TSTP Solution File: RNG006-3 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : RNG006-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n019.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 : Mon Jul 18 20:16:04 EDT 2022

% Result   : Unsatisfiable 15.17s 15.54s
% Output   : Refutation 15.17s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : RNG006-3 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14  % Command  : bliksem %s
% 0.15/0.36  % Computer : n019.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % DateTime : Mon May 30 19:00:40 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 14.16/14.50  *** allocated 10000 integers for termspace/termends
% 14.16/14.50  *** allocated 10000 integers for clauses
% 14.16/14.50  *** allocated 10000 integers for justifications
% 14.16/14.50  Bliksem 1.12
% 14.16/14.50  
% 14.16/14.50  
% 14.16/14.50  Automatic Strategy Selection
% 14.16/14.50  
% 14.16/14.50  Clauses:
% 14.16/14.50  [
% 14.16/14.50     [ sum( 'additive_identity', X, X ) ],
% 14.16/14.50     [ sum( X, 'additive_identity', X ) ],
% 14.16/14.50     [ product( X, Y, multiply( X, Y ) ) ],
% 14.16/14.50     [ sum( X, Y, add( X, Y ) ) ],
% 14.16/14.50     [ sum( 'additive_inverse'( X ), X, 'additive_identity' ) ],
% 14.16/14.50     [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ],
% 14.16/14.50     [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W ) ), sum( X
% 14.16/14.50    , U, W ) ],
% 14.16/14.50     [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, W ) ), sum( Z
% 14.16/14.50    , T, W ) ],
% 14.16/14.50     [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ],
% 14.16/14.50     [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product( Z, T, W
% 14.16/14.50     ) ), product( X, U, W ) ],
% 14.16/14.50     [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product( X, U, W
% 14.16/14.50     ) ), product( Z, T, W ) ],
% 14.16/14.50     [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, T, W ) )
% 14.16/14.50    , ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ],
% 14.16/14.50     [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, T, W ) )
% 14.16/14.50    , ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ],
% 14.16/14.50     [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum( X, T, W ) )
% 14.16/14.50    , ~( product( W, Y, V0 ) ), sum( Z, U, V0 ) ],
% 14.16/14.50     [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum( X, T, W ) )
% 14.16/14.50    , ~( sum( Z, U, V0 ) ), product( W, Y, V0 ) ],
% 14.16/14.50     [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ],
% 14.16/14.50     [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ],
% 14.16/14.50     [ sum( b, 'additive_inverse'( c ), 'bS_Ic' ) ],
% 14.16/14.50     [ product( a, b, aPb ) ],
% 14.16/14.50     [ product( a, c, aPc ) ],
% 14.16/14.50     [ sum( aPb, 'additive_inverse'( aPc ), 'aPb_S_IaPc' ) ],
% 14.16/14.50     [ ~( product( a, 'bS_Ic', 'aPb_S_IaPc' ) ) ]
% 14.16/14.50  ] .
% 14.16/14.50  
% 14.16/14.50  
% 14.16/14.50  percentage equality = 0.036364, percentage horn = 1.000000
% 14.16/14.50  This is a problem with some equality
% 14.16/14.50  
% 14.16/14.50  
% 14.16/14.50  
% 14.16/14.50  Options Used:
% 14.16/14.50  
% 14.16/14.50  useres =            1
% 14.16/14.50  useparamod =        1
% 14.16/14.50  useeqrefl =         1
% 14.16/14.50  useeqfact =         1
% 14.16/14.50  usefactor =         1
% 14.16/14.50  usesimpsplitting =  0
% 14.16/14.50  usesimpdemod =      5
% 14.16/14.50  usesimpres =        3
% 14.16/14.50  
% 14.16/14.50  resimpinuse      =  1000
% 14.16/14.50  resimpclauses =     20000
% 14.16/14.50  substype =          eqrewr
% 14.16/14.50  backwardsubs =      1
% 14.16/14.50  selectoldest =      5
% 14.16/14.50  
% 14.16/14.50  litorderings [0] =  split
% 14.16/14.50  litorderings [1] =  extend the termordering, first sorting on arguments
% 14.16/14.50  
% 14.16/14.50  termordering =      kbo
% 14.16/14.50  
% 14.16/14.50  litapriori =        0
% 14.16/14.50  termapriori =       1
% 14.16/14.50  litaposteriori =    0
% 14.16/14.50  termaposteriori =   0
% 14.16/14.50  demodaposteriori =  0
% 14.16/14.50  ordereqreflfact =   0
% 14.16/14.50  
% 14.16/14.50  litselect =         negord
% 14.16/14.50  
% 14.16/14.50  maxweight =         15
% 14.16/14.50  maxdepth =          30000
% 14.16/14.50  maxlength =         115
% 14.16/14.50  maxnrvars =         195
% 14.16/14.50  excuselevel =       1
