TSTP Solution File: SET245-6 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET245-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Mon Jul 18 22:48:23 EDT 2022
% Result : Unsatisfiable 1.02s 1.45s
% Output : Refutation 1.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET245-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13 % Command : bliksem %s
% 0.12/0.33 % Computer : n029.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 : Mon Jul 11 02:14:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.73/1.10 *** allocated 10000 integers for termspace/termends
% 0.73/1.10 *** allocated 10000 integers for clauses
% 0.73/1.10 *** allocated 10000 integers for justifications
% 0.73/1.10 Bliksem 1.12
% 0.73/1.10
% 0.73/1.10
% 0.73/1.10 Automatic Strategy Selection
% 0.73/1.10
% 0.73/1.10 Clauses:
% 0.73/1.10 [
% 0.73/1.10 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.73/1.10 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.73/1.10 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.73/1.10 ,
% 0.73/1.10 [ subclass( X, 'universal_class' ) ],
% 0.73/1.10 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.73/1.10 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.73/1.10 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.73/1.10 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.73/1.10 ,
% 0.73/1.10 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.73/1.10 ) ) ],
% 0.73/1.10 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.73/1.10 ) ) ],
% 0.73/1.10 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.73/1.10 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.73/1.10 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.73/1.10 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.73/1.10 X, Z ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.73/1.10 Y, T ) ],
% 0.73/1.10 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.73/1.10 ), 'cross_product'( Y, T ) ) ],
% 0.73/1.10 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.73/1.10 ), second( X ) ), X ) ],
% 0.73/1.10 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.73/1.10 'universal_class' ) ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.73/1.10 Y ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.73/1.10 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.73/1.10 , Y ), 'element_relation' ) ],
% 0.73/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.73/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.73/1.10 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.73/1.10 Z ) ) ],
% 0.73/1.10 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.73/1.10 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.73/1.10 member( X, Y ) ],
% 0.73/1.10 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.73/1.10 union( X, Y ) ) ],
% 0.73/1.10 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.73/1.10 intersection( complement( X ), complement( Y ) ) ) ),
% 0.73/1.10 'symmetric_difference'( X, Y ) ) ],
% 0.73/1.10 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.73/1.10 ,
% 0.73/1.10 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.73/1.10 ,
% 0.73/1.10 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.73/1.10 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.73/1.10 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.73/1.10 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.73/1.10 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.73/1.10 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.73/1.10 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.73/1.10 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.73/1.10 'cross_product'( 'universal_class', 'universal_class' ),
% 0.73/1.10 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.73/1.10 Y ), rotate( T ) ) ],
% 0.73/1.10 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.73/1.10 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.73/1.10 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.73/1.10 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.73/1.10 'cross_product'( 'universal_class', 'universal_class' ),
% 0.73/1.10 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.73/1.10 Z ), flip( T ) ) ],
% 0.73/1.10 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.73/1.10 inverse( X ) ) ],
% 0.73/1.10 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.73/1.10 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.73/1.10 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.73/1.10 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.73/1.10 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.73/1.10 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.73/1.10 ],
% 0.73/1.10 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.73/1.10 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.73/1.10 'universal_class' ) ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.73/1.10 successor( X ), Y ) ],
% 0.73/1.10 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.73/1.10 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.73/1.10 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.73/1.10 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.73/1.10 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.73/1.10 ,
% 0.73/1.10 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.73/1.10 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.73/1.10 [ inductive( omega ) ],
% 0.73/1.10 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.73/1.10 [ member( omega, 'universal_class' ) ],
% 0.73/1.10 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.73/1.10 , 'sum_class'( X ) ) ],
% 0.73/1.10 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.73/1.10 'universal_class' ) ],
% 0.73/1.10 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.73/1.10 'power_class'( X ) ) ],
% 0.73/1.10 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.73/1.10 'universal_class' ) ],
