TSTP Solution File: GRP180-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP180-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n011.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 07:35:51 EDT 2022
% Result : Unsatisfiable 119.18s 119.58s
% Output : Refutation 119.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP180-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Tue Jun 14 13:57:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 119.18/119.58 *** allocated 10000 integers for termspace/termends
% 119.18/119.58 *** allocated 10000 integers for clauses
% 119.18/119.58 *** allocated 10000 integers for justifications
% 119.18/119.58 Bliksem 1.12
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Automatic Strategy Selection
% 119.18/119.58
% 119.18/119.58 Clauses:
% 119.18/119.58 [
% 119.18/119.58 [ =( multiply( identity, X ), X ) ],
% 119.18/119.58 [ =( multiply( inverse( X ), X ), identity ) ],
% 119.18/119.58 [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply( Y, Z ) ) )
% 119.18/119.58 ],
% 119.18/119.58 [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, X ) ) ]
% 119.18/119.58 ,
% 119.18/119.58 [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ],
% 119.18/119.58 [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ),
% 119.18/119.58 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ],
% 119.18/119.58 [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.58 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ],
% 119.18/119.58 [ =( 'least_upper_bound'( X, X ), X ) ],
% 119.18/119.58 [ =( 'greatest_lower_bound'( X, X ), X ) ],
% 119.18/119.58 [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X ) ]
% 119.18/119.58 ,
% 119.18/119.58 [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ), X ) ]
% 119.18/119.58 ,
% 119.18/119.58 [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), 'least_upper_bound'(
% 119.18/119.58 multiply( X, Y ), multiply( X, Z ) ) ) ],
% 119.18/119.58 [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 119.18/119.58 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ],
% 119.18/119.58 [ =( multiply( 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'(
% 119.18/119.58 multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 119.18/119.58 [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 119.18/119.58 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 119.18/119.58 [ ~( =( multiply( a, multiply( inverse( 'greatest_lower_bound'( a, b ) )
% 119.18/119.58 , b ) ), 'least_upper_bound'( a, b ) ) ) ]
% 119.18/119.58 ] .
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 percentage equality = 1.000000, percentage horn = 1.000000
% 119.18/119.58 This is a pure equality problem
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Options Used:
% 119.18/119.58
% 119.18/119.58 useres = 1
% 119.18/119.58 useparamod = 1
% 119.18/119.58 useeqrefl = 1
% 119.18/119.58 useeqfact = 1
% 119.18/119.58 usefactor = 1
% 119.18/119.58 usesimpsplitting = 0
% 119.18/119.58 usesimpdemod = 5
% 119.18/119.58 usesimpres = 3
% 119.18/119.58
% 119.18/119.58 resimpinuse = 1000
% 119.18/119.58 resimpclauses = 20000
% 119.18/119.58 substype = eqrewr
% 119.18/119.58 backwardsubs = 1
% 119.18/119.58 selectoldest = 5
% 119.18/119.58
% 119.18/119.58 litorderings [0] = split
% 119.18/119.58 litorderings [1] = extend the termordering, first sorting on arguments
% 119.18/119.58
% 119.18/119.58 termordering = kbo
% 119.18/119.58
% 119.18/119.58 litapriori = 0
% 119.18/119.58 termapriori = 1
% 119.18/119.58 litaposteriori = 0
% 119.18/119.58 termaposteriori = 0
% 119.18/119.58 demodaposteriori = 0
% 119.18/119.58 ordereqreflfact = 0
% 119.18/119.58
% 119.18/119.58 litselect = negord
% 119.18/119.58
% 119.18/119.58 maxweight = 15
% 119.18/119.58 maxdepth = 30000
% 119.18/119.58 maxlength = 115
% 119.18/119.58 maxnrvars = 195
% 119.18/119.58 excuselevel = 1
% 119.18/119.58 increasemaxweight = 1
% 119.18/119.58
% 119.18/119.58 maxselected = 10000000
% 119.18/119.58 maxnrclauses = 10000000
% 119.18/119.58
% 119.18/119.58 showgenerated = 0
% 119.18/119.58 showkept = 0
% 119.18/119.58 showselected = 0
% 119.18/119.58 showdeleted = 0
% 119.18/119.58 showresimp = 1
% 119.18/119.58 showstatus = 2000
% 119.18/119.58
% 119.18/119.58 prologoutput = 1
% 119.18/119.58 nrgoals = 5000000
% 119.18/119.58 totalproof = 1
% 119.18/119.58
% 119.18/119.58 Symbols occurring in the translation:
% 119.18/119.58
% 119.18/119.58 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 119.18/119.58 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 119.18/119.58 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 119.18/119.58 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 119.18/119.58 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 119.18/119.58 identity [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 119.18/119.58 multiply [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 119.18/119.58 inverse [42, 1] (w:1, o:20, a:1, s:1, b:0),
% 119.18/119.58 'greatest_lower_bound' [45, 2] (w:1, o:48, a:1, s:1, b:0),
% 119.18/119.58 'least_upper_bound' [46, 2] (w:1, o:46, a:1, s:1, b:0),
% 119.18/119.58 a [47, 0] (w:1, o:13, a:1, s:1, b:0),
% 119.18/119.58 b [48, 0] (w:1, o:14, a:1, s:1, b:0).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Starting Search:
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 25055
% 119.18/119.58 Kept: 2004
% 119.18/119.58 Inuse: 197
% 119.18/119.58 Deleted: 13
% 119.18/119.58 Deletedinuse: 8
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 106659
% 119.18/119.58 Kept: 4005
% 119.18/119.58 Inuse: 441
% 119.18/119.58 Deleted: 28
% 119.18/119.58 Deletedinuse: 8
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 172335
% 119.18/119.58 Kept: 6011
% 119.18/119.58 Inuse: 602
% 119.18/119.58 Deleted: 82
% 119.18/119.58 Deletedinuse: 34
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 297984
% 119.18/119.58 Kept: 8012
% 119.18/119.58 Inuse: 777
% 119.18/119.58 Deleted: 133
% 119.18/119.58 Deletedinuse: 80
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 665659
% 119.18/119.58 Kept: 10018
% 119.18/119.58 Inuse: 1123
% 119.18/119.58 Deleted: 190
% 119.18/119.58 Deletedinuse: 80
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 1918125
% 119.18/119.58 Kept: 12023
% 119.18/119.58 Inuse: 1719
% 119.18/119.58 Deleted: 278
% 119.18/119.58 Deletedinuse: 80
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 2131236
% 119.18/119.58 Kept: 14120
% 119.18/119.58 Inuse: 1842
% 119.18/119.58 Deleted: 306
% 119.18/119.58 Deletedinuse: 81
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 2213924
% 119.18/119.58 Kept: 16162
% 119.18/119.58 Inuse: 1884
% 119.18/119.58 Deleted: 309
% 119.18/119.58 Deletedinuse: 81
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 2336861
% 119.18/119.58 Kept: 18167
% 119.18/119.58 Inuse: 1946
% 119.18/119.58 Deleted: 309
% 119.18/119.58 Deletedinuse: 81
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying clauses:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 2513840
% 119.18/119.58 Kept: 20179
% 119.18/119.58 Inuse: 2024
% 119.18/119.58 Deleted: 2162
% 119.18/119.58 Deletedinuse: 81
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 2825712
% 119.18/119.58 Kept: 22221
% 119.18/119.58 Inuse: 2159
% 119.18/119.58 Deleted: 2162
% 119.18/119.58 Deletedinuse: 81
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 3253561
% 119.18/119.58 Kept: 24227
% 119.18/119.58 Inuse: 2329
% 119.18/119.58 Deleted: 2162
% 119.18/119.58 Deletedinuse: 81
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 3858718
% 119.18/119.58 Kept: 26231
% 119.18/119.58 Inuse: 2553
% 119.18/119.58 Deleted: 2165
% 119.18/119.58 Deletedinuse: 81
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 4779497
% 119.18/119.58 Kept: 28234
% 119.18/119.58 Inuse: 2877
% 119.18/119.58 Deleted: 2170
% 119.18/119.58 Deletedinuse: 81
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 6237694
% 119.18/119.58 Kept: 30234
% 119.18/119.58 Inuse: 3279
% 119.18/119.58 Deleted: 2194
% 119.18/119.58 Deletedinuse: 81
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 8944931
% 119.18/119.58 Kept: 32234
% 119.18/119.58 Inuse: 3819
% 119.18/119.58 Deleted: 2194
% 119.18/119.58 Deletedinuse: 81
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 13985794
% 119.18/119.58 Kept: 34243
% 119.18/119.58 Inuse: 4911
% 119.18/119.58 Deleted: 2234
% 119.18/119.58 Deletedinuse: 81
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 17211489
% 119.18/119.58 Kept: 36251
% 119.18/119.58 Inuse: 5554
% 119.18/119.58 Deleted: 2388
% 119.18/119.58 Deletedinuse: 217
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 24914981
% 119.18/119.58 Kept: 38251
% 119.18/119.58 Inuse: 6561
% 119.18/119.58 Deleted: 2448
% 119.18/119.58 Deletedinuse: 249
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying clauses:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Intermediate Status:
% 119.18/119.58 Generated: 29859093
% 119.18/119.58 Kept: 40647
% 119.18/119.58 Inuse: 7142
% 119.18/119.58 Deleted: 16723
% 119.18/119.58 Deletedinuse: 1725
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58 Resimplifying inuse:
% 119.18/119.58 Done
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 Bliksems!, er is een bewijs:
% 119.18/119.58 % SZS status Unsatisfiable
% 119.18/119.58 % SZS output start Refutation
% 119.18/119.58
% 119.18/119.58 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 119.18/119.58 , Z ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 119.18/119.58 X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 119.18/119.58 ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) )
% 119.18/119.58 , 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.58 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 8, [ =( 'greatest_lower_bound'( X, X ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 119.18/119.58 ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 119.18/119.58 X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) )
% 119.18/119.58 , multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 12, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z )
% 119.18/119.58 ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 119.18/119.58 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 14, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z )
% 119.18/119.58 ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 15, [ ~( =( multiply( multiply( a, inverse( 'greatest_lower_bound'(
% 119.18/119.58 a, b ) ) ), b ), 'least_upper_bound'( a, b ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 16, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ), Y )
% 119.18/119.58 , identity ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 17, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 119.18/119.58 identity ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 18, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 119.18/119.58 ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 19, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X ),
% 119.18/119.58 X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 20, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) ),
% 119.18/119.58 X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 21, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), X ),
% 119.18/119.58 X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 23, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Z,
% 119.18/119.58 'least_upper_bound'( X, Y ) ), Y ), 'greatest_lower_bound'( Z, Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 26, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Z, X ),
% 119.18/119.58 'least_upper_bound'( X, Y ) ), 'greatest_lower_bound'( Z, X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 27, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z
% 119.18/119.58 ), 'greatest_lower_bound'( 'greatest_lower_bound'( Y, Z ), X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 28, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Z, Y ), X
% 119.18/119.58 ), 'greatest_lower_bound'( 'greatest_lower_bound'( Z, X ), Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 30, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Y, X ), X
% 119.18/119.58 ), 'greatest_lower_bound'( Y, X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 32, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), X
% 119.18/119.58 ), 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 33, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.58 'greatest_lower_bound'( X, Y ), Z ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 34, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Y ),
% 119.18/119.58 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 35, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 119.18/119.58 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 36, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) ),
% 119.18/119.58 X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 37, [ =( 'least_upper_bound'( 'greatest_lower_bound'( X, Y ), X ),
% 119.18/119.58 X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 39, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X ),
% 119.18/119.58 X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 40, [ =( 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.58 'greatest_lower_bound'( X, Y ), Z ), 'greatest_lower_bound'( Y, Z ) ),
% 119.18/119.58 'greatest_lower_bound'( Y, Z ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 42, [ =( 'least_upper_bound'( 'least_upper_bound'( Z,
% 119.18/119.58 'greatest_lower_bound'( X, Y ) ), Y ), 'least_upper_bound'( Z, Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 45, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, Z ),
% 119.18/119.58 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ),
% 119.18/119.58 'least_upper_bound'( Y, Z ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 49, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 119.18/119.58 'least_upper_bound'( 'least_upper_bound'( Y, Z ), X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 50, [ =( 'least_upper_bound'( 'least_upper_bound'( Z, Y ), X ),
% 119.18/119.58 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 53, [ =( 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.58 'greatest_lower_bound'( X, Y ), Z ), X ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 59, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.58 'least_upper_bound'( Z, X ), Y ), X ), 'least_upper_bound'(
% 119.18/119.58 'least_upper_bound'( Z, X ), Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 62, [ =( 'least_upper_bound'( multiply( multiply( X, Y ), Z ),
% 119.18/119.58 multiply( X, T ) ), multiply( X, 'least_upper_bound'( multiply( Y, Z ), T
% 119.18/119.58 ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 63, [ =( 'least_upper_bound'( multiply( X, T ), multiply( multiply(
% 119.18/119.58 X, Y ), Z ) ), multiply( X, 'least_upper_bound'( T, multiply( Y, Z ) ) )
% 119.18/119.58 ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 64, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), multiply( X,
% 119.18/119.58 'least_upper_bound'( Z, Y ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 65, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y )
% 119.18/119.58 ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 66, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ), identity
% 119.18/119.58 ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 67, [ =( multiply( inverse( identity ), X ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 68, [ =( multiply( multiply( Y, inverse( identity ) ), X ),
% 119.18/119.58 multiply( Y, X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 69, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.58 'greatest_lower_bound'( 'greatest_lower_bound'( 'least_upper_bound'( X, Y
% 119.18/119.58 ), Z ), T ), X ), Y ), 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 76, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ), multiply( X
% 119.18/119.58 , 'greatest_lower_bound'( Z, Y ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 80, [ =( 'greatest_lower_bound'( multiply( inverse( X ), Y ),
% 119.18/119.58 identity ), multiply( inverse( X ), 'greatest_lower_bound'( Y, X ) ) ) ]
% 119.18/119.58 )
% 119.18/119.58 .
% 119.18/119.58 clause( 114, [ =( multiply( 'least_upper_bound'( X, Z ), Y ), multiply(
% 119.18/119.58 'least_upper_bound'( Z, X ), Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 115, [ =( multiply( 'least_upper_bound'( inverse( X ), Y ), X ),
% 119.18/119.58 'least_upper_bound'( identity, multiply( Y, X ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 117, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 119.18/119.58 'least_upper_bound'( identity, Y ), X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 118, [ =( 'least_upper_bound'( multiply( Y, X ), X ), multiply(
% 119.18/119.58 'least_upper_bound'( Y, identity ), X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 138, [ =( multiply( inverse( inverse( identity ) ), X ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 144, [ =( 'least_upper_bound'( 'greatest_lower_bound'( multiply(
% 119.18/119.58 'greatest_lower_bound'( X, Z ), Y ), T ), multiply( X, Y ) ), multiply( X
% 119.18/119.58 , Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 150, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ), multiply(
% 119.18/119.58 'greatest_lower_bound'( Z, X ), Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 151, [ =( multiply( 'greatest_lower_bound'( inverse( X ), Y ), X )
% 119.18/119.58 , 'greatest_lower_bound'( identity, multiply( Y, X ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 153, [ =( 'greatest_lower_bound'( X, multiply( Y, X ) ), multiply(
% 119.18/119.58 'greatest_lower_bound'( identity, Y ), X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 154, [ =( 'greatest_lower_bound'( multiply( Y, X ), X ), multiply(
% 119.18/119.58 'greatest_lower_bound'( Y, identity ), X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 160, [ =( inverse( identity ), identity ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 163, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 119.18/119.58 ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 171, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X,
% 119.18/119.58 'least_upper_bound'( identity, Y ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 172, [ =( 'least_upper_bound'( multiply( X, Y ), X ), multiply( X,
% 119.18/119.58 'least_upper_bound'( Y, identity ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 180, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 182, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 119.18/119.58 X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 184, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 185, [ =( 'greatest_lower_bound'( identity, multiply( Y, inverse( X
% 119.18/119.58 ) ) ), multiply( 'greatest_lower_bound'( X, Y ), inverse( X ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 187, [ =( 'least_upper_bound'( identity, multiply( Y, inverse( X )
% 119.18/119.58 ) ), multiply( 'least_upper_bound'( X, Y ), inverse( X ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 192, [ =( multiply( X, 'least_upper_bound'( Y, inverse( X ) ) ),
% 119.18/119.58 'least_upper_bound'( multiply( X, Y ), identity ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 195, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y )
% 119.18/119.58 ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 199, [ =( multiply( 'least_upper_bound'( Z, multiply( X, Y ) ),
% 119.18/119.58 inverse( Y ) ), 'least_upper_bound'( multiply( Z, inverse( Y ) ), X ) ) ]
% 119.18/119.58 )
% 119.18/119.58 .
% 119.18/119.58 clause( 201, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X )
% 119.18/119.58 ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 202, [ =( multiply( inverse( Y ), inverse( X ) ), inverse( multiply(
% 119.18/119.58 X, Y ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 203, [ =( inverse( multiply( inverse( X ), Y ) ), multiply( inverse(
% 119.18/119.58 Y ), X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 211, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 119.18/119.58 inverse( X ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 212, [ =( multiply( X, 'greatest_lower_bound'( inverse( multiply( Y
% 119.18/119.58 , X ) ), Z ) ), 'greatest_lower_bound'( inverse( Y ), multiply( X, Z ) )
% 119.18/119.58 ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 215, [ =( multiply( X, 'least_upper_bound'( Z, inverse( multiply( Y
% 119.18/119.58 , X ) ) ) ), 'least_upper_bound'( multiply( X, Z ), inverse( Y ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 225, [ =( inverse( 'greatest_lower_bound'( Y, X ) ), inverse(
% 119.18/119.58 'greatest_lower_bound'( X, Y ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 230, [ =( multiply( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 119.18/119.58 T ), multiply( multiply( 'greatest_lower_bound'( Z, X ), Y ), T ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 241, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Z, X ),
% 119.18/119.58 'least_upper_bound'( Y, Z ) ), 'greatest_lower_bound'( X, Z ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 248, [ =( multiply( inverse( 'greatest_lower_bound'( Y, X ) ),
% 119.18/119.58 'greatest_lower_bound'( X, Y ) ), identity ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 259, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ),
% 119.18/119.58 'greatest_lower_bound'( X, Y ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 273, [ =( inverse( 'least_upper_bound'( Y, X ) ), inverse(
% 119.18/119.58 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 274, [ =( multiply( inverse( multiply( 'least_upper_bound'( Y, X )
% 119.18/119.58 , Z ) ), 'least_upper_bound'( X, Y ) ), inverse( Z ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 288, [ =( multiply( inverse( 'least_upper_bound'( Y, X ) ),
% 119.18/119.58 'least_upper_bound'( X, Y ) ), identity ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 416, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.58 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ), T ), X ),
% 119.18/119.58 'least_upper_bound'( X, T ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 506, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 119.18/119.58 X, 'greatest_lower_bound'( Y, identity ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 525, [ =( multiply( 'greatest_lower_bound'( X, multiply( X, Y ) ),
% 119.18/119.58 inverse( 'greatest_lower_bound'( identity, Y ) ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 528, [ =( multiply( inverse( Y ), 'greatest_lower_bound'( identity
% 119.18/119.58 , Y ) ), 'greatest_lower_bound'( inverse( Y ), identity ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 542, [ =( 'least_upper_bound'( multiply( X, 'greatest_lower_bound'(
% 119.18/119.58 identity, Y ) ), X ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 544, [ =( 'greatest_lower_bound'( Y, multiply( Y,
% 119.18/119.58 'least_upper_bound'( X, identity ) ) ), Y ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 546, [ =( 'greatest_lower_bound'( Y, multiply( Y,
% 119.18/119.58 'least_upper_bound'( identity, X ) ) ), Y ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 555, [ =( 'least_upper_bound'( multiply( X, 'greatest_lower_bound'(
% 119.18/119.58 Y, identity ) ), X ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 588, [ =( 'least_upper_bound'( X, multiply( X,
% 119.18/119.58 'greatest_lower_bound'( Y, identity ) ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 597, [ =( 'least_upper_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.58 identity, X ) ), identity ), inverse( 'greatest_lower_bound'( identity, X
% 119.18/119.58 ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 616, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.58 identity, X ) ), identity ), inverse( 'least_upper_bound'( identity, X )
% 119.18/119.58 ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 676, [ =( inverse( multiply( X, 'greatest_lower_bound'( Y, identity
% 119.18/119.58 ) ) ), inverse( 'greatest_lower_bound'( multiply( X, Y ), X ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 750, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X,
% 119.18/119.58 'least_upper_bound'( Y, identity ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 770, [ =( multiply( inverse( Y ), 'least_upper_bound'( identity, Y
% 119.18/119.58 ) ), 'least_upper_bound'( inverse( Y ), identity ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 781, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 119.18/119.58 'least_upper_bound'( multiply( X, Y ), X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 801, [ =( multiply( 'least_upper_bound'( X, multiply( X, Y ) ),
% 119.18/119.58 inverse( 'least_upper_bound'( Y, identity ) ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 818, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X,
% 119.18/119.58 'greatest_lower_bound'( Y, Z ) ), 'least_upper_bound'( X, Z ) ),
% 119.18/119.58 'least_upper_bound'( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 847, [ =( inverse( multiply( X, 'least_upper_bound'( Y, identity )
% 119.18/119.58 ) ), inverse( 'least_upper_bound'( X, multiply( X, Y ) ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 858, [ =( 'greatest_lower_bound'( Y, multiply( 'least_upper_bound'(
% 119.18/119.58 identity, X ), Y ) ), Y ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 928, [ =( 'least_upper_bound'( multiply( 'least_upper_bound'(
% 119.18/119.58 identity, Y ), X ), X ), multiply( 'least_upper_bound'( identity, Y ), X
% 119.18/119.58 ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 935, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 119.18/119.58 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( Y, X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1031, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'(
% 119.18/119.58 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'( Y, X ) ),
% 119.18/119.58 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1032, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), Z )
% 119.18/119.58 , 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), Z ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1065, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), Z )
% 119.18/119.58 , 'greatest_lower_bound'( Z, 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1087, [ =( 'greatest_lower_bound'( 'least_upper_bound'(
% 119.18/119.58 'least_upper_bound'( X, Z ), Y ), T ), 'greatest_lower_bound'( T,
% 119.18/119.58 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1199, [ =( multiply( inverse( 'greatest_lower_bound'( multiply( X,
% 119.18/119.58 Y ), Y ) ), 'greatest_lower_bound'( X, identity ) ), inverse( Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1205, [ =( 'greatest_lower_bound'( multiply( 'least_upper_bound'(
% 119.18/119.58 identity, Y ), X ), Z ), 'greatest_lower_bound'( 'least_upper_bound'(
% 119.18/119.58 multiply( Y, X ), X ), Z ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1206, [ =( multiply( X, 'least_upper_bound'( X, identity ) ),
% 119.18/119.58 multiply( 'least_upper_bound'( identity, X ), X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1207, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 119.18/119.58 'least_upper_bound'( X, identity ), Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1208, [ =( multiply( X, 'least_upper_bound'( identity, X ) ),
% 119.18/119.58 multiply( 'least_upper_bound'( identity, X ), X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1261, [ =( inverse( multiply( 'least_upper_bound'( Y, identity ), X
% 119.18/119.58 ) ), inverse( 'least_upper_bound'( multiply( Y, X ), X ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1265, [ =( multiply( 'least_upper_bound'( X, identity ), inverse( X
% 119.18/119.58 ) ), 'least_upper_bound'( inverse( X ), identity ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1313, [ =( multiply( inverse( 'least_upper_bound'( multiply( X, Y )
% 119.18/119.58 , Y ) ), 'least_upper_bound'( X, identity ) ), inverse( Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1314, [ =( multiply( multiply( 'least_upper_bound'( X, identity ),
% 119.18/119.58 X ), Y ), multiply( X, 'least_upper_bound'( multiply( X, Y ), Y ) ) ) ]
% 119.18/119.58 )
% 119.18/119.58 .
% 119.18/119.58 clause( 1320, [ =( multiply( inverse( 'least_upper_bound'( inverse( X ),
% 119.18/119.58 identity ) ), 'least_upper_bound'( X, identity ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1323, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.58 identity, X ) ), identity ), identity ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1324, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X,
% 119.18/119.58 identity ) ), identity ), identity ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1335, [ =( 'least_upper_bound'( 'least_upper_bound'( Y, inverse(
% 119.18/119.58 'least_upper_bound'( identity, X ) ) ), identity ), 'least_upper_bound'(
% 119.18/119.58 identity, Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1525, [ =( multiply( multiply( 'least_upper_bound'( identity, X ),
% 119.18/119.58 X ), inverse( 'least_upper_bound'( X, identity ) ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1545, [ =( multiply( X, 'least_upper_bound'( multiply( inverse( X )
% 119.18/119.58 , Y ), Z ) ), 'least_upper_bound'( Y, multiply( X, Z ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1547, [ =( multiply( inverse( X ), 'least_upper_bound'( multiply( X
% 119.18/119.58 , Y ), Z ) ), 'least_upper_bound'( Y, multiply( inverse( X ), Z ) ) ) ]
% 119.18/119.58 )
% 119.18/119.58 .
% 119.18/119.58 clause( 1586, [ =( multiply( inverse( X ), 'least_upper_bound'( Y, multiply(
% 119.18/119.58 X, Z ) ) ), 'least_upper_bound'( multiply( inverse( X ), Y ), Z ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1640, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y
% 119.18/119.58 ) ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1653, [ =( multiply( 'least_upper_bound'( identity, multiply(
% 119.18/119.58 inverse( X ), Y ) ), inverse( 'least_upper_bound'( X, Y ) ) ), inverse( X
% 119.18/119.58 ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1773, [ =( 'greatest_lower_bound'( identity, multiply( inverse( X )
% 119.18/119.58 , 'least_upper_bound'( Y, X ) ) ), identity ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 1781, [ =( 'greatest_lower_bound'( identity, multiply( inverse( Y )
% 119.18/119.58 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ), identity ) ]
% 119.18/119.58 )
% 119.18/119.58 .
% 119.18/119.58 clause( 2156, [ =( multiply( 'least_upper_bound'( identity, X ), inverse(
% 119.18/119.58 'least_upper_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 2166, [ =( multiply( 'greatest_lower_bound'( identity, X ), inverse(
% 119.18/119.58 'greatest_lower_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 2294, [ =( multiply( inverse( multiply( X, Y ) ),
% 119.18/119.58 'greatest_lower_bound'( X, multiply( X, Y ) ) ), 'greatest_lower_bound'(
% 119.18/119.58 inverse( Y ), identity ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 2633, [ =( 'least_upper_bound'( 'greatest_lower_bound'( inverse(
% 119.18/119.58 'least_upper_bound'( identity, X ) ), Y ), 'greatest_lower_bound'(
% 119.18/119.58 identity, Y ) ), 'greatest_lower_bound'( identity, Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 3103, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.58 'greatest_lower_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 3124, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( inverse(
% 119.18/119.58 'greatest_lower_bound'( inverse( X ), identity ) ), Y ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 3168, [ =( multiply( X, inverse( 'least_upper_bound'( identity,
% 119.18/119.58 multiply( Y, X ) ) ) ), inverse( 'least_upper_bound'( inverse( X ), Y ) )
% 119.18/119.58 ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 3237, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.58 inverse( X ), identity ) ), X ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 3242, [ =( multiply( 'least_upper_bound'( identity, inverse( X ) )
% 119.18/119.58 , inverse( 'least_upper_bound'( X, identity ) ) ), inverse( X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 3297, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X,
% 119.18/119.58 identity ) ), inverse( X ) ), inverse( X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 3308, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'( X
% 119.18/119.58 , identity ) ), inverse( X ) ), inverse( 'least_upper_bound'( X, identity
% 119.18/119.58 ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 4020, [ =( 'least_upper_bound'( 'greatest_lower_bound'( multiply(
% 119.18/119.58 'greatest_lower_bound'( X, Y ), inverse( X ) ), Z ), identity ), identity
% 119.18/119.58 ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 4025, [ =( multiply( 'least_upper_bound'( multiply( X, Y ), X ),
% 119.18/119.58 inverse( 'least_upper_bound'( inverse( Y ), identity ) ) ), multiply( X,
% 119.18/119.58 Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 4154, [ =( multiply( inverse( 'least_upper_bound'( multiply( X, Y )
% 119.18/119.58 , identity ) ), X ), inverse( 'least_upper_bound'( Y, inverse( X ) ) ) )
% 119.18/119.58 ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 4181, [ =( multiply( X, inverse( 'greatest_lower_bound'( identity,
% 119.18/119.58 multiply( Y, X ) ) ) ), inverse( 'greatest_lower_bound'( inverse( X ), Y
% 119.18/119.58 ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 4331, [ =( 'least_upper_bound'( multiply( 'greatest_lower_bound'( X
% 119.18/119.58 , Y ), inverse( X ) ), identity ), identity ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 4369, [ =( 'least_upper_bound'( identity, multiply( X, inverse(
% 119.18/119.58 'greatest_lower_bound'( X, Y ) ) ) ), multiply( X, inverse(
% 119.18/119.58 'greatest_lower_bound'( X, Y ) ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 4370, [ =( 'greatest_lower_bound'( identity, multiply( X, inverse(
% 119.18/119.58 'greatest_lower_bound'( X, Y ) ) ) ), identity ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 4427, [ =( 'least_upper_bound'( multiply( 'greatest_lower_bound'( Y
% 119.18/119.58 , X ), inverse( X ) ), identity ), identity ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 4805, [ =( 'greatest_lower_bound'( Z, multiply( multiply( Z, X ),
% 119.18/119.58 inverse( 'greatest_lower_bound'( X, Y ) ) ) ), Z ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 4935, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.58 'greatest_lower_bound'( inverse( X ), Y ) ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 4952, [ =( 'greatest_lower_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.58 inverse( X ), Y ) ), X ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 4962, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.58 'greatest_lower_bound'( Y, inverse( X ) ) ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 4973, [ =( 'greatest_lower_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.58 X, Y ) ), inverse( X ) ), inverse( X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 5003, [ =( 'greatest_lower_bound'( inverse( X ), inverse(
% 119.18/119.58 'greatest_lower_bound'( Y, X ) ) ), inverse( X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 5025, [ =( 'least_upper_bound'( inverse( 'greatest_lower_bound'( Y
% 119.18/119.58 , X ) ), inverse( X ) ), inverse( 'greatest_lower_bound'( Y, X ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 5051, [ =( 'least_upper_bound'( inverse( X ), inverse(
% 119.18/119.58 'greatest_lower_bound'( X, Y ) ) ), inverse( 'greatest_lower_bound'( X, Y
% 119.18/119.58 ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 5181, [ =( 'greatest_lower_bound'( identity, multiply( Y, inverse(
% 119.18/119.58 X ) ) ), multiply( 'greatest_lower_bound'( Y, X ), inverse( X ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 5547, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X, Y
% 119.18/119.58 ) ), inverse( Y ) ), inverse( Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 5563, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( Y,
% 119.18/119.58 inverse( X ) ) ), X ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 5571, [ =( 'least_upper_bound'( Y, inverse( 'least_upper_bound'( X
% 119.18/119.58 , inverse( Y ) ) ) ), Y ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 5591, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'( X
% 119.18/119.58 , inverse( Y ) ) ), Y ), inverse( 'least_upper_bound'( X, inverse( Y ) )
% 119.18/119.58 ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 8767, [ =( multiply( inverse( 'least_upper_bound'( identity,
% 119.18/119.58 multiply( Y, inverse( X ) ) ) ), 'least_upper_bound'( Y, X ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 12228, [ =( multiply( inverse( 'least_upper_bound'( X, inverse( Y )
% 119.18/119.58 ) ), 'least_upper_bound'( multiply( X, Y ), identity ) ), Y ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 12242, [ =( multiply( inverse( 'least_upper_bound'( X, inverse( Y )
% 119.18/119.58 ) ), 'least_upper_bound'( identity, multiply( X, Y ) ) ), Y ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 12249, [ =( inverse( 'least_upper_bound'( X, inverse(
% 119.18/119.58 'least_upper_bound'( identity, X ) ) ) ), inverse( 'least_upper_bound'( X
% 119.18/119.58 , identity ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 12259, [ =( 'least_upper_bound'( X, inverse( 'least_upper_bound'(
% 119.18/119.58 identity, X ) ) ), 'least_upper_bound'( identity, X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 12265, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.58 identity, X ) ), X ), 'least_upper_bound'( identity, X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 12284, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X,
% 119.18/119.58 identity ) ), X ), 'least_upper_bound'( identity, X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 12300, [ =( 'least_upper_bound'( inverse( multiply(
% 119.18/119.58 'least_upper_bound'( X, identity ), X ) ), identity ),
% 119.18/119.58 'least_upper_bound'( inverse( X ), identity ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 12414, [ =( multiply( inverse( 'greatest_lower_bound'( X, identity
% 119.18/119.58 ) ), 'greatest_lower_bound'( multiply( X, Y ), Y ) ), Y ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 12464, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.58 multiply( X, X ), X ) ), identity ), 'least_upper_bound'( inverse( X ),
% 119.18/119.58 identity ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 12466, [ =( 'least_upper_bound'( 'least_upper_bound'( multiply( X,
% 119.18/119.58 X ), X ), identity ), 'least_upper_bound'( multiply( X, X ), identity ) )
% 119.18/119.58 ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 12495, [ =( 'greatest_lower_bound'( identity, 'least_upper_bound'(
% 119.18/119.58 X, inverse( X ) ) ), identity ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 26875, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y,
% 119.18/119.58 identity ), 'least_upper_bound'( 'least_upper_bound'( Y, X ), inverse( X
% 119.18/119.58 ) ) ), 'least_upper_bound'( Y, identity ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 32636, [ =( multiply( multiply( inverse( 'least_upper_bound'(
% 119.18/119.58 inverse( Y ), X ) ), X ), 'least_upper_bound'( inverse( X ), Y ) ), Y ) ]
% 119.18/119.58 )
% 119.18/119.58 .
% 119.18/119.58 clause( 33848, [ =( 'least_upper_bound'( Y, multiply( X, inverse(
% 119.18/119.58 'least_upper_bound'( Z, multiply( inverse( Y ), X ) ) ) ) ), Y ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 35945, [ =( 'greatest_lower_bound'( 'least_upper_bound'( identity,
% 119.18/119.58 X ), 'least_upper_bound'( 'least_upper_bound'( X, Y ), inverse( Y ) ) ),
% 119.18/119.58 'least_upper_bound'( X, identity ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 35965, [ =( 'greatest_lower_bound'( 'least_upper_bound'(
% 119.18/119.58 'least_upper_bound'( Y, X ), inverse( Y ) ), 'least_upper_bound'(
% 119.18/119.58 identity, X ) ), 'least_upper_bound'( X, identity ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 39019, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.58 identity, inverse( X ) ) ), 'greatest_lower_bound'( identity, X ) ),
% 119.18/119.58 'greatest_lower_bound'( identity, X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 39036, [ =( 'least_upper_bound'( identity, inverse( X ) ), inverse(
% 119.18/119.58 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 39103, [ =( 'least_upper_bound'( inverse( X ), identity ), inverse(
% 119.18/119.58 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 39147, [ =( multiply( 'greatest_lower_bound'( identity, X ),
% 119.18/119.58 'least_upper_bound'( identity, X ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 39167, [ =( inverse( 'greatest_lower_bound'( inverse( Y ), X ) ),
% 119.18/119.58 'least_upper_bound'( Y, inverse( X ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 39178, [ =( inverse( 'greatest_lower_bound'( identity, multiply( X
% 119.18/119.58 , inverse( Y ) ) ) ), 'least_upper_bound'( identity, multiply( Y, inverse(
% 119.18/119.58 X ) ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 39226, [ =( 'greatest_lower_bound'( inverse( X ), identity ),
% 119.18/119.58 inverse( 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 39418, [ =( inverse( 'least_upper_bound'( inverse( Y ), X ) ),
% 119.18/119.58 'greatest_lower_bound'( inverse( X ), Y ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 39707, [ =( multiply( inverse( Y ), 'least_upper_bound'( identity,
% 119.18/119.58 Y ) ), inverse( 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 40349, [ =( multiply( 'greatest_lower_bound'( identity, multiply( Y
% 119.18/119.58 , X ) ), 'least_upper_bound'( inverse( X ), Y ) ), Y ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 40873, [ =( 'least_upper_bound'( multiply( X, inverse( Y ) ),
% 119.18/119.58 inverse( Z ) ), inverse( 'greatest_lower_bound'( multiply( Y, inverse( X
% 119.18/119.58 ) ), Z ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 41720, [ =( inverse( 'greatest_lower_bound'( multiply( X, inverse(
% 119.18/119.58 Y ) ), identity ) ), 'least_upper_bound'( identity, multiply( Y, inverse(
% 119.18/119.58 X ) ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 42447, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.58 inverse( Y ) ), 'least_upper_bound'( Y, X ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 42455, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.58 inverse( Y ) ), 'least_upper_bound'( X, Y ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 42462, [ =( multiply( multiply( 'greatest_lower_bound'( Y, X ),
% 119.18/119.58 inverse( Y ) ), 'least_upper_bound'( X, Y ) ), X ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 42464, [ =( multiply( multiply( X, inverse( 'greatest_lower_bound'(
% 119.18/119.58 X, Y ) ) ), Y ), 'least_upper_bound'( Y, X ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 42638, [ ~( =( 'least_upper_bound'( a, b ), 'least_upper_bound'( b
% 119.18/119.58 , a ) ) ) ] )
% 119.18/119.58 .
% 119.18/119.58 clause( 42639, [] )
% 119.18/119.58 .
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 % SZS output end Refutation
% 119.18/119.58 found a proof!
% 119.18/119.58
% 119.18/119.58 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 119.18/119.58
% 119.18/119.58 initialclauses(
% 119.18/119.58 [ clause( 42641, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.58 , clause( 42642, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.58 , clause( 42643, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 119.18/119.58 multiply( Y, Z ) ) ) ] )
% 119.18/119.58 , clause( 42644, [ =( 'greatest_lower_bound'( X, Y ),
% 119.18/119.58 'greatest_lower_bound'( Y, X ) ) ] )
% 119.18/119.58 , clause( 42645, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y,
% 119.18/119.58 X ) ) ] )
% 119.18/119.58 , clause( 42646, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y
% 119.18/119.58 , Z ) ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ]
% 119.18/119.58 )
% 119.18/119.58 , clause( 42647, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 119.18/119.58 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 , clause( 42648, [ =( 'least_upper_bound'( X, X ), X ) ] )
% 119.18/119.58 , clause( 42649, [ =( 'greatest_lower_bound'( X, X ), X ) ] )
% 119.18/119.58 , clause( 42650, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 119.18/119.58 ) ), X ) ] )
% 119.18/119.58 , clause( 42651, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 119.18/119.58 ) ), X ) ] )
% 119.18/119.58 , clause( 42652, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.58 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.58 , clause( 42653, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 119.18/119.58 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.58 , clause( 42654, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 119.18/119.58 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 119.18/119.58 , clause( 42655, [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 119.18/119.58 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 119.18/119.58 , clause( 42656, [ ~( =( multiply( a, multiply( inverse(
% 119.18/119.58 'greatest_lower_bound'( a, b ) ), b ) ), 'least_upper_bound'( a, b ) ) )
% 119.18/119.58 ] )
% 119.18/119.58 ] ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.58 , clause( 42641, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.58 , clause( 42642, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42662, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X
% 119.18/119.58 , Y ), Z ) ) ] )
% 119.18/119.58 , clause( 42643, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 119.18/119.58 multiply( Y, Z ) ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 119.18/119.58 , Z ) ) ] )
% 119.18/119.58 , clause( 42662, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply(
% 119.18/119.58 X, Y ), Z ) ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 119.18/119.58 X ) ) ] )
% 119.18/119.58 , clause( 42644, [ =( 'greatest_lower_bound'( X, Y ),
% 119.18/119.58 'greatest_lower_bound'( Y, X ) ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.58 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 119.18/119.58 ] )
% 119.18/119.58 , clause( 42645, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y,
% 119.18/119.58 X ) ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.58 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) )
% 119.18/119.58 , 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 , clause( 42646, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y
% 119.18/119.58 , Z ) ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ]
% 119.18/119.58 )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.58 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 , clause( 42647, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 119.18/119.58 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 8, [ =( 'greatest_lower_bound'( X, X ), X ) ] )
% 119.18/119.58 , clause( 42649, [ =( 'greatest_lower_bound'( X, X ), X ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 119.18/119.58 ) ] )
% 119.18/119.58 , clause( 42650, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 119.18/119.58 ) ), X ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.58 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 119.18/119.58 X ) ] )
% 119.18/119.58 , clause( 42651, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 119.18/119.58 ) ), X ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.58 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42711, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 119.18/119.58 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.58 , clause( 42652, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.58 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) )
% 119.18/119.58 , multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.58 , clause( 42711, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z
% 119.18/119.58 ) ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42722, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X,
% 119.18/119.58 Z ) ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.58 , clause( 42653, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 119.18/119.58 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 12, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z )
% 119.18/119.58 ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.58 , clause( 42722, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X
% 119.18/119.58 , Z ) ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42734, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 119.18/119.58 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 , clause( 42654, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 119.18/119.58 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 119.18/119.58 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 , clause( 42734, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z
% 119.18/119.58 ) ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42747, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y,
% 119.18/119.58 Z ) ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 , clause( 42655, [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 119.18/119.58 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 14, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z )
% 119.18/119.58 ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 , clause( 42747, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y
% 119.18/119.58 , Z ) ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42780, [ ~( =( multiply( multiply( a, inverse(
% 119.18/119.58 'greatest_lower_bound'( a, b ) ) ), b ), 'least_upper_bound'( a, b ) ) )
% 119.18/119.58 ] )
% 119.18/119.58 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 119.18/119.58 ), Z ) ) ] )
% 119.18/119.58 , 0, clause( 42656, [ ~( =( multiply( a, multiply( inverse(
% 119.18/119.58 'greatest_lower_bound'( a, b ) ), b ) ), 'least_upper_bound'( a, b ) ) )
% 119.18/119.58 ] )
% 119.18/119.58 , 0, 2, substitution( 0, [ :=( X, a ), :=( Y, inverse(
% 119.18/119.58 'greatest_lower_bound'( a, b ) ) ), :=( Z, b )] ), substitution( 1, [] )
% 119.18/119.58 ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 15, [ ~( =( multiply( multiply( a, inverse( 'greatest_lower_bound'(
% 119.18/119.58 a, b ) ) ), b ), 'least_upper_bound'( a, b ) ) ) ] )
% 119.18/119.58 , clause( 42780, [ ~( =( multiply( multiply( a, inverse(
% 119.18/119.58 'greatest_lower_bound'( a, b ) ) ), b ), 'least_upper_bound'( a, b ) ) )
% 119.18/119.58 ] )
% 119.18/119.58 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42782, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 119.18/119.58 Y, Z ) ) ) ] )
% 119.18/119.58 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 119.18/119.58 ), Z ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42785, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ), Y
% 119.18/119.58 ), identity ) ] )
% 119.18/119.58 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.58 , 0, clause( 42782, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 119.18/119.58 multiply( Y, Z ) ) ) ] )
% 119.18/119.58 , 0, 9, substitution( 0, [ :=( X, multiply( X, Y ) )] ), substitution( 1, [
% 119.18/119.58 :=( X, inverse( multiply( X, Y ) ) ), :=( Y, X ), :=( Z, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 16, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ), Y )
% 119.18/119.58 , identity ) ] )
% 119.18/119.58 , clause( 42785, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X )
% 119.18/119.58 , Y ), identity ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.58 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42791, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 119.18/119.58 Y, Z ) ) ) ] )
% 119.18/119.58 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 119.18/119.58 ), Z ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42796, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply( X
% 119.18/119.58 , identity ) ) ] )
% 119.18/119.58 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.58 , 0, clause( 42791, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 119.18/119.58 multiply( Y, Z ) ) ) ] )
% 119.18/119.58 , 0, 9, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.58 :=( Y, inverse( Y ) ), :=( Z, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 17, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 119.18/119.58 identity ) ) ] )
% 119.18/119.58 , clause( 42796, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply(
% 119.18/119.58 X, identity ) ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.58 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42801, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 119.18/119.58 Y, Z ) ) ) ] )
% 119.18/119.58 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 119.18/119.58 ), Z ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42806, [ =( multiply( multiply( X, identity ), Y ), multiply( X, Y
% 119.18/119.58 ) ) ] )
% 119.18/119.58 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.58 , 0, clause( 42801, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 119.18/119.58 multiply( Y, Z ) ) ) ] )
% 119.18/119.58 , 0, 8, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.58 :=( Y, identity ), :=( Z, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 18, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 119.18/119.58 ] )
% 119.18/119.58 , clause( 42806, [ =( multiply( multiply( X, identity ), Y ), multiply( X,
% 119.18/119.58 Y ) ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.58 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42811, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 119.18/119.58 ) ) ) ] )
% 119.18/119.58 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 119.18/119.58 , X ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42812, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y )
% 119.18/119.58 , X ) ) ] )
% 119.18/119.58 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 119.18/119.58 , X ) ) ] )
% 119.18/119.58 , 0, clause( 42811, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 119.18/119.58 X, Y ) ) ) ] )
% 119.18/119.58 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, 'least_upper_bound'( X, Y ) )] )
% 119.18/119.58 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42815, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X
% 119.18/119.58 ), X ) ] )
% 119.18/119.58 , clause( 42812, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y
% 119.18/119.58 ), X ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 19, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X ),
% 119.18/119.58 X ) ] )
% 119.18/119.58 , clause( 42815, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 119.18/119.58 X ), X ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.58 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42816, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 119.18/119.58 ) ) ) ] )
% 119.18/119.58 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 119.18/119.58 , X ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42817, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 119.18/119.58 ) ) ) ] )
% 119.18/119.58 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 119.18/119.58 ) ] )
% 119.18/119.58 , 0, clause( 42816, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 119.18/119.58 X, Y ) ) ) ] )
% 119.18/119.58 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.58 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42820, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X )
% 119.18/119.58 ), X ) ] )
% 119.18/119.58 , clause( 42817, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y
% 119.18/119.58 , X ) ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 20, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) ),
% 119.18/119.58 X ) ] )
% 119.18/119.58 , clause( 42820, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 119.18/119.58 ) ), X ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.58 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42821, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y )
% 119.18/119.58 , X ) ) ] )
% 119.18/119.58 , clause( 19, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 119.18/119.58 , X ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42822, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( Y, X )
% 119.18/119.58 , X ) ) ] )
% 119.18/119.58 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 119.18/119.58 ) ] )
% 119.18/119.58 , 0, clause( 42821, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X
% 119.18/119.58 , Y ), X ) ) ] )
% 119.18/119.58 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.58 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42825, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), X
% 119.18/119.58 ), X ) ] )
% 119.18/119.58 , clause( 42822, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( Y, X
% 119.18/119.58 ), X ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 21, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), X ),
% 119.18/119.58 X ) ] )
% 119.18/119.58 , clause( 42825, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 119.18/119.58 X ), X ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.58 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42827, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y )
% 119.18/119.58 , Z ), 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.58 , clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z )
% 119.18/119.58 ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42832, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X,
% 119.18/119.58 'least_upper_bound'( Y, Z ) ), Z ), 'greatest_lower_bound'( X, Z ) ) ] )
% 119.18/119.58 , clause( 21, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), X )
% 119.18/119.58 , X ) ] )
% 119.18/119.58 , 0, clause( 42827, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X
% 119.18/119.58 , Y ), Z ), 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ) )
% 119.18/119.58 ] )
% 119.18/119.58 , 0, 10, substitution( 0, [ :=( X, Z ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.58 :=( X, X ), :=( Y, 'least_upper_bound'( Y, Z ) ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 23, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Z,
% 119.18/119.58 'least_upper_bound'( X, Y ) ), Y ), 'greatest_lower_bound'( Z, Y ) ) ] )
% 119.18/119.58 , clause( 42832, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X,
% 119.18/119.58 'least_upper_bound'( Y, Z ) ), Z ), 'greatest_lower_bound'( X, Z ) ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 119.18/119.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42837, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y )
% 119.18/119.58 , Z ), 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.58 , clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z )
% 119.18/119.58 ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42840, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y )
% 119.18/119.58 , 'least_upper_bound'( Y, Z ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.58 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 119.18/119.58 , X ) ] )
% 119.18/119.58 , 0, clause( 42837, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X
% 119.18/119.58 , Y ), Z ), 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ) )
% 119.18/119.58 ] )
% 119.18/119.58 , 0, 10, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 119.18/119.58 :=( X, X ), :=( Y, Y ), :=( Z, 'least_upper_bound'( Y, Z ) )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 26, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Z, X ),
% 119.18/119.58 'least_upper_bound'( X, Y ) ), 'greatest_lower_bound'( Z, X ) ) ] )
% 119.18/119.58 , clause( 42840, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y
% 119.18/119.58 ), 'least_upper_bound'( Y, Z ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 119.18/119.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42844, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y )
% 119.18/119.58 , Z ), 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.58 , clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z )
% 119.18/119.58 ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42847, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y )
% 119.18/119.58 , Z ), 'greatest_lower_bound'( 'greatest_lower_bound'( Y, Z ), X ) ) ] )
% 119.18/119.58 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 119.18/119.58 , X ) ) ] )
% 119.18/119.58 , 0, clause( 42844, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X
% 119.18/119.58 , Y ), Z ), 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ) )
% 119.18/119.58 ] )
% 119.18/119.58 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, 'greatest_lower_bound'( Y, Z
% 119.18/119.58 ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 27, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z
% 119.18/119.58 ), 'greatest_lower_bound'( 'greatest_lower_bound'( Y, Z ), X ) ) ] )
% 119.18/119.58 , clause( 42847, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y
% 119.18/119.58 ), Z ), 'greatest_lower_bound'( 'greatest_lower_bound'( Y, Z ), X ) ) ]
% 119.18/119.58 )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42861, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y )
% 119.18/119.58 , Z ), 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.58 , clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z )
% 119.18/119.58 ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42866, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y )
% 119.18/119.58 , Z ), 'greatest_lower_bound'( X, 'greatest_lower_bound'( Z, Y ) ) ) ] )
% 119.18/119.58 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 119.18/119.58 , X ) ) ] )
% 119.18/119.58 , 0, clause( 42861, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X
% 119.18/119.58 , Y ), Z ), 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ) )
% 119.18/119.58 ] )
% 119.18/119.58 , 0, 8, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 119.18/119.58 :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42879, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y )
% 119.18/119.58 , Z ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Z ), Y ) ) ] )
% 119.18/119.58 , clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z )
% 119.18/119.58 ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 , 0, clause( 42866, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X
% 119.18/119.58 , Y ), Z ), 'greatest_lower_bound'( X, 'greatest_lower_bound'( Z, Y ) ) )
% 119.18/119.58 ] )
% 119.18/119.58 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 119.18/119.58 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 28, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Z, Y ), X
% 119.18/119.58 ), 'greatest_lower_bound'( 'greatest_lower_bound'( Z, X ), Y ) ) ] )
% 119.18/119.58 , clause( 42879, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y
% 119.18/119.58 ), Z ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Z ), Y ) ) ]
% 119.18/119.58 )
% 119.18/119.58 , substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 119.18/119.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42881, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y )
% 119.18/119.58 , Z ), 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.58 , clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z )
% 119.18/119.58 ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42887, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y )
% 119.18/119.58 , Y ), 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.58 , clause( 8, [ =( 'greatest_lower_bound'( X, X ), X ) ] )
% 119.18/119.58 , 0, clause( 42881, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X
% 119.18/119.58 , Y ), Z ), 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ) )
% 119.18/119.58 ] )
% 119.18/119.58 , 0, 8, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.58 :=( Y, Y ), :=( Z, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 30, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Y, X ), X
% 119.18/119.58 ), 'greatest_lower_bound'( Y, X ) ) ] )
% 119.18/119.58 , clause( 42887, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y
% 119.18/119.58 ), Y ), 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.58 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42893, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 119.18/119.58 ) ) ) ] )
% 119.18/119.58 , clause( 20, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) )
% 119.18/119.58 , X ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42896, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 119.18/119.58 'greatest_lower_bound'( X, Y ), X ) ) ] )
% 119.18/119.58 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 119.18/119.58 , X ) ] )
% 119.18/119.58 , 0, clause( 42893, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 119.18/119.58 Y, X ) ) ) ] )
% 119.18/119.58 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.58 :=( X, 'greatest_lower_bound'( X, Y ) ), :=( Y, X )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42897, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y )
% 119.18/119.58 , X ), 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.58 , clause( 42896, [ =( 'greatest_lower_bound'( X, Y ),
% 119.18/119.58 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), X ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 32, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), X
% 119.18/119.58 ), 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.58 , clause( 42897, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y
% 119.18/119.58 ), X ), 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.58 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42899, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 119.18/119.58 ) ) ) ] )
% 119.18/119.58 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 119.18/119.58 , X ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42900, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.58 'greatest_lower_bound'( X, Y ), Z ) ) ) ] )
% 119.18/119.58 , clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z )
% 119.18/119.58 ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.58 , 0, clause( 42899, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.58 X, Y ) ) ) ] )
% 119.18/119.58 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.58 substitution( 1, [ :=( X, X ), :=( Y, 'greatest_lower_bound'( Y, Z ) )] )
% 119.18/119.58 ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42901, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.58 'greatest_lower_bound'( X, Y ), Z ) ), X ) ] )
% 119.18/119.58 , clause( 42900, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.58 'greatest_lower_bound'( X, Y ), Z ) ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 33, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.58 'greatest_lower_bound'( X, Y ), Z ) ), X ) ] )
% 119.18/119.58 , clause( 42901, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.58 'greatest_lower_bound'( X, Y ), Z ) ), X ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.58 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42903, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 119.18/119.58 ) ) ) ] )
% 119.18/119.58 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 119.18/119.58 , X ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42906, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 119.18/119.58 'least_upper_bound'( X, Y ), Y ) ) ] )
% 119.18/119.58 , clause( 21, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), X )
% 119.18/119.58 , X ) ] )
% 119.18/119.58 , 0, clause( 42903, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.58 X, Y ) ) ) ] )
% 119.18/119.58 , 0, 8, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.58 :=( X, 'least_upper_bound'( X, Y ) ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42907, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Y ),
% 119.18/119.58 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.58 , clause( 42906, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 119.18/119.58 'least_upper_bound'( X, Y ), Y ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 34, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Y ),
% 119.18/119.58 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.58 , clause( 42907, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Y )
% 119.18/119.58 , 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.58 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42909, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 119.18/119.58 ) ) ) ] )
% 119.18/119.58 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 119.18/119.58 , X ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42912, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 119.18/119.58 'least_upper_bound'( X, Y ), X ) ) ] )
% 119.18/119.58 , clause( 19, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 119.18/119.58 , X ) ] )
% 119.18/119.58 , 0, clause( 42909, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.58 X, Y ) ) ) ] )
% 119.18/119.58 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.58 :=( X, 'least_upper_bound'( X, Y ) ), :=( Y, X )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42913, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 119.18/119.58 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.58 , clause( 42912, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 119.18/119.58 'least_upper_bound'( X, Y ), X ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 35, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 119.18/119.58 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.58 , clause( 42913, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X )
% 119.18/119.58 , 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.58 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42914, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 119.18/119.58 ) ) ) ] )
% 119.18/119.58 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 119.18/119.58 , X ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42915, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X
% 119.18/119.58 ) ) ) ] )
% 119.18/119.58 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 119.18/119.58 , X ) ) ] )
% 119.18/119.58 , 0, clause( 42914, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.58 X, Y ) ) ) ] )
% 119.18/119.58 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.58 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42918, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X )
% 119.18/119.58 ), X ) ] )
% 119.18/119.58 , clause( 42915, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y
% 119.18/119.58 , X ) ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 36, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) ),
% 119.18/119.58 X ) ] )
% 119.18/119.58 , clause( 42918, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X
% 119.18/119.58 ) ), X ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.58 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42919, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 119.18/119.58 ) ) ) ] )
% 119.18/119.58 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 119.18/119.58 , X ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 paramod(
% 119.18/119.58 clause( 42920, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( X, Y )
% 119.18/119.58 , X ) ) ] )
% 119.18/119.58 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 119.18/119.58 ) ] )
% 119.18/119.58 , 0, clause( 42919, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.58 X, Y ) ) ) ] )
% 119.18/119.58 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, 'greatest_lower_bound'( X, Y
% 119.18/119.58 ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42923, [ =( 'least_upper_bound'( 'greatest_lower_bound'( X, Y ), X
% 119.18/119.58 ), X ) ] )
% 119.18/119.58 , clause( 42920, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( X, Y
% 119.18/119.58 ), X ) ) ] )
% 119.18/119.58 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 subsumption(
% 119.18/119.58 clause( 37, [ =( 'least_upper_bound'( 'greatest_lower_bound'( X, Y ), X ),
% 119.18/119.58 X ) ] )
% 119.18/119.58 , clause( 42923, [ =( 'least_upper_bound'( 'greatest_lower_bound'( X, Y ),
% 119.18/119.58 X ), X ) ] )
% 119.18/119.58 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.58 )] ) ).
