TSTP Solution File: ALG377-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : ALG377-1 : 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 : Thu Jul 14 12:10:36 EDT 2022
% Result : Unsatisfiable 66.65s 67.05s
% Output : Refutation 66.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG377-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Wed Jun 8 05:37:06 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.87/1.23 *** allocated 10000 integers for termspace/termends
% 0.87/1.23 *** allocated 10000 integers for clauses
% 0.87/1.23 *** allocated 10000 integers for justifications
% 0.87/1.23 *** allocated 15000 integers for termspace/termends
% 0.87/1.23 Bliksem 1.12
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 Automatic Strategy Selection
% 0.87/1.23
% 0.87/1.23 Clauses:
% 0.87/1.23 [
% 0.87/1.23 [ 'c_lessequals'( 'c_RealDef_Oreal'( 'c_RComplete_Onatfloor'( X ),
% 0.87/1.23 'tc_nat' ), X, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' )
% 0.87/1.23 ) ],
% 0.87/1.23 [ =( 'c_RComplete_Onatfloor'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.23 ) ), ~( 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ =( 'c_RComplete_Onatfloor'( 'c_RealDef_Oreal'( X, 'tc_nat' ) ), X ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 0.87/1.23 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 0.87/1.23 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.87/1.23 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 0.87/1.23 X ) ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.23 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.23 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.23 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.87/1.23 , T, X ), X ), T, X ) ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 0.87/1.23 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.87/1.23 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.87/1.23 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 0.87/1.23 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 0.87/1.23 Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.87/1.23 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.87/1.23 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ =( 'c_RComplete_Onatfloor'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.87/1.23 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 0.87/1.23 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.23 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat'
% 0.87/1.23 ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.23 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ),
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ), 'tc_nat' ), Z, 'tc_nat' )
% 0.87/1.23 , 'tc_nat' ) ) ],
% 0.87/1.23 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 0.87/1.23 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ) ), Y, 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat'
% 0.87/1.23 ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ) ), Y, 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'c_RealDef_Oreal'( 'c_RComplete_Onatfloor'( X ), 'tc_nat' ),
% 0.87/1.23 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ) ],
% 0.87/1.23 [ =( 'c_RComplete_Onatfloor'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.87/1.23 'c_RealDef_Oreal'( Y, 'tc_nat' ), 'tc_RealDef_Oreal' ) ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_RComplete_Onatfloor'( X ), Y, 'tc_nat' ) )
% 0.87/1.23 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), X
% 0.87/1.23 , 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ =( 'c_RComplete_Onatfloor'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X
% 0.87/1.23 , 'c_HOL_Oplus__class_Oplus'( 'c_RealDef_Oreal'( Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( 'c_RealDef_Oreal'( Y, 'tc_nat'
% 0.87/1.23 ), X, 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 0.87/1.23 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.87/1.23 , X ), 'c_RealVector_Onorm__class_Onorm'( Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.23 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 Z, Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.87/1.23 , X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 0.87/1.23 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.87/1.23 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 0.87/1.23 , X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.87/1.23 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 0.87/1.23 , X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 0.87/1.23 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.87/1.23 , X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 0.87/1.23 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.87/1.23 , X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.87/1.23 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.87/1.23 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.87/1.23 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.87/1.23 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 0.87/1.23 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 0.87/1.23 [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( X, Y, 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_RealDef_Oreal' ), =( X, Y ), ~(
% 0.87/1.23 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( X, 'tc_RealDef_Oreal' ), Y, 'tc_RealDef_Oreal'
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_RealVector_Onorm__class_Onorm'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( T
% 0.87/1.23 , U, 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_RealVector_Onorm__class_Onorm'( Z, X ), U,
% 0.87/1.23 'tc_RealDef_Oreal' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_RealVector_Onorm__class_Onorm'( Y, X ), T, 'tc_RealDef_Oreal' ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.23 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.23 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.87/1.23 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 0.87/1.23 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.87/1.23 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 0.87/1.23 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.87/1.23 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 0.87/1.23 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.87/1.23 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.87/1.23 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.23 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.23 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 0.87/1.23 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 X, T, 'tc_nat' ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.87/1.23 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.87/1.23 ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.87/1.23 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.87/1.23 ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 0.87/1.23 Y, 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.87/1.23 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 0.87/1.23 ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.87/1.23 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.87/1.23 ],
% 0.87/1.23 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.87/1.23 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.23 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.23 ), 'tc_nat' ), X ) ],
% 0.87/1.23 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.87/1.23 , X, 'tc_nat' ), X ) ],
% 0.87/1.23 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.87/1.23 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 0.87/1.23 , X ), X ), 'c_HOL_Oinverse__class_Odivide'(
% 0.87/1.23 'c_RealVector_Onorm__class_Onorm'( Y, X ),
% 0.87/1.23 'c_RealVector_Onorm__class_Onorm'( Z, X ), 'tc_RealDef_Oreal' ) ), =( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ 'c_lessequals'( 'c_RealDef_Oreal'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' )
% 0.87/1.23 , 'tc_RealDef_Oreal' ) ],
% 0.87/1.23 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'(
% 0.87/1.23 'c_RealDef_Oreal'( X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'( X ), 'tc_nat' ),
% 0.87/1.23 'tc_RealDef_Oreal' ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ) ],
% 0.87/1.23 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( X, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), X,
% 0.87/1.23 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.23 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 0.87/1.23 ],
% 0.87/1.23 [ =( 'c_RComplete_Onatfloor'( 'c_HOL_Oinverse__class_Odivide'( X,
% 0.87/1.23 'c_RealDef_Oreal'( Y, 'tc_nat' ), 'tc_RealDef_Oreal' ) ),
% 0.87/1.23 'c_Divides_Odiv__class_Odiv'( 'c_RComplete_Onatfloor'( X ), Y, 'tc_nat' )
% 0.87/1.23 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.87/1.23 , Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 0.87/1.23 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ =( 'c_HOL_Oinverse__class_Odivide'( 'c_RealDef_Oreal'( X, 'tc_nat' ),
% 0.87/1.23 'c_RealDef_Oreal'( Y, 'tc_nat' ), 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_RealDef_Oreal'(
% 0.87/1.23 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( 'c_RealDef_Oreal'(
% 0.87/1.23 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 0.87/1.23 'c_RealDef_Oreal'( Y, 'tc_nat' ), 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 0.87/1.23 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 0.87/1.23 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 0.87/1.23 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 0.87/1.23 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.87/1.23 ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.87/1.23 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 0.87/1.23 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 0.87/1.23 ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.23 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.23 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.23 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 0.87/1.23 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 0.87/1.23 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 0.87/1.23 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.87/1.23 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 0.87/1.23 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.87/1.23 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.23 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 0.87/1.23 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 0.87/1.23 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.87/1.23 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.23 Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 0.87/1.23 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Z, Y, X ),
% 0.87/1.23 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.87/1.23 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.87/1.23 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.87/1.23 ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.87/1.23 ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.87/1.23 ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.87/1.23 ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.23 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.23 ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.87/1.23 ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.87/1.23 ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.87/1.23 ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.23 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.23 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 0.87/1.23 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.23 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.87/1.23 X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.23 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 Z, T, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 Z, T, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.23 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.87/1.23 X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.23 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 Y, T, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 Y, T, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.23 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.23 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.23 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.23 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.87/1.23 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.23 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.23 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 0.87/1.23 , X ), 'c_lessequals'( Y, Y, X ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 0.87/1.23 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.23 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.87/1.23 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.23 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 0.87/1.23 , X ), Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.23 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.23 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.23 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 0.87/1.23 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.23 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.23 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.23 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.23 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.23 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 0.87/1.23 , X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.23 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.87/1.23 , X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.23 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.23 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( =( 'c_RealDef_Oreal'( X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.87/1.23 ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.87/1.23 , X ), X ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.87/1.23 , X ), X ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 0.87/1.23 , Y, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.23 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.23 'c_Suc'( X ), 'tc_nat' ) ],
% 0.87/1.23 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 0.87/1.23 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.23 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 0.87/1.23 , 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.23 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.23 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_RealDef_Oreal'( X, 'tc_nat' ),
% 0.87/1.23 'c_RealDef_Oreal'( Y, 'tc_nat' ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_RealDef_Oreal'( X, 'tc_nat' ),
% 0.87/1.23 'c_RealDef_Oreal'( Y, 'tc_nat' ), 'tc_RealDef_Oreal' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.87/1.23 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_RealVector_Onorm__class_Onorm'( Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 0.87/1.23 ],
% 0.87/1.23 [ ~( 'c_HOL_Oord__class_Oless'( 'c_RealDef_Oreal'( X, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 0.87/1.23 ],
% 0.87/1.23 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.87/1.23 'c_RealVector_Onorm__class_Onorm'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_RealDef_Oreal' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal'
% 0.87/1.23 ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( X,
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Y, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 Y, X, 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ), Y,
% 0.87/1.23 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( X,
% 0.87/1.23 'tc_RealDef_Oreal' ), Y, 'tc_RealDef_Oreal' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal'
% 0.87/1.23 ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ =( 'c_HOL_Oabs__class_Oabs'( 'c_RealDef_Oreal'( X, 'tc_nat' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( X, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.23 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 0.87/1.23 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.23 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.23 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.23 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 0.87/1.23 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.23 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.87/1.23 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.87/1.23 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.23 Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X )
% 0.87/1.23 , 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.87/1.23 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.87/1.23 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.23 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 0.87/1.23 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.23 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 0.87/1.23 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.23 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 0.87/1.23 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 0.87/1.23 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 0.87/1.23 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.87/1.23 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.87/1.23 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.87/1.23 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 0.87/1.23 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.23 ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.23 ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.23 ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.23 ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 0.87/1.23 ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.23 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 0.87/1.23 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.23 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.87/1.23 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 0.87/1.23 ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.87/1.23 ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 0.87/1.23 ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.87/1.23 ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.23 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.23 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 0.87/1.23 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 0.87/1.23 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.87/1.23 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 0.87/1.23 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 0.87/1.23 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 0.87/1.23 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 0.87/1.23 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 0.87/1.23 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.87/1.23 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.87/1.23 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_RealVector_Oreal__normed__algebra__1'( X ) ), =(
