TSTP Solution File: GRP170-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP170-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.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 : Sat Jul 16 07:35:44 EDT 2022
% Result : Unsatisfiable 2.15s 2.57s
% Output : Refutation 2.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP170-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n006.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 : Tue Jun 14 03:54:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.15/2.57 *** allocated 10000 integers for termspace/termends
% 2.15/2.57 *** allocated 10000 integers for clauses
% 2.15/2.57 *** allocated 10000 integers for justifications
% 2.15/2.57 Bliksem 1.12
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 Automatic Strategy Selection
% 2.15/2.57
% 2.15/2.57 Clauses:
% 2.15/2.57 [
% 2.15/2.57 [ =( multiply( identity, X ), X ) ],
% 2.15/2.57 [ =( multiply( inverse( X ), X ), identity ) ],
% 2.15/2.57 [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply( Y, Z ) ) )
% 2.15/2.57 ],
% 2.15/2.57 [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, X ) ) ]
% 2.15/2.57 ,
% 2.15/2.57 [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ],
% 2.15/2.57 [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ),
% 2.15/2.57 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ],
% 2.15/2.57 [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 2.15/2.57 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ],
% 2.15/2.57 [ =( 'least_upper_bound'( X, X ), X ) ],
% 2.15/2.57 [ =( 'greatest_lower_bound'( X, X ), X ) ],
% 2.15/2.57 [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X ) ]
% 2.15/2.57 ,
% 2.15/2.57 [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ), X ) ]
% 2.15/2.57 ,
% 2.15/2.57 [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), 'least_upper_bound'(
% 2.15/2.57 multiply( X, Y ), multiply( X, Z ) ) ) ],
% 2.15/2.57 [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 2.15/2.57 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ],
% 2.15/2.57 [ =( multiply( 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'(
% 2.15/2.57 multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 2.15/2.57 [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 2.15/2.57 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 2.15/2.57 [ =( 'least_upper_bound'( a, b ), b ) ],
% 2.15/2.57 [ =( 'least_upper_bound'( c, d ), d ) ],
% 2.15/2.57 [ ~( =( 'least_upper_bound'( multiply( a, c ), multiply( b, d ) ),
% 2.15/2.57 multiply( b, d ) ) ) ]
% 2.15/2.57 ] .
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 percentage equality = 1.000000, percentage horn = 1.000000
% 2.15/2.57 This is a pure equality problem
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 Options Used:
% 2.15/2.57
% 2.15/2.57 useres = 1
% 2.15/2.57 useparamod = 1
% 2.15/2.57 useeqrefl = 1
% 2.15/2.57 useeqfact = 1
% 2.15/2.57 usefactor = 1
% 2.15/2.57 usesimpsplitting = 0
% 2.15/2.57 usesimpdemod = 5
% 2.15/2.57 usesimpres = 3
% 2.15/2.57
% 2.15/2.57 resimpinuse = 1000
% 2.15/2.57 resimpclauses = 20000
% 2.15/2.57 substype = eqrewr
% 2.15/2.57 backwardsubs = 1
% 2.15/2.57 selectoldest = 5
% 2.15/2.57
% 2.15/2.57 litorderings [0] = split
% 2.15/2.57 litorderings [1] = extend the termordering, first sorting on arguments
% 2.15/2.57
% 2.15/2.57 termordering = kbo
% 2.15/2.57
% 2.15/2.57 litapriori = 0
% 2.15/2.57 termapriori = 1
% 2.15/2.57 litaposteriori = 0
% 2.15/2.57 termaposteriori = 0
% 2.15/2.57 demodaposteriori = 0
% 2.15/2.57 ordereqreflfact = 0
% 2.15/2.57
% 2.15/2.57 litselect = negord
% 2.15/2.57
% 2.15/2.57 maxweight = 15
% 2.15/2.57 maxdepth = 30000
% 2.15/2.57 maxlength = 115
% 2.15/2.57 maxnrvars = 195
% 2.15/2.57 excuselevel = 1
% 2.15/2.57 increasemaxweight = 1
% 2.15/2.57
% 2.15/2.57 maxselected = 10000000
% 2.15/2.57 maxnrclauses = 10000000
% 2.15/2.57
% 2.15/2.57 showgenerated = 0
% 2.15/2.57 showkept = 0
% 2.15/2.57 showselected = 0
% 2.15/2.57 showdeleted = 0
% 2.15/2.57 showresimp = 1
% 2.15/2.57 showstatus = 2000
% 2.15/2.57
% 2.15/2.57 prologoutput = 1
% 2.15/2.57 nrgoals = 5000000
% 2.15/2.57 totalproof = 1
% 2.15/2.57
% 2.15/2.57 Symbols occurring in the translation:
% 2.15/2.57
% 2.15/2.57 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.15/2.57 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 2.15/2.57 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 2.15/2.57 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.15/2.57 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.15/2.57 identity [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 2.15/2.57 multiply [41, 2] (w:1, o:49, a:1, s:1, b:0),
% 2.15/2.57 inverse [42, 1] (w:1, o:22, a:1, s:1, b:0),
% 2.15/2.57 'greatest_lower_bound' [45, 2] (w:1, o:50, a:1, s:1, b:0),
% 2.15/2.57 'least_upper_bound' [46, 2] (w:1, o:48, a:1, s:1, b:0),
% 2.15/2.57 a [47, 0] (w:1, o:13, a:1, s:1, b:0),
% 2.15/2.57 b [48, 0] (w:1, o:14, a:1, s:1, b:0),
% 2.15/2.57 c [49, 0] (w:1, o:15, a:1, s:1, b:0),
% 2.15/2.57 d [50, 0] (w:1, o:16, a:1, s:1, b:0).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 Starting Search:
% 2.15/2.57
% 2.15/2.57 Resimplifying inuse:
% 2.15/2.57 Done
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 Intermediate Status:
% 2.15/2.57 Generated: 29492
% 2.15/2.57 Kept: 2009
% 2.15/2.57 Inuse: 263
% 2.15/2.57 Deleted: 17
% 2.15/2.57 Deletedinuse: 6
% 2.15/2.57
% 2.15/2.57 Resimplifying inuse:
% 2.15/2.57 Done
% 2.15/2.57
% 2.15/2.57 Resimplifying inuse:
% 2.15/2.57 Done
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 Intermediate Status:
% 2.15/2.57 Generated: 61539
% 2.15/2.57 Kept: 4020
% 2.15/2.57 Inuse: 471
% 2.15/2.57 Deleted: 30
% 2.15/2.57 Deletedinuse: 6
% 2.15/2.57
% 2.15/2.57 Resimplifying inuse:
% 2.15/2.57 Done
% 2.15/2.57
% 2.15/2.57 Resimplifying inuse:
% 2.15/2.57 Done
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 Intermediate Status:
% 2.15/2.57 Generated: 106531
% 2.15/2.57 Kept: 6022
% 2.15/2.57 Inuse: 681
% 2.15/2.57 Deleted: 46
% 2.15/2.57 Deletedinuse: 6
% 2.15/2.57
% 2.15/2.57 Resimplifying inuse:
% 2.15/2.57 Done
% 2.15/2.57
% 2.15/2.57 Resimplifying inuse:
% 2.15/2.57 Done
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 Intermediate Status:
% 2.15/2.57 Generated: 171286
% 2.15/2.57 Kept: 8063
% 2.15/2.57 Inuse: 816
% 2.15/2.57 Deleted: 46
% 2.15/2.57 Deletedinuse: 6
% 2.15/2.57
% 2.15/2.57 Resimplifying inuse:
% 2.15/2.57 Done
% 2.15/2.57
% 2.15/2.57 Resimplifying inuse:
% 2.15/2.57 Done
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 Intermediate Status:
% 2.15/2.57 Generated: 291582
% 2.15/2.57 Kept: 10074
% 2.15/2.57 Inuse: 1016
% 2.15/2.57 Deleted: 59
% 2.15/2.57 Deletedinuse: 6
% 2.15/2.57
% 2.15/2.57 Resimplifying inuse:
% 2.15/2.57 Done
% 2.15/2.57
% 2.15/2.57 Resimplifying inuse:
% 2.15/2.57 Done
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 Intermediate Status:
% 2.15/2.57 Generated: 376764
% 2.15/2.57 Kept: 12082
% 2.15/2.57 Inuse: 1182
% 2.15/2.57 Deleted: 83
% 2.15/2.57 Deletedinuse: 6
% 2.15/2.57
% 2.15/2.57 Resimplifying inuse:
% 2.15/2.57 Done
% 2.15/2.57
% 2.15/2.57 Resimplifying inuse:
% 2.15/2.57 Done
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 Intermediate Status:
% 2.15/2.57 Generated: 436473
% 2.15/2.57 Kept: 14085
% 2.15/2.57 Inuse: 1261
% 2.15/2.57 Deleted: 83
% 2.15/2.57 Deletedinuse: 6
% 2.15/2.57
% 2.15/2.57 Resimplifying inuse:
% 2.15/2.57 Done
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 Bliksems!, er is een bewijs:
% 2.15/2.57 % SZS status Unsatisfiable
% 2.15/2.57 % SZS output start Refutation
% 2.15/2.57
% 2.15/2.57 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 2.15/2.57 , Z ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 2.15/2.57 X ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 2.15/2.57 ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) )
% 2.15/2.57 , 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 2.15/2.57 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 2.15/2.57 ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 2.15/2.57 X ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) )
% 2.15/2.57 , multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 2.15/2.57 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 14, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z )
% 2.15/2.57 ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 15, [ =( 'least_upper_bound'( a, b ), b ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 16, [ =( 'least_upper_bound'( c, d ), d ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 17, [ ~( =( 'least_upper_bound'( multiply( a, c ), multiply( b, d )
% 2.15/2.57 ), multiply( b, d ) ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 18, [ =( 'least_upper_bound'( b, a ), b ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 19, [ =( 'least_upper_bound'( d, c ), d ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 20, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ), Y )
% 2.15/2.57 , identity ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 2.15/2.57 identity ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 22, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 2.15/2.57 ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 23, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X ),
% 2.15/2.57 X ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 24, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) ),
% 2.15/2.57 X ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 44, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, Z ),
% 2.15/2.57 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ),
% 2.15/2.57 'least_upper_bound'( Y, Z ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 49, [ =( 'least_upper_bound'( 'least_upper_bound'( X, b ), a ),
% 2.15/2.57 'least_upper_bound'( X, b ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 57, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), X
% 2.15/2.57 ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 58, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 2.15/2.57 'least_upper_bound'( X, Y ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 60, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) ),
% 2.15/2.57 X ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 63, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, Z ),
% 2.15/2.57 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ),
% 2.15/2.57 'greatest_lower_bound'( Y, Z ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 64, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X ),
% 2.15/2.57 X ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 75, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y )
% 2.15/2.57 ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 76, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ), identity
% 2.15/2.57 ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 105, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 2.15/2.57 'least_upper_bound'( identity, Y ), X ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 124, [ =( 'greatest_lower_bound'( multiply( Y, X ), X ), multiply(
% 2.15/2.57 'greatest_lower_bound'( Y, identity ), X ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 139, [ ~( =( 'least_upper_bound'( multiply( b, d ), multiply( a, c
% 2.15/2.57 ) ), multiply( b, d ) ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 151, [ =( 'least_upper_bound'( 'least_upper_bound'( a, X ), b ),
% 2.15/2.57 'least_upper_bound'( X, b ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 165, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 2.15/2.57 ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 173, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X,
% 2.15/2.57 'least_upper_bound'( identity, Y ) ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 365, [ =( multiply( X, identity ), X ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 373, [ =( inverse( inverse( X ) ), X ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 379, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 397, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y )
% 2.15/2.57 ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 401, [ =( multiply( 'least_upper_bound'( Z, multiply( X, Y ) ),
% 2.15/2.57 inverse( Y ) ), 'least_upper_bound'( multiply( Z, inverse( Y ) ), X ) ) ]
% 2.15/2.57 )
% 2.15/2.57 .