% 0.73/1.10 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.73/1.10 'universal_class' ) ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.73/1.10 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.73/1.10 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.73/1.10 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.73/1.10 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.73/1.10 ) ],
% 0.73/1.10 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.73/1.10 , 'identity_relation' ) ],
% 0.73/1.10 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.73/1.10 'single_valued_class'( X ) ],
% 0.73/1.10 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.73/1.10 'universal_class' ) ) ],
% 0.73/1.10 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.73/1.10 'identity_relation' ) ],
% 0.73/1.10 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.73/1.10 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.73/1.10 , function( X ) ],
% 0.73/1.10 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.73/1.10 X, Y ), 'universal_class' ) ],
% 0.73/1.10 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.73/1.10 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.73/1.10 ) ],
% 0.73/1.10 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.73/1.10 [ function( choice ) ],
% 0.73/1.10 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.73/1.10 apply( choice, X ), X ) ],
% 0.73/1.10 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.73/1.10 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.73/1.10 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.73/1.10 ,
% 0.73/1.10 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.73/1.10 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.73/1.10 , complement( compose( complement( 'element_relation' ), inverse(
% 0.73/1.10 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.73/1.10 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.73/1.10 'identity_relation' ) ],
% 0.73/1.10 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.73/1.10 , diagonalise( X ) ) ],
% 0.73/1.10 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.73/1.10 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.73/1.10 [ ~( operation( X ) ), function( X ) ],
% 0.73/1.10 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.73/1.10 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.73/1.10 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.73/1.10 'domain_of'( X ) ) ) ],
% 0.73/1.10 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.73/1.10 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.73/1.10 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.73/1.10 X ) ],
% 0.73/1.10 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.73/1.10 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.73/1.10 'domain_of'( X ) ) ],
% 0.73/1.10 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.73/1.10 'domain_of'( Z ) ) ) ],
% 0.73/1.10 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.73/1.10 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.73/1.10 ), compatible( X, Y, Z ) ],
% 0.73/1.10 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.73/1.10 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.73/1.10 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.73/1.10 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.73/1.10 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.73/1.10 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.73/1.10 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.73/1.10 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.73/1.10 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.73/1.10 , Y ) ],
% 0.73/1.10 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.73/1.10 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.73/1.10 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.73/1.10 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.73/1.10 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.73/1.10 [ subclass( 'compose_class'( X ), 'cross_product'( 'universal_class',
% 0.73/1.10 'universal_class' ) ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ), =(
% 0.73/1.10 compose( Z, X ), Y ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.73/1.10 , 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) ), member(
% 0.73/1.10 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ],
% 0.73/1.10 [ subclass( 'composition_function', 'cross_product'( 'universal_class',
% 0.73/1.10 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.73/1.10 'composition_function' ) ), =( compose( X, Y ), Z ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.73/1.10 , 'universal_class' ) ) ), member( 'ordered_pair'( X, 'ordered_pair'( Y,
% 0.73/1.10 compose( X, Y ) ) ), 'composition_function' ) ],
% 0.73/1.10 [ subclass( 'domain_relation', 'cross_product'( 'universal_class',
% 0.73/1.10 'universal_class' ) ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) ), =(
% 0.73/1.10 'domain_of'( X ), Y ) ],
% 0.73/1.10 [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X,
% 0.73/1.10 'domain_of'( X ) ), 'domain_relation' ) ],
% 0.73/1.10 [ =( first( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.73/1.10 'identity_relation' ) ), 'single_valued1'( X ) ) ],
% 0.73/1.10 [ =( second( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.73/1.10 'identity_relation' ) ), 'single_valued2'( X ) ) ],
% 0.73/1.10 [ =( domain( X, image( inverse( X ), singleton( 'single_valued1'( X ) )
% 0.73/1.10 ), 'single_valued2'( X ) ), 'single_valued3'( X ) ) ],
% 0.73/1.10 [ =( intersection( complement( compose( 'element_relation', complement(
% 0.73/1.10 'identity_relation' ) ) ), 'element_relation' ), 'singleton_relation' ) ]
% 0.73/1.10 ,
% 0.73/1.10 [ subclass( 'application_function', 'cross_product'( 'universal_class',
% 0.73/1.10 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.73/1.10 'application_function' ) ), member( Y, 'domain_of'( X ) ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.73/1.10 'application_function' ) ), =( apply( X, Y ), Z ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.73/1.10 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 0.73/1.10 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 0.73/1.10 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 0.73/1.10 'application_function' ) ],
