TSTP Solution File: SWV629-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV629-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n029.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 16:27:16 EDT 2022
% Result : Unsatisfiable 25.20s 25.60s
% Output : Refutation 25.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV629-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n029.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 19:42:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.44/1.17 *** allocated 10000 integers for termspace/termends
% 0.44/1.17 *** allocated 10000 integers for clauses
% 0.44/1.17 *** allocated 10000 integers for justifications
% 0.44/1.17 Bliksem 1.12
% 0.44/1.17
% 0.44/1.17
% 0.44/1.17 Automatic Strategy Selection
% 0.44/1.17
% 0.44/1.17 Clauses:
% 0.44/1.17 [
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( X, 'c_GCD_Ogcd__class_Ogcd'( X, Y,
% 0.44/1.17 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.44/1.17 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 0.44/1.17 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 0.44/1.17 Z, T, X ), X ) ) ],
% 0.44/1.17 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y, X ) ]
% 0.44/1.17 ,
% 0.44/1.17 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 0.44/1.17 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.44/1.17 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 0.44/1.17 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.44/1.17 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.44/1.17 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 0.44/1.17 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.44/1.17 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.44/1.17 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.44/1.17 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 0.44/1.17 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Olcm'( X, Y,
% 0.44/1.17 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Z, Y
% 0.44/1.17 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z
% 0.44/1.17 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z
% 0.44/1.17 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Z, Y
% 0.44/1.17 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.44/1.17 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.44/1.17 , Z, 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.44/1.17 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 0.44/1.17 , Z, 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z
% 0.44/1.17 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Z, Y
% 0.44/1.17 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.44/1.17 'tc_nat' ), 'tc_nat' ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 0.44/1.17 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 0.44/1.17 , 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.44/1.17 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.44/1.17 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.44/1.17 ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 0.44/1.17 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 0.44/1.17 'c_Divides_Odiv__class_Odiv'( T, U, X ), X ),
% 0.44/1.17 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( U, T, X ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.44/1.17 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X
% 0.44/1.17 ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.44/1.17 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.44/1.17 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.44/1.17 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.44/1.17 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.44/1.17 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.44/1.17 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 X ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 0.44/1.17 , 'tc_nat' ), Z, 'tc_nat' ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X, Y
% 0.44/1.17 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 0.44/1.17 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z,
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 0.44/1.17 , X, 'tc_nat' ), 'tc_nat' ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( X
% 0.44/1.17 , Y, 'tc_nat' ), 'tc_nat' ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X, Y
% 0.44/1.17 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 0.44/1.17 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z,
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 0.44/1.17 , X, 'tc_nat' ), 'tc_nat' ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( X
% 0.44/1.17 , Y, 'tc_nat' ), 'tc_nat' ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X, Y
% 0.44/1.17 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 0.44/1.17 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z,
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( X
% 0.44/1.17 , Y, 'tc_nat' ), 'tc_nat' ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 0.44/1.17 , X, 'tc_nat' ), 'tc_nat' ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X, Y
% 0.44/1.17 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 0.44/1.17 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z,
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X, Y
% 0.44/1.17 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 0.44/1.17 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z,
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X
% 0.44/1.17 , Y, 'tc_nat' ), Z, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.44/1.17 X, Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X,
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X
% 0.44/1.17 , Y, 'tc_nat' ), Z, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.44/1.17 Y, Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y,
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.44/1.17 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 0.44/1.17 ,
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.44/1.17 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 0.44/1.17 ,
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 0.44/1.17 , X ), Z, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 0.44/1.17 , X ), Z, X ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 0.44/1.17 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.44/1.17 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 0.44/1.17 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.44/1.17 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.44/1.17 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 0.44/1.17 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 0.44/1.17 ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 0.44/1.17 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.44/1.17 ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.44/1.17 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 0.44/1.17 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.44/1.17 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.44/1.17 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 0.44/1.17 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.44/1.17 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 0.44/1.17 Y, X ), Z, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 0.44/1.17 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 0.44/1.17 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.44/1.17 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.44/1.17 T, X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.44/1.17 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.44/1.17 X ), Z, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.44/1.17 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.44/1.17 T, X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.44/1.17 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.44/1.17 X ), T, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.44/1.17 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.44/1.17 T, X ), X ) ) ],
% 0.44/1.17 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 0.44/1.17 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.44/1.17 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.44/1.17 X ), T, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 0.44/1.17 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 0.44/1.17 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 0.44/1.17 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 0.44/1.17 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 X ) ) ],
% 0.44/1.17 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.44/1.17 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.44/1.17 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.44/1.17 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.44/1.17 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.44/1.17 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Osgn__class_Osgn'( Y, X ), X ),
% 0.44/1.17 'c_HOL_Osgn__class_Osgn'( Y, X ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X,
% 0.44/1.17 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 0.44/1.17 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_GCD_Ogcd__class_Olcm'( X, Z, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 0.44/1.17 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z,
% 0.44/1.17 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.44/1.17 'c_HOL_Osgn__class_Osgn'( Y, X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, T
% 0.44/1.17 , X ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 0.44/1.17 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, Z
% 0.44/1.17 , X ), 'c_Divides_Odiv__class_Odiv'( T, Z, X ), X ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 0.44/1.17 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.44/1.17 ,
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 0.44/1.17 , Z, 'tc_nat' ), 'tc_nat' ), 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X
% 0.44/1.17 , 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 0.44/1.17 ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 0.44/1.17 , Z, 'tc_nat' ), 'tc_nat' ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X
% 0.44/1.17 , 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' )
% 0.44/1.17 ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.44/1.17 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y
% 0.44/1.17 , X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.44/1.17 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Z
% 0.44/1.17 , X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ), =( Z,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.44/1.17 ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.44/1.17 , X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 0.44/1.17 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.44/1.17 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.44/1.17 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ), Z ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.44/1.17 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.44/1.17 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.44/1.17 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 0.44/1.17 , X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.44/1.17 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 0.44/1.17 , X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.44/1.17 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.44/1.17 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.44/1.17 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.44/1.17 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.44/1.17 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.44/1.17 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.44/1.17 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 0.44/1.17 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 0.44/1.17 ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), Y ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Z, 'c_HOL_Oone__class_Oone'(
% 0.44/1.17 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' )
% 0.44/1.17 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Z, 'c_HOL_Oone__class_Oone'(
% 0.44/1.17 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' )
% 0.44/1.17 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), X ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Y ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), X ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Y ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Y ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), X ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Y ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( Z, X,
% 0.44/1.17 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X, Z,
% 0.44/1.17 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 0.44/1.17 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.44/1.17 , Z, 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 0.44/1.17 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.44/1.17 , Y, 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( Z, X,
% 0.44/1.17 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X, Z,
% 0.44/1.17 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 0.44/1.17 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.44/1.17 , Y, 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 0.44/1.17 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.44/1.17 , Z, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Otimes__class_Otimes'( Z
% 0.44/1.17 , Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.44/1.17 , Z, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Otimes__class_Otimes'( Z
% 0.44/1.17 , Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 0.44/1.17 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 0.44/1.17 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 0.44/1.17 , X ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.44/1.17 ), X, 'tc_nat' ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.44/1.17 ), Y, 'tc_nat' ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.44/1.17 , Y, X ), X ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 0.44/1.17 , Z, X ), X ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 0.44/1.17 , Z, X ), X ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 0.44/1.17 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 0.44/1.17 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'(
% 0.44/1.17 'c_HOL_Oone__class_Oone'( X ), Y, X ), Z, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 0.44/1.17 ), X ), Y ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 0.44/1.17 , T, X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.44/1.17 Z, T, 'tc_nat' ), X ) ) ],
% 0.44/1.17 [ =( 'c_Complex_Ocnj'( 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex'
% 0.44/1.17 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.44/1.17 , Y, X ) ) ],
% 0.44/1.17 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.44/1.17 , Y, X ) ) ],
% 0.44/1.17 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.44/1.17 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 0.44/1.17 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 0.44/1.17 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 0.44/1.17 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'(
% 0.44/1.17 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X,
% 0.44/1.17 Z, 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X,
% 0.44/1.17 'c_GCD_Ogcd__class_Olcm'( Y, Z, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( X, X, 'tc_nat' ), X ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.44/1.17 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.44/1.17 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.44/1.17 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.44/1.17 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( Y, 'c_GCD_Ogcd__class_Ogcd'( Z
% 0.44/1.17 , X, 'tc_nat' ), 'tc_nat' ) ) ), ~( =( Z, 'c_HOL_Otimes__class_Otimes'( T
% 0.44/1.17 , 'c_GCD_Ogcd__class_Ogcd'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ), =(
% 0.44/1.17 'c_GCD_Ogcd__class_Ogcd'( Z, X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 'tc_nat' ) ), =( 'c_GCD_Ogcd__class_Ogcd'( T, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), T
% 0.44/1.17 , X ), 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.44/1.17 X ), Z, X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ]
% 0.44/1.17 ,
% 0.44/1.17 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.44/1.17 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.44/1.17 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 0.44/1.17 , 'c_Power_Opower__class_Opower'( Y, Z, X ) ), ~(
% 0.44/1.17 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 0.44/1.17 , 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X
% 0.44/1.17 ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 0.44/1.17 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 0.44/1.17 ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 0.44/1.17 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.44/1.17 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.44/1.17 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.44/1.17 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.44/1.17 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 0.44/1.17 , T, X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 0.44/1.17 Y, T, X ), Z, X ) ) ],
% 0.44/1.17 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 0.44/1.17 , X ), Z ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.44/1.17 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 0.44/1.17 , X ), Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.44/1.17 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.44/1.17 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Fact_Ofact__class_Ofact'( Y,
