TSTP Solution File: SET108-6 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : SET108-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n024.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 22:47:12 EDT 2022

% Result   : Unsatisfiable 0.75s 1.53s
% Output   : Refutation 0.75s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET108-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12  % Command  : bliksem %s
% 0.12/0.33  % Computer : n024.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 : Sun Jul 10 18:21:13 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.72/1.08  *** allocated 10000 integers for termspace/termends
% 0.72/1.08  *** allocated 10000 integers for clauses
% 0.72/1.08  *** allocated 10000 integers for justifications
% 0.72/1.08  Bliksem 1.12
% 0.72/1.08  
% 0.72/1.08  
% 0.72/1.08  Automatic Strategy Selection
% 0.72/1.08  
% 0.72/1.08  Clauses:
% 0.72/1.08  [
% 0.72/1.08     [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.72/1.08     [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.72/1.08     [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.72/1.08    ,
% 0.72/1.08     [ subclass( X, 'universal_class' ) ],
% 0.72/1.08     [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.72/1.08     [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.72/1.08     [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.72/1.08     [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.72/1.08    ,
% 0.72/1.08     [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.72/1.08     ) ) ],
% 0.72/1.08     [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.72/1.08     ) ) ],
% 0.72/1.08     [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.72/1.08     [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.72/1.08     [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.72/1.08     ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.72/1.08     [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member( 
% 0.72/1.08    X, Z ) ],
% 0.72/1.08     [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member( 
% 0.72/1.08    Y, T ) ],
% 0.72/1.08     [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.72/1.08     ), 'cross_product'( Y, T ) ) ],
% 0.72/1.08     [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.72/1.08     ), second( X ) ), X ) ],
% 0.72/1.08     [ subclass( 'element_relation', 'cross_product'( 'universal_class', 
% 0.72/1.08    'universal_class' ) ) ],
% 0.72/1.08     [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X, 
% 0.72/1.08    Y ) ],
% 0.72/1.08     [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.72/1.08    , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.72/1.08    , Y ), 'element_relation' ) ],
% 0.72/1.08     [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.72/1.08     [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.72/1.08     [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y, 
% 0.72/1.08    Z ) ) ],
% 0.72/1.08     [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.72/1.08     [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ), 
% 0.72/1.08    member( X, Y ) ],
% 0.72/1.08     [ =( complement( intersection( complement( X ), complement( Y ) ) ), 
% 0.72/1.08    union( X, Y ) ) ],
% 0.72/1.08     [ =( intersection( complement( intersection( X, Y ) ), complement( 
% 0.72/1.08    intersection( complement( X ), complement( Y ) ) ) ), 
% 0.72/1.08    'symmetric_difference'( X, Y ) ) ],
% 0.72/1.08     [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.72/1.08    ,
% 0.72/1.08     [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.72/1.08    ,
% 0.72/1.08     [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.72/1.08     ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.72/1.08     [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ), 
% 0.72/1.08    'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.72/1.08     [ subclass( rotate( X ), 'cross_product'( 'cross_product'( 
% 0.72/1.08    'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.72/1.08     [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.72/1.08     ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.72/1.08     [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~( 
% 0.72/1.08    member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'( 
% 0.72/1.08    'cross_product'( 'universal_class', 'universal_class' ), 
% 0.72/1.08    'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ), 
% 0.72/1.08    Y ), rotate( T ) ) ],
% 0.72/1.08     [ subclass( flip( X ), 'cross_product'( 'cross_product'( 
% 0.72/1.08    'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.72/1.08     [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.72/1.08    , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.72/1.08     [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~( 
% 0.72/1.08    member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'( 
% 0.72/1.08    'cross_product'( 'universal_class', 'universal_class' ), 
% 0.72/1.08    'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), 
% 0.72/1.08    Z ), flip( T ) ) ],
% 0.72/1.08     [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ), 
% 0.72/1.08    inverse( X ) ) ],
% 0.72/1.08     [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.72/1.08     [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ), 
% 0.72/1.08    'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.72/1.08     [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ), 
% 0.72/1.08    'null_class' ) ), range( X, Y, Z ) ) ],
% 0.72/1.08     [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.72/1.08     ],
% 0.72/1.08     [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.72/1.08     [ subclass( 'successor_relation', 'cross_product'( 'universal_class', 
% 0.72/1.08    'universal_class' ) ) ],
% 0.72/1.08     [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =( 
% 0.72/1.08    successor( X ), Y ) ],
