TSTP Solution File: GRP172-2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP172-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sat Jul 16 07:35:46 EDT 2022
% Result : Unsatisfiable 0.73s 1.14s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP172-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Mon Jun 13 19:26:23 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.73/1.14 *** allocated 10000 integers for termspace/termends
% 0.73/1.14 *** allocated 10000 integers for clauses
% 0.73/1.14 *** allocated 10000 integers for justifications
% 0.73/1.14 Bliksem 1.12
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 Automatic Strategy Selection
% 0.73/1.14
% 0.73/1.14 Clauses:
% 0.73/1.14 [
% 0.73/1.14 [ =( multiply( identity, X ), X ) ],
% 0.73/1.14 [ =( multiply( inverse( X ), X ), identity ) ],
% 0.73/1.14 [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply( Y, Z ) ) )
% 0.73/1.14 ],
% 0.73/1.14 [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, X ) ) ]
% 0.73/1.14 ,
% 0.73/1.14 [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ],
% 0.73/1.14 [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.73/1.14 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ],
% 0.73/1.14 [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.14 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ],
% 0.73/1.14 [ =( 'least_upper_bound'( X, X ), X ) ],
% 0.73/1.14 [ =( 'greatest_lower_bound'( X, X ), X ) ],
% 0.73/1.14 [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X ) ]
% 0.73/1.14 ,
% 0.73/1.14 [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ), X ) ]
% 0.73/1.14 ,
% 0.73/1.14 [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), 'least_upper_bound'(
% 0.73/1.14 multiply( X, Y ), multiply( X, Z ) ) ) ],
% 0.73/1.14 [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.73/1.14 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ],
% 0.73/1.14 [ =( multiply( 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'(
% 0.73/1.14 multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 0.73/1.14 [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 0.73/1.14 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 0.73/1.14 [ =( 'greatest_lower_bound'( identity, a ), identity ) ],
% 0.73/1.14 [ =( 'greatest_lower_bound'( identity, b ), identity ) ],
% 0.73/1.14 [ ~( =( 'least_upper_bound'( identity, multiply( a, b ) ), multiply( a,
% 0.73/1.14 b ) ) ) ]
% 0.73/1.14 ] .
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 percentage equality = 1.000000, percentage horn = 1.000000
% 0.73/1.14 This is a pure equality problem
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 Options Used:
% 0.73/1.14
% 0.73/1.14 useres = 1
% 0.73/1.14 useparamod = 1
% 0.73/1.14 useeqrefl = 1
% 0.73/1.14 useeqfact = 1
% 0.73/1.14 usefactor = 1
% 0.73/1.14 usesimpsplitting = 0
% 0.73/1.14 usesimpdemod = 5
% 0.73/1.14 usesimpres = 3
% 0.73/1.14
% 0.73/1.14 resimpinuse = 1000
% 0.73/1.14 resimpclauses = 20000
% 0.73/1.14 substype = eqrewr
% 0.73/1.14 backwardsubs = 1
% 0.73/1.14 selectoldest = 5
% 0.73/1.14
% 0.73/1.14 litorderings [0] = split
% 0.73/1.14 litorderings [1] = extend the termordering, first sorting on arguments
% 0.73/1.14
% 0.73/1.14 termordering = kbo
% 0.73/1.14
% 0.73/1.14 litapriori = 0
% 0.73/1.14 termapriori = 1
% 0.73/1.14 litaposteriori = 0
% 0.73/1.14 termaposteriori = 0
% 0.73/1.14 demodaposteriori = 0
% 0.73/1.14 ordereqreflfact = 0
% 0.73/1.14
% 0.73/1.14 litselect = negord
% 0.73/1.14
% 0.73/1.14 maxweight = 15
% 0.73/1.14 maxdepth = 30000
% 0.73/1.14 maxlength = 115
% 0.73/1.14 maxnrvars = 195
% 0.73/1.14 excuselevel = 1
% 0.73/1.14 increasemaxweight = 1
% 0.73/1.14
% 0.73/1.14 maxselected = 10000000
% 0.73/1.14 maxnrclauses = 10000000
% 0.73/1.14
% 0.73/1.14 showgenerated = 0
% 0.73/1.14 showkept = 0
% 0.73/1.14 showselected = 0
% 0.73/1.14 showdeleted = 0
% 0.73/1.14 showresimp = 1
% 0.73/1.14 showstatus = 2000
% 0.73/1.14
% 0.73/1.14 prologoutput = 1
% 0.73/1.14 nrgoals = 5000000
% 0.73/1.14 totalproof = 1
% 0.73/1.14
% 0.73/1.14 Symbols occurring in the translation:
% 0.73/1.14
% 0.73/1.14 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.73/1.14 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.73/1.14 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.73/1.14 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.14 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.14 identity [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.73/1.14 multiply [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.73/1.14 inverse [42, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.73/1.14 'greatest_lower_bound' [45, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.73/1.14 'least_upper_bound' [46, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.73/1.14 a [47, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.73/1.14 b [48, 0] (w:1, o:14, a:1, s:1, b:0).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 Starting Search:
% 0.73/1.14
% 0.73/1.14 Resimplifying inuse:
% 0.73/1.14 Done
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 Intermediate Status:
% 0.73/1.14 Generated: 27631
% 0.73/1.14 Kept: 2008
% 0.73/1.14 Inuse: 271
% 0.73/1.14 Deleted: 22
% 0.73/1.14 Deletedinuse: 6
% 0.73/1.14
% 0.73/1.14 Resimplifying inuse:
% 0.73/1.14
% 0.73/1.14 Bliksems!, er is een bewijs:
% 0.73/1.14 % SZS status Unsatisfiable
% 0.73/1.14 % SZS output start Refutation
% 0.73/1.14
% 0.73/1.14 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 0.73/1.14 , Z ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 0.73/1.14 X ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 0.73/1.14 ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.14 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 0.73/1.14 ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 0.73/1.14 X ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) )
