TSTP Solution File: SET184-6 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET184-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Mon Jul 18 22:47:57 EDT 2022
% Result : Unsatisfiable 0.46s 1.17s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET184-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.14 % Command : bliksem %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Sun Jul 10 03:38:25 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.46/1.12 *** allocated 10000 integers for termspace/termends
% 0.46/1.12 *** allocated 10000 integers for clauses
% 0.46/1.12 *** allocated 10000 integers for justifications
% 0.46/1.12 Bliksem 1.12
% 0.46/1.12
% 0.46/1.12
% 0.46/1.12 Automatic Strategy Selection
% 0.46/1.12
% 0.46/1.12 Clauses:
% 0.46/1.12 [
% 0.46/1.12 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.46/1.12 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.46/1.12 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.46/1.12 ,
% 0.46/1.12 [ subclass( X, 'universal_class' ) ],
% 0.46/1.12 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.46/1.12 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.46/1.12 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.46/1.12 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.46/1.12 ,
% 0.46/1.12 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.46/1.12 ) ) ],
% 0.46/1.12 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.46/1.12 ) ) ],
% 0.46/1.12 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.46/1.12 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.46/1.12 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.46/1.12 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.46/1.12 X, Z ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.46/1.12 Y, T ) ],
% 0.46/1.12 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.46/1.12 ), 'cross_product'( Y, T ) ) ],
% 0.46/1.12 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.46/1.12 ), second( X ) ), X ) ],
% 0.46/1.12 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.46/1.12 'universal_class' ) ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.46/1.12 Y ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.46/1.12 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.46/1.12 , Y ), 'element_relation' ) ],
% 0.46/1.12 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.46/1.12 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.46/1.12 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.46/1.12 Z ) ) ],
% 0.46/1.12 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.46/1.12 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.46/1.12 member( X, Y ) ],
% 0.46/1.12 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.46/1.12 union( X, Y ) ) ],
% 0.46/1.12 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.46/1.12 intersection( complement( X ), complement( Y ) ) ) ),
% 0.46/1.12 'symmetric_difference'( X, Y ) ) ],
% 0.46/1.12 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.46/1.12 ,
% 0.46/1.12 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.46/1.12 ,
% 0.46/1.12 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.46/1.12 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.46/1.12 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.46/1.12 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.46/1.12 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.46/1.12 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.46/1.12 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.46/1.12 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.46/1.12 'cross_product'( 'universal_class', 'universal_class' ),
% 0.46/1.12 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.46/1.12 Y ), rotate( T ) ) ],
% 0.46/1.12 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.46/1.12 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.46/1.12 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.46/1.12 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.46/1.12 'cross_product'( 'universal_class', 'universal_class' ),
% 0.46/1.12 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.46/1.12 Z ), flip( T ) ) ],
% 0.46/1.12 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.46/1.12 inverse( X ) ) ],
% 0.46/1.12 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.46/1.12 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.46/1.12 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.46/1.12 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.46/1.12 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.46/1.12 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.46/1.12 ],
% 0.46/1.12 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.46/1.12 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.46/1.12 'universal_class' ) ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.46/1.12 successor( X ), Y ) ],
% 0.46/1.12 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.46/1.12 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.46/1.12 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.46/1.12 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.46/1.12 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.46/1.12 ,
% 0.46/1.12 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.46/1.12 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.46/1.12 [ inductive( omega ) ],
% 0.46/1.12 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.46/1.12 [ member( omega, 'universal_class' ) ],
% 0.46/1.12 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.46/1.12 , 'sum_class'( X ) ) ],
% 0.46/1.12 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.46/1.12 'universal_class' ) ],
% 0.46/1.12 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.46/1.12 'power_class'( X ) ) ],
% 0.46/1.12 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.46/1.12 'universal_class' ) ],
% 0.46/1.12 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.46/1.12 'universal_class' ) ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.46/1.12 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.46/1.12 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.46/1.12 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.46/1.12 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.46/1.12 ) ],