% 0.87/1.23 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.87/1.23 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.87/1.23 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.23 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.23 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.23 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.23 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.23 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.87/1.23 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.23 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.87/1.23 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 0.87/1.23 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 0.87/1.23 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.87/1.23 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 0.87/1.23 , X ), X ), 'c_HOL_Oinverse__class_Odivide'(
% 0.87/1.23 'c_RealVector_Onorm__class_Onorm'( Y, X ),
% 0.87/1.23 'c_RealVector_Onorm__class_Onorm'( Z, X ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( X, Y, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), Y, 'tc_RealDef_Oreal' )
% 0.87/1.23 ) ],
% 0.87/1.23 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( X, Y, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), Y, 'tc_RealDef_Oreal' )
% 0.87/1.23 ) ],
% 0.87/1.23 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( X, Y, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( X,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 0.87/1.23 ],
% 0.87/1.23 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( X, Y, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( X,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 0.87/1.23 ],
% 0.87/1.23 [ 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), Y, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, X, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), X,
% 0.87/1.23 'tc_RealDef_Oreal' ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, X, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_RealDef_Oreal'( X, 'tc_nat' ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.23 [ 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( X, 'tc_RealDef_Oreal' ), Y,
% 0.87/1.23 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ) ),
% 0.87/1.23 ~( 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, 'tc_RealDef_Oreal'
% 0.87/1.23 ), X, 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal'
% 0.87/1.23 ), Y, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.23 Y, 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ), =( Y,
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.87/1.23 , 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ) ) ), =( X, Y ) ],
% 0.87/1.23 [ =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Y, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( X,
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ouminus__class_Ouminus'( X,
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 0.87/1.23 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~( =(
% 0.87/1.23 'c_RealVector_Onorm__class_Onorm'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( 'c_RealVector_Onorm__class_Onorm'( Y, X ),
% 0.87/1.23 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'( Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 0.87/1.23 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 0.87/1.23 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.87/1.23 [ =( 'c_HOL_Oabs__class_Oabs'( X, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.87/1.23 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.87/1.23 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.87/1.23 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.87/1.23 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.87/1.23 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 0.87/1.23 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 0.87/1.23 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal'
% 0.87/1.23 ), 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ozero__class_Ozero'( X ), X
% 0.87/1.23 ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 0.87/1.23 ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.23 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.23 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.87/1.23 ), =( Z, Y ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal'
% 0.87/1.23 ), 'c_RealVector_Onorm__class_Onorm'( Y, X ), 'tc_RealDef_Oreal' ), =( Y
% 0.87/1.23 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.87/1.23 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.23 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.23 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.23 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 0.87/1.23 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_RealVector_Onorm__class_Onorm'( Y, X ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 0.87/1.23 , X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 0.87/1.23 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 0.87/1.23 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.87/1.23 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 0.87/1.23 , X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 0.87/1.23 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.87/1.23 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 0.87/1.23 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.23 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 0.87/1.23 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 X ) ) ],
% 0.87/1.23 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.23 ), 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.87/1.23 ), 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.23 X, 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.87/1.23 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 0.87/1.23 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 X ) ) ],
% 0.87/1.23 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 0.87/1.23 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.23 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( X, 'tc_nat' ),
% 0.87/1.23 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( X, 'tc_nat' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.23 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.23 , Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.87/1.23 , X ) ) ],
% 0.87/1.23 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.23 , Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.23 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.23 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.87/1.23 'tc_nat' ) ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.87/1.23 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.23 [ =( 'c_HOL_Oabs__class_Oabs'( X, 'tc_RealDef_Oreal' ), X ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.87/1.23 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.87/1.23 [ =( 'c_RealDef_Oreal'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat'
% 0.87/1.23 ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.87/1.23 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.23 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 0.87/1.23 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 0.87/1.23 ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.23 Y, X ), X ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.23 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.23 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.23 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.23 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 0.87/1.23 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 0.87/1.23 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), X
% 0.87/1.23 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.23 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), Z
% 0.87/1.23 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.87/1.23 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_lessequals'(
% 0.87/1.23 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X )
% 0.87/1.23 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_RealVector_Onorm__class_Onorm'( Y,
% 0.87/1.23 X ), 'c_RealVector_Onorm__class_Onorm'( Z, X ), 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ) ],
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.23 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ),
% 0.87/1.23 'tc_nat' ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.23 [ =( 'c_RealDef_Oreal'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.87/1.23 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_lessequals'( 'c_RealDef_Oreal'( 'c_Divides_Odiv__class_Odiv'( X, Y
% 0.87/1.23 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oinverse__class_Odivide'(
% 0.87/1.23 'c_RealDef_Oreal'( X, 'tc_nat' ), 'c_RealDef_Oreal'( Y, 'tc_nat' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.23 [ 'c_lessequals'( X, 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 0.87/1.23 ],
% 0.87/1.23 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_RealDef_Oreal' )
% 0.87/1.23 , 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' )
% 0.87/1.23 , ~( 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( X,
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z,
% 0.87/1.23 'tc_RealDef_Oreal' ), 'c_HOL_Ouminus__class_Ouminus'( T,
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'( X,
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Z, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( T,
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.23 [ 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal'
% 0.87/1.23 ), Y, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'(
% 0.87/1.23 X, 'tc_RealDef_Oreal' ), Y, 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_RealDef_Oreal'( X,
% 0.87/1.23 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( Y, 'tc_nat' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_RealDef_Oreal'( X, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_RealDef_Oreal'( Y, 'tc_nat' ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), 'c_lessequals'( Y, X,
% 0.87/1.23 'tc_RealDef_Oreal' ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.87/1.23 'c_lessequals'( Z, Y, X ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 0.87/1.23 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 0.87/1.23 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.23 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.23 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 0.87/1.23 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 0.87/1.23 [ 'c_lessequals'( X, X, 'tc_RealDef_Oreal' ) ],
% 0.87/1.23 [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Z, Y,
% 0.87/1.23 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( X, Z, 'tc_RealDef_Oreal' ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 0.87/1.23 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ],
% 0.87/1.23 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.87/1.23 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.87/1.23 X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.87/1.23 X ) ) ],
% 0.87/1.23 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.87/1.23 X ) ) ],
% 0.87/1.23 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.87/1.23 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.87/1.23 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.23 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 0.87/1.23 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.87/1.23 X ) ) ), =( Y, T ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.87/1.23 X ) ) ), =( Z, T ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.87/1.23 X ) ) ), =( Z, T ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.23 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 0.87/1.23 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 0.87/1.23 X ), X ) ) ],
% 0.87/1.23 [ =( 'c_RealDef_Oreal'( 'c_Suc'( X ), 'tc_nat' ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_RealDef_Oreal'( X, 'tc_nat' ),
% 0.87/1.23 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.87/1.23 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 0.87/1.23 Y, X ), Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.87/1.23 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.87/1.23 [ 'c_lessequals'( 'c_RealDef_Oreal'( 'c_Suc'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'v_N1____', 'v_N2____', 'tc_nat' ) ), 'tc_nat' ), 'c_RealDef_Oreal'(
% 0.87/1.23 'c_Suc'( 'v_f____'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____',
% 0.87/1.23 'tc_nat' ) ) ), 'tc_nat' ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.23 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.87/1.23 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.23 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.23 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.87/1.23 X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.23 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.23 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.87/1.23 X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.87/1.23 ) ],
% 0.87/1.23 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_RealDef_Oreal' )
% 0.87/1.23 , 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_RealDef_Oreal' ),
% 0.87/1.23 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Y, Z, 'tc_RealDef_Oreal' ) ) ]
% 0.87/1.23 ,
% 0.87/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.87/1.23 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.87/1.23 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.87/1.23 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.23 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_RealDef_Oreal' ) ), ~(
% 0.87/1.23 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.87/1.23 , X ) ) ), =( Y, Z ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.87/1.23 , X ) ) ), =( Y, Z ) ],
% 0.87/1.23 [ ~( =( 'c_RealDef_Oreal'( X, 'tc_nat' ), 'c_RealDef_Oreal'( Y, 'tc_nat'
% 0.87/1.23 ) ) ), =( X, Y ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.87/1.23 , X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.23 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 0.87/1.23 ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.23 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.87/1.23 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.23 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.23 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.23 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.87/1.23 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.23 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.87/1.23 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.23 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.87/1.23 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.23 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.87/1.23 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ =( 'c_RealDef_Oreal'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 0.87/1.23 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_RealDef_Oreal'( X, 'tc_nat' )
% 0.87/1.23 , 'c_RealDef_Oreal'( Y, 'tc_nat' ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.87/1.23 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 0.87/1.23 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.23 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 0.87/1.23 Y, Z, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.87/1.23 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.23 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 0.87/1.23 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 0.87/1.23 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 0.87/1.23 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.87/1.23 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 0.87/1.23 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 0.87/1.23 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.87/1.23 ), Y ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.87/1.23 ) ) ],
% 0.87/1.23 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.87/1.23 ), Y ) ],
% 0.87/1.23 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.23 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.87/1.24 ), Y ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 0.87/1.24 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 0.87/1.24 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.87/1.24 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.24 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 0.87/1.24 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.87/1.24 [ 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'(
% 0.87/1.24 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 0.87/1.24 'c_Suc'( 'v_f____'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____',
% 0.87/1.24 'tc_nat' ) ) ), 'tc_nat' ), 'tc_RealDef_Oreal' ),
% 0.87/1.24 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 0.87/1.24 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ),
% 0.87/1.24 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.24 'c_HOL_Ouminus__class_Ouminus'( 'v_s____', 'tc_RealDef_Oreal' ),
% 0.87/1.24 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 0.87/1.24 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'( 'v_f____'(
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ) ),
% 0.87/1.24 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 0.87/1.24 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( 'v_s____',
% 0.87/1.24 'tc_RealDef_Oreal' ), 'c_HOL_Oinverse__class_Odivide'(
% 0.87/1.24 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 0.87/1.24 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) )
% 0.87/1.24 , 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 0.87/1.24 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.87/1.24 ],
% 0.87/1.24 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.87/1.24 ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 0.87/1.24 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 0.87/1.24 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_RealDef_Oreal'
% 0.87/1.24 ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 0.87/1.24 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 0.87/1.24 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_RealDef_Oreal'
% 0.87/1.24 ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_RealDef_Oreal' )
% 0.87/1.24 ],