% 0.73/1.14 , multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 15, [ =( 'greatest_lower_bound'( identity, a ), identity ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 16, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 17, [ ~( =( 'least_upper_bound'( identity, multiply( a, b ) ),
% 0.73/1.14 multiply( a, b ) ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 18, [ =( 'greatest_lower_bound'( a, identity ), identity ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 19, [ =( 'greatest_lower_bound'( b, identity ), identity ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 0.73/1.14 identity ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 22, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 0.73/1.14 ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 23, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.73/1.14 X ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 24, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) ),
% 0.73/1.14 X ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 43, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.73/1.14 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 44, [ =( 'least_upper_bound'( b, identity ), b ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 45, [ =( 'least_upper_bound'( a, identity ), a ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 48, [ =( 'least_upper_bound'( identity, b ), b ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 51, [ =( 'least_upper_bound'( 'least_upper_bound'( X, identity ), b
% 0.73/1.14 ), 'least_upper_bound'( X, b ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 54, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, Z ),
% 0.73/1.14 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ),
% 0.73/1.14 'least_upper_bound'( Y, Z ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 74, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y )
% 0.73/1.14 ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 75, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ), identity
% 0.73/1.14 ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 141, [ ~( =( 'least_upper_bound'( multiply( a, b ), identity ),
% 0.73/1.14 multiply( a, b ) ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 161, [ =( 'least_upper_bound'( 'least_upper_bound'( identity, X ),
% 0.73/1.14 b ), 'least_upper_bound'( X, b ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 173, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 179, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.73/1.14 ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 411, [ =( multiply( X, identity ), X ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 419, [ =( inverse( inverse( X ) ), X ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 465, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 0.73/1.14 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( Y, X ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 1180, [ =( 'least_upper_bound'( identity, inverse( a ) ), identity
% 0.73/1.14 ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 1200, [ =( 'least_upper_bound'( inverse( a ), b ), b ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 1206, [ =( 'least_upper_bound'( b, inverse( a ) ), b ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 1223, [ =( 'least_upper_bound'( multiply( a, b ), identity ),
% 0.73/1.14 multiply( a, b ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 2022, [] )
% 0.73/1.14 .
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 % SZS output end Refutation
% 0.73/1.14 found a proof!
% 0.73/1.14
% 0.73/1.14 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.73/1.14
% 0.73/1.14 initialclauses(
% 0.73/1.14 [ clause( 2024, [ =( multiply( identity, X ), X ) ] )
% 0.73/1.14 , clause( 2025, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.73/1.14 , clause( 2026, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.73/1.14 Y, Z ) ) ) ] )
% 0.73/1.14 , clause( 2027, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.14 Y, X ) ) ] )
% 0.73/1.14 , clause( 2028, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X
% 0.73/1.14 ) ) ] )
% 0.73/1.14 , clause( 2029, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y,
% 0.73/1.14 Z ) ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 0.73/1.14 , clause( 2030, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 0.73/1.14 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.73/1.14 , clause( 2031, [ =( 'least_upper_bound'( X, X ), X ) ] )
% 0.73/1.14 , clause( 2032, [ =( 'greatest_lower_bound'( X, X ), X ) ] )
% 0.73/1.14 , clause( 2033, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y )
% 0.73/1.14 ), X ) ] )
% 0.73/1.14 , clause( 2034, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y )
% 0.73/1.14 ), X ) ] )
% 0.73/1.14 , clause( 2035, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.14 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.73/1.14 , clause( 2036, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.73/1.14 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.73/1.14 , clause( 2037, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 0.73/1.14 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 0.73/1.14 , clause( 2038, [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 0.73/1.14 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 0.73/1.14 , clause( 2039, [ =( 'greatest_lower_bound'( identity, a ), identity ) ] )
% 0.73/1.14 , clause( 2040, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.73/1.14 , clause( 2041, [ ~( =( 'least_upper_bound'( identity, multiply( a, b ) ),
% 0.73/1.14 multiply( a, b ) ) ) ] )
% 0.73/1.14 ] ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.73/1.14 , clause( 2024, [ =( multiply( identity, X ), X ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.73/1.14 , clause( 2025, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2047, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X,
% 0.73/1.14 Y ), Z ) ) ] )
% 0.73/1.14 , clause( 2026, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.73/1.14 Y, Z ) ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 0.73/1.14 , Z ) ) ] )
