TSTP Solution File: RNG001-1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : RNG001-1 : 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 20:16:02 EDT 2022

% Result   : Unsatisfiable 0.75s 1.16s
% Output   : Refutation 0.75s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : RNG001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : bliksem %s
% 0.12/0.33  % Computer : n019.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % DateTime : Mon May 30 16:05:10 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.75/1.16  *** allocated 10000 integers for termspace/termends
% 0.75/1.16  *** allocated 10000 integers for clauses
% 0.75/1.16  *** allocated 10000 integers for justifications
% 0.75/1.16  Bliksem 1.12
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  Automatic Strategy Selection
% 0.75/1.16  
% 0.75/1.16  Clauses:
% 0.75/1.16  [
% 0.75/1.16     [ sum( 'additive_identity', X, X ) ],
% 0.75/1.16     [ sum( X, 'additive_identity', X ) ],
% 0.75/1.16     [ product( X, Y, multiply( X, Y ) ) ],
% 0.75/1.16     [ sum( X, Y, add( X, Y ) ) ],
% 0.75/1.16     [ sum( 'additive_inverse'( X ), X, 'additive_identity' ) ],
% 0.75/1.16     [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ],
% 0.75/1.16     [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W ) ), sum( X
% 0.75/1.16    , U, W ) ],
% 0.75/1.16     [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, W ) ), sum( Z
% 0.75/1.16    , T, W ) ],
% 0.75/1.16     [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ],
% 0.75/1.16     [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product( Z, T, W
% 0.75/1.16     ) ), product( X, U, W ) ],
% 0.75/1.16     [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product( X, U, W
% 0.75/1.16     ) ), product( Z, T, W ) ],
% 0.75/1.16     [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, T, W ) )
% 0.75/1.16    , ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ],
% 0.75/1.16     [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, T, W ) )
% 0.75/1.16    , ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ],
% 0.75/1.16     [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum( X, T, W ) )
% 0.75/1.16    , ~( product( W, Y, V0 ) ), sum( Z, U, V0 ) ],
% 0.75/1.16     [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum( X, T, W ) )
% 0.75/1.16    , ~( sum( Z, U, V0 ) ), product( W, Y, V0 ) ],
% 0.75/1.16     [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ],
% 0.75/1.16     [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ],
% 0.75/1.16     [ ~( product( a, 'additive_identity', 'additive_identity' ) ) ]
% 0.75/1.16  ] .
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  percentage equality = 0.039216, percentage horn = 1.000000
% 0.75/1.16  This is a problem with some equality
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  Options Used:
% 0.75/1.16  
% 0.75/1.16  useres =            1
% 0.75/1.16  useparamod =        1
% 0.75/1.16  useeqrefl =         1
% 0.75/1.16  useeqfact =         1
% 0.75/1.16  usefactor =         1
% 0.75/1.16  usesimpsplitting =  0
% 0.75/1.16  usesimpdemod =      5
% 0.75/1.16  usesimpres =        3
% 0.75/1.16  
% 0.75/1.16  resimpinuse      =  1000
% 0.75/1.16  resimpclauses =     20000
% 0.75/1.16  substype =          eqrewr
% 0.75/1.16  backwardsubs =      1
% 0.75/1.16  selectoldest =      5
% 0.75/1.16  
% 0.75/1.16  litorderings [0] =  split
% 0.75/1.16  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.75/1.16  
% 0.75/1.16  termordering =      kbo
% 0.75/1.16  
% 0.75/1.16  litapriori =        0
% 0.75/1.16  termapriori =       1
% 0.75/1.16  litaposteriori =    0
% 0.75/1.16  termaposteriori =   0
% 0.75/1.16  demodaposteriori =  0
% 0.75/1.16  ordereqreflfact =   0
% 0.75/1.16  
% 0.75/1.16  litselect =         negord
% 0.75/1.16  
% 0.75/1.16  maxweight =         15
% 0.75/1.16  maxdepth =          30000
% 0.75/1.16  maxlength =         115
% 0.75/1.16  maxnrvars =         195
% 0.75/1.16  excuselevel =       1
% 0.75/1.16  increasemaxweight = 1
% 0.75/1.16  
% 0.75/1.16  maxselected =       10000000
% 0.75/1.16  maxnrclauses =      10000000
% 0.75/1.16  
% 0.75/1.16  showgenerated =    0
