TSTP Solution File: GRP170-4 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP170-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n022.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 07:35:45 EDT 2022
% Result : Unsatisfiable 2.30s 2.67s
% Output : Refutation 2.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP170-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Mon Jun 13 21:59:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.30/2.67 *** allocated 10000 integers for termspace/termends
% 2.30/2.67 *** allocated 10000 integers for clauses
% 2.30/2.67 *** allocated 10000 integers for justifications
% 2.30/2.67 Bliksem 1.12
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 Automatic Strategy Selection
% 2.30/2.67
% 2.30/2.67 Clauses:
% 2.30/2.67 [
% 2.30/2.67 [ =( multiply( identity, X ), X ) ],
% 2.30/2.67 [ =( multiply( inverse( X ), X ), identity ) ],
% 2.30/2.67 [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply( Y, Z ) ) )
% 2.30/2.67 ],
% 2.30/2.67 [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, X ) ) ]
% 2.30/2.67 ,
% 2.30/2.67 [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ],
% 2.30/2.67 [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ),
% 2.30/2.67 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ],
% 2.30/2.67 [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 2.30/2.67 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ],
% 2.30/2.67 [ =( 'least_upper_bound'( X, X ), X ) ],
% 2.30/2.67 [ =( 'greatest_lower_bound'( X, X ), X ) ],
% 2.30/2.67 [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X ) ]
% 2.30/2.67 ,
% 2.30/2.67 [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ), X ) ]
% 2.30/2.67 ,
% 2.30/2.67 [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), 'least_upper_bound'(
% 2.30/2.67 multiply( X, Y ), multiply( X, Z ) ) ) ],
% 2.30/2.67 [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 2.30/2.67 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ],
% 2.30/2.67 [ =( multiply( 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'(
% 2.30/2.67 multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 2.30/2.67 [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 2.30/2.67 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 2.30/2.67 [ =( 'least_upper_bound'( a, b ), b ) ],
% 2.30/2.67 [ =( 'greatest_lower_bound'( c, d ), c ) ],
% 2.30/2.67 [ ~( =( 'least_upper_bound'( multiply( a, c ), multiply( b, d ) ),
% 2.30/2.67 multiply( b, d ) ) ) ]
% 2.30/2.67 ] .
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 percentage equality = 1.000000, percentage horn = 1.000000
% 2.30/2.67 This is a pure equality problem
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 Options Used:
% 2.30/2.67
% 2.30/2.67 useres = 1
% 2.30/2.67 useparamod = 1
% 2.30/2.67 useeqrefl = 1
% 2.30/2.67 useeqfact = 1
% 2.30/2.67 usefactor = 1
% 2.30/2.67 usesimpsplitting = 0
% 2.30/2.67 usesimpdemod = 5
% 2.30/2.67 usesimpres = 3
% 2.30/2.67
% 2.30/2.67 resimpinuse = 1000
% 2.30/2.67 resimpclauses = 20000
% 2.30/2.67 substype = eqrewr
% 2.30/2.67 backwardsubs = 1
% 2.30/2.67 selectoldest = 5
% 2.30/2.67
% 2.30/2.67 litorderings [0] = split
% 2.30/2.67 litorderings [1] = extend the termordering, first sorting on arguments
% 2.30/2.67
% 2.30/2.67 termordering = kbo
% 2.30/2.67
% 2.30/2.67 litapriori = 0
% 2.30/2.67 termapriori = 1
% 2.30/2.67 litaposteriori = 0
% 2.30/2.67 termaposteriori = 0
% 2.30/2.67 demodaposteriori = 0
% 2.30/2.67 ordereqreflfact = 0
% 2.30/2.67
% 2.30/2.67 litselect = negord
% 2.30/2.67
% 2.30/2.67 maxweight = 15
% 2.30/2.67 maxdepth = 30000
% 2.30/2.67 maxlength = 115
% 2.30/2.67 maxnrvars = 195
% 2.30/2.67 excuselevel = 1
% 2.30/2.67 increasemaxweight = 1
% 2.30/2.67
% 2.30/2.67 maxselected = 10000000
% 2.30/2.67 maxnrclauses = 10000000
% 2.30/2.67
% 2.30/2.67 showgenerated = 0
% 2.30/2.67 showkept = 0
% 2.30/2.67 showselected = 0
% 2.30/2.67 showdeleted = 0
% 2.30/2.67 showresimp = 1
% 2.30/2.67 showstatus = 2000
% 2.30/2.67
% 2.30/2.67 prologoutput = 1
% 2.30/2.67 nrgoals = 5000000
% 2.30/2.67 totalproof = 1
% 2.30/2.67
% 2.30/2.67 Symbols occurring in the translation:
% 2.30/2.67
% 2.30/2.67 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.30/2.67 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 2.30/2.67 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 2.30/2.67 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.30/2.67 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.30/2.67 identity [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 2.30/2.67 multiply [41, 2] (w:1, o:49, a:1, s:1, b:0),
% 2.30/2.67 inverse [42, 1] (w:1, o:22, a:1, s:1, b:0),
% 2.30/2.67 'greatest_lower_bound' [45, 2] (w:1, o:50, a:1, s:1, b:0),
% 2.30/2.67 'least_upper_bound' [46, 2] (w:1, o:48, a:1, s:1, b:0),
% 2.30/2.67 a [47, 0] (w:1, o:13, a:1, s:1, b:0),
% 2.30/2.67 b [48, 0] (w:1, o:14, a:1, s:1, b:0),
% 2.30/2.67 c [49, 0] (w:1, o:15, a:1, s:1, b:0),
% 2.30/2.67 d [50, 0] (w:1, o:16, a:1, s:1, b:0).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 Starting Search:
% 2.30/2.67
% 2.30/2.67 Resimplifying inuse:
% 2.30/2.67 Done
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 Intermediate Status:
% 2.30/2.67 Generated: 28612
% 2.30/2.67 Kept: 2006
% 2.30/2.67 Inuse: 259
% 2.30/2.67 Deleted: 15
% 2.30/2.67 Deletedinuse: 6
% 2.30/2.67
% 2.30/2.67 Resimplifying inuse:
% 2.30/2.67 Done
% 2.30/2.67
% 2.30/2.67 Resimplifying inuse:
% 2.30/2.67 Done
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 Intermediate Status:
% 2.30/2.67 Generated: 61600
% 2.30/2.67 Kept: 4010
% 2.30/2.67 Inuse: 471
% 2.30/2.67 Deleted: 30
% 2.30/2.67 Deletedinuse: 6
% 2.30/2.67
% 2.30/2.67 Resimplifying inuse:
% 2.30/2.67 Done
% 2.30/2.67
% 2.30/2.67 Resimplifying inuse:
% 2.30/2.67 Done
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 Intermediate Status:
% 2.30/2.67 Generated: 106821
% 2.30/2.67 Kept: 6015
% 2.30/2.67 Inuse: 682
% 2.30/2.67 Deleted: 52
% 2.30/2.67 Deletedinuse: 8
% 2.30/2.67
% 2.30/2.67 Resimplifying inuse:
% 2.30/2.67 Done
% 2.30/2.67
% 2.30/2.67 Resimplifying inuse:
% 2.30/2.67 Done
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 Intermediate Status:
% 2.30/2.67 Generated: 178389
% 2.30/2.67 Kept: 8032
% 2.30/2.67 Inuse: 839
% 2.30/2.67 Deleted: 54
% 2.30/2.67 Deletedinuse: 8
% 2.30/2.67
% 2.30/2.67 Resimplifying inuse:
% 2.30/2.67 Done
% 2.30/2.67
% 2.30/2.67 Resimplifying inuse:
% 2.30/2.67 Done
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 Intermediate Status:
% 2.30/2.67 Generated: 289940
% 2.30/2.67 Kept: 10035
% 2.30/2.67 Inuse: 1010
% 2.30/2.67 Deleted: 66
% 2.30/2.67 Deletedinuse: 8
% 2.30/2.67
% 2.30/2.67 Resimplifying inuse:
% 2.30/2.67 Done
% 2.30/2.67
% 2.30/2.67 Resimplifying inuse:
% 2.30/2.67 Done
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 Intermediate Status:
% 2.30/2.67 Generated: 405279
% 2.30/2.67 Kept: 12051
% 2.30/2.67 Inuse: 1225
% 2.30/2.67 Deleted: 87
% 2.30/2.67 Deletedinuse: 8
% 2.30/2.67
% 2.30/2.67 Resimplifying inuse:
% 2.30/2.67 Done
% 2.30/2.67
% 2.30/2.67 Resimplifying inuse:
% 2.30/2.67 Done
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 Intermediate Status:
% 2.30/2.67 Generated: 461749
% 2.30/2.67 Kept: 14250
% 2.30/2.67 Inuse: 1306
% 2.30/2.67 Deleted: 93
% 2.30/2.67 Deletedinuse: 8
% 2.30/2.67
% 2.30/2.67 Resimplifying inuse:
% 2.30/2.67 Done
% 2.30/2.67
% 2.30/2.67 Resimplifying inuse:
% 2.30/2.67
% 2.30/2.67 Bliksems!, er is een bewijs:
% 2.30/2.67 % SZS status Unsatisfiable
% 2.30/2.67 % SZS output start Refutation
% 2.30/2.67
% 2.30/2.67 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 2.30/2.67 , Z ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 2.30/2.67 X ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 2.30/2.67 ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) )
% 2.30/2.67 , 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 2.30/2.67 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 2.30/2.67 ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 2.30/2.67 X ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) )
% 2.30/2.67 , multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 2.30/2.67 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 14, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z )
% 2.30/2.67 ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 15, [ =( 'least_upper_bound'( a, b ), b ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 16, [ =( 'greatest_lower_bound'( c, d ), c ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 17, [ ~( =( 'least_upper_bound'( multiply( a, c ), multiply( b, d )
% 2.30/2.67 ), multiply( b, d ) ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 18, [ =( 'least_upper_bound'( b, a ), b ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 19, [ =( 'greatest_lower_bound'( d, c ), c ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 20, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ), Y )
% 2.30/2.67 , identity ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 2.30/2.67 identity ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 22, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 2.30/2.67 ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 23, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X ),
% 2.30/2.67 X ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 24, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) ),
% 2.30/2.67 X ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 29, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Z,
% 2.30/2.67 'least_upper_bound'( X, Y ) ), X ), 'greatest_lower_bound'( Z, X ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 45, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 2.30/2.67 'least_upper_bound'( X, Y ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 46, [ =( 'least_upper_bound'( d, c ), d ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 47, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) ),
% 2.30/2.67 X ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 48, [ =( 'least_upper_bound'( 'greatest_lower_bound'( X, Y ), X ),
% 2.30/2.67 X ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 52, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, Z ),
% 2.30/2.67 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ),
% 2.30/2.67 'least_upper_bound'( Y, Z ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 56, [ =( 'least_upper_bound'( 'least_upper_bound'( X, b ), a ),
% 2.30/2.67 'least_upper_bound'( X, b ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 74, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y )
% 2.30/2.67 ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 75, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ), identity
% 2.30/2.67 ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 109, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 2.30/2.67 'least_upper_bound'( identity, Y ), X ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 132, [ =( 'greatest_lower_bound'( multiply( Y, X ), X ), multiply(
% 2.30/2.67 'greatest_lower_bound'( Y, identity ), X ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 141, [ ~( =( 'least_upper_bound'( multiply( b, d ), multiply( a, c
% 2.30/2.67 ) ), multiply( b, d ) ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 158, [ =( 'least_upper_bound'( 'least_upper_bound'( a, X ), b ),
% 2.30/2.67 'least_upper_bound'( X, b ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 168, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 174, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 2.30/2.67 ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 177, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X,
% 2.30/2.67 'least_upper_bound'( identity, Y ) ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 211, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Y, X ),
% 2.30/2.67 'least_upper_bound'( Y, Z ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 388, [ =( multiply( X, identity ), X ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 396, [ =( inverse( inverse( X ) ), X ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 399, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 416, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y )
% 2.30/2.67 ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 420, [ =( multiply( 'least_upper_bound'( Z, multiply( X, Y ) ),
% 2.30/2.67 inverse( Y ) ), 'least_upper_bound'( multiply( Z, inverse( Y ) ), X ) ) ]
% 2.30/2.67 )
% 2.30/2.67 .
