TSTP Solution File: GRP185-1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP185-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n003.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 1.22s 1.61s
% Output : Refutation 1.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : GRP185-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.00/0.08 % Command : bliksem %s
% 0.07/0.28 % Computer : n003.cluster.edu
% 0.07/0.28 % Model : x86_64 x86_64
% 0.07/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28 % Memory : 8042.1875MB
% 0.07/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28 % CPULimit : 300
% 0.07/0.28 % DateTime : Tue Jun 14 08:15:40 EDT 2022
% 0.07/0.28 % CPUTime :
% 1.22/1.61 *** allocated 10000 integers for termspace/termends
% 1.22/1.61 *** allocated 10000 integers for clauses
% 1.22/1.61 *** allocated 10000 integers for justifications
% 1.22/1.61 Bliksem 1.12
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 Automatic Strategy Selection
% 1.22/1.61
% 1.22/1.61 Clauses:
% 1.22/1.61 [
% 1.22/1.61 [ =( multiply( identity, X ), X ) ],
% 1.22/1.61 [ =( multiply( inverse( X ), X ), identity ) ],
% 1.22/1.61 [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply( Y, Z ) ) )
% 1.22/1.61 ],
% 1.22/1.61 [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, X ) ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ],
% 1.22/1.61 [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ),
% 1.22/1.61 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ],
% 1.22/1.61 [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ],
% 1.22/1.61 [ =( 'least_upper_bound'( X, X ), X ) ],
% 1.22/1.61 [ =( 'greatest_lower_bound'( X, X ), X ) ],
% 1.22/1.61 [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ), X ) ]
% 1.22/1.61 ,
% 1.22/1.61 [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), 'least_upper_bound'(
% 1.22/1.61 multiply( X, Y ), multiply( X, Z ) ) ) ],
% 1.22/1.61 [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 1.22/1.61 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ],
% 1.22/1.61 [ =( multiply( 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'(
% 1.22/1.61 multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 1.22/1.61 [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 1.22/1.61 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 1.22/1.61 [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply( a, b ),
% 1.22/1.61 identity ), multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ) ), multiply( 'least_upper_bound'( a
% 1.22/1.61 , identity ), 'least_upper_bound'( b, identity ) ) ) ) ]
% 1.22/1.61 ] .
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 percentage equality = 1.000000, percentage horn = 1.000000
% 1.22/1.61 This is a pure equality problem
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 Options Used:
% 1.22/1.61
% 1.22/1.61 useres = 1
% 1.22/1.61 useparamod = 1
% 1.22/1.61 useeqrefl = 1
% 1.22/1.61 useeqfact = 1
% 1.22/1.61 usefactor = 1
% 1.22/1.61 usesimpsplitting = 0
% 1.22/1.61 usesimpdemod = 5
% 1.22/1.61 usesimpres = 3
% 1.22/1.61
% 1.22/1.61 resimpinuse = 1000
% 1.22/1.61 resimpclauses = 20000
% 1.22/1.61 substype = eqrewr
% 1.22/1.61 backwardsubs = 1
% 1.22/1.61 selectoldest = 5
% 1.22/1.61
% 1.22/1.61 litorderings [0] = split
% 1.22/1.61 litorderings [1] = extend the termordering, first sorting on arguments
% 1.22/1.61
% 1.22/1.61 termordering = kbo
% 1.22/1.61
% 1.22/1.61 litapriori = 0
% 1.22/1.61 termapriori = 1
% 1.22/1.61 litaposteriori = 0
% 1.22/1.61 termaposteriori = 0
% 1.22/1.61 demodaposteriori = 0
% 1.22/1.61 ordereqreflfact = 0
% 1.22/1.61
% 1.22/1.61 litselect = negord
% 1.22/1.61
% 1.22/1.61 maxweight = 15
% 1.22/1.61 maxdepth = 30000
% 1.22/1.61 maxlength = 115
% 1.22/1.61 maxnrvars = 195
% 1.22/1.61 excuselevel = 1
% 1.22/1.61 increasemaxweight = 1
% 1.22/1.61
% 1.22/1.61 maxselected = 10000000
% 1.22/1.61 maxnrclauses = 10000000
% 1.22/1.61
% 1.22/1.61 showgenerated = 0
% 1.22/1.61 showkept = 0
% 1.22/1.61 showselected = 0
% 1.22/1.61 showdeleted = 0
% 1.22/1.61 showresimp = 1
% 1.22/1.61 showstatus = 2000
% 1.22/1.61
% 1.22/1.61 prologoutput = 1
% 1.22/1.61 nrgoals = 5000000
% 1.22/1.61 totalproof = 1
% 1.22/1.61
% 1.22/1.61 Symbols occurring in the translation:
% 1.22/1.61