% 14.16/14.50  increasemaxweight = 1
% 14.16/14.50  
% 14.16/14.50  maxselected =       10000000
% 14.16/14.50  maxnrclauses =      10000000
% 14.16/14.50  
% 14.16/14.50  showgenerated =    0
% 14.16/14.50  showkept =         0
% 14.16/14.50  showselected =     0
% 14.16/14.50  showdeleted =      0
% 14.16/14.50  showresimp =       1
% 14.16/14.50  showstatus =       2000
% 14.16/14.50  
% 14.16/14.50  prologoutput =     1
% 14.16/14.50  nrgoals =          5000000
% 14.16/14.50  totalproof =       1
% 14.16/14.50  
% 14.16/14.50  Symbols occurring in the translation:
% 14.16/14.50  
% 14.16/14.50  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 14.16/14.50  .  [1, 2]      (w:1, o:33, a:1, s:1, b:0), 
% 14.16/14.50  !  [4, 1]      (w:0, o:27, a:1, s:1, b:0), 
% 14.16/14.50  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 14.16/14.50  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 14.16/14.50  'additive_identity'  [39, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 14.16/14.50  sum  [41, 3]      (w:1, o:60, a:1, s:1, b:0), 
% 14.16/14.50  multiply  [43, 2]      (w:1, o:58, a:1, s:1, b:0), 
% 14.16/14.50  product  [44, 3]      (w:1, o:61, a:1, s:1, b:0), 
% 14.16/14.50  add  [45, 2]      (w:1, o:59, a:1, s:1, b:0), 
% 14.16/14.50  'additive_inverse'  [46, 1]      (w:1, o:32, a:1, s:1, b:0), 
% 14.16/14.50  b  [55, 0]      (w:1, o:24, a:1, s:1, b:0), 
% 14.16/14.50  c  [56, 0]      (w:1, o:26, a:1, s:1, b:0), 
% 14.16/14.50  'bS_Ic'  [57, 0]      (w:1, o:25, a:1, s:1, b:0), 
% 14.16/14.50  a  [58, 0]      (w:1, o:20, a:1, s:1, b:0), 
% 14.16/14.50  aPb  [59, 0]      (w:1, o:21, a:1, s:1, b:0), 
% 14.16/14.50  aPc  [60, 0]      (w:1, o:23, a:1, s:1, b:0), 
% 14.16/14.50  'aPb_S_IaPc'  [61, 0]      (w:1, o:22, a:1, s:1, b:0).
% 14.16/14.50  
% 14.16/14.50  
% 14.16/14.50  Starting Search:
% 14.16/14.50  
% 14.16/14.50  Resimplifying inuse:
% 14.16/14.50  Done
% 14.16/14.50  
% 14.16/14.50  
% 14.16/14.50  Intermediate Status:
% 14.16/14.50  Generated:    6656
% 14.16/14.50  Kept:         2024
% 14.16/14.50  Inuse:        91
% 14.16/14.50  Deleted:      15
% 14.16/14.50  Deletedinuse: 7
% 14.16/14.50  
% 14.16/14.50  Resimplifying inuse:
% 14.16/14.50  Done
% 14.16/14.50  
% 14.16/14.50  Resimplifying inuse:
% 14.16/14.50  Done
% 14.16/14.50  
% 14.16/14.50  
% 14.16/14.50  Intermediate Status:
% 14.16/14.50  Generated:    17829
% 14.16/14.50  Kept:         4049
% 14.16/14.50  Inuse:        185
% 14.16/14.50  Deleted:      64
% 14.16/14.50  Deletedinuse: 38
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    24549
% 15.17/15.54  Kept:         6174
% 15.17/15.54  Inuse:        224
% 15.17/15.54  Deleted:      70
% 15.17/15.54  Deletedinuse: 44
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    33219
% 15.17/15.54  Kept:         8231
% 15.17/15.54  Inuse:        273
% 15.17/15.54  Deleted:      100
% 15.17/15.54  Deletedinuse: 67
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    40589
% 15.17/15.54  Kept:         10292
% 15.17/15.54  Inuse:        315
% 15.17/15.54  Deleted:      103
% 15.17/15.54  Deletedinuse: 67
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    49817
% 15.17/15.54  Kept:         12333
% 15.17/15.54  Inuse:        358
% 15.17/15.54  Deleted:      112
% 15.17/15.54  Deletedinuse: 67
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    56674
% 15.17/15.54  Kept:         14356
% 15.17/15.54  Inuse:        387
% 15.17/15.54  Deleted:      118
% 15.17/15.54  Deletedinuse: 68
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    63294
% 15.17/15.54  Kept:         16555
% 15.17/15.54  Inuse:        413
% 15.17/15.54  Deleted:      123
% 15.17/15.54  Deletedinuse: 68
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    73378
% 15.17/15.54  Kept:         18596
% 15.17/15.54  Inuse:        441
% 15.17/15.54  Deleted:      126
% 15.17/15.54  Deletedinuse: 70
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying clauses:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    80852
% 15.17/15.54  Kept:         20738
% 15.17/15.54  Inuse:        465
% 15.17/15.54  Deleted:      2672
% 15.17/15.54  Deletedinuse: 70
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    87179
% 15.17/15.54  Kept:         22771
% 15.17/15.54  Inuse:        479
% 15.17/15.54  Deleted:      2674
% 15.17/15.54  Deletedinuse: 72
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    93701
% 15.17/15.54  Kept:         24845
% 15.17/15.54  Inuse:        500
