TSTP Solution File: SET203-6 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET203-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.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 22:48:07 EDT 2022
% Result : Unsatisfiable 1.45s 1.89s
% Output : Refutation 1.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET203-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n025.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 06:07:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.69/1.10 *** allocated 10000 integers for termspace/termends
% 0.69/1.10 *** allocated 10000 integers for clauses
% 0.69/1.10 *** allocated 10000 integers for justifications
% 0.69/1.10 Bliksem 1.12
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 Automatic Strategy Selection
% 0.69/1.10
% 0.69/1.10 Clauses:
% 0.69/1.10 [
% 0.69/1.10 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.69/1.10 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.69/1.10 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ subclass( X, 'universal_class' ) ],
% 0.69/1.10 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.69/1.10 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.69/1.10 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.69/1.10 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.69/1.10 ) ) ],
% 0.69/1.10 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.69/1.10 ) ) ],
% 0.69/1.10 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.69/1.10 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.69/1.10 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.69/1.10 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.69/1.10 X, Z ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.69/1.10 Y, T ) ],
% 0.69/1.10 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.69/1.10 ), 'cross_product'( Y, T ) ) ],
% 0.69/1.10 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.69/1.10 ), second( X ) ), X ) ],
% 0.69/1.10 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.69/1.10 'universal_class' ) ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.69/1.10 Y ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.69/1.10 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.69/1.10 , Y ), 'element_relation' ) ],
% 0.69/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.69/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.69/1.10 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.69/1.10 Z ) ) ],
% 0.69/1.10 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.69/1.10 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.69/1.10 member( X, Y ) ],
% 0.69/1.10 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.69/1.10 union( X, Y ) ) ],
% 0.69/1.10 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.69/1.10 intersection( complement( X ), complement( Y ) ) ) ),
% 0.69/1.10 'symmetric_difference'( X, Y ) ) ],
% 0.69/1.10 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.69/1.10 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.69/1.10 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.69/1.10 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.69/1.10 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.69/1.10 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.69/1.10 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.69/1.10 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.69/1.10 'cross_product'( 'universal_class', 'universal_class' ),
% 0.69/1.10 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.69/1.10 Y ), rotate( T ) ) ],
% 0.69/1.10 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.69/1.10 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.69/1.10 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.69/1.10 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.69/1.10 'cross_product'( 'universal_class', 'universal_class' ),
% 0.69/1.10 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.69/1.10 Z ), flip( T ) ) ],
% 0.69/1.10 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.69/1.10 inverse( X ) ) ],
% 0.69/1.10 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.69/1.10 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.69/1.10 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.69/1.10 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.69/1.10 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.69/1.10 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.69/1.10 ],
% 0.69/1.10 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.69/1.10 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.69/1.10 'universal_class' ) ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.69/1.10 successor( X ), Y ) ],
% 0.69/1.10 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.69/1.10 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.69/1.10 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.69/1.10 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.69/1.10 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.69/1.10 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.69/1.10 [ inductive( omega ) ],
% 0.69/1.10 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.69/1.10 [ member( omega, 'universal_class' ) ],