% 0.73/1.14 , clause( 2047, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X
% 0.73/1.14 , Y ), Z ) ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.73/1.14 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 0.73/1.14 X ) ) ] )
% 0.73/1.14 , clause( 2027, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.14 Y, X ) ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.14 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 0.73/1.14 ] )
% 0.73/1.14 , clause( 2028, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X
% 0.73/1.14 ) ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.14 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.14 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.73/1.14 , clause( 2030, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 0.73/1.14 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.73/1.14 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 0.73/1.14 ) ] )
% 0.73/1.14 , clause( 2033, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y )
% 0.73/1.14 ), X ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.14 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 0.73/1.14 X ) ] )
% 0.73/1.14 , clause( 2034, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y )
% 0.73/1.14 ), X ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.14 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2085, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 0.73/1.14 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.73/1.14 , clause( 2035, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.14 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) )
% 0.73/1.14 , multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.73/1.14 , clause( 2085, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z
% 0.73/1.14 ) ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.73/1.14 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 15, [ =( 'greatest_lower_bound'( identity, a ), identity ) ] )
% 0.73/1.14 , clause( 2039, [ =( 'greatest_lower_bound'( identity, a ), identity ) ] )
% 0.73/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 16, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.73/1.14 , clause( 2040, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.73/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 17, [ ~( =( 'least_upper_bound'( identity, multiply( a, b ) ),
% 0.73/1.14 multiply( a, b ) ) ) ] )
% 0.73/1.14 , clause( 2041, [ ~( =( 'least_upper_bound'( identity, multiply( a, b ) ),
% 0.73/1.14 multiply( a, b ) ) ) ] )
% 0.73/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2131, [ =( identity, 'greatest_lower_bound'( identity, a ) ) ] )
% 0.73/1.14 , clause( 15, [ =( 'greatest_lower_bound'( identity, a ), identity ) ] )
% 0.73/1.14 , 0, substitution( 0, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2132, [ =( identity, 'greatest_lower_bound'( a, identity ) ) ] )
% 0.73/1.14 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 0.73/1.14 , X ) ) ] )
% 0.73/1.14 , 0, clause( 2131, [ =( identity, 'greatest_lower_bound'( identity, a ) ) ]
% 0.73/1.14 )
% 0.73/1.14 , 0, 2, substitution( 0, [ :=( X, identity ), :=( Y, a )] ), substitution(
% 0.73/1.14 1, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2135, [ =( 'greatest_lower_bound'( a, identity ), identity ) ] )
% 0.73/1.14 , clause( 2132, [ =( identity, 'greatest_lower_bound'( a, identity ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 18, [ =( 'greatest_lower_bound'( a, identity ), identity ) ] )
% 0.73/1.14 , clause( 2135, [ =( 'greatest_lower_bound'( a, identity ), identity ) ] )
% 0.73/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2136, [ =( identity, 'greatest_lower_bound'( identity, b ) ) ] )
% 0.73/1.14 , clause( 16, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.73/1.14 , 0, substitution( 0, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2137, [ =( identity, 'greatest_lower_bound'( b, identity ) ) ] )
% 0.73/1.14 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 0.73/1.14 , X ) ) ] )
% 0.73/1.14 , 0, clause( 2136, [ =( identity, 'greatest_lower_bound'( identity, b ) ) ]
% 0.73/1.14 )
% 0.73/1.14 , 0, 2, substitution( 0, [ :=( X, identity ), :=( Y, b )] ), substitution(
% 0.73/1.14 1, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2140, [ =( 'greatest_lower_bound'( b, identity ), identity ) ] )
% 0.73/1.14 , clause( 2137, [ =( identity, 'greatest_lower_bound'( b, identity ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 19, [ =( 'greatest_lower_bound'( b, identity ), identity ) ] )
% 0.73/1.14 , clause( 2140, [ =( 'greatest_lower_bound'( b, identity ), identity ) ] )
% 0.73/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2142, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.73/1.14 Y, Z ) ) ) ] )
% 0.73/1.14 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 0.73/1.14 ), Z ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2147, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply( X
% 0.73/1.14 , identity ) ) ] )
% 0.73/1.14 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.73/1.14 , 0, clause( 2142, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 0.73/1.14 multiply( Y, Z ) ) ) ] )
% 0.73/1.14 , 0, 9, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 0.73/1.14 :=( Y, inverse( Y ) ), :=( Z, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 0.73/1.14 identity ) ) ] )
% 0.73/1.14 , clause( 2147, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply(
% 0.73/1.14 X, identity ) ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.14 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2152, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.73/1.14 Y, Z ) ) ) ] )
% 0.73/1.14 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 0.73/1.14 ), Z ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2157, [ =( multiply( multiply( X, identity ), Y ), multiply( X, Y )
% 0.73/1.14 ) ] )
% 0.73/1.14 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.73/1.14 , 0, clause( 2152, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 0.73/1.14 multiply( Y, Z ) ) ) ] )