% 119.18/119.58
% 119.18/119.58
% 119.18/119.58 eqswap(
% 119.18/119.58 clause( 42924, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X
% 119.18/119.58 ) ) ) ] )
% 119.18/119.58 , clause( 36, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) )
% 119.18/119.58 , X ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 42925, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( Y, X )
% 119.18/119.59 , X ) ) ] )
% 119.18/119.59 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 119.18/119.59 ) ] )
% 119.18/119.59 , 0, clause( 42924, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.59 Y, X ) ) ) ] )
% 119.18/119.59 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, 'greatest_lower_bound'( Y, X
% 119.18/119.59 ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 42928, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X
% 119.18/119.59 ), X ) ] )
% 119.18/119.59 , clause( 42925, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( Y, X
% 119.18/119.59 ), X ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 39, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X ),
% 119.18/119.59 X ) ] )
% 119.18/119.59 , clause( 42928, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ),
% 119.18/119.59 X ), X ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 42930, [ =( Y, 'least_upper_bound'( 'greatest_lower_bound'( X, Y )
% 119.18/119.59 , Y ) ) ] )
% 119.18/119.59 , clause( 39, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X )
% 119.18/119.59 , X ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 42931, [ =( 'greatest_lower_bound'( X, Y ), 'least_upper_bound'(
% 119.18/119.59 'greatest_lower_bound'( 'greatest_lower_bound'( Z, X ), Y ),
% 119.18/119.59 'greatest_lower_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z )
% 119.18/119.59 ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 42930, [ =( Y, 'least_upper_bound'( 'greatest_lower_bound'( X
% 119.18/119.59 , Y ), Y ) ) ] )
% 119.18/119.59 , 0, 5, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 119.18/119.59 substitution( 1, [ :=( X, Z ), :=( Y, 'greatest_lower_bound'( X, Y ) )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 42932, [ =( 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( Z, X ), Y ), 'greatest_lower_bound'( X, Y ) ),
% 119.18/119.59 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.59 , clause( 42931, [ =( 'greatest_lower_bound'( X, Y ), 'least_upper_bound'(
% 119.18/119.59 'greatest_lower_bound'( 'greatest_lower_bound'( Z, X ), Y ),
% 119.18/119.59 'greatest_lower_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 40, [ =( 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( X, Y ), Z ), 'greatest_lower_bound'( Y, Z ) ),
% 119.18/119.59 'greatest_lower_bound'( Y, Z ) ) ] )
% 119.18/119.59 , clause( 42932, [ =( 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( Z, X ), Y ), 'greatest_lower_bound'( X, Y ) ),
% 119.18/119.59 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 42934, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 119.18/119.59 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 42939, [ =( 'least_upper_bound'( 'least_upper_bound'( X,
% 119.18/119.59 'greatest_lower_bound'( Y, Z ) ), Z ), 'least_upper_bound'( X, Z ) ) ] )
% 119.18/119.59 , clause( 39, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X )
% 119.18/119.59 , X ) ] )
% 119.18/119.59 , 0, clause( 42934, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ),
% 119.18/119.59 Z ), 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, 10, substitution( 0, [ :=( X, Z ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, 'greatest_lower_bound'( Y, Z ) ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 42, [ =( 'least_upper_bound'( 'least_upper_bound'( Z,
% 119.18/119.59 'greatest_lower_bound'( X, Y ) ), Y ), 'least_upper_bound'( Z, Y ) ) ] )
% 119.18/119.59 , clause( 42939, [ =( 'least_upper_bound'( 'least_upper_bound'( X,
% 119.18/119.59 'greatest_lower_bound'( Y, Z ) ), Z ), 'least_upper_bound'( X, Z ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 42944, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 119.18/119.59 ) ) ) ] )
% 119.18/119.59 , clause( 20, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) )
% 119.18/119.59 , X ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 42945, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), 'least_upper_bound'( 'least_upper_bound'( Z
% 119.18/119.59 , X ), Y ) ) ) ] )
% 119.18/119.59 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 42944, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 119.18/119.59 Y, X ) ) ) ] )
% 119.18/119.59 , 0, 8, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 119.18/119.59 substitution( 1, [ :=( X, 'least_upper_bound'( X, Y ) ), :=( Y, Z )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 42946, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ) ),
% 119.18/119.59 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.59 , clause( 42945, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), 'least_upper_bound'( 'least_upper_bound'( Z
% 119.18/119.59 , X ), Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 45, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, Z ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ),
% 119.18/119.59 'least_upper_bound'( Y, Z ) ) ] )
% 119.18/119.59 , clause( 42946, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ) ),
% 119.18/119.59 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 42947, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 119.18/119.59 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 42950, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( Y, Z ), X ) ) ] )
% 119.18/119.59 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 119.18/119.59 ) ] )
% 119.18/119.59 , 0, clause( 42947, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ),
% 119.18/119.59 Z ), 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, 'least_upper_bound'( Y, Z ) )] )
% 119.18/119.59 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 49, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( Y, Z ), X ) ) ] )
% 119.18/119.59 , clause( 42950, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z )
% 119.18/119.59 , 'least_upper_bound'( 'least_upper_bound'( Y, Z ), X ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 42964, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 119.18/119.59 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 42969, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 119.18/119.59 'least_upper_bound'( X, 'least_upper_bound'( Z, Y ) ) ) ] )
% 119.18/119.59 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 119.18/119.59 ) ] )
% 119.18/119.59 , 0, clause( 42964, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ),
% 119.18/119.59 Z ), 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, 8, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 42982, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( X, Z ), Y ) ) ] )
% 119.18/119.59 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 42969, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ),
% 119.18/119.59 Z ), 'least_upper_bound'( X, 'least_upper_bound'( Z, Y ) ) ) ] )
% 119.18/119.59 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 119.18/119.59 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 50, [ =( 'least_upper_bound'( 'least_upper_bound'( Z, Y ), X ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ) ) ] )
% 119.18/119.59 , clause( 42982, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z )
% 119.18/119.59 , 'least_upper_bound'( 'least_upper_bound'( X, Z ), Y ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 42984, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( X, Y )
% 119.18/119.59 , X ) ) ] )
% 119.18/119.59 , clause( 37, [ =( 'least_upper_bound'( 'greatest_lower_bound'( X, Y ), X )
% 119.18/119.59 , X ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 42985, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( X, Y ), Z ), X ) ) ] )
% 119.18/119.59 , clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z )
% 119.18/119.59 ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 42984, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( X
% 119.18/119.59 , Y ), X ) ) ] )
% 119.18/119.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.59 substitution( 1, [ :=( X, X ), :=( Y, 'greatest_lower_bound'( Y, Z ) )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 42986, [ =( 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( X, Y ), Z ), X ), X ) ] )
% 119.18/119.59 , clause( 42985, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( X, Y ), Z ), X ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 53, [ =( 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( X, Y ), Z ), X ), X ) ] )
% 119.18/119.59 , clause( 42986, [ =( 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( X, Y ), Z ), X ), X ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 42988, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 119.18/119.59 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43001, [ =( 'least_upper_bound'( 'least_upper_bound'( X,
% 119.18/119.59 'least_upper_bound'( Y, Z ) ), Y ), 'least_upper_bound'( X,
% 119.18/119.59 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , clause( 35, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 119.18/119.59 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.59 , 0, clause( 42988, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ),
% 119.18/119.59 Z ), 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, 10, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, 'least_upper_bound'( Y, Z ) ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43003, [ =( 'least_upper_bound'( 'least_upper_bound'( X,
% 119.18/119.59 'least_upper_bound'( Y, Z ) ), Y ), 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 43001, [ =( 'least_upper_bound'( 'least_upper_bound'( X,
% 119.18/119.59 'least_upper_bound'( Y, Z ) ), Y ), 'least_upper_bound'( X,
% 119.18/119.59 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.59 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43004, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), Z ), Y ), 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 43003, [ =( 'least_upper_bound'( 'least_upper_bound'( X,
% 119.18/119.59 'least_upper_bound'( Y, Z ) ), Y ), 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.59 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 59, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( Z, X ), Y ), X ), 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( Z, X ), Y ) ) ] )
% 119.18/119.59 , clause( 43004, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), Z ), Y ), 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43009, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 119.18/119.59 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43010, [ =( multiply( X, 'least_upper_bound'( multiply( Y, Z ), T )
% 119.18/119.59 ), 'least_upper_bound'( multiply( multiply( X, Y ), Z ), multiply( X, T
% 119.18/119.59 ) ) ) ] )
% 119.18/119.59 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 119.18/119.59 ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 43009, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , 0, 9, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.59 substitution( 1, [ :=( X, X ), :=( Y, multiply( Y, Z ) ), :=( Z, T )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43012, [ =( 'least_upper_bound'( multiply( multiply( X, Y ), Z ),
% 119.18/119.59 multiply( X, T ) ), multiply( X, 'least_upper_bound'( multiply( Y, Z ), T
% 119.18/119.59 ) ) ) ] )
% 119.18/119.59 , clause( 43010, [ =( multiply( X, 'least_upper_bound'( multiply( Y, Z ), T
% 119.18/119.59 ) ), 'least_upper_bound'( multiply( multiply( X, Y ), Z ), multiply( X,
% 119.18/119.59 T ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 62, [ =( 'least_upper_bound'( multiply( multiply( X, Y ), Z ),
% 119.18/119.59 multiply( X, T ) ), multiply( X, 'least_upper_bound'( multiply( Y, Z ), T
% 119.18/119.59 ) ) ) ] )
% 119.18/119.59 , clause( 43012, [ =( 'least_upper_bound'( multiply( multiply( X, Y ), Z )
% 119.18/119.59 , multiply( X, T ) ), multiply( X, 'least_upper_bound'( multiply( Y, Z )
% 119.18/119.59 , T ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43015, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 119.18/119.59 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43017, [ =( multiply( X, 'least_upper_bound'( Y, multiply( Z, T ) )
% 119.18/119.59 ), 'least_upper_bound'( multiply( X, Y ), multiply( multiply( X, Z ), T
% 119.18/119.59 ) ) ) ] )
% 119.18/119.59 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 119.18/119.59 ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 43015, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , 0, 12, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, T )] ),
% 119.18/119.59 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, multiply( Z, T ) )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43019, [ =( 'least_upper_bound'( multiply( X, Y ), multiply(
% 119.18/119.59 multiply( X, Z ), T ) ), multiply( X, 'least_upper_bound'( Y, multiply( Z
% 119.18/119.59 , T ) ) ) ) ] )
% 119.18/119.59 , clause( 43017, [ =( multiply( X, 'least_upper_bound'( Y, multiply( Z, T )
% 119.18/119.59 ) ), 'least_upper_bound'( multiply( X, Y ), multiply( multiply( X, Z ),
% 119.18/119.59 T ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 63, [ =( 'least_upper_bound'( multiply( X, T ), multiply( multiply(
% 119.18/119.59 X, Y ), Z ) ), multiply( X, 'least_upper_bound'( T, multiply( Y, Z ) ) )
% 119.18/119.59 ) ] )
% 119.18/119.59 , clause( 43019, [ =( 'least_upper_bound'( multiply( X, Y ), multiply(
% 119.18/119.59 multiply( X, Z ), T ) ), multiply( X, 'least_upper_bound'( Y, multiply( Z
% 119.18/119.59 , T ) ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, T ), :=( Z, Y ), :=( T, Z )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43020, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 119.18/119.59 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43022, [ =( multiply( X, 'least_upper_bound'( Z, Y ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 119.18/119.59 ) ] )
% 119.18/119.59 , 0, clause( 43020, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43024, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), multiply( X
% 119.18/119.59 , 'least_upper_bound'( Z, Y ) ) ) ] )
% 119.18/119.59 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 119.18/119.59 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, clause( 43022, [ =( multiply( X, 'least_upper_bound'( Z, Y ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 119.18/119.59 substitution( 1, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 64, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), multiply( X,
% 119.18/119.59 'least_upper_bound'( Z, Y ) ) ) ] )
% 119.18/119.59 , clause( 43024, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), multiply(
% 119.18/119.59 X, 'least_upper_bound'( Z, Y ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43026, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 119.18/119.59 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43028, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) ),
% 119.18/119.59 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 119.18/119.59 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.59 , 0, clause( 43026, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , 0, 8, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 119.18/119.59 X ) ), :=( Y, X ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43031, [ =( 'least_upper_bound'( identity, multiply( inverse( X ),
% 119.18/119.59 Y ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 43028, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) )
% 119.18/119.59 , 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 65, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y )
% 119.18/119.59 ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 43031, [ =( 'least_upper_bound'( identity, multiply( inverse( X )
% 119.18/119.59 , Y ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43034, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 119.18/119.59 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43037, [ =( multiply( inverse( X ), 'least_upper_bound'( Y, X ) ),
% 119.18/119.59 'least_upper_bound'( multiply( inverse( X ), Y ), identity ) ) ] )
% 119.18/119.59 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.59 , 0, clause( 43034, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , 0, 12, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.59 inverse( X ) ), :=( Y, Y ), :=( Z, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43040, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ),
% 119.18/119.59 identity ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.59 , clause( 43037, [ =( multiply( inverse( X ), 'least_upper_bound'( Y, X ) )
% 119.18/119.59 , 'least_upper_bound'( multiply( inverse( X ), Y ), identity ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 66, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ), identity
% 119.18/119.59 ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.59 , clause( 43040, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ),
% 119.18/119.59 identity ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43042, [ =( multiply( X, Y ), multiply( multiply( X, identity ), Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 18, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X )
% 119.18/119.59 ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43045, [ =( multiply( inverse( identity ), X ), multiply( identity
% 119.18/119.59 , X ) ) ] )
% 119.18/119.59 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.59 , 0, clause( 43042, [ =( multiply( X, Y ), multiply( multiply( X, identity
% 119.18/119.59 ), Y ) ) ] )
% 119.18/119.59 , 0, 6, substitution( 0, [ :=( X, identity )] ), substitution( 1, [ :=( X,
% 119.18/119.59 inverse( identity ) ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43046, [ =( multiply( inverse( identity ), X ), X ) ] )
% 119.18/119.59 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.59 , 0, clause( 43045, [ =( multiply( inverse( identity ), X ), multiply(
% 119.18/119.59 identity, X ) ) ] )
% 119.18/119.59 , 0, 5, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 67, [ =( multiply( inverse( identity ), X ), X ) ] )
% 119.18/119.59 , clause( 43046, [ =( multiply( inverse( identity ), X ), X ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43049, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 119.18/119.59 Y, Z ) ) ) ] )
% 119.18/119.59 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 119.18/119.59 ), Z ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43054, [ =( multiply( multiply( X, inverse( identity ) ), Y ),
% 119.18/119.59 multiply( X, Y ) ) ] )
% 119.18/119.59 , clause( 67, [ =( multiply( inverse( identity ), X ), X ) ] )
% 119.18/119.59 , 0, clause( 43049, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 119.18/119.59 multiply( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, 9, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.59 :=( Y, inverse( identity ) ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 68, [ =( multiply( multiply( Y, inverse( identity ) ), X ),
% 119.18/119.59 multiply( Y, X ) ) ] )
% 119.18/119.59 , clause( 43054, [ =( multiply( multiply( X, inverse( identity ) ), Y ),
% 119.18/119.59 multiply( X, Y ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43059, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( X, Y ), Z ), X ) ) ] )
% 119.18/119.59 , clause( 53, [ =( 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( X, Y ), Z ), X ), X ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43061, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( 'greatest_lower_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), Z ), T ), X ), Y ) ) ] )
% 119.18/119.59 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 43059, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( X, Y ), Z ), X ) ) ] )
% 119.18/119.59 , 0, 4, substitution( 0, [ :=( X, 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), Z ), T ) ), :=( Y, X
% 119.18/119.59 ), :=( Z, Y )] ), substitution( 1, [ :=( X, 'least_upper_bound'( X, Y )
% 119.18/119.59 ), :=( Y, Z ), :=( Z, T )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43062, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.59 'greatest_lower_bound'( 'greatest_lower_bound'( 'least_upper_bound'( X, Y
% 119.18/119.59 ), Z ), T ), X ), Y ), 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.59 , clause( 43061, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( 'greatest_lower_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), Z ), T ), X ), Y ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 69, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.59 'greatest_lower_bound'( 'greatest_lower_bound'( 'least_upper_bound'( X, Y
% 119.18/119.59 ), Z ), T ), X ), Y ), 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.59 , clause( 43062, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.59 'greatest_lower_bound'( 'greatest_lower_bound'( 'least_upper_bound'( X, Y
% 119.18/119.59 ), Z ), T ), X ), Y ), 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43063, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , clause( 12, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z
% 119.18/119.59 ) ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43065, [ =( multiply( X, 'greatest_lower_bound'( Z, Y ) ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 119.18/119.59 , X ) ) ] )
% 119.18/119.59 , 0, clause( 43063, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43067, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ), multiply(
% 119.18/119.59 X, 'greatest_lower_bound'( Z, Y ) ) ) ] )
% 119.18/119.59 , clause( 12, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z
% 119.18/119.59 ) ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, clause( 43065, [ =( multiply( X, 'greatest_lower_bound'( Z, Y ) ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 119.18/119.59 substitution( 1, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 76, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ), multiply( X
% 119.18/119.59 , 'greatest_lower_bound'( Z, Y ) ) ) ] )
% 119.18/119.59 , clause( 43067, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 119.18/119.59 multiply( X, 'greatest_lower_bound'( Z, Y ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43069, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , clause( 12, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z
% 119.18/119.59 ) ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43072, [ =( multiply( inverse( X ), 'greatest_lower_bound'( Y, X )
% 119.18/119.59 ), 'greatest_lower_bound'( multiply( inverse( X ), Y ), identity ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.59 , 0, clause( 43069, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , 0, 12, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.59 inverse( X ) ), :=( Y, Y ), :=( Z, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43075, [ =( 'greatest_lower_bound'( multiply( inverse( X ), Y ),
% 119.18/119.59 identity ), multiply( inverse( X ), 'greatest_lower_bound'( Y, X ) ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , clause( 43072, [ =( multiply( inverse( X ), 'greatest_lower_bound'( Y, X
% 119.18/119.59 ) ), 'greatest_lower_bound'( multiply( inverse( X ), Y ), identity ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 80, [ =( 'greatest_lower_bound'( multiply( inverse( X ), Y ),
% 119.18/119.59 identity ), multiply( inverse( X ), 'greatest_lower_bound'( Y, X ) ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , clause( 43075, [ =( 'greatest_lower_bound'( multiply( inverse( X ), Y ),
% 119.18/119.59 identity ), multiply( inverse( X ), 'greatest_lower_bound'( Y, X ) ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43076, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 119.18/119.59 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43078, [ =( multiply( 'least_upper_bound'( Y, X ), Z ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 119.18/119.59 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 119.18/119.59 ) ] )
% 119.18/119.59 , 0, clause( 43076, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43080, [ =( multiply( 'least_upper_bound'( X, Y ), Z ), multiply(
% 119.18/119.59 'least_upper_bound'( Y, X ), Z ) ) ] )
% 119.18/119.59 , clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 119.18/119.59 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 43078, [ =( multiply( 'least_upper_bound'( Y, X ), Z ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, 6, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 119.18/119.59 substitution( 1, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 114, [ =( multiply( 'least_upper_bound'( X, Z ), Y ), multiply(
% 119.18/119.59 'least_upper_bound'( Z, X ), Y ) ) ] )
% 119.18/119.59 , clause( 43080, [ =( multiply( 'least_upper_bound'( X, Y ), Z ), multiply(
% 119.18/119.59 'least_upper_bound'( Y, X ), Z ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43082, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 119.18/119.59 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43083, [ =( multiply( 'least_upper_bound'( inverse( X ), Y ), X ),
% 119.18/119.59 'least_upper_bound'( identity, multiply( Y, X ) ) ) ] )
% 119.18/119.59 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.59 , 0, clause( 43082, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , 0, 8, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 119.18/119.59 X ) ), :=( Y, X ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 115, [ =( multiply( 'least_upper_bound'( inverse( X ), Y ), X ),
% 119.18/119.59 'least_upper_bound'( identity, multiply( Y, X ) ) ) ] )
% 119.18/119.59 , clause( 43083, [ =( multiply( 'least_upper_bound'( inverse( X ), Y ), X )
% 119.18/119.59 , 'least_upper_bound'( identity, multiply( Y, X ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43088, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 119.18/119.59 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43089, [ =( multiply( 'least_upper_bound'( identity, X ), Y ),
% 119.18/119.59 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.59 , 0, clause( 43088, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , 0, 7, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X,
% 119.18/119.59 identity ), :=( Y, Y ), :=( Z, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43091, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 119.18/119.59 'least_upper_bound'( identity, X ), Y ) ) ] )
% 119.18/119.59 , clause( 43089, [ =( multiply( 'least_upper_bound'( identity, X ), Y ),
% 119.18/119.59 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 117, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 119.18/119.59 'least_upper_bound'( identity, Y ), X ) ) ] )
% 119.18/119.59 , clause( 43091, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 119.18/119.59 'least_upper_bound'( identity, X ), Y ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43094, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 119.18/119.59 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43096, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), Y ) ) ] )
% 119.18/119.59 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.59 , 0, clause( 43094, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , 0, 10, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.59 :=( Y, Y ), :=( Z, identity )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43098, [ =( 'least_upper_bound'( multiply( X, Y ), Y ), multiply(
% 119.18/119.59 'least_upper_bound'( X, identity ), Y ) ) ] )
% 119.18/119.59 , clause( 43096, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), Y ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 118, [ =( 'least_upper_bound'( multiply( Y, X ), X ), multiply(
% 119.18/119.59 'least_upper_bound'( Y, identity ), X ) ) ] )
% 119.18/119.59 , clause( 43098, [ =( 'least_upper_bound'( multiply( X, Y ), Y ), multiply(
% 119.18/119.59 'least_upper_bound'( X, identity ), Y ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43100, [ =( multiply( X, Y ), multiply( multiply( X, inverse(
% 119.18/119.59 identity ) ), Y ) ) ] )
% 119.18/119.59 , clause( 68, [ =( multiply( multiply( Y, inverse( identity ) ), X ),
% 119.18/119.59 multiply( Y, X ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43103, [ =( multiply( inverse( inverse( identity ) ), X ), multiply(
% 119.18/119.59 identity, X ) ) ] )
% 119.18/119.59 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.59 , 0, clause( 43100, [ =( multiply( X, Y ), multiply( multiply( X, inverse(
% 119.18/119.59 identity ) ), Y ) ) ] )
% 119.18/119.59 , 0, 7, substitution( 0, [ :=( X, inverse( identity ) )] ), substitution( 1
% 119.18/119.59 , [ :=( X, inverse( inverse( identity ) ) ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43104, [ =( multiply( inverse( inverse( identity ) ), X ), X ) ] )
% 119.18/119.59 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.59 , 0, clause( 43103, [ =( multiply( inverse( inverse( identity ) ), X ),
% 119.18/119.59 multiply( identity, X ) ) ] )
% 119.18/119.59 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 138, [ =( multiply( inverse( inverse( identity ) ), X ), X ) ] )
% 119.18/119.59 , clause( 43104, [ =( multiply( inverse( inverse( identity ) ), X ), X ) ]
% 119.18/119.59 )
% 119.18/119.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43107, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( X, Y ), Z ), X ) ) ] )
% 119.18/119.59 , clause( 53, [ =( 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( X, Y ), Z ), X ), X ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43108, [ =( multiply( X, Y ), 'least_upper_bound'(
% 119.18/119.59 'greatest_lower_bound'( multiply( 'greatest_lower_bound'( X, Z ), Y ), T
% 119.18/119.59 ), multiply( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 14, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z
% 119.18/119.59 ) ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 43107, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( X, Y ), Z ), X ) ) ] )
% 119.18/119.59 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 119.18/119.59 substitution( 1, [ :=( X, multiply( X, Y ) ), :=( Y, multiply( Z, Y ) ),
% 119.18/119.59 :=( Z, T )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43109, [ =( 'least_upper_bound'( 'greatest_lower_bound'( multiply(
% 119.18/119.59 'greatest_lower_bound'( X, Z ), Y ), T ), multiply( X, Y ) ), multiply( X
% 119.18/119.59 , Y ) ) ] )
% 119.18/119.59 , clause( 43108, [ =( multiply( X, Y ), 'least_upper_bound'(
% 119.18/119.59 'greatest_lower_bound'( multiply( 'greatest_lower_bound'( X, Z ), Y ), T
% 119.18/119.59 ), multiply( X, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 144, [ =( 'least_upper_bound'( 'greatest_lower_bound'( multiply(
% 119.18/119.59 'greatest_lower_bound'( X, Z ), Y ), T ), multiply( X, Y ) ), multiply( X
% 119.18/119.59 , Y ) ) ] )
% 119.18/119.59 , clause( 43109, [ =( 'least_upper_bound'( 'greatest_lower_bound'( multiply(
% 119.18/119.59 'greatest_lower_bound'( X, Z ), Y ), T ), multiply( X, Y ) ), multiply( X
% 119.18/119.59 , Y ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43110, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , clause( 14, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z
% 119.18/119.59 ) ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43112, [ =( multiply( 'greatest_lower_bound'( Y, X ), Z ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 119.18/119.59 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 119.18/119.59 , X ) ) ] )
% 119.18/119.59 , 0, clause( 43110, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43114, [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ), multiply(
% 119.18/119.59 'greatest_lower_bound'( Y, X ), Z ) ) ] )
% 119.18/119.59 , clause( 14, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z
% 119.18/119.59 ) ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 43112, [ =( multiply( 'greatest_lower_bound'( Y, X ), Z ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, 6, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 119.18/119.59 substitution( 1, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 150, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ), multiply(
% 119.18/119.59 'greatest_lower_bound'( Z, X ), Y ) ) ] )
% 119.18/119.59 , clause( 43114, [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 119.18/119.59 multiply( 'greatest_lower_bound'( Y, X ), Z ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43116, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , clause( 14, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z
% 119.18/119.59 ) ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43117, [ =( multiply( 'greatest_lower_bound'( inverse( X ), Y ), X
% 119.18/119.59 ), 'greatest_lower_bound'( identity, multiply( Y, X ) ) ) ] )
% 119.18/119.59 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.59 , 0, clause( 43116, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , 0, 8, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 119.18/119.59 X ) ), :=( Y, X ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 151, [ =( multiply( 'greatest_lower_bound'( inverse( X ), Y ), X )
% 119.18/119.59 , 'greatest_lower_bound'( identity, multiply( Y, X ) ) ) ] )
% 119.18/119.59 , clause( 43117, [ =( multiply( 'greatest_lower_bound'( inverse( X ), Y ),
% 119.18/119.59 X ), 'greatest_lower_bound'( identity, multiply( Y, X ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43122, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , clause( 14, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z
% 119.18/119.59 ) ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43123, [ =( multiply( 'greatest_lower_bound'( identity, X ), Y ),
% 119.18/119.59 'greatest_lower_bound'( Y, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.59 , 0, clause( 43122, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , 0, 7, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X,
% 119.18/119.59 identity ), :=( Y, Y ), :=( Z, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43125, [ =( 'greatest_lower_bound'( Y, multiply( X, Y ) ), multiply(
% 119.18/119.59 'greatest_lower_bound'( identity, X ), Y ) ) ] )
% 119.18/119.59 , clause( 43123, [ =( multiply( 'greatest_lower_bound'( identity, X ), Y )
% 119.18/119.59 , 'greatest_lower_bound'( Y, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 153, [ =( 'greatest_lower_bound'( X, multiply( Y, X ) ), multiply(
% 119.18/119.59 'greatest_lower_bound'( identity, Y ), X ) ) ] )
% 119.18/119.59 , clause( 43125, [ =( 'greatest_lower_bound'( Y, multiply( X, Y ) ),
% 119.18/119.59 multiply( 'greatest_lower_bound'( identity, X ), Y ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43128, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , clause( 14, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z
% 119.18/119.59 ) ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43130, [ =( multiply( 'greatest_lower_bound'( X, identity ), Y ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ] )
% 119.18/119.59 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.59 , 0, clause( 43128, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , 0, 10, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.59 :=( Y, Y ), :=( Z, identity )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43132, [ =( 'greatest_lower_bound'( multiply( X, Y ), Y ), multiply(
% 119.18/119.59 'greatest_lower_bound'( X, identity ), Y ) ) ] )
% 119.18/119.59 , clause( 43130, [ =( multiply( 'greatest_lower_bound'( X, identity ), Y )
% 119.18/119.59 , 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 154, [ =( 'greatest_lower_bound'( multiply( Y, X ), X ), multiply(
% 119.18/119.59 'greatest_lower_bound'( Y, identity ), X ) ) ] )
% 119.18/119.59 , clause( 43132, [ =( 'greatest_lower_bound'( multiply( X, Y ), Y ),
% 119.18/119.59 multiply( 'greatest_lower_bound'( X, identity ), Y ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43133, [ =( X, multiply( inverse( inverse( identity ) ), X ) ) ] )
% 119.18/119.59 , clause( 138, [ =( multiply( inverse( inverse( identity ) ), X ), X ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43135, [ =( inverse( identity ), identity ) ] )
% 119.18/119.59 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.59 , 0, clause( 43133, [ =( X, multiply( inverse( inverse( identity ) ), X ) )
% 119.18/119.59 ] )
% 119.18/119.59 , 0, 3, substitution( 0, [ :=( X, inverse( identity ) )] ), substitution( 1
% 119.18/119.59 , [ :=( X, inverse( identity ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 160, [ =( inverse( identity ), identity ) ] )
% 119.18/119.59 , clause( 43135, [ =( inverse( identity ), identity ) ] )
% 119.18/119.59 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43138, [ =( multiply( X, identity ), multiply( multiply( X, inverse(
% 119.18/119.59 Y ) ), Y ) ) ] )
% 119.18/119.59 , clause( 17, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 119.18/119.59 , identity ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43141, [ =( multiply( inverse( inverse( X ) ), identity ), multiply(
% 119.18/119.59 identity, X ) ) ] )
% 119.18/119.59 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.59 , 0, clause( 43138, [ =( multiply( X, identity ), multiply( multiply( X,
% 119.18/119.59 inverse( Y ) ), Y ) ) ] )
% 119.18/119.59 , 0, 7, substitution( 0, [ :=( X, inverse( X ) )] ), substitution( 1, [
% 119.18/119.59 :=( X, inverse( inverse( X ) ) ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43142, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 119.18/119.59 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.59 , 0, clause( 43141, [ =( multiply( inverse( inverse( X ) ), identity ),
% 119.18/119.59 multiply( identity, X ) ) ] )
% 119.18/119.59 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 163, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 119.18/119.59 , clause( 43142, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ]
% 119.18/119.59 )
% 119.18/119.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43145, [ =( multiply( X, Y ), multiply( multiply( X, identity ), Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 18, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X )
% 119.18/119.59 ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43148, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 163, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 119.18/119.59 , 0, clause( 43145, [ =( multiply( X, Y ), multiply( multiply( X, identity
% 119.18/119.59 ), Y ) ) ] )
% 119.18/119.59 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 119.18/119.59 inverse( X ) ) ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 119.18/119.59 ) ] )
% 119.18/119.59 , clause( 43148, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X,
% 119.18/119.59 Y ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43155, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 119.18/119.59 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43158, [ =( multiply( inverse( inverse( X ) ), 'least_upper_bound'(
% 119.18/119.59 identity, Y ) ), 'least_upper_bound'( X, multiply( inverse( inverse( X )
% 119.18/119.59 ), Y ) ) ) ] )
% 119.18/119.59 , clause( 163, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 119.18/119.59 , 0, clause( 43155, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , 0, 9, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 119.18/119.59 inverse( X ) ) ), :=( Y, identity ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43168, [ =( multiply( inverse( inverse( X ) ), 'least_upper_bound'(
% 119.18/119.59 identity, Y ) ), 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, clause( 43158, [ =( multiply( inverse( inverse( X ) ),
% 119.18/119.59 'least_upper_bound'( identity, Y ) ), 'least_upper_bound'( X, multiply(
% 119.18/119.59 inverse( inverse( X ) ), Y ) ) ) ] )
% 119.18/119.59 , 0, 10, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43170, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 119.18/119.59 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, clause( 43168, [ =( multiply( inverse( inverse( X ) ),
% 119.18/119.59 'least_upper_bound'( identity, Y ) ), 'least_upper_bound'( X, multiply( X
% 119.18/119.59 , Y ) ) ) ] )
% 119.18/119.59 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, 'least_upper_bound'( identity
% 119.18/119.59 , Y ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43171, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 119.18/119.59 , 'least_upper_bound'( identity, Y ) ) ) ] )
% 119.18/119.59 , clause( 43170, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 119.18/119.59 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 171, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X,
% 119.18/119.59 'least_upper_bound'( identity, Y ) ) ) ] )
% 119.18/119.59 , clause( 43171, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply(
% 119.18/119.59 X, 'least_upper_bound'( identity, Y ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43173, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 119.18/119.59 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43177, [ =( multiply( inverse( inverse( X ) ), 'least_upper_bound'(
% 119.18/119.59 Y, identity ) ), 'least_upper_bound'( multiply( inverse( inverse( X ) ),
% 119.18/119.59 Y ), X ) ) ] )
% 119.18/119.59 , clause( 163, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 119.18/119.59 , 0, clause( 43173, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , 0, 14, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.59 inverse( inverse( X ) ) ), :=( Y, Y ), :=( Z, identity )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43179, [ =( multiply( inverse( inverse( X ) ), 'least_upper_bound'(
% 119.18/119.59 Y, identity ) ), 'least_upper_bound'( multiply( X, Y ), X ) ) ] )
% 119.18/119.59 , clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, clause( 43177, [ =( multiply( inverse( inverse( X ) ),
% 119.18/119.59 'least_upper_bound'( Y, identity ) ), 'least_upper_bound'( multiply(
% 119.18/119.59 inverse( inverse( X ) ), Y ), X ) ) ] )
% 119.18/119.59 , 0, 9, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43181, [ =( multiply( X, 'least_upper_bound'( Y, identity ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), X ) ) ] )
% 119.18/119.59 , clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, clause( 43179, [ =( multiply( inverse( inverse( X ) ),
% 119.18/119.59 'least_upper_bound'( Y, identity ) ), 'least_upper_bound'( multiply( X, Y
% 119.18/119.59 ), X ) ) ] )
% 119.18/119.59 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, 'least_upper_bound'( Y,
% 119.18/119.59 identity ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43182, [ =( 'least_upper_bound'( multiply( X, Y ), X ), multiply( X
% 119.18/119.59 , 'least_upper_bound'( Y, identity ) ) ) ] )
% 119.18/119.59 , clause( 43181, [ =( multiply( X, 'least_upper_bound'( Y, identity ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), X ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 172, [ =( 'least_upper_bound'( multiply( X, Y ), X ), multiply( X,
% 119.18/119.59 'least_upper_bound'( Y, identity ) ) ) ] )
% 119.18/119.59 , clause( 43182, [ =( 'least_upper_bound'( multiply( X, Y ), X ), multiply(
% 119.18/119.59 X, 'least_upper_bound'( Y, identity ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43183, [ =( multiply( X, Y ), multiply( inverse( inverse( X ) ), Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43186, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.59 , clause( 163, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 119.18/119.59 , 0, clause( 43183, [ =( multiply( X, Y ), multiply( inverse( inverse( X )
% 119.18/119.59 ), Y ) ) ] )
% 119.18/119.59 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.59 :=( Y, identity )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.59 , clause( 43186, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43191, [ =( multiply( X, Y ), multiply( inverse( inverse( X ) ), Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43194, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 119.18/119.59 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.59 , 0, clause( 43191, [ =( multiply( X, Y ), multiply( inverse( inverse( X )
% 119.18/119.59 ), Y ) ) ] )
% 119.18/119.59 , 0, 5, substitution( 0, [ :=( X, inverse( X ) )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, inverse( X ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 180, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 119.18/119.59 , clause( 43194, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43197, [ =( X, multiply( X, identity ) ) ] )
% 119.18/119.59 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43200, [ =( inverse( inverse( X ) ), multiply( X, identity ) ) ] )
% 119.18/119.59 , clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, clause( 43197, [ =( X, multiply( X, identity ) ) ] )
% 119.18/119.59 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, identity )] ), substitution(
% 119.18/119.59 1, [ :=( X, inverse( inverse( X ) ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43201, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.59 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.59 , 0, clause( 43200, [ =( inverse( inverse( X ) ), multiply( X, identity ) )
% 119.18/119.59 ] )
% 119.18/119.59 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.59 , clause( 43201, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43204, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , clause( 12, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z
% 119.18/119.59 ) ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43205, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) ),
% 119.18/119.59 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.59 , 0, clause( 43204, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.59 :=( Y, identity ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43207, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 119.18/119.59 X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 119.18/119.59 , clause( 43205, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) )
% 119.18/119.59 , 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 182, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 119.18/119.59 X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 119.18/119.59 , clause( 43207, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ),
% 119.18/119.59 multiply( X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43210, [ =( multiply( X, identity ), multiply( multiply( X, inverse(
% 119.18/119.59 Y ) ), Y ) ) ] )
% 119.18/119.59 , clause( 17, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 119.18/119.59 , identity ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43212, [ =( multiply( X, identity ), multiply( multiply( X, Y ),
% 119.18/119.59 inverse( Y ) ) ) ] )
% 119.18/119.59 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.59 , 0, clause( 43210, [ =( multiply( X, identity ), multiply( multiply( X,
% 119.18/119.59 inverse( Y ) ), Y ) ) ] )
% 119.18/119.59 , 0, 7, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.59 :=( Y, inverse( Y ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43213, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 119.18/119.59 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.59 , 0, clause( 43212, [ =( multiply( X, identity ), multiply( multiply( X, Y
% 119.18/119.59 ), inverse( Y ) ) ) ] )
% 119.18/119.59 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.59 :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43214, [ =( multiply( multiply( X, Y ), inverse( Y ) ), X ) ] )
% 119.18/119.59 , clause( 43213, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 184, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 119.18/119.59 , clause( 43214, [ =( multiply( multiply( X, Y ), inverse( Y ) ), X ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43216, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , clause( 14, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z
% 119.18/119.59 ) ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43218, [ =( multiply( 'greatest_lower_bound'( X, Y ), inverse( X )
% 119.18/119.59 ), 'greatest_lower_bound'( identity, multiply( Y, inverse( X ) ) ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , clause( 180, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 119.18/119.59 , 0, clause( 43216, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , 0, 8, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.59 :=( Y, inverse( X ) ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43221, [ =( 'greatest_lower_bound'( identity, multiply( Y, inverse(
% 119.18/119.59 X ) ) ), multiply( 'greatest_lower_bound'( X, Y ), inverse( X ) ) ) ] )
% 119.18/119.59 , clause( 43218, [ =( multiply( 'greatest_lower_bound'( X, Y ), inverse( X
% 119.18/119.59 ) ), 'greatest_lower_bound'( identity, multiply( Y, inverse( X ) ) ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 185, [ =( 'greatest_lower_bound'( identity, multiply( Y, inverse( X
% 119.18/119.59 ) ) ), multiply( 'greatest_lower_bound'( X, Y ), inverse( X ) ) ) ] )
% 119.18/119.59 , clause( 43221, [ =( 'greatest_lower_bound'( identity, multiply( Y,
% 119.18/119.59 inverse( X ) ) ), multiply( 'greatest_lower_bound'( X, Y ), inverse( X )
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43224, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 119.18/119.59 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43226, [ =( multiply( 'least_upper_bound'( X, Y ), inverse( X ) ),
% 119.18/119.59 'least_upper_bound'( identity, multiply( Y, inverse( X ) ) ) ) ] )
% 119.18/119.59 , clause( 180, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 119.18/119.59 , 0, clause( 43224, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , 0, 8, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.59 :=( Y, inverse( X ) ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43229, [ =( 'least_upper_bound'( identity, multiply( Y, inverse( X
% 119.18/119.59 ) ) ), multiply( 'least_upper_bound'( X, Y ), inverse( X ) ) ) ] )
% 119.18/119.59 , clause( 43226, [ =( multiply( 'least_upper_bound'( X, Y ), inverse( X ) )
% 119.18/119.59 , 'least_upper_bound'( identity, multiply( Y, inverse( X ) ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 187, [ =( 'least_upper_bound'( identity, multiply( Y, inverse( X )
% 119.18/119.59 ) ), multiply( 'least_upper_bound'( X, Y ), inverse( X ) ) ) ] )
% 119.18/119.59 , clause( 43229, [ =( 'least_upper_bound'( identity, multiply( Y, inverse(
% 119.18/119.59 X ) ) ), multiply( 'least_upper_bound'( X, Y ), inverse( X ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43232, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 119.18/119.59 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43234, [ =( multiply( X, 'least_upper_bound'( Y, inverse( X ) ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), identity ) ) ] )
% 119.18/119.59 , clause( 180, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 119.18/119.59 , 0, clause( 43232, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , 0, 11, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.59 :=( Y, Y ), :=( Z, inverse( X ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 192, [ =( multiply( X, 'least_upper_bound'( Y, inverse( X ) ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), identity ) ) ] )