% 0.44/1.17 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 0.44/1.17 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 0.44/1.17 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), =( Z,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 0.44/1.17 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.44/1.17 ) ],
% 0.44/1.17 [ =( 'c_Complex_Ocnj'( 'c_Power_Opower__class_Opower'( X, Y,
% 0.44/1.17 'tc_Complex_Ocomplex' ) ), 'c_Power_Opower__class_Opower'(
% 0.44/1.17 'c_Complex_Ocnj'( X ), Y, 'tc_Complex_Ocomplex' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 0.44/1.17 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.44/1.17 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 0.44/1.17 Y, Z, 'tc_nat' ), 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.44/1.17 , Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat'
% 0.44/1.17 ) ) ],
% 0.44/1.17 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 0.44/1.17 Y, Z, 'tc_nat' ), 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.44/1.17 , Y, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 0.44/1.17 ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 0.44/1.17 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.44/1.17 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 0.44/1.17 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.44/1.17 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.44/1.17 , 'tc_nat' ), Y, 'tc_nat' ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.44/1.17 , 'tc_nat' ), X, 'tc_nat' ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.44/1.17 , 'tc_nat' ), X, 'tc_nat' ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.44/1.17 , 'tc_nat' ), Y, 'tc_nat' ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.44/1.17 , 'tc_nat' ), X, 'tc_nat' ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.44/1.17 , 'tc_nat' ), Y, 'tc_nat' ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 0.44/1.17 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.44/1.17 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 0.44/1.17 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.44/1.17 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 0.44/1.17 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 0.44/1.17 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 0.44/1.17 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 0.44/1.17 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 X ) ) ],
% 0.44/1.17 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' )
% 0.44/1.17 , 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 0.44/1.17 , 'tc_nat' ), X ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.44/1.17 , 'tc_nat' ), X ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.44/1.17 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.44/1.17 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.44/1.17 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 0.44/1.17 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.44/1.17 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.44/1.17 ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, X, 'tc_nat' ), X ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 0.44/1.17 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 0.44/1.17 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.44/1.17 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.44/1.17 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.44/1.17 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.44/1.17 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =(
% 0.44/1.17 'c_GCD_Ogcd__class_Ogcd'( X, Z, 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.44/1.17 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =(
% 0.44/1.17 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 0.44/1.17 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 0.44/1.17 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X,
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_Complex_Ocnj'( 'c_Complex_Ocnj'( X ) ), X ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_GCD_Ogcd__class_Olcm'( Y, X, 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_GCD_Ogcd__class_Olcm'( Y, X, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.44/1.17 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 0.44/1.17 Y, Z, X ), X ) ) ],
% 0.44/1.17 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 0.44/1.17 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 0.44/1.17 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 0.44/1.17 , X ) ) ],
% 0.44/1.17 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 'tc_nat' ), 'tc_nat' ) ],
% 0.44/1.17 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.44/1.17 'c_Power_Opower__class_Opower'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 0.44/1.17 T, X ), 'c_Divides_Odiv__class_Odiv'( 'c_Power_Opower__class_Opower'( Y,
% 0.44/1.17 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.44/1.17 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.44/1.17 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.44/1.17 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.44/1.17 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 0.44/1.17 , X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.44/1.17 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 0.44/1.17 Y, X ), Z, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z,
% 0.44/1.17 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( Y,
% 0.44/1.17 'c_GCD_Ogcd__class_Ogcd'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat'
% 0.44/1.17 ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 0.44/1.17 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat'
% 0.44/1.17 ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 0.44/1.17 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 'tc_nat' ), 'tc_nat' ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.44/1.17 , X ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 0.44/1.17 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 0.44/1.17 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.44/1.17 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.44/1.17 Z, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.44/1.17 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 0.44/1.17 ), X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 0.44/1.17 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( X, 'c_GCD_Ogcd__class_Olcm'( X, Y,
% 0.44/1.17 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ) ) ]
% 0.44/1.17 ,
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( 'c_GCD_Ogcd__class_Ogcd'(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), Y, 'tc_nat' ),
% 0.44/1.17 'c_GCD_Ogcd__class_Ogcd'( Z, Y, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 0.44/1.17 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 0.44/1.17 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.44/1.17 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( X, 'c_GCD_Ogcd__class_Olcm'( Y, Z,
% 0.44/1.17 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Olcm'( Y,
% 0.44/1.17 'c_GCD_Ogcd__class_Olcm'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat'
% 0.44/1.17 ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Olcm'( X, 'c_GCD_Ogcd__class_Olcm'(
% 0.44/1.17 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat'
% 0.44/1.17 ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Olcm'( X, 'c_GCD_Ogcd__class_Olcm'(
% 0.44/1.17 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.44/1.17 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.44/1.17 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( =( 'c_Complex_Ocnj'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 'tc_Complex_Ocomplex' ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 'tc_Complex_Ocomplex' ) ) ],
% 0.44/1.17 [ ~( =( 'c_Complex_Ocnj'( X ), 'c_Complex_Ocnj'( Y ) ) ), =( X, Y ) ]
% 0.44/1.17 ,
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.44/1.17 Y, 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 0.44/1.17 Z, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'(
% 0.44/1.17 Z, X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'(
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.44/1.17 [ ~( =( 'c_Complex_Oii', 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 'tc_Complex_Ocomplex' ) ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.44/1.17 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.44/1.17 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 0.44/1.17 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 0.44/1.17 Z, T, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.44/1.17 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), ~( =( 'c_GCD_Ogcd__class_Ogcd'(
% 0.44/1.17 X, Z, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =(
% 0.44/1.17 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat'
% 0.44/1.17 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.44/1.17 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 0.44/1.17 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 0.44/1.17 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( Y, X,
% 0.44/1.17 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'( X, Y,
% 0.44/1.17 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ) ]
% 0.44/1.17 ,
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 0.44/1.17 ), =( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.44/1.17 , U, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( U,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 0.44/1.17 , U, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 0.44/1.17 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.44/1.17 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 0.44/1.17 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 0.44/1.17 'c_Power_Opower__class_Opower'( Y, Z, X ), T, X ) ) ],
% 0.44/1.17 [ ~( 'class_RealVector_Oreal__normed__div__algebra'( X ) ), =(
% 0.44/1.17 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 0.44/1.17 'c_HOL_Osgn__class_Osgn'( Z, X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.44/1.17 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 0.44/1.17 'c_HOL_Osgn__class_Osgn'( Z, X ), X ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.44/1.17 , 'tc_nat' ), Z, 'tc_nat' ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X
% 0.44/1.17 , 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' )
% 0.44/1.17 ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 0.44/1.17 , 'tc_nat' ), Z, 'tc_nat' ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y
% 0.44/1.17 , 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' )
% 0.44/1.17 ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y, X ),
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_FFT__Mirabelle_Oroot'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.44/1.17 'tc_Complex_Ocomplex' ) ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'(
% 0.44/1.17 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.44/1.17 [ =( 'c_Complex_Ocnj'( 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' )
% 0.44/1.17 ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.44/1.17 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.44/1.17 X ), Y ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.44/1.17 X ), Y ) ],
% 0.44/1.17 [ ~( =( 'c_Complex_Oii', 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 0.44/1.17 ) ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.44/1.17 'tc_nat' ), X ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Olcm'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 0.44/1.17 'tc_nat' ), X ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.44/1.17 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.44/1.17 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.44/1.17 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 0.44/1.17 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.44/1.17 , 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.44/1.17 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 0.44/1.17 ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.44/1.17 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.44/1.17 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 0.44/1.17 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.44/1.17 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 0.44/1.17 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.44/1.17 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.44/1.17 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oone__class_Oone'(
% 0.44/1.17 'tc_nat' ), 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.44/1.17 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 0.44/1.17 X ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 0.44/1.17 'tc_nat' ), X, 'tc_nat' ) ],
% 0.44/1.17 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 0.44/1.17 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.44/1.17 [ =( 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'( X ), X,
% 0.44/1.17 'tc_Complex_Ocomplex' ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 0.44/1.17 ) ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.44/1.17 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.44/1.17 ), 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.44/1.17 ],
% 0.44/1.17 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.44/1.17 ],
% 0.44/1.17 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.44/1.17 ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.44/1.17 ],
% 0.44/1.17 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 0.44/1.17 , X, 'tc_nat' ), X ) ],
% 0.44/1.17 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.44/1.17 ), 'tc_nat' ), X ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.44/1.17 ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.44/1.17 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.44/1.17 ],
% 0.44/1.17 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 0.44/1.17 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_RealVector_Oreal__normed__algebra__1'( X ) ), =(
% 0.44/1.17 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.44/1.17 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 0.44/1.17 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ],
% 0.44/1.17 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.44/1.17 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 0.44/1.17 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 0.44/1.17 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.44/1.17 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 0.44/1.17 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 0.44/1.17 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 0.44/1.17 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.44/1.17 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.44/1.17 ],
% 0.44/1.17 [ ~( =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )
% 0.44/1.17 , 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ) ],
% 0.44/1.17 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.44/1.17 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.44/1.17 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.44/1.17 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 0.44/1.17 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 0.44/1.17 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.44/1.17 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 0.44/1.17 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.44/1.17 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 0.44/1.17 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 0.44/1.17 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 0.44/1.17 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 0.44/1.17 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 0.44/1.17 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 3.33/3.78 'tc_Complex_Ocomplex' ) ],
% 3.33/3.78 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 3.33/3.78 'tc_Complex_Ocomplex' ) ],
% 3.33/3.78 [ 'class_RealVector_Oreal__normed__div__algebra'( 'tc_Complex_Ocomplex'
% 3.33/3.78 ) ],
% 3.33/3.78 [ 'class_RealVector_Oreal__normed__algebra__1'( 'tc_Complex_Ocomplex' )
% 3.33/3.78 ],
% 3.33/3.78 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 3.33/3.78 ],
% 3.33/3.78 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 3.33/3.78 ],
% 3.33/3.78 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 3.33/3.78 ,
% 3.33/3.78 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 3.33/3.78 ,
% 3.33/3.78 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 3.33/3.78 ,
% 3.33/3.78 [ 'class_RealVector_Oreal__normed__vector'( 'tc_Complex_Ocomplex' ) ]
% 3.33/3.78 ,
% 3.33/3.78 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 3.33/3.78 ,
% 3.33/3.78 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_Complex_Ocomplex' ) ]
% 3.33/3.78 ,
% 3.33/3.78 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 3.33/3.78 ,
% 3.33/3.78 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 3.33/3.78 ,
% 3.33/3.78 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 3.33/3.78 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 3.33/3.78 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 3.33/3.78 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 3.33/3.78 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 3.33/3.78 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 3.33/3.78 [ 'class_Nat_Osemiring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 3.33/3.78 [ 'class_Ring__and__Field_Odvd'( 'tc_Complex_Ocomplex' ) ],
% 3.33/3.78 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 3.33/3.78 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ]
% 3.33/3.78 ] .