% 0.73/1.14 , 0, 8, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 0.73/1.14 :=( Y, identity ), :=( Z, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 22, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 0.73/1.14 ] )
% 0.73/1.14 , clause( 2157, [ =( multiply( multiply( X, identity ), Y ), multiply( X, Y
% 0.73/1.14 ) ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.14 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2162, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 0.73/1.14 ) ) ) ] )
% 0.73/1.14 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 0.73/1.14 , X ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2163, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.73/1.14 X ) ) ] )
% 0.73/1.14 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 0.73/1.14 , X ) ) ] )
% 0.73/1.14 , 0, clause( 2162, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 0.73/1.14 X, Y ) ) ) ] )
% 0.73/1.14 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, 'least_upper_bound'( X, Y ) )] )
% 0.73/1.14 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2166, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 0.73/1.14 , X ) ] )
% 0.73/1.14 , clause( 2163, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y )
% 0.73/1.14 , X ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 23, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.73/1.14 X ) ] )
% 0.73/1.14 , clause( 2166, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X
% 0.73/1.14 ), X ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.14 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2167, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 0.73/1.14 ) ) ) ] )
% 0.73/1.14 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 0.73/1.14 , X ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2168, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 0.73/1.14 ) ) ) ] )
% 0.73/1.14 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 0.73/1.14 ) ] )
% 0.73/1.14 , 0, clause( 2167, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 0.73/1.14 X, Y ) ) ) ] )
% 0.73/1.14 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.73/1.14 :=( X, X ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2171, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) )
% 0.73/1.14 , X ) ] )
% 0.73/1.14 , clause( 2168, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y,
% 0.73/1.14 X ) ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 24, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) ),
% 0.73/1.14 X ) ] )
% 0.73/1.14 , clause( 2171, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X )
% 0.73/1.14 ), X ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.14 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2173, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 0.73/1.14 ) ) ) ] )
% 0.73/1.14 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 0.73/1.14 , X ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2176, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 0.73/1.14 'least_upper_bound'( X, Y ), X ) ) ] )
% 0.73/1.14 , clause( 23, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 0.73/1.14 , X ) ] )
% 0.73/1.14 , 0, clause( 2173, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 0.73/1.14 X, Y ) ) ) ] )
% 0.73/1.14 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.73/1.14 :=( X, 'least_upper_bound'( X, Y ) ), :=( Y, X )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2177, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.73/1.14 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.14 , clause( 2176, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 0.73/1.14 'least_upper_bound'( X, Y ), X ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 43, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.73/1.14 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.14 , clause( 2177, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X )
% 0.73/1.14 , 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.14 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2179, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 0.73/1.14 ) ) ) ] )
% 0.73/1.14 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 0.73/1.14 , X ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2180, [ =( b, 'least_upper_bound'( b, identity ) ) ] )
% 0.73/1.14 , clause( 19, [ =( 'greatest_lower_bound'( b, identity ), identity ) ] )
% 0.73/1.14 , 0, clause( 2179, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 0.73/1.14 X, Y ) ) ) ] )
% 0.73/1.14 , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, b ), :=( Y,
% 0.73/1.14 identity )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2181, [ =( 'least_upper_bound'( b, identity ), b ) ] )
% 0.73/1.14 , clause( 2180, [ =( b, 'least_upper_bound'( b, identity ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 44, [ =( 'least_upper_bound'( b, identity ), b ) ] )
% 0.73/1.14 , clause( 2181, [ =( 'least_upper_bound'( b, identity ), b ) ] )
% 0.73/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2183, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 0.73/1.14 ) ) ) ] )
% 0.73/1.14 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 0.73/1.14 , X ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2184, [ =( a, 'least_upper_bound'( a, identity ) ) ] )
% 0.73/1.14 , clause( 18, [ =( 'greatest_lower_bound'( a, identity ), identity ) ] )
% 0.73/1.14 , 0, clause( 2183, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 0.73/1.14 X, Y ) ) ) ] )
% 0.73/1.14 , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y,
% 0.73/1.14 identity )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2185, [ =( 'least_upper_bound'( a, identity ), a ) ] )
% 0.73/1.14 , clause( 2184, [ =( a, 'least_upper_bound'( a, identity ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 45, [ =( 'least_upper_bound'( a, identity ), a ) ] )
% 0.73/1.14 , clause( 2185, [ =( 'least_upper_bound'( a, identity ), a ) ] )