% 1.22/1.61 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.22/1.61 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 1.22/1.61 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 1.22/1.61 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.22/1.61 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.22/1.61 identity [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.22/1.61 multiply [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 1.22/1.61 inverse [42, 1] (w:1, o:20, a:1, s:1, b:0),
% 1.22/1.61 'greatest_lower_bound' [45, 2] (w:1, o:48, a:1, s:1, b:0),
% 1.22/1.61 'least_upper_bound' [46, 2] (w:1, o:46, a:1, s:1, b:0),
% 1.22/1.61 a [47, 0] (w:1, o:13, a:1, s:1, b:0),
% 1.22/1.61 b [48, 0] (w:1, o:14, a:1, s:1, b:0).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 Starting Search:
% 1.22/1.61
% 1.22/1.61 Resimplifying inuse:
% 1.22/1.61 Done
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 Intermediate Status:
% 1.22/1.61 Generated: 25075
% 1.22/1.61 Kept: 2007
% 1.22/1.61 Inuse: 197
% 1.22/1.61 Deleted: 13
% 1.22/1.61 Deletedinuse: 8
% 1.22/1.61
% 1.22/1.61 Resimplifying inuse:
% 1.22/1.61 Done
% 1.22/1.61
% 1.22/1.61 Resimplifying inuse:
% 1.22/1.61 Done
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 Intermediate Status:
% 1.22/1.61 Generated: 106679
% 1.22/1.61 Kept: 4008
% 1.22/1.61 Inuse: 441
% 1.22/1.61 Deleted: 28
% 1.22/1.61 Deletedinuse: 8
% 1.22/1.61
% 1.22/1.61 Resimplifying inuse:
% 1.22/1.61 Done
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 Bliksems!, er is een bewijs:
% 1.22/1.61 % SZS status Unsatisfiable
% 1.22/1.61 % SZS output start Refutation
% 1.22/1.61
% 1.22/1.61 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 1.22/1.61 , Z ) ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 1.22/1.61 X ) ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 1.22/1.61 ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 1.22/1.61 ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 1.22/1.61 X ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) )
% 1.22/1.61 , multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 1.22/1.61 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 15, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply( a,
% 1.22/1.61 b ), identity ), multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ) ), multiply( 'least_upper_bound'( a
% 1.22/1.61 , identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 17, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 1.22/1.61 identity ) ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 18, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 1.22/1.61 ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 19, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X ),
% 1.22/1.61 X ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 35, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 1.22/1.61 'least_upper_bound'( X, Y ) ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 59, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( Z, X ), Y ), X ), 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( Z, X ), Y ) ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 61, [ =( 'least_upper_bound'( 'least_upper_bound'( T, multiply( X,
% 1.22/1.61 Y ) ), multiply( X, Z ) ), 'least_upper_bound'( T, multiply( X,
% 1.22/1.61 'least_upper_bound'( Y, Z ) ) ) ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 64, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), multiply( X,
% 1.22/1.61 'least_upper_bound'( Z, Y ) ) ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 117, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 1.22/1.61 'least_upper_bound'( identity, Y ), X ) ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 163, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 1.22/1.61 ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 171, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X,
% 1.22/1.61 'least_upper_bound'( identity, Y ) ) ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 173, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply(
% 1.22/1.61 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.22/1.61 , multiply( a, b ) ), identity ), multiply( 'least_upper_bound'( a,
% 1.22/1.61 identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 753, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X,
% 1.22/1.61 'least_upper_bound'( Y, identity ) ) ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 1210, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 1.22/1.61 'least_upper_bound'( X, identity ), Y ) ) ] )
% 1.22/1.61 .
% 1.22/1.61 clause( 4745, [] )
% 1.22/1.61 .
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 % SZS output end Refutation
% 1.22/1.61 found a proof!
