TSTP Solution File: GRP175-4 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP175-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.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 07:35:48 EDT 2022
% Result : Unsatisfiable 0.71s 1.23s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP175-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Mon Jun 13 05:05:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.71/1.22 *** allocated 10000 integers for termspace/termends
% 0.71/1.22 *** allocated 10000 integers for clauses
% 0.71/1.22 *** allocated 10000 integers for justifications
% 0.71/1.22 Bliksem 1.12
% 0.71/1.22
% 0.71/1.22
% 0.71/1.22 Automatic Strategy Selection
% 0.71/1.22
% 0.71/1.22 Clauses:
% 0.71/1.22 [
% 0.71/1.22 [ =( multiply( identity, X ), X ) ],
% 0.71/1.22 [ =( multiply( inverse( X ), X ), identity ) ],
% 0.71/1.22 [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply( Y, Z ) ) )
% 0.71/1.22 ],
% 0.71/1.22 [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, X ) ) ]
% 0.71/1.22 ,
% 0.71/1.22 [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ],
% 0.71/1.22 [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.71/1.22 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ],
% 0.71/1.22 [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 0.71/1.22 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ],
% 0.71/1.22 [ =( 'least_upper_bound'( X, X ), X ) ],
% 0.71/1.22 [ =( 'greatest_lower_bound'( X, X ), X ) ],
% 0.71/1.22 [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X ) ]
% 0.71/1.22 ,
% 0.71/1.22 [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ), X ) ]
% 0.71/1.22 ,
% 0.71/1.22 [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), 'least_upper_bound'(
% 0.71/1.22 multiply( X, Y ), multiply( X, Z ) ) ) ],
% 0.71/1.22 [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.71/1.22 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ],
% 0.71/1.22 [ =( multiply( 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'(
% 0.71/1.22 multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 0.71/1.22 [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 0.71/1.22 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 0.71/1.22 [ =( 'greatest_lower_bound'( identity, b ), identity ) ],
% 0.71/1.22 [ ~( =( 'least_upper_bound'( identity, multiply( inverse( a ), multiply(
% 0.71/1.22 b, a ) ) ), multiply( inverse( a ), multiply( b, a ) ) ) ) ]
% 0.71/1.22 ] .
% 0.71/1.22
% 0.71/1.22
% 0.71/1.22 percentage equality = 1.000000, percentage horn = 1.000000
% 0.71/1.22 This is a pure equality problem
% 0.71/1.22
% 0.71/1.22
% 0.71/1.22
% 0.71/1.22 Options Used:
% 0.71/1.22
% 0.71/1.22 useres = 1
% 0.71/1.22 useparamod = 1
% 0.71/1.22 useeqrefl = 1
% 0.71/1.22 useeqfact = 1
% 0.71/1.22 usefactor = 1
% 0.71/1.22 usesimpsplitting = 0
% 0.71/1.22 usesimpdemod = 5
% 0.71/1.22 usesimpres = 3
% 0.71/1.22
% 0.71/1.22 resimpinuse = 1000
% 0.71/1.22 resimpclauses = 20000
% 0.71/1.22 substype = eqrewr
% 0.71/1.22 backwardsubs = 1
% 0.71/1.22 selectoldest = 5
% 0.71/1.22
% 0.71/1.22 litorderings [0] = split
% 0.71/1.22 litorderings [1] = extend the termordering, first sorting on arguments
% 0.71/1.22
% 0.71/1.22 termordering = kbo
% 0.71/1.22
% 0.71/1.22 litapriori = 0
% 0.71/1.22 termapriori = 1
% 0.71/1.22 litaposteriori = 0
% 0.71/1.22 termaposteriori = 0
% 0.71/1.22 demodaposteriori = 0
% 0.71/1.22 ordereqreflfact = 0
% 0.71/1.22
% 0.71/1.22 litselect = negord
% 0.71/1.22
% 0.71/1.22 maxweight = 15
% 0.71/1.22 maxdepth = 30000
% 0.71/1.22 maxlength = 115
% 0.71/1.22 maxnrvars = 195
% 0.71/1.22 excuselevel = 1
% 0.71/1.22 increasemaxweight = 1
% 0.71/1.22
% 0.71/1.22 maxselected = 10000000
% 0.71/1.22 maxnrclauses = 10000000
% 0.71/1.22
% 0.71/1.22 showgenerated = 0
% 0.71/1.22 showkept = 0
% 0.71/1.22 showselected = 0
% 0.71/1.22 showdeleted = 0
% 0.71/1.22 showresimp = 1
% 0.71/1.22 showstatus = 2000
% 0.71/1.22
% 0.71/1.22 prologoutput = 1