% 119.18/119.59 , clause( 43234, [ =( multiply( X, 'least_upper_bound'( Y, inverse( X ) ) )
% 119.18/119.59 , 'least_upper_bound'( multiply( X, Y ), identity ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43238, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 119.18/119.59 , clause( 184, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43243, [ =( multiply( inverse( multiply( X, Y ) ), X ), multiply(
% 119.18/119.59 identity, inverse( Y ) ) ) ] )
% 119.18/119.59 , clause( 16, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ), Y
% 119.18/119.59 ), identity ) ] )
% 119.18/119.59 , 0, clause( 43238, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, multiply( inverse( multiply( X, Y ) ), X ) ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43244, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.59 , 0, clause( 43243, [ =( multiply( inverse( multiply( X, Y ) ), X ),
% 119.18/119.59 multiply( identity, inverse( Y ) ) ) ] )
% 119.18/119.59 , 0, 7, substitution( 0, [ :=( X, inverse( Y ) )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 195, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y )
% 119.18/119.59 ) ] )
% 119.18/119.59 , clause( 43244, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse(
% 119.18/119.59 Y ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43247, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 119.18/119.59 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43249, [ =( multiply( 'least_upper_bound'( X, multiply( Y, Z ) ),
% 119.18/119.59 inverse( Z ) ), 'least_upper_bound'( multiply( X, inverse( Z ) ), Y ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , clause( 184, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 119.18/119.59 , 0, clause( 43247, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 119.18/119.59 , 0, 14, substitution( 0, [ :=( X, Z ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, inverse( Z ) ), :=( Z, multiply( Y, Z ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 199, [ =( multiply( 'least_upper_bound'( Z, multiply( X, Y ) ),
% 119.18/119.59 inverse( Y ) ), 'least_upper_bound'( multiply( Z, inverse( Y ) ), X ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , clause( 43249, [ =( multiply( 'least_upper_bound'( X, multiply( Y, Z ) )
% 119.18/119.59 , inverse( Z ) ), 'least_upper_bound'( multiply( X, inverse( Z ) ), Y ) )
% 119.18/119.59 ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43252, [ =( inverse( Y ), multiply( inverse( multiply( X, Y ) ), X
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 195, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43256, [ =( inverse( X ), multiply( inverse( inverse( Y ) ),
% 119.18/119.59 inverse( multiply( X, Y ) ) ) ) ] )
% 119.18/119.59 , clause( 195, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, clause( 43252, [ =( inverse( Y ), multiply( inverse( multiply( X, Y )
% 119.18/119.59 ), X ) ) ] )
% 119.18/119.59 , 0, 5, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, inverse( multiply( X, Y ) ) ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43257, [ =( inverse( X ), multiply( Y, inverse( multiply( X, Y ) )
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, clause( 43256, [ =( inverse( X ), multiply( inverse( inverse( Y ) ),
% 119.18/119.59 inverse( multiply( X, Y ) ) ) ) ] )
% 119.18/119.59 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, inverse( multiply( X, Y ) ) )] )
% 119.18/119.59 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43258, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 43257, [ =( inverse( X ), multiply( Y, inverse( multiply( X, Y )
% 119.18/119.59 ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 201, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X )
% 119.18/119.59 ) ] )
% 119.18/119.59 , clause( 43258, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse(
% 119.18/119.59 X ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43260, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 119.18/119.59 , clause( 184, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43263, [ =( inverse( multiply( X, Y ) ), multiply( inverse( Y ),
% 119.18/119.59 inverse( X ) ) ) ] )
% 119.18/119.59 , clause( 195, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, clause( 43260, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, inverse( multiply( X, Y ) ) ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43264, [ =( multiply( inverse( Y ), inverse( X ) ), inverse(
% 119.18/119.59 multiply( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 43263, [ =( inverse( multiply( X, Y ) ), multiply( inverse( Y ),
% 119.18/119.59 inverse( X ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 202, [ =( multiply( inverse( Y ), inverse( X ) ), inverse( multiply(
% 119.18/119.59 X, Y ) ) ) ] )
% 119.18/119.59 , clause( 43264, [ =( multiply( inverse( Y ), inverse( X ) ), inverse(
% 119.18/119.59 multiply( X, Y ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43266, [ =( multiply( X, identity ), multiply( multiply( X, inverse(
% 119.18/119.59 Y ) ), Y ) ) ] )
% 119.18/119.59 , clause( 17, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 119.18/119.59 , identity ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43272, [ =( multiply( inverse( multiply( inverse( X ), Y ) ),
% 119.18/119.59 identity ), multiply( inverse( Y ), X ) ) ] )
% 119.18/119.59 , clause( 195, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, clause( 43266, [ =( multiply( X, identity ), multiply( multiply( X,
% 119.18/119.59 inverse( Y ) ), Y ) ) ] )
% 119.18/119.59 , 0, 9, substitution( 0, [ :=( X, inverse( X ) ), :=( Y, Y )] ),
% 119.18/119.59 substitution( 1, [ :=( X, inverse( multiply( inverse( X ), Y ) ) ), :=( Y
% 119.18/119.59 , X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43273, [ =( inverse( multiply( inverse( X ), Y ) ), multiply(
% 119.18/119.59 inverse( Y ), X ) ) ] )
% 119.18/119.59 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.59 , 0, clause( 43272, [ =( multiply( inverse( multiply( inverse( X ), Y ) ),
% 119.18/119.59 identity ), multiply( inverse( Y ), X ) ) ] )
% 119.18/119.59 , 0, 1, substitution( 0, [ :=( X, inverse( multiply( inverse( X ), Y ) ) )] )
% 119.18/119.59 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 203, [ =( inverse( multiply( inverse( X ), Y ) ), multiply( inverse(
% 119.18/119.59 Y ), X ) ) ] )
% 119.18/119.59 , clause( 43273, [ =( inverse( multiply( inverse( X ), Y ) ), multiply(
% 119.18/119.59 inverse( Y ), X ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43276, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X ) )
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 201, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43281, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 119.18/119.59 inverse( multiply( X, identity ) ) ) ) ] )
% 119.18/119.59 , clause( 17, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 119.18/119.59 , identity ) ) ] )
% 119.18/119.59 , 0, clause( 43276, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X
% 119.18/119.59 ) ) ) ) ] )
% 119.18/119.59 , 0, 9, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.59 :=( X, Y ), :=( Y, multiply( X, inverse( Y ) ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43282, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 119.18/119.59 inverse( X ) ) ) ] )
% 119.18/119.59 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.59 , 0, clause( 43281, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply(
% 119.18/119.59 Y, inverse( multiply( X, identity ) ) ) ) ] )
% 119.18/119.59 , 0, 9, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.59 :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 211, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 119.18/119.59 inverse( X ) ) ) ] )
% 119.18/119.59 , clause( 43282, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 119.18/119.59 inverse( X ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43285, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , clause( 12, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z
% 119.18/119.59 ) ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43286, [ =( multiply( X, 'greatest_lower_bound'( inverse( multiply(
% 119.18/119.59 Y, X ) ), Z ) ), 'greatest_lower_bound'( inverse( Y ), multiply( X, Z ) )
% 119.18/119.59 ) ] )
% 119.18/119.59 , clause( 201, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, clause( 43285, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , 0, 10, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, inverse( multiply( Y, X ) ) ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 212, [ =( multiply( X, 'greatest_lower_bound'( inverse( multiply( Y
% 119.18/119.59 , X ) ), Z ) ), 'greatest_lower_bound'( inverse( Y ), multiply( X, Z ) )
% 119.18/119.59 ) ] )
% 119.18/119.59 , clause( 43286, [ =( multiply( X, 'greatest_lower_bound'( inverse(
% 119.18/119.59 multiply( Y, X ) ), Z ) ), 'greatest_lower_bound'( inverse( Y ), multiply(
% 119.18/119.59 X, Z ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43291, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 119.18/119.59 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43293, [ =( multiply( X, 'least_upper_bound'( Y, inverse( multiply(
% 119.18/119.59 Z, X ) ) ) ), 'least_upper_bound'( multiply( X, Y ), inverse( Z ) ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , clause( 201, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, clause( 43291, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 119.18/119.59 , 0, 13, substitution( 0, [ :=( X, Z ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, Y ), :=( Z, inverse( multiply( Z, X ) ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 215, [ =( multiply( X, 'least_upper_bound'( Z, inverse( multiply( Y
% 119.18/119.59 , X ) ) ) ), 'least_upper_bound'( multiply( X, Z ), inverse( Y ) ) ) ] )
% 119.18/119.59 , clause( 43293, [ =( multiply( X, 'least_upper_bound'( Y, inverse(
% 119.18/119.59 multiply( Z, X ) ) ) ), 'least_upper_bound'( multiply( X, Y ), inverse( Z
% 119.18/119.59 ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43296, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X ) )
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 201, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43299, [ =( inverse( 'greatest_lower_bound'( X, Y ) ), multiply( Z
% 119.18/119.59 , inverse( multiply( 'greatest_lower_bound'( Y, X ), Z ) ) ) ) ] )
% 119.18/119.59 , clause( 150, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ), multiply(
% 119.18/119.59 'greatest_lower_bound'( Z, X ), Y ) ) ] )
% 119.18/119.59 , 0, clause( 43296, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X
% 119.18/119.59 ) ) ) ) ] )
% 119.18/119.59 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 119.18/119.59 substitution( 1, [ :=( X, Z ), :=( Y, 'greatest_lower_bound'( X, Y ) )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43302, [ =( inverse( 'greatest_lower_bound'( X, Y ) ), inverse(
% 119.18/119.59 'greatest_lower_bound'( Y, X ) ) ) ] )
% 119.18/119.59 , clause( 201, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, clause( 43299, [ =( inverse( 'greatest_lower_bound'( X, Y ) ),
% 119.18/119.59 multiply( Z, inverse( multiply( 'greatest_lower_bound'( Y, X ), Z ) ) ) )
% 119.18/119.59 ] )
% 119.18/119.59 , 0, 5, substitution( 0, [ :=( X, 'greatest_lower_bound'( Y, X ) ), :=( Y,
% 119.18/119.59 Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 225, [ =( inverse( 'greatest_lower_bound'( Y, X ) ), inverse(
% 119.18/119.59 'greatest_lower_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 43302, [ =( inverse( 'greatest_lower_bound'( X, Y ) ), inverse(
% 119.18/119.59 'greatest_lower_bound'( Y, X ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43324, [ =( multiply( 'greatest_lower_bound'( multiply( X, Y ),
% 119.18/119.59 multiply( Z, Y ) ), T ), multiply( multiply( 'greatest_lower_bound'( Z, X
% 119.18/119.59 ), Y ), T ) ) ] )
% 119.18/119.59 , clause( 14, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z
% 119.18/119.59 ) ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 150, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 119.18/119.59 multiply( 'greatest_lower_bound'( Z, X ), Y ) ) ] )
% 119.18/119.59 , 0, 11, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 119.18/119.59 substitution( 1, [ :=( X, multiply( X, Y ) ), :=( Y, T ), :=( Z, multiply(
% 119.18/119.59 Z, Y ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43326, [ =( multiply( multiply( 'greatest_lower_bound'( X, Z ), Y )
% 119.18/119.59 , T ), multiply( multiply( 'greatest_lower_bound'( Z, X ), Y ), T ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , clause( 14, [ =( 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z
% 119.18/119.59 ) ), multiply( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 43324, [ =( multiply( 'greatest_lower_bound'( multiply( X, Y )
% 119.18/119.59 , multiply( Z, Y ) ), T ), multiply( multiply( 'greatest_lower_bound'( Z
% 119.18/119.59 , X ), Y ), T ) ) ] )
% 119.18/119.59 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 119.18/119.59 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 230, [ =( multiply( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 119.18/119.59 T ), multiply( multiply( 'greatest_lower_bound'( Z, X ), Y ), T ) ) ] )
% 119.18/119.59 , clause( 43326, [ =( multiply( multiply( 'greatest_lower_bound'( X, Z ), Y
% 119.18/119.59 ), T ), multiply( multiply( 'greatest_lower_bound'( Z, X ), Y ), T ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43327, [ =( 'greatest_lower_bound'( X, Z ), 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( X, 'least_upper_bound'( Y, Z ) ), Z ) ) ] )
% 119.18/119.59 , clause( 23, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Z,
% 119.18/119.59 'least_upper_bound'( X, Y ) ), Y ), 'greatest_lower_bound'( Z, Y ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43330, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 119.18/119.59 Y, 'greatest_lower_bound'( X, 'least_upper_bound'( Z, Y ) ) ) ) ] )
% 119.18/119.59 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 119.18/119.59 , X ) ) ] )
% 119.18/119.59 , 0, clause( 43327, [ =( 'greatest_lower_bound'( X, Z ),
% 119.18/119.59 'greatest_lower_bound'( 'greatest_lower_bound'( X, 'least_upper_bound'( Y
% 119.18/119.59 , Z ) ), Z ) ) ] )
% 119.18/119.59 , 0, 4, substitution( 0, [ :=( X, 'greatest_lower_bound'( X,
% 119.18/119.59 'least_upper_bound'( Z, Y ) ) ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 119.18/119.59 , X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43343, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( Y, X ), 'least_upper_bound'( Z, Y ) ) ) ] )
% 119.18/119.59 , clause( 5, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z )
% 119.18/119.59 ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 43330, [ =( 'greatest_lower_bound'( X, Y ),
% 119.18/119.59 'greatest_lower_bound'( Y, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 119.18/119.59 Z, Y ) ) ) ) ] )
% 119.18/119.59 , 0, 4, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z,
% 119.18/119.59 'least_upper_bound'( Z, Y ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y
% 119.18/119.59 ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43344, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Y, X )
% 119.18/119.59 , 'least_upper_bound'( Z, Y ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.59 , clause( 43343, [ =( 'greatest_lower_bound'( X, Y ),
% 119.18/119.59 'greatest_lower_bound'( 'greatest_lower_bound'( Y, X ),
% 119.18/119.59 'least_upper_bound'( Z, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 241, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Z, X ),
% 119.18/119.59 'least_upper_bound'( Y, Z ) ), 'greatest_lower_bound'( X, Z ) ) ] )
% 119.18/119.59 , clause( 43344, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Y, X
% 119.18/119.59 ), 'least_upper_bound'( Z, Y ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43345, [ =( identity, multiply( inverse( X ), X ) ) ] )
% 119.18/119.59 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43346, [ =( identity, multiply( inverse( 'greatest_lower_bound'( Y
% 119.18/119.59 , X ) ), 'greatest_lower_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 225, [ =( inverse( 'greatest_lower_bound'( Y, X ) ), inverse(
% 119.18/119.59 'greatest_lower_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , 0, clause( 43345, [ =( identity, multiply( inverse( X ), X ) ) ] )
% 119.18/119.59 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.59 :=( X, 'greatest_lower_bound'( X, Y ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43349, [ =( multiply( inverse( 'greatest_lower_bound'( X, Y ) ),
% 119.18/119.59 'greatest_lower_bound'( Y, X ) ), identity ) ] )
% 119.18/119.59 , clause( 43346, [ =( identity, multiply( inverse( 'greatest_lower_bound'(
% 119.18/119.59 Y, X ) ), 'greatest_lower_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 248, [ =( multiply( inverse( 'greatest_lower_bound'( Y, X ) ),
% 119.18/119.59 'greatest_lower_bound'( X, Y ) ), identity ) ] )
% 119.18/119.59 , clause( 43349, [ =( multiply( inverse( 'greatest_lower_bound'( X, Y ) ),
% 119.18/119.59 'greatest_lower_bound'( Y, X ) ), identity ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43351, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( X, Y )
% 119.18/119.59 , X ) ) ] )
% 119.18/119.59 , clause( 37, [ =( 'least_upper_bound'( 'greatest_lower_bound'( X, Y ), X )
% 119.18/119.59 , X ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43354, [ =( 'greatest_lower_bound'( X, Y ), 'least_upper_bound'(
% 119.18/119.59 'greatest_lower_bound'( Y, X ), 'greatest_lower_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 241, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Z, X )
% 119.18/119.59 , 'least_upper_bound'( Y, Z ) ), 'greatest_lower_bound'( X, Z ) ) ] )
% 119.18/119.59 , 0, clause( 43351, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( X
% 119.18/119.59 , Y ), X ) ) ] )
% 119.18/119.59 , 0, 5, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 119.18/119.59 substitution( 1, [ :=( X, 'greatest_lower_bound'( X, Y ) ), :=( Y,
% 119.18/119.59 'least_upper_bound'( Z, X ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43355, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ),
% 119.18/119.59 'greatest_lower_bound'( X, Y ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.59 , clause( 43354, [ =( 'greatest_lower_bound'( X, Y ), 'least_upper_bound'(
% 119.18/119.59 'greatest_lower_bound'( Y, X ), 'greatest_lower_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 259, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ),
% 119.18/119.59 'greatest_lower_bound'( X, Y ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.59 , clause( 43355, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ),
% 119.18/119.59 'greatest_lower_bound'( X, Y ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43356, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X ) )
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 201, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43359, [ =( inverse( 'least_upper_bound'( X, Y ) ), multiply( Z,
% 119.18/119.59 inverse( multiply( 'least_upper_bound'( Y, X ), Z ) ) ) ) ] )
% 119.18/119.59 , clause( 114, [ =( multiply( 'least_upper_bound'( X, Z ), Y ), multiply(
% 119.18/119.59 'least_upper_bound'( Z, X ), Y ) ) ] )
% 119.18/119.59 , 0, clause( 43356, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X
% 119.18/119.59 ) ) ) ) ] )
% 119.18/119.59 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 119.18/119.59 substitution( 1, [ :=( X, Z ), :=( Y, 'least_upper_bound'( X, Y ) )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43362, [ =( inverse( 'least_upper_bound'( X, Y ) ), inverse(
% 119.18/119.59 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.59 , clause( 201, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, clause( 43359, [ =( inverse( 'least_upper_bound'( X, Y ) ), multiply(
% 119.18/119.59 Z, inverse( multiply( 'least_upper_bound'( Y, X ), Z ) ) ) ) ] )
% 119.18/119.59 , 0, 5, substitution( 0, [ :=( X, 'least_upper_bound'( Y, X ) ), :=( Y, Z )] )
% 119.18/119.59 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 273, [ =( inverse( 'least_upper_bound'( Y, X ) ), inverse(
% 119.18/119.59 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 43362, [ =( inverse( 'least_upper_bound'( X, Y ) ), inverse(
% 119.18/119.59 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43363, [ =( inverse( Y ), multiply( inverse( multiply( X, Y ) ), X
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 195, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43364, [ =( inverse( X ), multiply( inverse( multiply(
% 119.18/119.59 'least_upper_bound'( Z, Y ), X ) ), 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , clause( 114, [ =( multiply( 'least_upper_bound'( X, Z ), Y ), multiply(
% 119.18/119.59 'least_upper_bound'( Z, X ), Y ) ) ] )
% 119.18/119.59 , 0, clause( 43363, [ =( inverse( Y ), multiply( inverse( multiply( X, Y )
% 119.18/119.59 ), X ) ) ] )
% 119.18/119.59 , 0, 5, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 119.18/119.59 substitution( 1, [ :=( X, 'least_upper_bound'( Y, Z ) ), :=( Y, X )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43367, [ =( multiply( inverse( multiply( 'least_upper_bound'( Y, Z
% 119.18/119.59 ), X ) ), 'least_upper_bound'( Z, Y ) ), inverse( X ) ) ] )
% 119.18/119.59 , clause( 43364, [ =( inverse( X ), multiply( inverse( multiply(
% 119.18/119.59 'least_upper_bound'( Z, Y ), X ) ), 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 274, [ =( multiply( inverse( multiply( 'least_upper_bound'( Y, X )
% 119.18/119.59 , Z ) ), 'least_upper_bound'( X, Y ) ), inverse( Z ) ) ] )
% 119.18/119.59 , clause( 43367, [ =( multiply( inverse( multiply( 'least_upper_bound'( Y,
% 119.18/119.59 Z ), X ) ), 'least_upper_bound'( Z, Y ) ), inverse( X ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43368, [ =( identity, multiply( inverse( X ), X ) ) ] )
% 119.18/119.59 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43369, [ =( identity, multiply( inverse( 'least_upper_bound'( Y, X
% 119.18/119.59 ) ), 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 273, [ =( inverse( 'least_upper_bound'( Y, X ) ), inverse(
% 119.18/119.59 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , 0, clause( 43368, [ =( identity, multiply( inverse( X ), X ) ) ] )
% 119.18/119.59 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.59 :=( X, 'least_upper_bound'( X, Y ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43372, [ =( multiply( inverse( 'least_upper_bound'( X, Y ) ),
% 119.18/119.59 'least_upper_bound'( Y, X ) ), identity ) ] )
% 119.18/119.59 , clause( 43369, [ =( identity, multiply( inverse( 'least_upper_bound'( Y,
% 119.18/119.59 X ) ), 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 288, [ =( multiply( inverse( 'least_upper_bound'( Y, X ) ),
% 119.18/119.59 'least_upper_bound'( X, Y ) ), identity ) ] )
% 119.18/119.59 , clause( 43372, [ =( multiply( inverse( 'least_upper_bound'( X, Y ) ),
% 119.18/119.59 'least_upper_bound'( Y, X ) ), identity ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43374, [ =( 'least_upper_bound'( 'least_upper_bound'( Y, Z ), X ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , clause( 49, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( Y, Z ), X ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43390, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.59 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ), T ), X ),
% 119.18/119.59 'least_upper_bound'( X, T ) ) ] )
% 119.18/119.59 , clause( 33, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( X, Y ), Z ) ), X ) ] )
% 119.18/119.59 , 0, clause( 43374, [ =( 'least_upper_bound'( 'least_upper_bound'( Y, Z ),
% 119.18/119.59 X ), 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, 11, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.59 substitution( 1, [ :=( X, X ), :=( Y, 'greatest_lower_bound'(
% 119.18/119.59 'greatest_lower_bound'( X, Y ), Z ) ), :=( Z, T )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 416, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.59 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ), T ), X ),
% 119.18/119.59 'least_upper_bound'( X, T ) ) ] )
% 119.18/119.59 , clause( 43390, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.59 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ), T ), X ),
% 119.18/119.59 'least_upper_bound'( X, T ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43395, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) ),
% 119.18/119.59 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 182, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 119.18/119.59 X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43396, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 119.18/119.59 X, 'greatest_lower_bound'( Y, identity ) ) ) ] )
% 119.18/119.59 , clause( 43395, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) )
% 119.18/119.59 , 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , 0, clause( 76, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 119.18/119.59 multiply( X, 'greatest_lower_bound'( Z, Y ) ) ) ] )
% 119.18/119.59 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, identity ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 506, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 119.18/119.59 X, 'greatest_lower_bound'( Y, identity ) ) ) ] )
% 119.18/119.59 , clause( 43396, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ),
% 119.18/119.59 multiply( X, 'greatest_lower_bound'( Y, identity ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43398, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) ),
% 119.18/119.59 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 182, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 119.18/119.59 X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43399, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 119.18/119.59 , clause( 184, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43400, [ =( X, multiply( 'greatest_lower_bound'( X, multiply( X, Y
% 119.18/119.59 ) ), inverse( 'greatest_lower_bound'( identity, Y ) ) ) ) ] )
% 119.18/119.59 , clause( 43398, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) )
% 119.18/119.59 , 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , 0, clause( 43399, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, 'greatest_lower_bound'( identity, Y ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43401, [ =( multiply( 'greatest_lower_bound'( X, multiply( X, Y ) )
% 119.18/119.59 , inverse( 'greatest_lower_bound'( identity, Y ) ) ), X ) ] )
% 119.18/119.59 , clause( 43400, [ =( X, multiply( 'greatest_lower_bound'( X, multiply( X,
% 119.18/119.59 Y ) ), inverse( 'greatest_lower_bound'( identity, Y ) ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 525, [ =( multiply( 'greatest_lower_bound'( X, multiply( X, Y ) ),
% 119.18/119.59 inverse( 'greatest_lower_bound'( identity, Y ) ) ), X ) ] )
% 119.18/119.59 , clause( 43401, [ =( multiply( 'greatest_lower_bound'( X, multiply( X, Y )
% 119.18/119.59 ), inverse( 'greatest_lower_bound'( identity, Y ) ) ), X ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43403, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) ),
% 119.18/119.59 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 182, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 119.18/119.59 X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43422, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ),
% 119.18/119.59 'greatest_lower_bound'( identity, Y ) ), 'greatest_lower_bound'( multiply(
% 119.18/119.59 inverse( multiply( X, Y ) ), X ), identity ) ) ] )
% 119.18/119.59 , clause( 16, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ), Y
% 119.18/119.59 ), identity ) ] )
% 119.18/119.59 , 0, clause( 43403, [ =( multiply( X, 'greatest_lower_bound'( identity, Y )
% 119.18/119.59 ), 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , 0, 18, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, multiply( inverse( multiply( X, Y ) ), X ) ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43424, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ),
% 119.18/119.59 'greatest_lower_bound'( identity, Y ) ), 'greatest_lower_bound'( inverse(
% 119.18/119.59 Y ), identity ) ) ] )
% 119.18/119.59 , clause( 195, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, clause( 43422, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X
% 119.18/119.59 ), 'greatest_lower_bound'( identity, Y ) ), 'greatest_lower_bound'(
% 119.18/119.59 multiply( inverse( multiply( X, Y ) ), X ), identity ) ) ] )
% 119.18/119.59 , 0, 12, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43425, [ =( multiply( inverse( Y ), 'greatest_lower_bound'(
% 119.18/119.59 identity, Y ) ), 'greatest_lower_bound'( inverse( Y ), identity ) ) ] )
% 119.18/119.59 , clause( 195, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, clause( 43424, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X
% 119.18/119.59 ), 'greatest_lower_bound'( identity, Y ) ), 'greatest_lower_bound'(
% 119.18/119.59 inverse( Y ), identity ) ) ] )
% 119.18/119.59 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 528, [ =( multiply( inverse( Y ), 'greatest_lower_bound'( identity
% 119.18/119.59 , Y ) ), 'greatest_lower_bound'( inverse( Y ), identity ) ) ] )
% 119.18/119.59 , clause( 43425, [ =( multiply( inverse( Y ), 'greatest_lower_bound'(
% 119.18/119.59 identity, Y ) ), 'greatest_lower_bound'( inverse( Y ), identity ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Z ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43430, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( X, Y )
% 119.18/119.59 , X ) ) ] )
% 119.18/119.59 , clause( 37, [ =( 'least_upper_bound'( 'greatest_lower_bound'( X, Y ), X )
% 119.18/119.59 , X ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43431, [ =( X, 'least_upper_bound'( multiply( X,
% 119.18/119.59 'greatest_lower_bound'( identity, Y ) ), X ) ) ] )
% 119.18/119.59 , clause( 182, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 119.18/119.59 X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 119.18/119.59 , 0, clause( 43430, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( X
% 119.18/119.59 , Y ), X ) ) ] )
% 119.18/119.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, multiply( X, Y ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43432, [ =( 'least_upper_bound'( multiply( X,
% 119.18/119.59 'greatest_lower_bound'( identity, Y ) ), X ), X ) ] )
% 119.18/119.59 , clause( 43431, [ =( X, 'least_upper_bound'( multiply( X,
% 119.18/119.59 'greatest_lower_bound'( identity, Y ) ), X ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 542, [ =( 'least_upper_bound'( multiply( X, 'greatest_lower_bound'(
% 119.18/119.59 identity, Y ) ), X ), X ) ] )
% 119.18/119.59 , clause( 43432, [ =( 'least_upper_bound'( multiply( X,
% 119.18/119.59 'greatest_lower_bound'( identity, Y ) ), X ), X ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43434, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) ),
% 119.18/119.59 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 182, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 119.18/119.59 X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43436, [ =( multiply( X, identity ), 'greatest_lower_bound'( X,
% 119.18/119.59 multiply( X, 'least_upper_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.59 , clause( 20, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) )
% 119.18/119.59 , X ) ] )
% 119.18/119.59 , 0, clause( 43434, [ =( multiply( X, 'greatest_lower_bound'( identity, Y )
% 119.18/119.59 ), 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , 0, 3, substitution( 0, [ :=( X, identity ), :=( Y, Y )] ), substitution(
% 119.18/119.59 1, [ :=( X, X ), :=( Y, 'least_upper_bound'( Y, identity ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43437, [ =( X, 'greatest_lower_bound'( X, multiply( X,
% 119.18/119.59 'least_upper_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.59 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.59 , 0, clause( 43436, [ =( multiply( X, identity ), 'greatest_lower_bound'( X
% 119.18/119.59 , multiply( X, 'least_upper_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.59 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.59 :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43438, [ =( 'greatest_lower_bound'( X, multiply( X,
% 119.18/119.59 'least_upper_bound'( Y, identity ) ) ), X ) ] )
% 119.18/119.59 , clause( 43437, [ =( X, 'greatest_lower_bound'( X, multiply( X,
% 119.18/119.59 'least_upper_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 544, [ =( 'greatest_lower_bound'( Y, multiply( Y,
% 119.18/119.59 'least_upper_bound'( X, identity ) ) ), Y ) ] )
% 119.18/119.59 , clause( 43438, [ =( 'greatest_lower_bound'( X, multiply( X,
% 119.18/119.59 'least_upper_bound'( Y, identity ) ) ), X ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43440, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) ),
% 119.18/119.59 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 182, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 119.18/119.59 X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43442, [ =( multiply( X, identity ), 'greatest_lower_bound'( X,
% 119.18/119.59 multiply( X, 'least_upper_bound'( identity, Y ) ) ) ) ] )
% 119.18/119.59 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 119.18/119.59 , X ) ] )
% 119.18/119.59 , 0, clause( 43440, [ =( multiply( X, 'greatest_lower_bound'( identity, Y )
% 119.18/119.59 ), 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , 0, 3, substitution( 0, [ :=( X, identity ), :=( Y, Y )] ), substitution(
% 119.18/119.59 1, [ :=( X, X ), :=( Y, 'least_upper_bound'( identity, Y ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43443, [ =( X, 'greatest_lower_bound'( X, multiply( X,
% 119.18/119.59 'least_upper_bound'( identity, Y ) ) ) ) ] )
% 119.18/119.59 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.59 , 0, clause( 43442, [ =( multiply( X, identity ), 'greatest_lower_bound'( X
% 119.18/119.59 , multiply( X, 'least_upper_bound'( identity, Y ) ) ) ) ] )
% 119.18/119.59 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.59 :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43444, [ =( 'greatest_lower_bound'( X, multiply( X,
% 119.18/119.59 'least_upper_bound'( identity, Y ) ) ), X ) ] )
% 119.18/119.59 , clause( 43443, [ =( X, 'greatest_lower_bound'( X, multiply( X,
% 119.18/119.59 'least_upper_bound'( identity, Y ) ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 546, [ =( 'greatest_lower_bound'( Y, multiply( Y,
% 119.18/119.59 'least_upper_bound'( identity, X ) ) ), Y ) ] )
% 119.18/119.59 , clause( 43444, [ =( 'greatest_lower_bound'( X, multiply( X,
% 119.18/119.59 'least_upper_bound'( identity, Y ) ) ), X ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43445, [ =( X, 'least_upper_bound'( multiply( X,
% 119.18/119.59 'greatest_lower_bound'( identity, Y ) ), X ) ) ] )
% 119.18/119.59 , clause( 542, [ =( 'least_upper_bound'( multiply( X,
% 119.18/119.59 'greatest_lower_bound'( identity, Y ) ), X ), X ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43446, [ =( X, 'least_upper_bound'( multiply( X,
% 119.18/119.59 'greatest_lower_bound'( Y, identity ) ), X ) ) ] )
% 119.18/119.59 , clause( 76, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ), multiply(
% 119.18/119.59 X, 'greatest_lower_bound'( Z, Y ) ) ) ] )
% 119.18/119.59 , 0, clause( 43445, [ =( X, 'least_upper_bound'( multiply( X,
% 119.18/119.59 'greatest_lower_bound'( identity, Y ) ), X ) ) ] )
% 119.18/119.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, identity ), :=( Z, Y )] ),
% 119.18/119.59 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43449, [ =( 'least_upper_bound'( multiply( X,
% 119.18/119.59 'greatest_lower_bound'( Y, identity ) ), X ), X ) ] )
% 119.18/119.59 , clause( 43446, [ =( X, 'least_upper_bound'( multiply( X,
% 119.18/119.59 'greatest_lower_bound'( Y, identity ) ), X ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 555, [ =( 'least_upper_bound'( multiply( X, 'greatest_lower_bound'(
% 119.18/119.59 Y, identity ) ), X ), X ) ] )
% 119.18/119.59 , clause( 43449, [ =( 'least_upper_bound'( multiply( X,
% 119.18/119.59 'greatest_lower_bound'( Y, identity ) ), X ), X ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43451, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), X ) ) ] )
% 119.18/119.59 , clause( 35, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 119.18/119.59 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43453, [ =( 'least_upper_bound'( multiply( X,
% 119.18/119.59 'greatest_lower_bound'( Y, identity ) ), X ), 'least_upper_bound'( X,
% 119.18/119.59 multiply( X, 'greatest_lower_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.59 , clause( 555, [ =( 'least_upper_bound'( multiply( X,
% 119.18/119.59 'greatest_lower_bound'( Y, identity ) ), X ), X ) ] )
% 119.18/119.59 , 0, clause( 43451, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), X ) ) ] )
% 119.18/119.59 , 0, 9, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, multiply( X, 'greatest_lower_bound'( Y, identity ) ) ), :=( Y, X )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43454, [ =( X, 'least_upper_bound'( X, multiply( X,
% 119.18/119.59 'greatest_lower_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.59 , clause( 555, [ =( 'least_upper_bound'( multiply( X,
% 119.18/119.59 'greatest_lower_bound'( Y, identity ) ), X ), X ) ] )
% 119.18/119.59 , 0, clause( 43453, [ =( 'least_upper_bound'( multiply( X,
% 119.18/119.59 'greatest_lower_bound'( Y, identity ) ), X ), 'least_upper_bound'( X,
% 119.18/119.59 multiply( X, 'greatest_lower_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.59 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43456, [ =( 'least_upper_bound'( X, multiply( X,
% 119.18/119.59 'greatest_lower_bound'( Y, identity ) ) ), X ) ] )
% 119.18/119.59 , clause( 43454, [ =( X, 'least_upper_bound'( X, multiply( X,
% 119.18/119.59 'greatest_lower_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 588, [ =( 'least_upper_bound'( X, multiply( X,
% 119.18/119.59 'greatest_lower_bound'( Y, identity ) ) ), X ) ] )
% 119.18/119.59 , clause( 43456, [ =( 'least_upper_bound'( X, multiply( X,
% 119.18/119.59 'greatest_lower_bound'( Y, identity ) ) ), X ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43459, [ =( X, 'least_upper_bound'( X, multiply( X,
% 119.18/119.59 'greatest_lower_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.59 , clause( 588, [ =( 'least_upper_bound'( X, multiply( X,
% 119.18/119.59 'greatest_lower_bound'( Y, identity ) ) ), X ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43460, [ =( inverse( 'greatest_lower_bound'( identity, X ) ),
% 119.18/119.59 'least_upper_bound'( inverse( 'greatest_lower_bound'( identity, X ) ),
% 119.18/119.59 identity ) ) ] )
% 119.18/119.59 , clause( 248, [ =( multiply( inverse( 'greatest_lower_bound'( Y, X ) ),
% 119.18/119.59 'greatest_lower_bound'( X, Y ) ), identity ) ] )
% 119.18/119.59 , 0, clause( 43459, [ =( X, 'least_upper_bound'( X, multiply( X,
% 119.18/119.59 'greatest_lower_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.59 , 0, 10, substitution( 0, [ :=( X, X ), :=( Y, identity )] ),
% 119.18/119.59 substitution( 1, [ :=( X, inverse( 'greatest_lower_bound'( identity, X )
% 119.18/119.59 ) ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43461, [ =( 'least_upper_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.59 identity, X ) ), identity ), inverse( 'greatest_lower_bound'( identity, X
% 119.18/119.59 ) ) ) ] )
% 119.18/119.59 , clause( 43460, [ =( inverse( 'greatest_lower_bound'( identity, X ) ),
% 119.18/119.59 'least_upper_bound'( inverse( 'greatest_lower_bound'( identity, X ) ),
% 119.18/119.59 identity ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 597, [ =( 'least_upper_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.59 identity, X ) ), identity ), inverse( 'greatest_lower_bound'( identity, X
% 119.18/119.59 ) ) ) ] )
% 119.18/119.59 , clause( 43461, [ =( 'least_upper_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.59 identity, X ) ), identity ), inverse( 'greatest_lower_bound'( identity, X
% 119.18/119.59 ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43463, [ =( X, 'greatest_lower_bound'( X, multiply( X,
% 119.18/119.59 'least_upper_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.59 , clause( 544, [ =( 'greatest_lower_bound'( Y, multiply( Y,
% 119.18/119.59 'least_upper_bound'( X, identity ) ) ), Y ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43464, [ =( inverse( 'least_upper_bound'( identity, X ) ),
% 119.18/119.59 'greatest_lower_bound'( inverse( 'least_upper_bound'( identity, X ) ),
% 119.18/119.59 identity ) ) ] )
% 119.18/119.59 , clause( 288, [ =( multiply( inverse( 'least_upper_bound'( Y, X ) ),
% 119.18/119.59 'least_upper_bound'( X, Y ) ), identity ) ] )
% 119.18/119.59 , 0, clause( 43463, [ =( X, 'greatest_lower_bound'( X, multiply( X,
% 119.18/119.59 'least_upper_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.59 , 0, 10, substitution( 0, [ :=( X, X ), :=( Y, identity )] ),
% 119.18/119.59 substitution( 1, [ :=( X, inverse( 'least_upper_bound'( identity, X ) ) )
% 119.18/119.59 , :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43465, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.59 identity, X ) ), identity ), inverse( 'least_upper_bound'( identity, X )
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 43464, [ =( inverse( 'least_upper_bound'( identity, X ) ),
% 119.18/119.59 'greatest_lower_bound'( inverse( 'least_upper_bound'( identity, X ) ),
% 119.18/119.59 identity ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 616, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.59 identity, X ) ), identity ), inverse( 'least_upper_bound'( identity, X )
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 43465, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.59 identity, X ) ), identity ), inverse( 'least_upper_bound'( identity, X )
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43467, [ =( inverse( multiply( X, 'greatest_lower_bound'( Y,
% 119.18/119.59 identity ) ) ), inverse( 'greatest_lower_bound'( multiply( X, Y ), X ) )
% 119.18/119.59 ) ] )
% 119.18/119.59 , clause( 506, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 119.18/119.59 X, 'greatest_lower_bound'( Y, identity ) ) ) ] )
% 119.18/119.59 , 0, clause( 225, [ =( inverse( 'greatest_lower_bound'( Y, X ) ), inverse(
% 119.18/119.59 'greatest_lower_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, multiply( X, Y ) ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 676, [ =( inverse( multiply( X, 'greatest_lower_bound'( Y, identity
% 119.18/119.59 ) ) ), inverse( 'greatest_lower_bound'( multiply( X, Y ), X ) ) ) ] )
% 119.18/119.59 , clause( 43467, [ =( inverse( multiply( X, 'greatest_lower_bound'( Y,
% 119.18/119.59 identity ) ) ), inverse( 'greatest_lower_bound'( multiply( X, Y ), X ) )
% 119.18/119.59 ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43469, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 119.18/119.59 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 171, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 119.18/119.59 , 'least_upper_bound'( identity, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43470, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 119.18/119.59 , 'least_upper_bound'( Y, identity ) ) ) ] )
% 119.18/119.59 , clause( 43469, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 119.18/119.59 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , 0, clause( 64, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), multiply(
% 119.18/119.59 X, 'least_upper_bound'( Z, Y ) ) ) ] )
% 119.18/119.59 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, identity ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 750, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X,
% 119.18/119.59 'least_upper_bound'( Y, identity ) ) ) ] )
% 119.18/119.59 , clause( 43470, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply(
% 119.18/119.59 X, 'least_upper_bound'( Y, identity ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43473, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 119.18/119.59 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 171, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 119.18/119.59 , 'least_upper_bound'( identity, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43492, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ),
% 119.18/119.59 'least_upper_bound'( identity, Y ) ), 'least_upper_bound'( multiply(
% 119.18/119.59 inverse( multiply( X, Y ) ), X ), identity ) ) ] )
% 119.18/119.59 , clause( 16, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ), Y
% 119.18/119.59 ), identity ) ] )
% 119.18/119.59 , 0, clause( 43473, [ =( multiply( X, 'least_upper_bound'( identity, Y ) )
% 119.18/119.59 , 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , 0, 18, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, multiply( inverse( multiply( X, Y ) ), X ) ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43494, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X ),
% 119.18/119.59 'least_upper_bound'( identity, Y ) ), 'least_upper_bound'( inverse( Y ),
% 119.18/119.59 identity ) ) ] )
% 119.18/119.59 , clause( 195, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, clause( 43492, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X
% 119.18/119.59 ), 'least_upper_bound'( identity, Y ) ), 'least_upper_bound'( multiply(
% 119.18/119.59 inverse( multiply( X, Y ) ), X ), identity ) ) ] )
% 119.18/119.59 , 0, 12, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43495, [ =( multiply( inverse( Y ), 'least_upper_bound'( identity,
% 119.18/119.59 Y ) ), 'least_upper_bound'( inverse( Y ), identity ) ) ] )
% 119.18/119.59 , clause( 195, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, clause( 43494, [ =( multiply( multiply( inverse( multiply( X, Y ) ), X
% 119.18/119.59 ), 'least_upper_bound'( identity, Y ) ), 'least_upper_bound'( inverse( Y
% 119.18/119.59 ), identity ) ) ] )
% 119.18/119.59 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 770, [ =( multiply( inverse( Y ), 'least_upper_bound'( identity, Y
% 119.18/119.59 ) ), 'least_upper_bound'( inverse( Y ), identity ) ) ] )
% 119.18/119.59 , clause( 43495, [ =( multiply( inverse( Y ), 'least_upper_bound'( identity
% 119.18/119.59 , Y ) ), 'least_upper_bound'( inverse( Y ), identity ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Z ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43499, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 119.18/119.59 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 171, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 119.18/119.59 , 'least_upper_bound'( identity, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43501, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), X ) ) ] )
% 119.18/119.59 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 119.18/119.59 ) ] )
% 119.18/119.59 , 0, clause( 43499, [ =( multiply( X, 'least_upper_bound'( identity, Y ) )
% 119.18/119.59 , 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, multiply( X, Y ) )] ),
% 119.18/119.59 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 781, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), X ) ) ] )
% 119.18/119.59 , clause( 43501, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 119.18/119.59 'least_upper_bound'( multiply( X, Y ), X ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43508, [ =( multiply( X, 'least_upper_bound'( Y, identity ) ),
% 119.18/119.59 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 750, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 119.18/119.59 , 'least_upper_bound'( Y, identity ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43509, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 119.18/119.59 , clause( 184, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43510, [ =( X, multiply( 'least_upper_bound'( X, multiply( X, Y ) )
% 119.18/119.59 , inverse( 'least_upper_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.59 , clause( 43508, [ =( multiply( X, 'least_upper_bound'( Y, identity ) ),
% 119.18/119.59 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 119.18/119.59 , 0, clause( 43509, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, 'least_upper_bound'( Y, identity ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43511, [ =( multiply( 'least_upper_bound'( X, multiply( X, Y ) ),
% 119.18/119.59 inverse( 'least_upper_bound'( Y, identity ) ) ), X ) ] )
% 119.18/119.59 , clause( 43510, [ =( X, multiply( 'least_upper_bound'( X, multiply( X, Y )
% 119.18/119.59 ), inverse( 'least_upper_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 801, [ =( multiply( 'least_upper_bound'( X, multiply( X, Y ) ),
% 119.18/119.59 inverse( 'least_upper_bound'( Y, identity ) ) ), X ) ] )
% 119.18/119.59 , clause( 43511, [ =( multiply( 'least_upper_bound'( X, multiply( X, Y ) )
% 119.18/119.59 , inverse( 'least_upper_bound'( Y, identity ) ) ), X ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43513, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 119.18/119.59 ) ) ) ] )
% 119.18/119.59 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 119.18/119.59 , X ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43516, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, Z )
% 119.18/119.59 ), 'greatest_lower_bound'( 'least_upper_bound'( X,
% 119.18/119.59 'greatest_lower_bound'( Y, Z ) ), 'least_upper_bound'( X, Z ) ) ) ] )
% 119.18/119.59 , clause( 42, [ =( 'least_upper_bound'( 'least_upper_bound'( Z,
% 119.18/119.59 'greatest_lower_bound'( X, Y ) ), Y ), 'least_upper_bound'( Z, Y ) ) ] )
% 119.18/119.59 , 0, clause( 43513, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 119.18/119.59 X, Y ) ) ) ] )
% 119.18/119.59 , 0, 12, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 119.18/119.59 substitution( 1, [ :=( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.59 Y, Z ) ) ), :=( Y, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43517, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X,
% 119.18/119.59 'greatest_lower_bound'( Y, Z ) ), 'least_upper_bound'( X, Z ) ),
% 119.18/119.59 'least_upper_bound'( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , clause( 43516, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, Z
% 119.18/119.59 ) ), 'greatest_lower_bound'( 'least_upper_bound'( X,
% 119.18/119.59 'greatest_lower_bound'( Y, Z ) ), 'least_upper_bound'( X, Z ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 818, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X,
% 119.18/119.59 'greatest_lower_bound'( Y, Z ) ), 'least_upper_bound'( X, Z ) ),
% 119.18/119.59 'least_upper_bound'( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , clause( 43517, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X,
% 119.18/119.59 'greatest_lower_bound'( Y, Z ) ), 'least_upper_bound'( X, Z ) ),
% 119.18/119.59 'least_upper_bound'( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43519, [ =( inverse( multiply( X, 'least_upper_bound'( Y, identity
% 119.18/119.59 ) ) ), inverse( 'least_upper_bound'( X, multiply( X, Y ) ) ) ) ] )
% 119.18/119.59 , clause( 172, [ =( 'least_upper_bound'( multiply( X, Y ), X ), multiply( X
% 119.18/119.59 , 'least_upper_bound'( Y, identity ) ) ) ] )
% 119.18/119.59 , 0, clause( 273, [ =( inverse( 'least_upper_bound'( Y, X ) ), inverse(
