TSTP Solution File: SET041-3 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : SET041-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n004.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 22:46:00 EDT 2022

% Result   : Unsatisfiable 10.83s 11.23s
% Output   : Refutation 10.83s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET041-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : bliksem %s
% 0.12/0.33  % Computer : n004.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 13:00:52 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.73/1.12  *** allocated 10000 integers for termspace/termends
% 0.73/1.12  *** allocated 10000 integers for clauses
% 0.73/1.12  *** allocated 10000 integers for justifications
% 0.73/1.12  Bliksem 1.12
% 0.73/1.12  
% 0.73/1.12  
% 0.73/1.12  Automatic Strategy Selection
% 0.73/1.12  
% 0.73/1.12  Clauses:
% 0.73/1.12  [
% 0.73/1.12     [ ~( member( X, Y ) ), 'little_set'( X ) ],
% 0.73/1.12     [ 'little_set'( f1( X, Y ) ), =( X, Y ) ],
% 0.73/1.12     [ member( f1( X, Y ), X ), member( f1( X, Y ), Y ), =( X, Y ) ],
% 0.73/1.12     [ ~( member( f1( X, Y ), X ) ), ~( member( f1( X, Y ), Y ) ), =( X, Y )
% 0.73/1.12     ],
% 0.73/1.12     [ ~( member( X, 'non_ordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( X ) ), ~( 
% 0.73/1.12    =( X, Y ) ) ],
% 0.73/1.12     [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( X ) ), ~( 
% 0.73/1.12    =( X, Z ) ) ],
% 0.73/1.12     [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ],
% 0.73/1.12     [ =( 'singleton_set'( X ), 'non_ordered_pair'( X, X ) ) ],
% 0.73/1.12     [ =( 'ordered_pair'( X, Y ), 'non_ordered_pair'( 'singleton_set'( X ), 
% 0.73/1.12    'non_ordered_pair'( X, Y ) ) ) ],
% 0.73/1.12     [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f2( X ) ) ],
% 0.73/1.12     [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f3( X ) ) ],
% 0.73/1.12     [ ~( 'ordered_pair_predicate'( X ) ), =( X, 'ordered_pair'( f2( X ), f3( 
% 0.73/1.12    X ) ) ) ],
% 0.73/1.12     [ 'ordered_pair_predicate'( X ), ~( 'little_set'( Y ) ), ~( 'little_set'( 
% 0.73/1.12    Z ) ), ~( =( X, 'ordered_pair'( Y, Z ) ) ) ],
% 0.73/1.12     [ ~( member( X, first( Y ) ) ), 'little_set'( f4( X, Y ) ) ],
% 0.73/1.12     [ ~( member( X, first( Y ) ) ), 'little_set'( f5( X, Y ) ) ],
% 0.73/1.12     [ ~( member( X, first( Y ) ) ), =( Y, 'ordered_pair'( f4( X, Y ), f5( X
% 0.73/1.12    , Y ) ) ) ],
% 0.73/1.12     [ ~( member( X, first( Y ) ) ), member( X, f4( X, Y ) ) ],
% 0.73/1.12     [ member( X, first( Y ) ), ~( 'little_set'( Z ) ), ~( 'little_set'( T )
% 0.73/1.12     ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, Z ) ) ],
% 0.73/1.12     [ ~( member( X, second( Y ) ) ), 'little_set'( f6( X, Y ) ) ],
% 0.73/1.12     [ ~( member( X, second( Y ) ) ), 'little_set'( f7( X, Y ) ) ],
% 0.73/1.12     [ ~( member( X, second( Y ) ) ), =( Y, 'ordered_pair'( f6( X, Y ), f7( X
% 0.73/1.12    , Y ) ) ) ],
% 0.73/1.12     [ ~( member( X, second( Y ) ) ), member( X, f7( X, Y ) ) ],
% 0.73/1.12     [ member( X, second( Y ) ), ~( 'little_set'( Z ) ), ~( 'little_set'( T )
% 0.73/1.12     ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, T ) ) ],
% 0.73/1.12     [ ~( member( X, estin ) ), 'ordered_pair_predicate'( X ) ],
% 0.73/1.12     [ ~( member( X, estin ) ), member( first( X ), second( X ) ) ],
% 0.73/1.12     [ member( X, estin ), ~( 'little_set'( X ) ), ~( 
% 0.73/1.12    'ordered_pair_predicate'( X ) ), ~( member( first( X ), second( X ) ) ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.73/1.12     [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.73/1.12     [ member( X, intersection( Y, Z ) ), ~( member( X, Y ) ), ~( member( X, 
% 0.73/1.12    Z ) ) ],
% 0.73/1.12     [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.73/1.12     [ member( X, complement( Y ) ), ~( 'little_set'( X ) ), member( X, Y ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ =( union( X, Y ), complement( intersection( complement( X ), 
% 0.73/1.12    complement( Y ) ) ) ) ],
% 0.73/1.12     [ ~( member( X, 'domain_of'( Y ) ) ), 'ordered_pair_predicate'( f8( X, Y
% 0.73/1.12     ) ) ],
% 0.73/1.12     [ ~( member( X, 'domain_of'( Y ) ) ), member( f8( X, Y ), Y ) ],
% 0.73/1.12     [ ~( member( X, 'domain_of'( Y ) ) ), =( X, first( f8( X, Y ) ) ) ],
% 0.73/1.12     [ member( X, 'domain_of'( Y ) ), ~( 'little_set'( X ) ), ~( 
% 0.73/1.12    'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, first( Z )
% 0.73/1.12     ) ) ],
% 0.73/1.12     [ ~( member( X, 'cross_product'( Y, Z ) ) ), 'ordered_pair_predicate'( X
% 0.73/1.12     ) ],
% 0.73/1.12     [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( first( X ), Y ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( second( X ), Z ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ member( X, 'cross_product'( Y, Z ) ), ~( 'little_set'( X ) ), ~( 
% 0.73/1.12    'ordered_pair_predicate'( X ) ), ~( member( first( X ), Y ) ), ~( member( 
% 0.73/1.12    second( X ), Z ) ) ],
% 0.73/1.12     [ ~( member( X, converse( Y ) ) ), 'ordered_pair_predicate'( X ) ],
% 0.73/1.12     [ ~( member( X, converse( Y ) ) ), member( 'ordered_pair'( second( X ), 
% 0.73/1.12    first( X ) ), Y ) ],
% 0.73/1.12     [ member( X, converse( Y ) ), ~( 'little_set'( X ) ), ~( 
% 0.73/1.12    'ordered_pair_predicate'( X ) ), ~( member( 'ordered_pair'( second( X ), 
% 0.73/1.12    first( X ) ), Y ) ) ],
% 0.73/1.12     [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f9( X, Y ) ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f10( X, Y ) ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f11( X, Y ) ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ ~( member( X, 'rotate_right'( Y ) ) ), =( X, 'ordered_pair'( f9( X, Y
% 0.73/1.12     ), 'ordered_pair'( f10( X, Y ), f11( X, Y ) ) ) ) ],
% 0.73/1.12     [ ~( member( X, 'rotate_right'( Y ) ) ), member( 'ordered_pair'( f10( X
% 0.73/1.12    , Y ), 'ordered_pair'( f11( X, Y ), f9( X, Y ) ) ), Y ) ],
% 0.73/1.12     [ member( X, 'rotate_right'( Y ) ), ~( 'little_set'( X ) ), ~( 
% 0.73/1.12    'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) ), ~( 
% 0.73/1.12    =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member( 
% 0.73/1.12    'ordered_pair'( T, 'ordered_pair'( U, Z ) ), Y ) ) ],
% 0.73/1.12     [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f12( X, Y ) ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f13( X, Y ) ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f14( X, Y ) ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ ~( member( X, 'flip_range_of'( Y ) ) ), =( X, 'ordered_pair'( f12( X, 
% 0.73/1.12    Y ), 'ordered_pair'( f13( X, Y ), f14( X, Y ) ) ) ) ],
% 0.73/1.12     [ ~( member( X, 'flip_range_of'( Y ) ) ), member( 'ordered_pair'( f12( X
% 0.73/1.12    , Y ), 'ordered_pair'( f14( X, Y ), f13( X, Y ) ) ), Y ) ],
% 0.73/1.12     [ member( X, 'flip_range_of'( Y ) ), ~( 'little_set'( X ) ), ~( 
% 0.73/1.12    'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) ), ~( 
% 0.73/1.12    =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member( 
% 0.73/1.12    'ordered_pair'( Z, 'ordered_pair'( U, T ) ), Y ) ) ],
% 0.73/1.12     [ =( successor( X ), union( X, 'singleton_set'( X ) ) ) ],
% 0.73/1.12     [ ~( member( X, 'empty_set' ) ) ],
% 0.73/1.12     [ member( X, 'universal_set' ), ~( 'little_set'( X ) ) ],
% 0.73/1.12     [ 'little_set'( infinity ) ],
% 0.73/1.12     [ member( 'empty_set', infinity ) ],
% 0.73/1.12     [ ~( member( X, infinity ) ), member( successor( X ), infinity ) ],
% 0.73/1.12     [ ~( member( X, sigma( Y ) ) ), member( f16( X, Y ), Y ) ],
