TSTP Solution File: BOO005-1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : BOO005-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n020.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 : Thu Jul 14 23:30:34 EDT 2022

% Result   : Unsatisfiable 10.12s 10.50s
% Output   : Refutation 10.12s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : BOO005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13  % Command  : bliksem %s
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % DateTime : Wed Jun  1 17:51:38 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 10.12/10.50  *** allocated 10000 integers for termspace/termends
% 10.12/10.50  *** allocated 10000 integers for clauses
% 10.12/10.50  *** allocated 10000 integers for justifications
% 10.12/10.50  Bliksem 1.12
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  Automatic Strategy Selection
% 10.12/10.50  
% 10.12/10.50  Clauses:
% 10.12/10.50  [
% 10.12/10.50     [ sum( X, Y, add( X, Y ) ) ],
% 10.12/10.50     [ product( X, Y, multiply( X, Y ) ) ],
% 10.12/10.50     [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ],
% 10.12/10.50     [ ~( product( X, Y, Z ) ), product( Y, X, Z ) ],
% 10.12/10.50     [ sum( 'additive_identity', X, X ) ],
% 10.12/10.50     [ sum( X, 'additive_identity', X ) ],
% 10.12/10.50     [ product( 'multiplicative_identity', X, X ) ],
% 10.12/10.50     [ product( X, 'multiplicative_identity', X ) ],
% 10.12/10.50     [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, T, W ) )
% 10.12/10.50    , ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ],
% 10.12/10.50     [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, T, W ) )
% 10.12/10.50    , ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ],
% 10.12/10.50     [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum( X, T, W ) )
% 10.12/10.50    , ~( product( W, Y, V0 ) ), sum( Z, U, V0 ) ],
% 10.12/10.50     [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum( X, T, W ) )
% 10.12/10.50    , ~( sum( Z, U, V0 ) ), product( W, Y, V0 ) ],
% 10.12/10.50     [ ~( sum( X, Y, Z ) ), ~( sum( X, T, U ) ), ~( product( Y, T, W ) ), ~( 
% 10.12/10.50    sum( X, W, V0 ) ), product( Z, U, V0 ) ],
% 10.12/10.50     [ ~( sum( X, Y, Z ) ), ~( sum( X, T, U ) ), ~( product( Y, T, W ) ), ~( 
% 10.12/10.50    product( Z, U, V0 ) ), sum( X, W, V0 ) ],
% 10.12/10.50     [ ~( sum( X, Y, Z ) ), ~( sum( T, Y, U ) ), ~( product( X, T, W ) ), ~( 
% 10.12/10.50    sum( W, Y, V0 ) ), product( Z, U, V0 ) ],
% 10.12/10.50     [ ~( sum( X, Y, Z ) ), ~( sum( T, Y, U ) ), ~( product( X, T, W ) ), ~( 
% 10.12/10.50    product( Z, U, V0 ) ), sum( W, Y, V0 ) ],
% 10.12/10.50     [ sum( inverse( X ), X, 'multiplicative_identity' ) ],
% 10.12/10.50     [ sum( X, inverse( X ), 'multiplicative_identity' ) ],
% 10.12/10.50     [ product( inverse( X ), X, 'additive_identity' ) ],
% 10.12/10.50     [ product( X, inverse( X ), 'additive_identity' ) ],
% 10.12/10.50     [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ],
% 10.12/10.50     [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ],
% 10.12/10.50     [ ~( sum( x, 'multiplicative_identity', 'multiplicative_identity' ) ) ]
% 10.12/10.50    
% 10.12/10.50  ] .