% 0.75/1.16  showkept =         0
% 0.75/1.16  showselected =     0
% 0.75/1.16  showdeleted =      0
% 0.75/1.16  showresimp =       1
% 0.75/1.16  showstatus =       2000
% 0.75/1.16  
% 0.75/1.16  prologoutput =     1
% 0.75/1.16  nrgoals =          5000000
% 0.75/1.16  totalproof =       1
% 0.75/1.16  
% 0.75/1.16  Symbols occurring in the translation:
% 0.75/1.16  
% 0.75/1.16  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.75/1.16  .  [1, 2]      (w:1, o:27, a:1, s:1, b:0), 
% 0.75/1.16  !  [4, 1]      (w:0, o:21, a:1, s:1, b:0), 
% 0.75/1.16  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.75/1.16  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.75/1.16  'additive_identity'  [39, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 0.75/1.16  sum  [41, 3]      (w:1, o:54, a:1, s:1, b:0), 
% 0.75/1.16  multiply  [43, 2]      (w:1, o:52, a:1, s:1, b:0), 
% 0.75/1.16  product  [44, 3]      (w:1, o:55, a:1, s:1, b:0), 
% 0.75/1.16  add  [45, 2]      (w:1, o:53, a:1, s:1, b:0), 
% 0.75/1.16  'additive_inverse'  [46, 1]      (w:1, o:26, a:1, s:1, b:0), 
% 0.75/1.16  a  [55, 0]      (w:1, o:20, a:1, s:1, b:0).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  Starting Search:
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  Bliksems!, er is een bewijs:
% 0.75/1.16  % SZS status Unsatisfiable
% 0.75/1.16  % SZS output start Refutation
% 0.75/1.16  
% 0.75/1.16  clause( 0, [ sum( 'additive_identity', X, X ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 1, [ sum( X, 'additive_identity', X ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 2, [ product( X, Y, multiply( X, Y ) ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 5, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W ) )
% 0.75/1.16    , sum( X, U, W ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 11, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, 
% 0.75/1.16    T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 12, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, 
% 0.75/1.16    T, W ) ), ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 15, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 17, [ ~( product( a, 'additive_identity', 'additive_identity' ) ) ]
% 0.75/1.16     )
% 0.75/1.16  .
% 0.75/1.16  clause( 19, [ ~( sum( X, Y, Y ) ), ~( sum( Y, Z, T ) ), sum( X, T, T ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 228, [ ~( product( X, Y, Z ) ), ~( product( X, 'additive_identity'
% 0.75/1.16    , T ) ), ~( product( X, Y, U ) ), sum( Z, T, U ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 231, [ ~( product( X, 'additive_identity', Y ) ), ~( product( X, 
% 0.75/1.16    'additive_identity', Z ) ), sum( Y, Z, Z ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 232, [ ~( product( X, 'additive_identity', Y ) ), sum( Y, Y, Y ) ]
% 0.75/1.16     )
% 0.75/1.16  .
% 0.75/1.16  clause( 240, [ sum( multiply( X, 'additive_identity' ), multiply( X, 
% 0.75/1.16    'additive_identity' ), multiply( X, 'additive_identity' ) ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 281, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum( X
% 0.75/1.16    , Z, 'additive_identity' ) ), ~( sum( Y, T, 'additive_identity' ) ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 289, [ ~( product( a, X, X ) ), ~( product( a, Y, Y ) ), ~( sum( X
% 0.75/1.16    , Y, 'additive_identity' ) ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 290, [ ~( product( a, X, X ) ), ~( sum( X, X, 'additive_identity' )
% 0.75/1.16     ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 466, [ ~( sum( X, 'additive_identity', Y ) ), =( X, Y ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 716, [ ~( sum( X, Y, Y ) ), sum( X, 'additive_identity', 
% 0.75/1.16    'additive_identity' ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 726, [ sum( multiply( X, 'additive_identity' ), 'additive_identity'
% 0.75/1.16    , 'additive_identity' ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 806, [ =( multiply( X, 'additive_identity' ), 'additive_identity' )
% 0.75/1.16     ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 824, [ product( X, 'additive_identity', 'additive_identity' ) ] )
% 0.75/1.16  .