% 0.71/1.22 nrgoals = 5000000
% 0.71/1.22 totalproof = 1
% 0.71/1.22
% 0.71/1.22 Symbols occurring in the translation:
% 0.71/1.22
% 0.71/1.22 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.71/1.22 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.71/1.22 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.71/1.22 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.22 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.22 identity [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.71/1.23 multiply [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.71/1.23 inverse [42, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.71/1.23 'greatest_lower_bound' [45, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.71/1.23 'least_upper_bound' [46, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.71/1.23 b [47, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.71/1.23 a [48, 0] (w:1, o:13, a:1, s:1, b:0).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 Starting Search:
% 0.71/1.23
% 0.71/1.23 Resimplifying inuse:
% 0.71/1.23 Done
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 Intermediate Status:
% 0.71/1.23 Generated: 26803
% 0.71/1.23 Kept: 2008
% 0.71/1.23 Inuse: 249
% 0.71/1.23 Deleted: 18
% 0.71/1.23 Deletedinuse: 6
% 0.71/1.23
% 0.71/1.23 Resimplifying inuse:
% 0.71/1.23 Done
% 0.71/1.23
% 0.71/1.23 Resimplifying inuse:
% 0.71/1.23
% 0.71/1.23 Bliksems!, er is een bewijs:
% 0.71/1.23 % SZS status Unsatisfiable
% 0.71/1.23 % SZS output start Refutation
% 0.71/1.23
% 0.71/1.23 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 0.71/1.23 , Z ) ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 0.71/1.23 X ) ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 0.71/1.23 ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 0.71/1.23 ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 12, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z )
% 0.71/1.23 ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 0.71/1.23 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 15, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 16, [ ~( =( 'least_upper_bound'( identity, multiply( multiply(
% 0.71/1.23 inverse( a ), b ), a ) ), multiply( multiply( inverse( a ), b ), a ) ) )
% 0.71/1.23 ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 18, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 0.71/1.23 identity ) ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 19, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 0.71/1.23 ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 41, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) ),
% 0.71/1.23 X ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 55, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X ),
% 0.71/1.23 X ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 95, [ =( multiply( 'least_upper_bound'( inverse( X ), Y ), X ),
% 0.71/1.23 'least_upper_bound'( identity, multiply( Y, X ) ) ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 161, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 166, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.71/1.23 ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 167, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 0.71/1.23 X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 286, [ =( multiply( X, identity ), X ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 794, [ =( 'greatest_lower_bound'( X, multiply( X, b ) ), X ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 836, [ =( 'least_upper_bound'( X, multiply( X, b ) ), multiply( X,
% 0.71/1.23 b ) ) ] )
% 0.71/1.23 .
% 0.71/1.23 clause( 2072, [ =( 'least_upper_bound'( identity, multiply( multiply(
% 0.71/1.23 inverse( X ), b ), X ) ), multiply( multiply( inverse( X ), b ), X ) ) ]
% 0.71/1.23 )
% 0.71/1.23 .
% 0.71/1.23 clause( 3048, [] )
% 0.71/1.23 .
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 % SZS output end Refutation
% 0.71/1.23 found a proof!