% 0.72/1.08     [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ), 
% 0.72/1.08    'cross_product'( 'universal_class', 'universal_class' ) ) ), member( 
% 0.72/1.08    'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.72/1.08     [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.72/1.08     [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.72/1.08    ,
% 0.72/1.08     [ ~( member( 'null_class', X ) ), ~( subclass( image( 
% 0.72/1.08    'successor_relation', X ), X ) ), inductive( X ) ],
% 0.72/1.08     [ inductive( omega ) ],
% 0.72/1.08     [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.72/1.08     [ member( omega, 'universal_class' ) ],
% 0.72/1.08     [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.72/1.08    , 'sum_class'( X ) ) ],
% 0.72/1.08     [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ), 
% 0.72/1.08    'universal_class' ) ],
% 0.72/1.08     [ =( complement( image( 'element_relation', complement( X ) ) ), 
% 0.72/1.08    'power_class'( X ) ) ],
% 0.72/1.08     [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ), 
% 0.72/1.08    'universal_class' ) ],
% 0.72/1.08     [ subclass( compose( X, Y ), 'cross_product'( 'universal_class', 
% 0.72/1.08    'universal_class' ) ) ],
% 0.72/1.08     [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y, 
% 0.72/1.08    image( Z, image( T, singleton( X ) ) ) ) ],
% 0.72/1.08     [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member( 
% 0.72/1.08    'ordered_pair'( T, X ), 'cross_product'( 'universal_class', 
% 0.72/1.08    'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.72/1.08     ) ],
% 0.72/1.08     [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.72/1.08    , 'identity_relation' ) ],
% 0.72/1.08     [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ), 
% 0.72/1.08    'single_valued_class'( X ) ],
% 0.72/1.08     [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class', 
% 0.72/1.08    'universal_class' ) ) ],
% 0.72/1.08     [ ~( function( X ) ), subclass( compose( X, inverse( X ) ), 
% 0.72/1.08    'identity_relation' ) ],
% 0.72/1.08     [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.72/1.08     ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.72/1.08    , function( X ) ],
% 0.72/1.08     [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image( 
% 0.72/1.08    X, Y ), 'universal_class' ) ],
% 0.72/1.08     [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.72/1.08     [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.72/1.08     ) ],
% 0.72/1.08     [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.72/1.08     [ function( choice ) ],
% 0.72/1.08     [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member( 
% 0.72/1.08    apply( choice, X ), X ) ],
% 0.72/1.08     [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.72/1.08     [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.72/1.08     [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.72/1.08    ,
% 0.72/1.08     [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.72/1.08     ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.72/1.08    , complement( compose( complement( 'element_relation' ), inverse( 
% 0.72/1.08    'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.72/1.08     [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ), 
% 0.72/1.08    'identity_relation' ) ],
% 0.72/1.08     [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.72/1.08    , diagonalise( X ) ) ],
% 0.72/1.08     [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse( 
% 0.72/1.08    'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.72/1.08     [ ~( operation( X ) ), function( X ) ],
% 0.72/1.08     [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.72/1.08     ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.72/1.08     [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'( 
% 0.75/1.53    'domain_of'( X ) ) ) ],
% 0.75/1.53     [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.75/1.53     ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~( 
% 0.75/1.53    subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation( 
% 0.75/1.53    X ) ],
% 0.75/1.53     [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.75/1.53     [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ), 
% 0.75/1.53    'domain_of'( X ) ) ],
% 0.75/1.53     [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'( 
% 0.75/1.53    'domain_of'( Z ) ) ) ],
% 0.75/1.53     [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'( 
% 0.75/1.53    X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.75/1.53     ), compatible( X, Y, Z ) ],
% 0.75/1.53     [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.75/1.53     [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.75/1.53     [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.75/1.53     [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ), 
% 0.75/1.53    'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply( 
% 0.75/1.53    X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.75/1.53     [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ), 
% 0.75/1.53    member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 
% 0.75/1.53    'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.75/1.53    , Y ) ],
% 0.75/1.53     [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ), 
% 0.75/1.53    ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.75/1.53     ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X, 
% 0.75/1.53    'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.75/1.53    , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.75/1.53     [ member( 'ordered_pair'( y, z ), 'cross_product'( 'universal_class', 
% 0.75/1.53    'universal_class' ) ) ],
% 0.75/1.53     [ ~( member( 'ordered_pair'( first( 'ordered_pair'( y, z ) ), second( 
% 0.75/1.53    'ordered_pair'( y, z ) ) ), 'cross_product'( 'universal_class', 
% 0.75/1.53    'universal_class' ) ) ) ]
% 0.75/1.53  ] .
