TSTP Solution File: GRP123-9.003 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GRP123-9.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n018.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 07:35:02 EDT 2022

% Result   : Unsatisfiable 0.70s 1.10s
% Output   : Refutation 0.70s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP123-9.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13  % Command  : bliksem %s
% 0.13/0.33  % Computer : n018.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 05:57:12 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.70/1.10  *** allocated 10000 integers for termspace/termends
% 0.70/1.10  *** allocated 10000 integers for clauses
% 0.70/1.10  *** allocated 10000 integers for justifications
% 0.70/1.10  Bliksem 1.12
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  Automatic Strategy Selection
% 0.70/1.10  
% 0.70/1.10  Clauses:
% 0.70/1.10  [
% 0.70/1.10     [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product( 'e_1', 
% 0.70/1.10    X, Y ), product( 'e_2', X, Y ), product( 'e_3', X, Y ) ],
% 0.70/1.10     [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product( X, 
% 0.70/1.10    'e_1', Y ), product( X, 'e_2', Y ), product( X, 'e_3', Y ) ],
% 0.70/1.10     [ 'group_element'( 'e_1' ) ],
% 0.70/1.10     [ 'group_element'( 'e_2' ) ],
% 0.70/1.10     [ 'group_element'( 'e_3' ) ],
% 0.70/1.10     [ ~( equalish( 'e_1', 'e_2' ) ) ],
% 0.70/1.10     [ ~( equalish( 'e_1', 'e_3' ) ) ],
% 0.70/1.10     [ ~( equalish( 'e_2', 'e_1' ) ) ],
% 0.70/1.10     [ ~( equalish( 'e_2', 'e_3' ) ) ],
% 0.70/1.10     [ ~( equalish( 'e_3', 'e_1' ) ) ],
% 0.70/1.10     [ ~( equalish( 'e_3', 'e_2' ) ) ],
% 0.70/1.10     [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product1( X, Y, 
% 0.70/1.10    'e_1' ), product1( X, Y, 'e_2' ), product1( X, Y, 'e_3' ) ],
% 0.70/1.10     [ ~( product1( X, Y, Z ) ), ~( product1( X, Y, T ) ), equalish( Z, T ) ]
% 0.70/1.10    ,
% 0.70/1.10     [ ~( product1( X, Y, Z ) ), ~( product1( X, T, Z ) ), equalish( Y, T ) ]
% 0.70/1.10    ,
% 0.70/1.10     [ ~( product1( X, Y, Z ) ), ~( product1( T, Y, Z ) ), equalish( X, T ) ]
% 0.70/1.10    ,
% 0.70/1.10     [ product1( X, X, X ) ],
% 0.70/1.10     [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product2( X, Y, 
% 0.70/1.10    'e_1' ), product2( X, Y, 'e_2' ), product2( X, Y, 'e_3' ) ],
% 0.70/1.10     [ ~( product2( X, Y, Z ) ), ~( product2( X, Y, T ) ), equalish( Z, T ) ]
% 0.70/1.10    ,
% 0.70/1.10     [ ~( product2( X, Y, Z ) ), ~( product2( X, T, Z ) ), equalish( Y, T ) ]
% 0.70/1.10    ,
% 0.70/1.10     [ ~( product2( X, Y, Z ) ), ~( product2( T, Y, Z ) ), equalish( X, T ) ]
% 0.70/1.10    ,
% 0.70/1.10     [ product2( X, X, X ) ],
% 0.70/1.10     [ ~( product1( X, Y, Z ) ), ~( product1( Z, Y, T ) ), product2( T, X, Y
% 0.70/1.10     ) ]
% 0.70/1.10  ] .