% 0.69/1.10 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.69/1.10 , 'sum_class'( X ) ) ],
% 0.69/1.10 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.69/1.10 'universal_class' ) ],
% 0.69/1.10 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.69/1.10 'power_class'( X ) ) ],
% 0.69/1.10 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.69/1.10 'universal_class' ) ],
% 0.69/1.10 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.69/1.10 'universal_class' ) ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.69/1.10 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.69/1.10 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.69/1.10 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.69/1.10 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.69/1.10 ) ],
% 0.69/1.10 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.69/1.10 , 'identity_relation' ) ],
% 0.69/1.10 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.69/1.10 'single_valued_class'( X ) ],
% 0.69/1.10 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.69/1.10 'universal_class' ) ) ],
% 0.69/1.10 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.69/1.10 'identity_relation' ) ],
% 0.69/1.10 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.69/1.10 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.69/1.10 , function( X ) ],
% 0.69/1.10 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.69/1.10 X, Y ), 'universal_class' ) ],
% 0.69/1.10 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.69/1.10 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.69/1.10 ) ],
% 0.69/1.10 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.69/1.10 [ function( choice ) ],
% 0.69/1.10 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.69/1.10 apply( choice, X ), X ) ],
% 0.69/1.10 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.69/1.10 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.69/1.10 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.69/1.10 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.69/1.10 , complement( compose( complement( 'element_relation' ), inverse(
% 0.69/1.10 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.69/1.10 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.69/1.10 'identity_relation' ) ],
% 0.69/1.10 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.69/1.10 , diagonalise( X ) ) ],
% 0.69/1.10 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.69/1.10 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.69/1.10 [ ~( operation( X ) ), function( X ) ],
% 0.69/1.10 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.69/1.10 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.69/1.10 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.69/1.10 'domain_of'( X ) ) ) ],
% 0.69/1.10 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.69/1.10 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.69/1.10 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.69/1.10 X ) ],
% 0.69/1.10 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.69/1.10 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.69/1.10 'domain_of'( X ) ) ],
% 0.69/1.10 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.69/1.10 'domain_of'( Z ) ) ) ],
% 0.69/1.10 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.69/1.10 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.69/1.10 ), compatible( X, Y, Z ) ],
% 0.69/1.10 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.69/1.10 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.69/1.10 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.69/1.10 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.69/1.10 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.69/1.10 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.69/1.10 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.69/1.10 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.69/1.10 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.69/1.10 , Y ) ],
% 0.69/1.10 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.69/1.10 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.69/1.10 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.69/1.10 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.69/1.10 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.69/1.10 [ subclass( 'compose_class'( X ), 'cross_product'( 'universal_class',
% 0.69/1.10 'universal_class' ) ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ), =(
% 0.69/1.10 compose( Z, X ), Y ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.69/1.10 , 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) ), member(
% 0.69/1.10 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ],
% 0.69/1.10 [ subclass( 'composition_function', 'cross_product'( 'universal_class',
% 0.69/1.10 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.69/1.10 'composition_function' ) ), =( compose( X, Y ), Z ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.69/1.10 , 'universal_class' ) ) ), member( 'ordered_pair'( X, 'ordered_pair'( Y,
% 0.69/1.10 compose( X, Y ) ) ), 'composition_function' ) ],
% 0.69/1.10 [ subclass( 'domain_relation', 'cross_product'( 'universal_class',