% 0.73/1.12     [ ~( member( X, sigma( Y ) ) ), member( X, f16( X, Y ) ) ],
% 0.73/1.12     [ member( X, sigma( Y ) ), ~( member( Z, Y ) ), ~( member( X, Z ) ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ ~( 'little_set'( X ) ), 'little_set'( sigma( X ) ) ],
% 0.73/1.12     [ ~( subset( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.73/1.12     [ subset( X, Y ), member( f17( X, Y ), X ) ],
% 0.73/1.12     [ subset( X, Y ), ~( member( f17( X, Y ), Y ) ) ],
% 0.73/1.12     [ ~( 'proper_subset'( X, Y ) ), subset( X, Y ) ],
% 0.73/1.12     [ ~( 'proper_subset'( X, Y ) ), ~( =( X, Y ) ) ],
% 0.73/1.12     [ 'proper_subset'( X, Y ), ~( subset( X, Y ) ), =( X, Y ) ],
% 0.73/1.12     [ ~( member( X, powerset( Y ) ) ), subset( X, Y ) ],
% 0.73/1.12     [ member( X, powerset( Y ) ), ~( 'little_set'( X ) ), ~( subset( X, Y )
% 0.73/1.12     ) ],
% 0.73/1.12     [ ~( 'little_set'( X ) ), 'little_set'( powerset( X ) ) ],
% 0.73/1.12     [ ~( relation( X ) ), ~( member( Y, X ) ), 'ordered_pair_predicate'( Y )
% 0.73/1.12     ],
% 0.73/1.12     [ relation( X ), member( f18( X ), X ) ],
% 0.73/1.12     [ relation( X ), ~( 'ordered_pair_predicate'( f18( X ) ) ) ],
% 0.73/1.12     [ ~( 'single_valued_set'( X ) ), ~( 'little_set'( Y ) ), ~( 'little_set'( 
% 0.73/1.12    Z ) ), ~( 'little_set'( T ) ), ~( member( 'ordered_pair'( Y, Z ), X ) ), 
% 0.73/1.12    ~( member( 'ordered_pair'( Y, T ), X ) ), =( Z, T ) ],
% 0.73/1.12     [ 'single_valued_set'( X ), 'little_set'( f19( X ) ) ],
% 0.73/1.12     [ 'single_valued_set'( X ), 'little_set'( f20( X ) ) ],
% 0.73/1.12     [ 'single_valued_set'( X ), 'little_set'( f21( X ) ) ],
% 0.73/1.12     [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X ), f20( X ) )
% 0.73/1.12    , X ) ],
% 0.73/1.12     [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X ), f21( X ) )
% 0.73/1.12    , X ) ],
% 0.73/1.12     [ 'single_valued_set'( X ), ~( =( f20( X ), f21( X ) ) ) ],
% 0.73/1.12     [ ~( function( X ) ), relation( X ) ],
% 0.73/1.12     [ ~( function( X ) ), 'single_valued_set'( X ) ],
% 0.73/1.12     [ function( X ), ~( relation( X ) ), ~( 'single_valued_set'( X ) ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ ~( member( X, image( Y, Z ) ) ), 'ordered_pair_predicate'( f22( X, Y, 
% 0.73/1.12    Z ) ) ],
% 0.73/1.12     [ ~( member( X, image( Y, Z ) ) ), member( f22( X, Y, Z ), Z ) ],
% 0.73/1.12     [ ~( member( X, image( Y, Z ) ) ), member( first( f22( X, Y, Z ) ), Y )
% 0.73/1.12     ],
% 0.73/1.12     [ ~( member( X, image( Y, Z ) ) ), =( second( f22( X, Y, Z ) ), X ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ member( X, image( Y, Z ) ), ~( 'little_set'( X ) ), ~( 
% 0.73/1.12    'ordered_pair_predicate'( T ) ), ~( member( T, Z ) ), ~( member( first( T
% 0.73/1.12     ), Y ) ), ~( =( second( T ), X ) ) ],
% 0.73/1.12     [ ~( 'little_set'( X ) ), ~( function( Y ) ), 'little_set'( image( X, Y
% 0.73/1.12     ) ) ],
% 0.73/1.12     [ ~( disjoint( X, Y ) ), ~( member( Z, X ) ), ~( member( Z, Y ) ) ],
% 0.73/1.12     [ disjoint( X, Y ), member( f23( X, Y ), X ) ],
% 0.73/1.12     [ disjoint( X, Y ), member( f23( X, Y ), Y ) ],
% 0.73/1.12     [ =( X, 'empty_set' ), member( f24( X ), X ) ],
% 0.73/1.12     [ =( X, 'empty_set' ), disjoint( f24( X ), X ) ],
% 0.73/1.12     [ function( f25 ) ],
% 0.73/1.12     [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( f26( X ), X ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( 'ordered_pair'( X
% 0.73/1.12    , f26( X ) ), f25 ) ],
% 0.73/1.12     [ ~( member( X, 'range_of'( Y ) ) ), 'ordered_pair_predicate'( f27( X, Y
% 0.73/1.12     ) ) ],
% 0.73/1.12     [ ~( member( X, 'range_of'( Y ) ) ), member( f27( X, Y ), Y ) ],
% 0.73/1.12     [ ~( member( X, 'range_of'( Y ) ) ), =( X, second( f27( X, Y ) ) ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ member( X, 'range_of'( Y ) ), ~( 'little_set'( X ) ), ~( 
% 0.73/1.12    'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, second( Z
% 0.73/1.12     ) ) ) ],
% 0.73/1.12     [ ~( member( X, 'identity_relation' ) ), 'ordered_pair_predicate'( X ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ ~( member( X, 'identity_relation' ) ), =( first( X ), second( X ) ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ member( X, 'identity_relation' ), ~( 'little_set'( X ) ), ~( 
% 0.73/1.12    'ordered_pair_predicate'( X ) ), ~( =( first( X ), second( X ) ) ) ],
% 0.73/1.12     [ =( restrict( X, Y ), intersection( X, 'cross_product'( Y, 
% 0.73/1.12    'universal_set' ) ) ) ],
% 0.73/1.12     [ ~( 'one_to_one_function'( X ) ), function( X ) ],
% 0.73/1.12     [ ~( 'one_to_one_function'( X ) ), function( converse( X ) ) ],
% 0.73/1.12     [ 'one_to_one_function'( X ), ~( function( X ) ), ~( function( converse( 
% 0.73/1.12    X ) ) ) ],
% 0.73/1.12     [ ~( member( X, apply( Y, Z ) ) ), 'ordered_pair_predicate'( f28( X, Y, 
% 0.73/1.12    Z ) ) ],
% 0.73/1.12     [ ~( member( X, apply( Y, Z ) ) ), member( f28( X, Y, Z ), Y ) ],
% 0.73/1.12     [ ~( member( X, apply( Y, Z ) ) ), =( first( f28( X, Y, Z ) ), Z ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ ~( member( X, apply( Y, Z ) ) ), member( X, second( f28( X, Y, Z ) ) )
% 0.73/1.12     ],
% 0.73/1.12     [ member( X, apply( Y, Z ) ), ~( 'ordered_pair_predicate'( T ) ), ~( 
% 0.73/1.12    member( T, Y ) ), ~( =( first( T ), Z ) ), ~( member( X, second( T ) ) )
% 0.73/1.12     ],
% 0.73/1.12     [ =( 'apply_to_two_arguments'( X, Y, Z ), apply( X, 'ordered_pair'( Y, Z
% 0.73/1.12     ) ) ) ],
% 0.73/1.12     [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.73/1.12     [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 0.73/1.12     [ ~( maps( X, Y, Z ) ), subset( 'range_of'( X ), Z ) ],
% 0.73/1.12     [ maps( X, Y, Z ), ~( function( X ) ), ~( =( 'domain_of'( X ), Y ) ), 
% 0.73/1.12    ~( subset( 'range_of'( X ), Z ) ) ],
% 0.73/1.12     [ ~( closed( X, Y ) ), 'little_set'( X ) ],
% 0.73/1.12     [ ~( closed( X, Y ) ), 'little_set'( Y ) ],
% 0.73/1.12     [ ~( closed( X, Y ) ), maps( Y, 'cross_product'( X, X ), X ) ],
% 0.73/1.12     [ closed( X, Y ), ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( 
% 0.73/1.12    maps( Y, 'cross_product'( X, X ), X ) ) ],
% 0.73/1.12     [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f29( X, Y, Z ) ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f30( X, Y, Z ) ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f31( X, Y, Z ) ) ]
% 0.73/1.12    ,
% 0.73/1.12     [ ~( member( X, compose( Y, Z ) ) ), =( X, 'ordered_pair'( f29( X, Y, Z
% 0.73/1.12     ), f30( X, Y, Z ) ) ) ],
% 0.73/1.12     [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'( f29( X, Y, 
% 0.73/1.12    Z ), f31( X, Y, Z ) ), Y ) ],
% 0.73/1.12     [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'( f31( X, Y, 
% 0.73/1.12    Z ), f30( X, Y, Z ) ), Z ) ],
% 0.73/1.12     [ member( X, compose( Y, Z ) ), ~( 'little_set'( X ) ), ~( 'little_set'( 
% 0.73/1.12    T ) ), ~( 'little_set'( U ) ), ~( 'little_set'( W ) ), ~( =( X, 
% 0.73/1.12    'ordered_pair'( T, U ) ) ), ~( member( 'ordered_pair'( T, W ), Y ) ), ~( 
% 0.73/1.12    member( 'ordered_pair'( W, U ), Z ) ) ],
% 0.73/1.12     [ ~( homomorphism( X, Y, Z, T, U ) ), closed( Y, Z ) ],
% 0.73/1.12     [ ~( homomorphism( X, Y, Z, T, U ) ), closed( T, U ) ],
% 0.73/1.12     [ ~( homomorphism( X, Y, Z, T, U ) ), maps( X, Y, T ) ],
% 0.73/1.12     [ ~( homomorphism( X, Y, Z, T, U ) ), ~( member( W, Y ) ), ~( member( V0
% 0.73/1.12    , Y ) ), =( apply( X, 'apply_to_two_arguments'( Z, W, V0 ) ), 
