TSTP Solution File: GRP125-1.003 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n029.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 0s
% DateTime : Sat Jul 16 07:35:08 EDT 2022

% Result   : Unsatisfiable 0.42s 1.05s
% Output   : Refutation 0.42s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.12  % Command  : bliksem %s
% 0.13/0.33  % Computer : n029.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % DateTime : Mon Jun 13 23:23:25 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.42/1.05  *** allocated 10000 integers for termspace/termends
% 0.42/1.05  *** allocated 10000 integers for clauses
% 0.42/1.05  *** allocated 10000 integers for justifications
% 0.42/1.05  Bliksem 1.12
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  Automatic Strategy Selection
% 0.42/1.05  
% 0.42/1.05  Clauses:
% 0.42/1.05  [
% 0.42/1.05     [ 'group_element'( 'e_1' ) ],
% 0.42/1.05     [ 'group_element'( 'e_2' ) ],
% 0.42/1.05     [ 'group_element'( 'e_3' ) ],
% 0.42/1.05     [ ~( equalish( 'e_1', 'e_2' ) ) ],
% 0.42/1.05     [ ~( equalish( 'e_1', 'e_3' ) ) ],
% 0.42/1.05     [ ~( equalish( 'e_2', 'e_1' ) ) ],
% 0.42/1.05     [ ~( equalish( 'e_2', 'e_3' ) ) ],
% 0.42/1.05     [ ~( equalish( 'e_3', 'e_1' ) ) ],
% 0.42/1.05     [ ~( equalish( 'e_3', 'e_2' ) ) ],
% 0.42/1.05     [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product( X, Y, 
% 0.42/1.05    'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ],
% 0.42/1.05     [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), equalish( Z, T ) ]
% 0.42/1.05    ,
% 0.42/1.05     [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), equalish( Y, T ) ]
% 0.42/1.05    ,
% 0.42/1.05     [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish( X, T ) ]
% 0.42/1.05    ,
% 0.42/1.05     [ product( X, X, X ) ],
% 0.42/1.05     [ ~( product( X, Y, Z ) ), ~( product( Y, X, T ) ), product( Z, T, X ) ]
% 0.42/1.05    
% 0.42/1.05  ] .
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  percentage equality = 0.000000, percentage horn = 0.933333
% 0.42/1.05  This is a near-Horn, non-equality  problem
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  Options Used:
% 0.42/1.05  
% 0.42/1.05  useres =            1
% 0.42/1.05  useparamod =        0
% 0.42/1.05  useeqrefl =         0
% 0.42/1.05  useeqfact =         0
% 0.42/1.05  usefactor =         1
% 0.42/1.05  usesimpsplitting =  0
% 0.42/1.05  usesimpdemod =      0
% 0.42/1.05  usesimpres =        4
% 0.42/1.05  
% 0.42/1.05  resimpinuse      =  1000
% 0.42/1.05  resimpclauses =     20000
% 0.42/1.05  substype =          standard
% 0.42/1.05  backwardsubs =      1
% 0.42/1.05  selectoldest =      5
% 0.42/1.05  
% 0.42/1.05  litorderings [0] =  split
% 0.42/1.05  litorderings [1] =  liftord
% 0.42/1.05  
% 0.42/1.05  termordering =      none
% 0.42/1.05  
% 0.42/1.05  litapriori =        1
% 0.42/1.05  termapriori =       0
% 0.42/1.05  litaposteriori =    0
% 0.42/1.05  termaposteriori =   0
% 0.42/1.05  demodaposteriori =  0
% 0.42/1.05  ordereqreflfact =   0
% 0.42/1.05  
% 0.42/1.05  litselect =         negative
% 0.42/1.05  
% 0.42/1.05  maxweight =         30000
% 0.42/1.05  maxdepth =          30000
% 0.42/1.05  maxlength =         115
% 0.42/1.05  maxnrvars =         195
% 0.42/1.05  excuselevel =       0
% 0.42/1.05  increasemaxweight = 0
% 0.42/1.05  
% 0.42/1.05  maxselected =       10000000
% 0.42/1.05  maxnrclauses =      10000000
% 0.42/1.05  
% 0.42/1.05  showgenerated =    0
% 0.42/1.05  showkept =         0
% 0.42/1.05  showselected =     0
% 0.42/1.05  showdeleted =      0
% 0.42/1.05  showresimp =       1
% 0.42/1.05  showstatus =       2000
% 0.42/1.05  
% 0.42/1.05  prologoutput =     1
% 0.42/1.05  nrgoals =          5000000
% 0.42/1.05  totalproof =       1
% 0.42/1.05  
% 0.42/1.05  Symbols occurring in the translation:
% 0.42/1.05  
% 0.42/1.05  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.42/1.05  .  [1, 2]      (w:1, o:24, a:1, s:1, b:0), 
% 0.42/1.05  !  [4, 1]      (w:1, o:18, a:1, s:1, b:0), 
% 0.42/1.05  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.42/1.05  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.42/1.05  'e_1'  [39, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 0.42/1.05  'group_element'  [40, 1]      (w:1, o:23, a:1, s:1, b:0), 
% 0.42/1.05  'e_2'  [41, 0]      (w:1, o:10, a:1, s:1, b:0), 
% 0.42/1.05  'e_3'  [42, 0]      (w:1, o:11, a:1, s:1, b:0), 
% 0.42/1.05  equalish  [43, 2]      (w:1, o:49, a:1, s:1, b:0), 
% 0.42/1.05  product  [46, 3]      (w:1, o:50, a:1, s:1, b:0).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  Starting Search:
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  Bliksems!, er is een bewijs:
% 0.42/1.05  % SZS status Unsatisfiable
% 0.42/1.05  % SZS output start Refutation
% 0.42/1.05  
% 0.42/1.05  clause( 1, [ 'group_element'( 'e_2' ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 2, [ 'group_element'( 'e_3' ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 5, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 6, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 8, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 9, [ ~( 'group_element'( X ) ), product( X, Y, 'e_3' ), product( X
% 0.42/1.05    , Y, 'e_1' ), product( X, Y, 'e_2' ), ~( 'group_element'( Y ) ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 10, [ equalish( Z, T ), ~( product( X, Y, Z ) ), ~( product( X, Y, 
% 0.42/1.05    T ) ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 11, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T, 
% 0.42/1.05    Z ) ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 12, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y, 
% 0.42/1.05    Z ) ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 13, [ product( X, X, X ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 14, [ ~( product( X, Y, Z ) ), product( Z, T, X ), ~( product( Y, X
% 0.42/1.05    , T ) ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 21, [ product( X, 'e_2', 'e_3' ), product( X, 'e_2', 'e_1' ), 
% 0.42/1.05    product( X, 'e_2', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 22, [ product( X, 'e_3', 'e_3' ), product( X, 'e_3', 'e_1' ), 
% 0.42/1.05    product( X, 'e_3', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 24, [ equalish( X, Y ), ~( product( Y, Y, X ) ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 25, [ equalish( X, Y ), ~( product( X, Y, Y ) ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 26, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 41, [ product( 'e_3', 'e_2', 'e_1' ), product( 'e_3', 'e_2', 'e_2'
% 0.42/1.05     ), product( 'e_3', 'e_2', 'e_3' ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 47, [ product( 'e_3', 'e_2', 'e_1' ), product( 'e_3', 'e_2', 'e_2'
% 0.42/1.05     ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 49, [ product( 'e_2', 'e_3', 'e_1' ), product( 'e_2', 'e_3', 'e_2'
% 0.42/1.05     ), product( 'e_2', 'e_3', 'e_3' ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 53, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 54, [ product( X, 'e_1', 'e_2' ), ~( product( 'e_2', 'e_3', X ) ) ]
% 0.42/1.05     )
% 0.42/1.05  .
% 0.42/1.05  clause( 70, [ product( 'e_2', 'e_3', 'e_1' ), product( 'e_2', 'e_3', 'e_2'
% 0.42/1.05     ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 74, [ product( 'e_2', 'e_3', 'e_1' ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 75, [ product( 'e_1', 'e_1', 'e_2' ) ] )
% 0.42/1.05  .
% 0.42/1.05  clause( 87, [] )
% 0.42/1.05  .
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  % SZS output end Refutation
% 0.42/1.05  found a proof!