% 0.69/1.10 'universal_class' ) ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) ), =(
% 0.69/1.10 'domain_of'( X ), Y ) ],
% 0.69/1.10 [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X,
% 0.69/1.10 'domain_of'( X ) ), 'domain_relation' ) ],
% 0.69/1.10 [ =( first( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.69/1.10 'identity_relation' ) ), 'single_valued1'( X ) ) ],
% 0.69/1.10 [ =( second( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.69/1.10 'identity_relation' ) ), 'single_valued2'( X ) ) ],
% 0.69/1.10 [ =( domain( X, image( inverse( X ), singleton( 'single_valued1'( X ) )
% 0.69/1.10 ), 'single_valued2'( X ) ), 'single_valued3'( X ) ) ],
% 0.69/1.10 [ =( intersection( complement( compose( 'element_relation', complement(
% 0.69/1.10 'identity_relation' ) ) ), 'element_relation' ), 'singleton_relation' ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ subclass( 'application_function', 'cross_product'( 'universal_class',
% 0.69/1.10 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.69/1.10 'application_function' ) ), member( Y, 'domain_of'( X ) ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.69/1.10 'application_function' ) ), =( apply( X, Y ), Z ) ],
% 0.69/1.10 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.69/1.10 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 0.69/1.10 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 0.69/1.10 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 0.69/1.10 'application_function' ) ],
% 0.69/1.10 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.69/1.10 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 1.45/1.89 [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ],
% 1.45/1.89 [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ), maps( X,
% 1.45/1.89 'domain_of'( X ), Y ) ],
% 1.45/1.89 [ member( u, x ) ],
% 1.45/1.89 [ member( v, y ) ],
% 1.45/1.89 [ ~( member( 'ordered_pair'( u, v ), 'cross_product'( 'universal_class'
% 1.45/1.89 , 'universal_class' ) ) ) ]
% 1.45/1.89 ] .
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 percentage equality = 0.221719, percentage horn = 0.930435
% 1.45/1.89 This is a problem with some equality
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 Options Used:
% 1.45/1.89
% 1.45/1.89 useres = 1
% 1.45/1.89 useparamod = 1
% 1.45/1.89 useeqrefl = 1
% 1.45/1.89 useeqfact = 1
% 1.45/1.89 usefactor = 1
% 1.45/1.89 usesimpsplitting = 0
% 1.45/1.89 usesimpdemod = 5
% 1.45/1.89 usesimpres = 3
% 1.45/1.89
% 1.45/1.89 resimpinuse = 1000
% 1.45/1.89 resimpclauses = 20000
% 1.45/1.89 substype = eqrewr
% 1.45/1.89 backwardsubs = 1
% 1.45/1.89 selectoldest = 5
% 1.45/1.89
% 1.45/1.89 litorderings [0] = split
% 1.45/1.89 litorderings [1] = extend the termordering, first sorting on arguments
% 1.45/1.89
% 1.45/1.89 termordering = kbo
% 1.45/1.89
% 1.45/1.89 litapriori = 0
% 1.45/1.89 termapriori = 1
% 1.45/1.89 litaposteriori = 0
% 1.45/1.89 termaposteriori = 0
% 1.45/1.89 demodaposteriori = 0
% 1.45/1.89 ordereqreflfact = 0
% 1.45/1.89
% 1.45/1.89 litselect = negord
% 1.45/1.89
% 1.45/1.89 maxweight = 15
% 1.45/1.89 maxdepth = 30000
% 1.45/1.89 maxlength = 115
% 1.45/1.89 maxnrvars = 195
% 1.45/1.89 excuselevel = 1
% 1.45/1.89 increasemaxweight = 1
% 1.45/1.89
% 1.45/1.89 maxselected = 10000000
% 1.45/1.89 maxnrclauses = 10000000
% 1.45/1.89
% 1.45/1.89 showgenerated = 0
% 1.45/1.89 showkept = 0
% 1.45/1.89 showselected = 0
% 1.45/1.89 showdeleted = 0
% 1.45/1.89 showresimp = 1
% 1.45/1.89 showstatus = 2000
% 1.45/1.89
% 1.45/1.89 prologoutput = 1
% 1.45/1.89 nrgoals = 5000000
% 1.45/1.89 totalproof = 1
% 1.45/1.89
% 1.45/1.89 Symbols occurring in the translation:
% 1.45/1.89
% 1.45/1.89 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.45/1.89 . [1, 2] (w:1, o:66, a:1, s:1, b:0),
% 1.45/1.89 ! [4, 1] (w:0, o:37, a:1, s:1, b:0),
% 1.45/1.89 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.45/1.89 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.45/1.89 subclass [41, 2] (w:1, o:91, a:1, s:1, b:0),
% 1.45/1.89 member [43, 2] (w:1, o:92, a:1, s:1, b:0),
% 1.45/1.89 'not_subclass_element' [44, 2] (w:1, o:93, a:1, s:1, b:0),
% 1.45/1.89 'universal_class' [45, 0] (w:1, o:22, a:1, s:1, b:0),
% 1.45/1.89 'unordered_pair' [46, 2] (w:1, o:94, a:1, s:1, b:0),
% 1.45/1.89 singleton [47, 1] (w:1, o:45, a:1, s:1, b:0),
% 1.45/1.89 'ordered_pair' [48, 2] (w:1, o:95, a:1, s:1, b:0),
% 1.45/1.89 'cross_product' [50, 2] (w:1, o:96, a:1, s:1, b:0),
% 1.45/1.89 first [52, 1] (w:1, o:46, a:1, s:1, b:0),
% 1.45/1.89 second [53, 1] (w:1, o:47, a:1, s:1, b:0),
% 1.45/1.89 'element_relation' [54, 0] (w:1, o:27, a:1, s:1, b:0),
% 1.45/1.89 intersection [55, 2] (w:1, o:98, a:1, s:1, b:0),
% 1.45/1.89 complement [56, 1] (w:1, o:48, a:1, s:1, b:0),
% 1.45/1.89 union [57, 2] (w:1, o:99, a:1, s:1, b:0),
% 1.45/1.89 'symmetric_difference' [58, 2] (w:1, o:100, a:1, s:1, b:0),
% 1.45/1.89 restrict [60, 3] (w:1, o:103, a:1, s:1, b:0),
% 1.45/1.89 'null_class' [61, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.45/1.89 'domain_of' [62, 1] (w:1, o:51, a:1, s:1, b:0),
% 1.45/1.89 rotate [63, 1] (w:1, o:42, a:1, s:1, b:0),
