TSTP Solution File: GRP166-1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GRP166-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n006.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 07:35:40 EDT 2022

% Result   : Unsatisfiable 0.81s 1.20s
% Output   : Refutation 0.81s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP166-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12  % Command  : bliksem %s
% 0.12/0.33  % Computer : n006.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % DateTime : Tue Jun 14 07:44:11 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.81/1.20  *** allocated 10000 integers for termspace/termends
% 0.81/1.20  *** allocated 10000 integers for clauses
% 0.81/1.20  *** allocated 10000 integers for justifications
% 0.81/1.20  Bliksem 1.12
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  Automatic Strategy Selection
% 0.81/1.20  
% 0.81/1.20  Clauses:
% 0.81/1.20  [
% 0.81/1.20     [ =( multiply( identity, X ), X ) ],
% 0.81/1.20     [ =( multiply( inverse( X ), X ), identity ) ],
% 0.81/1.20     [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply( Y, Z ) ) )
% 0.81/1.20     ],
% 0.81/1.20     [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, X ) ) ]
% 0.81/1.20    ,
% 0.81/1.20     [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ],
% 0.81/1.20     [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ), 
% 0.81/1.20    'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ],
% 0.81/1.20     [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ), 
% 0.81/1.20    'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ],
% 0.81/1.20     [ =( 'least_upper_bound'( X, X ), X ) ],
% 0.81/1.20     [ =( 'greatest_lower_bound'( X, X ), X ) ],
% 0.81/1.20     [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X ) ]
% 0.81/1.20    ,
% 0.81/1.20     [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ), X ) ]
% 0.81/1.20    ,
% 0.81/1.20     [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), 'least_upper_bound'( 
% 0.81/1.20    multiply( X, Y ), multiply( X, Z ) ) ) ],
% 0.81/1.20     [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ), 
% 0.81/1.20    'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ],
% 0.81/1.20     [ =( multiply( 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'( 
% 0.81/1.20    multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 0.81/1.20     [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ), 
% 0.81/1.20    'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 0.81/1.20     [ =( 'least_upper_bound'( a, identity ), a ) ],
% 0.81/1.20     [ =( 'least_upper_bound'( b, identity ), b ) ],
% 0.81/1.20     [ ~( =( 'least_upper_bound'( a, multiply( a, b ) ), multiply( a, b ) ) )
% 0.81/1.20     ]
% 0.81/1.20  ] .
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  percentage equality = 1.000000, percentage horn = 1.000000
% 0.81/1.20  This is a pure equality problem
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  Options Used:
% 0.81/1.20  
% 0.81/1.20  useres =            1
% 0.81/1.20  useparamod =        1
% 0.81/1.20  useeqrefl =         1
% 0.81/1.20  useeqfact =         1
% 0.81/1.20  usefactor =         1
% 0.81/1.20  usesimpsplitting =  0
% 0.81/1.20  usesimpdemod =      5
% 0.81/1.20  usesimpres =        3
% 0.81/1.20  
% 0.81/1.20  resimpinuse      =  1000
% 0.81/1.20  resimpclauses =     20000
% 0.81/1.20  substype =          eqrewr
% 0.81/1.20  backwardsubs =      1
% 0.81/1.20  selectoldest =      5
% 0.81/1.20  
% 0.81/1.20  litorderings [0] =  split
% 0.81/1.20  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.81/1.20  
% 0.81/1.20  termordering =      kbo
% 0.81/1.20  
% 0.81/1.20  litapriori =        0
% 0.81/1.20  termapriori =       1
% 0.81/1.20  litaposteriori =    0
% 0.81/1.20  termaposteriori =   0
% 0.81/1.20  demodaposteriori =  0
% 0.81/1.20  ordereqreflfact =   0
% 0.81/1.20  
% 0.81/1.20  litselect =         negord
% 0.81/1.20  
% 0.81/1.20  maxweight =         15
% 0.81/1.20  maxdepth =          30000
% 0.81/1.20  maxlength =         115
% 0.81/1.20  maxnrvars =         195
% 0.81/1.20  excuselevel =       1
