TSTP Solution File: SET152-6 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET152-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Mon Jul 18 22:47:39 EDT 2022
% Result : Unsatisfiable 0.75s 1.39s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET152-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Mon Jul 11 06:13:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.71/1.11 *** allocated 10000 integers for termspace/termends
% 0.71/1.11 *** allocated 10000 integers for clauses
% 0.71/1.11 *** allocated 10000 integers for justifications
% 0.71/1.11 Bliksem 1.12
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Automatic Strategy Selection
% 0.71/1.11
% 0.71/1.11 Clauses:
% 0.71/1.11 [
% 0.71/1.11 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.71/1.11 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.71/1.11 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ subclass( X, 'universal_class' ) ],
% 0.71/1.11 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.71/1.11 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.71/1.11 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.71/1.11 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.71/1.11 ) ) ],
% 0.71/1.11 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.71/1.11 ) ) ],
% 0.71/1.11 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.71/1.11 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.71/1.11 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.71/1.11 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.71/1.11 X, Z ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.71/1.11 Y, T ) ],
% 0.71/1.11 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.71/1.11 ), 'cross_product'( Y, T ) ) ],
% 0.71/1.11 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.71/1.11 ), second( X ) ), X ) ],
% 0.71/1.11 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.71/1.11 'universal_class' ) ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.71/1.11 Y ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.71/1.11 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.71/1.11 , Y ), 'element_relation' ) ],
% 0.71/1.11 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.71/1.11 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.71/1.11 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.71/1.11 Z ) ) ],
% 0.71/1.11 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.71/1.11 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.71/1.11 member( X, Y ) ],
% 0.71/1.11 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.71/1.11 union( X, Y ) ) ],
% 0.71/1.11 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.71/1.11 intersection( complement( X ), complement( Y ) ) ) ),
% 0.71/1.11 'symmetric_difference'( X, Y ) ) ],
% 0.71/1.11 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.71/1.11 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.71/1.11 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.71/1.11 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.71/1.11 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.71/1.11 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.71/1.11 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.71/1.11 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.71/1.11 'cross_product'( 'universal_class', 'universal_class' ),
% 0.71/1.11 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.71/1.11 Y ), rotate( T ) ) ],
% 0.71/1.11 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.71/1.11 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.71/1.11 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.71/1.11 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.71/1.11 'cross_product'( 'universal_class', 'universal_class' ),
% 0.71/1.11 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.71/1.11 Z ), flip( T ) ) ],
% 0.71/1.11 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.71/1.11 inverse( X ) ) ],
% 0.71/1.11 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.71/1.11 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.71/1.11 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.71/1.11 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.71/1.11 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.71/1.11 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.71/1.11 ],
% 0.71/1.11 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.71/1.11 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.71/1.11 'universal_class' ) ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.71/1.11 successor( X ), Y ) ],
% 0.71/1.11 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.71/1.11 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.71/1.11 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.71/1.11 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.71/1.11 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.71/1.11 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.71/1.11 [ inductive( omega ) ],
% 0.71/1.11 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.71/1.11 [ member( omega, 'universal_class' ) ],
% 0.71/1.11 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.71/1.11 , 'sum_class'( X ) ) ],
% 0.71/1.11 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.71/1.11 'universal_class' ) ],
% 0.71/1.11 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.71/1.11 'power_class'( X ) ) ],
% 0.71/1.11 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.71/1.11 'universal_class' ) ],
% 0.71/1.11 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.71/1.11 'universal_class' ) ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.71/1.11 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.71/1.11 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.71/1.11 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.71/1.11 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.71/1.11 ) ],
% 0.71/1.11 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.71/1.11 , 'identity_relation' ) ],
% 0.71/1.11 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.71/1.11 'single_valued_class'( X ) ],
