%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP191-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n027.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 07:36:03 EDT 2022
% Result : Unsatisfiable 0.73s 1.24s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP191-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n027.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 00:13:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.73/1.24 *** allocated 10000 integers for termspace/termends
% 0.73/1.24 *** allocated 10000 integers for clauses
% 0.73/1.24 *** allocated 10000 integers for justifications
% 0.73/1.24 Bliksem 1.12
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Automatic Strategy Selection
% 0.73/1.24
% 0.73/1.24 Clauses:
% 0.73/1.24 [
% 0.73/1.24 [ =( multiply( identity, X ), X ) ],
% 0.73/1.24 [ =( multiply( inverse( X ), X ), identity ) ],
% 0.73/1.24 [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply( Y, Z ) ) )
% 0.73/1.24 ],
% 0.73/1.24 [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, X ) ) ]
% 0.73/1.24 ,
% 0.73/1.24 [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ],
% 0.73/1.24 [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.73/1.24 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ],
% 0.73/1.24 [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.24 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ],
% 0.73/1.24 [ =( 'least_upper_bound'( X, X ), X ) ],
% 0.73/1.24 [ =( 'greatest_lower_bound'( X, X ), X ) ],
% 0.73/1.24 [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X ) ]
% 0.73/1.24 ,
% 0.73/1.24 [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ), X ) ]
% 0.73/1.24 ,
% 0.73/1.24 [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), 'least_upper_bound'(
% 0.73/1.24 multiply( X, Y ), multiply( X, Z ) ) ) ],
% 0.73/1.24 [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.73/1.24 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ],
% 0.73/1.24 [ =( multiply( 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'(
% 0.73/1.24 multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 0.73/1.24 [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 0.73/1.24 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 0.73/1.24 [ =( 'greatest_lower_bound'( a, b ), b ) ],
% 0.73/1.24 [ ~( =( 'least_upper_bound'( inverse( a ), inverse( b ) ), inverse( b )
% 0.73/1.24 ) ) ]
% 0.73/1.24 ] .
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 percentage equality = 1.000000, percentage horn = 1.000000
% 0.73/1.24 This is a pure equality problem
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Options Used:
% 0.73/1.24
% 0.73/1.24 useres = 1
% 0.73/1.24 useparamod = 1
% 0.73/1.24 useeqrefl = 1
% 0.73/1.24 useeqfact = 1
% 0.73/1.24 usefactor = 1
% 0.73/1.24 usesimpsplitting = 0
% 0.73/1.24 usesimpdemod = 5
% 0.73/1.24 usesimpres = 3
% 0.73/1.24
% 0.73/1.24 resimpinuse = 1000
% 0.73/1.24 resimpclauses = 20000
% 0.73/1.24 substype = eqrewr
% 0.73/1.24 backwardsubs = 1
% 0.73/1.24 selectoldest = 5
% 0.73/1.24
% 0.73/1.24 litorderings [0] = split
% 0.73/1.24 litorderings [1] = extend the termordering, first sorting on arguments
% 0.73/1.24
% 0.73/1.24 termordering = kbo
% 0.73/1.24
% 0.73/1.24 litapriori = 0
% 0.73/1.24 termapriori = 1
% 0.73/1.24 litaposteriori = 0
% 0.73/1.24 termaposteriori = 0
% 0.73/1.24 demodaposteriori = 0
% 0.73/1.24 ordereqreflfact = 0
% 0.73/1.24
% 0.73/1.24 litselect = negord
% 0.73/1.24
% 0.73/1.24 maxweight = 15
% 0.73/1.24 maxdepth = 30000
% 0.73/1.24 maxlength = 115
% 0.73/1.24 maxnrvars = 195
% 0.73/1.24 excuselevel = 1
% 0.73/1.24 increasemaxweight = 1
% 0.73/1.24
% 0.73/1.24 maxselected = 10000000
% 0.73/1.24 maxnrclauses = 10000000
% 0.73/1.24
% 0.73/1.24 showgenerated = 0
% 0.73/1.24 showkept = 0
% 0.73/1.24 showselected = 0
% 0.73/1.24 showdeleted = 0
% 0.73/1.24 showresimp = 1
% 0.73/1.24 showstatus = 2000
% 0.73/1.24
% 0.73/1.24 prologoutput = 1
% 0.73/1.24 nrgoals = 5000000
% 0.73/1.24 totalproof = 1
% 0.73/1.24
% 0.73/1.24 Symbols occurring in the translation:
% 0.73/1.24