% 15.17/15.54  Deleted:      2674
% 15.17/15.54  Deletedinuse: 72
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    100539
% 15.17/15.54  Kept:         26865
% 15.17/15.54  Inuse:        524
% 15.17/15.54  Deleted:      2674
% 15.17/15.54  Deletedinuse: 72
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    104686
% 15.17/15.54  Kept:         28875
% 15.17/15.54  Inuse:        532
% 15.17/15.54  Deleted:      2676
% 15.17/15.54  Deletedinuse: 72
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    110757
% 15.17/15.54  Kept:         30903
% 15.17/15.54  Inuse:        553
% 15.17/15.54  Deleted:      2720
% 15.17/15.54  Deletedinuse: 110
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    115774
% 15.17/15.54  Kept:         32947
% 15.17/15.54  Inuse:        566
% 15.17/15.54  Deleted:      2723
% 15.17/15.54  Deletedinuse: 110
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    125515
% 15.17/15.54  Kept:         34991
% 15.17/15.54  Inuse:        595
% 15.17/15.54  Deleted:      2775
% 15.17/15.54  Deletedinuse: 153
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    131557
% 15.17/15.54  Kept:         37054
% 15.17/15.54  Inuse:        622
% 15.17/15.54  Deleted:      2777
% 15.17/15.54  Deletedinuse: 154
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    139355
% 15.17/15.54  Kept:         39083
% 15.17/15.54  Inuse:        651
% 15.17/15.54  Deleted:      2778
% 15.17/15.54  Deletedinuse: 155
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying clauses:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    149124
% 15.17/15.54  Kept:         41137
% 15.17/15.54  Inuse:        680
% 15.17/15.54  Deleted:      10678
% 15.17/15.54  Deletedinuse: 156
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    159520
% 15.17/15.54  Kept:         43198
% 15.17/15.54  Inuse:        713
% 15.17/15.54  Deleted:      10683
% 15.17/15.54  Deletedinuse: 160
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    166785
% 15.17/15.54  Kept:         45274
% 15.17/15.54  Inuse:        737
% 15.17/15.54  Deleted:      10687
% 15.17/15.54  Deletedinuse: 164
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    179668
% 15.17/15.54  Kept:         47346
% 15.17/15.54  Inuse:        768
% 15.17/15.54  Deleted:      10688
% 15.17/15.54  Deletedinuse: 164
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    193932
% 15.17/15.54  Kept:         49399
% 15.17/15.54  Inuse:        799
% 15.17/15.54  Deleted:      10688
% 15.17/15.54  Deletedinuse: 164
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    210802
% 15.17/15.54  Kept:         51478
% 15.17/15.54  Inuse:        829
% 15.17/15.54  Deleted:      10688
% 15.17/15.54  Deletedinuse: 164
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    227263
% 15.17/15.54  Kept:         53514
% 15.17/15.54  Inuse:        861
% 15.17/15.54  Deleted:      10688
% 15.17/15.54  Deletedinuse: 164
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  Resimplifying inuse:
% 15.17/15.54  Done
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Intermediate Status:
% 15.17/15.54  Generated:    238905
% 15.17/15.54  Kept:         55580
% 15.17/15.54  Inuse:        889
% 15.17/15.54  Deleted:      10688
% 15.17/15.54  Deletedinuse: 164
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  Bliksems!, er is een bewijs:
% 15.17/15.54  % SZS status Unsatisfiable
% 15.17/15.54  % SZS output start Refutation
% 15.17/15.54  
% 15.17/15.54  clause( 0, [ sum( 'additive_identity', X, X ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 2, [ product( X, Y, multiply( X, Y ) ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 3, [ sum( X, Y, add( X, Y ) ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 4, [ sum( 'additive_inverse'( X ), X, 'additive_identity' ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 5, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W ) )
% 15.17/15.54    , sum( X, U, W ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 7, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, W ) )
% 15.17/15.54    , sum( Z, T, W ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 8, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 11, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, 
% 15.17/15.54    T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 15, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 16, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ]
% 15.17/15.54     )
% 15.17/15.54  .