% 0.73/1.12    'apply_to_two_arguments'( U, apply( X, W ), apply( X, V0 ) ) ) ],
% 0.73/1.12     [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.73/1.12     ), ~( maps( X, Y, T ) ), member( f32( X, Y, Z, T, U ), Y ) ],
% 0.73/1.12     [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.73/1.12     ), ~( maps( X, Y, T ) ), member( f33( X, Y, Z, T, U ), Y ) ],
% 0.73/1.12     [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.76/1.23     ), ~( maps( X, Y, T ) ), ~( =( apply( X, 'apply_to_two_arguments'( Z, 
% 0.76/1.23    f32( X, Y, Z, T, U ), f33( X, Y, Z, T, U ) ) ), 'apply_to_two_arguments'( 
% 0.76/1.23    U, apply( X, f32( X, Y, Z, T, U ) ), apply( X, f33( X, Y, Z, T, U ) ) ) )
% 0.76/1.23     ) ],
% 0.76/1.23     [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( =( 'ordered_pair'( 
% 0.76/1.23    X, Z ), 'ordered_pair'( Y, T ) ) ), =( X, Y ) ],
% 0.76/1.23     [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( =( 
% 0.76/1.23    'non_ordered_pair'( Z, X ), 'non_ordered_pair'( Z, Y ) ) ), =( X, Y ) ]
% 0.76/1.23    ,
% 0.76/1.23     [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( 'little_set'( Z ) )
% 0.76/1.23    , ~( 'little_set'( T ) ), ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z
% 0.76/1.23    , T ) ) ), =( Y, T ) ],
% 0.76/1.23     [ ~( subset( X, Y ) ), ~( subset( Y, X ) ), =( X, Y ) ],
% 0.76/1.23     [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), =( first( 
% 0.76/1.23    'ordered_pair'( X, Y ) ), X ) ],
% 0.76/1.23     [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), =( second( 
% 0.76/1.23    'ordered_pair'( X, Y ) ), Y ) ],
% 0.76/1.23     [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( first( X ) ) ],
% 0.76/1.23     [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( second( X ) ) ],
% 0.76/1.23     [ ~( 'little_set'( X ) ), member( X, 'singleton_set'( X ) ) ],
% 0.76/1.23     [ 'little_set'( 'ordered_pair'( X, Y ) ) ],
% 0.76/1.23     [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( X ) ],
% 0.76/1.23     [ ~( subset( X, Y ) ), ~( subset( Y, Z ) ), subset( X, Z ) ],
% 0.76/1.23     [ subset( apply( X, Y ), sigma( image( 'singleton_set'( Y ), X ) ) ) ]
% 0.76/1.23    ,
% 0.76/1.23     [ subset( image( 'singleton_set'( X ), Y ), apply( Y, X ) ) ],
% 0.76/1.23     [ ~( function( X ) ), 'little_set'( apply( X, Y ) ) ],
% 0.76/1.23     [ relation( compose( X, Y ) ) ],
% 0.76/1.23     [ subset( 'range_of'( compose( X, Y ) ), 'range_of'( X ) ) ],
% 0.76/1.23     [ ~( subset( 'range_of'( X ), 'domain_of'( Y ) ) ), =( 'domain_of'( X )
% 0.76/1.23    , 'domain_of'( compose( Y, X ) ) ) ],
% 0.76/1.23     [ ~( function( X ) ), ~( function( Y ) ), function( compose( Y, X ) ) ]
% 0.76/1.23    ,
% 0.76/1.23     [ ~( maps( X, Y, Z ) ), ~( maps( T, Z, U ) ), maps( compose( T, X ), Y, 
% 0.76/1.23    U ) ],
% 0.76/1.23     [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( function( Z ) ), 
% 0.76/1.23    ~( member( 'ordered_pair'( X, Y ), Z ) ), =( apply( Z, X ), Y ) ],
% 0.76/1.23     [ ~( function( X ) ), ~( member( Y, 'domain_of'( X ) ) ), ~( =( apply( X
% 0.76/1.23    , Y ), Z ) ), member( 'ordered_pair'( Y, Z ), X ) ],
% 0.76/1.23     [ ~( maps( X, Y, Z ) ), ~( member( T, Y ) ), member( apply( X, T ), Z )
% 0.76/1.23     ],
% 0.76/1.23     [ ~( function( X ) ), ~( member( Y, 'domain_of'( X ) ) ), subset( apply( 
% 0.76/1.23    Z, apply( X, Y ) ), apply( compose( Z, X ), Y ) ) ],
% 0.76/1.23     [ ~( function( X ) ), subset( apply( compose( Y, X ), Z ), apply( Y, 
% 0.76/1.23    apply( X, Z ) ) ) ],
% 0.76/1.23     [ function( 'a_function' ) ],
% 0.76/1.23     [ member( a, 'domain_of'( 'a_function' ) ) ],
% 0.76/1.23     [ ~( =( apply( 'another_function', apply( 'a_function', a ) ), apply( 
% 0.76/1.23    compose( 'another_function', 'a_function' ), a ) ) ) ]
% 0.76/1.23  ] .
% 0.76/1.23  
% 0.76/1.23  
% 0.76/1.23  percentage equality = 0.141509, percentage horn = 0.881657
% 0.76/1.23  This is a problem with some equality
% 0.76/1.23  
% 0.76/1.23  
% 0.76/1.23  
% 0.76/1.23  Options Used:
% 0.76/1.23  
% 0.76/1.23  useres =            1
% 0.76/1.23  useparamod =        1
% 0.76/1.23  useeqrefl =         1
% 0.76/1.23  useeqfact =         1
% 0.76/1.23  usefactor =         1
% 0.76/1.23  usesimpsplitting =  0
% 0.76/1.23  usesimpdemod =      5
% 0.76/1.23  usesimpres =        3
% 0.76/1.23  
% 0.76/1.23  resimpinuse      =  1000
% 0.76/1.23  resimpclauses =     20000
% 0.76/1.23  substype =          eqrewr
% 0.76/1.23  backwardsubs =      1
% 0.76/1.23  selectoldest =      5
% 0.76/1.23  
% 0.76/1.23  litorderings [0] =  split
% 0.76/1.23  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.76/1.23  
% 0.76/1.23  termordering =      kbo
% 0.76/1.23  
% 0.76/1.23  litapriori =        0
% 0.76/1.23  termapriori =       1
% 0.76/1.23  litaposteriori =    0
% 0.76/1.23  termaposteriori =   0
% 0.76/1.23  demodaposteriori =  0
% 0.76/1.23  ordereqreflfact =   0
% 0.76/1.23  
% 0.76/1.23  litselect =         negord
% 0.76/1.23  
% 0.76/1.23  maxweight =         15
% 0.76/1.23  maxdepth =          30000
% 0.76/1.23  maxlength =         115
% 0.76/1.23  maxnrvars =         195
% 0.76/1.23  excuselevel =       1
% 0.76/1.23  increasemaxweight = 1
% 0.76/1.23  
% 0.76/1.23  maxselected =       10000000
% 0.76/1.23  maxnrclauses =      10000000
% 0.76/1.23  
% 0.76/1.23  showgenerated =    0
% 0.76/1.23  showkept =         0
% 0.76/1.23  showselected =     0
% 0.76/1.23  showdeleted =      0
% 0.76/1.23  showresimp =       1
% 0.76/1.23  showstatus =       2000
% 0.76/1.23  
% 0.76/1.23  prologoutput =     1
% 0.76/1.23  nrgoals =          5000000
% 0.76/1.23  totalproof =       1
% 0.76/1.23  
% 0.76/1.23  Symbols occurring in the translation:
% 0.76/1.23  
% 0.76/1.23  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.76/1.23  .  [1, 2]      (w:1, o:66, a:1, s:1, b:0), 
% 0.76/1.23  !  [4, 1]      (w:0, o:35, a:1, s:1, b:0), 
% 0.76/1.23  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.76/1.23  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.76/1.23  member  [41, 2]      (w:1, o:91, a:1, s:1, b:0), 
% 10.83/11.23  'little_set'  [42, 1]      (w:1, o:40, a:1, s:1, b:0), 
% 10.83/11.23  f1  [43, 2]      (w:1, o:92, a:1, s:1, b:0), 
% 10.83/11.23  'non_ordered_pair'  [45, 2]      (w:1, o:93, a:1, s:1, b:0), 
% 10.83/11.23  'singleton_set'  [46, 1]      (w:1, o:44, a:1, s:1, b:0), 
% 10.83/11.23  'ordered_pair'  [47, 2]      (w:1, o:94, a:1, s:1, b:0), 
% 10.83/11.23  'ordered_pair_predicate'  [48, 1]      (w:1, o:45, a:1, s:1, b:0), 
% 10.83/11.23  f2  [49, 1]      (w:1, o:48, a:1, s:1, b:0), 
% 10.83/11.23  f3  [50, 1]      (w:1, o:53, a:1, s:1, b:0), 
% 10.83/11.23  first  [52, 1]      (w:1, o:54, a:1, s:1, b:0), 
% 10.83/11.23  f4  [53, 2]      (w:1, o:95, a:1, s:1, b:0), 
% 10.83/11.23  f5  [54, 2]      (w:1, o:96, a:1, s:1, b:0), 
% 10.83/11.23  second  [56, 1]      (w:1, o:55, a:1, s:1, b:0), 
% 10.83/11.23  f6  [57, 2]      (w:1, o:97, a:1, s:1, b:0), 
% 10.83/11.23  f7  [58, 2]      (w:1, o:98, a:1, s:1, b:0), 
% 10.83/11.23  estin  [59, 0]      (w:1, o:26, a:1, s:1, b:0), 
% 10.83/11.23  intersection  [60, 2]      (w:1, o:100, a:1, s:1, b:0), 
% 10.83/11.23  complement  [61, 1]      (w:1, o:56, a:1, s:1, b:0), 
% 10.83/11.23  union  [62, 2]      (w:1, o:101, a:1, s:1, b:0), 
% 10.83/11.23  'domain_of'  [63, 1]      (w:1, o:58, a:1, s:1, b:0), 
% 10.83/11.23  f8  [64, 2]      (w:1, o:102, a:1, s:1, b:0), 
% 10.83/11.23  'cross_product'  [66, 2]      (w:1, o:103, a:1, s:1, b:0), 
% 10.83/11.23  converse  [67, 1]      (w:1, o:57, a:1, s:1, b:0), 