% 0.42/1.05  
% 0.42/1.05  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.42/1.05  
% 0.42/1.05  initialclauses(
% 0.42/1.05  [ clause( 89, [ 'group_element'( 'e_1' ) ] )
% 0.42/1.05  , clause( 90, [ 'group_element'( 'e_2' ) ] )
% 0.42/1.05  , clause( 91, [ 'group_element'( 'e_3' ) ] )
% 0.42/1.05  , clause( 92, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.42/1.05  , clause( 93, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.42/1.05  , clause( 94, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.42/1.05  , clause( 95, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.42/1.05  , clause( 96, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.42/1.05  , clause( 97, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.42/1.05  , clause( 98, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), 
% 0.42/1.05    product( X, Y, 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ]
% 0.42/1.05     )
% 0.42/1.05  , clause( 99, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), equalish( 
% 0.42/1.05    Z, T ) ] )
% 0.42/1.05  , clause( 100, [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), equalish( 
% 0.42/1.05    Y, T ) ] )
% 0.42/1.05  , clause( 101, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish( 
% 0.42/1.05    X, T ) ] )
% 0.42/1.05  , clause( 102, [ product( X, X, X ) ] )
% 0.42/1.05  , clause( 103, [ ~( product( X, Y, Z ) ), ~( product( Y, X, T ) ), product( 
% 0.42/1.05    Z, T, X ) ] )
% 0.42/1.05  ] ).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  subsumption(
% 0.42/1.05  clause( 1, [ 'group_element'( 'e_2' ) ] )
% 0.42/1.05  , clause( 90, [ 'group_element'( 'e_2' ) ] )
% 0.42/1.05  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  subsumption(
% 0.42/1.05  clause( 2, [ 'group_element'( 'e_3' ) ] )
% 0.42/1.05  , clause( 91, [ 'group_element'( 'e_3' ) ] )
% 0.42/1.05  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  subsumption(
% 0.42/1.05  clause( 5, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.42/1.05  , clause( 94, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.42/1.05  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  subsumption(
% 0.42/1.05  clause( 6, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.42/1.05  , clause( 95, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.42/1.05  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  subsumption(
% 0.42/1.05  clause( 8, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.42/1.05  , clause( 97, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.42/1.05  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  subsumption(
% 0.42/1.05  clause( 9, [ ~( 'group_element'( X ) ), product( X, Y, 'e_3' ), product( X
% 0.42/1.05    , Y, 'e_1' ), product( X, Y, 'e_2' ), ~( 'group_element'( Y ) ) ] )
% 0.42/1.05  , clause( 98, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), 
% 0.42/1.05    product( X, Y, 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ]
% 0.42/1.05     )
% 0.42/1.05  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.42/1.05     ), ==>( 1, 4 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 1 )] ) ).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  subsumption(
% 0.42/1.05  clause( 10, [ equalish( Z, T ), ~( product( X, Y, Z ) ), ~( product( X, Y, 
% 0.42/1.05    T ) ) ] )
% 0.42/1.05  , clause( 99, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), equalish( 
% 0.42/1.05    Z, T ) ] )
% 0.42/1.05  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 0.42/1.05    permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  subsumption(
% 0.42/1.05  clause( 11, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T, 
% 0.42/1.05    Z ) ) ] )
% 0.42/1.05  , clause( 100, [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), equalish( 
% 0.42/1.05    Y, T ) ] )
% 0.42/1.05  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 0.42/1.05    permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  subsumption(
% 0.42/1.05  clause( 12, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y, 
% 0.42/1.05    Z ) ) ] )