% 0.71/1.23
% 0.71/1.23 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.71/1.23
% 0.71/1.23 initialclauses(
% 0.71/1.23 [ clause( 3050, [ =( multiply( identity, X ), X ) ] )
% 0.71/1.23 , clause( 3051, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.71/1.23 , clause( 3052, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.71/1.23 Y, Z ) ) ) ] )
% 0.71/1.23 , clause( 3053, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 0.71/1.23 Y, X ) ) ] )
% 0.71/1.23 , clause( 3054, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X
% 0.71/1.23 ) ) ] )
% 0.71/1.23 , clause( 3055, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y,
% 0.71/1.23 Z ) ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 0.71/1.23 , clause( 3056, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 0.71/1.23 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.71/1.23 , clause( 3057, [ =( 'least_upper_bound'( X, X ), X ) ] )
% 0.71/1.23 , clause( 3058, [ =( 'greatest_lower_bound'( X, X ), X ) ] )
% 0.71/1.23 , clause( 3059, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y )
% 0.71/1.23 ), X ) ] )
% 0.71/1.23 , clause( 3060, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y )
% 0.71/1.23 ), X ) ] )
% 0.71/1.23 , clause( 3061, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 0.71/1.23 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.71/1.23 , clause( 3062, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.71/1.23 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.71/1.23 , clause( 3063, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 0.71/1.23 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 0.71/1.23 , clause( 3064, [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 0.71/1.23 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 0.71/1.23 , clause( 3065, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.71/1.23 , clause( 3066, [ ~( =( 'least_upper_bound'( identity, multiply( inverse( a
% 0.71/1.23 ), multiply( b, a ) ) ), multiply( inverse( a ), multiply( b, a ) ) ) )
% 0.71/1.23 ] )
% 0.71/1.23 ] ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 subsumption(
% 0.71/1.23 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.71/1.23 , clause( 3050, [ =( multiply( identity, X ), X ) ] )
% 0.71/1.23 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 subsumption(
% 0.71/1.23 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.71/1.23 , clause( 3051, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.71/1.23 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 eqswap(
% 0.71/1.23 clause( 3072, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X,
% 0.71/1.23 Y ), Z ) ) ] )
% 0.71/1.23 , clause( 3052, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.71/1.23 Y, Z ) ) ) ] )
% 0.71/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 subsumption(
% 0.71/1.23 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 0.71/1.23 , Z ) ) ] )
% 0.71/1.23 , clause( 3072, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X
% 0.71/1.23 , Y ), Z ) ) ] )
% 0.71/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.71/1.23 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 subsumption(
% 0.71/1.23 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 0.71/1.23 X ) ) ] )
% 0.71/1.23 , clause( 3053, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 0.71/1.23 Y, X ) ) ] )
% 0.71/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.23 )] ) ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 subsumption(
% 0.71/1.23 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 0.71/1.23 ] )
% 0.71/1.23 , clause( 3054, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X
% 0.71/1.23 ) ) ] )
% 0.71/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.23 )] ) ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 subsumption(
% 0.71/1.23 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 0.71/1.23 ) ] )
% 0.71/1.23 , clause( 3059, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y )
% 0.71/1.23 ), X ) ] )
% 0.71/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.23 )] ) ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 eqswap(
% 0.71/1.23 clause( 3097, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z
% 0.71/1.23 ) ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 0.71/1.23 , clause( 3062, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.71/1.23 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.71/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 subsumption(