% 0.73/1.24 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.73/1.24 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.73/1.24 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.73/1.24 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.24 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.24 identity [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.73/1.24 multiply [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.73/1.24 inverse [42, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.73/1.24 'greatest_lower_bound' [45, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.73/1.24 'least_upper_bound' [46, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.73/1.24 a [47, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.73/1.24 b [48, 0] (w:1, o:14, a:1, s:1, b:0).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Starting Search:
% 0.73/1.24
% 0.73/1.24 Resimplifying inuse:
% 0.73/1.24 Done
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Intermediate Status:
% 0.73/1.24 Generated: 28358
% 0.73/1.24 Kept: 2013
% 0.73/1.24 Inuse: 247
% 0.73/1.24 Deleted: 18
% 0.73/1.24 Deletedinuse: 6
% 0.73/1.24
% 0.73/1.24 Resimplifying inuse:
% 0.73/1.24 Done
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Bliksems!, er is een bewijs:
% 0.73/1.24 % SZS status Unsatisfiable
% 0.73/1.24 % SZS output start Refutation
% 0.73/1.24
% 0.73/1.24 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 0.73/1.24 , Z ) ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 0.73/1.24 X ) ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 0.73/1.24 ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.24 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 0.73/1.24 ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 0.73/1.24 X ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) )
% 0.73/1.24 , multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 0.73/1.24 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 15, [ =( 'greatest_lower_bound'( a, b ), b ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 16, [ ~( =( 'least_upper_bound'( inverse( a ), inverse( b ) ),
% 0.73/1.24 inverse( b ) ) ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 18, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 0.73/1.24 identity ) ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 19, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 0.73/1.24 ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 21, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.73/1.24 X ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 22, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) ),
% 0.73/1.24 X ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 32, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), X ),
% 0.73/1.24 X ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 38, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.73/1.24 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 42, [ =( 'least_upper_bound'( a, b ), a ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 44, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, Z ),
% 0.73/1.24 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ),
% 0.73/1.24 'least_upper_bound'( Y, Z ) ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 63, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y )
% 0.73/1.24 ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 90, [ =( 'least_upper_bound'( multiply( Y, X ), X ), multiply(
% 0.73/1.24 'least_upper_bound'( Y, identity ), X ) ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 141, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 146, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.73/1.24 ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 287, [ =( multiply( X, identity ), X ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 295, [ =( inverse( inverse( X ) ), X ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 300, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 453, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 0.73/1.24 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( Y, X ) ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 1021, [ =( 'least_upper_bound'( identity, multiply( inverse( a ), b
% 0.73/1.24 ) ), identity ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 1042, [ =( 'least_upper_bound'( multiply( inverse( a ), b ),
% 0.73/1.24 identity ), identity ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 2039, [ =( 'least_upper_bound'( multiply( multiply( inverse( a ), b
% 0.73/1.24 ), X ), X ), X ) ] )
% 0.73/1.24 .
% 0.73/1.24 clause( 2285, [] )
% 0.73/1.24 .
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 % SZS output end Refutation
% 0.73/1.24 found a proof!
