TSTP Solution File: FLD018-3 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : FLD018-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n029.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 01:50:59 EDT 2022

% Result   : Unsatisfiable 0.88s 1.31s
% Output   : Refutation 0.88s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : FLD018-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13  % Command  : bliksem %s
% 0.12/0.34  % Computer : n029.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % DateTime : Mon Jun  6 23:16:50 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.88/1.31  *** allocated 10000 integers for termspace/termends
% 0.88/1.31  *** allocated 10000 integers for clauses
% 0.88/1.31  *** allocated 10000 integers for justifications
% 0.88/1.31  Bliksem 1.12
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  Automatic Strategy Selection
% 0.88/1.31  
% 0.88/1.31  Clauses:
% 0.88/1.31  [
% 0.88/1.31     [ sum( X, Y, Z ), ~( sum( X, T, U ) ), ~( sum( T, W, Y ) ), ~( sum( U, W
% 0.88/1.31    , Z ) ) ],
% 0.88/1.31     [ sum( X, Y, Z ), ~( sum( T, U, X ) ), ~( sum( U, Y, W ) ), ~( sum( T, W
% 0.88/1.31    , Z ) ) ],
% 0.88/1.31     [ sum( 'additive_identity', X, X ), ~( defined( X ) ) ],
% 0.88/1.31     [ sum( 'additive_inverse'( X ), X, 'additive_identity' ), ~( defined( X
% 0.88/1.31     ) ) ],
% 0.88/1.31     [ sum( X, Y, Z ), ~( sum( Y, X, Z ) ) ],
% 0.88/1.31     [ product( X, Y, Z ), ~( product( X, T, U ) ), ~( product( T, W, Y ) ), 
% 0.88/1.31    ~( product( U, W, Z ) ) ],
% 0.88/1.31     [ product( X, Y, Z ), ~( product( T, U, X ) ), ~( product( U, Y, W ) ), 
% 0.88/1.31    ~( product( T, W, Z ) ) ],
% 0.88/1.31     [ product( 'multiplicative_identity', X, X ), ~( defined( X ) ) ],
% 0.88/1.31     [ product( 'multiplicative_inverse'( X ), X, 'multiplicative_identity' )
% 0.88/1.31    , sum( 'additive_identity', X, 'additive_identity' ), ~( defined( X ) ) ]
% 0.88/1.31    ,
% 0.88/1.31     [ product( X, Y, Z ), ~( product( Y, X, Z ) ) ],
% 0.88/1.31     [ sum( X, Y, Z ), ~( sum( T, U, W ) ), ~( product( W, V0, Z ) ), ~( 
% 0.88/1.31    product( T, V0, X ) ), ~( product( U, V0, Y ) ) ],
% 0.88/1.31     [ product( X, Y, Z ), ~( sum( T, U, X ) ), ~( product( T, Y, W ) ), ~( 
% 0.88/1.31    product( U, Y, V0 ) ), ~( sum( W, V0, Z ) ) ],
% 0.88/1.31     [ defined( add( X, Y ) ), ~( defined( X ) ), ~( defined( Y ) ) ],
% 0.88/1.31     [ defined( 'additive_identity' ) ],
% 0.88/1.31     [ defined( 'additive_inverse'( X ) ), ~( defined( X ) ) ],
% 0.88/1.31     [ defined( multiply( X, Y ) ), ~( defined( X ) ), ~( defined( Y ) ) ]
% 0.88/1.31    ,
% 0.88/1.31     [ defined( 'multiplicative_identity' ) ],
% 0.88/1.31     [ defined( 'multiplicative_inverse'( X ) ), ~( defined( X ) ), sum( 
% 0.88/1.31    'additive_identity', X, 'additive_identity' ) ],
% 0.88/1.31     [ sum( X, Y, add( X, Y ) ), ~( defined( X ) ), ~( defined( Y ) ) ],
% 0.88/1.31     [ product( X, Y, multiply( X, Y ) ), ~( defined( X ) ), ~( defined( Y )
% 0.88/1.31     ) ],
% 0.88/1.31     [ sum( 'additive_identity', X, Y ), ~( 'less_or_equal'( X, Y ) ), ~( 
% 0.88/1.31    'less_or_equal'( Y, X ) ) ],
% 0.88/1.31     [ 'less_or_equal'( X, Y ), ~( 'less_or_equal'( X, Z ) ), ~( 
% 0.88/1.31    'less_or_equal'( Z, Y ) ) ],
% 0.88/1.31     [ 'less_or_equal'( X, Y ), 'less_or_equal'( Y, X ), ~( defined( X ) ), 
% 0.88/1.31    ~( defined( Y ) ) ],
% 0.88/1.31     [ 'less_or_equal'( X, Y ), ~( 'less_or_equal'( Z, T ) ), ~( sum( Z, U, X
% 0.88/1.31     ) ), ~( sum( T, U, Y ) ) ],
% 0.88/1.31     [ 'less_or_equal'( 'additive_identity', X ), ~( 'less_or_equal'( 
% 0.88/1.31    'additive_identity', Y ) ), ~( 'less_or_equal'( 'additive_identity', Z )
% 0.88/1.31     ), ~( product( Y, Z, X ) ) ],
% 0.88/1.31     [ ~( sum( 'additive_identity', 'additive_identity', 
% 0.88/1.31    'multiplicative_identity' ) ) ],
% 0.88/1.31     [ defined( a ) ],
% 0.88/1.31     [ sum( 'additive_identity', a, 'additive_identity' ) ],
% 0.88/1.31     [ ~( sum( 'additive_identity', 'additive_inverse'( a ), 
% 0.88/1.31    'additive_identity' ) ) ]
% 0.88/1.31  ] .