% 3.33/3.78
% 3.33/3.78
% 3.33/3.78 percentage equality = 0.440299, percentage horn = 0.864516
% 3.33/3.78 This is a problem with some equality
% 3.33/3.78
% 3.33/3.78
% 3.33/3.78
% 3.33/3.78 Options Used:
% 3.33/3.78
% 3.33/3.78 useres = 1
% 3.33/3.78 useparamod = 1
% 3.33/3.78 useeqrefl = 1
% 3.33/3.78 useeqfact = 1
% 3.33/3.78 usefactor = 1
% 3.33/3.78 usesimpsplitting = 0
% 3.33/3.78 usesimpdemod = 5
% 3.33/3.78 usesimpres = 3
% 3.33/3.78
% 3.33/3.78 resimpinuse = 1000
% 3.33/3.78 resimpclauses = 20000
% 3.33/3.78 substype = eqrewr
% 3.33/3.78 backwardsubs = 1
% 3.33/3.78 selectoldest = 5
% 3.33/3.78
% 3.33/3.78 litorderings [0] = split
% 3.33/3.78 litorderings [1] = extend the termordering, first sorting on arguments
% 3.33/3.78
% 3.33/3.78 termordering = kbo
% 3.33/3.78
% 3.33/3.78 litapriori = 0
% 3.33/3.78 termapriori = 1
% 3.33/3.78 litaposteriori = 0
% 3.33/3.78 termaposteriori = 0
% 3.33/3.78 demodaposteriori = 0
% 3.33/3.78 ordereqreflfact = 0
% 3.33/3.78
% 3.33/3.78 litselect = negord
% 3.33/3.78
% 3.33/3.78 maxweight = 15
% 3.33/3.78 maxdepth = 30000
% 3.33/3.78 maxlength = 115
% 3.33/3.78 maxnrvars = 195
% 3.33/3.78 excuselevel = 1
% 3.33/3.78 increasemaxweight = 1
% 3.33/3.78
% 3.33/3.78 maxselected = 10000000
% 3.33/3.78 maxnrclauses = 10000000
% 3.33/3.78
% 3.33/3.78 showgenerated = 0
% 3.33/3.78 showkept = 0
% 3.33/3.78 showselected = 0
% 3.33/3.78 showdeleted = 0
% 3.33/3.78 showresimp = 1
% 3.33/3.78 showstatus = 2000
% 3.33/3.78
% 3.33/3.78 prologoutput = 1
% 3.33/3.78 nrgoals = 5000000
% 3.33/3.78 totalproof = 1
% 3.33/3.78
% 3.33/3.78 Symbols occurring in the translation:
% 3.33/3.78
% 3.33/3.78 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 3.33/3.78 . [1, 2] (w:1, o:76, a:1, s:1, b:0),
% 3.33/3.78 ! [4, 1] (w:0, o:37, a:1, s:1, b:0),
% 3.33/3.78 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.33/3.78 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.33/3.78 'tc_nat' [41, 0] (w:1, o:12, a:1, s:1, b:0),
% 3.33/3.78 'c_GCD_Ogcd__class_Ogcd' [42, 3] (w:1, o:108, a:1, s:1, b:0),
% 3.33/3.78 'c_GCD_Ogcd__class_Olcm' [43, 3] (w:1, o:109, a:1, s:1, b:0),
% 3.33/3.78 'class_Ring__and__Field_Ofield' [45, 1] (w:1, o:42, a:1, s:1, b:0),
% 3.33/3.78 'class_Ring__and__Field_Odivision__by__zero' [46, 1] (w:1, o:44, a:1
% 3.33/3.78 , s:1, b:0),
% 3.33/3.78 'c_HOL_Oinverse__class_Odivide' [49, 3] (w:1, o:110, a:1, s:1, b:0),
% 3.33/3.78
% 3.33/3.78 'c_Power_Opower__class_Opower' [51, 3] (w:1, o:111, a:1, s:1, b:0),
% 3.33/3.78 'c_Ring__and__Field_Odvd__class_Odvd' [52, 3] (w:1, o:112, a:1, s:1
% 3.33/3.78 , b:0),
% 3.33/3.78 'class_Ring__and__Field_Ocomm__semiring__1' [56, 1] (w:1, o:43, a:1
% 3.33/3.78 , s:1, b:0),
% 3.33/3.78 'c_HOL_Ozero__class_Ozero' [58, 1] (w:1, o:45, a:1, s:1, b:0),
% 3.33/3.78 'c_HOL_Otimes__class_Otimes' [59, 3] (w:1, o:113, a:1, s:1, b:0),
% 3.33/3.78 'class_Ring__and__Field_Oidom' [60, 1] (w:1, o:46, a:1, s:1, b:0),
% 3.33/3.78 'class_Ring__and__Field_Oordered__idom' [61, 1] (w:1, o:49, a:1, s:1
% 3.33/3.78 , b:0),
% 3.33/3.78 'c_HOL_Oabs__class_Oabs' [62, 2] (w:1, o:101, a:1, s:1, b:0),
% 25.20/25.60 'class_OrderedGroup_Oab__semigroup__idem__mult' [64, 1] (w:1, o:51
% 25.20/25.60 , a:1, s:1, b:0),
% 25.20/25.60 'class_Ring__and__Field_Ozero__neq__one' [65, 1] (w:1, o:52, a:1, s:1
% 25.20/25.60 , b:0),
% 25.20/25.60 'class_Ring__and__Field_Ono__zero__divisors' [66, 1] (w:1, o:48, a:1
% 25.20/25.60 , s:1, b:0),
% 25.20/25.60 'class_Ring__and__Field_Omult__zero' [67, 1] (w:1, o:47, a:1, s:1, b:
% 25.20/25.60 0),
% 25.20/25.60 'class_Power_Opower' [68, 1] (w:1, o:57, a:1, s:1, b:0),
% 25.20/25.60 'class_Ring__and__Field_Oring__1__no__zero__divisors' [69, 1] (w:1
% 25.20/25.60 , o:58, a:1, s:1, b:0),
% 25.20/25.60 'class_Divides_Osemiring__div' [70, 1] (w:1, o:59, a:1, s:1, b:0),
% 25.20/25.60 'c_Divides_Odiv__class_Odiv' [71, 3] (w:1, o:114, a:1, s:1, b:0),
% 25.20/25.60 'c_HOL_Oone__class_Oone' [72, 1] (w:1, o:60, a:1, s:1, b:0),
% 25.20/25.60 'class_Ring__and__Field_Osemiring__0' [73, 1] (w:1, o:62, a:1, s:1
% 25.20/25.60 , b:0),
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse' [76, 2] (w:1, o:102, a:1, s:1, b:0)
% 25.20/25.60 ,
% 25.20/25.60 'class_Ring__and__Field_Odivision__ring' [77, 1] (w:1, o:63, a:1, s:1
% 25.20/25.60 , b:0),
% 25.20/25.60 'class_OrderedGroup_Ocomm__monoid__mult' [79, 1] (w:1, o:53, a:1, s:1
% 25.20/25.60 , b:0),
% 25.20/25.60 'class_OrderedGroup_Oab__semigroup__mult' [80, 1] (w:1, o:54, a:1, s:
% 25.20/25.60 1, b:0),
% 25.20/25.60 'c_HOL_Osgn__class_Osgn' [85, 2] (w:1, o:103, a:1, s:1, b:0),
% 25.20/25.60 'c_Nat_Osemiring__1__class_Oof__nat' [86, 2] (w:1, o:104, a:1, s:1
% 25.20/25.60 , b:0),
% 25.20/25.60 'class_Ring__and__Field_Osemiring__1' [87, 1] (w:1, o:64, a:1, s:1
% 25.20/25.60 , b:0),
% 25.20/25.60 'c_Fact_Ofact__class_Ofact' [88, 2] (w:1, o:105, a:1, s:1, b:0),
% 25.20/25.60 'class_Ring__and__Field_Oring__no__zero__divisors' [89, 1] (w:1, o:61
% 25.20/25.60 , a:1, s:1, b:0),
% 25.20/25.60 'class_Nat_Osemiring__char__0' [90, 1] (w:1, o:50, a:1, s:1, b:0),
% 25.20/25.60 'class_Int_Onumber__ring' [92, 1] (w:1, o:65, a:1, s:1, b:0),
% 25.20/25.60 'class_Ring__and__Field_Odvd' [93, 1] (w:1, o:66, a:1, s:1, b:0),
% 25.20/25.60 'tc_Complex_Ocomplex' [95, 0] (w:1, o:33, a:1, s:1, b:0),
% 25.20/25.60 'c_Complex_Ocnj' [96, 1] (w:1, o:67, a:1, s:1, b:0),
% 25.20/25.60 'class_OrderedGroup_Opordered__ab__group__add__abs' [97, 1] (w:1, o:
% 25.20/25.60 55, a:1, s:1, b:0),
% 25.20/25.60 'class_RealVector_Oreal__normed__field' [98, 1] (w:1, o:68, a:1, s:1
% 25.20/25.60 , b:0),
% 25.20/25.60 'c_Parity_Oeven__odd__class_Oeven' [101, 2] (w:1, o:106, a:1, s:1, b:
% 25.20/25.60 0),
% 25.20/25.60 'class_Ring__and__Field_Oordered__field' [102, 1] (w:1, o:69, a:1, s:
% 25.20/25.60 1, b:0),
% 25.20/25.60 'class_RealVector_Oreal__normed__vector' [103, 1] (w:1, o:70, a:1, s:
% 25.20/25.60 1, b:0),
% 25.20/25.60 'class_OrderedGroup_Omonoid__mult' [104, 1] (w:1, o:56, a:1, s:1, b:0
% 25.20/25.60 ),
% 25.20/25.60 'class_RealVector_Oreal__normed__algebra' [105, 1] (w:1, o:71, a:1
% 25.20/25.60 , s:1, b:0),