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  percentage equality = 0.000000, percentage horn = 0.818182
% 0.70/1.10  This a non-horn, non-equality problem
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  Options Used:
% 0.70/1.10  
% 0.70/1.10  useres =            1
% 0.70/1.10  useparamod =        0
% 0.70/1.10  useeqrefl =         0
% 0.70/1.10  useeqfact =         0
% 0.70/1.10  usefactor =         1
% 0.70/1.10  usesimpsplitting =  0
% 0.70/1.10  usesimpdemod =      0
% 0.70/1.10  usesimpres =        3
% 0.70/1.10  
% 0.70/1.10  resimpinuse      =  1000
% 0.70/1.10  resimpclauses =     20000
% 0.70/1.10  substype =          standard
% 0.70/1.10  backwardsubs =      1
% 0.70/1.10  selectoldest =      5
% 0.70/1.10  
% 0.70/1.10  litorderings [0] =  split
% 0.70/1.10  litorderings [1] =  liftord
% 0.70/1.10  
% 0.70/1.10  termordering =      none
% 0.70/1.10  
% 0.70/1.10  litapriori =        1
% 0.70/1.10  termapriori =       0
% 0.70/1.10  litaposteriori =    0
% 0.70/1.10  termaposteriori =   0
% 0.70/1.10  demodaposteriori =  0
% 0.70/1.10  ordereqreflfact =   0
% 0.70/1.10  
% 0.70/1.10  litselect =         none
% 0.70/1.10  
% 0.70/1.10  maxweight =         15
% 0.70/1.10  maxdepth =          30000
% 0.70/1.10  maxlength =         115
% 0.70/1.10  maxnrvars =         195
% 0.70/1.10  excuselevel =       1
% 0.70/1.10  increasemaxweight = 1
% 0.70/1.10  
% 0.70/1.10  maxselected =       10000000
% 0.70/1.10  maxnrclauses =      10000000
% 0.70/1.10  
% 0.70/1.10  showgenerated =    0
% 0.70/1.10  showkept =         0
% 0.70/1.10  showselected =     0
% 0.70/1.10  showdeleted =      0
% 0.70/1.10  showresimp =       1
% 0.70/1.10  showstatus =       2000
% 0.70/1.10  
% 0.70/1.10  prologoutput =     1
% 0.70/1.10  nrgoals =          5000000
% 0.70/1.10  totalproof =       1
% 0.70/1.10  
% 0.70/1.10  Symbols occurring in the translation:
% 0.70/1.10  
% 0.70/1.10  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.70/1.10  .  [1, 2]      (w:1, o:24, a:1, s:1, b:0), 
% 0.70/1.10  !  [4, 1]      (w:0, o:18, a:1, s:1, b:0), 
% 0.70/1.10  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.70/1.10  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.70/1.10  'group_element'  [40, 1]      (w:1, o:23, a:1, s:1, b:0), 
% 0.70/1.10  'e_1'  [42, 0]      (w:1, o:12, a:1, s:1, b:0), 
% 0.70/1.10  product  [43, 3]      (w:1, o:50, a:1, s:1, b:0), 
% 0.70/1.10  'e_2'  [44, 0]      (w:1, o:13, a:1, s:1, b:0), 
% 0.70/1.10  'e_3'  [45, 0]      (w:1, o:14, a:1, s:1, b:0), 
% 0.70/1.10  equalish  [46, 2]      (w:1, o:49, a:1, s:1, b:0), 
% 0.70/1.10  product1  [47, 3]      (w:1, o:51, a:1, s:1, b:0), 
% 0.70/1.10  product2  [50, 3]      (w:1, o:52, a:1, s:1, b:0).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  Starting Search:
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  Bliksems!, er is een bewijs:
% 0.70/1.10  % SZS status Unsatisfiable
% 0.70/1.10  % SZS output start Refutation
% 0.70/1.10  
% 0.70/1.10  clause( 2, [ 'group_element'( 'e_1' ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 3, [ 'group_element'( 'e_2' ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 4, [ 'group_element'( 'e_3' ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 6, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 8, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 10, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 11, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), 
% 0.70/1.10    product1( X, Y, 'e_1' ), product1( X, Y, 'e_2' ), product1( X, Y, 'e_3' )
% 0.70/1.10     ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 13, [ equalish( Y, T ), ~( product1( X, Y, Z ) ), ~( product1( X, T
% 0.70/1.10    , Z ) ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 14, [ equalish( X, T ), ~( product1( X, Y, Z ) ), ~( product1( T, Y
% 0.70/1.10    , Z ) ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 15, [ product1( X, X, X ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 17, [ equalish( Z, T ), ~( product2( X, Y, Z ) ), ~( product2( X, Y
% 0.70/1.10    , T ) ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 18, [ equalish( Y, T ), ~( product2( X, Y, Z ) ), ~( product2( X, T
% 0.70/1.10    , Z ) ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 20, [ product2( X, X, X ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 21, [ ~( product1( X, Y, Z ) ), ~( product1( Z, Y, T ) ), product2( 
% 0.70/1.10    T, X, Y ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 42, [ equalish( X, Y ), ~( product1( X, Y, X ) ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 44, [ ~( 'group_element'( X ) ), equalish( 'e_3', X ), product1( 
% 0.70/1.10    'e_3', X, 'e_1' ), product1( 'e_3', X, 'e_2' ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 53, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 58, [ equalish( X, Y ), ~( product2( X, Y, X ) ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 72, [ equalish( X, Y ), ~( product2( X, X, Y ) ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 75, [ equalish( X, Y ), ~( product1( X, Y, Z ) ), ~( product1( Z, Y
% 0.70/1.10    , X ) ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 79, [ equalish( Y, X ), ~( product1( X, Y, Z ) ), ~( product1( Z, Y
% 0.70/1.10    , Y ) ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 176, [ equalish( 'e_3', 'e_2' ), product1( 'e_3', 'e_2', 'e_1' ) ]
% 0.70/1.10     )
% 0.70/1.10  .
