TSTP Solution File: NUM139-1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : NUM139-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n023.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 06:20:05 EDT 2022

% Result   : Unsatisfiable 2.55s 3.01s
% Output   : Refutation 2.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM139-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12  % Command  : bliksem %s
% 0.13/0.33  % Computer : n023.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 : Thu Jul  7 07:04:41 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.43/1.13  *** allocated 10000 integers for termspace/termends
% 0.43/1.13  *** allocated 10000 integers for clauses
% 0.43/1.13  *** allocated 10000 integers for justifications
% 0.43/1.13  Bliksem 1.12
% 0.43/1.13  
% 0.43/1.13  
% 0.43/1.13  Automatic Strategy Selection
% 0.43/1.13  
% 0.43/1.13  Clauses:
% 0.43/1.13  [
% 0.43/1.13     [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.43/1.13     [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.43/1.13     [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.43/1.13    ,
% 0.43/1.13     [ subclass( X, 'universal_class' ) ],
% 0.43/1.13     [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.43/1.13     [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.43/1.13     [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.43/1.13     [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.43/1.13    ,
% 0.43/1.13     [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.43/1.13     ) ) ],
% 0.43/1.13     [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.43/1.13     ) ) ],
% 0.43/1.13     [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.43/1.13     [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.43/1.13     [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.43/1.13     ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member( 
% 0.43/1.13    X, Z ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member( 
% 0.43/1.13    Y, T ) ],
% 0.43/1.13     [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.43/1.13     ), 'cross_product'( Y, T ) ) ],
% 0.43/1.13     [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.43/1.13     ), second( X ) ), X ) ],
% 0.43/1.13     [ subclass( 'element_relation', 'cross_product'( 'universal_class', 
% 0.43/1.13    'universal_class' ) ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X, 
% 0.43/1.13    Y ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.43/1.13    , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.43/1.13    , Y ), 'element_relation' ) ],
% 0.43/1.13     [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.43/1.13     [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.43/1.13     [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y, 
% 0.43/1.13    Z ) ) ],
% 0.43/1.13     [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.43/1.13     [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ), 
% 0.43/1.13    member( X, Y ) ],
% 0.43/1.13     [ =( complement( intersection( complement( X ), complement( Y ) ) ), 
% 0.43/1.13    union( X, Y ) ) ],
% 0.43/1.13     [ =( intersection( complement( intersection( X, Y ) ), complement( 
% 0.43/1.13    intersection( complement( X ), complement( Y ) ) ) ), 
% 0.43/1.13    'symmetric_difference'( X, Y ) ) ],
% 0.43/1.13     [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.43/1.13    ,
% 0.43/1.13     [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.43/1.13    ,
% 0.43/1.13     [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.43/1.13     ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.43/1.13     [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ), 
% 0.43/1.13    'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.43/1.13     [ subclass( rotate( X ), 'cross_product'( 'cross_product'( 
% 0.43/1.13    'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.43/1.13     ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~( 
% 0.43/1.13    member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'( 
% 0.43/1.13    'cross_product'( 'universal_class', 'universal_class' ), 
% 0.43/1.13    'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ), 
% 0.43/1.13    Y ), rotate( T ) ) ],
% 0.43/1.13     [ subclass( flip( X ), 'cross_product'( 'cross_product'( 
% 0.43/1.13    'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.43/1.13    , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~( 
% 0.43/1.13    member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'( 
% 0.43/1.13    'cross_product'( 'universal_class', 'universal_class' ), 
% 0.43/1.13    'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), 
% 0.43/1.13    Z ), flip( T ) ) ],
% 0.43/1.13     [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ), 
% 0.43/1.13    inverse( X ) ) ],
% 0.43/1.13     [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.43/1.13     [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ), 
% 0.43/1.13    'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.43/1.13     [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ), 
% 0.43/1.13    'null_class' ) ), range( X, Y, Z ) ) ],
% 0.43/1.13     [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.43/1.13     ],
% 0.43/1.13     [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.43/1.13     [ subclass( 'successor_relation', 'cross_product'( 'universal_class', 
% 0.43/1.13    'universal_class' ) ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =( 
% 0.43/1.13    successor( X ), Y ) ],
% 0.43/1.13     [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ), 
% 0.43/1.13    'cross_product'( 'universal_class', 'universal_class' ) ) ), member( 
% 0.43/1.13    'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.43/1.13     [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.43/1.13     [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.43/1.13    ,
% 0.43/1.13     [ ~( member( 'null_class', X ) ), ~( subclass( image( 
% 0.43/1.13    'successor_relation', X ), X ) ), inductive( X ) ],
% 0.43/1.13     [ inductive( omega ) ],
% 0.43/1.13     [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.43/1.13     [ member( omega, 'universal_class' ) ],
% 0.43/1.13     [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.43/1.13    , 'sum_class'( X ) ) ],
% 0.43/1.13     [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ), 
% 0.43/1.13    'universal_class' ) ],
% 0.43/1.13     [ =( complement( image( 'element_relation', complement( X ) ) ), 
% 0.43/1.13    'power_class'( X ) ) ],
% 0.43/1.13     [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ), 
% 0.43/1.13    'universal_class' ) ],
% 0.43/1.13     [ subclass( compose( X, Y ), 'cross_product'( 'universal_class', 
% 0.43/1.13    'universal_class' ) ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y, 
% 0.43/1.13    image( Z, image( T, singleton( X ) ) ) ) ],
% 0.43/1.13     [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member( 
% 0.43/1.13    'ordered_pair'( T, X ), 'cross_product'( 'universal_class', 
