TSTP Solution File: GRP185-2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP185-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n010.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 07:35:58 EDT 2022
% Result : Unsatisfiable 1.31s 1.73s
% Output : Refutation 1.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP185-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n010.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 : Mon Jun 13 07:11:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.31/1.73 *** allocated 10000 integers for termspace/termends
% 1.31/1.73 *** allocated 10000 integers for clauses
% 1.31/1.73 *** allocated 10000 integers for justifications
% 1.31/1.73 Bliksem 1.12
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 Automatic Strategy Selection
% 1.31/1.73
% 1.31/1.73 Clauses:
% 1.31/1.73 [
% 1.31/1.73 [ =( multiply( identity, X ), X ) ],
% 1.31/1.73 [ =( multiply( inverse( X ), X ), identity ) ],
% 1.31/1.73 [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply( Y, Z ) ) )
% 1.31/1.73 ],
% 1.31/1.73 [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, X ) ) ]
% 1.31/1.73 ,
% 1.31/1.73 [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ],
% 1.31/1.73 [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ),
% 1.31/1.73 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ],
% 1.31/1.73 [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ],
% 1.31/1.73 [ =( 'least_upper_bound'( X, X ), X ) ],
% 1.31/1.73 [ =( 'greatest_lower_bound'( X, X ), X ) ],
% 1.31/1.73 [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X ) ]
% 1.31/1.73 ,
% 1.31/1.73 [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ), X ) ]
% 1.31/1.73 ,
% 1.31/1.73 [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), 'least_upper_bound'(
% 1.31/1.73 multiply( X, Y ), multiply( X, Z ) ) ) ],
% 1.31/1.73 [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 1.31/1.73 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ],
% 1.31/1.73 [ =( multiply( 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'(
% 1.31/1.73 multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 1.31/1.73 [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 1.31/1.73 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 1.31/1.73 [ =( inverse( identity ), identity ) ],
% 1.31/1.73 [ =( inverse( inverse( X ) ), X ) ],
% 1.31/1.73 [ =( inverse( multiply( X, Y ) ), multiply( inverse( Y ), inverse( X ) )
% 1.31/1.73 ) ],
% 1.31/1.73 [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply( a, b ),
% 1.31/1.73 identity ), multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ) ), multiply( 'least_upper_bound'( a
% 1.31/1.73 , identity ), 'least_upper_bound'( b, identity ) ) ) ) ]
% 1.31/1.73 ] .
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 percentage equality = 1.000000, percentage horn = 1.000000
% 1.31/1.73 This is a pure equality problem
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 Options Used:
% 1.31/1.73
% 1.31/1.73 useres = 1
% 1.31/1.73 useparamod = 1
% 1.31/1.73 useeqrefl = 1
% 1.31/1.73 useeqfact = 1
% 1.31/1.73 usefactor = 1
% 1.31/1.73 usesimpsplitting = 0
% 1.31/1.73 usesimpdemod = 5
% 1.31/1.73 usesimpres = 3
% 1.31/1.73
% 1.31/1.73 resimpinuse = 1000
% 1.31/1.73 resimpclauses = 20000
% 1.31/1.73 substype = eqrewr
% 1.31/1.73 backwardsubs = 1
% 1.31/1.73 selectoldest = 5
% 1.31/1.73
% 1.31/1.73 litorderings [0] = split
% 1.31/1.73 litorderings [1] = extend the termordering, first sorting on arguments
% 1.31/1.73
% 1.31/1.73 termordering = kbo
% 1.31/1.73
% 1.31/1.73 litapriori = 0
% 1.31/1.73 termapriori = 1
% 1.31/1.73 litaposteriori = 0
% 1.31/1.73 termaposteriori = 0
% 1.31/1.73 demodaposteriori = 0
% 1.31/1.73 ordereqreflfact = 0
% 1.31/1.73
% 1.31/1.73 litselect = negord
% 1.31/1.73
% 1.31/1.73 maxweight = 15
% 1.31/1.73 maxdepth = 30000
% 1.31/1.73 maxlength = 115
% 1.31/1.73 maxnrvars = 195
% 1.31/1.73 excuselevel = 1
% 1.31/1.73 increasemaxweight = 1
% 1.31/1.73
% 1.31/1.73 maxselected = 10000000
% 1.31/1.73 maxnrclauses = 10000000
% 1.31/1.73
% 1.31/1.73 showgenerated = 0
% 1.31/1.73 showkept = 0
% 1.31/1.73 showselected = 0
% 1.31/1.73 showdeleted = 0
% 1.31/1.73 showresimp = 1
% 1.31/1.73 showstatus = 2000
% 1.31/1.73
% 1.31/1.73 prologoutput = 1
% 1.31/1.73 nrgoals = 5000000
% 1.31/1.73 totalproof = 1
% 1.31/1.73
% 1.31/1.73 Symbols occurring in the translation:
% 1.31/1.73