% 0.70/1.10  clause( 178, [ product1( 'e_3', 'e_2', 'e_1' ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 180, [ ~( product1( 'e_1', 'e_2', 'e_2' ) ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 181, [ ~( product1( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 183, [ equalish( X, 'e_3' ), ~( product1( X, 'e_2', 'e_1' ) ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 194, [ ~( 'group_element'( 'e_2' ) ), product1( 'e_1', 'e_2', 'e_1'
% 0.70/1.10     ), product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 195, [ product1( 'e_1', 'e_2', 'e_1' ) ] )
% 0.70/1.10  .
% 0.70/1.10  clause( 196, [] )
% 0.70/1.10  .
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  % SZS output end Refutation
% 0.70/1.10  found a proof!
% 0.70/1.10  
% 0.70/1.10  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.70/1.10  
% 0.70/1.10  initialclauses(
% 0.70/1.10  [ clause( 198, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), 
% 0.70/1.10    product( 'e_1', X, Y ), product( 'e_2', X, Y ), product( 'e_3', X, Y ) ]
% 0.70/1.10     )
% 0.70/1.10  , clause( 199, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), 
% 0.70/1.10    product( X, 'e_1', Y ), product( X, 'e_2', Y ), product( X, 'e_3', Y ) ]
% 0.70/1.10     )
% 0.70/1.10  , clause( 200, [ 'group_element'( 'e_1' ) ] )
% 0.70/1.10  , clause( 201, [ 'group_element'( 'e_2' ) ] )
% 0.70/1.10  , clause( 202, [ 'group_element'( 'e_3' ) ] )
% 0.70/1.10  , clause( 203, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.70/1.10  , clause( 204, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.70/1.10  , clause( 205, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.70/1.10  , clause( 206, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.70/1.10  , clause( 207, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.70/1.10  , clause( 208, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.70/1.10  , clause( 209, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), 
% 0.70/1.10    product1( X, Y, 'e_1' ), product1( X, Y, 'e_2' ), product1( X, Y, 'e_3' )
% 0.70/1.10     ] )
% 0.70/1.10  , clause( 210, [ ~( product1( X, Y, Z ) ), ~( product1( X, Y, T ) ), 
% 0.70/1.10    equalish( Z, T ) ] )
% 0.70/1.10  , clause( 211, [ ~( product1( X, Y, Z ) ), ~( product1( X, T, Z ) ), 
% 0.70/1.10    equalish( Y, T ) ] )
% 0.70/1.10  , clause( 212, [ ~( product1( X, Y, Z ) ), ~( product1( T, Y, Z ) ), 
% 0.70/1.10    equalish( X, T ) ] )
% 0.70/1.10  , clause( 213, [ product1( X, X, X ) ] )
% 0.70/1.10  , clause( 214, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), 
% 0.70/1.10    product2( X, Y, 'e_1' ), product2( X, Y, 'e_2' ), product2( X, Y, 'e_3' )
% 0.70/1.10     ] )
% 0.70/1.10  , clause( 215, [ ~( product2( X, Y, Z ) ), ~( product2( X, Y, T ) ), 
% 0.70/1.10    equalish( Z, T ) ] )
% 0.70/1.10  , clause( 216, [ ~( product2( X, Y, Z ) ), ~( product2( X, T, Z ) ), 
% 0.70/1.10    equalish( Y, T ) ] )
% 0.70/1.10  , clause( 217, [ ~( product2( X, Y, Z ) ), ~( product2( T, Y, Z ) ), 
% 0.70/1.10    equalish( X, T ) ] )
% 0.70/1.10  , clause( 218, [ product2( X, X, X ) ] )
% 0.70/1.10  , clause( 219, [ ~( product1( X, Y, Z ) ), ~( product1( Z, Y, T ) ), 
% 0.70/1.10    product2( T, X, Y ) ] )
% 0.70/1.10  ] ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 2, [ 'group_element'( 'e_1' ) ] )
% 0.70/1.10  , clause( 200, [ 'group_element'( 'e_1' ) ] )
% 0.70/1.10  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 3, [ 'group_element'( 'e_2' ) ] )
% 0.70/1.10  , clause( 201, [ 'group_element'( 'e_2' ) ] )
% 0.70/1.10  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 4, [ 'group_element'( 'e_3' ) ] )