% 2.15/2.57 clause( 403, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X )
% 2.15/2.57 ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 404, [ =( multiply( inverse( Y ), inverse( X ) ), inverse( multiply(
% 2.15/2.57 X, Y ) ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 405, [ =( inverse( multiply( inverse( X ), Y ) ), multiply( inverse(
% 2.15/2.57 Y ), X ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 413, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 2.15/2.57 inverse( X ) ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 483, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 2.15/2.57 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( Y, X ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 727, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ),
% 2.15/2.57 'greatest_lower_bound'( X, Y ) ), 'greatest_lower_bound'( Y, X ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 1257, [ =( 'least_upper_bound'( identity, multiply( inverse( X ),
% 2.15/2.57 'greatest_lower_bound'( X, Y ) ) ), identity ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 1260, [ =( 'least_upper_bound'( identity, multiply( inverse( d ), c
% 2.15/2.57 ) ), identity ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 1350, [ =( 'greatest_lower_bound'( identity, multiply( inverse( X )
% 2.15/2.57 , 'least_upper_bound'( Y, X ) ) ), identity ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 1485, [ =( 'greatest_lower_bound'( identity, multiply( inverse( c )
% 2.15/2.57 , d ) ), identity ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 1581, [ =( 'greatest_lower_bound'( multiply( inverse( c ), d ),
% 2.15/2.57 identity ), identity ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 3030, [ =( 'greatest_lower_bound'( multiply( multiply( inverse( c )
% 2.15/2.57 , d ), X ), X ), X ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 3205, [ =( 'greatest_lower_bound'( inverse( c ), inverse( d ) ),
% 2.15/2.57 inverse( d ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 3216, [ =( 'least_upper_bound'( identity, multiply( c, inverse( d )
% 2.15/2.57 ) ), identity ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 3266, [ =( 'least_upper_bound'( X, multiply( multiply( c, inverse(
% 2.15/2.57 d ) ), X ) ), X ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 4257, [ =( 'least_upper_bound'( X, multiply( multiply( X, c ),
% 2.15/2.57 inverse( d ) ) ), X ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 4347, [ =( 'least_upper_bound'( multiply( multiply( a, c ), inverse(
% 2.15/2.57 d ) ), b ), b ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 4507, [ =( 'least_upper_bound'( b, multiply( multiply( a, c ),
% 2.15/2.57 inverse( d ) ) ), b ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 14543, [ =( 'least_upper_bound'( multiply( b, d ), multiply( a, c )
% 2.15/2.57 ), multiply( b, d ) ) ] )
% 2.15/2.57 .
% 2.15/2.57 clause( 14997, [] )
% 2.15/2.57 .
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 % SZS output end Refutation
% 2.15/2.57 found a proof!
% 2.15/2.57
% 2.15/2.57 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.15/2.57
% 2.15/2.57 initialclauses(
% 2.15/2.57 [ clause( 14999, [ =( multiply( identity, X ), X ) ] )
% 2.15/2.57 , clause( 15000, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.15/2.57 , clause( 15001, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 2.15/2.57 multiply( Y, Z ) ) ) ] )
% 2.15/2.57 , clause( 15002, [ =( 'greatest_lower_bound'( X, Y ),
% 2.15/2.57 'greatest_lower_bound'( Y, X ) ) ] )
% 2.15/2.57 , clause( 15003, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y,
% 2.15/2.57 X ) ) ] )
% 2.15/2.57 , clause( 15004, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y
% 2.15/2.57 , Z ) ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ]
% 2.15/2.57 )
% 2.15/2.57 , clause( 15005, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 2.15/2.57 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.15/2.57 , clause( 15006, [ =( 'least_upper_bound'( X, X ), X ) ] )
% 2.15/2.57 , clause( 15007, [ =( 'greatest_lower_bound'( X, X ), X ) ] )
% 2.15/2.57 , clause( 15008, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 2.15/2.57 ) ), X ) ] )
% 2.15/2.57 , clause( 15009, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 2.15/2.57 ) ), X ) ] )
% 2.15/2.57 , clause( 15010, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 2.15/2.57 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.15/2.57 , clause( 15011, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 2.15/2.57 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.15/2.57 , clause( 15012, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 2.15/2.57 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 2.15/2.57 , clause( 15013, [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 2.15/2.57 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 2.15/2.57 , clause( 15014, [ =( 'least_upper_bound'( a, b ), b ) ] )
% 2.15/2.57 , clause( 15015, [ =( 'least_upper_bound'( c, d ), d ) ] )
% 2.15/2.57 , clause( 15016, [ ~( =( 'least_upper_bound'( multiply( a, c ), multiply( b
% 2.15/2.57 , d ) ), multiply( b, d ) ) ) ] )
% 2.15/2.57 ] ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.15/2.57 , clause( 14999, [ =( multiply( identity, X ), X ) ] )
% 2.15/2.57 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.15/2.57 , clause( 15000, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.15/2.57 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 eqswap(
% 2.15/2.57 clause( 15022, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X
% 2.15/2.57 , Y ), Z ) ) ] )
% 2.15/2.57 , clause( 15001, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 2.15/2.57 multiply( Y, Z ) ) ) ] )
% 2.15/2.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 2.15/2.57 , Z ) ) ] )
% 2.15/2.57 , clause( 15022, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply(
% 2.15/2.57 X, Y ), Z ) ) ] )
% 2.15/2.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.15/2.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 2.15/2.57 X ) ) ] )
% 2.15/2.57 , clause( 15002, [ =( 'greatest_lower_bound'( X, Y ),
% 2.15/2.57 'greatest_lower_bound'( Y, X ) ) ] )
% 2.15/2.57 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.57 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 2.15/2.57 ] )
% 2.15/2.57 , clause( 15003, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y,
% 2.15/2.57 X ) ) ] )
% 2.15/2.57 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.57 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) )
% 2.15/2.57 , 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 2.15/2.57 , clause( 15004, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y
% 2.15/2.57 , Z ) ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ]
% 2.15/2.57 )
% 2.15/2.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.15/2.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 2.15/2.57 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.15/2.57 , clause( 15005, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 2.15/2.57 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.15/2.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.15/2.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 2.15/2.57 ) ] )
% 2.15/2.57 , clause( 15008, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 2.15/2.57 ) ), X ) ] )
% 2.15/2.57 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.57 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 2.15/2.57 X ) ] )
% 2.15/2.57 , clause( 15009, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 2.15/2.57 ) ), X ) ] )
% 2.15/2.57 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.57 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 eqswap(
% 2.15/2.57 clause( 15064, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 2.15/2.57 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.15/2.57 , clause( 15010, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 2.15/2.57 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.15/2.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) )
% 2.15/2.57 , multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.15/2.57 , clause( 15064, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z
% 2.15/2.57 ) ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.15/2.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.15/2.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 eqswap(
% 2.15/2.57 clause( 15076, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 2.15/2.57 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.15/2.57 , clause( 15012, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 2.15/2.57 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 2.15/2.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 2.15/2.57 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.15/2.57 , clause( 15076, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z
% 2.15/2.57 ) ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.15/2.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.15/2.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 eqswap(
% 2.15/2.57 clause( 15089, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y,
% 2.15/2.57 Z ) ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 2.15/2.57 , clause( 15013, [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 2.15/2.57 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 2.15/2.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 14, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z )
% 2.15/2.57 ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 2.15/2.57 , clause( 15089, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y
% 2.15/2.57 , Z ) ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 2.15/2.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.15/2.57 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 15, [ =( 'least_upper_bound'( a, b ), b ) ] )
% 2.15/2.57 , clause( 15014, [ =( 'least_upper_bound'( a, b ), b ) ] )
% 2.15/2.57 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 16, [ =( 'least_upper_bound'( c, d ), d ) ] )
% 2.15/2.57 , clause( 15015, [ =( 'least_upper_bound'( c, d ), d ) ] )
% 2.15/2.57 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 17, [ ~( =( 'least_upper_bound'( multiply( a, c ), multiply( b, d )
% 2.15/2.57 ), multiply( b, d ) ) ) ] )
% 2.15/2.57 , clause( 15016, [ ~( =( 'least_upper_bound'( multiply( a, c ), multiply( b
% 2.15/2.57 , d ) ), multiply( b, d ) ) ) ] )
% 2.15/2.57 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 eqswap(
% 2.15/2.57 clause( 15135, [ =( b, 'least_upper_bound'( a, b ) ) ] )
% 2.15/2.57 , clause( 15, [ =( 'least_upper_bound'( a, b ), b ) ] )
% 2.15/2.57 , 0, substitution( 0, [] )).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 paramod(
% 2.15/2.57 clause( 15136, [ =( b, 'least_upper_bound'( b, a ) ) ] )
% 2.15/2.57 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 2.15/2.57 ) ] )
% 2.15/2.57 , 0, clause( 15135, [ =( b, 'least_upper_bound'( a, b ) ) ] )
% 2.15/2.57 , 0, 2, substitution( 0, [ :=( X, a ), :=( Y, b )] ), substitution( 1, [] )
% 2.15/2.57 ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 eqswap(
% 2.15/2.57 clause( 15139, [ =( 'least_upper_bound'( b, a ), b ) ] )
% 2.15/2.57 , clause( 15136, [ =( b, 'least_upper_bound'( b, a ) ) ] )
% 2.15/2.57 , 0, substitution( 0, [] )).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 18, [ =( 'least_upper_bound'( b, a ), b ) ] )
% 2.15/2.57 , clause( 15139, [ =( 'least_upper_bound'( b, a ), b ) ] )
% 2.15/2.57 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 eqswap(
% 2.15/2.57 clause( 15140, [ =( d, 'least_upper_bound'( c, d ) ) ] )
% 2.15/2.57 , clause( 16, [ =( 'least_upper_bound'( c, d ), d ) ] )
% 2.15/2.57 , 0, substitution( 0, [] )).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 paramod(
% 2.15/2.57 clause( 15141, [ =( d, 'least_upper_bound'( d, c ) ) ] )
% 2.15/2.57 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 2.15/2.57 ) ] )