% 0.87/1.24 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'class_RealVector_Oreal__normed__algebra__1'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.24 ,
% 0.87/1.24 [ 'class_RealVector_Oreal__normed__vector'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Oordered__field'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_RealVector_Oreal__normed__field'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Oab__group__add'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Omonoid__add'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_OrderedGroup_Ogroup__add'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Oabs__if'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Ofield'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_Ring__and__Field_Oidom'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_Nat_Osemiring__char__0'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_Orderings_Opreorder'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_Orderings_Olinorder'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_Orderings_Oorder'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.24 [ 'class_Int_Onumber__ring'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.24 ] .
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24 percentage equality = 0.206411, percentage horn = 0.865731
% 0.87/1.24 This is a problem with some equality
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24 Options Used:
% 0.87/1.24
% 0.87/1.24 useres = 1
% 0.87/1.24 useparamod = 1
% 0.87/1.24 useeqrefl = 1
% 0.87/1.24 useeqfact = 1
% 0.87/1.24 usefactor = 1
% 0.87/1.24 usesimpsplitting = 0
% 0.87/1.24 usesimpdemod = 5
% 0.87/1.24 usesimpres = 3
% 0.87/1.24
% 0.87/1.24 resimpinuse = 1000
% 0.87/1.24 resimpclauses = 20000
% 0.87/1.24 substype = eqrewr
% 0.87/1.24 backwardsubs = 1
% 0.87/1.24 selectoldest = 5
% 0.87/1.24
% 0.87/1.24 litorderings [0] = split
% 4.19/4.56 litorderings [1] = extend the termordering, first sorting on arguments
% 4.19/4.56
% 4.19/4.56 termordering = kbo
% 4.19/4.56
% 4.19/4.56 litapriori = 0
% 4.19/4.56 termapriori = 1
% 4.19/4.56 litaposteriori = 0
% 4.19/4.56 termaposteriori = 0
% 4.19/4.56 demodaposteriori = 0
% 4.19/4.56 ordereqreflfact = 0
% 4.19/4.56
% 4.19/4.56 litselect = negord
% 4.19/4.56
% 4.19/4.56 maxweight = 15
% 4.19/4.56 maxdepth = 30000
% 4.19/4.56 maxlength = 115
% 4.19/4.56 maxnrvars = 195
% 4.19/4.56 excuselevel = 1
% 4.19/4.56 increasemaxweight = 1
% 4.19/4.56
% 4.19/4.56 maxselected = 10000000
% 4.19/4.56 maxnrclauses = 10000000
% 4.19/4.56
% 4.19/4.56 showgenerated = 0
% 4.19/4.56 showkept = 0
% 4.19/4.56 showselected = 0
% 4.19/4.56 showdeleted = 0
% 4.19/4.56 showresimp = 1
% 4.19/4.56 showstatus = 2000
% 4.19/4.56
% 4.19/4.56 prologoutput = 1
% 4.19/4.56 nrgoals = 5000000
% 4.19/4.56 totalproof = 1
% 4.19/4.56
% 4.19/4.56 Symbols occurring in the translation:
% 4.19/4.56
% 4.19/4.56 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 4.19/4.56 . [1, 2] (w:1, o:86, a:1, s:1, b:0),
% 4.19/4.56 ! [4, 1] (w:0, o:39, a:1, s:1, b:0),
% 4.19/4.56 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 4.19/4.56 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 4.19/4.56 'c_RComplete_Onatfloor' [40, 1] (w:1, o:44, a:1, s:1, b:0),
% 4.19/4.56 'tc_nat' [41, 0] (w:1, o:11, a:1, s:1, b:0),
% 4.19/4.56 'c_RealDef_Oreal' [42, 2] (w:1, o:111, a:1, s:1, b:0),
% 4.19/4.56 'tc_RealDef_Oreal' [43, 0] (w:1, o:12, a:1, s:1, b:0),
% 4.19/4.56 'c_lessequals' [44, 3] (w:1, o:116, a:1, s:1, b:0),
% 4.19/4.56 'c_HOL_Ozero__class_Ozero' [45, 1] (w:1, o:45, a:1, s:1, b:0),
% 4.19/4.56 'c_Suc' [48, 1] (w:1, o:46, a:1, s:1, b:0),
% 4.19/4.56 'c_Divides_Odiv__class_Omod' [49, 3] (w:1, o:117, a:1, s:1, b:0),
% 4.19/4.56 'class_Divides_Oring__div' [51, 1] (w:1, o:47, a:1, s:1, b:0),
% 4.19/4.56 'c_HOL_Ouminus__class_Ouminus' [53, 2] (w:1, o:112, a:1, s:1, b:0),
% 4.19/4.56 'class_Divides_Osemiring__div' [56, 1] (w:1, o:48, a:1, s:1, b:0),
% 4.19/4.56 'c_HOL_Oplus__class_Oplus' [57, 3] (w:1, o:119, a:1, s:1, b:0),
% 4.19/4.56 'c_HOL_Oord__class_Oless' [60, 3] (w:1, o:118, a:1, s:1, b:0),
% 4.19/4.56 'c_HOL_Oone__class_Oone' [61, 1] (w:1, o:49, a:1, s:1, b:0),
% 4.19/4.56 'c_Divides_Odiv__class_Odiv' [62, 3] (w:1, o:120, a:1, s:1, b:0),
% 4.19/4.56 'class_OrderedGroup_Oordered__ab__group__add' [63, 1] (w:1, o:51, a:1
% 4.19/4.56 , s:1, b:0),
% 4.19/4.56 'class_OrderedGroup_Ogroup__add' [64, 1] (w:1, o:52, a:1, s:1, b:0),
% 4.19/4.56
% 4.19/4.56 'class_RealVector_Oreal__normed__vector' [65, 1] (w:1, o:53, a:1, s:1
% 4.19/4.56 , b:0),
% 4.19/4.56 'c_RealVector_Onorm__class_Onorm' [66, 2] (w:1, o:113, a:1, s:1, b:0)
% 4.19/4.56 ,
% 4.19/4.56 'class_OrderedGroup_Opordered__ab__group__add__abs' [67, 1] (w:1, o:
% 4.19/4.56 54, a:1, s:1, b:0),
% 4.19/4.56 'c_HOL_Oabs__class_Oabs' [68, 2] (w:1, o:114, a:1, s:1, b:0),
% 4.19/4.56 'class_OrderedGroup_Opordered__ab__group__add' [69, 1] (w:1, o:55, a:
% 4.19/4.56 1, s:1, b:0),
% 4.19/4.56 'class_Ring__and__Field_Ofield' [70, 1] (w:1, o:56, a:1, s:1, b:0),
% 4.19/4.56 'class_Ring__and__Field_Odivision__by__zero' [71, 1] (w:1, o:58, a:1
% 4.19/4.56 , s:1, b:0),
% 4.19/4.56 'c_HOL_Oinverse__class_Odivide' [72, 3] (w:1, o:121, a:1, s:1, b:0),
% 4.19/4.56
% 4.19/4.56 'class_RealVector_Oreal__normed__field' [73, 1] (w:1, o:59, a:1, s:1
% 4.19/4.56 , b:0),
% 4.19/4.56 'class_Ring__and__Field_Oordered__field' [75, 1] (w:1, o:60, a:1, s:1
% 4.19/4.56 , b:0),
% 4.19/4.56 'class_Ring__and__Field_Ozero__neq__one' [85, 1] (w:1, o:61, a:1, s:1
% 4.19/4.56 , b:0),
% 4.19/4.56 'class_Ring__and__Field_Oordered__idom' [86, 1] (w:1, o:62, a:1, s:1
% 4.19/4.56 , b:0),
% 4.19/4.56 'class_Ring__and__Field_Oordered__semidom' [88, 1] (w:1, o:63, a:1
% 4.19/4.56 , s:1, b:0),
% 4.19/4.56 'class_Ring__and__Field_Ocomm__semiring__1' [89, 1] (w:1, o:57, a:1
% 4.19/4.56 , s:1, b:0),
% 4.19/4.56 'class_OrderedGroup_Ocomm__monoid__add' [90, 1] (w:1, o:64, a:1, s:1
% 4.19/4.56 , b:0),
% 4.19/4.56 'class_Ring__and__Field_Oidom' [91, 1] (w:1, o:65, a:1, s:1, b:0),
% 4.19/4.56 'class_Int_Onumber__ring' [92, 1] (w:1, o:66, a:1, s:1, b:0),
% 4.19/4.56 'class_OrderedGroup_Omonoid__add' [93, 1] (w:1, o:69, a:1, s:1, b:0)
% 4.19/4.56 ,
% 4.19/4.56 'class_OrderedGroup_Olordered__ab__group__add' [94, 1] (w:1, o:67, a:
% 4.19/4.56 1, s:1, b:0),
% 4.19/4.56 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [95, 1]
% 4.19/4.56 (w:1, o:70, a:1, s:1, b:0),
% 4.19/4.56 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [96, 1]
% 4.19/4.56 (w:1, o:71, a:1, s:1, b:0),
% 4.19/4.56 'class_OrderedGroup_Opordered__comm__monoid__add' [97, 1] (w:1, o:72
% 4.19/4.56 , a:1, s:1, b:0),
% 4.19/4.56 'class_Orderings_Olinorder' [98, 1] (w:1, o:73, a:1, s:1, b:0),
% 4.19/4.56 'class_Orderings_Opreorder' [99, 1] (w:1, o:75, a:1, s:1, b:0),
% 26.87/27.30 'class_Orderings_Oorder' [100, 1] (w:1, o:74, a:1, s:1, b:0),
% 26.87/27.30 'c_Nat_Osemiring__1__class_Oof__nat' [101, 2] (w:1, o:115, a:1, s:1
% 26.87/27.30 , b:0),
% 26.87/27.30 'class_OrderedGroup_Olordered__ab__group__add__abs' [104, 1] (w:1, o:
% 26.87/27.30 68, a:1, s:1, b:0),
% 26.87/27.30 'class_OrderedGroup_Oab__group__add' [105, 1] (w:1, o:76, a:1, s:1
% 26.87/27.30 , b:0),
% 26.87/27.30 'class_Ring__and__Field_Osemiring__1' [106, 1] (w:1, o:77, a:1, s:1
% 26.87/27.30 , b:0),
% 26.87/27.30 'class_RealVector_Oreal__normed__algebra__1' [107, 1] (w:1, o:78, a:1
% 26.87/27.30 , s:1, b:0),
% 26.87/27.30 'class_Nat_Osemiring__char__0' [108, 1] (w:1, o:50, a:1, s:1, b:0),
% 26.87/27.30 'class_Ring__and__Field_Oabs__if' [109, 1] (w:1, o:79, a:1, s:1, b:0)
% 26.87/27.30 ,
% 26.87/27.30 'v_N1____' [110, 0] (w:1, o:34, a:1, s:1, b:0),
% 26.87/27.30 'v_N2____' [111, 0] (w:1, o:35, a:1, s:1, b:0),
% 26.87/27.30 'class_OrderedGroup_Opordered__ab__semigroup__add' [113, 1] (w:1, o:
% 26.87/27.30 80, a:1, s:1, b:0),
% 26.87/27.30 'class_OrderedGroup_Ocancel__semigroup__add' [115, 1] (w:1, o:81, a:1
% 26.87/27.30 , s:1, b:0),
% 26.87/27.30 'class_OrderedGroup_Ocancel__ab__semigroup__add' [116, 1] (w:1, o:82
% 26.87/27.30 , a:1, s:1, b:0),
% 26.87/27.30 'v_f____' [117, 1] (w:1, o:83, a:1, s:1, b:0),
% 26.87/27.30 'class_Lattices_Oboolean__algebra' [118, 1] (w:1, o:84, a:1, s:1, b:0
% 26.87/27.30 ),
% 26.87/27.30 'class_OrderedGroup_Oab__semigroup__add' [119, 1] (w:1, o:85, a:1, s:
% 26.87/27.30 1, b:0),
% 26.87/27.30 'v_s____' [121, 0] (w:1, o:38, a:1, s:1, b:0).
% 26.87/27.30
% 26.87/27.30
% 26.87/27.30 Starting Search:
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30
% 26.87/27.30 Intermediate Status:
% 26.87/27.30 Generated: 6914
% 26.87/27.30 Kept: 2571
% 26.87/27.30 Inuse: 208
% 26.87/27.30 Deleted: 3
% 26.87/27.30 Deletedinuse: 0
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30
% 26.87/27.30 Intermediate Status:
% 26.87/27.30 Generated: 13381
% 26.87/27.30 Kept: 4571
% 26.87/27.30 Inuse: 271
% 26.87/27.30 Deleted: 11
% 26.87/27.30 Deletedinuse: 7
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30
% 26.87/27.30 Intermediate Status:
% 26.87/27.30 Generated: 19227
% 26.87/27.30 Kept: 6589
% 26.87/27.30 Inuse: 297
% 26.87/27.30 Deleted: 14
% 26.87/27.30 Deletedinuse: 10
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30
% 26.87/27.30 Intermediate Status:
% 26.87/27.30 Generated: 26068
% 26.87/27.30 Kept: 8603
% 26.87/27.30 Inuse: 333
% 26.87/27.30 Deleted: 15
% 26.87/27.30 Deletedinuse: 10
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30
% 26.87/27.30 Intermediate Status:
% 26.87/27.30 Generated: 35501
% 26.87/27.30 Kept: 10633
% 26.87/27.30 Inuse: 411
% 26.87/27.30 Deleted: 17
% 26.87/27.30 Deletedinuse: 12
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30
% 26.87/27.30 Intermediate Status:
% 26.87/27.30 Generated: 47064
% 26.87/27.30 Kept: 12963
% 26.87/27.30 Inuse: 456
% 26.87/27.30 Deleted: 18
% 26.87/27.30 Deletedinuse: 13
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30
% 26.87/27.30 Intermediate Status:
% 26.87/27.30 Generated: 56327
% 26.87/27.30 Kept: 15005
% 26.87/27.30 Inuse: 511
% 26.87/27.30 Deleted: 18
% 26.87/27.30 Deletedinuse: 13
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30
% 26.87/27.30 Intermediate Status:
% 26.87/27.30 Generated: 66393
% 26.87/27.30 Kept: 17026
% 26.87/27.30 Inuse: 561
% 26.87/27.30 Deleted: 18
% 26.87/27.30 Deletedinuse: 13
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30
% 26.87/27.30 Intermediate Status:
% 26.87/27.30 Generated: 78692
% 26.87/27.30 Kept: 19628
% 26.87/27.30 Inuse: 611
% 26.87/27.30 Deleted: 20
% 26.87/27.30 Deletedinuse: 15
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30 Resimplifying clauses:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30
% 26.87/27.30 Intermediate Status:
% 26.87/27.30 Generated: 89888
% 26.87/27.30 Kept: 22094
% 26.87/27.30 Inuse: 633
% 26.87/27.30 Deleted: 992
% 26.87/27.30 Deletedinuse: 33
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30
% 26.87/27.30 Intermediate Status:
% 26.87/27.30 Generated: 97757
% 26.87/27.30 Kept: 24151
% 26.87/27.30 Inuse: 661
% 26.87/27.30 Deleted: 993
% 26.87/27.30 Deletedinuse: 34
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30
% 26.87/27.30 Intermediate Status:
% 26.87/27.30 Generated: 107944
% 26.87/27.30 Kept: 26156
% 26.87/27.30 Inuse: 712
% 26.87/27.30 Deleted: 993
% 26.87/27.30 Deletedinuse: 34
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30
% 26.87/27.30 Intermediate Status:
% 26.87/27.30 Generated: 116434
% 26.87/27.30 Kept: 28297
% 26.87/27.30 Inuse: 739
% 26.87/27.30 Deleted: 995
% 26.87/27.30 Deletedinuse: 34
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30
% 26.87/27.30 Intermediate Status:
% 26.87/27.30 Generated: 126312
% 26.87/27.30 Kept: 30429
% 26.87/27.30 Inuse: 789
% 26.87/27.30 Deleted: 995
% 26.87/27.30 Deletedinuse: 34
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30
% 26.87/27.30 Intermediate Status:
% 26.87/27.30 Generated: 139989
% 26.87/27.30 Kept: 32534
% 26.87/27.30 Inuse: 809
% 26.87/27.30 Deleted: 995
% 26.87/27.30 Deletedinuse: 34
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30
% 26.87/27.30 Intermediate Status:
% 26.87/27.30 Generated: 148802
% 26.87/27.30 Kept: 34542
% 26.87/27.30 Inuse: 848
% 26.87/27.30 Deleted: 995
% 26.87/27.30 Deletedinuse: 34
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 26.87/27.30 Done
% 26.87/27.30
% 26.87/27.30 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 157620
% 66.65/67.05 Kept: 36609
% 66.65/67.05 Inuse: 889
% 66.65/67.05 Deleted: 995
% 66.65/67.05 Deletedinuse: 34
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 167665
% 66.65/67.05 Kept: 38694
% 66.65/67.05 Inuse: 929
% 66.65/67.05 Deleted: 995
% 66.65/67.05 Deletedinuse: 34
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 177722
% 66.65/67.05 Kept: 40722
% 66.65/67.05 Inuse: 964
% 66.65/67.05 Deleted: 995
% 66.65/67.05 Deletedinuse: 34
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying clauses:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 188367
% 66.65/67.05 Kept: 43159
% 66.65/67.05 Inuse: 982
% 66.65/67.05 Deleted: 3827
% 66.65/67.05 Deletedinuse: 34
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 216568
% 66.65/67.05 Kept: 46472
% 66.65/67.05 Inuse: 1007
% 66.65/67.05 Deleted: 3829
% 66.65/67.05 Deletedinuse: 36
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 226547
% 66.65/67.05 Kept: 48792
% 66.65/67.05 Inuse: 1012
% 66.65/67.05 Deleted: 3829
% 66.65/67.05 Deletedinuse: 36
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 240426
% 66.65/67.05 Kept: 50797
% 66.65/67.05 Inuse: 1049
% 66.65/67.05 Deleted: 3829
% 66.65/67.05 Deletedinuse: 36
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 262466
% 66.65/67.05 Kept: 54393
% 66.65/67.05 Inuse: 1082
% 66.65/67.05 Deleted: 3832
% 66.65/67.05 Deletedinuse: 39
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 276260
% 66.65/67.05 Kept: 57185
% 66.65/67.05 Inuse: 1111
% 66.65/67.05 Deleted: 3835
% 66.65/67.05 Deletedinuse: 41
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 294463
% 66.65/67.05 Kept: 59207
% 66.65/67.05 Inuse: 1137
% 66.65/67.05 Deleted: 3835
% 66.65/67.05 Deletedinuse: 41
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 308984
% 66.65/67.05 Kept: 61376
% 66.65/67.05 Inuse: 1181
% 66.65/67.05 Deleted: 3835
% 66.65/67.05 Deletedinuse: 41
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying clauses:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 328785
% 66.65/67.05 Kept: 63627
% 66.65/67.05 Inuse: 1191
% 66.65/67.05 Deleted: 5515
% 66.65/67.05 Deletedinuse: 41
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 354198
% 66.65/67.05 Kept: 65887
% 66.65/67.05 Inuse: 1201
% 66.65/67.05 Deleted: 5515
% 66.65/67.05 Deletedinuse: 41
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 364963
% 66.65/67.05 Kept: 67905
% 66.65/67.05 Inuse: 1216
% 66.65/67.05 Deleted: 5591
% 66.65/67.05 Deletedinuse: 115
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 378015
% 66.65/67.05 Kept: 69909
% 66.65/67.05 Inuse: 1245
% 66.65/67.05 Deleted: 5593
% 66.65/67.05 Deletedinuse: 115
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 391729
% 66.65/67.05 Kept: 71959
% 66.65/67.05 Inuse: 1271
% 66.65/67.05 Deleted: 5594
% 66.65/67.05 Deletedinuse: 115
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 409903
% 66.65/67.05 Kept: 74799
% 66.65/67.05 Inuse: 1301
% 66.65/67.05 Deleted: 5594
% 66.65/67.05 Deletedinuse: 115
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 426167
% 66.65/67.05 Kept: 77933
% 66.65/67.05 Inuse: 1312
% 66.65/67.05 Deleted: 5594
% 66.65/67.05 Deletedinuse: 115
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 439630
% 66.65/67.05 Kept: 80153
% 66.65/67.05 Inuse: 1336
% 66.65/67.05 Deleted: 5596
% 66.65/67.05 Deletedinuse: 117
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 453681
% 66.65/67.05 Kept: 83218
% 66.65/67.05 Inuse: 1361
% 66.65/67.05 Deleted: 5597
% 66.65/67.05 Deletedinuse: 118
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying clauses:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 467060
% 66.65/67.05 Kept: 85696
% 66.65/67.05 Inuse: 1381
% 66.65/67.05 Deleted: 10549
% 66.65/67.05 Deletedinuse: 118
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 480168
% 66.65/67.05 Kept: 87720
% 66.65/67.05 Inuse: 1410
% 66.65/67.05 Deleted: 10549
% 66.65/67.05 Deletedinuse: 118
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 495241
% 66.65/67.05 Kept: 89761
% 66.65/67.05 Inuse: 1441
% 66.65/67.05 Deleted: 10549
% 66.65/67.05 Deletedinuse: 118
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 505872
% 66.65/67.05 Kept: 91770
% 66.65/67.05 Inuse: 1464
% 66.65/67.05 Deleted: 10549
% 66.65/67.05 Deletedinuse: 118
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 517404
% 66.65/67.05 Kept: 93980
% 66.65/67.05 Inuse: 1486
% 66.65/67.05 Deleted: 10549
% 66.65/67.05 Deletedinuse: 118
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 536107
% 66.65/67.05 Kept: 96961
% 66.65/67.05 Inuse: 1514
% 66.65/67.05 Deleted: 10559
% 66.65/67.05 Deletedinuse: 122
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 553279
% 66.65/67.05 Kept: 99432
% 66.65/67.05 Inuse: 1555
% 66.65/67.05 Deleted: 10559
% 66.65/67.05 Deletedinuse: 122
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 577356
% 66.65/67.05 Kept: 101747
% 66.65/67.05 Inuse: 1565
% 66.65/67.05 Deleted: 10576
% 66.65/67.05 Deletedinuse: 139
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 609191
% 66.65/67.05 Kept: 104458
% 66.65/67.05 Inuse: 1575
% 66.65/67.05 Deleted: 10599
% 66.65/67.05 Deletedinuse: 162
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying clauses:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 628144
% 66.65/67.05 Kept: 106970
% 66.65/67.05 Inuse: 1580
% 66.65/67.05 Deleted: 15231
% 66.65/67.05 Deletedinuse: 163
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 658996
% 66.65/67.05 Kept: 110655
% 66.65/67.05 Inuse: 1590
% 66.65/67.05 Deleted: 15231
% 66.65/67.05 Deletedinuse: 163
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 671586
% 66.65/67.05 Kept: 112668
% 66.65/67.05 Inuse: 1621
% 66.65/67.05 Deleted: 15263
% 66.65/67.05 Deletedinuse: 195
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 689329
% 66.65/67.05 Kept: 115451
% 66.65/67.05 Inuse: 1626
% 66.65/67.05 Deleted: 15263
% 66.65/67.05 Deletedinuse: 195
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 700265
% 66.65/67.05 Kept: 117461
% 66.65/67.05 Inuse: 1649
% 66.65/67.05 Deleted: 15263
% 66.65/67.05 Deletedinuse: 195
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 736209
% 66.65/67.05 Kept: 120822
% 66.65/67.05 Inuse: 1665
% 66.65/67.05 Deleted: 15263
% 66.65/67.05 Deletedinuse: 195
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 768532
% 66.65/67.05 Kept: 123779
% 66.65/67.05 Inuse: 1675
% 66.65/67.05 Deleted: 15263
% 66.65/67.05 Deletedinuse: 195
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 785856
% 66.65/67.05 Kept: 126928
% 66.65/67.05 Inuse: 1680
% 66.65/67.05 Deleted: 15263
% 66.65/67.05 Deletedinuse: 195
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying clauses:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 802391
% 66.65/67.05 Kept: 128928