% 0.46/1.12 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.46/1.12 , 'identity_relation' ) ],
% 0.46/1.12 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.46/1.12 'single_valued_class'( X ) ],
% 0.46/1.12 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.46/1.12 'universal_class' ) ) ],
% 0.46/1.12 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.46/1.12 'identity_relation' ) ],
% 0.46/1.12 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.46/1.12 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.46/1.12 , function( X ) ],
% 0.46/1.12 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.46/1.12 X, Y ), 'universal_class' ) ],
% 0.46/1.12 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.46/1.12 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.46/1.12 ) ],
% 0.46/1.12 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.46/1.12 [ function( choice ) ],
% 0.46/1.12 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.46/1.12 apply( choice, X ), X ) ],
% 0.46/1.12 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.46/1.12 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.46/1.12 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.46/1.12 ,
% 0.46/1.12 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.46/1.12 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.46/1.12 , complement( compose( complement( 'element_relation' ), inverse(
% 0.46/1.12 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.46/1.12 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.46/1.12 'identity_relation' ) ],
% 0.46/1.12 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.46/1.12 , diagonalise( X ) ) ],
% 0.46/1.12 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.46/1.12 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.46/1.12 [ ~( operation( X ) ), function( X ) ],
% 0.46/1.12 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.46/1.12 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.46/1.12 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.46/1.12 'domain_of'( X ) ) ) ],
% 0.46/1.12 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.46/1.12 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.46/1.12 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.46/1.12 X ) ],
% 0.46/1.12 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.46/1.12 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.46/1.12 'domain_of'( X ) ) ],
% 0.46/1.12 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.46/1.12 'domain_of'( Z ) ) ) ],
% 0.46/1.12 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.46/1.12 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.46/1.12 ), compatible( X, Y, Z ) ],
% 0.46/1.12 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.46/1.12 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.46/1.12 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.46/1.12 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.46/1.12 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.46/1.12 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.46/1.12 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.46/1.12 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.46/1.12 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.46/1.12 , Y ) ],
% 0.46/1.12 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.46/1.12 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.46/1.12 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.46/1.12 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.46/1.12 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.46/1.12 [ subclass( 'compose_class'( X ), 'cross_product'( 'universal_class',
% 0.46/1.12 'universal_class' ) ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ), =(
% 0.46/1.12 compose( Z, X ), Y ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.46/1.12 , 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) ), member(
% 0.46/1.12 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ],
% 0.46/1.12 [ subclass( 'composition_function', 'cross_product'( 'universal_class',
% 0.46/1.12 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.46/1.12 'composition_function' ) ), =( compose( X, Y ), Z ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.46/1.12 , 'universal_class' ) ) ), member( 'ordered_pair'( X, 'ordered_pair'( Y,
% 0.46/1.12 compose( X, Y ) ) ), 'composition_function' ) ],
% 0.46/1.12 [ subclass( 'domain_relation', 'cross_product'( 'universal_class',
% 0.46/1.12 'universal_class' ) ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) ), =(
% 0.46/1.12 'domain_of'( X ), Y ) ],
% 0.46/1.12 [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X,
% 0.46/1.12 'domain_of'( X ) ), 'domain_relation' ) ],
% 0.46/1.12 [ =( first( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.46/1.12 'identity_relation' ) ), 'single_valued1'( X ) ) ],
% 0.46/1.12 [ =( second( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.46/1.12 'identity_relation' ) ), 'single_valued2'( X ) ) ],
% 0.46/1.12 [ =( domain( X, image( inverse( X ), singleton( 'single_valued1'( X ) )
% 0.46/1.12 ), 'single_valued2'( X ) ), 'single_valued3'( X ) ) ],
% 0.46/1.12 [ =( intersection( complement( compose( 'element_relation', complement(
% 0.46/1.12 'identity_relation' ) ) ), 'element_relation' ), 'singleton_relation' ) ]
% 0.46/1.12 ,
% 0.46/1.12 [ subclass( 'application_function', 'cross_product'( 'universal_class',
% 0.46/1.12 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.46/1.12 'application_function' ) ), member( Y, 'domain_of'( X ) ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.46/1.12 'application_function' ) ), =( apply( X, Y ), Z ) ],
% 0.46/1.12 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.46/1.12 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 0.46/1.12 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 0.46/1.12 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 0.46/1.12 'application_function' ) ],
% 0.46/1.12 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.46/1.12 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 0.46/1.17 [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ],
% 0.46/1.17 [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ), maps( X,
% 0.46/1.17 'domain_of'( X ), Y ) ],
% 0.46/1.17 [ =( intersection( x, y ), x ) ],
% 0.46/1.17 [ ~( subclass( x, y ) ) ]
% 0.46/1.17 ] .