% 2.15/2.57 , 0, clause( 15140, [ =( d, 'least_upper_bound'( c, d ) ) ] )
% 2.15/2.57 , 0, 2, substitution( 0, [ :=( X, c ), :=( Y, d )] ), substitution( 1, [] )
% 2.15/2.57 ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 eqswap(
% 2.15/2.57 clause( 15144, [ =( 'least_upper_bound'( d, c ), d ) ] )
% 2.15/2.57 , clause( 15141, [ =( d, 'least_upper_bound'( d, c ) ) ] )
% 2.15/2.57 , 0, substitution( 0, [] )).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 19, [ =( 'least_upper_bound'( d, c ), d ) ] )
% 2.15/2.57 , clause( 15144, [ =( 'least_upper_bound'( d, c ), d ) ] )
% 2.15/2.57 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 eqswap(
% 2.15/2.57 clause( 15145, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 2.15/2.57 Y, Z ) ) ) ] )
% 2.15/2.57 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 2.15/2.57 ), Z ) ) ] )
% 2.15/2.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 paramod(
% 2.15/2.57 clause( 15148, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ), Y
% 2.15/2.57 ), identity ) ] )
% 2.15/2.57 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.15/2.57 , 0, clause( 15145, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 2.15/2.57 multiply( Y, Z ) ) ) ] )
% 2.15/2.57 , 0, 9, substitution( 0, [ :=( X, multiply( X, Y ) )] ), substitution( 1, [
% 2.15/2.57 :=( X, inverse( multiply( X, Y ) ) ), :=( Y, X ), :=( Z, Y )] )).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 20, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ), Y )
% 2.15/2.57 , identity ) ] )
% 2.15/2.57 , clause( 15148, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X )
% 2.15/2.57 , Y ), identity ) ] )
% 2.15/2.57 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.57 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 eqswap(
% 2.15/2.57 clause( 15154, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 2.15/2.57 Y, Z ) ) ) ] )
% 2.15/2.57 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 2.15/2.57 ), Z ) ) ] )
% 2.15/2.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 paramod(
% 2.15/2.57 clause( 15159, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply( X
% 2.15/2.57 , identity ) ) ] )
% 2.15/2.57 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.15/2.57 , 0, clause( 15154, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 2.15/2.57 multiply( Y, Z ) ) ) ] )
% 2.15/2.57 , 0, 9, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 2.15/2.57 :=( Y, inverse( Y ) ), :=( Z, Y )] )).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 2.15/2.57 identity ) ) ] )
% 2.15/2.57 , clause( 15159, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply(
% 2.15/2.57 X, identity ) ) ] )
% 2.15/2.57 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.57 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 eqswap(
% 2.15/2.57 clause( 15164, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 2.15/2.57 Y, Z ) ) ) ] )
% 2.15/2.57 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 2.15/2.57 ), Z ) ) ] )
% 2.15/2.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 paramod(
% 2.15/2.57 clause( 15169, [ =( multiply( multiply( X, identity ), Y ), multiply( X, Y
% 2.15/2.57 ) ) ] )
% 2.15/2.57 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.15/2.57 , 0, clause( 15164, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 2.15/2.57 multiply( Y, Z ) ) ) ] )
% 2.15/2.57 , 0, 8, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 2.15/2.57 :=( Y, identity ), :=( Z, Y )] )).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 subsumption(
% 2.15/2.57 clause( 22, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 2.15/2.57 ] )
% 2.15/2.57 , clause( 15169, [ =( multiply( multiply( X, identity ), Y ), multiply( X,
% 2.15/2.57 Y ) ) ] )
% 2.15/2.57 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.57 )] ) ).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 eqswap(
% 2.15/2.57 clause( 15174, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 2.15/2.57 ) ) ) ] )
% 2.15/2.57 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 2.15/2.57 , X ) ] )
% 2.15/2.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.57
% 2.15/2.57
% 2.15/2.57 paramod(
% 2.15/2.57 clause( 15175, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y )
% 2.15/2.57 , X ) ) ] )
% 2.15/2.57 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 2.15/2.58 , X ) ) ] )
% 2.15/2.58 , 0, clause( 15174, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 2.15/2.58 X, Y ) ) ) ] )
% 2.15/2.58 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, 'least_upper_bound'( X, Y ) )] )
% 2.15/2.58 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15178, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X
% 2.15/2.58 ), X ) ] )
% 2.15/2.58 , clause( 15175, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y
% 2.15/2.58 ), X ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 23, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X ),
% 2.15/2.58 X ) ] )
% 2.15/2.58 , clause( 15178, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 2.15/2.58 X ), X ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15179, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 2.15/2.58 ) ) ) ] )
% 2.15/2.58 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 2.15/2.58 , X ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15180, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 2.15/2.58 ) ) ) ] )
% 2.15/2.58 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 2.15/2.58 ) ] )
% 2.15/2.58 , 0, clause( 15179, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 2.15/2.58 X, Y ) ) ) ] )
% 2.15/2.58 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.15/2.58 :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15183, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X )
% 2.15/2.58 ), X ) ] )
% 2.15/2.58 , clause( 15180, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y
% 2.15/2.58 , X ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 24, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) ),
% 2.15/2.58 X ) ] )
% 2.15/2.58 , clause( 15183, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 2.15/2.58 ) ), X ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15185, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 2.15/2.58 ) ) ) ] )
% 2.15/2.58 , clause( 24, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) )
% 2.15/2.58 , X ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15186, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 2.15/2.58 'least_upper_bound'( X, Y ), 'least_upper_bound'( 'least_upper_bound'( Z
% 2.15/2.58 , X ), Y ) ) ) ] )
% 2.15/2.58 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 2.15/2.58 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.15/2.58 , 0, clause( 15185, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 2.15/2.58 Y, X ) ) ) ] )
% 2.15/2.58 , 0, 8, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 2.15/2.58 substitution( 1, [ :=( X, 'least_upper_bound'( X, Y ) ), :=( Y, Z )] )
% 2.15/2.58 ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15187, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 2.15/2.58 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ) ),
% 2.15/2.58 'least_upper_bound'( X, Y ) ) ] )
% 2.15/2.58 , clause( 15186, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 2.15/2.58 'least_upper_bound'( X, Y ), 'least_upper_bound'( 'least_upper_bound'( Z
% 2.15/2.58 , X ), Y ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 44, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, Z ),
% 2.15/2.58 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ),
% 2.15/2.58 'least_upper_bound'( Y, Z ) ) ] )
% 2.15/2.58 , clause( 15187, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 2.15/2.58 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ) ),
% 2.15/2.58 'least_upper_bound'( X, Y ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 2.15/2.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15189, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 2.15/2.58 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.15/2.58 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 2.15/2.58 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15191, [ =( 'least_upper_bound'( 'least_upper_bound'( X, b ), a ),
% 2.15/2.58 'least_upper_bound'( X, b ) ) ] )
% 2.15/2.58 , clause( 18, [ =( 'least_upper_bound'( b, a ), b ) ] )
% 2.15/2.58 , 0, clause( 15189, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ),
% 2.15/2.58 Z ), 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.15/2.58 , 0, 8, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, b ),
% 2.15/2.58 :=( Z, a )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 49, [ =( 'least_upper_bound'( 'least_upper_bound'( X, b ), a ),
% 2.15/2.58 'least_upper_bound'( X, b ) ) ] )
% 2.15/2.58 , clause( 15191, [ =( 'least_upper_bound'( 'least_upper_bound'( X, b ), a )
% 2.15/2.58 , 'least_upper_bound'( X, b ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15195, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 2.15/2.58 ) ) ) ] )
% 2.15/2.58 , clause( 24, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) )
% 2.15/2.58 , X ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15198, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 2.15/2.58 'greatest_lower_bound'( X, Y ), X ) ) ] )
% 2.15/2.58 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 2.15/2.58 , X ) ] )
% 2.15/2.58 , 0, clause( 15195, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 2.15/2.58 Y, X ) ) ) ] )
% 2.15/2.58 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.15/2.58 :=( X, 'greatest_lower_bound'( X, Y ) ), :=( Y, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15199, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y )
% 2.15/2.58 , X ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.15/2.58 , clause( 15198, [ =( 'greatest_lower_bound'( X, Y ),
% 2.15/2.58 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), X ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 57, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), X
% 2.15/2.58 ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.15/2.58 , clause( 15199, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y
% 2.15/2.58 ), X ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15201, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 2.15/2.58 ) ) ) ] )
% 2.15/2.58 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 2.15/2.58 , X ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15204, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 2.15/2.58 'least_upper_bound'( X, Y ), X ) ) ] )
% 2.15/2.58 , clause( 23, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 2.15/2.58 , X ) ] )
% 2.15/2.58 , 0, clause( 15201, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 2.15/2.58 X, Y ) ) ) ] )
% 2.15/2.58 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.15/2.58 :=( X, 'least_upper_bound'( X, Y ) ), :=( Y, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15205, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 2.15/2.58 'least_upper_bound'( X, Y ) ) ] )
% 2.15/2.58 , clause( 15204, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 2.15/2.58 'least_upper_bound'( X, Y ), X ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 58, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 2.15/2.58 'least_upper_bound'( X, Y ) ) ] )
% 2.15/2.58 , clause( 15205, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X )
% 2.15/2.58 , 'least_upper_bound'( X, Y ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15206, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 2.15/2.58 ) ) ) ] )
% 2.15/2.58 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 2.15/2.58 , X ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15207, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X
% 2.15/2.58 ) ) ) ] )
% 2.15/2.58 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 2.15/2.58 , X ) ) ] )