% 1.31/1.73 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.31/1.73 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 1.31/1.73 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 1.31/1.73 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.31/1.73 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.31/1.73 identity [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.31/1.73 multiply [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 1.31/1.73 inverse [42, 1] (w:1, o:20, a:1, s:1, b:0),
% 1.31/1.73 'greatest_lower_bound' [45, 2] (w:1, o:48, a:1, s:1, b:0),
% 1.31/1.73 'least_upper_bound' [46, 2] (w:1, o:46, a:1, s:1, b:0),
% 1.31/1.73 a [47, 0] (w:1, o:13, a:1, s:1, b:0),
% 1.31/1.73 b [48, 0] (w:1, o:14, a:1, s:1, b:0).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 Starting Search:
% 1.31/1.73
% 1.31/1.73 Resimplifying inuse:
% 1.31/1.73 Done
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 Intermediate Status:
% 1.31/1.73 Generated: 24329
% 1.31/1.73 Kept: 2011
% 1.31/1.73 Inuse: 194
% 1.31/1.73 Deleted: 12
% 1.31/1.73 Deletedinuse: 3
% 1.31/1.73
% 1.31/1.73 Resimplifying inuse:
% 1.31/1.73 Done
% 1.31/1.73
% 1.31/1.73 Resimplifying inuse:
% 1.31/1.73 Done
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 Intermediate Status:
% 1.31/1.73 Generated: 99674
% 1.31/1.73 Kept: 4029
% 1.31/1.73 Inuse: 421
% 1.31/1.73 Deleted: 28
% 1.31/1.73 Deletedinuse: 3
% 1.31/1.73
% 1.31/1.73 Resimplifying inuse:
% 1.31/1.73 Done
% 1.31/1.73
% 1.31/1.73 Resimplifying inuse:
% 1.31/1.73 Done
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 Bliksems!, er is een bewijs:
% 1.31/1.73 % SZS status Unsatisfiable
% 1.31/1.73 % SZS output start Refutation
% 1.31/1.73
% 1.31/1.73 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 1.31/1.73 , Z ) ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 1.31/1.73 X ) ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 1.31/1.73 ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 1.31/1.73 ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 1.31/1.73 X ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) )
% 1.31/1.73 , multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 1.31/1.73 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 16, [ =( inverse( inverse( X ) ), X ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 18, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply( a,
% 1.31/1.73 b ), identity ), multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ) ), multiply( 'least_upper_bound'( a
% 1.31/1.73 , identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 19, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 20, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X ),
% 1.31/1.73 X ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 22, [ =( multiply( multiply( Y, X ), inverse( X ) ), multiply( Y,
% 1.31/1.73 identity ) ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 29, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 1.31/1.73 'least_upper_bound'( X, Y ) ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 64, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( Z, X ), Y ), X ), 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( Z, X ), Y ) ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 67, [ =( 'least_upper_bound'( 'least_upper_bound'( T, multiply( X,
% 1.31/1.73 Y ) ), multiply( X, Z ) ), 'least_upper_bound'( T, multiply( X,
% 1.31/1.73 'least_upper_bound'( Y, Z ) ) ) ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 70, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), multiply( X,
% 1.31/1.73 'least_upper_bound'( Z, Y ) ) ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 144, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 1.31/1.73 'least_upper_bound'( identity, Y ), X ) ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 151, [ =( multiply( X, identity ), X ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 154, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X,
% 1.31/1.73 'least_upper_bound'( identity, Y ) ) ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 196, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply(
% 1.31/1.73 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.31/1.73 , multiply( a, b ) ), identity ), multiply( 'least_upper_bound'( a,
% 1.31/1.73 identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 1070, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 1.31/1.73 , 'least_upper_bound'( Y, identity ) ) ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 1190, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 1.31/1.73 'least_upper_bound'( X, identity ), Y ) ) ] )
% 1.31/1.73 .
% 1.31/1.73 clause( 5902, [] )
% 1.31/1.73 .
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 % SZS output end Refutation
% 1.31/1.73 found a proof!