% 0.81/1.20  increasemaxweight = 1
% 0.81/1.20  
% 0.81/1.20  maxselected =       10000000
% 0.81/1.20  maxnrclauses =      10000000
% 0.81/1.20  
% 0.81/1.20  showgenerated =    0
% 0.81/1.20  showkept =         0
% 0.81/1.20  showselected =     0
% 0.81/1.20  showdeleted =      0
% 0.81/1.20  showresimp =       1
% 0.81/1.20  showstatus =       2000
% 0.81/1.20  
% 0.81/1.20  prologoutput =     1
% 0.81/1.20  nrgoals =          5000000
% 0.81/1.20  totalproof =       1
% 0.81/1.20  
% 0.81/1.20  Symbols occurring in the translation:
% 0.81/1.20  
% 0.81/1.20  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.81/1.20  .  [1, 2]      (w:1, o:21, a:1, s:1, b:0), 
% 0.81/1.20  !  [4, 1]      (w:0, o:15, a:1, s:1, b:0), 
% 0.81/1.20  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.81/1.20  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.81/1.20  identity  [39, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 0.81/1.20  multiply  [41, 2]      (w:1, o:47, a:1, s:1, b:0), 
% 0.81/1.20  inverse  [42, 1]      (w:1, o:20, a:1, s:1, b:0), 
% 0.81/1.20  'greatest_lower_bound'  [45, 2]      (w:1, o:48, a:1, s:1, b:0), 
% 0.81/1.20  'least_upper_bound'  [46, 2]      (w:1, o:46, a:1, s:1, b:0), 
% 0.81/1.20  a  [47, 0]      (w:1, o:13, a:1, s:1, b:0), 
% 0.81/1.20  b  [48, 0]      (w:1, o:14, a:1, s:1, b:0).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  Starting Search:
% 0.81/1.20  
% 0.81/1.20  Resimplifying inuse:
% 0.81/1.20  Done
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  Intermediate Status:
% 0.81/1.20  Generated:    27623
% 0.81/1.20  Kept:         2010
% 0.81/1.20  Inuse:        273
% 0.81/1.20  Deleted:      17
% 0.81/1.20  Deletedinuse: 6
% 0.81/1.20  
% 0.81/1.20  Resimplifying inuse:
% 0.81/1.20  
% 0.81/1.20  Bliksems!, er is een bewijs:
% 0.81/1.20  % SZS status Unsatisfiable
% 0.81/1.20  % SZS output start Refutation
% 0.81/1.20  
% 0.81/1.20  clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 0.81/1.20    , Z ) ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, 
% 0.81/1.20    X ) ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 0.81/1.20     ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 0.81/1.20     ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ), 
% 0.81/1.20    X ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 12, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z )
% 0.81/1.20     ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 16, [ =( 'least_upper_bound'( b, identity ), b ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 17, [ ~( =( 'least_upper_bound'( a, multiply( a, b ) ), multiply( a
% 0.81/1.20    , b ) ) ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 19, [ =( 'least_upper_bound'( identity, b ), b ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y, 
% 0.81/1.20    identity ) ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 22, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 0.81/1.20     ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 24, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 60, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) ), 
% 0.81/1.20    X ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 141, [ ~( =( 'least_upper_bound'( multiply( a, b ), a ), multiply( 
% 0.81/1.20    a, b ) ) ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 174, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 179, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.81/1.20     ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 180, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply( 
% 0.81/1.20    X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 381, [ =( multiply( X, identity ), X ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 980, [ =( 'greatest_lower_bound'( X, multiply( X, b ) ), X ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 1059, [ =( 'least_upper_bound'( multiply( X, b ), X ), multiply( X
% 0.81/1.20    , b ) ) ] )
% 0.81/1.20  .
% 0.81/1.20  clause( 2029, [] )
% 0.81/1.20  .
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  % SZS output end Refutation
% 0.81/1.20  found a proof!