% 1.45/1.89 flip [65, 1] (w:1, o:52, a:1, s:1, b:0),
% 1.45/1.89 inverse [66, 1] (w:1, o:53, a:1, s:1, b:0),
% 1.45/1.89 'range_of' [67, 1] (w:1, o:43, a:1, s:1, b:0),
% 1.45/1.89 domain [68, 3] (w:1, o:105, a:1, s:1, b:0),
% 1.45/1.89 range [69, 3] (w:1, o:106, a:1, s:1, b:0),
% 1.45/1.89 image [70, 2] (w:1, o:97, a:1, s:1, b:0),
% 1.45/1.89 successor [71, 1] (w:1, o:54, a:1, s:1, b:0),
% 1.45/1.89 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 1.45/1.89 inductive [73, 1] (w:1, o:55, a:1, s:1, b:0),
% 1.45/1.89 omega [74, 0] (w:1, o:10, a:1, s:1, b:0),
% 1.45/1.89 'sum_class' [75, 1] (w:1, o:56, a:1, s:1, b:0),
% 1.45/1.89 'power_class' [76, 1] (w:1, o:59, a:1, s:1, b:0),
% 1.45/1.89 compose [78, 2] (w:1, o:101, a:1, s:1, b:0),
% 1.45/1.89 'single_valued_class' [79, 1] (w:1, o:60, a:1, s:1, b:0),
% 1.45/1.89 'identity_relation' [80, 0] (w:1, o:29, a:1, s:1, b:0),
% 1.45/1.89 function [82, 1] (w:1, o:61, a:1, s:1, b:0),
% 1.45/1.89 regular [83, 1] (w:1, o:44, a:1, s:1, b:0),
% 1.45/1.89 apply [84, 2] (w:1, o:102, a:1, s:1, b:0),
% 1.45/1.89 choice [85, 0] (w:1, o:30, a:1, s:1, b:0),
% 1.45/1.89 'one_to_one' [86, 1] (w:1, o:57, a:1, s:1, b:0),
% 1.45/1.89 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 1.45/1.89 diagonalise [88, 1] (w:1, o:62, a:1, s:1, b:0),
% 1.45/1.89 cantor [89, 1] (w:1, o:49, a:1, s:1, b:0),
% 1.45/1.89 operation [90, 1] (w:1, o:58, a:1, s:1, b:0),
% 1.45/1.89 compatible [94, 3] (w:1, o:104, a:1, s:1, b:0),
% 1.45/1.89 homomorphism [95, 3] (w:1, o:107, a:1, s:1, b:0),
% 1.45/1.89 'not_homomorphism1' [96, 3] (w:1, o:109, a:1, s:1, b:0),
% 1.45/1.89 'not_homomorphism2' [97, 3] (w:1, o:110, a:1, s:1, b:0),
% 1.45/1.89 'compose_class' [98, 1] (w:1, o:50, a:1, s:1, b:0),
% 1.45/1.89 'composition_function' [99, 0] (w:1, o:31, a:1, s:1, b:0),
% 1.45/1.89 'domain_relation' [100, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.45/1.89 'single_valued1' [101, 1] (w:1, o:63, a:1, s:1, b:0),
% 1.45/1.89 'single_valued2' [102, 1] (w:1, o:64, a:1, s:1, b:0),
% 1.45/1.89 'single_valued3' [103, 1] (w:1, o:65, a:1, s:1, b:0),
% 1.45/1.89 'singleton_relation' [104, 0] (w:1, o:7, a:1, s:1, b:0),
% 1.45/1.89 'application_function' [105, 0] (w:1, o:32, a:1, s:1, b:0),
% 1.45/1.89 maps [106, 3] (w:1, o:108, a:1, s:1, b:0),
% 1.45/1.89 u [107, 0] (w:1, o:33, a:1, s:1, b:0),
% 1.45/1.89 x [108, 0] (w:1, o:34, a:1, s:1, b:0),
% 1.45/1.89 v [109, 0] (w:1, o:35, a:1, s:1, b:0),
% 1.45/1.89 y [110, 0] (w:1, o:36, a:1, s:1, b:0).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 Starting Search:
% 1.45/1.89
% 1.45/1.89 Resimplifying inuse:
% 1.45/1.89 Done
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 Intermediate Status:
% 1.45/1.89 Generated: 5452
% 1.45/1.89 Kept: 2011
% 1.45/1.89 Inuse: 109
% 1.45/1.89 Deleted: 2
% 1.45/1.89 Deletedinuse: 2
% 1.45/1.89
% 1.45/1.89 Resimplifying inuse:
% 1.45/1.89 Done
% 1.45/1.89
% 1.45/1.89 Resimplifying inuse:
% 1.45/1.89 Done
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 Intermediate Status:
% 1.45/1.89 Generated: 10633
% 1.45/1.89 Kept: 4235
% 1.45/1.89 Inuse: 193
% 1.45/1.89 Deleted: 22
% 1.45/1.89 Deletedinuse: 14
% 1.45/1.89
% 1.45/1.89 Resimplifying inuse:
% 1.45/1.89 Done
% 1.45/1.89
% 1.45/1.89 Resimplifying inuse:
% 1.45/1.89 Done
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 Intermediate Status:
% 1.45/1.89 Generated: 14830
% 1.45/1.89 Kept: 6242
% 1.45/1.89 Inuse: 256
% 1.45/1.89 Deleted: 26
% 1.45/1.89 Deletedinuse: 17
% 1.45/1.89
% 1.45/1.89 Resimplifying inuse:
% 1.45/1.89 Done
% 1.45/1.89
% 1.45/1.89 Resimplifying inuse:
% 1.45/1.89 Done
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 Intermediate Status:
% 1.45/1.89 Generated: 19739
% 1.45/1.89 Kept: 8242
% 1.45/1.89 Inuse: 306
% 1.45/1.89 Deleted: 50
% 1.45/1.89 Deletedinuse: 38
% 1.45/1.89
% 1.45/1.89 Resimplifying inuse:
% 1.45/1.89 Done
% 1.45/1.89
% 1.45/1.89 Resimplifying inuse:
% 1.45/1.89 Done
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 Intermediate Status:
% 1.45/1.89 Generated: 25190
% 1.45/1.89 Kept: 10701
% 1.45/1.89 Inuse: 364
% 1.45/1.89 Deleted: 63
% 1.45/1.89 Deletedinuse: 46
% 1.45/1.89
% 1.45/1.89 Resimplifying inuse:
% 1.45/1.89 Done
% 1.45/1.89
% 1.45/1.89 Resimplifying inuse:
% 1.45/1.89 Done
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 Intermediate Status:
% 1.45/1.89 Generated: 28766
% 1.45/1.89 Kept: 12819
% 1.45/1.89 Inuse: 389
% 1.45/1.89 Deleted: 63
% 1.45/1.89 Deletedinuse: 46
% 1.45/1.89
% 1.45/1.89 Resimplifying inuse:
% 1.45/1.89 Done
% 1.45/1.89
% 1.45/1.89 Resimplifying inuse:
% 1.45/1.89 Done
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 Intermediate Status:
% 1.45/1.89 Generated: 32530
% 1.45/1.89 Kept: 14826
% 1.45/1.89 Inuse: 432
% 1.45/1.89 Deleted: 69
% 1.45/1.89 Deletedinuse: 52
% 1.45/1.89
% 1.45/1.89 Resimplifying inuse:
% 1.45/1.89 Done
% 1.45/1.89
% 1.45/1.89 Resimplifying inuse:
% 1.45/1.89 Done
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 Bliksems!, er is een bewijs:
% 1.45/1.89 % SZS status Unsatisfiable
% 1.45/1.89 % SZS output start Refutation
% 1.45/1.89
% 1.45/1.89 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 1.45/1.89 )
% 1.45/1.89 .
