TSTP Solution File: GRP190-2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP190-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 07:36:02 EDT 2022
% Result : Unsatisfiable 0.88s 1.27s
% Output : Refutation 0.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP190-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.14 % Command : bliksem %s
% 0.15/0.35 % Computer : n018.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % DateTime : Mon Jun 13 15:46:42 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.88/1.27 *** allocated 10000 integers for termspace/termends
% 0.88/1.27 *** allocated 10000 integers for clauses
% 0.88/1.27 *** allocated 10000 integers for justifications
% 0.88/1.27 Bliksem 1.12
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 Automatic Strategy Selection
% 0.88/1.27
% 0.88/1.27 Clauses:
% 0.88/1.27 [
% 0.88/1.27 [ =( multiply( identity, X ), X ) ],
% 0.88/1.27 [ =( multiply( inverse( X ), X ), identity ) ],
% 0.88/1.27 [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply( Y, Z ) ) )
% 0.88/1.27 ],
% 0.88/1.27 [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, X ) ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ],
% 0.88/1.27 [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.88/1.27 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ],
% 0.88/1.27 [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 0.88/1.27 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ],
% 0.88/1.27 [ =( 'least_upper_bound'( X, X ), X ) ],
% 0.88/1.27 [ =( 'greatest_lower_bound'( X, X ), X ) ],
% 0.88/1.27 [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ), X ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), 'least_upper_bound'(
% 0.88/1.27 multiply( X, Y ), multiply( X, Z ) ) ) ],
% 0.88/1.27 [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.88/1.27 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ],
% 0.88/1.27 [ =( multiply( 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'(
% 0.88/1.27 multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 0.88/1.27 [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 0.88/1.27 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 0.88/1.27 [ =( 'least_upper_bound'( a, b ), a ) ],
% 0.88/1.27 [ ~( =( 'greatest_lower_bound'( inverse( a ), inverse( b ) ), inverse( a
% 0.88/1.27 ) ) ) ]
% 0.88/1.27 ] .
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 percentage equality = 1.000000, percentage horn = 1.000000
% 0.88/1.27 This is a pure equality problem
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 Options Used:
% 0.88/1.27
% 0.88/1.27 useres = 1
% 0.88/1.27 useparamod = 1
% 0.88/1.27 useeqrefl = 1
% 0.88/1.27 useeqfact = 1
% 0.88/1.27 usefactor = 1
% 0.88/1.27 usesimpsplitting = 0
% 0.88/1.27 usesimpdemod = 5
% 0.88/1.27 usesimpres = 3
% 0.88/1.27
% 0.88/1.27 resimpinuse = 1000
% 0.88/1.27 resimpclauses = 20000
% 0.88/1.27 substype = eqrewr
% 0.88/1.27 backwardsubs = 1
% 0.88/1.27 selectoldest = 5
% 0.88/1.27
% 0.88/1.27 litorderings [0] = split
% 0.88/1.27 litorderings [1] = extend the termordering, first sorting on arguments
% 0.88/1.27
% 0.88/1.27 termordering = kbo
% 0.88/1.27
% 0.88/1.27 litapriori = 0
% 0.88/1.27 termapriori = 1
% 0.88/1.27 litaposteriori = 0
% 0.88/1.27 termaposteriori = 0
% 0.88/1.27 demodaposteriori = 0
% 0.88/1.27 ordereqreflfact = 0
% 0.88/1.27
% 0.88/1.27 litselect = negord
% 0.88/1.27
% 0.88/1.27 maxweight = 15
% 0.88/1.27 maxdepth = 30000
% 0.88/1.27 maxlength = 115
% 0.88/1.27 maxnrvars = 195
% 0.88/1.27 excuselevel = 1
% 0.88/1.27 increasemaxweight = 1
% 0.88/1.27
% 0.88/1.27 maxselected = 10000000
% 0.88/1.27 maxnrclauses = 10000000
% 0.88/1.27
% 0.88/1.27 showgenerated = 0
% 0.88/1.27 showkept = 0
% 0.88/1.27 showselected = 0
% 0.88/1.27 showdeleted = 0
% 0.88/1.27 showresimp = 1
% 0.88/1.27 showstatus = 2000
% 0.88/1.27
% 0.88/1.27 prologoutput = 1
% 0.88/1.27 nrgoals = 5000000
% 0.88/1.27 totalproof = 1
% 0.88/1.27
% 0.88/1.27 Symbols occurring in the translation:
% 0.88/1.27
% 0.88/1.27 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.88/1.27 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.88/1.27 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.88/1.27 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.88/1.27 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.88/1.27 identity [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.88/1.27 multiply [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.88/1.27 inverse [42, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.88/1.27 'greatest_lower_bound' [45, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.88/1.27 'least_upper_bound' [46, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.88/1.27 a [47, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.88/1.27 b [48, 0] (w:1, o:14, a:1, s:1, b:0).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 Starting Search:
% 0.88/1.27
% 0.88/1.27 Resimplifying inuse:
% 0.88/1.27 Done
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 Intermediate Status:
% 0.88/1.27 Generated: 28020
% 0.88/1.27 Kept: 2009
% 0.88/1.27 Inuse: 244
% 0.88/1.27 Deleted: 18
% 0.88/1.27 Deletedinuse: 6
% 0.88/1.27
% 0.88/1.27 Resimplifying inuse:
% 0.88/1.27 Done
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 Bliksems!, er is een bewijs:
% 0.88/1.27 % SZS status Unsatisfiable
% 0.88/1.27 % SZS output start Refutation
% 0.88/1.27
% 0.88/1.27 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 0.88/1.27 , Z ) ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 0.88/1.27 X ) ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 0.88/1.27 ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 0.88/1.27 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 0.88/1.27 ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 0.88/1.27 X ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) )