% 2.30/2.67 clause( 422, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X )
% 2.30/2.67 ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 423, [ =( multiply( inverse( Y ), inverse( X ) ), inverse( multiply(
% 2.30/2.67 X, Y ) ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 424, [ =( inverse( multiply( inverse( X ), Y ) ), multiply( inverse(
% 2.30/2.67 Y ), X ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 434, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 2.30/2.67 inverse( X ) ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 470, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 2.30/2.67 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( Y, X ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 618, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ),
% 2.30/2.67 'greatest_lower_bound'( X, Y ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 1230, [ =( 'least_upper_bound'( identity, multiply( inverse( d ), c
% 2.30/2.67 ) ), identity ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 1231, [ =( 'least_upper_bound'( identity, multiply( inverse( X ),
% 2.30/2.67 'greatest_lower_bound'( X, Y ) ) ), identity ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 1318, [ =( 'greatest_lower_bound'( identity, multiply( inverse( X )
% 2.30/2.67 , 'least_upper_bound'( Y, X ) ) ), identity ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 1489, [ =( 'greatest_lower_bound'( identity, multiply( inverse( c )
% 2.30/2.67 , d ) ), identity ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 1584, [ =( 'greatest_lower_bound'( multiply( inverse( c ), d ),
% 2.30/2.67 identity ), identity ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 3207, [ =( 'greatest_lower_bound'( multiply( multiply( inverse( c )
% 2.30/2.67 , d ), X ), X ), X ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 3278, [ =( 'greatest_lower_bound'( inverse( c ), inverse( d ) ),
% 2.30/2.67 inverse( d ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 3290, [ =( 'least_upper_bound'( identity, multiply( c, inverse( d )
% 2.30/2.67 ) ), identity ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 3356, [ =( 'least_upper_bound'( X, multiply( multiply( c, inverse(
% 2.30/2.67 d ) ), X ) ), X ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 4404, [ =( 'least_upper_bound'( X, multiply( multiply( X, c ),
% 2.30/2.67 inverse( d ) ) ), X ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 4516, [ =( 'least_upper_bound'( multiply( multiply( a, c ), inverse(
% 2.30/2.67 d ) ), b ), b ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 4625, [ =( 'least_upper_bound'( b, multiply( multiply( a, c ),
% 2.30/2.67 inverse( d ) ) ), b ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 15194, [ =( 'least_upper_bound'( multiply( b, d ), multiply( a, c )
% 2.30/2.67 ), multiply( b, d ) ) ] )
% 2.30/2.67 .
% 2.30/2.67 clause( 15262, [] )
% 2.30/2.67 .
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 % SZS output end Refutation
% 2.30/2.67 found a proof!
% 2.30/2.67
% 2.30/2.67 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.30/2.67
% 2.30/2.67 initialclauses(
% 2.30/2.67 [ clause( 15264, [ =( multiply( identity, X ), X ) ] )
% 2.30/2.67 , clause( 15265, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.30/2.67 , clause( 15266, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 2.30/2.67 multiply( Y, Z ) ) ) ] )
% 2.30/2.67 , clause( 15267, [ =( 'greatest_lower_bound'( X, Y ),
% 2.30/2.67 'greatest_lower_bound'( Y, X ) ) ] )
% 2.30/2.67 , clause( 15268, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y,
% 2.30/2.67 X ) ) ] )
% 2.30/2.67 , clause( 15269, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y
% 2.30/2.67 , Z ) ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ]
% 2.30/2.67 )
% 2.30/2.67 , clause( 15270, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 2.30/2.67 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.30/2.67 , clause( 15271, [ =( 'least_upper_bound'( X, X ), X ) ] )
% 2.30/2.67 , clause( 15272, [ =( 'greatest_lower_bound'( X, X ), X ) ] )
% 2.30/2.67 , clause( 15273, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 2.30/2.67 ) ), X ) ] )
% 2.30/2.67 , clause( 15274, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 2.30/2.67 ) ), X ) ] )
% 2.30/2.67 , clause( 15275, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 2.30/2.67 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.30/2.67 , clause( 15276, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 2.30/2.67 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.30/2.67 , clause( 15277, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 2.30/2.67 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 2.30/2.67 , clause( 15278, [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 2.30/2.67 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 2.30/2.67 , clause( 15279, [ =( 'least_upper_bound'( a, b ), b ) ] )
% 2.30/2.67 , clause( 15280, [ =( 'greatest_lower_bound'( c, d ), c ) ] )
% 2.30/2.67 , clause( 15281, [ ~( =( 'least_upper_bound'( multiply( a, c ), multiply( b
% 2.30/2.67 , d ) ), multiply( b, d ) ) ) ] )
% 2.30/2.67 ] ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.30/2.67 , clause( 15264, [ =( multiply( identity, X ), X ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.30/2.67 , clause( 15265, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15287, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X
% 2.30/2.67 , Y ), Z ) ) ] )
% 2.30/2.67 , clause( 15266, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 2.30/2.67 multiply( Y, Z ) ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 2.30/2.67 , Z ) ) ] )
% 2.30/2.67 , clause( 15287, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply(
% 2.30/2.67 X, Y ), Z ) ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.30/2.67 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 2.30/2.67 X ) ) ] )
% 2.30/2.67 , clause( 15267, [ =( 'greatest_lower_bound'( X, Y ),
% 2.30/2.67 'greatest_lower_bound'( Y, X ) ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.67 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 2.30/2.67 ] )
% 2.30/2.67 , clause( 15268, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y,
% 2.30/2.67 X ) ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.67 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) )
% 2.30/2.67 , 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 2.30/2.67 , clause( 15269, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y
% 2.30/2.67 , Z ) ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ]
% 2.30/2.67 )
% 2.30/2.67 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.30/2.67 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 2.30/2.67 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.30/2.67 , clause( 15270, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 2.30/2.67 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.30/2.67 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 2.30/2.67 ) ] )
% 2.30/2.67 , clause( 15273, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 2.30/2.67 ) ), X ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.67 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 2.30/2.67 X ) ] )
% 2.30/2.67 , clause( 15274, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 2.30/2.67 ) ), X ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.67 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15329, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 2.30/2.67 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.30/2.67 , clause( 15275, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 2.30/2.67 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) )
% 2.30/2.67 , multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.30/2.67 , clause( 15329, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z
% 2.30/2.67 ) ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.30/2.67 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15341, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 2.30/2.67 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.30/2.67 , clause( 15277, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 2.30/2.67 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 2.30/2.67 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.30/2.67 , clause( 15341, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z
% 2.30/2.67 ) ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.30/2.67 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15354, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y,
% 2.30/2.67 Z ) ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 2.30/2.67 , clause( 15278, [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 2.30/2.67 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 14, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z )
% 2.30/2.67 ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 2.30/2.67 , clause( 15354, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y
% 2.30/2.67 , Z ) ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.30/2.67 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 15, [ =( 'least_upper_bound'( a, b ), b ) ] )
% 2.30/2.67 , clause( 15279, [ =( 'least_upper_bound'( a, b ), b ) ] )
% 2.30/2.67 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 16, [ =( 'greatest_lower_bound'( c, d ), c ) ] )
% 2.30/2.67 , clause( 15280, [ =( 'greatest_lower_bound'( c, d ), c ) ] )
% 2.30/2.67 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 17, [ ~( =( 'least_upper_bound'( multiply( a, c ), multiply( b, d )
% 2.30/2.67 ), multiply( b, d ) ) ) ] )
% 2.30/2.67 , clause( 15281, [ ~( =( 'least_upper_bound'( multiply( a, c ), multiply( b
% 2.30/2.67 , d ) ), multiply( b, d ) ) ) ] )
% 2.30/2.67 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15400, [ =( b, 'least_upper_bound'( a, b ) ) ] )
% 2.30/2.67 , clause( 15, [ =( 'least_upper_bound'( a, b ), b ) ] )
% 2.30/2.67 , 0, substitution( 0, [] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 paramod(
% 2.30/2.67 clause( 15401, [ =( b, 'least_upper_bound'( b, a ) ) ] )
% 2.30/2.67 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 2.30/2.67 ) ] )
% 2.30/2.67 , 0, clause( 15400, [ =( b, 'least_upper_bound'( a, b ) ) ] )
% 2.30/2.67 , 0, 2, substitution( 0, [ :=( X, a ), :=( Y, b )] ), substitution( 1, [] )
% 2.30/2.67 ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15404, [ =( 'least_upper_bound'( b, a ), b ) ] )
% 2.30/2.67 , clause( 15401, [ =( b, 'least_upper_bound'( b, a ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 18, [ =( 'least_upper_bound'( b, a ), b ) ] )
% 2.30/2.67 , clause( 15404, [ =( 'least_upper_bound'( b, a ), b ) ] )
% 2.30/2.67 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15405, [ =( c, 'greatest_lower_bound'( c, d ) ) ] )
% 2.30/2.67 , clause( 16, [ =( 'greatest_lower_bound'( c, d ), c ) ] )
% 2.30/2.67 , 0, substitution( 0, [] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 paramod(
% 2.30/2.67 clause( 15406, [ =( c, 'greatest_lower_bound'( d, c ) ) ] )
% 2.30/2.67 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 2.30/2.67 , X ) ) ] )
% 2.30/2.67 , 0, clause( 15405, [ =( c, 'greatest_lower_bound'( c, d ) ) ] )
% 2.30/2.67 , 0, 2, substitution( 0, [ :=( X, c ), :=( Y, d )] ), substitution( 1, [] )
% 2.30/2.67 ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15409, [ =( 'greatest_lower_bound'( d, c ), c ) ] )
% 2.30/2.67 , clause( 15406, [ =( c, 'greatest_lower_bound'( d, c ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 19, [ =( 'greatest_lower_bound'( d, c ), c ) ] )
% 2.30/2.67 , clause( 15409, [ =( 'greatest_lower_bound'( d, c ), c ) ] )
% 2.30/2.67 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15410, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 2.30/2.67 Y, Z ) ) ) ] )
% 2.30/2.67 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 2.30/2.67 ), Z ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 paramod(
% 2.30/2.67 clause( 15413, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ), Y
% 2.30/2.67 ), identity ) ] )
% 2.30/2.67 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.30/2.67 , 0, clause( 15410, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 2.30/2.67 multiply( Y, Z ) ) ) ] )
% 2.30/2.67 , 0, 9, substitution( 0, [ :=( X, multiply( X, Y ) )] ), substitution( 1, [
% 2.30/2.67 :=( X, inverse( multiply( X, Y ) ) ), :=( Y, X ), :=( Z, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 20, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ), Y )