% 1.45/1.89 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 1.45/1.89 .
% 1.45/1.89 clause( 14, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.45/1.89 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.45/1.89 .
% 1.45/1.89 clause( 111, [ member( u, x ) ] )
% 1.45/1.89 .
% 1.45/1.89 clause( 112, [ member( v, y ) ] )
% 1.45/1.89 .
% 1.45/1.89 clause( 113, [ ~( member( 'ordered_pair'( u, v ), 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ) ] )
% 1.45/1.89 .
% 1.45/1.89 clause( 129, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ] )
% 1.45/1.89 .
% 1.45/1.89 clause( 385, [ member( u, 'universal_class' ) ] )
% 1.45/1.89 .
% 1.45/1.89 clause( 386, [ member( v, 'universal_class' ) ] )
% 1.45/1.89 .
% 1.45/1.89 clause( 16584, [ ~( member( v, 'universal_class' ) ) ] )
% 1.45/1.89 .
% 1.45/1.89 clause( 16656, [] )
% 1.45/1.89 .
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 % SZS output end Refutation
% 1.45/1.89 found a proof!
% 1.45/1.89
% 1.45/1.89 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.45/1.89
% 1.45/1.89 initialclauses(
% 1.45/1.89 [ clause( 16658, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.45/1.89 ) ] )
% 1.45/1.89 , clause( 16659, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 1.45/1.89 , Y ) ] )
% 1.45/1.89 , clause( 16660, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 1.45/1.89 subclass( X, Y ) ] )
% 1.45/1.89 , clause( 16661, [ subclass( X, 'universal_class' ) ] )
% 1.45/1.89 , clause( 16662, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.45/1.89 , clause( 16663, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 1.45/1.89 , clause( 16664, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 1.45/1.89 ] )
% 1.45/1.89 , clause( 16665, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 1.45/1.89 =( X, Z ) ] )
% 1.45/1.89 , clause( 16666, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.45/1.89 'unordered_pair'( X, Y ) ) ] )
% 1.45/1.89 , clause( 16667, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.45/1.89 'unordered_pair'( Y, X ) ) ] )
% 1.45/1.89 , clause( 16668, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 1.45/1.89 )
% 1.45/1.89 , clause( 16669, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.45/1.89 , clause( 16670, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 1.45/1.89 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.45/1.89 , clause( 16671, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.45/1.89 ) ) ), member( X, Z ) ] )
% 1.45/1.89 , clause( 16672, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.45/1.89 ) ) ), member( Y, T ) ] )
% 1.45/1.89 , clause( 16673, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.45/1.89 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.45/1.89 , clause( 16674, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 1.45/1.89 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 1.45/1.89 , clause( 16675, [ subclass( 'element_relation', 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ] )
% 1.45/1.89 , clause( 16676, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 1.45/1.89 ), member( X, Y ) ] )
% 1.45/1.89 , clause( 16677, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 1.45/1.89 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 1.45/1.89 , clause( 16678, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.45/1.89 )
% 1.45/1.89 , clause( 16679, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 1.45/1.89 )
% 1.45/1.89 , clause( 16680, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 1.45/1.89 intersection( Y, Z ) ) ] )
% 1.45/1.89 , clause( 16681, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 1.45/1.89 )
% 1.45/1.89 , clause( 16682, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.45/1.89 complement( Y ) ), member( X, Y ) ] )
% 1.45/1.89 , clause( 16683, [ =( complement( intersection( complement( X ), complement(
% 1.45/1.89 Y ) ) ), union( X, Y ) ) ] )
% 1.45/1.89 , clause( 16684, [ =( intersection( complement( intersection( X, Y ) ),
% 1.45/1.89 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 1.45/1.89 'symmetric_difference'( X, Y ) ) ] )
% 1.45/1.89 , clause( 16685, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 1.45/1.89 X, Y, Z ) ) ] )
% 1.45/1.89 , clause( 16686, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 1.45/1.89 Z, X, Y ) ) ] )
% 1.45/1.89 , clause( 16687, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 1.45/1.89 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 1.45/1.89 , clause( 16688, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 1.45/1.89 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 1.45/1.89 'domain_of'( Y ) ) ] )
% 1.45/1.89 , clause( 16689, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.45/1.89 , clause( 16690, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.45/1.89 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 1.45/1.89 ] )
% 1.45/1.89 , clause( 16691, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.45/1.89 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 1.45/1.89 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.45/1.89 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 1.45/1.89 , Y ), rotate( T ) ) ] )
% 1.45/1.89 , clause( 16692, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.45/1.89 , clause( 16693, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.45/1.89 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 1.45/1.89 )