% 119.18/119.59 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, multiply( X, Y ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 847, [ =( inverse( multiply( X, 'least_upper_bound'( Y, identity )
% 119.18/119.59 ) ), inverse( 'least_upper_bound'( X, multiply( X, Y ) ) ) ) ] )
% 119.18/119.59 , clause( 43519, [ =( inverse( multiply( X, 'least_upper_bound'( Y,
% 119.18/119.59 identity ) ) ), inverse( 'least_upper_bound'( X, multiply( X, Y ) ) ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43522, [ =( multiply( 'greatest_lower_bound'( identity, Y ), X ),
% 119.18/119.59 'greatest_lower_bound'( X, multiply( Y, X ) ) ) ] )
% 119.18/119.59 , clause( 153, [ =( 'greatest_lower_bound'( X, multiply( Y, X ) ), multiply(
% 119.18/119.59 'greatest_lower_bound'( identity, Y ), X ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43527, [ =( multiply( identity, Y ), 'greatest_lower_bound'( Y,
% 119.18/119.59 multiply( multiply( identity, 'least_upper_bound'( identity, X ) ), Y ) )
% 119.18/119.59 ) ] )
% 119.18/119.59 , clause( 546, [ =( 'greatest_lower_bound'( Y, multiply( Y,
% 119.18/119.59 'least_upper_bound'( identity, X ) ) ), Y ) ] )
% 119.18/119.59 , 0, clause( 43522, [ =( multiply( 'greatest_lower_bound'( identity, Y ), X
% 119.18/119.59 ), 'greatest_lower_bound'( X, multiply( Y, X ) ) ) ] )
% 119.18/119.59 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, identity )] ), substitution(
% 119.18/119.59 1, [ :=( X, Y ), :=( Y, multiply( identity, 'least_upper_bound'( identity
% 119.18/119.59 , X ) ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43530, [ =( multiply( identity, X ), 'greatest_lower_bound'( X,
% 119.18/119.59 multiply( 'least_upper_bound'( identity, Y ), X ) ) ) ] )
% 119.18/119.59 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.59 , 0, clause( 43527, [ =( multiply( identity, Y ), 'greatest_lower_bound'( Y
% 119.18/119.59 , multiply( multiply( identity, 'least_upper_bound'( identity, X ) ), Y )
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, 7, substitution( 0, [ :=( X, 'least_upper_bound'( identity, Y ) )] ),
% 119.18/119.59 substitution( 1, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43532, [ =( X, 'greatest_lower_bound'( X, multiply(
% 119.18/119.59 'least_upper_bound'( identity, Y ), X ) ) ) ] )
% 119.18/119.59 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.59 , 0, clause( 43530, [ =( multiply( identity, X ), 'greatest_lower_bound'( X
% 119.18/119.59 , multiply( 'least_upper_bound'( identity, Y ), X ) ) ) ] )
% 119.18/119.59 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.59 :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43533, [ =( 'greatest_lower_bound'( X, multiply(
% 119.18/119.59 'least_upper_bound'( identity, Y ), X ) ), X ) ] )
% 119.18/119.59 , clause( 43532, [ =( X, 'greatest_lower_bound'( X, multiply(
% 119.18/119.59 'least_upper_bound'( identity, Y ), X ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 858, [ =( 'greatest_lower_bound'( Y, multiply( 'least_upper_bound'(
% 119.18/119.59 identity, X ), Y ) ), Y ) ] )
% 119.18/119.59 , clause( 43533, [ =( 'greatest_lower_bound'( X, multiply(
% 119.18/119.59 'least_upper_bound'( identity, Y ), X ) ), X ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43535, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X
% 119.18/119.59 ) ) ) ] )
% 119.18/119.59 , clause( 36, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) )
% 119.18/119.59 , X ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43538, [ =( multiply( 'least_upper_bound'( identity, X ), Y ),
% 119.18/119.59 'least_upper_bound'( multiply( 'least_upper_bound'( identity, X ), Y ), Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 858, [ =( 'greatest_lower_bound'( Y, multiply(
% 119.18/119.59 'least_upper_bound'( identity, X ), Y ) ), Y ) ] )
% 119.18/119.59 , 0, clause( 43535, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.59 Y, X ) ) ) ] )
% 119.18/119.59 , 0, 12, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, multiply( 'least_upper_bound'( identity, X ), Y ) ), :=( Y, Y )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43539, [ =( 'least_upper_bound'( multiply( 'least_upper_bound'(
% 119.18/119.59 identity, X ), Y ), Y ), multiply( 'least_upper_bound'( identity, X ), Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 43538, [ =( multiply( 'least_upper_bound'( identity, X ), Y ),
% 119.18/119.59 'least_upper_bound'( multiply( 'least_upper_bound'( identity, X ), Y ), Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 928, [ =( 'least_upper_bound'( multiply( 'least_upper_bound'(
% 119.18/119.59 identity, Y ), X ), X ), multiply( 'least_upper_bound'( identity, Y ), X
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 43539, [ =( 'least_upper_bound'( multiply( 'least_upper_bound'(
% 119.18/119.59 identity, X ), Y ), Y ), multiply( 'least_upper_bound'( identity, X ), Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43541, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), 'least_upper_bound'( 'least_upper_bound'( Z
% 119.18/119.59 , X ), Y ) ) ) ] )
% 119.18/119.59 , clause( 45, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, Z ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ),
% 119.18/119.59 'least_upper_bound'( Y, Z ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43544, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.59 , clause( 35, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 119.18/119.59 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.59 , 0, clause( 43541, [ =( 'least_upper_bound'( X, Y ),
% 119.18/119.59 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( Z, X ), Y ) ) ) ] )
% 119.18/119.59 , 0, 8, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.59 :=( X, X ), :=( Y, Y ), :=( Z, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43550, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 119.18/119.59 'least_upper_bound'( Y, X ) ), 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.59 , clause( 43544, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 935, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 119.18/119.59 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( Y, X ) ) ] )
% 119.18/119.59 , clause( 43550, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 119.18/119.59 'least_upper_bound'( Y, X ) ), 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.59 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43554, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'( Y, X ) ),
% 119.18/119.59 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , clause( 935, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 119.18/119.59 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( Y, X ) ) ] )
% 119.18/119.59 , 0, clause( 28, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Z, Y
% 119.18/119.59 ), X ), 'greatest_lower_bound'( 'greatest_lower_bound'( Z, X ), Y ) ) ]
% 119.18/119.59 )
% 119.18/119.59 , 0, 11, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.59 :=( X, 'least_upper_bound'( Y, X ) ), :=( Y, Z ), :=( Z,
% 119.18/119.59 'least_upper_bound'( X, Y ) )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 1031, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'( Y, X ) ),
% 119.18/119.59 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , clause( 43554, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'( Y, X ) ),
% 119.18/119.59 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43556, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Y, Z )
% 119.18/119.59 , X ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , clause( 27, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ),
% 119.18/119.59 Z ), 'greatest_lower_bound'( 'greatest_lower_bound'( Y, Z ), X ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43559, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'( Y, X ) ),
% 119.18/119.59 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), Z ) ) ] )
% 119.18/119.59 , clause( 935, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 119.18/119.59 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( Y, X ) ) ] )
% 119.18/119.59 , 0, clause( 43556, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Y
% 119.18/119.59 , Z ), X ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) )
% 119.18/119.59 ] )
% 119.18/119.59 , 0, 11, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.59 :=( X, 'least_upper_bound'( Y, X ) ), :=( Y, 'least_upper_bound'( X, Y )
% 119.18/119.59 ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43560, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), Z
% 119.18/119.59 ), 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), Z ) ) ] )
% 119.18/119.59 , clause( 1031, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'( Y, X ) ),
% 119.18/119.59 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 43559, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'(
% 119.18/119.59 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'( Y, X ) ),
% 119.18/119.59 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), Z ) ) ] )
% 119.18/119.59 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.59 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 1032, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), Z )
% 119.18/119.59 , 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), Z ) ) ] )
% 119.18/119.59 , clause( 43560, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 119.18/119.59 Z ), 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), Z ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43561, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), Z
% 119.18/119.59 ), 'greatest_lower_bound'( Z, 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 1032, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), Z
% 119.18/119.59 ), 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 119.18/119.59 Y, X ) ) ] )
% 119.18/119.59 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.59 substitution( 1, [ :=( X, 'least_upper_bound'( X, Y ) ), :=( Y, Z )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 1065, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), Z )
% 119.18/119.59 , 'greatest_lower_bound'( Z, 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , clause( 43561, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 119.18/119.59 Z ), 'greatest_lower_bound'( Z, 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43565, [ =( 'greatest_lower_bound'( Z, 'least_upper_bound'( Y, X )
% 119.18/119.59 ), 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , clause( 1065, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), Z
% 119.18/119.59 ), 'greatest_lower_bound'( Z, 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43568, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y,
% 119.18/119.59 'least_upper_bound'( Z, T ) ) ), 'greatest_lower_bound'(
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( Z, Y ), T ), X ) ) ] )
% 119.18/119.59 , clause( 50, [ =( 'least_upper_bound'( 'least_upper_bound'( Z, Y ), X ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ) ) ] )
% 119.18/119.59 , 0, clause( 43565, [ =( 'greatest_lower_bound'( Z, 'least_upper_bound'( Y
% 119.18/119.59 , X ) ), 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, 9, substitution( 0, [ :=( X, Y ), :=( Y, T ), :=( Z, Z )] ),
% 119.18/119.59 substitution( 1, [ :=( X, 'least_upper_bound'( Z, T ) ), :=( Y, Y ), :=(
% 119.18/119.59 Z, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43571, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( Y, Z ), T ) ), 'greatest_lower_bound'(
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( Z, Y ), T ), X ) ) ] )
% 119.18/119.59 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.59 , 0, clause( 43568, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y
% 119.18/119.59 , 'least_upper_bound'( Z, T ) ) ), 'greatest_lower_bound'(
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( Z, Y ), T ), X ) ) ] )
% 119.18/119.59 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T )] ),
% 119.18/119.59 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43572, [ =( 'greatest_lower_bound'( 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( Z, Y ), T ), X ), 'greatest_lower_bound'( X,
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( Y, Z ), T ) ) ) ] )
% 119.18/119.59 , clause( 43571, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( Y, Z ), T ) ), 'greatest_lower_bound'(
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( Z, Y ), T ), X ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 119.18/119.59 ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 subsumption(
% 119.18/119.59 clause( 1087, [ =( 'greatest_lower_bound'( 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( X, Z ), Y ), T ), 'greatest_lower_bound'( T,
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ) ) ) ] )
% 119.18/119.59 , clause( 43572, [ =( 'greatest_lower_bound'( 'least_upper_bound'(
% 119.18/119.59 'least_upper_bound'( Z, Y ), T ), X ), 'greatest_lower_bound'( X,
% 119.18/119.59 'least_upper_bound'( 'least_upper_bound'( Y, Z ), T ) ) ) ] )
% 119.18/119.59 , substitution( 0, [ :=( X, T ), :=( Y, Z ), :=( Z, X ), :=( T, Y )] ),
% 119.18/119.59 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43573, [ =( multiply( 'greatest_lower_bound'( X, identity ), Y ),
% 119.18/119.59 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ] )
% 119.18/119.59 , clause( 154, [ =( 'greatest_lower_bound'( multiply( Y, X ), X ), multiply(
% 119.18/119.59 'greatest_lower_bound'( Y, identity ), X ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 eqswap(
% 119.18/119.59 clause( 43574, [ =( inverse( Y ), multiply( inverse( multiply( X, Y ) ), X
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , clause( 195, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 119.18/119.59 ) ) ] )
% 119.18/119.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.59
% 119.18/119.59
% 119.18/119.59 paramod(
% 119.18/119.59 clause( 43575, [ =( inverse( X ), multiply( inverse( 'greatest_lower_bound'(
% 119.18/119.60 multiply( Y, X ), X ) ), 'greatest_lower_bound'( Y, identity ) ) ) ] )
% 119.18/119.60 , clause( 43573, [ =( multiply( 'greatest_lower_bound'( X, identity ), Y )
% 119.18/119.60 , 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ] )
% 119.18/119.60 , 0, clause( 43574, [ =( inverse( Y ), multiply( inverse( multiply( X, Y )
% 119.18/119.60 ), X ) ) ] )
% 119.18/119.60 , 0, 5, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, 'greatest_lower_bound'( Y, identity ) ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43576, [ =( multiply( inverse( 'greatest_lower_bound'( multiply( Y
% 119.18/119.60 , X ), X ) ), 'greatest_lower_bound'( Y, identity ) ), inverse( X ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , clause( 43575, [ =( inverse( X ), multiply( inverse(
% 119.18/119.60 'greatest_lower_bound'( multiply( Y, X ), X ) ), 'greatest_lower_bound'(
% 119.18/119.60 Y, identity ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1199, [ =( multiply( inverse( 'greatest_lower_bound'( multiply( X,
% 119.18/119.60 Y ), Y ) ), 'greatest_lower_bound'( X, identity ) ), inverse( Y ) ) ] )
% 119.18/119.60 , clause( 43576, [ =( multiply( inverse( 'greatest_lower_bound'( multiply(
% 119.18/119.60 Y, X ), X ) ), 'greatest_lower_bound'( Y, identity ) ), inverse( X ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43578, [ =( 'greatest_lower_bound'( multiply( 'least_upper_bound'(
% 119.18/119.60 identity, Y ), X ), Z ), 'greatest_lower_bound'( 'least_upper_bound'(
% 119.18/119.60 multiply( Y, X ), X ), Z ) ) ] )
% 119.18/119.60 , clause( 117, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 119.18/119.60 'least_upper_bound'( identity, Y ), X ) ) ] )
% 119.18/119.60 , 0, clause( 1032, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y )
% 119.18/119.60 , Z ), 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), Z ) ) ] )
% 119.18/119.60 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.60 :=( X, X ), :=( Y, multiply( Y, X ) ), :=( Z, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1205, [ =( 'greatest_lower_bound'( multiply( 'least_upper_bound'(
% 119.18/119.60 identity, Y ), X ), Z ), 'greatest_lower_bound'( 'least_upper_bound'(
% 119.18/119.60 multiply( Y, X ), X ), Z ) ) ] )
% 119.18/119.60 , clause( 43578, [ =( 'greatest_lower_bound'( multiply( 'least_upper_bound'(
% 119.18/119.60 identity, Y ), X ), Z ), 'greatest_lower_bound'( 'least_upper_bound'(
% 119.18/119.60 multiply( Y, X ), X ), Z ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43580, [ =( multiply( 'least_upper_bound'( identity, Y ), X ),
% 119.18/119.60 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 119.18/119.60 , clause( 117, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 119.18/119.60 'least_upper_bound'( identity, Y ), X ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43601, [ =( multiply( 'least_upper_bound'( identity, X ), X ),
% 119.18/119.60 multiply( X, 'least_upper_bound'( X, identity ) ) ) ] )
% 119.18/119.60 , clause( 750, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 119.18/119.60 , 'least_upper_bound'( Y, identity ) ) ) ] )
% 119.18/119.60 , 0, clause( 43580, [ =( multiply( 'least_upper_bound'( identity, Y ), X )
% 119.18/119.60 , 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 119.18/119.60 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, X ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43603, [ =( multiply( X, 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 multiply( 'least_upper_bound'( identity, X ), X ) ) ] )
% 119.18/119.60 , clause( 43601, [ =( multiply( 'least_upper_bound'( identity, X ), X ),
% 119.18/119.60 multiply( X, 'least_upper_bound'( X, identity ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1206, [ =( multiply( X, 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 multiply( 'least_upper_bound'( identity, X ), X ) ) ] )
% 119.18/119.60 , clause( 43603, [ =( multiply( X, 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 multiply( 'least_upper_bound'( identity, X ), X ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43605, [ =( multiply( 'least_upper_bound'( identity, Y ), X ),
% 119.18/119.60 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 119.18/119.60 , clause( 117, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 119.18/119.60 'least_upper_bound'( identity, Y ), X ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43618, [ =( multiply( multiply( identity, 'least_upper_bound'( X,
% 119.18/119.60 identity ) ), Y ), 'least_upper_bound'( Y, multiply( multiply( identity,
% 119.18/119.60 X ), Y ) ) ) ] )
% 119.18/119.60 , clause( 750, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 119.18/119.60 , 'least_upper_bound'( Y, identity ) ) ) ] )
% 119.18/119.60 , 0, clause( 43605, [ =( multiply( 'least_upper_bound'( identity, Y ), X )
% 119.18/119.60 , 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 119.18/119.60 , 0, 2, substitution( 0, [ :=( X, identity ), :=( Y, X )] ), substitution(
% 119.18/119.60 1, [ :=( X, Y ), :=( Y, multiply( identity, X ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43621, [ =( multiply( multiply( identity, 'least_upper_bound'( X,
% 119.18/119.60 identity ) ), Y ), 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 119.18/119.60 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.60 , 0, clause( 43618, [ =( multiply( multiply( identity, 'least_upper_bound'(
% 119.18/119.60 X, identity ) ), Y ), 'least_upper_bound'( Y, multiply( multiply(
% 119.18/119.60 identity, X ), Y ) ) ) ] )
% 119.18/119.60 , 0, 11, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43623, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 119.18/119.60 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 119.18/119.60 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.60 , 0, clause( 43621, [ =( multiply( multiply( identity, 'least_upper_bound'(
% 119.18/119.60 X, identity ) ), Y ), 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 119.18/119.60 , 0, 2, substitution( 0, [ :=( X, 'least_upper_bound'( X, identity ) )] ),
% 119.18/119.60 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43624, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 119.18/119.60 'least_upper_bound'( X, identity ), Y ) ) ] )
% 119.18/119.60 , clause( 43623, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 119.18/119.60 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1207, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 119.18/119.60 'least_upper_bound'( X, identity ), Y ) ) ] )
% 119.18/119.60 , clause( 43624, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 119.18/119.60 'least_upper_bound'( X, identity ), Y ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43625, [ =( multiply( 'least_upper_bound'( identity, Y ), X ),
% 119.18/119.60 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 119.18/119.60 , clause( 117, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 119.18/119.60 'least_upper_bound'( identity, Y ), X ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43646, [ =( multiply( 'least_upper_bound'( identity, X ), X ),
% 119.18/119.60 multiply( X, 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.60 , clause( 171, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 119.18/119.60 , 'least_upper_bound'( identity, Y ) ) ) ] )
% 119.18/119.60 , 0, clause( 43625, [ =( multiply( 'least_upper_bound'( identity, Y ), X )
% 119.18/119.60 , 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 119.18/119.60 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, X ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43648, [ =( multiply( X, 'least_upper_bound'( identity, X ) ),
% 119.18/119.60 multiply( 'least_upper_bound'( identity, X ), X ) ) ] )
% 119.18/119.60 , clause( 43646, [ =( multiply( 'least_upper_bound'( identity, X ), X ),
% 119.18/119.60 multiply( X, 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1208, [ =( multiply( X, 'least_upper_bound'( identity, X ) ),
% 119.18/119.60 multiply( 'least_upper_bound'( identity, X ), X ) ) ] )
% 119.18/119.60 , clause( 43648, [ =( multiply( X, 'least_upper_bound'( identity, X ) ),
% 119.18/119.60 multiply( 'least_upper_bound'( identity, X ), X ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43650, [ =( inverse( multiply( 'least_upper_bound'( Y, identity ),
% 119.18/119.60 X ) ), inverse( 'least_upper_bound'( multiply( Y, X ), X ) ) ) ] )
% 119.18/119.60 , clause( 1207, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 119.18/119.60 'least_upper_bound'( X, identity ), Y ) ) ] )
% 119.18/119.60 , 0, clause( 273, [ =( inverse( 'least_upper_bound'( Y, X ) ), inverse(
% 119.18/119.60 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.60 , 0, 2, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, multiply( Y, X ) ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1261, [ =( inverse( multiply( 'least_upper_bound'( Y, identity ), X
% 119.18/119.60 ) ), inverse( 'least_upper_bound'( multiply( Y, X ), X ) ) ) ] )
% 119.18/119.60 , clause( 43650, [ =( inverse( multiply( 'least_upper_bound'( Y, identity )
% 119.18/119.60 , X ) ), inverse( 'least_upper_bound'( multiply( Y, X ), X ) ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43653, [ =( multiply( 'least_upper_bound'( Y, identity ), X ),
% 119.18/119.60 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 119.18/119.60 , clause( 1207, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 119.18/119.60 'least_upper_bound'( X, identity ), Y ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43657, [ =( multiply( 'least_upper_bound'( X, identity ), inverse(
% 119.18/119.60 X ) ), 'least_upper_bound'( inverse( X ), identity ) ) ] )
% 119.18/119.60 , clause( 180, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 119.18/119.60 , 0, clause( 43653, [ =( multiply( 'least_upper_bound'( Y, identity ), X )
% 119.18/119.60 , 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 119.18/119.60 , 0, 10, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.60 inverse( X ) ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1265, [ =( multiply( 'least_upper_bound'( X, identity ), inverse( X
% 119.18/119.60 ) ), 'least_upper_bound'( inverse( X ), identity ) ) ] )
% 119.18/119.60 , clause( 43657, [ =( multiply( 'least_upper_bound'( X, identity ), inverse(
% 119.18/119.60 X ) ), 'least_upper_bound'( inverse( X ), identity ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43660, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 119.18/119.60 'least_upper_bound'( multiply( X, Y ), Y ) ) ] )
% 119.18/119.60 , clause( 118, [ =( 'least_upper_bound'( multiply( Y, X ), X ), multiply(
% 119.18/119.60 'least_upper_bound'( Y, identity ), X ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43661, [ =( inverse( Y ), multiply( inverse( multiply( X, Y ) ), X
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , clause( 195, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43662, [ =( inverse( X ), multiply( inverse( 'least_upper_bound'(
% 119.18/119.60 multiply( Y, X ), X ) ), 'least_upper_bound'( Y, identity ) ) ) ] )
% 119.18/119.60 , clause( 43660, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 119.18/119.60 'least_upper_bound'( multiply( X, Y ), Y ) ) ] )
% 119.18/119.60 , 0, clause( 43661, [ =( inverse( Y ), multiply( inverse( multiply( X, Y )
% 119.18/119.60 ), X ) ) ] )
% 119.18/119.60 , 0, 5, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, 'least_upper_bound'( Y, identity ) ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43663, [ =( multiply( inverse( 'least_upper_bound'( multiply( Y, X
% 119.18/119.60 ), X ) ), 'least_upper_bound'( Y, identity ) ), inverse( X ) ) ] )
% 119.18/119.60 , clause( 43662, [ =( inverse( X ), multiply( inverse( 'least_upper_bound'(
% 119.18/119.60 multiply( Y, X ), X ) ), 'least_upper_bound'( Y, identity ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1313, [ =( multiply( inverse( 'least_upper_bound'( multiply( X, Y )
% 119.18/119.60 , Y ) ), 'least_upper_bound'( X, identity ) ), inverse( Y ) ) ] )
% 119.18/119.60 , clause( 43663, [ =( multiply( inverse( 'least_upper_bound'( multiply( Y,
% 119.18/119.60 X ), X ) ), 'least_upper_bound'( Y, identity ) ), inverse( X ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43664, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 119.18/119.60 'least_upper_bound'( multiply( X, Y ), Y ) ) ] )
% 119.18/119.60 , clause( 118, [ =( 'least_upper_bound'( multiply( Y, X ), X ), multiply(
% 119.18/119.60 'least_upper_bound'( Y, identity ), X ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43681, [ =( multiply( 'least_upper_bound'( X, identity ), multiply(
% 119.18/119.60 X, Y ) ), multiply( X, 'least_upper_bound'( multiply( X, Y ), Y ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 119.18/119.60 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.60 , 0, clause( 43664, [ =( multiply( 'least_upper_bound'( X, identity ), Y )
% 119.18/119.60 , 'least_upper_bound'( multiply( X, Y ), Y ) ) ] )
% 119.18/119.60 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, multiply( X, Y ) ), :=( Z, Y
% 119.18/119.60 )] ), substitution( 1, [ :=( X, X ), :=( Y, multiply( X, Y ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43682, [ =( multiply( multiply( 'least_upper_bound'( X, identity )
% 119.18/119.60 , X ), Y ), multiply( X, 'least_upper_bound'( multiply( X, Y ), Y ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 119.18/119.60 ), Z ) ) ] )
% 119.18/119.60 , 0, clause( 43681, [ =( multiply( 'least_upper_bound'( X, identity ),
% 119.18/119.60 multiply( X, Y ) ), multiply( X, 'least_upper_bound'( multiply( X, Y ), Y
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 :=( Y, X ), :=( Z, Y )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1314, [ =( multiply( multiply( 'least_upper_bound'( X, identity ),
% 119.18/119.60 X ), Y ), multiply( X, 'least_upper_bound'( multiply( X, Y ), Y ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , clause( 43682, [ =( multiply( multiply( 'least_upper_bound'( X, identity
% 119.18/119.60 ), X ), Y ), multiply( X, 'least_upper_bound'( multiply( X, Y ), Y ) ) )
% 119.18/119.60 ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43685, [ =( inverse( Y ), multiply( inverse( multiply( X, Y ) ), X
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , clause( 195, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43687, [ =( inverse( inverse( X ) ), multiply( inverse(
% 119.18/119.60 'least_upper_bound'( inverse( X ), identity ) ), 'least_upper_bound'( X,
% 119.18/119.60 identity ) ) ) ] )
% 119.18/119.60 , clause( 1265, [ =( multiply( 'least_upper_bound'( X, identity ), inverse(
% 119.18/119.60 X ) ), 'least_upper_bound'( inverse( X ), identity ) ) ] )
% 119.18/119.60 , 0, clause( 43685, [ =( inverse( Y ), multiply( inverse( multiply( X, Y )
% 119.18/119.60 ), X ) ) ] )
% 119.18/119.60 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.60 'least_upper_bound'( X, identity ) ), :=( Y, inverse( X ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43688, [ =( X, multiply( inverse( 'least_upper_bound'( inverse( X )
% 119.18/119.60 , identity ) ), 'least_upper_bound'( X, identity ) ) ) ] )
% 119.18/119.60 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43687, [ =( inverse( inverse( X ) ), multiply( inverse(
% 119.18/119.60 'least_upper_bound'( inverse( X ), identity ) ), 'least_upper_bound'( X,
% 119.18/119.60 identity ) ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43689, [ =( multiply( inverse( 'least_upper_bound'( inverse( X ),
% 119.18/119.60 identity ) ), 'least_upper_bound'( X, identity ) ), X ) ] )
% 119.18/119.60 , clause( 43688, [ =( X, multiply( inverse( 'least_upper_bound'( inverse( X
% 119.18/119.60 ), identity ) ), 'least_upper_bound'( X, identity ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1320, [ =( multiply( inverse( 'least_upper_bound'( inverse( X ),
% 119.18/119.60 identity ) ), 'least_upper_bound'( X, identity ) ), X ) ] )
% 119.18/119.60 , clause( 43689, [ =( multiply( inverse( 'least_upper_bound'( inverse( X )
% 119.18/119.60 , identity ) ), 'least_upper_bound'( X, identity ) ), X ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43691, [ =( 'least_upper_bound'( inverse( X ), identity ), multiply(
% 119.18/119.60 'least_upper_bound'( X, identity ), inverse( X ) ) ) ] )
% 119.18/119.60 , clause( 1265, [ =( multiply( 'least_upper_bound'( X, identity ), inverse(
% 119.18/119.60 X ) ), 'least_upper_bound'( inverse( X ), identity ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43693, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ), identity ), multiply( 'least_upper_bound'( identity, X )
% 119.18/119.60 , inverse( 'least_upper_bound'( identity, X ) ) ) ) ] )
% 119.18/119.60 , clause( 35, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 119.18/119.60 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.60 , 0, clause( 43691, [ =( 'least_upper_bound'( inverse( X ), identity ),
% 119.18/119.60 multiply( 'least_upper_bound'( X, identity ), inverse( X ) ) ) ] )
% 119.18/119.60 , 0, 8, substitution( 0, [ :=( X, identity ), :=( Y, X )] ), substitution(
% 119.18/119.60 1, [ :=( X, 'least_upper_bound'( identity, X ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43694, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ), identity ), identity ) ] )
% 119.18/119.60 , clause( 180, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 119.18/119.60 , 0, clause( 43693, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ), identity ), multiply( 'least_upper_bound'( identity, X )
% 119.18/119.60 , inverse( 'least_upper_bound'( identity, X ) ) ) ) ] )
% 119.18/119.60 , 0, 7, substitution( 0, [ :=( X, 'least_upper_bound'( identity, X ) )] ),
% 119.18/119.60 substitution( 1, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1323, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ), identity ), identity ) ] )
% 119.18/119.60 , clause( 43694, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ), identity ), identity ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43697, [ =( 'least_upper_bound'( inverse( X ), identity ), multiply(
% 119.18/119.60 'least_upper_bound'( X, identity ), inverse( X ) ) ) ] )
% 119.18/119.60 , clause( 1265, [ =( multiply( 'least_upper_bound'( X, identity ), inverse(
% 119.18/119.60 X ) ), 'least_upper_bound'( inverse( X ), identity ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43699, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X,
% 119.18/119.60 identity ) ), identity ), multiply( 'least_upper_bound'( X, identity ),
% 119.18/119.60 inverse( 'least_upper_bound'( X, identity ) ) ) ) ] )
% 119.18/119.60 , clause( 34, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Y ),
% 119.18/119.60 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.60 , 0, clause( 43697, [ =( 'least_upper_bound'( inverse( X ), identity ),
% 119.18/119.60 multiply( 'least_upper_bound'( X, identity ), inverse( X ) ) ) ] )
% 119.18/119.60 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, identity )] ), substitution(
% 119.18/119.60 1, [ :=( X, 'least_upper_bound'( X, identity ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43700, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X,
% 119.18/119.60 identity ) ), identity ), identity ) ] )
% 119.18/119.60 , clause( 180, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 119.18/119.60 , 0, clause( 43699, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 X, identity ) ), identity ), multiply( 'least_upper_bound'( X, identity )
% 119.18/119.60 , inverse( 'least_upper_bound'( X, identity ) ) ) ) ] )
% 119.18/119.60 , 0, 7, substitution( 0, [ :=( X, 'least_upper_bound'( X, identity ) )] ),
% 119.18/119.60 substitution( 1, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1324, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X,
% 119.18/119.60 identity ) ), identity ), identity ) ] )
% 119.18/119.60 , clause( 43700, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X
% 119.18/119.60 , identity ) ), identity ), identity ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43703, [ =( 'least_upper_bound'( 'least_upper_bound'( Y, Z ), X ),
% 119.18/119.60 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.60 , clause( 49, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 119.18/119.60 'least_upper_bound'( 'least_upper_bound'( Y, Z ), X ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43704, [ =( 'least_upper_bound'( identity, Y ), 'least_upper_bound'(
% 119.18/119.60 'least_upper_bound'( Y, inverse( 'least_upper_bound'( identity, X ) ) ),
% 119.18/119.60 identity ) ) ] )
% 119.18/119.60 , clause( 1323, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ), identity ), identity ) ] )
% 119.18/119.60 , 0, clause( 43703, [ =( 'least_upper_bound'( 'least_upper_bound'( Y, Z ),
% 119.18/119.60 X ), 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.60 , 0, 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, Y ),
% 119.18/119.60 :=( Y, inverse( 'least_upper_bound'( identity, X ) ) ), :=( Z, identity )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43706, [ =( 'least_upper_bound'( 'least_upper_bound'( X, inverse(
% 119.18/119.60 'least_upper_bound'( identity, Y ) ) ), identity ), 'least_upper_bound'(
% 119.18/119.60 identity, X ) ) ] )
% 119.18/119.60 , clause( 43704, [ =( 'least_upper_bound'( identity, Y ),
% 119.18/119.60 'least_upper_bound'( 'least_upper_bound'( Y, inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ) ), identity ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1335, [ =( 'least_upper_bound'( 'least_upper_bound'( Y, inverse(
% 119.18/119.60 'least_upper_bound'( identity, X ) ) ), identity ), 'least_upper_bound'(
% 119.18/119.60 identity, Y ) ) ] )
% 119.18/119.60 , clause( 43706, [ =( 'least_upper_bound'( 'least_upper_bound'( X, inverse(
% 119.18/119.60 'least_upper_bound'( identity, Y ) ) ), identity ), 'least_upper_bound'(
% 119.18/119.60 identity, X ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43709, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 119.18/119.60 , clause( 184, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43710, [ =( X, multiply( multiply( 'least_upper_bound'( identity, X
% 119.18/119.60 ), X ), inverse( 'least_upper_bound'( X, identity ) ) ) ) ] )
% 119.18/119.60 , clause( 1206, [ =( multiply( X, 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 multiply( 'least_upper_bound'( identity, X ), X ) ) ] )
% 119.18/119.60 , 0, clause( 43709, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , 0, 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, 'least_upper_bound'( X, identity ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43711, [ =( multiply( multiply( 'least_upper_bound'( identity, X )
% 119.18/119.60 , X ), inverse( 'least_upper_bound'( X, identity ) ) ), X ) ] )
% 119.18/119.60 , clause( 43710, [ =( X, multiply( multiply( 'least_upper_bound'( identity
% 119.18/119.60 , X ), X ), inverse( 'least_upper_bound'( X, identity ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1525, [ =( multiply( multiply( 'least_upper_bound'( identity, X ),
% 119.18/119.60 X ), inverse( 'least_upper_bound'( X, identity ) ) ), X ) ] )
% 119.18/119.60 , clause( 43711, [ =( multiply( multiply( 'least_upper_bound'( identity, X
% 119.18/119.60 ), X ), inverse( 'least_upper_bound'( X, identity ) ) ), X ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43713, [ =( multiply( X, 'least_upper_bound'( multiply( Y, Z ), T )
% 119.18/119.60 ), 'least_upper_bound'( multiply( multiply( X, Y ), Z ), multiply( X, T
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , clause( 62, [ =( 'least_upper_bound'( multiply( multiply( X, Y ), Z ),
% 119.18/119.60 multiply( X, T ) ), multiply( X, 'least_upper_bound'( multiply( Y, Z ), T
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43717, [ =( multiply( X, 'least_upper_bound'( multiply( inverse( X
% 119.18/119.60 ), Y ), Z ) ), 'least_upper_bound'( multiply( identity, Y ), multiply( X
% 119.18/119.60 , Z ) ) ) ] )
% 119.18/119.60 , clause( 180, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 119.18/119.60 , 0, clause( 43713, [ =( multiply( X, 'least_upper_bound'( multiply( Y, Z )
% 119.18/119.60 , T ) ), 'least_upper_bound'( multiply( multiply( X, Y ), Z ), multiply(
% 119.18/119.60 X, T ) ) ) ] )
% 119.18/119.60 , 0, 11, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, inverse( X ) ), :=( Z, Y ), :=( T, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43719, [ =( multiply( X, 'least_upper_bound'( multiply( inverse( X
% 119.18/119.60 ), Y ), Z ) ), 'least_upper_bound'( Y, multiply( X, Z ) ) ) ] )
% 119.18/119.60 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.60 , 0, clause( 43717, [ =( multiply( X, 'least_upper_bound'( multiply(
% 119.18/119.60 inverse( X ), Y ), Z ) ), 'least_upper_bound'( multiply( identity, Y ),
% 119.18/119.60 multiply( X, Z ) ) ) ] )
% 119.18/119.60 , 0, 10, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1545, [ =( multiply( X, 'least_upper_bound'( multiply( inverse( X )
% 119.18/119.60 , Y ), Z ) ), 'least_upper_bound'( Y, multiply( X, Z ) ) ) ] )
% 119.18/119.60 , clause( 43719, [ =( multiply( X, 'least_upper_bound'( multiply( inverse(
% 119.18/119.60 X ), Y ), Z ) ), 'least_upper_bound'( Y, multiply( X, Z ) ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43722, [ =( multiply( X, 'least_upper_bound'( multiply( Y, Z ), T )
% 119.18/119.60 ), 'least_upper_bound'( multiply( multiply( X, Y ), Z ), multiply( X, T
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , clause( 62, [ =( 'least_upper_bound'( multiply( multiply( X, Y ), Z ),
% 119.18/119.60 multiply( X, T ) ), multiply( X, 'least_upper_bound'( multiply( Y, Z ), T
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43726, [ =( multiply( inverse( X ), 'least_upper_bound'( multiply(
% 119.18/119.60 X, Y ), Z ) ), 'least_upper_bound'( multiply( identity, Y ), multiply(
% 119.18/119.60 inverse( X ), Z ) ) ) ] )
% 119.18/119.60 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.60 , 0, clause( 43722, [ =( multiply( X, 'least_upper_bound'( multiply( Y, Z )
% 119.18/119.60 , T ) ), 'least_upper_bound'( multiply( multiply( X, Y ), Z ), multiply(
% 119.18/119.60 X, T ) ) ) ] )
% 119.18/119.60 , 0, 11, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.60 inverse( X ) ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43728, [ =( multiply( inverse( X ), 'least_upper_bound'( multiply(
% 119.18/119.60 X, Y ), Z ) ), 'least_upper_bound'( Y, multiply( inverse( X ), Z ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.60 , 0, clause( 43726, [ =( multiply( inverse( X ), 'least_upper_bound'(
% 119.18/119.60 multiply( X, Y ), Z ) ), 'least_upper_bound'( multiply( identity, Y ),
% 119.18/119.60 multiply( inverse( X ), Z ) ) ) ] )
% 119.18/119.60 , 0, 10, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1547, [ =( multiply( inverse( X ), 'least_upper_bound'( multiply( X
% 119.18/119.60 , Y ), Z ) ), 'least_upper_bound'( Y, multiply( inverse( X ), Z ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , clause( 43728, [ =( multiply( inverse( X ), 'least_upper_bound'( multiply(
% 119.18/119.60 X, Y ), Z ) ), 'least_upper_bound'( Y, multiply( inverse( X ), Z ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43731, [ =( multiply( X, 'least_upper_bound'( Y, multiply( Z, T ) )
% 119.18/119.60 ), 'least_upper_bound'( multiply( X, Y ), multiply( multiply( X, Z ), T
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , clause( 63, [ =( 'least_upper_bound'( multiply( X, T ), multiply(
% 119.18/119.60 multiply( X, Y ), Z ) ), multiply( X, 'least_upper_bound'( T, multiply( Y
% 119.18/119.60 , Z ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, T ), :=( T, Y )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43736, [ =( multiply( inverse( X ), 'least_upper_bound'( Y,
% 119.18/119.60 multiply( X, Z ) ) ), 'least_upper_bound'( multiply( inverse( X ), Y ),
% 119.18/119.60 multiply( identity, Z ) ) ) ] )
% 119.18/119.60 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 119.18/119.60 , 0, clause( 43731, [ =( multiply( X, 'least_upper_bound'( Y, multiply( Z,
% 119.18/119.60 T ) ) ), 'least_upper_bound'( multiply( X, Y ), multiply( multiply( X, Z
% 119.18/119.60 ), T ) ) ) ] )
% 119.18/119.60 , 0, 15, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.60 inverse( X ) ), :=( Y, Y ), :=( Z, X ), :=( T, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43737, [ =( multiply( inverse( X ), 'least_upper_bound'( Y,
% 119.18/119.60 multiply( X, Z ) ) ), 'least_upper_bound'( multiply( inverse( X ), Y ), Z
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.60 , 0, clause( 43736, [ =( multiply( inverse( X ), 'least_upper_bound'( Y,
% 119.18/119.60 multiply( X, Z ) ) ), 'least_upper_bound'( multiply( inverse( X ), Y ),
% 119.18/119.60 multiply( identity, Z ) ) ) ] )
% 119.18/119.60 , 0, 14, substitution( 0, [ :=( X, Z )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1586, [ =( multiply( inverse( X ), 'least_upper_bound'( Y, multiply(
% 119.18/119.60 X, Z ) ) ), 'least_upper_bound'( multiply( inverse( X ), Y ), Z ) ) ] )
% 119.18/119.60 , clause( 43737, [ =( multiply( inverse( X ), 'least_upper_bound'( Y,
% 119.18/119.60 multiply( X, Z ) ) ), 'least_upper_bound'( multiply( inverse( X ), Y ), Z
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43739, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) ),
% 119.18/119.60 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 119.18/119.60 , clause( 65, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y
% 119.18/119.60 ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43740, [ =( 'least_upper_bound'( identity, multiply( inverse( X ),
% 119.18/119.60 Y ) ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.60 , clause( 43739, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) )
% 119.18/119.60 , 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 119.18/119.60 , 0, clause( 64, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), multiply(
% 119.18/119.60 X, 'least_upper_bound'( Z, Y ) ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.60 :=( X, inverse( X ) ), :=( Y, X ), :=( Z, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1640, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y
% 119.18/119.60 ) ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.60 , clause( 43740, [ =( 'least_upper_bound'( identity, multiply( inverse( X )
% 119.18/119.60 , Y ) ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43742, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) ),
% 119.18/119.60 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 119.18/119.60 , clause( 65, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y
% 119.18/119.60 ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43743, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 119.18/119.60 , clause( 184, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43744, [ =( inverse( X ), multiply( 'least_upper_bound'( identity,
% 119.18/119.60 multiply( inverse( X ), Y ) ), inverse( 'least_upper_bound'( X, Y ) ) ) )
% 119.18/119.60 ] )
% 119.18/119.60 , clause( 43742, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) )
% 119.18/119.60 , 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 119.18/119.60 , 0, clause( 43743, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.60 :=( X, inverse( X ) ), :=( Y, 'least_upper_bound'( X, Y ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43745, [ =( multiply( 'least_upper_bound'( identity, multiply(
% 119.18/119.60 inverse( X ), Y ) ), inverse( 'least_upper_bound'( X, Y ) ) ), inverse( X
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , clause( 43744, [ =( inverse( X ), multiply( 'least_upper_bound'( identity
% 119.18/119.60 , multiply( inverse( X ), Y ) ), inverse( 'least_upper_bound'( X, Y ) ) )
% 119.18/119.60 ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1653, [ =( multiply( 'least_upper_bound'( identity, multiply(
% 119.18/119.60 inverse( X ), Y ) ), inverse( 'least_upper_bound'( X, Y ) ) ), inverse( X
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , clause( 43745, [ =( multiply( 'least_upper_bound'( identity, multiply(
% 119.18/119.60 inverse( X ), Y ) ), inverse( 'least_upper_bound'( X, Y ) ) ), inverse( X
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43747, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , clause( 20, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) )
% 119.18/119.60 , X ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43748, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 119.18/119.60 inverse( X ), 'least_upper_bound'( Y, X ) ) ) ) ] )
% 119.18/119.60 , clause( 66, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ),
% 119.18/119.60 identity ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.60 , 0, clause( 43747, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 119.18/119.60 Y, X ) ) ) ] )
% 119.18/119.60 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.60 :=( X, identity ), :=( Y, multiply( inverse( X ), Y ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43749, [ =( 'greatest_lower_bound'( identity, multiply( inverse( X
% 119.18/119.60 ), 'least_upper_bound'( Y, X ) ) ), identity ) ] )
% 119.18/119.60 , clause( 43748, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 119.18/119.60 inverse( X ), 'least_upper_bound'( Y, X ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1773, [ =( 'greatest_lower_bound'( identity, multiply( inverse( X )
% 119.18/119.60 , 'least_upper_bound'( Y, X ) ) ), identity ) ] )
% 119.18/119.60 , clause( 43749, [ =( 'greatest_lower_bound'( identity, multiply( inverse(
% 119.18/119.60 X ), 'least_upper_bound'( Y, X ) ) ), identity ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43751, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 119.18/119.60 inverse( X ), 'least_upper_bound'( Y, X ) ) ) ) ] )
% 119.18/119.60 , clause( 1773, [ =( 'greatest_lower_bound'( identity, multiply( inverse( X
% 119.18/119.60 ), 'least_upper_bound'( Y, X ) ) ), identity ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43752, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 119.18/119.60 inverse( X ), 'least_upper_bound'( 'least_upper_bound'( Y, X ), Z ) ) ) )
% 119.18/119.60 ] )
% 119.18/119.60 , clause( 59, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.60 'least_upper_bound'( Z, X ), Y ), X ), 'least_upper_bound'(
% 119.18/119.60 'least_upper_bound'( Z, X ), Y ) ) ] )
% 119.18/119.60 , 0, clause( 43751, [ =( identity, 'greatest_lower_bound'( identity,
% 119.18/119.60 multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ) ] )
% 119.18/119.60 , 0, 7, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 119.18/119.60 substitution( 1, [ :=( X, X ), :=( Y, 'least_upper_bound'(
% 119.18/119.60 'least_upper_bound'( Y, X ), Z ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43753, [ =( 'greatest_lower_bound'( identity, multiply( inverse( X
% 119.18/119.60 ), 'least_upper_bound'( 'least_upper_bound'( Y, X ), Z ) ) ), identity )
% 119.18/119.60 ] )
% 119.18/119.60 , clause( 43752, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 119.18/119.60 inverse( X ), 'least_upper_bound'( 'least_upper_bound'( Y, X ), Z ) ) ) )
% 119.18/119.60 ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 1781, [ =( 'greatest_lower_bound'( identity, multiply( inverse( Y )
% 119.18/119.60 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ), identity ) ]
% 119.18/119.60 )
% 119.18/119.60 , clause( 43753, [ =( 'greatest_lower_bound'( identity, multiply( inverse(
% 119.18/119.60 X ), 'least_upper_bound'( 'least_upper_bound'( Y, X ), Z ) ) ), identity
% 119.18/119.60 ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 119.18/119.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43755, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X ) )
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , clause( 201, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43757, [ =( inverse( inverse( X ) ), multiply( 'least_upper_bound'(
% 119.18/119.60 identity, X ), inverse( 'least_upper_bound'( inverse( X ), identity ) ) )
% 119.18/119.60 ) ] )
% 119.18/119.60 , clause( 770, [ =( multiply( inverse( Y ), 'least_upper_bound'( identity,
% 119.18/119.60 Y ) ), 'least_upper_bound'( inverse( Y ), identity ) ) ] )
% 119.18/119.60 , 0, clause( 43755, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X
% 119.18/119.60 ) ) ) ) ] )
% 119.18/119.60 , 0, 9, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, 'least_upper_bound'( identity, X ) ), :=( Y, inverse( X ) )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43758, [ =( X, multiply( 'least_upper_bound'( identity, X ),
% 119.18/119.60 inverse( 'least_upper_bound'( inverse( X ), identity ) ) ) ) ] )
% 119.18/119.60 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43757, [ =( inverse( inverse( X ) ), multiply(
% 119.18/119.60 'least_upper_bound'( identity, X ), inverse( 'least_upper_bound'( inverse(
% 119.18/119.60 X ), identity ) ) ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43759, [ =( multiply( 'least_upper_bound'( identity, X ), inverse(
% 119.18/119.60 'least_upper_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.60 , clause( 43758, [ =( X, multiply( 'least_upper_bound'( identity, X ),
% 119.18/119.60 inverse( 'least_upper_bound'( inverse( X ), identity ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 2156, [ =( multiply( 'least_upper_bound'( identity, X ), inverse(
% 119.18/119.60 'least_upper_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.60 , clause( 43759, [ =( multiply( 'least_upper_bound'( identity, X ), inverse(
% 119.18/119.60 'least_upper_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43761, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X ) )