% 0.42/1.05  , clause( 101, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish( 
% 0.42/1.05    X, T ) ] )
% 0.42/1.05  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 0.42/1.05    permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  subsumption(
% 0.42/1.05  clause( 13, [ product( X, X, X ) ] )
% 0.42/1.05  , clause( 102, [ product( X, X, X ) ] )
% 0.42/1.05  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  subsumption(
% 0.42/1.05  clause( 14, [ ~( product( X, Y, Z ) ), product( Z, T, X ), ~( product( Y, X
% 0.42/1.05    , T ) ) ] )
% 0.42/1.05  , clause( 103, [ ~( product( X, Y, Z ) ), ~( product( Y, X, T ) ), product( 
% 0.42/1.05    Z, T, X ) ] )
% 0.42/1.05  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 0.42/1.05    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  resolution(
% 0.42/1.05  clause( 124, [ ~( 'group_element'( X ) ), product( X, 'e_2', 'e_3' ), 
% 0.42/1.05    product( X, 'e_2', 'e_1' ), product( X, 'e_2', 'e_2' ) ] )
% 0.42/1.05  , clause( 9, [ ~( 'group_element'( X ) ), product( X, Y, 'e_3' ), product( 
% 0.42/1.05    X, Y, 'e_1' ), product( X, Y, 'e_2' ), ~( 'group_element'( Y ) ) ] )
% 0.42/1.05  , 4, clause( 1, [ 'group_element'( 'e_2' ) ] )
% 0.42/1.05  , 0, substitution( 0, [ :=( X, X ), :=( Y, 'e_2' )] ), substitution( 1, [] )
% 0.42/1.05    ).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  subsumption(
% 0.42/1.05  clause( 21, [ product( X, 'e_2', 'e_3' ), product( X, 'e_2', 'e_1' ), 
% 0.42/1.05    product( X, 'e_2', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.42/1.05  , clause( 124, [ ~( 'group_element'( X ) ), product( X, 'e_2', 'e_3' ), 
% 0.42/1.05    product( X, 'e_2', 'e_1' ), product( X, 'e_2', 'e_2' ) ] )
% 0.42/1.05  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 3 ), ==>( 1, 
% 0.42/1.05    0 ), ==>( 2, 1 ), ==>( 3, 2 )] ) ).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  resolution(
% 0.42/1.05  clause( 126, [ ~( 'group_element'( X ) ), product( X, 'e_3', 'e_3' ), 
% 0.42/1.05    product( X, 'e_3', 'e_1' ), product( X, 'e_3', 'e_2' ) ] )
% 0.42/1.05  , clause( 9, [ ~( 'group_element'( X ) ), product( X, Y, 'e_3' ), product( 
% 0.42/1.05    X, Y, 'e_1' ), product( X, Y, 'e_2' ), ~( 'group_element'( Y ) ) ] )
% 0.42/1.05  , 4, clause( 2, [ 'group_element'( 'e_3' ) ] )
% 0.42/1.05  , 0, substitution( 0, [ :=( X, X ), :=( Y, 'e_3' )] ), substitution( 1, [] )
% 0.42/1.05    ).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  subsumption(
% 0.42/1.05  clause( 22, [ product( X, 'e_3', 'e_3' ), product( X, 'e_3', 'e_1' ), 
% 0.42/1.05    product( X, 'e_3', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.42/1.05  , clause( 126, [ ~( 'group_element'( X ) ), product( X, 'e_3', 'e_3' ), 
% 0.42/1.05    product( X, 'e_3', 'e_1' ), product( X, 'e_3', 'e_2' ) ] )
% 0.42/1.05  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 3 ), ==>( 1, 
% 0.42/1.05    0 ), ==>( 2, 1 ), ==>( 3, 2 )] ) ).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  resolution(
% 0.42/1.05  clause( 128, [ equalish( X, Y ), ~( product( Y, Y, X ) ) ] )
% 0.42/1.05  , clause( 10, [ equalish( Z, T ), ~( product( X, Y, Z ) ), ~( product( X, Y
% 0.42/1.05    , T ) ) ] )
% 0.42/1.05  , 2, clause( 13, [ product( X, X, X ) ] )
% 0.42/1.05  , 0, substitution( 0, [ :=( X, Y ), :=( Y, Y ), :=( Z, X ), :=( T, Y )] ), 
% 0.42/1.05    substitution( 1, [ :=( X, Y )] )).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  subsumption(
% 0.42/1.05  clause( 24, [ equalish( X, Y ), ~( product( Y, Y, X ) ) ] )
% 0.42/1.05  , clause( 128, [ equalish( X, Y ), ~( product( Y, Y, X ) ) ] )
% 0.42/1.05  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.42/1.05     ), ==>( 1, 1 )] ) ).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  resolution(
% 0.42/1.05  clause( 130, [ equalish( X, Y ), ~( product( X, Y, Y ) ) ] )
% 0.42/1.05  , clause( 12, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y
% 0.42/1.05    , Z ) ) ] )
% 0.42/1.05  , 2, clause( 13, [ product( X, X, X ) ] )
% 0.42/1.05  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y ), :=( T, Y )] ), 
% 0.42/1.05    substitution( 1, [ :=( X, Y )] )).