% 66.65/67.05 Inuse: 1712
% 66.65/67.05 Deleted: 17047
% 66.65/67.05 Deletedinuse: 199
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 820082
% 66.65/67.05 Kept: 131026
% 66.65/67.05 Inuse: 1745
% 66.65/67.05 Deleted: 17047
% 66.65/67.05 Deletedinuse: 199
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 845651
% 66.65/67.05 Kept: 134620
% 66.65/67.05 Inuse: 1751
% 66.65/67.05 Deleted: 17052
% 66.65/67.05 Deletedinuse: 204
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Intermediate Status:
% 66.65/67.05 Generated: 853165
% 66.65/67.05 Kept: 136801
% 66.65/67.05 Inuse: 1780
% 66.65/67.05 Deleted: 17296
% 66.65/67.05 Deletedinuse: 448
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05 Resimplifying inuse:
% 66.65/67.05 Done
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 Bliksems!, er is een bewijs:
% 66.65/67.05 % SZS status Unsatisfiable
% 66.65/67.05 % SZS output start Refutation
% 66.65/67.05
% 66.65/67.05 clause( 396, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'( X, Z,
% 66.65/67.05 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Y, Z,
% 66.65/67.05 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 .
% 66.65/67.05 clause( 423, [ 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.05 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 66.65/67.05 'c_Suc'( 'v_f____'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____',
% 66.65/67.05 'tc_nat' ) ) ), 'tc_nat' ), 'tc_RealDef_Oreal' ),
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ),
% 66.65/67.05 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ] )
% 66.65/67.05 .
% 66.65/67.05 clause( 424, [ ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( 'v_s____', 'tc_RealDef_Oreal' ),
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'( 'v_f____'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ) ),
% 66.65/67.05 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( 'v_s____',
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.05 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 66.65/67.05 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) )
% 66.65/67.05 , 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.05 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 .
% 66.65/67.05 clause( 136985, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X,
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'( 'v_f____'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ) ),
% 66.65/67.05 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.05 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 66.65/67.05 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) )
% 66.65/67.05 , 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.05 'tc_RealDef_Oreal' ) ] )
% 66.65/67.05 .
% 66.65/67.05 clause( 137950, [] )
% 66.65/67.05 .
% 66.65/67.05
% 66.65/67.05
% 66.65/67.05 % SZS output end Refutation
% 66.65/67.05 found a proof!
% 66.65/67.05
% 66.65/67.05 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 66.65/67.05
% 66.65/67.05 initialclauses(
% 66.65/67.05 [ clause( 137952, [ 'c_lessequals'( 'c_RealDef_Oreal'(
% 66.65/67.05 'c_RComplete_Onatfloor'( X ), 'tc_nat' ), X, 'tc_RealDef_Oreal' ), ~(
% 66.65/67.05 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), X,
% 66.65/67.05 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 137953, [ =( 'c_RComplete_Onatfloor'( X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 66.65/67.05 ] )
% 66.65/67.05 , clause( 137954, [ =( 'c_RComplete_Onatfloor'( 'c_RealDef_Oreal'( X,
% 66.65/67.05 'tc_nat' ) ), X ) ] )
% 66.65/67.05 , clause( 137955, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 66.65/67.05 'tc_nat' ), 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ),
% 66.65/67.05 =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ] )
% 66.65/67.05 , clause( 137956, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 66.65/67.05 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 137957, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 66.65/67.05 X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ] )
% 66.65/67.05 , clause( 137958, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 66.65/67.05 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 66.65/67.05 X ) ) ] )
% 66.65/67.05 , clause( 137959, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 66.65/67.05 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 66.65/67.05 , clause( 137960, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 66.65/67.05 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 66.65/67.05 , clause( 137961, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 66.65/67.05 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 66.65/67.05 , T, X ), X ), T, X ) ) ] )
% 66.65/67.05 , clause( 137962, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 66.65/67.05 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ] )
% 66.65/67.05 , clause( 137963, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 66.65/67.05 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 66.65/67.05 , clause( 137964, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 66.65/67.05 ) ) ] )
% 66.65/67.05 , clause( 137965, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 66.65/67.05 ) ) ] )
% 66.65/67.05 , clause( 137966, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 66.65/67.05 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 66.65/67.05 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 66.65/67.05 Z, X ) ) ] )
% 66.65/67.05 , clause( 137967, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 137968, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X )
% 66.65/67.05 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 137969, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 66.65/67.05 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 66.65/67.05 , clause( 137970, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 66.65/67.05 ) ] )
% 66.65/67.05 , clause( 137971, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 66.65/67.05 ) ] )
% 66.65/67.05 , clause( 137972, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 137973, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 66.65/67.05 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 137974, [ =( 'c_RComplete_Onatfloor'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_RealDef_Oreal' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 137975, [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'(
% 66.65/67.05 X, Y, 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 137976, [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 66.65/67.05 'tc_nat' ) ), Y ) ), =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 66.65/67.05 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 137977, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 137978, [ =( 'c_Divides_Odiv__class_Odiv'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat' ),
% 66.65/67.05 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 66.65/67.05 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ),
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ), 'tc_nat' ), Z, 'tc_nat' )
% 66.65/67.05 , 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 137979, [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), Y,
% 66.65/67.05 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 66.65/67.05 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_nat' ) ), Y, 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat'
% 66.65/67.05 ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_nat' ) ), Y, 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 137980, [ 'c_HOL_Oord__class_Oless'( X,
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'c_RealDef_Oreal'( 'c_RComplete_Onatfloor'( X
% 66.65/67.05 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 66.65/67.05 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ] )
% 66.65/67.05 , clause( 137981, [ =( 'c_RComplete_Onatfloor'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 X, 'c_RealDef_Oreal'( Y, 'tc_nat' ), 'tc_RealDef_Oreal' ) ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'c_RComplete_Onatfloor'( X ), Y, 'tc_nat' ) )
% 66.65/67.05 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), X
% 66.65/67.05 , 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 137982, [ =( 'c_RComplete_Onatfloor'( X ), Y ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 'c_RealDef_Oreal'( Y, 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ), ~(
% 66.65/67.05 'c_lessequals'( 'c_RealDef_Oreal'( Y, 'tc_nat' ), X, 'tc_RealDef_Oreal' )
% 66.65/67.05 ) ] )
% 66.65/67.05 , clause( 137983, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 66.65/67.05 , =( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 66.65/67.05 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 137984, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 137985, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 137986, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 66.65/67.05 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 66.65/67.05 , X ), 'c_RealVector_Onorm__class_Onorm'( Y, X ) ) ] )
% 66.65/67.05 , clause( 137987, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.05 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 66.65/67.05 ), X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ] )
% 66.65/67.05 , clause( 137988, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 66.65/67.05 , ~( =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 137989, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 66.65/67.05 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 137990, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 Z, Y, X ) ) ] )
% 66.65/67.05 , clause( 137991, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 66.65/67.05 , X ), X ) ) ] )
% 66.65/67.05 , clause( 137992, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 66.65/67.05 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ] )
% 66.65/67.05 , clause( 137993, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 66.65/67.05 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X
% 66.65/67.05 ), Y, X ) ) ] )
% 66.65/67.05 , clause( 137994, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 66.65/67.05 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X
% 66.65/67.05 ), Y, X ) ) ] )
% 66.65/67.05 , clause( 137995, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X )
% 66.65/67.05 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y
% 66.65/67.05 , X ), X ) ) ] )
% 66.65/67.05 , clause( 137996, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X )
% 66.65/67.05 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y
% 66.65/67.05 , X ), X ) ) ] )
% 66.65/67.05 , clause( 137997, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 137998, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 66.65/67.05 )
% 66.65/67.05 , clause( 137999, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 66.65/67.05 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138000, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 66.65/67.05 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138001, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 66.65/67.05 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138002, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 66.65/67.05 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138003, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 66.65/67.05 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 66.65/67.05 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 66.65/67.05 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 66.65/67.05 , clause( 138004, [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( X, Y, 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138005, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_RealDef_Oreal' ),
% 66.65/67.05 =( X, Y ), ~( 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138006, [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), ~(
% 66.65/67.05 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( X, 'tc_RealDef_Oreal' ), Y,
% 66.65/67.05 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138007, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_RealVector_Onorm__class_Onorm'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( T
% 66.65/67.05 , U, 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_RealVector_Onorm__class_Onorm'( Z, X ), U,
% 66.65/67.05 'tc_RealDef_Oreal' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_RealVector_Onorm__class_Onorm'( Y, X ), T, 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138008, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_nat' ) ) ) ] )
% 66.65/67.05 , clause( 138009, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_nat' ) ) ) ] )
% 66.65/67.05 , clause( 138010, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 66.65/67.05 , ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138011, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X
% 66.65/67.05 ), 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 66.65/67.05 , clause( 138012, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y
% 66.65/67.05 ), 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 66.65/67.05 , clause( 138013, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' )
% 66.65/67.05 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 66.65/67.05 , clause( 138014, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138015, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 66.65/67.05 , clause( 138016, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138017, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' )
% 66.65/67.05 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138018, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' )
% 66.65/67.05 ] )
% 66.65/67.05 , clause( 138019, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' )
% 66.65/67.05 ] )
% 66.65/67.05 , clause( 138020, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' )
% 66.65/67.05 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138021, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 66.65/67.05 X ) ) ) ] )
% 66.65/67.05 , clause( 138022, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 66.65/67.05 X ) ) ) ] )
% 66.65/67.05 , clause( 138023, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' )
% 66.65/67.05 , =( 'c_Suc'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 66.65/67.05 ] )
% 66.65/67.05 , clause( 138024, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 66.65/67.05 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138025, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138026, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 66.65/67.05 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138027, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat'
% 66.65/67.05 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138028, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138029, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat'
% 66.65/67.05 ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138030, [ ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138031, [ ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138032, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat'
% 66.65/67.05 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138033, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 X, T, 'tc_nat' ) ] )
% 66.65/67.05 , clause( 138034, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138035, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138036, [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) )
% 66.65/67.05 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138037, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X )
% 66.65/67.05 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138038, [ 'c_HOL_Oord__class_Oless'( X,
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138039, [ 'c_HOL_Oord__class_Oless'( X,
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138040, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 66.65/67.05 Y, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138041, [ 'c_HOL_Oord__class_Oless'( X,
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138042, [ 'c_HOL_Oord__class_Oless'( X,
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138043, [ =( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138044, [ =( X, 'c_HOL_Oplus__class_Oplus'( X,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138045, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 66.65/67.05 , clause( 138046, [ =( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 66.65/67.05 , clause( 138047, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 66.65/67.05 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 66.65/67.05 , X ), X ), 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.05 'c_RealVector_Onorm__class_Onorm'( Y, X ),
% 66.65/67.05 'c_RealVector_Onorm__class_Onorm'( Z, X ), 'tc_RealDef_Oreal' ) ), =( Z,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138048, [ 'c_lessequals'( 'c_RealDef_Oreal'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ]
% 66.65/67.05 )
% 66.65/67.05 , clause( 138049, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 66.65/67.05 'c_lessequals'( 'c_RealDef_Oreal'( X, 'tc_nat' ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 66.65/67.05 ] )
% 66.65/67.05 , clause( 138050, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'( X ), 'tc_nat' ),
% 66.65/67.05 'tc_RealDef_Oreal' ) ] )
% 66.65/67.05 , clause( 138051, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' )
% 66.65/67.05 , 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ) ] )
% 66.65/67.05 , clause( 138052, [ ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( X,
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 66.65/67.05 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138053, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 X, Y, 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 Y, 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ),
% 66.65/67.05 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138054, [ 'c_HOL_Oord__class_Oless'( X,
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( Y, 'tc_RealDef_Oreal' ),
% 66.65/67.05 'tc_RealDef_Oreal' ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_RealDef_Oreal' ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 66.65/67.05 ] )
% 66.65/67.05 , clause( 138055, [ =( 'c_RComplete_Onatfloor'(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( X, 'c_RealDef_Oreal'( Y, 'tc_nat' ),
% 66.65/67.05 'tc_RealDef_Oreal' ) ), 'c_Divides_Odiv__class_Odiv'(
% 66.65/67.05 'c_RComplete_Onatfloor'( X ), Y, 'tc_nat' ) ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 66.65/67.05 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.05 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138056, [ =( 'c_HOL_Oinverse__class_Odivide'( 'c_RealDef_Oreal'(