% 0.81/1.20  
% 0.81/1.20  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.81/1.20  
% 0.81/1.20  initialclauses(
% 0.81/1.20  [ clause( 2031, [ =( multiply( identity, X ), X ) ] )
% 0.81/1.20  , clause( 2032, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.81/1.20  , clause( 2033, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply( 
% 0.81/1.20    Y, Z ) ) ) ] )
% 0.81/1.20  , clause( 2034, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( 
% 0.81/1.20    Y, X ) ) ] )
% 0.81/1.20  , clause( 2035, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X
% 0.81/1.20     ) ) ] )
% 0.81/1.20  , clause( 2036, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, 
% 0.81/1.20    Z ) ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 0.81/1.20  , clause( 2037, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 0.81/1.20    , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.81/1.20  , clause( 2038, [ =( 'least_upper_bound'( X, X ), X ) ] )
% 0.81/1.20  , clause( 2039, [ =( 'greatest_lower_bound'( X, X ), X ) ] )
% 0.81/1.20  , clause( 2040, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y )
% 0.81/1.20     ), X ) ] )
% 0.81/1.20  , clause( 2041, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y )
% 0.81/1.20     ), X ) ] )
% 0.81/1.20  , clause( 2042, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), 
% 0.81/1.20    'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.81/1.20  , clause( 2043, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ), 
% 0.81/1.20    'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.81/1.20  , clause( 2044, [ =( multiply( 'least_upper_bound'( X, Y ), Z ), 
% 0.81/1.20    'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 0.81/1.20  , clause( 2045, [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ), 
% 0.81/1.20    'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 0.81/1.20  , clause( 2046, [ =( 'least_upper_bound'( a, identity ), a ) ] )
% 0.81/1.20  , clause( 2047, [ =( 'least_upper_bound'( b, identity ), b ) ] )
% 0.81/1.20  , clause( 2048, [ ~( =( 'least_upper_bound'( a, multiply( a, b ) ), 
% 0.81/1.20    multiply( a, b ) ) ) ] )
% 0.81/1.20  ] ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.81/1.20  , clause( 2031, [ =( multiply( identity, X ), X ) ] )
% 0.81/1.20  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.81/1.20  , clause( 2032, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.81/1.20  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2054, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, 
% 0.81/1.20    Y ), Z ) ) ] )
% 0.81/1.20  , clause( 2033, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply( 
% 0.81/1.20    Y, Z ) ) ) ] )
% 0.81/1.20  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 0.81/1.20    , Z ) ) ] )
% 0.81/1.20  , clause( 2054, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X
% 0.81/1.20    , Y ), Z ) ) ] )
% 0.81/1.20  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 0.81/1.20    permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, 
% 0.81/1.20    X ) ) ] )
% 0.81/1.20  , clause( 2034, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( 
% 0.81/1.20    Y, X ) ) ] )
% 0.81/1.20  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.81/1.20     )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 0.81/1.20     ] )
% 0.81/1.20  , clause( 2035, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X
% 0.81/1.20     ) ) ] )
% 0.81/1.20  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.81/1.20     )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 0.81/1.20     ) ] )
% 0.81/1.20  , clause( 2040, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y )
% 0.81/1.20     ), X ) ] )
% 0.81/1.20  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.81/1.20     )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ), 
% 0.81/1.20    X ) ] )
% 0.81/1.20  , clause( 2041, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y )
% 0.81/1.20     ), X ) ] )
% 0.81/1.20  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.81/1.20     )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2088, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z
% 0.81/1.20     ) ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 0.81/1.20  , clause( 2043, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ), 
% 0.81/1.20    'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.81/1.20  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 12, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z )
% 0.81/1.20     ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 0.81/1.20  , clause( 2088, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X