% 2.30/2.67 , identity ) ] )
% 2.30/2.67 , clause( 15413, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X )
% 2.30/2.67 , Y ), identity ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.67 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15419, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 2.30/2.67 Y, Z ) ) ) ] )
% 2.30/2.67 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 2.30/2.67 ), Z ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 paramod(
% 2.30/2.67 clause( 15424, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply( X
% 2.30/2.67 , identity ) ) ] )
% 2.30/2.67 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.30/2.67 , 0, clause( 15419, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 2.30/2.67 multiply( Y, Z ) ) ) ] )
% 2.30/2.67 , 0, 9, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 2.30/2.67 :=( Y, inverse( Y ) ), :=( Z, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 2.30/2.67 identity ) ) ] )
% 2.30/2.67 , clause( 15424, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply(
% 2.30/2.67 X, identity ) ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.67 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15429, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 2.30/2.67 Y, Z ) ) ) ] )
% 2.30/2.67 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 2.30/2.67 ), Z ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 paramod(
% 2.30/2.67 clause( 15434, [ =( multiply( multiply( X, identity ), Y ), multiply( X, Y
% 2.30/2.67 ) ) ] )
% 2.30/2.67 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.30/2.67 , 0, clause( 15429, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 2.30/2.67 multiply( Y, Z ) ) ) ] )
% 2.30/2.67 , 0, 8, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 2.30/2.67 :=( Y, identity ), :=( Z, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 22, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 2.30/2.67 ] )
% 2.30/2.67 , clause( 15434, [ =( multiply( multiply( X, identity ), Y ), multiply( X,
% 2.30/2.67 Y ) ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.67 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15439, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 2.30/2.67 ) ) ) ] )
% 2.30/2.67 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 2.30/2.67 , X ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 paramod(
% 2.30/2.67 clause( 15440, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y )
% 2.30/2.67 , X ) ) ] )
% 2.30/2.67 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 2.30/2.67 , X ) ) ] )
% 2.30/2.67 , 0, clause( 15439, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 2.30/2.67 X, Y ) ) ) ] )
% 2.30/2.67 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, 'least_upper_bound'( X, Y ) )] )
% 2.30/2.67 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15443, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X
% 2.30/2.67 ), X ) ] )
% 2.30/2.67 , clause( 15440, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y
% 2.30/2.67 ), X ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 23, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X ),
% 2.30/2.67 X ) ] )
% 2.30/2.67 , clause( 15443, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 2.30/2.67 X ), X ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.67 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15444, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 2.30/2.67 ) ) ) ] )
% 2.30/2.67 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 2.30/2.67 , X ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 paramod(
% 2.30/2.67 clause( 15445, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 2.30/2.67 ) ) ) ] )
% 2.30/2.67 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 2.30/2.67 ) ] )
% 2.30/2.67 , 0, clause( 15444, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 2.30/2.67 X, Y ) ) ) ] )
% 2.30/2.67 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.30/2.67 :=( X, X ), :=( Y, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15448, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X )
% 2.30/2.67 ), X ) ] )
% 2.30/2.67 , clause( 15445, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y
% 2.30/2.67 , X ) ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 24, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) ),
% 2.30/2.67 X ) ] )
% 2.30/2.67 , clause( 15448, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 2.30/2.67 ) ), X ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.67 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15450, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y )
% 2.30/2.67 , Z ), 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 2.30/2.67 , clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z )
% 2.30/2.67 ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 paramod(
% 2.30/2.67 clause( 15455, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X,
% 2.30/2.67 'least_upper_bound'( Y, Z ) ), Y ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.30/2.67 , clause( 23, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 2.30/2.67 , X ) ] )
% 2.30/2.67 , 0, clause( 15450, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X
% 2.30/2.67 , Y ), Z ), 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ) )
% 2.30/2.67 ] )
% 2.30/2.67 , 0, 10, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 2.30/2.67 :=( X, X ), :=( Y, 'least_upper_bound'( Y, Z ) ), :=( Z, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 29, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Z,
% 2.30/2.67 'least_upper_bound'( X, Y ) ), X ), 'greatest_lower_bound'( Z, X ) ) ] )
% 2.30/2.67 , clause( 15455, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X,
% 2.30/2.67 'least_upper_bound'( Y, Z ) ), Y ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 2.30/2.67 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15460, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 2.30/2.67 ) ) ) ] )
% 2.30/2.67 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 2.30/2.67 , X ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 paramod(
% 2.30/2.67 clause( 15463, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 2.30/2.67 'least_upper_bound'( X, Y ), X ) ) ] )
% 2.30/2.67 , clause( 23, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 2.30/2.67 , X ) ] )
% 2.30/2.67 , 0, clause( 15460, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 2.30/2.67 X, Y ) ) ) ] )
% 2.30/2.67 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.30/2.67 :=( X, 'least_upper_bound'( X, Y ) ), :=( Y, X )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15464, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 2.30/2.67 'least_upper_bound'( X, Y ) ) ] )
% 2.30/2.67 , clause( 15463, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 2.30/2.67 'least_upper_bound'( X, Y ), X ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 45, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 2.30/2.67 'least_upper_bound'( X, Y ) ) ] )
% 2.30/2.67 , clause( 15464, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X )
% 2.30/2.67 , 'least_upper_bound'( X, Y ) ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.67 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15466, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 2.30/2.67 ) ) ) ] )
% 2.30/2.67 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 2.30/2.67 , X ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 paramod(
% 2.30/2.67 clause( 15467, [ =( d, 'least_upper_bound'( d, c ) ) ] )
% 2.30/2.67 , clause( 19, [ =( 'greatest_lower_bound'( d, c ), c ) ] )
% 2.30/2.67 , 0, clause( 15466, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 2.30/2.67 X, Y ) ) ) ] )
% 2.30/2.67 , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, d ), :=( Y, c )] )
% 2.30/2.67 ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15468, [ =( 'least_upper_bound'( d, c ), d ) ] )
% 2.30/2.67 , clause( 15467, [ =( d, 'least_upper_bound'( d, c ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 46, [ =( 'least_upper_bound'( d, c ), d ) ] )
% 2.30/2.67 , clause( 15468, [ =( 'least_upper_bound'( d, c ), d ) ] )
% 2.30/2.67 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15469, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 2.30/2.67 ) ) ) ] )
% 2.30/2.67 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 2.30/2.67 , X ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 paramod(
% 2.30/2.67 clause( 15470, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X
% 2.30/2.67 ) ) ) ] )
% 2.30/2.67 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 2.30/2.67 , X ) ) ] )
% 2.30/2.67 , 0, clause( 15469, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 2.30/2.67 X, Y ) ) ) ] )
% 2.30/2.67 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.30/2.67 :=( X, X ), :=( Y, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15473, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X )
% 2.30/2.67 ), X ) ] )
% 2.30/2.67 , clause( 15470, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y
% 2.30/2.67 , X ) ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 47, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) ),
% 2.30/2.67 X ) ] )
% 2.30/2.67 , clause( 15473, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X
% 2.30/2.67 ) ), X ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.67 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15474, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 2.30/2.67 ) ) ) ] )
% 2.30/2.67 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 2.30/2.67 , X ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 paramod(
% 2.30/2.67 clause( 15475, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( X, Y )
% 2.30/2.67 , X ) ) ] )
% 2.30/2.67 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 2.30/2.67 ) ] )
% 2.30/2.67 , 0, clause( 15474, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 2.30/2.67 X, Y ) ) ) ] )
% 2.30/2.67 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, 'greatest_lower_bound'( X, Y
% 2.30/2.67 ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15478, [ =( 'least_upper_bound'( 'greatest_lower_bound'( X, Y ), X
% 2.30/2.67 ), X ) ] )
% 2.30/2.67 , clause( 15475, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( X, Y
% 2.30/2.67 ), X ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 48, [ =( 'least_upper_bound'( 'greatest_lower_bound'( X, Y ), X ),
% 2.30/2.67 X ) ] )
% 2.30/2.67 , clause( 15478, [ =( 'least_upper_bound'( 'greatest_lower_bound'( X, Y ),
% 2.30/2.67 X ), X ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.67 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15480, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 2.30/2.67 ) ) ) ] )
% 2.30/2.67 , clause( 24, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) )
% 2.30/2.67 , X ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 paramod(
% 2.30/2.67 clause( 15481, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 2.30/2.67 'least_upper_bound'( X, Y ), 'least_upper_bound'( 'least_upper_bound'( Z
% 2.30/2.67 , X ), Y ) ) ) ] )
% 2.30/2.67 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 2.30/2.67 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.30/2.67 , 0, clause( 15480, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 2.30/2.67 Y, X ) ) ) ] )
% 2.30/2.67 , 0, 8, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 2.30/2.67 substitution( 1, [ :=( X, 'least_upper_bound'( X, Y ) ), :=( Y, Z )] )
% 2.30/2.67 ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15482, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 2.30/2.67 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ) ),
% 2.30/2.67 'least_upper_bound'( X, Y ) ) ] )
% 2.30/2.67 , clause( 15481, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 2.30/2.67 'least_upper_bound'( X, Y ), 'least_upper_bound'( 'least_upper_bound'( Z
% 2.30/2.67 , X ), Y ) ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 52, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, Z ),
% 2.30/2.67 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ),
% 2.30/2.67 'least_upper_bound'( Y, Z ) ) ] )
% 2.30/2.67 , clause( 15482, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 2.30/2.67 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ) ),
% 2.30/2.67 'least_upper_bound'( X, Y ) ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 2.30/2.67 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15484, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 2.30/2.67 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.30/2.67 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 2.30/2.67 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 paramod(