% 0.73/1.24
% 0.73/1.24 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.73/1.24
% 0.73/1.24 initialclauses(
% 0.73/1.24 [ clause( 2287, [ =( multiply( identity, X ), X ) ] )
% 0.73/1.24 , clause( 2288, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.73/1.24 , clause( 2289, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.73/1.24 Y, Z ) ) ) ] )
% 0.73/1.24 , clause( 2290, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.24 Y, X ) ) ] )
% 0.73/1.24 , clause( 2291, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X
% 0.73/1.24 ) ) ] )
% 0.73/1.24 , clause( 2292, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y,
% 0.73/1.24 Z ) ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 0.73/1.24 , clause( 2293, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 0.73/1.24 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.73/1.24 , clause( 2294, [ =( 'least_upper_bound'( X, X ), X ) ] )
% 0.73/1.24 , clause( 2295, [ =( 'greatest_lower_bound'( X, X ), X ) ] )
% 0.73/1.24 , clause( 2296, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y )
% 0.73/1.24 ), X ) ] )
% 0.73/1.24 , clause( 2297, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y )
% 0.73/1.24 ), X ) ] )
% 0.73/1.24 , clause( 2298, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.24 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.73/1.24 , clause( 2299, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.73/1.24 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.73/1.24 , clause( 2300, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 0.73/1.24 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 0.73/1.24 , clause( 2301, [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 0.73/1.24 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 0.73/1.24 , clause( 2302, [ =( 'greatest_lower_bound'( a, b ), b ) ] )
% 0.73/1.24 , clause( 2303, [ ~( =( 'least_upper_bound'( inverse( a ), inverse( b ) ),
% 0.73/1.24 inverse( b ) ) ) ] )
% 0.73/1.24 ] ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.73/1.24 , clause( 2287, [ =( multiply( identity, X ), X ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.73/1.24 , clause( 2288, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2309, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X,
% 0.73/1.24 Y ), Z ) ) ] )
% 0.73/1.24 , clause( 2289, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.73/1.24 Y, Z ) ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 0.73/1.24 , Z ) ) ] )
% 0.73/1.24 , clause( 2309, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X
% 0.73/1.24 , Y ), Z ) ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.73/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 0.73/1.24 X ) ) ] )
% 0.73/1.24 , clause( 2290, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.24 Y, X ) ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.24 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 0.73/1.24 ] )
% 0.73/1.24 , clause( 2291, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X
% 0.73/1.24 ) ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.24 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.24 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.73/1.24 , clause( 2293, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 0.73/1.24 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.73/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 0.73/1.24 ) ] )
% 0.73/1.24 , clause( 2296, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y )
% 0.73/1.24 ), X ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.24 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 0.73/1.24 X ) ] )
% 0.73/1.24 , clause( 2297, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y )
% 0.73/1.24 ), X ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.24 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2347, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 0.73/1.24 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.73/1.24 , clause( 2298, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.24 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) )
% 0.73/1.24 , multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.73/1.24 , clause( 2347, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z
% 0.73/1.24 ) ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.73/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2359, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 0.73/1.24 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.73/1.24 , clause( 2300, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 0.73/1.24 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 0.73/1.24 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.73/1.24 , clause( 2359, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z
% 0.73/1.24 ) ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.73/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 15, [ =( 'greatest_lower_bound'( a, b ), b ) ] )
% 0.73/1.24 , clause( 2302, [ =( 'greatest_lower_bound'( a, b ), b ) ] )
% 0.73/1.24 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 16, [ ~( =( 'least_upper_bound'( inverse( a ), inverse( b ) ),
% 0.73/1.24 inverse( b ) ) ) ] )
% 0.73/1.24 , clause( 2303, [ ~( =( 'least_upper_bound'( inverse( a ), inverse( b ) ),
% 0.73/1.24 inverse( b ) ) ) ] )
% 0.73/1.24 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2390, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.73/1.24 Y, Z ) ) ) ] )