% 0.42/1.05  
% 0.42/1.05  
% 0.42/1.05  subsumption(
% 0.42/1.05  clause( 25, [ equalish( X, Y ), ~( product( X, Y, Y ) ) ] )
% 0.42/1.05  , clause( 130, [ equalish( X, Y ), ~( product( X, Y, Y ) ) ] )
% 0.42/1.05  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.42/1.05     ), ==>( 1, 1 )] ) ).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  resolution(
% 0.71/1.05  clause( 132, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.71/1.05  , clause( 11, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T
% 0.71/1.05    , Z ) ) ] )
% 0.71/1.05  , 2, clause( 13, [ product( X, X, X ) ] )
% 0.71/1.05  , 0, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Y ), :=( T, Y )] ), 
% 0.71/1.05    substitution( 1, [ :=( X, Y )] )).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  subsumption(
% 0.71/1.05  clause( 26, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.71/1.05  , clause( 132, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.71/1.05  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.05     ), ==>( 1, 1 )] ) ).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  resolution(
% 0.71/1.05  clause( 133, [ product( 'e_3', 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1'
% 0.71/1.05     ), product( 'e_3', 'e_2', 'e_2' ) ] )
% 0.71/1.05  , clause( 21, [ product( X, 'e_2', 'e_3' ), product( X, 'e_2', 'e_1' ), 
% 0.71/1.05    product( X, 'e_2', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.71/1.05  , 3, clause( 2, [ 'group_element'( 'e_3' ) ] )
% 0.71/1.05  , 0, substitution( 0, [ :=( X, 'e_3' )] ), substitution( 1, [] )).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  subsumption(
% 0.71/1.05  clause( 41, [ product( 'e_3', 'e_2', 'e_1' ), product( 'e_3', 'e_2', 'e_2'
% 0.71/1.05     ), product( 'e_3', 'e_2', 'e_3' ) ] )
% 0.71/1.05  , clause( 133, [ product( 'e_3', 'e_2', 'e_3' ), product( 'e_3', 'e_2', 
% 0.71/1.05    'e_1' ), product( 'e_3', 'e_2', 'e_2' ) ] )
% 0.71/1.05  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2
% 0.71/1.05    , 1 )] ) ).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  resolution(
% 0.71/1.05  clause( 134, [ equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1' ), 
% 0.71/1.05    product( 'e_3', 'e_2', 'e_2' ) ] )
% 0.71/1.05  , clause( 26, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.71/1.05  , 1, clause( 41, [ product( 'e_3', 'e_2', 'e_1' ), product( 'e_3', 'e_2', 
% 0.71/1.05    'e_2' ), product( 'e_3', 'e_2', 'e_3' ) ] )
% 0.71/1.05  , 2, substitution( 0, [ :=( X, 'e_2' ), :=( Y, 'e_3' )] ), substitution( 1
% 0.71/1.05    , [] )).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  resolution(
% 0.71/1.05  clause( 135, [ product( 'e_3', 'e_2', 'e_1' ), product( 'e_3', 'e_2', 'e_2'
% 0.71/1.05     ) ] )
% 0.71/1.05  , clause( 6, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.71/1.05  , 0, clause( 134, [ equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1'
% 0.71/1.05     ), product( 'e_3', 'e_2', 'e_2' ) ] )
% 0.71/1.05  , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  subsumption(
% 0.71/1.05  clause( 47, [ product( 'e_3', 'e_2', 'e_1' ), product( 'e_3', 'e_2', 'e_2'
% 0.71/1.05     ) ] )
% 0.71/1.05  , clause( 135, [ product( 'e_3', 'e_2', 'e_1' ), product( 'e_3', 'e_2', 
% 0.71/1.05    'e_2' ) ] )
% 0.71/1.05  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 0.71/1.05     ).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  resolution(
% 0.71/1.05  clause( 136, [ product( 'e_2', 'e_3', 'e_3' ), product( 'e_2', 'e_3', 'e_1'
% 0.71/1.05     ), product( 'e_2', 'e_3', 'e_2' ) ] )