% 1.22/1.61
% 1.22/1.61 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.22/1.61
% 1.22/1.61 initialclauses(
% 1.22/1.61 [ clause( 4747, [ =( multiply( identity, X ), X ) ] )
% 1.22/1.61 , clause( 4748, [ =( multiply( inverse( X ), X ), identity ) ] )
% 1.22/1.61 , clause( 4749, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 1.22/1.61 Y, Z ) ) ) ] )
% 1.22/1.61 , clause( 4750, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 1.22/1.61 Y, X ) ) ] )
% 1.22/1.61 , clause( 4751, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X
% 1.22/1.61 ) ) ] )
% 1.22/1.61 , clause( 4752, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y,
% 1.22/1.61 Z ) ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 , clause( 4753, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 1.22/1.61 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 , clause( 4754, [ =( 'least_upper_bound'( X, X ), X ) ] )
% 1.22/1.61 , clause( 4755, [ =( 'greatest_lower_bound'( X, X ), X ) ] )
% 1.22/1.61 , clause( 4756, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y )
% 1.22/1.61 ), X ) ] )
% 1.22/1.61 , clause( 4757, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y )
% 1.22/1.61 ), X ) ] )
% 1.22/1.61 , clause( 4758, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 1.22/1.61 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.22/1.61 , clause( 4759, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 1.22/1.61 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.22/1.61 , clause( 4760, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 1.22/1.61 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 1.22/1.61 , clause( 4761, [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 1.22/1.61 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 1.22/1.61 , clause( 4762, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply(
% 1.22/1.61 a, b ), identity ), multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ) ), multiply( 'least_upper_bound'( a
% 1.22/1.61 , identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.22/1.61 ] ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 1.22/1.61 , clause( 4747, [ =( multiply( identity, X ), X ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 1.22/1.61 , clause( 4748, [ =( multiply( inverse( X ), X ), identity ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4768, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X,
% 1.22/1.61 Y ), Z ) ) ] )
% 1.22/1.61 , clause( 4749, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 1.22/1.61 Y, Z ) ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 1.22/1.61 , Z ) ) ] )
% 1.22/1.61 , clause( 4768, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X
% 1.22/1.61 , Y ), Z ) ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.22/1.61 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 1.22/1.61 X ) ) ] )
% 1.22/1.61 , clause( 4750, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 1.22/1.61 Y, X ) ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.22/1.61 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 1.22/1.61 ] )
% 1.22/1.61 , clause( 4751, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X
% 1.22/1.61 ) ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.22/1.61 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 , clause( 4753, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 1.22/1.61 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.22/1.61 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 1.22/1.61 ) ] )
% 1.22/1.61 , clause( 4756, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y )
% 1.22/1.61 ), X ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.22/1.61 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 1.22/1.61 X ) ] )
% 1.22/1.61 , clause( 4757, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y )
% 1.22/1.61 ), X ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.22/1.61 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4806, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 1.22/1.61 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.22/1.61 , clause( 4758, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 1.22/1.61 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) )
% 1.22/1.61 , multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.22/1.61 , clause( 4806, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z
% 1.22/1.61 ) ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.22/1.61 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4818, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 1.22/1.61 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 , clause( 4760, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 1.22/1.61 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 1.22/1.61 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 , clause( 4818, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z
% 1.22/1.61 ) ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.22/1.61 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 15, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply( a,
% 1.22/1.61 b ), identity ), multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ) ), multiply( 'least_upper_bound'( a
% 1.22/1.61 , identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.22/1.61 , clause( 4762, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply(
% 1.22/1.61 a, b ), identity ), multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ) ), multiply( 'least_upper_bound'( a
% 1.22/1.61 , identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.22/1.61 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4834, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 1.22/1.61 Y, Z ) ) ) ] )
% 1.22/1.61 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 1.22/1.61 ), Z ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4839, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply( X
% 1.22/1.61 , identity ) ) ] )