% 66.65/67.05 X, 'tc_nat' ), 'c_RealDef_Oreal'( Y, 'tc_nat' ), 'tc_RealDef_Oreal' ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'c_RealDef_Oreal'(
% 66.65/67.05 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( 'c_RealDef_Oreal'(
% 66.65/67.05 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 66.65/67.05 'c_RealDef_Oreal'( Y, 'tc_nat' ), 'tc_RealDef_Oreal' ),
% 66.65/67.05 'tc_RealDef_Oreal' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138057, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.05 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 66.65/67.05 ) ) ] )
% 66.65/67.05 , clause( 138058, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.05 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 66.65/67.05 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 66.65/67.05 ) ] )
% 66.65/67.05 , clause( 138059, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 66.65/67.05 ) ) ] )
% 66.65/67.05 , clause( 138060, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 66.65/67.05 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 66.65/67.05 ) ] )
% 66.65/67.05 , clause( 138061, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 66.65/67.05 ] )
% 66.65/67.05 , clause( 138062, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 66.65/67.05 =( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 66.65/67.05 )
% 66.65/67.05 , clause( 138063, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 66.65/67.05 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 66.65/67.05 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 66.65/67.05 , clause( 138064, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 66.65/67.05 =( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 66.65/67.05 )
% 66.65/67.05 , clause( 138065, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138066, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 66.65/67.05 , clause( 138067, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ] )
% 66.65/67.05 , clause( 138068, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 66.65/67.05 , clause( 138069, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 66.65/67.05 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 66.65/67.05 ] )
% 66.65/67.05 , clause( 138070, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 66.65/67.05 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138071, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 66.65/67.05 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138072, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 66.65/67.05 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 66.65/67.05 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138073, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 66.65/67.05 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 66.65/67.05 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138074, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 66.65/67.05 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 66.65/67.05 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138075, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 66.65/67.05 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 66.65/67.05 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 66.65/67.05 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138076, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.05 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), ~( 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138077, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.05 X ) ), 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'(
% 66.65/67.05 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 66.65/67.05 ) ] )
% 66.65/67.05 , clause( 138078, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 66.65/67.05 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Z, Y, X ),
% 66.65/67.05 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 66.65/67.05 ) ) ] )
% 66.65/67.05 , clause( 138079, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.05 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 66.65/67.05 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 66.65/67.05 ) ) ] )
% 66.65/67.05 , clause( 138080, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 66.65/67.05 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 66.65/67.05 , clause( 138081, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 66.65/67.05 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 66.65/67.05 ) ] )
% 66.65/67.05 , clause( 138082, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 66.65/67.05 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 66.65/67.05 ) ] )
% 66.65/67.05 , clause( 138083, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 66.65/67.05 ] )
% 66.65/67.05 , clause( 138084, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 66.65/67.05 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 66.65/67.05 ) ] )
% 66.65/67.05 , clause( 138085, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 66.65/67.05 'class_Int_Onumber__ring'( X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138086, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 66.65/67.05 ] )
% 66.65/67.05 , clause( 138087, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 66.65/67.05 ] )
% 66.65/67.05 , clause( 138088, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 66.65/67.05 ] )
% 66.65/67.05 , clause( 138089, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 66.65/67.05 ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 66.65/67.05 )
% 66.65/67.05 , clause( 138090, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 66.65/67.05 'class_Int_Onumber__ring'( X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y
% 66.65/67.05 , Z, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138091, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 66.65/67.05 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 66.65/67.05 ) ) ] )
% 66.65/67.05 , clause( 138092, [ ~(
% 66.65/67.05 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 66.65/67.05 , clause( 138093, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.05 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 66.65/67.05 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 66.65/67.05 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 66.65/67.05 , clause( 138094, [ ~(
% 66.65/67.05 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 66.65/67.05 X ), X ) ) ] )
% 66.65/67.05 , clause( 138095, [ ~(
% 66.65/67.05 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 Z, T, X ) ) ] )
% 66.65/67.05 , clause( 138096, [ ~(
% 66.65/67.05 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 Z, T, X ) ) ] )
% 66.65/67.05 , clause( 138097, [ ~(
% 66.65/67.05 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 66.65/67.05 X ), X ) ) ] )
% 66.65/67.05 , clause( 138098, [ ~(
% 66.65/67.05 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 Y, T, X ) ) ] )
% 66.65/67.05 , clause( 138099, [ ~(
% 66.65/67.05 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 Y, T, X ) ) ] )
% 66.65/67.05 , clause( 138100, [ ~(
% 66.65/67.05 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 66.65/67.05 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 66.65/67.05 , clause( 138101, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 66.65/67.05 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138102, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 66.65/67.05 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138103, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 66.65/67.05 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138104, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 66.65/67.05 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138105, [ ~(
% 66.65/67.05 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 66.65/67.05 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X
% 66.65/67.05 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 66.65/67.05 ) ) ] )
% 66.65/67.05 , clause( 138106, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 66.65/67.05 'c_lessequals'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ]
% 66.65/67.05 )
% 66.65/67.05 , clause( 138107, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 66.65/67.05 , clause( 138108, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 66.65/67.05 Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 66.65/67.05 , clause( 138109, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 66.65/67.05 )
% 66.65/67.05 , clause( 138110, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Y, X ), 'c_lessequals'( Y, Y, X ) ] )
% 66.65/67.05 , clause( 138111, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 66.65/67.05 'c_lessequals'( Y, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ]
% 66.65/67.05 )
% 66.65/67.05 , clause( 138112, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 66.65/67.05 , clause( 138113, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 66.65/67.05 'c_lessequals'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ]
% 66.65/67.05 )
% 66.65/67.05 , clause( 138114, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.05 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 66.65/67.05 , clause( 138115, [ ~( 'class_Orderings_Oorder'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 66.65/67.05 , X ) ) ] )
% 66.65/67.05 , clause( 138116, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 66.65/67.05 , clause( 138117, [ ~( 'class_Orderings_Oorder'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 66.65/67.05 , X ) ) ] )
% 66.65/67.05 , clause( 138118, [ ~( 'class_Orderings_Oorder'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 66.65/67.05 Y, Z ) ] )
% 66.65/67.05 , clause( 138119, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 66.65/67.05 'c_lessequals'( Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ] )
% 66.65/67.05 , clause( 138120, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 66.65/67.05 , clause( 138121, [ ~( 'class_Orderings_Oorder'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 66.65/67.05 Z, Y ) ] )
% 66.65/67.05 , clause( 138122, [ ~( 'class_Orderings_Oorder'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ), ~( 'c_lessequals'( Y, Z
% 66.65/67.05 , X ) ) ] )
% 66.65/67.05 , clause( 138123, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.05 X ) ), 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 66.65/67.05 , clause( 138124, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 66.65/67.05 'c_lessequals'( Y, Z, X ) ) ] )
% 66.65/67.05 , clause( 138125, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y,
% 66.65/67.05 Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 66.65/67.05 , clause( 138126, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'(
% 66.65/67.05 Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 66.65/67.05 , clause( 138127, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 66.65/67.05 , X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 66.65/67.05 , clause( 138128, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 66.65/67.05 , clause( 138129, [ ~( 'class_Orderings_Oorder'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 66.65/67.05 , X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 66.65/67.05 , clause( 138130, [ ~( 'class_Orderings_Oorder'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 66.65/67.05 , clause( 138131, [ ~( =( 'c_RealDef_Oreal'( X, 'tc_nat' ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ), =( X,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138132, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 66.65/67.05 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 66.65/67.05 , clause( 138133, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 66.65/67.05 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 66.65/67.05 , clause( 138134, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138135, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138136, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138137, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138138, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 66.65/67.05 ~( 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X
% 66.65/67.05 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138139, [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 66.65/67.05 , Y, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138140, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.05 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138141, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 66.65/67.05 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138142, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 66.65/67.05 , clause( 138143, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 66.65/67.05 , clause( 138144, [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 66.65/67.05 ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_Suc'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138145, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138146, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.05 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 66.65/67.05 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138147, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 66.65/67.05 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 66.65/67.05 , clause( 138148, [ ~( 'class_Orderings_Oorder'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 66.65/67.05 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 66.65/67.05 , clause( 138149, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_RealDef_Oreal'( X, 'tc_nat' ),
% 66.65/67.05 'c_RealDef_Oreal'( Y, 'tc_nat' ), 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138150, [ 'c_HOL_Oord__class_Oless'( 'c_RealDef_Oreal'( X,
% 66.65/67.05 'tc_nat' ), 'c_RealDef_Oreal'( Y, 'tc_nat' ), 'tc_RealDef_Oreal' ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138151, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138152, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 66.65/67.05 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138153, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138154, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_RealVector_Onorm__class_Onorm'( Y, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 66.65/67.05 ] )
% 66.65/67.05 , clause( 138155, [ ~( 'c_HOL_Oord__class_Oless'( 'c_RealDef_Oreal'( X,
% 66.65/67.05 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 66.65/67.05 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138156, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 66.65/67.05 Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 66.65/67.05 'c_RealVector_Onorm__class_Onorm'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138157, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_RealDef_Oreal' ),
% 66.65/67.05 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ),
% 66.65/67.05 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138158, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'( X,
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( Y, 'tc_RealDef_Oreal' ),
% 66.65/67.05 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 Y, X, 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138159, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'( X, Y,
% 66.65/67.05 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ), Y,
% 66.65/67.05 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138160, [ 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ), Y,
% 66.65/67.05 'tc_RealDef_Oreal' ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_RealDef_Oreal' ),
% 66.65/67.05 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138161, [ =( 'c_HOL_Oabs__class_Oabs'( 'c_RealDef_Oreal'( X,
% 66.65/67.05 'tc_nat' ), 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( X, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138162, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 66.65/67.05 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138163, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138164, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 66.65/67.05 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138165, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138166, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 66.65/67.05 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 66.65/67.05 , clause( 138167, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 66.65/67.05 ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138168, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 66.65/67.05 X ) ), 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 66.65/67.05 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ] )
% 66.65/67.05 , clause( 138169, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 66.65/67.05 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138170, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 66.65/67.05 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138171, [ ~(
% 66.65/67.05 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 66.65/67.05 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 66.65/67.05 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 66.65/67.05 , clause( 138172, [ ~(
% 66.65/67.05 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 66.65/67.05 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 66.65/67.05 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 66.65/67.05 , clause( 138173, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 66.65/67.05 ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 66.65/67.05 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 66.65/67.05 )
% 66.65/67.05 , clause( 138174, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.05 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 66.65/67.05 X ) ] )
% 66.65/67.05 , clause( 138175, [ ~(
% 66.65/67.05 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 66.65/67.05 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 66.65/67.05 , clause( 138176, [ ~(
% 66.65/67.05 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 66.65/67.05 , clause( 138177, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 66.65/67.05 ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138178, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 66.65/67.05 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'(
% 66.65/67.05 X ), X ) ] )