% 0.71/1.05  , clause( 22, [ product( X, 'e_3', 'e_3' ), product( X, 'e_3', 'e_1' ), 
% 0.71/1.05    product( X, 'e_3', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.71/1.05  , 3, clause( 1, [ 'group_element'( 'e_2' ) ] )
% 0.71/1.05  , 0, substitution( 0, [ :=( X, 'e_2' )] ), substitution( 1, [] )).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  subsumption(
% 0.71/1.05  clause( 49, [ product( 'e_2', 'e_3', 'e_1' ), product( 'e_2', 'e_3', 'e_2'
% 0.71/1.05     ), product( 'e_2', 'e_3', 'e_3' ) ] )
% 0.71/1.05  , clause( 136, [ product( 'e_2', 'e_3', 'e_3' ), product( 'e_2', 'e_3', 
% 0.71/1.05    'e_1' ), product( 'e_2', 'e_3', 'e_2' ) ] )
% 0.71/1.05  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2
% 0.71/1.05    , 1 )] ) ).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  resolution(
% 0.71/1.05  clause( 137, [ equalish( 'e_3', 'e_2' ), product( 'e_3', 'e_2', 'e_1' ) ]
% 0.71/1.05     )
% 0.71/1.05  , clause( 25, [ equalish( X, Y ), ~( product( X, Y, Y ) ) ] )
% 0.71/1.05  , 1, clause( 47, [ product( 'e_3', 'e_2', 'e_1' ), product( 'e_3', 'e_2', 
% 0.71/1.05    'e_2' ) ] )
% 0.71/1.05  , 1, substitution( 0, [ :=( X, 'e_3' ), :=( Y, 'e_2' )] ), substitution( 1
% 0.71/1.05    , [] )).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  resolution(
% 0.71/1.05  clause( 138, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.71/1.05  , clause( 8, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.71/1.05  , 0, clause( 137, [ equalish( 'e_3', 'e_2' ), product( 'e_3', 'e_2', 'e_1'
% 0.71/1.05     ) ] )
% 0.71/1.05  , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  subsumption(
% 0.71/1.05  clause( 53, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.71/1.05  , clause( 138, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.71/1.05  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  resolution(
% 0.71/1.05  clause( 140, [ ~( product( 'e_2', 'e_3', X ) ), product( X, 'e_1', 'e_2' )
% 0.71/1.05     ] )
% 0.71/1.05  , clause( 14, [ ~( product( X, Y, Z ) ), product( Z, T, X ), ~( product( Y
% 0.71/1.05    , X, T ) ) ] )
% 0.71/1.05  , 2, clause( 53, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.71/1.05  , 0, substitution( 0, [ :=( X, 'e_2' ), :=( Y, 'e_3' ), :=( Z, X ), :=( T, 
% 0.71/1.05    'e_1' )] ), substitution( 1, [] )).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  subsumption(
% 0.71/1.05  clause( 54, [ product( X, 'e_1', 'e_2' ), ~( product( 'e_2', 'e_3', X ) ) ]
% 0.71/1.05     )
% 0.71/1.05  , clause( 140, [ ~( product( 'e_2', 'e_3', X ) ), product( X, 'e_1', 'e_2'
% 0.71/1.05     ) ] )
% 0.71/1.05  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 
% 0.71/1.05    0 )] ) ).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  resolution(
% 0.71/1.05  clause( 141, [ equalish( 'e_2', 'e_3' ), product( 'e_2', 'e_3', 'e_1' ), 
% 0.71/1.05    product( 'e_2', 'e_3', 'e_2' ) ] )
% 0.71/1.05  , clause( 25, [ equalish( X, Y ), ~( product( X, Y, Y ) ) ] )
% 0.71/1.05  , 1, clause( 49, [ product( 'e_2', 'e_3', 'e_1' ), product( 'e_2', 'e_3', 
% 0.71/1.05    'e_2' ), product( 'e_2', 'e_3', 'e_3' ) ] )
% 0.71/1.05  , 2, substitution( 0, [ :=( X, 'e_2' ), :=( Y, 'e_3' )] ), substitution( 1
% 0.71/1.05    , [] )).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  resolution(
% 0.71/1.05  clause( 142, [ product( 'e_2', 'e_3', 'e_1' ), product( 'e_2', 'e_3', 'e_2'
% 0.71/1.05     ) ] )
% 0.71/1.05  , clause( 6, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.71/1.05  , 0, clause( 141, [ equalish( 'e_2', 'e_3' ), product( 'e_2', 'e_3', 'e_1'
% 0.71/1.05     ), product( 'e_2', 'e_3', 'e_2' ) ] )