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 percentage equality = 0.227273, percentage horn = 0.929825
% 0.46/1.17 This is a problem with some equality
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 Options Used:
% 0.46/1.17
% 0.46/1.17 useres = 1
% 0.46/1.17 useparamod = 1
% 0.46/1.17 useeqrefl = 1
% 0.46/1.17 useeqfact = 1
% 0.46/1.17 usefactor = 1
% 0.46/1.17 usesimpsplitting = 0
% 0.46/1.17 usesimpdemod = 5
% 0.46/1.17 usesimpres = 3
% 0.46/1.17
% 0.46/1.17 resimpinuse = 1000
% 0.46/1.17 resimpclauses = 20000
% 0.46/1.17 substype = eqrewr
% 0.46/1.17 backwardsubs = 1
% 0.46/1.17 selectoldest = 5
% 0.46/1.17
% 0.46/1.17 litorderings [0] = split
% 0.46/1.17 litorderings [1] = extend the termordering, first sorting on arguments
% 0.46/1.17
% 0.46/1.17 termordering = kbo
% 0.46/1.17
% 0.46/1.17 litapriori = 0
% 0.46/1.17 termapriori = 1
% 0.46/1.17 litaposteriori = 0
% 0.46/1.17 termaposteriori = 0
% 0.46/1.17 demodaposteriori = 0
% 0.46/1.17 ordereqreflfact = 0
% 0.46/1.17
% 0.46/1.17 litselect = negord
% 0.46/1.17
% 0.46/1.17 maxweight = 15
% 0.46/1.17 maxdepth = 30000
% 0.46/1.17 maxlength = 115
% 0.46/1.17 maxnrvars = 195
% 0.46/1.17 excuselevel = 1
% 0.46/1.17 increasemaxweight = 1
% 0.46/1.17
% 0.46/1.17 maxselected = 10000000
% 0.46/1.17 maxnrclauses = 10000000
% 0.46/1.17
% 0.46/1.17 showgenerated = 0
% 0.46/1.17 showkept = 0
% 0.46/1.17 showselected = 0
% 0.46/1.17 showdeleted = 0
% 0.46/1.17 showresimp = 1
% 0.46/1.17 showstatus = 2000
% 0.46/1.17
% 0.46/1.17 prologoutput = 1
% 0.46/1.17 nrgoals = 5000000
% 0.46/1.17 totalproof = 1
% 0.46/1.17
% 0.46/1.17 Symbols occurring in the translation:
% 0.46/1.17
% 0.46/1.17 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.46/1.17 . [1, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.46/1.17 ! [4, 1] (w:0, o:35, a:1, s:1, b:0),
% 0.46/1.17 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.46/1.17 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.46/1.17 subclass [41, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.46/1.17 member [43, 2] (w:1, o:90, a:1, s:1, b:0),
% 0.46/1.17 'not_subclass_element' [44, 2] (w:1, o:91, a:1, s:1, b:0),
% 0.46/1.17 'universal_class' [45, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.46/1.17 'unordered_pair' [46, 2] (w:1, o:92, a:1, s:1, b:0),
% 0.46/1.17 singleton [47, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.46/1.17 'ordered_pair' [48, 2] (w:1, o:93, a:1, s:1, b:0),
% 0.46/1.17 'cross_product' [50, 2] (w:1, o:94, a:1, s:1, b:0),
% 0.46/1.17 first [52, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.46/1.17 second [53, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.46/1.17 'element_relation' [54, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.46/1.17 intersection [55, 2] (w:1, o:96, a:1, s:1, b:0),
% 0.46/1.17 complement [56, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.46/1.17 union [57, 2] (w:1, o:97, a:1, s:1, b:0),
% 0.46/1.17 'symmetric_difference' [58, 2] (w:1, o:98, a:1, s:1, b:0),
% 0.46/1.17 restrict [60, 3] (w:1, o:101, a:1, s:1, b:0),
% 0.46/1.17 'null_class' [61, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.46/1.17 'domain_of' [62, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.46/1.17 rotate [63, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.46/1.17 flip [65, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.46/1.17 inverse [66, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.46/1.17 'range_of' [67, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.46/1.17 domain [68, 3] (w:1, o:103, a:1, s:1, b:0),