% 1.31/1.73
% 1.31/1.73 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.31/1.73
% 1.31/1.73 initialclauses(
% 1.31/1.73 [ clause( 5904, [ =( multiply( identity, X ), X ) ] )
% 1.31/1.73 , clause( 5905, [ =( multiply( inverse( X ), X ), identity ) ] )
% 1.31/1.73 , clause( 5906, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 1.31/1.73 Y, Z ) ) ) ] )
% 1.31/1.73 , clause( 5907, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 1.31/1.73 Y, X ) ) ] )
% 1.31/1.73 , clause( 5908, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X
% 1.31/1.73 ) ) ] )
% 1.31/1.73 , clause( 5909, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y,
% 1.31/1.73 Z ) ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 , clause( 5910, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 1.31/1.73 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 , clause( 5911, [ =( 'least_upper_bound'( X, X ), X ) ] )
% 1.31/1.73 , clause( 5912, [ =( 'greatest_lower_bound'( X, X ), X ) ] )
% 1.31/1.73 , clause( 5913, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y )
% 1.31/1.73 ), X ) ] )
% 1.31/1.73 , clause( 5914, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y )
% 1.31/1.73 ), X ) ] )
% 1.31/1.73 , clause( 5915, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 1.31/1.73 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.31/1.73 , clause( 5916, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 1.31/1.73 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.31/1.73 , clause( 5917, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 1.31/1.73 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 1.31/1.73 , clause( 5918, [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 1.31/1.73 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 1.31/1.73 , clause( 5919, [ =( inverse( identity ), identity ) ] )
% 1.31/1.73 , clause( 5920, [ =( inverse( inverse( X ) ), X ) ] )
% 1.31/1.73 , clause( 5921, [ =( inverse( multiply( X, Y ) ), multiply( inverse( Y ),
% 1.31/1.73 inverse( X ) ) ) ] )
% 1.31/1.73 , clause( 5922, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply(
% 1.31/1.73 a, b ), identity ), multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ) ), multiply( 'least_upper_bound'( a
% 1.31/1.73 , identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.31/1.73 ] ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 1.31/1.73 , clause( 5904, [ =( multiply( identity, X ), X ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 1.31/1.73 , clause( 5905, [ =( multiply( inverse( X ), X ), identity ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 5928, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X,
% 1.31/1.73 Y ), Z ) ) ] )
% 1.31/1.73 , clause( 5906, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 1.31/1.73 Y, Z ) ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 1.31/1.73 , Z ) ) ] )
% 1.31/1.73 , clause( 5928, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X
% 1.31/1.73 , Y ), Z ) ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.31/1.73 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 1.31/1.73 X ) ) ] )
% 1.31/1.73 , clause( 5907, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 1.31/1.73 Y, X ) ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.31/1.73 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 1.31/1.73 ] )
% 1.31/1.73 , clause( 5908, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X
% 1.31/1.73 ) ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.31/1.73 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 , clause( 5910, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 1.31/1.73 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.31/1.73 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 1.31/1.73 ) ] )
% 1.31/1.73 , clause( 5913, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y )
% 1.31/1.73 ), X ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.31/1.73 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 1.31/1.73 X ) ] )
% 1.31/1.73 , clause( 5914, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y )
% 1.31/1.73 ), X ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.31/1.73 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 5966, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 1.31/1.73 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.31/1.73 , clause( 5915, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 1.31/1.73 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) )
% 1.31/1.73 , multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.31/1.73 , clause( 5966, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z
% 1.31/1.73 ) ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.31/1.73 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 5978, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 1.31/1.73 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 , clause( 5917, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 1.31/1.73 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 1.31/1.73 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 , clause( 5978, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z
% 1.31/1.73 ) ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.31/1.73 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 16, [ =( inverse( inverse( X ) ), X ) ] )
% 1.31/1.73 , clause( 5920, [ =( inverse( inverse( X ) ), X ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 18, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply( a,
% 1.31/1.73 b ), identity ), multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ) ), multiply( 'least_upper_bound'( a