% 0.43/1.13    'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.43/1.13     ) ],
% 0.43/1.13     [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.43/1.13    , 'identity_relation' ) ],
% 0.43/1.13     [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ), 
% 0.43/1.13    'single_valued_class'( X ) ],
% 0.43/1.13     [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class', 
% 0.43/1.13    'universal_class' ) ) ],
% 0.43/1.13     [ ~( function( X ) ), subclass( compose( X, inverse( X ) ), 
% 0.43/1.13    'identity_relation' ) ],
% 0.43/1.13     [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.43/1.13     ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.43/1.13    , function( X ) ],
% 0.43/1.13     [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image( 
% 0.43/1.13    X, Y ), 'universal_class' ) ],
% 0.43/1.13     [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.43/1.13     [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.43/1.13     ) ],
% 0.43/1.13     [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.43/1.13     [ function( choice ) ],
% 0.43/1.13     [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member( 
% 0.43/1.13    apply( choice, X ), X ) ],
% 0.43/1.13     [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.43/1.13     [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.43/1.13     [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.43/1.13    ,
% 0.43/1.13     [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.43/1.13     ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.43/1.13    , complement( compose( complement( 'element_relation' ), inverse( 
% 0.43/1.13    'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.43/1.13     [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ), 
% 0.43/1.13    'identity_relation' ) ],
% 0.43/1.13     [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.43/1.13    , diagonalise( X ) ) ],
% 0.43/1.13     [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse( 
% 0.43/1.13    'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.43/1.13     [ ~( operation( X ) ), function( X ) ],
% 0.43/1.13     [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.43/1.13     ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.43/1.13     [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'( 
% 0.43/1.13    'domain_of'( X ) ) ) ],
% 0.43/1.13     [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.43/1.13     ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~( 
% 0.43/1.13    subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation( 
% 0.43/1.13    X ) ],
% 0.43/1.13     [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.43/1.13     [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ), 
% 0.43/1.13    'domain_of'( X ) ) ],
% 0.43/1.13     [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'( 
% 0.43/1.13    'domain_of'( Z ) ) ) ],
% 0.43/1.13     [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'( 
% 0.43/1.13    X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.43/1.13     ), compatible( X, Y, Z ) ],
% 0.43/1.13     [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.43/1.13     [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.43/1.13     [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.43/1.13     [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ), 
% 0.43/1.13    'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply( 
% 0.43/1.13    X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.43/1.13     [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ), 
% 0.43/1.13    member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 
% 0.43/1.13    'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.43/1.13    , Y ) ],
% 0.43/1.13     [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ), 
% 0.43/1.13    ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.43/1.13     ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X, 
% 0.43/1.13    'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.43/1.13    , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.43/1.13     [ subclass( 'compose_class'( X ), 'cross_product'( 'universal_class', 
% 0.43/1.13    'universal_class' ) ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ), =( 
% 0.43/1.13    compose( Z, X ), Y ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.43/1.13    , 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) ), member( 
% 0.43/1.13    'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ],
% 0.43/1.13     [ subclass( 'composition_function', 'cross_product'( 'universal_class', 
% 0.43/1.13    'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ), 
% 0.43/1.13    'composition_function' ) ), =( compose( X, Y ), Z ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.43/1.13    , 'universal_class' ) ) ), member( 'ordered_pair'( X, 'ordered_pair'( Y, 
% 0.43/1.13    compose( X, Y ) ) ), 'composition_function' ) ],
% 0.43/1.13     [ subclass( 'domain_relation', 'cross_product'( 'universal_class', 
% 0.43/1.13    'universal_class' ) ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) ), =( 
% 0.43/1.13    'domain_of'( X ), Y ) ],
% 0.43/1.13     [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X, 
% 0.43/1.13    'domain_of'( X ) ), 'domain_relation' ) ],
% 0.43/1.13     [ =( first( 'not_subclass_element'( compose( X, inverse( X ) ), 
% 0.43/1.13    'identity_relation' ) ), 'single_valued1'( X ) ) ],
% 0.43/1.13     [ =( second( 'not_subclass_element'( compose( X, inverse( X ) ), 
% 0.43/1.13    'identity_relation' ) ), 'single_valued2'( X ) ) ],
% 0.43/1.13     [ =( domain( X, image( inverse( X ), singleton( 'single_valued1'( X ) )
% 0.43/1.13     ), 'single_valued2'( X ) ), 'single_valued3'( X ) ) ],
% 0.43/1.13     [ =( intersection( complement( compose( 'element_relation', complement( 
% 0.43/1.13    'identity_relation' ) ) ), 'element_relation' ), 'singleton_relation' ) ]
% 0.43/1.13    ,
% 0.43/1.13     [ subclass( 'application_function', 'cross_product'( 'universal_class', 
% 0.43/1.13    'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ), 
% 0.43/1.13    'application_function' ) ), member( Y, 'domain_of'( X ) ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ), 
% 0.43/1.13    'application_function' ) ), =( apply( X, Y ), Z ) ],
% 0.43/1.13     [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ), 
% 0.43/1.13    'cross_product'( 'universal_class', 'cross_product'( 'universal_class', 
% 0.43/1.13    'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member( 
% 0.43/1.13    'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ), 
% 0.43/1.13    'application_function' ) ],
% 0.43/1.13     [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.43/1.13     [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 0.77/1.13     [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ],
% 0.77/1.13     [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ), maps( X, 
% 0.77/1.13    'domain_of'( X ), Y ) ],
% 0.77/1.13     [ =( union( X, inverse( X ) ), 'symmetrization_of'( X ) ) ],