% 0.71/1.23 clause( 12, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z )
% 0.71/1.23 ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 0.71/1.23 , clause( 3097, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X
% 0.71/1.23 , Z ) ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 0.71/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.71/1.23 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 eqswap(
% 0.71/1.23 clause( 3109, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 0.71/1.23 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.71/1.23 , clause( 3063, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 0.71/1.23 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 0.71/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 subsumption(
% 0.71/1.23 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 0.71/1.23 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.71/1.23 , clause( 3109, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z
% 0.71/1.23 ) ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.71/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.71/1.23 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 subsumption(
% 0.71/1.23 clause( 15, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.71/1.23 , clause( 3065, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.71/1.23 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 paramod(
% 0.71/1.23 clause( 3159, [ ~( =( 'least_upper_bound'( identity, multiply( inverse( a )
% 0.71/1.23 , multiply( b, a ) ) ), multiply( multiply( inverse( a ), b ), a ) ) ) ]
% 0.71/1.23 )
% 0.71/1.23 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 0.71/1.23 ), Z ) ) ] )
% 0.71/1.23 , 0, clause( 3066, [ ~( =( 'least_upper_bound'( identity, multiply( inverse(
% 0.71/1.23 a ), multiply( b, a ) ) ), multiply( inverse( a ), multiply( b, a ) ) ) )
% 0.71/1.23 ] )
% 0.71/1.23 , 0, 10, substitution( 0, [ :=( X, inverse( a ) ), :=( Y, b ), :=( Z, a )] )
% 0.71/1.23 , substitution( 1, [] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 paramod(
% 0.71/1.23 clause( 3160, [ ~( =( 'least_upper_bound'( identity, multiply( multiply(
% 0.71/1.23 inverse( a ), b ), a ) ), multiply( multiply( inverse( a ), b ), a ) ) )
% 0.71/1.23 ] )
% 0.71/1.23 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 0.71/1.23 ), Z ) ) ] )
% 0.71/1.23 , 0, clause( 3159, [ ~( =( 'least_upper_bound'( identity, multiply( inverse(
% 0.71/1.23 a ), multiply( b, a ) ) ), multiply( multiply( inverse( a ), b ), a ) ) )
% 0.71/1.23 ] )
% 0.71/1.23 , 0, 4, substitution( 0, [ :=( X, inverse( a ) ), :=( Y, b ), :=( Z, a )] )
% 0.71/1.23 , substitution( 1, [] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 subsumption(
% 0.71/1.23 clause( 16, [ ~( =( 'least_upper_bound'( identity, multiply( multiply(
% 0.71/1.23 inverse( a ), b ), a ) ), multiply( multiply( inverse( a ), b ), a ) ) )
% 0.71/1.23 ] )
% 0.71/1.23 , clause( 3160, [ ~( =( 'least_upper_bound'( identity, multiply( multiply(
% 0.71/1.23 inverse( a ), b ), a ) ), multiply( multiply( inverse( a ), b ), a ) ) )
% 0.71/1.23 ] )
% 0.71/1.23 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 eqswap(
% 0.71/1.23 clause( 3165, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.71/1.23 Y, Z ) ) ) ] )
% 0.71/1.23 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 0.71/1.23 ), Z ) ) ] )
% 0.71/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 paramod(
% 0.71/1.23 clause( 3170, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply( X
% 0.71/1.23 , identity ) ) ] )
% 0.71/1.23 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.71/1.23 , 0, clause( 3165, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 0.71/1.23 multiply( Y, Z ) ) ) ] )
% 0.71/1.23 , 0, 9, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 0.71/1.23 :=( Y, inverse( Y ) ), :=( Z, Y )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 subsumption(
% 0.71/1.23 clause( 18, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 0.71/1.23 identity ) ) ] )
% 0.71/1.23 , clause( 3170, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply(
% 0.71/1.23 X, identity ) ) ] )
% 0.71/1.23 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.23 )] ) ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 eqswap(
% 0.71/1.23 clause( 3175, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.71/1.23 Y, Z ) ) ) ] )
% 0.71/1.23 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 0.71/1.23 ), Z ) ) ] )