% 0.75/1.53  
% 0.75/1.53  
% 0.75/1.53  percentage equality = 0.213115, percentage horn = 0.913978
% 0.75/1.53  This is a problem with some equality
% 0.75/1.53  
% 0.75/1.53  
% 0.75/1.53  
% 0.75/1.53  Options Used:
% 0.75/1.53  
% 0.75/1.53  useres =            1
% 0.75/1.53  useparamod =        1
% 0.75/1.53  useeqrefl =         1
% 0.75/1.53  useeqfact =         1
% 0.75/1.53  usefactor =         1
% 0.75/1.53  usesimpsplitting =  0
% 0.75/1.53  usesimpdemod =      5
% 0.75/1.53  usesimpres =        3
% 0.75/1.53  
% 0.75/1.53  resimpinuse      =  1000
% 0.75/1.53  resimpclauses =     20000
% 0.75/1.53  substype =          eqrewr
% 0.75/1.53  backwardsubs =      1
% 0.75/1.53  selectoldest =      5
% 0.75/1.53  
% 0.75/1.53  litorderings [0] =  split
% 0.75/1.53  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.75/1.53  
% 0.75/1.53  termordering =      kbo
% 0.75/1.53  
% 0.75/1.53  litapriori =        0
% 0.75/1.53  termapriori =       1
% 0.75/1.53  litaposteriori =    0
% 0.75/1.53  termaposteriori =   0
% 0.75/1.53  demodaposteriori =  0
% 0.75/1.53  ordereqreflfact =   0
% 0.75/1.53  
% 0.75/1.53  litselect =         negord
% 0.75/1.53  
% 0.75/1.53  maxweight =         15
% 0.75/1.53  maxdepth =          30000
% 0.75/1.53  maxlength =         115
% 0.75/1.53  maxnrvars =         195
% 0.75/1.53  excuselevel =       1
% 0.75/1.53  increasemaxweight = 1
% 0.75/1.53  
% 0.75/1.53  maxselected =       10000000
% 0.75/1.53  maxnrclauses =      10000000
% 0.75/1.53  
% 0.75/1.53  showgenerated =    0
% 0.75/1.53  showkept =         0
% 0.75/1.53  showselected =     0
% 0.75/1.53  showdeleted =      0
% 0.75/1.53  showresimp =       1
% 0.75/1.53  showstatus =       2000
% 0.75/1.53  
% 0.75/1.53  prologoutput =     1
% 0.75/1.53  nrgoals =          5000000
% 0.75/1.53  totalproof =       1
% 0.75/1.53  
% 0.75/1.53  Symbols occurring in the translation:
% 0.75/1.53  
% 0.75/1.53  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.75/1.53  .  [1, 2]      (w:1, o:56, a:1, s:1, b:0), 
% 0.75/1.53  !  [4, 1]      (w:0, o:31, a:1, s:1, b:0), 
% 0.75/1.53  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.75/1.53  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.75/1.53  subclass  [41, 2]      (w:1, o:81, a:1, s:1, b:0), 
% 0.75/1.53  member  [43, 2]      (w:1, o:82, a:1, s:1, b:0), 
% 0.75/1.53  'not_subclass_element'  [44, 2]      (w:1, o:83, a:1, s:1, b:0), 
% 0.75/1.53  'universal_class'  [45, 0]      (w:1, o:21, a:1, s:1, b:0), 
% 0.75/1.53  'unordered_pair'  [46, 2]      (w:1, o:84, a:1, s:1, b:0), 
% 0.75/1.53  singleton  [47, 1]      (w:1, o:39, a:1, s:1, b:0), 
% 0.75/1.53  'ordered_pair'  [48, 2]      (w:1, o:85, a:1, s:1, b:0), 
% 0.75/1.53  'cross_product'  [50, 2]      (w:1, o:86, a:1, s:1, b:0), 
% 0.75/1.53  first  [52, 1]      (w:1, o:40, a:1, s:1, b:0), 
% 0.75/1.53  second  [53, 1]      (w:1, o:41, a:1, s:1, b:0), 
% 0.75/1.53  'element_relation'  [54, 0]      (w:1, o:25, a:1, s:1, b:0), 
% 0.75/1.53  intersection  [55, 2]      (w:1, o:88, a:1, s:1, b:0), 
% 0.75/1.53  complement  [56, 1]      (w:1, o:42, a:1, s:1, b:0), 
% 0.75/1.53  union  [57, 2]      (w:1, o:89, a:1, s:1, b:0), 
% 0.75/1.53  'symmetric_difference'  [58, 2]      (w:1, o:90, a:1, s:1, b:0), 
% 0.75/1.53  restrict  [60, 3]      (w:1, o:93, a:1, s:1, b:0), 
% 0.75/1.53  'null_class'  [61, 0]      (w:1, o:26, a:1, s:1, b:0), 
% 0.75/1.53  'domain_of'  [62, 1]      (w:1, o:44, a:1, s:1, b:0), 
% 0.75/1.53  rotate  [63, 1]      (w:1, o:36, a:1, s:1, b:0), 
% 0.75/1.53  flip  [65, 1]      (w:1, o:45, a:1, s:1, b:0), 
% 0.75/1.53  inverse  [66, 1]      (w:1, o:46, a:1, s:1, b:0), 
% 0.75/1.53  'range_of'  [67, 1]      (w:1, o:37, a:1, s:1, b:0), 
% 0.75/1.53  domain  [68, 3]      (w:1, o:95, a:1, s:1, b:0), 