% 0.88/1.27 , multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 0.88/1.27 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 15, [ =( 'least_upper_bound'( a, b ), a ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 16, [ ~( =( 'greatest_lower_bound'( inverse( a ), inverse( b ) ),
% 0.88/1.27 inverse( a ) ) ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 18, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 0.88/1.27 identity ) ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 19, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 0.88/1.27 ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 21, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.88/1.27 X ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 23, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) ),
% 0.88/1.27 X ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 34, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), X ),
% 0.88/1.27 X ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 37, [ =( 'greatest_lower_bound'( 'least_upper_bound'(
% 0.88/1.27 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'( Y, Z ) ),
% 0.88/1.27 'least_upper_bound'( Y, Z ) ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 50, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.88/1.27 'least_upper_bound'( X, Y ) ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 64, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y )
% 0.88/1.27 ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 69, [ ~( =( 'greatest_lower_bound'( inverse( b ), inverse( a ) ),
% 0.88/1.27 inverse( a ) ) ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 90, [ =( 'least_upper_bound'( multiply( Y, X ), X ), multiply(
% 0.88/1.27 'least_upper_bound'( Y, identity ), X ) ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 141, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 146, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.88/1.27 ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 287, [ =( multiply( X, identity ), X ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 295, [ =( inverse( inverse( X ) ), X ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 300, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 366, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.88/1.27 'least_upper_bound'( Y, X ) ), 'least_upper_bound'( Y, X ) ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 1079, [ =( 'least_upper_bound'( identity, multiply( inverse( a ), b
% 0.88/1.27 ) ), identity ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 1095, [ =( 'least_upper_bound'( multiply( inverse( a ), b ),
% 0.88/1.27 identity ), identity ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 2085, [ =( 'least_upper_bound'( multiply( multiply( inverse( a ), b
% 0.88/1.27 ), X ), X ), X ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 2330, [ =( 'least_upper_bound'( inverse( a ), inverse( b ) ),
% 0.88/1.27 inverse( b ) ) ] )
% 0.88/1.27 .
% 0.88/1.27 clause( 2353, [] )
% 0.88/1.27 .
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 % SZS output end Refutation
% 0.88/1.27 found a proof!
% 0.88/1.27
% 0.88/1.27 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.88/1.27
% 0.88/1.27 initialclauses(
% 0.88/1.27 [ clause( 2355, [ =( multiply( identity, X ), X ) ] )
% 0.88/1.27 , clause( 2356, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.88/1.27 , clause( 2357, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.88/1.27 Y, Z ) ) ) ] )
% 0.88/1.27 , clause( 2358, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 0.88/1.27 Y, X ) ) ] )
% 0.88/1.27 , clause( 2359, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X
% 0.88/1.27 ) ) ] )
% 0.88/1.27 , clause( 2360, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y,
% 0.88/1.27 Z ) ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 0.88/1.27 , clause( 2361, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 0.88/1.27 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.88/1.27 , clause( 2362, [ =( 'least_upper_bound'( X, X ), X ) ] )
% 0.88/1.27 , clause( 2363, [ =( 'greatest_lower_bound'( X, X ), X ) ] )
% 0.88/1.27 , clause( 2364, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y )
% 0.88/1.27 ), X ) ] )
% 0.88/1.27 , clause( 2365, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y )
% 0.88/1.27 ), X ) ] )
% 0.88/1.27 , clause( 2366, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 0.88/1.27 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.88/1.27 , clause( 2367, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.88/1.27 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.88/1.27 , clause( 2368, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 0.88/1.27 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 0.88/1.27 , clause( 2369, [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 0.88/1.27 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 0.88/1.27 , clause( 2370, [ =( 'least_upper_bound'( a, b ), a ) ] )
% 0.88/1.27 , clause( 2371, [ ~( =( 'greatest_lower_bound'( inverse( a ), inverse( b )
% 0.88/1.27 ), inverse( a ) ) ) ] )
% 0.88/1.27 ] ).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 subsumption(
% 0.88/1.27 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.88/1.27 , clause( 2355, [ =( multiply( identity, X ), X ) ] )
% 0.88/1.27 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 subsumption(