% 0.81/1.20    , Z ) ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 0.81/1.20  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 0.81/1.20    permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 16, [ =( 'least_upper_bound'( b, identity ), b ) ] )
% 0.81/1.20  , clause( 2047, [ =( 'least_upper_bound'( b, identity ), b ) ] )
% 0.81/1.20  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 17, [ ~( =( 'least_upper_bound'( a, multiply( a, b ) ), multiply( a
% 0.81/1.20    , b ) ) ) ] )
% 0.81/1.20  , clause( 2048, [ ~( =( 'least_upper_bound'( a, multiply( a, b ) ), 
% 0.81/1.20    multiply( a, b ) ) ) ] )
% 0.81/1.20  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2120, [ =( b, 'least_upper_bound'( b, identity ) ) ] )
% 0.81/1.20  , clause( 16, [ =( 'least_upper_bound'( b, identity ), b ) ] )
% 0.81/1.20  , 0, substitution( 0, [] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  paramod(
% 0.81/1.20  clause( 2121, [ =( b, 'least_upper_bound'( identity, b ) ) ] )
% 0.81/1.20  , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 0.81/1.20     ) ] )
% 0.81/1.20  , 0, clause( 2120, [ =( b, 'least_upper_bound'( b, identity ) ) ] )
% 0.81/1.20  , 0, 2, substitution( 0, [ :=( X, b ), :=( Y, identity )] ), substitution( 
% 0.81/1.20    1, [] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2124, [ =( 'least_upper_bound'( identity, b ), b ) ] )
% 0.81/1.20  , clause( 2121, [ =( b, 'least_upper_bound'( identity, b ) ) ] )
% 0.81/1.20  , 0, substitution( 0, [] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 19, [ =( 'least_upper_bound'( identity, b ), b ) ] )
% 0.81/1.20  , clause( 2124, [ =( 'least_upper_bound'( identity, b ), b ) ] )
% 0.81/1.20  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2126, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply( 
% 0.81/1.20    Y, Z ) ) ) ] )
% 0.81/1.20  , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 0.81/1.20     ), Z ) ) ] )
% 0.81/1.20  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  paramod(
% 0.81/1.20  clause( 2131, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply( X
% 0.81/1.20    , identity ) ) ] )
% 0.81/1.20  , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.81/1.20  , 0, clause( 2126, [ =( multiply( multiply( X, Y ), Z ), multiply( X, 
% 0.81/1.20    multiply( Y, Z ) ) ) ] )
% 0.81/1.20  , 0, 9, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ), 
% 0.81/1.20    :=( Y, inverse( Y ) ), :=( Z, Y )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y, 
% 0.81/1.20    identity ) ) ] )
% 0.81/1.20  , clause( 2131, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply( 
% 0.81/1.20    X, identity ) ) ] )
% 0.81/1.20  , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.81/1.20     )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2136, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply( 
% 0.81/1.20    Y, Z ) ) ) ] )
% 0.81/1.20  , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 0.81/1.20     ), Z ) ) ] )
% 0.81/1.20  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  paramod(
% 0.81/1.20  clause( 2141, [ =( multiply( multiply( X, identity ), Y ), multiply( X, Y )
% 0.81/1.20     ) ] )
% 0.81/1.20  , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.81/1.20  , 0, clause( 2136, [ =( multiply( multiply( X, Y ), Z ), multiply( X, 
% 0.81/1.20    multiply( Y, Z ) ) ) ] )
% 0.81/1.20  , 0, 8, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ), 
% 0.81/1.20    :=( Y, identity ), :=( Z, Y )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 22, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 0.81/1.20     ] )
% 0.81/1.20  , clause( 2141, [ =( multiply( multiply( X, identity ), Y ), multiply( X, Y
% 0.81/1.20     ) ) ] )
% 0.81/1.20  , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.81/1.20     )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2147, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 0.81/1.20     ) ) ) ] )
% 0.81/1.20  , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 0.81/1.20    , X ) ] )
% 0.81/1.20  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  paramod(
% 0.81/1.20  clause( 2148, [ =( identity, 'greatest_lower_bound'( identity, b ) ) ] )
% 0.81/1.20  , clause( 19, [ =( 'least_upper_bound'( identity, b ), b ) ] )
% 0.81/1.20  , 0, clause( 2147, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( 
% 0.81/1.20    X, Y ) ) ) ] )
% 0.81/1.20  , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, identity ), :=( Y
% 0.81/1.20    , b )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2149, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.81/1.20  , clause( 2148, [ =( identity, 'greatest_lower_bound'( identity, b ) ) ] )