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  percentage equality = 0.000000, percentage horn = 0.896552
% 0.88/1.31  This a non-horn, non-equality problem
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  Options Used:
% 0.88/1.31  
% 0.88/1.31  useres =            1
% 0.88/1.31  useparamod =        0
% 0.88/1.31  useeqrefl =         0
% 0.88/1.31  useeqfact =         0
% 0.88/1.31  usefactor =         1
% 0.88/1.31  usesimpsplitting =  0
% 0.88/1.31  usesimpdemod =      0
% 0.88/1.31  usesimpres =        3
% 0.88/1.31  
% 0.88/1.31  resimpinuse      =  1000
% 0.88/1.31  resimpclauses =     20000
% 0.88/1.31  substype =          standard
% 0.88/1.31  backwardsubs =      1
% 0.88/1.31  selectoldest =      5
% 0.88/1.31  
% 0.88/1.31  litorderings [0] =  split
% 0.88/1.31  litorderings [1] =  liftord
% 0.88/1.31  
% 0.88/1.31  termordering =      none
% 0.88/1.31  
% 0.88/1.31  litapriori =        1
% 0.88/1.31  termapriori =       0
% 0.88/1.31  litaposteriori =    0
% 0.88/1.31  termaposteriori =   0
% 0.88/1.31  demodaposteriori =  0
% 0.88/1.31  ordereqreflfact =   0
% 0.88/1.31  
% 0.88/1.31  litselect =         none
% 0.88/1.31  
% 0.88/1.31  maxweight =         15
% 0.88/1.31  maxdepth =          30000
% 0.88/1.31  maxlength =         115
% 0.88/1.31  maxnrvars =         195
% 0.88/1.31  excuselevel =       1
% 0.88/1.31  increasemaxweight = 1
% 0.88/1.31  
% 0.88/1.31  maxselected =       10000000
% 0.88/1.31  maxnrclauses =      10000000
% 0.88/1.31  
% 0.88/1.31  showgenerated =    0
% 0.88/1.31  showkept =         0
% 0.88/1.31  showselected =     0
% 0.88/1.31  showdeleted =      0
% 0.88/1.31  showresimp =       1
% 0.88/1.31  showstatus =       2000
% 0.88/1.31  
% 0.88/1.31  prologoutput =     1
% 0.88/1.31  nrgoals =          5000000
% 0.88/1.31  totalproof =       1
% 0.88/1.31  
% 0.88/1.31  Symbols occurring in the translation:
% 0.88/1.31  
% 0.88/1.31  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.88/1.31  .  [1, 2]      (w:1, o:30, a:1, s:1, b:0), 
% 0.88/1.31  !  [4, 1]      (w:0, o:22, a:1, s:1, b:0), 
% 0.88/1.31  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.88/1.31  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.88/1.31  sum  [42, 3]      (w:1, o:58, a:1, s:1, b:0), 
% 0.88/1.31  'additive_identity'  [46, 0]      (w:1, o:15, a:1, s:1, b:0), 
% 0.88/1.31  defined  [47, 1]      (w:1, o:27, a:1, s:1, b:0), 
% 0.88/1.31  'additive_inverse'  [48, 1]      (w:1, o:28, a:1, s:1, b:0), 
% 0.88/1.31  product  [49, 3]      (w:1, o:59, a:1, s:1, b:0), 
% 0.88/1.31  'multiplicative_identity'  [50, 0]      (w:1, o:16, a:1, s:1, b:0), 
% 0.88/1.31  'multiplicative_inverse'  [51, 1]      (w:1, o:29, a:1, s:1, b:0), 
% 0.88/1.31  add  [56, 2]      (w:1, o:55, a:1, s:1, b:0), 
% 0.88/1.31  multiply  [57, 2]      (w:1, o:57, a:1, s:1, b:0), 
% 0.88/1.31  'less_or_equal'  [58, 2]      (w:1, o:56, a:1, s:1, b:0), 
% 0.88/1.31  a  [59, 0]      (w:1, o:21, a:1, s:1, b:0).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  Starting Search:
% 0.88/1.31  
% 0.88/1.31  Resimplifying inuse:
% 0.88/1.31  Done
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  Intermediate Status:
% 0.88/1.31  Generated:    2925
% 0.88/1.31  Kept:         2025
% 0.88/1.31  Inuse:        130
% 0.88/1.31  Deleted:      0
% 0.88/1.31  Deletedinuse: 0
% 0.88/1.31  