% 0.88/1.27 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.88/1.27 , clause( 2356, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.88/1.27 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 eqswap(
% 0.88/1.27 clause( 2377, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X,
% 0.88/1.27 Y ), Z ) ) ] )
% 0.88/1.27 , clause( 2357, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.88/1.27 Y, Z ) ) ) ] )
% 0.88/1.27 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 subsumption(
% 0.88/1.27 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 0.88/1.27 , Z ) ) ] )
% 0.88/1.27 , clause( 2377, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X
% 0.88/1.27 , Y ), Z ) ) ] )
% 0.88/1.27 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.88/1.27 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 subsumption(
% 0.88/1.27 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 0.88/1.27 X ) ) ] )
% 0.88/1.27 , clause( 2358, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 0.88/1.27 Y, X ) ) ] )
% 0.88/1.27 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.88/1.27 )] ) ).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 subsumption(
% 0.88/1.27 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 0.88/1.27 ] )
% 0.88/1.27 , clause( 2359, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X
% 0.88/1.27 ) ) ] )
% 0.88/1.27 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.88/1.27 )] ) ).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 subsumption(
% 0.88/1.27 clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 0.88/1.27 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.88/1.27 , clause( 2361, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 0.88/1.27 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.88/1.27 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.88/1.27 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 subsumption(
% 0.88/1.27 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 0.88/1.27 ) ] )
% 0.88/1.27 , clause( 2364, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y )
% 0.88/1.27 ), X ) ] )
% 0.88/1.27 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.88/1.27 )] ) ).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 subsumption(
% 0.88/1.27 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 0.88/1.27 X ) ] )
% 0.88/1.27 , clause( 2365, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y )
% 0.88/1.27 ), X ) ] )
% 0.88/1.27 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.88/1.27 )] ) ).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 eqswap(
% 0.88/1.27 clause( 2415, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 0.88/1.27 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.88/1.27 , clause( 2366, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 0.88/1.27 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.88/1.27 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 subsumption(
% 0.88/1.27 clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) )
% 0.88/1.27 , multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.88/1.27 , clause( 2415, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z
% 0.88/1.27 ) ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.88/1.27 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.88/1.27 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 eqswap(
% 0.88/1.27 clause( 2427, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 0.88/1.27 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.88/1.27 , clause( 2368, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 0.88/1.27 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 0.88/1.27 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 subsumption(
% 0.88/1.27 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 0.88/1.27 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.88/1.27 , clause( 2427, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z
% 0.88/1.27 ) ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.88/1.27 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.88/1.27 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 subsumption(
% 0.88/1.27 clause( 15, [ =( 'least_upper_bound'( a, b ), a ) ] )
% 0.88/1.27 , clause( 2370, [ =( 'least_upper_bound'( a, b ), a ) ] )
% 0.88/1.27 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 subsumption(
% 0.88/1.27 clause( 16, [ ~( =( 'greatest_lower_bound'( inverse( a ), inverse( b ) ),
% 0.88/1.27 inverse( a ) ) ) ] )
% 0.88/1.27 , clause( 2371, [ ~( =( 'greatest_lower_bound'( inverse( a ), inverse( b )
% 0.88/1.27 ), inverse( a ) ) ) ] )
% 0.88/1.27 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 eqswap(
% 0.88/1.27 clause( 2458, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.88/1.27 Y, Z ) ) ) ] )
% 0.88/1.27 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 0.88/1.27 ), Z ) ) ] )
% 0.88/1.27 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 paramod(
% 0.88/1.27 clause( 2463, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply( X
% 0.88/1.27 , identity ) ) ] )
% 0.88/1.27 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.88/1.27 , 0, clause( 2458, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 0.88/1.27 multiply( Y, Z ) ) ) ] )
% 0.88/1.27 , 0, 9, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 0.88/1.27 :=( Y, inverse( Y ) ), :=( Z, Y )] )).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 subsumption(
% 0.88/1.27 clause( 18, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 0.88/1.27 identity ) ) ] )
% 0.88/1.27 , clause( 2463, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply(
% 0.88/1.27 X, identity ) ) ] )
% 0.88/1.27 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.88/1.27 )] ) ).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 eqswap(
