TSTP Solution File: GRP172-2 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GRP172-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 0s
% DateTime : Sat Jul 16 07:35:46 EDT 2022

% Result   : Unsatisfiable 0.73s 1.14s
% Output   : Refutation 0.73s
% Verified : 
% SZS Type : -

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