% 0.77/1.13     [ ~( irreflexive( X, Y ) ), subclass( restrict( X, Y, Y ), complement( 
% 0.77/1.13    'identity_relation' ) ) ],
% 0.77/1.13     [ ~( subclass( restrict( X, Y, Y ), complement( 'identity_relation' ) )
% 0.77/1.13     ), irreflexive( X, Y ) ],
% 0.77/1.13     [ ~( connected( X, Y ) ), subclass( 'cross_product'( Y, Y ), union( 
% 0.77/1.13    'identity_relation', 'symmetrization_of'( X ) ) ) ],
% 0.77/1.13     [ ~( subclass( 'cross_product'( X, X ), union( 'identity_relation', 
% 0.77/1.13    'symmetrization_of'( Y ) ) ) ), connected( Y, X ) ],
% 0.77/1.13     [ ~( transitive( X, Y ) ), subclass( compose( restrict( X, Y, Y ), 
% 0.77/1.13    restrict( X, Y, Y ) ), restrict( X, Y, Y ) ) ],
% 0.77/1.13     [ ~( subclass( compose( restrict( X, Y, Y ), restrict( X, Y, Y ) ), 
% 0.77/1.13    restrict( X, Y, Y ) ) ), transitive( X, Y ) ],
% 0.77/1.13     [ ~( asymmetric( X, Y ) ), =( restrict( intersection( X, inverse( X ) )
% 0.77/1.13    , Y, Y ), 'null_class' ) ],
% 0.77/1.13     [ ~( =( restrict( intersection( X, inverse( X ) ), Y, Y ), 'null_class'
% 0.77/1.13     ) ), asymmetric( X, Y ) ],
% 0.77/1.13     [ =( segment( X, Y, Z ), 'domain_of'( restrict( X, Y, singleton( Z ) ) )
% 0.77/1.13     ) ],
% 0.77/1.13     [ ~( 'well_ordering'( X, Y ) ), connected( X, Y ) ],
% 0.77/1.13     [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), =( Z, 
% 0.77/1.13    'null_class' ), member( least( X, Z ), Z ) ],
% 0.77/1.13     [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), ~( member( T, Z )
% 0.77/1.13     ), member( least( X, Z ), Z ) ],
% 0.77/1.13     [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), =( segment( X, Z
% 0.77/1.13    , least( X, Z ) ), 'null_class' ) ],
% 0.77/1.13     [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), ~( member( T, Z )
% 0.77/1.13     ), ~( member( 'ordered_pair'( T, least( X, Z ) ), X ) ) ],
% 0.77/1.13     [ ~( connected( X, Y ) ), ~( =( 'not_well_ordering'( X, Y ), 
% 0.77/1.13    'null_class' ) ), 'well_ordering'( X, Y ) ],
% 0.77/1.13     [ ~( connected( X, Y ) ), subclass( 'not_well_ordering'( X, Y ), Y ), 
% 0.77/1.13    'well_ordering'( X, Y ) ],
% 0.77/1.13     [ ~( member( X, 'not_well_ordering'( Y, Z ) ) ), ~( =( segment( Y, 
% 0.77/1.13    'not_well_ordering'( Y, Z ), X ), 'null_class' ) ), ~( connected( Y, Z )
% 0.77/1.13     ), 'well_ordering'( Y, Z ) ],
% 0.77/1.13     [ ~( section( X, Y, Z ) ), subclass( Y, Z ) ],
% 0.77/1.13     [ ~( section( X, Y, Z ) ), subclass( 'domain_of'( restrict( X, Z, Y ) )
% 0.77/1.13    , Y ) ],
% 0.77/1.13     [ ~( subclass( X, Y ) ), ~( subclass( 'domain_of'( restrict( Z, Y, X ) )
% 0.77/1.13    , X ) ), section( Z, X, Y ) ],
% 0.77/1.13     [ ~( member( X, 'ordinal_numbers' ) ), 'well_ordering'( 
% 0.77/1.13    'element_relation', X ) ],
% 0.77/1.13     [ ~( member( X, 'ordinal_numbers' ) ), subclass( 'sum_class'( X ), X ) ]
% 0.77/1.13    ,
% 0.77/1.13     [ ~( 'well_ordering'( 'element_relation', X ) ), ~( subclass( 
% 0.77/1.13    'sum_class'( X ), X ) ), ~( member( X, 'universal_class' ) ), member( X, 
% 0.77/1.13    'ordinal_numbers' ) ],
% 0.77/1.13     [ ~( 'well_ordering'( 'element_relation', X ) ), ~( subclass( 
% 0.77/1.13    'sum_class'( X ), X ) ), member( X, 'ordinal_numbers' ), =( X, 
% 0.77/1.13    'ordinal_numbers' ) ],
% 0.77/1.13     [ =( union( singleton( 'null_class' ), image( 'successor_relation', 
% 0.77/1.13    'ordinal_numbers' ) ), 'kind_1_ordinals' ) ],
% 0.77/1.13     [ =( intersection( complement( 'kind_1_ordinals' ), 'ordinal_numbers' )
% 0.77/1.13    , 'limit_ordinals' ) ],
% 0.77/1.13     [ subclass( 'rest_of'( X ), 'cross_product'( 'universal_class', 
% 0.77/1.13    'universal_class' ) ) ],
% 0.77/1.13     [ ~( member( 'ordered_pair'( X, Y ), 'rest_of'( Z ) ) ), member( X, 
% 0.77/1.13    'domain_of'( Z ) ) ],
% 0.77/1.13     [ ~( member( 'ordered_pair'( X, Y ), 'rest_of'( Z ) ) ), =( restrict( Z
% 0.77/1.13    , X, 'universal_class' ), Y ) ],
% 0.77/1.13     [ ~( member( X, 'domain_of'( Y ) ) ), ~( =( restrict( Y, X, 
% 0.77/1.13    'universal_class' ), Z ) ), member( 'ordered_pair'( X, Z ), 'rest_of'( Y
% 0.77/1.13     ) ) ],
% 0.77/1.13     [ subclass( 'rest_relation', 'cross_product'( 'universal_class', 
% 0.77/1.13    'universal_class' ) ) ],
% 0.77/1.13     [ ~( member( 'ordered_pair'( X, Y ), 'rest_relation' ) ), =( 'rest_of'( 
% 0.77/1.13    X ), Y ) ],
% 0.77/1.13     [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X, 
% 0.77/1.13    'rest_of'( X ) ), 'rest_relation' ) ],
% 0.77/1.13     [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), function( Y ) ]
% 0.77/1.13    ,
% 0.77/1.13     [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), function( X ) ]
% 0.77/1.13    ,
% 0.77/1.13     [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), member( 
% 1.32/1.69    'domain_of'( X ), 'ordinal_numbers' ) ],
% 1.32/1.69     [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), =( compose( Y, 
% 1.32/1.69    'rest_of'( X ) ), X ) ],
% 1.32/1.69     [ ~( function( X ) ), ~( function( Y ) ), ~( member( 'domain_of'( Y ), 
% 1.32/1.69    'ordinal_numbers' ) ), ~( =( compose( X, 'rest_of'( Y ) ), Y ) ), member( 
% 1.32/1.69    Y, 'recursion_equation_functions'( X ) ) ],
% 1.32/1.69     [ subclass( 'union_of_range_map', 'cross_product'( 'universal_class', 
% 1.32/1.69    'universal_class' ) ) ],
% 1.32/1.69     [ ~( member( 'ordered_pair'( X, Y ), 'union_of_range_map' ) ), =( 
% 1.32/1.69    'sum_class'( 'range_of'( X ) ), Y ) ],
% 1.32/1.69     [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 1.32/1.69    , 'universal_class' ) ) ), ~( =( 'sum_class'( 'range_of'( X ) ), Y ) ), 
% 1.32/1.69    member( 'ordered_pair'( X, Y ), 'union_of_range_map' ) ],
% 1.32/1.69     [ =( apply( recursion( X, 'successor_relation', 'union_of_range_map' ), 
% 1.32/1.69    Y ), 'ordinal_add'( X, Y ) ) ],
% 1.32/1.69     [ =( recursion( 'null_class', apply( 'add_relation', X ), 
% 1.32/1.69    'union_of_range_map' ), 'ordinal_multiply'( X, Y ) ) ],
% 1.32/1.69     [ ~( member( X, omega ) ), =( 'integer_of'( X ), X ) ],
% 1.32/1.69     [ member( X, omega ), =( 'integer_of'( X ), 'null_class' ) ],
% 1.32/1.69     [ ~( member( 'not_subclass_element'( intersection( 'power_class'( x ), z
% 1.32/1.69     ), x ), z ) ) ],
% 1.32/1.69     [ ~( subclass( intersection( 'power_class'( x ), z ), x ) ) ]
% 1.32/1.69  ] .
% 1.32/1.69  
% 1.32/1.69  
% 1.32/1.69  percentage equality = 0.219136, percentage horn = 0.925000
% 1.32/1.69  This is a problem with some equality
% 1.32/1.69  
% 1.32/1.69  
% 1.32/1.69  
% 1.32/1.69  Options Used:
% 1.32/1.69  
% 1.32/1.69  useres =            1
% 1.32/1.69  useparamod =        1
% 1.32/1.69  useeqrefl =         1
% 1.32/1.69  useeqfact =         1
% 1.32/1.69  usefactor =         1
% 1.32/1.69  usesimpsplitting =  0
% 1.32/1.69  usesimpdemod =      5
% 1.32/1.69  usesimpres =        3
% 1.32/1.69  
% 1.32/1.69  resimpinuse      =  1000
% 1.32/1.69  resimpclauses =     20000
% 1.32/1.69  substype =          eqrewr
% 1.32/1.69  backwardsubs =      1
% 1.32/1.69  selectoldest =      5
% 1.32/1.69  