% 0.70/1.10  , clause( 202, [ 'group_element'( 'e_3' ) ] )
% 0.70/1.10  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 6, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.70/1.10  , clause( 204, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.70/1.10  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 8, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.70/1.10  , clause( 206, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.70/1.10  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 10, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.70/1.10  , clause( 208, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.70/1.10  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 11, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), 
% 0.70/1.10    product1( X, Y, 'e_1' ), product1( X, Y, 'e_2' ), product1( X, Y, 'e_3' )
% 0.70/1.10     ] )
% 0.70/1.10  , clause( 209, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), 
% 0.70/1.10    product1( X, Y, 'e_1' ), product1( X, Y, 'e_2' ), product1( X, Y, 'e_3' )
% 0.70/1.10     ] )
% 0.70/1.10  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.70/1.10     ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 4 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 13, [ equalish( Y, T ), ~( product1( X, Y, Z ) ), ~( product1( X, T
% 0.70/1.10    , Z ) ) ] )
% 0.70/1.10  , clause( 211, [ ~( product1( X, Y, Z ) ), ~( product1( X, T, Z ) ), 
% 0.70/1.10    equalish( Y, T ) ] )
% 0.70/1.10  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 0.70/1.10    permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 14, [ equalish( X, T ), ~( product1( X, Y, Z ) ), ~( product1( T, Y
% 0.70/1.10    , Z ) ) ] )
% 0.70/1.10  , clause( 212, [ ~( product1( X, Y, Z ) ), ~( product1( T, Y, Z ) ), 
% 0.70/1.10    equalish( X, T ) ] )
% 0.70/1.10  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 0.70/1.10    permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 15, [ product1( X, X, X ) ] )
% 0.70/1.10  , clause( 213, [ product1( X, X, X ) ] )
% 0.70/1.10  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 17, [ equalish( Z, T ), ~( product2( X, Y, Z ) ), ~( product2( X, Y
% 0.70/1.10    , T ) ) ] )
% 0.70/1.10  , clause( 215, [ ~( product2( X, Y, Z ) ), ~( product2( X, Y, T ) ), 
% 0.70/1.10    equalish( Z, T ) ] )
% 0.70/1.10  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 0.70/1.10    permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 18, [ equalish( Y, T ), ~( product2( X, Y, Z ) ), ~( product2( X, T
% 0.70/1.10    , Z ) ) ] )
% 0.70/1.10  , clause( 216, [ ~( product2( X, Y, Z ) ), ~( product2( X, T, Z ) ), 
% 0.70/1.10    equalish( Y, T ) ] )
% 0.70/1.10  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 0.70/1.10    permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 20, [ product2( X, X, X ) ] )
% 0.70/1.10  , clause( 218, [ product2( X, X, X ) ] )
% 0.70/1.10  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 21, [ ~( product1( X, Y, Z ) ), ~( product1( Z, Y, T ) ), product2( 
% 0.70/1.10    T, X, Y ) ] )
% 0.70/1.10  , clause( 219, [ ~( product1( X, Y, Z ) ), ~( product1( Z, Y, T ) ), 
% 0.70/1.10    product2( T, X, Y ) ] )
% 0.70/1.10  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 0.70/1.10    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 290, [ equalish( X, Y ), ~( product1( X, Y, X ) ) ] )
% 0.70/1.10  , clause( 13, [ equalish( Y, T ), ~( product1( X, Y, Z ) ), ~( product1( X
% 0.70/1.10    , T, Z ) ) ] )
% 0.70/1.10  , 1, clause( 15, [ product1( X, X, X ) ] )
% 0.70/1.10  , 0, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, X ), :=( T, Y )] ), 