% 1.22/1.61 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 1.22/1.61 , 0, clause( 4834, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 1.22/1.61 multiply( Y, Z ) ) ) ] )
% 1.22/1.61 , 0, 9, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 1.22/1.61 :=( Y, inverse( Y ) ), :=( Z, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 17, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 1.22/1.61 identity ) ) ] )
% 1.22/1.61 , clause( 4839, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply(
% 1.22/1.61 X, identity ) ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 1.22/1.61 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4844, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 1.22/1.61 Y, Z ) ) ) ] )
% 1.22/1.61 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 1.22/1.61 ), Z ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4849, [ =( multiply( multiply( X, identity ), Y ), multiply( X, Y )
% 1.22/1.61 ) ] )
% 1.22/1.61 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 1.22/1.61 , 0, clause( 4844, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 1.22/1.61 multiply( Y, Z ) ) ) ] )
% 1.22/1.61 , 0, 8, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 1.22/1.61 :=( Y, identity ), :=( Z, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 18, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 1.22/1.61 ] )
% 1.22/1.61 , clause( 4849, [ =( multiply( multiply( X, identity ), Y ), multiply( X, Y
% 1.22/1.61 ) ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 1.22/1.61 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4854, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 1.22/1.61 ) ) ) ] )
% 1.22/1.61 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 1.22/1.61 , X ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4855, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y ),
% 1.22/1.61 X ) ) ] )
% 1.22/1.61 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 1.22/1.61 , X ) ) ] )
% 1.22/1.61 , 0, clause( 4854, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 1.22/1.61 X, Y ) ) ) ] )
% 1.22/1.61 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, 'least_upper_bound'( X, Y ) )] )
% 1.22/1.61 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4858, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 1.22/1.61 , X ) ] )
% 1.22/1.61 , clause( 4855, [ =( X, 'greatest_lower_bound'( 'least_upper_bound'( X, Y )
% 1.22/1.61 , X ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 19, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X ),
% 1.22/1.61 X ) ] )
% 1.22/1.61 , clause( 4858, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X
% 1.22/1.61 ), X ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.22/1.61 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4860, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 1.22/1.61 ) ) ) ] )
% 1.22/1.61 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 1.22/1.61 , X ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4863, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( X, Y ), X ) ) ] )
% 1.22/1.61 , clause( 19, [ =( 'greatest_lower_bound'( 'least_upper_bound'( X, Y ), X )
% 1.22/1.61 , X ) ] )
% 1.22/1.61 , 0, clause( 4860, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 1.22/1.61 X, Y ) ) ) ] )
% 1.22/1.61 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 1.22/1.61 :=( X, 'least_upper_bound'( X, Y ) ), :=( Y, X )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4864, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 1.22/1.61 'least_upper_bound'( X, Y ) ) ] )
% 1.22/1.61 , clause( 4863, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( X, Y ), X ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 35, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 1.22/1.61 'least_upper_bound'( X, Y ) ) ] )
% 1.22/1.61 , clause( 4864, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X )
% 1.22/1.61 , 'least_upper_bound'( X, Y ) ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.22/1.61 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4866, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 1.22/1.61 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.22/1.61 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4879, [ =( 'least_upper_bound'( 'least_upper_bound'( X,
% 1.22/1.61 'least_upper_bound'( Y, Z ) ), Y ), 'least_upper_bound'( X,
% 1.22/1.61 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.22/1.61 , clause( 35, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 1.22/1.61 'least_upper_bound'( X, Y ) ) ] )
% 1.22/1.61 , 0, clause( 4866, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z
% 1.22/1.61 ), 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.22/1.61 , 0, 10, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 1.22/1.61 :=( X, X ), :=( Y, 'least_upper_bound'( Y, Z ) ), :=( Z, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4881, [ =( 'least_upper_bound'( 'least_upper_bound'( X,
% 1.22/1.61 'least_upper_bound'( Y, Z ) ), Y ), 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 , 0, clause( 4879, [ =( 'least_upper_bound'( 'least_upper_bound'( X,
% 1.22/1.61 'least_upper_bound'( Y, Z ) ), Y ), 'least_upper_bound'( X,
% 1.22/1.61 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.22/1.61 , 0, 8, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.22/1.61 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4882, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( X, Y ), Z ), Y ), 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 , 0, clause( 4881, [ =( 'least_upper_bound'( 'least_upper_bound'( X,
% 1.22/1.61 'least_upper_bound'( Y, Z ) ), Y ), 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.22/1.61 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 59, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( Z, X ), Y ), X ), 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( Z, X ), Y ) ) ] )