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  percentage equality = 0.032787, percentage horn = 1.000000
% 10.12/10.50  This is a problem with some equality
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  Options Used:
% 10.12/10.50  
% 10.12/10.50  useres =            1
% 10.12/10.50  useparamod =        1
% 10.12/10.50  useeqrefl =         1
% 10.12/10.50  useeqfact =         1
% 10.12/10.50  usefactor =         1
% 10.12/10.50  usesimpsplitting =  0
% 10.12/10.50  usesimpdemod =      5
% 10.12/10.50  usesimpres =        3
% 10.12/10.50  
% 10.12/10.50  resimpinuse      =  1000
% 10.12/10.50  resimpclauses =     20000
% 10.12/10.50  substype =          eqrewr
% 10.12/10.50  backwardsubs =      1
% 10.12/10.50  selectoldest =      5
% 10.12/10.50  
% 10.12/10.50  litorderings [0] =  split
% 10.12/10.50  litorderings [1] =  extend the termordering, first sorting on arguments
% 10.12/10.50  
% 10.12/10.50  termordering =      kbo
% 10.12/10.50  
% 10.12/10.50  litapriori =        0
% 10.12/10.50  termapriori =       1
% 10.12/10.50  litaposteriori =    0
% 10.12/10.50  termaposteriori =   0
% 10.12/10.50  demodaposteriori =  0
% 10.12/10.50  ordereqreflfact =   0
% 10.12/10.50  
% 10.12/10.50  litselect =         negord
% 10.12/10.50  
% 10.12/10.50  maxweight =         15
% 10.12/10.50  maxdepth =          30000
% 10.12/10.50  maxlength =         115
% 10.12/10.50  maxnrvars =         195
% 10.12/10.50  excuselevel =       1
% 10.12/10.50  increasemaxweight = 1
% 10.12/10.50  
% 10.12/10.50  maxselected =       10000000
% 10.12/10.50  maxnrclauses =      10000000
% 10.12/10.50  
% 10.12/10.50  showgenerated =    0
% 10.12/10.50  showkept =         0
% 10.12/10.50  showselected =     0
% 10.12/10.50  showdeleted =      0
% 10.12/10.50  showresimp =       1
% 10.12/10.50  showstatus =       2000
% 10.12/10.50  
% 10.12/10.50  prologoutput =     1
% 10.12/10.50  nrgoals =          5000000
% 10.12/10.50  totalproof =       1
% 10.12/10.50  
% 10.12/10.50  Symbols occurring in the translation:
% 10.12/10.50  
% 10.12/10.50  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 10.12/10.50  .  [1, 2]      (w:1, o:27, a:1, s:1, b:0), 
% 10.12/10.50  !  [4, 1]      (w:0, o:21, a:1, s:1, b:0), 
% 10.12/10.50  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 10.12/10.50  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 10.12/10.50  add  [41, 2]      (w:1, o:52, a:1, s:1, b:0), 
% 10.12/10.50  sum  [42, 3]      (w:1, o:54, a:1, s:1, b:0), 
% 10.12/10.50  multiply  [43, 2]      (w:1, o:53, a:1, s:1, b:0), 
% 10.12/10.50  product  [44, 3]      (w:1, o:55, a:1, s:1, b:0), 
% 10.12/10.50  'additive_identity'  [46, 0]      (w:1, o:12, a:1, s:1, b:0), 
% 10.12/10.50  'multiplicative_identity'  [47, 0]      (w:1, o:13, a:1, s:1, b:0), 
% 10.12/10.50  inverse  [52, 1]      (w:1, o:26, a:1, s:1, b:0), 
% 10.12/10.50  x  [55, 0]      (w:1, o:20, a:1, s:1, b:0).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  Starting Search:
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  Intermediate Status:
% 10.12/10.50  Generated:    11039
% 10.12/10.50  Kept:         2007
% 10.12/10.50  Inuse:        126
% 10.12/10.50  Deleted:      0
% 10.12/10.50  Deletedinuse: 0
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  Intermediate Status:
% 10.12/10.50  Generated:    25584
% 10.12/10.50  Kept:         4011
% 10.12/10.50  Inuse:        233
% 10.12/10.50  Deleted:      3
% 10.12/10.50  Deletedinuse: 3
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  Intermediate Status:
% 10.12/10.50  Generated:    41515
% 10.12/10.50  Kept:         6055
% 10.12/10.50  Inuse:        328
% 10.12/10.50  Deleted:      6
% 10.12/10.50  Deletedinuse: 3
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  Intermediate Status:
% 10.12/10.50  Generated:    54930
% 10.12/10.50  Kept:         8067
% 10.12/10.50  Inuse:        389
% 10.12/10.50  Deleted:      154
% 10.12/10.50  Deletedinuse: 127
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  Intermediate Status:
% 10.12/10.50  Generated:    92944
% 10.12/10.50  Kept:         10068
% 10.12/10.50  Inuse:        504
% 10.12/10.50  Deleted:      185
% 10.12/10.50  Deletedinuse: 140
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  Intermediate Status:
% 10.12/10.50  Generated:    119674
% 10.12/10.50  Kept:         12104
% 10.12/10.50  Inuse:        569
% 10.12/10.50  Deleted:      193
% 10.12/10.50  Deletedinuse: 146
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  Intermediate Status:
% 10.12/10.50  Generated:    135302
% 10.12/10.50  Kept:         14282
% 10.12/10.50  Inuse:        601
% 10.12/10.50  Deleted:      196
% 10.12/10.50  Deletedinuse: 146
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  Intermediate Status:
% 10.12/10.50  Generated:    152578
% 10.12/10.50  Kept:         16289
% 10.12/10.50  Inuse:        655
% 10.12/10.50  Deleted:      200
% 10.12/10.50  Deletedinuse: 148
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  Intermediate Status:
% 10.12/10.50  Generated:    177580
% 10.12/10.50  Kept:         18324
% 10.12/10.50  Inuse:        707
% 10.12/10.50  Deleted:      206
% 10.12/10.50  Deletedinuse: 149
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  Resimplifying clauses:
% 10.12/10.50  Done
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  Intermediate Status:
% 10.12/10.50  Generated:    195477
% 10.12/10.50  Kept:         20339
% 10.12/10.50  Inuse:        755
% 10.12/10.50  Deleted:      4330
% 10.12/10.50  Deletedinuse: 149
% 10.12/10.50  
% 10.12/10.50  Resimplifying inuse:
% 10.12/10.50  
% 10.12/10.50  Bliksems!, er is een bewijs:
% 10.12/10.50  % SZS status Unsatisfiable
% 10.12/10.50  % SZS output start Refutation
% 10.12/10.50  
% 10.12/10.50  clause( 0, [ sum( X, Y, add( X, Y ) ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 1, [ product( X, Y, multiply( X, Y ) ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 2, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 3, [ ~( product( X, Y, Z ) ), product( Y, X, Z ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 4, [ sum( 'additive_identity', X, X ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 5, [ sum( X, 'additive_identity', X ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 6, [ product( 'multiplicative_identity', X, X ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 7, [ product( X, 'multiplicative_identity', X ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 8, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, T
% 10.12/10.50    , W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 14, [ ~( sum( X, Y, Z ) ), ~( sum( T, Y, U ) ), ~( product( X, T, W
% 10.12/10.50     ) ), ~( sum( W, Y, V0 ) ), product( Z, U, V0 ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 15, [ ~( sum( X, Y, Z ) ), ~( sum( T, Y, U ) ), ~( product( X, T, W
% 10.12/10.50     ) ), ~( product( Z, U, V0 ) ), sum( W, Y, V0 ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 19, [ product( X, inverse( X ), 'additive_identity' ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 20, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 21, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ]
% 10.12/10.50     )
% 10.12/10.50  .
% 10.12/10.50  clause( 22, [ ~( sum( x, 'multiplicative_identity', 
% 10.12/10.50    'multiplicative_identity' ) ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 46, [ ~( sum( X, Y, Z ) ), ~( sum( T, Y, U ) ), ~( product( X, T, T
% 10.12/10.50     ) ), product( Z, U, U ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 48, [ ~( sum( X, Y, Z ) ), ~( product( X, X, T ) ), ~( product( Z, 
% 10.12/10.50    Z, U ) ), sum( T, Y, U ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 51, [ product( X, Y, multiply( Y, X ) ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 52, [ sum( X, Y, add( Y, X ) ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 53, [ ~( sum( 'multiplicative_identity', x, 
% 10.12/10.50    'multiplicative_identity' ) ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 73, [ ~( product( X, Y, Z ) ), ~( product( X, 'additive_identity', 
% 10.12/10.50    T ) ), ~( product( X, Y, U ) ), sum( Z, T, U ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 87, [ ~( product( X, Y, Z ) ), ~( product( X, 'additive_identity', 
% 10.12/10.50    T ) ), sum( Z, T, Z ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 146, [ ~( product( 'multiplicative_identity', X, Y ) ), =( X, Y ) ]
% 10.12/10.50     )
% 10.12/10.50  .