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , clause( 201, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43763, [ =( inverse( inverse( X ) ), multiply(
% 119.18/119.60 'greatest_lower_bound'( identity, X ), inverse( 'greatest_lower_bound'(
% 119.18/119.60 inverse( X ), identity ) ) ) ) ] )
% 119.18/119.60 , clause( 528, [ =( multiply( inverse( Y ), 'greatest_lower_bound'(
% 119.18/119.60 identity, Y ) ), 'greatest_lower_bound'( inverse( Y ), identity ) ) ] )
% 119.18/119.60 , 0, clause( 43761, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X
% 119.18/119.60 ) ) ) ) ] )
% 119.18/119.60 , 0, 9, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, 'greatest_lower_bound'( identity, X ) ), :=( Y, inverse( X ) )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43764, [ =( X, multiply( 'greatest_lower_bound'( identity, X ),
% 119.18/119.60 inverse( 'greatest_lower_bound'( inverse( X ), identity ) ) ) ) ] )
% 119.18/119.60 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43763, [ =( inverse( inverse( X ) ), multiply(
% 119.18/119.60 'greatest_lower_bound'( identity, X ), inverse( 'greatest_lower_bound'(
% 119.18/119.60 inverse( X ), identity ) ) ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43765, [ =( multiply( 'greatest_lower_bound'( identity, X ),
% 119.18/119.60 inverse( 'greatest_lower_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.60 , clause( 43764, [ =( X, multiply( 'greatest_lower_bound'( identity, X ),
% 119.18/119.60 inverse( 'greatest_lower_bound'( inverse( X ), identity ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 2166, [ =( multiply( 'greatest_lower_bound'( identity, X ), inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.60 , clause( 43765, [ =( multiply( 'greatest_lower_bound'( identity, X ),
% 119.18/119.60 inverse( 'greatest_lower_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43767, [ =( multiply( inverse( X ), 'greatest_lower_bound'( Y, X )
% 119.18/119.60 ), 'greatest_lower_bound'( multiply( inverse( X ), Y ), identity ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , clause( 80, [ =( 'greatest_lower_bound'( multiply( inverse( X ), Y ),
% 119.18/119.60 identity ), multiply( inverse( X ), 'greatest_lower_bound'( Y, X ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43770, [ =( multiply( inverse( multiply( X, Y ) ),
% 119.18/119.60 'greatest_lower_bound'( X, multiply( X, Y ) ) ), 'greatest_lower_bound'(
% 119.18/119.60 inverse( Y ), identity ) ) ] )
% 119.18/119.60 , clause( 195, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , 0, clause( 43767, [ =( multiply( inverse( X ), 'greatest_lower_bound'( Y
% 119.18/119.60 , X ) ), 'greatest_lower_bound'( multiply( inverse( X ), Y ), identity )
% 119.18/119.60 ) ] )
% 119.18/119.60 , 0, 12, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.60 :=( X, multiply( X, Y ) ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 2294, [ =( multiply( inverse( multiply( X, Y ) ),
% 119.18/119.60 'greatest_lower_bound'( X, multiply( X, Y ) ) ), 'greatest_lower_bound'(
% 119.18/119.60 inverse( Y ), identity ) ) ] )
% 119.18/119.60 , clause( 43770, [ =( multiply( inverse( multiply( X, Y ) ),
% 119.18/119.60 'greatest_lower_bound'( X, multiply( X, Y ) ) ), 'greatest_lower_bound'(
% 119.18/119.60 inverse( Y ), identity ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43773, [ =( 'greatest_lower_bound'( Y, Z ), 'least_upper_bound'(
% 119.18/119.60 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ),
% 119.18/119.60 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.60 , clause( 40, [ =( 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.60 'greatest_lower_bound'( X, Y ), Z ), 'greatest_lower_bound'( Y, Z ) ),
% 119.18/119.60 'greatest_lower_bound'( Y, Z ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43776, [ =( 'greatest_lower_bound'( identity, X ),
% 119.18/119.60 'least_upper_bound'( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 identity, Y ) ), X ), 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.60 , clause( 616, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ), identity ), inverse( 'least_upper_bound'( identity, X )
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , 0, clause( 43773, [ =( 'greatest_lower_bound'( Y, Z ),
% 119.18/119.60 'least_upper_bound'( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y
% 119.18/119.60 ), Z ), 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.60 , 0, 6, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, inverse(
% 119.18/119.60 'least_upper_bound'( identity, Y ) ) ), :=( Y, identity ), :=( Z, X )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43781, [ =( 'least_upper_bound'( 'greatest_lower_bound'( inverse(
% 119.18/119.60 'least_upper_bound'( identity, Y ) ), X ), 'greatest_lower_bound'(
% 119.18/119.60 identity, X ) ), 'greatest_lower_bound'( identity, X ) ) ] )
% 119.18/119.60 , clause( 43776, [ =( 'greatest_lower_bound'( identity, X ),
% 119.18/119.60 'least_upper_bound'( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 identity, Y ) ), X ), 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 2633, [ =( 'least_upper_bound'( 'greatest_lower_bound'( inverse(
% 119.18/119.60 'least_upper_bound'( identity, X ) ), Y ), 'greatest_lower_bound'(
% 119.18/119.60 identity, Y ) ), 'greatest_lower_bound'( identity, Y ) ) ] )
% 119.18/119.60 , clause( 43781, [ =( 'least_upper_bound'( 'greatest_lower_bound'( inverse(
% 119.18/119.60 'least_upper_bound'( identity, Y ) ), X ), 'greatest_lower_bound'(
% 119.18/119.60 identity, X ) ), 'greatest_lower_bound'( identity, X ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43783, [ =( multiply( 'greatest_lower_bound'( X, identity ), Y ),
% 119.18/119.60 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ] )
% 119.18/119.60 , clause( 154, [ =( 'greatest_lower_bound'( multiply( Y, X ), X ), multiply(
% 119.18/119.60 'greatest_lower_bound'( Y, identity ), X ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43788, [ =( multiply( 'greatest_lower_bound'(
% 119.18/119.60 'greatest_lower_bound'( identity, X ), identity ), inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), identity ) ) ),
% 119.18/119.60 'greatest_lower_bound'( X, inverse( 'greatest_lower_bound'( inverse( X )
% 119.18/119.60 , identity ) ) ) ) ] )
% 119.18/119.60 , clause( 2166, [ =( multiply( 'greatest_lower_bound'( identity, X ),
% 119.18/119.60 inverse( 'greatest_lower_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43783, [ =( multiply( 'greatest_lower_bound'( X, identity ), Y
% 119.18/119.60 ), 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ] )
% 119.18/119.60 , 0, 13, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.60 'greatest_lower_bound'( identity, X ) ), :=( Y, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), identity ) ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43789, [ =( multiply( 'greatest_lower_bound'( identity, X ),
% 119.18/119.60 inverse( 'greatest_lower_bound'( inverse( X ), identity ) ) ),
% 119.18/119.60 'greatest_lower_bound'( X, inverse( 'greatest_lower_bound'( inverse( X )
% 119.18/119.60 , identity ) ) ) ) ] )
% 119.18/119.60 , clause( 32, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ),
% 119.18/119.60 X ), 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.60 , 0, clause( 43788, [ =( multiply( 'greatest_lower_bound'(
% 119.18/119.60 'greatest_lower_bound'( identity, X ), identity ), inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), identity ) ) ),
% 119.18/119.60 'greatest_lower_bound'( X, inverse( 'greatest_lower_bound'( inverse( X )
% 119.18/119.60 , identity ) ) ) ) ] )
% 119.18/119.60 , 0, 2, substitution( 0, [ :=( X, identity ), :=( Y, X )] ), substitution(
% 119.18/119.60 1, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43790, [ =( X, 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), identity ) ) ) ) ] )
% 119.18/119.60 , clause( 2166, [ =( multiply( 'greatest_lower_bound'( identity, X ),
% 119.18/119.60 inverse( 'greatest_lower_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43789, [ =( multiply( 'greatest_lower_bound'( identity, X ),
% 119.18/119.60 inverse( 'greatest_lower_bound'( inverse( X ), identity ) ) ),
% 119.18/119.60 'greatest_lower_bound'( X, inverse( 'greatest_lower_bound'( inverse( X )
% 119.18/119.60 , identity ) ) ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43791, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.60 , clause( 43790, [ =( X, 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), identity ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 3103, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.60 , clause( 43791, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43793, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 119.18/119.60 'greatest_lower_bound'( X, Y ), 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.60 , clause( 26, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Z, X ),
% 119.18/119.60 'least_upper_bound'( X, Y ) ), 'greatest_lower_bound'( Z, X ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43795, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), identity ) ) ),
% 119.18/119.60 'greatest_lower_bound'( X, 'least_upper_bound'( inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), identity ) ), Y ) ) ) ] )
% 119.18/119.60 , clause( 3103, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43793, [ =( 'greatest_lower_bound'( X, Y ),
% 119.18/119.60 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ),
% 119.18/119.60 'least_upper_bound'( Y, Z ) ) ) ] )
% 119.18/119.60 , 0, 9, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, inverse( 'greatest_lower_bound'( inverse( X ), identity ) ) ),
% 119.18/119.60 :=( Z, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43796, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 119.18/119.60 inverse( 'greatest_lower_bound'( inverse( X ), identity ) ), Y ) ) ) ] )
% 119.18/119.60 , clause( 3103, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43795, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), identity ) ) ),
% 119.18/119.60 'greatest_lower_bound'( X, 'least_upper_bound'( inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), identity ) ), Y ) ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43798, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), identity ) ), Y ) ), X ) ] )
% 119.18/119.60 , clause( 43796, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 119.18/119.60 inverse( 'greatest_lower_bound'( inverse( X ), identity ) ), Y ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 3124, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), identity ) ), Y ) ), X ) ] )
% 119.18/119.60 , clause( 43798, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'(
% 119.18/119.60 inverse( 'greatest_lower_bound'( inverse( X ), identity ) ), Y ) ), X ) ]
% 119.18/119.60 )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43801, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X ) )
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , clause( 201, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43804, [ =( inverse( 'least_upper_bound'( inverse( X ), Y ) ),
% 119.18/119.60 multiply( X, inverse( 'least_upper_bound'( identity, multiply( Y, X ) ) )
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , clause( 115, [ =( multiply( 'least_upper_bound'( inverse( X ), Y ), X ),
% 119.18/119.60 'least_upper_bound'( identity, multiply( Y, X ) ) ) ] )
% 119.18/119.60 , 0, clause( 43801, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X
% 119.18/119.60 ) ) ) ) ] )
% 119.18/119.60 , 0, 9, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.60 :=( X, X ), :=( Y, 'least_upper_bound'( inverse( X ), Y ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43805, [ =( multiply( X, inverse( 'least_upper_bound'( identity,
% 119.18/119.60 multiply( Y, X ) ) ) ), inverse( 'least_upper_bound'( inverse( X ), Y ) )
% 119.18/119.60 ) ] )
% 119.18/119.60 , clause( 43804, [ =( inverse( 'least_upper_bound'( inverse( X ), Y ) ),
% 119.18/119.60 multiply( X, inverse( 'least_upper_bound'( identity, multiply( Y, X ) ) )
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 3168, [ =( multiply( X, inverse( 'least_upper_bound'( identity,
% 119.18/119.60 multiply( Y, X ) ) ) ), inverse( 'least_upper_bound'( inverse( X ), Y ) )
% 119.18/119.60 ) ] )
% 119.18/119.60 , clause( 43805, [ =( multiply( X, inverse( 'least_upper_bound'( identity,
% 119.18/119.60 multiply( Y, X ) ) ) ), inverse( 'least_upper_bound'( inverse( X ), Y ) )
% 119.18/119.60 ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43807, [ =( multiply( 'least_upper_bound'( Y, identity ), X ),
% 119.18/119.60 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 119.18/119.60 , clause( 1207, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 119.18/119.60 'least_upper_bound'( X, identity ), Y ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43813, [ =( multiply( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.60 identity, X ), identity ), inverse( 'least_upper_bound'( inverse( X ),
% 119.18/119.60 identity ) ) ), 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 inverse( X ), identity ) ), X ) ) ] )
% 119.18/119.60 , clause( 2156, [ =( multiply( 'least_upper_bound'( identity, X ), inverse(
% 119.18/119.60 'least_upper_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43807, [ =( multiply( 'least_upper_bound'( Y, identity ), X )
% 119.18/119.60 , 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 119.18/119.60 , 0, 18, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.60 inverse( 'least_upper_bound'( inverse( X ), identity ) ) ), :=( Y,
% 119.18/119.60 'least_upper_bound'( identity, X ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43814, [ =( multiply( 'least_upper_bound'( identity, X ), inverse(
% 119.18/119.60 'least_upper_bound'( inverse( X ), identity ) ) ), 'least_upper_bound'(
% 119.18/119.60 inverse( 'least_upper_bound'( inverse( X ), identity ) ), X ) ) ] )
% 119.18/119.60 , clause( 35, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 119.18/119.60 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.60 , 0, clause( 43813, [ =( multiply( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.60 identity, X ), identity ), inverse( 'least_upper_bound'( inverse( X ),
% 119.18/119.60 identity ) ) ), 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 inverse( X ), identity ) ), X ) ) ] )
% 119.18/119.60 , 0, 2, substitution( 0, [ :=( X, identity ), :=( Y, X )] ), substitution(
% 119.18/119.60 1, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43815, [ =( X, 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 inverse( X ), identity ) ), X ) ) ] )
% 119.18/119.60 , clause( 2156, [ =( multiply( 'least_upper_bound'( identity, X ), inverse(
% 119.18/119.60 'least_upper_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43814, [ =( multiply( 'least_upper_bound'( identity, X ),
% 119.18/119.60 inverse( 'least_upper_bound'( inverse( X ), identity ) ) ),
% 119.18/119.60 'least_upper_bound'( inverse( 'least_upper_bound'( inverse( X ), identity
% 119.18/119.60 ) ), X ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43816, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 inverse( X ), identity ) ), X ), X ) ] )
% 119.18/119.60 , clause( 43815, [ =( X, 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 inverse( X ), identity ) ), X ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 3237, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 inverse( X ), identity ) ), X ), X ) ] )
% 119.18/119.60 , clause( 43816, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 inverse( X ), identity ) ), X ), X ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43818, [ =( X, multiply( 'least_upper_bound'( identity, X ),
% 119.18/119.60 inverse( 'least_upper_bound'( inverse( X ), identity ) ) ) ) ] )
% 119.18/119.60 , clause( 2156, [ =( multiply( 'least_upper_bound'( identity, X ), inverse(
% 119.18/119.60 'least_upper_bound'( inverse( X ), identity ) ) ), X ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43819, [ =( inverse( X ), multiply( 'least_upper_bound'( identity,
% 119.18/119.60 inverse( X ) ), inverse( 'least_upper_bound'( X, identity ) ) ) ) ] )
% 119.18/119.60 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43818, [ =( X, multiply( 'least_upper_bound'( identity, X ),
% 119.18/119.60 inverse( 'least_upper_bound'( inverse( X ), identity ) ) ) ) ] )
% 119.18/119.60 , 0, 10, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.60 inverse( X ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43820, [ =( multiply( 'least_upper_bound'( identity, inverse( X ) )
% 119.18/119.60 , inverse( 'least_upper_bound'( X, identity ) ) ), inverse( X ) ) ] )
% 119.18/119.60 , clause( 43819, [ =( inverse( X ), multiply( 'least_upper_bound'( identity
% 119.18/119.60 , inverse( X ) ), inverse( 'least_upper_bound'( X, identity ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 3242, [ =( multiply( 'least_upper_bound'( identity, inverse( X ) )
% 119.18/119.60 , inverse( 'least_upper_bound'( X, identity ) ) ), inverse( X ) ) ] )
% 119.18/119.60 , clause( 43820, [ =( multiply( 'least_upper_bound'( identity, inverse( X )
% 119.18/119.60 ), inverse( 'least_upper_bound'( X, identity ) ) ), inverse( X ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43822, [ =( X, 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 inverse( X ), identity ) ), X ) ) ] )
% 119.18/119.60 , clause( 3237, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 inverse( X ), identity ) ), X ), X ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43823, [ =( inverse( X ), 'least_upper_bound'( inverse(
% 119.18/119.60 'least_upper_bound'( X, identity ) ), inverse( X ) ) ) ] )
% 119.18/119.60 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43822, [ =( X, 'least_upper_bound'( inverse(
% 119.18/119.60 'least_upper_bound'( inverse( X ), identity ) ), X ) ) ] )
% 119.18/119.60 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 119.18/119.60 X ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43824, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X,
% 119.18/119.60 identity ) ), inverse( X ) ), inverse( X ) ) ] )
% 119.18/119.60 , clause( 43823, [ =( inverse( X ), 'least_upper_bound'( inverse(
% 119.18/119.60 'least_upper_bound'( X, identity ) ), inverse( X ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 3297, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X,
% 119.18/119.60 identity ) ), inverse( X ) ), inverse( X ) ) ] )
% 119.18/119.60 , clause( 43824, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X
% 119.18/119.60 , identity ) ), inverse( X ) ), inverse( X ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43826, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 119.18/119.60 , X ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43827, [ =( inverse( 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 'greatest_lower_bound'( inverse( 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 inverse( X ) ) ) ] )
% 119.18/119.60 , clause( 3297, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X,
% 119.18/119.60 identity ) ), inverse( X ) ), inverse( X ) ) ] )
% 119.18/119.60 , 0, clause( 43826, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 119.18/119.60 X, Y ) ) ) ] )
% 119.18/119.60 , 0, 10, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.60 inverse( 'least_upper_bound'( X, identity ) ) ), :=( Y, inverse( X ) )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43828, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'( X
% 119.18/119.60 , identity ) ), inverse( X ) ), inverse( 'least_upper_bound'( X, identity
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , clause( 43827, [ =( inverse( 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 'greatest_lower_bound'( inverse( 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 inverse( X ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 3308, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'( X
% 119.18/119.60 , identity ) ), inverse( X ) ), inverse( 'least_upper_bound'( X, identity
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , clause( 43828, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 X, identity ) ), inverse( X ) ), inverse( 'least_upper_bound'( X,
% 119.18/119.60 identity ) ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43830, [ =( multiply( X, Z ), 'least_upper_bound'(
% 119.18/119.60 'greatest_lower_bound'( multiply( 'greatest_lower_bound'( X, Y ), Z ), T
% 119.18/119.60 ), multiply( X, Z ) ) ) ] )
% 119.18/119.60 , clause( 144, [ =( 'least_upper_bound'( 'greatest_lower_bound'( multiply(
% 119.18/119.60 'greatest_lower_bound'( X, Z ), Y ), T ), multiply( X, Y ) ), multiply( X
% 119.18/119.60 , Y ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T, T )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43832, [ =( multiply( X, inverse( X ) ), 'least_upper_bound'(
% 119.18/119.60 'greatest_lower_bound'( multiply( 'greatest_lower_bound'( X, Y ), inverse(
% 119.18/119.60 X ) ), Z ), identity ) ) ] )
% 119.18/119.60 , clause( 180, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 119.18/119.60 , 0, clause( 43830, [ =( multiply( X, Z ), 'least_upper_bound'(
% 119.18/119.60 'greatest_lower_bound'( multiply( 'greatest_lower_bound'( X, Y ), Z ), T
% 119.18/119.60 ), multiply( X, Z ) ) ) ] )
% 119.18/119.60 , 0, 14, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, Y ), :=( Z, inverse( X ) ), :=( T, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43834, [ =( identity, 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.60 multiply( 'greatest_lower_bound'( X, Y ), inverse( X ) ), Z ), identity )
% 119.18/119.60 ) ] )
% 119.18/119.60 , clause( 180, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 119.18/119.60 , 0, clause( 43832, [ =( multiply( X, inverse( X ) ), 'least_upper_bound'(
% 119.18/119.60 'greatest_lower_bound'( multiply( 'greatest_lower_bound'( X, Y ), inverse(
% 119.18/119.60 X ) ), Z ), identity ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43836, [ =( 'least_upper_bound'( 'greatest_lower_bound'( multiply(
% 119.18/119.60 'greatest_lower_bound'( X, Y ), inverse( X ) ), Z ), identity ), identity
% 119.18/119.60 ) ] )
% 119.18/119.60 , clause( 43834, [ =( identity, 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.60 multiply( 'greatest_lower_bound'( X, Y ), inverse( X ) ), Z ), identity )
% 119.18/119.60 ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 4020, [ =( 'least_upper_bound'( 'greatest_lower_bound'( multiply(
% 119.18/119.60 'greatest_lower_bound'( X, Y ), inverse( X ) ), Z ), identity ), identity
% 119.18/119.60 ) ] )
% 119.18/119.60 , clause( 43836, [ =( 'least_upper_bound'( 'greatest_lower_bound'( multiply(
% 119.18/119.60 'greatest_lower_bound'( X, Y ), inverse( X ) ), Z ), identity ), identity
% 119.18/119.60 ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43840, [ =( X, multiply( 'least_upper_bound'( X, multiply( X, Y ) )
% 119.18/119.60 , inverse( 'least_upper_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.60 , clause( 801, [ =( multiply( 'least_upper_bound'( X, multiply( X, Y ) ),
% 119.18/119.60 inverse( 'least_upper_bound'( Y, identity ) ) ), X ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43843, [ =( multiply( X, Y ), multiply( 'least_upper_bound'(
% 119.18/119.60 multiply( X, Y ), X ), inverse( 'least_upper_bound'( inverse( Y ),
% 119.18/119.60 identity ) ) ) ) ] )
% 119.18/119.60 , clause( 184, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 119.18/119.60 , 0, clause( 43840, [ =( X, multiply( 'least_upper_bound'( X, multiply( X,
% 119.18/119.60 Y ) ), inverse( 'least_upper_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.60 , 0, 9, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, multiply( X, Y ) ), :=( Y, inverse( Y ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43844, [ =( multiply( 'least_upper_bound'( multiply( X, Y ), X ),
% 119.18/119.60 inverse( 'least_upper_bound'( inverse( Y ), identity ) ) ), multiply( X,
% 119.18/119.60 Y ) ) ] )
% 119.18/119.60 , clause( 43843, [ =( multiply( X, Y ), multiply( 'least_upper_bound'(
% 119.18/119.60 multiply( X, Y ), X ), inverse( 'least_upper_bound'( inverse( Y ),
% 119.18/119.60 identity ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 4025, [ =( multiply( 'least_upper_bound'( multiply( X, Y ), X ),
% 119.18/119.60 inverse( 'least_upper_bound'( inverse( Y ), identity ) ) ), multiply( X,
% 119.18/119.60 Y ) ) ] )
% 119.18/119.60 , clause( 43844, [ =( multiply( 'least_upper_bound'( multiply( X, Y ), X )
% 119.18/119.60 , inverse( 'least_upper_bound'( inverse( Y ), identity ) ) ), multiply( X
% 119.18/119.60 , Y ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43846, [ =( inverse( Y ), multiply( inverse( multiply( X, Y ) ), X
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , clause( 195, [ =( multiply( inverse( multiply( X, Y ) ), X ), inverse( Y
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43849, [ =( inverse( 'least_upper_bound'( X, inverse( Y ) ) ),
% 119.18/119.60 multiply( inverse( 'least_upper_bound'( multiply( Y, X ), identity ) ), Y
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , clause( 192, [ =( multiply( X, 'least_upper_bound'( Y, inverse( X ) ) ),
% 119.18/119.60 'least_upper_bound'( multiply( X, Y ), identity ) ) ] )
% 119.18/119.60 , 0, clause( 43846, [ =( inverse( Y ), multiply( inverse( multiply( X, Y )
% 119.18/119.60 ), X ) ) ] )
% 119.18/119.60 , 0, 8, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, Y ), :=( Y, 'least_upper_bound'( X, inverse( Y ) ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43850, [ =( multiply( inverse( 'least_upper_bound'( multiply( Y, X
% 119.18/119.60 ), identity ) ), Y ), inverse( 'least_upper_bound'( X, inverse( Y ) ) )
% 119.18/119.60 ) ] )
% 119.18/119.60 , clause( 43849, [ =( inverse( 'least_upper_bound'( X, inverse( Y ) ) ),
% 119.18/119.60 multiply( inverse( 'least_upper_bound'( multiply( Y, X ), identity ) ), Y
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 4154, [ =( multiply( inverse( 'least_upper_bound'( multiply( X, Y )
% 119.18/119.60 , identity ) ), X ), inverse( 'least_upper_bound'( Y, inverse( X ) ) ) )
% 119.18/119.60 ] )
% 119.18/119.60 , clause( 43850, [ =( multiply( inverse( 'least_upper_bound'( multiply( Y,
% 119.18/119.60 X ), identity ) ), Y ), inverse( 'least_upper_bound'( X, inverse( Y ) ) )
% 119.18/119.60 ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43852, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X ) )
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , clause( 201, [ =( multiply( Y, inverse( multiply( X, Y ) ) ), inverse( X
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43855, [ =( inverse( 'greatest_lower_bound'( inverse( X ), Y ) ),
% 119.18/119.60 multiply( X, inverse( 'greatest_lower_bound'( identity, multiply( Y, X )
% 119.18/119.60 ) ) ) ) ] )
% 119.18/119.60 , clause( 151, [ =( multiply( 'greatest_lower_bound'( inverse( X ), Y ), X
% 119.18/119.60 ), 'greatest_lower_bound'( identity, multiply( Y, X ) ) ) ] )
% 119.18/119.60 , 0, clause( 43852, [ =( inverse( Y ), multiply( X, inverse( multiply( Y, X
% 119.18/119.60 ) ) ) ) ] )
% 119.18/119.60 , 0, 9, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.60 :=( X, X ), :=( Y, 'greatest_lower_bound'( inverse( X ), Y ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43856, [ =( multiply( X, inverse( 'greatest_lower_bound'( identity
% 119.18/119.60 , multiply( Y, X ) ) ) ), inverse( 'greatest_lower_bound'( inverse( X ),
% 119.18/119.60 Y ) ) ) ] )
% 119.18/119.60 , clause( 43855, [ =( inverse( 'greatest_lower_bound'( inverse( X ), Y ) )
% 119.18/119.60 , multiply( X, inverse( 'greatest_lower_bound'( identity, multiply( Y, X
% 119.18/119.60 ) ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 4181, [ =( multiply( X, inverse( 'greatest_lower_bound'( identity,
% 119.18/119.60 multiply( Y, X ) ) ) ), inverse( 'greatest_lower_bound'( inverse( X ), Y
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , clause( 43856, [ =( multiply( X, inverse( 'greatest_lower_bound'(
% 119.18/119.60 identity, multiply( Y, X ) ) ) ), inverse( 'greatest_lower_bound'(
% 119.18/119.60 inverse( X ), Y ) ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43858, [ =( identity, 'least_upper_bound'( 'greatest_lower_bound'(
% 119.18/119.60 multiply( 'greatest_lower_bound'( X, Y ), inverse( X ) ), Z ), identity )
% 119.18/119.60 ) ] )
% 119.18/119.60 , clause( 4020, [ =( 'least_upper_bound'( 'greatest_lower_bound'( multiply(
% 119.18/119.60 'greatest_lower_bound'( X, Y ), inverse( X ) ), Z ), identity ), identity
% 119.18/119.60 ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43859, [ =( identity, 'least_upper_bound'( multiply(
% 119.18/119.60 'greatest_lower_bound'( X, Y ), inverse( X ) ), identity ) ) ] )
% 119.18/119.60 , clause( 3124, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'(
% 119.18/119.60 inverse( 'greatest_lower_bound'( inverse( X ), identity ) ), Y ) ), X ) ]
% 119.18/119.60 )
% 119.18/119.60 , 0, clause( 43858, [ =( identity, 'least_upper_bound'(
% 119.18/119.60 'greatest_lower_bound'( multiply( 'greatest_lower_bound'( X, Y ), inverse(
% 119.18/119.60 X ) ), Z ), identity ) ) ] )
% 119.18/119.60 , 0, 3, substitution( 0, [ :=( X, multiply( 'greatest_lower_bound'( X, Y )
% 119.18/119.60 , inverse( X ) ) ), :=( Y, Z )] ), substitution( 1, [ :=( X, X ), :=( Y,
% 119.18/119.60 Y ), :=( Z, 'least_upper_bound'( inverse( 'greatest_lower_bound'( inverse(
% 119.18/119.60 multiply( 'greatest_lower_bound'( X, Y ), inverse( X ) ) ), identity ) )
% 119.18/119.60 , Z ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43861, [ =( 'least_upper_bound'( multiply( 'greatest_lower_bound'(
% 119.18/119.60 X, Y ), inverse( X ) ), identity ), identity ) ] )
% 119.18/119.60 , clause( 43859, [ =( identity, 'least_upper_bound'( multiply(
% 119.18/119.60 'greatest_lower_bound'( X, Y ), inverse( X ) ), identity ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 4331, [ =( 'least_upper_bound'( multiply( 'greatest_lower_bound'( X
% 119.18/119.60 , Y ), inverse( X ) ), identity ), identity ) ] )
% 119.18/119.60 , clause( 43861, [ =( 'least_upper_bound'( multiply( 'greatest_lower_bound'(
% 119.18/119.60 X, Y ), inverse( X ) ), identity ), identity ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43864, [ =( inverse( X ), multiply( 'least_upper_bound'( identity,
% 119.18/119.60 inverse( X ) ), inverse( 'least_upper_bound'( X, identity ) ) ) ) ] )
% 119.18/119.60 , clause( 3242, [ =( multiply( 'least_upper_bound'( identity, inverse( X )
% 119.18/119.60 ), inverse( 'least_upper_bound'( X, identity ) ) ), inverse( X ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43868, [ =( inverse( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.60 inverse( X ) ) ), multiply( 'least_upper_bound'( identity, inverse(
% 119.18/119.60 multiply( 'greatest_lower_bound'( X, Y ), inverse( X ) ) ) ), inverse(
% 119.18/119.60 identity ) ) ) ] )
% 119.18/119.60 , clause( 4331, [ =( 'least_upper_bound'( multiply( 'greatest_lower_bound'(
% 119.18/119.60 X, Y ), inverse( X ) ), identity ), identity ) ] )
% 119.18/119.60 , 0, clause( 43864, [ =( inverse( X ), multiply( 'least_upper_bound'(
% 119.18/119.60 identity, inverse( X ) ), inverse( 'least_upper_bound'( X, identity ) ) )
% 119.18/119.60 ) ] )
% 119.18/119.60 , 0, 19, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.60 :=( X, multiply( 'greatest_lower_bound'( X, Y ), inverse( X ) ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43870, [ =( inverse( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.60 inverse( X ) ) ), multiply( 'least_upper_bound'( identity, multiply( X,
% 119.18/119.60 inverse( 'greatest_lower_bound'( X, Y ) ) ) ), inverse( identity ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , clause( 211, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 119.18/119.60 inverse( X ) ) ) ] )
% 119.18/119.60 , 0, clause( 43868, [ =( inverse( multiply( 'greatest_lower_bound'( X, Y )
% 119.18/119.60 , inverse( X ) ) ), multiply( 'least_upper_bound'( identity, inverse(
% 119.18/119.60 multiply( 'greatest_lower_bound'( X, Y ), inverse( X ) ) ) ), inverse(
% 119.18/119.60 identity ) ) ) ] )
% 119.18/119.60 , 0, 11, substitution( 0, [ :=( X, 'greatest_lower_bound'( X, Y ) ), :=( Y
% 119.18/119.60 , X )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43871, [ =( multiply( X, inverse( 'greatest_lower_bound'( X, Y ) )
% 119.18/119.60 ), multiply( 'least_upper_bound'( identity, multiply( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ) ), inverse( identity ) ) ) ] )
% 119.18/119.60 , clause( 211, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 119.18/119.60 inverse( X ) ) ) ] )
% 119.18/119.60 , 0, clause( 43870, [ =( inverse( multiply( 'greatest_lower_bound'( X, Y )
% 119.18/119.60 , inverse( X ) ) ), multiply( 'least_upper_bound'( identity, multiply( X
% 119.18/119.60 , inverse( 'greatest_lower_bound'( X, Y ) ) ) ), inverse( identity ) ) )
% 119.18/119.60 ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, 'greatest_lower_bound'( X, Y ) ), :=( Y,
% 119.18/119.60 X )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43875, [ =( multiply( X, inverse( 'greatest_lower_bound'( X, Y ) )
% 119.18/119.60 ), multiply( 'least_upper_bound'( identity, multiply( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ) ), identity ) ) ] )
% 119.18/119.60 , clause( 160, [ =( inverse( identity ), identity ) ] )
% 119.18/119.60 , 0, clause( 43871, [ =( multiply( X, inverse( 'greatest_lower_bound'( X, Y
% 119.18/119.60 ) ) ), multiply( 'least_upper_bound'( identity, multiply( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ) ), inverse( identity ) ) ) ] )
% 119.18/119.60 , 0, 16, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43876, [ =( multiply( X, inverse( 'greatest_lower_bound'( X, Y ) )
% 119.18/119.60 ), 'least_upper_bound'( identity, multiply( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ) ) ) ] )
% 119.18/119.60 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.60 , 0, clause( 43875, [ =( multiply( X, inverse( 'greatest_lower_bound'( X, Y
% 119.18/119.60 ) ) ), multiply( 'least_upper_bound'( identity, multiply( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ) ), identity ) ) ] )
% 119.18/119.60 , 0, 7, substitution( 0, [ :=( X, 'least_upper_bound'( identity, multiply(
% 119.18/119.60 X, inverse( 'greatest_lower_bound'( X, Y ) ) ) ) )] ), substitution( 1, [
% 119.18/119.60 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43877, [ =( 'least_upper_bound'( identity, multiply( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ) ), multiply( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ) ) ] )
% 119.18/119.60 , clause( 43876, [ =( multiply( X, inverse( 'greatest_lower_bound'( X, Y )
% 119.18/119.60 ) ), 'least_upper_bound'( identity, multiply( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 4369, [ =( 'least_upper_bound'( identity, multiply( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ) ), multiply( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ) ) ] )
% 119.18/119.60 , clause( 43877, [ =( 'least_upper_bound'( identity, multiply( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ) ), multiply( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43879, [ =( inverse( 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 'greatest_lower_bound'( inverse( 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 inverse( X ) ) ) ] )
% 119.18/119.60 , clause( 3308, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 X, identity ) ), inverse( X ) ), inverse( 'least_upper_bound'( X,
% 119.18/119.60 identity ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43884, [ =( inverse( 'least_upper_bound'( multiply(
% 119.18/119.60 'greatest_lower_bound'( X, Y ), inverse( X ) ), identity ) ),
% 119.18/119.60 'greatest_lower_bound'( inverse( identity ), inverse( multiply(
% 119.18/119.60 'greatest_lower_bound'( X, Y ), inverse( X ) ) ) ) ) ] )
% 119.18/119.60 , clause( 4331, [ =( 'least_upper_bound'( multiply( 'greatest_lower_bound'(
% 119.18/119.60 X, Y ), inverse( X ) ), identity ), identity ) ] )
% 119.18/119.60 , 0, clause( 43879, [ =( inverse( 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 'greatest_lower_bound'( inverse( 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 inverse( X ) ) ) ] )
% 119.18/119.60 , 0, 12, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.60 :=( X, multiply( 'greatest_lower_bound'( X, Y ), inverse( X ) ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43885, [ =( inverse( identity ), 'greatest_lower_bound'( inverse(
% 119.18/119.60 identity ), inverse( multiply( 'greatest_lower_bound'( X, Y ), inverse( X
% 119.18/119.60 ) ) ) ) ) ] )
% 119.18/119.60 , clause( 4331, [ =( 'least_upper_bound'( multiply( 'greatest_lower_bound'(
% 119.18/119.60 X, Y ), inverse( X ) ), identity ), identity ) ] )
% 119.18/119.60 , 0, clause( 43884, [ =( inverse( 'least_upper_bound'( multiply(
% 119.18/119.60 'greatest_lower_bound'( X, Y ), inverse( X ) ), identity ) ),
% 119.18/119.60 'greatest_lower_bound'( inverse( identity ), inverse( multiply(
% 119.18/119.60 'greatest_lower_bound'( X, Y ), inverse( X ) ) ) ) ) ] )
% 119.18/119.60 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.60 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43890, [ =( inverse( identity ), 'greatest_lower_bound'( identity,
% 119.18/119.60 inverse( multiply( 'greatest_lower_bound'( X, Y ), inverse( X ) ) ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , clause( 160, [ =( inverse( identity ), identity ) ] )
% 119.18/119.60 , 0, clause( 43885, [ =( inverse( identity ), 'greatest_lower_bound'(
% 119.18/119.60 inverse( identity ), inverse( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.60 inverse( X ) ) ) ) ) ] )
% 119.18/119.60 , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43891, [ =( identity, 'greatest_lower_bound'( identity, inverse(
% 119.18/119.60 multiply( 'greatest_lower_bound'( X, Y ), inverse( X ) ) ) ) ) ] )
% 119.18/119.60 , clause( 160, [ =( inverse( identity ), identity ) ] )
% 119.18/119.60 , 0, clause( 43890, [ =( inverse( identity ), 'greatest_lower_bound'(
% 119.18/119.60 identity, inverse( multiply( 'greatest_lower_bound'( X, Y ), inverse( X )
% 119.18/119.60 ) ) ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43894, [ =( identity, 'greatest_lower_bound'( identity, multiply( X
% 119.18/119.60 , inverse( 'greatest_lower_bound'( X, Y ) ) ) ) ) ] )
% 119.18/119.60 , clause( 211, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 119.18/119.60 inverse( X ) ) ) ] )
% 119.18/119.60 , 0, clause( 43891, [ =( identity, 'greatest_lower_bound'( identity,
% 119.18/119.60 inverse( multiply( 'greatest_lower_bound'( X, Y ), inverse( X ) ) ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , 0, 4, substitution( 0, [ :=( X, 'greatest_lower_bound'( X, Y ) ), :=( Y,
% 119.18/119.60 X )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43895, [ =( 'greatest_lower_bound'( identity, multiply( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ) ), identity ) ] )
% 119.18/119.60 , clause( 43894, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 119.18/119.60 X, inverse( 'greatest_lower_bound'( X, Y ) ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 4370, [ =( 'greatest_lower_bound'( identity, multiply( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ) ), identity ) ] )
% 119.18/119.60 , clause( 43895, [ =( 'greatest_lower_bound'( identity, multiply( X,
% 119.18/119.60 inverse( 'greatest_lower_bound'( X, Y ) ) ) ), identity ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43896, [ =( identity, 'least_upper_bound'( multiply(
% 119.18/119.60 'greatest_lower_bound'( X, Y ), inverse( X ) ), identity ) ) ] )
% 119.18/119.60 , clause( 4331, [ =( 'least_upper_bound'( multiply( 'greatest_lower_bound'(
% 119.18/119.60 X, Y ), inverse( X ) ), identity ), identity ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43897, [ =( identity, 'least_upper_bound'( multiply(
% 119.18/119.60 'greatest_lower_bound'( Y, X ), inverse( X ) ), identity ) ) ] )
% 119.18/119.60 , clause( 150, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ), multiply(
% 119.18/119.60 'greatest_lower_bound'( Z, X ), Y ) ) ] )
% 119.18/119.60 , 0, clause( 43896, [ =( identity, 'least_upper_bound'( multiply(
% 119.18/119.60 'greatest_lower_bound'( X, Y ), inverse( X ) ), identity ) ) ] )
% 119.18/119.60 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, inverse( X ) ), :=( Z, Y )] )
% 119.18/119.60 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43900, [ =( 'least_upper_bound'( multiply( 'greatest_lower_bound'(
% 119.18/119.60 X, Y ), inverse( Y ) ), identity ), identity ) ] )
% 119.18/119.60 , clause( 43897, [ =( identity, 'least_upper_bound'( multiply(
% 119.18/119.60 'greatest_lower_bound'( Y, X ), inverse( X ) ), identity ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 4427, [ =( 'least_upper_bound'( multiply( 'greatest_lower_bound'( Y
% 119.18/119.60 , X ), inverse( X ) ), identity ), identity ) ] )
% 119.18/119.60 , clause( 43900, [ =( 'least_upper_bound'( multiply( 'greatest_lower_bound'(
% 119.18/119.60 X, Y ), inverse( Y ) ), identity ), identity ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43902, [ =( X, multiply( 'greatest_lower_bound'( X, multiply( X, Y
% 119.18/119.60 ) ), inverse( 'greatest_lower_bound'( identity, Y ) ) ) ) ] )
% 119.18/119.60 , clause( 525, [ =( multiply( 'greatest_lower_bound'( X, multiply( X, Y ) )
% 119.18/119.60 , inverse( 'greatest_lower_bound'( identity, Y ) ) ), X ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43907, [ =( X, multiply( 'greatest_lower_bound'( X, multiply( X,
% 119.18/119.60 multiply( Y, inverse( 'greatest_lower_bound'( Y, Z ) ) ) ) ), inverse(
% 119.18/119.60 identity ) ) ) ] )
% 119.18/119.60 , clause( 4370, [ =( 'greatest_lower_bound'( identity, multiply( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ) ), identity ) ] )
% 119.18/119.60 , 0, clause( 43902, [ =( X, multiply( 'greatest_lower_bound'( X, multiply(
% 119.18/119.60 X, Y ) ), inverse( 'greatest_lower_bound'( identity, Y ) ) ) ) ] )
% 119.18/119.60 , 0, 14, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 119.18/119.60 :=( X, X ), :=( Y, multiply( Y, inverse( 'greatest_lower_bound'( Y, Z ) )
% 119.18/119.60 ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43908, [ =( X, multiply( 'greatest_lower_bound'( X, multiply(
% 119.18/119.60 multiply( X, Y ), inverse( 'greatest_lower_bound'( Y, Z ) ) ) ), inverse(
% 119.18/119.60 identity ) ) ) ] )
% 119.18/119.60 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 119.18/119.60 ), Z ) ) ] )
% 119.18/119.60 , 0, clause( 43907, [ =( X, multiply( 'greatest_lower_bound'( X, multiply(
% 119.18/119.60 X, multiply( Y, inverse( 'greatest_lower_bound'( Y, Z ) ) ) ) ), inverse(
% 119.18/119.60 identity ) ) ) ] )
% 119.18/119.60 , 0, 5, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, inverse(
% 119.18/119.60 'greatest_lower_bound'( Y, Z ) ) )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43909, [ =( X, multiply( 'greatest_lower_bound'( X, multiply(
% 119.18/119.60 multiply( X, Y ), inverse( 'greatest_lower_bound'( Y, Z ) ) ) ), identity
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , clause( 160, [ =( inverse( identity ), identity ) ] )
% 119.18/119.60 , 0, clause( 43908, [ =( X, multiply( 'greatest_lower_bound'( X, multiply(
% 119.18/119.60 multiply( X, Y ), inverse( 'greatest_lower_bound'( Y, Z ) ) ) ), inverse(
% 119.18/119.60 identity ) ) ) ] )
% 119.18/119.60 , 0, 13, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, Y ),
% 119.18/119.60 :=( Z, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43910, [ =( X, 'greatest_lower_bound'( X, multiply( multiply( X, Y
% 119.18/119.60 ), inverse( 'greatest_lower_bound'( Y, Z ) ) ) ) ) ] )
% 119.18/119.60 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.60 , 0, clause( 43909, [ =( X, multiply( 'greatest_lower_bound'( X, multiply(
% 119.18/119.60 multiply( X, Y ), inverse( 'greatest_lower_bound'( Y, Z ) ) ) ), identity
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , 0, 2, substitution( 0, [ :=( X, 'greatest_lower_bound'( X, multiply(
% 119.18/119.60 multiply( X, Y ), inverse( 'greatest_lower_bound'( Y, Z ) ) ) ) )] ),
% 119.18/119.60 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43911, [ =( 'greatest_lower_bound'( X, multiply( multiply( X, Y ),
% 119.18/119.60 inverse( 'greatest_lower_bound'( Y, Z ) ) ) ), X ) ] )
% 119.18/119.60 , clause( 43910, [ =( X, 'greatest_lower_bound'( X, multiply( multiply( X,
% 119.18/119.60 Y ), inverse( 'greatest_lower_bound'( Y, Z ) ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 4805, [ =( 'greatest_lower_bound'( Z, multiply( multiply( Z, X ),
% 119.18/119.60 inverse( 'greatest_lower_bound'( X, Y ) ) ) ), Z ) ] )
% 119.18/119.60 , clause( 43911, [ =( 'greatest_lower_bound'( X, multiply( multiply( X, Y )
% 119.18/119.60 , inverse( 'greatest_lower_bound'( Y, Z ) ) ) ), X ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 119.18/119.60 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43913, [ =( X, 'greatest_lower_bound'( X, multiply( multiply( X, Y
% 119.18/119.60 ), inverse( 'greatest_lower_bound'( Y, Z ) ) ) ) ) ] )
% 119.18/119.60 , clause( 4805, [ =( 'greatest_lower_bound'( Z, multiply( multiply( Z, X )
% 119.18/119.60 , inverse( 'greatest_lower_bound'( X, Y ) ) ) ), Z ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43915, [ =( X, 'greatest_lower_bound'( X, multiply( identity,
% 119.18/119.60 inverse( 'greatest_lower_bound'( inverse( X ), Y ) ) ) ) ) ] )
% 119.18/119.60 , clause( 180, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 119.18/119.60 , 0, clause( 43913, [ =( X, 'greatest_lower_bound'( X, multiply( multiply(
% 119.18/119.60 X, Y ), inverse( 'greatest_lower_bound'( Y, Z ) ) ) ) ) ] )
% 119.18/119.60 , 0, 5, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, inverse( X ) ), :=( Z, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43916, [ =( X, 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), Y ) ) ) ) ] )
% 119.18/119.60 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.60 , 0, clause( 43915, [ =( X, 'greatest_lower_bound'( X, multiply( identity,
% 119.18/119.60 inverse( 'greatest_lower_bound'( inverse( X ), Y ) ) ) ) ) ] )
% 119.18/119.60 , 0, 4, substitution( 0, [ :=( X, inverse( 'greatest_lower_bound'( inverse(
% 119.18/119.60 X ), Y ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43917, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), Y ) ) ), X ) ] )
% 119.18/119.60 , clause( 43916, [ =( X, 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), Y ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 4935, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), Y ) ) ), X ) ] )
% 119.18/119.60 , clause( 43917, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), Y ) ) ), X ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43919, [ =( 'greatest_lower_bound'( Y, X ), 'least_upper_bound'(
% 119.18/119.60 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, X ) ) ) ] )
% 119.18/119.60 , clause( 259, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ),
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ), 'greatest_lower_bound'( X, Y ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43923, [ =( 'greatest_lower_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.60 inverse( X ), Y ) ), X ), 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.60 inverse( 'greatest_lower_bound'( inverse( X ), Y ) ), X ) ) ) ] )
% 119.18/119.60 , clause( 4935, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), Y ) ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43919, [ =( 'greatest_lower_bound'( Y, X ),
% 119.18/119.60 'least_upper_bound'( 'greatest_lower_bound'( X, Y ),
% 119.18/119.60 'greatest_lower_bound'( Y, X ) ) ) ] )
% 119.18/119.60 , 0, 9, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.60 :=( X, X ), :=( Y, inverse( 'greatest_lower_bound'( inverse( X ), Y ) ) )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43925, [ =( 'greatest_lower_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.60 inverse( X ), Y ) ), X ), X ) ] )
% 119.18/119.60 , clause( 36, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) )
% 119.18/119.60 , X ) ] )
% 119.18/119.60 , 0, clause( 43923, [ =( 'greatest_lower_bound'( inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), Y ) ), X ), 'least_upper_bound'( X
% 119.18/119.60 , 'greatest_lower_bound'( inverse( 'greatest_lower_bound'( inverse( X ),
% 119.18/119.60 Y ) ), X ) ) ) ] )
% 119.18/119.60 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), Y ) ) )] ), substitution( 1, [ :=(
% 119.18/119.60 X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 4952, [ =( 'greatest_lower_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.60 inverse( X ), Y ) ), X ), X ) ] )
% 119.18/119.60 , clause( 43925, [ =( 'greatest_lower_bound'( inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), Y ) ), X ), X ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43927, [ =( X, 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), Y ) ) ) ) ] )
% 119.18/119.60 , clause( 4935, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), Y ) ) ), X ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43928, [ =( X, 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( Y, inverse( X ) ) ) ) ) ] )
% 119.18/119.60 , clause( 225, [ =( inverse( 'greatest_lower_bound'( Y, X ) ), inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ) ] )
% 119.18/119.60 , 0, clause( 43927, [ =( X, 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), Y ) ) ) ) ] )
% 119.18/119.60 , 0, 4, substitution( 0, [ :=( X, Y ), :=( Y, inverse( X ) )] ),
% 119.18/119.60 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43934, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( Y, inverse( X ) ) ) ), X ) ] )
% 119.18/119.60 , clause( 43928, [ =( X, 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( Y, inverse( X ) ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 4962, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( Y, inverse( X ) ) ) ), X ) ] )
% 119.18/119.60 , clause( 43934, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( Y, inverse( X ) ) ) ), X ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43938, [ =( X, 'greatest_lower_bound'( inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), Y ) ), X ) ) ] )
% 119.18/119.60 , clause( 4952, [ =( 'greatest_lower_bound'( inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), Y ) ), X ), X ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43939, [ =( inverse( X ), 'greatest_lower_bound'( inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ), inverse( X ) ) ) ] )
% 119.18/119.60 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43938, [ =( X, 'greatest_lower_bound'( inverse(
% 119.18/119.60 'greatest_lower_bound'( inverse( X ), Y ) ), X ) ) ] )
% 119.18/119.60 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 119.18/119.60 X ) ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43940, [ =( 'greatest_lower_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.60 X, Y ) ), inverse( X ) ), inverse( X ) ) ] )
% 119.18/119.60 , clause( 43939, [ =( inverse( X ), 'greatest_lower_bound'( inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ), inverse( X ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 4973, [ =( 'greatest_lower_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.60 X, Y ) ), inverse( X ) ), inverse( X ) ) ] )
% 119.18/119.60 , clause( 43940, [ =( 'greatest_lower_bound'( inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ), inverse( X ) ), inverse( X ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43942, [ =( X, 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( Y, inverse( X ) ) ) ) ) ] )