% 25.20/25.60 'c_Int_Oiszero' [106, 2] (w:1, o:107, a:1, s:1, b:0),
% 25.20/25.60 'class_Ring__and__Field_Osgn__if' [107, 1] (w:1, o:72, a:1, s:1, b:0)
% 25.20/25.60 ,
% 25.20/25.60 'c_Complex_Oii' [108, 0] (w:1, o:34, a:1, s:1, b:0),
% 25.20/25.60 'class_RealVector_Oreal__normed__div__algebra' [109, 1] (w:1, o:73
% 25.20/25.60 , a:1, s:1, b:0),
% 25.20/25.60 'c_FFT__Mirabelle_Oroot' [113, 1] (w:1, o:74, a:1, s:1, b:0),
% 25.20/25.60 'class_RealVector_Oreal__normed__algebra__1' [114, 1] (w:1, o:75, a:1
% 25.20/25.60 , s:1, b:0).
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Starting Search:
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 6432
% 25.20/25.60 Kept: 2007
% 25.20/25.60 Inuse: 167
% 25.20/25.60 Deleted: 4
% 25.20/25.60 Deletedinuse: 0
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 23049
% 25.20/25.60 Kept: 4009
% 25.20/25.60 Inuse: 245
% 25.20/25.60 Deleted: 7
% 25.20/25.60 Deletedinuse: 0
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 36624
% 25.20/25.60 Kept: 6071
% 25.20/25.60 Inuse: 288
% 25.20/25.60 Deleted: 8
% 25.20/25.60 Deletedinuse: 0
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 53198
% 25.20/25.60 Kept: 8512
% 25.20/25.60 Inuse: 347
% 25.20/25.60 Deleted: 14
% 25.20/25.60 Deletedinuse: 0
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 74387
% 25.20/25.60 Kept: 11071
% 25.20/25.60 Inuse: 384
% 25.20/25.60 Deleted: 17
% 25.20/25.60 Deletedinuse: 0
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 95912
% 25.20/25.60 Kept: 13094
% 25.20/25.60 Inuse: 409
% 25.20/25.60 Deleted: 17
% 25.20/25.60 Deletedinuse: 0
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 123347
% 25.20/25.60 Kept: 15670
% 25.20/25.60 Inuse: 475
% 25.20/25.60 Deleted: 23
% 25.20/25.60 Deletedinuse: 2
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 141446
% 25.20/25.60 Kept: 17701
% 25.20/25.60 Inuse: 542
% 25.20/25.60 Deleted: 27
% 25.20/25.60 Deletedinuse: 3
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 155521
% 25.20/25.60 Kept: 19729
% 25.20/25.60 Inuse: 589
% 25.20/25.60 Deleted: 31
% 25.20/25.60 Deletedinuse: 3
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying clauses:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 166787
% 25.20/25.60 Kept: 21732
% 25.20/25.60 Inuse: 604
% 25.20/25.60 Deleted: 617
% 25.20/25.60 Deletedinuse: 3
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 182663
% 25.20/25.60 Kept: 23737
% 25.20/25.60 Inuse: 635
% 25.20/25.60 Deleted: 618
% 25.20/25.60 Deletedinuse: 4
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 199365
% 25.20/25.60 Kept: 26042
% 25.20/25.60 Inuse: 653
% 25.20/25.60 Deleted: 632
% 25.20/25.60 Deletedinuse: 18
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 217181
% 25.20/25.60 Kept: 28138
% 25.20/25.60 Inuse: 678
% 25.20/25.60 Deleted: 632
% 25.20/25.60 Deletedinuse: 18
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 229009
% 25.20/25.60 Kept: 30261
% 25.20/25.60 Inuse: 703
% 25.20/25.60 Deleted: 633
% 25.20/25.60 Deletedinuse: 19
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 263548
% 25.20/25.60 Kept: 32281
% 25.20/25.60 Inuse: 718
% 25.20/25.60 Deleted: 638
% 25.20/25.60 Deletedinuse: 24
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 277732
% 25.20/25.60 Kept: 34573
% 25.20/25.60 Inuse: 742
% 25.20/25.60 Deleted: 640
% 25.20/25.60 Deletedinuse: 25
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 299982
% 25.20/25.60 Kept: 36579
% 25.20/25.60 Inuse: 774
% 25.20/25.60 Deleted: 640
% 25.20/25.60 Deletedinuse: 25
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 312650
% 25.20/25.60 Kept: 39542
% 25.20/25.60 Inuse: 797
% 25.20/25.60 Deleted: 640
% 25.20/25.60 Deletedinuse: 25
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying clauses:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 325084
% 25.20/25.60 Kept: 41627
% 25.20/25.60 Inuse: 837
% 25.20/25.60 Deleted: 2495
% 25.20/25.60 Deletedinuse: 35
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 339444
% 25.20/25.60 Kept: 44380
% 25.20/25.60 Inuse: 852
% 25.20/25.60 Deleted: 2495
% 25.20/25.60 Deletedinuse: 35
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 355452
% 25.20/25.60 Kept: 46468
% 25.20/25.60 Inuse: 879
% 25.20/25.60 Deleted: 2495
% 25.20/25.60 Deletedinuse: 35
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 366576
% 25.20/25.60 Kept: 49634
% 25.20/25.60 Inuse: 887
% 25.20/25.60 Deleted: 2495
% 25.20/25.60 Deletedinuse: 35
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 412498
% 25.20/25.60 Kept: 51911
% 25.20/25.60 Inuse: 902
% 25.20/25.60 Deleted: 2495
% 25.20/25.60 Deletedinuse: 35
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 426214
% 25.20/25.60 Kept: 54624
% 25.20/25.60 Inuse: 922
% 25.20/25.60 Deleted: 2495
% 25.20/25.60 Deletedinuse: 35
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 438047
% 25.20/25.60 Kept: 57159
% 25.20/25.60 Inuse: 930
% 25.20/25.60 Deleted: 2495
% 25.20/25.60 Deletedinuse: 35
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Intermediate Status:
% 25.20/25.60 Generated: 451304
% 25.20/25.60 Kept: 60250
% 25.20/25.60 Inuse: 940
% 25.20/25.60 Deleted: 2497
% 25.20/25.60 Deletedinuse: 35
% 25.20/25.60
% 25.20/25.60 Resimplifying inuse:
% 25.20/25.60 Done
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 Bliksems!, er is een bewijs:
% 25.20/25.60 % SZS status Unsatisfiable
% 25.20/25.60 % SZS output start Refutation
% 25.20/25.60
% 25.20/25.60 clause( 231, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 25.20/25.60 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 25.20/25.60 X ), Y ) ] )
% 25.20/25.60 .
% 25.20/25.60 clause( 251, [ =( 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'(
% 25.20/25.60 X ), X, 'tc_Complex_Ocomplex' ), 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_Complex_Ocomplex' ) ) ] )
% 25.20/25.60 .
% 25.20/25.60 clause( 263, [ ~( =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ) ] )
% 25.20/25.60 .
% 25.20/25.60 clause( 294, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' )
% 25.20/25.60 ] )
% 25.20/25.60 .