% 0.88/1.31  Resimplifying inuse:
% 0.88/1.31  Done
% 0.88/1.31  
% 0.88/1.31  Resimplifying inuse:
% 0.88/1.31  Done
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  Intermediate Status:
% 0.88/1.31  Generated:    5864
% 0.88/1.31  Kept:         4025
% 0.88/1.31  Inuse:        235
% 0.88/1.31  Deleted:      1
% 0.88/1.31  Deletedinuse: 0
% 0.88/1.31  
% 0.88/1.31  Resimplifying inuse:
% 0.88/1.31  Done
% 0.88/1.31  
% 0.88/1.31  Resimplifying inuse:
% 0.88/1.31  Done
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  Bliksems!, er is een bewijs:
% 0.88/1.31  % SZS status Unsatisfiable
% 0.88/1.31  % SZS output start Refutation
% 0.88/1.31  
% 0.88/1.31  clause( 0, [ ~( sum( X, T, U ) ), ~( sum( T, W, Y ) ), ~( sum( U, W, Z ) )
% 0.88/1.31    , sum( X, Y, Z ) ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 1, [ ~( sum( T, U, X ) ), ~( sum( U, Y, W ) ), ~( sum( T, W, Z ) )
% 0.88/1.31    , sum( X, Y, Z ) ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 2, [ ~( defined( X ) ), sum( 'additive_identity', X, X ) ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 3, [ ~( defined( X ) ), sum( 'additive_inverse'( X ), X, 
% 0.88/1.31    'additive_identity' ) ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 4, [ ~( sum( Y, X, Z ) ), sum( X, Y, Z ) ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 13, [ defined( 'additive_identity' ) ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 26, [ defined( a ) ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 27, [ sum( 'additive_identity', a, 'additive_identity' ) ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 28, [ ~( sum( 'additive_identity', 'additive_inverse'( a ), 
% 0.88/1.31    'additive_identity' ) ) ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 56, [ ~( sum( 'additive_identity', X, Z ) ), sum( 
% 0.88/1.31    'additive_identity', Y, Z ), ~( sum( a, X, Y ) ) ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 71, [ ~( sum( Y, 'additive_inverse'( a ), Z ) ), ~( sum( X, Z, 
% 0.88/1.31    'additive_identity' ) ), ~( sum( X, Y, 'additive_identity' ) ) ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 79, [ ~( sum( 'additive_identity', Y, Z ) ), sum( 
% 0.88/1.31    'additive_identity', X, Z ), ~( sum( a, X, Y ) ) ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 85, [ ~( sum( Y, X, 'additive_identity' ) ), ~( sum( X, 
% 0.88/1.31    'additive_inverse'( a ), X ) ) ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 133, [ ~( defined( X ) ), sum( X, 'additive_identity', X ) ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 5443, [ sum( 'additive_identity', X, 'additive_identity' ), ~( sum( 
% 0.88/1.31    a, X, 'additive_identity' ) ) ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 5966, [ ~( sum( 'additive_identity', Y, 'additive_identity' ) ), 
% 0.88/1.31    ~( sum( a, Y, X ) ), ~( sum( X, 'additive_inverse'( a ), X ) ) ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 5974, [ ~( sum( a, 'additive_inverse'( a ), 'additive_identity' ) )
% 0.88/1.31     ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 5976, [ ~( sum( 'additive_inverse'( a ), a, 'additive_identity' ) )
% 0.88/1.31     ] )
% 0.88/1.31  .
% 0.88/1.31  clause( 5981, [] )
% 0.88/1.31  .
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  % SZS output end Refutation
% 0.88/1.31  found a proof!