% 119.18/119.60 , clause( 4962, [ =( 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( Y, inverse( X ) ) ) ), X ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43943, [ =( inverse( X ), 'greatest_lower_bound'( inverse( X ),
% 119.18/119.60 inverse( 'greatest_lower_bound'( Y, X ) ) ) ) ] )
% 119.18/119.60 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43942, [ =( X, 'greatest_lower_bound'( X, inverse(
% 119.18/119.60 'greatest_lower_bound'( Y, inverse( X ) ) ) ) ) ] )
% 119.18/119.60 , 0, 9, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 119.18/119.60 X ) ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43944, [ =( 'greatest_lower_bound'( inverse( X ), inverse(
% 119.18/119.60 'greatest_lower_bound'( Y, X ) ) ), inverse( X ) ) ] )
% 119.18/119.60 , clause( 43943, [ =( inverse( X ), 'greatest_lower_bound'( inverse( X ),
% 119.18/119.60 inverse( 'greatest_lower_bound'( Y, X ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 5003, [ =( 'greatest_lower_bound'( inverse( X ), inverse(
% 119.18/119.60 'greatest_lower_bound'( Y, X ) ) ), inverse( X ) ) ] )
% 119.18/119.60 , clause( 43944, [ =( 'greatest_lower_bound'( inverse( X ), inverse(
% 119.18/119.60 'greatest_lower_bound'( Y, X ) ) ), inverse( X ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43946, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , clause( 36, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) )
% 119.18/119.60 , X ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43947, [ =( inverse( 'greatest_lower_bound'( X, Y ) ),
% 119.18/119.60 'least_upper_bound'( inverse( 'greatest_lower_bound'( X, Y ) ), inverse(
% 119.18/119.60 Y ) ) ) ] )
% 119.18/119.60 , clause( 5003, [ =( 'greatest_lower_bound'( inverse( X ), inverse(
% 119.18/119.60 'greatest_lower_bound'( Y, X ) ) ), inverse( X ) ) ] )
% 119.18/119.60 , 0, clause( 43946, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.60 Y, X ) ) ) ] )
% 119.18/119.60 , 0, 10, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, inverse( 'greatest_lower_bound'( X, Y ) ) ), :=( Y, inverse( Y ) )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43948, [ =( 'least_upper_bound'( inverse( 'greatest_lower_bound'( X
% 119.18/119.60 , Y ) ), inverse( Y ) ), inverse( 'greatest_lower_bound'( X, Y ) ) ) ] )
% 119.18/119.60 , clause( 43947, [ =( inverse( 'greatest_lower_bound'( X, Y ) ),
% 119.18/119.60 'least_upper_bound'( inverse( 'greatest_lower_bound'( X, Y ) ), inverse(
% 119.18/119.60 Y ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 5025, [ =( 'least_upper_bound'( inverse( 'greatest_lower_bound'( Y
% 119.18/119.60 , X ) ), inverse( X ) ), inverse( 'greatest_lower_bound'( Y, X ) ) ) ] )
% 119.18/119.60 , clause( 43948, [ =( 'least_upper_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.60 X, Y ) ), inverse( Y ) ), inverse( 'greatest_lower_bound'( X, Y ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43950, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( X, Y )
% 119.18/119.60 , X ) ) ] )
% 119.18/119.60 , clause( 37, [ =( 'least_upper_bound'( 'greatest_lower_bound'( X, Y ), X )
% 119.18/119.60 , X ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43951, [ =( inverse( 'greatest_lower_bound'( X, Y ) ),
% 119.18/119.60 'least_upper_bound'( inverse( X ), inverse( 'greatest_lower_bound'( X, Y
% 119.18/119.60 ) ) ) ) ] )
% 119.18/119.60 , clause( 4973, [ =( 'greatest_lower_bound'( inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ), inverse( X ) ), inverse( X ) ) ] )
% 119.18/119.60 , 0, clause( 43950, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( X
% 119.18/119.60 , Y ), X ) ) ] )
% 119.18/119.60 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.60 :=( X, inverse( 'greatest_lower_bound'( X, Y ) ) ), :=( Y, inverse( X ) )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43952, [ =( 'least_upper_bound'( inverse( X ), inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ), inverse( 'greatest_lower_bound'( X, Y
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , clause( 43951, [ =( inverse( 'greatest_lower_bound'( X, Y ) ),
% 119.18/119.60 'least_upper_bound'( inverse( X ), inverse( 'greatest_lower_bound'( X, Y
% 119.18/119.60 ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 5051, [ =( 'least_upper_bound'( inverse( X ), inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ), inverse( 'greatest_lower_bound'( X, Y
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , clause( 43952, [ =( 'least_upper_bound'( inverse( X ), inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ), inverse( 'greatest_lower_bound'( X, Y
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43953, [ =( multiply( 'greatest_lower_bound'( Y, X ), inverse( Y )
% 119.18/119.60 ), 'greatest_lower_bound'( identity, multiply( X, inverse( Y ) ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , clause( 185, [ =( 'greatest_lower_bound'( identity, multiply( Y, inverse(
% 119.18/119.60 X ) ) ), multiply( 'greatest_lower_bound'( X, Y ), inverse( X ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43954, [ =( 'greatest_lower_bound'( identity, multiply( Y, inverse(
% 119.18/119.60 X ) ) ), multiply( 'greatest_lower_bound'( Y, X ), inverse( X ) ) ) ] )
% 119.18/119.60 , clause( 43953, [ =( multiply( 'greatest_lower_bound'( Y, X ), inverse( Y
% 119.18/119.60 ) ), 'greatest_lower_bound'( identity, multiply( X, inverse( Y ) ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , 0, clause( 150, [ =( multiply( 'greatest_lower_bound'( X, Z ), Y ),
% 119.18/119.60 multiply( 'greatest_lower_bound'( Z, X ), Y ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, X ), :=( Y, inverse( X ) ), :=( Z, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 5181, [ =( 'greatest_lower_bound'( identity, multiply( Y, inverse(
% 119.18/119.60 X ) ) ), multiply( 'greatest_lower_bound'( Y, X ), inverse( X ) ) ) ] )
% 119.18/119.60 , clause( 43954, [ =( 'greatest_lower_bound'( identity, multiply( Y,
% 119.18/119.60 inverse( X ) ) ), multiply( 'greatest_lower_bound'( Y, X ), inverse( X )
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43957, [ =( inverse( 'greatest_lower_bound'( X, Y ) ),
% 119.18/119.60 'least_upper_bound'( inverse( X ), inverse( 'greatest_lower_bound'( X, Y
% 119.18/119.60 ) ) ) ) ] )
% 119.18/119.60 , clause( 5051, [ =( 'least_upper_bound'( inverse( X ), inverse(
% 119.18/119.60 'greatest_lower_bound'( X, Y ) ) ), inverse( 'greatest_lower_bound'( X, Y
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43961, [ =( inverse( 'greatest_lower_bound'( 'least_upper_bound'( X
% 119.18/119.60 , Y ), Y ) ), 'least_upper_bound'( inverse( 'least_upper_bound'( X, Y ) )
% 119.18/119.60 , inverse( Y ) ) ) ] )
% 119.18/119.60 , clause( 21, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), X )
% 119.18/119.60 , X ) ] )
% 119.18/119.60 , 0, clause( 43957, [ =( inverse( 'greatest_lower_bound'( X, Y ) ),
% 119.18/119.60 'least_upper_bound'( inverse( X ), inverse( 'greatest_lower_bound'( X, Y
% 119.18/119.60 ) ) ) ) ] )
% 119.18/119.60 , 0, 13, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, 'least_upper_bound'( X, Y ) ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43962, [ =( inverse( Y ), 'least_upper_bound'( inverse(
% 119.18/119.60 'least_upper_bound'( X, Y ) ), inverse( Y ) ) ) ] )
% 119.18/119.60 , clause( 21, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), X )
% 119.18/119.60 , X ) ] )
% 119.18/119.60 , 0, clause( 43961, [ =( inverse( 'greatest_lower_bound'(
% 119.18/119.60 'least_upper_bound'( X, Y ), Y ) ), 'least_upper_bound'( inverse(
% 119.18/119.60 'least_upper_bound'( X, Y ) ), inverse( Y ) ) ) ] )
% 119.18/119.60 , 0, 2, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43964, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( Y, X
% 119.18/119.60 ) ), inverse( X ) ), inverse( X ) ) ] )
% 119.18/119.60 , clause( 43962, [ =( inverse( Y ), 'least_upper_bound'( inverse(
% 119.18/119.60 'least_upper_bound'( X, Y ) ), inverse( Y ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 5547, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X, Y
% 119.18/119.60 ) ), inverse( Y ) ), inverse( Y ) ) ] )
% 119.18/119.60 , clause( 43964, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( Y
% 119.18/119.60 , X ) ), inverse( X ) ), inverse( X ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43967, [ =( inverse( Y ), 'least_upper_bound'( inverse(
% 119.18/119.60 'least_upper_bound'( X, Y ) ), inverse( Y ) ) ) ] )
% 119.18/119.60 , clause( 5547, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X,
% 119.18/119.60 Y ) ), inverse( Y ) ), inverse( Y ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43969, [ =( inverse( inverse( X ) ), 'least_upper_bound'( inverse(
% 119.18/119.60 'least_upper_bound'( Y, inverse( X ) ) ), X ) ) ] )
% 119.18/119.60 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43967, [ =( inverse( Y ), 'least_upper_bound'( inverse(
% 119.18/119.60 'least_upper_bound'( X, Y ) ), inverse( Y ) ) ) ] )
% 119.18/119.60 , 0, 10, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, Y ),
% 119.18/119.60 :=( Y, inverse( X ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43970, [ =( X, 'least_upper_bound'( inverse( 'least_upper_bound'( Y
% 119.18/119.60 , inverse( X ) ) ), X ) ) ] )
% 119.18/119.60 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43969, [ =( inverse( inverse( X ) ), 'least_upper_bound'(
% 119.18/119.60 inverse( 'least_upper_bound'( Y, inverse( X ) ) ), X ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43972, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( Y,
% 119.18/119.60 inverse( X ) ) ), X ), X ) ] )
% 119.18/119.60 , clause( 43970, [ =( X, 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 Y, inverse( X ) ) ), X ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 5563, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( Y,
% 119.18/119.60 inverse( X ) ) ), X ), X ) ] )
% 119.18/119.60 , clause( 43972, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( Y
% 119.18/119.60 , inverse( X ) ) ), X ), X ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43975, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 119.18/119.60 'least_upper_bound'( 'greatest_lower_bound'( 'greatest_lower_bound'(
% 119.18/119.60 'least_upper_bound'( X, Y ), Z ), T ), X ), Y ) ) ] )
% 119.18/119.60 , clause( 69, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.60 'greatest_lower_bound'( 'greatest_lower_bound'( 'least_upper_bound'( X, Y
% 119.18/119.60 ), Z ), T ), X ), Y ), 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43979, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X,
% 119.18/119.60 inverse( Y ) ) ), Y ), 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.60 'greatest_lower_bound'( 'greatest_lower_bound'( Y, Z ), T ), inverse(
% 119.18/119.60 'least_upper_bound'( X, inverse( Y ) ) ) ), Y ) ) ] )
% 119.18/119.60 , clause( 5563, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( Y,
% 119.18/119.60 inverse( X ) ) ), X ), X ) ] )
% 119.18/119.60 , 0, clause( 43975, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 119.18/119.60 'least_upper_bound'( 'greatest_lower_bound'( 'greatest_lower_bound'(
% 119.18/119.60 'least_upper_bound'( X, Y ), Z ), T ), X ), Y ) ) ] )
% 119.18/119.60 , 0, 12, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, inverse( 'least_upper_bound'( X, inverse( Y ) ) ) ), :=( Y, Y ),
% 119.18/119.60 :=( Z, Z ), :=( T, T )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43980, [ =( Y, 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.60 'greatest_lower_bound'( 'greatest_lower_bound'( Y, Z ), T ), inverse(
% 119.18/119.60 'least_upper_bound'( X, inverse( Y ) ) ) ), Y ) ) ] )
% 119.18/119.60 , clause( 5563, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( Y,
% 119.18/119.60 inverse( X ) ) ), X ), X ) ] )
% 119.18/119.60 , 0, clause( 43979, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 X, inverse( Y ) ) ), Y ), 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.60 'greatest_lower_bound'( 'greatest_lower_bound'( Y, Z ), T ), inverse(
% 119.18/119.60 'least_upper_bound'( X, inverse( Y ) ) ) ), Y ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43983, [ =( X, 'least_upper_bound'( X, inverse( 'least_upper_bound'(
% 119.18/119.60 T, inverse( X ) ) ) ) ) ] )
% 119.18/119.60 , clause( 416, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.60 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ), T ), X ),
% 119.18/119.60 'least_upper_bound'( X, T ) ) ] )
% 119.18/119.60 , 0, clause( 43980, [ =( Y, 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.60 'greatest_lower_bound'( 'greatest_lower_bound'( Y, Z ), T ), inverse(
% 119.18/119.60 'least_upper_bound'( X, inverse( Y ) ) ) ), Y ) ) ] )
% 119.18/119.60 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 119.18/119.60 inverse( 'least_upper_bound'( T, inverse( X ) ) ) )] ), substitution( 1
% 119.18/119.60 , [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43984, [ =( 'least_upper_bound'( X, inverse( 'least_upper_bound'( Y
% 119.18/119.60 , inverse( X ) ) ) ), X ) ] )
% 119.18/119.60 , clause( 43983, [ =( X, 'least_upper_bound'( X, inverse(
% 119.18/119.60 'least_upper_bound'( T, inverse( X ) ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, T ), :=( T, Y )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 5571, [ =( 'least_upper_bound'( Y, inverse( 'least_upper_bound'( X
% 119.18/119.60 , inverse( Y ) ) ) ), Y ) ] )
% 119.18/119.60 , clause( 43984, [ =( 'least_upper_bound'( X, inverse( 'least_upper_bound'(
% 119.18/119.60 Y, inverse( X ) ) ) ), X ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43986, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 119.18/119.60 , X ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43987, [ =( inverse( 'least_upper_bound'( X, inverse( Y ) ) ),
% 119.18/119.60 'greatest_lower_bound'( inverse( 'least_upper_bound'( X, inverse( Y ) ) )
% 119.18/119.60 , Y ) ) ] )
% 119.18/119.60 , clause( 5563, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( Y,
% 119.18/119.60 inverse( X ) ) ), X ), X ) ] )
% 119.18/119.60 , 0, clause( 43986, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 119.18/119.60 X, Y ) ) ) ] )
% 119.18/119.60 , 0, 12, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, inverse( 'least_upper_bound'( X, inverse( Y ) ) ) ), :=( Y, Y )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43988, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'( X
% 119.18/119.60 , inverse( Y ) ) ), Y ), inverse( 'least_upper_bound'( X, inverse( Y ) )
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , clause( 43987, [ =( inverse( 'least_upper_bound'( X, inverse( Y ) ) ),
% 119.18/119.60 'greatest_lower_bound'( inverse( 'least_upper_bound'( X, inverse( Y ) ) )
% 119.18/119.60 , Y ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 5591, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'( X
% 119.18/119.60 , inverse( Y ) ) ), Y ), inverse( 'least_upper_bound'( X, inverse( Y ) )
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , clause( 43988, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 X, inverse( Y ) ) ), Y ), inverse( 'least_upper_bound'( X, inverse( Y ) )
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43989, [ =( multiply( 'least_upper_bound'( Y, X ), inverse( Y ) ),
% 119.18/119.60 'least_upper_bound'( identity, multiply( X, inverse( Y ) ) ) ) ] )
% 119.18/119.60 , clause( 187, [ =( 'least_upper_bound'( identity, multiply( Y, inverse( X
% 119.18/119.60 ) ) ), multiply( 'least_upper_bound'( X, Y ), inverse( X ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43990, [ =( inverse( Z ), multiply( inverse( multiply(
% 119.18/119.60 'least_upper_bound'( X, Y ), Z ) ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.60 , clause( 274, [ =( multiply( inverse( multiply( 'least_upper_bound'( Y, X
% 119.18/119.60 ), Z ) ), 'least_upper_bound'( X, Y ) ), inverse( Z ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43992, [ =( inverse( inverse( X ) ), multiply( inverse(
% 119.18/119.60 'least_upper_bound'( identity, multiply( Y, inverse( X ) ) ) ),
% 119.18/119.60 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.60 , clause( 43989, [ =( multiply( 'least_upper_bound'( Y, X ), inverse( Y ) )
% 119.18/119.60 , 'least_upper_bound'( identity, multiply( X, inverse( Y ) ) ) ) ] )
% 119.18/119.60 , 0, clause( 43990, [ =( inverse( Z ), multiply( inverse( multiply(
% 119.18/119.60 'least_upper_bound'( X, Y ), Z ) ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.60 , 0, 6, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, X ), :=( Y, Y ), :=( Z, inverse( X ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43993, [ =( X, multiply( inverse( 'least_upper_bound'( identity,
% 119.18/119.60 multiply( Y, inverse( X ) ) ) ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.60 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43992, [ =( inverse( inverse( X ) ), multiply( inverse(
% 119.18/119.60 'least_upper_bound'( identity, multiply( Y, inverse( X ) ) ) ),
% 119.18/119.60 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43994, [ =( multiply( inverse( 'least_upper_bound'( identity,
% 119.18/119.60 multiply( Y, inverse( X ) ) ) ), 'least_upper_bound'( Y, X ) ), X ) ] )
% 119.18/119.60 , clause( 43993, [ =( X, multiply( inverse( 'least_upper_bound'( identity,
% 119.18/119.60 multiply( Y, inverse( X ) ) ) ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 8767, [ =( multiply( inverse( 'least_upper_bound'( identity,
% 119.18/119.60 multiply( Y, inverse( X ) ) ) ), 'least_upper_bound'( Y, X ) ), X ) ] )
% 119.18/119.60 , clause( 43994, [ =( multiply( inverse( 'least_upper_bound'( identity,
% 119.18/119.60 multiply( Y, inverse( X ) ) ) ), 'least_upper_bound'( Y, X ) ), X ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 43996, [ =( inverse( Y ), multiply( inverse( 'least_upper_bound'(
% 119.18/119.60 multiply( X, Y ), Y ) ), 'least_upper_bound'( X, identity ) ) ) ] )
% 119.18/119.60 , clause( 1313, [ =( multiply( inverse( 'least_upper_bound'( multiply( X, Y
% 119.18/119.60 ), Y ) ), 'least_upper_bound'( X, identity ) ), inverse( Y ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 43999, [ =( inverse( inverse( X ) ), multiply( inverse(
% 119.18/119.60 'least_upper_bound'( Y, inverse( X ) ) ), 'least_upper_bound'( multiply(
% 119.18/119.60 Y, X ), identity ) ) ) ] )
% 119.18/119.60 , clause( 184, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 119.18/119.60 , 0, clause( 43996, [ =( inverse( Y ), multiply( inverse(
% 119.18/119.60 'least_upper_bound'( multiply( X, Y ), Y ) ), 'least_upper_bound'( X,
% 119.18/119.60 identity ) ) ) ] )
% 119.18/119.60 , 0, 7, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.60 :=( X, multiply( Y, X ) ), :=( Y, inverse( X ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44000, [ =( X, multiply( inverse( 'least_upper_bound'( Y, inverse(
% 119.18/119.60 X ) ) ), 'least_upper_bound'( multiply( Y, X ), identity ) ) ) ] )
% 119.18/119.60 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.60 , 0, clause( 43999, [ =( inverse( inverse( X ) ), multiply( inverse(
% 119.18/119.60 'least_upper_bound'( Y, inverse( X ) ) ), 'least_upper_bound'( multiply(
% 119.18/119.60 Y, X ), identity ) ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 44001, [ =( multiply( inverse( 'least_upper_bound'( Y, inverse( X )
% 119.18/119.60 ) ), 'least_upper_bound'( multiply( Y, X ), identity ) ), X ) ] )
% 119.18/119.60 , clause( 44000, [ =( X, multiply( inverse( 'least_upper_bound'( Y, inverse(
% 119.18/119.60 X ) ) ), 'least_upper_bound'( multiply( Y, X ), identity ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 12228, [ =( multiply( inverse( 'least_upper_bound'( X, inverse( Y )
% 119.18/119.60 ) ), 'least_upper_bound'( multiply( X, Y ), identity ) ), Y ) ] )
% 119.18/119.60 , clause( 44001, [ =( multiply( inverse( 'least_upper_bound'( Y, inverse( X
% 119.18/119.60 ) ) ), 'least_upper_bound'( multiply( Y, X ), identity ) ), X ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 44003, [ =( 'least_upper_bound'( multiply( X, Y ), X ), multiply( X
% 119.18/119.60 , 'least_upper_bound'( identity, Y ) ) ) ] )
% 119.18/119.60 , clause( 781, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 119.18/119.60 'least_upper_bound'( multiply( X, Y ), X ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44010, [ =( 'least_upper_bound'( Y, inverse( 'least_upper_bound'( X
% 119.18/119.60 , inverse( Y ) ) ) ), multiply( inverse( 'least_upper_bound'( X, inverse(
% 119.18/119.60 Y ) ) ), 'least_upper_bound'( identity, 'least_upper_bound'( multiply( X
% 119.18/119.60 , Y ), identity ) ) ) ) ] )
% 119.18/119.60 , clause( 12228, [ =( multiply( inverse( 'least_upper_bound'( X, inverse( Y
% 119.18/119.60 ) ) ), 'least_upper_bound'( multiply( X, Y ), identity ) ), Y ) ] )
% 119.18/119.60 , 0, clause( 44003, [ =( 'least_upper_bound'( multiply( X, Y ), X ),
% 119.18/119.60 multiply( X, 'least_upper_bound'( identity, Y ) ) ) ] )
% 119.18/119.60 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.60 :=( X, inverse( 'least_upper_bound'( X, inverse( Y ) ) ) ), :=( Y,
% 119.18/119.60 'least_upper_bound'( multiply( X, Y ), identity ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44011, [ =( 'least_upper_bound'( X, inverse( 'least_upper_bound'( Y
% 119.18/119.60 , inverse( X ) ) ) ), multiply( inverse( 'least_upper_bound'( Y, inverse(
% 119.18/119.60 X ) ) ), 'least_upper_bound'( 'least_upper_bound'( identity, multiply( Y
% 119.18/119.60 , X ) ), identity ) ) ) ] )
% 119.18/119.60 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.60 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.60 , 0, clause( 44010, [ =( 'least_upper_bound'( Y, inverse(
% 119.18/119.60 'least_upper_bound'( X, inverse( Y ) ) ) ), multiply( inverse(
% 119.18/119.60 'least_upper_bound'( X, inverse( Y ) ) ), 'least_upper_bound'( identity,
% 119.18/119.60 'least_upper_bound'( multiply( X, Y ), identity ) ) ) ) ] )
% 119.18/119.60 , 0, 14, substitution( 0, [ :=( X, identity ), :=( Y, multiply( Y, X ) ),
% 119.18/119.60 :=( Z, identity )] ), substitution( 1, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44012, [ =( 'least_upper_bound'( X, inverse( 'least_upper_bound'( Y
% 119.18/119.60 , inverse( X ) ) ) ), multiply( inverse( 'least_upper_bound'( Y, inverse(
% 119.18/119.60 X ) ) ), 'least_upper_bound'( identity, multiply( Y, X ) ) ) ) ] )
% 119.18/119.60 , clause( 35, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 119.18/119.60 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.60 , 0, clause( 44011, [ =( 'least_upper_bound'( X, inverse(
% 119.18/119.60 'least_upper_bound'( Y, inverse( X ) ) ) ), multiply( inverse(
% 119.18/119.60 'least_upper_bound'( Y, inverse( X ) ) ), 'least_upper_bound'(
% 119.18/119.60 'least_upper_bound'( identity, multiply( Y, X ) ), identity ) ) ) ] )
% 119.18/119.60 , 0, 14, substitution( 0, [ :=( X, identity ), :=( Y, multiply( Y, X ) )] )
% 119.18/119.60 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44013, [ =( X, multiply( inverse( 'least_upper_bound'( Y, inverse(
% 119.18/119.60 X ) ) ), 'least_upper_bound'( identity, multiply( Y, X ) ) ) ) ] )
% 119.18/119.60 , clause( 5571, [ =( 'least_upper_bound'( Y, inverse( 'least_upper_bound'(
% 119.18/119.60 X, inverse( Y ) ) ) ), Y ) ] )
% 119.18/119.60 , 0, clause( 44012, [ =( 'least_upper_bound'( X, inverse(
% 119.18/119.60 'least_upper_bound'( Y, inverse( X ) ) ) ), multiply( inverse(
% 119.18/119.60 'least_upper_bound'( Y, inverse( X ) ) ), 'least_upper_bound'( identity,
% 119.18/119.60 multiply( Y, X ) ) ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 44014, [ =( multiply( inverse( 'least_upper_bound'( Y, inverse( X )
% 119.18/119.60 ) ), 'least_upper_bound'( identity, multiply( Y, X ) ) ), X ) ] )
% 119.18/119.60 , clause( 44013, [ =( X, multiply( inverse( 'least_upper_bound'( Y, inverse(
% 119.18/119.60 X ) ) ), 'least_upper_bound'( identity, multiply( Y, X ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 12242, [ =( multiply( inverse( 'least_upper_bound'( X, inverse( Y )
% 119.18/119.60 ) ), 'least_upper_bound'( identity, multiply( X, Y ) ) ), Y ) ] )
% 119.18/119.60 , clause( 44014, [ =( multiply( inverse( 'least_upper_bound'( Y, inverse( X
% 119.18/119.60 ) ) ), 'least_upper_bound'( identity, multiply( Y, X ) ) ), X ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 44016, [ =( Y, multiply( inverse( 'least_upper_bound'( X, inverse(
% 119.18/119.60 Y ) ) ), 'least_upper_bound'( identity, multiply( X, Y ) ) ) ) ] )
% 119.18/119.60 , clause( 12242, [ =( multiply( inverse( 'least_upper_bound'( X, inverse( Y
% 119.18/119.60 ) ) ), 'least_upper_bound'( identity, multiply( X, Y ) ) ), Y ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44021, [ =( inverse( 'least_upper_bound'( X, identity ) ), multiply(
% 119.18/119.60 inverse( 'least_upper_bound'( multiply( 'least_upper_bound'( identity, X
% 119.18/119.60 ), X ), inverse( inverse( 'least_upper_bound'( X, identity ) ) ) ) ),
% 119.18/119.60 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.60 , clause( 1525, [ =( multiply( multiply( 'least_upper_bound'( identity, X )
% 119.18/119.60 , X ), inverse( 'least_upper_bound'( X, identity ) ) ), X ) ] )
% 119.18/119.60 , 0, clause( 44016, [ =( Y, multiply( inverse( 'least_upper_bound'( X,
% 119.18/119.60 inverse( Y ) ) ), 'least_upper_bound'( identity, multiply( X, Y ) ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , 0, 20, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.60 multiply( 'least_upper_bound'( identity, X ), X ) ), :=( Y, inverse(
% 119.18/119.60 'least_upper_bound'( X, identity ) ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44022, [ =( inverse( 'least_upper_bound'( X, identity ) ), multiply(
% 119.18/119.60 inverse( 'least_upper_bound'( multiply( 'least_upper_bound'( identity, X
% 119.18/119.60 ), X ), 'least_upper_bound'( X, identity ) ) ), 'least_upper_bound'(
% 119.18/119.60 identity, X ) ) ) ] )
% 119.18/119.60 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.60 , 0, clause( 44021, [ =( inverse( 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 multiply( inverse( 'least_upper_bound'( multiply( 'least_upper_bound'(
% 119.18/119.60 identity, X ), X ), inverse( inverse( 'least_upper_bound'( X, identity )
% 119.18/119.60 ) ) ) ), 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.60 , 0, 13, substitution( 0, [ :=( X, 'least_upper_bound'( X, identity ) )] )
% 119.18/119.60 , substitution( 1, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44023, [ =( inverse( 'least_upper_bound'( X, identity ) ), multiply(
% 119.18/119.60 inverse( 'least_upper_bound'( 'least_upper_bound'( multiply(
% 119.18/119.60 'least_upper_bound'( identity, X ), X ), X ), identity ) ),
% 119.18/119.60 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.60 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.60 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.60 , 0, clause( 44022, [ =( inverse( 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 multiply( inverse( 'least_upper_bound'( multiply( 'least_upper_bound'(
% 119.18/119.60 identity, X ), X ), 'least_upper_bound'( X, identity ) ) ),
% 119.18/119.60 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.60 , 0, 7, substitution( 0, [ :=( X, multiply( 'least_upper_bound'( identity,
% 119.18/119.60 X ), X ) ), :=( Y, X ), :=( Z, identity )] ), substitution( 1, [ :=( X, X
% 119.18/119.60 )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44024, [ =( inverse( 'least_upper_bound'( X, identity ) ), multiply(
% 119.18/119.60 inverse( 'least_upper_bound'( multiply( 'least_upper_bound'( identity, X
% 119.18/119.60 ), X ), identity ) ), 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.60 , clause( 928, [ =( 'least_upper_bound'( multiply( 'least_upper_bound'(
% 119.18/119.60 identity, Y ), X ), X ), multiply( 'least_upper_bound'( identity, Y ), X
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , 0, clause( 44023, [ =( inverse( 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 multiply( inverse( 'least_upper_bound'( 'least_upper_bound'( multiply(
% 119.18/119.60 'least_upper_bound'( identity, X ), X ), X ), identity ) ),
% 119.18/119.60 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.60 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44025, [ =( inverse( 'least_upper_bound'( X, identity ) ), inverse(
% 119.18/119.60 'least_upper_bound'( X, inverse( 'least_upper_bound'( identity, X ) ) ) )
% 119.18/119.60 ) ] )
% 119.18/119.60 , clause( 4154, [ =( multiply( inverse( 'least_upper_bound'( multiply( X, Y
% 119.18/119.60 ), identity ) ), X ), inverse( 'least_upper_bound'( Y, inverse( X ) ) )
% 119.18/119.60 ) ] )
% 119.18/119.60 , 0, clause( 44024, [ =( inverse( 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 multiply( inverse( 'least_upper_bound'( multiply( 'least_upper_bound'(
% 119.18/119.60 identity, X ), X ), identity ) ), 'least_upper_bound'( identity, X ) ) )
% 119.18/119.60 ] )
% 119.18/119.60 , 0, 5, substitution( 0, [ :=( X, 'least_upper_bound'( identity, X ) ),
% 119.18/119.60 :=( Y, X )] ), substitution( 1, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 44026, [ =( inverse( 'least_upper_bound'( X, inverse(
% 119.18/119.60 'least_upper_bound'( identity, X ) ) ) ), inverse( 'least_upper_bound'( X
% 119.18/119.60 , identity ) ) ) ] )
% 119.18/119.60 , clause( 44025, [ =( inverse( 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 inverse( 'least_upper_bound'( X, inverse( 'least_upper_bound'( identity,
% 119.18/119.60 X ) ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 12249, [ =( inverse( 'least_upper_bound'( X, inverse(
% 119.18/119.60 'least_upper_bound'( identity, X ) ) ) ), inverse( 'least_upper_bound'( X
% 119.18/119.60 , identity ) ) ) ] )
% 119.18/119.60 , clause( 44026, [ =( inverse( 'least_upper_bound'( X, inverse(
% 119.18/119.60 'least_upper_bound'( identity, X ) ) ) ), inverse( 'least_upper_bound'( X
% 119.18/119.60 , identity ) ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 44028, [ =( X, multiply( inverse( 'least_upper_bound'( inverse( X )
% 119.18/119.60 , identity ) ), 'least_upper_bound'( X, identity ) ) ) ] )
% 119.18/119.60 , clause( 1320, [ =( multiply( inverse( 'least_upper_bound'( inverse( X ),
% 119.18/119.60 identity ) ), 'least_upper_bound'( X, identity ) ), X ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44033, [ =( 'least_upper_bound'( X, inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ) ), multiply( inverse( 'least_upper_bound'( inverse(
% 119.18/119.60 'least_upper_bound'( X, identity ) ), identity ) ), 'least_upper_bound'(
% 119.18/119.60 'least_upper_bound'( X, inverse( 'least_upper_bound'( identity, X ) ) ),
% 119.18/119.60 identity ) ) ) ] )
% 119.18/119.60 , clause( 12249, [ =( inverse( 'least_upper_bound'( X, inverse(
% 119.18/119.60 'least_upper_bound'( identity, X ) ) ) ), inverse( 'least_upper_bound'( X
% 119.18/119.60 , identity ) ) ) ] )
% 119.18/119.60 , 0, clause( 44028, [ =( X, multiply( inverse( 'least_upper_bound'( inverse(
% 119.18/119.60 X ), identity ) ), 'least_upper_bound'( X, identity ) ) ) ] )
% 119.18/119.60 , 0, 10, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.60 'least_upper_bound'( X, inverse( 'least_upper_bound'( identity, X ) ) ) )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44034, [ =( 'least_upper_bound'( X, inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ) ), multiply( inverse( identity ), 'least_upper_bound'(
% 119.18/119.60 'least_upper_bound'( X, inverse( 'least_upper_bound'( identity, X ) ) ),
% 119.18/119.60 identity ) ) ) ] )
% 119.18/119.60 , clause( 1324, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X,
% 119.18/119.60 identity ) ), identity ), identity ) ] )
% 119.18/119.60 , 0, clause( 44033, [ =( 'least_upper_bound'( X, inverse(
% 119.18/119.60 'least_upper_bound'( identity, X ) ) ), multiply( inverse(
% 119.18/119.60 'least_upper_bound'( inverse( 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 identity ) ), 'least_upper_bound'( 'least_upper_bound'( X, inverse(
% 119.18/119.60 'least_upper_bound'( identity, X ) ) ), identity ) ) ) ] )
% 119.18/119.60 , 0, 9, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44035, [ =( 'least_upper_bound'( X, inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ) ), multiply( identity, 'least_upper_bound'(
% 119.18/119.60 'least_upper_bound'( X, inverse( 'least_upper_bound'( identity, X ) ) ),
% 119.18/119.60 identity ) ) ) ] )
% 119.18/119.60 , clause( 160, [ =( inverse( identity ), identity ) ] )
% 119.18/119.60 , 0, clause( 44034, [ =( 'least_upper_bound'( X, inverse(
% 119.18/119.60 'least_upper_bound'( identity, X ) ) ), multiply( inverse( identity ),
% 119.18/119.60 'least_upper_bound'( 'least_upper_bound'( X, inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ) ), identity ) ) ) ] )
% 119.18/119.60 , 0, 8, substitution( 0, [] ), substitution( 1, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44036, [ =( 'least_upper_bound'( X, inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ) ), 'least_upper_bound'( 'least_upper_bound'( X, inverse(
% 119.18/119.60 'least_upper_bound'( identity, X ) ) ), identity ) ) ] )
% 119.18/119.60 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.60 , 0, clause( 44035, [ =( 'least_upper_bound'( X, inverse(
% 119.18/119.60 'least_upper_bound'( identity, X ) ) ), multiply( identity,
% 119.18/119.60 'least_upper_bound'( 'least_upper_bound'( X, inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ) ), identity ) ) ) ] )
% 119.18/119.60 , 0, 7, substitution( 0, [ :=( X, 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.60 X, inverse( 'least_upper_bound'( identity, X ) ) ), identity ) )] ),
% 119.18/119.60 substitution( 1, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44037, [ =( 'least_upper_bound'( X, inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ) ), 'least_upper_bound'( identity, X ) ) ] )
% 119.18/119.60 , clause( 1335, [ =( 'least_upper_bound'( 'least_upper_bound'( Y, inverse(
% 119.18/119.60 'least_upper_bound'( identity, X ) ) ), identity ), 'least_upper_bound'(
% 119.18/119.60 identity, Y ) ) ] )
% 119.18/119.60 , 0, clause( 44036, [ =( 'least_upper_bound'( X, inverse(
% 119.18/119.60 'least_upper_bound'( identity, X ) ) ), 'least_upper_bound'(
% 119.18/119.60 'least_upper_bound'( X, inverse( 'least_upper_bound'( identity, X ) ) ),
% 119.18/119.60 identity ) ) ] )
% 119.18/119.60 , 0, 7, substitution( 0, [ :=( X, X ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 12259, [ =( 'least_upper_bound'( X, inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ) ), 'least_upper_bound'( identity, X ) ) ] )
% 119.18/119.60 , clause( 44037, [ =( 'least_upper_bound'( X, inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ) ), 'least_upper_bound'( identity, X ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 44040, [ =( Y, multiply( inverse( 'least_upper_bound'( X, inverse(
% 119.18/119.60 Y ) ) ), 'least_upper_bound'( identity, multiply( X, Y ) ) ) ) ] )
% 119.18/119.60 , clause( 12242, [ =( multiply( inverse( 'least_upper_bound'( X, inverse( Y
% 119.18/119.60 ) ) ), 'least_upper_bound'( identity, multiply( X, Y ) ) ), Y ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44044, [ =( 'least_upper_bound'( identity, X ), multiply( inverse(
% 119.18/119.60 'least_upper_bound'( identity, X ) ), 'least_upper_bound'( identity,
% 119.18/119.60 multiply( X, 'least_upper_bound'( identity, X ) ) ) ) ) ] )
% 119.18/119.60 , clause( 12259, [ =( 'least_upper_bound'( X, inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ) ), 'least_upper_bound'( identity, X ) ) ] )
% 119.18/119.60 , 0, clause( 44040, [ =( Y, multiply( inverse( 'least_upper_bound'( X,
% 119.18/119.60 inverse( Y ) ) ), 'least_upper_bound'( identity, multiply( X, Y ) ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, 'least_upper_bound'( identity, X ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44045, [ =( 'least_upper_bound'( identity, X ), multiply( inverse(
% 119.18/119.60 'least_upper_bound'( identity, X ) ), 'least_upper_bound'( identity,
% 119.18/119.60 multiply( 'least_upper_bound'( identity, X ), X ) ) ) ) ] )
% 119.18/119.60 , clause( 1208, [ =( multiply( X, 'least_upper_bound'( identity, X ) ),
% 119.18/119.60 multiply( 'least_upper_bound'( identity, X ), X ) ) ] )
% 119.18/119.60 , 0, clause( 44044, [ =( 'least_upper_bound'( identity, X ), multiply(
% 119.18/119.60 inverse( 'least_upper_bound'( identity, X ) ), 'least_upper_bound'(
% 119.18/119.60 identity, multiply( X, 'least_upper_bound'( identity, X ) ) ) ) ) ] )
% 119.18/119.60 , 0, 11, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44046, [ =( 'least_upper_bound'( identity, X ), 'least_upper_bound'(
% 119.18/119.60 multiply( inverse( 'least_upper_bound'( identity, X ) ), identity ), X )
% 119.18/119.60 ) ] )
% 119.18/119.60 , clause( 1586, [ =( multiply( inverse( X ), 'least_upper_bound'( Y,
% 119.18/119.60 multiply( X, Z ) ) ), 'least_upper_bound'( multiply( inverse( X ), Y ), Z
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , 0, clause( 44045, [ =( 'least_upper_bound'( identity, X ), multiply(
% 119.18/119.60 inverse( 'least_upper_bound'( identity, X ) ), 'least_upper_bound'(
% 119.18/119.60 identity, multiply( 'least_upper_bound'( identity, X ), X ) ) ) ) ] )
% 119.18/119.60 , 0, 4, substitution( 0, [ :=( X, 'least_upper_bound'( identity, X ) ),
% 119.18/119.60 :=( Y, identity ), :=( Z, X )] ), substitution( 1, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44047, [ =( 'least_upper_bound'( identity, X ), 'least_upper_bound'(
% 119.18/119.60 inverse( 'least_upper_bound'( identity, X ) ), X ) ) ] )
% 119.18/119.60 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.60 , 0, clause( 44046, [ =( 'least_upper_bound'( identity, X ),
% 119.18/119.60 'least_upper_bound'( multiply( inverse( 'least_upper_bound'( identity, X
% 119.18/119.60 ) ), identity ), X ) ) ] )
% 119.18/119.60 , 0, 5, substitution( 0, [ :=( X, inverse( 'least_upper_bound'( identity, X
% 119.18/119.60 ) ) )] ), substitution( 1, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 44048, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ), X ), 'least_upper_bound'( identity, X ) ) ] )
% 119.18/119.60 , clause( 44047, [ =( 'least_upper_bound'( identity, X ),
% 119.18/119.60 'least_upper_bound'( inverse( 'least_upper_bound'( identity, X ) ), X ) )
% 119.18/119.60 ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 12265, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ), X ), 'least_upper_bound'( identity, X ) ) ] )
% 119.18/119.60 , clause( 44048, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ), X ), 'least_upper_bound'( identity, X ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 44049, [ =( inverse( 'least_upper_bound'( X, multiply( X, Y ) ) ),
% 119.18/119.60 inverse( multiply( X, 'least_upper_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.60 , clause( 847, [ =( inverse( multiply( X, 'least_upper_bound'( Y, identity
% 119.18/119.60 ) ) ), inverse( 'least_upper_bound'( X, multiply( X, Y ) ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 44050, [ =( 'least_upper_bound'( identity, X ), 'least_upper_bound'(
% 119.18/119.60 inverse( 'least_upper_bound'( identity, X ) ), X ) ) ] )
% 119.18/119.60 , clause( 12265, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.60 identity, X ) ), X ), 'least_upper_bound'( identity, X ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44053, [ =( 'least_upper_bound'( identity, multiply( identity, X )
% 119.18/119.60 ), 'least_upper_bound'( inverse( multiply( identity, 'least_upper_bound'(
% 119.18/119.60 X, identity ) ) ), multiply( identity, X ) ) ) ] )
% 119.18/119.60 , clause( 44049, [ =( inverse( 'least_upper_bound'( X, multiply( X, Y ) ) )
% 119.18/119.60 , inverse( multiply( X, 'least_upper_bound'( Y, identity ) ) ) ) ] )
% 119.18/119.60 , 0, clause( 44050, [ =( 'least_upper_bound'( identity, X ),
% 119.18/119.60 'least_upper_bound'( inverse( 'least_upper_bound'( identity, X ) ), X ) )
% 119.18/119.60 ] )
% 119.18/119.60 , 0, 7, substitution( 0, [ :=( X, identity ), :=( Y, X )] ), substitution(
% 119.18/119.60 1, [ :=( X, multiply( identity, X ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44056, [ =( 'least_upper_bound'( identity, multiply( identity, X )
% 119.18/119.60 ), 'least_upper_bound'( inverse( 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 multiply( identity, X ) ) ) ] )
% 119.18/119.60 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.60 , 0, clause( 44053, [ =( 'least_upper_bound'( identity, multiply( identity
% 119.18/119.60 , X ) ), 'least_upper_bound'( inverse( multiply( identity,
% 119.18/119.60 'least_upper_bound'( X, identity ) ) ), multiply( identity, X ) ) ) ] )
% 119.18/119.60 , 0, 8, substitution( 0, [ :=( X, 'least_upper_bound'( X, identity ) )] ),
% 119.18/119.60 substitution( 1, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44062, [ =( 'least_upper_bound'( identity, multiply( identity, X )
% 119.18/119.60 ), 'least_upper_bound'( inverse( 'least_upper_bound'( X, identity ) ), X
% 119.18/119.60 ) ) ] )
% 119.18/119.60 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.60 , 0, clause( 44056, [ =( 'least_upper_bound'( identity, multiply( identity
% 119.18/119.60 , X ) ), 'least_upper_bound'( inverse( 'least_upper_bound'( X, identity )
% 119.18/119.60 ), multiply( identity, X ) ) ) ] )
% 119.18/119.60 , 0, 11, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44063, [ =( 'least_upper_bound'( identity, X ), 'least_upper_bound'(
% 119.18/119.60 inverse( 'least_upper_bound'( X, identity ) ), X ) ) ] )
% 119.18/119.60 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.60 , 0, clause( 44062, [ =( 'least_upper_bound'( identity, multiply( identity
% 119.18/119.60 , X ) ), 'least_upper_bound'( inverse( 'least_upper_bound'( X, identity )
% 119.18/119.60 ), X ) ) ] )
% 119.18/119.60 , 0, 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 44065, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X,
% 119.18/119.60 identity ) ), X ), 'least_upper_bound'( identity, X ) ) ] )
% 119.18/119.60 , clause( 44063, [ =( 'least_upper_bound'( identity, X ),
% 119.18/119.60 'least_upper_bound'( inverse( 'least_upper_bound'( X, identity ) ), X ) )
% 119.18/119.60 ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 12284, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X,
% 119.18/119.60 identity ) ), X ), 'least_upper_bound'( identity, X ) ) ] )
% 119.18/119.60 , clause( 44065, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X
% 119.18/119.60 , identity ) ), X ), 'least_upper_bound'( identity, X ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 44068, [ =( multiply( inverse( X ), 'least_upper_bound'( Y, X ) ),
% 119.18/119.60 'least_upper_bound'( multiply( inverse( X ), Y ), identity ) ) ] )
% 119.18/119.60 , clause( 66, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ),
% 119.18/119.60 identity ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44072, [ =( multiply( inverse( X ), 'least_upper_bound'( identity,
% 119.18/119.60 X ) ), 'least_upper_bound'( multiply( inverse( X ), inverse(
% 119.18/119.60 'least_upper_bound'( X, identity ) ) ), identity ) ) ] )
% 119.18/119.60 , clause( 12284, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'( X
% 119.18/119.60 , identity ) ), X ), 'least_upper_bound'( identity, X ) ) ] )
% 119.18/119.60 , 0, clause( 44068, [ =( multiply( inverse( X ), 'least_upper_bound'( Y, X
% 119.18/119.60 ) ), 'least_upper_bound'( multiply( inverse( X ), Y ), identity ) ) ] )
% 119.18/119.60 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, inverse( 'least_upper_bound'( X, identity ) ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44073, [ =( multiply( inverse( X ), 'least_upper_bound'( identity,
% 119.18/119.60 X ) ), 'least_upper_bound'( inverse( multiply( 'least_upper_bound'( X,
% 119.18/119.60 identity ), X ) ), identity ) ) ] )
% 119.18/119.60 , clause( 202, [ =( multiply( inverse( Y ), inverse( X ) ), inverse(
% 119.18/119.60 multiply( X, Y ) ) ) ] )
% 119.18/119.60 , 0, clause( 44072, [ =( multiply( inverse( X ), 'least_upper_bound'(
% 119.18/119.60 identity, X ) ), 'least_upper_bound'( multiply( inverse( X ), inverse(
% 119.18/119.60 'least_upper_bound'( X, identity ) ) ), identity ) ) ] )
% 119.18/119.60 , 0, 8, substitution( 0, [ :=( X, 'least_upper_bound'( X, identity ) ),
% 119.18/119.60 :=( Y, X )] ), substitution( 1, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44074, [ =( 'least_upper_bound'( inverse( X ), identity ),
% 119.18/119.60 'least_upper_bound'( inverse( multiply( 'least_upper_bound'( X, identity
% 119.18/119.60 ), X ) ), identity ) ) ] )
% 119.18/119.60 , clause( 770, [ =( multiply( inverse( Y ), 'least_upper_bound'( identity,
% 119.18/119.60 Y ) ), 'least_upper_bound'( inverse( Y ), identity ) ) ] )
% 119.18/119.60 , 0, clause( 44073, [ =( multiply( inverse( X ), 'least_upper_bound'(
% 119.18/119.60 identity, X ) ), 'least_upper_bound'( inverse( multiply(
% 119.18/119.60 'least_upper_bound'( X, identity ), X ) ), identity ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.60 :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 44075, [ =( 'least_upper_bound'( inverse( multiply(
% 119.18/119.60 'least_upper_bound'( X, identity ), X ) ), identity ),
% 119.18/119.60 'least_upper_bound'( inverse( X ), identity ) ) ] )
% 119.18/119.60 , clause( 44074, [ =( 'least_upper_bound'( inverse( X ), identity ),
% 119.18/119.60 'least_upper_bound'( inverse( multiply( 'least_upper_bound'( X, identity
% 119.18/119.60 ), X ) ), identity ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 12300, [ =( 'least_upper_bound'( inverse( multiply(
% 119.18/119.60 'least_upper_bound'( X, identity ), X ) ), identity ),
% 119.18/119.60 'least_upper_bound'( inverse( X ), identity ) ) ] )
% 119.18/119.60 , clause( 44075, [ =( 'least_upper_bound'( inverse( multiply(
% 119.18/119.60 'least_upper_bound'( X, identity ), X ) ), identity ),
% 119.18/119.60 'least_upper_bound'( inverse( X ), identity ) ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 44077, [ =( inverse( 'greatest_lower_bound'( multiply( X, Y ), X )
% 119.18/119.60 ), inverse( multiply( X, 'greatest_lower_bound'( Y, identity ) ) ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , clause( 676, [ =( inverse( multiply( X, 'greatest_lower_bound'( Y,
% 119.18/119.60 identity ) ) ), inverse( 'greatest_lower_bound'( multiply( X, Y ), X ) )
% 119.18/119.60 ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44085, [ =( inverse( 'greatest_lower_bound'( inverse( Y ), inverse(
% 119.18/119.60 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ) ), inverse( multiply(
% 119.18/119.60 inverse( 'greatest_lower_bound'( multiply( X, Y ), Y ) ),
% 119.18/119.60 'greatest_lower_bound'( 'greatest_lower_bound'( X, identity ), identity )
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , clause( 1199, [ =( multiply( inverse( 'greatest_lower_bound'( multiply( X
% 119.18/119.60 , Y ), Y ) ), 'greatest_lower_bound'( X, identity ) ), inverse( Y ) ) ]
% 119.18/119.60 )
% 119.18/119.60 , 0, clause( 44077, [ =( inverse( 'greatest_lower_bound'( multiply( X, Y )
% 119.18/119.60 , X ) ), inverse( multiply( X, 'greatest_lower_bound'( Y, identity ) ) )
% 119.18/119.60 ) ] )
% 119.18/119.60 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.60 :=( X, inverse( 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ), :=( Y
% 119.18/119.60 , 'greatest_lower_bound'( X, identity ) )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44087, [ =( inverse( 'greatest_lower_bound'( inverse( X ), inverse(
% 119.18/119.60 'greatest_lower_bound'( multiply( Y, X ), X ) ) ) ), multiply( inverse(
% 119.18/119.60 'greatest_lower_bound'( 'greatest_lower_bound'( Y, identity ), identity )
% 119.18/119.60 ), 'greatest_lower_bound'( multiply( Y, X ), X ) ) ) ] )
% 119.18/119.60 , clause( 203, [ =( inverse( multiply( inverse( X ), Y ) ), multiply(
% 119.18/119.60 inverse( Y ), X ) ) ] )
% 119.18/119.60 , 0, clause( 44085, [ =( inverse( 'greatest_lower_bound'( inverse( Y ),
% 119.18/119.60 inverse( 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ) ), inverse(
% 119.18/119.60 multiply( inverse( 'greatest_lower_bound'( multiply( X, Y ), Y ) ),
% 119.18/119.60 'greatest_lower_bound'( 'greatest_lower_bound'( X, identity ), identity )
% 119.18/119.60 ) ) ) ] )
% 119.18/119.60 , 0, 11, substitution( 0, [ :=( X, 'greatest_lower_bound'( multiply( Y, X )
% 119.18/119.60 , X ) ), :=( Y, 'greatest_lower_bound'( 'greatest_lower_bound'( Y,
% 119.18/119.60 identity ), identity ) )] ), substitution( 1, [ :=( X, Y ), :=( Y, X )] )
% 119.18/119.60 ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44088, [ =( inverse( 'greatest_lower_bound'( inverse( X ), inverse(
% 119.18/119.60 'greatest_lower_bound'( multiply( Y, X ), X ) ) ) ), multiply( inverse(
% 119.18/119.60 'greatest_lower_bound'( Y, identity ) ), 'greatest_lower_bound'( multiply(
% 119.18/119.60 Y, X ), X ) ) ) ] )
% 119.18/119.60 , clause( 30, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Y, X ),
% 119.18/119.60 X ), 'greatest_lower_bound'( Y, X ) ) ] )
% 119.18/119.60 , 0, clause( 44087, [ =( inverse( 'greatest_lower_bound'( inverse( X ),
% 119.18/119.60 inverse( 'greatest_lower_bound'( multiply( Y, X ), X ) ) ) ), multiply(
% 119.18/119.60 inverse( 'greatest_lower_bound'( 'greatest_lower_bound'( Y, identity ),
% 119.18/119.60 identity ) ), 'greatest_lower_bound'( multiply( Y, X ), X ) ) ) ] )
% 119.18/119.60 , 0, 13, substitution( 0, [ :=( X, identity ), :=( Y, Y )] ),
% 119.18/119.60 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44089, [ =( inverse( inverse( X ) ), multiply( inverse(
% 119.18/119.60 'greatest_lower_bound'( Y, identity ) ), 'greatest_lower_bound'( multiply(
% 119.18/119.60 Y, X ), X ) ) ) ] )
% 119.18/119.60 , clause( 5003, [ =( 'greatest_lower_bound'( inverse( X ), inverse(
% 119.18/119.60 'greatest_lower_bound'( Y, X ) ) ), inverse( X ) ) ] )
% 119.18/119.60 , 0, clause( 44088, [ =( inverse( 'greatest_lower_bound'( inverse( X ),
% 119.18/119.60 inverse( 'greatest_lower_bound'( multiply( Y, X ), X ) ) ) ), multiply(
% 119.18/119.60 inverse( 'greatest_lower_bound'( Y, identity ) ), 'greatest_lower_bound'(
% 119.18/119.60 multiply( Y, X ), X ) ) ) ] )
% 119.18/119.60 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, multiply( Y, X ) )] ),
% 119.18/119.60 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 paramod(
% 119.18/119.60 clause( 44090, [ =( X, multiply( inverse( 'greatest_lower_bound'( Y,
% 119.18/119.60 identity ) ), 'greatest_lower_bound'( multiply( Y, X ), X ) ) ) ] )
% 119.18/119.60 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.60 , 0, clause( 44089, [ =( inverse( inverse( X ) ), multiply( inverse(
% 119.18/119.60 'greatest_lower_bound'( Y, identity ) ), 'greatest_lower_bound'( multiply(
% 119.18/119.60 Y, X ), X ) ) ) ] )
% 119.18/119.60 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.60 :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 44091, [ =( multiply( inverse( 'greatest_lower_bound'( Y, identity
% 119.18/119.60 ) ), 'greatest_lower_bound'( multiply( Y, X ), X ) ), X ) ] )
% 119.18/119.60 , clause( 44090, [ =( X, multiply( inverse( 'greatest_lower_bound'( Y,
% 119.18/119.60 identity ) ), 'greatest_lower_bound'( multiply( Y, X ), X ) ) ) ] )
% 119.18/119.60 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 subsumption(
% 119.18/119.60 clause( 12414, [ =( multiply( inverse( 'greatest_lower_bound'( X, identity
% 119.18/119.60 ) ), 'greatest_lower_bound'( multiply( X, Y ), Y ) ), Y ) ] )
% 119.18/119.60 , clause( 44091, [ =( multiply( inverse( 'greatest_lower_bound'( Y,
% 119.18/119.60 identity ) ), 'greatest_lower_bound'( multiply( Y, X ), X ) ), X ) ] )
% 119.18/119.60 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.60 )] ) ).