% 1.31/1.73 , identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.31/1.73 , clause( 5922, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply(
% 1.31/1.73 a, b ), identity ), multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ) ), multiply( 'least_upper_bound'( a
% 1.31/1.73 , identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.31/1.73 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6012, [ =( identity, multiply( inverse( X ), X ) ) ] )
% 1.31/1.73 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6013, [ =( identity, multiply( X, inverse( X ) ) ) ] )
% 1.31/1.73 , clause( 16, [ =( inverse( inverse( X ) ), X ) ] )
% 1.31/1.73 , 0, clause( 6012, [ =( identity, multiply( inverse( X ), X ) ) ] )
% 1.31/1.73 , 0, 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 1.31/1.73 X ) )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6014, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 1.31/1.73 , clause( 6013, [ =( identity, multiply( X, inverse( X ) ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 19, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 1.31/1.73 , clause( 6014, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6015, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 1.31/1.73 ) ) ) ] )
% 1.31/1.73 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 1.31/1.73 , X ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6016, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 1.31/1.73 X ) ) ] )
% 1.31/1.73 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 1.31/1.73 , X ) ) ] )
% 1.31/1.73 , 0, clause( 6015, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 1.31/1.73 X, Y ) ) ) ] )
% 1.31/1.73 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, 'least_upper_bound'( X, Y ) )] )
% 1.31/1.73 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6019, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 1.31/1.73 , X ) ] )
% 1.31/1.73 , clause( 6016, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y )
% 1.31/1.73 , X ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 20, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X ),
% 1.31/1.73 X ) ] )
% 1.31/1.73 , clause( 6019, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X
% 1.31/1.73 ), X ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.31/1.73 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6021, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 1.31/1.73 Y, Z ) ) ) ] )
% 1.31/1.73 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 1.31/1.73 ), Z ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6024, [ =( multiply( multiply( X, Y ), inverse( Y ) ), multiply( X
% 1.31/1.73 , identity ) ) ] )
% 1.31/1.73 , clause( 19, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 1.31/1.73 , 0, clause( 6021, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 1.31/1.73 multiply( Y, Z ) ) ) ] )
% 1.31/1.73 , 0, 9, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 1.31/1.73 :=( Y, Y ), :=( Z, inverse( Y ) )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 22, [ =( multiply( multiply( Y, X ), inverse( X ) ), multiply( Y,
% 1.31/1.73 identity ) ) ] )
% 1.31/1.73 , clause( 6024, [ =( multiply( multiply( X, Y ), inverse( Y ) ), multiply(
% 1.31/1.73 X, identity ) ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 1.31/1.73 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6029, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 1.31/1.73 ) ) ) ] )
% 1.31/1.73 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 1.31/1.73 , X ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6032, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( X, Y ), X ) ) ] )
% 1.31/1.73 , clause( 20, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 1.31/1.73 , X ) ] )
% 1.31/1.73 , 0, clause( 6029, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 1.31/1.73 X, Y ) ) ) ] )
% 1.31/1.73 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 1.31/1.73 :=( X, 'least_upper_bound'( X, Y ) ), :=( Y, X )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6033, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 1.31/1.73 'least_upper_bound'( X, Y ) ) ] )
% 1.31/1.73 , clause( 6032, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( X, Y ), X ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 29, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 1.31/1.73 'least_upper_bound'( X, Y ) ) ] )
% 1.31/1.73 , clause( 6033, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X )
% 1.31/1.73 , 'least_upper_bound'( X, Y ) ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.31/1.73 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6035, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 1.31/1.73 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.31/1.73 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6048, [ =( 'least_upper_bound'( 'least_upper_bound'( X,
% 1.31/1.73 'least_upper_bound'( Y, Z ) ), Y ), 'least_upper_bound'( X,
% 1.31/1.73 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.31/1.73 , clause( 29, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 1.31/1.73 'least_upper_bound'( X, Y ) ) ] )
% 1.31/1.73 , 0, clause( 6035, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z
% 1.31/1.73 ), 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.31/1.73 , 0, 10, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 1.31/1.73 :=( X, X ), :=( Y, 'least_upper_bound'( Y, Z ) ), :=( Z, Y )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6050, [ =( 'least_upper_bound'( 'least_upper_bound'( X,
% 1.31/1.73 'least_upper_bound'( Y, Z ) ), Y ), 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 , 0, clause( 6048, [ =( 'least_upper_bound'( 'least_upper_bound'( X,