% 15.17/15.54  clause( 17, [ sum( b, 'additive_inverse'( c ), 'bS_Ic' ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 18, [ product( a, b, aPb ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 19, [ product( a, c, aPc ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 20, [ sum( aPb, 'additive_inverse'( aPc ), 'aPb_S_IaPc' ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 21, [ ~( product( a, 'bS_Ic', 'aPb_S_IaPc' ) ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 48, [ sum( 'additive_inverse'( aPc ), aPb, 'aPb_S_IaPc' ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 56, [ ~( sum( X, 'additive_inverse'( aPc ), Y ) ), ~( sum( Y, aPb, 
% 15.17/15.54    Z ) ), sum( X, 'aPb_S_IaPc', Z ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 74, [ ~( sum( X, Y, Z ) ), ~( sum( 'additive_identity', Y, T ) ), 
% 15.17/15.54    sum( 'additive_inverse'( X ), Z, T ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 79, [ ~( sum( X, Y, Z ) ), ~( sum( Y, 'additive_inverse'( Z ), T )
% 15.17/15.54     ), sum( X, T, 'additive_identity' ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 82, [ ~( sum( X, Y, 'additive_identity' ) ), ~( sum( Y, Z, T ) ), 
% 15.17/15.54    sum( X, T, Z ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 86, [ ~( sum( 'additive_identity', X, Y ) ), sum( 
% 15.17/15.54    'additive_inverse'( 'additive_identity' ), Y, Y ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 97, [ sum( 'additive_inverse'( 'additive_identity' ), X, X ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 125, [ ~( sum( 'additive_inverse'( aPc ), X, Y ) ), ~( sum( X, Z, 
% 15.17/15.54    aPb ) ), sum( Y, Z, 'aPb_S_IaPc' ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 133, [ ~( sum( X, Y, Z ) ), ~( sum( T, Z, U ) ), sum( add( T, X ), 
% 15.17/15.54    Y, U ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 136, [ ~( sum( 'additive_inverse'( c ), X, Y ) ), ~( sum( b, Y, Z )
% 15.17/15.54     ), sum( 'bS_Ic', X, Z ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 154, [ ~( sum( X, Y, Y ) ), sum( add( X, X ), Y, Y ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 162, [ sum( add( 'additive_inverse'( 'additive_identity' ), 
% 15.17/15.54    'additive_inverse'( 'additive_identity' ) ), X, X ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 248, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum( X
% 15.17/15.54    , Z, b ) ), sum( Y, T, aPb ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 274, [ sum( X, add( 'additive_inverse'( 'additive_identity' ), 
% 15.17/15.54    'additive_inverse'( 'additive_identity' ) ), X ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 490, [ ~( sum( 'additive_identity', X, Y ) ), =( X, Y ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 545, [ =( add( 'additive_inverse'( 'additive_identity' ), 
% 15.17/15.54    'additive_inverse'( 'additive_identity' ) ), 'additive_identity' ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 593, [ sum( Y, X, Y ), ~( sum( 'additive_identity', 
% 15.17/15.54    'additive_identity', X ) ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 599, [ sum( X, Y, Y ), ~( sum( 'additive_identity', 
% 15.17/15.54    'additive_identity', X ) ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 737, [ ~( product( a, c, X ) ), =( aPc, X ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 4350, [ ~( sum( 'additive_identity', aPb, X ) ), sum( aPc, 
% 15.17/15.54    'aPb_S_IaPc', X ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 4385, [ sum( aPc, 'aPb_S_IaPc', aPb ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 4483, [ sum( 'aPb_S_IaPc', aPc, aPb ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 10228, [ ~( sum( X, 'aPb_S_IaPc', 'additive_identity' ) ), sum( X, 
% 15.17/15.54    aPb, aPc ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 12929, [ sum( 'additive_inverse'( 'aPb_S_IaPc' ), aPb, aPc ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 13022, [ sum( aPb, 'additive_inverse'( 'aPb_S_IaPc' ), aPc ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 13094, [ ~( sum( X, aPb, 'aPb_S_IaPc' ) ), sum( X, aPc, 
% 15.17/15.54    'additive_identity' ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 13239, [ sum( X, aPc, 'additive_identity' ), ~( sum( aPb, X, 
% 15.17/15.54    'aPb_S_IaPc' ) ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 21475, [ ~( sum( aPc, X, aPb ) ), sum( 'additive_identity', X, 
% 15.17/15.54    'aPb_S_IaPc' ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 21728, [ ~( sum( aPc, X, aPb ) ), =( X, 'aPb_S_IaPc' ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 21816, [ =( X, 'aPb_S_IaPc' ), ~( sum( X, aPc, aPb ) ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 22663, [ ~( product( a, 'bS_Ic', X ) ), ~( sum( X, aPc, aPb ) ) ]
% 15.17/15.54     )
% 15.17/15.54  .
% 15.17/15.54  clause( 22750, [ ~( product( a, 'bS_Ic', Y ) ), ~( sum( Y, X, aPb ) ), ~( 
% 15.17/15.54    product( a, c, X ) ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 27388, [ ~( sum( b, 'additive_identity', X ) ), sum( 'bS_Ic', c, X
% 15.17/15.54     ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 27500, [ sum( 'bS_Ic', c, b ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 55615, [ ~( product( a, 'bS_Ic', X ) ), ~( product( a, c, Y ) ) ]
% 15.17/15.54     )
% 15.17/15.54  .
% 15.17/15.54  clause( 55686, [ ~( product( a, c, X ) ) ] )
% 15.17/15.54  .
% 15.17/15.54  clause( 55721, [] )
% 15.17/15.54  .
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  % SZS output end Refutation
% 15.17/15.54  found a proof!