% 0.73/1.24 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 0.73/1.24 ), Z ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2395, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply( X
% 0.73/1.24 , identity ) ) ] )
% 0.73/1.24 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.73/1.24 , 0, clause( 2390, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 0.73/1.24 multiply( Y, Z ) ) ) ] )
% 0.73/1.24 , 0, 9, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 0.73/1.24 :=( Y, inverse( Y ) ), :=( Z, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 18, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 0.73/1.24 identity ) ) ] )
% 0.73/1.24 , clause( 2395, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply(
% 0.73/1.24 X, identity ) ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.24 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2400, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.73/1.24 Y, Z ) ) ) ] )
% 0.73/1.24 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 0.73/1.24 ), Z ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2405, [ =( multiply( multiply( X, identity ), Y ), multiply( X, Y )
% 0.73/1.24 ) ] )
% 0.73/1.24 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.73/1.24 , 0, clause( 2400, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 0.73/1.24 multiply( Y, Z ) ) ) ] )
% 0.73/1.24 , 0, 8, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 0.73/1.24 :=( Y, identity ), :=( Z, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 19, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 0.73/1.24 ] )
% 0.73/1.24 , clause( 2405, [ =( multiply( multiply( X, identity ), Y ), multiply( X, Y
% 0.73/1.24 ) ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.24 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2410, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 0.73/1.24 ) ) ) ] )
% 0.73/1.24 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 0.73/1.24 , X ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2411, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.73/1.24 X ) ) ] )
% 0.73/1.24 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 0.73/1.24 , X ) ) ] )
% 0.73/1.24 , 0, clause( 2410, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 0.73/1.24 X, Y ) ) ) ] )
% 0.73/1.24 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, 'least_upper_bound'( X, Y ) )] )
% 0.73/1.24 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2414, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 0.73/1.24 , X ) ] )
% 0.73/1.24 , clause( 2411, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y )
% 0.73/1.24 , X ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 21, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.73/1.24 X ) ] )
% 0.73/1.24 , clause( 2414, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X
% 0.73/1.24 ), X ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.24 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2415, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 0.73/1.24 ) ) ) ] )
% 0.73/1.24 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 0.73/1.24 , X ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2416, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 0.73/1.24 ) ) ) ] )
% 0.73/1.24 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 0.73/1.24 ) ] )
% 0.73/1.24 , 0, clause( 2415, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 0.73/1.24 X, Y ) ) ) ] )
% 0.73/1.24 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.73/1.24 :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2419, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) )
% 0.73/1.24 , X ) ] )
% 0.73/1.24 , clause( 2416, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y,
% 0.73/1.24 X ) ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 22, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) ),
% 0.73/1.24 X ) ] )
% 0.73/1.24 , clause( 2419, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X )
% 0.73/1.24 ), X ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.24 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2420, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.73/1.24 X ) ) ] )
% 0.73/1.24 , clause( 21, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 0.73/1.24 , X ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2421, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 0.73/1.24 X ) ) ] )
% 0.73/1.24 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 0.73/1.24 ) ] )
% 0.73/1.24 , 0, clause( 2420, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X,
% 0.73/1.24 Y ), X ) ) ] )
% 0.73/1.24 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.73/1.24 :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2424, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), X )
% 0.73/1.24 , X ) ] )
% 0.73/1.24 , clause( 2421, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( Y, X )
% 0.73/1.24 , X ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 32, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), X ),
% 0.73/1.24 X ) ] )
% 0.73/1.24 , clause( 2424, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), X
% 0.73/1.24 ), X ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.24 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2426, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 0.73/1.24 ) ) ) ] )