% 10.83/11.23  'rotate_right'  [68, 1]      (w:1, o:41, a:1, s:1, b:0), 
% 10.83/11.23  f9  [69, 2]      (w:1, o:104, a:1, s:1, b:0), 
% 10.83/11.23  f10  [70, 2]      (w:1, o:105, a:1, s:1, b:0), 
% 10.83/11.23  f11  [71, 2]      (w:1, o:106, a:1, s:1, b:0), 
% 10.83/11.23  'flip_range_of'  [73, 1]      (w:1, o:59, a:1, s:1, b:0), 
% 10.83/11.23  f12  [74, 2]      (w:1, o:107, a:1, s:1, b:0), 
% 10.83/11.23  f13  [75, 2]      (w:1, o:108, a:1, s:1, b:0), 
% 10.83/11.23  f14  [76, 2]      (w:1, o:109, a:1, s:1, b:0), 
% 10.83/11.23  successor  [77, 1]      (w:1, o:60, a:1, s:1, b:0), 
% 10.83/11.23  'empty_set'  [78, 0]      (w:1, o:27, a:1, s:1, b:0), 
% 10.83/11.23  'universal_set'  [79, 0]      (w:1, o:28, a:1, s:1, b:0), 
% 10.83/11.23  infinity  [80, 0]      (w:1, o:29, a:1, s:1, b:0), 
% 10.83/11.23  sigma  [81, 1]      (w:1, o:61, a:1, s:1, b:0), 
% 10.83/11.23  f16  [82, 2]      (w:1, o:110, a:1, s:1, b:0), 
% 10.83/11.23  subset  [83, 2]      (w:1, o:112, a:1, s:1, b:0), 
% 10.83/11.23  f17  [84, 2]      (w:1, o:113, a:1, s:1, b:0), 
% 10.83/11.23  'proper_subset'  [85, 2]      (w:1, o:114, a:1, s:1, b:0), 
% 10.83/11.23  powerset  [86, 1]      (w:1, o:63, a:1, s:1, b:0), 
% 10.83/11.23  relation  [87, 1]      (w:1, o:42, a:1, s:1, b:0), 
% 10.83/11.23  f18  [88, 1]      (w:1, o:46, a:1, s:1, b:0), 
% 10.83/11.23  'single_valued_set'  [89, 1]      (w:1, o:64, a:1, s:1, b:0), 
% 10.83/11.23  f19  [90, 1]      (w:1, o:47, a:1, s:1, b:0), 
% 10.83/11.23  f20  [91, 1]      (w:1, o:49, a:1, s:1, b:0), 
% 10.83/11.23  f21  [92, 1]      (w:1, o:50, a:1, s:1, b:0), 
% 10.83/11.23  function  [94, 1]      (w:1, o:65, a:1, s:1, b:0), 
% 10.83/11.23  image  [95, 2]      (w:1, o:99, a:1, s:1, b:0), 
% 10.83/11.23  f22  [96, 3]      (w:1, o:121, a:1, s:1, b:0), 
% 10.83/11.23  disjoint  [97, 2]      (w:1, o:117, a:1, s:1, b:0), 
% 10.83/11.23  f23  [98, 2]      (w:1, o:118, a:1, s:1, b:0), 
% 10.83/11.23  f24  [99, 1]      (w:1, o:51, a:1, s:1, b:0), 
% 10.83/11.23  f25  [100, 0]      (w:1, o:30, a:1, s:1, b:0), 
% 10.83/11.23  f26  [101, 1]      (w:1, o:52, a:1, s:1, b:0), 
% 10.83/11.23  'range_of'  [102, 1]      (w:1, o:43, a:1, s:1, b:0), 
% 10.83/11.23  f27  [103, 2]      (w:1, o:119, a:1, s:1, b:0), 
% 10.83/11.23  'identity_relation'  [104, 0]      (w:1, o:31, a:1, s:1, b:0), 
% 10.83/11.23  restrict  [105, 2]      (w:1, o:111, a:1, s:1, b:0), 
% 10.83/11.23  'one_to_one_function'  [106, 1]      (w:1, o:62, a:1, s:1, b:0), 
% 10.83/11.23  apply  [107, 2]      (w:1, o:120, a:1, s:1, b:0), 
% 10.83/11.23  f28  [108, 3]      (w:1, o:122, a:1, s:1, b:0), 
% 10.83/11.23  'apply_to_two_arguments'  [109, 3]      (w:1, o:123, a:1, s:1, b:0), 
% 10.83/11.23  maps  [110, 3]      (w:1, o:124, a:1, s:1, b:0), 
% 10.83/11.23  closed  [112, 2]      (w:1, o:115, a:1, s:1, b:0), 
% 10.83/11.23  compose  [114, 2]      (w:1, o:116, a:1, s:1, b:0), 
% 10.83/11.23  f29  [115, 3]      (w:1, o:125, a:1, s:1, b:0), 
% 10.83/11.23  f30  [116, 3]      (w:1, o:126, a:1, s:1, b:0), 
% 10.83/11.23  f31  [117, 3]      (w:1, o:127, a:1, s:1, b:0), 
% 10.83/11.23  homomorphism  [123, 5]      (w:1, o:128, a:1, s:1, b:0), 
% 10.83/11.23  f32  [124, 5]      (w:1, o:129, a:1, s:1, b:0), 
% 10.83/11.23  f33  [125, 5]      (w:1, o:130, a:1, s:1, b:0), 
% 10.83/11.23  'a_function'  [128, 0]      (w:1, o:32, a:1, s:1, b:0), 
% 10.83/11.23  a  [129, 0]      (w:1, o:33, a:1, s:1, b:0), 
% 10.83/11.23  'another_function'  [130, 0]      (w:1, o:34, a:1, s:1, b:0).
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Starting Search:
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    3582
% 10.83/11.23  Kept:         2012
% 10.83/11.23  Inuse:        91
% 10.83/11.23  Deleted:      0
% 10.83/11.23  Deletedinuse: 0
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    6999
% 10.83/11.23  Kept:         4030
% 10.83/11.23  Inuse:        148
% 10.83/11.23  Deleted:      1
% 10.83/11.23  Deletedinuse: 0
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    10296
% 10.83/11.23  Kept:         6042
% 10.83/11.23  Inuse:        200
% 10.83/11.23  Deleted:      3
% 10.83/11.23  Deletedinuse: 0
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    14971
% 10.83/11.23  Kept:         8064
% 10.83/11.23  Inuse:        257
% 10.83/11.23  Deleted:      19
% 10.83/11.23  Deletedinuse: 10
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    19170
% 10.83/11.23  Kept:         10071
% 10.83/11.23  Inuse:        297
% 10.83/11.23  Deleted:      20
% 10.83/11.23  Deletedinuse: 10
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    21910
% 10.83/11.23  Kept:         12089
% 10.83/11.23  Inuse:        323
% 10.83/11.23  Deleted:      20
% 10.83/11.23  Deletedinuse: 10
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    28301
% 10.83/11.23  Kept:         14202
% 10.83/11.23  Inuse:        374
% 10.83/11.23  Deleted:      23
% 10.83/11.23  Deletedinuse: 11
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    34764
% 10.83/11.23  Kept:         16243
% 10.83/11.23  Inuse:        403
% 10.83/11.23  Deleted:      130
% 10.83/11.23  Deletedinuse: 107
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    39134
% 10.83/11.23  Kept:         18259
% 10.83/11.23  Inuse:        439
% 10.83/11.23  Deleted:      155
% 10.83/11.23  Deletedinuse: 108
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  Resimplifying clauses:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    45708
% 10.83/11.23  Kept:         20263
% 10.83/11.23  Inuse:        468
% 10.83/11.23  Deleted:      3866
% 10.83/11.23  Deletedinuse: 108
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    56061
% 10.83/11.23  Kept:         22788
% 10.83/11.23  Inuse:        512
% 10.83/11.23  Deleted:      3879
% 10.83/11.23  Deletedinuse: 116
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    68022
% 10.83/11.23  Kept:         24905
% 10.83/11.23  Inuse:        527
% 10.83/11.23  Deleted:      3879
% 10.83/11.23  Deletedinuse: 116
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    72593
% 10.83/11.23  Kept:         26934
% 10.83/11.23  Inuse:        565
% 10.83/11.23  Deleted:      3879
% 10.83/11.23  Deletedinuse: 116
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    79123
% 10.83/11.23  Kept:         29063
% 10.83/11.23  Inuse:        597
% 10.83/11.23  Deleted:      3879
% 10.83/11.23  Deletedinuse: 116
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    84154
% 10.83/11.23  Kept:         31701
% 10.83/11.23  Inuse:        617
% 10.83/11.23  Deleted:      3880
% 10.83/11.23  Deletedinuse: 117
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    93181
% 10.83/11.23  Kept:         34914
% 10.83/11.23  Inuse:        627
% 10.83/11.23  Deleted:      3880
% 10.83/11.23  Deletedinuse: 117
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    99074
% 10.83/11.23  Kept:         36942
% 10.83/11.23  Inuse:        660
% 10.83/11.23  Deleted:      3880
% 10.83/11.23  Deletedinuse: 117
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  Intermediate Status:
% 10.83/11.23  Generated:    107418
% 10.83/11.23  Kept:         38957
% 10.83/11.23  Inuse:        690
% 10.83/11.23  Deleted:      3885
% 10.83/11.23  Deletedinuse: 118
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  Resimplifying inuse:
% 10.83/11.23  Done
% 10.83/11.23  
% 10.83/11.23  Resimplifying clauses:
% 10.83/11.23  
% 10.83/11.23  Bliksems!, er is een bewijs:
% 10.83/11.23  % SZS status Unsatisfiable
% 10.83/11.23  % SZS output start Refutation
% 10.83/11.23  
% 10.83/11.23  clause( 144, [ ~( subset( X, Y ) ), ~( subset( Y, X ) ), =( X, Y ) ] )
% 10.83/11.23  .