% 0.46/1.17 range [69, 3] (w:1, o:104, a:1, s:1, b:0),
% 0.46/1.17 image [70, 2] (w:1, o:95, a:1, s:1, b:0),
% 0.46/1.17 successor [71, 1] (w:1, o:52, a:1, s:1, b:0),
% 0.46/1.17 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.46/1.17 inductive [73, 1] (w:1, o:53, a:1, s:1, b:0),
% 0.46/1.17 omega [74, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.46/1.17 'sum_class' [75, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.46/1.17 'power_class' [76, 1] (w:1, o:57, a:1, s:1, b:0),
% 0.46/1.17 compose [78, 2] (w:1, o:99, a:1, s:1, b:0),
% 0.46/1.17 'single_valued_class' [79, 1] (w:1, o:58, a:1, s:1, b:0),
% 0.46/1.17 'identity_relation' [80, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.46/1.17 function [82, 1] (w:1, o:59, a:1, s:1, b:0),
% 0.46/1.17 regular [83, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.46/1.17 apply [84, 2] (w:1, o:100, a:1, s:1, b:0),
% 0.46/1.17 choice [85, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.46/1.17 'one_to_one' [86, 1] (w:1, o:55, a:1, s:1, b:0),
% 0.46/1.17 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 0.46/1.17 diagonalise [88, 1] (w:1, o:60, a:1, s:1, b:0),
% 0.46/1.17 cantor [89, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.46/1.17 operation [90, 1] (w:1, o:56, a:1, s:1, b:0),
% 0.46/1.17 compatible [94, 3] (w:1, o:102, a:1, s:1, b:0),
% 0.46/1.17 homomorphism [95, 3] (w:1, o:105, a:1, s:1, b:0),
% 0.46/1.17 'not_homomorphism1' [96, 3] (w:1, o:107, a:1, s:1, b:0),
% 0.46/1.17 'not_homomorphism2' [97, 3] (w:1, o:108, a:1, s:1, b:0),
% 0.46/1.17 'compose_class' [98, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.46/1.17 'composition_function' [99, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.46/1.17 'domain_relation' [100, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.46/1.17 'single_valued1' [101, 1] (w:1, o:61, a:1, s:1, b:0),
% 0.46/1.17 'single_valued2' [102, 1] (w:1, o:62, a:1, s:1, b:0),
% 0.46/1.17 'single_valued3' [103, 1] (w:1, o:63, a:1, s:1, b:0),
% 0.46/1.17 'singleton_relation' [104, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.46/1.17 'application_function' [105, 0] (w:1, o:32, a:1, s:1, b:0),
% 0.46/1.17 maps [106, 3] (w:1, o:106, a:1, s:1, b:0),
% 0.46/1.17 x [107, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.46/1.17 y [108, 0] (w:1, o:34, a:1, s:1, b:0).
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 Starting Search:
% 0.46/1.17
% 0.46/1.17 Resimplifying inuse:
% 0.46/1.17 Done
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 Bliksems!, er is een bewijs:
% 0.46/1.17 % SZS status Unsatisfiable
% 0.46/1.17 % SZS output start Refutation
% 0.46/1.17
% 0.46/1.17 clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y )
% 0.46/1.17 ] )
% 0.46/1.17 .
% 0.46/1.17 clause( 2, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X
% 0.46/1.17 , Y ) ] )
% 0.46/1.17 .
% 0.46/1.17 clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 0.46/1.17 .
% 0.46/1.17 clause( 111, [ =( intersection( x, y ), x ) ] )
% 0.46/1.17 .
% 0.46/1.17 clause( 112, [ ~( subclass( x, y ) ) ] )
% 0.46/1.17 .
% 0.46/1.17 clause( 132, [ member( 'not_subclass_element'( x, y ), x ) ] )
% 0.46/1.17 .
% 0.46/1.17 clause( 140, [ ~( member( 'not_subclass_element'( x, y ), y ) ) ] )
% 0.46/1.17 .
% 0.46/1.17 clause( 1433, [ ~( member( X, x ) ), member( X, y ) ] )
% 0.46/1.17 .
% 0.46/1.17 clause( 1452, [] )
% 0.46/1.17 .
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 % SZS output end Refutation
% 0.46/1.17 found a proof!