% 0.73/1.10 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.73/1.10 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 1.02/1.44 [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ],
% 1.02/1.44 [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ), maps( X,
% 1.02/1.44 'domain_of'( X ), Y ) ],
% 1.02/1.44 [ ~( =( restrict( 'null_class', x, y ), 'null_class' ) ) ]
% 1.02/1.44 ] .
% 1.02/1.44
% 1.02/1.44
% 1.02/1.44 percentage equality = 0.228311, percentage horn = 0.929204
% 1.02/1.44 This is a problem with some equality
% 1.02/1.44
% 1.02/1.44
% 1.02/1.44
% 1.02/1.44 Options Used:
% 1.02/1.44
% 1.02/1.44 useres = 1
% 1.02/1.44 useparamod = 1
% 1.02/1.44 useeqrefl = 1
% 1.02/1.44 useeqfact = 1
% 1.02/1.44 usefactor = 1
% 1.02/1.44 usesimpsplitting = 0
% 1.02/1.44 usesimpdemod = 5
% 1.02/1.44 usesimpres = 3
% 1.02/1.44
% 1.02/1.44 resimpinuse = 1000
% 1.02/1.44 resimpclauses = 20000
% 1.02/1.44 substype = eqrewr
% 1.02/1.44 backwardsubs = 1
% 1.02/1.44 selectoldest = 5
% 1.02/1.44
% 1.02/1.44 litorderings [0] = split
% 1.02/1.44 litorderings [1] = extend the termordering, first sorting on arguments
% 1.02/1.44
% 1.02/1.44 termordering = kbo
% 1.02/1.44
% 1.02/1.44 litapriori = 0
% 1.02/1.44 termapriori = 1
% 1.02/1.44 litaposteriori = 0
% 1.02/1.44 termaposteriori = 0
% 1.02/1.44 demodaposteriori = 0
% 1.02/1.44 ordereqreflfact = 0
% 1.02/1.44
% 1.02/1.44 litselect = negord
% 1.02/1.44
% 1.02/1.44 maxweight = 15
% 1.02/1.44 maxdepth = 30000
% 1.02/1.44 maxlength = 115
% 1.02/1.44 maxnrvars = 195
% 1.02/1.44 excuselevel = 1
% 1.02/1.44 increasemaxweight = 1
% 1.02/1.44
% 1.02/1.44 maxselected = 10000000
% 1.02/1.44 maxnrclauses = 10000000
% 1.02/1.44
% 1.02/1.44 showgenerated = 0
% 1.02/1.44 showkept = 0
% 1.02/1.44 showselected = 0
% 1.02/1.44 showdeleted = 0
% 1.02/1.44 showresimp = 1
% 1.02/1.44 showstatus = 2000
% 1.02/1.44
% 1.02/1.44 prologoutput = 1
% 1.02/1.44 nrgoals = 5000000
% 1.02/1.44 totalproof = 1
% 1.02/1.44
% 1.02/1.44 Symbols occurring in the translation:
% 1.02/1.44
% 1.02/1.44 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.02/1.44 . [1, 2] (w:1, o:64, a:1, s:1, b:0),
% 1.02/1.44 ! [4, 1] (w:0, o:35, a:1, s:1, b:0),
% 1.02/1.44 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.02/1.44 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.02/1.44 subclass [41, 2] (w:1, o:89, a:1, s:1, b:0),
% 1.02/1.44 member [43, 2] (w:1, o:90, a:1, s:1, b:0),
% 1.02/1.44 'not_subclass_element' [44, 2] (w:1, o:91, a:1, s:1, b:0),
% 1.02/1.44 'universal_class' [45, 0] (w:1, o:22, a:1, s:1, b:0),
% 1.02/1.44 'unordered_pair' [46, 2] (w:1, o:92, a:1, s:1, b:0),
% 1.02/1.44 singleton [47, 1] (w:1, o:43, a:1, s:1, b:0),
% 1.02/1.44 'ordered_pair' [48, 2] (w:1, o:93, a:1, s:1, b:0),
% 1.02/1.44 'cross_product' [50, 2] (w:1, o:94, a:1, s:1, b:0),
% 1.02/1.44 first [52, 1] (w:1, o:44, a:1, s:1, b:0),
% 1.02/1.44 second [53, 1] (w:1, o:45, a:1, s:1, b:0),
% 1.02/1.44 'element_relation' [54, 0] (w:1, o:27, a:1, s:1, b:0),
% 1.02/1.44 intersection [55, 2] (w:1, o:96, a:1, s:1, b:0),
% 1.02/1.44 complement [56, 1] (w:1, o:46, a:1, s:1, b:0),
% 1.02/1.44 union [57, 2] (w:1, o:97, a:1, s:1, b:0),
% 1.02/1.44 'symmetric_difference' [58, 2] (w:1, o:98, a:1, s:1, b:0),
% 1.02/1.44 restrict [60, 3] (w:1, o:101, a:1, s:1, b:0),
% 1.02/1.44 'null_class' [61, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.02/1.44 'domain_of' [62, 1] (w:1, o:49, a:1, s:1, b:0),
% 1.02/1.44 rotate [63, 1] (w:1, o:40, a:1, s:1, b:0),
% 1.02/1.44 flip [65, 1] (w:1, o:50, a:1, s:1, b:0),
% 1.02/1.44 inverse [66, 1] (w:1, o:51, a:1, s:1, b:0),
% 1.02/1.44 'range_of' [67, 1] (w:1, o:41, a:1, s:1, b:0),
% 1.02/1.44 domain [68, 3] (w:1, o:103, a:1, s:1, b:0),
% 1.02/1.44 range [69, 3] (w:1, o:104, a:1, s:1, b:0),
% 1.02/1.44 image [70, 2] (w:1, o:95, a:1, s:1, b:0),
% 1.02/1.44 successor [71, 1] (w:1, o:52, a:1, s:1, b:0),
% 1.02/1.44 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 1.02/1.44 inductive [73, 1] (w:1, o:53, a:1, s:1, b:0),
% 1.02/1.44 omega [74, 0] (w:1, o:10, a:1, s:1, b:0),
% 1.02/1.44 'sum_class' [75, 1] (w:1, o:54, a:1, s:1, b:0),
% 1.02/1.44 'power_class' [76, 1] (w:1, o:57, a:1, s:1, b:0),
% 1.02/1.44 compose [78, 2] (w:1, o:99, a:1, s:1, b:0),
% 1.02/1.44 'single_valued_class' [79, 1] (w:1, o:58, a:1, s:1, b:0),
% 1.02/1.44 'identity_relation' [80, 0] (w:1, o:29, a:1, s:1, b:0),
% 1.02/1.44 function [82, 1] (w:1, o:59, a:1, s:1, b:0),
% 1.02/1.44 regular [83, 1] (w:1, o:42, a:1, s:1, b:0),
% 1.02/1.44 apply [84, 2] (w:1, o:100, a:1, s:1, b:0),
% 1.02/1.44 choice [85, 0] (w:1, o:30, a:1, s:1, b:0),
% 1.02/1.44 'one_to_one' [86, 1] (w:1, o:55, a:1, s:1, b:0),
% 1.02/1.44 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 1.02/1.44 diagonalise [88, 1] (w:1, o:60, a:1, s:1, b:0),
% 1.02/1.44 cantor [89, 1] (w:1, o:47, a:1, s:1, b:0),
% 1.02/1.44 operation [90, 1] (w:1, o:56, a:1, s:1, b:0),
% 1.02/1.44 compatible [94, 3] (w:1, o:102, a:1, s:1, b:0),
% 1.02/1.44 homomorphism [95, 3] (w:1, o:105, a:1, s:1, b:0),
% 1.02/1.44 'not_homomorphism1' [96, 3] (w:1, o:107, a:1, s:1, b:0),
% 1.02/1.44 'not_homomorphism2' [97, 3] (w:1, o:108, a:1, s:1, b:0),
% 1.02/1.44 'compose_class' [98, 1] (w:1, o:48, a:1, s:1, b:0),
% 1.02/1.44 'composition_function' [99, 0] (w:1, o:31, a:1, s:1, b:0),
% 1.02/1.44 'domain_relation' [100, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.02/1.44 'single_valued1' [101, 1] (w:1, o:61, a:1, s:1, b:0),
% 1.02/1.44 'single_valued2' [102, 1] (w:1, o:62, a:1, s:1, b:0),
% 1.02/1.44 'single_valued3' [103, 1] (w:1, o:63, a:1, s:1, b:0),
% 1.02/1.44 'singleton_relation' [104, 0] (w:1, o:7, a:1, s:1, b:0),
% 1.02/1.44 'application_function' [105, 0] (w:1, o:32, a:1, s:1, b:0),
% 1.02/1.44 maps [106, 3] (w:1, o:106, a:1, s:1, b:0),
% 1.02/1.44 x [107, 0] (w:1, o:33, a:1, s:1, b:0),
% 1.02/1.44 y [108, 0] (w:1, o:34, a:1, s:1, b:0).