% 0.73/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2186, [ =( b, 'least_upper_bound'( b, identity ) ) ] )
% 0.73/1.14 , clause( 44, [ =( 'least_upper_bound'( b, identity ), b ) ] )
% 0.73/1.14 , 0, substitution( 0, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2187, [ =( b, 'least_upper_bound'( identity, b ) ) ] )
% 0.73/1.14 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 0.73/1.14 ) ] )
% 0.73/1.14 , 0, clause( 2186, [ =( b, 'least_upper_bound'( b, identity ) ) ] )
% 0.73/1.14 , 0, 2, substitution( 0, [ :=( X, b ), :=( Y, identity )] ), substitution(
% 0.73/1.14 1, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2190, [ =( 'least_upper_bound'( identity, b ), b ) ] )
% 0.73/1.14 , clause( 2187, [ =( b, 'least_upper_bound'( identity, b ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 48, [ =( 'least_upper_bound'( identity, b ), b ) ] )
% 0.73/1.14 , clause( 2190, [ =( 'least_upper_bound'( identity, b ), b ) ] )
% 0.73/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2192, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 0.73/1.14 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.73/1.14 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.14 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2194, [ =( 'least_upper_bound'( 'least_upper_bound'( X, identity )
% 0.73/1.14 , b ), 'least_upper_bound'( X, b ) ) ] )
% 0.73/1.14 , clause( 48, [ =( 'least_upper_bound'( identity, b ), b ) ] )
% 0.73/1.14 , 0, clause( 2192, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z
% 0.73/1.14 ), 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.73/1.14 , 0, 8, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y,
% 0.73/1.14 identity ), :=( Z, b )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 51, [ =( 'least_upper_bound'( 'least_upper_bound'( X, identity ), b
% 0.73/1.14 ), 'least_upper_bound'( X, b ) ) ] )
% 0.73/1.14 , clause( 2194, [ =( 'least_upper_bound'( 'least_upper_bound'( X, identity
% 0.73/1.14 ), b ), 'least_upper_bound'( X, b ) ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2198, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X
% 0.73/1.14 ) ) ) ] )
% 0.73/1.14 , clause( 24, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( Y, X ) )
% 0.73/1.14 , X ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2199, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.14 'least_upper_bound'( X, Y ), 'least_upper_bound'( 'least_upper_bound'( Z
% 0.73/1.14 , X ), Y ) ) ) ] )
% 0.73/1.14 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.14 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.73/1.14 , 0, clause( 2198, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 0.73/1.14 Y, X ) ) ) ] )
% 0.73/1.14 , 0, 8, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 0.73/1.14 substitution( 1, [ :=( X, 'least_upper_bound'( X, Y ) ), :=( Y, Z )] )
% 0.73/1.14 ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2200, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.73/1.14 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ) ),
% 0.73/1.14 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.14 , clause( 2199, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.14 'least_upper_bound'( X, Y ), 'least_upper_bound'( 'least_upper_bound'( Z
% 0.73/1.14 , X ), Y ) ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 54, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, Z ),
% 0.73/1.14 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ),
% 0.73/1.14 'least_upper_bound'( Y, Z ) ) ] )
% 0.73/1.14 , clause( 2200, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.73/1.14 'least_upper_bound'( 'least_upper_bound'( Z, X ), Y ) ),
% 0.73/1.14 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 0.73/1.14 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2202, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.14 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.73/1.14 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 0.73/1.14 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2204, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) ),
% 0.73/1.14 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 0.73/1.14 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.73/1.14 , 0, clause( 2202, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.14 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.73/1.14 , 0, 8, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 0.73/1.14 X ) ), :=( Y, X ), :=( Z, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2207, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y
% 0.73/1.14 ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 0.73/1.14 , clause( 2204, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) )
% 0.73/1.14 , 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 74, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y )
% 0.73/1.14 ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 0.73/1.14 , clause( 2207, [ =( 'least_upper_bound'( identity, multiply( inverse( X )
% 0.73/1.14 , Y ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.14 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2210, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.14 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.73/1.14 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 0.73/1.14 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2213, [ =( multiply( inverse( X ), 'least_upper_bound'( Y, X ) ),
% 0.73/1.14 'least_upper_bound'( multiply( inverse( X ), Y ), identity ) ) ] )
% 0.73/1.14 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.73/1.14 , 0, clause( 2210, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 0.73/1.14 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.73/1.14 , 0, 12, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 0.73/1.14 inverse( X ) ), :=( Y, Y ), :=( Z, X )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2216, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ),