% 0.75/1.16  clause( 825, [] )
% 0.75/1.16  .
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  % SZS output end Refutation
% 0.75/1.16  found a proof!
% 0.75/1.16  
% 0.75/1.16  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.75/1.16  
% 0.75/1.16  initialclauses(
% 0.75/1.16  [ clause( 827, [ sum( 'additive_identity', X, X ) ] )
% 0.75/1.16  , clause( 828, [ sum( X, 'additive_identity', X ) ] )
% 0.75/1.16  , clause( 829, [ product( X, Y, multiply( X, Y ) ) ] )
% 0.75/1.16  , clause( 830, [ sum( X, Y, add( X, Y ) ) ] )
% 0.75/1.16  , clause( 831, [ sum( 'additive_inverse'( X ), X, 'additive_identity' ) ]
% 0.75/1.16     )
% 0.75/1.16  , clause( 832, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ]
% 0.75/1.16     )
% 0.75/1.16  , clause( 833, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W
% 0.75/1.16     ) ), sum( X, U, W ) ] )
% 0.75/1.16  , clause( 834, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, W
% 0.75/1.16     ) ), sum( Z, T, W ) ] )
% 0.75/1.16  , clause( 835, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 0.75/1.16  , clause( 836, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( 
% 0.75/1.16    product( Z, T, W ) ), product( X, U, W ) ] )
% 0.75/1.16  , clause( 837, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( 
% 0.75/1.16    product( X, U, W ) ), product( Z, T, W ) ] )
% 0.75/1.16  , clause( 838, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( 
% 0.75/1.16    Y, T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 0.75/1.16  , clause( 839, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( 
% 0.75/1.16    Y, T, W ) ), ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ] )
% 0.75/1.16  , clause( 840, [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum( 
% 0.75/1.16    X, T, W ) ), ~( product( W, Y, V0 ) ), sum( Z, U, V0 ) ] )
% 0.75/1.16  , clause( 841, [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum( 
% 0.75/1.16    X, T, W ) ), ~( sum( Z, U, V0 ) ), product( W, Y, V0 ) ] )
% 0.75/1.16  , clause( 842, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 0.75/1.16  , clause( 843, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T
% 0.75/1.16     ) ] )
% 0.75/1.16  , clause( 844, [ ~( product( a, 'additive_identity', 'additive_identity' )
% 0.75/1.16     ) ] )
% 0.75/1.16  ] ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 0, [ sum( 'additive_identity', X, X ) ] )
% 0.75/1.16  , clause( 827, [ sum( 'additive_identity', X, X ) ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 1, [ sum( X, 'additive_identity', X ) ] )
% 0.75/1.16  , clause( 828, [ sum( X, 'additive_identity', X ) ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 2, [ product( X, Y, multiply( X, Y ) ) ] )
% 0.75/1.16  , clause( 829, [ product( X, Y, multiply( X, Y ) ) ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.75/1.16     )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 5, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ] )
% 0.75/1.16  , clause( 832, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ]
% 0.75/1.16     )
% 0.75/1.16  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W ) )
% 0.75/1.16    , sum( X, U, W ) ] )
% 0.75/1.16  , clause( 833, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W
% 0.75/1.16     ) ), sum( X, U, W ) ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.75/1.16    , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2
% 0.75/1.16    , 2 ), ==>( 3, 3 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 11, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, 
% 0.75/1.16    T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 0.75/1.16  , clause( 838, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( 