% 0.46/1.17
% 0.46/1.17 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.46/1.17
% 0.46/1.17 initialclauses(
% 0.46/1.17 [ clause( 1454, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 0.46/1.17 ) ] )
% 0.46/1.17 , clause( 1455, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 0.46/1.17 , Y ) ] )
% 0.46/1.17 , clause( 1456, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 0.46/1.17 subclass( X, Y ) ] )
% 0.46/1.17 , clause( 1457, [ subclass( X, 'universal_class' ) ] )
% 0.46/1.17 , clause( 1458, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 0.46/1.17 , clause( 1459, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 0.46/1.17 , clause( 1460, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ]
% 0.46/1.17 )
% 0.46/1.17 , clause( 1461, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 0.46/1.17 =( X, Z ) ] )
% 0.46/1.17 , clause( 1462, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.46/1.17 'unordered_pair'( X, Y ) ) ] )
% 0.46/1.17 , clause( 1463, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.46/1.17 'unordered_pair'( Y, X ) ) ] )
% 0.46/1.17 , clause( 1464, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 0.46/1.17 )
% 0.46/1.17 , clause( 1465, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 0.46/1.17 , clause( 1466, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 0.46/1.17 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.46/1.17 , clause( 1467, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.46/1.17 ) ) ), member( X, Z ) ] )
% 0.46/1.17 , clause( 1468, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.46/1.17 ) ) ), member( Y, T ) ] )
% 0.46/1.17 , clause( 1469, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 0.46/1.17 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 0.46/1.17 , clause( 1470, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 0.46/1.17 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 0.46/1.17 , clause( 1471, [ subclass( 'element_relation', 'cross_product'(
% 0.46/1.17 'universal_class', 'universal_class' ) ) ] )
% 0.46/1.17 , clause( 1472, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) )
% 0.46/1.17 , member( X, Y ) ] )
% 0.46/1.17 , clause( 1473, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.46/1.17 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 0.46/1.17 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 0.46/1.17 , clause( 1474, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.46/1.17 )
% 0.46/1.17 , clause( 1475, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 0.46/1.17 )
% 0.46/1.17 , clause( 1476, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 0.46/1.17 intersection( Y, Z ) ) ] )
% 0.46/1.17 , clause( 1477, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 0.46/1.17 )
% 0.46/1.17 , clause( 1478, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.46/1.17 complement( Y ) ), member( X, Y ) ] )
% 0.46/1.17 , clause( 1479, [ =( complement( intersection( complement( X ), complement(
% 0.46/1.17 Y ) ) ), union( X, Y ) ) ] )
% 0.46/1.17 , clause( 1480, [ =( intersection( complement( intersection( X, Y ) ),
% 0.46/1.17 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 0.46/1.17 'symmetric_difference'( X, Y ) ) ] )
% 0.46/1.17 , clause( 1481, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 0.46/1.17 X, Y, Z ) ) ] )
% 0.46/1.17 , clause( 1482, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 0.46/1.17 Z, X, Y ) ) ] )
% 0.46/1.17 , clause( 1483, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 0.46/1.17 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 0.46/1.17 , clause( 1484, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 0.46/1.17 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 0.46/1.17 'domain_of'( Y ) ) ] )
% 0.46/1.17 , clause( 1485, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.46/1.17 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.46/1.17 , clause( 1486, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.46/1.17 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 0.46/1.17 ] )
% 0.46/1.17 , clause( 1487, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.46/1.17 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 0.46/1.17 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.46/1.17 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 0.46/1.17 , Y ), rotate( T ) ) ] )
% 0.46/1.17 , clause( 1488, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.46/1.17 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.46/1.17 , clause( 1489, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.46/1.17 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 0.46/1.17 )
% 0.46/1.17 , clause( 1490, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.46/1.17 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 0.46/1.17 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.46/1.17 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 0.46/1.17 , Z ), flip( T ) ) ] )
% 0.46/1.17 , clause( 1491, [ =( 'domain_of'( flip( 'cross_product'( X,
% 0.46/1.17 'universal_class' ) ) ), inverse( X ) ) ] )
% 0.46/1.17 , clause( 1492, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 0.46/1.17 , clause( 1493, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 0.46/1.17 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 0.46/1.17 , clause( 1494, [ =( second( 'not_subclass_element'( restrict( X, singleton(