% 0.73/1.14 identity ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 0.73/1.14 , clause( 2213, [ =( multiply( inverse( X ), 'least_upper_bound'( Y, X ) )
% 0.73/1.14 , 'least_upper_bound'( multiply( inverse( X ), Y ), identity ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 75, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ), identity
% 0.73/1.14 ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 0.73/1.14 , clause( 2216, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ),
% 0.73/1.14 identity ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.14 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2217, [ ~( =( multiply( a, b ), 'least_upper_bound'( identity,
% 0.73/1.14 multiply( a, b ) ) ) ) ] )
% 0.73/1.14 , clause( 17, [ ~( =( 'least_upper_bound'( identity, multiply( a, b ) ),
% 0.73/1.14 multiply( a, b ) ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2218, [ ~( =( multiply( a, b ), 'least_upper_bound'( multiply( a, b
% 0.73/1.14 ), identity ) ) ) ] )
% 0.73/1.14 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 0.73/1.14 ) ] )
% 0.73/1.14 , 0, clause( 2217, [ ~( =( multiply( a, b ), 'least_upper_bound'( identity
% 0.73/1.14 , multiply( a, b ) ) ) ) ] )
% 0.73/1.14 , 0, 5, substitution( 0, [ :=( X, identity ), :=( Y, multiply( a, b ) )] )
% 0.73/1.14 , substitution( 1, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2221, [ ~( =( 'least_upper_bound'( multiply( a, b ), identity ),
% 0.73/1.14 multiply( a, b ) ) ) ] )
% 0.73/1.14 , clause( 2218, [ ~( =( multiply( a, b ), 'least_upper_bound'( multiply( a
% 0.73/1.14 , b ), identity ) ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 141, [ ~( =( 'least_upper_bound'( multiply( a, b ), identity ),
% 0.73/1.14 multiply( a, b ) ) ) ] )
% 0.73/1.14 , clause( 2221, [ ~( =( 'least_upper_bound'( multiply( a, b ), identity ),
% 0.73/1.14 multiply( a, b ) ) ) ] )
% 0.73/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2222, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 0.73/1.14 'least_upper_bound'( X, identity ), b ) ) ] )
% 0.73/1.14 , clause( 51, [ =( 'least_upper_bound'( 'least_upper_bound'( X, identity )
% 0.73/1.14 , b ), 'least_upper_bound'( X, b ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2225, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 0.73/1.14 'least_upper_bound'( identity, X ), b ) ) ] )
% 0.73/1.14 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 0.73/1.14 ) ] )
% 0.73/1.14 , 0, clause( 2222, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 0.73/1.14 'least_upper_bound'( X, identity ), b ) ) ] )
% 0.73/1.14 , 0, 5, substitution( 0, [ :=( X, X ), :=( Y, identity )] ), substitution(
% 0.73/1.14 1, [ :=( X, X )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2238, [ =( 'least_upper_bound'( 'least_upper_bound'( identity, X )
% 0.73/1.14 , b ), 'least_upper_bound'( X, b ) ) ] )
% 0.73/1.14 , clause( 2225, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 0.73/1.14 'least_upper_bound'( identity, X ), b ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 161, [ =( 'least_upper_bound'( 'least_upper_bound'( identity, X ),
% 0.73/1.14 b ), 'least_upper_bound'( X, b ) ) ] )
% 0.73/1.14 , clause( 2238, [ =( 'least_upper_bound'( 'least_upper_bound'( identity, X
% 0.73/1.14 ), b ), 'least_upper_bound'( X, b ) ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2240, [ =( multiply( X, identity ), multiply( multiply( X, inverse(
% 0.73/1.14 Y ) ), Y ) ) ] )
% 0.73/1.14 , clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 0.73/1.14 , identity ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2243, [ =( multiply( inverse( inverse( X ) ), identity ), multiply(
% 0.73/1.14 identity, X ) ) ] )
% 0.73/1.14 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.73/1.14 , 0, clause( 2240, [ =( multiply( X, identity ), multiply( multiply( X,
% 0.73/1.14 inverse( Y ) ), Y ) ) ] )
% 0.73/1.14 , 0, 7, substitution( 0, [ :=( X, inverse( X ) )] ), substitution( 1, [
% 0.73/1.14 :=( X, inverse( inverse( X ) ) ), :=( Y, X )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2244, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.73/1.14 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.73/1.14 , 0, clause( 2243, [ =( multiply( inverse( inverse( X ) ), identity ),
% 0.73/1.14 multiply( identity, X ) ) ] )
% 0.73/1.14 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.73/1.14 ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 173, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.73/1.14 , clause( 2244, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ]
% 0.73/1.14 )
% 0.73/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2247, [ =( multiply( X, Y ), multiply( multiply( X, identity ), Y )
% 0.73/1.14 ) ] )
% 0.73/1.14 , clause( 22, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X )
% 0.73/1.14 ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2250, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.73/1.14 ) ] )
% 0.73/1.14 , clause( 173, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.73/1.14 , 0, clause( 2247, [ =( multiply( X, Y ), multiply( multiply( X, identity )
% 0.73/1.14 , Y ) ) ] )
% 0.73/1.14 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 0.73/1.14 inverse( X ) ) ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 179, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.73/1.14 ) ] )
% 0.73/1.14 , clause( 2250, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.73/1.14 ) ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.14 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2256, [ =( multiply( X, Y ), multiply( inverse( inverse( X ) ), Y )
% 0.73/1.14 ) ] )
% 0.73/1.14 , clause( 179, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.73/1.14 ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2259, [ =( multiply( X, identity ), X ) ] )
% 0.73/1.14 , clause( 173, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.73/1.14 , 0, clause( 2256, [ =( multiply( X, Y ), multiply( inverse( inverse( X ) )
% 0.73/1.14 , Y ) ) ] )