% 66.65/67.05 , clause( 138179, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 66.65/67.05 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 66.65/67.05 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 66.65/67.05 , clause( 138180, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.05 X ) ), 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 66.65/67.05 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 66.65/67.05 , clause( 138181, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 66.65/67.05 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 66.65/67.05 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138182, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 66.65/67.05 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 66.65/67.05 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138183, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 66.65/67.05 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 66.65/67.05 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138184, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 66.65/67.05 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 66.65/67.05 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 66.65/67.05 , clause( 138185, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 66.65/67.05 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138186, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 66.65/67.05 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138187, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 66.65/67.05 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138188, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 66.65/67.05 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 66.65/67.05 , clause( 138189, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138190, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 66.65/67.05 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 66.65/67.05 , clause( 138191, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.05 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 66.65/67.05 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 66.65/67.05 'c_lessequals'( Y, Z, X ) ) ] )
% 66.65/67.05 , clause( 138192, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.05 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 66.65/67.05 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 66.65/67.05 'c_lessequals'( Y, Z, X ) ) ] )
% 66.65/67.05 , clause( 138193, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.05 X ) ), 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 66.65/67.05 ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 66.65/67.05 , clause( 138194, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138195, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 66.65/67.05 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138196, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 66.65/67.05 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 66.65/67.05 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138197, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 66.65/67.05 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 66.65/67.05 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138198, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 66.65/67.05 ), X ) ) ] )
% 66.65/67.05 , clause( 138199, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 66.65/67.05 ), X ) ) ] )
% 66.65/67.05 , clause( 138200, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 66.65/67.05 ), X ) ) ] )
% 66.65/67.05 , clause( 138201, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 66.65/67.05 ), X ) ) ] )
% 66.65/67.05 , clause( 138202, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 66.65/67.05 )
% 66.65/67.05 , clause( 138203, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 66.65/67.05 ] )
% 66.65/67.05 , clause( 138204, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 66.65/67.05 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 66.65/67.05 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138205, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 66.65/67.05 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 66.65/67.05 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.05 , clause( 138206, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 66.65/67.05 ), X ) ) ] )
% 66.65/67.05 , clause( 138207, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 66.65/67.05 ), X ) ) ] )
% 66.65/67.05 , clause( 138208, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 66.65/67.05 ), X ) ) ] )
% 66.65/67.05 , clause( 138209, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 66.65/67.05 ), X ) ) ] )
% 66.65/67.05 , clause( 138210, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 66.65/67.05 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ] )
% 66.65/67.05 , clause( 138211, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 66.65/67.05 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ] )
% 66.65/67.05 , clause( 138212, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 66.65/67.05 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138213, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 66.65/67.05 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138214, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 66.65/67.05 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138215, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 66.65/67.05 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138216, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 66.65/67.05 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ] )
% 66.65/67.05 , clause( 138217, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 66.65/67.05 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 66.65/67.05 , clause( 138218, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 66.65/67.05 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138219, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 66.65/67.05 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138220, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 66.65/67.05 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 66.65/67.05 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 66.65/67.05 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 66.65/67.05 , clause( 138221, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138222, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 66.65/67.05 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138223, [ ~( 'class_RealVector_Oreal__normed__algebra__1'( X ) )
% 66.65/67.05 , =( 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oone__class_Oone'( X ), X
% 66.65/67.05 ), 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138224, [ =( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 66.65/67.05 , clause( 138225, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 66.65/67.05 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138226, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 66.65/67.05 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 66.65/67.05 , clause( 138227, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 66.65/67.05 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138228, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 66.65/67.05 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138229, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 66.65/67.05 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 66.65/67.05 , clause( 138230, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 66.65/67.05 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138231, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 66.65/67.05 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 66.65/67.05 , clause( 138232, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 66.65/67.05 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138233, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 66.65/67.05 , clause( 138234, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ), 'tc_nat' ) ] )
% 66.65/67.05 , clause( 138235, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 66.65/67.05 , clause( 138236, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 66.65/67.05 ) ] )
% 66.65/67.05 , clause( 138237, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 66.65/67.05 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 66.65/67.05 , clause( 138238, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 66.65/67.05 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138239, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 66.65/67.05 'tc_RealDef_Oreal' ) ] )
% 66.65/67.05 , clause( 138240, [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) )
% 66.65/67.05 , ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 66.65/67.05 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 66.65/67.05 , X ), X ), 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.05 'c_RealVector_Onorm__class_Onorm'( Y, X ),
% 66.65/67.05 'c_RealVector_Onorm__class_Onorm'( Z, X ), 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138241, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_HOL_Oinverse__class_Odivide'( X, Y,
% 66.65/67.05 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 66.65/67.05 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), Y
% 66.65/67.05 , 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138242, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_HOL_Oinverse__class_Odivide'( X, Y,
% 66.65/67.05 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' )
% 66.65/67.05 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 66.65/67.05 Y, 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138243, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_HOL_Oinverse__class_Odivide'( X, Y,
% 66.65/67.05 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 66.65/67.05 , ~( 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' )
% 66.65/67.05 , 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138244, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_HOL_Oinverse__class_Odivide'( X, Y,
% 66.65/67.05 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' )
% 66.65/67.05 ), ~( 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal'
% 66.65/67.05 ), 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138245, [ 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), Y, 'tc_RealDef_Oreal' )
% 66.65/67.05 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Y, X, 'tc_RealDef_Oreal' ),
% 66.65/67.05 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138246, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' ), 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.05 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( Y, X, 'tc_RealDef_Oreal' ),
% 66.65/67.05 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138247, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( X, 'tc_nat' ),
% 66.65/67.05 'tc_RealDef_Oreal' ) ] )
% 66.65/67.05 , clause( 138248, [ 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( X,
% 66.65/67.05 'tc_RealDef_Oreal' ), Y, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( X, Y,
% 66.65/67.05 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'(
% 66.65/67.05 Y, 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138249, [ 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( X,
% 66.65/67.05 'tc_RealDef_Oreal' ), Y, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 66.65/67.05 'c_HOL_Oabs__class_Oabs'( Y, 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal'
% 66.65/67.05 ) ) ] )
% 66.65/67.05 , clause( 138250, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) )
% 66.65/67.05 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138251, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( Y, 'tc_RealDef_Oreal' ),
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) )
% 66.65/67.05 ), =( X, Y ) ] )
% 66.65/67.05 , clause( 138252, [ =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.05 X, 'c_HOL_Ouminus__class_Ouminus'( Y, 'tc_RealDef_Oreal' ),
% 66.65/67.05 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'c_HOL_Oabs__class_Oabs'(
% 66.65/67.05 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( X,
% 66.65/67.05 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.05 , clause( 138253, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ),
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) )
% 66.65/67.05 ] )
% 66.65/67.05 , clause( 138254, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 66.65/67.05 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138255, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 66.65/67.05 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 66.65/67.05 , clause( 138256, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.05 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 66.65/67.05 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.05 , clause( 138257, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ),
% 66.65/67.05 'c_lessequals'( 'c_RealVector_Onorm__class_Onorm'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ] )
% 66.65/67.05 , clause( 138258, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 66.65/67.05 =( 'c_RealVector_Onorm__class_Onorm'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.05 'tc_RealDef_Oreal' ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.05 , clause( 138259, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 66.65/67.05 'c_HOL_Oabs__class_Oabs'( 'c_RealVector_Onorm__class_Onorm'( Y, X ),
% 66.65/67.05 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'( Y, X ) ) ] )
% 66.65/67.05 , clause( 138260, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 66.65/67.05 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 66.65/67.05 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ] )
% 66.65/67.05 , clause( 138261, [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 66.65/67.05 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.05 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 66.65/67.05 , clause( 138262, [ =( 'c_HOL_Oabs__class_Oabs'( X, 'tc_RealDef_Oreal' ),
% 66.65/67.05 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ) ), ~(
% 66.65/67.05 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , clause( 138263, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 66.65/67.06 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 66.65/67.06 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 66.65/67.06 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 66.65/67.06 ) ] )
% 66.65/67.06 , clause( 138264, [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 66.65/67.06 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 66.65/67.06 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 66.65/67.06 ) ] )
% 66.65/67.06 , clause( 138265, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.06 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 66.65/67.06 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.06 , clause( 138266, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.06 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.06 , clause( 138267, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.06 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.06 , clause( 138268, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.06 , clause( 138269, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.06 , clause( 138270, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 66.65/67.06 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 66.65/67.06 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.06 , clause( 138271, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 66.65/67.06 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.06 , clause( 138272, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 66.65/67.06 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 66.65/67.06 ) ] )
% 66.65/67.06 , clause( 138273, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 66.65/67.06 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 66.65/67.06 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 66.65/67.06 ) ) ] )
% 66.65/67.06 , clause( 138274, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal'
% 66.65/67.06 ), 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ozero__class_Ozero'( X ), X
% 66.65/67.06 ), 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , clause( 138275, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.06 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 66.65/67.06 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 66.65/67.06 ] )
% 66.65/67.06 , clause( 138276, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 66.65/67.06 ), =( Z, Y ) ] )
% 66.65/67.06 , clause( 138277, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 66.65/67.06 , clause( 138278, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 66.65/67.06 , clause( 138279, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 66.65/67.06 , clause( 138280, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 66.65/67.06 ) ] )
% 66.65/67.06 , clause( 138281, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 66.65/67.06 ) ] )
% 66.65/67.06 , clause( 138282, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 66.65/67.06 ), =( Z, Y ) ] )
% 66.65/67.06 , clause( 138283, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.06 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.06 , clause( 138284, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal'
% 66.65/67.06 ), 'c_RealVector_Onorm__class_Onorm'( Y, X ), 'tc_RealDef_Oreal' ), =( Y
% 66.65/67.06 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.06 , clause( 138285, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 66.65/67.06 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 66.65/67.06 , clause( 138286, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 66.65/67.06 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 66.65/67.06 , clause( 138287, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ] )
% 66.65/67.06 , clause( 138288, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ] )
% 66.65/67.06 , clause( 138289, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ] )
% 66.65/67.06 , clause( 138290, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ] )
% 66.65/67.06 , clause( 138291, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.06 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 66.65/67.06 'tc_nat' ) ) ] )
% 66.65/67.06 , clause( 138292, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.06 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 66.65/67.06 'tc_nat' ) ) ] )
% 66.65/67.06 , clause( 138293, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 66.65/67.06 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 66.65/67.06 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 66.65/67.06 , clause( 138294, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 66.65/67.06 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.06 , clause( 138295, [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ] )
% 66.65/67.06 , clause( 138296, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ),
% 66.65/67.06 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_RealVector_Onorm__class_Onorm'( Y, X ), 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138297, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 66.65/67.06 , X ) ) ] )