% 1.02/1.44
% 1.02/1.44
% 1.02/1.44 Starting Search:
% 1.02/1.44
% 1.02/1.44 Resimplifying inuse:
% 1.02/1.44 Done
% 1.02/1.44
% 1.02/1.44
% 1.02/1.44 Intermediate Status:
% 1.02/1.44 Generated: 4939
% 1.02/1.44 Kept: 2019
% 1.02/1.44 Inuse: 100
% 1.02/1.44 Deleted: 8
% 1.02/1.44 Deletedinuse: 2
% 1.02/1.44
% 1.02/1.44 Resimplifying inuse:
% 1.02/1.44 Done
% 1.02/1.44
% 1.02/1.44 Resimplifying inuse:
% 1.02/1.44 Done
% 1.02/1.44
% 1.02/1.44
% 1.02/1.44 Intermediate Status:
% 1.02/1.44 Generated: 9532
% 1.02/1.44 Kept: 4024
% 1.02/1.44 Inuse: 181
% 1.02/1.45 Deleted: 18
% 1.02/1.45 Deletedinuse: 6
% 1.02/1.45
% 1.02/1.45 Resimplifying inuse:
% 1.02/1.45 Done
% 1.02/1.45
% 1.02/1.45 Resimplifying inuse:
% 1.02/1.45 Done
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 Intermediate Status:
% 1.02/1.45 Generated: 13399
% 1.02/1.45 Kept: 6048
% 1.02/1.45 Inuse: 234
% 1.02/1.45 Deleted: 21
% 1.02/1.45 Deletedinuse: 7
% 1.02/1.45
% 1.02/1.45 Resimplifying inuse:
% 1.02/1.45 Done
% 1.02/1.45
% 1.02/1.45 Resimplifying inuse:
% 1.02/1.45 Done
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 Intermediate Status:
% 1.02/1.45 Generated: 18145
% 1.02/1.45 Kept: 8110
% 1.02/1.45 Inuse: 285
% 1.02/1.45 Deleted: 79
% 1.02/1.45 Deletedinuse: 63
% 1.02/1.45
% 1.02/1.45 Resimplifying inuse:
% 1.02/1.45
% 1.02/1.45 Bliksems!, er is een bewijs:
% 1.02/1.45 % SZS status Unsatisfiable
% 1.02/1.45 % SZS output start Refutation
% 1.02/1.45
% 1.02/1.45 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 1.02/1.45 )
% 1.02/1.45 .
% 1.02/1.45 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 1.02/1.45 .
% 1.02/1.45 clause( 19, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ] )
% 1.02/1.45 .
% 1.02/1.45 clause( 22, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ] )
% 1.02/1.45 .
% 1.02/1.45 clause( 26, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y
% 1.02/1.45 , Z ) ) ] )
% 1.02/1.45 .
% 1.02/1.45 clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.02/1.45 .
% 1.02/1.45 clause( 111, [ ~( =( restrict( 'null_class', x, y ), 'null_class' ) ) ] )
% 1.02/1.45 .
% 1.02/1.45 clause( 127, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ] )
% 1.02/1.45 .
% 1.02/1.45 clause( 1856, [ ~( member( X, complement( 'universal_class' ) ) ), ~(
% 1.02/1.45 member( X, Y ) ) ] )
% 1.02/1.45 .
% 1.02/1.45 clause( 1880, [ ~( member( X, complement( 'universal_class' ) ) ) ] )
% 1.02/1.45 .
% 1.02/1.45 clause( 1884, [ ~( member( X, intersection( complement( 'universal_class' )
% 1.02/1.45 , Y ) ) ) ] )
% 1.02/1.45 .
% 1.02/1.45 clause( 6848, [ =( intersection( complement( 'universal_class' ), X ),
% 1.02/1.45 'null_class' ) ] )
% 1.02/1.45 .
% 1.02/1.45 clause( 7437, [ ~( member( X, 'null_class' ) ) ] )
% 1.02/1.45 .
% 1.02/1.45 clause( 7464, [ ~( member( X, intersection( 'null_class', Y ) ) ) ] )
% 1.02/1.45 .
% 1.02/1.45 clause( 8285, [ =( intersection( 'null_class', X ), 'null_class' ) ] )
% 1.02/1.45 .
% 1.02/1.45 clause( 8348, [ =( restrict( 'null_class', X, Y ), 'null_class' ) ] )
% 1.02/1.45 .
% 1.02/1.45 clause( 8488, [] )
% 1.02/1.45 .
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 % SZS output end Refutation
% 1.02/1.45 found a proof!
% 1.02/1.45
% 1.02/1.45 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.02/1.45
% 1.02/1.45 initialclauses(
% 1.02/1.45 [ clause( 8490, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.02/1.45 ) ] )
% 1.02/1.45 , clause( 8491, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 1.02/1.45 , Y ) ] )
% 1.02/1.45 , clause( 8492, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 1.02/1.45 subclass( X, Y ) ] )
% 1.02/1.45 , clause( 8493, [ subclass( X, 'universal_class' ) ] )
% 1.02/1.45 , clause( 8494, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.02/1.45 , clause( 8495, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 1.02/1.45 , clause( 8496, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ]
% 1.02/1.45 )
% 1.02/1.45 , clause( 8497, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 1.02/1.45 =( X, Z ) ] )
% 1.02/1.45 , clause( 8498, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.02/1.45 'unordered_pair'( X, Y ) ) ] )
% 1.02/1.45 , clause( 8499, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.02/1.45 'unordered_pair'( Y, X ) ) ] )
% 1.02/1.45 , clause( 8500, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 1.02/1.45 )
% 1.02/1.45 , clause( 8501, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.02/1.45 , clause( 8502, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 1.02/1.45 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.02/1.45 , clause( 8503, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.02/1.45 ) ) ), member( X, Z ) ] )
% 1.02/1.45 , clause( 8504, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.02/1.45 ) ) ), member( Y, T ) ] )
% 1.02/1.45 , clause( 8505, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.02/1.45 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.02/1.45 , clause( 8506, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 1.02/1.45 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 1.02/1.45 , clause( 8507, [ subclass( 'element_relation', 'cross_product'(
% 1.02/1.45 'universal_class', 'universal_class' ) ) ] )
% 1.02/1.45 , clause( 8508, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) )
% 1.02/1.45 , member( X, Y ) ] )
% 1.02/1.45 , clause( 8509, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.02/1.45 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 1.02/1.45 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 1.02/1.45 , clause( 8510, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.02/1.45 )
% 1.02/1.45 , clause( 8511, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 1.02/1.45 )
% 1.02/1.45 , clause( 8512, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 1.02/1.45 intersection( Y, Z ) ) ] )
% 1.02/1.45 , clause( 8513, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 1.02/1.45 )
% 1.02/1.45 , clause( 8514, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.02/1.45 complement( Y ) ), member( X, Y ) ] )