% 10.83/11.23  clause( 164, [ ~( function( X ) ), ~( member( Y, 'domain_of'( X ) ) ), 
% 10.83/11.23    subset( apply( Z, apply( X, Y ) ), apply( compose( Z, X ), Y ) ) ] )
% 10.83/11.23  .
% 10.83/11.23  clause( 165, [ ~( function( X ) ), subset( apply( compose( Y, X ), Z ), 
% 10.83/11.23    apply( Y, apply( X, Z ) ) ) ] )
% 10.83/11.23  .
% 10.83/11.23  clause( 166, [ function( 'a_function' ) ] )
% 10.83/11.23  .
% 10.83/11.23  clause( 167, [ member( a, 'domain_of'( 'a_function' ) ) ] )
% 10.83/11.23  .
% 10.83/11.23  clause( 168, [ ~( =( apply( 'another_function', apply( 'a_function', a ) )
% 10.83/11.23    , apply( compose( 'another_function', 'a_function' ), a ) ) ) ] )
% 10.83/11.23  .
% 10.83/11.23  clause( 29263, [ subset( apply( X, apply( 'a_function', a ) ), apply( 
% 10.83/11.23    compose( X, 'a_function' ), a ) ) ] )
% 10.83/11.23  .
% 10.83/11.23  clause( 29483, [ subset( apply( compose( X, 'a_function' ), Y ), apply( X, 
% 10.83/11.23    apply( 'a_function', Y ) ) ) ] )
% 10.83/11.23  .
% 10.83/11.23  clause( 29754, [ ~( =( X, apply( compose( 'another_function', 'a_function'
% 10.83/11.23     ), a ) ) ), ~( subset( apply( 'another_function', apply( 'a_function', a
% 10.83/11.23     ) ), X ) ), ~( subset( X, apply( 'another_function', apply( 'a_function'
% 10.83/11.23    , a ) ) ) ) ] )
% 10.83/11.23  .
% 10.83/11.23  clause( 29849, [ ~( subset( apply( compose( 'another_function', 
% 10.83/11.23    'a_function' ), a ), apply( 'another_function', apply( 'a_function', a )
% 10.83/11.23     ) ) ) ] )
% 10.83/11.23  .
% 10.83/11.23  clause( 40340, [] )
% 10.83/11.23  .
% 10.83/11.23  
% 10.83/11.23  
% 10.83/11.23  % SZS output end Refutation
% 10.83/11.23  found a proof!
% 10.83/11.23  
% 10.83/11.23  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 10.83/11.23  
% 10.83/11.23  initialclauses(
% 10.83/11.23  [ clause( 40342, [ ~( member( X, Y ) ), 'little_set'( X ) ] )
% 10.83/11.23  , clause( 40343, [ 'little_set'( f1( X, Y ) ), =( X, Y ) ] )
% 10.83/11.23  , clause( 40344, [ member( f1( X, Y ), X ), member( f1( X, Y ), Y ), =( X, 
% 10.83/11.23    Y ) ] )
% 10.83/11.23  , clause( 40345, [ ~( member( f1( X, Y ), X ) ), ~( member( f1( X, Y ), Y )
% 10.83/11.23     ), =( X, Y ) ] )
% 10.83/11.23  , clause( 40346, [ ~( member( X, 'non_ordered_pair'( Y, Z ) ) ), =( X, Y )
% 10.83/11.23    , =( X, Z ) ] )
% 10.83/11.23  , clause( 40347, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( 
% 10.83/11.23    X ) ), ~( =( X, Y ) ) ] )
% 10.83/11.23  , clause( 40348, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( 
% 10.83/11.23    X ) ), ~( =( X, Z ) ) ] )
% 10.83/11.23  , clause( 40349, [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ] )
% 10.83/11.23  , clause( 40350, [ =( 'singleton_set'( X ), 'non_ordered_pair'( X, X ) ) ]
% 10.83/11.23     )
% 10.83/11.23  , clause( 40351, [ =( 'ordered_pair'( X, Y ), 'non_ordered_pair'( 
% 10.83/11.23    'singleton_set'( X ), 'non_ordered_pair'( X, Y ) ) ) ] )
% 10.83/11.23  , clause( 40352, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f2( X
% 10.83/11.23     ) ) ] )
% 10.83/11.23  , clause( 40353, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f3( X
% 10.83/11.23     ) ) ] )
% 10.83/11.23  , clause( 40354, [ ~( 'ordered_pair_predicate'( X ) ), =( X, 'ordered_pair'( 
% 10.83/11.23    f2( X ), f3( X ) ) ) ] )
% 10.83/11.23  , clause( 40355, [ 'ordered_pair_predicate'( X ), ~( 'little_set'( Y ) ), 
% 10.83/11.23    ~( 'little_set'( Z ) ), ~( =( X, 'ordered_pair'( Y, Z ) ) ) ] )
% 10.83/11.23  , clause( 40356, [ ~( member( X, first( Y ) ) ), 'little_set'( f4( X, Y ) )
% 10.83/11.23     ] )
% 10.83/11.23  , clause( 40357, [ ~( member( X, first( Y ) ) ), 'little_set'( f5( X, Y ) )
% 10.83/11.23     ] )
% 10.83/11.23  , clause( 40358, [ ~( member( X, first( Y ) ) ), =( Y, 'ordered_pair'( f4( 
% 10.83/11.23    X, Y ), f5( X, Y ) ) ) ] )
% 10.83/11.23  , clause( 40359, [ ~( member( X, first( Y ) ) ), member( X, f4( X, Y ) ) ]
% 10.83/11.23     )
% 10.83/11.23  , clause( 40360, [ member( X, first( Y ) ), ~( 'little_set'( Z ) ), ~( 
% 10.83/11.23    'little_set'( T ) ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, Z
% 10.83/11.23     ) ) ] )
% 10.83/11.23  , clause( 40361, [ ~( member( X, second( Y ) ) ), 'little_set'( f6( X, Y )
% 10.83/11.23     ) ] )
% 10.83/11.23  , clause( 40362, [ ~( member( X, second( Y ) ) ), 'little_set'( f7( X, Y )
% 10.83/11.23     ) ] )
% 10.83/11.23  , clause( 40363, [ ~( member( X, second( Y ) ) ), =( Y, 'ordered_pair'( f6( 
% 10.83/11.23    X, Y ), f7( X, Y ) ) ) ] )
% 10.83/11.23  , clause( 40364, [ ~( member( X, second( Y ) ) ), member( X, f7( X, Y ) ) ]
% 10.83/11.23     )
% 10.83/11.23  , clause( 40365, [ member( X, second( Y ) ), ~( 'little_set'( Z ) ), ~( 
% 10.83/11.23    'little_set'( T ) ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, T
% 10.83/11.23     ) ) ] )
% 10.83/11.23  , clause( 40366, [ ~( member( X, estin ) ), 'ordered_pair_predicate'( X ) ]
% 10.83/11.23     )
% 10.83/11.23  , clause( 40367, [ ~( member( X, estin ) ), member( first( X ), second( X )
% 10.83/11.23     ) ] )
% 10.83/11.23  , clause( 40368, [ member( X, estin ), ~( 'little_set'( X ) ), ~( 
% 10.83/11.23    'ordered_pair_predicate'( X ) ), ~( member( first( X ), second( X ) ) ) ]
% 10.83/11.23     )
% 10.83/11.23  , clause( 40369, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 10.83/11.23     )
% 10.83/11.23  , clause( 40370, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 10.83/11.23     )
% 10.83/11.23  , clause( 40371, [ member( X, intersection( Y, Z ) ), ~( member( X, Y ) ), 
% 10.83/11.23    ~( member( X, Z ) ) ] )
% 10.83/11.23  , clause( 40372, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 10.83/11.23     )
% 10.83/11.23  , clause( 40373, [ member( X, complement( Y ) ), ~( 'little_set'( X ) ), 
% 10.83/11.23    member( X, Y ) ] )
% 10.83/11.23  , clause( 40374, [ =( union( X, Y ), complement( intersection( complement( 
% 10.83/11.23    X ), complement( Y ) ) ) ) ] )
% 10.83/11.23  , clause( 40375, [ ~( member( X, 'domain_of'( Y ) ) ), 
% 10.83/11.23    'ordered_pair_predicate'( f8( X, Y ) ) ] )
% 10.83/11.23  , clause( 40376, [ ~( member( X, 'domain_of'( Y ) ) ), member( f8( X, Y ), 
% 10.83/11.23    Y ) ] )
% 10.83/11.23  , clause( 40377, [ ~( member( X, 'domain_of'( Y ) ) ), =( X, first( f8( X, 
% 10.83/11.23    Y ) ) ) ] )
% 10.83/11.23  , clause( 40378, [ member( X, 'domain_of'( Y ) ), ~( 'little_set'( X ) ), 
% 10.83/11.23    ~( 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, first( 
% 10.83/11.23    Z ) ) ) ] )
% 10.83/11.23  , clause( 40379, [ ~( member( X, 'cross_product'( Y, Z ) ) ), 
% 10.83/11.23    'ordered_pair_predicate'( X ) ] )
% 10.83/11.23  , clause( 40380, [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( first( 
% 10.83/11.23    X ), Y ) ] )
% 10.83/11.23  , clause( 40381, [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( 
% 10.83/11.23    second( X ), Z ) ] )
% 10.83/11.23  , clause( 40382, [ member( X, 'cross_product'( Y, Z ) ), ~( 'little_set'( X