% 1.22/1.61 , clause( 4882, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( X, Y ), Z ), Y ), 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 1.22/1.61 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4887, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ),
% 1.22/1.61 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.22/1.61 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4891, [ =( 'least_upper_bound'( 'least_upper_bound'( X, multiply( Y
% 1.22/1.61 , Z ) ), multiply( Y, T ) ), 'least_upper_bound'( X, multiply( Y,
% 1.22/1.61 'least_upper_bound'( Z, T ) ) ) ) ] )
% 1.22/1.61 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 1.22/1.61 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.22/1.61 , 0, clause( 4887, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z
% 1.22/1.61 ), 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.22/1.61 , 0, 12, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T )] ),
% 1.22/1.61 substitution( 1, [ :=( X, X ), :=( Y, multiply( Y, Z ) ), :=( Z, multiply(
% 1.22/1.61 Y, T ) )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 61, [ =( 'least_upper_bound'( 'least_upper_bound'( T, multiply( X,
% 1.22/1.61 Y ) ), multiply( X, Z ) ), 'least_upper_bound'( T, multiply( X,
% 1.22/1.61 'least_upper_bound'( Y, Z ) ) ) ) ] )
% 1.22/1.61 , clause( 4891, [ =( 'least_upper_bound'( 'least_upper_bound'( X, multiply(
% 1.22/1.61 Y, Z ) ), multiply( Y, T ) ), 'least_upper_bound'( X, multiply( Y,
% 1.22/1.61 'least_upper_bound'( Z, T ) ) ) ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z )] ),
% 1.22/1.61 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4894, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 1.22/1.61 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.22/1.61 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 1.22/1.61 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4896, [ =( multiply( X, 'least_upper_bound'( Z, Y ) ),
% 1.22/1.61 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.22/1.61 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 1.22/1.61 ) ] )
% 1.22/1.61 , 0, clause( 4894, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 1.22/1.61 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.22/1.61 , 0, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 1.22/1.61 :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4898, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), multiply( X
% 1.22/1.61 , 'least_upper_bound'( Z, Y ) ) ) ] )
% 1.22/1.61 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 1.22/1.61 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.22/1.61 , 0, clause( 4896, [ =( multiply( X, 'least_upper_bound'( Z, Y ) ),
% 1.22/1.61 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.22/1.61 , 0, 6, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 1.22/1.61 substitution( 1, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 64, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), multiply( X,
% 1.22/1.61 'least_upper_bound'( Z, Y ) ) ) ] )
% 1.22/1.61 , clause( 4898, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), multiply(
% 1.22/1.61 X, 'least_upper_bound'( Z, Y ) ) ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.22/1.61 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4900, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 1.22/1.61 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 1.22/1.61 , clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 1.22/1.61 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4901, [ =( multiply( 'least_upper_bound'( identity, X ), Y ),
% 1.22/1.61 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 1.22/1.61 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 1.22/1.61 , 0, clause( 4900, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 1.22/1.61 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 1.22/1.61 , 0, 7, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X,
% 1.22/1.61 identity ), :=( Y, Y ), :=( Z, X )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4903, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 1.22/1.61 'least_upper_bound'( identity, X ), Y ) ) ] )
% 1.22/1.61 , clause( 4901, [ =( multiply( 'least_upper_bound'( identity, X ), Y ),
% 1.22/1.61 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 117, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 1.22/1.61 'least_upper_bound'( identity, Y ), X ) ) ] )
% 1.22/1.61 , clause( 4903, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 1.22/1.61 'least_upper_bound'( identity, X ), Y ) ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 1.22/1.61 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4906, [ =( multiply( X, identity ), multiply( multiply( X, inverse(
% 1.22/1.61 Y ) ), Y ) ) ] )
% 1.22/1.61 , clause( 17, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 1.22/1.61 , identity ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4909, [ =( multiply( inverse( inverse( X ) ), identity ), multiply(
% 1.22/1.61 identity, X ) ) ] )
% 1.22/1.61 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 1.22/1.61 , 0, clause( 4906, [ =( multiply( X, identity ), multiply( multiply( X,
% 1.22/1.61 inverse( Y ) ), Y ) ) ] )
% 1.22/1.61 , 0, 7, substitution( 0, [ :=( X, inverse( X ) )] ), substitution( 1, [
% 1.22/1.61 :=( X, inverse( inverse( X ) ) ), :=( Y, X )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4910, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 1.22/1.61 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 1.22/1.61 , 0, clause( 4909, [ =( multiply( inverse( inverse( X ) ), identity ),
% 1.22/1.61 multiply( identity, X ) ) ] )
% 1.22/1.61 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 1.22/1.61 ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 163, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 1.22/1.61 , clause( 4910, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ]
% 1.22/1.61 )
% 1.22/1.61 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4913, [ =( multiply( X, Y ), multiply( multiply( X, identity ), Y )
% 1.22/1.61 ) ] )