% 0.75/1.16    Y, T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.75/1.16    , U ), :=( W, W ), :=( V0, V0 )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1
% 0.75/1.16    , 1 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 4 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 12, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, 
% 0.75/1.16    T, W ) ), ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ] )
% 0.75/1.16  , clause( 839, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( 
% 0.75/1.16    Y, T, W ) ), ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.75/1.16    , U ), :=( W, W ), :=( V0, V0 )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1
% 0.75/1.16    , 1 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 4 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 15, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 0.75/1.16  , clause( 842, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 0.75/1.16    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 17, [ ~( product( a, 'additive_identity', 'additive_identity' ) ) ]
% 0.75/1.16     )
% 0.75/1.16  , clause( 844, [ ~( product( a, 'additive_identity', 'additive_identity' )
% 0.75/1.16     ) ] )
% 0.75/1.16  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  factor(
% 0.75/1.16  clause( 957, [ ~( sum( X, Y, Y ) ), ~( sum( Y, Z, T ) ), sum( X, T, T ) ]
% 0.75/1.16     )
% 0.75/1.16  , clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W )
% 0.75/1.16     ), sum( X, U, W ) ] )
% 0.75/1.16  , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y ), :=( T, Z ), 
% 0.75/1.16    :=( U, T ), :=( W, T )] )).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 19, [ ~( sum( X, Y, Y ) ), ~( sum( Y, Z, T ) ), sum( X, T, T ) ] )
% 0.75/1.16  , clause( 957, [ ~( sum( X, Y, Y ) ), ~( sum( Y, Z, T ) ), sum( X, T, T ) ]
% 0.75/1.16     )
% 0.75/1.16  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 0.75/1.16    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  resolution(
% 0.75/1.16  clause( 959, [ ~( product( X, Y, Z ) ), ~( product( X, 'additive_identity'
% 0.75/1.16    , T ) ), ~( product( X, Y, U ) ), sum( Z, T, U ) ] )
% 0.75/1.16  , clause( 11, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y
% 0.75/1.16    , T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 0.75/1.16  , 2, clause( 1, [ sum( X, 'additive_identity', X ) ] )
% 0.75/1.16  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, 
% 0.75/1.16    'additive_identity' ), :=( U, T ), :=( W, Y ), :=( V0, U )] ), 
% 0.75/1.16    substitution( 1, [ :=( X, Y )] )).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 228, [ ~( product( X, Y, Z ) ), ~( product( X, 'additive_identity'
% 0.75/1.16    , T ) ), ~( product( X, Y, U ) ), sum( Z, T, U ) ] )
% 0.75/1.16  , clause( 959, [ ~( product( X, Y, Z ) ), ~( product( X, 
% 0.75/1.16    'additive_identity', T ) ), ~( product( X, Y, U ) ), sum( Z, T, U ) ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.75/1.16    , U )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3
% 0.75/1.16    , 3 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  factor(
% 0.75/1.16  clause( 966, [ ~( product( X, 'additive_identity', Y ) ), ~( product( X, 
% 0.75/1.16    'additive_identity', Z ) ), sum( Y, Z, Z ) ] )
% 0.75/1.16  , clause( 228, [ ~( product( X, Y, Z ) ), ~( product( X, 
% 0.75/1.16    'additive_identity', T ) ), ~( product( X, Y, U ) ), sum( Z, T, U ) ] )
% 0.75/1.16  , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, 'additive_identity' ), :=( Z
% 0.75/1.16    , Y ), :=( T, Z ), :=( U, Z )] )).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 231, [ ~( product( X, 'additive_identity', Y ) ), ~( product( X, 
% 0.75/1.16    'additive_identity', Z ) ), sum( Y, Z, Z ) ] )
% 0.75/1.16  , clause( 966, [ ~( product( X, 'additive_identity', Y ) ), ~( product( X, 