% 1.32/1.69  litorderings [0] =  split
% 1.32/1.69  litorderings [1] =  extend the termordering, first sorting on arguments
% 1.32/1.69  
% 1.32/1.69  termordering =      kbo
% 1.32/1.69  
% 1.32/1.69  litapriori =        0
% 1.32/1.69  termapriori =       1
% 1.32/1.69  litaposteriori =    0
% 1.32/1.69  termaposteriori =   0
% 1.32/1.69  demodaposteriori =  0
% 1.32/1.69  ordereqreflfact =   0
% 1.32/1.69  
% 1.32/1.69  litselect =         negord
% 1.32/1.69  
% 1.32/1.69  maxweight =         15
% 1.32/1.69  maxdepth =          30000
% 1.32/1.69  maxlength =         115
% 1.32/1.69  maxnrvars =         195
% 1.32/1.69  excuselevel =       1
% 1.32/1.69  increasemaxweight = 1
% 1.32/1.69  
% 1.32/1.69  maxselected =       10000000
% 1.32/1.69  maxnrclauses =      10000000
% 1.32/1.69  
% 1.32/1.69  showgenerated =    0
% 1.32/1.69  showkept =         0
% 1.32/1.69  showselected =     0
% 1.32/1.69  showdeleted =      0
% 1.32/1.69  showresimp =       1
% 1.32/1.69  showstatus =       2000
% 1.32/1.69  
% 1.32/1.69  prologoutput =     1
% 1.32/1.69  nrgoals =          5000000
% 1.32/1.69  totalproof =       1
% 1.32/1.69  
% 1.32/1.69  Symbols occurring in the translation:
% 1.32/1.69  
% 1.32/1.69  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 1.32/1.69  .  [1, 2]      (w:1, o:74, a:1, s:1, b:0), 
% 1.32/1.69  !  [4, 1]      (w:0, o:41, a:1, s:1, b:0), 
% 1.32/1.69  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.32/1.69  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.32/1.69  subclass  [41, 2]      (w:1, o:99, a:1, s:1, b:0), 
% 1.32/1.69  member  [43, 2]      (w:1, o:101, a:1, s:1, b:0), 
% 1.32/1.69  'not_subclass_element'  [44, 2]      (w:1, o:102, a:1, s:1, b:0), 
% 1.32/1.69  'universal_class'  [45, 0]      (w:1, o:24, a:1, s:1, b:0), 
% 1.32/1.69  'unordered_pair'  [46, 2]      (w:1, o:104, a:1, s:1, b:0), 
% 1.32/1.69  singleton  [47, 1]      (w:1, o:51, a:1, s:1, b:0), 
% 1.32/1.69  'ordered_pair'  [48, 2]      (w:1, o:106, a:1, s:1, b:0), 
% 1.32/1.69  'cross_product'  [50, 2]      (w:1, o:107, a:1, s:1, b:0), 
% 1.32/1.69  first  [52, 1]      (w:1, o:52, a:1, s:1, b:0), 
% 1.32/1.69  second  [53, 1]      (w:1, o:53, a:1, s:1, b:0), 
% 1.32/1.69  'element_relation'  [54, 0]      (w:1, o:29, a:1, s:1, b:0), 
% 1.32/1.69  intersection  [55, 2]      (w:1, o:109, a:1, s:1, b:0), 
% 1.32/1.69  complement  [56, 1]      (w:1, o:54, a:1, s:1, b:0), 
% 1.32/1.69  union  [57, 2]      (w:1, o:110, a:1, s:1, b:0), 
% 1.32/1.69  'symmetric_difference'  [58, 2]      (w:1, o:111, a:1, s:1, b:0), 
% 1.32/1.69  restrict  [60, 3]      (w:1, o:120, a:1, s:1, b:0), 
% 1.32/1.69  'null_class'  [61, 0]      (w:1, o:30, a:1, s:1, b:0), 
% 1.32/1.69  'domain_of'  [62, 1]      (w:1, o:57, a:1, s:1, b:0), 
% 1.32/1.69  rotate  [63, 1]      (w:1, o:46, a:1, s:1, b:0), 
% 1.32/1.69  flip  [65, 1]      (w:1, o:58, a:1, s:1, b:0), 
% 1.32/1.69  inverse  [66, 1]      (w:1, o:59, a:1, s:1, b:0), 
% 1.32/1.69  'range_of'  [67, 1]      (w:1, o:47, a:1, s:1, b:0), 
% 1.32/1.69  domain  [68, 3]      (w:1, o:122, a:1, s:1, b:0), 
% 1.32/1.69  range  [69, 3]      (w:1, o:123, a:1, s:1, b:0), 
% 1.32/1.69  image  [70, 2]      (w:1, o:108, a:1, s:1, b:0), 
% 1.32/1.69  successor  [71, 1]      (w:1, o:60, a:1, s:1, b:0), 
% 1.32/1.69  'successor_relation'  [72, 0]      (w:1, o:7, a:1, s:1, b:0), 
% 2.55/3.01  inductive  [73, 1]      (w:1, o:61, a:1, s:1, b:0), 
% 2.55/3.01  omega  [74, 0]      (w:1, o:11, a:1, s:1, b:0), 
% 2.55/3.01  'sum_class'  [75, 1]      (w:1, o:62, a:1, s:1, b:0), 
% 2.55/3.01  'power_class'  [76, 1]      (w:1, o:65, a:1, s:1, b:0), 
% 2.55/3.01  compose  [78, 2]      (w:1, o:112, a:1, s:1, b:0), 
% 2.55/3.01  'single_valued_class'  [79, 1]      (w:1, o:66, a:1, s:1, b:0), 
% 2.55/3.01  'identity_relation'  [80, 0]      (w:1, o:31, a:1, s:1, b:0), 
% 2.55/3.01  function  [82, 1]      (w:1, o:67, a:1, s:1, b:0), 
% 2.55/3.01  regular  [83, 1]      (w:1, o:48, a:1, s:1, b:0), 
% 2.55/3.01  apply  [84, 2]      (w:1, o:113, a:1, s:1, b:0), 
% 2.55/3.01  choice  [85, 0]      (w:1, o:32, a:1, s:1, b:0), 
% 2.55/3.01  'one_to_one'  [86, 1]      (w:1, o:63, a:1, s:1, b:0), 
% 2.55/3.01  'subset_relation'  [87, 0]      (w:1, o:6, a:1, s:1, b:0), 
% 2.55/3.01  diagonalise  [88, 1]      (w:1, o:68, a:1, s:1, b:0), 
% 2.55/3.01  cantor  [89, 1]      (w:1, o:55, a:1, s:1, b:0), 
% 2.55/3.01  operation  [90, 1]      (w:1, o:64, a:1, s:1, b:0), 
% 2.55/3.01  compatible  [94, 3]      (w:1, o:121, a:1, s:1, b:0), 
% 2.55/3.01  homomorphism  [95, 3]      (w:1, o:124, a:1, s:1, b:0), 
% 2.55/3.01  'not_homomorphism1'  [96, 3]      (w:1, o:126, a:1, s:1, b:0), 
% 2.55/3.01  'not_homomorphism2'  [97, 3]      (w:1, o:127, a:1, s:1, b:0), 
% 2.55/3.01  'compose_class'  [98, 1]      (w:1, o:56, a:1, s:1, b:0), 
% 2.55/3.01  'composition_function'  [99, 0]      (w:1, o:33, a:1, s:1, b:0), 
% 2.55/3.01  'domain_relation'  [100, 0]      (w:1, o:28, a:1, s:1, b:0), 
% 2.55/3.01  'single_valued1'  [101, 1]      (w:1, o:69, a:1, s:1, b:0), 
% 2.55/3.01  'single_valued2'  [102, 1]      (w:1, o:70, a:1, s:1, b:0), 
% 2.55/3.01  'single_valued3'  [103, 1]      (w:1, o:71, a:1, s:1, b:0), 
% 2.55/3.01  'singleton_relation'  [104, 0]      (w:1, o:8, a:1, s:1, b:0), 
% 2.55/3.01  'application_function'  [105, 0]      (w:1, o:34, a:1, s:1, b:0), 
% 2.55/3.01  maps  [106, 3]      (w:1, o:125, a:1, s:1, b:0), 
% 2.55/3.01  'symmetrization_of'  [107, 1]      (w:1, o:72, a:1, s:1, b:0), 
% 2.55/3.01  irreflexive  [108, 2]      (w:1, o:114, a:1, s:1, b:0), 
% 2.55/3.01  connected  [109, 2]      (w:1, o:115, a:1, s:1, b:0), 
% 2.55/3.01  transitive  [110, 2]      (w:1, o:103, a:1, s:1, b:0), 
% 2.55/3.01  asymmetric  [111, 2]      (w:1, o:116, a:1, s:1, b:0), 
% 2.55/3.01  segment  [112, 3]      (w:1, o:129, a:1, s:1, b:0), 
% 2.55/3.01  'well_ordering'  [113, 2]      (w:1, o:117, a:1, s:1, b:0), 
% 2.55/3.01  least  [114, 2]      (w:1, o:100, a:1, s:1, b:0), 
% 2.55/3.01  'not_well_ordering'  [115, 2]      (w:1, o:105, a:1, s:1, b:0), 
% 2.55/3.01  section  [116, 3]      (w:1, o:130, a:1, s:1, b:0), 
% 2.55/3.01  'ordinal_numbers'  [117, 0]      (w:1, o:12, a:1, s:1, b:0), 
% 2.55/3.01  'kind_1_ordinals'  [118, 0]      (w:1, o:35, a:1, s:1, b:0), 
% 2.55/3.01  'limit_ordinals'  [119, 0]      (w:1, o:36, a:1, s:1, b:0), 
% 2.55/3.01  'rest_of'  [120, 1]      (w:1, o:49, a:1, s:1, b:0), 
% 2.55/3.01  'rest_relation'  [121, 0]      (w:1, o:5, a:1, s:1, b:0), 
% 2.55/3.01  'recursion_equation_functions'  [122, 1]      (w:1, o:50, a:1, s:1, b:0), 
% 2.55/3.01  'union_of_range_map'  [123, 0]      (w:1, o:37, a:1, s:1, b:0), 
% 2.55/3.01  recursion  [124, 3]      (w:1, o:128, a:1, s:1, b:0), 
% 2.55/3.01  'ordinal_add'  [125, 2]      (w:1, o:118, a:1, s:1, b:0), 
% 2.55/3.01  'add_relation'  [126, 0]      (w:1, o:38, a:1, s:1, b:0), 
% 2.55/3.01  'ordinal_multiply'  [127, 2]      (w:1, o:119, a:1, s:1, b:0), 
% 2.55/3.01  'integer_of'  [128, 1]      (w:1, o:73, a:1, s:1, b:0), 
% 2.55/3.01  x  [129, 0]      (w:1, o:39, a:1, s:1, b:0), 
% 2.55/3.01  z  [130, 0]      (w:1, o:40, a:1, s:1, b:0).