% 0.88/1.31  
% 0.88/1.31  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.88/1.31  
% 0.88/1.31  initialclauses(
% 0.88/1.31  [ clause( 5983, [ sum( X, Y, Z ), ~( sum( X, T, U ) ), ~( sum( T, W, Y ) )
% 0.88/1.31    , ~( sum( U, W, Z ) ) ] )
% 0.88/1.31  , clause( 5984, [ sum( X, Y, Z ), ~( sum( T, U, X ) ), ~( sum( U, Y, W ) )
% 0.88/1.31    , ~( sum( T, W, Z ) ) ] )
% 0.88/1.31  , clause( 5985, [ sum( 'additive_identity', X, X ), ~( defined( X ) ) ] )
% 0.88/1.31  , clause( 5986, [ sum( 'additive_inverse'( X ), X, 'additive_identity' ), 
% 0.88/1.31    ~( defined( X ) ) ] )
% 0.88/1.31  , clause( 5987, [ sum( X, Y, Z ), ~( sum( Y, X, Z ) ) ] )
% 0.88/1.31  , clause( 5988, [ product( X, Y, Z ), ~( product( X, T, U ) ), ~( product( 
% 0.88/1.31    T, W, Y ) ), ~( product( U, W, Z ) ) ] )
% 0.88/1.31  , clause( 5989, [ product( X, Y, Z ), ~( product( T, U, X ) ), ~( product( 
% 0.88/1.31    U, Y, W ) ), ~( product( T, W, Z ) ) ] )
% 0.88/1.31  , clause( 5990, [ product( 'multiplicative_identity', X, X ), ~( defined( X
% 0.88/1.31     ) ) ] )
% 0.88/1.31  , clause( 5991, [ product( 'multiplicative_inverse'( X ), X, 
% 0.88/1.31    'multiplicative_identity' ), sum( 'additive_identity', X, 
% 0.88/1.31    'additive_identity' ), ~( defined( X ) ) ] )
% 0.88/1.31  , clause( 5992, [ product( X, Y, Z ), ~( product( Y, X, Z ) ) ] )
% 0.88/1.31  , clause( 5993, [ sum( X, Y, Z ), ~( sum( T, U, W ) ), ~( product( W, V0, Z
% 0.88/1.31     ) ), ~( product( T, V0, X ) ), ~( product( U, V0, Y ) ) ] )
% 0.88/1.31  , clause( 5994, [ product( X, Y, Z ), ~( sum( T, U, X ) ), ~( product( T, Y
% 0.88/1.31    , W ) ), ~( product( U, Y, V0 ) ), ~( sum( W, V0, Z ) ) ] )
% 0.88/1.31  , clause( 5995, [ defined( add( X, Y ) ), ~( defined( X ) ), ~( defined( Y
% 0.88/1.31     ) ) ] )
% 0.88/1.31  , clause( 5996, [ defined( 'additive_identity' ) ] )
% 0.88/1.31  , clause( 5997, [ defined( 'additive_inverse'( X ) ), ~( defined( X ) ) ]
% 0.88/1.31     )
% 0.88/1.31  , clause( 5998, [ defined( multiply( X, Y ) ), ~( defined( X ) ), ~( 
% 0.88/1.31    defined( Y ) ) ] )
% 0.88/1.31  , clause( 5999, [ defined( 'multiplicative_identity' ) ] )
% 0.88/1.31  , clause( 6000, [ defined( 'multiplicative_inverse'( X ) ), ~( defined( X )
% 0.88/1.31     ), sum( 'additive_identity', X, 'additive_identity' ) ] )
% 0.88/1.31  , clause( 6001, [ sum( X, Y, add( X, Y ) ), ~( defined( X ) ), ~( defined( 
% 0.88/1.31    Y ) ) ] )
% 0.88/1.31  , clause( 6002, [ product( X, Y, multiply( X, Y ) ), ~( defined( X ) ), ~( 
% 0.88/1.31    defined( Y ) ) ] )
% 0.88/1.31  , clause( 6003, [ sum( 'additive_identity', X, Y ), ~( 'less_or_equal'( X, 
% 0.88/1.31    Y ) ), ~( 'less_or_equal'( Y, X ) ) ] )
% 0.88/1.31  , clause( 6004, [ 'less_or_equal'( X, Y ), ~( 'less_or_equal'( X, Z ) ), 
% 0.88/1.31    ~( 'less_or_equal'( Z, Y ) ) ] )
% 0.88/1.31  , clause( 6005, [ 'less_or_equal'( X, Y ), 'less_or_equal'( Y, X ), ~( 
% 0.88/1.31    defined( X ) ), ~( defined( Y ) ) ] )
% 0.88/1.31  , clause( 6006, [ 'less_or_equal'( X, Y ), ~( 'less_or_equal'( Z, T ) ), 
% 0.88/1.31    ~( sum( Z, U, X ) ), ~( sum( T, U, Y ) ) ] )
% 0.88/1.31  , clause( 6007, [ 'less_or_equal'( 'additive_identity', X ), ~( 
% 0.88/1.31    'less_or_equal'( 'additive_identity', Y ) ), ~( 'less_or_equal'( 
% 0.88/1.31    'additive_identity', Z ) ), ~( product( Y, Z, X ) ) ] )
% 0.88/1.31  , clause( 6008, [ ~( sum( 'additive_identity', 'additive_identity', 
% 0.88/1.31    'multiplicative_identity' ) ) ] )
% 0.88/1.31  , clause( 6009, [ defined( a ) ] )
% 0.88/1.31  , clause( 6010, [ sum( 'additive_identity', a, 'additive_identity' ) ] )
% 0.88/1.31  , clause( 6011, [ ~( sum( 'additive_identity', 'additive_inverse'( a ), 
% 0.88/1.31    'additive_identity' ) ) ] )
% 0.88/1.31  ] ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  subsumption(