% 0.75/1.53  range  [69, 3]      (w:1, o:96, a:1, s:1, b:0), 
% 0.75/1.53  image  [70, 2]      (w:1, o:87, a:1, s:1, b:0), 
% 0.75/1.53  successor  [71, 1]      (w:1, o:47, a:1, s:1, b:0), 
% 0.75/1.53  'successor_relation'  [72, 0]      (w:1, o:6, a:1, s:1, b:0), 
% 0.75/1.53  inductive  [73, 1]      (w:1, o:48, a:1, s:1, b:0), 
% 0.75/1.53  omega  [74, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 0.75/1.53  'sum_class'  [75, 1]      (w:1, o:49, a:1, s:1, b:0), 
% 0.75/1.53  'power_class'  [76, 1]      (w:1, o:52, a:1, s:1, b:0), 
% 0.75/1.53  compose  [78, 2]      (w:1, o:91, a:1, s:1, b:0), 
% 0.75/1.53  'single_valued_class'  [79, 1]      (w:1, o:53, a:1, s:1, b:0), 
% 0.75/1.53  'identity_relation'  [80, 0]      (w:1, o:27, a:1, s:1, b:0), 
% 0.75/1.53  function  [82, 1]      (w:1, o:54, a:1, s:1, b:0), 
% 0.75/1.53  regular  [83, 1]      (w:1, o:38, a:1, s:1, b:0), 
% 0.75/1.53  apply  [84, 2]      (w:1, o:92, a:1, s:1, b:0), 
% 0.75/1.53  choice  [85, 0]      (w:1, o:28, a:1, s:1, b:0), 
% 0.75/1.53  'one_to_one'  [86, 1]      (w:1, o:50, a:1, s:1, b:0), 
% 0.75/1.53  'subset_relation'  [87, 0]      (w:1, o:5, a:1, s:1, b:0), 
% 0.75/1.53  diagonalise  [88, 1]      (w:1, o:55, a:1, s:1, b:0), 
% 0.75/1.53  cantor  [89, 1]      (w:1, o:43, a:1, s:1, b:0), 
% 0.75/1.53  operation  [90, 1]      (w:1, o:51, a:1, s:1, b:0), 
% 0.75/1.53  compatible  [94, 3]      (w:1, o:94, a:1, s:1, b:0), 
% 0.75/1.53  homomorphism  [95, 3]      (w:1, o:97, a:1, s:1, b:0), 
% 0.75/1.53  'not_homomorphism1'  [96, 3]      (w:1, o:98, a:1, s:1, b:0), 
% 0.75/1.53  'not_homomorphism2'  [97, 3]      (w:1, o:99, a:1, s:1, b:0), 
% 0.75/1.53  y  [98, 0]      (w:1, o:29, a:1, s:1, b:0), 
% 0.75/1.53  z  [99, 0]      (w:1, o:30, a:1, s:1, b:0).
% 0.75/1.53  
% 0.75/1.53  
% 0.75/1.53  Starting Search:
% 0.75/1.53  
% 0.75/1.53  Resimplifying inuse:
% 0.75/1.53  Done
% 0.75/1.53  
% 0.75/1.53  
% 0.75/1.53  Intermediate Status:
% 0.75/1.53  Generated:    5497
% 0.75/1.53  Kept:         2041
% 0.75/1.53  Inuse:        103
% 0.75/1.53  Deleted:      5
% 0.75/1.53  Deletedinuse: 2
% 0.75/1.53  
% 0.75/1.53  Resimplifying inuse:
% 0.75/1.53  Done
% 0.75/1.53  
% 0.75/1.53  Resimplifying inuse:
% 0.75/1.53  Done
% 0.75/1.53  
% 0.75/1.53  
% 0.75/1.53  Intermediate Status:
% 0.75/1.53  Generated:    10253
% 0.75/1.53  Kept:         4049
% 0.75/1.53  Inuse:        188
% 0.75/1.53  Deleted:      23
% 0.75/1.53  Deletedinuse: 14
% 0.75/1.53  
% 0.75/1.53  Resimplifying inuse:
% 0.75/1.53  Done
% 0.75/1.53  
% 0.75/1.53  Resimplifying inuse:
% 0.75/1.53  Done
% 0.75/1.53  
% 0.75/1.53  
% 0.75/1.53  Intermediate Status:
% 0.75/1.53  Generated:    14126
% 0.75/1.53  Kept:         6081
% 0.75/1.53  Inuse:        239
% 0.75/1.53  Deleted:      27
% 0.75/1.53  Deletedinuse: 15
% 0.75/1.53  
% 0.75/1.53  Resimplifying inuse:
% 0.75/1.53  Done
% 0.75/1.53  
% 0.75/1.53  Resimplifying inuse:
% 0.75/1.53  Done
% 0.75/1.53  
% 0.75/1.53  
% 0.75/1.53  Intermediate Status:
% 0.75/1.53  Generated:    18824
% 0.75/1.53  Kept:         8090
% 0.75/1.53  Inuse:        291
% 0.75/1.53  Deleted:      84
% 0.75/1.53  Deletedinuse: 71
% 0.75/1.53  
% 0.75/1.53  Resimplifying inuse:
% 0.75/1.53  Done
% 0.75/1.53  
% 0.75/1.53  Resimplifying inuse:
% 0.75/1.53  Done
% 0.75/1.53  
% 0.75/1.53  
% 0.75/1.53  Bliksems!, er is een bewijs:
% 0.75/1.53  % SZS status Unsatisfiable
% 0.75/1.53  % SZS output start Refutation
% 0.75/1.53  
% 0.75/1.53  clause( 15, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( 
% 0.75/1.53    first( X ), second( X ) ), X ) ] )
% 0.75/1.53  .
% 0.75/1.53  clause( 90, [ member( 'ordered_pair'( y, z ), 'cross_product'( 
% 0.75/1.53    'universal_class', 'universal_class' ) ) ] )
% 0.75/1.53  .