% 2.30/2.67 clause( 15486, [ =( 'least_upper_bound'( 'least_upper_bound'( X, b ), a ),
% 2.30/2.67 'least_upper_bound'( X, b ) ) ] )
% 2.30/2.67 , clause( 18, [ =( 'least_upper_bound'( b, a ), b ) ] )
% 2.30/2.67 , 0, clause( 15484, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ),
% 2.30/2.67 Z ), 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.30/2.67 , 0, 8, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, b ),
% 2.30/2.67 :=( Z, a )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 subsumption(
% 2.30/2.67 clause( 56, [ =( 'least_upper_bound'( 'least_upper_bound'( X, b ), a ),
% 2.30/2.67 'least_upper_bound'( X, b ) ) ] )
% 2.30/2.67 , clause( 15486, [ =( 'least_upper_bound'( 'least_upper_bound'( X, b ), a )
% 2.30/2.67 , 'least_upper_bound'( X, b ) ) ] )
% 2.30/2.67 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 eqswap(
% 2.30/2.67 clause( 15490, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 2.30/2.67 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.30/2.67 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 2.30/2.67 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.30/2.67 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.30/2.67
% 2.30/2.67
% 2.30/2.67 paramod(
% 2.30/2.67 clause( 15492, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) ),
% 2.30/2.67 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 2.30/2.67 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.30/2.67 , 0, clause( 15490, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 2.30/2.67 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.30/2.68 , 0, 8, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 2.30/2.68 X ) ), :=( Y, X ), :=( Z, Y )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15495, [ =( 'least_upper_bound'( identity, multiply( inverse( X ),
% 2.30/2.68 Y ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 2.30/2.68 , clause( 15492, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) )
% 2.30/2.68 , 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 subsumption(
% 2.30/2.68 clause( 74, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y )
% 2.30/2.68 ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 2.30/2.68 , clause( 15495, [ =( 'least_upper_bound'( identity, multiply( inverse( X )
% 2.30/2.68 , Y ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 2.30/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.68 )] ) ).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15498, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 2.30/2.68 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.30/2.68 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 2.30/2.68 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15501, [ =( multiply( inverse( X ), 'least_upper_bound'( Y, X ) ),
% 2.30/2.68 'least_upper_bound'( multiply( inverse( X ), Y ), identity ) ) ] )
% 2.30/2.68 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.30/2.68 , 0, clause( 15498, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 2.30/2.68 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.30/2.68 , 0, 12, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 2.30/2.68 inverse( X ) ), :=( Y, Y ), :=( Z, X )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15504, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ),
% 2.30/2.68 identity ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 2.30/2.68 , clause( 15501, [ =( multiply( inverse( X ), 'least_upper_bound'( Y, X ) )
% 2.30/2.68 , 'least_upper_bound'( multiply( inverse( X ), Y ), identity ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 subsumption(
% 2.30/2.68 clause( 75, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ), identity
% 2.30/2.68 ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 2.30/2.68 , clause( 15504, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ),
% 2.30/2.68 identity ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 2.30/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.68 )] ) ).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15506, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 2.30/2.68 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 2.30/2.68 , clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 2.30/2.68 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15507, [ =( multiply( 'least_upper_bound'( identity, X ), Y ),
% 2.30/2.68 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 2.30/2.68 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.30/2.68 , 0, clause( 15506, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 2.30/2.68 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 2.30/2.68 , 0, 7, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X,
% 2.30/2.68 identity ), :=( Y, Y ), :=( Z, X )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15509, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 2.30/2.68 'least_upper_bound'( identity, X ), Y ) ) ] )
% 2.30/2.68 , clause( 15507, [ =( multiply( 'least_upper_bound'( identity, X ), Y ),
% 2.30/2.68 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 subsumption(
% 2.30/2.68 clause( 109, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 2.30/2.68 'least_upper_bound'( identity, Y ), X ) ) ] )
% 2.30/2.68 , clause( 15509, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 2.30/2.68 'least_upper_bound'( identity, X ), Y ) ) ] )
% 2.30/2.68 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.68 )] ) ).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15512, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 2.30/2.68 'greatest_lower_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 2.30/2.68 , clause( 14, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z
% 2.30/2.68 ) ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15514, [ =( multiply( 'greatest_lower_bound'( X, identity ), Y ),
% 2.30/2.68 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ] )
% 2.30/2.68 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.30/2.68 , 0, clause( 15512, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 2.30/2.68 'greatest_lower_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 2.30/2.68 , 0, 10, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 2.30/2.68 :=( Y, Y ), :=( Z, identity )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15516, [ =( 'greatest_lower_bound'( multiply( X, Y ), Y ), multiply(
% 2.30/2.68 'greatest_lower_bound'( X, identity ), Y ) ) ] )
% 2.30/2.68 , clause( 15514, [ =( multiply( 'greatest_lower_bound'( X, identity ), Y )
% 2.30/2.68 , 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 subsumption(
% 2.30/2.68 clause( 132, [ =( 'greatest_lower_bound'( multiply( Y, X ), X ), multiply(
% 2.30/2.68 'greatest_lower_bound'( Y, identity ), X ) ) ] )
% 2.30/2.68 , clause( 15516, [ =( 'greatest_lower_bound'( multiply( X, Y ), Y ),
% 2.30/2.68 multiply( 'greatest_lower_bound'( X, identity ), Y ) ) ] )
% 2.30/2.68 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.68 )] ) ).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15517, [ ~( =( multiply( b, d ), 'least_upper_bound'( multiply( a,
% 2.30/2.68 c ), multiply( b, d ) ) ) ) ] )
% 2.30/2.68 , clause( 17, [ ~( =( 'least_upper_bound'( multiply( a, c ), multiply( b, d
% 2.30/2.68 ) ), multiply( b, d ) ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15518, [ ~( =( multiply( b, d ), 'least_upper_bound'( multiply( b,
% 2.30/2.68 d ), multiply( a, c ) ) ) ) ] )
% 2.30/2.68 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 2.30/2.68 ) ] )
% 2.30/2.68 , 0, clause( 15517, [ ~( =( multiply( b, d ), 'least_upper_bound'( multiply(
% 2.30/2.68 a, c ), multiply( b, d ) ) ) ) ] )
% 2.30/2.68 , 0, 5, substitution( 0, [ :=( X, multiply( a, c ) ), :=( Y, multiply( b, d
% 2.30/2.68 ) )] ), substitution( 1, [] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15521, [ ~( =( 'least_upper_bound'( multiply( b, d ), multiply( a,
% 2.30/2.68 c ) ), multiply( b, d ) ) ) ] )
% 2.30/2.68 , clause( 15518, [ ~( =( multiply( b, d ), 'least_upper_bound'( multiply( b
% 2.30/2.68 , d ), multiply( a, c ) ) ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 subsumption(
% 2.30/2.68 clause( 141, [ ~( =( 'least_upper_bound'( multiply( b, d ), multiply( a, c
% 2.30/2.68 ) ), multiply( b, d ) ) ) ] )
% 2.30/2.68 , clause( 15521, [ ~( =( 'least_upper_bound'( multiply( b, d ), multiply( a
% 2.30/2.68 , c ) ), multiply( b, d ) ) ) ] )
% 2.30/2.68 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15522, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 2.30/2.68 'least_upper_bound'( X, b ), a ) ) ] )
% 2.30/2.68 , clause( 56, [ =( 'least_upper_bound'( 'least_upper_bound'( X, b ), a ),
% 2.30/2.68 'least_upper_bound'( X, b ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, X )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15526, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'( a,
% 2.30/2.68 'least_upper_bound'( X, b ) ) ) ] )
% 2.30/2.68 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 2.30/2.68 ) ] )
% 2.30/2.68 , 0, clause( 15522, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 2.30/2.68 'least_upper_bound'( X, b ), a ) ) ] )
% 2.30/2.68 , 0, 4, substitution( 0, [ :=( X, 'least_upper_bound'( X, b ) ), :=( Y, a )] )
% 2.30/2.68 , substitution( 1, [ :=( X, X )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15532, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 2.30/2.68 'least_upper_bound'( a, X ), b ) ) ] )
% 2.30/2.68 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 2.30/2.68 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.30/2.68 , 0, clause( 15526, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 2.30/2.68 a, 'least_upper_bound'( X, b ) ) ) ] )
% 2.30/2.68 , 0, 4, substitution( 0, [ :=( X, a ), :=( Y, X ), :=( Z, b )] ),
% 2.30/2.68 substitution( 1, [ :=( X, X )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15533, [ =( 'least_upper_bound'( 'least_upper_bound'( a, X ), b ),
% 2.30/2.68 'least_upper_bound'( X, b ) ) ] )
% 2.30/2.68 , clause( 15532, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 2.30/2.68 'least_upper_bound'( a, X ), b ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, X )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 subsumption(
% 2.30/2.68 clause( 158, [ =( 'least_upper_bound'( 'least_upper_bound'( a, X ), b ),
% 2.30/2.68 'least_upper_bound'( X, b ) ) ] )
% 2.30/2.68 , clause( 15533, [ =( 'least_upper_bound'( 'least_upper_bound'( a, X ), b )
% 2.30/2.68 , 'least_upper_bound'( X, b ) ) ] )
% 2.30/2.68 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15535, [ =( multiply( X, identity ), multiply( multiply( X, inverse(
% 2.30/2.68 Y ) ), Y ) ) ] )
% 2.30/2.68 , clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 2.30/2.68 , identity ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15538, [ =( multiply( inverse( inverse( X ) ), identity ), multiply(
% 2.30/2.68 identity, X ) ) ] )
% 2.30/2.68 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.30/2.68 , 0, clause( 15535, [ =( multiply( X, identity ), multiply( multiply( X,
% 2.30/2.68 inverse( Y ) ), Y ) ) ] )
% 2.30/2.68 , 0, 7, substitution( 0, [ :=( X, inverse( X ) )] ), substitution( 1, [
% 2.30/2.68 :=( X, inverse( inverse( X ) ) ), :=( Y, X )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15539, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 2.30/2.68 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.30/2.68 , 0, clause( 15538, [ =( multiply( inverse( inverse( X ) ), identity ),
% 2.30/2.68 multiply( identity, X ) ) ] )
% 2.30/2.68 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 2.30/2.68 ).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 subsumption(
% 2.30/2.68 clause( 168, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 2.30/2.68 , clause( 15539, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ]
% 2.30/2.68 )
% 2.30/2.68 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15542, [ =( multiply( X, Y ), multiply( multiply( X, identity ), Y
% 2.30/2.68 ) ) ] )
% 2.30/2.68 , clause( 22, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X )
% 2.30/2.68 ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15545, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 2.30/2.68 ) ) ] )
% 2.30/2.68 , clause( 168, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 2.30/2.68 , 0, clause( 15542, [ =( multiply( X, Y ), multiply( multiply( X, identity
% 2.30/2.68 ), Y ) ) ] )