% 0.46/1.17 Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 0.46/1.17 , clause( 1495, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 0.46/1.17 image( X, Y ) ) ] )
% 0.46/1.17 , clause( 1496, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 0.46/1.17 , clause( 1497, [ subclass( 'successor_relation', 'cross_product'(
% 0.46/1.17 'universal_class', 'universal_class' ) ) ] )
% 0.46/1.17 , clause( 1498, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' )
% 0.46/1.17 ), =( successor( X ), Y ) ] )
% 0.46/1.17 , clause( 1499, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X
% 0.46/1.17 , Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 0.46/1.17 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 0.46/1.17 , clause( 1500, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 0.46/1.17 , clause( 1501, [ ~( inductive( X ) ), subclass( image(
% 0.46/1.17 'successor_relation', X ), X ) ] )
% 0.46/1.17 , clause( 1502, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.46/1.17 'successor_relation', X ), X ) ), inductive( X ) ] )
% 0.46/1.17 , clause( 1503, [ inductive( omega ) ] )
% 0.46/1.17 , clause( 1504, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 0.46/1.17 , clause( 1505, [ member( omega, 'universal_class' ) ] )
% 0.46/1.17 , clause( 1506, [ =( 'domain_of'( restrict( 'element_relation',
% 0.46/1.17 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 0.46/1.17 , clause( 1507, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 0.46/1.17 X ), 'universal_class' ) ] )
% 0.46/1.17 , clause( 1508, [ =( complement( image( 'element_relation', complement( X )
% 0.46/1.17 ) ), 'power_class'( X ) ) ] )
% 0.46/1.17 , clause( 1509, [ ~( member( X, 'universal_class' ) ), member(
% 0.46/1.17 'power_class'( X ), 'universal_class' ) ] )
% 0.46/1.17 , clause( 1510, [ subclass( compose( X, Y ), 'cross_product'(
% 0.46/1.17 'universal_class', 'universal_class' ) ) ] )
% 0.46/1.17 , clause( 1511, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 0.46/1.17 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 0.46/1.17 , clause( 1512, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 0.46/1.17 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.46/1.17 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.46/1.17 ) ] )
% 0.46/1.17 , clause( 1513, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 0.46/1.17 inverse( X ) ), 'identity_relation' ) ] )
% 0.46/1.17 , clause( 1514, [ ~( subclass( compose( X, inverse( X ) ),
% 0.46/1.17 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 0.46/1.17 , clause( 1515, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 0.46/1.17 'universal_class', 'universal_class' ) ) ] )
% 0.46/1.17 , clause( 1516, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 0.46/1.17 , 'identity_relation' ) ] )
% 0.46/1.17 , clause( 1517, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 0.46/1.17 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 0.46/1.17 'identity_relation' ) ), function( X ) ] )
% 0.46/1.17 , clause( 1518, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ),
% 0.46/1.17 member( image( X, Y ), 'universal_class' ) ] )
% 0.46/1.17 , clause( 1519, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.46/1.17 , clause( 1520, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 0.46/1.17 , 'null_class' ) ] )
% 0.46/1.17 , clause( 1521, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y
% 0.46/1.17 ) ) ] )
% 0.46/1.17 , clause( 1522, [ function( choice ) ] )
% 0.46/1.17 , clause( 1523, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' )
% 0.46/1.17 , member( apply( choice, X ), X ) ] )
% 0.46/1.17 , clause( 1524, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 0.46/1.17 , clause( 1525, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 0.46/1.17 , clause( 1526, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 0.46/1.17 'one_to_one'( X ) ] )
% 0.46/1.17 , clause( 1527, [ =( intersection( 'cross_product'( 'universal_class',
% 0.46/1.17 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 0.46/1.17 'universal_class' ), complement( compose( complement( 'element_relation'
% 0.46/1.17 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 0.46/1.17 , clause( 1528, [ =( intersection( inverse( 'subset_relation' ),
% 0.46/1.17 'subset_relation' ), 'identity_relation' ) ] )
% 0.46/1.17 , clause( 1529, [ =( complement( 'domain_of'( intersection( X,
% 0.46/1.17 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 0.46/1.17 , clause( 1530, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 0.46/1.17 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 0.46/1.17 , clause( 1531, [ ~( operation( X ) ), function( X ) ] )
% 0.46/1.17 , clause( 1532, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 0.46/1.17 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.46/1.17 ] )
% 0.46/1.17 , clause( 1533, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 0.46/1.17 'domain_of'( 'domain_of'( X ) ) ) ] )
% 0.46/1.17 , clause( 1534, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 0.46/1.17 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.46/1.17 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 0.46/1.17 operation( X ) ] )
% 0.46/1.17 , clause( 1535, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 0.46/1.17 , clause( 1536, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 0.46/1.17 Y ) ), 'domain_of'( X ) ) ] )