% 1.02/1.45 , clause( 8515, [ =( complement( intersection( complement( X ), complement(
% 1.02/1.45 Y ) ) ), union( X, Y ) ) ] )
% 1.02/1.45 , clause( 8516, [ =( intersection( complement( intersection( X, Y ) ),
% 1.02/1.45 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 1.02/1.45 'symmetric_difference'( X, Y ) ) ] )
% 1.02/1.45 , clause( 8517, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 1.02/1.45 X, Y, Z ) ) ] )
% 1.02/1.45 , clause( 8518, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 1.02/1.45 Z, X, Y ) ) ] )
% 1.02/1.45 , clause( 8519, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 1.02/1.45 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 1.02/1.45 , clause( 8520, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 1.02/1.45 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 1.02/1.45 'domain_of'( Y ) ) ] )
% 1.02/1.45 , clause( 8521, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 1.02/1.45 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.02/1.45 , clause( 8522, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.02/1.45 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 1.02/1.45 ] )
% 1.02/1.45 , clause( 8523, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 1.02/1.45 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 1.02/1.45 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.02/1.45 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 1.02/1.45 , Y ), rotate( T ) ) ] )
% 1.02/1.45 , clause( 8524, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 1.02/1.45 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.02/1.45 , clause( 8525, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.02/1.45 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 1.02/1.45 )
% 1.02/1.45 , clause( 8526, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 1.02/1.45 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 1.02/1.45 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.02/1.45 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 1.02/1.45 , Z ), flip( T ) ) ] )
% 1.02/1.45 , clause( 8527, [ =( 'domain_of'( flip( 'cross_product'( X,
% 1.02/1.45 'universal_class' ) ) ), inverse( X ) ) ] )
% 1.02/1.45 , clause( 8528, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 1.02/1.45 , clause( 8529, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 1.02/1.45 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 1.02/1.45 , clause( 8530, [ =( second( 'not_subclass_element'( restrict( X, singleton(
% 1.02/1.45 Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 1.02/1.45 , clause( 8531, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 1.02/1.45 image( X, Y ) ) ] )
% 1.02/1.45 , clause( 8532, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 1.02/1.45 , clause( 8533, [ subclass( 'successor_relation', 'cross_product'(
% 1.02/1.45 'universal_class', 'universal_class' ) ) ] )
% 1.02/1.45 , clause( 8534, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' )
% 1.02/1.45 ), =( successor( X ), Y ) ] )
% 1.02/1.45 , clause( 8535, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X
% 1.02/1.45 , Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 1.02/1.45 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 1.02/1.45 , clause( 8536, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 1.02/1.45 , clause( 8537, [ ~( inductive( X ) ), subclass( image(
% 1.02/1.45 'successor_relation', X ), X ) ] )
% 1.02/1.45 , clause( 8538, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 1.02/1.45 'successor_relation', X ), X ) ), inductive( X ) ] )
% 1.02/1.45 , clause( 8539, [ inductive( omega ) ] )
% 1.02/1.45 , clause( 8540, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 1.02/1.45 , clause( 8541, [ member( omega, 'universal_class' ) ] )
% 1.02/1.45 , clause( 8542, [ =( 'domain_of'( restrict( 'element_relation',
% 1.02/1.45 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 1.02/1.45 , clause( 8543, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 1.02/1.45 X ), 'universal_class' ) ] )
% 1.02/1.45 , clause( 8544, [ =( complement( image( 'element_relation', complement( X )
% 1.02/1.45 ) ), 'power_class'( X ) ) ] )
% 1.02/1.45 , clause( 8545, [ ~( member( X, 'universal_class' ) ), member(
% 1.02/1.45 'power_class'( X ), 'universal_class' ) ] )
% 1.02/1.45 , clause( 8546, [ subclass( compose( X, Y ), 'cross_product'(
% 1.02/1.45 'universal_class', 'universal_class' ) ) ] )
% 1.02/1.45 , clause( 8547, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 1.02/1.45 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 1.02/1.45 , clause( 8548, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 1.02/1.45 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 1.02/1.45 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 1.02/1.45 ) ] )
% 1.02/1.45 , clause( 8549, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 1.02/1.45 inverse( X ) ), 'identity_relation' ) ] )
% 1.02/1.45 , clause( 8550, [ ~( subclass( compose( X, inverse( X ) ),
% 1.02/1.45 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 1.02/1.45 , clause( 8551, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 1.02/1.45 'universal_class', 'universal_class' ) ) ] )
% 1.02/1.45 , clause( 8552, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 1.02/1.45 , 'identity_relation' ) ] )
% 1.02/1.45 , clause( 8553, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 1.02/1.45 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 1.02/1.45 'identity_relation' ) ), function( X ) ] )
% 1.02/1.45 , clause( 8554, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ),
% 1.02/1.45 member( image( X, Y ), 'universal_class' ) ] )
% 1.02/1.45 , clause( 8555, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.02/1.45 , clause( 8556, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 1.02/1.45 , 'null_class' ) ] )
% 1.02/1.45 , clause( 8557, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y
% 1.02/1.45 ) ) ] )
% 1.02/1.45 , clause( 8558, [ function( choice ) ] )
% 1.02/1.45 , clause( 8559, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' )