% 66.65/67.06 , clause( 138298, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 66.65/67.06 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 66.65/67.06 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 66.65/67.06 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 66.65/67.06 , clause( 138299, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 66.65/67.06 , X ) ) ] )
% 66.65/67.06 , clause( 138300, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 66.65/67.06 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 66.65/67.06 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 66.65/67.06 , clause( 138301, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.06 , clause( 138302, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.06 , clause( 138303, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.06 , clause( 138304, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.06 , clause( 138305, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 66.65/67.06 , clause( 138306, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 66.65/67.06 , clause( 138307, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 66.65/67.06 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 66.65/67.06 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ] )
% 66.65/67.06 , clause( 138308, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.06 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 66.65/67.06 ) ] )
% 66.65/67.06 , clause( 138309, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 66.65/67.06 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.06 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.06 , clause( 138310, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 66.65/67.06 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 66.65/67.06 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 66.65/67.06 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.06 X ) ) ] )
% 66.65/67.06 , clause( 138311, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 66.65/67.06 , clause( 138312, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 66.65/67.06 , clause( 138313, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_HOL_Oabs__class_Oabs'(
% 66.65/67.06 X, 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138314, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 66.65/67.06 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 66.65/67.06 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.06 , clause( 138315, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.06 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X )
% 66.65/67.06 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ] )
% 66.65/67.06 , clause( 138316, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.06 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.06 X ) ) ] )
% 66.65/67.06 , clause( 138317, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 66.65/67.06 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , clause( 138318, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.06 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( X,
% 66.65/67.06 'tc_nat' ), 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , clause( 138319, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( X, 'tc_nat' ),
% 66.65/67.06 'tc_RealDef_Oreal' ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 66.65/67.06 , clause( 138320, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.06 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 66.65/67.06 ] )
% 66.65/67.06 , clause( 138321, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 66.65/67.06 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.06 , clause( 138322, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.06 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 66.65/67.06 , clause( 138323, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 66.65/67.06 , clause( 138324, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 66.65/67.06 , clause( 138325, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_RealDef_Oreal'
% 66.65/67.06 ) ) ] )
% 66.65/67.06 , clause( 138326, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 66.65/67.06 , clause( 138327, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 66.65/67.06 , clause( 138328, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 66.65/67.06 , clause( 138329, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 66.65/67.06 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.06 , clause( 138330, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.06 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.06 , clause( 138331, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.06 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 66.65/67.06 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 66.65/67.06 , clause( 138332, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 66.65/67.06 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 66.65/67.06 , clause( 138333, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_HOL_Oone__class_Oone'( X ), X ) ] )
% 66.65/67.06 , clause( 138334, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 66.65/67.06 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 66.65/67.06 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 66.65/67.06 , clause( 138335, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 66.65/67.06 'tc_nat' ) ) ] )
% 66.65/67.06 , clause( 138336, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.06 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 66.65/67.06 ] )
% 66.65/67.06 , clause( 138337, [ ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.06 'tc_nat' ), 'tc_nat' ) ) ] )
% 66.65/67.06 , clause( 138338, [ =( 'c_HOL_Oabs__class_Oabs'( X, 'tc_RealDef_Oreal' ), X
% 66.65/67.06 ), 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138339, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 66.65/67.06 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 66.65/67.06 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 66.65/67.06 , clause( 138340, [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 66.65/67.06 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 66.65/67.06 , clause( 138341, [ =( 'c_RealDef_Oreal'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.06 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' )
% 66.65/67.06 ) ] )
% 66.65/67.06 , clause( 138342, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.06 X ) ), ~( =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.06 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 66.65/67.06 , clause( 138343, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.06 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 66.65/67.06 )
% 66.65/67.06 , clause( 138344, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.06 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.06 , clause( 138345, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.06 , clause( 138346, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.06 , clause( 138347, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.06 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.06 , clause( 138348, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.06 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 66.65/67.06 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 66.65/67.06 , clause( 138349, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.06 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 66.65/67.06 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.06 , clause( 138350, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 66.65/67.06 ) ] )
% 66.65/67.06 , clause( 138351, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 66.65/67.06 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 66.65/67.06 ] )
% 66.65/67.06 , clause( 138352, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.06 X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 66.65/67.06 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 66.65/67.06 , clause( 138353, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 66.65/67.06 Y, X ) ) ] )
% 66.65/67.06 , clause( 138354, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 66.65/67.06 Y, X ) ) ] )
% 66.65/67.06 , clause( 138355, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 66.65/67.06 Y, X ) ) ] )
% 66.65/67.06 , clause( 138356, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 66.65/67.06 Y, X ) ) ] )
% 66.65/67.06 , clause( 138357, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 66.65/67.06 , clause( 138358, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 66.65/67.06 , clause( 138359, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ] )
% 66.65/67.06 , clause( 138360, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), X
% 66.65/67.06 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 66.65/67.06 , clause( 138361, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 66.65/67.06 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), Z
% 66.65/67.06 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 66.65/67.06 , clause( 138362, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 66.65/67.06 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 66.65/67.06 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 66.65/67.06 , clause( 138363, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ),
% 66.65/67.06 'c_lessequals'( 'c_RealVector_Onorm__class_Onorm'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.06 'c_RealVector_Onorm__class_Onorm'( Y, X ),
% 66.65/67.06 'c_RealVector_Onorm__class_Onorm'( Z, X ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138364, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ),
% 66.65/67.06 'tc_nat' ), 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138365, [ =( 'c_RealDef_Oreal'( 'c_Suc'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 66.65/67.06 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , clause( 138366, [ 'c_lessequals'( 'c_RealDef_Oreal'(
% 66.65/67.06 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_RealDef_Oreal'( X, 'tc_nat' ),
% 66.65/67.06 'c_RealDef_Oreal'( Y, 'tc_nat' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138367, [ 'c_lessequals'( X, 'c_HOL_Ouminus__class_Ouminus'( Y,
% 66.65/67.06 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 66.65/67.06 ] )
% 66.65/67.06 , clause( 138368, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Y,
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , clause( 138369, [ 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( Z, 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( T, 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 66.65/67.06 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'( Y,
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( T, 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138370, [ 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( X,
% 66.65/67.06 'tc_RealDef_Oreal' ), Y, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 66.65/67.06 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , clause( 138371, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'( X, Y,
% 66.65/67.06 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ), Y,
% 66.65/67.06 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , clause( 138372, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.06 'c_RealDef_Oreal'( X, 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( Y,
% 66.65/67.06 'tc_nat' ), 'tc_RealDef_Oreal' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 66.65/67.06 'tc_nat' ) ) ] )
% 66.65/67.06 , clause( 138373, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 66.65/67.06 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_RealDef_Oreal'( X,
% 66.65/67.06 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( Y, 'tc_nat' ),
% 66.65/67.06 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , clause( 138374, [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_lessequals'( Y, X, 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138375, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 66.65/67.06 Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 66.65/67.06 , clause( 138376, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 66.65/67.06 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 66.65/67.06 , clause( 138377, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 66.65/67.06 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 66.65/67.06 , clause( 138378, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y,
% 66.65/67.06 Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 66.65/67.06 )
% 66.65/67.06 , clause( 138379, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'(
% 66.65/67.06 Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 66.65/67.06 ] )
% 66.65/67.06 , clause( 138380, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.06 ), 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 66.65/67.06 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ] )
% 66.65/67.06 , clause( 138381, [ 'c_lessequals'( X, X, 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138382, [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), ~(
% 66.65/67.06 'c_lessequals'( Z, Y, 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( X, Z,
% 66.65/67.06 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , clause( 138383, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y,
% 66.65/67.06 Y, X ) ] )
% 66.65/67.06 , clause( 138384, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'(
% 66.65/67.06 Y, Y, X ) ] )
% 66.65/67.06 , clause( 138385, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138386, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ] )
% 66.65/67.06 , clause( 138387, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ] )
% 66.65/67.06 , clause( 138388, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 66.65/67.06 , clause( 138389, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 66.65/67.06 , clause( 138390, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 66.65/67.06 X ) ) ] )
% 66.65/67.06 , clause( 138391, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 66.65/67.06 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 66.65/67.06 Y, X ) ) ] )
% 66.65/67.06 , clause( 138392, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ] )
% 66.65/67.06 , clause( 138393, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 66.65/67.06 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 66.65/67.06 Y, X ) ) ] )
% 66.65/67.06 , clause( 138394, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ),
% 66.65/67.06 'tc_nat' ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ]
% 66.65/67.06 )
% 66.65/67.06 , clause( 138395, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y,
% 66.65/67.06 'tc_nat' ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ]
% 66.65/67.06 )
% 66.65/67.06 , clause( 138396, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 66.65/67.06 X ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 66.65/67.06 ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 66.65/67.06 , clause( 138397, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 66.65/67.06 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ] )
% 66.65/67.06 , clause( 138398, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y,
% 66.65/67.06 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 66.65/67.06 )
% 66.65/67.06 , clause( 138399, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) )
% 66.65/67.06 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.06 T, Z, X ) ) ), =( Y, T ) ] )
% 66.65/67.06 , clause( 138400, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) )
% 66.65/67.06 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.06 Y, T, X ) ) ), =( Z, T ) ] )
% 66.65/67.06 , clause( 138401, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X
% 66.65/67.06 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 66.65/67.06 , clause( 138402, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 66.65/67.06 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 66.65/67.06 , X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 66.65/67.06 , clause( 138403, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 66.65/67.06 , clause( 138404, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 66.65/67.06 , clause( 138405, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ] )
% 66.65/67.06 , clause( 138406, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 66.65/67.06 ) ] )
% 66.65/67.06 , clause( 138407, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 66.65/67.06 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 66.65/67.06 X ), X ) ) ] )
% 66.65/67.06 , clause( 138408, [ =( 'c_RealDef_Oreal'( 'c_Suc'( X ), 'tc_nat' ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'c_RealDef_Oreal'( X, 'tc_nat' ),
% 66.65/67.06 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ]
% 66.65/67.06 )
% 66.65/67.06 , clause( 138409, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 66.65/67.06 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 66.65/67.06 Y, X ), Z, X ) ) ] )
% 66.65/67.06 , clause( 138410, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 66.65/67.06 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 66.65/67.06 , clause( 138411, [ 'c_lessequals'( 'c_RealDef_Oreal'( 'c_Suc'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ),
% 66.65/67.06 'tc_nat' ), 'c_RealDef_Oreal'( 'c_Suc'( 'v_f____'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ) ),
% 66.65/67.06 'tc_nat' ), 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138412, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 66.65/67.06 , clause( 138413, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 66.65/67.06 , clause( 138414, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ] )
% 66.65/67.06 , clause( 138415, [ ~(
% 66.65/67.06 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 66.65/67.06 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 66.65/67.06 ) ] )
% 66.65/67.06 , clause( 138416, [ ~(
% 66.65/67.06 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 66.65/67.06 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.06 Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 66.65/67.06 , clause( 138417, [ ~(
% 66.65/67.06 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 66.65/67.06 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 66.65/67.06 ) ] )
% 66.65/67.06 , clause( 138418, [ ~(
% 66.65/67.06 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 66.65/67.06 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.06 T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ) ) ] )
% 66.65/67.06 , clause( 138419, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 66.65/67.06 X ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 66.65/67.06 ) ] )
% 66.65/67.06 , clause( 138420, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 66.65/67.06 X ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 66.65/67.06 ) ] )