% 15.17/15.54  
% 15.17/15.54  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 15.17/15.54  
% 15.17/15.54  initialclauses(
% 15.17/15.54  [ clause( 55723, [ sum( 'additive_identity', X, X ) ] )
% 15.17/15.54  , clause( 55724, [ sum( X, 'additive_identity', X ) ] )
% 15.17/15.54  , clause( 55725, [ product( X, Y, multiply( X, Y ) ) ] )
% 15.17/15.54  , clause( 55726, [ sum( X, Y, add( X, Y ) ) ] )
% 15.17/15.54  , clause( 55727, [ sum( 'additive_inverse'( X ), X, 'additive_identity' ) ]
% 15.17/15.54     )
% 15.17/15.54  , clause( 55728, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ]
% 15.17/15.54     )
% 15.17/15.54  , clause( 55729, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, 
% 15.17/15.54    W ) ), sum( X, U, W ) ] )
% 15.17/15.54  , clause( 55730, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, 
% 15.17/15.54    W ) ), sum( Z, T, W ) ] )
% 15.17/15.54  , clause( 55731, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 15.17/15.54  , clause( 55732, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( 
% 15.17/15.54    product( Z, T, W ) ), product( X, U, W ) ] )
% 15.17/15.54  , clause( 55733, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( 
% 15.17/15.54    product( X, U, W ) ), product( Z, T, W ) ] )
% 15.17/15.54  , clause( 55734, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( 
% 15.17/15.54    Y, T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 15.17/15.54  , clause( 55735, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( 
% 15.17/15.54    Y, T, W ) ), ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ] )
% 15.17/15.54  , clause( 55736, [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum( 
% 15.17/15.54    X, T, W ) ), ~( product( W, Y, V0 ) ), sum( Z, U, V0 ) ] )
% 15.17/15.54  , clause( 55737, [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum( 
% 15.17/15.54    X, T, W ) ), ~( sum( Z, U, V0 ) ), product( W, Y, V0 ) ] )
% 15.17/15.54  , clause( 55738, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 15.17/15.54  , clause( 55739, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, 
% 15.17/15.54    T ) ] )
% 15.17/15.54  , clause( 55740, [ sum( b, 'additive_inverse'( c ), 'bS_Ic' ) ] )
% 15.17/15.54  , clause( 55741, [ product( a, b, aPb ) ] )
% 15.17/15.54  , clause( 55742, [ product( a, c, aPc ) ] )
% 15.17/15.54  , clause( 55743, [ sum( aPb, 'additive_inverse'( aPc ), 'aPb_S_IaPc' ) ] )
% 15.17/15.54  , clause( 55744, [ ~( product( a, 'bS_Ic', 'aPb_S_IaPc' ) ) ] )
% 15.17/15.54  ] ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 0, [ sum( 'additive_identity', X, X ) ] )
% 15.17/15.54  , clause( 55723, [ sum( 'additive_identity', X, X ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 2, [ product( X, Y, multiply( X, Y ) ) ] )
% 15.17/15.54  , clause( 55725, [ product( X, Y, multiply( X, Y ) ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 15.17/15.54     )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 3, [ sum( X, Y, add( X, Y ) ) ] )
% 15.17/15.54  , clause( 55726, [ sum( X, Y, add( X, Y ) ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 15.17/15.54     )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 4, [ sum( 'additive_inverse'( X ), X, 'additive_identity' ) ] )
% 15.17/15.54  , clause( 55727, [ sum( 'additive_inverse'( X ), X, 'additive_identity' ) ]
% 15.17/15.54     )
% 15.17/15.54  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 5, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ] )
% 15.17/15.54  , clause( 55728, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ]
% 15.17/15.54     )
% 15.17/15.54  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W ) )
% 15.17/15.54    , sum( X, U, W ) ] )
% 15.17/15.54  , clause( 55729, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, 
% 15.17/15.54    W ) ), sum( X, U, W ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 15.17/15.54    , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2
% 15.17/15.54    , 2 ), ==>( 3, 3 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 7, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, W ) )
% 15.17/15.54    , sum( Z, T, W ) ] )
% 15.17/15.54  , clause( 55730, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, 
% 15.17/15.54    W ) ), sum( Z, T, W ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 15.17/15.54    , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2
% 15.17/15.54    , 2 ), ==>( 3, 3 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 8, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 15.17/15.54  , clause( 55731, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 15.17/15.54    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 11, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, 