% 1.45/1.89 , clause( 16694, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.45/1.89 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 1.45/1.89 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.45/1.89 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 1.45/1.89 , Z ), flip( T ) ) ] )
% 1.45/1.89 , clause( 16695, [ =( 'domain_of'( flip( 'cross_product'( X,
% 1.45/1.89 'universal_class' ) ) ), inverse( X ) ) ] )
% 1.45/1.89 , clause( 16696, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 1.45/1.89 , clause( 16697, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 1.45/1.89 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 1.45/1.89 , clause( 16698, [ =( second( 'not_subclass_element'( restrict( X,
% 1.45/1.89 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 1.45/1.89 , clause( 16699, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 1.45/1.89 image( X, Y ) ) ] )
% 1.45/1.89 , clause( 16700, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 1.45/1.89 , clause( 16701, [ subclass( 'successor_relation', 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ] )
% 1.45/1.89 , clause( 16702, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 1.45/1.89 ) ), =( successor( X ), Y ) ] )
% 1.45/1.89 , clause( 16703, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 1.45/1.89 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 1.45/1.89 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 1.45/1.89 , clause( 16704, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 1.45/1.89 , clause( 16705, [ ~( inductive( X ) ), subclass( image(
% 1.45/1.89 'successor_relation', X ), X ) ] )
% 1.45/1.89 , clause( 16706, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 1.45/1.89 'successor_relation', X ), X ) ), inductive( X ) ] )
% 1.45/1.89 , clause( 16707, [ inductive( omega ) ] )
% 1.45/1.89 , clause( 16708, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 1.45/1.89 , clause( 16709, [ member( omega, 'universal_class' ) ] )
% 1.45/1.89 , clause( 16710, [ =( 'domain_of'( restrict( 'element_relation',
% 1.45/1.89 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 1.45/1.89 , clause( 16711, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 1.45/1.89 X ), 'universal_class' ) ] )
% 1.45/1.89 , clause( 16712, [ =( complement( image( 'element_relation', complement( X
% 1.45/1.89 ) ) ), 'power_class'( X ) ) ] )
% 1.45/1.89 , clause( 16713, [ ~( member( X, 'universal_class' ) ), member(
% 1.45/1.89 'power_class'( X ), 'universal_class' ) ] )
% 1.45/1.89 , clause( 16714, [ subclass( compose( X, Y ), 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ] )
% 1.45/1.89 , clause( 16715, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 1.45/1.89 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 1.45/1.89 , clause( 16716, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 1.45/1.89 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 1.45/1.89 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 1.45/1.89 ) ] )
% 1.45/1.89 , clause( 16717, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 1.45/1.89 inverse( X ) ), 'identity_relation' ) ] )
% 1.45/1.89 , clause( 16718, [ ~( subclass( compose( X, inverse( X ) ),
% 1.45/1.89 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 1.45/1.89 , clause( 16719, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ] )
% 1.45/1.89 , clause( 16720, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 1.45/1.89 , 'identity_relation' ) ] )
% 1.45/1.89 , clause( 16721, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 1.45/1.89 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 1.45/1.89 'identity_relation' ) ), function( X ) ] )
% 1.45/1.89 , clause( 16722, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 1.45/1.89 , member( image( X, Y ), 'universal_class' ) ] )
% 1.45/1.89 , clause( 16723, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.45/1.89 , clause( 16724, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 1.45/1.89 , 'null_class' ) ] )
% 1.45/1.89 , clause( 16725, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 1.45/1.89 Y ) ) ] )
% 1.45/1.89 , clause( 16726, [ function( choice ) ] )
% 1.45/1.89 , clause( 16727, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 1.45/1.89 ), member( apply( choice, X ), X ) ] )
% 1.45/1.89 , clause( 16728, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 1.45/1.89 , clause( 16729, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 1.45/1.89 , clause( 16730, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 1.45/1.89 'one_to_one'( X ) ] )
% 1.45/1.89 , clause( 16731, [ =( intersection( 'cross_product'( 'universal_class',
% 1.45/1.89 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 1.45/1.89 'universal_class' ), complement( compose( complement( 'element_relation'
% 1.45/1.89 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 1.45/1.89 , clause( 16732, [ =( intersection( inverse( 'subset_relation' ),
% 1.45/1.89 'subset_relation' ), 'identity_relation' ) ] )
% 1.45/1.89 , clause( 16733, [ =( complement( 'domain_of'( intersection( X,
% 1.45/1.89 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 1.45/1.89 , clause( 16734, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 1.45/1.89 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 1.45/1.89 , clause( 16735, [ ~( operation( X ) ), function( X ) ] )