% 0.71/1.11 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.71/1.11 'universal_class' ) ) ],
% 0.71/1.11 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.71/1.11 'identity_relation' ) ],
% 0.71/1.11 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.71/1.11 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.71/1.11 , function( X ) ],
% 0.71/1.11 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.71/1.11 X, Y ), 'universal_class' ) ],
% 0.71/1.11 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.71/1.11 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.71/1.11 ) ],
% 0.71/1.11 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.71/1.11 [ function( choice ) ],
% 0.71/1.11 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.71/1.11 apply( choice, X ), X ) ],
% 0.71/1.11 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.71/1.11 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.71/1.11 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.71/1.11 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.71/1.11 , complement( compose( complement( 'element_relation' ), inverse(
% 0.71/1.11 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.71/1.11 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.71/1.11 'identity_relation' ) ],
% 0.71/1.11 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.71/1.11 , diagonalise( X ) ) ],
% 0.71/1.11 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.71/1.11 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.71/1.11 [ ~( operation( X ) ), function( X ) ],
% 0.71/1.11 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.71/1.11 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.71/1.11 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.71/1.11 'domain_of'( X ) ) ) ],
% 0.71/1.11 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.71/1.11 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.71/1.11 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.71/1.11 X ) ],
% 0.71/1.11 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.71/1.11 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.71/1.11 'domain_of'( X ) ) ],
% 0.71/1.11 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.71/1.11 'domain_of'( Z ) ) ) ],
% 0.71/1.11 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.71/1.11 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.71/1.11 ), compatible( X, Y, Z ) ],
% 0.71/1.11 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.71/1.11 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.71/1.11 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.71/1.11 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.71/1.11 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.71/1.11 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.71/1.11 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.71/1.11 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.71/1.11 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.71/1.11 , Y ) ],
% 0.71/1.11 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.71/1.11 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.71/1.11 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.71/1.11 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.71/1.11 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.71/1.11 [ subclass( 'compose_class'( X ), 'cross_product'( 'universal_class',
% 0.71/1.11 'universal_class' ) ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ), =(
% 0.71/1.11 compose( Z, X ), Y ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.71/1.11 , 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) ), member(
% 0.71/1.11 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ],
% 0.71/1.11 [ subclass( 'composition_function', 'cross_product'( 'universal_class',
% 0.71/1.11 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.71/1.11 'composition_function' ) ), =( compose( X, Y ), Z ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.71/1.11 , 'universal_class' ) ) ), member( 'ordered_pair'( X, 'ordered_pair'( Y,
% 0.71/1.11 compose( X, Y ) ) ), 'composition_function' ) ],
% 0.71/1.11 [ subclass( 'domain_relation', 'cross_product'( 'universal_class',
% 0.71/1.11 'universal_class' ) ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) ), =(
% 0.71/1.11 'domain_of'( X ), Y ) ],
% 0.71/1.11 [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X,
% 0.71/1.11 'domain_of'( X ) ), 'domain_relation' ) ],
% 0.71/1.11 [ =( first( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.71/1.11 'identity_relation' ) ), 'single_valued1'( X ) ) ],
% 0.71/1.11 [ =( second( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.71/1.11 'identity_relation' ) ), 'single_valued2'( X ) ) ],
% 0.71/1.11 [ =( domain( X, image( inverse( X ), singleton( 'single_valued1'( X ) )
% 0.71/1.11 ), 'single_valued2'( X ) ), 'single_valued3'( X ) ) ],
% 0.71/1.11 [ =( intersection( complement( compose( 'element_relation', complement(
% 0.71/1.11 'identity_relation' ) ) ), 'element_relation' ), 'singleton_relation' ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ subclass( 'application_function', 'cross_product'( 'universal_class',
% 0.71/1.11 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.71/1.11 'application_function' ) ), member( Y, 'domain_of'( X ) ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.71/1.11 'application_function' ) ), =( apply( X, Y ), Z ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.71/1.11 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 0.71/1.11 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 0.71/1.11 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 0.71/1.11 'application_function' ) ],
% 0.71/1.11 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.71/1.11 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 0.75/1.39 [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ],
% 0.75/1.39 [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ), maps( X,
% 0.75/1.39 'domain_of'( X ), Y ) ],
% 0.75/1.39 [ ~( =( complement( 'universal_class' ), 'null_class' ) ) ]
% 0.75/1.39 ] .