% 10.12/10.50  clause( 147, [ ~( product( X, 'multiplicative_identity', Y ) ), =( X, Y ) ]
% 10.12/10.50     )
% 10.12/10.50  .
% 10.12/10.50  clause( 150, [ sum( Y, X, Z ), ~( product( T, U, add( X, Y ) ) ), ~( 
% 10.12/10.50    product( T, U, Z ) ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 174, [ ~( product( X, Y, Z ) ), =( Y, Z ), ~( product( 
% 10.12/10.50    'multiplicative_identity', X, 'multiplicative_identity' ) ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 342, [ product( Y, X, Y ), ~( product( X, 'multiplicative_identity'
% 10.12/10.50    , 'multiplicative_identity' ) ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 797, [ ~( sum( 'additive_identity', X, Y ) ), =( X, Y ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 2934, [ ~( sum( X, Y, Z ) ), ~( product( X, 'additive_identity', 
% 10.12/10.50    'additive_identity' ) ), product( Z, Y, Y ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 3112, [ ~( sum( X, x, Y ) ), ~( product( X, X, 
% 10.12/10.50    'multiplicative_identity' ) ), ~( product( Y, Y, 
% 10.12/10.50    'multiplicative_identity' ) ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 3117, [ ~( sum( X, x, X ) ), ~( product( X, X, 
% 10.12/10.50    'multiplicative_identity' ) ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 6734, [ ~( product( X, 'additive_identity', Y ) ), sum( 
% 10.12/10.50    'additive_identity', Y, 'additive_identity' ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 6749, [ sum( 'additive_identity', multiply( 'additive_identity', X
% 10.12/10.50     ), 'additive_identity' ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 6789, [ =( multiply( 'additive_identity', X ), 'additive_identity'
% 10.12/10.50     ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 6808, [ product( X, 'additive_identity', 'additive_identity' ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 14226, [ ~( product( X, Y, add( x, Z ) ) ), ~( product( X, Y, Z ) )
% 10.12/10.50    , ~( product( Z, Z, 'multiplicative_identity' ) ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 14271, [ ~( product( 'multiplicative_identity', 
% 10.12/10.50    'multiplicative_identity', add( x, 'multiplicative_identity' ) ) ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 17575, [ ~( product( 'multiplicative_identity', 
% 10.12/10.50    'multiplicative_identity', X ) ), ~( product( Y, add( x, 
% 10.12/10.50    'multiplicative_identity' ), X ) ), ~( product( 'multiplicative_identity'
% 10.12/10.50    , Y, 'multiplicative_identity' ) ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 17736, [ ~( product( 'multiplicative_identity', add( x, 
% 10.12/10.50    'multiplicative_identity' ), 'multiplicative_identity' ) ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 18265, [ ~( product( add( x, 'multiplicative_identity' ), 
% 10.12/10.50    'multiplicative_identity', 'multiplicative_identity' ) ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 20025, [ ~( sum( X, Y, Z ) ), product( Z, Y, Y ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 20174, [ product( add( X, Y ), Y, Y ) ] )
% 10.12/10.50  .
% 10.12/10.50  clause( 20517, [] )
% 10.12/10.50  .
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  % SZS output end Refutation
% 10.12/10.50  found a proof!