% 0.71/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 paramod(
% 0.71/1.23 clause( 3180, [ =( multiply( multiply( X, identity ), Y ), multiply( X, Y )
% 0.71/1.23 ) ] )
% 0.71/1.23 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.71/1.23 , 0, clause( 3175, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 0.71/1.23 multiply( Y, Z ) ) ) ] )
% 0.71/1.23 , 0, 8, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 0.71/1.23 :=( Y, identity ), :=( Z, Y )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 subsumption(
% 0.71/1.23 clause( 19, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 0.71/1.23 ] )
% 0.71/1.23 , clause( 3180, [ =( multiply( multiply( X, identity ), Y ), multiply( X, Y
% 0.71/1.23 ) ) ] )
% 0.71/1.23 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.23 )] ) ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 eqswap(
% 0.71/1.23 clause( 3185, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 0.71/1.23 ) ) ) ] )
% 0.71/1.23 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 0.71/1.23 , X ) ] )
% 0.71/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 paramod(
% 0.71/1.23 clause( 3186, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X
% 0.71/1.23 ) ) ) ] )
% 0.71/1.23 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 0.71/1.23 , X ) ) ] )
% 0.71/1.23 , 0, clause( 3185, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 0.71/1.23 X, Y ) ) ) ] )
% 0.71/1.23 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.71/1.23 :=( X, X ), :=( Y, Y )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 eqswap(
% 0.71/1.23 clause( 3189, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) )
% 0.71/1.23 , X ) ] )
% 0.71/1.23 , clause( 3186, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y,
% 0.71/1.23 X ) ) ) ] )
% 0.71/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 subsumption(
% 0.71/1.23 clause( 41, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) ),
% 0.71/1.23 X ) ] )
% 0.71/1.23 , clause( 3189, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X )
% 0.71/1.23 ), X ) ] )
% 0.71/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.23 )] ) ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 eqswap(
% 0.71/1.23 clause( 3190, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X
% 0.71/1.23 ) ) ) ] )
% 0.71/1.23 , clause( 41, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) )
% 0.71/1.23 , X ) ] )
% 0.71/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 paramod(
% 0.71/1.23 clause( 3191, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( Y, X ),
% 0.71/1.23 X ) ) ] )
% 0.71/1.23 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 0.71/1.23 ) ] )
% 0.71/1.23 , 0, clause( 3190, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 0.71/1.23 Y, X ) ) ) ] )
% 0.71/1.23 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, 'greatest_lower_bound'( Y, X
% 0.71/1.23 ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 eqswap(
% 0.71/1.23 clause( 3194, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X )
% 0.71/1.23 , X ) ] )
% 0.71/1.23 , clause( 3191, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( Y, X )
% 0.71/1.23 , X ) ) ] )
% 0.71/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 subsumption(
% 0.71/1.23 clause( 55, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X ),
% 0.71/1.23 X ) ] )
% 0.71/1.23 , clause( 3194, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X
% 0.71/1.23 ), X ) ] )
% 0.71/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.23 )] ) ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 eqswap(
% 0.71/1.23 clause( 3196, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 0.71/1.23 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 0.71/1.23 , clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 0.71/1.23 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.71/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 paramod(
% 0.71/1.23 clause( 3197, [ =( multiply( 'least_upper_bound'( inverse( X ), Y ), X ),
% 0.71/1.23 'least_upper_bound'( identity, multiply( Y, X ) ) ) ] )
% 0.71/1.23 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.71/1.23 , 0, clause( 3196, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 0.71/1.23 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 0.71/1.23 , 0, 8, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 0.71/1.23 X ) ), :=( Y, X ), :=( Z, Y )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 subsumption(