% 2.15/2.58 , 0, clause( 15206, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 2.15/2.58 X, Y ) ) ) ] )
% 2.15/2.58 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.15/2.58 :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15210, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X )
% 2.15/2.58 ), X ) ] )
% 2.15/2.58 , clause( 15207, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y
% 2.15/2.58 , X ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 60, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) ),
% 2.15/2.58 X ) ] )
% 2.15/2.58 , clause( 15210, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X
% 2.15/2.58 ) ), X ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15212, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X
% 2.15/2.58 ) ) ) ] )
% 2.15/2.58 , clause( 60, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) )
% 2.15/2.58 , X ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15213, [ =( 'greatest_lower_bound'( X, Y ), 'least_upper_bound'(
% 2.15/2.58 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 2.15/2.58 'greatest_lower_bound'( Z, X ), Y ) ) ) ] )
% 2.15/2.58 , clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z )
% 2.15/2.58 ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 2.15/2.58 , 0, clause( 15212, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 2.15/2.58 Y, X ) ) ) ] )
% 2.15/2.58 , 0, 8, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 2.15/2.58 substitution( 1, [ :=( X, 'greatest_lower_bound'( X, Y ) ), :=( Y, Z )] )
% 2.15/2.58 ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15214, [ =( 'least_upper_bound'( 'greatest_lower_bound'( X, Y ),
% 2.15/2.58 'greatest_lower_bound'( 'greatest_lower_bound'( Z, X ), Y ) ),
% 2.15/2.58 'greatest_lower_bound'( X, Y ) ) ] )
% 2.15/2.58 , clause( 15213, [ =( 'greatest_lower_bound'( X, Y ), 'least_upper_bound'(
% 2.15/2.58 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 2.15/2.58 'greatest_lower_bound'( Z, X ), Y ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 63, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, Z ),
% 2.15/2.58 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ),
% 2.15/2.58 'greatest_lower_bound'( Y, Z ) ) ] )
% 2.15/2.58 , clause( 15214, [ =( 'least_upper_bound'( 'greatest_lower_bound'( X, Y ),
% 2.15/2.58 'greatest_lower_bound'( 'greatest_lower_bound'( Z, X ), Y ) ),
% 2.15/2.58 'greatest_lower_bound'( X, Y ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 2.15/2.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15215, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X
% 2.15/2.58 ) ) ) ] )
% 2.15/2.58 , clause( 60, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) )
% 2.15/2.58 , X ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15216, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( Y, X )
% 2.15/2.58 , X ) ) ] )
% 2.15/2.58 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 2.15/2.58 ) ] )
% 2.15/2.58 , 0, clause( 15215, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 2.15/2.58 Y, X ) ) ) ] )
% 2.15/2.58 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, 'greatest_lower_bound'( Y, X
% 2.15/2.58 ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15219, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X
% 2.15/2.58 ), X ) ] )
% 2.15/2.58 , clause( 15216, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( Y, X
% 2.15/2.58 ), X ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 64, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X ),
% 2.15/2.58 X ) ] )
% 2.15/2.58 , clause( 15219, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ),
% 2.15/2.58 X ), X ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15221, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 2.15/2.58 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.15/2.58 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 2.15/2.58 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15223, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) ),
% 2.15/2.58 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 2.15/2.58 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.15/2.58 , 0, clause( 15221, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 2.15/2.58 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.15/2.58 , 0, 8, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 2.15/2.58 X ) ), :=( Y, X ), :=( Z, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15226, [ =( 'least_upper_bound'( identity, multiply( inverse( X ),
% 2.15/2.58 Y ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 2.15/2.58 , clause( 15223, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) )
% 2.15/2.58 , 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 75, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y )
% 2.15/2.58 ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 2.15/2.58 , clause( 15226, [ =( 'least_upper_bound'( identity, multiply( inverse( X )
% 2.15/2.58 , Y ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15229, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 2.15/2.58 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.15/2.58 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 2.15/2.58 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15232, [ =( multiply( inverse( X ), 'least_upper_bound'( Y, X ) ),
% 2.15/2.58 'least_upper_bound'( multiply( inverse( X ), Y ), identity ) ) ] )
% 2.15/2.58 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.15/2.58 , 0, clause( 15229, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 2.15/2.58 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.15/2.58 , 0, 12, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 2.15/2.58 inverse( X ) ), :=( Y, Y ), :=( Z, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15235, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ),
% 2.15/2.58 identity ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 2.15/2.58 , clause( 15232, [ =( multiply( inverse( X ), 'least_upper_bound'( Y, X ) )
% 2.15/2.58 , 'least_upper_bound'( multiply( inverse( X ), Y ), identity ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 76, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ), identity
% 2.15/2.58 ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 2.15/2.58 , clause( 15235, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ),
% 2.15/2.58 identity ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15237, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 2.15/2.58 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 2.15/2.58 , clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 2.15/2.58 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15238, [ =( multiply( 'least_upper_bound'( identity, X ), Y ),
% 2.15/2.58 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 2.15/2.58 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.15/2.58 , 0, clause( 15237, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 2.15/2.58 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 2.15/2.58 , 0, 7, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X,
% 2.15/2.58 identity ), :=( Y, Y ), :=( Z, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15240, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 2.15/2.58 'least_upper_bound'( identity, X ), Y ) ) ] )
% 2.15/2.58 , clause( 15238, [ =( multiply( 'least_upper_bound'( identity, X ), Y ),
% 2.15/2.58 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 105, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 2.15/2.58 'least_upper_bound'( identity, Y ), X ) ) ] )
% 2.15/2.58 , clause( 15240, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 2.15/2.58 'least_upper_bound'( identity, X ), Y ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15243, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 2.15/2.58 'greatest_lower_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 2.15/2.58 , clause( 14, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z
% 2.15/2.58 ) ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15245, [ =( multiply( 'greatest_lower_bound'( X, identity ), Y ),
% 2.15/2.58 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ] )
% 2.15/2.58 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.15/2.58 , 0, clause( 15243, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 2.15/2.58 'greatest_lower_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 2.15/2.58 , 0, 10, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 2.15/2.58 :=( Y, Y ), :=( Z, identity )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15247, [ =( 'greatest_lower_bound'( multiply( X, Y ), Y ), multiply(
% 2.15/2.58 'greatest_lower_bound'( X, identity ), Y ) ) ] )
% 2.15/2.58 , clause( 15245, [ =( multiply( 'greatest_lower_bound'( X, identity ), Y )
% 2.15/2.58 , 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 124, [ =( 'greatest_lower_bound'( multiply( Y, X ), X ), multiply(
% 2.15/2.58 'greatest_lower_bound'( Y, identity ), X ) ) ] )
% 2.15/2.58 , clause( 15247, [ =( 'greatest_lower_bound'( multiply( X, Y ), Y ),
% 2.15/2.58 multiply( 'greatest_lower_bound'( X, identity ), Y ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15248, [ ~( =( multiply( b, d ), 'least_upper_bound'( multiply( a,
% 2.15/2.58 c ), multiply( b, d ) ) ) ) ] )
% 2.15/2.58 , clause( 17, [ ~( =( 'least_upper_bound'( multiply( a, c ), multiply( b, d
% 2.15/2.58 ) ), multiply( b, d ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15249, [ ~( =( multiply( b, d ), 'least_upper_bound'( multiply( b,
% 2.15/2.58 d ), multiply( a, c ) ) ) ) ] )
% 2.15/2.58 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 2.15/2.58 ) ] )
% 2.15/2.58 , 0, clause( 15248, [ ~( =( multiply( b, d ), 'least_upper_bound'( multiply(
% 2.15/2.58 a, c ), multiply( b, d ) ) ) ) ] )
% 2.15/2.58 , 0, 5, substitution( 0, [ :=( X, multiply( a, c ) ), :=( Y, multiply( b, d
% 2.15/2.58 ) )] ), substitution( 1, [] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15252, [ ~( =( 'least_upper_bound'( multiply( b, d ), multiply( a,
% 2.15/2.58 c ) ), multiply( b, d ) ) ) ] )
% 2.15/2.58 , clause( 15249, [ ~( =( multiply( b, d ), 'least_upper_bound'( multiply( b
% 2.15/2.58 , d ), multiply( a, c ) ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 139, [ ~( =( 'least_upper_bound'( multiply( b, d ), multiply( a, c
% 2.15/2.58 ) ), multiply( b, d ) ) ) ] )
% 2.15/2.58 , clause( 15252, [ ~( =( 'least_upper_bound'( multiply( b, d ), multiply( a
% 2.15/2.58 , c ) ), multiply( b, d ) ) ) ] )
% 2.15/2.58 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15253, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 2.15/2.58 'least_upper_bound'( X, b ), a ) ) ] )
% 2.15/2.58 , clause( 49, [ =( 'least_upper_bound'( 'least_upper_bound'( X, b ), a ),
% 2.15/2.58 'least_upper_bound'( X, b ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15257, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'( a,
% 2.15/2.58 'least_upper_bound'( X, b ) ) ) ] )
% 2.15/2.58 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 2.15/2.58 ) ] )
% 2.15/2.58 , 0, clause( 15253, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 2.15/2.58 'least_upper_bound'( X, b ), a ) ) ] )
% 2.15/2.58 , 0, 4, substitution( 0, [ :=( X, 'least_upper_bound'( X, b ) ), :=( Y, a )] )
% 2.15/2.58 , substitution( 1, [ :=( X, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15263, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 2.15/2.58 'least_upper_bound'( a, X ), b ) ) ] )
% 2.15/2.58 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 2.15/2.58 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.15/2.58 , 0, clause( 15257, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 2.15/2.58 a, 'least_upper_bound'( X, b ) ) ) ] )
% 2.15/2.58 , 0, 4, substitution( 0, [ :=( X, a ), :=( Y, X ), :=( Z, b )] ),
% 2.15/2.58 substitution( 1, [ :=( X, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15264, [ =( 'least_upper_bound'( 'least_upper_bound'( a, X ), b ),