% 1.31/1.73 'least_upper_bound'( Y, Z ) ), Y ), 'least_upper_bound'( X,
% 1.31/1.73 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.31/1.73 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.31/1.73 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6051, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( X, Y ), Z ), Y ), 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 , 0, clause( 6050, [ =( 'least_upper_bound'( 'least_upper_bound'( X,
% 1.31/1.73 'least_upper_bound'( Y, Z ) ), Y ), 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.31/1.73 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 64, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( Z, X ), Y ), X ), 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( Z, X ), Y ) ) ] )
% 1.31/1.73 , clause( 6051, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( X, Y ), Z ), Y ), 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 1.31/1.73 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6056, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 1.31/1.73 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.31/1.73 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6060, [ =( 'least_upper_bound'( 'least_upper_bound'( X, multiply( Y
% 1.31/1.73 , Z ) ), multiply( Y, T ) ), 'least_upper_bound'( X, multiply( Y,
% 1.31/1.73 'least_upper_bound'( Z, T ) ) ) ) ] )
% 1.31/1.73 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 1.31/1.73 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.31/1.73 , 0, clause( 6056, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z
% 1.31/1.73 ), 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.31/1.73 , 0, 12, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T )] ),
% 1.31/1.73 substitution( 1, [ :=( X, X ), :=( Y, multiply( Y, Z ) ), :=( Z, multiply(
% 1.31/1.73 Y, T ) )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 67, [ =( 'least_upper_bound'( 'least_upper_bound'( T, multiply( X,
% 1.31/1.73 Y ) ), multiply( X, Z ) ), 'least_upper_bound'( T, multiply( X,
% 1.31/1.73 'least_upper_bound'( Y, Z ) ) ) ) ] )
% 1.31/1.73 , clause( 6060, [ =( 'least_upper_bound'( 'least_upper_bound'( X, multiply(
% 1.31/1.73 Y, Z ) ), multiply( Y, T ) ), 'least_upper_bound'( X, multiply( Y,
% 1.31/1.73 'least_upper_bound'( Z, T ) ) ) ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] ),
% 1.31/1.73 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6063, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 1.31/1.73 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.31/1.73 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 1.31/1.73 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6065, [ =( multiply( X, 'least_upper_bound'( Z, Y ) ),
% 1.31/1.73 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.31/1.73 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 1.31/1.73 ) ] )
% 1.31/1.73 , 0, clause( 6063, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 1.31/1.73 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.31/1.73 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 1.31/1.73 :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6067, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), multiply( X
% 1.31/1.73 , 'least_upper_bound'( Z, Y ) ) ) ] )
% 1.31/1.73 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 1.31/1.73 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.31/1.73 , 0, clause( 6065, [ =( multiply( X, 'least_upper_bound'( Z, Y ) ),
% 1.31/1.73 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.31/1.73 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 1.31/1.73 substitution( 1, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 70, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), multiply( X,
% 1.31/1.73 'least_upper_bound'( Z, Y ) ) ) ] )
% 1.31/1.73 , clause( 6067, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), multiply(
% 1.31/1.73 X, 'least_upper_bound'( Z, Y ) ) ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.31/1.73 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6069, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 1.31/1.73 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 1.31/1.73 , clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 1.31/1.73 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6070, [ =( multiply( 'least_upper_bound'( identity, X ), Y ),
% 1.31/1.73 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 1.31/1.73 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 1.31/1.73 , 0, clause( 6069, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 1.31/1.73 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 1.31/1.73 , 0, 7, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X,
% 1.31/1.73 identity ), :=( Y, Y ), :=( Z, X )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6072, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 1.31/1.73 'least_upper_bound'( identity, X ), Y ) ) ] )
% 1.31/1.73 , clause( 6070, [ =( multiply( 'least_upper_bound'( identity, X ), Y ),
% 1.31/1.73 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 144, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 1.31/1.73 'least_upper_bound'( identity, Y ), X ) ) ] )
% 1.31/1.73 , clause( 6072, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 1.31/1.73 'least_upper_bound'( identity, X ), Y ) ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 1.31/1.73 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6075, [ =( multiply( X, identity ), multiply( multiply( X, Y ),
% 1.31/1.73 inverse( Y ) ) ) ] )
% 1.31/1.73 , clause( 22, [ =( multiply( multiply( Y, X ), inverse( X ) ), multiply( Y
% 1.31/1.73 , identity ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6078, [ =( multiply( X, identity ), multiply( identity, inverse(