% 10.12/10.50  
% 10.12/10.50  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 10.12/10.50  
% 10.12/10.50  initialclauses(
% 10.12/10.50  [ clause( 20519, [ sum( X, Y, add( X, Y ) ) ] )
% 10.12/10.50  , clause( 20520, [ product( X, Y, multiply( X, Y ) ) ] )
% 10.12/10.50  , clause( 20521, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 10.12/10.50  , clause( 20522, [ ~( product( X, Y, Z ) ), product( Y, X, Z ) ] )
% 10.12/10.50  , clause( 20523, [ sum( 'additive_identity', X, X ) ] )
% 10.12/10.50  , clause( 20524, [ sum( X, 'additive_identity', X ) ] )
% 10.12/10.50  , clause( 20525, [ product( 'multiplicative_identity', X, X ) ] )
% 10.12/10.50  , clause( 20526, [ product( X, 'multiplicative_identity', X ) ] )
% 10.12/10.50  , clause( 20527, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( 
% 10.12/10.50    Y, T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 10.12/10.50  , clause( 20528, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( 
% 10.12/10.50    Y, T, W ) ), ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ] )
% 10.12/10.50  , clause( 20529, [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum( 
% 10.12/10.50    X, T, W ) ), ~( product( W, Y, V0 ) ), sum( Z, U, V0 ) ] )
% 10.12/10.50  , clause( 20530, [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum( 
% 10.12/10.50    X, T, W ) ), ~( sum( Z, U, V0 ) ), product( W, Y, V0 ) ] )
% 10.12/10.50  , clause( 20531, [ ~( sum( X, Y, Z ) ), ~( sum( X, T, U ) ), ~( product( Y
% 10.12/10.50    , T, W ) ), ~( sum( X, W, V0 ) ), product( Z, U, V0 ) ] )
% 10.12/10.50  , clause( 20532, [ ~( sum( X, Y, Z ) ), ~( sum( X, T, U ) ), ~( product( Y
% 10.12/10.50    , T, W ) ), ~( product( Z, U, V0 ) ), sum( X, W, V0 ) ] )
% 10.12/10.50  , clause( 20533, [ ~( sum( X, Y, Z ) ), ~( sum( T, Y, U ) ), ~( product( X
% 10.12/10.50    , T, W ) ), ~( sum( W, Y, V0 ) ), product( Z, U, V0 ) ] )
% 10.12/10.50  , clause( 20534, [ ~( sum( X, Y, Z ) ), ~( sum( T, Y, U ) ), ~( product( X
% 10.12/10.50    , T, W ) ), ~( product( Z, U, V0 ) ), sum( W, Y, V0 ) ] )
% 10.12/10.50  , clause( 20535, [ sum( inverse( X ), X, 'multiplicative_identity' ) ] )
% 10.12/10.50  , clause( 20536, [ sum( X, inverse( X ), 'multiplicative_identity' ) ] )
% 10.12/10.50  , clause( 20537, [ product( inverse( X ), X, 'additive_identity' ) ] )
% 10.12/10.50  , clause( 20538, [ product( X, inverse( X ), 'additive_identity' ) ] )
% 10.12/10.50  , clause( 20539, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 10.12/10.50  , clause( 20540, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, 
% 10.12/10.50    T ) ] )
% 10.12/10.50  , clause( 20541, [ ~( sum( x, 'multiplicative_identity', 
% 10.12/10.50    'multiplicative_identity' ) ) ] )
% 10.12/10.50  ] ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 0, [ sum( X, Y, add( X, Y ) ) ] )
% 10.12/10.50  , clause( 20519, [ sum( X, Y, add( X, Y ) ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 10.12/10.50     )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 1, [ product( X, Y, multiply( X, Y ) ) ] )
% 10.12/10.50  , clause( 20520, [ product( X, Y, multiply( X, Y ) ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 10.12/10.50     )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 2, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 10.12/10.50  , clause( 20521, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 10.12/10.50    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 3, [ ~( product( X, Y, Z ) ), product( Y, X, Z ) ] )
% 10.12/10.50  , clause( 20522, [ ~( product( X, Y, Z ) ), product( Y, X, Z ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 10.12/10.50    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 4, [ sum( 'additive_identity', X, X ) ] )
% 10.12/10.50  , clause( 20523, [ sum( 'additive_identity', X, X ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 5, [ sum( X, 'additive_identity', X ) ] )
% 10.12/10.50  , clause( 20524, [ sum( X, 'additive_identity', X ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 6, [ product( 'multiplicative_identity', X, X ) ] )
% 10.12/10.50  , clause( 20525, [ product( 'multiplicative_identity', X, X ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 7, [ product( X, 'multiplicative_identity', X ) ] )