% 2.30/2.68 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 2.30/2.68 inverse( X ) ) ), :=( Y, Y )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 subsumption(
% 2.30/2.68 clause( 174, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 2.30/2.68 ) ] )
% 2.30/2.68 , clause( 15545, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X,
% 2.30/2.68 Y ) ) ] )
% 2.30/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.68 )] ) ).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15552, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 2.30/2.68 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.30/2.68 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 2.30/2.68 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15555, [ =( multiply( inverse( inverse( X ) ), 'least_upper_bound'(
% 2.30/2.68 identity, Y ) ), 'least_upper_bound'( X, multiply( inverse( inverse( X )
% 2.30/2.68 ), Y ) ) ) ] )
% 2.30/2.68 , clause( 168, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 2.30/2.68 , 0, clause( 15552, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 2.30/2.68 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 2.30/2.68 , 0, 9, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 2.30/2.68 inverse( X ) ) ), :=( Y, identity ), :=( Z, Y )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15565, [ =( multiply( inverse( inverse( X ) ), 'least_upper_bound'(
% 2.30/2.68 identity, Y ) ), 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 2.30/2.68 , clause( 174, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 2.30/2.68 ) ) ] )
% 2.30/2.68 , 0, clause( 15555, [ =( multiply( inverse( inverse( X ) ),
% 2.30/2.68 'least_upper_bound'( identity, Y ) ), 'least_upper_bound'( X, multiply(
% 2.30/2.68 inverse( inverse( X ) ), Y ) ) ) ] )
% 2.30/2.68 , 0, 10, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.30/2.68 :=( X, X ), :=( Y, Y )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15567, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 2.30/2.68 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 2.30/2.68 , clause( 174, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 2.30/2.68 ) ) ] )
% 2.30/2.68 , 0, clause( 15565, [ =( multiply( inverse( inverse( X ) ),
% 2.30/2.68 'least_upper_bound'( identity, Y ) ), 'least_upper_bound'( X, multiply( X
% 2.30/2.68 , Y ) ) ) ] )
% 2.30/2.68 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, 'least_upper_bound'( identity
% 2.30/2.68 , Y ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15568, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 2.30/2.68 , 'least_upper_bound'( identity, Y ) ) ) ] )
% 2.30/2.68 , clause( 15567, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 2.30/2.68 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 subsumption(
% 2.30/2.68 clause( 177, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X,
% 2.30/2.68 'least_upper_bound'( identity, Y ) ) ) ] )
% 2.30/2.68 , clause( 15568, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply(
% 2.30/2.68 X, 'least_upper_bound'( identity, Y ) ) ) ] )
% 2.30/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.30/2.68 )] ) ).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15569, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 2.30/2.68 'greatest_lower_bound'( X, 'least_upper_bound'( Y, Z ) ), Y ) ) ] )
% 2.30/2.68 , clause( 29, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Z,
% 2.30/2.68 'least_upper_bound'( X, Y ) ), X ), 'greatest_lower_bound'( Z, X ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15572, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 2.30/2.68 Y, 'greatest_lower_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ) ] )
% 2.30/2.68 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 2.30/2.68 , X ) ) ] )
% 2.30/2.68 , 0, clause( 15569, [ =( 'greatest_lower_bound'( X, Y ),
% 2.30/2.68 'greatest_lower_bound'( 'greatest_lower_bound'( X, 'least_upper_bound'( Y
% 2.30/2.68 , Z ) ), Y ) ) ] )
% 2.30/2.68 , 0, 4, substitution( 0, [ :=( X, 'greatest_lower_bound'( X,
% 2.30/2.68 'least_upper_bound'( Y, Z ) ) ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 2.30/2.68 , X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15585, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 2.30/2.68 'greatest_lower_bound'( Y, X ), 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.30/2.68 , clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z )
% 2.30/2.68 ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 2.30/2.68 , 0, clause( 15572, [ =( 'greatest_lower_bound'( X, Y ),
% 2.30/2.68 'greatest_lower_bound'( Y, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 2.30/2.68 Y, Z ) ) ) ) ] )
% 2.30/2.68 , 0, 4, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z,
% 2.30/2.68 'least_upper_bound'( Y, Z ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y
% 2.30/2.68 ), :=( Z, Z )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15586, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Y, X )
% 2.30/2.68 , 'least_upper_bound'( Y, Z ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.30/2.68 , clause( 15585, [ =( 'greatest_lower_bound'( X, Y ),
% 2.30/2.68 'greatest_lower_bound'( 'greatest_lower_bound'( Y, X ),
% 2.30/2.68 'least_upper_bound'( Y, Z ) ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 subsumption(
% 2.30/2.68 clause( 211, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Y, X ),
% 2.30/2.68 'least_upper_bound'( Y, Z ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.30/2.68 , clause( 15586, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Y, X
% 2.30/2.68 ), 'least_upper_bound'( Y, Z ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.30/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.30/2.68 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15587, [ =( multiply( X, Y ), multiply( inverse( inverse( X ) ), Y
% 2.30/2.68 ) ) ] )
% 2.30/2.68 , clause( 174, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 2.30/2.68 ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15590, [ =( multiply( X, identity ), X ) ] )
% 2.30/2.68 , clause( 168, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 2.30/2.68 , 0, clause( 15587, [ =( multiply( X, Y ), multiply( inverse( inverse( X )
% 2.30/2.68 ), Y ) ) ] )
% 2.30/2.68 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 2.30/2.68 :=( Y, identity )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 subsumption(
% 2.30/2.68 clause( 388, [ =( multiply( X, identity ), X ) ] )
% 2.30/2.68 , clause( 15590, [ =( multiply( X, identity ), X ) ] )
% 2.30/2.68 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15595, [ =( X, multiply( X, identity ) ) ] )
% 2.30/2.68 , clause( 388, [ =( multiply( X, identity ), X ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, X )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15598, [ =( inverse( inverse( X ) ), multiply( X, identity ) ) ] )
% 2.30/2.68 , clause( 174, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 2.30/2.68 ) ) ] )
% 2.30/2.68 , 0, clause( 15595, [ =( X, multiply( X, identity ) ) ] )
% 2.30/2.68 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, identity )] ), substitution(
% 2.30/2.68 1, [ :=( X, inverse( inverse( X ) ) )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15599, [ =( inverse( inverse( X ) ), X ) ] )
% 2.30/2.68 , clause( 388, [ =( multiply( X, identity ), X ) ] )
% 2.30/2.68 , 0, clause( 15598, [ =( inverse( inverse( X ) ), multiply( X, identity ) )
% 2.30/2.68 ] )
% 2.30/2.68 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 2.30/2.68 ).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 subsumption(
% 2.30/2.68 clause( 396, [ =( inverse( inverse( X ) ), X ) ] )
% 2.30/2.68 , clause( 15599, [ =( inverse( inverse( X ) ), X ) ] )
% 2.30/2.68 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 eqswap(
% 2.30/2.68 clause( 15602, [ =( multiply( X, identity ), multiply( multiply( X, inverse(
% 2.30/2.68 Y ) ), Y ) ) ] )
% 2.30/2.68 , clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 2.30/2.68 , identity ) ) ] )
% 2.30/2.68 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 paramod(
% 2.30/2.68 clause( 15604, [ =( multiply( X, identity ), multiply( multiply( X, Y ),
% 2.33/2.68 inverse( Y ) ) ) ] )
% 2.33/2.68 , clause( 396, [ =( inverse( inverse( X ) ), X ) ] )
% 2.33/2.68 , 0, clause( 15602, [ =( multiply( X, identity ), multiply( multiply( X,
% 2.33/2.68 inverse( Y ) ), Y ) ) ] )
% 2.33/2.68 , 0, 7, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 2.33/2.68 :=( Y, inverse( Y ) )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15605, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 2.33/2.68 , clause( 388, [ =( multiply( X, identity ), X ) ] )
% 2.33/2.68 , 0, clause( 15604, [ =( multiply( X, identity ), multiply( multiply( X, Y
% 2.33/2.68 ), inverse( Y ) ) ) ] )
% 2.33/2.68 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 2.33/2.68 :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15606, [ =( multiply( multiply( X, Y ), inverse( Y ) ), X ) ] )
% 2.33/2.68 , clause( 15605, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 399, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 2.33/2.68 , clause( 15606, [ =( multiply( multiply( X, Y ), inverse( Y ) ), X ) ] )
% 2.33/2.68 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 2.33/2.68 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15608, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 2.33/2.68 , clause( 399, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15613, [ =( multiply( inverse( multiply( X, Y ) ), X ), multiply(
% 2.33/2.68 identity, inverse( Y ) ) ) ] )
% 2.33/2.68 , clause( 20, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ), Y
% 2.33/2.68 ), identity ) ] )
% 2.33/2.68 , 0, clause( 15608, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ]
% 2.33/2.68 )
% 2.33/2.68 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.33/2.68 :=( X, multiply( inverse( multiply( X, Y ) ), X ) ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15614, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 2.33/2.68 ) ) ] )
% 2.33/2.68 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.33/2.68 , 0, clause( 15613, [ =( multiply( inverse( multiply( X, Y ) ), X ),
% 2.33/2.68 multiply( identity, inverse( Y ) ) ) ] )
% 2.33/2.68 , 0, 7, substitution( 0, [ :=( X, inverse( Y ) )] ), substitution( 1, [
% 2.33/2.68 :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 416, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y )
% 2.33/2.68 ) ] )
% 2.33/2.68 , clause( 15614, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse(
% 2.33/2.68 Y ) ) ] )
% 2.33/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.33/2.68 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15617, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 2.33/2.68 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 2.33/2.68 , clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 2.33/2.68 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15619, [ =( multiply( 'least_upper_bound'( X, multiply( Y, Z ) ),
% 2.33/2.68 inverse( Z ) ), 'least_upper_bound'( multiply( X, inverse( Z ) ), Y ) ) ]
% 2.33/2.68 )
% 2.33/2.68 , clause( 399, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 2.33/2.68 , 0, clause( 15617, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 2.33/2.68 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 2.33/2.68 , 0, 14, substitution( 0, [ :=( X, Z ), :=( Y, Y )] ), substitution( 1, [
% 2.33/2.68 :=( X, X ), :=( Y, inverse( Z ) ), :=( Z, multiply( Y, Z ) )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 420, [ =( multiply( 'least_upper_bound'( Z, multiply( X, Y ) ),
% 2.33/2.68 inverse( Y ) ), 'least_upper_bound'( multiply( Z, inverse( Y ) ), X ) ) ]
% 2.33/2.68 )
% 2.33/2.68 , clause( 15619, [ =( multiply( 'least_upper_bound'( X, multiply( Y, Z ) )
% 2.33/2.68 , inverse( Z ) ), 'least_upper_bound'( multiply( X, inverse( Z ) ), Y ) )
% 2.33/2.68 ] )
% 2.33/2.68 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 2.33/2.68 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15622, [ =( inverse( Y ), multiply( inverse( multiply( X, Y ) ), X
% 2.33/2.68 ) ) ] )
% 2.33/2.68 , clause( 416, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 2.33/2.68 ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15626, [ =( inverse( X ), multiply( inverse( inverse( Y ) ),
% 2.33/2.68 inverse( multiply( X, Y ) ) ) ) ] )
% 2.33/2.68 , clause( 416, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 2.33/2.68 ) ) ] )