% 0.73/1.14 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.73/1.14 :=( Y, identity )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 411, [ =( multiply( X, identity ), X ) ] )
% 0.73/1.14 , clause( 2259, [ =( multiply( X, identity ), X ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2264, [ =( X, multiply( X, identity ) ) ] )
% 0.73/1.14 , clause( 411, [ =( multiply( X, identity ), X ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2267, [ =( inverse( inverse( X ) ), multiply( X, identity ) ) ] )
% 0.73/1.14 , clause( 179, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.73/1.14 ) ) ] )
% 0.73/1.14 , 0, clause( 2264, [ =( X, multiply( X, identity ) ) ] )
% 0.73/1.14 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, identity )] ), substitution(
% 0.73/1.14 1, [ :=( X, inverse( inverse( X ) ) )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2268, [ =( inverse( inverse( X ) ), X ) ] )
% 0.73/1.14 , clause( 411, [ =( multiply( X, identity ), X ) ] )
% 0.73/1.14 , 0, clause( 2267, [ =( inverse( inverse( X ) ), multiply( X, identity ) )
% 0.73/1.14 ] )
% 0.73/1.14 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.73/1.14 ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 419, [ =( inverse( inverse( X ) ), X ) ] )
% 0.73/1.14 , clause( 2268, [ =( inverse( inverse( X ) ), X ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2271, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.14 'least_upper_bound'( X, Y ), 'least_upper_bound'( 'least_upper_bound'( Z
% 0.73/1.14 , X ), Y ) ) ) ] )
% 0.73/1.14 , clause( 54, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, Z ),
% 0.73/1.14 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ),
% 0.73/1.14 'least_upper_bound'( Y, Z ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2274, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.14 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 0.73/1.14 , clause( 43, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 0.73/1.14 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.14 , 0, clause( 2271, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.14 'least_upper_bound'( X, Y ), 'least_upper_bound'( 'least_upper_bound'( Z
% 0.73/1.14 , X ), Y ) ) ) ] )
% 0.73/1.14 , 0, 8, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 0.73/1.14 :=( X, X ), :=( Y, Y ), :=( Z, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2280, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.73/1.14 'least_upper_bound'( Y, X ) ), 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.14 , clause( 2274, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.14 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 465, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 0.73/1.14 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( Y, X ) ) ] )
% 0.73/1.14 , clause( 2280, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 0.73/1.14 'least_upper_bound'( Y, X ) ), 'least_upper_bound'( X, Y ) ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.14 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2283, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y ) ),
% 0.73/1.14 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 0.73/1.14 , clause( 74, [ =( 'least_upper_bound'( identity, multiply( inverse( X ), Y
% 0.73/1.14 ) ), multiply( inverse( X ), 'least_upper_bound'( X, Y ) ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2286, [ =( multiply( inverse( a ), a ), 'least_upper_bound'(
% 0.73/1.14 identity, multiply( inverse( a ), identity ) ) ) ] )
% 0.73/1.14 , clause( 45, [ =( 'least_upper_bound'( a, identity ), a ) ] )
% 0.73/1.14 , 0, clause( 2283, [ =( multiply( inverse( X ), 'least_upper_bound'( X, Y )
% 0.73/1.14 ), 'least_upper_bound'( identity, multiply( inverse( X ), Y ) ) ) ] )
% 0.73/1.14 , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y,
% 0.73/1.14 identity )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2287, [ =( multiply( inverse( a ), a ), 'least_upper_bound'(
% 0.73/1.14 identity, inverse( a ) ) ) ] )
% 0.73/1.14 , clause( 411, [ =( multiply( X, identity ), X ) ] )
% 0.73/1.14 , 0, clause( 2286, [ =( multiply( inverse( a ), a ), 'least_upper_bound'(
% 0.73/1.14 identity, multiply( inverse( a ), identity ) ) ) ] )
% 0.73/1.14 , 0, 7, substitution( 0, [ :=( X, inverse( a ) )] ), substitution( 1, [] )
% 0.73/1.14 ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2288, [ =( identity, 'least_upper_bound'( identity, inverse( a ) )
% 0.73/1.14 ) ] )
% 0.73/1.14 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.73/1.14 , 0, clause( 2287, [ =( multiply( inverse( a ), a ), 'least_upper_bound'(
% 0.73/1.14 identity, inverse( a ) ) ) ] )
% 0.73/1.14 , 0, 1, substitution( 0, [ :=( X, a )] ), substitution( 1, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2289, [ =( 'least_upper_bound'( identity, inverse( a ) ), identity
% 0.73/1.14 ) ] )
% 0.73/1.14 , clause( 2288, [ =( identity, 'least_upper_bound'( identity, inverse( a )
% 0.73/1.14 ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 1180, [ =( 'least_upper_bound'( identity, inverse( a ) ), identity
% 0.73/1.14 ) ] )
% 0.73/1.14 , clause( 2289, [ =( 'least_upper_bound'( identity, inverse( a ) ),
% 0.73/1.14 identity ) ] )
% 0.73/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2291, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 0.73/1.14 'least_upper_bound'( identity, X ), b ) ) ] )
% 0.73/1.14 , clause( 161, [ =( 'least_upper_bound'( 'least_upper_bound'( identity, X )
% 0.73/1.14 , b ), 'least_upper_bound'( X, b ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2293, [ =( 'least_upper_bound'( inverse( a ), b ),
% 0.73/1.14 'least_upper_bound'( identity, b ) ) ] )
% 0.73/1.14 , clause( 1180, [ =( 'least_upper_bound'( identity, inverse( a ) ),
% 0.73/1.14 identity ) ] )
% 0.73/1.14 , 0, clause( 2291, [ =( 'least_upper_bound'( X, b ), 'least_upper_bound'(
% 0.73/1.14 'least_upper_bound'( identity, X ), b ) ) ] )
% 0.73/1.14 , 0, 6, substitution( 0, [] ), substitution( 1, [ :=( X, inverse( a ) )] )