% 0.70/1.10    substitution( 1, [ :=( X, X )] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 42, [ equalish( X, Y ), ~( product1( X, Y, X ) ) ] )
% 0.70/1.10  , clause( 290, [ equalish( X, Y ), ~( product1( X, Y, X ) ) ] )
% 0.70/1.10  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.70/1.10     ), ==>( 1, 1 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 294, [ equalish( 'e_3', X ), ~( 'group_element'( 'e_3' ) ), ~( 
% 0.70/1.10    'group_element'( X ) ), product1( 'e_3', X, 'e_1' ), product1( 'e_3', X, 
% 0.70/1.10    'e_2' ) ] )
% 0.70/1.10  , clause( 42, [ equalish( X, Y ), ~( product1( X, Y, X ) ) ] )
% 0.70/1.10  , 1, clause( 11, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), 
% 0.70/1.10    product1( X, Y, 'e_1' ), product1( X, Y, 'e_2' ), product1( X, Y, 'e_3' )
% 0.70/1.10     ] )
% 0.70/1.10  , 4, substitution( 0, [ :=( X, 'e_3' ), :=( Y, X )] ), substitution( 1, [ 
% 0.70/1.10    :=( X, 'e_3' ), :=( Y, X )] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 299, [ equalish( 'e_3', X ), ~( 'group_element'( X ) ), product1( 
% 0.70/1.10    'e_3', X, 'e_1' ), product1( 'e_3', X, 'e_2' ) ] )
% 0.70/1.10  , clause( 294, [ equalish( 'e_3', X ), ~( 'group_element'( 'e_3' ) ), ~( 
% 0.70/1.10    'group_element'( X ) ), product1( 'e_3', X, 'e_1' ), product1( 'e_3', X, 
% 0.70/1.10    'e_2' ) ] )
% 0.70/1.10  , 1, clause( 4, [ 'group_element'( 'e_3' ) ] )
% 0.70/1.10  , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 44, [ ~( 'group_element'( X ) ), equalish( 'e_3', X ), product1( 
% 0.70/1.10    'e_3', X, 'e_1' ), product1( 'e_3', X, 'e_2' ) ] )
% 0.70/1.10  , clause( 299, [ equalish( 'e_3', X ), ~( 'group_element'( X ) ), product1( 
% 0.70/1.10    'e_3', X, 'e_1' ), product1( 'e_3', X, 'e_2' ) ] )
% 0.70/1.10  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 
% 0.70/1.10    0 ), ==>( 2, 2 ), ==>( 3, 3 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 301, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.70/1.10  , clause( 14, [ equalish( X, T ), ~( product1( X, Y, Z ) ), ~( product1( T
% 0.70/1.10    , Y, Z ) ) ] )
% 0.70/1.10  , 2, clause( 15, [ product1( X, X, X ) ] )
% 0.70/1.10  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y ), :=( T, Y )] ), 
% 0.70/1.10    substitution( 1, [ :=( X, Y )] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 53, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.70/1.10  , clause( 301, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.70/1.10  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.70/1.10     ), ==>( 1, 1 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 302, [ equalish( X, Y ), ~( product2( X, Y, X ) ) ] )
% 0.70/1.10  , clause( 18, [ equalish( Y, T ), ~( product2( X, Y, Z ) ), ~( product2( X
% 0.70/1.10    , T, Z ) ) ] )
% 0.70/1.10  , 1, clause( 20, [ product2( X, X, X ) ] )
% 0.70/1.10  , 0, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, X ), :=( T, Y )] ), 
% 0.70/1.10    substitution( 1, [ :=( X, X )] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 58, [ equalish( X, Y ), ~( product2( X, Y, X ) ) ] )
% 0.70/1.10  , clause( 302, [ equalish( X, Y ), ~( product2( X, Y, X ) ) ] )
% 0.70/1.10  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.70/1.10     ), ==>( 1, 1 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 304, [ equalish( X, Y ), ~( product2( X, X, Y ) ) ] )
% 0.70/1.10  , clause( 17, [ equalish( Z, T ), ~( product2( X, Y, Z ) ), ~( product2( X
% 0.70/1.10    , Y, T ) ) ] )
% 0.70/1.10  , 1, clause( 20, [ product2( X, X, X ) ] )
% 0.70/1.10  , 0, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, X ), :=( T, Y )] ), 