% 0.73/1.24 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 0.73/1.24 , X ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2429, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 0.73/1.24 'least_upper_bound'( X, Y ), X ) ) ] )
% 0.73/1.24 , clause( 21, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 0.73/1.24 , X ) ] )
% 0.73/1.24 , 0, clause( 2426, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 0.73/1.24 X, Y ) ) ) ] )
% 0.73/1.24 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.73/1.24 :=( X, 'least_upper_bound'( X, Y ) ), :=( Y, X )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2430, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.73/1.24 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.24 , clause( 2429, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 0.73/1.24 'least_upper_bound'( X, Y ), X ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 38, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.73/1.24 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.24 , clause( 2430, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X )
% 0.73/1.24 , 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.24 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2432, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 0.73/1.24 ) ) ) ] )
% 0.73/1.24 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 0.73/1.24 , X ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2433, [ =( a, 'least_upper_bound'( a, b ) ) ] )
% 0.73/1.24 , clause( 15, [ =( 'greatest_lower_bound'( a, b ), b ) ] )
% 0.73/1.24 , 0, clause( 2432, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 0.73/1.24 X, Y ) ) ) ] )
% 0.73/1.24 , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, b )] )
% 0.73/1.24 ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2434, [ =( 'least_upper_bound'( a, b ), a ) ] )
% 0.73/1.24 , clause( 2433, [ =( a, 'least_upper_bound'( a, b ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 42, [ =( 'least_upper_bound'( a, b ), a ) ] )
% 0.73/1.24 , clause( 2434, [ =( 'least_upper_bound'( a, b ), a ) ] )
% 0.73/1.24 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2436, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 0.73/1.24 ) ) ) ] )
% 0.73/1.24 , clause( 22, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) )
% 0.73/1.24 , X ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2437, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.24 'least_upper_bound'( X, Y ), 'least_upper_bound'( 'least_upper_bound'( Z
% 0.73/1.24 , X ), Y ) ) ) ] )
% 0.73/1.24 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.24 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.73/1.24 , 0, clause( 2436, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 0.73/1.24 Y, X ) ) ) ] )
% 0.73/1.24 , 0, 8, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 0.73/1.24 substitution( 1, [ :=( X, 'least_upper_bound'( X, Y ) ), :=( Y, Z )] )
% 0.73/1.24 ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2438, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.73/1.24 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ) ),
% 0.73/1.24 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.24 , clause( 2437, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.24 'least_upper_bound'( X, Y ), 'least_upper_bound'( 'least_upper_bound'( Z
% 0.73/1.24 , X ), Y ) ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 44, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, Z ),
% 0.73/1.24 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ),
% 0.73/1.24 'least_upper_bound'( Y, Z ) ) ] )
% 0.73/1.24 , clause( 2438, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.73/1.24 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ) ),
% 0.73/1.24 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 0.73/1.24 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2440, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.24 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.73/1.24 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 0.73/1.24 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2442, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) ),
% 0.73/1.24 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 0.73/1.24 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.73/1.24 , 0, clause( 2440, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.24 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.73/1.24 , 0, 8, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 0.73/1.24 X ) ), :=( Y, X ), :=( Z, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2445, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y
% 0.73/1.24 ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 0.73/1.24 , clause( 2442, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) )
% 0.73/1.24 , 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 63, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y )
% 0.73/1.24 ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 0.73/1.24 , clause( 2445, [ =( 'least_upper_bound'( identity, multiply( inverse( X )
% 0.73/1.24 , Y ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.24 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2448, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 0.73/1.24 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 0.73/1.24 , clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 0.73/1.24 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2450, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 0.73/1.24 'least_upper_bound'( multiply( X, Y ), Y ) ) ] )