% 0.46/1.17 , clause( 1537, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 0.46/1.17 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 0.46/1.17 , clause( 1538, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) )
% 0.46/1.17 , 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 0.46/1.17 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 0.46/1.17 , clause( 1539, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 0.46/1.17 , clause( 1540, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 0.46/1.17 , clause( 1541, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 0.46/1.17 , clause( 1542, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 0.46/1.17 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 0.46/1.17 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 0.46/1.17 )
% 0.46/1.17 , clause( 1543, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 0.46/1.17 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.46/1.17 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.46/1.17 , Y ) ] )
% 0.46/1.17 , clause( 1544, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 0.46/1.17 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 0.46/1.17 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 0.46/1.17 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 0.46/1.17 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 0.46/1.17 )
% 0.46/1.17 , clause( 1545, [ subclass( 'compose_class'( X ), 'cross_product'(
% 0.46/1.17 'universal_class', 'universal_class' ) ) ] )
% 0.46/1.17 , clause( 1546, [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) )
% 0.46/1.17 ), =( compose( Z, X ), Y ) ] )
% 0.46/1.17 , clause( 1547, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.46/1.17 'universal_class', 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) )
% 0.46/1.17 , member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ] )
% 0.46/1.17 , clause( 1548, [ subclass( 'composition_function', 'cross_product'(
% 0.46/1.17 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 0.46/1.17 ) ) ) ] )
% 0.46/1.17 , clause( 1549, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.46/1.17 'composition_function' ) ), =( compose( X, Y ), Z ) ] )
% 0.46/1.17 , clause( 1550, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.46/1.17 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( X,
% 0.46/1.17 'ordered_pair'( Y, compose( X, Y ) ) ), 'composition_function' ) ] )
% 0.46/1.17 , clause( 1551, [ subclass( 'domain_relation', 'cross_product'(
% 0.46/1.17 'universal_class', 'universal_class' ) ) ] )
% 0.46/1.17 , clause( 1552, [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) )
% 0.46/1.17 , =( 'domain_of'( X ), Y ) ] )
% 0.46/1.17 , clause( 1553, [ ~( member( X, 'universal_class' ) ), member(
% 0.46/1.17 'ordered_pair'( X, 'domain_of'( X ) ), 'domain_relation' ) ] )
% 0.46/1.17 , clause( 1554, [ =( first( 'not_subclass_element'( compose( X, inverse( X
% 0.46/1.17 ) ), 'identity_relation' ) ), 'single_valued1'( X ) ) ] )
% 0.46/1.17 , clause( 1555, [ =( second( 'not_subclass_element'( compose( X, inverse( X
% 0.46/1.17 ) ), 'identity_relation' ) ), 'single_valued2'( X ) ) ] )
% 0.46/1.17 , clause( 1556, [ =( domain( X, image( inverse( X ), singleton(
% 0.46/1.17 'single_valued1'( X ) ) ), 'single_valued2'( X ) ), 'single_valued3'( X )
% 0.46/1.17 ) ] )
% 0.46/1.17 , clause( 1557, [ =( intersection( complement( compose( 'element_relation'
% 0.46/1.17 , complement( 'identity_relation' ) ) ), 'element_relation' ),
% 0.46/1.17 'singleton_relation' ) ] )
% 0.46/1.17 , clause( 1558, [ subclass( 'application_function', 'cross_product'(
% 0.46/1.17 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 0.46/1.17 ) ) ) ] )
% 0.46/1.17 , clause( 1559, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.46/1.17 'application_function' ) ), member( Y, 'domain_of'( X ) ) ] )
% 0.46/1.17 , clause( 1560, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.46/1.17 'application_function' ) ), =( apply( X, Y ), Z ) ] )
% 0.46/1.17 , clause( 1561, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.46/1.17 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 0.46/1.17 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 0.46/1.17 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 0.46/1.17 'application_function' ) ] )
% 0.46/1.17 , clause( 1562, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 0.46/1.17 , clause( 1563, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 0.46/1.17 , clause( 1564, [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ] )
% 0.46/1.17 , clause( 1565, [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ),
% 0.46/1.17 maps( X, 'domain_of'( X ), Y ) ] )
% 0.46/1.17 , clause( 1566, [ =( intersection( x, y ), x ) ] )
% 0.46/1.17 , clause( 1567, [ ~( subclass( x, y ) ) ] )
% 0.46/1.17 ] ).
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 subsumption(
% 0.46/1.17 clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y )
% 0.46/1.17 ] )
% 0.46/1.17 , clause( 1455, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 0.46/1.17 , Y ) ] )
% 0.46/1.17 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.46/1.17 ), ==>( 1, 1 )] ) ).
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 subsumption(
% 0.46/1.17 clause( 2, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X
% 0.46/1.17 , Y ) ] )
% 0.46/1.17 , clause( 1456, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 0.46/1.17 subclass( X, Y ) ] )
% 0.46/1.17 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.46/1.17 ), ==>( 1, 1 )] ) ).