% 0.70/1.10    substitution( 1, [ :=( X, X )] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 72, [ equalish( X, Y ), ~( product2( X, X, Y ) ) ] )
% 0.70/1.10  , clause( 304, [ equalish( X, Y ), ~( product2( X, X, Y ) ) ] )
% 0.70/1.10  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.70/1.10     ), ==>( 1, 1 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 306, [ equalish( X, Y ), ~( product1( X, Y, Z ) ), ~( product1( Z, 
% 0.70/1.10    Y, X ) ) ] )
% 0.70/1.10  , clause( 72, [ equalish( X, Y ), ~( product2( X, X, Y ) ) ] )
% 0.70/1.10  , 1, clause( 21, [ ~( product1( X, Y, Z ) ), ~( product1( Z, Y, T ) ), 
% 0.70/1.10    product2( T, X, Y ) ] )
% 0.70/1.10  , 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 0.70/1.10    , X ), :=( Y, Y ), :=( Z, Z ), :=( T, X )] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 75, [ equalish( X, Y ), ~( product1( X, Y, Z ) ), ~( product1( Z, Y
% 0.70/1.10    , X ) ) ] )
% 0.70/1.10  , clause( 306, [ equalish( X, Y ), ~( product1( X, Y, Z ) ), ~( product1( Z
% 0.70/1.10    , Y, X ) ) ] )
% 0.70/1.10  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 0.70/1.10    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 308, [ equalish( X, Y ), ~( product1( Y, X, Z ) ), ~( product1( Z, 
% 0.70/1.10    X, X ) ) ] )
% 0.70/1.10  , clause( 58, [ equalish( X, Y ), ~( product2( X, Y, X ) ) ] )
% 0.70/1.10  , 1, clause( 21, [ ~( product1( X, Y, Z ) ), ~( product1( Z, Y, T ) ), 
% 0.70/1.10    product2( T, X, Y ) ] )
% 0.70/1.10  , 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 0.70/1.10    , Y ), :=( Y, X ), :=( Z, Z ), :=( T, X )] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 79, [ equalish( Y, X ), ~( product1( X, Y, Z ) ), ~( product1( Z, Y
% 0.70/1.10    , Y ) ) ] )
% 0.70/1.10  , clause( 308, [ equalish( X, Y ), ~( product1( Y, X, Z ) ), ~( product1( Z
% 0.70/1.10    , X, X ) ) ] )
% 0.70/1.10  , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ), 
% 0.70/1.10    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 311, [ equalish( 'e_3', 'e_2' ), ~( 'group_element'( 'e_2' ) ), 
% 0.70/1.10    equalish( 'e_3', 'e_2' ), product1( 'e_3', 'e_2', 'e_1' ) ] )
% 0.70/1.10  , clause( 53, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.70/1.10  , 1, clause( 44, [ ~( 'group_element'( X ) ), equalish( 'e_3', X ), 
% 0.70/1.10    product1( 'e_3', X, 'e_1' ), product1( 'e_3', X, 'e_2' ) ] )
% 0.70/1.10  , 3, substitution( 0, [ :=( X, 'e_3' ), :=( Y, 'e_2' )] ), substitution( 1
% 0.70/1.10    , [ :=( X, 'e_2' )] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 314, [ equalish( 'e_3', 'e_2' ), equalish( 'e_3', 'e_2' ), product1( 
% 0.70/1.10    'e_3', 'e_2', 'e_1' ) ] )
% 0.70/1.10  , clause( 311, [ equalish( 'e_3', 'e_2' ), ~( 'group_element'( 'e_2' ) ), 
% 0.70/1.10    equalish( 'e_3', 'e_2' ), product1( 'e_3', 'e_2', 'e_1' ) ] )
% 0.70/1.10  , 1, clause( 3, [ 'group_element'( 'e_2' ) ] )
% 0.70/1.10  , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  factor(
% 0.70/1.10  clause( 315, [ equalish( 'e_3', 'e_2' ), product1( 'e_3', 'e_2', 'e_1' ) ]
% 0.70/1.10     )
% 0.70/1.10  , clause( 314, [ equalish( 'e_3', 'e_2' ), equalish( 'e_3', 'e_2' ), 
% 0.70/1.10    product1( 'e_3', 'e_2', 'e_1' ) ] )
% 0.70/1.10  , 0, 1, substitution( 0, [] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 176, [ equalish( 'e_3', 'e_2' ), product1( 'e_3', 'e_2', 'e_1' ) ]
% 0.70/1.10     )
% 0.70/1.10  , clause( 315, [ equalish( 'e_3', 'e_2' ), product1( 'e_3', 'e_2', 'e_1' )
% 0.70/1.10     ] )