% 1.22/1.61 , clause( 18, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X )
% 1.22/1.61 ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4916, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 1.22/1.61 ) ] )
% 1.22/1.61 , clause( 163, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 1.22/1.61 , 0, clause( 4913, [ =( multiply( X, Y ), multiply( multiply( X, identity )
% 1.22/1.61 , Y ) ) ] )
% 1.22/1.61 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 1.22/1.61 inverse( X ) ) ), :=( Y, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 1.22/1.61 ) ] )
% 1.22/1.61 , clause( 4916, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 1.22/1.61 ) ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.22/1.61 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4923, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 1.22/1.61 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.22/1.61 , clause( 11, [ =( 'least_upper_bound'( multiply( X, Y ), multiply( X, Z )
% 1.22/1.61 ), multiply( X, 'least_upper_bound'( Y, Z ) ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4926, [ =( multiply( inverse( inverse( X ) ), 'least_upper_bound'(
% 1.22/1.61 identity, Y ) ), 'least_upper_bound'( X, multiply( inverse( inverse( X )
% 1.22/1.61 ), Y ) ) ) ] )
% 1.22/1.61 , clause( 163, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 1.22/1.61 , 0, clause( 4923, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 1.22/1.61 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 1.22/1.61 , 0, 9, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 1.22/1.61 inverse( X ) ) ), :=( Y, identity ), :=( Z, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4936, [ =( multiply( inverse( inverse( X ) ), 'least_upper_bound'(
% 1.22/1.61 identity, Y ) ), 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 1.22/1.61 , clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 1.22/1.61 ) ) ] )
% 1.22/1.61 , 0, clause( 4926, [ =( multiply( inverse( inverse( X ) ),
% 1.22/1.61 'least_upper_bound'( identity, Y ) ), 'least_upper_bound'( X, multiply(
% 1.22/1.61 inverse( inverse( X ) ), Y ) ) ) ] )
% 1.22/1.61 , 0, 10, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 1.22/1.61 :=( X, X ), :=( Y, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4938, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 1.22/1.61 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 1.22/1.61 , clause( 170, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 1.22/1.61 ) ) ] )
% 1.22/1.61 , 0, clause( 4936, [ =( multiply( inverse( inverse( X ) ),
% 1.22/1.61 'least_upper_bound'( identity, Y ) ), 'least_upper_bound'( X, multiply( X
% 1.22/1.61 , Y ) ) ) ] )
% 1.22/1.61 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, 'least_upper_bound'( identity
% 1.22/1.61 , Y ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4939, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 1.22/1.61 , 'least_upper_bound'( identity, Y ) ) ) ] )
% 1.22/1.61 , clause( 4938, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 1.22/1.61 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 171, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X,
% 1.22/1.61 'least_upper_bound'( identity, Y ) ) ) ] )
% 1.22/1.61 , clause( 4939, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply(
% 1.22/1.61 X, 'least_upper_bound'( identity, Y ) ) ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.22/1.61 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 4940, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ), 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( multiply( a, b ), identity ), multiply(
% 1.22/1.61 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.22/1.61 ) ) ) ] )
% 1.22/1.61 , clause( 15, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply( a
% 1.22/1.61 , b ), identity ), multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ) ), multiply( 'least_upper_bound'( a
% 1.22/1.61 , identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 4946, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ), 'least_upper_bound'( multiply(
% 1.22/1.61 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.22/1.61 , 'least_upper_bound'( multiply( a, b ), identity ) ) ) ) ] )
% 1.22/1.61 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 1.22/1.61 ) ] )
% 1.22/1.61 , 0, clause( 4940, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ), 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( multiply( a, b ), identity ), multiply(
% 1.22/1.61 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.22/1.61 ) ) ) ] )
% 1.22/1.61 , 0, 9, substitution( 0, [ :=( X, 'least_upper_bound'( multiply( a, b ),
% 1.22/1.61 identity ) ), :=( Y, multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ) )] ), substitution( 1, [] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 5016, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ), 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ), multiply( a, b ) ), identity ) ) )
% 1.22/1.61 ] )
% 1.22/1.61 , clause( 6, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 1.22/1.61 , 0, clause( 4946, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ), 'least_upper_bound'( multiply(
% 1.22/1.61 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.22/1.61 , 'least_upper_bound'( multiply( a, b ), identity ) ) ) ) ] )
% 1.22/1.61 , 0, 9, substitution( 0, [ :=( X, multiply( 'least_upper_bound'( a,
% 1.22/1.61 identity ), 'least_upper_bound'( b, identity ) ) ), :=( Y, multiply( a, b
% 1.22/1.61 ) ), :=( Z, identity )] ), substitution( 1, [] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 5017, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply(
% 1.22/1.61 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.22/1.61 , multiply( a, b ) ), identity ), multiply( 'least_upper_bound'( a,
% 1.22/1.61 identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.22/1.61 , clause( 5016, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ), 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ), multiply( a, b ) ), identity ) ) )