% 10.83/11.23     ) ), ~( 'ordered_pair_predicate'( X ) ), ~( member( first( X ), Y ) ), 
% 10.83/11.23    ~( member( second( X ), Z ) ) ] )
% 10.83/11.23  , clause( 40383, [ ~( member( X, converse( Y ) ) ), 
% 10.83/11.23    'ordered_pair_predicate'( X ) ] )
% 10.83/11.23  , clause( 40384, [ ~( member( X, converse( Y ) ) ), member( 'ordered_pair'( 
% 10.83/11.23    second( X ), first( X ) ), Y ) ] )
% 10.83/11.23  , clause( 40385, [ member( X, converse( Y ) ), ~( 'little_set'( X ) ), ~( 
% 10.83/11.23    'ordered_pair_predicate'( X ) ), ~( member( 'ordered_pair'( second( X ), 
% 10.83/11.23    first( X ) ), Y ) ) ] )
% 10.83/11.23  , clause( 40386, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f9( 
% 10.83/11.23    X, Y ) ) ] )
% 10.83/11.23  , clause( 40387, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f10( 
% 10.83/11.23    X, Y ) ) ] )
% 10.83/11.23  , clause( 40388, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f11( 
% 10.83/11.23    X, Y ) ) ] )
% 10.83/11.23  , clause( 40389, [ ~( member( X, 'rotate_right'( Y ) ) ), =( X, 
% 10.83/11.23    'ordered_pair'( f9( X, Y ), 'ordered_pair'( f10( X, Y ), f11( X, Y ) ) )
% 10.83/11.23     ) ] )
% 10.83/11.23  , clause( 40390, [ ~( member( X, 'rotate_right'( Y ) ) ), member( 
% 10.83/11.23    'ordered_pair'( f10( X, Y ), 'ordered_pair'( f11( X, Y ), f9( X, Y ) ) )
% 10.83/11.23    , Y ) ] )
% 10.83/11.23  , clause( 40391, [ member( X, 'rotate_right'( Y ) ), ~( 'little_set'( X ) )
% 10.83/11.23    , ~( 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) )
% 10.83/11.23    , ~( =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member( 
% 10.83/11.23    'ordered_pair'( T, 'ordered_pair'( U, Z ) ), Y ) ) ] )
% 10.83/11.23  , clause( 40392, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( 
% 10.83/11.23    f12( X, Y ) ) ] )
% 10.83/11.23  , clause( 40393, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( 
% 10.83/11.23    f13( X, Y ) ) ] )
% 10.83/11.23  , clause( 40394, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( 
% 10.83/11.23    f14( X, Y ) ) ] )
% 10.83/11.23  , clause( 40395, [ ~( member( X, 'flip_range_of'( Y ) ) ), =( X, 
% 10.83/11.23    'ordered_pair'( f12( X, Y ), 'ordered_pair'( f13( X, Y ), f14( X, Y ) ) )
% 10.83/11.23     ) ] )
% 10.83/11.23  , clause( 40396, [ ~( member( X, 'flip_range_of'( Y ) ) ), member( 
% 10.83/11.23    'ordered_pair'( f12( X, Y ), 'ordered_pair'( f14( X, Y ), f13( X, Y ) ) )
% 10.83/11.23    , Y ) ] )
% 10.83/11.23  , clause( 40397, [ member( X, 'flip_range_of'( Y ) ), ~( 'little_set'( X )
% 10.83/11.23     ), ~( 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U )
% 10.83/11.23     ), ~( =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member( 
% 10.83/11.23    'ordered_pair'( Z, 'ordered_pair'( U, T ) ), Y ) ) ] )
% 10.83/11.23  , clause( 40398, [ =( successor( X ), union( X, 'singleton_set'( X ) ) ) ]
% 10.83/11.23     )
% 10.83/11.23  , clause( 40399, [ ~( member( X, 'empty_set' ) ) ] )
% 10.83/11.23  , clause( 40400, [ member( X, 'universal_set' ), ~( 'little_set'( X ) ) ]
% 10.83/11.23     )
% 10.83/11.23  , clause( 40401, [ 'little_set'( infinity ) ] )
% 10.83/11.23  , clause( 40402, [ member( 'empty_set', infinity ) ] )
% 10.83/11.23  , clause( 40403, [ ~( member( X, infinity ) ), member( successor( X ), 
% 10.83/11.23    infinity ) ] )
% 10.83/11.23  , clause( 40404, [ ~( member( X, sigma( Y ) ) ), member( f16( X, Y ), Y ) ]
% 10.83/11.23     )
% 10.83/11.23  , clause( 40405, [ ~( member( X, sigma( Y ) ) ), member( X, f16( X, Y ) ) ]
% 10.83/11.23     )
% 10.83/11.23  , clause( 40406, [ member( X, sigma( Y ) ), ~( member( Z, Y ) ), ~( member( 
% 10.83/11.23    X, Z ) ) ] )
% 10.83/11.23  , clause( 40407, [ ~( 'little_set'( X ) ), 'little_set'( sigma( X ) ) ] )
% 10.83/11.23  , clause( 40408, [ ~( subset( X, Y ) ), ~( member( Z, X ) ), member( Z, Y )
% 10.83/11.23     ] )
% 10.83/11.23  , clause( 40409, [ subset( X, Y ), member( f17( X, Y ), X ) ] )
% 10.83/11.23  , clause( 40410, [ subset( X, Y ), ~( member( f17( X, Y ), Y ) ) ] )
% 10.83/11.23  , clause( 40411, [ ~( 'proper_subset'( X, Y ) ), subset( X, Y ) ] )
% 10.83/11.23  , clause( 40412, [ ~( 'proper_subset'( X, Y ) ), ~( =( X, Y ) ) ] )
% 10.83/11.23  , clause( 40413, [ 'proper_subset'( X, Y ), ~( subset( X, Y ) ), =( X, Y )
% 10.83/11.23     ] )
% 10.83/11.23  , clause( 40414, [ ~( member( X, powerset( Y ) ) ), subset( X, Y ) ] )
% 10.83/11.23  , clause( 40415, [ member( X, powerset( Y ) ), ~( 'little_set'( X ) ), ~( 
% 10.83/11.23    subset( X, Y ) ) ] )
% 10.83/11.23  , clause( 40416, [ ~( 'little_set'( X ) ), 'little_set'( powerset( X ) ) ]
% 10.83/11.23     )
% 10.83/11.23  , clause( 40417, [ ~( relation( X ) ), ~( member( Y, X ) ), 
% 10.83/11.23    'ordered_pair_predicate'( Y ) ] )
% 10.83/11.23  , clause( 40418, [ relation( X ), member( f18( X ), X ) ] )
% 10.83/11.23  , clause( 40419, [ relation( X ), ~( 'ordered_pair_predicate'( f18( X ) ) )
% 10.83/11.23     ] )
% 10.83/11.23  , clause( 40420, [ ~( 'single_valued_set'( X ) ), ~( 'little_set'( Y ) ), 
% 10.83/11.23    ~( 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( member( 'ordered_pair'( 
% 10.83/11.23    Y, Z ), X ) ), ~( member( 'ordered_pair'( Y, T ), X ) ), =( Z, T ) ] )
% 10.83/11.23  , clause( 40421, [ 'single_valued_set'( X ), 'little_set'( f19( X ) ) ] )
% 10.83/11.23  , clause( 40422, [ 'single_valued_set'( X ), 'little_set'( f20( X ) ) ] )
% 10.83/11.23  , clause( 40423, [ 'single_valued_set'( X ), 'little_set'( f21( X ) ) ] )
% 10.83/11.23  , clause( 40424, [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X
% 10.83/11.23     ), f20( X ) ), X ) ] )
% 10.83/11.23  , clause( 40425, [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X
% 10.83/11.23     ), f21( X ) ), X ) ] )
% 10.83/11.23  , clause( 40426, [ 'single_valued_set'( X ), ~( =( f20( X ), f21( X ) ) ) ]
% 10.83/11.23     )
% 10.83/11.23  , clause( 40427, [ ~( function( X ) ), relation( X ) ] )
% 10.83/11.23  , clause( 40428, [ ~( function( X ) ), 'single_valued_set'( X ) ] )
% 10.83/11.23  , clause( 40429, [ function( X ), ~( relation( X ) ), ~( 
% 10.83/11.23    'single_valued_set'( X ) ) ] )
% 10.83/11.23  , clause( 40430, [ ~( member( X, image( Y, Z ) ) ), 
% 10.83/11.23    'ordered_pair_predicate'( f22( X, Y, Z ) ) ] )
% 10.83/11.23  , clause( 40431, [ ~( member( X, image( Y, Z ) ) ), member( f22( X, Y, Z )
% 10.83/11.23    , Z ) ] )
% 10.83/11.23  , clause( 40432, [ ~( member( X, image( Y, Z ) ) ), member( first( f22( X, 
% 10.83/11.23    Y, Z ) ), Y ) ] )
% 10.83/11.23  , clause( 40433, [ ~( member( X, image( Y, Z ) ) ), =( second( f22( X, Y, Z
% 10.83/11.23     ) ), X ) ] )
% 10.83/11.23  , clause( 40434, [ member( X, image( Y, Z ) ), ~( 'little_set'( X ) ), ~( 
% 10.83/11.23    'ordered_pair_predicate'( T ) ), ~( member( T, Z ) ), ~( member( first( T
% 10.83/11.23     ), Y ) ), ~( =( second( T ), X ) ) ] )
% 10.83/11.23  , clause( 40435, [ ~( 'little_set'( X ) ), ~( function( Y ) ), 'little_set'( 
% 10.83/11.23    image( X, Y ) ) ] )