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  Starting Search:
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  Intermediate Status:
% 2.55/3.01  Generated:    5321
% 2.55/3.01  Kept:         2006
% 2.55/3.01  Inuse:        110
% 2.55/3.01  Deleted:      8
% 2.55/3.01  Deletedinuse: 2
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  Intermediate Status:
% 2.55/3.01  Generated:    9915
% 2.55/3.01  Kept:         4013
% 2.55/3.01  Inuse:        188
% 2.55/3.01  Deleted:      31
% 2.55/3.01  Deletedinuse: 18
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  Intermediate Status:
% 2.55/3.01  Generated:    13892
% 2.55/3.01  Kept:         6033
% 2.55/3.01  Inuse:        247
% 2.55/3.01  Deleted:      37
% 2.55/3.01  Deletedinuse: 20
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  Intermediate Status:
% 2.55/3.01  Generated:    18866
% 2.55/3.01  Kept:         8062
% 2.55/3.01  Inuse:        294
% 2.55/3.01  Deleted:      72
% 2.55/3.01  Deletedinuse: 45
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  Intermediate Status:
% 2.55/3.01  Generated:    23564
% 2.55/3.01  Kept:         10146
% 2.55/3.01  Inuse:        354
% 2.55/3.01  Deleted:      96
% 2.55/3.01  Deletedinuse: 69
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  Intermediate Status:
% 2.55/3.01  Generated:    27124
% 2.55/3.01  Kept:         12173
% 2.55/3.01  Inuse:        384
% 2.55/3.01  Deleted:      101
% 2.55/3.01  Deletedinuse: 74
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  Intermediate Status:
% 2.55/3.01  Generated:    31112
% 2.55/3.01  Kept:         14198
% 2.55/3.01  Inuse:        421
% 2.55/3.01  Deleted:      102
% 2.55/3.01  Deletedinuse: 75
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  Intermediate Status:
% 2.55/3.01  Generated:    34520
% 2.55/3.01  Kept:         16206
% 2.55/3.01  Inuse:        451
% 2.55/3.01  Deleted:      102
% 2.55/3.01  Deletedinuse: 75
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  Intermediate Status:
% 2.55/3.01  Generated:    39756
% 2.55/3.01  Kept:         18212
% 2.55/3.01  Inuse:        500
% 2.55/3.01  Deleted:      104
% 2.55/3.01  Deletedinuse: 76
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  Resimplifying clauses:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  Intermediate Status:
% 2.55/3.01  Generated:    45172
% 2.55/3.01  Kept:         20228
% 2.55/3.01  Inuse:        544
% 2.55/3.01  Deleted:      2650
% 2.55/3.01  Deletedinuse: 80
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  Intermediate Status:
% 2.55/3.01  Generated:    49881
% 2.55/3.01  Kept:         22527
% 2.55/3.01  Inuse:        573
% 2.55/3.01  Deleted:      2653
% 2.55/3.01  Deletedinuse: 83
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  Intermediate Status:
% 2.55/3.01  Generated:    53928
% 2.55/3.01  Kept:         24533
% 2.55/3.01  Inuse:        601
% 2.55/3.01  Deleted:      2653
% 2.55/3.01  Deletedinuse: 83
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  Intermediate Status:
% 2.55/3.01  Generated:    57386
% 2.55/3.01  Kept:         26578
% 2.55/3.01  Inuse:        617
% 2.55/3.01  Deleted:      2655
% 2.55/3.01  Deletedinuse: 85
% 2.55/3.01  
% 2.55/3.01  Resimplifying inuse:
% 2.55/3.01  Done
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  Bliksems!, er is een bewijs:
% 2.55/3.01  % SZS status Unsatisfiable
% 2.55/3.01  % SZS output start Refutation
% 2.55/3.01  
% 2.55/3.01  clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y )
% 2.55/3.01     ] )
% 2.55/3.01  .
% 2.55/3.01  clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 2.55/3.01  .
% 2.55/3.01  clause( 157, [ ~( member( 'not_subclass_element'( intersection( 
% 2.55/3.01    'power_class'( x ), z ), x ), z ) ) ] )
% 2.55/3.01  .
% 2.55/3.01  clause( 158, [ ~( subclass( intersection( 'power_class'( x ), z ), x ) ) ]
% 2.55/3.01     )
% 2.55/3.01  .
% 2.55/3.01  clause( 27500, [ ~( member( 'not_subclass_element'( intersection( 
% 2.55/3.01    'power_class'( x ), z ), x ), intersection( X, z ) ) ) ] )
% 2.55/3.01  .
% 2.55/3.01  clause( 27755, [] )
% 2.55/3.01  .
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  % SZS output end Refutation
% 2.55/3.01  found a proof!
% 2.55/3.01  
% 2.55/3.01  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.55/3.01  
% 2.55/3.01  initialclauses(
% 2.55/3.01  [ clause( 27757, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 2.55/3.01     ) ] )
% 2.55/3.01  , clause( 27758, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 2.55/3.01    , Y ) ] )
% 2.55/3.01  , clause( 27759, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), 
% 2.55/3.01    subclass( X, Y ) ] )
% 2.55/3.01  , clause( 27760, [ subclass( X, 'universal_class' ) ] )
% 2.55/3.01  , clause( 27761, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.55/3.01  , clause( 27762, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 2.55/3.01  , clause( 27763, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 2.55/3.01     ] )
% 2.55/3.01  , clause( 27764, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), 
% 2.55/3.01    =( X, Z ) ] )
% 2.55/3.01  , clause( 27765, [ ~( member( X, 'universal_class' ) ), member( X, 
% 2.55/3.01    'unordered_pair'( X, Y ) ) ] )
% 2.55/3.01  , clause( 27766, [ ~( member( X, 'universal_class' ) ), member( X, 
% 2.55/3.01    'unordered_pair'( Y, X ) ) ] )
% 2.55/3.01  , clause( 27767, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 2.55/3.01     )
% 2.55/3.01  , clause( 27768, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.55/3.01  , clause( 27769, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 2.55/3.01    , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 2.55/3.01  , clause( 27770, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.55/3.01     ) ) ), member( X, Z ) ] )
% 2.55/3.01  , clause( 27771, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.55/3.01     ) ) ), member( Y, T ) ] )
% 2.55/3.01  , clause( 27772, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 
% 2.55/3.01    'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 2.55/3.01  , clause( 27773, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 
% 2.55/3.01    'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 2.55/3.01  , clause( 27774, [ subclass( 'element_relation', 'cross_product'( 
% 2.55/3.01    'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01  , clause( 27775, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 2.55/3.01     ), member( X, Y ) ] )
% 2.55/3.01  , clause( 27776, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 
% 2.55/3.01    'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member( 
% 2.55/3.01    'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 2.55/3.01  , clause( 27777, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 2.55/3.01     )
% 2.55/3.01  , clause( 27778, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 2.55/3.01     )
% 2.55/3.01  , clause( 27779, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, 
% 2.55/3.01    intersection( Y, Z ) ) ] )
% 2.55/3.01  , clause( 27780, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 2.55/3.01     )
% 2.55/3.01  , clause( 27781, [ ~( member( X, 'universal_class' ) ), member( X, 
% 2.55/3.01    complement( Y ) ), member( X, Y ) ] )
% 2.55/3.01  , clause( 27782, [ =( complement( intersection( complement( X ), complement( 
% 2.55/3.01    Y ) ) ), union( X, Y ) ) ] )
% 2.55/3.01  , clause( 27783, [ =( intersection( complement( intersection( X, Y ) ), 
% 2.55/3.01    complement( intersection( complement( X ), complement( Y ) ) ) ), 
% 2.55/3.01    'symmetric_difference'( X, Y ) ) ] )
% 2.55/3.01  , clause( 27784, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( 
% 2.55/3.01    X, Y, Z ) ) ] )
% 2.55/3.01  , clause( 27785, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( 
% 2.55/3.01    Z, X, Y ) ) ] )
% 2.55/3.01  , clause( 27786, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 
% 2.55/3.01    'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 2.55/3.01  , clause( 27787, [ ~( member( X, 'universal_class' ) ), =( restrict( Y, 
% 2.55/3.01    singleton( X ), 'universal_class' ), 'null_class' ), member( X, 