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 subsumption(
% 0.46/1.17 clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 0.46/1.17 , clause( 1475, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 0.46/1.17 )
% 0.46/1.17 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.46/1.17 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 subsumption(
% 0.46/1.17 clause( 111, [ =( intersection( x, y ), x ) ] )
% 0.46/1.17 , clause( 1566, [ =( intersection( x, y ), x ) ] )
% 0.46/1.17 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 subsumption(
% 0.46/1.17 clause( 112, [ ~( subclass( x, y ) ) ] )
% 0.46/1.17 , clause( 1567, [ ~( subclass( x, y ) ) ] )
% 0.46/1.17 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 resolution(
% 0.46/1.17 clause( 1702, [ member( 'not_subclass_element'( x, y ), x ) ] )
% 0.46/1.17 , clause( 112, [ ~( subclass( x, y ) ) ] )
% 0.46/1.17 , 0, clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 0.46/1.17 , Y ) ] )
% 0.46/1.17 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, x ), :=( Y, y )] )
% 0.46/1.17 ).
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 subsumption(
% 0.46/1.17 clause( 132, [ member( 'not_subclass_element'( x, y ), x ) ] )
% 0.46/1.17 , clause( 1702, [ member( 'not_subclass_element'( x, y ), x ) ] )
% 0.46/1.17 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 resolution(
% 0.46/1.17 clause( 1703, [ ~( member( 'not_subclass_element'( x, y ), y ) ) ] )
% 0.46/1.17 , clause( 112, [ ~( subclass( x, y ) ) ] )
% 0.46/1.17 , 0, clause( 2, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 0.46/1.17 subclass( X, Y ) ] )
% 0.46/1.17 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, x ), :=( Y, y )] )
% 0.46/1.17 ).
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 subsumption(
% 0.46/1.17 clause( 140, [ ~( member( 'not_subclass_element'( x, y ), y ) ) ] )
% 0.46/1.17 , clause( 1703, [ ~( member( 'not_subclass_element'( x, y ), y ) ) ] )
% 0.46/1.17 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 paramod(
% 0.46/1.17 clause( 1705, [ ~( member( X, x ) ), member( X, y ) ] )
% 0.46/1.17 , clause( 111, [ =( intersection( x, y ), x ) ] )
% 0.46/1.17 , 0, clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 0.46/1.17 )
% 0.46/1.17 , 0, 3, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, x ),
% 0.46/1.17 :=( Z, y )] )).
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 subsumption(
% 0.46/1.17 clause( 1433, [ ~( member( X, x ) ), member( X, y ) ] )
% 0.46/1.17 , clause( 1705, [ ~( member( X, x ) ), member( X, y ) ] )
% 0.46/1.17 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.46/1.17 1 )] ) ).
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 resolution(
% 0.46/1.17 clause( 1706, [ ~( member( 'not_subclass_element'( x, y ), x ) ) ] )
% 0.46/1.17 , clause( 140, [ ~( member( 'not_subclass_element'( x, y ), y ) ) ] )
% 0.46/1.17 , 0, clause( 1433, [ ~( member( X, x ) ), member( X, y ) ] )
% 0.46/1.17 , 1, substitution( 0, [] ), substitution( 1, [ :=( X,
% 0.46/1.17 'not_subclass_element'( x, y ) )] )).
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 resolution(
% 0.46/1.17 clause( 1707, [] )
% 0.46/1.17 , clause( 1706, [ ~( member( 'not_subclass_element'( x, y ), x ) ) ] )
% 0.46/1.17 , 0, clause( 132, [ member( 'not_subclass_element'( x, y ), x ) ] )
% 0.46/1.17 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 subsumption(
% 0.46/1.17 clause( 1452, [] )
% 0.46/1.17 , clause( 1707, [] )
% 0.46/1.17 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 end.
% 0.46/1.17
% 0.46/1.17 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.46/1.17
% 0.46/1.17 Memory use:
% 0.46/1.17
% 0.46/1.17 space for terms: 23046
% 0.46/1.17 space for clauses: 72268
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 clauses generated: 3468
% 0.46/1.17 clauses kept: 1453
% 0.46/1.17 clauses selected: 91
% 0.46/1.17 clauses deleted: 3
% 0.46/1.17 clauses inuse deleted: 2
% 0.46/1.17
% 0.46/1.17 subsentry: 8082
% 0.46/1.17 literals s-matched: 6751
% 0.46/1.17 literals matched: 6664
% 0.46/1.17 full subsumption: 3622
% 0.46/1.17
% 0.46/1.17 checksum: -2008697580
% 0.46/1.17
% 0.46/1.17
% 0.46/1.17 Bliksem ended
%------------------------------------------------------------------------------