% 119.18/119.60
% 119.18/119.60
% 119.18/119.60 eqswap(
% 119.18/119.60 clause( 44093, [ =( 'least_upper_bound'( inverse( X ), identity ),
% 119.18/119.60 'least_upper_bound'( inverse( multiply( 'least_upper_bound'( X, identity
% 119.18/119.60 ), X ) ), identity ) ) ] )
% 119.18/119.60 , clause( 12300, [ =( 'least_upper_bound'( inverse( multiply(
% 119.18/119.61 'least_upper_bound'( X, identity ), X ) ), identity ),
% 119.18/119.61 'least_upper_bound'( inverse( X ), identity ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44101, [ =( 'least_upper_bound'( inverse( X ), identity ),
% 119.18/119.61 'least_upper_bound'( inverse( 'least_upper_bound'( multiply( X, X ), X )
% 119.18/119.61 ), identity ) ) ] )
% 119.18/119.61 , clause( 1261, [ =( inverse( multiply( 'least_upper_bound'( Y, identity )
% 119.18/119.61 , X ) ), inverse( 'least_upper_bound'( multiply( Y, X ), X ) ) ) ] )
% 119.18/119.61 , 0, clause( 44093, [ =( 'least_upper_bound'( inverse( X ), identity ),
% 119.18/119.61 'least_upper_bound'( inverse( multiply( 'least_upper_bound'( X, identity
% 119.18/119.61 ), X ) ), identity ) ) ] )
% 119.18/119.61 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.61 :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44105, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.61 multiply( X, X ), X ) ), identity ), 'least_upper_bound'( inverse( X ),
% 119.18/119.61 identity ) ) ] )
% 119.18/119.61 , clause( 44101, [ =( 'least_upper_bound'( inverse( X ), identity ),
% 119.18/119.61 'least_upper_bound'( inverse( 'least_upper_bound'( multiply( X, X ), X )
% 119.18/119.61 ), identity ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 12464, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.61 multiply( X, X ), X ) ), identity ), 'least_upper_bound'( inverse( X ),
% 119.18/119.61 identity ) ) ] )
% 119.18/119.61 , clause( 44105, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.61 multiply( X, X ), X ) ), identity ), 'least_upper_bound'( inverse( X ),
% 119.18/119.61 identity ) ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44107, [ =( 'least_upper_bound'( inverse( X ), identity ),
% 119.18/119.61 'least_upper_bound'( inverse( multiply( 'least_upper_bound'( X, identity
% 119.18/119.61 ), X ) ), identity ) ) ] )
% 119.18/119.61 , clause( 12300, [ =( 'least_upper_bound'( inverse( multiply(
% 119.18/119.61 'least_upper_bound'( X, identity ), X ) ), identity ),
% 119.18/119.61 'least_upper_bound'( inverse( X ), identity ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44113, [ =( 'least_upper_bound'( inverse( inverse(
% 119.18/119.61 'least_upper_bound'( multiply( X, X ), X ) ) ), identity ),
% 119.18/119.61 'least_upper_bound'( inverse( multiply( 'least_upper_bound'( inverse( X )
% 119.18/119.61 , identity ), inverse( 'least_upper_bound'( multiply( X, X ), X ) ) ) ),
% 119.18/119.61 identity ) ) ] )
% 119.18/119.61 , clause( 12464, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.61 multiply( X, X ), X ) ), identity ), 'least_upper_bound'( inverse( X ),
% 119.18/119.61 identity ) ) ] )
% 119.18/119.61 , 0, clause( 44107, [ =( 'least_upper_bound'( inverse( X ), identity ),
% 119.18/119.61 'least_upper_bound'( inverse( multiply( 'least_upper_bound'( X, identity
% 119.18/119.61 ), X ) ), identity ) ) ] )
% 119.18/119.61 , 0, 13, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.61 inverse( 'least_upper_bound'( multiply( X, X ), X ) ) )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44114, [ =( 'least_upper_bound'( inverse( inverse(
% 119.18/119.61 'least_upper_bound'( multiply( X, X ), X ) ) ), identity ),
% 119.18/119.61 'least_upper_bound'( multiply( 'least_upper_bound'( multiply( X, X ), X )
% 119.18/119.61 , inverse( 'least_upper_bound'( inverse( X ), identity ) ) ), identity )
% 119.18/119.61 ) ] )
% 119.18/119.61 , clause( 211, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 119.18/119.61 inverse( X ) ) ) ] )
% 119.18/119.61 , 0, clause( 44113, [ =( 'least_upper_bound'( inverse( inverse(
% 119.18/119.61 'least_upper_bound'( multiply( X, X ), X ) ) ), identity ),
% 119.18/119.61 'least_upper_bound'( inverse( multiply( 'least_upper_bound'( inverse( X )
% 119.18/119.61 , identity ), inverse( 'least_upper_bound'( multiply( X, X ), X ) ) ) ),
% 119.18/119.61 identity ) ) ] )
% 119.18/119.61 , 0, 11, substitution( 0, [ :=( X, 'least_upper_bound'( inverse( X ),
% 119.18/119.61 identity ) ), :=( Y, 'least_upper_bound'( multiply( X, X ), X ) )] ),
% 119.18/119.61 substitution( 1, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44115, [ =( 'least_upper_bound'( inverse( inverse(
% 119.18/119.61 'least_upper_bound'( multiply( X, X ), X ) ) ), identity ),
% 119.18/119.61 'least_upper_bound'( multiply( X, X ), identity ) ) ] )
% 119.18/119.61 , clause( 4025, [ =( multiply( 'least_upper_bound'( multiply( X, Y ), X ),
% 119.18/119.61 inverse( 'least_upper_bound'( inverse( Y ), identity ) ) ), multiply( X,
% 119.18/119.61 Y ) ) ] )
% 119.18/119.61 , 0, clause( 44114, [ =( 'least_upper_bound'( inverse( inverse(
% 119.18/119.61 'least_upper_bound'( multiply( X, X ), X ) ) ), identity ),
% 119.18/119.61 'least_upper_bound'( multiply( 'least_upper_bound'( multiply( X, X ), X )
% 119.18/119.61 , inverse( 'least_upper_bound'( inverse( X ), identity ) ) ), identity )
% 119.18/119.61 ) ] )
% 119.18/119.61 , 0, 11, substitution( 0, [ :=( X, X ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.61 :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44116, [ =( 'least_upper_bound'( 'least_upper_bound'( multiply( X,
% 119.18/119.61 X ), X ), identity ), 'least_upper_bound'( multiply( X, X ), identity ) )
% 119.18/119.61 ] )
% 119.18/119.61 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.61 , 0, clause( 44115, [ =( 'least_upper_bound'( inverse( inverse(
% 119.18/119.61 'least_upper_bound'( multiply( X, X ), X ) ) ), identity ),
% 119.18/119.61 'least_upper_bound'( multiply( X, X ), identity ) ) ] )
% 119.18/119.61 , 0, 2, substitution( 0, [ :=( X, 'least_upper_bound'( multiply( X, X ), X
% 119.18/119.61 ) )] ), substitution( 1, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 12466, [ =( 'least_upper_bound'( 'least_upper_bound'( multiply( X,
% 119.18/119.61 X ), X ), identity ), 'least_upper_bound'( multiply( X, X ), identity ) )
% 119.18/119.61 ] )
% 119.18/119.61 , clause( 44116, [ =( 'least_upper_bound'( 'least_upper_bound'( multiply( X
% 119.18/119.61 , X ), X ), identity ), 'least_upper_bound'( multiply( X, X ), identity )
% 119.18/119.61 ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44119, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 119.18/119.61 inverse( X ), 'least_upper_bound'( 'least_upper_bound'( Y, X ), Z ) ) ) )
% 119.18/119.61 ] )
% 119.18/119.61 , clause( 1781, [ =( 'greatest_lower_bound'( identity, multiply( inverse( Y
% 119.18/119.61 ), 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ), identity )
% 119.18/119.61 ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44122, [ =( identity, 'greatest_lower_bound'( identity, multiply(
% 119.18/119.61 inverse( X ), 'least_upper_bound'( multiply( X, X ), identity ) ) ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , clause( 12466, [ =( 'least_upper_bound'( 'least_upper_bound'( multiply( X
% 119.18/119.61 , X ), X ), identity ), 'least_upper_bound'( multiply( X, X ), identity )
% 119.18/119.61 ) ] )
% 119.18/119.61 , 0, clause( 44119, [ =( identity, 'greatest_lower_bound'( identity,
% 119.18/119.61 multiply( inverse( X ), 'least_upper_bound'( 'least_upper_bound'( Y, X )
% 119.18/119.61 , Z ) ) ) ) ] )
% 119.18/119.61 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.61 :=( Y, multiply( X, X ) ), :=( Z, identity )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44124, [ =( identity, 'greatest_lower_bound'( identity,
% 119.18/119.61 'least_upper_bound'( X, multiply( inverse( X ), identity ) ) ) ) ] )
% 119.18/119.61 , clause( 1547, [ =( multiply( inverse( X ), 'least_upper_bound'( multiply(
% 119.18/119.61 X, Y ), Z ) ), 'least_upper_bound'( Y, multiply( inverse( X ), Z ) ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , 0, clause( 44122, [ =( identity, 'greatest_lower_bound'( identity,
% 119.18/119.61 multiply( inverse( X ), 'least_upper_bound'( multiply( X, X ), identity )
% 119.18/119.61 ) ) ) ] )
% 119.18/119.61 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, identity )] ),
% 119.18/119.61 substitution( 1, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44125, [ =( identity, 'greatest_lower_bound'( identity,
% 119.18/119.61 'least_upper_bound'( X, inverse( X ) ) ) ) ] )
% 119.18/119.61 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.61 , 0, clause( 44124, [ =( identity, 'greatest_lower_bound'( identity,
% 119.18/119.61 'least_upper_bound'( X, multiply( inverse( X ), identity ) ) ) ) ] )
% 119.18/119.61 , 0, 6, substitution( 0, [ :=( X, inverse( X ) )] ), substitution( 1, [
% 119.18/119.61 :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44126, [ =( 'greatest_lower_bound'( identity, 'least_upper_bound'(
% 119.18/119.61 X, inverse( X ) ) ), identity ) ] )
% 119.18/119.61 , clause( 44125, [ =( identity, 'greatest_lower_bound'( identity,
% 119.18/119.61 'least_upper_bound'( X, inverse( X ) ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 12495, [ =( 'greatest_lower_bound'( identity, 'least_upper_bound'(
% 119.18/119.61 X, inverse( X ) ) ), identity ) ] )
% 119.18/119.61 , clause( 44126, [ =( 'greatest_lower_bound'( identity, 'least_upper_bound'(
% 119.18/119.61 X, inverse( X ) ) ), identity ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44128, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, Z )
% 119.18/119.61 ), 'greatest_lower_bound'( 'least_upper_bound'( X,
% 119.18/119.61 'greatest_lower_bound'( Y, Z ) ), 'least_upper_bound'( X, Z ) ) ) ] )
% 119.18/119.61 , clause( 818, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X,
% 119.18/119.61 'greatest_lower_bound'( Y, Z ) ), 'least_upper_bound'( X, Z ) ),
% 119.18/119.61 'least_upper_bound'( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44131, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.61 identity, 'least_upper_bound'( Y, inverse( Y ) ) ) ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'least_upper_bound'( X, 'least_upper_bound'( Y, inverse( Y ) ) ) ) ) ] )
% 119.18/119.61 , clause( 12495, [ =( 'greatest_lower_bound'( identity, 'least_upper_bound'(
% 119.18/119.61 X, inverse( X ) ) ), identity ) ] )
% 119.18/119.61 , 0, clause( 44128, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y
% 119.18/119.61 , Z ) ), 'greatest_lower_bound'( 'least_upper_bound'( X,
% 119.18/119.61 'greatest_lower_bound'( Y, Z ) ), 'least_upper_bound'( X, Z ) ) ) ] )
% 119.18/119.61 , 0, 12, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.61 :=( Y, identity ), :=( Z, 'least_upper_bound'( Y, inverse( Y ) ) )] )
% 119.18/119.61 ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44132, [ =( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'least_upper_bound'( X, 'least_upper_bound'( Y, inverse( Y ) ) ) ) ) ] )
% 119.18/119.61 , clause( 12495, [ =( 'greatest_lower_bound'( identity, 'least_upper_bound'(
% 119.18/119.61 X, inverse( X ) ) ), identity ) ] )
% 119.18/119.61 , 0, clause( 44131, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'(
% 119.18/119.61 identity, 'least_upper_bound'( Y, inverse( Y ) ) ) ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'least_upper_bound'( X, 'least_upper_bound'( Y, inverse( Y ) ) ) ) ) ] )
% 119.18/119.61 , 0, 3, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.61 :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44135, [ =( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), inverse( Y ) ) ) ) ] )
% 119.18/119.61 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.61 , 0, clause( 44132, [ =( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'least_upper_bound'( X, 'least_upper_bound'( Y, inverse( Y ) ) ) ) ) ] )
% 119.18/119.61 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, inverse( Y ) )] )
% 119.18/119.61 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44136, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X,
% 119.18/119.61 identity ), 'least_upper_bound'( 'least_upper_bound'( X, Y ), inverse( Y
% 119.18/119.61 ) ) ), 'least_upper_bound'( X, identity ) ) ] )
% 119.18/119.61 , clause( 44135, [ =( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), inverse( Y ) ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 26875, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y,
% 119.18/119.61 identity ), 'least_upper_bound'( 'least_upper_bound'( Y, X ), inverse( X
% 119.18/119.61 ) ) ), 'least_upper_bound'( Y, identity ) ) ] )
% 119.18/119.61 , clause( 44136, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X,
% 119.18/119.61 identity ), 'least_upper_bound'( 'least_upper_bound'( X, Y ), inverse( Y
% 119.18/119.61 ) ) ), 'least_upper_bound'( X, identity ) ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.61 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44138, [ =( Y, multiply( inverse( 'least_upper_bound'( identity,
% 119.18/119.61 multiply( X, inverse( Y ) ) ) ), 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.61 , clause( 8767, [ =( multiply( inverse( 'least_upper_bound'( identity,
% 119.18/119.61 multiply( Y, inverse( X ) ) ) ), 'least_upper_bound'( Y, X ) ), X ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44141, [ =( X, multiply( inverse( multiply( inverse( Y ),
% 119.18/119.61 'least_upper_bound'( inverse( X ), Y ) ) ), 'least_upper_bound'( inverse(
% 119.18/119.61 Y ), X ) ) ) ] )
% 119.18/119.61 , clause( 1640, [ =( 'least_upper_bound'( identity, multiply( inverse( X )
% 119.18/119.61 , Y ) ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.61 , 0, clause( 44138, [ =( Y, multiply( inverse( 'least_upper_bound'(
% 119.18/119.61 identity, multiply( X, inverse( Y ) ) ) ), 'least_upper_bound'( X, Y ) )
% 119.18/119.61 ) ] )
% 119.18/119.61 , 0, 4, substitution( 0, [ :=( X, Y ), :=( Y, inverse( X ) )] ),
% 119.18/119.61 substitution( 1, [ :=( X, inverse( Y ) ), :=( Y, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44145, [ =( X, multiply( multiply( inverse( 'least_upper_bound'(
% 119.18/119.61 inverse( X ), Y ) ), Y ), 'least_upper_bound'( inverse( Y ), X ) ) ) ] )
% 119.18/119.61 , clause( 203, [ =( inverse( multiply( inverse( X ), Y ) ), multiply(
% 119.18/119.61 inverse( Y ), X ) ) ] )
% 119.18/119.61 , 0, clause( 44141, [ =( X, multiply( inverse( multiply( inverse( Y ),
% 119.18/119.61 'least_upper_bound'( inverse( X ), Y ) ) ), 'least_upper_bound'( inverse(
% 119.18/119.61 Y ), X ) ) ) ] )
% 119.18/119.61 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, 'least_upper_bound'( inverse(
% 119.18/119.61 X ), Y ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44146, [ =( multiply( multiply( inverse( 'least_upper_bound'(
% 119.18/119.61 inverse( X ), Y ) ), Y ), 'least_upper_bound'( inverse( Y ), X ) ), X ) ]
% 119.18/119.61 )
% 119.18/119.61 , clause( 44145, [ =( X, multiply( multiply( inverse( 'least_upper_bound'(
% 119.18/119.61 inverse( X ), Y ) ), Y ), 'least_upper_bound'( inverse( Y ), X ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 32636, [ =( multiply( multiply( inverse( 'least_upper_bound'(
% 119.18/119.61 inverse( Y ), X ) ), X ), 'least_upper_bound'( inverse( X ), Y ) ), Y ) ]
% 119.18/119.61 )
% 119.18/119.61 , clause( 44146, [ =( multiply( multiply( inverse( 'least_upper_bound'(
% 119.18/119.61 inverse( X ), Y ) ), Y ), 'least_upper_bound'( inverse( Y ), X ) ), X ) ]
% 119.18/119.61 )
% 119.18/119.61 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.61 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44148, [ =( 'least_upper_bound'( Y, multiply( X, Z ) ), multiply( X
% 119.18/119.61 , 'least_upper_bound'( multiply( inverse( X ), Y ), Z ) ) ) ] )
% 119.18/119.61 , clause( 1545, [ =( multiply( X, 'least_upper_bound'( multiply( inverse( X
% 119.18/119.61 ), Y ), Z ) ), 'least_upper_bound'( Y, multiply( X, Z ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44153, [ =( 'least_upper_bound'( X, multiply( Y, inverse(
% 119.18/119.61 'least_upper_bound'( Z, inverse( multiply( inverse( Y ), X ) ) ) ) ) ),
% 119.18/119.61 multiply( Y, multiply( inverse( Y ), X ) ) ) ] )
% 119.18/119.61 , clause( 5571, [ =( 'least_upper_bound'( Y, inverse( 'least_upper_bound'(
% 119.18/119.61 X, inverse( Y ) ) ) ), Y ) ] )
% 119.18/119.61 , 0, clause( 44148, [ =( 'least_upper_bound'( Y, multiply( X, Z ) ),
% 119.18/119.61 multiply( X, 'least_upper_bound'( multiply( inverse( X ), Y ), Z ) ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , 0, 15, substitution( 0, [ :=( X, Z ), :=( Y, multiply( inverse( Y ), X )
% 119.18/119.61 )] ), substitution( 1, [ :=( X, Y ), :=( Y, X ), :=( Z, inverse(
% 119.18/119.61 'least_upper_bound'( Z, inverse( multiply( inverse( Y ), X ) ) ) ) )] )
% 119.18/119.61 ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44154, [ =( 'least_upper_bound'( X, multiply( Y, inverse(
% 119.18/119.61 'least_upper_bound'( Z, inverse( multiply( inverse( Y ), X ) ) ) ) ) ),
% 119.18/119.61 multiply( multiply( Y, inverse( Y ) ), X ) ) ] )
% 119.18/119.61 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 119.18/119.61 ), Z ) ) ] )
% 119.18/119.61 , 0, clause( 44153, [ =( 'least_upper_bound'( X, multiply( Y, inverse(
% 119.18/119.61 'least_upper_bound'( Z, inverse( multiply( inverse( Y ), X ) ) ) ) ) ),
% 119.18/119.61 multiply( Y, multiply( inverse( Y ), X ) ) ) ] )
% 119.18/119.61 , 0, 13, substitution( 0, [ :=( X, Y ), :=( Y, inverse( Y ) ), :=( Z, X )] )
% 119.18/119.61 , substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44155, [ =( 'least_upper_bound'( X, multiply( Y, inverse(
% 119.18/119.61 'least_upper_bound'( Z, inverse( multiply( inverse( Y ), X ) ) ) ) ) ),
% 119.18/119.61 multiply( identity, X ) ) ] )
% 119.18/119.61 , clause( 180, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 119.18/119.61 , 0, clause( 44154, [ =( 'least_upper_bound'( X, multiply( Y, inverse(
% 119.18/119.61 'least_upper_bound'( Z, inverse( multiply( inverse( Y ), X ) ) ) ) ) ),
% 119.18/119.61 multiply( multiply( Y, inverse( Y ) ), X ) ) ] )
% 119.18/119.61 , 0, 14, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.61 :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44156, [ =( 'least_upper_bound'( X, multiply( Y, inverse(
% 119.18/119.61 'least_upper_bound'( Z, inverse( multiply( inverse( Y ), X ) ) ) ) ) ), X
% 119.18/119.61 ) ] )
% 119.18/119.61 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.61 , 0, clause( 44155, [ =( 'least_upper_bound'( X, multiply( Y, inverse(
% 119.18/119.61 'least_upper_bound'( Z, inverse( multiply( inverse( Y ), X ) ) ) ) ) ),
% 119.18/119.61 multiply( identity, X ) ) ] )
% 119.18/119.61 , 0, 13, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.61 :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44157, [ =( 'least_upper_bound'( X, multiply( Y, inverse(
% 119.18/119.61 'least_upper_bound'( Z, multiply( inverse( X ), Y ) ) ) ) ), X ) ] )
% 119.18/119.61 , clause( 203, [ =( inverse( multiply( inverse( X ), Y ) ), multiply(
% 119.18/119.61 inverse( Y ), X ) ) ] )
% 119.18/119.61 , 0, clause( 44156, [ =( 'least_upper_bound'( X, multiply( Y, inverse(
% 119.18/119.61 'least_upper_bound'( Z, inverse( multiply( inverse( Y ), X ) ) ) ) ) ), X
% 119.18/119.61 ) ] )
% 119.18/119.61 , 0, 8, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.61 :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 33848, [ =( 'least_upper_bound'( Y, multiply( X, inverse(
% 119.18/119.61 'least_upper_bound'( Z, multiply( inverse( Y ), X ) ) ) ) ), Y ) ] )
% 119.18/119.61 , clause( 44157, [ =( 'least_upper_bound'( X, multiply( Y, inverse(
% 119.18/119.61 'least_upper_bound'( Z, multiply( inverse( X ), Y ) ) ) ) ), X ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 119.18/119.61 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44159, [ =( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), inverse( Y ) ) ) ) ] )
% 119.18/119.61 , clause( 26875, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y,
% 119.18/119.61 identity ), 'least_upper_bound'( 'least_upper_bound'( Y, X ), inverse( X
% 119.18/119.61 ) ) ), 'least_upper_bound'( Y, identity ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44160, [ =( 'greatest_lower_bound'( 'least_upper_bound'( multiply(
% 119.18/119.61 X, Y ), Y ), Z ), 'greatest_lower_bound'( multiply( 'least_upper_bound'(
% 119.18/119.61 identity, X ), Y ), Z ) ) ] )
% 119.18/119.61 , clause( 1205, [ =( 'greatest_lower_bound'( multiply( 'least_upper_bound'(
% 119.18/119.61 identity, Y ), X ), Z ), 'greatest_lower_bound'( 'least_upper_bound'(
% 119.18/119.61 multiply( Y, X ), X ), Z ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44163, [ =( 'least_upper_bound'( multiply( X, identity ), identity
% 119.18/119.61 ), 'greatest_lower_bound'( multiply( 'least_upper_bound'( identity, X )
% 119.18/119.61 , identity ), 'least_upper_bound'( 'least_upper_bound'( multiply( X,
% 119.18/119.61 identity ), Y ), inverse( Y ) ) ) ) ] )
% 119.18/119.61 , clause( 44160, [ =( 'greatest_lower_bound'( 'least_upper_bound'( multiply(
% 119.18/119.61 X, Y ), Y ), Z ), 'greatest_lower_bound'( multiply( 'least_upper_bound'(
% 119.18/119.61 identity, X ), Y ), Z ) ) ] )
% 119.18/119.61 , 0, clause( 44159, [ =( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), inverse( Y ) ) ) ) ] )
% 119.18/119.61 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, identity ), :=( Z,
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( multiply( X, identity ), Y ),
% 119.18/119.61 inverse( Y ) ) )] ), substitution( 1, [ :=( X, multiply( X, identity ) )
% 119.18/119.61 , :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44166, [ =( 'least_upper_bound'( multiply( X, identity ), identity
% 119.18/119.61 ), 'greatest_lower_bound'( 'least_upper_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( multiply( X, identity ), Y ),
% 119.18/119.61 inverse( Y ) ) ) ) ] )
% 119.18/119.61 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.61 , 0, clause( 44163, [ =( 'least_upper_bound'( multiply( X, identity ),
% 119.18/119.61 identity ), 'greatest_lower_bound'( multiply( 'least_upper_bound'(
% 119.18/119.61 identity, X ), identity ), 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.61 multiply( X, identity ), Y ), inverse( Y ) ) ) ) ] )
% 119.18/119.61 , 0, 7, substitution( 0, [ :=( X, 'least_upper_bound'( identity, X ) )] ),
% 119.18/119.61 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44172, [ =( 'least_upper_bound'( multiply( X, identity ), identity
% 119.18/119.61 ), 'greatest_lower_bound'( 'least_upper_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), inverse( Y ) ) ) ) ] )
% 119.18/119.61 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.61 , 0, clause( 44166, [ =( 'least_upper_bound'( multiply( X, identity ),
% 119.18/119.61 identity ), 'greatest_lower_bound'( 'least_upper_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( multiply( X, identity ), Y ),
% 119.18/119.61 inverse( Y ) ) ) ) ] )
% 119.18/119.61 , 0, 12, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.61 :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44173, [ =( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), inverse( Y ) ) ) ) ] )
% 119.18/119.61 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.61 , 0, clause( 44172, [ =( 'least_upper_bound'( multiply( X, identity ),
% 119.18/119.61 identity ), 'greatest_lower_bound'( 'least_upper_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), inverse( Y ) ) ) ) ] )
% 119.18/119.61 , 0, 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.61 :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44175, [ =( 'greatest_lower_bound'( 'least_upper_bound'( identity,
% 119.18/119.61 X ), 'least_upper_bound'( 'least_upper_bound'( X, Y ), inverse( Y ) ) ),
% 119.18/119.61 'least_upper_bound'( X, identity ) ) ] )
% 119.18/119.61 , clause( 44173, [ =( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), inverse( Y ) ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 35945, [ =( 'greatest_lower_bound'( 'least_upper_bound'( identity,
% 119.18/119.61 X ), 'least_upper_bound'( 'least_upper_bound'( X, Y ), inverse( Y ) ) ),
% 119.18/119.61 'least_upper_bound'( X, identity ) ) ] )
% 119.18/119.61 , clause( 44175, [ =( 'greatest_lower_bound'( 'least_upper_bound'( identity
% 119.18/119.61 , X ), 'least_upper_bound'( 'least_upper_bound'( X, Y ), inverse( Y ) ) )
% 119.18/119.61 , 'least_upper_bound'( X, identity ) ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.61 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44177, [ =( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), inverse( Y ) ) ) ) ] )
% 119.18/119.61 , clause( 35945, [ =( 'greatest_lower_bound'( 'least_upper_bound'( identity
% 119.18/119.61 , X ), 'least_upper_bound'( 'least_upper_bound'( X, Y ), inverse( Y ) ) )
% 119.18/119.61 , 'least_upper_bound'( X, identity ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44178, [ =( 'greatest_lower_bound'( T, 'least_upper_bound'(
% 119.18/119.61 'least_upper_bound'( Y, X ), Z ) ), 'greatest_lower_bound'(
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ), T ) ) ] )
% 119.18/119.61 , clause( 1087, [ =( 'greatest_lower_bound'( 'least_upper_bound'(
% 119.18/119.61 'least_upper_bound'( X, Z ), Y ), T ), 'greatest_lower_bound'( T,
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y ), :=( T, T )] )
% 119.18/119.61 ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44179, [ =( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( 'least_upper_bound'( Y, X )
% 119.18/119.61 , inverse( Y ) ), 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , clause( 44178, [ =( 'greatest_lower_bound'( T, 'least_upper_bound'(
% 119.18/119.61 'least_upper_bound'( Y, X ), Z ) ), 'greatest_lower_bound'(
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ), T ) ) ] )
% 119.18/119.61 , 0, clause( 44177, [ =( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), inverse( Y ) ) ) ) ] )
% 119.18/119.61 , 0, 4, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, inverse( Y ) ),
% 119.18/119.61 :=( T, 'least_upper_bound'( identity, X ) )] ), substitution( 1, [ :=( X
% 119.18/119.61 , X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44180, [ =( 'greatest_lower_bound'( 'least_upper_bound'(
% 119.18/119.61 'least_upper_bound'( Y, X ), inverse( Y ) ), 'least_upper_bound'(
% 119.18/119.61 identity, X ) ), 'least_upper_bound'( X, identity ) ) ] )
% 119.18/119.61 , clause( 44179, [ =( 'least_upper_bound'( X, identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( 'least_upper_bound'( Y, X )
% 119.18/119.61 , inverse( Y ) ), 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 35965, [ =( 'greatest_lower_bound'( 'least_upper_bound'(
% 119.18/119.61 'least_upper_bound'( Y, X ), inverse( Y ) ), 'least_upper_bound'(
% 119.18/119.61 identity, X ) ), 'least_upper_bound'( X, identity ) ) ] )
% 119.18/119.61 , clause( 44180, [ =( 'greatest_lower_bound'( 'least_upper_bound'(
% 119.18/119.61 'least_upper_bound'( Y, X ), inverse( Y ) ), 'least_upper_bound'(
% 119.18/119.61 identity, X ) ), 'least_upper_bound'( X, identity ) ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.61 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44182, [ =( 'greatest_lower_bound'( identity, Y ),
% 119.18/119.61 'least_upper_bound'( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.61 identity, X ) ), Y ), 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 119.18/119.61 , clause( 2633, [ =( 'least_upper_bound'( 'greatest_lower_bound'( inverse(
% 119.18/119.61 'least_upper_bound'( identity, X ) ), Y ), 'greatest_lower_bound'(
% 119.18/119.61 identity, Y ) ), 'greatest_lower_bound'( identity, Y ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44183, [ =( 'greatest_lower_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( inverse( 'least_upper_bound'( identity, inverse( X )
% 119.18/119.61 ) ), 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , clause( 5591, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.61 X, inverse( Y ) ) ), Y ), inverse( 'least_upper_bound'( X, inverse( Y ) )
% 119.18/119.61 ) ) ] )
% 119.18/119.61 , 0, clause( 44182, [ =( 'greatest_lower_bound'( identity, Y ),
% 119.18/119.61 'least_upper_bound'( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.61 identity, X ) ), Y ), 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 119.18/119.61 , 0, 5, substitution( 0, [ :=( X, identity ), :=( Y, X )] ), substitution(
% 119.18/119.61 1, [ :=( X, inverse( X ) ), :=( Y, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44184, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.61 identity, inverse( X ) ) ), 'greatest_lower_bound'( identity, X ) ),
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ] )
% 119.18/119.61 , clause( 44183, [ =( 'greatest_lower_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( inverse( 'least_upper_bound'( identity, inverse( X )
% 119.18/119.61 ) ), 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 39019, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.61 identity, inverse( X ) ) ), 'greatest_lower_bound'( identity, X ) ),
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ] )
% 119.18/119.61 , clause( 44184, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.61 identity, inverse( X ) ) ), 'greatest_lower_bound'( identity, X ) ),
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44186, [ =( inverse( X ), multiply( 'least_upper_bound'( identity,
% 119.18/119.61 multiply( inverse( X ), Y ) ), inverse( 'least_upper_bound'( X, Y ) ) ) )
% 119.18/119.61 ] )
% 119.18/119.61 , clause( 1653, [ =( multiply( 'least_upper_bound'( identity, multiply(
% 119.18/119.61 inverse( X ), Y ) ), inverse( 'least_upper_bound'( X, Y ) ) ), inverse( X
% 119.18/119.61 ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44193, [ =( inverse( inverse( 'least_upper_bound'( identity,
% 119.18/119.61 inverse( X ) ) ) ), multiply( 'least_upper_bound'( identity, multiply(
% 119.18/119.61 inverse( inverse( 'least_upper_bound'( identity, inverse( X ) ) ) ),
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ), inverse(
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ) ) ] )
% 119.18/119.61 , clause( 39019, [ =( 'least_upper_bound'( inverse( 'least_upper_bound'(
% 119.18/119.61 identity, inverse( X ) ) ), 'greatest_lower_bound'( identity, X ) ),
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ] )
% 119.18/119.61 , 0, clause( 44186, [ =( inverse( X ), multiply( 'least_upper_bound'(
% 119.18/119.61 identity, multiply( inverse( X ), Y ) ), inverse( 'least_upper_bound'( X
% 119.18/119.61 , Y ) ) ) ) ] )
% 119.18/119.61 , 0, 21, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.61 inverse( 'least_upper_bound'( identity, inverse( X ) ) ) ), :=( Y,
% 119.18/119.61 'greatest_lower_bound'( identity, X ) )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44194, [ =( inverse( inverse( 'least_upper_bound'( identity,
% 119.18/119.61 inverse( X ) ) ) ), 'least_upper_bound'( multiply( identity, inverse(
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ), inverse( inverse(
% 119.18/119.61 'least_upper_bound'( identity, inverse( X ) ) ) ) ) ) ] )
% 119.18/119.61 , clause( 199, [ =( multiply( 'least_upper_bound'( Z, multiply( X, Y ) ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( multiply( Z, inverse( Y ) ), X ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , 0, clause( 44193, [ =( inverse( inverse( 'least_upper_bound'( identity,
% 119.18/119.61 inverse( X ) ) ) ), multiply( 'least_upper_bound'( identity, multiply(
% 119.18/119.61 inverse( inverse( 'least_upper_bound'( identity, inverse( X ) ) ) ),
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ), inverse(
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ) ) ] )
% 119.18/119.61 , 0, 7, substitution( 0, [ :=( X, inverse( inverse( 'least_upper_bound'(
% 119.18/119.61 identity, inverse( X ) ) ) ) ), :=( Y, 'greatest_lower_bound'( identity,
% 119.18/119.61 X ) ), :=( Z, identity )] ), substitution( 1, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44195, [ =( inverse( inverse( 'least_upper_bound'( identity,
% 119.18/119.61 inverse( X ) ) ) ), 'least_upper_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.61 identity, X ) ), inverse( inverse( 'least_upper_bound'( identity, inverse(
% 119.18/119.61 X ) ) ) ) ) ) ] )
% 119.18/119.61 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.61 , 0, clause( 44194, [ =( inverse( inverse( 'least_upper_bound'( identity,
% 119.18/119.61 inverse( X ) ) ) ), 'least_upper_bound'( multiply( identity, inverse(
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ), inverse( inverse(
% 119.18/119.61 'least_upper_bound'( identity, inverse( X ) ) ) ) ) ) ] )
% 119.18/119.61 , 0, 8, substitution( 0, [ :=( X, inverse( 'greatest_lower_bound'( identity
% 119.18/119.61 , X ) ) )] ), substitution( 1, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44197, [ =( inverse( inverse( 'least_upper_bound'( identity,
% 119.18/119.61 inverse( X ) ) ) ), 'least_upper_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.61 identity, X ) ), 'least_upper_bound'( identity, inverse( X ) ) ) ) ] )
% 119.18/119.61 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.61 , 0, clause( 44195, [ =( inverse( inverse( 'least_upper_bound'( identity,
% 119.18/119.61 inverse( X ) ) ) ), 'least_upper_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.61 identity, X ) ), inverse( inverse( 'least_upper_bound'( identity, inverse(
% 119.18/119.61 X ) ) ) ) ) ) ] )
% 119.18/119.61 , 0, 12, substitution( 0, [ :=( X, 'least_upper_bound'( identity, inverse(
% 119.18/119.61 X ) ) )] ), substitution( 1, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44198, [ =( 'least_upper_bound'( identity, inverse( X ) ),
% 119.18/119.61 'least_upper_bound'( inverse( 'greatest_lower_bound'( identity, X ) ),
% 119.18/119.61 'least_upper_bound'( identity, inverse( X ) ) ) ) ] )
% 119.18/119.61 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.61 , 0, clause( 44197, [ =( inverse( inverse( 'least_upper_bound'( identity,
% 119.18/119.61 inverse( X ) ) ) ), 'least_upper_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.61 identity, X ) ), 'least_upper_bound'( identity, inverse( X ) ) ) ) ] )
% 119.18/119.61 , 0, 1, substitution( 0, [ :=( X, 'least_upper_bound'( identity, inverse( X
% 119.18/119.61 ) ) )] ), substitution( 1, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44203, [ =( 'least_upper_bound'( identity, inverse( X ) ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.61 identity, X ) ), identity ), inverse( X ) ) ) ] )
% 119.18/119.61 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.61 , 0, clause( 44198, [ =( 'least_upper_bound'( identity, inverse( X ) ),
% 119.18/119.61 'least_upper_bound'( inverse( 'greatest_lower_bound'( identity, X ) ),
% 119.18/119.61 'least_upper_bound'( identity, inverse( X ) ) ) ) ] )
% 119.18/119.61 , 0, 5, substitution( 0, [ :=( X, inverse( 'greatest_lower_bound'( identity
% 119.18/119.61 , X ) ) ), :=( Y, identity ), :=( Z, inverse( X ) )] ), substitution( 1
% 119.18/119.61 , [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44204, [ =( 'least_upper_bound'( identity, inverse( X ) ),
% 119.18/119.61 'least_upper_bound'( inverse( 'greatest_lower_bound'( identity, X ) ),
% 119.18/119.61 inverse( X ) ) ) ] )
% 119.18/119.61 , clause( 597, [ =( 'least_upper_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.61 identity, X ) ), identity ), inverse( 'greatest_lower_bound'( identity, X
% 119.18/119.61 ) ) ) ] )
% 119.18/119.61 , 0, clause( 44203, [ =( 'least_upper_bound'( identity, inverse( X ) ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.61 identity, X ) ), identity ), inverse( X ) ) ) ] )
% 119.18/119.61 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.61 ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44205, [ =( 'least_upper_bound'( identity, inverse( X ) ), inverse(
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , clause( 5025, [ =( 'least_upper_bound'( inverse( 'greatest_lower_bound'(
% 119.18/119.61 Y, X ) ), inverse( X ) ), inverse( 'greatest_lower_bound'( Y, X ) ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , 0, clause( 44204, [ =( 'least_upper_bound'( identity, inverse( X ) ),
% 119.18/119.61 'least_upper_bound'( inverse( 'greatest_lower_bound'( identity, X ) ),
% 119.18/119.61 inverse( X ) ) ) ] )
% 119.18/119.61 , 0, 5, substitution( 0, [ :=( X, X ), :=( Y, identity )] ), substitution(
% 119.18/119.61 1, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 39036, [ =( 'least_upper_bound'( identity, inverse( X ) ), inverse(
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , clause( 44205, [ =( 'least_upper_bound'( identity, inverse( X ) ),
% 119.18/119.61 inverse( 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44208, [ =( 'least_upper_bound'( Y, identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( 'least_upper_bound'( X, Y )
% 119.18/119.61 , inverse( X ) ), 'least_upper_bound'( identity, Y ) ) ) ] )
% 119.18/119.61 , clause( 35965, [ =( 'greatest_lower_bound'( 'least_upper_bound'(
% 119.18/119.61 'least_upper_bound'( Y, X ), inverse( Y ) ), 'least_upper_bound'(
% 119.18/119.61 identity, X ) ), 'least_upper_bound'( X, identity ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44211, [ =( 'least_upper_bound'( inverse( X ), identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.61 identity, inverse( X ) ), inverse( identity ) ), inverse(
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ) ) ] )
% 119.18/119.61 , clause( 39036, [ =( 'least_upper_bound'( identity, inverse( X ) ),
% 119.18/119.61 inverse( 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , 0, clause( 44208, [ =( 'least_upper_bound'( Y, identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( 'least_upper_bound'( X, Y )
% 119.18/119.61 , inverse( X ) ), 'least_upper_bound'( identity, Y ) ) ) ] )
% 119.18/119.61 , 0, 13, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.61 identity ), :=( Y, inverse( X ) )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44213, [ =( 'least_upper_bound'( inverse( X ), identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( inverse(
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ), inverse( identity ) ), inverse(
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ) ) ] )
% 119.18/119.61 , clause( 39036, [ =( 'least_upper_bound'( identity, inverse( X ) ),
% 119.18/119.61 inverse( 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , 0, clause( 44211, [ =( 'least_upper_bound'( inverse( X ), identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( 'least_upper_bound'(
% 119.18/119.61 identity, inverse( X ) ), inverse( identity ) ), inverse(
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ) ) ] )
% 119.18/119.61 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.61 ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44214, [ =( 'least_upper_bound'( inverse( X ), identity ), inverse(
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , clause( 19, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 119.18/119.61 , X ) ] )
% 119.18/119.61 , 0, clause( 44213, [ =( 'least_upper_bound'( inverse( X ), identity ),
% 119.18/119.61 'greatest_lower_bound'( 'least_upper_bound'( inverse(
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ), inverse( identity ) ), inverse(
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ) ) ] )
% 119.18/119.61 , 0, 5, substitution( 0, [ :=( X, inverse( 'greatest_lower_bound'( identity
% 119.18/119.61 , X ) ) ), :=( Y, inverse( identity ) )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.61 ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 39103, [ =( 'least_upper_bound'( inverse( X ), identity ), inverse(
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , clause( 44214, [ =( 'least_upper_bound'( inverse( X ), identity ),
% 119.18/119.61 inverse( 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44217, [ =( Y, multiply( inverse( 'least_upper_bound'( X, inverse(
% 119.18/119.61 Y ) ) ), 'least_upper_bound'( identity, multiply( X, Y ) ) ) ) ] )
% 119.18/119.61 , clause( 12242, [ =( multiply( inverse( 'least_upper_bound'( X, inverse( Y
% 119.18/119.61 ) ) ), 'least_upper_bound'( identity, multiply( X, Y ) ) ), Y ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44220, [ =( X, multiply( inverse( inverse( 'greatest_lower_bound'(
% 119.18/119.61 identity, X ) ) ), 'least_upper_bound'( identity, multiply( identity, X )
% 119.18/119.61 ) ) ) ] )
% 119.18/119.61 , clause( 39036, [ =( 'least_upper_bound'( identity, inverse( X ) ),
% 119.18/119.61 inverse( 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , 0, clause( 44217, [ =( Y, multiply( inverse( 'least_upper_bound'( X,
% 119.18/119.61 inverse( Y ) ) ), 'least_upper_bound'( identity, multiply( X, Y ) ) ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.61 identity ), :=( Y, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44221, [ =( X, multiply( 'greatest_lower_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( identity, multiply( identity, X ) ) ) ) ] )
% 119.18/119.61 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.61 , 0, clause( 44220, [ =( X, multiply( inverse( inverse(
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ), 'least_upper_bound'( identity
% 119.18/119.61 , multiply( identity, X ) ) ) ) ] )
% 119.18/119.61 , 0, 3, substitution( 0, [ :=( X, 'greatest_lower_bound'( identity, X ) )] )
% 119.18/119.61 , substitution( 1, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44222, [ =( X, multiply( 'greatest_lower_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.61 , 0, clause( 44221, [ =( X, multiply( 'greatest_lower_bound'( identity, X )
% 119.18/119.61 , 'least_upper_bound'( identity, multiply( identity, X ) ) ) ) ] )
% 119.18/119.61 , 0, 8, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.61 ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44223, [ =( multiply( 'greatest_lower_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( identity, X ) ), X ) ] )
% 119.18/119.61 , clause( 44222, [ =( X, multiply( 'greatest_lower_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 39147, [ =( multiply( 'greatest_lower_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( identity, X ) ), X ) ] )
% 119.18/119.61 , clause( 44223, [ =( multiply( 'greatest_lower_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( identity, X ) ), X ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44225, [ =( 'least_upper_bound'( multiply( X, Y ), inverse( Z ) ),
% 119.18/119.61 multiply( X, 'least_upper_bound'( Y, inverse( multiply( Z, X ) ) ) ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , clause( 215, [ =( multiply( X, 'least_upper_bound'( Z, inverse( multiply(
% 119.18/119.61 Y, X ) ) ) ), 'least_upper_bound'( multiply( X, Z ), inverse( Y ) ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44228, [ =( 'least_upper_bound'( multiply( X, identity ), inverse(
% 119.18/119.61 Y ) ), multiply( X, inverse( 'greatest_lower_bound'( identity, multiply(
% 119.18/119.61 Y, X ) ) ) ) ) ] )
% 119.18/119.61 , clause( 39036, [ =( 'least_upper_bound'( identity, inverse( X ) ),
% 119.18/119.61 inverse( 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , 0, clause( 44225, [ =( 'least_upper_bound'( multiply( X, Y ), inverse( Z
% 119.18/119.61 ) ), multiply( X, 'least_upper_bound'( Y, inverse( multiply( Z, X ) ) )
% 119.18/119.61 ) ) ] )
% 119.18/119.61 , 0, 9, substitution( 0, [ :=( X, multiply( Y, X ) )] ), substitution( 1, [
% 119.18/119.61 :=( X, X ), :=( Y, identity ), :=( Z, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44229, [ =( 'least_upper_bound'( multiply( X, identity ), inverse(
% 119.18/119.61 Y ) ), inverse( 'greatest_lower_bound'( inverse( X ), Y ) ) ) ] )