% 1.02/1.45 , member( apply( choice, X ), X ) ] )
% 1.02/1.45 , clause( 8560, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 1.02/1.45 , clause( 8561, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 1.02/1.45 , clause( 8562, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 1.02/1.45 'one_to_one'( X ) ] )
% 1.02/1.45 , clause( 8563, [ =( intersection( 'cross_product'( 'universal_class',
% 1.02/1.45 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 1.02/1.45 'universal_class' ), complement( compose( complement( 'element_relation'
% 1.02/1.45 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 1.02/1.45 , clause( 8564, [ =( intersection( inverse( 'subset_relation' ),
% 1.02/1.45 'subset_relation' ), 'identity_relation' ) ] )
% 1.02/1.45 , clause( 8565, [ =( complement( 'domain_of'( intersection( X,
% 1.02/1.45 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 1.02/1.45 , clause( 8566, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 1.02/1.45 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 1.02/1.45 , clause( 8567, [ ~( operation( X ) ), function( X ) ] )
% 1.02/1.45 , clause( 8568, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 1.02/1.45 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.02/1.45 ] )
% 1.02/1.45 , clause( 8569, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 1.02/1.45 'domain_of'( 'domain_of'( X ) ) ) ] )
% 1.02/1.45 , clause( 8570, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 1.02/1.45 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.02/1.45 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 1.02/1.45 operation( X ) ] )
% 1.02/1.45 , clause( 8571, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 1.02/1.45 , clause( 8572, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 1.02/1.45 Y ) ), 'domain_of'( X ) ) ] )
% 1.02/1.45 , clause( 8573, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 1.02/1.45 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 1.02/1.45 , clause( 8574, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) )
% 1.02/1.45 , 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 1.02/1.45 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 1.02/1.45 , clause( 8575, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 1.02/1.45 , clause( 8576, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 1.02/1.45 , clause( 8577, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 1.02/1.45 , clause( 8578, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 1.02/1.45 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 1.02/1.45 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 1.02/1.45 )
% 1.02/1.45 , clause( 8579, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.02/1.45 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.02/1.45 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.02/1.45 , Y ) ] )
% 1.02/1.45 , clause( 8580, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.02/1.45 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 1.02/1.45 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 1.02/1.45 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 1.02/1.45 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 1.02/1.45 )
% 1.02/1.45 , clause( 8581, [ subclass( 'compose_class'( X ), 'cross_product'(
% 1.02/1.45 'universal_class', 'universal_class' ) ) ] )
% 1.02/1.45 , clause( 8582, [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) )
% 1.02/1.45 ), =( compose( Z, X ), Y ) ] )
% 1.02/1.45 , clause( 8583, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.02/1.45 'universal_class', 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) )
% 1.02/1.45 , member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ] )
% 1.02/1.45 , clause( 8584, [ subclass( 'composition_function', 'cross_product'(
% 1.02/1.45 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 1.02/1.45 ) ) ) ] )
% 1.02/1.45 , clause( 8585, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.02/1.45 'composition_function' ) ), =( compose( X, Y ), Z ) ] )
% 1.02/1.45 , clause( 8586, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.02/1.45 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( X,
% 1.02/1.45 'ordered_pair'( Y, compose( X, Y ) ) ), 'composition_function' ) ] )
% 1.02/1.45 , clause( 8587, [ subclass( 'domain_relation', 'cross_product'(
% 1.02/1.45 'universal_class', 'universal_class' ) ) ] )
% 1.02/1.45 , clause( 8588, [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) )
% 1.02/1.45 , =( 'domain_of'( X ), Y ) ] )
% 1.02/1.45 , clause( 8589, [ ~( member( X, 'universal_class' ) ), member(
% 1.02/1.45 'ordered_pair'( X, 'domain_of'( X ) ), 'domain_relation' ) ] )
% 1.02/1.45 , clause( 8590, [ =( first( 'not_subclass_element'( compose( X, inverse( X
% 1.02/1.45 ) ), 'identity_relation' ) ), 'single_valued1'( X ) ) ] )
% 1.02/1.45 , clause( 8591, [ =( second( 'not_subclass_element'( compose( X, inverse( X
% 1.02/1.45 ) ), 'identity_relation' ) ), 'single_valued2'( X ) ) ] )
% 1.02/1.45 , clause( 8592, [ =( domain( X, image( inverse( X ), singleton(
% 1.02/1.45 'single_valued1'( X ) ) ), 'single_valued2'( X ) ), 'single_valued3'( X )
% 1.02/1.45 ) ] )
% 1.02/1.45 , clause( 8593, [ =( intersection( complement( compose( 'element_relation'
% 1.02/1.45 , complement( 'identity_relation' ) ) ), 'element_relation' ),
% 1.02/1.45 'singleton_relation' ) ] )
% 1.02/1.45 , clause( 8594, [ subclass( 'application_function', 'cross_product'(
% 1.02/1.45 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 1.02/1.45 ) ) ) ] )
% 1.02/1.45 , clause( 8595, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.02/1.45 'application_function' ) ), member( Y, 'domain_of'( X ) ) ] )
% 1.02/1.45 , clause( 8596, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.02/1.45 'application_function' ) ), =( apply( X, Y ), Z ) ] )
% 1.02/1.45 , clause( 8597, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.02/1.45 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 1.02/1.45 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 1.02/1.45 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 1.02/1.45 'application_function' ) ] )