% 25.20/25.60 clause( 60597, [ ~( 'class_OrderedGroup_Omonoid__mult'(
% 25.20/25.60 'tc_Complex_Ocomplex' ) ) ] )
% 25.20/25.60 .
% 25.20/25.60 clause( 60669, [] )
% 25.20/25.60 .
% 25.20/25.60
% 25.20/25.60
% 25.20/25.60 % SZS output end Refutation
% 25.20/25.60 found a proof!
% 25.20/25.60
% 25.20/25.60 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 25.20/25.60
% 25.20/25.60 initialclauses(
% 25.20/25.60 [ clause( 60671, [ =( 'c_GCD_Ogcd__class_Olcm'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 25.20/25.60 X, Y, 'tc_nat' ), 'tc_nat' ), X ) ] )
% 25.20/25.60 , clause( 60672, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 25.20/25.60 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 25.20/25.60 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 25.20/25.60 Z, T, X ), X ) ) ] )
% 25.20/25.60 , clause( 60673, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 25.20/25.60 ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y
% 25.20/25.60 , X ) ] )
% 25.20/25.60 , clause( 60674, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 25.20/25.60 ) ), =( Y, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 25.20/25.60 ) ) ] )
% 25.20/25.60 , clause( 60675, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 Y, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 25.20/25.60 ) ) ] )
% 25.20/25.60 , clause( 60676, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 25.20/25.60 X, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 25.20/25.60 ) ) ] )
% 25.20/25.60 , clause( 60677, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 25.20/25.60 ) ), =( Y, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 25.20/25.60 ) ) ] )
% 25.20/25.60 , clause( 60678, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 25.20/25.60 X, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 25.20/25.60 ) ) ] )
% 25.20/25.60 , clause( 60679, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 25.20/25.60 X, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 25.20/25.60 ) ) ] )
% 25.20/25.60 , clause( 60680, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Olcm'(
% 25.20/25.60 X, Y, 'tc_nat' ), 'tc_nat' ), X ) ] )
% 25.20/25.60 , clause( 60681, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 25.20/25.60 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 25.20/25.60 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60682, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 25.20/25.60 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 25.20/25.60 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60683, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 25.20/25.60 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 25.20/25.60 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60684, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 25.20/25.60 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 25.20/25.60 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60685, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60686, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60687, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 25.20/25.60 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 25.20/25.60 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60688, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 25.20/25.60 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 25.20/25.60 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60689, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 25.20/25.60 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60690, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 25.20/25.60 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60691, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' )
% 25.20/25.60 ] )
% 25.20/25.60 , clause( 60692, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ] )
% 25.20/25.60 , clause( 60693, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 25.20/25.60 , clause( 60694, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 25.20/25.60 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60695, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ] )
% 25.20/25.60 , clause( 60696, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ] )
% 25.20/25.60 , clause( 60697, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 25.20/25.60 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 25.20/25.60 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 25.20/25.60 , clause( 60698, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 25.20/25.60 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 25.20/25.60 , 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 25.20/25.60 , clause( 60699, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 25.20/25.60 ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y,
% 25.20/25.60 Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 25.20/25.60 , clause( 60700, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 25.20/25.60 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 25.20/25.60 ) ) ] )
% 25.20/25.60 , clause( 60701, [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 25.20/25.60 X ) ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 25.20/25.60 ) ) ] )
% 25.20/25.60 , clause( 60702, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 25.20/25.60 'c_Divides_Odiv__class_Odiv'( T, U, X ), X ),
% 25.20/25.60 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( U, T, X ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 25.20/25.60 , clause( 60703, [ ~( 'class_Power_Opower'( X ) ), =(
% 25.20/25.60 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 25.20/25.60 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 25.20/25.60 , clause( 60704, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 25.20/25.60 , clause( 60705, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 25.20/25.60 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 25.20/25.60 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60706, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 25.20/25.60 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 25.20/25.60 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60707, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 25.20/25.60 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 X ) ) ] )
% 25.20/25.60 , clause( 60708, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 25.20/25.60 , 'tc_nat' ), Z, 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60709, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60710, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( Y, X, 'tc_nat' ), 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60711, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60712, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60713, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( Y, X, 'tc_nat' ), 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60714, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60715, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60716, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60717, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( Y, X, 'tc_nat' ), 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60718, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60719, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60720, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60721, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60722, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 25.20/25.60 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 25.20/25.60 , clause( 60723, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 25.20/25.60 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 25.20/25.60 , clause( 60724, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 25.20/25.60 , X ), Z, X ) ) ] )
% 25.20/25.60 , clause( 60725, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 25.20/25.60 , X ), Z, X ) ) ] )
% 25.20/25.60 , clause( 60726, [ =( 'c_GCD_Ogcd__class_Olcm'( 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60727, [ =( 'c_GCD_Ogcd__class_Olcm'( X,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60728, [ =( 'c_GCD_Ogcd__class_Olcm'( 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60729, [ =( 'c_GCD_Ogcd__class_Olcm'( X,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60730, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 25.20/25.60 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60731, [ =( 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 25.20/25.60 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60732, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 25.20/25.60 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ] )
% 25.20/25.60 , clause( 60733, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 25.20/25.60 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 25.20/25.60 ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ] )
% 25.20/25.60 , clause( 60734, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 25.20/25.60 ), =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 25.20/25.60 , clause( 60735, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ] )
% 25.20/25.60 , clause( 60736, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 25.20/25.60 =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 25.20/25.60 ) ] )
% 25.20/25.60 , clause( 60737, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60738, [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 25.20/25.60 =( 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 25.20/25.60 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60739, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 25.20/25.60 ), T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'(
% 25.20/25.60 Y, T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ] )
% 25.20/25.60 , clause( 60740, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 25.20/25.60 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 25.20/25.60 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 25.20/25.60 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ] )
% 25.20/25.60 , clause( 60741, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 25.20/25.60 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 25.20/25.60 Y, X ), Z, X ) ) ] )
% 25.20/25.60 , clause( 60742, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 25.20/25.60 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ] )
% 25.20/25.60 , clause( 60743, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 25.20/25.60 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 25.20/25.60 T, X ), X ) ) ] )
% 25.20/25.60 , clause( 60744, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 25.20/25.60 , T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y,
% 25.20/25.60 T, X ), Z, X ) ) ] )
% 25.20/25.60 , clause( 60745, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 25.20/25.60 , T, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 Z, T, X ), X ) ) ] )
% 25.20/25.60 , clause( 60746, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 25.20/25.60 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 25.20/25.60 , X ), T, X ) ) ] )
% 25.20/25.60 , clause( 60747, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 25.20/25.60 ), X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y
% 25.20/25.60 , T, X ), X ) ) ] )
% 25.20/25.60 , clause( 60748, [ =( 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 25.20/25.60 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60749, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 25.20/25.60 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 25.20/25.60 , X ), T, X ) ) ] )
% 25.20/25.60 , clause( 60750, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 25.20/25.60 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 X ) ) ] )
% 25.20/25.60 , clause( 60751, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 25.20/25.60 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 X ) ) ] )
% 25.20/25.60 , clause( 60752, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 25.20/25.60 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 X ) ) ] )
% 25.20/25.60 , clause( 60753, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 25.20/25.60 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 X ) ) ] )
% 25.20/25.60 , clause( 60754, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 25.20/25.60 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 25.20/25.60 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60755, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 25.20/25.60 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 25.20/25.60 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60756, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 25.20/25.60 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Osgn__class_Osgn'( Y, X ), X ),
% 25.20/25.60 'c_HOL_Osgn__class_Osgn'( Y, X ) ) ] )
% 25.20/25.60 , clause( 60757, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ),
% 25.20/25.60 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Olcm'( X, Y,
% 25.20/25.60 'tc_nat' ), 'c_GCD_Ogcd__class_Olcm'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 25.20/25.60 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60758, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' )
% 25.20/25.60 , 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60759, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 25.20/25.60 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 25.20/25.60 'c_HOL_Osgn__class_Osgn'( Y, X ), X ) ) ] )
% 25.20/25.60 , clause( 60760, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, T
% 25.20/25.60 , X ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ] )
% 25.20/25.60 , clause( 60761, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, Z
% 25.20/25.60 , X ), 'c_Divides_Odiv__class_Odiv'( T, Z, X ), X ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 25.20/25.60 , clause( 60762, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 25.20/25.60 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 25.20/25.60 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ] )
% 25.20/25.60 , clause( 60763, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 25.20/25.60 )
% 25.20/25.60 , clause( 60764, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60765, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60766, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 25.20/25.60 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y
% 25.20/25.60 , X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ] )
% 25.20/25.60 , clause( 60767, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 25.20/25.60 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Z
% 25.20/25.60 , X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ), =( Z,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 25.20/25.60 ) ] )