% 0.88/1.27 clause( 2468, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.88/1.27 Y, Z ) ) ) ] )
% 0.88/1.27 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 0.88/1.27 ), Z ) ) ] )
% 0.88/1.27 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 paramod(
% 0.88/1.27 clause( 2473, [ =( multiply( multiply( X, identity ), Y ), multiply( X, Y )
% 0.88/1.27 ) ] )
% 0.88/1.27 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.88/1.27 , 0, clause( 2468, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 0.88/1.27 multiply( Y, Z ) ) ) ] )
% 0.88/1.27 , 0, 8, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 0.88/1.28 :=( Y, identity ), :=( Z, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 19, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 0.88/1.28 ] )
% 0.88/1.28 , clause( 2473, [ =( multiply( multiply( X, identity ), Y ), multiply( X, Y
% 0.88/1.28 ) ) ] )
% 0.88/1.28 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.88/1.28 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2478, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 0.88/1.28 ) ) ) ] )
% 0.88/1.28 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 0.88/1.28 , X ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2479, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.88/1.28 X ) ) ] )
% 0.88/1.28 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 0.88/1.28 , X ) ) ] )
% 0.88/1.28 , 0, clause( 2478, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 0.88/1.28 X, Y ) ) ) ] )
% 0.88/1.28 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, 'least_upper_bound'( X, Y ) )] )
% 0.88/1.28 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2482, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 0.88/1.28 , X ) ] )
% 0.88/1.28 , clause( 2479, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y )
% 0.88/1.28 , X ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 21, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.88/1.28 X ) ] )
% 0.88/1.28 , clause( 2482, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X
% 0.88/1.28 ), X ) ] )
% 0.88/1.28 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.88/1.28 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2483, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 0.88/1.28 ) ) ) ] )
% 0.88/1.28 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 0.88/1.28 , X ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2484, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 0.88/1.28 ) ) ) ] )
% 0.88/1.28 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 0.88/1.28 ) ] )
% 0.88/1.28 , 0, clause( 2483, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 0.88/1.28 X, Y ) ) ) ] )
% 0.88/1.28 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.88/1.28 :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2487, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) )
% 0.88/1.28 , X ) ] )
% 0.88/1.28 , clause( 2484, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y,
% 0.88/1.28 X ) ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 23, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) ),
% 0.88/1.28 X ) ] )
% 0.88/1.28 , clause( 2487, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X )
% 0.88/1.28 ), X ) ] )
% 0.88/1.28 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.88/1.28 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2488, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.88/1.28 X ) ) ] )
% 0.88/1.28 , clause( 21, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 0.88/1.28 , X ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2489, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 0.88/1.28 X ) ) ] )
% 0.88/1.28 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 0.88/1.28 ) ] )
% 0.88/1.28 , 0, clause( 2488, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X,
% 0.88/1.28 Y ), X ) ) ] )
% 0.88/1.28 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.88/1.28 :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2492, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), X )
% 0.88/1.28 , X ) ] )
% 0.88/1.28 , clause( 2489, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( Y, X )
% 0.88/1.28 , X ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 34, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), X ),
% 0.88/1.28 X ) ] )
% 0.88/1.28 , clause( 2492, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), X
% 0.88/1.28 ), X ) ] )
% 0.88/1.28 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.88/1.28 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2494, [ =( Y, 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.88/1.28 Y ) ) ] )
% 0.88/1.28 , clause( 34, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), X )
% 0.88/1.28 , X ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2495, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.88/1.28 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ),
% 0.88/1.28 'least_upper_bound'( X, Y ) ) ) ] )
% 0.88/1.28 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 0.88/1.28 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.88/1.28 , 0, clause( 2494, [ =( Y, 'greatest_lower_bound'( 'least_upper_bound'( X,
% 0.88/1.28 Y ), Y ) ) ] )
% 0.88/1.28 , 0, 5, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 0.88/1.28 substitution( 1, [ :=( X, Z ), :=( Y, 'least_upper_bound'( X, Y ) )] )
% 0.88/1.28 ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2496, [ =( 'greatest_lower_bound'( 'least_upper_bound'(
% 0.88/1.28 'least_upper_bound'( Z, X ), Y ), 'least_upper_bound'( X, Y ) ),
% 0.88/1.28 'least_upper_bound'( X, Y ) ) ] )