% 0.81/1.20  , 0, substitution( 0, [] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 24, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.81/1.20  , clause( 2149, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.81/1.20  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2150, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 0.81/1.20     ) ) ) ] )
% 0.81/1.20  , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 0.81/1.20    , X ) ] )
% 0.81/1.20  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  paramod(
% 0.81/1.20  clause( 2151, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X
% 0.81/1.20     ) ) ) ] )
% 0.81/1.20  , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 0.81/1.20    , X ) ) ] )
% 0.81/1.20  , 0, clause( 2150, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( 
% 0.81/1.20    X, Y ) ) ) ] )
% 0.81/1.20  , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ 
% 0.81/1.20    :=( X, X ), :=( Y, Y )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2154, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) )
% 0.81/1.20    , X ) ] )
% 0.81/1.20  , clause( 2151, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y, 
% 0.81/1.20    X ) ) ) ] )
% 0.81/1.20  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 60, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) ), 
% 0.81/1.20    X ) ] )
% 0.81/1.20  , clause( 2154, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X )
% 0.81/1.20     ), X ) ] )
% 0.81/1.20  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.81/1.20     )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2155, [ ~( =( multiply( a, b ), 'least_upper_bound'( a, multiply( a
% 0.81/1.20    , b ) ) ) ) ] )
% 0.81/1.20  , clause( 17, [ ~( =( 'least_upper_bound'( a, multiply( a, b ) ), multiply( 
% 0.81/1.20    a, b ) ) ) ] )
% 0.81/1.20  , 0, substitution( 0, [] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  paramod(
% 0.81/1.20  clause( 2156, [ ~( =( multiply( a, b ), 'least_upper_bound'( multiply( a, b
% 0.81/1.20     ), a ) ) ) ] )
% 0.81/1.20  , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 0.81/1.20     ) ] )
% 0.81/1.20  , 0, clause( 2155, [ ~( =( multiply( a, b ), 'least_upper_bound'( a, 
% 0.81/1.20    multiply( a, b ) ) ) ) ] )
% 0.81/1.20  , 0, 5, substitution( 0, [ :=( X, a ), :=( Y, multiply( a, b ) )] ), 
% 0.81/1.20    substitution( 1, [] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2159, [ ~( =( 'least_upper_bound'( multiply( a, b ), a ), multiply( 
% 0.81/1.20    a, b ) ) ) ] )
% 0.81/1.20  , clause( 2156, [ ~( =( multiply( a, b ), 'least_upper_bound'( multiply( a
% 0.81/1.20    , b ), a ) ) ) ] )
% 0.81/1.20  , 0, substitution( 0, [] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 141, [ ~( =( 'least_upper_bound'( multiply( a, b ), a ), multiply( 
% 0.81/1.20    a, b ) ) ) ] )
% 0.81/1.20  , clause( 2159, [ ~( =( 'least_upper_bound'( multiply( a, b ), a ), 
% 0.81/1.20    multiply( a, b ) ) ) ] )
% 0.81/1.20  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2161, [ =( multiply( X, identity ), multiply( multiply( X, inverse( 
% 0.81/1.20    Y ) ), Y ) ) ] )
% 0.81/1.20  , clause( 21, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 0.81/1.20    , identity ) ) ] )
% 0.81/1.20  , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  paramod(
% 0.81/1.20  clause( 2164, [ =( multiply( inverse( inverse( X ) ), identity ), multiply( 
% 0.81/1.20    identity, X ) ) ] )
% 0.81/1.20  , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.81/1.20  , 0, clause( 2161, [ =( multiply( X, identity ), multiply( multiply( X, 
% 0.81/1.20    inverse( Y ) ), Y ) ) ] )
% 0.81/1.20  , 0, 7, substitution( 0, [ :=( X, inverse( X ) )] ), substitution( 1, [ 
% 0.81/1.20    :=( X, inverse( inverse( X ) ) ), :=( Y, X )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  paramod(
% 0.81/1.20  clause( 2165, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.81/1.20  , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.81/1.20  , 0, clause( 2164, [ =( multiply( inverse( inverse( X ) ), identity ), 
% 0.81/1.20    multiply( identity, X ) ) ] )
% 0.81/1.20  , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.81/1.20    ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 174, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.81/1.20  , clause( 2165, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ]
% 0.81/1.20     )
% 0.81/1.20  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2168, [ =( multiply( X, Y ), multiply( multiply( X, identity ), Y )
% 0.81/1.20     ) ] )
% 0.81/1.20  , clause( 22, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X )
% 0.81/1.20     ) ] )
% 0.81/1.20  , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  paramod(
% 0.81/1.20  clause( 2171, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.81/1.20     ) ] )