% 0.71/1.05  , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  subsumption(
% 0.71/1.05  clause( 70, [ product( 'e_2', 'e_3', 'e_1' ), product( 'e_2', 'e_3', 'e_2'
% 0.71/1.05     ) ] )
% 0.71/1.05  , clause( 142, [ product( 'e_2', 'e_3', 'e_1' ), product( 'e_2', 'e_3', 
% 0.71/1.05    'e_2' ) ] )
% 0.71/1.05  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 0.71/1.05     ).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  resolution(
% 0.71/1.05  clause( 143, [ equalish( 'e_3', 'e_2' ), product( 'e_2', 'e_3', 'e_1' ) ]
% 0.71/1.05     )
% 0.71/1.05  , clause( 26, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.71/1.05  , 1, clause( 70, [ product( 'e_2', 'e_3', 'e_1' ), product( 'e_2', 'e_3', 
% 0.71/1.05    'e_2' ) ] )
% 0.71/1.05  , 1, substitution( 0, [ :=( X, 'e_3' ), :=( Y, 'e_2' )] ), substitution( 1
% 0.71/1.05    , [] )).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  resolution(
% 0.71/1.05  clause( 144, [ product( 'e_2', 'e_3', 'e_1' ) ] )
% 0.71/1.05  , clause( 8, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.71/1.05  , 0, clause( 143, [ equalish( 'e_3', 'e_2' ), product( 'e_2', 'e_3', 'e_1'
% 0.71/1.05     ) ] )
% 0.71/1.05  , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  subsumption(
% 0.71/1.05  clause( 74, [ product( 'e_2', 'e_3', 'e_1' ) ] )
% 0.71/1.05  , clause( 144, [ product( 'e_2', 'e_3', 'e_1' ) ] )
% 0.71/1.05  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  resolution(
% 0.71/1.05  clause( 145, [ product( 'e_1', 'e_1', 'e_2' ) ] )
% 0.71/1.05  , clause( 54, [ product( X, 'e_1', 'e_2' ), ~( product( 'e_2', 'e_3', X ) )
% 0.71/1.05     ] )
% 0.71/1.05  , 1, clause( 74, [ product( 'e_2', 'e_3', 'e_1' ) ] )
% 0.71/1.05  , 0, substitution( 0, [ :=( X, 'e_1' )] ), substitution( 1, [] )).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  subsumption(
% 0.71/1.05  clause( 75, [ product( 'e_1', 'e_1', 'e_2' ) ] )
% 0.71/1.05  , clause( 145, [ product( 'e_1', 'e_1', 'e_2' ) ] )
% 0.71/1.05  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  resolution(
% 0.71/1.05  clause( 146, [ equalish( 'e_2', 'e_1' ) ] )
% 0.71/1.05  , clause( 24, [ equalish( X, Y ), ~( product( Y, Y, X ) ) ] )
% 0.71/1.05  , 1, clause( 75, [ product( 'e_1', 'e_1', 'e_2' ) ] )
% 0.71/1.05  , 0, substitution( 0, [ :=( X, 'e_2' ), :=( Y, 'e_1' )] ), substitution( 1
% 0.71/1.05    , [] )).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  resolution(
% 0.71/1.05  clause( 147, [] )
% 0.71/1.05  , clause( 5, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.71/1.05  , 0, clause( 146, [ equalish( 'e_2', 'e_1' ) ] )
% 0.71/1.05  , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  subsumption(
% 0.71/1.05  clause( 87, [] )
% 0.71/1.05  , clause( 147, [] )
% 0.71/1.05  , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  end.
% 0.71/1.05  
% 0.71/1.05  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.71/1.05  
% 0.71/1.05  Memory use:
% 0.71/1.05  
% 0.71/1.05  space for terms:        1195
% 0.71/1.05  space for clauses:      4422
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  clauses generated:      143
% 0.71/1.05  clauses kept:           88
% 0.71/1.05  clauses selected:       53
% 0.71/1.05  clauses deleted:        4
% 0.71/1.05  clauses inuse deleted:  0
% 0.71/1.05  
% 0.71/1.05  subsentry:          329
% 0.71/1.05  literals s-matched: 187
% 0.71/1.05  literals matched:   136
% 0.71/1.05  full subsumption:   36
% 0.71/1.05  
% 0.71/1.05  checksum:           -705076530
% 0.71/1.05  
% 0.71/1.05  
% 0.71/1.05  Bliksem ended
%------------------------------------------------------------------------------