% 2.15/2.58 'least_upper_bound'( X, b ) ) ] )
% 2.15/2.58 , clause( 15263, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 2.15/2.58 'least_upper_bound'( a, X ), b ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 151, [ =( 'least_upper_bound'( 'least_upper_bound'( a, X ), b ),
% 2.15/2.58 'least_upper_bound'( X, b ) ) ] )
% 2.15/2.58 , clause( 15264, [ =( 'least_upper_bound'( 'least_upper_bound'( a, X ), b )
% 2.15/2.58 , 'least_upper_bound'( X, b ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15266, [ =( multiply( X, identity ), multiply( multiply( X, inverse(
% 2.15/2.58 Y ) ), Y ) ) ] )
% 2.15/2.58 , clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 2.15/2.58 , identity ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15269, [ =( multiply( inverse( inverse( X ) ), identity ), multiply(
% 2.15/2.58 identity, X ) ) ] )
% 2.15/2.58 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.15/2.58 , 0, clause( 15266, [ =( multiply( X, identity ), multiply( multiply( X,
% 2.15/2.58 inverse( Y ) ), Y ) ) ] )
% 2.15/2.58 , 0, 7, substitution( 0, [ :=( X, inverse( X ) )] ), substitution( 1, [
% 2.15/2.58 :=( X, inverse( inverse( X ) ) ), :=( Y, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15270, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 2.15/2.58 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.15/2.58 , 0, clause( 15269, [ =( multiply( inverse( inverse( X ) ), identity ),
% 2.15/2.58 multiply( identity, X ) ) ] )
% 2.15/2.58 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 2.15/2.58 ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 165, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 2.15/2.58 , clause( 15270, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ]
% 2.15/2.58 )
% 2.15/2.58 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15273, [ =( multiply( X, Y ), multiply( multiply( X, identity ), Y
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , clause( 22, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X )
% 2.15/2.58 ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15276, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , clause( 165, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 2.15/2.58 , 0, clause( 15273, [ =( multiply( X, Y ), multiply( multiply( X, identity
% 2.15/2.58 ), Y ) ) ] )
% 2.15/2.58 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 2.15/2.58 inverse( X ) ) ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 2.15/2.58 ) ] )
% 2.15/2.58 , clause( 15276, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X,
% 2.15/2.58 Y ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15283, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 2.15/2.58 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.15/2.58 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 2.15/2.58 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15286, [ =( multiply( inverse( inverse( X ) ), 'least_upper_bound'(
% 2.15/2.58 identity, Y ) ), 'least_upper_bound'( X, multiply( inverse( inverse( X )
% 2.15/2.58 ), Y ) ) ) ] )
% 2.15/2.58 , clause( 165, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 2.15/2.58 , 0, clause( 15283, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 2.15/2.58 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.15/2.58 , 0, 9, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 2.15/2.58 inverse( X ) ) ), :=( Y, identity ), :=( Z, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15296, [ =( multiply( inverse( inverse( X ) ), 'least_upper_bound'(
% 2.15/2.58 identity, Y ) ), 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 2.15/2.58 , clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , 0, clause( 15286, [ =( multiply( inverse( inverse( X ) ),
% 2.15/2.58 'least_upper_bound'( identity, Y ) ), 'least_upper_bound'( X, multiply(
% 2.15/2.58 inverse( inverse( X ) ), Y ) ) ) ] )
% 2.15/2.58 , 0, 10, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.15/2.58 :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15298, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 2.15/2.58 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 2.15/2.58 , clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , 0, clause( 15296, [ =( multiply( inverse( inverse( X ) ),
% 2.15/2.58 'least_upper_bound'( identity, Y ) ), 'least_upper_bound'( X, multiply( X
% 2.15/2.58 , Y ) ) ) ] )
% 2.15/2.58 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, 'least_upper_bound'( identity
% 2.15/2.58 , Y ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15299, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 2.15/2.58 , 'least_upper_bound'( identity, Y ) ) ) ] )
% 2.15/2.58 , clause( 15298, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 2.15/2.58 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 173, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X,
% 2.15/2.58 'least_upper_bound'( identity, Y ) ) ) ] )
% 2.15/2.58 , clause( 15299, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply(
% 2.15/2.58 X, 'least_upper_bound'( identity, Y ) ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15300, [ =( multiply( X, Y ), multiply( inverse( inverse( X ) ), Y
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15303, [ =( multiply( X, identity ), X ) ] )
% 2.15/2.58 , clause( 165, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 2.15/2.58 , 0, clause( 15300, [ =( multiply( X, Y ), multiply( inverse( inverse( X )
% 2.15/2.58 ), Y ) ) ] )
% 2.15/2.58 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 2.15/2.58 :=( Y, identity )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 365, [ =( multiply( X, identity ), X ) ] )
% 2.15/2.58 , clause( 15303, [ =( multiply( X, identity ), X ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15308, [ =( X, multiply( X, identity ) ) ] )
% 2.15/2.58 , clause( 365, [ =( multiply( X, identity ), X ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15311, [ =( inverse( inverse( X ) ), multiply( X, identity ) ) ] )
% 2.15/2.58 , clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , 0, clause( 15308, [ =( X, multiply( X, identity ) ) ] )
% 2.15/2.58 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, identity )] ), substitution(
% 2.15/2.58 1, [ :=( X, inverse( inverse( X ) ) )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15312, [ =( inverse( inverse( X ) ), X ) ] )
% 2.15/2.58 , clause( 365, [ =( multiply( X, identity ), X ) ] )
% 2.15/2.58 , 0, clause( 15311, [ =( inverse( inverse( X ) ), multiply( X, identity ) )
% 2.15/2.58 ] )
% 2.15/2.58 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 2.15/2.58 ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 373, [ =( inverse( inverse( X ) ), X ) ] )
% 2.15/2.58 , clause( 15312, [ =( inverse( inverse( X ) ), X ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15315, [ =( multiply( X, identity ), multiply( multiply( X, inverse(
% 2.15/2.58 Y ) ), Y ) ) ] )
% 2.15/2.58 , clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 2.15/2.58 , identity ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15317, [ =( multiply( X, identity ), multiply( multiply( X, Y ),
% 2.15/2.58 inverse( Y ) ) ) ] )
% 2.15/2.58 , clause( 373, [ =( inverse( inverse( X ) ), X ) ] )
% 2.15/2.58 , 0, clause( 15315, [ =( multiply( X, identity ), multiply( multiply( X,
% 2.15/2.58 inverse( Y ) ), Y ) ) ] )
% 2.15/2.58 , 0, 7, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 2.15/2.58 :=( Y, inverse( Y ) )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15318, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 2.15/2.58 , clause( 365, [ =( multiply( X, identity ), X ) ] )
% 2.15/2.58 , 0, clause( 15317, [ =( multiply( X, identity ), multiply( multiply( X, Y
% 2.15/2.58 ), inverse( Y ) ) ) ] )
% 2.15/2.58 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 2.15/2.58 :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15319, [ =( multiply( multiply( X, Y ), inverse( Y ) ), X ) ] )
% 2.15/2.58 , clause( 15318, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 379, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 2.15/2.58 , clause( 15319, [ =( multiply( multiply( X, Y ), inverse( Y ) ), X ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15321, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 2.15/2.58 , clause( 379, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15326, [ =( multiply( inverse( multiply( X, Y ) ), X ), multiply(
% 2.15/2.58 identity, inverse( Y ) ) ) ] )
% 2.15/2.58 , clause( 20, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ), Y
% 2.15/2.58 ), identity ) ] )
% 2.15/2.58 , 0, clause( 15321, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ]
% 2.15/2.58 )
% 2.15/2.58 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.15/2.58 :=( X, multiply( inverse( multiply( X, Y ) ), X ) ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15327, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.15/2.58 , 0, clause( 15326, [ =( multiply( inverse( multiply( X, Y ) ), X ),
% 2.15/2.58 multiply( identity, inverse( Y ) ) ) ] )
% 2.15/2.58 , 0, 7, substitution( 0, [ :=( X, inverse( Y ) )] ), substitution( 1, [
% 2.15/2.58 :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 397, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y )
% 2.15/2.58 ) ] )
% 2.15/2.58 , clause( 15327, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse(
% 2.15/2.58 Y ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15330, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 2.15/2.58 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 2.15/2.58 , clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 2.15/2.58 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15332, [ =( multiply( 'least_upper_bound'( X, multiply( Y, Z ) ),
% 2.15/2.58 inverse( Z ) ), 'least_upper_bound'( multiply( X, inverse( Z ) ), Y ) ) ]
% 2.15/2.58 )
% 2.15/2.58 , clause( 379, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 2.15/2.58 , 0, clause( 15330, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 2.15/2.58 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 2.15/2.58 , 0, 14, substitution( 0, [ :=( X, Z ), :=( Y, Y )] ), substitution( 1, [
% 2.15/2.58 :=( X, X ), :=( Y, inverse( Z ) ), :=( Z, multiply( Y, Z ) )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 401, [ =( multiply( 'least_upper_bound'( Z, multiply( X, Y ) ),
% 2.15/2.58 inverse( Y ) ), 'least_upper_bound'( multiply( Z, inverse( Y ) ), X ) ) ]
% 2.15/2.58 )
% 2.15/2.58 , clause( 15332, [ =( multiply( 'least_upper_bound'( X, multiply( Y, Z ) )
% 2.15/2.58 , inverse( Z ) ), 'least_upper_bound'( multiply( X, inverse( Z ) ), Y ) )
% 2.15/2.58 ] )
% 2.15/2.58 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 2.15/2.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15335, [ =( inverse( Y ), multiply( inverse( multiply( X, Y ) ), X
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , clause( 397, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15339, [ =( inverse( X ), multiply( inverse( inverse( Y ) ),
% 2.15/2.58 inverse( multiply( X, Y ) ) ) ) ] )
% 2.15/2.58 , clause( 397, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , 0, clause( 15335, [ =( inverse( Y ), multiply( inverse( multiply( X, Y )
% 2.15/2.58 ), X ) ) ] )
% 2.15/2.58 , 0, 5, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.15/2.58 :=( X, inverse( multiply( X, Y ) ) ), :=( Y, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15340, [ =( inverse( X ), multiply( Y, inverse( multiply( X, Y ) )
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , 0, clause( 15339, [ =( inverse( X ), multiply( inverse( inverse( Y ) ),
% 2.15/2.58 inverse( multiply( X, Y ) ) ) ) ] )
% 2.15/2.58 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, inverse( multiply( X, Y ) ) )] )
% 2.15/2.58 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15341, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , clause( 15340, [ =( inverse( X ), multiply( Y, inverse( multiply( X, Y )