% 0.73/1.24 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.73/1.24 , 0, clause( 2448, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 0.73/1.24 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 0.73/1.24 , 0, 10, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 0.73/1.24 :=( Y, Y ), :=( Z, identity )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2452, [ =( 'least_upper_bound'( multiply( X, Y ), Y ), multiply(
% 0.73/1.24 'least_upper_bound'( X, identity ), Y ) ) ] )
% 0.73/1.24 , clause( 2450, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 0.73/1.24 'least_upper_bound'( multiply( X, Y ), Y ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 90, [ =( 'least_upper_bound'( multiply( Y, X ), X ), multiply(
% 0.73/1.24 'least_upper_bound'( Y, identity ), X ) ) ] )
% 0.73/1.24 , clause( 2452, [ =( 'least_upper_bound'( multiply( X, Y ), Y ), multiply(
% 0.73/1.24 'least_upper_bound'( X, identity ), Y ) ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.24 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2454, [ =( multiply( X, identity ), multiply( multiply( X, inverse(
% 0.73/1.24 Y ) ), Y ) ) ] )
% 0.73/1.24 , clause( 18, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 0.73/1.24 , identity ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2457, [ =( multiply( inverse( inverse( X ) ), identity ), multiply(
% 0.73/1.24 identity, X ) ) ] )
% 0.73/1.24 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.73/1.24 , 0, clause( 2454, [ =( multiply( X, identity ), multiply( multiply( X,
% 0.73/1.24 inverse( Y ) ), Y ) ) ] )
% 0.73/1.24 , 0, 7, substitution( 0, [ :=( X, inverse( X ) )] ), substitution( 1, [
% 0.73/1.24 :=( X, inverse( inverse( X ) ) ), :=( Y, X )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2458, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.73/1.24 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.73/1.24 , 0, clause( 2457, [ =( multiply( inverse( inverse( X ) ), identity ),
% 0.73/1.24 multiply( identity, X ) ) ] )
% 0.73/1.24 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.73/1.24 ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 141, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.73/1.24 , clause( 2458, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ]
% 0.73/1.24 )
% 0.73/1.24 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2461, [ =( multiply( X, Y ), multiply( multiply( X, identity ), Y )
% 0.73/1.24 ) ] )
% 0.73/1.24 , clause( 19, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X )
% 0.73/1.24 ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2464, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.73/1.24 ) ] )
% 0.73/1.24 , clause( 141, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.73/1.24 , 0, clause( 2461, [ =( multiply( X, Y ), multiply( multiply( X, identity )
% 0.73/1.24 , Y ) ) ] )
% 0.73/1.24 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 0.73/1.24 inverse( X ) ) ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 146, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.73/1.24 ) ] )
% 0.73/1.24 , clause( 2464, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.73/1.24 ) ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.24 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2470, [ =( multiply( X, Y ), multiply( inverse( inverse( X ) ), Y )
% 0.73/1.24 ) ] )
% 0.73/1.24 , clause( 146, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.73/1.24 ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2473, [ =( multiply( X, identity ), X ) ] )
% 0.73/1.24 , clause( 141, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.73/1.24 , 0, clause( 2470, [ =( multiply( X, Y ), multiply( inverse( inverse( X ) )
% 0.73/1.24 , Y ) ) ] )
% 0.73/1.24 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.73/1.24 :=( Y, identity )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 287, [ =( multiply( X, identity ), X ) ] )
% 0.73/1.24 , clause( 2473, [ =( multiply( X, identity ), X ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2478, [ =( X, multiply( X, identity ) ) ] )
% 0.73/1.24 , clause( 287, [ =( multiply( X, identity ), X ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2481, [ =( inverse( inverse( X ) ), multiply( X, identity ) ) ] )
% 0.73/1.24 , clause( 146, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.73/1.24 ) ) ] )
% 0.73/1.24 , 0, clause( 2478, [ =( X, multiply( X, identity ) ) ] )
% 0.73/1.24 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, identity )] ), substitution(
% 0.73/1.24 1, [ :=( X, inverse( inverse( X ) ) )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2482, [ =( inverse( inverse( X ) ), X ) ] )
% 0.73/1.24 , clause( 287, [ =( multiply( X, identity ), X ) ] )
% 0.73/1.24 , 0, clause( 2481, [ =( inverse( inverse( X ) ), multiply( X, identity ) )
% 0.73/1.24 ] )
% 0.73/1.24 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.73/1.24 ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 295, [ =( inverse( inverse( X ) ), X ) ] )
% 0.73/1.24 , clause( 2482, [ =( inverse( inverse( X ) ), X ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2485, [ =( multiply( X, identity ), multiply( multiply( X, inverse(
% 0.73/1.24 Y ) ), Y ) ) ] )