% 10.83/11.23  , clause( 40436, [ ~( disjoint( X, Y ) ), ~( member( Z, X ) ), ~( member( Z
% 10.83/11.23    , Y ) ) ] )
% 10.83/11.23  , clause( 40437, [ disjoint( X, Y ), member( f23( X, Y ), X ) ] )
% 10.83/11.23  , clause( 40438, [ disjoint( X, Y ), member( f23( X, Y ), Y ) ] )
% 10.83/11.23  , clause( 40439, [ =( X, 'empty_set' ), member( f24( X ), X ) ] )
% 10.83/11.23  , clause( 40440, [ =( X, 'empty_set' ), disjoint( f24( X ), X ) ] )
% 10.83/11.23  , clause( 40441, [ function( f25 ) ] )
% 10.83/11.23  , clause( 40442, [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( f26( 
% 10.83/11.23    X ), X ) ] )
% 10.83/11.23  , clause( 40443, [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( 
% 10.83/11.23    'ordered_pair'( X, f26( X ) ), f25 ) ] )
% 10.83/11.23  , clause( 40444, [ ~( member( X, 'range_of'( Y ) ) ), 
% 10.83/11.23    'ordered_pair_predicate'( f27( X, Y ) ) ] )
% 10.83/11.23  , clause( 40445, [ ~( member( X, 'range_of'( Y ) ) ), member( f27( X, Y ), 
% 10.83/11.23    Y ) ] )
% 10.83/11.23  , clause( 40446, [ ~( member( X, 'range_of'( Y ) ) ), =( X, second( f27( X
% 10.83/11.23    , Y ) ) ) ] )
% 10.83/11.23  , clause( 40447, [ member( X, 'range_of'( Y ) ), ~( 'little_set'( X ) ), 
% 10.83/11.23    ~( 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, second( 
% 10.83/11.23    Z ) ) ) ] )
% 10.83/11.23  , clause( 40448, [ ~( member( X, 'identity_relation' ) ), 
% 10.83/11.23    'ordered_pair_predicate'( X ) ] )
% 10.83/11.23  , clause( 40449, [ ~( member( X, 'identity_relation' ) ), =( first( X ), 
% 10.83/11.23    second( X ) ) ] )
% 10.83/11.23  , clause( 40450, [ member( X, 'identity_relation' ), ~( 'little_set'( X ) )
% 10.83/11.23    , ~( 'ordered_pair_predicate'( X ) ), ~( =( first( X ), second( X ) ) ) ]
% 10.83/11.23     )
% 10.83/11.23  , clause( 40451, [ =( restrict( X, Y ), intersection( X, 'cross_product'( Y
% 10.83/11.23    , 'universal_set' ) ) ) ] )
% 10.83/11.23  , clause( 40452, [ ~( 'one_to_one_function'( X ) ), function( X ) ] )
% 10.83/11.23  , clause( 40453, [ ~( 'one_to_one_function'( X ) ), function( converse( X )
% 10.83/11.23     ) ] )
% 10.83/11.23  , clause( 40454, [ 'one_to_one_function'( X ), ~( function( X ) ), ~( 
% 10.83/11.23    function( converse( X ) ) ) ] )
% 10.83/11.23  , clause( 40455, [ ~( member( X, apply( Y, Z ) ) ), 
% 10.83/11.23    'ordered_pair_predicate'( f28( X, Y, Z ) ) ] )
% 10.83/11.23  , clause( 40456, [ ~( member( X, apply( Y, Z ) ) ), member( f28( X, Y, Z )
% 10.83/11.23    , Y ) ] )
% 10.83/11.23  , clause( 40457, [ ~( member( X, apply( Y, Z ) ) ), =( first( f28( X, Y, Z
% 10.83/11.23     ) ), Z ) ] )
% 10.83/11.23  , clause( 40458, [ ~( member( X, apply( Y, Z ) ) ), member( X, second( f28( 
% 10.83/11.23    X, Y, Z ) ) ) ] )
% 10.83/11.23  , clause( 40459, [ member( X, apply( Y, Z ) ), ~( 'ordered_pair_predicate'( 
% 10.83/11.23    T ) ), ~( member( T, Y ) ), ~( =( first( T ), Z ) ), ~( member( X, second( 
% 10.83/11.23    T ) ) ) ] )
% 10.83/11.23  , clause( 40460, [ =( 'apply_to_two_arguments'( X, Y, Z ), apply( X, 
% 10.83/11.23    'ordered_pair'( Y, Z ) ) ) ] )
% 10.83/11.23  , clause( 40461, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 10.83/11.23  , clause( 40462, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 10.83/11.23  , clause( 40463, [ ~( maps( X, Y, Z ) ), subset( 'range_of'( X ), Z ) ] )
% 10.83/11.23  , clause( 40464, [ maps( X, Y, Z ), ~( function( X ) ), ~( =( 'domain_of'( 
% 10.83/11.23    X ), Y ) ), ~( subset( 'range_of'( X ), Z ) ) ] )
% 10.83/11.23  , clause( 40465, [ ~( closed( X, Y ) ), 'little_set'( X ) ] )
% 10.83/11.23  , clause( 40466, [ ~( closed( X, Y ) ), 'little_set'( Y ) ] )
% 10.83/11.23  , clause( 40467, [ ~( closed( X, Y ) ), maps( Y, 'cross_product'( X, X ), X
% 10.83/11.23     ) ] )
% 10.83/11.23  , clause( 40468, [ closed( X, Y ), ~( 'little_set'( X ) ), ~( 'little_set'( 
% 10.83/11.23    Y ) ), ~( maps( Y, 'cross_product'( X, X ), X ) ) ] )
% 10.83/11.23  , clause( 40469, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f29( X
% 10.83/11.23    , Y, Z ) ) ] )
% 10.83/11.23  , clause( 40470, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f30( X
% 10.83/11.23    , Y, Z ) ) ] )
% 10.83/11.23  , clause( 40471, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f31( X
% 10.83/11.23    , Y, Z ) ) ] )
% 10.83/11.23  , clause( 40472, [ ~( member( X, compose( Y, Z ) ) ), =( X, 'ordered_pair'( 
% 10.83/11.23    f29( X, Y, Z ), f30( X, Y, Z ) ) ) ] )
% 10.83/11.23  , clause( 40473, [ ~( member( X, compose( Y, Z ) ) ), member( 
% 10.83/11.23    'ordered_pair'( f29( X, Y, Z ), f31( X, Y, Z ) ), Y ) ] )
% 10.83/11.23  , clause( 40474, [ ~( member( X, compose( Y, Z ) ) ), member( 
% 10.83/11.23    'ordered_pair'( f31( X, Y, Z ), f30( X, Y, Z ) ), Z ) ] )
% 10.83/11.23  , clause( 40475, [ member( X, compose( Y, Z ) ), ~( 'little_set'( X ) ), 
% 10.83/11.23    ~( 'little_set'( T ) ), ~( 'little_set'( U ) ), ~( 'little_set'( W ) ), 
% 10.83/11.23    ~( =( X, 'ordered_pair'( T, U ) ) ), ~( member( 'ordered_pair'( T, W ), Y
% 10.83/11.23     ) ), ~( member( 'ordered_pair'( W, U ), Z ) ) ] )
% 10.83/11.23  , clause( 40476, [ ~( homomorphism( X, Y, Z, T, U ) ), closed( Y, Z ) ] )
% 10.83/11.23  , clause( 40477, [ ~( homomorphism( X, Y, Z, T, U ) ), closed( T, U ) ] )
% 10.83/11.23  , clause( 40478, [ ~( homomorphism( X, Y, Z, T, U ) ), maps( X, Y, T ) ] )
% 10.83/11.23  , clause( 40479, [ ~( homomorphism( X, Y, Z, T, U ) ), ~( member( W, Y ) )
% 10.83/11.23    , ~( member( V0, Y ) ), =( apply( X, 'apply_to_two_arguments'( Z, W, V0 )
% 10.83/11.23     ), 'apply_to_two_arguments'( U, apply( X, W ), apply( X, V0 ) ) ) ] )
% 10.83/11.23  , clause( 40480, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( 
% 10.83/11.23    closed( T, U ) ), ~( maps( X, Y, T ) ), member( f32( X, Y, Z, T, U ), Y )
% 10.83/11.23     ] )
% 10.83/11.23  , clause( 40481, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( 
% 10.83/11.23    closed( T, U ) ), ~( maps( X, Y, T ) ), member( f33( X, Y, Z, T, U ), Y )
% 10.83/11.23     ] )
% 10.83/11.23  , clause( 40482, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( 
% 10.83/11.23    closed( T, U ) ), ~( maps( X, Y, T ) ), ~( =( apply( X, 
% 10.83/11.23    'apply_to_two_arguments'( Z, f32( X, Y, Z, T, U ), f33( X, Y, Z, T, U ) )
% 10.83/11.23     ), 'apply_to_two_arguments'( U, apply( X, f32( X, Y, Z, T, U ) ), apply( 
% 10.83/11.23    X, f33( X, Y, Z, T, U ) ) ) ) ) ] )
% 10.83/11.23  , clause( 40483, [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( =( 
% 10.83/11.23    'ordered_pair'( X, Z ), 'ordered_pair'( Y, T ) ) ), =( X, Y ) ] )
% 10.83/11.23  , clause( 40484, [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( =( 
% 10.83/11.23    'non_ordered_pair'( Z, X ), 'non_ordered_pair'( Z, Y ) ) ), =( X, Y ) ]
% 10.83/11.23     )
% 10.83/11.23  , clause( 40485, [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( 
% 10.83/11.23    'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( =( 'ordered_pair'( X, Y )
% 10.83/11.23    , 'ordered_pair'( Z, T ) ) ), =( Y, T ) ] )