% 2.55/3.01    'domain_of'( Y ) ) ] )
% 2.55/3.01  , clause( 27788, [ subclass( rotate( X ), 'cross_product'( 'cross_product'( 
% 2.55/3.01    'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.55/3.01  , clause( 27789, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), 
% 2.55/3.01    rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 2.55/3.01     ] )
% 2.55/3.01  , clause( 27790, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), 
% 2.55/3.01    T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 
% 2.55/3.01    'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.55/3.01    , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 2.55/3.01    , Y ), rotate( T ) ) ] )
% 2.55/3.01  , clause( 27791, [ subclass( flip( X ), 'cross_product'( 'cross_product'( 
% 2.55/3.01    'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.55/3.01  , clause( 27792, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), 
% 2.55/3.01    flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 2.55/3.01     )
% 2.55/3.01  , clause( 27793, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), 
% 2.55/3.01    T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 
% 2.55/3.01    'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.55/3.01    , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 2.55/3.01    , Z ), flip( T ) ) ] )
% 2.55/3.01  , clause( 27794, [ =( 'domain_of'( flip( 'cross_product'( X, 
% 2.55/3.01    'universal_class' ) ) ), inverse( X ) ) ] )
% 2.55/3.01  , clause( 27795, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 2.55/3.01  , clause( 27796, [ =( first( 'not_subclass_element'( restrict( X, Y, 
% 2.55/3.01    singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 2.55/3.01  , clause( 27797, [ =( second( 'not_subclass_element'( restrict( X, 
% 2.55/3.01    singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 2.55/3.01  , clause( 27798, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), 
% 2.55/3.01    image( X, Y ) ) ] )
% 2.55/3.01  , clause( 27799, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 2.55/3.01  , clause( 27800, [ subclass( 'successor_relation', 'cross_product'( 
% 2.55/3.01    'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01  , clause( 27801, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 2.55/3.01     ) ), =( successor( X ), Y ) ] )
% 2.55/3.01  , clause( 27802, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( 
% 2.55/3.01    X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ), 
% 2.55/3.01    member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 2.55/3.01  , clause( 27803, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 2.55/3.01  , clause( 27804, [ ~( inductive( X ) ), subclass( image( 
% 2.55/3.01    'successor_relation', X ), X ) ] )
% 2.55/3.01  , clause( 27805, [ ~( member( 'null_class', X ) ), ~( subclass( image( 
% 2.55/3.01    'successor_relation', X ), X ) ), inductive( X ) ] )
% 2.55/3.01  , clause( 27806, [ inductive( omega ) ] )
% 2.55/3.01  , clause( 27807, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 2.55/3.01  , clause( 27808, [ member( omega, 'universal_class' ) ] )
% 2.55/3.01  , clause( 27809, [ =( 'domain_of'( restrict( 'element_relation', 
% 2.55/3.01    'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 2.55/3.01  , clause( 27810, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( 
% 2.55/3.01    X ), 'universal_class' ) ] )
% 2.55/3.01  , clause( 27811, [ =( complement( image( 'element_relation', complement( X
% 2.55/3.01     ) ) ), 'power_class'( X ) ) ] )
% 2.55/3.01  , clause( 27812, [ ~( member( X, 'universal_class' ) ), member( 
% 2.55/3.01    'power_class'( X ), 'universal_class' ) ] )
% 2.55/3.01  , clause( 27813, [ subclass( compose( X, Y ), 'cross_product'( 
% 2.55/3.01    'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01  , clause( 27814, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), 
% 2.55/3.01    member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 2.55/3.01  , clause( 27815, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 2.55/3.01    , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class', 
% 2.55/3.01    'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 2.55/3.01     ) ] )
% 2.55/3.01  , clause( 27816, [ ~( 'single_valued_class'( X ) ), subclass( compose( X, 
% 2.55/3.01    inverse( X ) ), 'identity_relation' ) ] )
% 2.55/3.01  , clause( 27817, [ ~( subclass( compose( X, inverse( X ) ), 
% 2.55/3.01    'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 2.55/3.01  , clause( 27818, [ ~( function( X ) ), subclass( X, 'cross_product'( 
% 2.55/3.01    'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01  , clause( 27819, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 2.55/3.01    , 'identity_relation' ) ] )
% 2.55/3.01  , clause( 27820, [ ~( subclass( X, 'cross_product'( 'universal_class', 
% 2.55/3.01    'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ), 
% 2.55/3.01    'identity_relation' ) ), function( X ) ] )
% 2.55/3.01  , clause( 27821, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 2.55/3.01    , member( image( X, Y ), 'universal_class' ) ] )
% 2.55/3.01  , clause( 27822, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 2.55/3.01  , clause( 27823, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 2.55/3.01    , 'null_class' ) ] )
% 2.55/3.01  , clause( 27824, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, 
% 2.55/3.01    Y ) ) ] )
% 2.55/3.01  , clause( 27825, [ function( choice ) ] )
% 2.55/3.01  , clause( 27826, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 2.55/3.01     ), member( apply( choice, X ), X ) ] )
% 2.55/3.01  , clause( 27827, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 2.55/3.01  , clause( 27828, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 2.55/3.01  , clause( 27829, [ ~( function( inverse( X ) ) ), ~( function( X ) ), 
% 2.55/3.01    'one_to_one'( X ) ] )
% 2.55/3.01  , clause( 27830, [ =( intersection( 'cross_product'( 'universal_class', 
% 2.55/3.01    'universal_class' ), intersection( 'cross_product'( 'universal_class', 
% 2.55/3.01    'universal_class' ), complement( compose( complement( 'element_relation'
% 2.55/3.01     ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 2.55/3.01  , clause( 27831, [ =( intersection( inverse( 'subset_relation' ), 
% 2.55/3.01    'subset_relation' ), 'identity_relation' ) ] )
% 2.55/3.01  , clause( 27832, [ =( complement( 'domain_of'( intersection( X, 
% 2.55/3.01    'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 2.55/3.01  , clause( 27833, [ =( intersection( 'domain_of'( X ), diagonalise( compose( 
% 2.55/3.01    inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 2.55/3.01  , clause( 27834, [ ~( operation( X ) ), function( X ) ] )
% 2.55/3.01  , clause( 27835, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 
% 2.55/3.01    'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.55/3.01     ] )
% 2.55/3.01  , clause( 27836, [ ~( operation( X ) ), subclass( 'range_of'( X ), 
% 2.55/3.01    'domain_of'( 'domain_of'( X ) ) ) ] )
% 2.55/3.01  , clause( 27837, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 
% 2.55/3.01    'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.55/3.01     ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), 
% 2.55/3.01    operation( X ) ] )
% 2.55/3.01  , clause( 27838, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 2.55/3.01  , clause( 27839, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( 
% 2.55/3.01    Y ) ), 'domain_of'( X ) ) ] )
% 2.55/3.01  , clause( 27840, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 
% 2.55/3.01    'domain_of'( 'domain_of'( Z ) ) ) ] )
% 2.55/3.01  , clause( 27841, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 2.55/3.01     ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 
% 2.55/3.01    'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 2.55/3.01  , clause( 27842, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 2.55/3.01  , clause( 27843, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 2.55/3.01  , clause( 27844, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 2.55/3.01  , clause( 27845, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( 