% 0.75/1.53  clause( 91, [ ~( member( 'ordered_pair'( first( 'ordered_pair'( y, z ) ), 
% 0.75/1.53    second( 'ordered_pair'( y, z ) ) ), 'cross_product'( 'universal_class', 
% 0.75/1.53    'universal_class' ) ) ) ] )
% 0.75/1.53  .
% 0.75/1.53  clause( 9775, [ =( 'ordered_pair'( first( 'ordered_pair'( y, z ) ), second( 
% 0.75/1.54    'ordered_pair'( y, z ) ) ), 'ordered_pair'( y, z ) ) ] )
% 0.75/1.54  .
% 0.75/1.54  clause( 9874, [] )
% 0.75/1.54  .
% 0.75/1.54  
% 0.75/1.54  
% 0.75/1.54  % SZS output end Refutation
% 0.75/1.54  found a proof!
% 0.75/1.54  
% 0.75/1.54  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.75/1.54  
% 0.75/1.54  initialclauses(
% 0.75/1.54  [ clause( 9876, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 0.75/1.54     ) ] )
% 0.75/1.54  , clause( 9877, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 0.75/1.54    , Y ) ] )
% 0.75/1.54  , clause( 9878, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), 
% 0.75/1.54    subclass( X, Y ) ] )
% 0.75/1.54  , clause( 9879, [ subclass( X, 'universal_class' ) ] )
% 0.75/1.54  , clause( 9880, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 0.75/1.54  , clause( 9881, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 0.75/1.54  , clause( 9882, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ]
% 0.75/1.54     )
% 0.75/1.54  , clause( 9883, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), 
% 0.75/1.54    =( X, Z ) ] )
% 0.75/1.54  , clause( 9884, [ ~( member( X, 'universal_class' ) ), member( X, 
% 0.75/1.54    'unordered_pair'( X, Y ) ) ] )
% 0.75/1.54  , clause( 9885, [ ~( member( X, 'universal_class' ) ), member( X, 
% 0.75/1.54    'unordered_pair'( Y, X ) ) ] )
% 0.75/1.54  , clause( 9886, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 0.75/1.54     )
% 0.75/1.54  , clause( 9887, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 0.75/1.54  , clause( 9888, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 0.75/1.54    , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.75/1.54  , clause( 9889, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.75/1.54     ) ) ), member( X, Z ) ] )
% 0.75/1.54  , clause( 9890, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.75/1.54     ) ) ), member( Y, T ) ] )
% 0.75/1.54  , clause( 9891, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 
% 0.75/1.54    'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 0.75/1.54  , clause( 9892, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 
% 0.75/1.54    'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 0.75/1.54  , clause( 9893, [ subclass( 'element_relation', 'cross_product'( 
% 0.75/1.54    'universal_class', 'universal_class' ) ) ] )
% 0.75/1.54  , clause( 9894, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) )
% 0.75/1.54    , member( X, Y ) ] )
% 0.75/1.54  , clause( 9895, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 
% 0.75/1.54    'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member( 
% 0.75/1.54    'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 0.75/1.54  , clause( 9896, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.75/1.54     )
% 0.75/1.54  , clause( 9897, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 0.75/1.54     )
% 0.75/1.54  , clause( 9898, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, 
% 0.75/1.54    intersection( Y, Z ) ) ] )
% 0.75/1.54  , clause( 9899, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 0.75/1.54     )
% 0.75/1.54  , clause( 9900, [ ~( member( X, 'universal_class' ) ), member( X, 
% 0.75/1.54    complement( Y ) ), member( X, Y ) ] )
% 0.75/1.54  , clause( 9901, [ =( complement( intersection( complement( X ), complement( 
% 0.75/1.54    Y ) ) ), union( X, Y ) ) ] )
% 0.75/1.54  , clause( 9902, [ =( intersection( complement( intersection( X, Y ) ), 
% 0.75/1.54    complement( intersection( complement( X ), complement( Y ) ) ) ), 
% 0.75/1.54    'symmetric_difference'( X, Y ) ) ] )
% 0.75/1.54  , clause( 9903, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( 
% 0.75/1.54    X, Y, Z ) ) ] )
% 0.75/1.54  , clause( 9904, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( 
% 0.75/1.54    Z, X, Y ) ) ] )
% 0.75/1.54  , clause( 9905, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 
% 0.75/1.54    'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 0.75/1.54  , clause( 9906, [ ~( member( X, 'universal_class' ) ), =( restrict( Y, 
% 0.75/1.54    singleton( X ), 'universal_class' ), 'null_class' ), member( X, 
% 0.75/1.54    'domain_of'( Y ) ) ] )
% 0.75/1.54  , clause( 9907, [ subclass( rotate( X ), 'cross_product'( 'cross_product'( 
% 0.75/1.54    'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.75/1.54  , clause( 9908, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), 
% 0.75/1.54    rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 0.75/1.54     ] )
% 0.75/1.54  , clause( 9909, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.75/1.54     ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 
% 0.75/1.54    'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.75/1.54    , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 0.75/1.54    , Y ), rotate( T ) ) ] )
% 0.75/1.54  , clause( 9910, [ subclass( flip( X ), 'cross_product'( 'cross_product'( 
% 0.75/1.54    'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.75/1.54  , clause( 9911, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), 