% 66.65/67.06 , clause( 138421, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'( X, Z,
% 66.65/67.06 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Y, Z,
% 66.65/67.06 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , clause( 138422, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 66.65/67.06 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 66.65/67.06 , clause( 138423, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 66.65/67.06 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 66.65/67.06 , clause( 138424, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 66.65/67.06 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 66.65/67.06 , clause( 138425, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_RealDef_Oreal'
% 66.65/67.06 ) ), ~( 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , clause( 138426, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 66.65/67.06 , X ) ) ), =( Y, Z ) ] )
% 66.65/67.06 , clause( 138427, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 66.65/67.06 , X ) ) ), =( Y, Z ) ] )
% 66.65/67.06 , clause( 138428, [ ~( =( 'c_RealDef_Oreal'( X, 'tc_nat' ),
% 66.65/67.06 'c_RealDef_Oreal'( Y, 'tc_nat' ) ) ), =( X, Y ) ] )
% 66.65/67.06 , clause( 138429, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.06 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 66.65/67.06 , X ), X ) ) ] )
% 66.65/67.06 , clause( 138430, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.06 ), 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 66.65/67.06 ) ] )
% 66.65/67.06 , clause( 138431, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 66.65/67.06 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 66.65/67.06 ) ) ] )
% 66.65/67.06 , clause( 138432, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 66.65/67.06 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 66.65/67.06 ) ) ] )
% 66.65/67.06 , clause( 138433, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 66.65/67.06 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 66.65/67.06 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 66.65/67.06 , X ) ) ] )
% 66.65/67.06 , clause( 138434, [ =( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat'
% 66.65/67.06 ), 'tc_nat' ) ) ] )
% 66.65/67.06 , clause( 138435, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 66.65/67.06 ), 'tc_nat' ) ) ] )
% 66.65/67.06 , clause( 138436, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 66.65/67.06 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 66.65/67.06 ) ) ] )
% 66.65/67.06 , clause( 138437, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 66.65/67.06 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 66.65/67.06 ) ) ] )
% 66.65/67.06 , clause( 138438, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 66.65/67.06 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 66.65/67.06 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 66.65/67.06 , X ) ) ] )
% 66.65/67.06 , clause( 138439, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 66.65/67.06 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 66.65/67.06 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z
% 66.65/67.06 , X ) ) ] )
% 66.65/67.06 , clause( 138440, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 66.65/67.06 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 66.65/67.06 X ), 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X )
% 66.65/67.06 , X ) ) ] )
% 66.65/67.06 , clause( 138441, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 66.65/67.06 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 66.65/67.06 X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 66.65/67.06 , X ) ) ] )
% 66.65/67.06 , clause( 138442, [ =( 'c_RealDef_Oreal'( 'c_HOL_Oplus__class_Oplus'( X, Y
% 66.65/67.06 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_RealDef_Oreal'(
% 66.65/67.06 X, 'tc_nat' ), 'c_RealDef_Oreal'( Y, 'tc_nat' ), 'tc_RealDef_Oreal' ) ) ]
% 66.65/67.06 )
% 66.65/67.06 , clause( 138443, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 66.65/67.06 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ] )
% 66.65/67.06 , clause( 138444, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 66.65/67.06 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 Y, Z, X ), X ) ) ] )
% 66.65/67.06 , clause( 138445, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 66.65/67.06 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ] )
% 66.65/67.06 , clause( 138446, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 66.65/67.06 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 66.65/67.06 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 66.65/67.06 , clause( 138447, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 66.65/67.06 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 66.65/67.06 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 66.65/67.06 , clause( 138448, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 66.65/67.06 ), Y ) ] )
% 66.65/67.06 , clause( 138449, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 66.65/67.06 ) ) ] )
% 66.65/67.06 , clause( 138450, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 66.65/67.06 ) ) ] )
% 66.65/67.06 , clause( 138451, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 66.65/67.06 ), Y ) ] )
% 66.65/67.06 , clause( 138452, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 66.65/67.06 ), Y ) ] )
% 66.65/67.06 , clause( 138453, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.06 ), 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 66.65/67.06 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ] )
% 66.65/67.06 , clause( 138454, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.06 ), 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 66.65/67.06 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ] )
% 66.65/67.06 , clause( 138455, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.06 ), 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 66.65/67.06 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 66.65/67.06 , clause( 138456, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 66.65/67.06 ), 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 66.65/67.06 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 66.65/67.06 , clause( 138457, [ 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 66.65/67.06 'c_Suc'( 'v_f____'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____',
% 66.65/67.06 'tc_nat' ) ) ), 'tc_nat' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ),
% 66.65/67.06 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138458, [ ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( 'v_s____', 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'( 'v_f____'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ) ),
% 66.65/67.06 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( 'v_s____',
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 66.65/67.06 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) )
% 66.65/67.06 , 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , clause( 138459, [
% 66.65/67.06 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 66.65/67.06 )
% 66.65/67.06 , clause( 138460, [
% 66.65/67.06 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 66.65/67.06 )
% 66.65/67.06 , clause( 138461, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 66.65/67.06 'tc_nat' ) ] )
% 66.65/67.06 , clause( 138462, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 66.65/67.06 'tc_nat' ) ] )
% 66.65/67.06 , clause( 138463, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 66.65/67.06 'tc_nat' ) ] )
% 66.65/67.06 , clause( 138464, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat'
% 66.65/67.06 ) ] )
% 66.65/67.06 , clause( 138465, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' )
% 66.65/67.06 ] )
% 66.65/67.06 , clause( 138466, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' )
% 66.65/67.06 ] )
% 66.65/67.06 , clause( 138467, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ]
% 66.65/67.06 )
% 66.65/67.06 , clause( 138468, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ]
% 66.65/67.06 )
% 66.65/67.06 , clause( 138469, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ]
% 66.65/67.06 )
% 66.65/67.06 , clause( 138470, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 66.65/67.06 , clause( 138471, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 66.65/67.06 , clause( 138472, [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ] )
% 66.65/67.06 , clause( 138473, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 66.65/67.06 , clause( 138474, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 66.65/67.06 , clause( 138475, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 66.65/67.06 , clause( 138476, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 66.65/67.06 , clause( 138477, [
% 66.65/67.06 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138478, [
% 66.65/67.06 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138479, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138480, [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138481, [ 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138482, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138483, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138484, [ 'class_OrderedGroup_Opordered__ab__group__add'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138485, [ 'class_OrderedGroup_Olordered__ab__group__add'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138486, [ 'class_OrderedGroup_Oordered__ab__group__add'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138487, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138488, [ 'class_RealVector_Oreal__normed__algebra__1'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138489, [ 'class_Ring__and__Field_Odivision__by__zero'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138490, [ 'class_Ring__and__Field_Oordered__semidom'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138491, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138492, [ 'class_RealVector_Oreal__normed__vector'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138493, [ 'class_OrderedGroup_Oab__semigroup__add'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138494, [ 'class_Ring__and__Field_Oordered__field'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138495, [ 'class_RealVector_Oreal__normed__field'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138496, [ 'class_OrderedGroup_Ocomm__monoid__add'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138497, [ 'class_Ring__and__Field_Ozero__neq__one'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138498, [ 'class_Ring__and__Field_Oordered__idom'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138499, [ 'class_Ring__and__Field_Osemiring__1'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138500, [ 'class_OrderedGroup_Oab__group__add'(
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138501, [ 'class_OrderedGroup_Omonoid__add'( 'tc_RealDef_Oreal' )
% 66.65/67.06 ] )
% 66.65/67.06 , clause( 138502, [ 'class_OrderedGroup_Ogroup__add'( 'tc_RealDef_Oreal' )
% 66.65/67.06 ] )
% 66.65/67.06 , clause( 138503, [ 'class_Ring__and__Field_Oabs__if'( 'tc_RealDef_Oreal' )
% 66.65/67.06 ] )
% 66.65/67.06 , clause( 138504, [ 'class_Ring__and__Field_Ofield'( 'tc_RealDef_Oreal' ) ]
% 66.65/67.06 )
% 66.65/67.06 , clause( 138505, [ 'class_Ring__and__Field_Oidom'( 'tc_RealDef_Oreal' ) ]
% 66.65/67.06 )
% 66.65/67.06 , clause( 138506, [ 'class_Nat_Osemiring__char__0'( 'tc_RealDef_Oreal' ) ]
% 66.65/67.06 )
% 66.65/67.06 , clause( 138507, [ 'class_Orderings_Opreorder'( 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138508, [ 'class_Orderings_Olinorder'( 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138509, [ 'class_Orderings_Oorder'( 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138510, [ 'class_Int_Onumber__ring'( 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 ] ).
% 66.65/67.06
% 66.65/67.06
% 66.65/67.06
% 66.65/67.06 subsumption(
% 66.65/67.06 clause( 396, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'( X, Z,
% 66.65/67.06 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Y, Z,
% 66.65/67.06 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , clause( 138421, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'( X, Z,
% 66.65/67.06 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Y, Z,
% 66.65/67.06 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 66.65/67.06 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 66.65/67.06
% 66.65/67.06
% 66.65/67.06 subsumption(
% 66.65/67.06 clause( 423, [ 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 66.65/67.06 'c_Suc'( 'v_f____'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____',
% 66.65/67.06 'tc_nat' ) ) ), 'tc_nat' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ),
% 66.65/67.06 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 138457, [ 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 66.65/67.06 'c_Suc'( 'v_f____'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____',
% 66.65/67.06 'tc_nat' ) ) ), 'tc_nat' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ),
% 66.65/67.06 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 66.65/67.06
% 66.65/67.06
% 66.65/67.06 subsumption(
% 66.65/67.06 clause( 424, [ ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( 'v_s____', 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'( 'v_f____'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ) ),
% 66.65/67.06 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( 'v_s____',
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 66.65/67.06 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) )
% 66.65/67.06 , 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , clause( 138458, [ ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( 'v_s____', 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'( 'v_f____'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ) ),
% 66.65/67.06 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( 'v_s____',
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 66.65/67.06 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) )
% 66.65/67.06 , 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 66.65/67.06
% 66.65/67.06
% 66.65/67.06 resolution(
% 66.65/67.06 clause( 139883, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X,
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'( 'v_f____'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ) ),
% 66.65/67.06 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 66.65/67.06 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) )
% 66.65/67.06 , 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 396, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'( X, Z,
% 66.65/67.06 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Y, Z,
% 66.65/67.06 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , 1, clause( 423, [ 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 66.65/67.06 'c_Suc'( 'v_f____'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____',
% 66.65/67.06 'tc_nat' ) ) ), 'tc_nat' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ),
% 66.65/67.06 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 66.65/67.06 'c_Suc'( 'v_f____'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____',
% 66.65/67.06 'tc_nat' ) ) ), 'tc_nat' ), 'tc_RealDef_Oreal' ) ), :=( Z,
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ),
% 66.65/67.06 'tc_nat' ), 'tc_RealDef_Oreal' ) )] ), substitution( 1, [] )).
% 66.65/67.06
% 66.65/67.06
% 66.65/67.06 subsumption(
% 66.65/67.06 clause( 136985, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X,
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'( 'v_f____'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ) ),
% 66.65/67.06 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 66.65/67.06 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) )
% 66.65/67.06 , 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , clause( 139883, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X,
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'( 'v_f____'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ) ),
% 66.65/67.06 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 66.65/67.06 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) )
% 66.65/67.06 , 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 66.65/67.06
% 66.65/67.06
% 66.65/67.06 resolution(
% 66.65/67.06 clause( 139884, [] )
% 66.65/67.06 , clause( 424, [ ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( 'v_s____', 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'( 'v_f____'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ) ),
% 66.65/67.06 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( 'v_s____',
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 66.65/67.06 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) )
% 66.65/67.06 , 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ) ) ] )
% 66.65/67.06 , 0, clause( 136985, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X,
% 66.65/67.06 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 66.65/67.06 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'( 'c_Suc'( 'v_f____'(
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) ) ),
% 66.65/67.06 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oinverse__class_Odivide'(
% 66.65/67.06 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_RealDef_Oreal'(
% 66.65/67.06 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( 'v_N1____', 'v_N2____', 'tc_nat' ) )
% 66.65/67.06 , 'tc_nat' ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 66.65/67.06 'tc_RealDef_Oreal' ) ] )
% 66.65/67.06 , 0, substitution( 0, [] ), substitution( 1, [ :=( X,
% 66.65/67.06 'c_HOL_Ouminus__class_Ouminus'( 'v_s____', 'tc_RealDef_Oreal' ) )] )).
% 66.65/67.06
% 66.65/67.06
% 66.65/67.06 subsumption(
% 66.65/67.06 clause( 137950, [] )
% 66.65/67.06 , clause( 139884, [] )
% 66.65/67.06 , substitution( 0, [] ), permutation( 0, [] ) ).
% 66.65/67.06
% 66.65/67.06
% 66.65/67.06 end.
% 66.65/67.06
% 66.65/67.06 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 66.65/67.06
% 66.65/67.06 Memory use:
% 66.65/67.06
% 66.65/67.06 space for terms: 3222330
% 66.65/67.06 space for clauses: 6065982
% 66.65/67.06
% 66.65/67.06
% 66.65/67.06 clauses generated: 857186
% 66.65/67.06 clauses kept: 137951
% 66.65/67.06 clauses selected: 1789
% 66.65/67.06 clauses deleted: 17297
% 66.65/67.06 clauses inuse deleted: 448
% 66.65/67.06
% 66.65/67.06 subsentry: 4162189
% 66.65/67.06 literals s-matched: 2583385
% 66.65/67.06 literals matched: 2413824
% 66.65/67.06 full subsumption: 1038084
% 66.65/67.06
% 66.65/67.06 checksum: 1882290903
% 66.65/67.06
% 66.65/67.06
% 66.65/67.06 Bliksem ended
%------------------------------------------------------------------------------