% 1.22/1.61 ] )
% 1.22/1.61 , 0, substitution( 0, [] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 173, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply(
% 1.22/1.61 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.22/1.61 , multiply( a, b ) ), identity ), multiply( 'least_upper_bound'( a,
% 1.22/1.61 identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.22/1.61 , clause( 5017, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply(
% 1.22/1.61 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.22/1.61 , multiply( a, b ) ), identity ), multiply( 'least_upper_bound'( a,
% 1.22/1.61 identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.22/1.61 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 5018, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 1.22/1.61 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 1.22/1.61 , clause( 171, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 1.22/1.61 , 'least_upper_bound'( identity, Y ) ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 5019, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 1.22/1.61 , 'least_upper_bound'( Y, identity ) ) ) ] )
% 1.22/1.61 , clause( 5018, [ =( multiply( X, 'least_upper_bound'( identity, Y ) ),
% 1.22/1.61 'least_upper_bound'( X, multiply( X, Y ) ) ) ] )
% 1.22/1.61 , 0, clause( 64, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), multiply(
% 1.22/1.61 X, 'least_upper_bound'( Z, Y ) ) ) ] )
% 1.22/1.61 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 1.22/1.61 :=( X, X ), :=( Y, identity ), :=( Z, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 753, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X,
% 1.22/1.61 'least_upper_bound'( Y, identity ) ) ) ] )
% 1.22/1.61 , clause( 5019, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply(
% 1.22/1.61 X, 'least_upper_bound'( Y, identity ) ) ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.22/1.61 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 5022, [ =( multiply( 'least_upper_bound'( identity, Y ), X ),
% 1.22/1.61 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 1.22/1.61 , clause( 117, [ =( 'least_upper_bound'( X, multiply( Y, X ) ), multiply(
% 1.22/1.61 'least_upper_bound'( identity, Y ), X ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 5035, [ =( multiply( multiply( identity, 'least_upper_bound'( X,
% 1.22/1.61 identity ) ), Y ), 'least_upper_bound'( Y, multiply( multiply( identity,
% 1.22/1.61 X ), Y ) ) ) ] )
% 1.22/1.61 , clause( 753, [ =( 'least_upper_bound'( X, multiply( X, Y ) ), multiply( X
% 1.22/1.61 , 'least_upper_bound'( Y, identity ) ) ) ] )
% 1.22/1.61 , 0, clause( 5022, [ =( multiply( 'least_upper_bound'( identity, Y ), X ),
% 1.22/1.61 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 1.22/1.61 , 0, 2, substitution( 0, [ :=( X, identity ), :=( Y, X )] ), substitution(
% 1.22/1.61 1, [ :=( X, Y ), :=( Y, multiply( identity, X ) )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 5038, [ =( multiply( multiply( identity, 'least_upper_bound'( X,
% 1.22/1.61 identity ) ), Y ), 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 1.22/1.61 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 1.22/1.61 , 0, clause( 5035, [ =( multiply( multiply( identity, 'least_upper_bound'(
% 1.22/1.61 X, identity ) ), Y ), 'least_upper_bound'( Y, multiply( multiply(
% 1.22/1.61 identity, X ), Y ) ) ) ] )
% 1.22/1.61 , 0, 11, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 1.22/1.61 :=( Y, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 5040, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 1.22/1.61 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 1.22/1.61 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 1.22/1.61 , 0, clause( 5038, [ =( multiply( multiply( identity, 'least_upper_bound'(
% 1.22/1.61 X, identity ) ), Y ), 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 1.22/1.61 , 0, 2, substitution( 0, [ :=( X, 'least_upper_bound'( X, identity ) )] ),
% 1.22/1.61 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 5041, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 1.22/1.61 'least_upper_bound'( X, identity ), Y ) ) ] )
% 1.22/1.61 , clause( 5040, [ =( multiply( 'least_upper_bound'( X, identity ), Y ),
% 1.22/1.61 'least_upper_bound'( Y, multiply( X, Y ) ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 1210, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 1.22/1.61 'least_upper_bound'( X, identity ), Y ) ) ] )
% 1.22/1.61 , clause( 5041, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 1.22/1.61 'least_upper_bound'( X, identity ), Y ) ) ] )
% 1.22/1.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.22/1.61 )] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 5042, [ =( multiply( 'least_upper_bound'( Y, identity ), X ),
% 1.22/1.61 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 1.22/1.61 , clause( 1210, [ =( 'least_upper_bound'( Y, multiply( X, Y ) ), multiply(
% 1.22/1.61 'least_upper_bound'( X, identity ), Y ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqswap(
% 1.22/1.61 clause( 5043, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ), 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ), multiply( a, b ) ), identity ) ) )
% 1.22/1.61 ] )
% 1.22/1.61 , clause( 173, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( multiply(
% 1.22/1.61 'least_upper_bound'( a, identity ), 'least_upper_bound'( b, identity ) )
% 1.22/1.61 , multiply( a, b ) ), identity ), multiply( 'least_upper_bound'( a,
% 1.22/1.61 identity ), 'least_upper_bound'( b, identity ) ) ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 5048, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ), 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( 'least_upper_bound'( b,
% 1.22/1.61 identity ), multiply( a, 'least_upper_bound'( b, identity ) ) ), multiply(
% 1.22/1.61 a, b ) ), identity ) ) ) ] )
% 1.22/1.61 , clause( 5042, [ =( multiply( 'least_upper_bound'( Y, identity ), X ),