% 2.55/3.01    T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 2.55/3.01    , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 2.55/3.01     )
% 2.55/3.01  , clause( 27846, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( 
% 2.55/3.01    Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 
% 2.55/3.01    'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 2.55/3.01    , Y ) ] )
% 2.55/3.01  , clause( 27847, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( 
% 2.55/3.01    Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z, 
% 2.55/3.01    'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 2.55/3.01     ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X, 
% 2.55/3.01    Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 2.55/3.01     )
% 2.55/3.01  , clause( 27848, [ subclass( 'compose_class'( X ), 'cross_product'( 
% 2.55/3.01    'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01  , clause( 27849, [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z )
% 2.55/3.01     ) ), =( compose( Z, X ), Y ) ] )
% 2.55/3.01  , clause( 27850, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 
% 2.55/3.01    'universal_class', 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) )
% 2.55/3.01    , member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ] )
% 2.55/3.01  , clause( 27851, [ subclass( 'composition_function', 'cross_product'( 
% 2.55/3.01    'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 2.55/3.01     ) ) ) ] )
% 2.55/3.01  , clause( 27852, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ), 
% 2.55/3.01    'composition_function' ) ), =( compose( X, Y ), Z ) ] )
% 2.55/3.01  , clause( 27853, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 
% 2.55/3.01    'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( X, 
% 2.55/3.01    'ordered_pair'( Y, compose( X, Y ) ) ), 'composition_function' ) ] )
% 2.55/3.01  , clause( 27854, [ subclass( 'domain_relation', 'cross_product'( 
% 2.55/3.01    'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01  , clause( 27855, [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) )
% 2.55/3.01    , =( 'domain_of'( X ), Y ) ] )
% 2.55/3.01  , clause( 27856, [ ~( member( X, 'universal_class' ) ), member( 
% 2.55/3.01    'ordered_pair'( X, 'domain_of'( X ) ), 'domain_relation' ) ] )
% 2.55/3.01  , clause( 27857, [ =( first( 'not_subclass_element'( compose( X, inverse( X
% 2.55/3.01     ) ), 'identity_relation' ) ), 'single_valued1'( X ) ) ] )
% 2.55/3.01  , clause( 27858, [ =( second( 'not_subclass_element'( compose( X, inverse( 
% 2.55/3.01    X ) ), 'identity_relation' ) ), 'single_valued2'( X ) ) ] )
% 2.55/3.01  , clause( 27859, [ =( domain( X, image( inverse( X ), singleton( 
% 2.55/3.01    'single_valued1'( X ) ) ), 'single_valued2'( X ) ), 'single_valued3'( X )
% 2.55/3.01     ) ] )
% 2.55/3.01  , clause( 27860, [ =( intersection( complement( compose( 'element_relation'
% 2.55/3.01    , complement( 'identity_relation' ) ) ), 'element_relation' ), 
% 2.55/3.01    'singleton_relation' ) ] )
% 2.55/3.01  , clause( 27861, [ subclass( 'application_function', 'cross_product'( 
% 2.55/3.01    'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 2.55/3.01     ) ) ) ] )
% 2.55/3.01  , clause( 27862, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ), 
% 2.55/3.01    'application_function' ) ), member( Y, 'domain_of'( X ) ) ] )
% 2.55/3.01  , clause( 27863, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ), 
% 2.55/3.01    'application_function' ) ), =( apply( X, Y ), Z ) ] )
% 2.55/3.01  , clause( 27864, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ), 
% 2.55/3.01    'cross_product'( 'universal_class', 'cross_product'( 'universal_class', 
% 2.55/3.01    'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member( 
% 2.55/3.01    'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ), 
% 2.55/3.01    'application_function' ) ] )
% 2.55/3.01  , clause( 27865, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 2.55/3.01  , clause( 27866, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 2.55/3.01  , clause( 27867, [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ]
% 2.55/3.01     )
% 2.55/3.01  , clause( 27868, [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) )
% 2.55/3.01    , maps( X, 'domain_of'( X ), Y ) ] )
% 2.55/3.01  , clause( 27869, [ =( union( X, inverse( X ) ), 'symmetrization_of'( X ) )
% 2.55/3.01     ] )
% 2.55/3.01  , clause( 27870, [ ~( irreflexive( X, Y ) ), subclass( restrict( X, Y, Y )
% 2.55/3.01    , complement( 'identity_relation' ) ) ] )
% 2.55/3.01  , clause( 27871, [ ~( subclass( restrict( X, Y, Y ), complement( 
% 2.55/3.01    'identity_relation' ) ) ), irreflexive( X, Y ) ] )
% 2.55/3.01  , clause( 27872, [ ~( connected( X, Y ) ), subclass( 'cross_product'( Y, Y
% 2.55/3.01     ), union( 'identity_relation', 'symmetrization_of'( X ) ) ) ] )
% 2.55/3.01  , clause( 27873, [ ~( subclass( 'cross_product'( X, X ), union( 
% 2.55/3.01    'identity_relation', 'symmetrization_of'( Y ) ) ) ), connected( Y, X ) ]
% 2.55/3.01     )
% 2.55/3.01  , clause( 27874, [ ~( transitive( X, Y ) ), subclass( compose( restrict( X
% 2.55/3.01    , Y, Y ), restrict( X, Y, Y ) ), restrict( X, Y, Y ) ) ] )
% 2.55/3.01  , clause( 27875, [ ~( subclass( compose( restrict( X, Y, Y ), restrict( X, 
% 2.55/3.01    Y, Y ) ), restrict( X, Y, Y ) ) ), transitive( X, Y ) ] )
% 2.55/3.01  , clause( 27876, [ ~( asymmetric( X, Y ) ), =( restrict( intersection( X, 
% 2.55/3.01    inverse( X ) ), Y, Y ), 'null_class' ) ] )
% 2.55/3.01  , clause( 27877, [ ~( =( restrict( intersection( X, inverse( X ) ), Y, Y )
% 2.55/3.01    , 'null_class' ) ), asymmetric( X, Y ) ] )
% 2.55/3.01  , clause( 27878, [ =( segment( X, Y, Z ), 'domain_of'( restrict( X, Y, 
% 2.55/3.01    singleton( Z ) ) ) ) ] )
% 2.55/3.01  , clause( 27879, [ ~( 'well_ordering'( X, Y ) ), connected( X, Y ) ] )
% 2.55/3.01  , clause( 27880, [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), =( 
% 2.55/3.01    Z, 'null_class' ), member( least( X, Z ), Z ) ] )
% 2.55/3.01  , clause( 27881, [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), ~( 
% 2.55/3.01    member( T, Z ) ), member( least( X, Z ), Z ) ] )
% 2.55/3.01  , clause( 27882, [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), =( 
% 2.55/3.01    segment( X, Z, least( X, Z ) ), 'null_class' ) ] )
% 2.55/3.01  , clause( 27883, [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), ~( 
% 2.55/3.01    member( T, Z ) ), ~( member( 'ordered_pair'( T, least( X, Z ) ), X ) ) ]
% 2.55/3.01     )
% 2.55/3.01  , clause( 27884, [ ~( connected( X, Y ) ), ~( =( 'not_well_ordering'( X, Y
% 2.55/3.01     ), 'null_class' ) ), 'well_ordering'( X, Y ) ] )
% 2.55/3.01  , clause( 27885, [ ~( connected( X, Y ) ), subclass( 'not_well_ordering'( X
% 2.55/3.01    , Y ), Y ), 'well_ordering'( X, Y ) ] )
% 2.55/3.01  , clause( 27886, [ ~( member( X, 'not_well_ordering'( Y, Z ) ) ), ~( =( 
% 2.55/3.01    segment( Y, 'not_well_ordering'( Y, Z ), X ), 'null_class' ) ), ~( 
% 2.55/3.01    connected( Y, Z ) ), 'well_ordering'( Y, Z ) ] )
% 2.55/3.01  , clause( 27887, [ ~( section( X, Y, Z ) ), subclass( Y, Z ) ] )
% 2.55/3.01  , clause( 27888, [ ~( section( X, Y, Z ) ), subclass( 'domain_of'( restrict( 
% 2.55/3.01    X, Z, Y ) ), Y ) ] )
% 2.55/3.01  , clause( 27889, [ ~( subclass( X, Y ) ), ~( subclass( 'domain_of'( 
% 2.55/3.01    restrict( Z, Y, X ) ), X ) ), section( Z, X, Y ) ] )
% 2.55/3.01  , clause( 27890, [ ~( member( X, 'ordinal_numbers' ) ), 'well_ordering'( 
% 2.55/3.01    'element_relation', X ) ] )
% 2.55/3.01  , clause( 27891, [ ~( member( X, 'ordinal_numbers' ) ), subclass( 
% 2.55/3.01    'sum_class'( X ), X ) ] )
% 2.55/3.01  , clause( 27892, [ ~( 'well_ordering'( 'element_relation', X ) ), ~( 
% 2.55/3.01    subclass( 'sum_class'( X ), X ) ), ~( member( X, 'universal_class' ) ), 
% 2.55/3.01    member( X, 'ordinal_numbers' ) ] )
% 2.55/3.01  , clause( 27893, [ ~( 'well_ordering'( 'element_relation', X ) ), ~( 