% 1.31/1.73 inverse( X ) ) ) ) ] )
% 1.31/1.73 , clause( 19, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 1.31/1.73 , 0, clause( 6075, [ =( multiply( X, identity ), multiply( multiply( X, Y )
% 1.31/1.73 , inverse( Y ) ) ) ] )
% 1.31/1.73 , 0, 5, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 1.31/1.73 :=( Y, inverse( X ) )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6079, [ =( multiply( X, identity ), inverse( inverse( X ) ) ) ] )
% 1.31/1.73 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 1.31/1.73 , 0, clause( 6078, [ =( multiply( X, identity ), multiply( identity,
% 1.31/1.73 inverse( inverse( X ) ) ) ) ] )
% 1.31/1.73 , 0, 4, substitution( 0, [ :=( X, inverse( inverse( X ) ) )] ),
% 1.31/1.73 substitution( 1, [ :=( X, X )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6080, [ =( multiply( X, identity ), X ) ] )
% 1.31/1.73 , clause( 16, [ =( inverse( inverse( X ) ), X ) ] )
% 1.31/1.73 , 0, clause( 6079, [ =( multiply( X, identity ), inverse( inverse( X ) ) )
% 1.31/1.73 ] )
% 1.31/1.73 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 1.31/1.73 ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 151, [ =( multiply( X, identity ), X ) ] )
% 1.31/1.73 , clause( 6080, [ =( multiply( X, identity ), X ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6083, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 1.31/1.73 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.31/1.73 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 1.31/1.73 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6084, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 1.31/1.73 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 1.31/1.73 , clause( 151, [ =( multiply( X, identity ), X ) ] )
% 1.31/1.73 , 0, clause( 6083, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 1.31/1.73 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.31/1.73 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 1.31/1.73 :=( Y, identity ), :=( Z, Y )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6086, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 1.31/1.73 , 'least_upper_bound'( identity, Y ) ) ) ] )
% 1.31/1.73 , clause( 6084, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 1.31/1.73 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 154, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X,
% 1.31/1.73 'least_upper_bound'( identity, Y ) ) ) ] )
% 1.31/1.73 , clause( 6086, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply(
% 1.31/1.73 X, 'least_upper_bound'( identity, Y ) ) ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.31/1.73 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6088, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ), 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( multiply( a, b ), identity ), multiply(
% 1.31/1.73 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.31/1.73 ) ) ) ] )
% 1.31/1.73 , clause( 18, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply( a
% 1.31/1.73 , b ), identity ), multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ) ), multiply( 'least_upper_bound'( a
% 1.31/1.73 , identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6094, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ), 'least_upper_bound'( multiply(
% 1.31/1.73 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.31/1.73 , 'least_upper_bound'( multiply( a, b ), identity ) ) ) ) ] )
% 1.31/1.73 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 1.31/1.73 ) ] )
% 1.31/1.73 , 0, clause( 6088, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ), 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( multiply( a, b ), identity ), multiply(
% 1.31/1.73 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.31/1.73 ) ) ) ] )
% 1.31/1.73 , 0, 9, substitution( 0, [ :=( X, 'least_upper_bound'( multiply( a, b ),
% 1.31/1.73 identity ) ), :=( Y, multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ) )] ), substitution( 1, [] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6164, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ), 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ), multiply( a, b ) ), identity ) ) )
% 1.31/1.73 ] )
% 1.31/1.73 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.31/1.73 , 0, clause( 6094, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ), 'least_upper_bound'( multiply(
% 1.31/1.73 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.31/1.73 , 'least_upper_bound'( multiply( a, b ), identity ) ) ) ) ] )
% 1.31/1.73 , 0, 9, substitution( 0, [ :=( X, multiply( 'least_upper_bound'( a,
% 1.31/1.73 identity ), 'least_upper_bound'( b, identity ) ) ), :=( Y, multiply( a, b
% 1.31/1.73 ) ), :=( Z, identity )] ), substitution( 1, [] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6165, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply(
% 1.31/1.73 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.31/1.73 , multiply( a, b ) ), identity ), multiply( 'least_upper_bound'( a,
% 1.31/1.73 identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.31/1.73 , clause( 6164, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ), 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ), multiply( a, b ) ), identity ) ) )
% 1.31/1.73 ] )
% 1.31/1.73 , 0, substitution( 0, [] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 196, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply(
% 1.31/1.73 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.31/1.73 , multiply( a, b ) ), identity ), multiply( 'least_upper_bound'( a,
% 1.31/1.73 identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.31/1.73 , clause( 6165, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply(