% 1.22/1.61 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 1.22/1.61 , 0, clause( 5043, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ), 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ), multiply( a, b ) ), identity ) ) )
% 1.22/1.61 ] )
% 1.22/1.61 , 0, 11, substitution( 0, [ :=( X, 'least_upper_bound'( b, identity ) ),
% 1.22/1.61 :=( Y, a )] ), substitution( 1, [] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 5049, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( b, identity
% 1.22/1.61 ), multiply( a, 'least_upper_bound'( b, identity ) ) ),
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( b, identity ), multiply( a, 'least_upper_bound'( b,
% 1.22/1.61 identity ) ) ), multiply( a, b ) ), identity ) ) ) ] )
% 1.22/1.61 , clause( 5042, [ =( multiply( 'least_upper_bound'( Y, identity ), X ),
% 1.22/1.61 'least_upper_bound'( X, multiply( Y, X ) ) ) ] )
% 1.22/1.61 , 0, clause( 5048, [ ~( =( multiply( 'least_upper_bound'( a, identity ),
% 1.22/1.61 'least_upper_bound'( b, identity ) ), 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( 'least_upper_bound'( b,
% 1.22/1.61 identity ), multiply( a, 'least_upper_bound'( b, identity ) ) ), multiply(
% 1.22/1.61 a, b ) ), identity ) ) ) ] )
% 1.22/1.61 , 0, 2, substitution( 0, [ :=( X, 'least_upper_bound'( b, identity ) ),
% 1.22/1.61 :=( Y, a )] ), substitution( 1, [] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 5053, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( b, identity
% 1.22/1.61 ), multiply( a, 'least_upper_bound'( b, identity ) ) ),
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( 'least_upper_bound'( b,
% 1.22/1.61 identity ), multiply( a, 'least_upper_bound'( 'least_upper_bound'( b,
% 1.22/1.61 identity ), b ) ) ), identity ) ) ) ] )
% 1.22/1.61 , clause( 61, [ =( 'least_upper_bound'( 'least_upper_bound'( T, multiply( X
% 1.22/1.61 , Y ) ), multiply( X, Z ) ), 'least_upper_bound'( T, multiply( X,
% 1.22/1.61 'least_upper_bound'( Y, Z ) ) ) ) ] )
% 1.22/1.61 , 0, clause( 5049, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( b,
% 1.22/1.61 identity ), multiply( a, 'least_upper_bound'( b, identity ) ) ),
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( b, identity ), multiply( a, 'least_upper_bound'( b,
% 1.22/1.61 identity ) ) ), multiply( a, b ) ), identity ) ) ) ] )
% 1.22/1.61 , 0, 12, substitution( 0, [ :=( X, a ), :=( Y, 'least_upper_bound'( b,
% 1.22/1.61 identity ) ), :=( Z, b ), :=( T, 'least_upper_bound'( b, identity ) )] )
% 1.22/1.61 , substitution( 1, [] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 5054, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( b, identity
% 1.22/1.61 ), multiply( a, 'least_upper_bound'( b, identity ) ) ),
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( b, identity ), multiply( a,
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( b, identity ), b ) ) ) ) ) ] )
% 1.22/1.61 , clause( 59, [ =( 'least_upper_bound'( 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( Z, X ), Y ), X ), 'least_upper_bound'(
% 1.22/1.61 'least_upper_bound'( Z, X ), Y ) ) ] )
% 1.22/1.61 , 0, clause( 5053, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( b,
% 1.22/1.61 identity ), multiply( a, 'least_upper_bound'( b, identity ) ) ),
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( 'least_upper_bound'( b,
% 1.22/1.61 identity ), multiply( a, 'least_upper_bound'( 'least_upper_bound'( b,
% 1.22/1.61 identity ), b ) ) ), identity ) ) ) ] )
% 1.22/1.61 , 0, 11, substitution( 0, [ :=( X, identity ), :=( Y, multiply( a,
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( b, identity ), b ) ) ), :=( Z,
% 1.22/1.61 b )] ), substitution( 1, [] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 paramod(
% 1.22/1.61 clause( 5055, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( b, identity
% 1.22/1.61 ), multiply( a, 'least_upper_bound'( b, identity ) ) ),
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( b, identity ), multiply( a,
% 1.22/1.61 'least_upper_bound'( b, identity ) ) ) ) ) ] )
% 1.22/1.61 , clause( 35, [ =( 'least_upper_bound'( 'least_upper_bound'( X, Y ), X ),
% 1.22/1.61 'least_upper_bound'( X, Y ) ) ] )
% 1.22/1.61 , 0, clause( 5054, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( b,
% 1.22/1.61 identity ), multiply( a, 'least_upper_bound'( b, identity ) ) ),
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( b, identity ), multiply( a,
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( b, identity ), b ) ) ) ) ) ] )
% 1.22/1.61 , 0, 17, substitution( 0, [ :=( X, b ), :=( Y, identity )] ),
% 1.22/1.61 substitution( 1, [] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 eqrefl(
% 1.22/1.61 clause( 5056, [] )
% 1.22/1.61 , clause( 5055, [ ~( =( 'least_upper_bound'( 'least_upper_bound'( b,
% 1.22/1.61 identity ), multiply( a, 'least_upper_bound'( b, identity ) ) ),
% 1.22/1.61 'least_upper_bound'( 'least_upper_bound'( b, identity ), multiply( a,
% 1.22/1.61 'least_upper_bound'( b, identity ) ) ) ) ) ] )
% 1.22/1.61 , 0, substitution( 0, [] )).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 subsumption(
% 1.22/1.61 clause( 4745, [] )
% 1.22/1.61 , clause( 5056, [] )
% 1.22/1.61 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 end.
% 1.22/1.61
% 1.22/1.61 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.22/1.61
% 1.22/1.61 Memory use:
% 1.22/1.61
% 1.22/1.61 space for terms: 64827
% 1.22/1.61 space for clauses: 515042
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 clauses generated: 130929
% 1.22/1.61 clauses kept: 4746
% 1.22/1.61 clauses selected: 521
% 1.22/1.61 clauses deleted: 43
% 1.22/1.61 clauses inuse deleted: 8
% 1.22/1.61
% 1.22/1.61 subsentry: 9643
% 1.22/1.61 literals s-matched: 7768
% 1.22/1.61 literals matched: 7755
% 1.22/1.61 full subsumption: 0
% 1.22/1.61
% 1.22/1.61 checksum: 1810097168
% 1.22/1.61
% 1.22/1.61
% 1.22/1.61 Bliksem ended
%------------------------------------------------------------------------------