% 0.75/1.54    flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 0.75/1.54     )
% 0.75/1.54  , clause( 9912, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.75/1.54     ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 
% 0.75/1.54    'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.75/1.54    , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 0.75/1.54    , Z ), flip( T ) ) ] )
% 0.75/1.54  , clause( 9913, [ =( 'domain_of'( flip( 'cross_product'( X, 
% 0.75/1.54    'universal_class' ) ) ), inverse( X ) ) ] )
% 0.75/1.54  , clause( 9914, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 0.75/1.54  , clause( 9915, [ =( first( 'not_subclass_element'( restrict( X, Y, 
% 0.75/1.54    singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 0.75/1.54  , clause( 9916, [ =( second( 'not_subclass_element'( restrict( X, singleton( 
% 0.75/1.54    Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 0.75/1.54  , clause( 9917, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), 
% 0.75/1.54    image( X, Y ) ) ] )
% 0.75/1.54  , clause( 9918, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 0.75/1.54  , clause( 9919, [ subclass( 'successor_relation', 'cross_product'( 
% 0.75/1.54    'universal_class', 'universal_class' ) ) ] )
% 0.75/1.54  , clause( 9920, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' )
% 0.75/1.54     ), =( successor( X ), Y ) ] )
% 0.75/1.54  , clause( 9921, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X
% 0.75/1.54    , Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ), 
% 0.75/1.54    member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 0.75/1.54  , clause( 9922, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 0.75/1.54  , clause( 9923, [ ~( inductive( X ) ), subclass( image( 
% 0.75/1.54    'successor_relation', X ), X ) ] )
% 0.75/1.54  , clause( 9924, [ ~( member( 'null_class', X ) ), ~( subclass( image( 
% 0.75/1.54    'successor_relation', X ), X ) ), inductive( X ) ] )
% 0.75/1.54  , clause( 9925, [ inductive( omega ) ] )
% 0.75/1.54  , clause( 9926, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 0.75/1.54  , clause( 9927, [ member( omega, 'universal_class' ) ] )
% 0.75/1.54  , clause( 9928, [ =( 'domain_of'( restrict( 'element_relation', 
% 0.75/1.54    'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 0.75/1.54  , clause( 9929, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( 
% 0.75/1.54    X ), 'universal_class' ) ] )
% 0.75/1.54  , clause( 9930, [ =( complement( image( 'element_relation', complement( X )
% 0.75/1.54     ) ), 'power_class'( X ) ) ] )
% 0.75/1.54  , clause( 9931, [ ~( member( X, 'universal_class' ) ), member( 
% 0.75/1.54    'power_class'( X ), 'universal_class' ) ] )
% 0.75/1.54  , clause( 9932, [ subclass( compose( X, Y ), 'cross_product'( 
% 0.75/1.54    'universal_class', 'universal_class' ) ) ] )
% 0.75/1.54  , clause( 9933, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), 
% 0.75/1.54    member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 0.75/1.54  , clause( 9934, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 0.75/1.54    , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class', 
% 0.75/1.54    'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.75/1.54     ) ] )
% 0.75/1.54  , clause( 9935, [ ~( 'single_valued_class'( X ) ), subclass( compose( X, 
% 0.75/1.54    inverse( X ) ), 'identity_relation' ) ] )
% 0.75/1.54  , clause( 9936, [ ~( subclass( compose( X, inverse( X ) ), 
% 0.75/1.54    'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 0.75/1.54  , clause( 9937, [ ~( function( X ) ), subclass( X, 'cross_product'( 
% 0.75/1.54    'universal_class', 'universal_class' ) ) ] )
% 0.75/1.54  , clause( 9938, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 0.75/1.54    , 'identity_relation' ) ] )
% 0.75/1.54  , clause( 9939, [ ~( subclass( X, 'cross_product'( 'universal_class', 
% 0.75/1.54    'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ), 
% 0.75/1.54    'identity_relation' ) ), function( X ) ] )
% 0.75/1.54  , clause( 9940, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), 
% 0.75/1.54    member( image( X, Y ), 'universal_class' ) ] )
% 0.75/1.54  , clause( 9941, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.75/1.54  , clause( 9942, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 0.75/1.54    , 'null_class' ) ] )
% 0.75/1.54  , clause( 9943, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y
% 0.75/1.54     ) ) ] )
% 0.75/1.54  , clause( 9944, [ function( choice ) ] )
% 0.75/1.54  , clause( 9945, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' )
% 0.75/1.54    , member( apply( choice, X ), X ) ] )
% 0.75/1.54  , clause( 9946, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 0.75/1.54  , clause( 9947, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 0.75/1.54  , clause( 9948, [ ~( function( inverse( X ) ) ), ~( function( X ) ), 
% 0.75/1.54    'one_to_one'( X ) ] )
% 0.75/1.54  , clause( 9949, [ =( intersection( 'cross_product'( 'universal_class', 
% 0.75/1.54    'universal_class' ), intersection( 'cross_product'( 'universal_class', 
% 0.75/1.54    'universal_class' ), complement( compose( complement( 'element_relation'
% 0.75/1.54     ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 0.75/1.54  , clause( 9950, [ =( intersection( inverse( 'subset_relation' ), 
% 0.75/1.54    'subset_relation' ), 'identity_relation' ) ] )
% 0.75/1.54  , clause( 9951, [ =( complement( 'domain_of'( intersection( X, 