% 2.15/2.58 ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 403, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X )
% 2.15/2.58 ) ] )
% 2.15/2.58 , clause( 15341, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse(
% 2.15/2.58 X ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15343, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 2.15/2.58 , clause( 379, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15346, [ =( inverse( multiply( X, Y ) ), multiply( inverse( Y ),
% 2.15/2.58 inverse( X ) ) ) ] )
% 2.15/2.58 , clause( 397, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , 0, clause( 15343, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ]
% 2.15/2.58 )
% 2.15/2.58 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.15/2.58 :=( X, inverse( multiply( X, Y ) ) ), :=( Y, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15347, [ =( multiply( inverse( Y ), inverse( X ) ), inverse(
% 2.15/2.58 multiply( X, Y ) ) ) ] )
% 2.15/2.58 , clause( 15346, [ =( inverse( multiply( X, Y ) ), multiply( inverse( Y ),
% 2.15/2.58 inverse( X ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 404, [ =( multiply( inverse( Y ), inverse( X ) ), inverse( multiply(
% 2.15/2.58 X, Y ) ) ) ] )
% 2.15/2.58 , clause( 15347, [ =( multiply( inverse( Y ), inverse( X ) ), inverse(
% 2.15/2.58 multiply( X, Y ) ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15349, [ =( multiply( X, identity ), multiply( multiply( X, inverse(
% 2.15/2.58 Y ) ), Y ) ) ] )
% 2.15/2.58 , clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 2.15/2.58 , identity ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15355, [ =( multiply( inverse( multiply( inverse( X ), Y ) ),
% 2.15/2.58 identity ), multiply( inverse( Y ), X ) ) ] )
% 2.15/2.58 , clause( 397, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , 0, clause( 15349, [ =( multiply( X, identity ), multiply( multiply( X,
% 2.15/2.58 inverse( Y ) ), Y ) ) ] )
% 2.15/2.58 , 0, 9, substitution( 0, [ :=( X, inverse( X ) ), :=( Y, Y )] ),
% 2.15/2.58 substitution( 1, [ :=( X, inverse( multiply( inverse( X ), Y ) ) ), :=( Y
% 2.15/2.58 , X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15356, [ =( inverse( multiply( inverse( X ), Y ) ), multiply(
% 2.15/2.58 inverse( Y ), X ) ) ] )
% 2.15/2.58 , clause( 365, [ =( multiply( X, identity ), X ) ] )
% 2.15/2.58 , 0, clause( 15355, [ =( multiply( inverse( multiply( inverse( X ), Y ) ),
% 2.15/2.58 identity ), multiply( inverse( Y ), X ) ) ] )
% 2.15/2.58 , 0, 1, substitution( 0, [ :=( X, inverse( multiply( inverse( X ), Y ) ) )] )
% 2.15/2.58 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 405, [ =( inverse( multiply( inverse( X ), Y ) ), multiply( inverse(
% 2.15/2.58 Y ), X ) ) ] )
% 2.15/2.58 , clause( 15356, [ =( inverse( multiply( inverse( X ), Y ) ), multiply(
% 2.15/2.58 inverse( Y ), X ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15359, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X ) )
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , clause( 403, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X
% 2.15/2.58 ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15364, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 2.15/2.58 inverse( multiply( X, identity ) ) ) ) ] )
% 2.15/2.58 , clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 2.15/2.58 , identity ) ) ] )
% 2.15/2.58 , 0, clause( 15359, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X
% 2.15/2.58 ) ) ) ) ] )
% 2.15/2.58 , 0, 9, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 2.15/2.58 :=( X, Y ), :=( Y, multiply( X, inverse( Y ) ) )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15365, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 2.15/2.58 inverse( X ) ) ) ] )
% 2.15/2.58 , clause( 365, [ =( multiply( X, identity ), X ) ] )
% 2.15/2.58 , 0, clause( 15364, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply(
% 2.15/2.58 Y, inverse( multiply( X, identity ) ) ) ) ] )
% 2.15/2.58 , 0, 9, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 2.15/2.58 :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 413, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 2.15/2.58 inverse( X ) ) ) ] )
% 2.15/2.58 , clause( 15365, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 2.15/2.58 inverse( X ) ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15368, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 2.15/2.58 'least_upper_bound'( X, Y ), 'least_upper_bound'( 'least_upper_bound'( Z
% 2.15/2.58 , X ), Y ) ) ) ] )
% 2.15/2.58 , clause( 44, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, Z ),
% 2.15/2.58 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ),
% 2.15/2.58 'least_upper_bound'( Y, Z ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15371, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 2.15/2.58 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 2.15/2.58 , clause( 58, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 2.15/2.58 'least_upper_bound'( X, Y ) ) ] )
% 2.15/2.58 , 0, clause( 15368, [ =( 'least_upper_bound'( X, Y ),
% 2.15/2.58 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 2.15/2.58 'least_upper_bound'( Z, X ), Y ) ) ) ] )
% 2.15/2.58 , 0, 8, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 2.15/2.58 :=( X, X ), :=( Y, Y ), :=( Z, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15377, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 2.15/2.58 'least_upper_bound'( Y, X ) ), 'least_upper_bound'( X, Y ) ) ] )
% 2.15/2.58 , clause( 15371, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 2.15/2.58 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 483, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 2.15/2.58 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( Y, X ) ) ] )
% 2.15/2.58 , clause( 15377, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 2.15/2.58 'least_upper_bound'( Y, X ) ), 'least_upper_bound'( X, Y ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15380, [ =( 'greatest_lower_bound'( X, Y ), 'least_upper_bound'(
% 2.15/2.58 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 2.15/2.58 'greatest_lower_bound'( Z, X ), Y ) ) ) ] )
% 2.15/2.58 , clause( 63, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, Z ),
% 2.15/2.58 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ),
% 2.15/2.58 'greatest_lower_bound'( Y, Z ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15383, [ =( 'greatest_lower_bound'( X, Y ), 'least_upper_bound'(
% 2.15/2.58 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, X ) ) ) ] )
% 2.15/2.58 , clause( 57, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ),
% 2.15/2.58 X ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.15/2.58 , 0, clause( 15380, [ =( 'greatest_lower_bound'( X, Y ),
% 2.15/2.58 'least_upper_bound'( 'greatest_lower_bound'( X, Y ),
% 2.15/2.58 'greatest_lower_bound'( 'greatest_lower_bound'( Z, X ), Y ) ) ) ] )
% 2.15/2.58 , 0, 8, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 2.15/2.58 :=( X, X ), :=( Y, Y ), :=( Z, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15389, [ =( 'least_upper_bound'( 'greatest_lower_bound'( X, Y ),
% 2.15/2.58 'greatest_lower_bound'( Y, X ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.15/2.58 , clause( 15383, [ =( 'greatest_lower_bound'( X, Y ), 'least_upper_bound'(
% 2.15/2.58 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, X ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 727, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ),
% 2.15/2.58 'greatest_lower_bound'( X, Y ) ), 'greatest_lower_bound'( Y, X ) ) ] )
% 2.15/2.58 , clause( 15389, [ =( 'least_upper_bound'( 'greatest_lower_bound'( X, Y ),
% 2.15/2.58 'greatest_lower_bound'( Y, X ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15392, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) ),
% 2.15/2.58 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 2.15/2.58 , clause( 75, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y
% 2.15/2.58 ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15394, [ =( multiply( inverse( X ), X ), 'least_upper_bound'(
% 2.15/2.58 identity, multiply( inverse( X ), 'greatest_lower_bound'( X, Y ) ) ) ) ]
% 2.15/2.58 )
% 2.15/2.58 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 2.15/2.58 , X ) ] )
% 2.15/2.58 , 0, clause( 15392, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y
% 2.15/2.58 ) ), 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 2.15/2.58 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.15/2.58 :=( X, X ), :=( Y, 'greatest_lower_bound'( X, Y ) )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15395, [ =( identity, 'least_upper_bound'( identity, multiply(
% 2.15/2.58 inverse( X ), 'greatest_lower_bound'( X, Y ) ) ) ) ] )
% 2.15/2.58 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.15/2.58 , 0, clause( 15394, [ =( multiply( inverse( X ), X ), 'least_upper_bound'(
% 2.15/2.58 identity, multiply( inverse( X ), 'greatest_lower_bound'( X, Y ) ) ) ) ]
% 2.15/2.58 )
% 2.15/2.58 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 2.15/2.58 :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15396, [ =( 'least_upper_bound'( identity, multiply( inverse( X ),
% 2.15/2.58 'greatest_lower_bound'( X, Y ) ) ), identity ) ] )
% 2.15/2.58 , clause( 15395, [ =( identity, 'least_upper_bound'( identity, multiply(
% 2.15/2.58 inverse( X ), 'greatest_lower_bound'( X, Y ) ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 1257, [ =( 'least_upper_bound'( identity, multiply( inverse( X ),
% 2.15/2.58 'greatest_lower_bound'( X, Y ) ) ), identity ) ] )
% 2.15/2.58 , clause( 15396, [ =( 'least_upper_bound'( identity, multiply( inverse( X )
% 2.15/2.58 , 'greatest_lower_bound'( X, Y ) ) ), identity ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15398, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) ),
% 2.15/2.58 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 2.15/2.58 , clause( 75, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y
% 2.15/2.58 ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15400, [ =( multiply( inverse( d ), d ), 'least_upper_bound'(
% 2.15/2.58 identity, multiply( inverse( d ), c ) ) ) ] )
% 2.15/2.58 , clause( 19, [ =( 'least_upper_bound'( d, c ), d ) ] )
% 2.15/2.58 , 0, clause( 15398, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y
% 2.15/2.58 ) ), 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 2.15/2.58 , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, d ), :=( Y, c )] )
% 2.15/2.58 ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15401, [ =( identity, 'least_upper_bound'( identity, multiply(
% 2.15/2.58 inverse( d ), c ) ) ) ] )
% 2.15/2.58 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.15/2.58 , 0, clause( 15400, [ =( multiply( inverse( d ), d ), 'least_upper_bound'(
% 2.15/2.58 identity, multiply( inverse( d ), c ) ) ) ] )
% 2.15/2.58 , 0, 1, substitution( 0, [ :=( X, d )] ), substitution( 1, [] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15402, [ =( 'least_upper_bound'( identity, multiply( inverse( d ),
% 2.15/2.58 c ) ), identity ) ] )
% 2.15/2.58 , clause( 15401, [ =( identity, 'least_upper_bound'( identity, multiply(
% 2.15/2.58 inverse( d ), c ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 1260, [ =( 'least_upper_bound'( identity, multiply( inverse( d ), c
% 2.15/2.58 ) ), identity ) ] )
% 2.15/2.58 , clause( 15402, [ =( 'least_upper_bound'( identity, multiply( inverse( d )
% 2.15/2.58 , c ) ), identity ) ] )
% 2.15/2.58 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15404, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 2.15/2.58 ) ) ) ] )
% 2.15/2.58 , clause( 24, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) )
% 2.15/2.58 , X ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15405, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 2.15/2.58 inverse( X ), 'least_upper_bound'( Y, X ) ) ) ) ] )
% 2.15/2.58 , clause( 76, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ),