% 0.88/1.31  clause( 0, [ ~( sum( X, T, U ) ), ~( sum( T, W, Y ) ), ~( sum( U, W, Z ) )
% 0.88/1.31    , sum( X, Y, Z ) ] )
% 0.88/1.31  , clause( 5983, [ sum( X, Y, Z ), ~( sum( X, T, U ) ), ~( sum( T, W, Y ) )
% 0.88/1.31    , ~( sum( U, W, Z ) ) ] )
% 0.88/1.31  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.88/1.31    , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 3 ), ==>( 1, 0 ), ==>( 2
% 0.88/1.31    , 1 ), ==>( 3, 2 )] ) ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  subsumption(
% 0.88/1.31  clause( 1, [ ~( sum( T, U, X ) ), ~( sum( U, Y, W ) ), ~( sum( T, W, Z ) )
% 0.88/1.31    , sum( X, Y, Z ) ] )
% 0.88/1.31  , clause( 5984, [ sum( X, Y, Z ), ~( sum( T, U, X ) ), ~( sum( U, Y, W ) )
% 0.88/1.31    , ~( sum( T, W, Z ) ) ] )
% 0.88/1.31  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.88/1.31    , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 3 ), ==>( 1, 0 ), ==>( 2
% 0.88/1.31    , 1 ), ==>( 3, 2 )] ) ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  subsumption(
% 0.88/1.31  clause( 2, [ ~( defined( X ) ), sum( 'additive_identity', X, X ) ] )
% 0.88/1.31  , clause( 5985, [ sum( 'additive_identity', X, X ), ~( defined( X ) ) ] )
% 0.88/1.31  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 
% 0.88/1.31    0 )] ) ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  subsumption(
% 0.88/1.31  clause( 3, [ ~( defined( X ) ), sum( 'additive_inverse'( X ), X, 
% 0.88/1.31    'additive_identity' ) ] )
% 0.88/1.31  , clause( 5986, [ sum( 'additive_inverse'( X ), X, 'additive_identity' ), 
% 0.88/1.31    ~( defined( X ) ) ] )
% 0.88/1.31  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 
% 0.88/1.31    0 )] ) ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  subsumption(
% 0.88/1.31  clause( 4, [ ~( sum( Y, X, Z ) ), sum( X, Y, Z ) ] )
% 0.88/1.31  , clause( 5987, [ sum( X, Y, Z ), ~( sum( Y, X, Z ) ) ] )
% 0.88/1.31  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 0.88/1.31    permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  subsumption(
% 0.88/1.31  clause( 13, [ defined( 'additive_identity' ) ] )
% 0.88/1.31  , clause( 5996, [ defined( 'additive_identity' ) ] )
% 0.88/1.31  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  subsumption(
% 0.88/1.31  clause( 26, [ defined( a ) ] )
% 0.88/1.31  , clause( 6009, [ defined( a ) ] )
% 0.88/1.31  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  subsumption(
% 0.88/1.31  clause( 27, [ sum( 'additive_identity', a, 'additive_identity' ) ] )
% 0.88/1.31  , clause( 6010, [ sum( 'additive_identity', a, 'additive_identity' ) ] )
% 0.88/1.31  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  subsumption(
% 0.88/1.31  clause( 28, [ ~( sum( 'additive_identity', 'additive_inverse'( a ), 
% 0.88/1.31    'additive_identity' ) ) ] )
% 0.88/1.31  , clause( 6011, [ ~( sum( 'additive_identity', 'additive_inverse'( a ), 
% 0.88/1.31    'additive_identity' ) ) ] )
% 0.88/1.31  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  resolution(
% 0.88/1.31  clause( 6171, [ ~( sum( a, X, Y ) ), ~( sum( 'additive_identity', X, Z ) )
% 0.88/1.31    , sum( 'additive_identity', Y, Z ) ] )
% 0.88/1.31  , clause( 0, [ ~( sum( X, T, U ) ), ~( sum( T, W, Y ) ), ~( sum( U, W, Z )
% 0.88/1.31     ), sum( X, Y, Z ) ] )
% 0.88/1.31  , 0, clause( 27, [ sum( 'additive_identity', a, 'additive_identity' ) ] )
% 0.88/1.31  , 0, substitution( 0, [ :=( X, 'additive_identity' ), :=( Y, Y ), :=( Z, Z
% 0.88/1.31     ), :=( T, a ), :=( U, 'additive_identity' ), :=( W, X )] ), 
% 0.88/1.31    substitution( 1, [] )).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  subsumption(
% 0.88/1.31  clause( 56, [ ~( sum( 'additive_identity', X, Z ) ), sum( 
% 0.88/1.31    'additive_identity', Y, Z ), ~( sum( a, X, Y ) ) ] )