% 0.88/1.28 , clause( 2495, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.88/1.28 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ),
% 0.88/1.28 'least_upper_bound'( X, Y ) ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 37, [ =( 'greatest_lower_bound'( 'least_upper_bound'(
% 0.88/1.28 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'( Y, Z ) ),
% 0.88/1.28 'least_upper_bound'( Y, Z ) ) ] )
% 0.88/1.28 , clause( 2496, [ =( 'greatest_lower_bound'( 'least_upper_bound'(
% 0.88/1.28 'least_upper_bound'( Z, X ), Y ), 'least_upper_bound'( X, Y ) ),
% 0.88/1.28 'least_upper_bound'( X, Y ) ) ] )
% 0.88/1.28 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 0.88/1.28 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2498, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 0.88/1.28 ) ) ) ] )
% 0.88/1.28 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 0.88/1.28 , X ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2501, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 0.88/1.28 'least_upper_bound'( X, Y ), X ) ) ] )
% 0.88/1.28 , clause( 21, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 0.88/1.28 , X ) ] )
% 0.88/1.28 , 0, clause( 2498, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 0.88/1.28 X, Y ) ) ) ] )
% 0.88/1.28 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.88/1.28 :=( X, 'least_upper_bound'( X, Y ) ), :=( Y, X )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2502, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.88/1.28 'least_upper_bound'( X, Y ) ) ] )
% 0.88/1.28 , clause( 2501, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 0.88/1.28 'least_upper_bound'( X, Y ), X ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 50, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.88/1.28 'least_upper_bound'( X, Y ) ) ] )
% 0.88/1.28 , clause( 2502, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X )
% 0.88/1.28 , 'least_upper_bound'( X, Y ) ) ] )
% 0.88/1.28 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.88/1.28 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2504, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 0.88/1.28 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.88/1.28 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 0.88/1.28 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2506, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) ),
% 0.88/1.28 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 0.88/1.28 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.88/1.28 , 0, clause( 2504, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 0.88/1.28 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.88/1.28 , 0, 8, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 0.88/1.28 X ) ), :=( Y, X ), :=( Z, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2509, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y
% 0.88/1.28 ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 0.88/1.28 , clause( 2506, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) )
% 0.88/1.28 , 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 64, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y )
% 0.88/1.28 ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 0.88/1.28 , clause( 2509, [ =( 'least_upper_bound'( identity, multiply( inverse( X )
% 0.88/1.28 , Y ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 0.88/1.28 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.88/1.28 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2511, [ ~( =( inverse( a ), 'greatest_lower_bound'( inverse( a ),
% 0.88/1.28 inverse( b ) ) ) ) ] )
% 0.88/1.28 , clause( 16, [ ~( =( 'greatest_lower_bound'( inverse( a ), inverse( b ) )
% 0.88/1.28 , inverse( a ) ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2512, [ ~( =( inverse( a ), 'greatest_lower_bound'( inverse( b ),
% 0.88/1.28 inverse( a ) ) ) ) ] )
% 0.88/1.28 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 0.88/1.28 , X ) ) ] )
% 0.88/1.28 , 0, clause( 2511, [ ~( =( inverse( a ), 'greatest_lower_bound'( inverse( a
% 0.88/1.28 ), inverse( b ) ) ) ) ] )
% 0.88/1.28 , 0, 4, substitution( 0, [ :=( X, inverse( a ) ), :=( Y, inverse( b ) )] )
% 0.88/1.28 , substitution( 1, [] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2515, [ ~( =( 'greatest_lower_bound'( inverse( b ), inverse( a ) )
% 0.88/1.28 , inverse( a ) ) ) ] )
% 0.88/1.28 , clause( 2512, [ ~( =( inverse( a ), 'greatest_lower_bound'( inverse( b )
% 0.88/1.28 , inverse( a ) ) ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 69, [ ~( =( 'greatest_lower_bound'( inverse( b ), inverse( a ) ),
% 0.88/1.28 inverse( a ) ) ) ] )
% 0.88/1.28 , clause( 2515, [ ~( =( 'greatest_lower_bound'( inverse( b ), inverse( a )
% 0.88/1.28 ), inverse( a ) ) ) ] )
% 0.88/1.28 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2517, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 0.88/1.28 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 0.88/1.28 , clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 0.88/1.28 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2519, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 0.88/1.28 'least_upper_bound'( multiply( X, Y ), Y ) ) ] )
% 0.88/1.28 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.88/1.28 , 0, clause( 2517, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 0.88/1.28 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 0.88/1.28 , 0, 10, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 0.88/1.28 :=( Y, Y ), :=( Z, identity )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2521, [ =( 'least_upper_bound'( multiply( X, Y ), Y ), multiply(
% 0.88/1.28 'least_upper_bound'( X, identity ), Y ) ) ] )