% 15.17/15.54    T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 15.17/15.54  , clause( 55734, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( 
% 15.17/15.54    Y, T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 15.17/15.54    , U ), :=( W, W ), :=( V0, V0 )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1
% 15.17/15.54    , 1 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 4 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 15, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 15.17/15.54  , clause( 55738, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 15.17/15.54    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 16, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ]
% 15.17/15.54     )
% 15.17/15.54  , clause( 55739, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, 
% 15.17/15.54    T ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 15.17/15.54    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 17, [ sum( b, 'additive_inverse'( c ), 'bS_Ic' ) ] )
% 15.17/15.54  , clause( 55740, [ sum( b, 'additive_inverse'( c ), 'bS_Ic' ) ] )
% 15.17/15.54  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 18, [ product( a, b, aPb ) ] )
% 15.17/15.54  , clause( 55741, [ product( a, b, aPb ) ] )
% 15.17/15.54  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 19, [ product( a, c, aPc ) ] )
% 15.17/15.54  , clause( 55742, [ product( a, c, aPc ) ] )
% 15.17/15.54  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 20, [ sum( aPb, 'additive_inverse'( aPc ), 'aPb_S_IaPc' ) ] )
% 15.17/15.54  , clause( 55743, [ sum( aPb, 'additive_inverse'( aPc ), 'aPb_S_IaPc' ) ] )
% 15.17/15.54  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 21, [ ~( product( a, 'bS_Ic', 'aPb_S_IaPc' ) ) ] )
% 15.17/15.54  , clause( 55744, [ ~( product( a, 'bS_Ic', 'aPb_S_IaPc' ) ) ] )
% 15.17/15.54  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  resolution(
% 15.17/15.54  clause( 56008, [ sum( 'additive_inverse'( aPc ), aPb, 'aPb_S_IaPc' ) ] )
% 15.17/15.54  , clause( 8, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 15.17/15.54  , 0, clause( 20, [ sum( aPb, 'additive_inverse'( aPc ), 'aPb_S_IaPc' ) ] )
% 15.17/15.54  , 0, substitution( 0, [ :=( X, aPb ), :=( Y, 'additive_inverse'( aPc ) ), 
% 15.17/15.54    :=( Z, 'aPb_S_IaPc' )] ), substitution( 1, [] )).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 48, [ sum( 'additive_inverse'( aPc ), aPb, 'aPb_S_IaPc' ) ] )
% 15.17/15.54  , clause( 56008, [ sum( 'additive_inverse'( aPc ), aPb, 'aPb_S_IaPc' ) ] )
% 15.17/15.54  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  resolution(
% 15.17/15.54  clause( 56010, [ ~( sum( X, 'additive_inverse'( aPc ), Y ) ), ~( sum( Y, 
% 15.17/15.54    aPb, Z ) ), sum( X, 'aPb_S_IaPc', Z ) ] )
% 15.17/15.54  , clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W )
% 15.17/15.54     ), sum( X, U, W ) ] )
% 15.17/15.54  , 1, clause( 48, [ sum( 'additive_inverse'( aPc ), aPb, 'aPb_S_IaPc' ) ] )
% 15.17/15.54  , 0, substitution( 0, [ :=( X, X ), :=( Y, 'additive_inverse'( aPc ) ), 
% 15.17/15.54    :=( Z, Y ), :=( T, aPb ), :=( U, 'aPb_S_IaPc' ), :=( W, Z )] ), 
% 15.17/15.54    substitution( 1, [] )).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 56, [ ~( sum( X, 'additive_inverse'( aPc ), Y ) ), ~( sum( Y, aPb, 
% 15.17/15.54    Z ) ), sum( X, 'aPb_S_IaPc', Z ) ] )
% 15.17/15.54  , clause( 56010, [ ~( sum( X, 'additive_inverse'( aPc ), Y ) ), ~( sum( Y, 
% 15.17/15.54    aPb, Z ) ), sum( X, 'aPb_S_IaPc', Z ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 15.17/15.54    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  resolution(
% 15.17/15.54  clause( 56013, [ ~( sum( X, Y, Z ) ), ~( sum( 'additive_identity', Y, T ) )
% 15.17/15.54    , sum( 'additive_inverse'( X ), Z, T ) ] )
% 15.17/15.54  , clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W )
% 15.17/15.54     ), sum( X, U, W ) ] )
% 15.17/15.54  , 0, clause( 4, [ sum( 'additive_inverse'( X ), X, 'additive_identity' ) ]
% 15.17/15.54     )
% 15.17/15.54  , 0, substitution( 0, [ :=( X, 'additive_inverse'( X ) ), :=( Y, X ), :=( Z
% 15.17/15.54    , 'additive_identity' ), :=( T, Y ), :=( U, Z ), :=( W, T )] ), 
% 15.17/15.54    substitution( 1, [ :=( X, X )] )).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 74, [ ~( sum( X, Y, Z ) ), ~( sum( 'additive_identity', Y, T ) ), 
% 15.17/15.54    sum( 'additive_inverse'( X ), Z, T ) ] )
% 15.17/15.54  , clause( 56013, [ ~( sum( X, Y, Z ) ), ~( sum( 'additive_identity', Y, T )