% 10.12/10.50  , clause( 20526, [ product( X, 'multiplicative_identity', X ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 8, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, T
% 10.12/10.50    , W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 10.12/10.50  , clause( 20527, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( 
% 10.12/10.50    Y, T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 10.12/10.50    , U ), :=( W, W ), :=( V0, V0 )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1
% 10.12/10.50    , 1 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 4 )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 14, [ ~( sum( X, Y, Z ) ), ~( sum( T, Y, U ) ), ~( product( X, T, W
% 10.12/10.50     ) ), ~( sum( W, Y, V0 ) ), product( Z, U, V0 ) ] )
% 10.12/10.50  , clause( 20533, [ ~( sum( X, Y, Z ) ), ~( sum( T, Y, U ) ), ~( product( X
% 10.12/10.50    , T, W ) ), ~( sum( W, Y, V0 ) ), product( Z, U, V0 ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 10.12/10.50    , U ), :=( W, W ), :=( V0, V0 )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1
% 10.12/10.50    , 1 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 4 )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 15, [ ~( sum( X, Y, Z ) ), ~( sum( T, Y, U ) ), ~( product( X, T, W
% 10.12/10.50     ) ), ~( product( Z, U, V0 ) ), sum( W, Y, V0 ) ] )
% 10.12/10.50  , clause( 20534, [ ~( sum( X, Y, Z ) ), ~( sum( T, Y, U ) ), ~( product( X
% 10.12/10.50    , T, W ) ), ~( product( Z, U, V0 ) ), sum( W, Y, V0 ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 10.12/10.50    , U ), :=( W, W ), :=( V0, V0 )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1
% 10.12/10.50    , 1 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 4 )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 19, [ product( X, inverse( X ), 'additive_identity' ) ] )
% 10.12/10.50  , clause( 20538, [ product( X, inverse( X ), 'additive_identity' ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 20, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 10.12/10.50  , clause( 20539, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 10.12/10.50    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 21, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ]
% 10.12/10.50     )
% 10.12/10.50  , clause( 20540, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, 
% 10.12/10.50    T ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 10.12/10.50    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 22, [ ~( sum( x, 'multiplicative_identity', 
% 10.12/10.50    'multiplicative_identity' ) ) ] )
% 10.12/10.50  , clause( 20541, [ ~( sum( x, 'multiplicative_identity', 
% 10.12/10.50    'multiplicative_identity' ) ) ] )
% 10.12/10.50  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  factor(
% 10.12/10.50  clause( 20718, [ ~( sum( X, Y, Z ) ), ~( sum( T, Y, U ) ), ~( product( X, T
% 10.12/10.50    , T ) ), product( Z, U, U ) ] )
% 10.12/10.50  , clause( 14, [ ~( sum( X, Y, Z ) ), ~( sum( T, Y, U ) ), ~( product( X, T
% 10.12/10.50    , W ) ), ~( sum( W, Y, V0 ) ), product( Z, U, V0 ) ] )
% 10.12/10.50  , 1, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), 
% 10.12/10.50    :=( U, U ), :=( W, T ), :=( V0, U )] )).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 46, [ ~( sum( X, Y, Z ) ), ~( sum( T, Y, U ) ), ~( product( X, T, T
% 10.12/10.50     ) ), product( Z, U, U ) ] )
% 10.12/10.50  , clause( 20718, [ ~( sum( X, Y, Z ) ), ~( sum( T, Y, U ) ), ~( product( X
% 10.12/10.50    , T, T ) ), product( Z, U, U ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 10.12/10.50    , U )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3
% 10.12/10.50    , 3 )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  factor(
% 10.12/10.50  clause( 20720, [ ~( sum( X, Y, Z ) ), ~( product( X, X, T ) ), ~( product( 
% 10.12/10.50    Z, Z, U ) ), sum( T, Y, U ) ] )
% 10.12/10.50  , clause( 15, [ ~( sum( X, Y, Z ) ), ~( sum( T, Y, U ) ), ~( product( X, T
% 10.12/10.50    , W ) ), ~( product( Z, U, V0 ) ), sum( W, Y, V0 ) ] )
% 10.12/10.50  , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, X ), 