% 0.75/1.16    'additive_identity', Z ) ), sum( Y, Z, Z ) ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 0.75/1.16    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  factor(
% 0.75/1.16  clause( 968, [ ~( product( X, 'additive_identity', Y ) ), sum( Y, Y, Y ) ]
% 0.75/1.16     )
% 0.75/1.16  , clause( 231, [ ~( product( X, 'additive_identity', Y ) ), ~( product( X, 
% 0.75/1.16    'additive_identity', Z ) ), sum( Y, Z, Z ) ] )
% 0.75/1.16  , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y )] )).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 232, [ ~( product( X, 'additive_identity', Y ) ), sum( Y, Y, Y ) ]
% 0.75/1.16     )
% 0.75/1.16  , clause( 968, [ ~( product( X, 'additive_identity', Y ) ), sum( Y, Y, Y )
% 0.75/1.16     ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.75/1.16     ), ==>( 1, 1 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  resolution(
% 0.75/1.16  clause( 969, [ sum( multiply( X, 'additive_identity' ), multiply( X, 
% 0.75/1.16    'additive_identity' ), multiply( X, 'additive_identity' ) ) ] )
% 0.75/1.16  , clause( 232, [ ~( product( X, 'additive_identity', Y ) ), sum( Y, Y, Y )
% 0.75/1.16     ] )
% 0.75/1.16  , 0, clause( 2, [ product( X, Y, multiply( X, Y ) ) ] )
% 0.75/1.16  , 0, substitution( 0, [ :=( X, X ), :=( Y, multiply( X, 'additive_identity'
% 0.75/1.16     ) )] ), substitution( 1, [ :=( X, X ), :=( Y, 'additive_identity' )] )
% 0.75/1.16    ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 240, [ sum( multiply( X, 'additive_identity' ), multiply( X, 
% 0.75/1.16    'additive_identity' ), multiply( X, 'additive_identity' ) ) ] )
% 0.75/1.16  , clause( 969, [ sum( multiply( X, 'additive_identity' ), multiply( X, 
% 0.75/1.16    'additive_identity' ), multiply( X, 'additive_identity' ) ) ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  resolution(
% 0.75/1.16  clause( 970, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum( X
% 0.75/1.16    , Z, 'additive_identity' ) ), ~( sum( Y, T, 'additive_identity' ) ) ] )
% 0.75/1.16  , clause( 17, [ ~( product( a, 'additive_identity', 'additive_identity' ) )
% 0.75/1.16     ] )
% 0.75/1.16  , 0, clause( 12, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( 
% 0.75/1.16    Y, T, W ) ), ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ] )
% 0.75/1.16  , 4, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, X ), :=( 
% 0.75/1.16    Z, Y ), :=( T, Z ), :=( U, T ), :=( W, 'additive_identity' ), :=( V0, 
% 0.75/1.16    'additive_identity' )] )).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 281, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum( X
% 0.75/1.16    , Z, 'additive_identity' ) ), ~( sum( Y, T, 'additive_identity' ) ) ] )
% 0.75/1.16  , clause( 970, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum( 
% 0.75/1.16    X, Z, 'additive_identity' ) ), ~( sum( Y, T, 'additive_identity' ) ) ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 0.75/1.16    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 )] )
% 0.75/1.16     ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  factor(
% 0.75/1.16  clause( 975, [ ~( product( a, X, X ) ), ~( product( a, Y, Y ) ), ~( sum( X
% 0.75/1.16    , Y, 'additive_identity' ) ) ] )
% 0.75/1.16  , clause( 281, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum( 
% 0.75/1.16    X, Z, 'additive_identity' ) ), ~( sum( Y, T, 'additive_identity' ) ) ] )
% 0.75/1.16  , 2, 3, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, Y ), :=( T, Y )] )
% 0.75/1.16    ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 289, [ ~( product( a, X, X ) ), ~( product( a, Y, Y ) ), ~( sum( X
% 0.75/1.16    , Y, 'additive_identity' ) ) ] )
% 0.75/1.16  , clause( 975, [ ~( product( a, X, X ) ), ~( product( a, Y, Y ) ), ~( sum( 