% 0.70/1.10  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 0.70/1.10     ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 316, [ product1( 'e_3', 'e_2', 'e_1' ) ] )
% 0.70/1.10  , clause( 10, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.70/1.10  , 0, clause( 176, [ equalish( 'e_3', 'e_2' ), product1( 'e_3', 'e_2', 'e_1'
% 0.70/1.10     ) ] )
% 0.70/1.10  , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 178, [ product1( 'e_3', 'e_2', 'e_1' ) ] )
% 0.70/1.10  , clause( 316, [ product1( 'e_3', 'e_2', 'e_1' ) ] )
% 0.70/1.10  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 317, [ equalish( 'e_2', 'e_3' ), ~( product1( 'e_1', 'e_2', 'e_2' )
% 0.70/1.10     ) ] )
% 0.70/1.10  , clause( 79, [ equalish( Y, X ), ~( product1( X, Y, Z ) ), ~( product1( Z
% 0.70/1.10    , Y, Y ) ) ] )
% 0.70/1.10  , 1, clause( 178, [ product1( 'e_3', 'e_2', 'e_1' ) ] )
% 0.70/1.10  , 0, substitution( 0, [ :=( X, 'e_3' ), :=( Y, 'e_2' ), :=( Z, 'e_1' )] ), 
% 0.70/1.10    substitution( 1, [] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 318, [ ~( product1( 'e_1', 'e_2', 'e_2' ) ) ] )
% 0.70/1.10  , clause( 8, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.70/1.10  , 0, clause( 317, [ equalish( 'e_2', 'e_3' ), ~( product1( 'e_1', 'e_2', 
% 0.70/1.10    'e_2' ) ) ] )
% 0.70/1.10  , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 180, [ ~( product1( 'e_1', 'e_2', 'e_2' ) ) ] )
% 0.70/1.10  , clause( 318, [ ~( product1( 'e_1', 'e_2', 'e_2' ) ) ] )
% 0.70/1.10  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 319, [ equalish( 'e_3', 'e_2' ), ~( product1( 'e_1', 'e_2', 'e_3' )
% 0.70/1.10     ) ] )
% 0.70/1.10  , clause( 75, [ equalish( X, Y ), ~( product1( X, Y, Z ) ), ~( product1( Z
% 0.70/1.10    , Y, X ) ) ] )
% 0.70/1.10  , 1, clause( 178, [ product1( 'e_3', 'e_2', 'e_1' ) ] )
% 0.70/1.10  , 0, substitution( 0, [ :=( X, 'e_3' ), :=( Y, 'e_2' ), :=( Z, 'e_1' )] ), 
% 0.70/1.10    substitution( 1, [] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 321, [ ~( product1( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.70/1.10  , clause( 10, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.70/1.10  , 0, clause( 319, [ equalish( 'e_3', 'e_2' ), ~( product1( 'e_1', 'e_2', 
% 0.70/1.10    'e_3' ) ) ] )
% 0.70/1.10  , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 181, [ ~( product1( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.70/1.10  , clause( 321, [ ~( product1( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.70/1.10  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 323, [ equalish( X, 'e_3' ), ~( product1( X, 'e_2', 'e_1' ) ) ] )
% 0.70/1.10  , clause( 14, [ equalish( X, T ), ~( product1( X, Y, Z ) ), ~( product1( T
% 0.70/1.10    , Y, Z ) ) ] )
% 0.70/1.10  , 2, clause( 178, [ product1( 'e_3', 'e_2', 'e_1' ) ] )
% 0.70/1.10  , 0, substitution( 0, [ :=( X, X ), :=( Y, 'e_2' ), :=( Z, 'e_1' ), :=( T, 
% 0.70/1.10    'e_3' )] ), substitution( 1, [] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 183, [ equalish( X, 'e_3' ), ~( product1( X, 'e_2', 'e_1' ) ) ] )
% 0.70/1.10  , clause( 323, [ equalish( X, 'e_3' ), ~( product1( X, 'e_2', 'e_1' ) ) ]
% 0.70/1.10     )
% 0.70/1.10  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 
% 0.70/1.10    1 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 324, [ ~( 'group_element'( 'e_1' ) ), ~( 'group_element'( 'e_2' ) )
% 0.70/1.10    , product1( 'e_1', 'e_2', 'e_1' ), product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.70/1.10  , clause( 181, [ ~( product1( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.70/1.10  , 0, clause( 11, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), 