% 0.75/1.54    'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 0.75/1.54  , clause( 9952, [ =( intersection( 'domain_of'( X ), diagonalise( compose( 
% 0.75/1.54    inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 0.75/1.54  , clause( 9953, [ ~( operation( X ) ), function( X ) ] )
% 0.75/1.54  , clause( 9954, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 
% 0.75/1.54    'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.75/1.54     ] )
% 0.75/1.54  , clause( 9955, [ ~( operation( X ) ), subclass( 'range_of'( X ), 
% 0.75/1.54    'domain_of'( 'domain_of'( X ) ) ) ] )
% 0.75/1.54  , clause( 9956, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 
% 0.75/1.54    'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.75/1.54     ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), 
% 0.75/1.54    operation( X ) ] )
% 0.75/1.54  , clause( 9957, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 0.75/1.54  , clause( 9958, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( 
% 0.75/1.54    Y ) ), 'domain_of'( X ) ) ] )
% 0.75/1.54  , clause( 9959, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 
% 0.75/1.54    'domain_of'( 'domain_of'( Z ) ) ) ] )
% 0.75/1.54  , clause( 9960, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) )
% 0.75/1.54    , 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 
% 0.75/1.54    'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 0.75/1.54  , clause( 9961, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 0.75/1.54  , clause( 9962, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 0.75/1.54  , clause( 9963, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 0.75/1.54  , clause( 9964, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( 
% 0.75/1.54    T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 0.75/1.54    , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 0.75/1.54     )
% 0.75/1.54  , clause( 9965, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( 
% 0.75/1.54    Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 
% 0.75/1.54    'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.75/1.54    , Y ) ] )
% 0.75/1.54  , clause( 9966, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( 
% 0.75/1.54    Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z, 
% 0.75/1.54    'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 0.75/1.54     ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X, 
% 0.75/1.54    Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 0.75/1.54     )
% 0.75/1.54  , clause( 9967, [ member( 'ordered_pair'( y, z ), 'cross_product'( 
% 0.75/1.54    'universal_class', 'universal_class' ) ) ] )
% 0.75/1.54  , clause( 9968, [ ~( member( 'ordered_pair'( first( 'ordered_pair'( y, z )
% 0.75/1.54     ), second( 'ordered_pair'( y, z ) ) ), 'cross_product'( 
% 0.75/1.54    'universal_class', 'universal_class' ) ) ) ] )
% 0.75/1.54  ] ).
% 0.75/1.54  
% 0.75/1.54  
% 0.75/1.54  
% 0.75/1.54  subsumption(
% 0.75/1.54  clause( 15, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( 
% 0.75/1.54    first( X ), second( X ) ), X ) ] )
% 0.75/1.54  , clause( 9892, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 
% 0.75/1.54    'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 0.75/1.54  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 0.75/1.54    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 0.75/1.54  
% 0.75/1.54  
% 0.75/1.54  subsumption(
% 0.75/1.54  clause( 90, [ member( 'ordered_pair'( y, z ), 'cross_product'( 
% 0.75/1.54    'universal_class', 'universal_class' ) ) ] )
% 0.75/1.54  , clause( 9967, [ member( 'ordered_pair'( y, z ), 'cross_product'( 
% 0.75/1.54    'universal_class', 'universal_class' ) ) ] )
% 0.75/1.54  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.54  
% 0.75/1.54  
% 0.75/1.54  subsumption(
% 0.75/1.54  clause( 91, [ ~( member( 'ordered_pair'( first( 'ordered_pair'( y, z ) ), 
% 0.75/1.54    second( 'ordered_pair'( y, z ) ) ), 'cross_product'( 'universal_class', 
% 0.75/1.54    'universal_class' ) ) ) ] )
% 0.75/1.54  , clause( 9968, [ ~( member( 'ordered_pair'( first( 'ordered_pair'( y, z )
% 0.75/1.54     ), second( 'ordered_pair'( y, z ) ) ), 'cross_product'( 
% 0.75/1.54    'universal_class', 'universal_class' ) ) ) ] )
% 0.75/1.54  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.54  
% 0.75/1.54  
% 0.75/1.54  eqswap(
% 0.75/1.54  clause( 10081, [ =( X, 'ordered_pair'( first( X ), second( X ) ) ), ~( 
% 0.75/1.54    member( X, 'cross_product'( Y, Z ) ) ) ] )
% 0.75/1.54  , clause( 15, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 
% 0.75/1.54    'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 0.75/1.54  , 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.75/1.54  
% 0.75/1.54  
% 0.75/1.54  resolution(
% 0.75/1.54  clause( 10082, [ =( 'ordered_pair'( y, z ), 'ordered_pair'( first( 
% 0.75/1.54    'ordered_pair'( y, z ) ), second( 'ordered_pair'( y, z ) ) ) ) ] )
% 0.75/1.54  , clause( 10081, [ =( X, 'ordered_pair'( first( X ), second( X ) ) ), ~( 
% 0.75/1.54    member( X, 'cross_product'( Y, Z ) ) ) ] )
% 0.75/1.54  , 1, clause( 90, [ member( 'ordered_pair'( y, z ), 'cross_product'( 
% 0.75/1.54    'universal_class', 'universal_class' ) ) ] )
% 0.75/1.54  , 0, substitution( 0, [ :=( X, 'ordered_pair'( y, z ) ), :=( Y, 
% 0.75/1.54    'universal_class' ), :=( Z, 'universal_class' )] ), substitution( 1, [] )
% 0.75/1.54    ).