% 10.12/10.50    :=( U, Z ), :=( W, T ), :=( V0, U )] )).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 48, [ ~( sum( X, Y, Z ) ), ~( product( X, X, T ) ), ~( product( Z, 
% 10.12/10.50    Z, U ) ), sum( T, Y, U ) ] )
% 10.12/10.50  , clause( 20720, [ ~( sum( X, Y, Z ) ), ~( product( X, X, T ) ), ~( product( 
% 10.12/10.50    Z, Z, U ) ), sum( T, Y, U ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 10.12/10.50    , U )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3
% 10.12/10.50    , 3 )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  resolution(
% 10.12/10.50  clause( 20723, [ product( Y, X, multiply( X, Y ) ) ] )
% 10.12/10.50  , clause( 3, [ ~( product( X, Y, Z ) ), product( Y, X, Z ) ] )
% 10.12/10.50  , 0, clause( 1, [ product( X, Y, multiply( X, Y ) ) ] )
% 10.12/10.50  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, multiply( X, Y ) )] )
% 10.12/10.50    , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 51, [ product( X, Y, multiply( Y, X ) ) ] )
% 10.12/10.50  , clause( 20723, [ product( Y, X, multiply( X, Y ) ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 10.12/10.50     )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  resolution(
% 10.12/10.50  clause( 20724, [ sum( Y, X, add( X, Y ) ) ] )
% 10.12/10.50  , clause( 2, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 10.12/10.50  , 0, clause( 0, [ sum( X, Y, add( X, Y ) ) ] )
% 10.12/10.50  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, add( X, Y ) )] ), 
% 10.12/10.50    substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 52, [ sum( X, Y, add( Y, X ) ) ] )
% 10.12/10.50  , clause( 20724, [ sum( Y, X, add( X, Y ) ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 10.12/10.50     )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  resolution(
% 10.12/10.50  clause( 20725, [ ~( sum( 'multiplicative_identity', x, 
% 10.12/10.50    'multiplicative_identity' ) ) ] )
% 10.12/10.50  , clause( 22, [ ~( sum( x, 'multiplicative_identity', 
% 10.12/10.50    'multiplicative_identity' ) ) ] )
% 10.12/10.50  , 0, clause( 2, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 10.12/10.50  , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 
% 10.12/10.50    'multiplicative_identity' ), :=( Y, x ), :=( Z, 'multiplicative_identity'
% 10.12/10.50     )] )).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 53, [ ~( sum( 'multiplicative_identity', x, 
% 10.12/10.50    'multiplicative_identity' ) ) ] )
% 10.12/10.50  , clause( 20725, [ ~( sum( 'multiplicative_identity', x, 
% 10.12/10.50    'multiplicative_identity' ) ) ] )
% 10.12/10.50  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  resolution(
% 10.12/10.50  clause( 20726, [ ~( product( X, Y, Z ) ), ~( product( X, 
% 10.12/10.50    'additive_identity', T ) ), ~( product( X, Y, U ) ), sum( Z, T, U ) ] )
% 10.12/10.50  , clause( 8, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y
% 10.12/10.50    , T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 10.12/10.50  , 2, clause( 5, [ sum( X, 'additive_identity', X ) ] )
% 10.12/10.50  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, 
% 10.12/10.50    'additive_identity' ), :=( U, T ), :=( W, Y ), :=( V0, U )] ), 
% 10.12/10.50    substitution( 1, [ :=( X, Y )] )).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  subsumption(
% 10.12/10.50  clause( 73, [ ~( product( X, Y, Z ) ), ~( product( X, 'additive_identity', 
% 10.12/10.50    T ) ), ~( product( X, Y, U ) ), sum( Z, T, U ) ] )
% 10.12/10.50  , clause( 20726, [ ~( product( X, Y, Z ) ), ~( product( X, 
% 10.12/10.50    'additive_identity', T ) ), ~( product( X, Y, U ) ), sum( Z, T, U ) ] )
% 10.12/10.50  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 10.12/10.50    , U )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3
% 10.12/10.50    , 3 )] ) ).
% 10.12/10.50  
% 10.12/10.50  
% 10.12/10.50  factor(
% 10.12/10.50  clause( 20732, [ ~( product( X, Y, Z ) ), ~( product( X, 
% 10.12/10.50    'additive_identity', T ) ), sum( Z, T, Z ) ] )
% 10.12/10.50  , clause( 73, [ ~( product( X, Y, Z ) ), ~( product( X, 'additive_identity'
% 10.12/10.50    , T ) ), ~( product( X, Y, U ) ), sum( Z, T, U ) ] )
% 21.24/21.66  , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), 
% 21.24/21.66    :=( U, Z )] )).