% 0.88/1.28 , clause( 2519, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 0.88/1.28 'least_upper_bound'( multiply( X, Y ), Y ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 90, [ =( 'least_upper_bound'( multiply( Y, X ), X ), multiply(
% 0.88/1.28 'least_upper_bound'( Y, identity ), X ) ) ] )
% 0.88/1.28 , clause( 2521, [ =( 'least_upper_bound'( multiply( X, Y ), Y ), multiply(
% 0.88/1.28 'least_upper_bound'( X, identity ), Y ) ) ] )
% 0.88/1.28 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.88/1.28 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2523, [ =( multiply( X, identity ), multiply( multiply( X, inverse(
% 0.88/1.28 Y ) ), Y ) ) ] )
% 0.88/1.28 , clause( 18, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 0.88/1.28 , identity ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2526, [ =( multiply( inverse( inverse( X ) ), identity ), multiply(
% 0.88/1.28 identity, X ) ) ] )
% 0.88/1.28 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.88/1.28 , 0, clause( 2523, [ =( multiply( X, identity ), multiply( multiply( X,
% 0.88/1.28 inverse( Y ) ), Y ) ) ] )
% 0.88/1.28 , 0, 7, substitution( 0, [ :=( X, inverse( X ) )] ), substitution( 1, [
% 0.88/1.28 :=( X, inverse( inverse( X ) ) ), :=( Y, X )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2527, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.88/1.28 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.88/1.28 , 0, clause( 2526, [ =( multiply( inverse( inverse( X ) ), identity ),
% 0.88/1.28 multiply( identity, X ) ) ] )
% 0.88/1.28 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.88/1.28 ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 141, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.88/1.28 , clause( 2527, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ]
% 0.88/1.28 )
% 0.88/1.28 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2530, [ =( multiply( X, Y ), multiply( multiply( X, identity ), Y )
% 0.88/1.28 ) ] )
% 0.88/1.28 , clause( 19, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X )
% 0.88/1.28 ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2533, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.88/1.28 ) ] )
% 0.88/1.28 , clause( 141, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.88/1.28 , 0, clause( 2530, [ =( multiply( X, Y ), multiply( multiply( X, identity )
% 0.88/1.28 , Y ) ) ] )
% 0.88/1.28 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 0.88/1.28 inverse( X ) ) ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 146, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.88/1.28 ) ] )
% 0.88/1.28 , clause( 2533, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.88/1.28 ) ) ] )
% 0.88/1.28 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.88/1.28 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2539, [ =( multiply( X, Y ), multiply( inverse( inverse( X ) ), Y )
% 0.88/1.28 ) ] )
% 0.88/1.28 , clause( 146, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.88/1.28 ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2542, [ =( multiply( X, identity ), X ) ] )
% 0.88/1.28 , clause( 141, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.88/1.28 , 0, clause( 2539, [ =( multiply( X, Y ), multiply( inverse( inverse( X ) )
% 0.88/1.28 , Y ) ) ] )
% 0.88/1.28 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.88/1.28 :=( Y, identity )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 287, [ =( multiply( X, identity ), X ) ] )
% 0.88/1.28 , clause( 2542, [ =( multiply( X, identity ), X ) ] )
% 0.88/1.28 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2547, [ =( X, multiply( X, identity ) ) ] )
% 0.88/1.28 , clause( 287, [ =( multiply( X, identity ), X ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2550, [ =( inverse( inverse( X ) ), multiply( X, identity ) ) ] )
% 0.88/1.28 , clause( 146, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.88/1.28 ) ) ] )
% 0.88/1.28 , 0, clause( 2547, [ =( X, multiply( X, identity ) ) ] )
% 0.88/1.28 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, identity )] ), substitution(
% 0.88/1.28 1, [ :=( X, inverse( inverse( X ) ) )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2551, [ =( inverse( inverse( X ) ), X ) ] )
% 0.88/1.28 , clause( 287, [ =( multiply( X, identity ), X ) ] )
% 0.88/1.28 , 0, clause( 2550, [ =( inverse( inverse( X ) ), multiply( X, identity ) )
% 0.88/1.28 ] )
% 0.88/1.28 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.88/1.28 ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 295, [ =( inverse( inverse( X ) ), X ) ] )
% 0.88/1.28 , clause( 2551, [ =( inverse( inverse( X ) ), X ) ] )
% 0.88/1.28 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2554, [ =( multiply( X, identity ), multiply( multiply( X, inverse(
% 0.88/1.28 Y ) ), Y ) ) ] )
% 0.88/1.28 , clause( 18, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 0.88/1.28 , identity ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2556, [ =( multiply( X, identity ), multiply( multiply( X, Y ),
% 0.88/1.28 inverse( Y ) ) ) ] )
% 0.88/1.28 , clause( 295, [ =( inverse( inverse( X ) ), X ) ] )
% 0.88/1.28 , 0, clause( 2554, [ =( multiply( X, identity ), multiply( multiply( X,
% 0.88/1.28 inverse( Y ) ), Y ) ) ] )
% 0.88/1.28 , 0, 7, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 0.88/1.28 :=( Y, inverse( Y ) )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2557, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 0.88/1.28 , clause( 287, [ =( multiply( X, identity ), X ) ] )
% 0.88/1.28 , 0, clause( 2556, [ =( multiply( X, identity ), multiply( multiply( X, Y )
% 0.88/1.28 , inverse( Y ) ) ) ] )