% 0.71/1.23 clause( 95, [ =( multiply( 'least_upper_bound'( inverse( X ), Y ), X ),
% 0.71/1.23 'least_upper_bound'( identity, multiply( Y, X ) ) ) ] )
% 0.71/1.23 , clause( 3197, [ =( multiply( 'least_upper_bound'( inverse( X ), Y ), X )
% 0.71/1.23 , 'least_upper_bound'( identity, multiply( Y, X ) ) ) ] )
% 0.71/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.23 )] ) ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 eqswap(
% 0.71/1.23 clause( 3202, [ =( multiply( X, identity ), multiply( multiply( X, inverse(
% 0.71/1.23 Y ) ), Y ) ) ] )
% 0.71/1.23 , clause( 18, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 0.71/1.23 , identity ) ) ] )
% 0.71/1.23 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 paramod(
% 0.71/1.23 clause( 3205, [ =( multiply( inverse( inverse( X ) ), identity ), multiply(
% 0.71/1.23 identity, X ) ) ] )
% 0.71/1.23 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.71/1.23 , 0, clause( 3202, [ =( multiply( X, identity ), multiply( multiply( X,
% 0.71/1.23 inverse( Y ) ), Y ) ) ] )
% 0.71/1.23 , 0, 7, substitution( 0, [ :=( X, inverse( X ) )] ), substitution( 1, [
% 0.71/1.23 :=( X, inverse( inverse( X ) ) ), :=( Y, X )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 paramod(
% 0.71/1.23 clause( 3206, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.71/1.23 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.71/1.23 , 0, clause( 3205, [ =( multiply( inverse( inverse( X ) ), identity ),
% 0.71/1.23 multiply( identity, X ) ) ] )
% 0.71/1.23 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.71/1.23 ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 subsumption(
% 0.71/1.23 clause( 161, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.71/1.23 , clause( 3206, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ]
% 0.71/1.23 )
% 0.71/1.23 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 eqswap(
% 0.71/1.23 clause( 3209, [ =( multiply( X, Y ), multiply( multiply( X, identity ), Y )
% 0.71/1.23 ) ] )
% 0.71/1.23 , clause( 19, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X )
% 0.71/1.23 ) ] )
% 0.71/1.23 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.71/1.23
% 0.71/1.23
% 0.71/1.23 paramod(
% 0.71/1.23 clause( 3212, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.71/1.23 ) ] )
% 0.71/1.23 , clause( 161, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.87/1.23 , 0, clause( 3209, [ =( multiply( X, Y ), multiply( multiply( X, identity )
% 0.87/1.23 , Y ) ) ] )
% 0.87/1.23 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 0.87/1.23 inverse( X ) ) ), :=( Y, Y )] )).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 subsumption(
% 0.87/1.23 clause( 166, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.87/1.23 ) ] )
% 0.87/1.23 , clause( 3212, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.87/1.23 ) ) ] )
% 0.87/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.87/1.23 )] ) ).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 eqswap(
% 0.87/1.23 clause( 3219, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.87/1.23 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.87/1.23 , clause( 12, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z
% 0.87/1.23 ) ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 0.87/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 paramod(
% 0.87/1.23 clause( 3222, [ =( multiply( inverse( inverse( X ) ),
% 0.87/1.23 'greatest_lower_bound'( identity, Y ) ), 'greatest_lower_bound'( X,
% 0.87/1.23 multiply( inverse( inverse( X ) ), Y ) ) ) ] )
% 0.87/1.23 , clause( 161, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.87/1.23 , 0, clause( 3219, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.87/1.23 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.87/1.23 , 0, 9, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 0.87/1.23 inverse( X ) ) ), :=( Y, identity ), :=( Z, Y )] )).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 paramod(
% 0.87/1.23 clause( 3232, [ =( multiply( inverse( inverse( X ) ),
% 0.87/1.23 'greatest_lower_bound'( identity, Y ) ), 'greatest_lower_bound'( X,
% 0.87/1.23 multiply( X, Y ) ) ) ] )
% 0.87/1.23 , clause( 166, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.87/1.23 ) ) ] )
% 0.87/1.23 , 0, clause( 3222, [ =( multiply( inverse( inverse( X ) ),
% 0.87/1.23 'greatest_lower_bound'( identity, Y ) ), 'greatest_lower_bound'( X,
% 0.87/1.23 multiply( inverse( inverse( X ) ), Y ) ) ) ] )