% 0.81/1.20  , clause( 174, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.81/1.20  , 0, clause( 2168, [ =( multiply( X, Y ), multiply( multiply( X, identity )
% 0.81/1.20    , Y ) ) ] )
% 0.81/1.20  , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse( 
% 0.81/1.20    inverse( X ) ) ), :=( Y, Y )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 179, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.81/1.20     ) ] )
% 0.81/1.20  , clause( 2171, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.81/1.20     ) ) ] )
% 0.81/1.20  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.81/1.20     )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2178, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ), 
% 0.81/1.20    'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.81/1.20  , clause( 12, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z
% 0.81/1.20     ) ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 0.81/1.20  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  paramod(
% 0.81/1.20  clause( 2181, [ =( multiply( inverse( inverse( X ) ), 
% 0.81/1.20    'greatest_lower_bound'( identity, Y ) ), 'greatest_lower_bound'( X, 
% 0.81/1.20    multiply( inverse( inverse( X ) ), Y ) ) ) ] )
% 0.81/1.20  , clause( 174, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.81/1.20  , 0, clause( 2178, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ), 
% 0.81/1.20    'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.81/1.20  , 0, 9, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse( 
% 0.81/1.20    inverse( X ) ) ), :=( Y, identity ), :=( Z, Y )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  paramod(
% 0.81/1.20  clause( 2191, [ =( multiply( inverse( inverse( X ) ), 
% 0.81/1.20    'greatest_lower_bound'( identity, Y ) ), 'greatest_lower_bound'( X, 
% 0.81/1.20    multiply( X, Y ) ) ) ] )
% 0.81/1.20  , clause( 179, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.81/1.20     ) ) ] )
% 0.81/1.20  , 0, clause( 2181, [ =( multiply( inverse( inverse( X ) ), 
% 0.81/1.20    'greatest_lower_bound'( identity, Y ) ), 'greatest_lower_bound'( X, 
% 0.81/1.20    multiply( inverse( inverse( X ) ), Y ) ) ) ] )
% 0.81/1.20  , 0, 10, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ 
% 0.81/1.20    :=( X, X ), :=( Y, Y )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  paramod(
% 0.81/1.20  clause( 2193, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) ), 
% 0.81/1.20    'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 0.81/1.20  , clause( 179, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.81/1.20     ) ) ] )
% 0.81/1.20  , 0, clause( 2191, [ =( multiply( inverse( inverse( X ) ), 
% 0.81/1.20    'greatest_lower_bound'( identity, Y ) ), 'greatest_lower_bound'( X, 
% 0.81/1.20    multiply( X, Y ) ) ) ] )
% 0.81/1.20  , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, 'greatest_lower_bound'( 
% 0.81/1.20    identity, Y ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2194, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply( 
% 0.81/1.20    X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 0.81/1.20  , clause( 2193, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) ), 
% 0.81/1.20    'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 0.81/1.20  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 180, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply( 
% 0.81/1.20    X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 0.81/1.20  , clause( 2194, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), 
% 0.81/1.20    multiply( X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 0.81/1.20  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.81/1.20     )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2195, [ =( multiply( X, Y ), multiply( inverse( inverse( X ) ), Y )
% 0.81/1.20     ) ] )
% 0.81/1.20  , clause( 179, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.81/1.20     ) ) ] )
% 0.81/1.20  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  paramod(
% 0.81/1.20  clause( 2198, [ =( multiply( X, identity ), X ) ] )
% 0.81/1.20  , clause( 174, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.81/1.20  , 0, clause( 2195, [ =( multiply( X, Y ), multiply( inverse( inverse( X ) )
% 0.81/1.20    , Y ) ) ] )
% 0.81/1.20  , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ), 
% 0.81/1.20    :=( Y, identity )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 381, [ =( multiply( X, identity ), X ) ] )
% 0.81/1.20  , clause( 2198, [ =( multiply( X, identity ), X ) ] )
% 0.81/1.20  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2204, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) ), 