% 15.17/15.54     ), sum( 'additive_inverse'( X ), Z, T ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 15.17/15.54    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  resolution(
% 15.17/15.54  clause( 56020, [ ~( sum( X, Y, Z ) ), ~( sum( Y, 'additive_inverse'( Z ), T
% 15.17/15.54     ) ), sum( X, T, 'additive_identity' ) ] )
% 15.17/15.54  , clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W )
% 15.17/15.54     ), sum( X, U, W ) ] )
% 15.17/15.54  , 2, clause( 5, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ]
% 15.17/15.54     )
% 15.17/15.54  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, 
% 15.17/15.54    'additive_inverse'( Z ) ), :=( U, T ), :=( W, 'additive_identity' )] ), 
% 15.17/15.54    substitution( 1, [ :=( X, Z )] )).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 79, [ ~( sum( X, Y, Z ) ), ~( sum( Y, 'additive_inverse'( Z ), T )
% 15.17/15.54     ), sum( X, T, 'additive_identity' ) ] )
% 15.17/15.54  , clause( 56020, [ ~( sum( X, Y, Z ) ), ~( sum( Y, 'additive_inverse'( Z )
% 15.17/15.54    , T ) ), sum( X, T, 'additive_identity' ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 15.17/15.54    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  resolution(
% 15.17/15.54  clause( 56024, [ ~( sum( X, Y, 'additive_identity' ) ), ~( sum( Y, Z, T ) )
% 15.17/15.54    , sum( X, T, Z ) ] )
% 15.17/15.54  , clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W )
% 15.17/15.54     ), sum( X, U, W ) ] )
% 15.17/15.54  , 2, clause( 0, [ sum( 'additive_identity', X, X ) ] )
% 15.17/15.54  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, 'additive_identity'
% 15.17/15.54     ), :=( T, Z ), :=( U, T ), :=( W, Z )] ), substitution( 1, [ :=( X, Z )] )
% 15.17/15.54    ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 82, [ ~( sum( X, Y, 'additive_identity' ) ), ~( sum( Y, Z, T ) ), 
% 15.17/15.54    sum( X, T, Z ) ] )
% 15.17/15.54  , clause( 56024, [ ~( sum( X, Y, 'additive_identity' ) ), ~( sum( Y, Z, T )
% 15.17/15.54     ), sum( X, T, Z ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 15.17/15.54    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  factor(
% 15.17/15.54  clause( 56028, [ ~( sum( 'additive_identity', X, Y ) ), sum( 
% 15.17/15.54    'additive_inverse'( 'additive_identity' ), Y, Y ) ] )
% 15.17/15.54  , clause( 74, [ ~( sum( X, Y, Z ) ), ~( sum( 'additive_identity', Y, T ) )
% 15.17/15.54    , sum( 'additive_inverse'( X ), Z, T ) ] )
% 15.17/15.54  , 0, 1, substitution( 0, [ :=( X, 'additive_identity' ), :=( Y, X ), :=( Z
% 15.17/15.54    , Y ), :=( T, Y )] )).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 86, [ ~( sum( 'additive_identity', X, Y ) ), sum( 
% 15.17/15.54    'additive_inverse'( 'additive_identity' ), Y, Y ) ] )
% 15.17/15.54  , clause( 56028, [ ~( sum( 'additive_identity', X, Y ) ), sum( 
% 15.17/15.54    'additive_inverse'( 'additive_identity' ), Y, Y ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 15.17/15.54     ), ==>( 1, 1 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  resolution(
% 15.17/15.54  clause( 56029, [ sum( 'additive_inverse'( 'additive_identity' ), X, X ) ]
% 15.17/15.54     )
% 15.17/15.54  , clause( 86, [ ~( sum( 'additive_identity', X, Y ) ), sum( 
% 15.17/15.54    'additive_inverse'( 'additive_identity' ), Y, Y ) ] )
% 15.17/15.54  , 0, clause( 0, [ sum( 'additive_identity', X, X ) ] )
% 15.17/15.54  , 0, substitution( 0, [ :=( X, X ), :=( Y, X )] ), substitution( 1, [ :=( X
% 15.17/15.54    , X )] )).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 97, [ sum( 'additive_inverse'( 'additive_identity' ), X, X ) ] )
% 15.17/15.54  , clause( 56029, [ sum( 'additive_inverse'( 'additive_identity' ), X, X ) ]
% 15.17/15.54     )
% 15.17/15.54  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  resolution(
% 15.17/15.54  clause( 56032, [ ~( sum( 'additive_inverse'( aPc ), X, Y ) ), ~( sum( X, Z
% 15.17/15.54    , aPb ) ), sum( Y, Z, 'aPb_S_IaPc' ) ] )
% 15.17/15.54  , clause( 7, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, W )
% 15.17/15.54     ), sum( Z, T, W ) ] )
% 15.17/15.54  , 2, clause( 48, [ sum( 'additive_inverse'( aPc ), aPb, 'aPb_S_IaPc' ) ] )
% 15.17/15.54  , 0, substitution( 0, [ :=( X, 'additive_inverse'( aPc ) ), :=( Y, X ), 
% 15.17/15.54    :=( Z, Y ), :=( T, Z ), :=( U, aPb ), :=( W, 'aPb_S_IaPc' )] ), 
% 15.17/15.54    substitution( 1, [] )).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 125, [ ~( sum( 'additive_inverse'( aPc ), X, Y ) ), ~( sum( X, Z, 
% 15.17/15.54    aPb ) ), sum( Y, Z, 'aPb_S_IaPc' ) ] )
% 15.17/15.54  , clause( 56032, [ ~( sum( 'additive_inverse'( aPc ), X, Y ) ), ~( sum( X, 