% 0.87/1.23 , 0, 10, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.87/1.23 :=( X, X ), :=( Y, Y )] )).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 paramod(
% 0.87/1.23 clause( 3234, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) ),
% 0.87/1.23 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 0.87/1.23 , clause( 166, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.87/1.23 ) ) ] )
% 0.87/1.23 , 0, clause( 3232, [ =( multiply( inverse( inverse( X ) ),
% 0.87/1.23 'greatest_lower_bound'( identity, Y ) ), 'greatest_lower_bound'( X,
% 0.87/1.23 multiply( X, Y ) ) ) ] )
% 0.87/1.23 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, 'greatest_lower_bound'(
% 0.87/1.23 identity, Y ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 eqswap(
% 0.87/1.23 clause( 3235, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 0.87/1.23 X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 0.87/1.23 , clause( 3234, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) ),
% 0.87/1.23 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 0.87/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 subsumption(
% 0.87/1.23 clause( 167, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 0.87/1.23 X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 0.87/1.23 , clause( 3235, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ),
% 0.87/1.23 multiply( X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 0.87/1.23 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.87/1.23 )] ) ).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 eqswap(
% 0.87/1.23 clause( 3236, [ =( multiply( X, Y ), multiply( inverse( inverse( X ) ), Y )
% 0.87/1.23 ) ] )
% 0.87/1.23 , clause( 166, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.87/1.23 ) ) ] )
% 0.87/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 paramod(
% 0.87/1.23 clause( 3239, [ =( multiply( X, identity ), X ) ] )
% 0.87/1.23 , clause( 161, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.87/1.23 , 0, clause( 3236, [ =( multiply( X, Y ), multiply( inverse( inverse( X ) )
% 0.87/1.23 , Y ) ) ] )
% 0.87/1.23 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.87/1.23 :=( Y, identity )] )).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 subsumption(
% 0.87/1.23 clause( 286, [ =( multiply( X, identity ), X ) ] )
% 0.87/1.23 , clause( 3239, [ =( multiply( X, identity ), X ) ] )
% 0.87/1.23 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 eqswap(
% 0.87/1.23 clause( 3245, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) ),
% 0.87/1.23 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 0.87/1.23 , clause( 167, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 0.87/1.23 X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 0.87/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 paramod(
% 0.87/1.23 clause( 3247, [ =( multiply( X, identity ), 'greatest_lower_bound'( X,
% 0.87/1.23 multiply( X, b ) ) ) ] )
% 0.87/1.23 , clause( 15, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.87/1.23 , 0, clause( 3245, [ =( multiply( X, 'greatest_lower_bound'( identity, Y )
% 0.87/1.23 ), 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 0.87/1.23 , 0, 3, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, b )] )
% 0.87/1.23 ).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 paramod(
% 0.87/1.23 clause( 3248, [ =( X, 'greatest_lower_bound'( X, multiply( X, b ) ) ) ] )
% 0.87/1.23 , clause( 286, [ =( multiply( X, identity ), X ) ] )
% 0.87/1.23 , 0, clause( 3247, [ =( multiply( X, identity ), 'greatest_lower_bound'( X
% 0.87/1.23 , multiply( X, b ) ) ) ] )
% 0.87/1.23 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.87/1.23 ).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 eqswap(
% 0.87/1.23 clause( 3249, [ =( 'greatest_lower_bound'( X, multiply( X, b ) ), X ) ] )
% 0.87/1.23 , clause( 3248, [ =( X, 'greatest_lower_bound'( X, multiply( X, b ) ) ) ]
% 0.87/1.23 )
% 0.87/1.23 , 0, substitution( 0, [ :=( X, X )] )).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 subsumption(
% 0.87/1.23 clause( 794, [ =( 'greatest_lower_bound'( X, multiply( X, b ) ), X ) ] )
% 0.87/1.23 , clause( 3249, [ =( 'greatest_lower_bound'( X, multiply( X, b ) ), X ) ]
% 0.87/1.23 )
% 0.87/1.23 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 eqswap(
% 0.87/1.23 clause( 3251, [ =( Y, 'least_upper_bound'( 'greatest_lower_bound'( X, Y ),
% 0.87/1.23 Y ) ) ] )
% 0.87/1.23 , clause( 55, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X )
% 0.87/1.23 , X ) ] )