% 0.81/1.20    'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 0.81/1.20  , clause( 180, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply( 
% 0.81/1.20    X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 0.81/1.20  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  paramod(
% 0.81/1.20  clause( 2206, [ =( multiply( X, identity ), 'greatest_lower_bound'( X, 
% 0.81/1.20    multiply( X, b ) ) ) ] )
% 0.81/1.20  , clause( 24, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.81/1.20  , 0, clause( 2204, [ =( multiply( X, 'greatest_lower_bound'( identity, Y )
% 0.81/1.20     ), 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 0.81/1.20  , 0, 3, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, b )] )
% 0.81/1.20    ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  paramod(
% 0.81/1.20  clause( 2207, [ =( X, 'greatest_lower_bound'( X, multiply( X, b ) ) ) ] )
% 0.81/1.20  , clause( 381, [ =( multiply( X, identity ), X ) ] )
% 0.81/1.20  , 0, clause( 2206, [ =( multiply( X, identity ), 'greatest_lower_bound'( X
% 0.81/1.20    , multiply( X, b ) ) ) ] )
% 0.81/1.20  , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.81/1.20    ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2208, [ =( 'greatest_lower_bound'( X, multiply( X, b ) ), X ) ] )
% 0.81/1.20  , clause( 2207, [ =( X, 'greatest_lower_bound'( X, multiply( X, b ) ) ) ]
% 0.81/1.20     )
% 0.81/1.20  , 0, substitution( 0, [ :=( X, X )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 980, [ =( 'greatest_lower_bound'( X, multiply( X, b ) ), X ) ] )
% 0.81/1.20  , clause( 2208, [ =( 'greatest_lower_bound'( X, multiply( X, b ) ), X ) ]
% 0.81/1.20     )
% 0.81/1.20  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2210, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X
% 0.81/1.20     ) ) ) ] )
% 0.81/1.20  , clause( 60, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) )
% 0.81/1.20    , X ) ] )
% 0.81/1.20  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  paramod(
% 0.81/1.20  clause( 2211, [ =( multiply( X, b ), 'least_upper_bound'( multiply( X, b )
% 0.81/1.20    , X ) ) ] )
% 0.81/1.20  , clause( 980, [ =( 'greatest_lower_bound'( X, multiply( X, b ) ), X ) ] )
% 0.81/1.20  , 0, clause( 2210, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( 
% 0.81/1.20    Y, X ) ) ) ] )
% 0.81/1.20  , 0, 8, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, 
% 0.81/1.20    multiply( X, b ) ), :=( Y, X )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqswap(
% 0.81/1.20  clause( 2212, [ =( 'least_upper_bound'( multiply( X, b ), X ), multiply( X
% 0.81/1.20    , b ) ) ] )
% 0.81/1.20  , clause( 2211, [ =( multiply( X, b ), 'least_upper_bound'( multiply( X, b
% 0.81/1.20     ), X ) ) ] )
% 0.81/1.20  , 0, substitution( 0, [ :=( X, X )] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 1059, [ =( 'least_upper_bound'( multiply( X, b ), X ), multiply( X
% 0.81/1.20    , b ) ) ] )
% 0.81/1.20  , clause( 2212, [ =( 'least_upper_bound'( multiply( X, b ), X ), multiply( 
% 0.81/1.20    X, b ) ) ] )
% 0.81/1.20  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  paramod(
% 0.81/1.20  clause( 2215, [ ~( =( multiply( a, b ), multiply( a, b ) ) ) ] )
% 0.81/1.20  , clause( 1059, [ =( 'least_upper_bound'( multiply( X, b ), X ), multiply( 
% 0.81/1.20    X, b ) ) ] )
% 0.81/1.20  , 0, clause( 141, [ ~( =( 'least_upper_bound'( multiply( a, b ), a ), 
% 0.81/1.20    multiply( a, b ) ) ) ] )
% 0.81/1.20  , 0, 2, substitution( 0, [ :=( X, a )] ), substitution( 1, [] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  eqrefl(
% 0.81/1.20  clause( 2216, [] )
% 0.81/1.20  , clause( 2215, [ ~( =( multiply( a, b ), multiply( a, b ) ) ) ] )
% 0.81/1.20  , 0, substitution( 0, [] )).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  subsumption(
% 0.81/1.20  clause( 2029, [] )
% 0.81/1.20  , clause( 2216, [] )
% 0.81/1.20  , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  end.
% 0.81/1.20  
% 0.81/1.20  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.81/1.20  
% 0.81/1.20  Memory use:
% 0.81/1.20  
% 0.81/1.20  space for terms:        25353
% 0.81/1.20  space for clauses:      207341
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  clauses generated:      27700
% 0.81/1.20  clauses kept:           2030
% 0.81/1.20  clauses selected:       274
% 0.81/1.20  clauses deleted:        18
% 0.81/1.20  clauses inuse deleted:  7
% 0.81/1.20  
% 0.81/1.20  subsentry:          4521
% 0.81/1.20  literals s-matched: 4098
% 0.81/1.20  literals matched:   4086
% 0.81/1.20  full subsumption:   0
% 0.81/1.20  
% 0.81/1.20  checksum:           1507496237
% 0.81/1.20  
% 0.81/1.20  
% 0.81/1.20  Bliksem ended
%------------------------------------------------------------------------------