% 1.02/1.45 , clause( 8598, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 1.02/1.45 , clause( 8599, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 1.02/1.45 , clause( 8600, [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ] )
% 1.02/1.45 , clause( 8601, [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ),
% 1.02/1.45 maps( X, 'domain_of'( X ), Y ) ] )
% 1.02/1.45 , clause( 8602, [ ~( =( restrict( 'null_class', x, y ), 'null_class' ) ) ]
% 1.02/1.45 )
% 1.02/1.45 ] ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 1.02/1.45 )
% 1.02/1.45 , clause( 8490, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.02/1.45 ) ] )
% 1.02/1.45 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.02/1.45 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 1.02/1.45 , clause( 8493, [ subclass( X, 'universal_class' ) ] )
% 1.02/1.45 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 19, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ] )
% 1.02/1.45 , clause( 8510, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.02/1.45 )
% 1.02/1.45 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.02/1.45 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 22, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ] )
% 1.02/1.45 , clause( 8513, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 1.02/1.45 )
% 1.02/1.45 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.02/1.45 ), ==>( 1, 1 )] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 26, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y
% 1.02/1.45 , Z ) ) ] )
% 1.02/1.45 , clause( 8517, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 1.02/1.45 X, Y, Z ) ) ] )
% 1.02/1.45 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.02/1.45 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.02/1.45 , clause( 8555, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.02/1.45 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.02/1.45 1 )] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 111, [ ~( =( restrict( 'null_class', x, y ), 'null_class' ) ) ] )
% 1.02/1.45 , clause( 8602, [ ~( =( restrict( 'null_class', x, y ), 'null_class' ) ) ]
% 1.02/1.45 )
% 1.02/1.45 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 resolution(
% 1.02/1.45 clause( 8737, [ ~( member( Y, X ) ), member( Y, 'universal_class' ) ] )
% 1.02/1.45 , clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 1.02/1.45 )
% 1.02/1.45 , 0, clause( 3, [ subclass( X, 'universal_class' ) ] )
% 1.02/1.45 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'universal_class' ), :=( Z, Y )] )
% 1.02/1.45 , substitution( 1, [ :=( X, X )] )).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 127, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ] )
% 1.02/1.45 , clause( 8737, [ ~( member( Y, X ) ), member( Y, 'universal_class' ) ] )
% 1.02/1.45 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 1.02/1.45 ), ==>( 1, 1 )] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 resolution(
% 1.02/1.45 clause( 8738, [ ~( member( X, complement( 'universal_class' ) ) ), ~(
% 1.02/1.45 member( X, Y ) ) ] )
% 1.02/1.45 , clause( 22, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ] )
% 1.02/1.45 , 1, clause( 127, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ]
% 1.02/1.45 )
% 1.02/1.45 , 1, substitution( 0, [ :=( X, X ), :=( Y, 'universal_class' )] ),
% 1.02/1.45 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 1856, [ ~( member( X, complement( 'universal_class' ) ) ), ~(
% 1.02/1.45 member( X, Y ) ) ] )
% 1.02/1.45 , clause( 8738, [ ~( member( X, complement( 'universal_class' ) ) ), ~(
% 1.02/1.45 member( X, Y ) ) ] )
% 1.02/1.45 , substitution( 0, [ :=( X, X ), :=( Y, complement( 'universal_class' ) )] )
% 1.02/1.45 , permutation( 0, [ ==>( 0, 0 ), ==>( 1, 0 )] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 factor(
% 1.02/1.45 clause( 8740, [ ~( member( X, complement( 'universal_class' ) ) ) ] )
% 1.02/1.45 , clause( 1856, [ ~( member( X, complement( 'universal_class' ) ) ), ~(
% 1.02/1.45 member( X, Y ) ) ] )
% 1.02/1.45 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, complement( 'universal_class'
% 1.02/1.45 ) )] )).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 1880, [ ~( member( X, complement( 'universal_class' ) ) ) ] )
% 1.02/1.45 , clause( 8740, [ ~( member( X, complement( 'universal_class' ) ) ) ] )
% 1.02/1.45 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 resolution(
% 1.02/1.45 clause( 8741, [ ~( member( X, intersection( complement( 'universal_class' )
% 1.02/1.45 , Y ) ) ) ] )
% 1.02/1.45 , clause( 1880, [ ~( member( X, complement( 'universal_class' ) ) ) ] )
% 1.02/1.45 , 0, clause( 19, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.02/1.45 )
% 1.02/1.45 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ), :=( Y
% 1.02/1.45 , complement( 'universal_class' ) ), :=( Z, Y )] )).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 1884, [ ~( member( X, intersection( complement( 'universal_class' )
% 1.02/1.45 , Y ) ) ) ] )
% 1.02/1.45 , clause( 8741, [ ~( member( X, intersection( complement( 'universal_class'
% 1.02/1.45 ), Y ) ) ) ] )
% 1.02/1.45 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.02/1.45 )] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 eqswap(
% 1.02/1.45 clause( 8742, [ =( 'null_class', X ), member( regular( X ), X ) ] )
% 1.02/1.45 , clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.02/1.45 , 0, substitution( 0, [ :=( X, X )] )).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 resolution(
% 1.02/1.45 clause( 8743, [ =( 'null_class', intersection( complement(
% 1.02/1.45 'universal_class' ), X ) ) ] )
% 1.02/1.45 , clause( 1884, [ ~( member( X, intersection( complement( 'universal_class'
% 1.02/1.45 ), Y ) ) ) ] )
% 1.02/1.45 , 0, clause( 8742, [ =( 'null_class', X ), member( regular( X ), X ) ] )
% 1.02/1.45 , 1, substitution( 0, [ :=( X, regular( intersection( complement(
% 1.02/1.45 'universal_class' ), X ) ) ), :=( Y, X )] ), substitution( 1, [ :=( X,