% 2.55/3.01    subclass( 'sum_class'( X ), X ) ), member( X, 'ordinal_numbers' ), =( X, 
% 2.55/3.01    'ordinal_numbers' ) ] )
% 2.55/3.01  , clause( 27894, [ =( union( singleton( 'null_class' ), image( 
% 2.55/3.01    'successor_relation', 'ordinal_numbers' ) ), 'kind_1_ordinals' ) ] )
% 2.55/3.01  , clause( 27895, [ =( intersection( complement( 'kind_1_ordinals' ), 
% 2.55/3.01    'ordinal_numbers' ), 'limit_ordinals' ) ] )
% 2.55/3.01  , clause( 27896, [ subclass( 'rest_of'( X ), 'cross_product'( 
% 2.55/3.01    'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01  , clause( 27897, [ ~( member( 'ordered_pair'( X, Y ), 'rest_of'( Z ) ) ), 
% 2.55/3.01    member( X, 'domain_of'( Z ) ) ] )
% 2.55/3.01  , clause( 27898, [ ~( member( 'ordered_pair'( X, Y ), 'rest_of'( Z ) ) ), 
% 2.55/3.01    =( restrict( Z, X, 'universal_class' ), Y ) ] )
% 2.55/3.01  , clause( 27899, [ ~( member( X, 'domain_of'( Y ) ) ), ~( =( restrict( Y, X
% 2.55/3.01    , 'universal_class' ), Z ) ), member( 'ordered_pair'( X, Z ), 'rest_of'( 
% 2.55/3.01    Y ) ) ] )
% 2.55/3.01  , clause( 27900, [ subclass( 'rest_relation', 'cross_product'( 
% 2.55/3.01    'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01  , clause( 27901, [ ~( member( 'ordered_pair'( X, Y ), 'rest_relation' ) ), 
% 2.55/3.01    =( 'rest_of'( X ), Y ) ] )
% 2.55/3.01  , clause( 27902, [ ~( member( X, 'universal_class' ) ), member( 
% 2.55/3.01    'ordered_pair'( X, 'rest_of'( X ) ), 'rest_relation' ) ] )
% 2.55/3.01  , clause( 27903, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), 
% 2.55/3.01    function( Y ) ] )
% 2.55/3.01  , clause( 27904, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), 
% 2.55/3.01    function( X ) ] )
% 2.55/3.01  , clause( 27905, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), 
% 2.55/3.01    member( 'domain_of'( X ), 'ordinal_numbers' ) ] )
% 2.55/3.01  , clause( 27906, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), 
% 2.55/3.01    =( compose( Y, 'rest_of'( X ) ), X ) ] )
% 2.55/3.01  , clause( 27907, [ ~( function( X ) ), ~( function( Y ) ), ~( member( 
% 2.55/3.01    'domain_of'( Y ), 'ordinal_numbers' ) ), ~( =( compose( X, 'rest_of'( Y )
% 2.55/3.01     ), Y ) ), member( Y, 'recursion_equation_functions'( X ) ) ] )
% 2.55/3.01  , clause( 27908, [ subclass( 'union_of_range_map', 'cross_product'( 
% 2.55/3.01    'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01  , clause( 27909, [ ~( member( 'ordered_pair'( X, Y ), 'union_of_range_map'
% 2.55/3.01     ) ), =( 'sum_class'( 'range_of'( X ) ), Y ) ] )
% 2.55/3.01  , clause( 27910, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 
% 2.55/3.01    'universal_class', 'universal_class' ) ) ), ~( =( 'sum_class'( 'range_of'( 
% 2.55/3.01    X ) ), Y ) ), member( 'ordered_pair'( X, Y ), 'union_of_range_map' ) ] )
% 2.55/3.01  , clause( 27911, [ =( apply( recursion( X, 'successor_relation', 
% 2.55/3.01    'union_of_range_map' ), Y ), 'ordinal_add'( X, Y ) ) ] )
% 2.55/3.01  , clause( 27912, [ =( recursion( 'null_class', apply( 'add_relation', X ), 
% 2.55/3.01    'union_of_range_map' ), 'ordinal_multiply'( X, Y ) ) ] )
% 2.55/3.01  , clause( 27913, [ ~( member( X, omega ) ), =( 'integer_of'( X ), X ) ] )
% 2.55/3.01  , clause( 27914, [ member( X, omega ), =( 'integer_of'( X ), 'null_class' )
% 2.55/3.01     ] )
% 2.55/3.01  , clause( 27915, [ ~( member( 'not_subclass_element'( intersection( 
% 2.55/3.01    'power_class'( x ), z ), x ), z ) ) ] )
% 2.55/3.01  , clause( 27916, [ ~( subclass( intersection( 'power_class'( x ), z ), x )
% 2.55/3.01     ) ] )
% 2.55/3.01  ] ).
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  subsumption(
% 2.55/3.01  clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y )
% 2.55/3.01     ] )
% 2.55/3.01  , clause( 27758, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 2.55/3.01    , Y ) ] )
% 2.55/3.01  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.55/3.01     ), ==>( 1, 1 )] ) ).
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  subsumption(
% 2.55/3.01  clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 2.55/3.01  , clause( 27778, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 2.55/3.01     )
% 2.55/3.01  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 2.55/3.01    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  subsumption(
% 2.55/3.01  clause( 157, [ ~( member( 'not_subclass_element'( intersection( 
% 2.55/3.01    'power_class'( x ), z ), x ), z ) ) ] )
% 2.55/3.01  , clause( 27915, [ ~( member( 'not_subclass_element'( intersection( 
% 2.55/3.01    'power_class'( x ), z ), x ), z ) ) ] )
% 2.55/3.01  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  subsumption(
% 2.55/3.01  clause( 158, [ ~( subclass( intersection( 'power_class'( x ), z ), x ) ) ]
% 2.55/3.01     )
% 2.55/3.01  , clause( 27916, [ ~( subclass( intersection( 'power_class'( x ), z ), x )
% 2.55/3.01     ) ] )
% 2.55/3.01  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  resolution(
% 2.55/3.01  clause( 28097, [ ~( member( 'not_subclass_element'( intersection( 
% 2.55/3.01    'power_class'( x ), z ), x ), intersection( X, z ) ) ) ] )
% 2.55/3.01  , clause( 157, [ ~( member( 'not_subclass_element'( intersection( 
% 2.55/3.01    'power_class'( x ), z ), x ), z ) ) ] )
% 2.55/3.01  , 0, clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 2.55/3.01     )
% 2.55/3.01  , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 
% 2.55/3.01    'not_subclass_element'( intersection( 'power_class'( x ), z ), x ) ), 
% 2.55/3.01    :=( Y, X ), :=( Z, z )] )).
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  subsumption(
% 2.55/3.01  clause( 27500, [ ~( member( 'not_subclass_element'( intersection( 
% 2.55/3.01    'power_class'( x ), z ), x ), intersection( X, z ) ) ) ] )
% 2.55/3.01  , clause( 28097, [ ~( member( 'not_subclass_element'( intersection( 
% 2.55/3.01    'power_class'( x ), z ), x ), intersection( X, z ) ) ) ] )
% 2.55/3.01  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  resolution(
% 2.55/3.01  clause( 28098, [ member( 'not_subclass_element'( intersection( 
% 2.55/3.01    'power_class'( x ), z ), x ), intersection( 'power_class'( x ), z ) ) ]
% 2.55/3.01     )
% 2.55/3.01  , clause( 158, [ ~( subclass( intersection( 'power_class'( x ), z ), x ) )
% 2.55/3.01     ] )
% 2.55/3.01  , 0, clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 2.55/3.01    , Y ) ] )
% 2.55/3.01  , 1, substitution( 0, [] ), substitution( 1, [ :=( X, intersection( 
% 2.55/3.01    'power_class'( x ), z ) ), :=( Y, x )] )).
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  resolution(
% 2.55/3.01  clause( 28099, [] )
% 2.55/3.01  , clause( 27500, [ ~( member( 'not_subclass_element'( intersection( 
% 2.55/3.01    'power_class'( x ), z ), x ), intersection( X, z ) ) ) ] )
% 2.55/3.01  , 0, clause( 28098, [ member( 'not_subclass_element'( intersection( 
% 2.55/3.01    'power_class'( x ), z ), x ), intersection( 'power_class'( x ), z ) ) ]
% 2.55/3.01     )
% 2.55/3.01  , 0, substitution( 0, [ :=( X, 'power_class'( x ) )] ), substitution( 1, [] )
% 2.55/3.01    ).
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  subsumption(
% 2.55/3.01  clause( 27755, [] )
% 2.55/3.01  , clause( 28099, [] )
% 2.55/3.01  , substitution( 0, [] ), permutation( 0, [] ) ).
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  end.
% 2.55/3.01  
% 2.55/3.01  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.55/3.01  
% 2.55/3.01  Memory use:
% 2.55/3.01  
% 2.55/3.01  space for terms:        455418
% 2.55/3.01  space for clauses:      1316275
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  clauses generated:      59980
% 2.55/3.01  clauses kept:           27756
% 2.55/3.01  clauses selected:       642
% 2.55/3.01  clauses deleted:        2656
% 2.55/3.01  clauses inuse deleted:  85
% 2.55/3.01  
% 2.55/3.01  subsentry:          197658
% 2.55/3.01  literals s-matched: 141935
% 2.55/3.01  literals matched:   139559
% 2.55/3.01  full subsumption:   61464
% 2.55/3.01  
% 2.55/3.01  checksum:           2119345189
% 2.55/3.01  
% 2.55/3.01  
% 2.55/3.01  Bliksem ended
%------------------------------------------------------------------------------