% 0.88/1.31  , clause( 6171, [ ~( sum( a, X, Y ) ), ~( sum( 'additive_identity', X, Z )
% 0.88/1.31     ), sum( 'additive_identity', Y, Z ) ] )
% 0.88/1.31  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 0.88/1.31    permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  resolution(
% 0.88/1.31  clause( 6175, [ ~( sum( X, Y, 'additive_identity' ) ), ~( sum( Y, 
% 0.88/1.31    'additive_inverse'( a ), Z ) ), ~( sum( X, Z, 'additive_identity' ) ) ]
% 0.88/1.31     )
% 0.88/1.31  , clause( 28, [ ~( sum( 'additive_identity', 'additive_inverse'( a ), 
% 0.88/1.31    'additive_identity' ) ) ] )
% 0.88/1.31  , 0, clause( 1, [ ~( sum( T, U, X ) ), ~( sum( U, Y, W ) ), ~( sum( T, W, Z
% 0.88/1.31     ) ), sum( X, Y, Z ) ] )
% 0.88/1.31  , 3, substitution( 0, [] ), substitution( 1, [ :=( X, 'additive_identity' )
% 0.88/1.31    , :=( Y, 'additive_inverse'( a ) ), :=( Z, 'additive_identity' ), :=( T, 
% 0.88/1.31    X ), :=( U, Y ), :=( W, Z )] )).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  subsumption(
% 0.88/1.31  clause( 71, [ ~( sum( Y, 'additive_inverse'( a ), Z ) ), ~( sum( X, Z, 
% 0.88/1.31    'additive_identity' ) ), ~( sum( X, Y, 'additive_identity' ) ) ] )
% 0.88/1.31  , clause( 6175, [ ~( sum( X, Y, 'additive_identity' ) ), ~( sum( Y, 
% 0.88/1.31    'additive_inverse'( a ), Z ) ), ~( sum( X, Z, 'additive_identity' ) ) ]
% 0.88/1.31     )
% 0.88/1.31  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 0.88/1.31    permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  resolution(
% 0.88/1.31  clause( 6178, [ ~( sum( a, X, Y ) ), ~( sum( 'additive_identity', Y, Z ) )
% 0.88/1.31    , sum( 'additive_identity', X, Z ) ] )
% 0.88/1.31  , clause( 1, [ ~( sum( T, U, X ) ), ~( sum( U, Y, W ) ), ~( sum( T, W, Z )
% 0.88/1.31     ), sum( X, Y, Z ) ] )
% 0.88/1.31  , 0, clause( 27, [ sum( 'additive_identity', a, 'additive_identity' ) ] )
% 0.88/1.31  , 0, substitution( 0, [ :=( X, 'additive_identity' ), :=( Y, X ), :=( Z, Z
% 0.88/1.31     ), :=( T, 'additive_identity' ), :=( U, a ), :=( W, Y )] ), 
% 0.88/1.31    substitution( 1, [] )).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  subsumption(
% 0.88/1.31  clause( 79, [ ~( sum( 'additive_identity', Y, Z ) ), sum( 
% 0.88/1.31    'additive_identity', X, Z ), ~( sum( a, X, Y ) ) ] )
% 0.88/1.31  , clause( 6178, [ ~( sum( a, X, Y ) ), ~( sum( 'additive_identity', Y, Z )
% 0.88/1.31     ), sum( 'additive_identity', X, Z ) ] )
% 0.88/1.31  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 0.88/1.31    permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  factor(
% 0.88/1.31  clause( 6184, [ ~( sum( X, 'additive_inverse'( a ), X ) ), ~( sum( Y, X, 
% 0.88/1.31    'additive_identity' ) ) ] )
% 0.88/1.31  , clause( 71, [ ~( sum( Y, 'additive_inverse'( a ), Z ) ), ~( sum( X, Z, 
% 0.88/1.31    'additive_identity' ) ), ~( sum( X, Y, 'additive_identity' ) ) ] )
% 0.88/1.31  , 1, 2, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, X )] )).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  subsumption(
% 0.88/1.31  clause( 85, [ ~( sum( Y, X, 'additive_identity' ) ), ~( sum( X, 
% 0.88/1.31    'additive_inverse'( a ), X ) ) ] )
% 0.88/1.31  , clause( 6184, [ ~( sum( X, 'additive_inverse'( a ), X ) ), ~( sum( Y, X, 
% 0.88/1.31    'additive_identity' ) ) ] )
% 0.88/1.31  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 0.88/1.31     ), ==>( 1, 0 )] ) ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  resolution(
% 0.88/1.31  clause( 6185, [ sum( X, 'additive_identity', X ), ~( defined( X ) ) ] )
% 0.88/1.31  , clause( 4, [ ~( sum( Y, X, Z ) ), sum( X, Y, Z ) ] )
% 0.88/1.31  , 0, clause( 2, [ ~( defined( X ) ), sum( 'additive_identity', X, X ) ] )
% 0.88/1.31  , 1, substitution( 0, [ :=( X, X ), :=( Y, 'additive_identity' ), :=( Z, X