% 2.33/2.68 , 0, clause( 15622, [ =( inverse( Y ), multiply( inverse( multiply( X, Y )
% 2.33/2.68 ), X ) ) ] )
% 2.33/2.68 , 0, 5, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.33/2.68 :=( X, inverse( multiply( X, Y ) ) ), :=( Y, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15627, [ =( inverse( X ), multiply( Y, inverse( multiply( X, Y ) )
% 2.33/2.68 ) ) ] )
% 2.33/2.68 , clause( 174, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 2.33/2.68 ) ) ] )
% 2.33/2.68 , 0, clause( 15626, [ =( inverse( X ), multiply( inverse( inverse( Y ) ),
% 2.33/2.68 inverse( multiply( X, Y ) ) ) ) ] )
% 2.33/2.68 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, inverse( multiply( X, Y ) ) )] )
% 2.33/2.68 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15628, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X
% 2.33/2.68 ) ) ] )
% 2.33/2.68 , clause( 15627, [ =( inverse( X ), multiply( Y, inverse( multiply( X, Y )
% 2.33/2.68 ) ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 422, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X )
% 2.33/2.68 ) ] )
% 2.33/2.68 , clause( 15628, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse(
% 2.33/2.68 X ) ) ] )
% 2.33/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.33/2.68 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15630, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 2.33/2.68 , clause( 399, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15633, [ =( inverse( multiply( X, Y ) ), multiply( inverse( Y ),
% 2.33/2.68 inverse( X ) ) ) ] )
% 2.33/2.68 , clause( 416, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 2.33/2.68 ) ) ] )
% 2.33/2.68 , 0, clause( 15630, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ]
% 2.33/2.68 )
% 2.33/2.68 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.33/2.68 :=( X, inverse( multiply( X, Y ) ) ), :=( Y, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15634, [ =( multiply( inverse( Y ), inverse( X ) ), inverse(
% 2.33/2.68 multiply( X, Y ) ) ) ] )
% 2.33/2.68 , clause( 15633, [ =( inverse( multiply( X, Y ) ), multiply( inverse( Y ),
% 2.33/2.68 inverse( X ) ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 423, [ =( multiply( inverse( Y ), inverse( X ) ), inverse( multiply(
% 2.33/2.68 X, Y ) ) ) ] )
% 2.33/2.68 , clause( 15634, [ =( multiply( inverse( Y ), inverse( X ) ), inverse(
% 2.33/2.68 multiply( X, Y ) ) ) ] )
% 2.33/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.33/2.68 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15636, [ =( multiply( X, identity ), multiply( multiply( X, inverse(
% 2.33/2.68 Y ) ), Y ) ) ] )
% 2.33/2.68 , clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 2.33/2.68 , identity ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15642, [ =( multiply( inverse( multiply( inverse( X ), Y ) ),
% 2.33/2.68 identity ), multiply( inverse( Y ), X ) ) ] )
% 2.33/2.68 , clause( 416, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 2.33/2.68 ) ) ] )
% 2.33/2.68 , 0, clause( 15636, [ =( multiply( X, identity ), multiply( multiply( X,
% 2.33/2.68 inverse( Y ) ), Y ) ) ] )
% 2.33/2.68 , 0, 9, substitution( 0, [ :=( X, inverse( X ) ), :=( Y, Y )] ),
% 2.33/2.68 substitution( 1, [ :=( X, inverse( multiply( inverse( X ), Y ) ) ), :=( Y
% 2.33/2.68 , X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15643, [ =( inverse( multiply( inverse( X ), Y ) ), multiply(
% 2.33/2.68 inverse( Y ), X ) ) ] )
% 2.33/2.68 , clause( 388, [ =( multiply( X, identity ), X ) ] )
% 2.33/2.68 , 0, clause( 15642, [ =( multiply( inverse( multiply( inverse( X ), Y ) ),
% 2.33/2.68 identity ), multiply( inverse( Y ), X ) ) ] )
% 2.33/2.68 , 0, 1, substitution( 0, [ :=( X, inverse( multiply( inverse( X ), Y ) ) )] )
% 2.33/2.68 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 424, [ =( inverse( multiply( inverse( X ), Y ) ), multiply( inverse(
% 2.33/2.68 Y ), X ) ) ] )
% 2.33/2.68 , clause( 15643, [ =( inverse( multiply( inverse( X ), Y ) ), multiply(
% 2.33/2.68 inverse( Y ), X ) ) ] )
% 2.33/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.33/2.68 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15646, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X ) )
% 2.33/2.68 ) ) ] )
% 2.33/2.68 , clause( 422, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X
% 2.33/2.68 ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15651, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 2.33/2.68 inverse( multiply( X, identity ) ) ) ) ] )
% 2.33/2.68 , clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 2.33/2.68 , identity ) ) ] )
% 2.33/2.68 , 0, clause( 15646, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X
% 2.33/2.68 ) ) ) ) ] )
% 2.33/2.68 , 0, 9, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 2.33/2.68 :=( X, Y ), :=( Y, multiply( X, inverse( Y ) ) )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15652, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 2.33/2.68 inverse( X ) ) ) ] )
% 2.33/2.68 , clause( 388, [ =( multiply( X, identity ), X ) ] )
% 2.33/2.68 , 0, clause( 15651, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply(
% 2.33/2.68 Y, inverse( multiply( X, identity ) ) ) ) ] )
% 2.33/2.68 , 0, 9, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 2.33/2.68 :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 434, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 2.33/2.68 inverse( X ) ) ) ] )
% 2.33/2.68 , clause( 15652, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 2.33/2.68 inverse( X ) ) ) ] )
% 2.33/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.33/2.68 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15655, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 2.33/2.68 'least_upper_bound'( X, Y ), 'least_upper_bound'( 'least_upper_bound'( Z
% 2.33/2.68 , X ), Y ) ) ) ] )
% 2.33/2.68 , clause( 52, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, Z ),
% 2.33/2.68 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ),
% 2.33/2.68 'least_upper_bound'( Y, Z ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15658, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 2.33/2.68 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 2.33/2.68 , clause( 45, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 2.33/2.68 'least_upper_bound'( X, Y ) ) ] )
% 2.33/2.68 , 0, clause( 15655, [ =( 'least_upper_bound'( X, Y ),
% 2.33/2.68 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 2.33/2.68 'least_upper_bound'( Z, X ), Y ) ) ) ] )
% 2.33/2.68 , 0, 8, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 2.33/2.68 :=( X, X ), :=( Y, Y ), :=( Z, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15664, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 2.33/2.68 'least_upper_bound'( Y, X ) ), 'least_upper_bound'( X, Y ) ) ] )
% 2.33/2.68 , clause( 15658, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 2.33/2.68 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 470, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 2.33/2.68 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( Y, X ) ) ] )
% 2.33/2.68 , clause( 15664, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 2.33/2.68 'least_upper_bound'( Y, X ) ), 'least_upper_bound'( X, Y ) ) ] )
% 2.33/2.68 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 2.33/2.68 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15667, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( X, Y )
% 2.33/2.68 , X ) ) ] )
% 2.33/2.68 , clause( 48, [ =( 'least_upper_bound'( 'greatest_lower_bound'( X, Y ), X )
% 2.33/2.68 , X ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15670, [ =( 'greatest_lower_bound'( X, Y ), 'least_upper_bound'(
% 2.33/2.68 'greatest_lower_bound'( Y, X ), 'greatest_lower_bound'( X, Y ) ) ) ] )
% 2.33/2.68 , clause( 211, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Y, X )
% 2.33/2.68 , 'least_upper_bound'( Y, Z ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.33/2.68 , 0, clause( 15667, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( X
% 2.33/2.68 , Y ), X ) ) ] )
% 2.33/2.68 , 0, 5, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 2.33/2.68 substitution( 1, [ :=( X, 'greatest_lower_bound'( X, Y ) ), :=( Y,
% 2.33/2.68 'least_upper_bound'( X, Z ) )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15671, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ),
% 2.33/2.68 'greatest_lower_bound'( X, Y ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.33/2.68 , clause( 15670, [ =( 'greatest_lower_bound'( X, Y ), 'least_upper_bound'(
% 2.33/2.68 'greatest_lower_bound'( Y, X ), 'greatest_lower_bound'( X, Y ) ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 618, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ),
% 2.33/2.68 'greatest_lower_bound'( X, Y ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.33/2.68 , clause( 15671, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ),
% 2.33/2.68 'greatest_lower_bound'( X, Y ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.33/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.33/2.68 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15673, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) ),
% 2.33/2.68 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 2.33/2.68 , clause( 74, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y
% 2.33/2.68 ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15675, [ =( multiply( inverse( d ), d ), 'least_upper_bound'(
% 2.33/2.68 identity, multiply( inverse( d ), c ) ) ) ] )
% 2.33/2.68 , clause( 46, [ =( 'least_upper_bound'( d, c ), d ) ] )
% 2.33/2.68 , 0, clause( 15673, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y
% 2.33/2.68 ) ), 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 2.33/2.68 , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, d ), :=( Y, c )] )
% 2.33/2.68 ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15676, [ =( identity, 'least_upper_bound'( identity, multiply(
% 2.33/2.68 inverse( d ), c ) ) ) ] )
% 2.33/2.68 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.33/2.68 , 0, clause( 15675, [ =( multiply( inverse( d ), d ), 'least_upper_bound'(
% 2.33/2.68 identity, multiply( inverse( d ), c ) ) ) ] )
% 2.33/2.68 , 0, 1, substitution( 0, [ :=( X, d )] ), substitution( 1, [] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15677, [ =( 'least_upper_bound'( identity, multiply( inverse( d ),
% 2.33/2.68 c ) ), identity ) ] )
% 2.33/2.68 , clause( 15676, [ =( identity, 'least_upper_bound'( identity, multiply(
% 2.33/2.68 inverse( d ), c ) ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 1230, [ =( 'least_upper_bound'( identity, multiply( inverse( d ), c
% 2.33/2.68 ) ), identity ) ] )
% 2.33/2.68 , clause( 15677, [ =( 'least_upper_bound'( identity, multiply( inverse( d )
% 2.33/2.68 , c ) ), identity ) ] )
% 2.33/2.68 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15679, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) ),
% 2.33/2.68 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 2.33/2.68 , clause( 74, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y
% 2.33/2.68 ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15681, [ =( multiply( inverse( X ), X ), 'least_upper_bound'(
% 2.33/2.68 identity, multiply( inverse( X ), 'greatest_lower_bound'( X, Y ) ) ) ) ]
% 2.33/2.68 )
% 2.33/2.68 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 2.33/2.68 , X ) ] )
% 2.33/2.68 , 0, clause( 15679, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y
% 2.33/2.68 ) ), 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 2.33/2.68 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.33/2.68 :=( X, X ), :=( Y, 'greatest_lower_bound'( X, Y ) )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15682, [ =( identity, 'least_upper_bound'( identity, multiply(
% 2.33/2.68 inverse( X ), 'greatest_lower_bound'( X, Y ) ) ) ) ] )
% 2.33/2.68 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 2.33/2.68 , 0, clause( 15681, [ =( multiply( inverse( X ), X ), 'least_upper_bound'(
% 2.33/2.68 identity, multiply( inverse( X ), 'greatest_lower_bound'( X, Y ) ) ) ) ]
% 2.33/2.68 )
% 2.33/2.68 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 2.33/2.68 :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15683, [ =( 'least_upper_bound'( identity, multiply( inverse( X ),
% 2.33/2.68 'greatest_lower_bound'( X, Y ) ) ), identity ) ] )
% 2.33/2.68 , clause( 15682, [ =( identity, 'least_upper_bound'( identity, multiply(
% 2.33/2.68 inverse( X ), 'greatest_lower_bound'( X, Y ) ) ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 1231, [ =( 'least_upper_bound'( identity, multiply( inverse( X ),