% 1.45/1.89 , clause( 16736, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 1.45/1.89 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.45/1.89 ] )
% 1.45/1.89 , clause( 16737, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 1.45/1.89 'domain_of'( 'domain_of'( X ) ) ) ] )
% 1.45/1.89 , clause( 16738, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 1.45/1.89 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.45/1.89 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 1.45/1.89 operation( X ) ] )
% 1.45/1.89 , clause( 16739, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 1.45/1.89 , clause( 16740, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 1.45/1.89 Y ) ), 'domain_of'( X ) ) ] )
% 1.45/1.89 , clause( 16741, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 1.45/1.89 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 1.45/1.89 , clause( 16742, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 1.45/1.89 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 1.45/1.89 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 1.45/1.89 , clause( 16743, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 1.45/1.89 , clause( 16744, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 1.45/1.89 , clause( 16745, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 1.45/1.89 , clause( 16746, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 1.45/1.89 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 1.45/1.89 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 1.45/1.89 )
% 1.45/1.89 , clause( 16747, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.45/1.89 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.45/1.89 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.45/1.89 , Y ) ] )
% 1.45/1.89 , clause( 16748, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.45/1.89 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 1.45/1.89 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 1.45/1.89 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 1.45/1.89 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 1.45/1.89 )
% 1.45/1.89 , clause( 16749, [ subclass( 'compose_class'( X ), 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ] )
% 1.45/1.89 , clause( 16750, [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z )
% 1.45/1.89 ) ), =( compose( Z, X ), Y ) ] )
% 1.45/1.89 , clause( 16751, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) )
% 1.45/1.89 , member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ] )
% 1.45/1.89 , clause( 16752, [ subclass( 'composition_function', 'cross_product'(
% 1.45/1.89 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 1.45/1.89 ) ) ) ] )
% 1.45/1.89 , clause( 16753, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.45/1.89 'composition_function' ) ), =( compose( X, Y ), Z ) ] )
% 1.45/1.89 , clause( 16754, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( X,
% 1.45/1.89 'ordered_pair'( Y, compose( X, Y ) ) ), 'composition_function' ) ] )
% 1.45/1.89 , clause( 16755, [ subclass( 'domain_relation', 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ] )
% 1.45/1.89 , clause( 16756, [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) )
% 1.45/1.89 , =( 'domain_of'( X ), Y ) ] )
% 1.45/1.89 , clause( 16757, [ ~( member( X, 'universal_class' ) ), member(
% 1.45/1.89 'ordered_pair'( X, 'domain_of'( X ) ), 'domain_relation' ) ] )
% 1.45/1.89 , clause( 16758, [ =( first( 'not_subclass_element'( compose( X, inverse( X
% 1.45/1.89 ) ), 'identity_relation' ) ), 'single_valued1'( X ) ) ] )
% 1.45/1.89 , clause( 16759, [ =( second( 'not_subclass_element'( compose( X, inverse(
% 1.45/1.89 X ) ), 'identity_relation' ) ), 'single_valued2'( X ) ) ] )
% 1.45/1.89 , clause( 16760, [ =( domain( X, image( inverse( X ), singleton(
% 1.45/1.89 'single_valued1'( X ) ) ), 'single_valued2'( X ) ), 'single_valued3'( X )
% 1.45/1.89 ) ] )
% 1.45/1.89 , clause( 16761, [ =( intersection( complement( compose( 'element_relation'
% 1.45/1.89 , complement( 'identity_relation' ) ) ), 'element_relation' ),
% 1.45/1.89 'singleton_relation' ) ] )
% 1.45/1.89 , clause( 16762, [ subclass( 'application_function', 'cross_product'(
% 1.45/1.89 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 1.45/1.89 ) ) ) ] )
% 1.45/1.89 , clause( 16763, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.45/1.89 'application_function' ) ), member( Y, 'domain_of'( X ) ) ] )
% 1.45/1.89 , clause( 16764, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.45/1.89 'application_function' ) ), =( apply( X, Y ), Z ) ] )
% 1.45/1.89 , clause( 16765, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.45/1.89 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 1.45/1.89 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 1.45/1.89 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 1.45/1.89 'application_function' ) ] )
% 1.45/1.89 , clause( 16766, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 1.45/1.89 , clause( 16767, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 1.45/1.89 , clause( 16768, [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ]
% 1.45/1.89 )
% 1.45/1.89 , clause( 16769, [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) )
% 1.45/1.89 , maps( X, 'domain_of'( X ), Y ) ] )
% 1.45/1.89 , clause( 16770, [ member( u, x ) ] )
% 1.45/1.89 , clause( 16771, [ member( v, y ) ] )
% 1.45/1.89 , clause( 16772, [ ~( member( 'ordered_pair'( u, v ), 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ) ] )