% 0.73/1.14 ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2294, [ =( 'least_upper_bound'( inverse( a ), b ), b ) ] )
% 0.73/1.14 , clause( 48, [ =( 'least_upper_bound'( identity, b ), b ) ] )
% 0.73/1.14 , 0, clause( 2293, [ =( 'least_upper_bound'( inverse( a ), b ),
% 0.73/1.14 'least_upper_bound'( identity, b ) ) ] )
% 0.73/1.14 , 0, 5, substitution( 0, [] ), substitution( 1, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 1200, [ =( 'least_upper_bound'( inverse( a ), b ), b ) ] )
% 0.73/1.14 , clause( 2294, [ =( 'least_upper_bound'( inverse( a ), b ), b ) ] )
% 0.73/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2297, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.14 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 0.73/1.14 , clause( 465, [ =( 'greatest_lower_bound'( 'least_upper_bound'( Y, X ),
% 0.73/1.14 'least_upper_bound'( X, Y ) ), 'least_upper_bound'( Y, X ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2301, [ =( 'least_upper_bound'( b, inverse( a ) ),
% 0.73/1.14 'greatest_lower_bound'( 'least_upper_bound'( b, inverse( a ) ), b ) ) ]
% 0.73/1.14 )
% 0.73/1.14 , clause( 1200, [ =( 'least_upper_bound'( inverse( a ), b ), b ) ] )
% 0.73/1.14 , 0, clause( 2297, [ =( 'least_upper_bound'( X, Y ), 'greatest_lower_bound'(
% 0.73/1.14 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ) ] )
% 0.73/1.14 , 0, 10, substitution( 0, [] ), substitution( 1, [ :=( X, b ), :=( Y,
% 0.73/1.14 inverse( a ) )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2303, [ =( 'least_upper_bound'( b, inverse( a ) ), b ) ] )
% 0.73/1.14 , clause( 23, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 0.73/1.14 , X ) ] )
% 0.73/1.14 , 0, clause( 2301, [ =( 'least_upper_bound'( b, inverse( a ) ),
% 0.73/1.14 'greatest_lower_bound'( 'least_upper_bound'( b, inverse( a ) ), b ) ) ]
% 0.73/1.14 )
% 0.73/1.14 , 0, 5, substitution( 0, [ :=( X, b ), :=( Y, inverse( a ) )] ),
% 0.73/1.14 substitution( 1, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 1206, [ =( 'least_upper_bound'( b, inverse( a ) ), b ) ] )
% 0.73/1.14 , clause( 2303, [ =( 'least_upper_bound'( b, inverse( a ) ), b ) ] )
% 0.73/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2306, [ =( multiply( inverse( X ), 'least_upper_bound'( Y, X ) ),
% 0.73/1.14 'least_upper_bound'( multiply( inverse( X ), Y ), identity ) ) ] )
% 0.73/1.14 , clause( 75, [ =( 'least_upper_bound'( multiply( inverse( X ), Y ),
% 0.73/1.14 identity ), multiply( inverse( X ), 'least_upper_bound'( Y, X ) ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2308, [ =( multiply( inverse( inverse( a ) ), b ),
% 0.73/1.14 'least_upper_bound'( multiply( inverse( inverse( a ) ), b ), identity ) )
% 0.73/1.14 ] )
% 0.73/1.14 , clause( 1206, [ =( 'least_upper_bound'( b, inverse( a ) ), b ) ] )
% 0.73/1.14 , 0, clause( 2306, [ =( multiply( inverse( X ), 'least_upper_bound'( Y, X )
% 0.73/1.14 ), 'least_upper_bound'( multiply( inverse( X ), Y ), identity ) ) ] )
% 0.73/1.14 , 0, 5, substitution( 0, [] ), substitution( 1, [ :=( X, inverse( a ) ),
% 0.73/1.14 :=( Y, b )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2310, [ =( multiply( inverse( inverse( a ) ), b ),
% 0.73/1.14 'least_upper_bound'( multiply( a, b ), identity ) ) ] )
% 0.73/1.14 , clause( 419, [ =( inverse( inverse( X ) ), X ) ] )
% 0.73/1.14 , 0, clause( 2308, [ =( multiply( inverse( inverse( a ) ), b ),
% 0.73/1.14 'least_upper_bound'( multiply( inverse( inverse( a ) ), b ), identity ) )
% 0.73/1.14 ] )
% 0.73/1.14 , 0, 8, substitution( 0, [ :=( X, a )] ), substitution( 1, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2311, [ =( multiply( a, b ), 'least_upper_bound'( multiply( a, b )
% 0.73/1.14 , identity ) ) ] )
% 0.73/1.14 , clause( 419, [ =( inverse( inverse( X ) ), X ) ] )
% 0.73/1.14 , 0, clause( 2310, [ =( multiply( inverse( inverse( a ) ), b ),
% 0.73/1.14 'least_upper_bound'( multiply( a, b ), identity ) ) ] )
% 0.73/1.14 , 0, 2, substitution( 0, [ :=( X, a )] ), substitution( 1, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqswap(
% 0.73/1.14 clause( 2313, [ =( 'least_upper_bound'( multiply( a, b ), identity ),
% 0.73/1.14 multiply( a, b ) ) ] )
% 0.73/1.14 , clause( 2311, [ =( multiply( a, b ), 'least_upper_bound'( multiply( a, b
% 0.73/1.14 ), identity ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 1223, [ =( 'least_upper_bound'( multiply( a, b ), identity ),
% 0.73/1.14 multiply( a, b ) ) ] )
% 0.73/1.14 , clause( 2313, [ =( 'least_upper_bound'( multiply( a, b ), identity ),
% 0.73/1.14 multiply( a, b ) ) ] )
% 0.73/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 paramod(
% 0.73/1.14 clause( 2317, [ ~( =( multiply( a, b ), multiply( a, b ) ) ) ] )
% 0.73/1.14 , clause( 1223, [ =( 'least_upper_bound'( multiply( a, b ), identity ),
% 0.73/1.14 multiply( a, b ) ) ] )
% 0.73/1.14 , 0, clause( 141, [ ~( =( 'least_upper_bound'( multiply( a, b ), identity )
% 0.73/1.14 , multiply( a, b ) ) ) ] )
% 0.73/1.14 , 0, 2, substitution( 0, [] ), substitution( 1, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 eqrefl(
% 0.73/1.14 clause( 2318, [] )
% 0.73/1.14 , clause( 2317, [ ~( =( multiply( a, b ), multiply( a, b ) ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 2022, [] )
% 0.73/1.14 , clause( 2318, [] )
% 0.73/1.14 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 end.
% 0.73/1.14
% 0.73/1.14 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.73/1.14
% 0.73/1.14 Memory use:
% 0.73/1.14
% 0.73/1.14 space for terms: 25305
% 0.73/1.14 space for clauses: 207301
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 clauses generated: 27843
% 0.73/1.14 clauses kept: 2023
% 0.73/1.14 clauses selected: 274
% 0.73/1.14 clauses deleted: 23
% 0.73/1.14 clauses inuse deleted: 7
% 0.73/1.14
% 0.73/1.14 subsentry: 5167
% 0.73/1.14 literals s-matched: 4253
% 0.73/1.14 literals matched: 4229
% 0.73/1.14 full subsumption: 0
% 0.73/1.14
% 0.73/1.14 checksum: -2038013604
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 Bliksem ended
%------------------------------------------------------------------------------