% 25.20/25.60 , clause( 60768, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 25.20/25.60 , X ) ) ] )
% 25.20/25.60 , clause( 60769, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 25.20/25.60 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60770, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 25.20/25.60 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60771, [ ~( =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 25.20/25.60 , clause( 60772, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 25.20/25.60 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60773, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ) ) ] )
% 25.20/25.60 , clause( 60774, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ), Z ) ] )
% 25.20/25.60 , clause( 60775, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 25.20/25.60 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60776, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 25.20/25.60 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60777, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 25.20/25.60 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 25.20/25.60 , clause( 60778, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 25.20/25.60 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 25.20/25.60 , clause( 60779, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 25.20/25.60 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 25.20/25.60 , clause( 60780, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 25.20/25.60 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 25.20/25.60 , X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60781, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 25.20/25.60 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 25.20/25.60 , X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60782, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 25.20/25.60 ) ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 25.20/25.60 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60783, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 25.20/25.60 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60784, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 25.20/25.60 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60785, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60786, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 25.20/25.60 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60787, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 25.20/25.60 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60788, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 25.20/25.60 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 25.20/25.60 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ] )
% 25.20/25.60 , clause( 60789, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 25.20/25.60 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 25.20/25.60 ) ] )
% 25.20/25.60 , clause( 60790, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 25.20/25.60 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), Y ) ] )
% 25.20/25.60 , clause( 60791, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Z, 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' )
% 25.20/25.60 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60792, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Z, 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' )
% 25.20/25.60 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60793, [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), X ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60794, [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Y ) )
% 25.20/25.60 , 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60795, [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), X ) )
% 25.20/25.60 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60796, [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), X ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60797, [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Y ) )
% 25.20/25.60 , 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60798, [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Y ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60799, [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), X ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60800, [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Y ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60801, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 25.20/25.60 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( Z,
% 25.20/25.60 X, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60802, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 25.20/25.60 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X,
% 25.20/25.60 Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60803, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60804, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60805, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 25.20/25.60 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( Z,
% 25.20/25.60 X, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60806, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 25.20/25.60 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X,
% 25.20/25.60 Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60807, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60808, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60809, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Otimes__class_Otimes'( Z
% 25.20/25.60 , Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 25.20/25.60 , Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60810, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Otimes__class_Otimes'( Z
% 25.20/25.60 , Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60811, [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60812, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 25.20/25.60 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 25.20/25.60 , clause( 60813, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 25.20/25.60 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 25.20/25.60 , X ) ) ] )
% 25.20/25.60 , clause( 60814, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 25.20/25.60 ), X, 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60815, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 25.20/25.60 ), Y, 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60816, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 25.20/25.60 , Y, X ), X ) ] )
% 25.20/25.60 , clause( 60817, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 25.20/25.60 , Z, X ), X ) ] )
% 25.20/25.60 , clause( 60818, [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 25.20/25.60 , Z, X ), X ) ] )
% 25.20/25.60 , clause( 60819, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 25.20/25.60 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 25.20/25.60 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'(
% 25.20/25.60 'c_HOL_Oone__class_Oone'( X ), Y, X ), Z, X ) ) ] )
% 25.20/25.60 , clause( 60820, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 25.20/25.60 ), X ), Y ) ] )
% 25.20/25.60 , clause( 60821, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z,
% 25.20/25.60 X ), T, X ), 'c_Power_Opower__class_Opower'( Y,
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X ) ) ] )
% 25.20/25.60 , clause( 60822, [ =( 'c_Complex_Ocnj'( 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 'tc_Complex_Ocomplex' ) ), 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 'tc_Complex_Ocomplex' ) ) ] )
% 25.20/25.60 , clause( 60823, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 Z, Y, X ) ) ] )
% 25.20/25.60 , clause( 60824, [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60825, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 Z, Y, X ) ) ] )
% 25.20/25.60 , clause( 60826, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 25.20/25.60 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 25.20/25.60 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60827, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 25.20/25.60 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 25.20/25.60 , clause( 60828, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 25.20/25.60 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 25.20/25.60 , clause( 60829, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 25.20/25.60 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60830, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 25.20/25.60 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60831, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Olcm'( Y, Z, 'tc_nat' ),
% 25.20/25.60 'tc_nat' ), 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60832, [ =( 'c_GCD_Ogcd__class_Olcm'( X, X, 'tc_nat' ), X ) ] )
% 25.20/25.60 , clause( 60833, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 25.20/25.60 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60834, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 25.20/25.60 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60835, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 25.20/25.60 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60836, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 25.20/25.60 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60837, [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ), ~( =( Z,
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( T, 'c_GCD_Ogcd__class_Ogcd'( Z, X, 'tc_nat'
% 25.20/25.60 ), 'tc_nat' ) ) ), =( 'c_GCD_Ogcd__class_Ogcd'( Z, X, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( 'c_GCD_Ogcd__class_Ogcd'( T
% 25.20/25.60 , Y, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60838, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), T
% 25.20/25.60 , X ), 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 25.20/25.60 X ), Z, X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 25.20/25.60 , clause( 60839, [ =( 'c_Fact_Ofact__class_Ofact'(
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60840, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 25.20/25.60 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 25.20/25.60 , 'c_Power_Opower__class_Opower'( Y, Z, X ) ), ~(
% 25.20/25.60 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60841, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 25.20/25.60 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 25.20/25.60 , 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X
% 25.20/25.60 ) ) ] )
% 25.20/25.60 , clause( 60842, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 25.20/25.60 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 25.20/25.60 , clause( 60843, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 25.20/25.60 ] )
% 25.20/25.60 , clause( 60844, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 25.20/25.60 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 25.20/25.60 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 25.20/25.60 , clause( 60845, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 25.20/25.60 =( 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 25.20/25.60 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60846, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 25.20/25.60 =( 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 25.20/25.60 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60847, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 25.20/25.60 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60848, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 25.20/25.60 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60849, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 25.20/25.60 , T, X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 Y, T, X ), Z, X ) ) ] )
% 25.20/25.60 , clause( 60850, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 25.20/25.60 , X ), Z ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 25.20/25.60 , clause( 60851, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 25.20/25.60 , X ), Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 25.20/25.60 , clause( 60852, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 25.20/25.60 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Fact_Ofact__class_Ofact'( Y,
% 25.20/25.60 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 25.20/25.60 , clause( 60853, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 25.20/25.60 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 25.20/25.60 , clause( 60854, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 25.20/25.60 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 25.20/25.60 , clause( 60855, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 25.20/25.60 , =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 25.20/25.60 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 25.20/25.60 ) ] )
% 25.20/25.60 , clause( 60856, [ =( 'c_Complex_Ocnj'( 'c_Power_Opower__class_Opower'( X,
% 25.20/25.60 Y, 'tc_Complex_Ocomplex' ) ), 'c_Power_Opower__class_Opower'(
% 25.20/25.60 'c_Complex_Ocnj'( X ), Y, 'tc_Complex_Ocomplex' ) ) ] )
% 25.20/25.60 , clause( 60857, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60858, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60859, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60860, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60861, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60862, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y, 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60863, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X, 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60864, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X, 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60865, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y, 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60866, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X, 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60867, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y, 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60868, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60869, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60870, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60871, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 25.20/25.60 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60872, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 25.20/25.60 ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60873, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 25.20/25.60 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 25.20/25.60 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60874, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 25.20/25.60 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 25.20/25.60 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 25.20/25.60 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 X ) ) ] )