% 1.45/1.89 ] ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 1.45/1.89 )
% 1.45/1.89 , clause( 16658, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.45/1.89 ) ] )
% 1.45/1.89 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.45/1.89 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 1.45/1.89 , clause( 16661, [ subclass( X, 'universal_class' ) ] )
% 1.45/1.89 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 14, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.45/1.89 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.45/1.89 , clause( 16673, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.45/1.89 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.45/1.89 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.45/1.89 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 111, [ member( u, x ) ] )
% 1.45/1.89 , clause( 16770, [ member( u, x ) ] )
% 1.45/1.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 112, [ member( v, y ) ] )
% 1.45/1.89 , clause( 16771, [ member( v, y ) ] )
% 1.45/1.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 113, [ ~( member( 'ordered_pair'( u, v ), 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ) ] )
% 1.45/1.89 , clause( 16772, [ ~( member( 'ordered_pair'( u, v ), 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ) ] )
% 1.45/1.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 resolution(
% 1.45/1.89 clause( 16964, [ ~( member( Y, X ) ), member( Y, 'universal_class' ) ] )
% 1.45/1.89 , clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 1.45/1.89 )
% 1.45/1.89 , 0, clause( 3, [ subclass( X, 'universal_class' ) ] )
% 1.45/1.89 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'universal_class' ), :=( Z, Y )] )
% 1.45/1.89 , substitution( 1, [ :=( X, X )] )).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 129, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ] )
% 1.45/1.89 , clause( 16964, [ ~( member( Y, X ) ), member( Y, 'universal_class' ) ] )
% 1.45/1.89 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 1.45/1.89 ), ==>( 1, 1 )] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 resolution(
% 1.45/1.89 clause( 16965, [ member( u, 'universal_class' ) ] )
% 1.45/1.89 , clause( 129, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ] )
% 1.45/1.89 , 0, clause( 111, [ member( u, x ) ] )
% 1.45/1.89 , 0, substitution( 0, [ :=( X, u ), :=( Y, x )] ), substitution( 1, [] )
% 1.45/1.89 ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 385, [ member( u, 'universal_class' ) ] )
% 1.45/1.89 , clause( 16965, [ member( u, 'universal_class' ) ] )
% 1.45/1.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 resolution(
% 1.45/1.89 clause( 16966, [ member( v, 'universal_class' ) ] )
% 1.45/1.89 , clause( 129, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ] )
% 1.45/1.89 , 0, clause( 112, [ member( v, y ) ] )
% 1.45/1.89 , 0, substitution( 0, [ :=( X, v ), :=( Y, y )] ), substitution( 1, [] )
% 1.45/1.89 ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 386, [ member( v, 'universal_class' ) ] )
% 1.45/1.89 , clause( 16966, [ member( v, 'universal_class' ) ] )
% 1.45/1.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 resolution(
% 1.45/1.89 clause( 16967, [ ~( member( u, 'universal_class' ) ), ~( member( v,
% 1.45/1.89 'universal_class' ) ) ] )
% 1.45/1.89 , clause( 113, [ ~( member( 'ordered_pair'( u, v ), 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ) ] )
% 1.45/1.89 , 0, clause( 14, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.45/1.89 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.45/1.89 , 2, substitution( 0, [] ), substitution( 1, [ :=( X, u ), :=( Y,
% 1.45/1.89 'universal_class' ), :=( Z, v ), :=( T, 'universal_class' )] )).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 resolution(
% 1.45/1.89 clause( 16968, [ ~( member( v, 'universal_class' ) ) ] )
% 1.45/1.89 , clause( 16967, [ ~( member( u, 'universal_class' ) ), ~( member( v,
% 1.45/1.89 'universal_class' ) ) ] )
% 1.45/1.89 , 0, clause( 385, [ member( u, 'universal_class' ) ] )
% 1.45/1.89 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 16584, [ ~( member( v, 'universal_class' ) ) ] )
% 1.45/1.89 , clause( 16968, [ ~( member( v, 'universal_class' ) ) ] )
% 1.45/1.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 resolution(
% 1.45/1.89 clause( 16969, [] )
% 1.45/1.89 , clause( 16584, [ ~( member( v, 'universal_class' ) ) ] )
% 1.45/1.89 , 0, clause( 386, [ member( v, 'universal_class' ) ] )
% 1.45/1.89 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 16656, [] )
% 1.45/1.89 , clause( 16969, [] )
% 1.45/1.89 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 end.
% 1.45/1.89
% 1.45/1.89 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.45/1.89
% 1.45/1.89 Memory use:
% 1.45/1.89
% 1.45/1.89 space for terms: 263005
% 1.45/1.89 space for clauses: 811024
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 clauses generated: 35439
% 1.45/1.89 clauses kept: 16657
% 1.45/1.89 clauses selected: 454
% 1.45/1.89 clauses deleted: 70
% 1.45/1.89 clauses inuse deleted: 52
% 1.45/1.89
% 1.45/1.89 subsentry: 72470
% 1.45/1.89 literals s-matched: 52971
% 1.45/1.89 literals matched: 51882
% 1.45/1.89 full subsumption: 20990
% 1.45/1.89
% 1.45/1.89 checksum: -1473107863
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 Bliksem ended
%------------------------------------------------------------------------------