% 0.88/1.31     )] ), substitution( 1, [ :=( X, X )] )).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  subsumption(
% 0.88/1.31  clause( 133, [ ~( defined( X ) ), sum( X, 'additive_identity', X ) ] )
% 0.88/1.31  , clause( 6185, [ sum( X, 'additive_identity', X ), ~( defined( X ) ) ] )
% 0.88/1.31  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 
% 0.88/1.31    0 )] ) ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  resolution(
% 0.88/1.31  clause( 6186, [ sum( 'additive_identity', X, 'additive_identity' ), ~( sum( 
% 0.88/1.31    a, X, 'additive_identity' ) ), ~( defined( 'additive_identity' ) ) ] )
% 0.88/1.31  , clause( 79, [ ~( sum( 'additive_identity', Y, Z ) ), sum( 
% 0.88/1.31    'additive_identity', X, Z ), ~( sum( a, X, Y ) ) ] )
% 0.88/1.31  , 0, clause( 133, [ ~( defined( X ) ), sum( X, 'additive_identity', X ) ]
% 0.88/1.31     )
% 0.88/1.31  , 1, substitution( 0, [ :=( X, X ), :=( Y, 'additive_identity' ), :=( Z, 
% 0.88/1.31    'additive_identity' )] ), substitution( 1, [ :=( X, 'additive_identity' )] )
% 0.88/1.31    ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  resolution(
% 0.88/1.31  clause( 6188, [ sum( 'additive_identity', X, 'additive_identity' ), ~( sum( 
% 0.88/1.31    a, X, 'additive_identity' ) ) ] )
% 0.88/1.31  , clause( 6186, [ sum( 'additive_identity', X, 'additive_identity' ), ~( 
% 0.88/1.31    sum( a, X, 'additive_identity' ) ), ~( defined( 'additive_identity' ) ) ]
% 0.88/1.31     )
% 0.88/1.31  , 2, clause( 13, [ defined( 'additive_identity' ) ] )
% 0.88/1.31  , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  subsumption(
% 0.88/1.31  clause( 5443, [ sum( 'additive_identity', X, 'additive_identity' ), ~( sum( 
% 0.88/1.31    a, X, 'additive_identity' ) ) ] )
% 0.88/1.31  , clause( 6188, [ sum( 'additive_identity', X, 'additive_identity' ), ~( 
% 0.88/1.31    sum( a, X, 'additive_identity' ) ) ] )
% 0.88/1.31  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 
% 0.88/1.31    1 )] ) ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  resolution(
% 0.88/1.31  clause( 6189, [ ~( sum( X, 'additive_inverse'( a ), X ) ), ~( sum( 
% 0.88/1.31    'additive_identity', Y, 'additive_identity' ) ), ~( sum( a, Y, X ) ) ] )
% 0.88/1.31  , clause( 85, [ ~( sum( Y, X, 'additive_identity' ) ), ~( sum( X, 
% 0.88/1.31    'additive_inverse'( a ), X ) ) ] )
% 0.88/1.31  , 0, clause( 56, [ ~( sum( 'additive_identity', X, Z ) ), sum( 
% 0.88/1.31    'additive_identity', Y, Z ), ~( sum( a, X, Y ) ) ] )
% 0.88/1.31  , 1, substitution( 0, [ :=( X, X ), :=( Y, 'additive_identity' )] ), 
% 0.88/1.31    substitution( 1, [ :=( X, Y ), :=( Y, X ), :=( Z, 'additive_identity' )] )
% 0.88/1.31    ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  subsumption(
% 0.88/1.31  clause( 5966, [ ~( sum( 'additive_identity', Y, 'additive_identity' ) ), 
% 0.88/1.31    ~( sum( a, Y, X ) ), ~( sum( X, 'additive_inverse'( a ), X ) ) ] )
% 0.88/1.31  , clause( 6189, [ ~( sum( X, 'additive_inverse'( a ), X ) ), ~( sum( 
% 0.88/1.31    'additive_identity', Y, 'additive_identity' ) ), ~( sum( a, Y, X ) ) ] )
% 0.88/1.31  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 2
% 0.88/1.31     ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 0.88/1.31  
% 0.88/1.31  
% 0.88/1.31  factor(
% 0.88/1.31  clause( 6194, [ ~( sum( 'additive_identity', 'additive_inverse'( a ), 
% 0.88/1.31    'additive_identity' ) ), ~( sum( a, 'additive_inverse'( a ), 
% 0.88/1.32    'additive_identity' ) ) ] )
% 0.88/1.32  , clause( 5966, [ ~( sum( 'additive_identity', Y, 'additive_identity' ) ), 
% 0.88/1.32    ~( sum( a, Y, X ) ), ~( sum( X, 'additive_inverse'( a ), X ) ) ] )
% 0.88/1.32  , 0, 2, substitution( 0, [ :=( X, 'additive_identity' ), :=( Y, 
% 0.88/1.32    'additive_inverse'( a ) )] )).