% 0.75/1.54  
% 0.75/1.54  
% 0.75/1.54  eqswap(
% 0.75/1.54  clause( 10083, [ =( 'ordered_pair'( first( 'ordered_pair'( y, z ) ), second( 
% 0.75/1.54    'ordered_pair'( y, z ) ) ), 'ordered_pair'( y, z ) ) ] )
% 0.75/1.54  , clause( 10082, [ =( 'ordered_pair'( y, z ), 'ordered_pair'( first( 
% 0.75/1.54    'ordered_pair'( y, z ) ), second( 'ordered_pair'( y, z ) ) ) ) ] )
% 0.75/1.54  , 0, substitution( 0, [] )).
% 0.75/1.54  
% 0.75/1.54  
% 0.75/1.54  subsumption(
% 0.75/1.54  clause( 9775, [ =( 'ordered_pair'( first( 'ordered_pair'( y, z ) ), second( 
% 0.75/1.54    'ordered_pair'( y, z ) ) ), 'ordered_pair'( y, z ) ) ] )
% 0.75/1.54  , clause( 10083, [ =( 'ordered_pair'( first( 'ordered_pair'( y, z ) ), 
% 0.75/1.54    second( 'ordered_pair'( y, z ) ) ), 'ordered_pair'( y, z ) ) ] )
% 0.75/1.54  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.54  
% 0.75/1.54  
% 0.75/1.54  paramod(
% 0.75/1.54  clause( 10085, [ ~( member( 'ordered_pair'( y, z ), 'cross_product'( 
% 0.75/1.54    'universal_class', 'universal_class' ) ) ) ] )
% 0.75/1.54  , clause( 9775, [ =( 'ordered_pair'( first( 'ordered_pair'( y, z ) ), 
% 0.75/1.54    second( 'ordered_pair'( y, z ) ) ), 'ordered_pair'( y, z ) ) ] )
% 0.75/1.54  , 0, clause( 91, [ ~( member( 'ordered_pair'( first( 'ordered_pair'( y, z )
% 0.75/1.54     ), second( 'ordered_pair'( y, z ) ) ), 'cross_product'( 
% 0.75/1.54    'universal_class', 'universal_class' ) ) ) ] )
% 0.75/1.54  , 0, 2, substitution( 0, [] ), substitution( 1, [] )).
% 0.75/1.54  
% 0.75/1.54  
% 0.75/1.54  resolution(
% 0.75/1.54  clause( 10086, [] )
% 0.75/1.54  , clause( 10085, [ ~( member( 'ordered_pair'( y, z ), 'cross_product'( 
% 0.75/1.54    'universal_class', 'universal_class' ) ) ) ] )
% 0.75/1.54  , 0, clause( 90, [ member( 'ordered_pair'( y, z ), 'cross_product'( 
% 0.75/1.54    'universal_class', 'universal_class' ) ) ] )
% 0.75/1.54  , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.75/1.54  
% 0.75/1.54  
% 0.75/1.54  subsumption(
% 0.75/1.54  clause( 9874, [] )
% 0.75/1.54  , clause( 10086, [] )
% 0.75/1.54  , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.75/1.54  
% 0.75/1.54  
% 0.75/1.54  end.
% 0.75/1.54  
% 0.75/1.54  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.75/1.54  
% 0.75/1.54  Memory use:
% 0.75/1.54  
% 0.75/1.54  space for terms:        152076
% 0.75/1.54  space for clauses:      469172
% 0.75/1.54  
% 0.75/1.54  
% 0.75/1.54  clauses generated:      23581
% 0.75/1.54  clauses kept:           9875
% 0.75/1.54  clauses selected:       370
% 0.75/1.54  clauses deleted:        96
% 0.75/1.54  clauses inuse deleted:  80
% 0.75/1.54  
% 0.75/1.54  subsentry:          51356
% 0.75/1.54  literals s-matched: 39915
% 0.75/1.54  literals matched:   39293
% 0.75/1.54  full subsumption:   17768
% 0.75/1.54  
% 0.75/1.54  checksum:           1256904251
% 0.75/1.54  
% 0.75/1.54  
% 0.75/1.54  Bliksem ended
%------------------------------------------------------------------------------