% 25.20/25.60 , clause( 60875, [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' )
% 25.20/25.60 , 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60876, [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 25.20/25.60 , clause( 60877, [ =( 'c_GCD_Ogcd__class_Ogcd'( X,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 25.20/25.60 , clause( 60878, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 25.20/25.60 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 25.20/25.60 X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 25.20/25.60 , clause( 60879, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 25.20/25.60 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 25.20/25.60 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60880, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 Z, Y, 'tc_nat' ), 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60881, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, X, 'tc_nat' ), X ) ] )
% 25.20/25.60 , clause( 60882, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60883, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 25.20/25.60 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ] )
% 25.20/25.60 , clause( 60884, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 25.20/25.60 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 25.20/25.60 , clause( 60885, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 25.20/25.60 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X )
% 25.20/25.60 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ] )
% 25.20/25.60 , clause( 60886, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X,
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( 'c_GCD_Ogcd__class_Ogcd'( X
% 25.20/25.60 , Z, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60887, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X,
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( 'c_GCD_Ogcd__class_Ogcd'( X
% 25.20/25.60 , Y, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60888, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 25.20/25.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60889, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 25.20/25.60 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60890, [ =( 'c_Complex_Ocnj'( 'c_Complex_Ocnj'( X ) ), X ) ] )
% 25.20/25.60 , clause( 60891, [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( Y, X, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60892, [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( Y, X, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60893, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 25.20/25.60 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 25.20/25.60 Y, Z, X ), X ) ) ] )
% 25.20/25.60 , clause( 60894, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ] )
% 25.20/25.60 , clause( 60895, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ] )
% 25.20/25.60 , clause( 60896, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60897, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 25.20/25.60 , X ) ) ] )
% 25.20/25.60 , clause( 60898, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60899, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 25.20/25.60 'c_Power_Opower__class_Opower'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 25.20/25.60 T, X ), 'c_Divides_Odiv__class_Odiv'( 'c_Power_Opower__class_Opower'( Y,
% 25.20/25.60 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 25.20/25.60 , clause( 60900, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 25.20/25.60 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 25.20/25.60 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 25.20/25.60 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 25.20/25.60 , clause( 60901, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 25.20/25.60 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 25.20/25.60 , X ) ) ] )
% 25.20/25.60 , clause( 60902, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 25.20/25.60 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 25.20/25.60 Y, X ), Z, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60903, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 25.20/25.60 Y, Z, 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( Y,
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60904, [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Ogcd'( X
% 25.20/25.60 , Y, 'tc_nat' ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60905, [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Ogcd'( X
% 25.20/25.60 , Y, 'tc_nat' ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60906, [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' )
% 25.20/25.60 ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60907, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60908, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 25.20/25.60 , X ) ] )
% 25.20/25.60 , clause( 60909, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 25.20/25.60 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60910, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 25.20/25.60 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60911, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 25.20/25.60 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60912, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 25.20/25.60 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60913, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60914, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60915, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60916, [ =( 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60917, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60918, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60919, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 25.20/25.60 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60920, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60921, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60922, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 25.20/25.60 ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 25.20/25.60 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60923, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 25.20/25.60 ) ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 25.20/25.60 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60924, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ] )
% 25.20/25.60 , clause( 60925, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 25.20/25.60 Z, X ) ) ] )
% 25.20/25.60 , clause( 60926, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 25.20/25.60 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 25.20/25.60 , clause( 60927, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 25.20/25.60 ), X ) ) ] )
% 25.20/25.60 , clause( 60928, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 25.20/25.60 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 25.20/25.60 , clause( 60929, [ =( 'c_GCD_Ogcd__class_Olcm'( X, 'c_GCD_Ogcd__class_Olcm'(
% 25.20/25.60 X, Y, 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' )
% 25.20/25.60 ) ] )
% 25.20/25.60 , clause( 60930, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( 'c_GCD_Ogcd__class_Ogcd'(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), Y, 'tc_nat' ),
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( Z, Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60931, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 25.20/25.60 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60932, [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 25.20/25.60 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60933, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 25.20/25.60 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60934, [ =( 'c_GCD_Ogcd__class_Olcm'( X, 'c_GCD_Ogcd__class_Olcm'(
% 25.20/25.60 Y, Z, 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Olcm'( Y,
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60935, [ =( 'c_GCD_Ogcd__class_Olcm'( 'c_GCD_Ogcd__class_Olcm'( X
% 25.20/25.60 , Y, 'tc_nat' ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Olcm'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60936, [ =( 'c_GCD_Ogcd__class_Olcm'( 'c_GCD_Ogcd__class_Olcm'( X
% 25.20/25.60 , Y, 'tc_nat' ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Olcm'( X,
% 25.20/25.60 'c_GCD_Ogcd__class_Olcm'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60937, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 25.20/25.60 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60938, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 25.20/25.60 =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60939, [ ~( =( 'c_Complex_Ocnj'( X ), 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 'tc_Complex_Ocomplex' ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 'tc_Complex_Ocomplex' ) ) ] )
% 25.20/25.60 , clause( 60940, [ ~( =( 'c_Complex_Ocnj'( X ), 'c_Complex_Ocnj'( Y ) ) ),
% 25.20/25.60 =( X, Y ) ] )
% 25.20/25.60 , clause( 60941, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 Y, 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ] )
% 25.20/25.60 , clause( 60942, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 25.20/25.60 Z, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'(
% 25.20/25.60 Z, X ), X ) ) ] )
% 25.20/25.60 , clause( 60943, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ),
% 25.20/25.60 'c_Int_Oiszero'( 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 25.20/25.60 , clause( 60944, [ ~( =( 'c_Complex_Oii', 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 'tc_Complex_Ocomplex' ) ) ) ] )
% 25.20/25.60 , clause( 60945, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 25.20/25.60 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 25.20/25.60 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 25.20/25.60 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 25.20/25.60 Z, T, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60946, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 25.20/25.60 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 25.20/25.60 , clause( 60947, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), ~( =( 'c_GCD_Ogcd__class_Ogcd'(
% 25.20/25.60 X, Z, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =(
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat'
% 25.20/25.60 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60948, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60949, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60950, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X ) )
% 25.20/25.60 , 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ] )
% 25.20/25.60 , clause( 60951, [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60952, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 25.20/25.60 X ) ), ~( =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60953, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 25.20/25.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 25.20/25.60 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( Y, X,
% 25.20/25.60 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60954, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60955, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60956, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 25.20/25.60 , clause( 60957, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 25.20/25.60 X, Y, 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' )
% 25.20/25.60 ) ] )
% 25.20/25.60 , clause( 60958, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 25.20/25.60 ), =( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ] )
% 25.20/25.60 , clause( 60959, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 25.20/25.60 , U, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( U,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 25.20/25.60 , U, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ] )
% 25.20/25.60 , clause( 60960, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 25.20/25.60 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 25.20/25.60 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 25.20/25.60 'c_Power_Opower__class_Opower'( Y, Z, X ), T, X ) ) ] )
% 25.20/25.60 , clause( 60961, [ ~( 'class_RealVector_Oreal__normed__div__algebra'( X ) )
% 25.20/25.60 , =( 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 25.20/25.60 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 25.20/25.60 'c_HOL_Osgn__class_Osgn'( Z, X ), X ) ) ] )
% 25.20/25.60 , clause( 60962, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 25.20/25.60 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 25.20/25.60 'c_HOL_Osgn__class_Osgn'( Z, X ), X ) ) ] )
% 25.20/25.60 , clause( 60963, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60964, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60965, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60966, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60967, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60968, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60969, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y, X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 25.20/25.60 , clause( 60970, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 25.20/25.60 =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 25.20/25.60 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ] )
% 25.20/25.60 , clause( 60971, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 25.20/25.60 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60972, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 25.20/25.60 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60973, [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60974, [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( Y,
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60975, [ ~( =( 'c_FFT__Mirabelle_Oroot'( X ),
% 25.20/25.60 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ) ] )
% 25.20/25.60 , clause( 60976, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~(
% 25.20/25.60 'c_Int_Oiszero'( 'c_HOL_Oone__class_Oone'( X ), X ) ) ] )
% 25.20/25.60 , clause( 60977, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 25.20/25.60 , clause( 60978, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 25.20/25.60 , clause( 60979, [ =( 'c_Complex_Ocnj'( 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_Complex_Ocomplex' ) ), 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_Complex_Ocomplex' ) ) ] )
% 25.20/25.60 , clause( 60980, [ =( 'c_GCD_Ogcd__class_Olcm'( 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60981, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 25.20/25.60 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 25.20/25.60 X ), Y ) ] )