% 1.31/1.73 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.31/1.73 , multiply( a, b ) ), identity ), multiply( 'least_upper_bound'( a,
% 1.31/1.73 identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.31/1.73 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6166, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 1.31/1.73 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 1.31/1.73 , clause( 154, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 1.31/1.73 , 'least_upper_bound'( identity, Y ) ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6167, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 1.31/1.73 , 'least_upper_bound'( Y, identity ) ) ) ] )
% 1.31/1.73 , clause( 6166, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 1.31/1.73 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 1.31/1.73 , 0, clause( 70, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), multiply(
% 1.31/1.73 X, 'least_upper_bound'( Z, Y ) ) ) ] )
% 1.31/1.73 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 1.31/1.73 :=( X, X ), :=( Y, identity ), :=( Z, Y )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 1070, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 1.31/1.73 , 'least_upper_bound'( Y, identity ) ) ) ] )
% 1.31/1.73 , clause( 6167, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply(
% 1.31/1.73 X, 'least_upper_bound'( Y, identity ) ) ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.31/1.73 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6170, [ =( multiply( 'least_upper_bound'( identity, Y ), X ),
% 1.31/1.73 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 1.31/1.73 , clause( 144, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 1.31/1.73 'least_upper_bound'( identity, Y ), X ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6183, [ =( multiply( multiply( identity, 'least_upper_bound'( X,
% 1.31/1.73 identity ) ), Y ), 'least_upper_bound'( Y, multiply( multiply( identity,
% 1.31/1.73 X ), Y ) ) ) ] )
% 1.31/1.73 , clause( 1070, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply(
% 1.31/1.73 X, 'least_upper_bound'( Y, identity ) ) ) ] )
% 1.31/1.73 , 0, clause( 6170, [ =( multiply( 'least_upper_bound'( identity, Y ), X ),
% 1.31/1.73 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 1.31/1.73 , 0, 2, substitution( 0, [ :=( X, identity ), :=( Y, X )] ), substitution(
% 1.31/1.73 1, [ :=( X, Y ), :=( Y, multiply( identity, X ) )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6186, [ =( multiply( multiply( identity, 'least_upper_bound'( X,
% 1.31/1.73 identity ) ), Y ), 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 1.31/1.73 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 1.31/1.73 , 0, clause( 6183, [ =( multiply( multiply( identity, 'least_upper_bound'(
% 1.31/1.73 X, identity ) ), Y ), 'least_upper_bound'( Y, multiply( multiply(
% 1.31/1.73 identity, X ), Y ) ) ) ] )
% 1.31/1.73 , 0, 11, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 1.31/1.73 :=( Y, Y )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6188, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 1.31/1.73 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 1.31/1.73 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 1.31/1.73 , 0, clause( 6186, [ =( multiply( multiply( identity, 'least_upper_bound'(
% 1.31/1.73 X, identity ) ), Y ), 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 1.31/1.73 , 0, 2, substitution( 0, [ :=( X, 'least_upper_bound'( X, identity ) )] ),
% 1.31/1.73 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6189, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 1.31/1.73 'least_upper_bound'( X, identity ), Y ) ) ] )
% 1.31/1.73 , clause( 6188, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 1.31/1.73 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 1190, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 1.31/1.73 'least_upper_bound'( X, identity ), Y ) ) ] )
% 1.31/1.73 , clause( 6189, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 1.31/1.73 'least_upper_bound'( X, identity ), Y ) ) ] )
% 1.31/1.73 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.31/1.73 )] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6190, [ =( multiply( 'least_upper_bound'( Y, identity ), X ),
% 1.31/1.73 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 1.31/1.73 , clause( 1190, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 1.31/1.73 'least_upper_bound'( X, identity ), Y ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqswap(
% 1.31/1.73 clause( 6191, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ), 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ), multiply( a, b ) ), identity ) ) )
% 1.31/1.73 ] )
% 1.31/1.73 , clause( 196, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply(
% 1.31/1.73 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.31/1.73 , multiply( a, b ) ), identity ), multiply( 'least_upper_bound'( a,
% 1.31/1.73 identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6196, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ), 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( 'least_upper_bound'( b,
% 1.31/1.73 identity ), multiply( a, 'least_upper_bound'( b, identity ) ) ), multiply(
% 1.31/1.73 a, b ) ), identity ) ) ) ] )
% 1.31/1.73 , clause( 6190, [ =( multiply( 'least_upper_bound'( Y, identity ), X ),
% 1.31/1.73 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 1.31/1.73 , 0, clause( 6191, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ), 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ), multiply( a, b ) ), identity ) ) )
% 1.31/1.73 ] )