% 2.33/2.68 'greatest_lower_bound'( X, Y ) ) ), identity ) ] )
% 2.33/2.68 , clause( 15683, [ =( 'least_upper_bound'( identity, multiply( inverse( X )
% 2.33/2.68 , 'greatest_lower_bound'( X, Y ) ) ), identity ) ] )
% 2.33/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.33/2.68 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15685, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 2.33/2.68 ) ) ) ] )
% 2.33/2.68 , clause( 24, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) )
% 2.33/2.68 , X ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15686, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 2.33/2.68 inverse( X ), 'least_upper_bound'( Y, X ) ) ) ) ] )
% 2.33/2.68 , clause( 75, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ),
% 2.33/2.68 identity ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 2.33/2.68 , 0, clause( 15685, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 2.33/2.68 Y, X ) ) ) ] )
% 2.33/2.68 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 2.33/2.68 :=( X, identity ), :=( Y, multiply( inverse( X ), Y ) )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15687, [ =( 'greatest_lower_bound'( identity, multiply( inverse( X
% 2.33/2.68 ), 'least_upper_bound'( Y, X ) ) ), identity ) ] )
% 2.33/2.68 , clause( 15686, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 2.33/2.68 inverse( X ), 'least_upper_bound'( Y, X ) ) ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 1318, [ =( 'greatest_lower_bound'( identity, multiply( inverse( X )
% 2.33/2.68 , 'least_upper_bound'( Y, X ) ) ), identity ) ] )
% 2.33/2.68 , clause( 15687, [ =( 'greatest_lower_bound'( identity, multiply( inverse(
% 2.33/2.68 X ), 'least_upper_bound'( Y, X ) ) ), identity ) ] )
% 2.33/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.33/2.68 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15689, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 2.33/2.68 inverse( X ), 'least_upper_bound'( Y, X ) ) ) ) ] )
% 2.33/2.68 , clause( 1318, [ =( 'greatest_lower_bound'( identity, multiply( inverse( X
% 2.33/2.68 ), 'least_upper_bound'( Y, X ) ) ), identity ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15692, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 2.33/2.68 inverse( multiply( inverse( d ), c ) ), identity ) ) ) ] )
% 2.33/2.68 , clause( 1230, [ =( 'least_upper_bound'( identity, multiply( inverse( d )
% 2.33/2.68 , c ) ), identity ) ] )
% 2.33/2.68 , 0, clause( 15689, [ =( identity, 'greatest_lower_bound'( identity,
% 2.33/2.68 multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ) ] )
% 2.33/2.68 , 0, 10, substitution( 0, [] ), substitution( 1, [ :=( X, multiply( inverse(
% 2.33/2.68 d ), c ) ), :=( Y, identity )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15693, [ =( identity, 'greatest_lower_bound'( identity, inverse(
% 2.33/2.68 multiply( inverse( d ), c ) ) ) ) ] )
% 2.33/2.68 , clause( 388, [ =( multiply( X, identity ), X ) ] )
% 2.33/2.68 , 0, clause( 15692, [ =( identity, 'greatest_lower_bound'( identity,
% 2.33/2.68 multiply( inverse( multiply( inverse( d ), c ) ), identity ) ) ) ] )
% 2.33/2.68 , 0, 4, substitution( 0, [ :=( X, inverse( multiply( inverse( d ), c ) ) )] )
% 2.33/2.68 , substitution( 1, [] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15694, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 2.33/2.68 inverse( c ), d ) ) ) ] )
% 2.33/2.68 , clause( 424, [ =( inverse( multiply( inverse( X ), Y ) ), multiply(
% 2.33/2.68 inverse( Y ), X ) ) ] )
% 2.33/2.68 , 0, clause( 15693, [ =( identity, 'greatest_lower_bound'( identity,
% 2.33/2.68 inverse( multiply( inverse( d ), c ) ) ) ) ] )
% 2.33/2.68 , 0, 4, substitution( 0, [ :=( X, d ), :=( Y, c )] ), substitution( 1, [] )
% 2.33/2.68 ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15695, [ =( 'greatest_lower_bound'( identity, multiply( inverse( c
% 2.33/2.68 ), d ) ), identity ) ] )
% 2.33/2.68 , clause( 15694, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 2.33/2.68 inverse( c ), d ) ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 1489, [ =( 'greatest_lower_bound'( identity, multiply( inverse( c )
% 2.33/2.68 , d ) ), identity ) ] )
% 2.33/2.68 , clause( 15695, [ =( 'greatest_lower_bound'( identity, multiply( inverse(
% 2.33/2.68 c ), d ) ), identity ) ] )
% 2.33/2.68 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15697, [ =( 'greatest_lower_bound'( Y, X ), 'least_upper_bound'(
% 2.33/2.68 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, X ) ) ) ] )
% 2.33/2.68 , clause( 618, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ),
% 2.33/2.68 'greatest_lower_bound'( X, Y ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15701, [ =( 'greatest_lower_bound'( multiply( inverse( c ), d ),
% 2.33/2.68 identity ), 'least_upper_bound'( identity, 'greatest_lower_bound'(
% 2.33/2.68 multiply( inverse( c ), d ), identity ) ) ) ] )
% 2.33/2.68 , clause( 1489, [ =( 'greatest_lower_bound'( identity, multiply( inverse( c
% 2.33/2.68 ), d ) ), identity ) ] )
% 2.33/2.68 , 0, clause( 15697, [ =( 'greatest_lower_bound'( Y, X ),
% 2.33/2.68 'least_upper_bound'( 'greatest_lower_bound'( X, Y ),
% 2.33/2.68 'greatest_lower_bound'( Y, X ) ) ) ] )
% 2.33/2.68 , 0, 8, substitution( 0, [] ), substitution( 1, [ :=( X, identity ), :=( Y
% 2.33/2.68 , multiply( inverse( c ), d ) )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15703, [ =( 'greatest_lower_bound'( multiply( inverse( c ), d ),
% 2.33/2.68 identity ), identity ) ] )
% 2.33/2.68 , clause( 47, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) )
% 2.33/2.68 , X ) ] )
% 2.33/2.68 , 0, clause( 15701, [ =( 'greatest_lower_bound'( multiply( inverse( c ), d
% 2.33/2.68 ), identity ), 'least_upper_bound'( identity, 'greatest_lower_bound'(
% 2.33/2.68 multiply( inverse( c ), d ), identity ) ) ) ] )
% 2.33/2.68 , 0, 7, substitution( 0, [ :=( X, identity ), :=( Y, multiply( inverse( c )
% 2.33/2.68 , d ) )] ), substitution( 1, [] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 1584, [ =( 'greatest_lower_bound'( multiply( inverse( c ), d ),
% 2.33/2.68 identity ), identity ) ] )
% 2.33/2.68 , clause( 15703, [ =( 'greatest_lower_bound'( multiply( inverse( c ), d ),
% 2.33/2.68 identity ), identity ) ] )
% 2.33/2.68 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15706, [ =( multiply( 'greatest_lower_bound'( X, identity ), Y ),
% 2.33/2.68 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ] )
% 2.33/2.68 , clause( 132, [ =( 'greatest_lower_bound'( multiply( Y, X ), X ), multiply(
% 2.33/2.68 'greatest_lower_bound'( Y, identity ), X ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15708, [ =( multiply( identity, X ), 'greatest_lower_bound'(
% 2.33/2.68 multiply( multiply( inverse( c ), d ), X ), X ) ) ] )
% 2.33/2.68 , clause( 1584, [ =( 'greatest_lower_bound'( multiply( inverse( c ), d ),
% 2.33/2.68 identity ), identity ) ] )
% 2.33/2.68 , 0, clause( 15706, [ =( multiply( 'greatest_lower_bound'( X, identity ), Y
% 2.33/2.68 ), 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ] )
% 2.33/2.68 , 0, 2, substitution( 0, [] ), substitution( 1, [ :=( X, multiply( inverse(
% 2.33/2.68 c ), d ) ), :=( Y, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15709, [ =( X, 'greatest_lower_bound'( multiply( multiply( inverse(
% 2.33/2.68 c ), d ), X ), X ) ) ] )
% 2.33/2.68 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.33/2.68 , 0, clause( 15708, [ =( multiply( identity, X ), 'greatest_lower_bound'(
% 2.33/2.68 multiply( multiply( inverse( c ), d ), X ), X ) ) ] )
% 2.33/2.68 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 2.33/2.68 ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15710, [ =( 'greatest_lower_bound'( multiply( multiply( inverse( c
% 2.33/2.68 ), d ), X ), X ), X ) ] )
% 2.33/2.68 , clause( 15709, [ =( X, 'greatest_lower_bound'( multiply( multiply(
% 2.33/2.68 inverse( c ), d ), X ), X ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 3207, [ =( 'greatest_lower_bound'( multiply( multiply( inverse( c )
% 2.33/2.68 , d ), X ), X ), X ) ] )
% 2.33/2.68 , clause( 15710, [ =( 'greatest_lower_bound'( multiply( multiply( inverse(
% 2.33/2.68 c ), d ), X ), X ), X ) ] )
% 2.33/2.68 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15712, [ =( X, 'greatest_lower_bound'( multiply( multiply( inverse(
% 2.33/2.68 c ), d ), X ), X ) ) ] )
% 2.33/2.68 , clause( 3207, [ =( 'greatest_lower_bound'( multiply( multiply( inverse( c
% 2.33/2.68 ), d ), X ), X ), X ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15713, [ =( inverse( d ), 'greatest_lower_bound'( inverse( c ),
% 2.33/2.68 inverse( d ) ) ) ] )
% 2.33/2.68 , clause( 399, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 2.33/2.68 , 0, clause( 15712, [ =( X, 'greatest_lower_bound'( multiply( multiply(
% 2.33/2.68 inverse( c ), d ), X ), X ) ) ] )
% 2.33/2.68 , 0, 4, substitution( 0, [ :=( X, d ), :=( Y, inverse( c ) )] ),
% 2.33/2.68 substitution( 1, [ :=( X, inverse( d ) )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15714, [ =( 'greatest_lower_bound'( inverse( c ), inverse( d ) ),
% 2.33/2.68 inverse( d ) ) ] )
% 2.33/2.68 , clause( 15713, [ =( inverse( d ), 'greatest_lower_bound'( inverse( c ),
% 2.33/2.68 inverse( d ) ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 3278, [ =( 'greatest_lower_bound'( inverse( c ), inverse( d ) ),
% 2.33/2.68 inverse( d ) ) ] )
% 2.33/2.68 , clause( 15714, [ =( 'greatest_lower_bound'( inverse( c ), inverse( d ) )
% 2.33/2.68 , inverse( d ) ) ] )
% 2.33/2.68 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15716, [ =( identity, 'least_upper_bound'( identity, multiply(
% 2.33/2.68 inverse( X ), 'greatest_lower_bound'( X, Y ) ) ) ) ] )
% 2.33/2.68 , clause( 1231, [ =( 'least_upper_bound'( identity, multiply( inverse( X )
% 2.33/2.68 , 'greatest_lower_bound'( X, Y ) ) ), identity ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15719, [ =( identity, 'least_upper_bound'( identity, multiply(
% 2.33/2.68 inverse( inverse( c ) ), inverse( d ) ) ) ) ] )
% 2.33/2.68 , clause( 3278, [ =( 'greatest_lower_bound'( inverse( c ), inverse( d ) ),
% 2.33/2.68 inverse( d ) ) ] )
% 2.33/2.68 , 0, clause( 15716, [ =( identity, 'least_upper_bound'( identity, multiply(
% 2.33/2.68 inverse( X ), 'greatest_lower_bound'( X, Y ) ) ) ) ] )
% 2.33/2.68 , 0, 8, substitution( 0, [] ), substitution( 1, [ :=( X, inverse( c ) ),
% 2.33/2.68 :=( Y, inverse( d ) )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15720, [ =( identity, 'least_upper_bound'( identity, inverse(
% 2.33/2.68 multiply( d, inverse( c ) ) ) ) ) ] )
% 2.33/2.68 , clause( 423, [ =( multiply( inverse( Y ), inverse( X ) ), inverse(
% 2.33/2.68 multiply( X, Y ) ) ) ] )
% 2.33/2.68 , 0, clause( 15719, [ =( identity, 'least_upper_bound'( identity, multiply(
% 2.33/2.68 inverse( inverse( c ) ), inverse( d ) ) ) ) ] )
% 2.33/2.68 , 0, 4, substitution( 0, [ :=( X, d ), :=( Y, inverse( c ) )] ),
% 2.33/2.68 substitution( 1, [] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15721, [ =( identity, 'least_upper_bound'( identity, multiply( c,
% 2.33/2.68 inverse( d ) ) ) ) ] )
% 2.33/2.68 , clause( 434, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 2.33/2.68 inverse( X ) ) ) ] )
% 2.33/2.68 , 0, clause( 15720, [ =( identity, 'least_upper_bound'( identity, inverse(
% 2.33/2.68 multiply( d, inverse( c ) ) ) ) ) ] )
% 2.33/2.68 , 0, 4, substitution( 0, [ :=( X, d ), :=( Y, c )] ), substitution( 1, [] )
% 2.33/2.68 ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15722, [ =( 'least_upper_bound'( identity, multiply( c, inverse( d
% 2.33/2.68 ) ) ), identity ) ] )
% 2.33/2.68 , clause( 15721, [ =( identity, 'least_upper_bound'( identity, multiply( c
% 2.33/2.68 , inverse( d ) ) ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 3290, [ =( 'least_upper_bound'( identity, multiply( c, inverse( d )
% 2.33/2.68 ) ), identity ) ] )
% 2.33/2.68 , clause( 15722, [ =( 'least_upper_bound'( identity, multiply( c, inverse(
% 2.33/2.68 d ) ) ), identity ) ] )
% 2.33/2.68 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15724, [ =( multiply( 'least_upper_bound'( identity, Y ), X ),
% 2.33/2.68 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 2.33/2.68 , clause( 109, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 2.33/2.68 'least_upper_bound'( identity, Y ), X ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15726, [ =( multiply( identity, X ), 'least_upper_bound'( X,
% 2.33/2.68 multiply( multiply( c, inverse( d ) ), X ) ) ) ] )