% 0.88/1.28 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.88/1.28 :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2558, [ =( multiply( multiply( X, Y ), inverse( Y ) ), X ) ] )
% 0.88/1.28 , clause( 2557, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 300, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 0.88/1.28 , clause( 2558, [ =( multiply( multiply( X, Y ), inverse( Y ) ), X ) ] )
% 0.88/1.28 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.88/1.28 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2560, [ =( 'least_upper_bound'( Y, Z ), 'greatest_lower_bound'(
% 0.88/1.28 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 0.88/1.28 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.88/1.28 , clause( 37, [ =( 'greatest_lower_bound'( 'least_upper_bound'(
% 0.88/1.28 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'( Y, Z ) ),
% 0.88/1.28 'least_upper_bound'( Y, Z ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2563, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.88/1.28 'least_upper_bound'( Y, X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 0.88/1.28 , clause( 50, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.88/1.28 'least_upper_bound'( X, Y ) ) ] )
% 0.88/1.28 , 0, clause( 2560, [ =( 'least_upper_bound'( Y, Z ), 'greatest_lower_bound'(
% 0.88/1.28 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 0.88/1.28 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.88/1.28 , 0, 5, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 0.88/1.28 :=( X, Y ), :=( Y, X ), :=( Z, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2569, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 0.88/1.28 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( X, Y ) ) ] )
% 0.88/1.28 , clause( 2563, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.88/1.28 'least_upper_bound'( Y, X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 366, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.88/1.28 'least_upper_bound'( Y, X ) ), 'least_upper_bound'( Y, X ) ) ] )
% 0.88/1.28 , clause( 2569, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 0.88/1.28 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( X, Y ) ) ] )
% 0.88/1.28 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.88/1.28 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2572, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) ),
% 0.88/1.28 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 0.88/1.28 , clause( 64, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y
% 0.88/1.28 ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2574, [ =( multiply( inverse( a ), a ), 'least_upper_bound'(
% 0.88/1.28 identity, multiply( inverse( a ), b ) ) ) ] )
% 0.88/1.28 , clause( 15, [ =( 'least_upper_bound'( a, b ), a ) ] )
% 0.88/1.28 , 0, clause( 2572, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y )
% 0.88/1.28 ), 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 0.88/1.28 , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, b )] )
% 0.88/1.28 ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2575, [ =( identity, 'least_upper_bound'( identity, multiply(
% 0.88/1.28 inverse( a ), b ) ) ) ] )
% 0.88/1.28 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.88/1.28 , 0, clause( 2574, [ =( multiply( inverse( a ), a ), 'least_upper_bound'(
% 0.88/1.28 identity, multiply( inverse( a ), b ) ) ) ] )
% 0.88/1.28 , 0, 1, substitution( 0, [ :=( X, a )] ), substitution( 1, [] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2576, [ =( 'least_upper_bound'( identity, multiply( inverse( a ), b
% 0.88/1.28 ) ), identity ) ] )
% 0.88/1.28 , clause( 2575, [ =( identity, 'least_upper_bound'( identity, multiply(
% 0.88/1.28 inverse( a ), b ) ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 1079, [ =( 'least_upper_bound'( identity, multiply( inverse( a ), b
% 0.88/1.28 ) ), identity ) ] )
% 0.88/1.28 , clause( 2576, [ =( 'least_upper_bound'( identity, multiply( inverse( a )
% 0.88/1.28 , b ) ), identity ) ] )
% 0.88/1.28 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2578, [ =( 'least_upper_bound'( Y, X ), 'greatest_lower_bound'(
% 0.88/1.28 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 0.88/1.28 , clause( 366, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.88/1.28 'least_upper_bound'( Y, X ) ), 'least_upper_bound'( Y, X ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2582, [ =( 'least_upper_bound'( multiply( inverse( a ), b ),
% 0.88/1.28 identity ), 'greatest_lower_bound'( identity, 'least_upper_bound'(
% 0.88/1.28 multiply( inverse( a ), b ), identity ) ) ) ] )
% 0.88/1.28 , clause( 1079, [ =( 'least_upper_bound'( identity, multiply( inverse( a )
% 0.88/1.28 , b ) ), identity ) ] )
% 0.88/1.28 , 0, clause( 2578, [ =( 'least_upper_bound'( Y, X ), 'greatest_lower_bound'(
% 0.88/1.28 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 0.88/1.28 , 0, 8, substitution( 0, [] ), substitution( 1, [ :=( X, identity ), :=( Y
% 0.88/1.28 , multiply( inverse( a ), b ) )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2584, [ =( 'least_upper_bound'( multiply( inverse( a ), b ),
% 0.88/1.28 identity ), identity ) ] )
% 0.88/1.28 , clause( 23, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) )
% 0.88/1.28 , X ) ] )
% 0.88/1.28 , 0, clause( 2582, [ =( 'least_upper_bound'( multiply( inverse( a ), b ),
% 0.88/1.28 identity ), 'greatest_lower_bound'( identity, 'least_upper_bound'(
% 0.88/1.28 multiply( inverse( a ), b ), identity ) ) ) ] )
% 0.88/1.28 , 0, 7, substitution( 0, [ :=( X, identity ), :=( Y, multiply( inverse( a )
% 0.88/1.28 , b ) )] ), substitution( 1, [] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 1095, [ =( 'least_upper_bound'( multiply( inverse( a ), b ),