% 2.15/2.58 identity ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 2.15/2.58 , 0, clause( 15404, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 2.15/2.58 Y, X ) ) ) ] )
% 2.15/2.58 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.15/2.58 :=( X, identity ), :=( Y, multiply( inverse( X ), Y ) )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15406, [ =( 'greatest_lower_bound'( identity, multiply( inverse( X
% 2.15/2.58 ), 'least_upper_bound'( Y, X ) ) ), identity ) ] )
% 2.15/2.58 , clause( 15405, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 2.15/2.58 inverse( X ), 'least_upper_bound'( Y, X ) ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 1350, [ =( 'greatest_lower_bound'( identity, multiply( inverse( X )
% 2.15/2.58 , 'least_upper_bound'( Y, X ) ) ), identity ) ] )
% 2.15/2.58 , clause( 15406, [ =( 'greatest_lower_bound'( identity, multiply( inverse(
% 2.15/2.58 X ), 'least_upper_bound'( Y, X ) ) ), identity ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.15/2.58 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15408, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 2.15/2.58 inverse( X ), 'least_upper_bound'( Y, X ) ) ) ) ] )
% 2.15/2.58 , clause( 1350, [ =( 'greatest_lower_bound'( identity, multiply( inverse( X
% 2.15/2.58 ), 'least_upper_bound'( Y, X ) ) ), identity ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15411, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 2.15/2.58 inverse( multiply( inverse( d ), c ) ), identity ) ) ) ] )
% 2.15/2.58 , clause( 1260, [ =( 'least_upper_bound'( identity, multiply( inverse( d )
% 2.15/2.58 , c ) ), identity ) ] )
% 2.15/2.58 , 0, clause( 15408, [ =( identity, 'greatest_lower_bound'( identity,
% 2.15/2.58 multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ) ] )
% 2.15/2.58 , 0, 10, substitution( 0, [] ), substitution( 1, [ :=( X, multiply( inverse(
% 2.15/2.58 d ), c ) ), :=( Y, identity )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15412, [ =( identity, 'greatest_lower_bound'( identity, inverse(
% 2.15/2.58 multiply( inverse( d ), c ) ) ) ) ] )
% 2.15/2.58 , clause( 365, [ =( multiply( X, identity ), X ) ] )
% 2.15/2.58 , 0, clause( 15411, [ =( identity, 'greatest_lower_bound'( identity,
% 2.15/2.58 multiply( inverse( multiply( inverse( d ), c ) ), identity ) ) ) ] )
% 2.15/2.58 , 0, 4, substitution( 0, [ :=( X, inverse( multiply( inverse( d ), c ) ) )] )
% 2.15/2.58 , substitution( 1, [] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15413, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 2.15/2.58 inverse( c ), d ) ) ) ] )
% 2.15/2.58 , clause( 405, [ =( inverse( multiply( inverse( X ), Y ) ), multiply(
% 2.15/2.58 inverse( Y ), X ) ) ] )
% 2.15/2.58 , 0, clause( 15412, [ =( identity, 'greatest_lower_bound'( identity,
% 2.15/2.58 inverse( multiply( inverse( d ), c ) ) ) ) ] )
% 2.15/2.58 , 0, 4, substitution( 0, [ :=( X, d ), :=( Y, c )] ), substitution( 1, [] )
% 2.15/2.58 ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15414, [ =( 'greatest_lower_bound'( identity, multiply( inverse( c
% 2.15/2.58 ), d ) ), identity ) ] )
% 2.15/2.58 , clause( 15413, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 2.15/2.58 inverse( c ), d ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 1485, [ =( 'greatest_lower_bound'( identity, multiply( inverse( c )
% 2.15/2.58 , d ) ), identity ) ] )
% 2.15/2.58 , clause( 15414, [ =( 'greatest_lower_bound'( identity, multiply( inverse(
% 2.15/2.58 c ), d ) ), identity ) ] )
% 2.15/2.58 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15416, [ =( 'greatest_lower_bound'( X, Y ), 'least_upper_bound'(
% 2.15/2.58 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, X ) ) ) ] )
% 2.15/2.58 , clause( 727, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ),
% 2.15/2.58 'greatest_lower_bound'( X, Y ) ), 'greatest_lower_bound'( Y, X ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15420, [ =( 'greatest_lower_bound'( multiply( inverse( c ), d ),
% 2.15/2.58 identity ), 'least_upper_bound'( 'greatest_lower_bound'( multiply(
% 2.15/2.58 inverse( c ), d ), identity ), identity ) ) ] )
% 2.15/2.58 , clause( 1485, [ =( 'greatest_lower_bound'( identity, multiply( inverse( c
% 2.15/2.58 ), d ) ), identity ) ] )
% 2.15/2.58 , 0, clause( 15416, [ =( 'greatest_lower_bound'( X, Y ),
% 2.15/2.58 'least_upper_bound'( 'greatest_lower_bound'( X, Y ),
% 2.15/2.58 'greatest_lower_bound'( Y, X ) ) ) ] )
% 2.15/2.58 , 0, 14, substitution( 0, [] ), substitution( 1, [ :=( X, multiply( inverse(
% 2.15/2.58 c ), d ) ), :=( Y, identity )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15422, [ =( 'greatest_lower_bound'( multiply( inverse( c ), d ),
% 2.15/2.58 identity ), identity ) ] )
% 2.15/2.58 , clause( 64, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X )
% 2.15/2.58 , X ) ] )
% 2.15/2.58 , 0, clause( 15420, [ =( 'greatest_lower_bound'( multiply( inverse( c ), d
% 2.15/2.58 ), identity ), 'least_upper_bound'( 'greatest_lower_bound'( multiply(
% 2.15/2.58 inverse( c ), d ), identity ), identity ) ) ] )
% 2.15/2.58 , 0, 7, substitution( 0, [ :=( X, identity ), :=( Y, multiply( inverse( c )
% 2.15/2.58 , d ) )] ), substitution( 1, [] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 1581, [ =( 'greatest_lower_bound'( multiply( inverse( c ), d ),
% 2.15/2.58 identity ), identity ) ] )
% 2.15/2.58 , clause( 15422, [ =( 'greatest_lower_bound'( multiply( inverse( c ), d ),
% 2.15/2.58 identity ), identity ) ] )
% 2.15/2.58 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15425, [ =( multiply( 'greatest_lower_bound'( X, identity ), Y ),
% 2.15/2.58 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ] )
% 2.15/2.58 , clause( 124, [ =( 'greatest_lower_bound'( multiply( Y, X ), X ), multiply(
% 2.15/2.58 'greatest_lower_bound'( Y, identity ), X ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15427, [ =( multiply( identity, X ), 'greatest_lower_bound'(
% 2.15/2.58 multiply( multiply( inverse( c ), d ), X ), X ) ) ] )
% 2.15/2.58 , clause( 1581, [ =( 'greatest_lower_bound'( multiply( inverse( c ), d ),
% 2.15/2.58 identity ), identity ) ] )
% 2.15/2.58 , 0, clause( 15425, [ =( multiply( 'greatest_lower_bound'( X, identity ), Y
% 2.15/2.58 ), 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ] )
% 2.15/2.58 , 0, 2, substitution( 0, [] ), substitution( 1, [ :=( X, multiply( inverse(
% 2.15/2.58 c ), d ) ), :=( Y, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15428, [ =( X, 'greatest_lower_bound'( multiply( multiply( inverse(
% 2.15/2.58 c ), d ), X ), X ) ) ] )
% 2.15/2.58 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.15/2.58 , 0, clause( 15427, [ =( multiply( identity, X ), 'greatest_lower_bound'(
% 2.15/2.58 multiply( multiply( inverse( c ), d ), X ), X ) ) ] )
% 2.15/2.58 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 2.15/2.58 ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15429, [ =( 'greatest_lower_bound'( multiply( multiply( inverse( c
% 2.15/2.58 ), d ), X ), X ), X ) ] )
% 2.15/2.58 , clause( 15428, [ =( X, 'greatest_lower_bound'( multiply( multiply(
% 2.15/2.58 inverse( c ), d ), X ), X ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 3030, [ =( 'greatest_lower_bound'( multiply( multiply( inverse( c )
% 2.15/2.58 , d ), X ), X ), X ) ] )
% 2.15/2.58 , clause( 15429, [ =( 'greatest_lower_bound'( multiply( multiply( inverse(
% 2.15/2.58 c ), d ), X ), X ), X ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15431, [ =( X, 'greatest_lower_bound'( multiply( multiply( inverse(
% 2.15/2.58 c ), d ), X ), X ) ) ] )
% 2.15/2.58 , clause( 3030, [ =( 'greatest_lower_bound'( multiply( multiply( inverse( c
% 2.15/2.58 ), d ), X ), X ), X ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15432, [ =( inverse( d ), 'greatest_lower_bound'( inverse( c ),
% 2.15/2.58 inverse( d ) ) ) ] )
% 2.15/2.58 , clause( 379, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 2.15/2.58 , 0, clause( 15431, [ =( X, 'greatest_lower_bound'( multiply( multiply(
% 2.15/2.58 inverse( c ), d ), X ), X ) ) ] )
% 2.15/2.58 , 0, 4, substitution( 0, [ :=( X, d ), :=( Y, inverse( c ) )] ),
% 2.15/2.58 substitution( 1, [ :=( X, inverse( d ) )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15433, [ =( 'greatest_lower_bound'( inverse( c ), inverse( d ) ),
% 2.15/2.58 inverse( d ) ) ] )
% 2.15/2.58 , clause( 15432, [ =( inverse( d ), 'greatest_lower_bound'( inverse( c ),
% 2.15/2.58 inverse( d ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 3205, [ =( 'greatest_lower_bound'( inverse( c ), inverse( d ) ),
% 2.15/2.58 inverse( d ) ) ] )
% 2.15/2.58 , clause( 15433, [ =( 'greatest_lower_bound'( inverse( c ), inverse( d ) )
% 2.15/2.58 , inverse( d ) ) ] )
% 2.15/2.58 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15435, [ =( identity, 'least_upper_bound'( identity, multiply(
% 2.15/2.58 inverse( X ), 'greatest_lower_bound'( X, Y ) ) ) ) ] )
% 2.15/2.58 , clause( 1257, [ =( 'least_upper_bound'( identity, multiply( inverse( X )
% 2.15/2.58 , 'greatest_lower_bound'( X, Y ) ) ), identity ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15438, [ =( identity, 'least_upper_bound'( identity, multiply(
% 2.15/2.58 inverse( inverse( c ) ), inverse( d ) ) ) ) ] )
% 2.15/2.58 , clause( 3205, [ =( 'greatest_lower_bound'( inverse( c ), inverse( d ) ),
% 2.15/2.58 inverse( d ) ) ] )
% 2.15/2.58 , 0, clause( 15435, [ =( identity, 'least_upper_bound'( identity, multiply(
% 2.15/2.58 inverse( X ), 'greatest_lower_bound'( X, Y ) ) ) ) ] )
% 2.15/2.58 , 0, 8, substitution( 0, [] ), substitution( 1, [ :=( X, inverse( c ) ),
% 2.15/2.58 :=( Y, inverse( d ) )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15439, [ =( identity, 'least_upper_bound'( identity, inverse(
% 2.15/2.58 multiply( d, inverse( c ) ) ) ) ) ] )
% 2.15/2.58 , clause( 404, [ =( multiply( inverse( Y ), inverse( X ) ), inverse(
% 2.15/2.58 multiply( X, Y ) ) ) ] )
% 2.15/2.58 , 0, clause( 15438, [ =( identity, 'least_upper_bound'( identity, multiply(
% 2.15/2.58 inverse( inverse( c ) ), inverse( d ) ) ) ) ] )
% 2.15/2.58 , 0, 4, substitution( 0, [ :=( X, d ), :=( Y, inverse( c ) )] ),
% 2.15/2.58 substitution( 1, [] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15440, [ =( identity, 'least_upper_bound'( identity, multiply( c,
% 2.15/2.58 inverse( d ) ) ) ) ] )
% 2.15/2.58 , clause( 413, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 2.15/2.58 inverse( X ) ) ) ] )
% 2.15/2.58 , 0, clause( 15439, [ =( identity, 'least_upper_bound'( identity, inverse(
% 2.15/2.58 multiply( d, inverse( c ) ) ) ) ) ] )
% 2.15/2.58 , 0, 4, substitution( 0, [ :=( X, d ), :=( Y, c )] ), substitution( 1, [] )
% 2.15/2.58 ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15441, [ =( 'least_upper_bound'( identity, multiply( c, inverse( d
% 2.15/2.58 ) ) ), identity ) ] )
% 2.15/2.58 , clause( 15440, [ =( identity, 'least_upper_bound'( identity, multiply( c
% 2.15/2.58 , inverse( d ) ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 3216, [ =( 'least_upper_bound'( identity, multiply( c, inverse( d )
% 2.15/2.58 ) ), identity ) ] )
% 2.15/2.58 , clause( 15441, [ =( 'least_upper_bound'( identity, multiply( c, inverse(
% 2.15/2.58 d ) ) ), identity ) ] )
% 2.15/2.58 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15443, [ =( multiply( 'least_upper_bound'( identity, Y ), X ),
% 2.15/2.58 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 2.15/2.58 , clause( 105, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 2.15/2.58 'least_upper_bound'( identity, Y ), X ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15445, [ =( multiply( identity, X ), 'least_upper_bound'( X,
% 2.15/2.58 multiply( multiply( c, inverse( d ) ), X ) ) ) ] )
% 2.15/2.58 , clause( 3216, [ =( 'least_upper_bound'( identity, multiply( c, inverse( d
% 2.15/2.58 ) ) ), identity ) ] )
% 2.15/2.58 , 0, clause( 15443, [ =( multiply( 'least_upper_bound'( identity, Y ), X )
% 2.15/2.58 , 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 2.15/2.58 , 0, 2, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y,