% 2.33/2.68 , clause( 3290, [ =( 'least_upper_bound'( identity, multiply( c, inverse( d
% 2.33/2.68 ) ) ), identity ) ] )
% 2.33/2.68 , 0, clause( 15724, [ =( multiply( 'least_upper_bound'( identity, Y ), X )
% 2.33/2.68 , 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 2.33/2.68 , 0, 2, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y,
% 2.33/2.68 multiply( c, inverse( d ) ) )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15727, [ =( X, 'least_upper_bound'( X, multiply( multiply( c,
% 2.33/2.68 inverse( d ) ), X ) ) ) ] )
% 2.33/2.68 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 2.33/2.68 , 0, clause( 15726, [ =( multiply( identity, X ), 'least_upper_bound'( X,
% 2.33/2.68 multiply( multiply( c, inverse( d ) ), X ) ) ) ] )
% 2.33/2.68 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 2.33/2.68 ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15728, [ =( 'least_upper_bound'( X, multiply( multiply( c, inverse(
% 2.33/2.68 d ) ), X ) ), X ) ] )
% 2.33/2.68 , clause( 15727, [ =( X, 'least_upper_bound'( X, multiply( multiply( c,
% 2.33/2.68 inverse( d ) ), X ) ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 3356, [ =( 'least_upper_bound'( X, multiply( multiply( c, inverse(
% 2.33/2.68 d ) ), X ) ), X ) ] )
% 2.33/2.68 , clause( 15728, [ =( 'least_upper_bound'( X, multiply( multiply( c,
% 2.33/2.68 inverse( d ) ), X ) ), X ) ] )
% 2.33/2.68 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15730, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 2.33/2.68 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 2.33/2.68 , clause( 177, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 2.33/2.68 , 'least_upper_bound'( identity, Y ) ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15737, [ =( multiply( X, identity ), 'least_upper_bound'( X,
% 2.33/2.68 multiply( X, multiply( multiply( c, inverse( d ) ), identity ) ) ) ) ] )
% 2.33/2.68 , clause( 3356, [ =( 'least_upper_bound'( X, multiply( multiply( c, inverse(
% 2.33/2.68 d ) ), X ) ), X ) ] )
% 2.33/2.68 , 0, clause( 15730, [ =( multiply( X, 'least_upper_bound'( identity, Y ) )
% 2.33/2.68 , 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 2.33/2.68 , 0, 3, substitution( 0, [ :=( X, identity )] ), substitution( 1, [ :=( X,
% 2.33/2.68 X ), :=( Y, multiply( multiply( c, inverse( d ) ), identity ) )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15739, [ =( multiply( X, identity ), 'least_upper_bound'( X,
% 2.33/2.68 multiply( multiply( X, multiply( c, inverse( d ) ) ), identity ) ) ) ] )
% 2.33/2.68 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 2.33/2.68 ), Z ) ) ] )
% 2.33/2.68 , 0, clause( 15737, [ =( multiply( X, identity ), 'least_upper_bound'( X,
% 2.33/2.68 multiply( X, multiply( multiply( c, inverse( d ) ), identity ) ) ) ) ] )
% 2.33/2.68 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, multiply( c, inverse( d ) ) )
% 2.33/2.68 , :=( Z, identity )] ), substitution( 1, [ :=( X, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15742, [ =( multiply( X, identity ), 'least_upper_bound'( X,
% 2.33/2.68 multiply( X, multiply( c, inverse( d ) ) ) ) ) ] )
% 2.33/2.68 , clause( 388, [ =( multiply( X, identity ), X ) ] )
% 2.33/2.68 , 0, clause( 15739, [ =( multiply( X, identity ), 'least_upper_bound'( X,
% 2.33/2.68 multiply( multiply( X, multiply( c, inverse( d ) ) ), identity ) ) ) ] )
% 2.33/2.68 , 0, 6, substitution( 0, [ :=( X, multiply( X, multiply( c, inverse( d ) )
% 2.33/2.68 ) )] ), substitution( 1, [ :=( X, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15744, [ =( multiply( X, identity ), 'least_upper_bound'( X,
% 2.33/2.68 multiply( multiply( X, c ), inverse( d ) ) ) ) ] )
% 2.33/2.68 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 2.33/2.68 ), Z ) ) ] )
% 2.33/2.68 , 0, clause( 15742, [ =( multiply( X, identity ), 'least_upper_bound'( X,
% 2.33/2.68 multiply( X, multiply( c, inverse( d ) ) ) ) ) ] )
% 2.33/2.68 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, c ), :=( Z, inverse( d ) )] )
% 2.33/2.68 , substitution( 1, [ :=( X, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15745, [ =( X, 'least_upper_bound'( X, multiply( multiply( X, c ),
% 2.33/2.68 inverse( d ) ) ) ) ] )
% 2.33/2.68 , clause( 388, [ =( multiply( X, identity ), X ) ] )
% 2.33/2.68 , 0, clause( 15744, [ =( multiply( X, identity ), 'least_upper_bound'( X,
% 2.33/2.68 multiply( multiply( X, c ), inverse( d ) ) ) ) ] )
% 2.33/2.68 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 2.33/2.68 ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15746, [ =( 'least_upper_bound'( X, multiply( multiply( X, c ),
% 2.33/2.68 inverse( d ) ) ), X ) ] )
% 2.33/2.68 , clause( 15745, [ =( X, 'least_upper_bound'( X, multiply( multiply( X, c )
% 2.33/2.68 , inverse( d ) ) ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 4404, [ =( 'least_upper_bound'( X, multiply( multiply( X, c ),
% 2.33/2.68 inverse( d ) ) ), X ) ] )
% 2.33/2.68 , clause( 15746, [ =( 'least_upper_bound'( X, multiply( multiply( X, c ),
% 2.33/2.68 inverse( d ) ) ), X ) ] )
% 2.33/2.68 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15748, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 2.33/2.68 'least_upper_bound'( a, X ), b ) ) ] )
% 2.33/2.68 , clause( 158, [ =( 'least_upper_bound'( 'least_upper_bound'( a, X ), b ),
% 2.33/2.68 'least_upper_bound'( X, b ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15750, [ =( 'least_upper_bound'( multiply( multiply( a, c ),
% 2.33/2.68 inverse( d ) ), b ), 'least_upper_bound'( a, b ) ) ] )
% 2.33/2.68 , clause( 4404, [ =( 'least_upper_bound'( X, multiply( multiply( X, c ),
% 2.33/2.68 inverse( d ) ) ), X ) ] )
% 2.33/2.68 , 0, clause( 15748, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 2.33/2.68 'least_upper_bound'( a, X ), b ) ) ] )
% 2.33/2.68 , 0, 10, substitution( 0, [ :=( X, a )] ), substitution( 1, [ :=( X,
% 2.33/2.68 multiply( multiply( a, c ), inverse( d ) ) )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15751, [ =( 'least_upper_bound'( multiply( multiply( a, c ),
% 2.33/2.68 inverse( d ) ), b ), b ) ] )
% 2.33/2.68 , clause( 15, [ =( 'least_upper_bound'( a, b ), b ) ] )
% 2.33/2.68 , 0, clause( 15750, [ =( 'least_upper_bound'( multiply( multiply( a, c ),
% 2.33/2.68 inverse( d ) ), b ), 'least_upper_bound'( a, b ) ) ] )
% 2.33/2.68 , 0, 9, substitution( 0, [] ), substitution( 1, [] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 4516, [ =( 'least_upper_bound'( multiply( multiply( a, c ), inverse(
% 2.33/2.68 d ) ), b ), b ) ] )
% 2.33/2.68 , clause( 15751, [ =( 'least_upper_bound'( multiply( multiply( a, c ),
% 2.33/2.68 inverse( d ) ), b ), b ) ] )
% 2.33/2.68 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15754, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 2.33/2.68 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 2.33/2.68 , clause( 470, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 2.33/2.68 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( Y, X ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15758, [ =( 'least_upper_bound'( b, multiply( multiply( a, c ),
% 2.33/2.68 inverse( d ) ) ), 'greatest_lower_bound'( 'least_upper_bound'( b,
% 2.33/2.68 multiply( multiply( a, c ), inverse( d ) ) ), b ) ) ] )
% 2.33/2.68 , clause( 4516, [ =( 'least_upper_bound'( multiply( multiply( a, c ),
% 2.33/2.68 inverse( d ) ), b ), b ) ] )
% 2.33/2.68 , 0, clause( 15754, [ =( 'least_upper_bound'( X, Y ),
% 2.33/2.68 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 2.33/2.68 Y, X ) ) ) ] )
% 2.33/2.68 , 0, 18, substitution( 0, [] ), substitution( 1, [ :=( X, b ), :=( Y,
% 2.33/2.68 multiply( multiply( a, c ), inverse( d ) ) )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15760, [ =( 'least_upper_bound'( b, multiply( multiply( a, c ),
% 2.33/2.68 inverse( d ) ) ), b ) ] )
% 2.33/2.68 , clause( 23, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 2.33/2.68 , X ) ] )
% 2.33/2.68 , 0, clause( 15758, [ =( 'least_upper_bound'( b, multiply( multiply( a, c )
% 2.33/2.68 , inverse( d ) ) ), 'greatest_lower_bound'( 'least_upper_bound'( b,
% 2.33/2.68 multiply( multiply( a, c ), inverse( d ) ) ), b ) ) ] )
% 2.33/2.68 , 0, 9, substitution( 0, [ :=( X, b ), :=( Y, multiply( multiply( a, c ),
% 2.33/2.68 inverse( d ) ) )] ), substitution( 1, [] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 4625, [ =( 'least_upper_bound'( b, multiply( multiply( a, c ),
% 2.33/2.68 inverse( d ) ) ), b ) ] )
% 2.33/2.68 , clause( 15760, [ =( 'least_upper_bound'( b, multiply( multiply( a, c ),
% 2.33/2.68 inverse( d ) ) ), b ) ] )
% 2.33/2.68 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqswap(
% 2.33/2.68 clause( 15763, [ =( 'least_upper_bound'( multiply( X, inverse( Z ) ), Y ),
% 2.33/2.68 multiply( 'least_upper_bound'( X, multiply( Y, Z ) ), inverse( Z ) ) ) ]
% 2.33/2.68 )
% 2.33/2.68 , clause( 420, [ =( multiply( 'least_upper_bound'( Z, multiply( X, Y ) ),
% 2.33/2.68 inverse( Y ) ), 'least_upper_bound'( multiply( Z, inverse( Y ) ), X ) ) ]
% 2.33/2.68 )
% 2.33/2.68 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15765, [ =( 'least_upper_bound'( multiply( b, inverse( inverse( d )
% 2.33/2.68 ) ), multiply( a, c ) ), multiply( b, inverse( inverse( d ) ) ) ) ] )
% 2.33/2.68 , clause( 4625, [ =( 'least_upper_bound'( b, multiply( multiply( a, c ),
% 2.33/2.68 inverse( d ) ) ), b ) ] )
% 2.33/2.68 , 0, clause( 15763, [ =( 'least_upper_bound'( multiply( X, inverse( Z ) ),
% 2.33/2.68 Y ), multiply( 'least_upper_bound'( X, multiply( Y, Z ) ), inverse( Z ) )
% 2.33/2.68 ) ] )
% 2.33/2.68 , 0, 11, substitution( 0, [] ), substitution( 1, [ :=( X, b ), :=( Y,
% 2.33/2.68 multiply( a, c ) ), :=( Z, inverse( d ) )] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15767, [ =( 'least_upper_bound'( multiply( b, inverse( inverse( d )
% 2.33/2.68 ) ), multiply( a, c ) ), multiply( b, d ) ) ] )
% 2.33/2.68 , clause( 396, [ =( inverse( inverse( X ) ), X ) ] )
% 2.33/2.68 , 0, clause( 15765, [ =( 'least_upper_bound'( multiply( b, inverse( inverse(
% 2.33/2.68 d ) ) ), multiply( a, c ) ), multiply( b, inverse( inverse( d ) ) ) ) ]
% 2.33/2.68 )
% 2.33/2.68 , 0, 12, substitution( 0, [ :=( X, d )] ), substitution( 1, [] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15768, [ =( 'least_upper_bound'( multiply( b, d ), multiply( a, c )
% 2.33/2.68 ), multiply( b, d ) ) ] )
% 2.33/2.68 , clause( 396, [ =( inverse( inverse( X ) ), X ) ] )
% 2.33/2.68 , 0, clause( 15767, [ =( 'least_upper_bound'( multiply( b, inverse( inverse(
% 2.33/2.68 d ) ) ), multiply( a, c ) ), multiply( b, d ) ) ] )
% 2.33/2.68 , 0, 4, substitution( 0, [ :=( X, d )] ), substitution( 1, [] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 15194, [ =( 'least_upper_bound'( multiply( b, d ), multiply( a, c )
% 2.33/2.68 ), multiply( b, d ) ) ] )
% 2.33/2.68 , clause( 15768, [ =( 'least_upper_bound'( multiply( b, d ), multiply( a, c
% 2.33/2.68 ) ), multiply( b, d ) ) ] )
% 2.33/2.68 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 paramod(
% 2.33/2.68 clause( 15774, [ ~( =( multiply( b, d ), multiply( b, d ) ) ) ] )
% 2.33/2.68 , clause( 15194, [ =( 'least_upper_bound'( multiply( b, d ), multiply( a, c
% 2.33/2.68 ) ), multiply( b, d ) ) ] )
% 2.33/2.68 , 0, clause( 141, [ ~( =( 'least_upper_bound'( multiply( b, d ), multiply(
% 2.33/2.68 a, c ) ), multiply( b, d ) ) ) ] )
% 2.33/2.68 , 0, 2, substitution( 0, [] ), substitution( 1, [] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 eqrefl(
% 2.33/2.68 clause( 15775, [] )
% 2.33/2.68 , clause( 15774, [ ~( =( multiply( b, d ), multiply( b, d ) ) ) ] )
% 2.33/2.68 , 0, substitution( 0, [] )).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 subsumption(
% 2.33/2.68 clause( 15262, [] )
% 2.33/2.68 , clause( 15775, [] )
% 2.33/2.68 , substitution( 0, [] ), permutation( 0, [] ) ).
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 end.
% 2.33/2.68
% 2.33/2.68 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.33/2.68
% 2.33/2.68 Memory use:
% 2.33/2.68
% 2.33/2.68 space for terms: 205267
% 2.33/2.68 space for clauses: 1624900
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 clauses generated: 488039
% 2.33/2.68 clauses kept: 15263
% 2.33/2.68 clauses selected: 1355
% 2.33/2.68 clauses deleted: 191
% 2.33/2.68 clauses inuse deleted: 106
% 2.33/2.68
% 2.33/2.68 subsentry: 32288
% 2.33/2.68 literals s-matched: 31006
% 2.33/2.68 literals matched: 30963
% 2.33/2.68 full subsumption: 0
% 2.33/2.68
% 2.33/2.68 checksum: 1777638015
% 2.33/2.68
% 2.33/2.68
% 2.33/2.68 Bliksem ended
%------------------------------------------------------------------------------