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  resolution(
% 0.88/1.32  clause( 6196, [ ~( sum( a, 'additive_inverse'( a ), 'additive_identity' ) )
% 0.88/1.32    , ~( sum( a, 'additive_inverse'( a ), 'additive_identity' ) ) ] )
% 0.88/1.32  , clause( 6194, [ ~( sum( 'additive_identity', 'additive_inverse'( a ), 
% 0.88/1.32    'additive_identity' ) ), ~( sum( a, 'additive_inverse'( a ), 
% 0.88/1.32    'additive_identity' ) ) ] )
% 0.88/1.32  , 0, clause( 5443, [ sum( 'additive_identity', X, 'additive_identity' ), 
% 0.88/1.32    ~( sum( a, X, 'additive_identity' ) ) ] )
% 0.88/1.32  , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'additive_inverse'( a
% 0.88/1.32     ) )] )).
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  factor(
% 0.88/1.32  clause( 6197, [ ~( sum( a, 'additive_inverse'( a ), 'additive_identity' ) )
% 0.88/1.32     ] )
% 0.88/1.32  , clause( 6196, [ ~( sum( a, 'additive_inverse'( a ), 'additive_identity' )
% 0.88/1.32     ), ~( sum( a, 'additive_inverse'( a ), 'additive_identity' ) ) ] )
% 0.88/1.32  , 0, 1, substitution( 0, [] )).
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  subsumption(
% 0.88/1.32  clause( 5974, [ ~( sum( a, 'additive_inverse'( a ), 'additive_identity' ) )
% 0.88/1.32     ] )
% 0.88/1.32  , clause( 6197, [ ~( sum( a, 'additive_inverse'( a ), 'additive_identity' )
% 0.88/1.32     ) ] )
% 0.88/1.32  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  resolution(
% 0.88/1.32  clause( 6198, [ ~( sum( 'additive_inverse'( a ), a, 'additive_identity' ) )
% 0.88/1.32     ] )
% 0.88/1.32  , clause( 5974, [ ~( sum( a, 'additive_inverse'( a ), 'additive_identity' )
% 0.88/1.32     ) ] )
% 0.88/1.32  , 0, clause( 4, [ ~( sum( Y, X, Z ) ), sum( X, Y, Z ) ] )
% 0.88/1.32  , 1, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, 
% 0.88/1.32    'additive_inverse'( a ) ), :=( Z, 'additive_identity' )] )).
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  subsumption(
% 0.88/1.32  clause( 5976, [ ~( sum( 'additive_inverse'( a ), a, 'additive_identity' ) )
% 0.88/1.32     ] )
% 0.88/1.32  , clause( 6198, [ ~( sum( 'additive_inverse'( a ), a, 'additive_identity' )
% 0.88/1.32     ) ] )
% 0.88/1.32  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  resolution(
% 0.88/1.32  clause( 6199, [ ~( defined( a ) ) ] )
% 0.88/1.32  , clause( 5976, [ ~( sum( 'additive_inverse'( a ), a, 'additive_identity' )
% 0.88/1.32     ) ] )
% 0.88/1.32  , 0, clause( 3, [ ~( defined( X ) ), sum( 'additive_inverse'( X ), X, 
% 0.88/1.32    'additive_identity' ) ] )
% 0.88/1.32  , 1, substitution( 0, [] ), substitution( 1, [ :=( X, a )] )).
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  resolution(
% 0.88/1.32  clause( 6200, [] )
% 0.88/1.32  , clause( 6199, [ ~( defined( a ) ) ] )
% 0.88/1.32  , 0, clause( 26, [ defined( a ) ] )
% 0.88/1.32  , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  subsumption(
% 0.88/1.32  clause( 5981, [] )
% 0.88/1.32  , clause( 6200, [] )
% 0.88/1.32  , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  end.
% 0.88/1.32  
% 0.88/1.32  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.88/1.32  
% 0.88/1.32  Memory use:
% 0.88/1.32  
% 0.88/1.32  space for terms:        56485
% 0.88/1.32  space for clauses:      291438
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  clauses generated:      10409
% 0.88/1.32  clauses kept:           5982
% 0.88/1.32  clauses selected:       348
% 0.88/1.32  clauses deleted:        6
% 0.88/1.32  clauses inuse deleted:  1
% 0.88/1.32  
% 0.88/1.32  subsentry:          33719
% 0.88/1.32  literals s-matched: 11734
% 0.88/1.32  literals matched:   10906
% 0.88/1.32  full subsumption:   8698
% 0.88/1.32  
% 0.88/1.32  checksum:           -607895072
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  Bliksem ended
%------------------------------------------------------------------------------