% 0.75/1.16    X, Y, 'additive_identity' ) ) ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.75/1.16     ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  factor(
% 0.75/1.16  clause( 977, [ ~( product( a, X, X ) ), ~( sum( X, X, 'additive_identity' )
% 0.75/1.16     ) ] )
% 0.75/1.16  , clause( 289, [ ~( product( a, X, X ) ), ~( product( a, Y, Y ) ), ~( sum( 
% 0.75/1.16    X, Y, 'additive_identity' ) ) ] )
% 0.75/1.16  , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, X )] )).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 290, [ ~( product( a, X, X ) ), ~( sum( X, X, 'additive_identity' )
% 0.75/1.16     ) ] )
% 0.75/1.16  , clause( 977, [ ~( product( a, X, X ) ), ~( sum( X, X, 'additive_identity'
% 0.75/1.16     ) ) ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 
% 0.75/1.16    1 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  resolution(
% 0.75/1.16  clause( 978, [ ~( sum( X, 'additive_identity', Y ) ), =( X, Y ) ] )
% 0.75/1.16  , clause( 15, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 0.75/1.16  , 0, clause( 1, [ sum( X, 'additive_identity', X ) ] )
% 0.75/1.16  , 0, substitution( 0, [ :=( X, X ), :=( Y, 'additive_identity' ), :=( Z, X
% 0.75/1.16     ), :=( T, Y )] ), substitution( 1, [ :=( X, X )] )).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 466, [ ~( sum( X, 'additive_identity', Y ) ), =( X, Y ) ] )
% 0.75/1.16  , clause( 978, [ ~( sum( X, 'additive_identity', Y ) ), =( X, Y ) ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.75/1.16     ), ==>( 1, 1 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  resolution(
% 0.75/1.16  clause( 980, [ ~( sum( X, Y, Y ) ), sum( X, 'additive_identity', 
% 0.75/1.16    'additive_identity' ) ] )
% 0.75/1.16  , clause( 19, [ ~( sum( X, Y, Y ) ), ~( sum( Y, Z, T ) ), sum( X, T, T ) ]
% 0.75/1.16     )
% 0.75/1.16  , 1, clause( 5, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ]
% 0.75/1.16     )
% 0.75/1.16  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, 'additive_inverse'( 
% 0.75/1.16    Y ) ), :=( T, 'additive_identity' )] ), substitution( 1, [ :=( X, Y )] )
% 0.75/1.16    ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 716, [ ~( sum( X, Y, Y ) ), sum( X, 'additive_identity', 
% 0.75/1.16    'additive_identity' ) ] )
% 0.75/1.16  , clause( 980, [ ~( sum( X, Y, Y ) ), sum( X, 'additive_identity', 
% 0.75/1.16    'additive_identity' ) ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.75/1.16     ), ==>( 1, 1 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  resolution(
% 0.75/1.16  clause( 981, [ sum( multiply( X, 'additive_identity' ), 'additive_identity'
% 0.75/1.16    , 'additive_identity' ) ] )
% 0.75/1.16  , clause( 716, [ ~( sum( X, Y, Y ) ), sum( X, 'additive_identity', 
% 0.75/1.16    'additive_identity' ) ] )
% 0.75/1.16  , 0, clause( 240, [ sum( multiply( X, 'additive_identity' ), multiply( X, 
% 0.75/1.16    'additive_identity' ), multiply( X, 'additive_identity' ) ) ] )
% 0.75/1.16  , 0, substitution( 0, [ :=( X, multiply( X, 'additive_identity' ) ), :=( Y
% 0.75/1.16    , multiply( X, 'additive_identity' ) )] ), substitution( 1, [ :=( X, X )] )
% 0.75/1.16    ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 726, [ sum( multiply( X, 'additive_identity' ), 'additive_identity'
% 0.75/1.16    , 'additive_identity' ) ] )
% 0.75/1.16  , clause( 981, [ sum( multiply( X, 'additive_identity' ), 
% 0.75/1.16    'additive_identity', 'additive_identity' ) ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  eqswap(
% 0.75/1.16  clause( 982, [ =( Y, X ), ~( sum( X, 'additive_identity', Y ) ) ] )
% 0.75/1.16  , clause( 466, [ ~( sum( X, 'additive_identity', Y ) ), =( X, Y ) ] )
% 0.75/1.16  , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  resolution(