% 0.73/1.24 , clause( 18, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 0.73/1.24 , identity ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2487, [ =( multiply( X, identity ), multiply( multiply( X, Y ),
% 0.73/1.24 inverse( Y ) ) ) ] )
% 0.73/1.24 , clause( 295, [ =( inverse( inverse( X ) ), X ) ] )
% 0.73/1.24 , 0, clause( 2485, [ =( multiply( X, identity ), multiply( multiply( X,
% 0.73/1.24 inverse( Y ) ), Y ) ) ] )
% 0.73/1.24 , 0, 7, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 0.73/1.24 :=( Y, inverse( Y ) )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2488, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 0.73/1.24 , clause( 287, [ =( multiply( X, identity ), X ) ] )
% 0.73/1.24 , 0, clause( 2487, [ =( multiply( X, identity ), multiply( multiply( X, Y )
% 0.73/1.24 , inverse( Y ) ) ) ] )
% 0.73/1.24 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.73/1.24 :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2489, [ =( multiply( multiply( X, Y ), inverse( Y ) ), X ) ] )
% 0.73/1.24 , clause( 2488, [ =( X, multiply( multiply( X, Y ), inverse( Y ) ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 300, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 0.73/1.24 , clause( 2489, [ =( multiply( multiply( X, Y ), inverse( Y ) ), X ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.24 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2491, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.24 'least_upper_bound'( X, Y ), 'least_upper_bound'( 'least_upper_bound'( Z
% 0.73/1.24 , X ), Y ) ) ) ] )
% 0.73/1.24 , clause( 44, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, Z ),
% 0.73/1.24 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ),
% 0.73/1.24 'least_upper_bound'( Y, Z ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2494, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.24 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 0.73/1.24 , clause( 38, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.73/1.24 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.24 , 0, clause( 2491, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.24 'least_upper_bound'( X, Y ), 'least_upper_bound'( 'least_upper_bound'( Z
% 0.73/1.24 , X ), Y ) ) ) ] )
% 0.73/1.24 , 0, 8, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 0.73/1.24 :=( X, X ), :=( Y, Y ), :=( Z, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2500, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.73/1.24 'least_upper_bound'( Y, X ) ), 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.24 , clause( 2494, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.24 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 453, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 0.73/1.24 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( Y, X ) ) ] )
% 0.73/1.24 , clause( 2500, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.73/1.24 'least_upper_bound'( Y, X ) ), 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.24 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2503, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) ),
% 0.73/1.24 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 0.73/1.24 , clause( 63, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y
% 0.73/1.24 ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2505, [ =( multiply( inverse( a ), a ), 'least_upper_bound'(
% 0.73/1.24 identity, multiply( inverse( a ), b ) ) ) ] )
% 0.73/1.24 , clause( 42, [ =( 'least_upper_bound'( a, b ), a ) ] )
% 0.73/1.24 , 0, clause( 2503, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y )
% 0.73/1.24 ), 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 0.73/1.24 , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, b )] )
% 0.73/1.24 ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2506, [ =( identity, 'least_upper_bound'( identity, multiply(
% 0.73/1.24 inverse( a ), b ) ) ) ] )
% 0.73/1.24 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.73/1.24 , 0, clause( 2505, [ =( multiply( inverse( a ), a ), 'least_upper_bound'(
% 0.73/1.24 identity, multiply( inverse( a ), b ) ) ) ] )
% 0.73/1.24 , 0, 1, substitution( 0, [ :=( X, a )] ), substitution( 1, [] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2507, [ =( 'least_upper_bound'( identity, multiply( inverse( a ), b
% 0.73/1.24 ) ), identity ) ] )
% 0.73/1.24 , clause( 2506, [ =( identity, 'least_upper_bound'( identity, multiply(
% 0.73/1.24 inverse( a ), b ) ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 1021, [ =( 'least_upper_bound'( identity, multiply( inverse( a ), b
% 0.73/1.24 ) ), identity ) ] )
% 0.73/1.24 , clause( 2507, [ =( 'least_upper_bound'( identity, multiply( inverse( a )
% 0.73/1.24 , b ) ), identity ) ] )
% 0.73/1.24 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2509, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.24 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 0.73/1.24 , clause( 453, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 0.73/1.24 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( Y, X ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2513, [ =( 'least_upper_bound'( multiply( inverse( a ), b ),
% 0.73/1.24 identity ), 'greatest_lower_bound'( 'least_upper_bound'( multiply(
% 0.73/1.24 inverse( a ), b ), identity ), identity ) ) ] )
% 0.73/1.24 , clause( 1021, [ =( 'least_upper_bound'( identity, multiply( inverse( a )
% 0.73/1.24 , b ) ), identity ) ] )