% 25.20/25.60 , clause( 60982, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 25.20/25.60 ), X ), Y ) ] )
% 25.20/25.60 , clause( 60983, [ ~( =( 'c_Complex_Oii', 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_Complex_Ocomplex' ) ) ) ] )
% 25.20/25.60 , clause( 60984, [ =( 'c_GCD_Ogcd__class_Olcm'( X, 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ), 'tc_nat' ), X ) ] )
% 25.20/25.60 , clause( 60985, [ =( 'c_GCD_Ogcd__class_Olcm'( 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 25.20/25.60 , clause( 60986, [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60987, [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60988, [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60989, [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60990, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 25.20/25.60 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 25.20/25.60 , clause( 60991, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 25.20/25.60 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 25.20/25.60 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 25.20/25.60 , clause( 60992, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 25.20/25.60 =( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 25.20/25.60 )
% 25.20/25.60 , clause( 60993, [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Ozero__class_Ozero'(
% 25.20/25.60 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ] )
% 25.20/25.60 , clause( 60994, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 25.20/25.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 25.20/25.60 ) ] )
% 25.20/25.60 , clause( 60995, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 25.20/25.60 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 25.20/25.60 , clause( 60996, [ ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60997, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60998, [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 60999, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 61000, [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 61001, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 25.20/25.60 X ) ] )
% 25.20/25.60 , clause( 61002, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ] )
% 25.20/25.60 , clause( 61003, [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 61004, [ =( 'c_Power_Opower__class_Opower'(
% 25.20/25.60 'c_FFT__Mirabelle_Oroot'( X ), X, 'tc_Complex_Ocomplex' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ] )
% 25.20/25.60 , clause( 61005, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 25.20/25.60 =( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 25.20/25.60 )
% 25.20/25.60 , clause( 61006, [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 61007, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 25.20/25.60 ] )
% 25.20/25.60 , clause( 61008, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 25.20/25.60 ] )
% 25.20/25.60 , clause( 61009, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 25.20/25.60 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 25.20/25.60 ] )
% 25.20/25.60 , clause( 61010, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y
% 25.20/25.60 ) ] )
% 25.20/25.60 , clause( 61011, [ =( 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 25.20/25.60 , clause( 61012, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 25.20/25.60 , clause( 61013, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 25.20/25.60 ) ] )
% 25.20/25.60 , clause( 61014, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 25.20/25.60 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y
% 25.20/25.60 ) ] )
% 25.20/25.60 , clause( 61015, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 61016, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 61017, [ ~( 'class_RealVector_Oreal__normed__algebra__1'( X ) ),
% 25.20/25.60 =( 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 25.20/25.60 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 25.20/25.60 , clause( 61018, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 25.20/25.60 ), 'tc_nat' ) ] )
% 25.20/25.60 , clause( 61019, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 25.20/25.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 25.20/25.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 25.20/25.60 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 25.20/25.60 , clause( 61020, [ =( 'c_HOL_Otimes__class_Otimes'(
% 25.20/25.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 25.20/25.60 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 25.20/25.60 , clause( 61021, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 25.20/25.60 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 25.20/25.60 ] )
% 25.20/25.60 , clause( 61022, [ ~( =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Oone__class_Oone'(
% 25.20/25.60 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ) ] )
% 25.20/25.60 , clause( 61023, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 25.20/25.60 ] )
% 25.20/25.60 , clause( 61024, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' )
% 25.20/25.60 ] )
% 25.20/25.60 , clause( 61025, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 25.20/25.60 )
% 25.20/25.60 , clause( 61026, [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ]
% 25.20/25.60 )
% 25.20/25.60 , clause( 61027, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ]
% 25.20/25.60 )
% 25.20/25.60 , clause( 61028, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 25.20/25.60 , clause( 61029, [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ] )
% 25.20/25.60 , clause( 61030, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 25.20/25.60 , clause( 61031, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 25.20/25.60 , clause( 61032, [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ] )
% 25.20/25.60 , clause( 61033, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 25.20/25.60 , clause( 61034, [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ] )
% 25.20/25.60 , clause( 61035, [ 'class_Power_Opower'( 'tc_nat' ) ] )
% 25.20/25.60 , clause( 61036, [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 25.20/25.60 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.60 , clause( 61037, [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 25.20/25.60 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.60 , clause( 61038, [ 'class_RealVector_Oreal__normed__div__algebra'(
% 25.20/25.60 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.60 , clause( 61039, [ 'class_RealVector_Oreal__normed__algebra__1'(
% 25.20/25.60 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.60 , clause( 61040, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 25.20/25.60 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.60 , clause( 61041, [ 'class_Ring__and__Field_Odivision__by__zero'(
% 25.20/25.60 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.60 , clause( 61042, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 25.20/25.60 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.60 , clause( 61043, [ 'class_RealVector_Oreal__normed__algebra'(
% 25.20/25.61 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.61 , clause( 61044, [ 'class_OrderedGroup_Oab__semigroup__mult'(
% 25.20/25.61 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.61 , clause( 61045, [ 'class_RealVector_Oreal__normed__vector'(
% 25.20/25.61 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.61 , clause( 61046, [ 'class_OrderedGroup_Ocomm__monoid__mult'(
% 25.20/25.61 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.61 , clause( 61047, [ 'class_Ring__and__Field_Odivision__ring'(
% 25.20/25.61 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.61 , clause( 61048, [ 'class_RealVector_Oreal__normed__field'(
% 25.20/25.61 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.61 , clause( 61049, [ 'class_Ring__and__Field_Ozero__neq__one'(
% 25.20/25.61 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.61 , clause( 61050, [ 'class_Ring__and__Field_Osemiring__1'(
% 25.20/25.61 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.61 , clause( 61051, [ 'class_Ring__and__Field_Osemiring__0'(
% 25.20/25.61 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.61 , clause( 61052, [ 'class_Ring__and__Field_Omult__zero'(
% 25.20/25.61 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.61 , clause( 61053, [ 'class_OrderedGroup_Omonoid__mult'(
% 25.20/25.61 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.61 , clause( 61054, [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' )
% 25.20/25.61 ] )
% 25.20/25.61 , clause( 61055, [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' )
% 25.20/25.61 ] )
% 25.20/25.61 , clause( 61056, [ 'class_Nat_Osemiring__char__0'( 'tc_Complex_Ocomplex' )
% 25.20/25.61 ] )
% 25.20/25.61 , clause( 61057, [ 'class_Ring__and__Field_Odvd'( 'tc_Complex_Ocomplex' ) ]
% 25.20/25.61 )
% 25.20/25.61 , clause( 61058, [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.61 , clause( 61059, [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.61 ] ).
% 25.20/25.61
% 25.20/25.61
% 25.20/25.61
% 25.20/25.61 subsumption(
% 25.20/25.61 clause( 231, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 25.20/25.61 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 25.20/25.61 X ), Y ) ] )
% 25.20/25.61 , clause( 60981, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 25.20/25.61 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 25.20/25.61 X ), Y ) ] )
% 25.20/25.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 25.20/25.61 ), ==>( 1, 1 )] ) ).
% 25.20/25.61
% 25.20/25.61
% 25.20/25.61 subsumption(
% 25.20/25.61 clause( 251, [ =( 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'(
% 25.20/25.61 X ), X, 'tc_Complex_Ocomplex' ), 'c_HOL_Oone__class_Oone'(
% 25.20/25.61 'tc_Complex_Ocomplex' ) ) ] )
% 25.20/25.61 , clause( 61004, [ =( 'c_Power_Opower__class_Opower'(
% 25.20/25.61 'c_FFT__Mirabelle_Oroot'( X ), X, 'tc_Complex_Ocomplex' ),
% 25.20/25.61 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ] )
% 25.20/25.61 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 25.20/25.61
% 25.20/25.61
% 25.20/25.61 subsumption(
% 25.20/25.61 clause( 263, [ ~( =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Oone__class_Oone'(
% 25.20/25.61 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ) ] )
% 25.20/25.61 , clause( 61022, [ ~( =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Oone__class_Oone'(
% 25.20/25.61 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ) ] )
% 25.20/25.61 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 25.20/25.61
% 25.20/25.61
% 25.20/25.61 subsumption(
% 25.20/25.61 clause( 294, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' )
% 25.20/25.61 ] )
% 25.20/25.61 , clause( 61053, [ 'class_OrderedGroup_Omonoid__mult'(
% 25.20/25.61 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.61 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 25.20/25.61
% 25.20/25.61
% 25.20/25.61 eqswap(
% 25.20/25.61 clause( 63246, [ =( X, 'c_Power_Opower__class_Opower'( X,
% 25.20/25.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y ) ), ~(
% 25.20/25.61 'class_OrderedGroup_Omonoid__mult'( Y ) ) ] )
% 25.20/25.62 , clause( 231, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 25.20/25.62 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 25.20/25.62 X ), Y ) ] )
% 25.20/25.62 , 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 25.20/25.62
% 25.20/25.62
% 25.20/25.62 paramod(
% 25.20/25.62 clause( 63249, [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Oone__class_Oone'(
% 25.20/25.62 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ), ~(
% 25.20/25.62 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ) ] )
% 25.20/25.62 , clause( 251, [ =( 'c_Power_Opower__class_Opower'(
% 25.20/25.62 'c_FFT__Mirabelle_Oroot'( X ), X, 'tc_Complex_Ocomplex' ),
% 25.20/25.62 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ] )
% 25.20/25.62 , 0, clause( 63246, [ =( X, 'c_Power_Opower__class_Opower'( X,
% 25.20/25.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y ) ), ~(
% 25.20/25.62 'class_OrderedGroup_Omonoid__mult'( Y ) ) ] )
% 25.20/25.62 , 0, 4, substitution( 0, [ :=( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )] )
% 25.20/25.62 , substitution( 1, [ :=( X, 'c_FFT__Mirabelle_Oroot'(
% 25.20/25.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), :=( Y, 'tc_Complex_Ocomplex' )] )
% 25.20/25.62 ).
% 25.20/25.62
% 25.20/25.62
% 25.20/25.62 resolution(
% 25.20/25.62 clause( 63250, [ ~( 'class_OrderedGroup_Omonoid__mult'(
% 25.20/25.62 'tc_Complex_Ocomplex' ) ) ] )
% 25.20/25.62 , clause( 263, [ ~( =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Oone__class_Oone'(
% 25.20/25.62 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ) ] )
% 25.20/25.62 , 0, clause( 63249, [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Oone__class_Oone'(
% 25.20/25.62 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ), ~(
% 25.20/25.62 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ) ] )
% 25.20/25.62 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 25.20/25.62
% 25.20/25.62
% 25.20/25.62 subsumption(
% 25.20/25.62 clause( 60597, [ ~( 'class_OrderedGroup_Omonoid__mult'(
% 25.20/25.62 'tc_Complex_Ocomplex' ) ) ] )
% 25.20/25.62 , clause( 63250, [ ~( 'class_OrderedGroup_Omonoid__mult'(
% 25.20/25.62 'tc_Complex_Ocomplex' ) ) ] )
% 25.20/25.62 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 25.20/25.62
% 25.20/25.62
% 25.20/25.62 resolution(
% 25.20/25.62 clause( 63251, [] )
% 25.20/25.62 , clause( 60597, [ ~( 'class_OrderedGroup_Omonoid__mult'(
% 25.20/25.62 'tc_Complex_Ocomplex' ) ) ] )
% 25.20/25.62 , 0, clause( 294, [ 'class_OrderedGroup_Omonoid__mult'(
% 25.20/25.62 'tc_Complex_Ocomplex' ) ] )
% 25.20/25.62 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 25.20/25.62
% 25.20/25.62
% 25.20/25.62 subsumption(
% 25.20/25.62 clause( 60669, [] )
% 25.20/25.62 , clause( 63251, [] )
% 25.20/25.62 , substitution( 0, [] ), permutation( 0, [] ) ).
% 25.20/25.62
% 25.20/25.62
% 25.20/25.62 end.
% 25.20/25.62
% 25.20/25.62 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 25.20/25.62
% 25.20/25.62 Memory use:
% 25.20/25.62
% 25.20/25.62 space for terms: 1376722
% 25.20/25.62 space for clauses: 2717327
% 25.20/25.62
% 25.20/25.62
% 25.20/25.62 clauses generated: 453936
% 25.20/25.62 clauses kept: 60670
% 25.20/25.62 clauses selected: 946
% 25.20/25.62 clauses deleted: 2502
% 25.20/25.62 clauses inuse deleted: 35
% 25.20/25.62
% 25.20/25.62 subsentry: 1034061
% 25.20/25.62 literals s-matched: 667847
% 25.20/25.62 literals matched: 600701
% 25.20/25.62 full subsumption: 379391
% 25.20/25.62
% 25.20/25.62 checksum: 109094082
% 25.20/25.62
% 25.20/25.62
% 25.20/25.62 Bliksem ended
%------------------------------------------------------------------------------