% 119.18/119.61 , clause( 4181, [ =( multiply( X, inverse( 'greatest_lower_bound'( identity
% 119.18/119.61 , multiply( Y, X ) ) ) ), inverse( 'greatest_lower_bound'( inverse( X ),
% 119.18/119.61 Y ) ) ) ] )
% 119.18/119.61 , 0, clause( 44228, [ =( 'least_upper_bound'( multiply( X, identity ),
% 119.18/119.61 inverse( Y ) ), multiply( X, inverse( 'greatest_lower_bound'( identity,
% 119.18/119.61 multiply( Y, X ) ) ) ) ) ] )
% 119.18/119.61 , 0, 7, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.61 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44230, [ =( 'least_upper_bound'( X, inverse( Y ) ), inverse(
% 119.18/119.61 'greatest_lower_bound'( inverse( X ), Y ) ) ) ] )
% 119.18/119.61 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.61 , 0, clause( 44229, [ =( 'least_upper_bound'( multiply( X, identity ),
% 119.18/119.61 inverse( Y ) ), inverse( 'greatest_lower_bound'( inverse( X ), Y ) ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , 0, 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.61 :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44231, [ =( inverse( 'greatest_lower_bound'( inverse( X ), Y ) ),
% 119.18/119.61 'least_upper_bound'( X, inverse( Y ) ) ) ] )
% 119.18/119.61 , clause( 44230, [ =( 'least_upper_bound'( X, inverse( Y ) ), inverse(
% 119.18/119.61 'greatest_lower_bound'( inverse( X ), Y ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 39167, [ =( inverse( 'greatest_lower_bound'( inverse( Y ), X ) ),
% 119.18/119.61 'least_upper_bound'( Y, inverse( X ) ) ) ] )
% 119.18/119.61 , clause( 44231, [ =( inverse( 'greatest_lower_bound'( inverse( X ), Y ) )
% 119.18/119.61 , 'least_upper_bound'( X, inverse( Y ) ) ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.61 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44233, [ =( inverse( 'greatest_lower_bound'( identity, X ) ),
% 119.18/119.61 'least_upper_bound'( identity, inverse( X ) ) ) ] )
% 119.18/119.61 , clause( 39036, [ =( 'least_upper_bound'( identity, inverse( X ) ),
% 119.18/119.61 inverse( 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44234, [ =( inverse( 'greatest_lower_bound'( identity, multiply( X
% 119.18/119.61 , inverse( Y ) ) ) ), 'least_upper_bound'( identity, multiply( Y, inverse(
% 119.18/119.61 X ) ) ) ) ] )
% 119.18/119.61 , clause( 211, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 119.18/119.61 inverse( X ) ) ) ] )
% 119.18/119.61 , 0, clause( 44233, [ =( inverse( 'greatest_lower_bound'( identity, X ) ),
% 119.18/119.61 'least_upper_bound'( identity, inverse( X ) ) ) ] )
% 119.18/119.61 , 0, 10, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.61 :=( X, multiply( X, inverse( Y ) ) )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 39178, [ =( inverse( 'greatest_lower_bound'( identity, multiply( X
% 119.18/119.61 , inverse( Y ) ) ) ), 'least_upper_bound'( identity, multiply( Y, inverse(
% 119.18/119.61 X ) ) ) ) ] )
% 119.18/119.61 , clause( 44234, [ =( inverse( 'greatest_lower_bound'( identity, multiply(
% 119.18/119.61 X, inverse( Y ) ) ) ), 'least_upper_bound'( identity, multiply( Y,
% 119.18/119.61 inverse( X ) ) ) ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.61 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44237, [ =( 'greatest_lower_bound'( inverse( Y ), identity ),
% 119.18/119.61 multiply( inverse( multiply( X, Y ) ), 'greatest_lower_bound'( X,
% 119.18/119.61 multiply( X, Y ) ) ) ) ] )
% 119.18/119.61 , clause( 2294, [ =( multiply( inverse( multiply( X, Y ) ),
% 119.18/119.61 'greatest_lower_bound'( X, multiply( X, Y ) ) ), 'greatest_lower_bound'(
% 119.18/119.61 inverse( Y ), identity ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44242, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.61 identity, X ) ), identity ), multiply( inverse( multiply(
% 119.18/119.61 'greatest_lower_bound'( identity, X ), 'least_upper_bound'( identity, X )
% 119.18/119.61 ) ), 'greatest_lower_bound'( 'greatest_lower_bound'( identity, X ), X )
% 119.18/119.61 ) ) ] )
% 119.18/119.61 , clause( 39147, [ =( multiply( 'greatest_lower_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( identity, X ) ), X ) ] )
% 119.18/119.61 , 0, clause( 44237, [ =( 'greatest_lower_bound'( inverse( Y ), identity ),
% 119.18/119.61 multiply( inverse( multiply( X, Y ) ), 'greatest_lower_bound'( X,
% 119.18/119.61 multiply( X, Y ) ) ) ) ] )
% 119.18/119.61 , 0, 20, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ), :=( Y, 'least_upper_bound'(
% 119.18/119.61 identity, X ) )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44243, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.61 identity, X ) ), identity ), multiply( inverse( X ),
% 119.18/119.61 'greatest_lower_bound'( 'greatest_lower_bound'( identity, X ), X ) ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , clause( 39147, [ =( multiply( 'greatest_lower_bound'( identity, X ),
% 119.18/119.61 'least_upper_bound'( identity, X ) ), X ) ] )
% 119.18/119.61 , 0, clause( 44242, [ =( 'greatest_lower_bound'( inverse(
% 119.18/119.61 'least_upper_bound'( identity, X ) ), identity ), multiply( inverse(
% 119.18/119.61 multiply( 'greatest_lower_bound'( identity, X ), 'least_upper_bound'(
% 119.18/119.61 identity, X ) ) ), 'greatest_lower_bound'( 'greatest_lower_bound'(
% 119.18/119.61 identity, X ), X ) ) ) ] )
% 119.18/119.61 , 0, 9, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.61 ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44245, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.61 identity, X ) ), identity ), multiply( inverse( X ),
% 119.18/119.61 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , clause( 30, [ =( 'greatest_lower_bound'( 'greatest_lower_bound'( Y, X ),
% 119.18/119.61 X ), 'greatest_lower_bound'( Y, X ) ) ] )
% 119.18/119.61 , 0, clause( 44243, [ =( 'greatest_lower_bound'( inverse(
% 119.18/119.61 'least_upper_bound'( identity, X ) ), identity ), multiply( inverse( X )
% 119.18/119.61 , 'greatest_lower_bound'( 'greatest_lower_bound'( identity, X ), X ) ) )
% 119.18/119.61 ] )
% 119.18/119.61 , 0, 10, substitution( 0, [ :=( X, X ), :=( Y, identity )] ),
% 119.18/119.61 substitution( 1, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44246, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.61 identity, X ) ), identity ), 'greatest_lower_bound'( inverse( X ),
% 119.18/119.61 identity ) ) ] )
% 119.18/119.61 , clause( 528, [ =( multiply( inverse( Y ), 'greatest_lower_bound'(
% 119.18/119.61 identity, Y ) ), 'greatest_lower_bound'( inverse( Y ), identity ) ) ] )
% 119.18/119.61 , 0, clause( 44245, [ =( 'greatest_lower_bound'( inverse(
% 119.18/119.61 'least_upper_bound'( identity, X ) ), identity ), multiply( inverse( X )
% 119.18/119.61 , 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , 0, 7, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.61 :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44247, [ =( inverse( 'least_upper_bound'( identity, X ) ),
% 119.18/119.61 'greatest_lower_bound'( inverse( X ), identity ) ) ] )
% 119.18/119.61 , clause( 616, [ =( 'greatest_lower_bound'( inverse( 'least_upper_bound'(
% 119.18/119.61 identity, X ) ), identity ), inverse( 'least_upper_bound'( identity, X )
% 119.18/119.61 ) ) ] )
% 119.18/119.61 , 0, clause( 44246, [ =( 'greatest_lower_bound'( inverse(
% 119.18/119.61 'least_upper_bound'( identity, X ) ), identity ), 'greatest_lower_bound'(
% 119.18/119.61 inverse( X ), identity ) ) ] )
% 119.18/119.61 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 119.18/119.61 ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44248, [ =( 'greatest_lower_bound'( inverse( X ), identity ),
% 119.18/119.61 inverse( 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , clause( 44247, [ =( inverse( 'least_upper_bound'( identity, X ) ),
% 119.18/119.61 'greatest_lower_bound'( inverse( X ), identity ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 39226, [ =( 'greatest_lower_bound'( inverse( X ), identity ),
% 119.18/119.61 inverse( 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , clause( 44248, [ =( 'greatest_lower_bound'( inverse( X ), identity ),
% 119.18/119.61 inverse( 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44250, [ =( 'greatest_lower_bound'( inverse( Y ), multiply( X, Z )
% 119.18/119.61 ), multiply( X, 'greatest_lower_bound'( inverse( multiply( Y, X ) ), Z )
% 119.18/119.61 ) ) ] )
% 119.18/119.61 , clause( 212, [ =( multiply( X, 'greatest_lower_bound'( inverse( multiply(
% 119.18/119.61 Y, X ) ), Z ) ), 'greatest_lower_bound'( inverse( Y ), multiply( X, Z ) )
% 119.18/119.61 ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44253, [ =( 'greatest_lower_bound'( inverse( X ), multiply( Y,
% 119.18/119.61 identity ) ), multiply( Y, inverse( 'least_upper_bound'( identity,
% 119.18/119.61 multiply( X, Y ) ) ) ) ) ] )
% 119.18/119.61 , clause( 39226, [ =( 'greatest_lower_bound'( inverse( X ), identity ),
% 119.18/119.61 inverse( 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , 0, clause( 44250, [ =( 'greatest_lower_bound'( inverse( Y ), multiply( X
% 119.18/119.61 , Z ) ), multiply( X, 'greatest_lower_bound'( inverse( multiply( Y, X ) )
% 119.18/119.61 , Z ) ) ) ] )
% 119.18/119.61 , 0, 9, substitution( 0, [ :=( X, multiply( X, Y ) )] ), substitution( 1, [
% 119.18/119.61 :=( X, Y ), :=( Y, X ), :=( Z, identity )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44254, [ =( 'greatest_lower_bound'( inverse( X ), multiply( Y,
% 119.18/119.61 identity ) ), inverse( 'least_upper_bound'( inverse( Y ), X ) ) ) ] )
% 119.18/119.61 , clause( 3168, [ =( multiply( X, inverse( 'least_upper_bound'( identity,
% 119.18/119.61 multiply( Y, X ) ) ) ), inverse( 'least_upper_bound'( inverse( X ), Y ) )
% 119.18/119.61 ) ] )
% 119.18/119.61 , 0, clause( 44253, [ =( 'greatest_lower_bound'( inverse( X ), multiply( Y
% 119.18/119.61 , identity ) ), multiply( Y, inverse( 'least_upper_bound'( identity,
% 119.18/119.61 multiply( X, Y ) ) ) ) ) ] )
% 119.18/119.61 , 0, 7, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.61 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44255, [ =( 'greatest_lower_bound'( inverse( X ), Y ), inverse(
% 119.18/119.61 'least_upper_bound'( inverse( Y ), X ) ) ) ] )
% 119.18/119.61 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.61 , 0, clause( 44254, [ =( 'greatest_lower_bound'( inverse( X ), multiply( Y
% 119.18/119.61 , identity ) ), inverse( 'least_upper_bound'( inverse( Y ), X ) ) ) ] )
% 119.18/119.61 , 0, 4, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.61 :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44256, [ =( inverse( 'least_upper_bound'( inverse( Y ), X ) ),
% 119.18/119.61 'greatest_lower_bound'( inverse( X ), Y ) ) ] )
% 119.18/119.61 , clause( 44255, [ =( 'greatest_lower_bound'( inverse( X ), Y ), inverse(
% 119.18/119.61 'least_upper_bound'( inverse( Y ), X ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 39418, [ =( inverse( 'least_upper_bound'( inverse( Y ), X ) ),
% 119.18/119.61 'greatest_lower_bound'( inverse( X ), Y ) ) ] )
% 119.18/119.61 , clause( 44256, [ =( inverse( 'least_upper_bound'( inverse( Y ), X ) ),
% 119.18/119.61 'greatest_lower_bound'( inverse( X ), Y ) ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.61 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44259, [ =( multiply( inverse( X ), 'least_upper_bound'( identity,
% 119.18/119.61 X ) ), inverse( 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , clause( 39103, [ =( 'least_upper_bound'( inverse( X ), identity ),
% 119.18/119.61 inverse( 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , 0, clause( 770, [ =( multiply( inverse( Y ), 'least_upper_bound'(
% 119.18/119.61 identity, Y ) ), 'least_upper_bound'( inverse( Y ), identity ) ) ] )
% 119.18/119.61 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, Y ),
% 119.18/119.61 :=( Y, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 39707, [ =( multiply( inverse( Y ), 'least_upper_bound'( identity,
% 119.18/119.61 Y ) ), inverse( 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 119.18/119.61 , clause( 44259, [ =( multiply( inverse( X ), 'least_upper_bound'( identity
% 119.18/119.61 , X ) ), inverse( 'greatest_lower_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, Y )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44264, [ =( multiply( multiply( 'greatest_lower_bound'( inverse( Y
% 119.18/119.61 ), X ), Y ), 'least_upper_bound'( inverse( Y ), X ) ), X ) ] )
% 119.18/119.61 , clause( 39418, [ =( inverse( 'least_upper_bound'( inverse( Y ), X ) ),
% 119.18/119.61 'greatest_lower_bound'( inverse( X ), Y ) ) ] )
% 119.18/119.61 , 0, clause( 32636, [ =( multiply( multiply( inverse( 'least_upper_bound'(
% 119.18/119.61 inverse( Y ), X ) ), X ), 'least_upper_bound'( inverse( X ), Y ) ), Y ) ]
% 119.18/119.61 )
% 119.18/119.61 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.61 :=( X, Y ), :=( Y, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44265, [ =( multiply( 'greatest_lower_bound'( identity, multiply( Y
% 119.18/119.61 , X ) ), 'least_upper_bound'( inverse( X ), Y ) ), Y ) ] )
% 119.18/119.61 , clause( 151, [ =( multiply( 'greatest_lower_bound'( inverse( X ), Y ), X
% 119.18/119.61 ), 'greatest_lower_bound'( identity, multiply( Y, X ) ) ) ] )
% 119.18/119.61 , 0, clause( 44264, [ =( multiply( multiply( 'greatest_lower_bound'(
% 119.18/119.61 inverse( Y ), X ), Y ), 'least_upper_bound'( inverse( Y ), X ) ), X ) ]
% 119.18/119.61 )
% 119.18/119.61 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.61 :=( X, Y ), :=( Y, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 40349, [ =( multiply( 'greatest_lower_bound'( identity, multiply( Y
% 119.18/119.61 , X ) ), 'least_upper_bound'( inverse( X ), Y ) ), Y ) ] )
% 119.18/119.61 , clause( 44265, [ =( multiply( 'greatest_lower_bound'( identity, multiply(
% 119.18/119.61 Y, X ) ), 'least_upper_bound'( inverse( X ), Y ) ), Y ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.61 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44268, [ =( 'least_upper_bound'( X, inverse( Y ) ), inverse(
% 119.18/119.61 'greatest_lower_bound'( inverse( X ), Y ) ) ) ] )
% 119.18/119.61 , clause( 39167, [ =( inverse( 'greatest_lower_bound'( inverse( Y ), X ) )
% 119.18/119.61 , 'least_upper_bound'( Y, inverse( X ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44274, [ =( 'least_upper_bound'( multiply( X, inverse( Y ) ),
% 119.18/119.61 inverse( Z ) ), inverse( 'greatest_lower_bound'( multiply( Y, inverse( X
% 119.18/119.61 ) ), Z ) ) ) ] )
% 119.18/119.61 , clause( 211, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 119.18/119.61 inverse( X ) ) ) ] )
% 119.18/119.61 , 0, clause( 44268, [ =( 'least_upper_bound'( X, inverse( Y ) ), inverse(
% 119.18/119.61 'greatest_lower_bound'( inverse( X ), Y ) ) ) ] )
% 119.18/119.61 , 0, 10, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.61 :=( X, multiply( X, inverse( Y ) ) ), :=( Y, Z )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 40873, [ =( 'least_upper_bound'( multiply( X, inverse( Y ) ),
% 119.18/119.61 inverse( Z ) ), inverse( 'greatest_lower_bound'( multiply( Y, inverse( X
% 119.18/119.61 ) ), Z ) ) ) ] )
% 119.18/119.61 , clause( 44274, [ =( 'least_upper_bound'( multiply( X, inverse( Y ) ),
% 119.18/119.61 inverse( Z ) ), inverse( 'greatest_lower_bound'( multiply( Y, inverse( X
% 119.18/119.61 ) ), Z ) ) ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 119.18/119.61 permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44278, [ =( inverse( 'greatest_lower_bound'( identity, X ) ),
% 119.18/119.61 multiply( inverse( X ), 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , clause( 39707, [ =( multiply( inverse( Y ), 'least_upper_bound'( identity
% 119.18/119.61 , Y ) ), inverse( 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44289, [ =( inverse( 'greatest_lower_bound'( identity, multiply( X
% 119.18/119.61 , inverse( 'least_upper_bound'( Y, multiply( inverse( identity ), X ) ) )
% 119.18/119.61 ) ) ), multiply( inverse( multiply( X, inverse( 'least_upper_bound'( Y,
% 119.18/119.61 multiply( inverse( identity ), X ) ) ) ) ), identity ) ) ] )
% 119.18/119.61 , clause( 33848, [ =( 'least_upper_bound'( Y, multiply( X, inverse(
% 119.18/119.61 'least_upper_bound'( Z, multiply( inverse( Y ), X ) ) ) ) ), Y ) ] )
% 119.18/119.61 , 0, clause( 44278, [ =( inverse( 'greatest_lower_bound'( identity, X ) ),
% 119.18/119.61 multiply( inverse( X ), 'least_upper_bound'( identity, X ) ) ) ] )
% 119.18/119.61 , 0, 24, substitution( 0, [ :=( X, X ), :=( Y, identity ), :=( Z, Y )] ),
% 119.18/119.61 substitution( 1, [ :=( X, multiply( X, inverse( 'least_upper_bound'( Y,
% 119.18/119.61 multiply( inverse( identity ), X ) ) ) ) )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44290, [ =( inverse( 'greatest_lower_bound'( identity, multiply( X
% 119.18/119.61 , inverse( 'least_upper_bound'( Y, multiply( inverse( identity ), X ) ) )
% 119.18/119.61 ) ) ), inverse( multiply( X, inverse( 'least_upper_bound'( Y, multiply(
% 119.18/119.61 inverse( identity ), X ) ) ) ) ) ) ] )
% 119.18/119.61 , clause( 174, [ =( multiply( X, identity ), X ) ] )
% 119.18/119.61 , 0, clause( 44289, [ =( inverse( 'greatest_lower_bound'( identity,
% 119.18/119.61 multiply( X, inverse( 'least_upper_bound'( Y, multiply( inverse( identity
% 119.18/119.61 ), X ) ) ) ) ) ), multiply( inverse( multiply( X, inverse(
% 119.18/119.61 'least_upper_bound'( Y, multiply( inverse( identity ), X ) ) ) ) ),
% 119.18/119.61 identity ) ) ] )
% 119.18/119.61 , 0, 13, substitution( 0, [ :=( X, inverse( multiply( X, inverse(
% 119.18/119.61 'least_upper_bound'( Y, multiply( inverse( identity ), X ) ) ) ) ) )] ),
% 119.18/119.61 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44291, [ =( inverse( 'greatest_lower_bound'( identity, multiply( X
% 119.18/119.61 , inverse( 'least_upper_bound'( Y, multiply( inverse( identity ), X ) ) )
% 119.18/119.61 ) ) ), multiply( 'least_upper_bound'( Y, multiply( inverse( identity ),
% 119.18/119.61 X ) ), inverse( X ) ) ) ] )
% 119.18/119.61 , clause( 211, [ =( inverse( multiply( X, inverse( Y ) ) ), multiply( Y,
% 119.18/119.61 inverse( X ) ) ) ] )
% 119.18/119.61 , 0, clause( 44290, [ =( inverse( 'greatest_lower_bound'( identity,
% 119.18/119.61 multiply( X, inverse( 'least_upper_bound'( Y, multiply( inverse( identity
% 119.18/119.61 ), X ) ) ) ) ) ), inverse( multiply( X, inverse( 'least_upper_bound'( Y
% 119.18/119.61 , multiply( inverse( identity ), X ) ) ) ) ) ) ] )
% 119.18/119.61 , 0, 13, substitution( 0, [ :=( X, X ), :=( Y, 'least_upper_bound'( Y,
% 119.18/119.61 multiply( inverse( identity ), X ) ) )] ), substitution( 1, [ :=( X, X )
% 119.18/119.61 , :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44292, [ =( inverse( 'greatest_lower_bound'( identity, multiply( X
% 119.18/119.61 , inverse( 'least_upper_bound'( Y, multiply( inverse( identity ), X ) ) )
% 119.18/119.61 ) ) ), 'least_upper_bound'( multiply( Y, inverse( X ) ), inverse(
% 119.18/119.61 identity ) ) ) ] )
% 119.18/119.61 , clause( 199, [ =( multiply( 'least_upper_bound'( Z, multiply( X, Y ) ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( multiply( Z, inverse( Y ) ), X ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , 0, clause( 44291, [ =( inverse( 'greatest_lower_bound'( identity,
% 119.18/119.61 multiply( X, inverse( 'least_upper_bound'( Y, multiply( inverse( identity
% 119.18/119.61 ), X ) ) ) ) ) ), multiply( 'least_upper_bound'( Y, multiply( inverse(
% 119.18/119.61 identity ), X ) ), inverse( X ) ) ) ] )
% 119.18/119.61 , 0, 13, substitution( 0, [ :=( X, inverse( identity ) ), :=( Y, X ), :=( Z
% 119.18/119.61 , Y )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44293, [ =( inverse( 'greatest_lower_bound'( identity, multiply( X
% 119.18/119.61 , inverse( 'least_upper_bound'( Y, multiply( inverse( identity ), X ) ) )
% 119.18/119.61 ) ) ), inverse( 'greatest_lower_bound'( multiply( X, inverse( Y ) ),
% 119.18/119.61 identity ) ) ) ] )
% 119.18/119.61 , clause( 40873, [ =( 'least_upper_bound'( multiply( X, inverse( Y ) ),
% 119.18/119.61 inverse( Z ) ), inverse( 'greatest_lower_bound'( multiply( Y, inverse( X
% 119.18/119.61 ) ), Z ) ) ) ] )
% 119.18/119.61 , 0, clause( 44292, [ =( inverse( 'greatest_lower_bound'( identity,
% 119.18/119.61 multiply( X, inverse( 'least_upper_bound'( Y, multiply( inverse( identity
% 119.18/119.61 ), X ) ) ) ) ) ), 'least_upper_bound'( multiply( Y, inverse( X ) ),
% 119.18/119.61 inverse( identity ) ) ) ] )
% 119.18/119.61 , 0, 13, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, identity )] ),
% 119.18/119.61 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44294, [ =( 'least_upper_bound'( identity, multiply(
% 119.18/119.61 'least_upper_bound'( Y, multiply( inverse( identity ), X ) ), inverse( X
% 119.18/119.61 ) ) ), inverse( 'greatest_lower_bound'( multiply( X, inverse( Y ) ),
% 119.18/119.61 identity ) ) ) ] )
% 119.18/119.61 , clause( 39178, [ =( inverse( 'greatest_lower_bound'( identity, multiply(
% 119.18/119.61 X, inverse( Y ) ) ) ), 'least_upper_bound'( identity, multiply( Y,
% 119.18/119.61 inverse( X ) ) ) ) ] )
% 119.18/119.61 , 0, clause( 44293, [ =( inverse( 'greatest_lower_bound'( identity,
% 119.18/119.61 multiply( X, inverse( 'least_upper_bound'( Y, multiply( inverse( identity
% 119.18/119.61 ), X ) ) ) ) ) ), inverse( 'greatest_lower_bound'( multiply( X, inverse(
% 119.18/119.61 Y ) ), identity ) ) ) ] )
% 119.18/119.61 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, 'least_upper_bound'( Y,
% 119.18/119.61 multiply( inverse( identity ), X ) ) )] ), substitution( 1, [ :=( X, X )
% 119.18/119.61 , :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44295, [ =( 'least_upper_bound'( identity, 'least_upper_bound'(
% 119.18/119.61 multiply( X, inverse( Y ) ), inverse( identity ) ) ), inverse(
% 119.18/119.61 'greatest_lower_bound'( multiply( Y, inverse( X ) ), identity ) ) ) ] )
% 119.18/119.61 , clause( 199, [ =( multiply( 'least_upper_bound'( Z, multiply( X, Y ) ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( multiply( Z, inverse( Y ) ), X ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , 0, clause( 44294, [ =( 'least_upper_bound'( identity, multiply(
% 119.18/119.61 'least_upper_bound'( Y, multiply( inverse( identity ), X ) ), inverse( X
% 119.18/119.61 ) ) ), inverse( 'greatest_lower_bound'( multiply( X, inverse( Y ) ),
% 119.18/119.61 identity ) ) ) ] )
% 119.18/119.61 , 0, 3, substitution( 0, [ :=( X, inverse( identity ) ), :=( Y, Y ), :=( Z
% 119.18/119.61 , X )] ), substitution( 1, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44296, [ =( 'least_upper_bound'( 'least_upper_bound'( identity,
% 119.18/119.61 multiply( X, inverse( Y ) ) ), inverse( identity ) ), inverse(
% 119.18/119.61 'greatest_lower_bound'( multiply( Y, inverse( X ) ), identity ) ) ) ] )
% 119.18/119.61 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.61 , 0, clause( 44295, [ =( 'least_upper_bound'( identity, 'least_upper_bound'(
% 119.18/119.61 multiply( X, inverse( Y ) ), inverse( identity ) ) ), inverse(
% 119.18/119.61 'greatest_lower_bound'( multiply( Y, inverse( X ) ), identity ) ) ) ] )
% 119.18/119.61 , 0, 1, substitution( 0, [ :=( X, identity ), :=( Y, multiply( X, inverse(
% 119.18/119.61 Y ) ) ), :=( Z, inverse( identity ) )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.61 :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44297, [ =( 'least_upper_bound'( 'least_upper_bound'( identity,
% 119.18/119.61 multiply( X, inverse( Y ) ) ), identity ), inverse(
% 119.18/119.61 'greatest_lower_bound'( multiply( Y, inverse( X ) ), identity ) ) ) ] )
% 119.18/119.61 , clause( 160, [ =( inverse( identity ), identity ) ] )
% 119.18/119.61 , 0, clause( 44296, [ =( 'least_upper_bound'( 'least_upper_bound'( identity
% 119.18/119.61 , multiply( X, inverse( Y ) ) ), inverse( identity ) ), inverse(
% 119.18/119.61 'greatest_lower_bound'( multiply( Y, inverse( X ) ), identity ) ) ) ] )
% 119.18/119.61 , 0, 8, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 119.18/119.61 ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44298, [ =( 'least_upper_bound'( identity, multiply( X, inverse( Y
% 119.18/119.61 ) ) ), inverse( 'greatest_lower_bound'( multiply( Y, inverse( X ) ),
% 119.18/119.61 identity ) ) ) ] )
% 119.18/119.61 , clause( 35, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 119.18/119.61 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.61 , 0, clause( 44297, [ =( 'least_upper_bound'( 'least_upper_bound'( identity
% 119.18/119.61 , multiply( X, inverse( Y ) ) ), identity ), inverse(
% 119.18/119.61 'greatest_lower_bound'( multiply( Y, inverse( X ) ), identity ) ) ) ] )
% 119.18/119.61 , 0, 1, substitution( 0, [ :=( X, identity ), :=( Y, multiply( X, inverse(
% 119.18/119.61 Y ) ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44299, [ =( inverse( 'greatest_lower_bound'( multiply( Y, inverse(
% 119.18/119.61 X ) ), identity ) ), 'least_upper_bound'( identity, multiply( X, inverse(
% 119.18/119.61 Y ) ) ) ) ] )
% 119.18/119.61 , clause( 44298, [ =( 'least_upper_bound'( identity, multiply( X, inverse(
% 119.18/119.61 Y ) ) ), inverse( 'greatest_lower_bound'( multiply( Y, inverse( X ) ),
% 119.18/119.61 identity ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 41720, [ =( inverse( 'greatest_lower_bound'( multiply( X, inverse(
% 119.18/119.61 Y ) ), identity ) ), 'least_upper_bound'( identity, multiply( Y, inverse(
% 119.18/119.61 X ) ) ) ) ] )
% 119.18/119.61 , clause( 44299, [ =( inverse( 'greatest_lower_bound'( multiply( Y, inverse(
% 119.18/119.61 X ) ), identity ) ), 'least_upper_bound'( identity, multiply( X, inverse(
% 119.18/119.61 Y ) ) ) ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.61 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44301, [ =( X, multiply( 'greatest_lower_bound'( identity, multiply(
% 119.18/119.61 X, Y ) ), 'least_upper_bound'( inverse( Y ), X ) ) ) ] )
% 119.18/119.61 , clause( 40349, [ =( multiply( 'greatest_lower_bound'( identity, multiply(
% 119.18/119.61 Y, X ) ), 'least_upper_bound'( inverse( X ), Y ) ), Y ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44309, [ =( X, multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( inverse( inverse( Y ) ), X ) ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , clause( 5181, [ =( 'greatest_lower_bound'( identity, multiply( Y, inverse(
% 119.18/119.61 X ) ) ), multiply( 'greatest_lower_bound'( Y, X ), inverse( X ) ) ) ] )
% 119.18/119.61 , 0, clause( 44301, [ =( X, multiply( 'greatest_lower_bound'( identity,
% 119.18/119.61 multiply( X, Y ) ), 'least_upper_bound'( inverse( Y ), X ) ) ) ] )
% 119.18/119.61 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.61 :=( X, X ), :=( Y, inverse( Y ) )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44310, [ =( X, multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.61 , clause( 181, [ =( inverse( inverse( X ) ), X ) ] )
% 119.18/119.61 , 0, clause( 44309, [ =( X, multiply( multiply( 'greatest_lower_bound'( X,
% 119.18/119.61 Y ), inverse( Y ) ), 'least_upper_bound'( inverse( inverse( Y ) ), X ) )
% 119.18/119.61 ) ] )
% 119.18/119.61 , 0, 10, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.61 :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44311, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( Y, X ) ), X ) ] )
% 119.18/119.61 , clause( 44310, [ =( X, multiply( multiply( 'greatest_lower_bound'( X, Y )
% 119.18/119.61 , inverse( Y ) ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 42447, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( Y, X ) ), X ) ] )
% 119.18/119.61 , clause( 44311, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( Y, X ) ), X ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.61 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44313, [ =( multiply( X, 'least_upper_bound'( multiply( X, Y ), Y )
% 119.18/119.61 ), multiply( multiply( 'least_upper_bound'( X, identity ), X ), Y ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , clause( 1314, [ =( multiply( multiply( 'least_upper_bound'( X, identity )
% 119.18/119.61 , X ), Y ), multiply( X, 'least_upper_bound'( multiply( X, Y ), Y ) ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44320, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( X, 'least_upper_bound'( Y, X ) ) ),
% 119.18/119.61 multiply( multiply( 'least_upper_bound'( multiply( 'greatest_lower_bound'(
% 119.18/119.61 X, Y ), inverse( Y ) ), identity ), multiply( 'greatest_lower_bound'( X,
% 119.18/119.61 Y ), inverse( Y ) ) ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.61 , clause( 42447, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( Y, X ) ), X ) ] )
% 119.18/119.61 , 0, clause( 44313, [ =( multiply( X, 'least_upper_bound'( multiply( X, Y )
% 119.18/119.61 , Y ) ), multiply( multiply( 'least_upper_bound'( X, identity ), X ), Y )
% 119.18/119.61 ) ] )
% 119.18/119.61 , 0, 9, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.61 :=( X, multiply( 'greatest_lower_bound'( X, Y ), inverse( Y ) ) ), :=( Y
% 119.18/119.61 , 'least_upper_bound'( Y, X ) )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44321, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( X, 'least_upper_bound'( Y, X ) ) ),
% 119.18/119.61 multiply( multiply( multiply( 'least_upper_bound'( multiply(
% 119.18/119.61 'greatest_lower_bound'( X, Y ), inverse( Y ) ), identity ),
% 119.18/119.61 'greatest_lower_bound'( X, Y ) ), inverse( Y ) ), 'least_upper_bound'( Y
% 119.18/119.61 , X ) ) ) ] )
% 119.18/119.61 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 119.18/119.61 ), Z ) ) ] )
% 119.18/119.61 , 0, clause( 44320, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y )
% 119.18/119.61 , inverse( Y ) ), 'least_upper_bound'( X, 'least_upper_bound'( Y, X ) ) )
% 119.18/119.61 , multiply( multiply( 'least_upper_bound'( multiply(
% 119.18/119.61 'greatest_lower_bound'( X, Y ), inverse( Y ) ), identity ), multiply(
% 119.18/119.61 'greatest_lower_bound'( X, Y ), inverse( Y ) ) ), 'least_upper_bound'( Y
% 119.18/119.61 , X ) ) ) ] )
% 119.18/119.61 , 0, 14, substitution( 0, [ :=( X, 'least_upper_bound'( multiply(
% 119.18/119.61 'greatest_lower_bound'( X, Y ), inverse( Y ) ), identity ) ), :=( Y,
% 119.18/119.61 'greatest_lower_bound'( X, Y ) ), :=( Z, inverse( Y ) )] ),
% 119.18/119.61 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44322, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( X, 'least_upper_bound'( Y, X ) ) ),
% 119.18/119.61 multiply( multiply( multiply( identity, 'greatest_lower_bound'( X, Y ) )
% 119.18/119.61 , inverse( Y ) ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.61 , clause( 4427, [ =( 'least_upper_bound'( multiply( 'greatest_lower_bound'(
% 119.18/119.61 Y, X ), inverse( X ) ), identity ), identity ) ] )
% 119.18/119.61 , 0, clause( 44321, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y )
% 119.18/119.61 , inverse( Y ) ), 'least_upper_bound'( X, 'least_upper_bound'( Y, X ) ) )
% 119.18/119.61 , multiply( multiply( multiply( 'least_upper_bound'( multiply(
% 119.18/119.61 'greatest_lower_bound'( X, Y ), inverse( Y ) ), identity ),
% 119.18/119.61 'greatest_lower_bound'( X, Y ) ), inverse( Y ) ), 'least_upper_bound'( Y
% 119.18/119.61 , X ) ) ) ] )
% 119.18/119.61 , 0, 16, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.61 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44323, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( X, 'least_upper_bound'( Y, X ) ) ),
% 119.18/119.61 multiply( multiply( 'greatest_lower_bound'( X, Y ), inverse( Y ) ),
% 119.18/119.61 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.61 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 119.18/119.61 , 0, clause( 44322, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y )
% 119.18/119.61 , inverse( Y ) ), 'least_upper_bound'( X, 'least_upper_bound'( Y, X ) ) )
% 119.18/119.61 , multiply( multiply( multiply( identity, 'greatest_lower_bound'( X, Y )
% 119.18/119.61 ), inverse( Y ) ), 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.61 , 0, 15, substitution( 0, [ :=( X, 'greatest_lower_bound'( X, Y ) )] ),
% 119.18/119.61 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44324, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( X, 'least_upper_bound'( Y, X ) ) ),
% 119.18/119.61 X ) ] )
% 119.18/119.61 , clause( 42447, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( Y, X ) ), X ) ] )
% 119.18/119.61 , 0, clause( 44323, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y )
% 119.18/119.61 , inverse( Y ) ), 'least_upper_bound'( X, 'least_upper_bound'( Y, X ) ) )
% 119.18/119.61 , multiply( multiply( 'greatest_lower_bound'( X, Y ), inverse( Y ) ),
% 119.18/119.61 'least_upper_bound'( Y, X ) ) ) ] )
% 119.18/119.61 , 0, 13, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.61 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44325, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ) ),
% 119.18/119.61 X ) ] )
% 119.18/119.61 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 119.18/119.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 119.18/119.61 , 0, clause( 44324, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y )
% 119.18/119.61 , inverse( Y ) ), 'least_upper_bound'( X, 'least_upper_bound'( Y, X ) ) )
% 119.18/119.61 , X ) ] )
% 119.18/119.61 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, X )] ),
% 119.18/119.61 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44326, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( X, Y ) ), X ) ] )
% 119.18/119.61 , clause( 35, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 119.18/119.61 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.61 , 0, clause( 44325, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y )
% 119.18/119.61 , inverse( Y ) ), 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ) )
% 119.18/119.61 , X ) ] )
% 119.18/119.61 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.61 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 42455, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( X, Y ) ), X ) ] )
% 119.18/119.61 , clause( 44326, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( X, Y ) ), X ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.61 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44328, [ =( X, multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.61 , clause( 42455, [ =( multiply( multiply( 'greatest_lower_bound'( X, Y ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( X, Y ) ), X ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44329, [ =( X, multiply( multiply( 'greatest_lower_bound'( Y, X ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.61 , clause( 230, [ =( multiply( multiply( 'greatest_lower_bound'( X, Z ), Y )
% 119.18/119.61 , T ), multiply( multiply( 'greatest_lower_bound'( Z, X ), Y ), T ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , 0, clause( 44328, [ =( X, multiply( multiply( 'greatest_lower_bound'( X,
% 119.18/119.61 Y ), inverse( Y ) ), 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.61 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, inverse( Y ) ), :=( Z, Y ),
% 119.18/119.61 :=( T, 'least_upper_bound'( X, Y ) )] ), substitution( 1, [ :=( X, X ),
% 119.18/119.61 :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44332, [ =( multiply( multiply( 'greatest_lower_bound'( Y, X ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( X, Y ) ), X ) ] )
% 119.18/119.61 , clause( 44329, [ =( X, multiply( multiply( 'greatest_lower_bound'( Y, X )
% 119.18/119.61 , inverse( Y ) ), 'least_upper_bound'( X, Y ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 42462, [ =( multiply( multiply( 'greatest_lower_bound'( Y, X ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( X, Y ) ), X ) ] )
% 119.18/119.61 , clause( 44332, [ =( multiply( multiply( 'greatest_lower_bound'( Y, X ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( X, Y ) ), X ) ] )
% 119.18/119.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.61 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44334, [ =( Y, multiply( inverse( 'greatest_lower_bound'( X,
% 119.18/119.61 identity ) ), 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ) ] )
% 119.18/119.61 , clause( 12414, [ =( multiply( inverse( 'greatest_lower_bound'( X,
% 119.18/119.61 identity ) ), 'greatest_lower_bound'( multiply( X, Y ), Y ) ), Y ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44338, [ =( 'least_upper_bound'( X, Y ), multiply( inverse(
% 119.18/119.61 'greatest_lower_bound'( multiply( 'greatest_lower_bound'( Y, X ), inverse(
% 119.18/119.61 Y ) ), identity ) ), 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 119.18/119.61 ) ) ) ) ] )
% 119.18/119.61 , clause( 42462, [ =( multiply( multiply( 'greatest_lower_bound'( Y, X ),
% 119.18/119.61 inverse( Y ) ), 'least_upper_bound'( X, Y ) ), X ) ] )
% 119.18/119.61 , 0, clause( 44334, [ =( Y, multiply( inverse( 'greatest_lower_bound'( X,
% 119.18/119.61 identity ) ), 'greatest_lower_bound'( multiply( X, Y ), Y ) ) ) ] )
% 119.18/119.61 , 0, 15, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.61 :=( X, multiply( 'greatest_lower_bound'( Y, X ), inverse( Y ) ) ), :=( Y
% 119.18/119.61 , 'least_upper_bound'( X, Y ) )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44339, [ =( 'least_upper_bound'( X, Y ), multiply(
% 119.18/119.61 'least_upper_bound'( identity, multiply( Y, inverse(
% 119.18/119.61 'greatest_lower_bound'( Y, X ) ) ) ), 'greatest_lower_bound'( X,
% 119.18/119.61 'least_upper_bound'( X, Y ) ) ) ) ] )
% 119.18/119.61 , clause( 41720, [ =( inverse( 'greatest_lower_bound'( multiply( X, inverse(
% 119.18/119.61 Y ) ), identity ) ), 'least_upper_bound'( identity, multiply( Y, inverse(
% 119.18/119.61 X ) ) ) ) ] )
% 119.18/119.61 , 0, clause( 44338, [ =( 'least_upper_bound'( X, Y ), multiply( inverse(
% 119.18/119.61 'greatest_lower_bound'( multiply( 'greatest_lower_bound'( Y, X ), inverse(
% 119.18/119.61 Y ) ), identity ) ), 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 119.18/119.61 ) ) ) ) ] )
% 119.18/119.61 , 0, 5, substitution( 0, [ :=( X, 'greatest_lower_bound'( Y, X ) ), :=( Y,
% 119.18/119.61 Y )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44340, [ =( 'least_upper_bound'( X, Y ), multiply( multiply( Y,
% 119.18/119.61 inverse( 'greatest_lower_bound'( Y, X ) ) ), 'greatest_lower_bound'( X,
% 119.18/119.61 'least_upper_bound'( X, Y ) ) ) ) ] )
% 119.18/119.61 , clause( 4369, [ =( 'least_upper_bound'( identity, multiply( X, inverse(
% 119.18/119.61 'greatest_lower_bound'( X, Y ) ) ) ), multiply( X, inverse(
% 119.18/119.61 'greatest_lower_bound'( X, Y ) ) ) ) ] )
% 119.18/119.61 , 0, clause( 44339, [ =( 'least_upper_bound'( X, Y ), multiply(
% 119.18/119.61 'least_upper_bound'( identity, multiply( Y, inverse(
% 119.18/119.61 'greatest_lower_bound'( Y, X ) ) ) ), 'greatest_lower_bound'( X,
% 119.18/119.61 'least_upper_bound'( X, Y ) ) ) ) ] )
% 119.18/119.61 , 0, 5, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 119.18/119.61 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44341, [ =( 'least_upper_bound'( X, Y ), multiply( multiply( Y,
% 119.18/119.61 inverse( 'greatest_lower_bound'( Y, X ) ) ), X ) ) ] )
% 119.18/119.61 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 119.18/119.61 , X ) ] )
% 119.18/119.61 , 0, clause( 44340, [ =( 'least_upper_bound'( X, Y ), multiply( multiply( Y
% 119.18/119.61 , inverse( 'greatest_lower_bound'( Y, X ) ) ), 'greatest_lower_bound'( X
% 119.18/119.61 , 'least_upper_bound'( X, Y ) ) ) ) ] )
% 119.18/119.61 , 0, 11, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 119.18/119.61 :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44342, [ =( multiply( multiply( Y, inverse( 'greatest_lower_bound'(
% 119.18/119.61 Y, X ) ) ), X ), 'least_upper_bound'( X, Y ) ) ] )
% 119.18/119.61 , clause( 44341, [ =( 'least_upper_bound'( X, Y ), multiply( multiply( Y,
% 119.18/119.61 inverse( 'greatest_lower_bound'( Y, X ) ) ), X ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 42464, [ =( multiply( multiply( X, inverse( 'greatest_lower_bound'(
% 119.18/119.61 X, Y ) ) ), Y ), 'least_upper_bound'( Y, X ) ) ] )
% 119.18/119.61 , clause( 44342, [ =( multiply( multiply( Y, inverse(
% 119.18/119.61 'greatest_lower_bound'( Y, X ) ) ), X ), 'least_upper_bound'( X, Y ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 119.18/119.61 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44344, [ ~( =( 'least_upper_bound'( a, b ), multiply( multiply( a,
% 119.18/119.61 inverse( 'greatest_lower_bound'( a, b ) ) ), b ) ) ) ] )
% 119.18/119.61 , clause( 15, [ ~( =( multiply( multiply( a, inverse(
% 119.18/119.61 'greatest_lower_bound'( a, b ) ) ), b ), 'least_upper_bound'( a, b ) ) )
% 119.18/119.61 ] )
% 119.18/119.61 , 0, substitution( 0, [] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44345, [ ~( =( 'least_upper_bound'( a, b ), 'least_upper_bound'( b
% 119.18/119.61 , a ) ) ) ] )
% 119.18/119.61 , clause( 42464, [ =( multiply( multiply( X, inverse(
% 119.18/119.61 'greatest_lower_bound'( X, Y ) ) ), Y ), 'least_upper_bound'( Y, X ) ) ]
% 119.18/119.61 )
% 119.18/119.61 , 0, clause( 44344, [ ~( =( 'least_upper_bound'( a, b ), multiply( multiply(
% 119.18/119.61 a, inverse( 'greatest_lower_bound'( a, b ) ) ), b ) ) ) ] )
% 119.18/119.61 , 0, 5, substitution( 0, [ :=( X, a ), :=( Y, b )] ), substitution( 1, [] )
% 119.18/119.61 ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 42638, [ ~( =( 'least_upper_bound'( a, b ), 'least_upper_bound'( b
% 119.18/119.61 , a ) ) ) ] )
% 119.18/119.61 , clause( 44345, [ ~( =( 'least_upper_bound'( a, b ), 'least_upper_bound'(
% 119.18/119.61 b, a ) ) ) ] )
% 119.18/119.61 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqswap(
% 119.18/119.61 clause( 44347, [ ~( =( 'least_upper_bound'( b, a ), 'least_upper_bound'( a
% 119.18/119.61 , b ) ) ) ] )
% 119.18/119.61 , clause( 42638, [ ~( =( 'least_upper_bound'( a, b ), 'least_upper_bound'(
% 119.18/119.61 b, a ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 paramod(
% 119.18/119.61 clause( 44349, [ ~( =( 'least_upper_bound'( b, a ), 'least_upper_bound'( b
% 119.18/119.61 , a ) ) ) ] )
% 119.18/119.61 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 119.18/119.61 ) ] )
% 119.18/119.61 , 0, clause( 44347, [ ~( =( 'least_upper_bound'( b, a ),
% 119.18/119.61 'least_upper_bound'( a, b ) ) ) ] )
% 119.18/119.61 , 0, 5, substitution( 0, [ :=( X, a ), :=( Y, b )] ), substitution( 1, [] )
% 119.18/119.61 ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 eqrefl(
% 119.18/119.61 clause( 44352, [] )
% 119.18/119.61 , clause( 44349, [ ~( =( 'least_upper_bound'( b, a ), 'least_upper_bound'(
% 119.18/119.61 b, a ) ) ) ] )
% 119.18/119.61 , 0, substitution( 0, [] )).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 subsumption(
% 119.18/119.61 clause( 42639, [] )
% 119.18/119.61 , clause( 44352, [] )
% 119.18/119.61 , substitution( 0, [] ), permutation( 0, [] ) ).
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 end.
% 119.18/119.61
% 119.18/119.61 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 119.18/119.61
% 119.18/119.61 Memory use:
% 119.18/119.61
% 119.18/119.61 space for terms: 612882
% 119.18/119.61 space for clauses: 4470702
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 clauses generated: 30802258
% 119.18/119.61 clauses kept: 42640
% 119.18/119.61 clauses selected: 7352
% 119.18/119.61 clauses deleted: 17270
% 119.18/119.61 clauses inuse deleted: 2260
% 119.18/119.61
% 119.18/119.61 subsentry: 1340157
% 119.18/119.61 literals s-matched: 1335559
% 119.18/119.61 literals matched: 1335051
% 119.18/119.61 full subsumption: 0
% 119.18/119.61
% 119.18/119.61 checksum: 123525017
% 119.18/119.61
% 119.18/119.61
% 119.18/119.61 Bliksem ended
%------------------------------------------------------------------------------