% 21.24/21.66  
% 21.24/21.66  
% 21.24/21.66  subsumption(
% 21.24/21.66  clause( 87, [ ~( product( X, Y, Z ) ), ~( product( X, 'additive_identity', 
% 21.24/21.66    T ) ), sum( Z, T, Z ) ] )
% 21.24/21.66  , clause( 20732, [ ~( product( X, Y, Z ) ), ~( product( X, 
% 21.24/21.66    'additive_identity', T ) ), sum( Z, T, Z ) ] )
% 21.24/21.66  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 21.24/21.66    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 21.24/21.66  
% 21.24/21.66  
% 21.24/21.66  resolution(
% 21.24/21.66  clause( 20735, [ ~( product( 'multiplicative_identity', X, Y ) ), =( X, Y )
% 21.24/21.66     ] )
% 21.24/21.66  , clause( 21, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T )
% 21.24/21.66     ] )
% 21.24/21.66  , 0, clause( 6, [ product( 'multiplicative_identity', X, X ) ] )
% 21.24/21.66  , 0, substitution( 0, [ :=( X, 'multiplicative_identity' ), :=( Y, X ), 
% 21.24/21.66    :=( Z, X ), :=( T, Y )] ), substitution( 1, [ :=( X, X )] )).
% 21.24/21.66  
% 21.24/21.66  
% 21.24/21.66  subsumption(
% 21.24/21.66  clause( 146, [ ~( product( 'multiplicative_identity', X, Y ) ), =( X, Y ) ]
% 21.24/21.66     )
% 21.24/21.66  , clause( 20735, [ ~( product( 'multiplicative_identity', X, Y ) ), =( X, Y
% 21.24/21.66     ) ] )
% 21.24/21.66  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 21.24/21.66     ), ==>( 1, 1 )] ) ).
% 21.24/21.66  
% 21.24/21.66  
% 21.24/21.66  resolution(
% 21.24/21.66  clause( 20737, [ ~( product( X, 'multiplicative_identity', Y ) ), =( X, Y )
% 21.24/21.66     ] )
% 21.24/21.66  , clause( 21, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T )
% 21.24/21.66     ] )
% 21.24/21.66  , 0, clause( 7, [ product( X, 'multiplicative_identity', X ) ] )
% 21.24/21.66  , 0, substitution( 0, [ :=( X, X ), :=( Y, 'multiplicative_identity' ), 
% 21.24/21.66    :=( Z, X ), :=( T, Y )] ), substitution( 1, [ :=( X, X )] )).
% 21.24/21.66  
% 21.24/21.66  
% 21.24/21.66  subsumption(
% 21.24/21.66  clause( 147, [ ~( product( X, 'multiplicative_identity', Y ) ), =( X, Y ) ]
% 21.24/21.66     )
% 21.24/21.66  , clause( 20737, [ ~( product( X, 'multiplicative_identity', Y ) ), =( X, Y
% 21.24/21.66     ) ] )
% 21.24/21.66  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 21.24/21.66     ), ==>( 1, 1 )] ) ).
% 21.24/21.66  
% 21.24/21.66  
% 21.24/21.66  assignments is full
% 21.24/21.66  
% 21.24/21.66  Memory use:
% 21.24/21.66  
% 21.24/21.66  space for terms:        308116
% 21.24/21.66  space for clauses:      794360
% 21.24/21.66  
% 21.24/21.66  
% 21.24/21.66  clauses generated:      196271
% 21.24/21.66  clauses kept:           20518
% 21.24/21.66  clauses selected:       759
% 21.24/21.66  clauses deleted:        4343
% 21.24/21.66  clauses inuse deleted:  162
% 21.24/21.66  
% 21.24/21.66  subsentry:          2540081
% 21.24/21.66  literals s-matched: 992008
% 21.24/21.66  literals matched:   596244
% 21.24/21.66  full subsumption:   243891
% 21.24/21.66  
% 21.24/21.66  checksum:           1938336894
% 21.24/21.66  
% 21.24/21.66  
% 21.24/21.66  Bliksem ended
%------------------------------------------------------------------------------