% 1.02/1.45 intersection( complement( 'universal_class' ), X ) )] )).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 eqswap(
% 1.02/1.45 clause( 8744, [ =( intersection( complement( 'universal_class' ), X ),
% 1.02/1.45 'null_class' ) ] )
% 1.02/1.45 , clause( 8743, [ =( 'null_class', intersection( complement(
% 1.02/1.45 'universal_class' ), X ) ) ] )
% 1.02/1.45 , 0, substitution( 0, [ :=( X, X )] )).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 6848, [ =( intersection( complement( 'universal_class' ), X ),
% 1.02/1.45 'null_class' ) ] )
% 1.02/1.45 , clause( 8744, [ =( intersection( complement( 'universal_class' ), X ),
% 1.02/1.45 'null_class' ) ] )
% 1.02/1.45 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 paramod(
% 1.02/1.45 clause( 8746, [ ~( member( X, 'null_class' ) ) ] )
% 1.02/1.45 , clause( 6848, [ =( intersection( complement( 'universal_class' ), X ),
% 1.02/1.45 'null_class' ) ] )
% 1.02/1.45 , 0, clause( 1884, [ ~( member( X, intersection( complement(
% 1.02/1.45 'universal_class' ), Y ) ) ) ] )
% 1.02/1.45 , 0, 3, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 1.02/1.45 :=( Y, Y )] )).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 7437, [ ~( member( X, 'null_class' ) ) ] )
% 1.02/1.45 , clause( 8746, [ ~( member( X, 'null_class' ) ) ] )
% 1.02/1.45 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 resolution(
% 1.02/1.45 clause( 8747, [ ~( member( X, intersection( 'null_class', Y ) ) ) ] )
% 1.02/1.45 , clause( 7437, [ ~( member( X, 'null_class' ) ) ] )
% 1.02/1.45 , 0, clause( 19, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.02/1.45 )
% 1.02/1.45 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ), :=( Y
% 1.02/1.45 , 'null_class' ), :=( Z, Y )] )).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 7464, [ ~( member( X, intersection( 'null_class', Y ) ) ) ] )
% 1.02/1.45 , clause( 8747, [ ~( member( X, intersection( 'null_class', Y ) ) ) ] )
% 1.02/1.45 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.02/1.45 )] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 eqswap(
% 1.02/1.45 clause( 8748, [ =( 'null_class', X ), member( regular( X ), X ) ] )
% 1.02/1.45 , clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.02/1.45 , 0, substitution( 0, [ :=( X, X )] )).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 resolution(
% 1.02/1.45 clause( 8749, [ =( 'null_class', intersection( 'null_class', X ) ) ] )
% 1.02/1.45 , clause( 7464, [ ~( member( X, intersection( 'null_class', Y ) ) ) ] )
% 1.02/1.45 , 0, clause( 8748, [ =( 'null_class', X ), member( regular( X ), X ) ] )
% 1.02/1.45 , 1, substitution( 0, [ :=( X, regular( intersection( 'null_class', X ) ) )
% 1.02/1.45 , :=( Y, X )] ), substitution( 1, [ :=( X, intersection( 'null_class', X
% 1.02/1.45 ) )] )).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 eqswap(
% 1.02/1.45 clause( 8750, [ =( intersection( 'null_class', X ), 'null_class' ) ] )
% 1.02/1.45 , clause( 8749, [ =( 'null_class', intersection( 'null_class', X ) ) ] )
% 1.02/1.45 , 0, substitution( 0, [ :=( X, X )] )).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 8285, [ =( intersection( 'null_class', X ), 'null_class' ) ] )
% 1.02/1.45 , clause( 8750, [ =( intersection( 'null_class', X ), 'null_class' ) ] )
% 1.02/1.45 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 eqswap(
% 1.02/1.45 clause( 8751, [ =( 'null_class', intersection( 'null_class', X ) ) ] )
% 1.02/1.45 , clause( 8285, [ =( intersection( 'null_class', X ), 'null_class' ) ] )
% 1.02/1.45 , 0, substitution( 0, [ :=( X, X )] )).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 paramod(
% 1.02/1.45 clause( 8753, [ =( 'null_class', restrict( 'null_class', X, Y ) ) ] )
% 1.02/1.45 , clause( 26, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X
% 1.02/1.45 , Y, Z ) ) ] )
% 1.02/1.45 , 0, clause( 8751, [ =( 'null_class', intersection( 'null_class', X ) ) ]
% 1.02/1.45 )
% 1.02/1.45 , 0, 2, substitution( 0, [ :=( X, 'null_class' ), :=( Y, X ), :=( Z, Y )] )
% 1.02/1.45 , substitution( 1, [ :=( X, 'cross_product'( X, Y ) )] )).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 eqswap(
% 1.02/1.45 clause( 8754, [ =( restrict( 'null_class', X, Y ), 'null_class' ) ] )
% 1.02/1.45 , clause( 8753, [ =( 'null_class', restrict( 'null_class', X, Y ) ) ] )
% 1.02/1.45 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 8348, [ =( restrict( 'null_class', X, Y ), 'null_class' ) ] )
% 1.02/1.45 , clause( 8754, [ =( restrict( 'null_class', X, Y ), 'null_class' ) ] )
% 1.02/1.45 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.02/1.45 )] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 paramod(
% 1.02/1.45 clause( 8757, [ ~( =( 'null_class', 'null_class' ) ) ] )
% 1.02/1.45 , clause( 8348, [ =( restrict( 'null_class', X, Y ), 'null_class' ) ] )
% 1.02/1.45 , 0, clause( 111, [ ~( =( restrict( 'null_class', x, y ), 'null_class' ) )
% 1.02/1.45 ] )
% 1.02/1.45 , 0, 2, substitution( 0, [ :=( X, x ), :=( Y, y )] ), substitution( 1, [] )
% 1.02/1.45 ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 eqrefl(
% 1.02/1.45 clause( 8758, [] )
% 1.02/1.45 , clause( 8757, [ ~( =( 'null_class', 'null_class' ) ) ] )
% 1.02/1.45 , 0, substitution( 0, [] )).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 8488, [] )
% 1.02/1.45 , clause( 8758, [] )
% 1.02/1.45 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 end.
% 1.02/1.45
% 1.02/1.45 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.02/1.45
% 1.02/1.45 Memory use:
% 1.02/1.45
% 1.02/1.45 space for terms: 125761
% 1.02/1.45 space for clauses: 403329
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 clauses generated: 19331
% 1.02/1.45 clauses kept: 8489
% 1.02/1.45 clauses selected: 303
% 1.02/1.45 clauses deleted: 90
% 1.02/1.45 clauses inuse deleted: 72
% 1.02/1.45
% 1.02/1.45 subsentry: 43188
% 1.02/1.45 literals s-matched: 33639
% 1.02/1.45 literals matched: 33143
% 1.02/1.45 full subsumption: 14803
% 1.02/1.45
% 1.02/1.45 checksum: -367024961
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 Bliksem ended
%------------------------------------------------------------------------------