% 15.17/15.54    Z, aPb ) ), sum( Y, Z, 'aPb_S_IaPc' ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 15.17/15.54    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  resolution(
% 15.17/15.54  clause( 56034, [ ~( sum( Y, Z, T ) ), ~( sum( X, T, U ) ), sum( add( X, Y )
% 15.17/15.54    , Z, U ) ] )
% 15.17/15.54  , clause( 7, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, W )
% 15.17/15.54     ), sum( Z, T, W ) ] )
% 15.17/15.54  , 0, clause( 3, [ sum( X, Y, add( X, Y ) ) ] )
% 15.17/15.54  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, add( X, Y ) ), :=( T
% 15.17/15.54    , Z ), :=( U, T ), :=( W, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y
% 15.17/15.54     )] )).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 133, [ ~( sum( X, Y, Z ) ), ~( sum( T, Z, U ) ), sum( add( T, X ), 
% 15.17/15.54    Y, U ) ] )
% 15.17/15.54  , clause( 56034, [ ~( sum( Y, Z, T ) ), ~( sum( X, T, U ) ), sum( add( X, Y
% 15.17/15.54     ), Z, U ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z ), :=( U
% 15.17/15.54    , U )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] )
% 15.17/15.54     ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  resolution(
% 15.17/15.54  clause( 56039, [ ~( sum( 'additive_inverse'( c ), X, Y ) ), ~( sum( b, Y, Z
% 15.17/15.54     ) ), sum( 'bS_Ic', X, Z ) ] )
% 15.17/15.54  , clause( 7, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, W )
% 15.17/15.54     ), sum( Z, T, W ) ] )
% 15.17/15.54  , 0, clause( 17, [ sum( b, 'additive_inverse'( c ), 'bS_Ic' ) ] )
% 15.17/15.54  , 0, substitution( 0, [ :=( X, b ), :=( Y, 'additive_inverse'( c ) ), :=( Z
% 15.17/15.54    , 'bS_Ic' ), :=( T, X ), :=( U, Y ), :=( W, Z )] ), substitution( 1, [] )
% 15.17/15.54    ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 136, [ ~( sum( 'additive_inverse'( c ), X, Y ) ), ~( sum( b, Y, Z )
% 15.17/15.54     ), sum( 'bS_Ic', X, Z ) ] )
% 15.17/15.54  , clause( 56039, [ ~( sum( 'additive_inverse'( c ), X, Y ) ), ~( sum( b, Y
% 15.17/15.54    , Z ) ), sum( 'bS_Ic', X, Z ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 15.17/15.54    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  factor(
% 15.17/15.54  clause( 56043, [ ~( sum( X, Y, Y ) ), sum( add( X, X ), Y, Y ) ] )
% 15.17/15.54  , clause( 133, [ ~( sum( X, Y, Z ) ), ~( sum( T, Z, U ) ), sum( add( T, X )
% 15.17/15.54    , Y, U ) ] )
% 15.17/15.54  , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y ), :=( T, X ), 
% 15.17/15.54    :=( U, Y )] )).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 154, [ ~( sum( X, Y, Y ) ), sum( add( X, X ), Y, Y ) ] )
% 15.17/15.54  , clause( 56043, [ ~( sum( X, Y, Y ) ), sum( add( X, X ), Y, Y ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 15.17/15.54     ), ==>( 1, 1 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  resolution(
% 15.17/15.54  clause( 56044, [ sum( add( 'additive_inverse'( 'additive_identity' ), 
% 15.17/15.54    'additive_inverse'( 'additive_identity' ) ), X, X ) ] )
% 15.17/15.54  , clause( 154, [ ~( sum( X, Y, Y ) ), sum( add( X, X ), Y, Y ) ] )
% 15.17/15.54  , 0, clause( 97, [ sum( 'additive_inverse'( 'additive_identity' ), X, X ) ]
% 15.17/15.54     )
% 15.17/15.54  , 0, substitution( 0, [ :=( X, 'additive_inverse'( 'additive_identity' ) )
% 15.17/15.54    , :=( Y, X )] ), substitution( 1, [ :=( X, X )] )).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 162, [ sum( add( 'additive_inverse'( 'additive_identity' ), 
% 15.17/15.54    'additive_inverse'( 'additive_identity' ) ), X, X ) ] )
% 15.17/15.54  , clause( 56044, [ sum( add( 'additive_inverse'( 'additive_identity' ), 
% 15.17/15.54    'additive_inverse'( 'additive_identity' ) ), X, X ) ] )
% 15.17/15.54  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  resolution(
% 15.17/15.54  clause( 56047, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum( 
% 15.17/15.54    X, Z, b ) ), sum( Y, T, aPb ) ] )
% 15.17/15.54  , clause( 11, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y
% 15.17/15.54    , T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 15.17/15.54  , 3, clause( 18, [ product( a, b, aPb ) ] )
% 15.17/15.54  , 0, substitution( 0, [ :=( X, a ), :=( Y, X ), :=( Z, Y ), :=( T, Z ), 
% 15.17/15.54    :=( U, T ), :=( W, b ), :=( V0, aPb )] ), substitution( 1, [] )).
% 15.17/15.54  
% 15.17/15.54  
% 15.17/15.54  subsumption(
% 15.17/15.54  clause( 248, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum( X
% 15.17/15.54    , Z, b ) ), sum( Y, T, aPb ) ] )
% 15.17/15.54  , clause( 56047, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum( 
% 15.17/15.54    X, Z, b ) ), sum( Y, T, aPb ) ] )
% 15.17/15.54  , substitCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------