% 2.15/2.58 multiply( c, inverse( d ) ) )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15446, [ =( X, 'least_upper_bound'( X, multiply( multiply( c,
% 2.15/2.58 inverse( d ) ), X ) ) ) ] )
% 2.15/2.58 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.15/2.58 , 0, clause( 15445, [ =( multiply( identity, X ), 'least_upper_bound'( X,
% 2.15/2.58 multiply( multiply( c, inverse( d ) ), X ) ) ) ] )
% 2.15/2.58 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 2.15/2.58 ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15447, [ =( 'least_upper_bound'( X, multiply( multiply( c, inverse(
% 2.15/2.58 d ) ), X ) ), X ) ] )
% 2.15/2.58 , clause( 15446, [ =( X, 'least_upper_bound'( X, multiply( multiply( c,
% 2.15/2.58 inverse( d ) ), X ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 3266, [ =( 'least_upper_bound'( X, multiply( multiply( c, inverse(
% 2.15/2.58 d ) ), X ) ), X ) ] )
% 2.15/2.58 , clause( 15447, [ =( 'least_upper_bound'( X, multiply( multiply( c,
% 2.15/2.58 inverse( d ) ), X ) ), X ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15449, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 2.15/2.58 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 2.15/2.58 , clause( 173, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 2.15/2.58 , 'least_upper_bound'( identity, Y ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15456, [ =( multiply( X, identity ), 'least_upper_bound'( X,
% 2.15/2.58 multiply( X, multiply( multiply( c, inverse( d ) ), identity ) ) ) ) ] )
% 2.15/2.58 , clause( 3266, [ =( 'least_upper_bound'( X, multiply( multiply( c, inverse(
% 2.15/2.58 d ) ), X ) ), X ) ] )
% 2.15/2.58 , 0, clause( 15449, [ =( multiply( X, 'least_upper_bound'( identity, Y ) )
% 2.15/2.58 , 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 2.15/2.58 , 0, 3, substitution( 0, [ :=( X, identity )] ), substitution( 1, [ :=( X,
% 2.15/2.58 X ), :=( Y, multiply( multiply( c, inverse( d ) ), identity ) )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15458, [ =( multiply( X, identity ), 'least_upper_bound'( X,
% 2.15/2.58 multiply( multiply( X, multiply( c, inverse( d ) ) ), identity ) ) ) ] )
% 2.15/2.58 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 2.15/2.58 ), Z ) ) ] )
% 2.15/2.58 , 0, clause( 15456, [ =( multiply( X, identity ), 'least_upper_bound'( X,
% 2.15/2.58 multiply( X, multiply( multiply( c, inverse( d ) ), identity ) ) ) ) ] )
% 2.15/2.58 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, multiply( c, inverse( d ) ) )
% 2.15/2.58 , :=( Z, identity )] ), substitution( 1, [ :=( X, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15461, [ =( multiply( X, identity ), 'least_upper_bound'( X,
% 2.15/2.58 multiply( X, multiply( c, inverse( d ) ) ) ) ) ] )
% 2.15/2.58 , clause( 365, [ =( multiply( X, identity ), X ) ] )
% 2.15/2.58 , 0, clause( 15458, [ =( multiply( X, identity ), 'least_upper_bound'( X,
% 2.15/2.58 multiply( multiply( X, multiply( c, inverse( d ) ) ), identity ) ) ) ] )
% 2.15/2.58 , 0, 6, substitution( 0, [ :=( X, multiply( X, multiply( c, inverse( d ) )
% 2.15/2.58 ) )] ), substitution( 1, [ :=( X, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15463, [ =( multiply( X, identity ), 'least_upper_bound'( X,
% 2.15/2.58 multiply( multiply( X, c ), inverse( d ) ) ) ) ] )
% 2.15/2.58 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 2.15/2.58 ), Z ) ) ] )
% 2.15/2.58 , 0, clause( 15461, [ =( multiply( X, identity ), 'least_upper_bound'( X,
% 2.15/2.58 multiply( X, multiply( c, inverse( d ) ) ) ) ) ] )
% 2.15/2.58 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, c ), :=( Z, inverse( d ) )] )
% 2.15/2.58 , substitution( 1, [ :=( X, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15464, [ =( X, 'least_upper_bound'( X, multiply( multiply( X, c ),
% 2.15/2.58 inverse( d ) ) ) ) ] )
% 2.15/2.58 , clause( 365, [ =( multiply( X, identity ), X ) ] )
% 2.15/2.58 , 0, clause( 15463, [ =( multiply( X, identity ), 'least_upper_bound'( X,
% 2.15/2.58 multiply( multiply( X, c ), inverse( d ) ) ) ) ] )
% 2.15/2.58 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 2.15/2.58 ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15465, [ =( 'least_upper_bound'( X, multiply( multiply( X, c ),
% 2.15/2.58 inverse( d ) ) ), X ) ] )
% 2.15/2.58 , clause( 15464, [ =( X, 'least_upper_bound'( X, multiply( multiply( X, c )
% 2.15/2.58 , inverse( d ) ) ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 4257, [ =( 'least_upper_bound'( X, multiply( multiply( X, c ),
% 2.15/2.58 inverse( d ) ) ), X ) ] )
% 2.15/2.58 , clause( 15465, [ =( 'least_upper_bound'( X, multiply( multiply( X, c ),
% 2.15/2.58 inverse( d ) ) ), X ) ] )
% 2.15/2.58 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15467, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 2.15/2.58 'least_upper_bound'( a, X ), b ) ) ] )
% 2.15/2.58 , clause( 151, [ =( 'least_upper_bound'( 'least_upper_bound'( a, X ), b ),
% 2.15/2.58 'least_upper_bound'( X, b ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15469, [ =( 'least_upper_bound'( multiply( multiply( a, c ),
% 2.15/2.58 inverse( d ) ), b ), 'least_upper_bound'( a, b ) ) ] )
% 2.15/2.58 , clause( 4257, [ =( 'least_upper_bound'( X, multiply( multiply( X, c ),
% 2.15/2.58 inverse( d ) ) ), X ) ] )
% 2.15/2.58 , 0, clause( 15467, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 2.15/2.58 'least_upper_bound'( a, X ), b ) ) ] )
% 2.15/2.58 , 0, 10, substitution( 0, [ :=( X, a )] ), substitution( 1, [ :=( X,
% 2.15/2.58 multiply( multiply( a, c ), inverse( d ) ) )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15470, [ =( 'least_upper_bound'( multiply( multiply( a, c ),
% 2.15/2.58 inverse( d ) ), b ), b ) ] )
% 2.15/2.58 , clause( 15, [ =( 'least_upper_bound'( a, b ), b ) ] )
% 2.15/2.58 , 0, clause( 15469, [ =( 'least_upper_bound'( multiply( multiply( a, c ),
% 2.15/2.58 inverse( d ) ), b ), 'least_upper_bound'( a, b ) ) ] )
% 2.15/2.58 , 0, 9, substitution( 0, [] ), substitution( 1, [] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 4347, [ =( 'least_upper_bound'( multiply( multiply( a, c ), inverse(
% 2.15/2.58 d ) ), b ), b ) ] )
% 2.15/2.58 , clause( 15470, [ =( 'least_upper_bound'( multiply( multiply( a, c ),
% 2.15/2.58 inverse( d ) ), b ), b ) ] )
% 2.15/2.58 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15473, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 2.15/2.58 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 2.15/2.58 , clause( 483, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 2.15/2.58 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( Y, X ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15477, [ =( 'least_upper_bound'( b, multiply( multiply( a, c ),
% 2.15/2.58 inverse( d ) ) ), 'greatest_lower_bound'( 'least_upper_bound'( b,
% 2.15/2.58 multiply( multiply( a, c ), inverse( d ) ) ), b ) ) ] )
% 2.15/2.58 , clause( 4347, [ =( 'least_upper_bound'( multiply( multiply( a, c ),
% 2.15/2.58 inverse( d ) ), b ), b ) ] )
% 2.15/2.58 , 0, clause( 15473, [ =( 'least_upper_bound'( X, Y ),
% 2.15/2.58 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 2.15/2.58 Y, X ) ) ) ] )
% 2.15/2.58 , 0, 18, substitution( 0, [] ), substitution( 1, [ :=( X, b ), :=( Y,
% 2.15/2.58 multiply( multiply( a, c ), inverse( d ) ) )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15479, [ =( 'least_upper_bound'( b, multiply( multiply( a, c ),
% 2.15/2.58 inverse( d ) ) ), b ) ] )
% 2.15/2.58 , clause( 23, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 2.15/2.58 , X ) ] )
% 2.15/2.58 , 0, clause( 15477, [ =( 'least_upper_bound'( b, multiply( multiply( a, c )
% 2.15/2.58 , inverse( d ) ) ), 'greatest_lower_bound'( 'least_upper_bound'( b,
% 2.15/2.58 multiply( multiply( a, c ), inverse( d ) ) ), b ) ) ] )
% 2.15/2.58 , 0, 9, substitution( 0, [ :=( X, b ), :=( Y, multiply( multiply( a, c ),
% 2.15/2.58 inverse( d ) ) )] ), substitution( 1, [] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 4507, [ =( 'least_upper_bound'( b, multiply( multiply( a, c ),
% 2.15/2.58 inverse( d ) ) ), b ) ] )
% 2.15/2.58 , clause( 15479, [ =( 'least_upper_bound'( b, multiply( multiply( a, c ),
% 2.15/2.58 inverse( d ) ) ), b ) ] )
% 2.15/2.58 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 eqswap(
% 2.15/2.58 clause( 15482, [ =( 'least_upper_bound'( multiply( X, inverse( Z ) ), Y ),
% 2.15/2.58 multiply( 'least_upper_bound'( X, multiply( Y, Z ) ), inverse( Z ) ) ) ]
% 2.15/2.58 )
% 2.15/2.58 , clause( 401, [ =( multiply( 'least_upper_bound'( Z, multiply( X, Y ) ),
% 2.15/2.58 inverse( Y ) ), 'least_upper_bound'( multiply( Z, inverse( Y ) ), X ) ) ]
% 2.15/2.58 )
% 2.15/2.58 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15484, [ =( 'least_upper_bound'( multiply( b, inverse( inverse( d )
% 2.15/2.58 ) ), multiply( a, c ) ), multiply( b, inverse( inverse( d ) ) ) ) ] )
% 2.15/2.58 , clause( 4507, [ =( 'least_upper_bound'( b, multiply( multiply( a, c ),
% 2.15/2.58 inverse( d ) ) ), b ) ] )
% 2.15/2.58 , 0, clause( 15482, [ =( 'least_upper_bound'( multiply( X, inverse( Z ) ),
% 2.15/2.58 Y ), multiply( 'least_upper_bound'( X, multiply( Y, Z ) ), inverse( Z ) )
% 2.15/2.58 ) ] )
% 2.15/2.58 , 0, 11, substitution( 0, [] ), substitution( 1, [ :=( X, b ), :=( Y,
% 2.15/2.58 multiply( a, c ) ), :=( Z, inverse( d ) )] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15486, [ =( 'least_upper_bound'( multiply( b, inverse( inverse( d )
% 2.15/2.58 ) ), multiply( a, c ) ), multiply( b, d ) ) ] )
% 2.15/2.58 , clause( 373, [ =( inverse( inverse( X ) ), X ) ] )
% 2.15/2.58 , 0, clause( 15484, [ =( 'least_upper_bound'( multiply( b, inverse( inverse(
% 2.15/2.58 d ) ) ), multiply( a, c ) ), multiply( b, inverse( inverse( d ) ) ) ) ]
% 2.15/2.58 )
% 2.15/2.58 , 0, 12, substitution( 0, [ :=( X, d )] ), substitution( 1, [] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 paramod(
% 2.15/2.58 clause( 15487, [ =( 'least_upper_bound'( multiply( b, d ), multiply( a, c )
% 2.15/2.58 ), multiply( b, d ) ) ] )
% 2.15/2.58 , clause( 373, [ =( inverse( inverse( X ) ), X ) ] )
% 2.15/2.58 , 0, clause( 15486, [ =( 'least_upper_bound'( multiply( b, inverse( inverse(
% 2.15/2.58 d ) ) ), multiply( a, c ) ), multiply( b, d ) ) ] )
% 2.15/2.58 , 0, 4, substitution( 0, [ :=( X, d )] ), substitution( 1, [] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 14543, [ =( 'least_upper_bound'( multiply( b, d ), multiply( a, c )
% 2.15/2.58 ), multiply( b, d ) ) ] )
% 2.15/2.58 , clause( 15487, [ =( 'least_upper_bound'( multiply( b, d ), multiply( a, c
% 2.15/2.58 ) ), multiply( b, d ) ) ] )
% 2.15/2.58 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 resolution(
% 2.15/2.58 clause( 15493, [] )
% 2.15/2.58 , clause( 139, [ ~( =( 'least_upper_bound'( multiply( b, d ), multiply( a,
% 2.15/2.58 c ) ), multiply( b, d ) ) ) ] )
% 2.15/2.58 , 0, clause( 14543, [ =( 'least_upper_bound'( multiply( b, d ), multiply( a
% 2.15/2.58 , c ) ), multiply( b, d ) ) ] )
% 2.15/2.58 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 subsumption(
% 2.15/2.58 clause( 14997, [] )
% 2.15/2.58 , clause( 15493, [] )
% 2.15/2.58 , substitution( 0, [] ), permutation( 0, [] ) ).
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 end.
% 2.15/2.58
% 2.15/2.58 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.15/2.58
% 2.15/2.58 Memory use:
% 2.15/2.58
% 2.15/2.58 space for terms: 201528
% 2.15/2.58 space for clauses: 1597265
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 clauses generated: 464093
% 2.15/2.58 clauses kept: 14998
% 2.15/2.58 clauses selected: 1323
% 2.15/2.58 clauses deleted: 122
% 2.15/2.58 clauses inuse deleted: 42
% 2.15/2.58
% 2.15/2.58 subsentry: 27337
% 2.15/2.58 literals s-matched: 26127
% 2.15/2.58 literals matched: 26087
% 2.15/2.58 full subsumption: 0
% 2.15/2.58
% 2.15/2.58 checksum: 1074326152
% 2.15/2.58
% 2.15/2.58
% 2.15/2.58 Bliksem ended
%------------------------------------------------------------------------------