% 0.87/1.23 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 paramod(
% 0.87/1.23 clause( 3252, [ =( multiply( X, b ), 'least_upper_bound'( X, multiply( X, b
% 0.87/1.23 ) ) ) ] )
% 0.87/1.23 , clause( 794, [ =( 'greatest_lower_bound'( X, multiply( X, b ) ), X ) ] )
% 0.87/1.23 , 0, clause( 3251, [ =( Y, 'least_upper_bound'( 'greatest_lower_bound'( X,
% 0.87/1.23 Y ), Y ) ) ] )
% 0.87/1.23 , 0, 5, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.87/1.23 :=( Y, multiply( X, b ) )] )).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 eqswap(
% 0.87/1.23 clause( 3253, [ =( 'least_upper_bound'( X, multiply( X, b ) ), multiply( X
% 0.87/1.23 , b ) ) ] )
% 0.87/1.23 , clause( 3252, [ =( multiply( X, b ), 'least_upper_bound'( X, multiply( X
% 0.87/1.23 , b ) ) ) ] )
% 0.87/1.23 , 0, substitution( 0, [ :=( X, X )] )).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 subsumption(
% 0.87/1.23 clause( 836, [ =( 'least_upper_bound'( X, multiply( X, b ) ), multiply( X,
% 0.87/1.23 b ) ) ] )
% 0.87/1.23 , clause( 3253, [ =( 'least_upper_bound'( X, multiply( X, b ) ), multiply(
% 0.87/1.23 X, b ) ) ] )
% 0.87/1.23 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 eqswap(
% 0.87/1.23 clause( 3255, [ =( 'least_upper_bound'( identity, multiply( Y, X ) ),
% 0.87/1.23 multiply( 'least_upper_bound'( inverse( X ), Y ), X ) ) ] )
% 0.87/1.23 , clause( 95, [ =( multiply( 'least_upper_bound'( inverse( X ), Y ), X ),
% 0.87/1.23 'least_upper_bound'( identity, multiply( Y, X ) ) ) ] )
% 0.87/1.23 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 paramod(
% 0.87/1.23 clause( 3263, [ =( 'least_upper_bound'( identity, multiply( multiply(
% 0.87/1.23 inverse( X ), b ), X ) ), multiply( multiply( inverse( X ), b ), X ) ) ]
% 0.87/1.23 )
% 0.87/1.23 , clause( 836, [ =( 'least_upper_bound'( X, multiply( X, b ) ), multiply( X
% 0.87/1.23 , b ) ) ] )
% 0.87/1.23 , 0, clause( 3255, [ =( 'least_upper_bound'( identity, multiply( Y, X ) ),
% 0.87/1.23 multiply( 'least_upper_bound'( inverse( X ), Y ), X ) ) ] )
% 0.87/1.23 , 0, 10, substitution( 0, [ :=( X, inverse( X ) )] ), substitution( 1, [
% 0.87/1.23 :=( X, X ), :=( Y, multiply( inverse( X ), b ) )] )).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 subsumption(
% 0.87/1.23 clause( 2072, [ =( 'least_upper_bound'( identity, multiply( multiply(
% 0.87/1.23 inverse( X ), b ), X ) ), multiply( multiply( inverse( X ), b ), X ) ) ]
% 0.87/1.23 )
% 0.87/1.23 , clause( 3263, [ =( 'least_upper_bound'( identity, multiply( multiply(
% 0.87/1.23 inverse( X ), b ), X ) ), multiply( multiply( inverse( X ), b ), X ) ) ]
% 0.87/1.23 )
% 0.87/1.23 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 paramod(
% 0.87/1.23 clause( 3268, [ ~( =( multiply( multiply( inverse( a ), b ), a ), multiply(
% 0.87/1.23 multiply( inverse( a ), b ), a ) ) ) ] )
% 0.87/1.23 , clause( 2072, [ =( 'least_upper_bound'( identity, multiply( multiply(
% 0.87/1.23 inverse( X ), b ), X ) ), multiply( multiply( inverse( X ), b ), X ) ) ]
% 0.87/1.23 )
% 0.87/1.23 , 0, clause( 16, [ ~( =( 'least_upper_bound'( identity, multiply( multiply(
% 0.87/1.23 inverse( a ), b ), a ) ), multiply( multiply( inverse( a ), b ), a ) ) )
% 0.87/1.23 ] )
% 0.87/1.23 , 0, 2, substitution( 0, [ :=( X, a )] ), substitution( 1, [] )).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 eqrefl(
% 0.87/1.23 clause( 3269, [] )
% 0.87/1.23 , clause( 3268, [ ~( =( multiply( multiply( inverse( a ), b ), a ),
% 0.87/1.23 multiply( multiply( inverse( a ), b ), a ) ) ) ] )
% 0.87/1.23 , 0, substitution( 0, [] )).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 subsumption(
% 0.87/1.23 clause( 3048, [] )
% 0.87/1.23 , clause( 3269, [] )
% 0.87/1.23 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 end.
% 0.87/1.23
% 0.87/1.23 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.87/1.23
% 0.87/1.23 Memory use:
% 0.87/1.23
% 0.87/1.23 space for terms: 39435
% 0.87/1.23 space for clauses: 324130
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 clauses generated: 40092
% 0.87/1.23 clauses kept: 3049
% 0.87/1.23 clauses selected: 315
% 0.87/1.23 clauses deleted: 27
% 0.87/1.23 clauses inuse deleted: 11
% 0.87/1.23
% 0.87/1.23 subsentry: 5161
% 0.87/1.23 literals s-matched: 4662
% 0.87/1.23 literals matched: 4650
% 0.87/1.23 full subsumption: 0
% 0.87/1.23
% 0.87/1.23 checksum: 1890843805
% 0.87/1.23
% 0.87/1.23
% 0.87/1.23 Bliksem ended
%------------------------------------------------------------------------------