% 0.75/1.16  clause( 983, [ =( 'additive_identity', multiply( X, 'additive_identity' ) )
% 0.75/1.16     ] )
% 0.75/1.16  , clause( 982, [ =( Y, X ), ~( sum( X, 'additive_identity', Y ) ) ] )
% 0.75/1.16  , 1, clause( 726, [ sum( multiply( X, 'additive_identity' ), 
% 0.75/1.16    'additive_identity', 'additive_identity' ) ] )
% 0.75/1.16  , 0, substitution( 0, [ :=( X, multiply( X, 'additive_identity' ) ), :=( Y
% 0.75/1.16    , 'additive_identity' )] ), substitution( 1, [ :=( X, X )] )).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  eqswap(
% 0.75/1.16  clause( 984, [ =( multiply( X, 'additive_identity' ), 'additive_identity' )
% 0.75/1.16     ] )
% 0.75/1.16  , clause( 983, [ =( 'additive_identity', multiply( X, 'additive_identity' )
% 0.75/1.16     ) ] )
% 0.75/1.16  , 0, substitution( 0, [ :=( X, X )] )).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 806, [ =( multiply( X, 'additive_identity' ), 'additive_identity' )
% 0.75/1.16     ] )
% 0.75/1.16  , clause( 984, [ =( multiply( X, 'additive_identity' ), 'additive_identity'
% 0.75/1.16     ) ] )
% 0.75/1.16  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  paramod(
% 0.75/1.16  clause( 986, [ product( X, 'additive_identity', 'additive_identity' ) ] )
% 0.75/1.16  , clause( 806, [ =( multiply( X, 'additive_identity' ), 'additive_identity'
% 0.75/1.16     ) ] )
% 0.75/1.16  , 0, clause( 2, [ product( X, Y, multiply( X, Y ) ) ] )
% 0.75/1.16  , 0, 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ), 
% 0.75/1.16    :=( Y, 'additive_identity' )] )).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 824, [ product( X, 'additive_identity', 'additive_identity' ) ] )
% 0.75/1.16  , clause( 986, [ product( X, 'additive_identity', 'additive_identity' ) ]
% 0.75/1.16     )
% 0.75/1.16  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  resolution(
% 0.75/1.16  clause( 987, [ ~( sum( 'additive_identity', 'additive_identity', 
% 0.75/1.16    'additive_identity' ) ) ] )
% 0.75/1.16  , clause( 290, [ ~( product( a, X, X ) ), ~( sum( X, X, 'additive_identity'
% 0.75/1.16     ) ) ] )
% 0.75/1.16  , 0, clause( 824, [ product( X, 'additive_identity', 'additive_identity' )
% 0.75/1.16     ] )
% 0.75/1.16  , 0, substitution( 0, [ :=( X, 'additive_identity' )] ), substitution( 1, [
% 0.75/1.16     :=( X, a )] )).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  resolution(
% 0.75/1.16  clause( 988, [] )
% 0.75/1.16  , clause( 987, [ ~( sum( 'additive_identity', 'additive_identity', 
% 0.75/1.16    'additive_identity' ) ) ] )
% 0.75/1.16  , 0, clause( 0, [ sum( 'additive_identity', X, X ) ] )
% 0.75/1.16  , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'additive_identity' )] )
% 0.75/1.16    ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  subsumption(
% 0.75/1.16  clause( 825, [] )
% 0.75/1.16  , clause( 988, [] )
% 0.75/1.16  , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  end.
% 0.75/1.16  
% 0.75/1.16  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.75/1.16  
% 0.75/1.16  Memory use:
% 0.75/1.16  
% 0.75/1.16  space for terms:        14478
% 0.75/1.16  space for clauses:      36101
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  clauses generated:      3922
% 0.75/1.16  clauses kept:           826
% 0.75/1.16  clauses selected:       65
% 0.75/1.16  clauses deleted:        8
% 0.75/1.16  clauses inuse deleted:  0
% 0.75/1.16  
% 0.75/1.16  subsentry:          46098
% 0.75/1.16  literals s-matched: 17508
% 0.75/1.16  literals matched:   16628
% 0.75/1.16  full subsumption:   14219
% 0.75/1.16  
% 0.75/1.16  checksum:           -1109926917
% 0.75/1.16  
% 0.75/1.16  
% 0.75/1.16  Bliksem ended
%------------------------------------------------------------------------------