% 0.88/1.28 identity ), identity ) ] )
% 0.88/1.28 , clause( 2584, [ =( 'least_upper_bound'( multiply( inverse( a ), b ),
% 0.88/1.28 identity ), identity ) ] )
% 0.88/1.28 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2587, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 0.88/1.28 'least_upper_bound'( multiply( X, Y ), Y ) ) ] )
% 0.88/1.28 , clause( 90, [ =( 'least_upper_bound'( multiply( Y, X ), X ), multiply(
% 0.88/1.28 'least_upper_bound'( Y, identity ), X ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2589, [ =( multiply( identity, X ), 'least_upper_bound'( multiply(
% 0.88/1.28 multiply( inverse( a ), b ), X ), X ) ) ] )
% 0.88/1.28 , clause( 1095, [ =( 'least_upper_bound'( multiply( inverse( a ), b ),
% 0.88/1.28 identity ), identity ) ] )
% 0.88/1.28 , 0, clause( 2587, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 0.88/1.28 'least_upper_bound'( multiply( X, Y ), Y ) ) ] )
% 0.88/1.28 , 0, 2, substitution( 0, [] ), substitution( 1, [ :=( X, multiply( inverse(
% 0.88/1.28 a ), b ) ), :=( Y, X )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2590, [ =( X, 'least_upper_bound'( multiply( multiply( inverse( a )
% 0.88/1.28 , b ), X ), X ) ) ] )
% 0.88/1.28 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.88/1.28 , 0, clause( 2589, [ =( multiply( identity, X ), 'least_upper_bound'(
% 0.88/1.28 multiply( multiply( inverse( a ), b ), X ), X ) ) ] )
% 0.88/1.28 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.88/1.28 ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2591, [ =( 'least_upper_bound'( multiply( multiply( inverse( a ), b
% 0.88/1.28 ), X ), X ), X ) ] )
% 0.88/1.28 , clause( 2590, [ =( X, 'least_upper_bound'( multiply( multiply( inverse( a
% 0.88/1.28 ), b ), X ), X ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 2085, [ =( 'least_upper_bound'( multiply( multiply( inverse( a ), b
% 0.88/1.28 ), X ), X ), X ) ] )
% 0.88/1.28 , clause( 2591, [ =( 'least_upper_bound'( multiply( multiply( inverse( a )
% 0.88/1.28 , b ), X ), X ), X ) ] )
% 0.88/1.28 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2593, [ =( X, 'least_upper_bound'( multiply( multiply( inverse( a )
% 0.88/1.28 , b ), X ), X ) ) ] )
% 0.88/1.28 , clause( 2085, [ =( 'least_upper_bound'( multiply( multiply( inverse( a )
% 0.88/1.28 , b ), X ), X ), X ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2594, [ =( inverse( b ), 'least_upper_bound'( inverse( a ), inverse(
% 0.88/1.28 b ) ) ) ] )
% 0.88/1.28 , clause( 300, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 0.88/1.28 , 0, clause( 2593, [ =( X, 'least_upper_bound'( multiply( multiply( inverse(
% 0.88/1.28 a ), b ), X ), X ) ) ] )
% 0.88/1.28 , 0, 4, substitution( 0, [ :=( X, b ), :=( Y, inverse( a ) )] ),
% 0.88/1.28 substitution( 1, [ :=( X, inverse( b ) )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2595, [ =( 'least_upper_bound'( inverse( a ), inverse( b ) ),
% 0.88/1.28 inverse( b ) ) ] )
% 0.88/1.28 , clause( 2594, [ =( inverse( b ), 'least_upper_bound'( inverse( a ),
% 0.88/1.28 inverse( b ) ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 2330, [ =( 'least_upper_bound'( inverse( a ), inverse( b ) ),
% 0.88/1.28 inverse( b ) ) ] )
% 0.88/1.28 , clause( 2595, [ =( 'least_upper_bound'( inverse( a ), inverse( b ) ),
% 0.88/1.28 inverse( b ) ) ] )
% 0.88/1.28 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2597, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.88/1.28 X ) ) ] )
% 0.88/1.28 , clause( 21, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 0.88/1.28 , X ) ] )
% 0.88/1.28 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 eqswap(
% 0.88/1.28 clause( 2598, [ ~( =( inverse( a ), 'greatest_lower_bound'( inverse( b ),
% 0.88/1.28 inverse( a ) ) ) ) ] )
% 0.88/1.28 , clause( 69, [ ~( =( 'greatest_lower_bound'( inverse( b ), inverse( a ) )
% 0.88/1.28 , inverse( a ) ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 paramod(
% 0.88/1.28 clause( 2599, [ =( inverse( a ), 'greatest_lower_bound'( inverse( b ),
% 0.88/1.28 inverse( a ) ) ) ] )
% 0.88/1.28 , clause( 2330, [ =( 'least_upper_bound'( inverse( a ), inverse( b ) ),
% 0.88/1.28 inverse( b ) ) ] )
% 0.88/1.28 , 0, clause( 2597, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X,
% 0.88/1.28 Y ), X ) ) ] )
% 0.88/1.28 , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, inverse( a ) ),
% 0.88/1.28 :=( Y, inverse( b ) )] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 resolution(
% 0.88/1.28 clause( 2600, [] )
% 0.88/1.28 , clause( 2598, [ ~( =( inverse( a ), 'greatest_lower_bound'( inverse( b )
% 0.88/1.28 , inverse( a ) ) ) ) ] )
% 0.88/1.28 , 0, clause( 2599, [ =( inverse( a ), 'greatest_lower_bound'( inverse( b )
% 0.88/1.28 , inverse( a ) ) ) ] )
% 0.88/1.28 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 subsumption(
% 0.88/1.28 clause( 2353, [] )
% 0.88/1.28 , clause( 2600, [] )
% 0.88/1.28 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 end.
% 0.88/1.28
% 0.88/1.28 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.88/1.28
% 0.88/1.28 Memory use:
% 0.88/1.28
% 0.88/1.28 space for terms: 30892
% 0.88/1.28 space for clauses: 258296
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 clauses generated: 33019
% 0.88/1.28 clauses kept: 2354
% 0.88/1.28 clauses selected: 274
% 0.88/1.28 clauses deleted: 20
% 0.88/1.28 clauses inuse deleted: 6
% 0.88/1.28
% 0.88/1.28 subsentry: 4587
% 0.88/1.28 literals s-matched: 3993
% 0.88/1.28 literals matched: 3961
% 0.88/1.28 full subsumption: 0
% 0.88/1.28
% 0.88/1.28 checksum: -641894630
% 0.88/1.28
% 0.88/1.28
% 0.88/1.28 Bliksem ended
%------------------------------------------------------------------------------