% 1.31/1.73 , 0, 11, substitution( 0, [ :=( X, 'least_upper_bound'( b, identity ) ),
% 1.31/1.73 :=( Y, a )] ), substitution( 1, [] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6197, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( b, identity
% 1.31/1.73 ), multiply( a, 'least_upper_bound'( b, identity ) ) ),
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( b, identity ), multiply( a, 'least_upper_bound'( b,
% 1.31/1.73 identity ) ) ), multiply( a, b ) ), identity ) ) ) ] )
% 1.31/1.73 , clause( 6190, [ =( multiply( 'least_upper_bound'( Y, identity ), X ),
% 1.31/1.73 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 1.31/1.73 , 0, clause( 6196, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.31/1.73 'least_upper_bound'( b, identity ) ), 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( 'least_upper_bound'( b,
% 1.31/1.73 identity ), multiply( a, 'least_upper_bound'( b, identity ) ) ), multiply(
% 1.31/1.73 a, b ) ), identity ) ) ) ] )
% 1.31/1.73 , 0, 2, substitution( 0, [ :=( X, 'least_upper_bound'( b, identity ) ),
% 1.31/1.73 :=( Y, a )] ), substitution( 1, [] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6201, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( b, identity
% 1.31/1.73 ), multiply( a, 'least_upper_bound'( b, identity ) ) ),
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( 'least_upper_bound'( b,
% 1.31/1.73 identity ), multiply( a, 'least_upper_bound'( 'least_upper_bound'( b,
% 1.31/1.73 identity ), b ) ) ), identity ) ) ) ] )
% 1.31/1.73 , clause( 67, [ =( 'least_upper_bound'( 'least_upper_bound'( T, multiply( X
% 1.31/1.73 , Y ) ), multiply( X, Z ) ), 'least_upper_bound'( T, multiply( X,
% 1.31/1.73 'least_upper_bound'( Y, Z ) ) ) ) ] )
% 1.31/1.73 , 0, clause( 6197, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( b,
% 1.31/1.73 identity ), multiply( a, 'least_upper_bound'( b, identity ) ) ),
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( b, identity ), multiply( a, 'least_upper_bound'( b,
% 1.31/1.73 identity ) ) ), multiply( a, b ) ), identity ) ) ) ] )
% 1.31/1.73 , 0, 12, substitution( 0, [ :=( X, a ), :=( Y, 'least_upper_bound'( b,
% 1.31/1.73 identity ) ), :=( Z, b ), :=( T, 'least_upper_bound'( b, identity ) )] )
% 1.31/1.73 , substitution( 1, [] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6202, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( b, identity
% 1.31/1.73 ), multiply( a, 'least_upper_bound'( b, identity ) ) ),
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( b, identity ), multiply( a,
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( b, identity ), b ) ) ) ) ) ] )
% 1.31/1.73 , clause( 64, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( Z, X ), Y ), X ), 'least_upper_bound'(
% 1.31/1.73 'least_upper_bound'( Z, X ), Y ) ) ] )
% 1.31/1.73 , 0, clause( 6201, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( b,
% 1.31/1.73 identity ), multiply( a, 'least_upper_bound'( b, identity ) ) ),
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( 'least_upper_bound'( b,
% 1.31/1.73 identity ), multiply( a, 'least_upper_bound'( 'least_upper_bound'( b,
% 1.31/1.73 identity ), b ) ) ), identity ) ) ) ] )
% 1.31/1.73 , 0, 11, substitution( 0, [ :=( X, identity ), :=( Y, multiply( a,
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( b, identity ), b ) ) ), :=( Z,
% 1.31/1.73 b )] ), substitution( 1, [] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 paramod(
% 1.31/1.73 clause( 6203, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( b, identity
% 1.31/1.73 ), multiply( a, 'least_upper_bound'( b, identity ) ) ),
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( b, identity ), multiply( a,
% 1.31/1.73 'least_upper_bound'( b, identity ) ) ) ) ) ] )
% 1.31/1.73 , clause( 29, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 1.31/1.73 'least_upper_bound'( X, Y ) ) ] )
% 1.31/1.73 , 0, clause( 6202, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( b,
% 1.31/1.73 identity ), multiply( a, 'least_upper_bound'( b, identity ) ) ),
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( b, identity ), multiply( a,
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( b, identity ), b ) ) ) ) ) ] )
% 1.31/1.73 , 0, 17, substitution( 0, [ :=( X, b ), :=( Y, identity )] ),
% 1.31/1.73 substitution( 1, [] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 eqrefl(
% 1.31/1.73 clause( 6204, [] )
% 1.31/1.73 , clause( 6203, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( b,
% 1.31/1.73 identity ), multiply( a, 'least_upper_bound'( b, identity ) ) ),
% 1.31/1.73 'least_upper_bound'( 'least_upper_bound'( b, identity ), multiply( a,
% 1.31/1.73 'least_upper_bound'( b, identity ) ) ) ) ) ] )
% 1.31/1.73 , 0, substitution( 0, [] )).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 subsumption(
% 1.31/1.73 clause( 5902, [] )
% 1.31/1.73 , clause( 6204, [] )
% 1.31/1.73 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 end.
% 1.31/1.73
% 1.31/1.73 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.31/1.73
% 1.31/1.73 Memory use:
% 1.31/1.73
% 1.31/1.73 space for terms: 80699
% 1.31/1.73 space for clauses: 634840
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 clauses generated: 175545
% 1.31/1.73 clauses kept: 5903
% 1.31/1.73 clauses selected: 608
% 1.31/1.73 clauses deleted: 72
% 1.31/1.73 clauses inuse deleted: 34
% 1.31/1.73
% 1.31/1.73 subsentry: 10481
% 1.31/1.73 literals s-matched: 8628
% 1.31/1.73 literals matched: 8622
% 1.31/1.73 full subsumption: 0
% 1.31/1.73
% 1.31/1.73 checksum: 710980522
% 1.31/1.73
% 1.31/1.73
% 1.31/1.73 Bliksem ended
%------------------------------------------------------------------------------