% 0.70/1.10    product1( X, Y, 'e_1' ), product1( X, Y, 'e_2' ), product1( X, Y, 'e_3' )
% 0.70/1.10     ] )
% 0.70/1.10  , 4, substitution( 0, [] ), substitution( 1, [ :=( X, 'e_1' ), :=( Y, 'e_2'
% 0.70/1.10     )] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 325, [ ~( 'group_element'( 'e_2' ) ), product1( 'e_1', 'e_2', 'e_1'
% 0.70/1.10     ), product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.70/1.10  , clause( 324, [ ~( 'group_element'( 'e_1' ) ), ~( 'group_element'( 'e_2' )
% 0.70/1.10     ), product1( 'e_1', 'e_2', 'e_1' ), product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.70/1.10  , 0, clause( 2, [ 'group_element'( 'e_1' ) ] )
% 0.70/1.10  , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 194, [ ~( 'group_element'( 'e_2' ) ), product1( 'e_1', 'e_2', 'e_1'
% 0.70/1.10     ), product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.70/1.10  , clause( 325, [ ~( 'group_element'( 'e_2' ) ), product1( 'e_1', 'e_2', 
% 0.70/1.10    'e_1' ), product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.70/1.10  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2
% 0.70/1.10    , 2 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 326, [ product1( 'e_1', 'e_2', 'e_1' ), product1( 'e_1', 'e_2', 
% 0.70/1.10    'e_2' ) ] )
% 0.70/1.10  , clause( 194, [ ~( 'group_element'( 'e_2' ) ), product1( 'e_1', 'e_2', 
% 0.70/1.10    'e_1' ), product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.70/1.10  , 0, clause( 3, [ 'group_element'( 'e_2' ) ] )
% 0.70/1.10  , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 327, [ product1( 'e_1', 'e_2', 'e_1' ) ] )
% 0.70/1.10  , clause( 180, [ ~( product1( 'e_1', 'e_2', 'e_2' ) ) ] )
% 0.70/1.10  , 0, clause( 326, [ product1( 'e_1', 'e_2', 'e_1' ), product1( 'e_1', 'e_2'
% 0.70/1.10    , 'e_2' ) ] )
% 0.70/1.10  , 1, substitution( 0, [] ), substitution( 1, [] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 195, [ product1( 'e_1', 'e_2', 'e_1' ) ] )
% 0.70/1.10  , clause( 327, [ product1( 'e_1', 'e_2', 'e_1' ) ] )
% 0.70/1.10  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 328, [ equalish( 'e_1', 'e_3' ) ] )
% 0.70/1.10  , clause( 183, [ equalish( X, 'e_3' ), ~( product1( X, 'e_2', 'e_1' ) ) ]
% 0.70/1.10     )
% 0.70/1.10  , 1, clause( 195, [ product1( 'e_1', 'e_2', 'e_1' ) ] )
% 0.70/1.10  , 0, substitution( 0, [ :=( X, 'e_1' )] ), substitution( 1, [] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  resolution(
% 0.70/1.10  clause( 329, [] )
% 0.70/1.10  , clause( 6, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.70/1.10  , 0, clause( 328, [ equalish( 'e_1', 'e_3' ) ] )
% 0.70/1.10  , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  subsumption(
% 0.70/1.10  clause( 196, [] )
% 0.70/1.10  , clause( 329, [] )
% 0.70/1.10  , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  end.
% 0.70/1.10  
% 0.70/1.10  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.70/1.10  
% 0.70/1.10  Memory use:
% 0.70/1.10  
% 0.70/1.10  space for terms:        3229
% 0.70/1.10  space for clauses:      7665
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  clauses generated:      757
% 0.70/1.11  clauses kept:           197
% 0.70/1.11  clauses selected:       105
% 0.70/1.11  clauses deleted:        8
% 0.70/1.11  clauses inuse deleted:  0
% 0.70/1.11  
% 0.70/1.11  subsentry:          2320
% 0.70/1.11  literals s-matched: 1789
% 0.70/1.11  literals matched:   1701
% 0.70/1.11  full subsumption:   945
% 0.70/1.11  
% 0.70/1.11  checksum:           -2127556372
% 0.70/1.11  
% 0.70/1.11  
% 0.70/1.11  Bliksem ended
%------------------------------------------------------------------------------