% 10.83/11.23  , clause( 40486, [ ~( subset( X, Y ) ), ~( subset( Y, X ) ), =( X, Y ) ] )
% 10.83/11.23  , clause( 40487, [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), =( first( 
% 10.83/11.23    'ordered_pair'( X, Y ) ), X ) ] )
% 10.83/11.23  , clause( 40488, [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), =( 
% 10.83/11.23    second( 'ordered_pair'( X, Y ) ), Y ) ] )
% 10.83/11.23  , clause( 40489, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( first( 
% 10.83/11.23    X ) ) ] )
% 10.83/11.23  , clause( 40490, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( second( 
% 10.83/11.23    X ) ) ] )
% 10.83/11.23  , clause( 40491, [ ~( 'little_set'( X ) ), member( X, 'singleton_set'( X )
% 10.83/11.23     ) ] )
% 10.83/11.23  , clause( 40492, [ 'little_set'( 'ordered_pair'( X, Y ) ) ] )
% 10.83/11.23  , clause( 40493, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( X ) ]
% 10.83/11.23     )
% 10.83/11.23  , clause( 40494, [ ~( subset( X, Y ) ), ~( subset( Y, Z ) ), subset( X, Z )
% 10.83/11.23     ] )
% 10.83/11.23  , clause( 40495, [ subset( apply( X, Y ), sigma( image( 'singleton_set'( Y
% 10.83/11.23     ), X ) ) ) ] )
% 10.83/11.23  , clause( 40496, [ subset( image( 'singleton_set'( X ), Y ), apply( Y, X )
% 10.83/11.23     ) ] )
% 10.83/11.23  , clause( 40497, [ ~( function( X ) ), 'little_set'( apply( X, Y ) ) ] )
% 10.83/11.23  , clause( 40498, [ relation( compose( X, Y ) ) ] )
% 10.83/11.23  , clause( 40499, [ subset( 'range_of'( compose( X, Y ) ), 'range_of'( X ) )
% 10.83/11.24     ] )
% 10.83/11.24  , clause( 40500, [ ~( subset( 'range_of'( X ), 'domain_of'( Y ) ) ), =( 
% 10.83/11.24    'domain_of'( X ), 'domain_of'( compose( Y, X ) ) ) ] )
% 10.83/11.24  , clause( 40501, [ ~( function( X ) ), ~( function( Y ) ), function( 
% 10.83/11.24    compose( Y, X ) ) ] )
% 10.83/11.24  , clause( 40502, [ ~( maps( X, Y, Z ) ), ~( maps( T, Z, U ) ), maps( 
% 10.83/11.24    compose( T, X ), Y, U ) ] )
% 10.83/11.24  , clause( 40503, [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( 
% 10.83/11.24    function( Z ) ), ~( member( 'ordered_pair'( X, Y ), Z ) ), =( apply( Z, X
% 10.83/11.24     ), Y ) ] )
% 10.83/11.24  , clause( 40504, [ ~( function( X ) ), ~( member( Y, 'domain_of'( X ) ) ), 
% 10.83/11.24    ~( =( apply( X, Y ), Z ) ), member( 'ordered_pair'( Y, Z ), X ) ] )
% 10.83/11.24  , clause( 40505, [ ~( maps( X, Y, Z ) ), ~( member( T, Y ) ), member( apply( 
% 10.83/11.24    X, T ), Z ) ] )
% 10.83/11.24  , clause( 40506, [ ~( function( X ) ), ~( member( Y, 'domain_of'( X ) ) ), 
% 10.83/11.24    subset( apply( Z, apply( X, Y ) ), apply( compose( Z, X ), Y ) ) ] )
% 10.83/11.24  , clause( 40507, [ ~( function( X ) ), subset( apply( compose( Y, X ), Z )
% 10.83/11.24    , apply( Y, apply( X, Z ) ) ) ] )
% 10.83/11.24  , clause( 40508, [ function( 'a_function' ) ] )
% 10.83/11.24  , clause( 40509, [ member( a, 'domain_of'( 'a_function' ) ) ] )
% 10.83/11.24  , clause( 40510, [ ~( =( apply( 'another_function', apply( 'a_function', a
% 10.83/11.24     ) ), apply( compose( 'another_function', 'a_function' ), a ) ) ) ] )
% 10.83/11.24  ] ).
% 10.83/11.24  
% 10.83/11.24  
% 10.83/11.24  
% 10.83/11.24  subsumption(
% 10.83/11.24  clause( 144, [ ~( subset( X, Y ) ), ~( subset( Y, X ) ), =( X, Y ) ] )
% 10.83/11.24  , clause( 40486, [ ~( subset( X, Y ) ), ~( subset( Y, X ) ), =( X, Y ) ] )
% 10.83/11.24  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 10.83/11.24     ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 10.83/11.24  
% 10.83/11.24  
% 10.83/11.24  subsumption(
% 10.83/11.24  clause( 164, [ ~( function( X ) ), ~( member( Y, 'domain_of'( X ) ) ), 
% 10.83/11.24    subset( apply( Z, apply( X, Y ) ), apply( compose( Z, X ), Y ) ) ] )
% 10.83/11.24  , clause( 40506, [ ~( function( X ) ), ~( member( Y, 'domain_of'( X ) ) ), 
% 10.83/11.24    subset( apply( Z, apply( X, Y ) ), apply( compose( Z, X ), Y ) ) ] )
% 10.83/11.24  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 10.83/11.24    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 10.83/11.24  
% 10.83/11.24  
% 10.83/11.24  subsumption(
% 10.83/11.24  clause( 165, [ ~( function( X ) ), subset( apply( compose( Y, X ), Z ), 
% 10.83/11.24    apply( Y, apply( X, Z ) ) ) ] )
% 10.83/11.24  , clause( 40507, [ ~( function( X ) ), subset( apply( compose( Y, X ), Z )
% 10.83/11.24    , apply( Y, apply( X, Z ) ) ) ] )
% 10.83/11.24  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 10.83/11.24    permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 10.83/11.24  
% 10.83/11.24  
% 10.83/11.24  subsumption(
% 10.83/11.24  clause( 166, [ function( 'a_function' ) ] )
% 10.83/11.24  , clause( 40508, [ function( 'a_function' ) ] )
% 10.83/11.24  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 10.83/11.24  
% 10.83/11.24  
% 10.83/11.24  subsumption(
% 10.83/11.24  clause( 167, [ member( a, 'domain_of'( 'a_function' ) ) ] )
% 10.83/11.24  , clause( 40509, [ member( a, 'domain_of'( 'a_function' ) ) ] )
% 10.83/11.24  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 10.83/11.24  
% 10.83/11.24  
% 10.83/11.24  subsumption(
% 10.83/11.24  clause( 168, [ ~( =( apply( 'another_function', apply( 'a_function', a ) )
% 10.83/11.24    , apply( compose( 'another_function', 'a_function' ), a ) ) ) ] )
% 10.83/11.24  , clause( 40510, [ ~( =( apply( 'another_function', apply( 'a_function', a
% 10.83/11.24     ) ), apply( compose( 'another_function', 'a_function' ), a ) ) ) ] )
% 10.83/11.24  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 10.83/11.24  
% 10.83/11.24  
% 10.83/11.24  resolution(
% 10.83/11.24  clause( 41788, [ ~( function( 'a_function' ) ), subset( apply( X, apply( 
% 10.83/11.24    'a_function', a ) ), apply( compose( X, 'a_function' ), a ) ) ] )
% 10.83/11.24  , clause( 164, [ ~( function( X ) ), ~( member( Y, 'domain_of'( X ) ) ), 
% 10.83/11.24    subset( apply( Z, apply( X, Y ) ), apply( compose( Z, X ), Y ) ) ] )
% 10.83/11.24  , 1, clause( 167, [ member( a, 'domain_of'( 'a_function' ) ) ] )
% 10.83/11.24  , 0, substitution( 0, [ :=( X, 'a_function' ), :=( Y, a ), :=( Z, X )] ), 
% 10.83/11.24    substitution( 1, [] )).
% 10.83/11.24  
% 10.83/11.24  
% 10.83/11.24  resolution(
% 10.83/11.24  clause( 41789, [ subset( apply( X, apply( 'a_function', a ) ), apply( 
% 10.83/11.24    compose( X, 'a_function' ), a ) ) ] )
% 10.83/11.24  , clause( 41788, [ ~( function( 'a_function' ) ), subset( apply( X, apply( 
% 10.83/11.24    'a_function', a ) ), apply( compose( X, 'a_function' ), a ) ) ] )
% 10.83/11.24  , 0, clause( 166, [ function( 'a_function' ) ] )
% 10.83/11.24  , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 10.83/11.24  
% 10.83/11.24  
% 10.83/11.24  subsumption(
% 10.83/11.24  clause( 29263, [ subset( apply( X, apply( 'a_function', a ) ), apply( 
% 10.83/11.24    compose( X, 'a_function' ), a ) ) ] )
% 10.83/11.24  , clause( 41789, [ subset( apply( X, apply( 'a_fuCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------