% 0.73/1.24 , 0, clause( 2509, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.24 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 0.73/1.24 , 0, 14, substitution( 0, [] ), substitution( 1, [ :=( X, multiply( inverse(
% 0.73/1.24 a ), b ) ), :=( Y, identity )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2515, [ =( 'least_upper_bound'( multiply( inverse( a ), b ),
% 0.73/1.24 identity ), identity ) ] )
% 0.73/1.24 , clause( 32, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ), X )
% 0.73/1.24 , X ) ] )
% 0.73/1.24 , 0, clause( 2513, [ =( 'least_upper_bound'( multiply( inverse( a ), b ),
% 0.73/1.24 identity ), 'greatest_lower_bound'( 'least_upper_bound'( multiply(
% 0.73/1.24 inverse( a ), b ), identity ), identity ) ) ] )
% 0.73/1.24 , 0, 7, substitution( 0, [ :=( X, identity ), :=( Y, multiply( inverse( a )
% 0.73/1.24 , b ) )] ), substitution( 1, [] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 1042, [ =( 'least_upper_bound'( multiply( inverse( a ), b ),
% 0.73/1.24 identity ), identity ) ] )
% 0.73/1.24 , clause( 2515, [ =( 'least_upper_bound'( multiply( inverse( a ), b ),
% 0.73/1.24 identity ), identity ) ] )
% 0.73/1.24 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2518, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 0.73/1.24 'least_upper_bound'( multiply( X, Y ), Y ) ) ] )
% 0.73/1.24 , clause( 90, [ =( 'least_upper_bound'( multiply( Y, X ), X ), multiply(
% 0.73/1.24 'least_upper_bound'( Y, identity ), X ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2520, [ =( multiply( identity, X ), 'least_upper_bound'( multiply(
% 0.73/1.24 multiply( inverse( a ), b ), X ), X ) ) ] )
% 0.73/1.24 , clause( 1042, [ =( 'least_upper_bound'( multiply( inverse( a ), b ),
% 0.73/1.24 identity ), identity ) ] )
% 0.73/1.24 , 0, clause( 2518, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 0.73/1.24 'least_upper_bound'( multiply( X, Y ), Y ) ) ] )
% 0.73/1.24 , 0, 2, substitution( 0, [] ), substitution( 1, [ :=( X, multiply( inverse(
% 0.73/1.24 a ), b ) ), :=( Y, X )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2521, [ =( X, 'least_upper_bound'( multiply( multiply( inverse( a )
% 0.73/1.24 , b ), X ), X ) ) ] )
% 0.73/1.24 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.73/1.24 , 0, clause( 2520, [ =( multiply( identity, X ), 'least_upper_bound'(
% 0.73/1.24 multiply( multiply( inverse( a ), b ), X ), X ) ) ] )
% 0.73/1.24 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.73/1.24 ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2522, [ =( 'least_upper_bound'( multiply( multiply( inverse( a ), b
% 0.73/1.24 ), X ), X ), X ) ] )
% 0.73/1.24 , clause( 2521, [ =( X, 'least_upper_bound'( multiply( multiply( inverse( a
% 0.73/1.24 ), b ), X ), X ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 2039, [ =( 'least_upper_bound'( multiply( multiply( inverse( a ), b
% 0.73/1.24 ), X ), X ), X ) ] )
% 0.73/1.24 , clause( 2522, [ =( 'least_upper_bound'( multiply( multiply( inverse( a )
% 0.73/1.24 , b ), X ), X ), X ) ] )
% 0.73/1.24 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2524, [ =( X, 'least_upper_bound'( multiply( multiply( inverse( a )
% 0.73/1.24 , b ), X ), X ) ) ] )
% 0.73/1.24 , clause( 2039, [ =( 'least_upper_bound'( multiply( multiply( inverse( a )
% 0.73/1.24 , b ), X ), X ), X ) ] )
% 0.73/1.24 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 eqswap(
% 0.73/1.24 clause( 2525, [ ~( =( inverse( b ), 'least_upper_bound'( inverse( a ),
% 0.73/1.24 inverse( b ) ) ) ) ] )
% 0.73/1.24 , clause( 16, [ ~( =( 'least_upper_bound'( inverse( a ), inverse( b ) ),
% 0.73/1.24 inverse( b ) ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 paramod(
% 0.73/1.24 clause( 2526, [ =( inverse( b ), 'least_upper_bound'( inverse( a ), inverse(
% 0.73/1.24 b ) ) ) ] )
% 0.73/1.24 , clause( 300, [ =( multiply( multiply( Y, X ), inverse( X ) ), Y ) ] )
% 0.73/1.24 , 0, clause( 2524, [ =( X, 'least_upper_bound'( multiply( multiply( inverse(
% 0.73/1.24 a ), b ), X ), X ) ) ] )
% 0.73/1.24 , 0, 4, substitution( 0, [ :=( X, b ), :=( Y, inverse( a ) )] ),
% 0.73/1.24 substitution( 1, [ :=( X, inverse( b ) )] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 resolution(
% 0.73/1.24 clause( 2527, [] )
% 0.73/1.24 , clause( 2525, [ ~( =( inverse( b ), 'least_upper_bound'( inverse( a ),
% 0.73/1.24 inverse( b ) ) ) ) ] )
% 0.73/1.24 , 0, clause( 2526, [ =( inverse( b ), 'least_upper_bound'( inverse( a ),
% 0.73/1.24 inverse( b ) ) ) ] )
% 0.73/1.24 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 subsumption(
% 0.73/1.24 clause( 2285, [] )
% 0.73/1.24 , clause( 2527, [] )
% 0.73/1.24 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 end.
% 0.73/1.24
% 0.73/1.24 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.73/1.24
% 0.73/1.24 Memory use:
% 0.73/1.24
% 0.73/1.24 space for terms: 30027
% 0.73/1.24 space for clauses: 251878
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 clauses generated: 32677
% 0.73/1.24 clauses kept: 2286
% 0.73/1.24 clauses selected: 273
% 0.73/1.24 clauses deleted: 20
% 0.73/1.24 clauses inuse deleted: 6
% 0.73/1.24
% 0.73/1.24 subsentry: 4471
% 0.73/1.24 literals s-matched: 3891
% 0.73/1.24 literals matched: 3863
% 0.73/1.24 full subsumption: 0
% 0.73/1.24
% 0.73/1.24 checksum: 2051754227
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Bliksem ended
%------------------------------------------------------------------------------