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 percentage equality = 0.228311, percentage horn = 0.929204
% 0.75/1.39 This is a problem with some equality
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 Options Used:
% 0.75/1.39
% 0.75/1.39 useres = 1
% 0.75/1.39 useparamod = 1
% 0.75/1.39 useeqrefl = 1
% 0.75/1.39 useeqfact = 1
% 0.75/1.39 usefactor = 1
% 0.75/1.39 usesimpsplitting = 0
% 0.75/1.39 usesimpdemod = 5
% 0.75/1.39 usesimpres = 3
% 0.75/1.39
% 0.75/1.39 resimpinuse = 1000
% 0.75/1.39 resimpclauses = 20000
% 0.75/1.39 substype = eqrewr
% 0.75/1.39 backwardsubs = 1
% 0.75/1.39 selectoldest = 5
% 0.75/1.39
% 0.75/1.39 litorderings [0] = split
% 0.75/1.39 litorderings [1] = extend the termordering, first sorting on arguments
% 0.75/1.39
% 0.75/1.39 termordering = kbo
% 0.75/1.39
% 0.75/1.39 litapriori = 0
% 0.75/1.39 termapriori = 1
% 0.75/1.39 litaposteriori = 0
% 0.75/1.39 termaposteriori = 0
% 0.75/1.39 demodaposteriori = 0
% 0.75/1.39 ordereqreflfact = 0
% 0.75/1.39
% 0.75/1.39 litselect = negord
% 0.75/1.39
% 0.75/1.39 maxweight = 15
% 0.75/1.39 maxdepth = 30000
% 0.75/1.39 maxlength = 115
% 0.75/1.39 maxnrvars = 195
% 0.75/1.39 excuselevel = 1
% 0.75/1.39 increasemaxweight = 1
% 0.75/1.39
% 0.75/1.39 maxselected = 10000000
% 0.75/1.39 maxnrclauses = 10000000
% 0.75/1.39
% 0.75/1.39 showgenerated = 0
% 0.75/1.39 showkept = 0
% 0.75/1.39 showselected = 0
% 0.75/1.39 showdeleted = 0
% 0.75/1.39 showresimp = 1
% 0.75/1.39 showstatus = 2000
% 0.75/1.39
% 0.75/1.39 prologoutput = 1
% 0.75/1.39 nrgoals = 5000000
% 0.75/1.39 totalproof = 1
% 0.75/1.39
% 0.75/1.39 Symbols occurring in the translation:
% 0.75/1.39
% 0.75/1.39 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.75/1.39 . [1, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.75/1.39 ! [4, 1] (w:0, o:33, a:1, s:1, b:0),
% 0.75/1.39 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.39 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.39 subclass [41, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.75/1.39 member [43, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.75/1.39 'not_subclass_element' [44, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.75/1.39 'universal_class' [45, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.75/1.39 'unordered_pair' [46, 2] (w:1, o:90, a:1, s:1, b:0),
% 0.75/1.39 singleton [47, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.75/1.39 'ordered_pair' [48, 2] (w:1, o:91, a:1, s:1, b:0),
% 0.75/1.39 'cross_product' [50, 2] (w:1, o:92, a:1, s:1, b:0),
% 0.75/1.39 first [52, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.75/1.39 second [53, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.75/1.39 'element_relation' [54, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.75/1.39 intersection [55, 2] (w:1, o:94, a:1, s:1, b:0),
% 0.75/1.39 complement [56, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.75/1.39 union [57, 2] (w:1, o:95, a:1, s:1, b:0),
% 0.75/1.39 'symmetric_difference' [58, 2] (w:1, o:96, a:1, s:1, b:0),
% 0.75/1.39 restrict [60, 3] (w:1, o:99, a:1, s:1, b:0),
% 0.75/1.39 'null_class' [61, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.75/1.39 'domain_of' [62, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.75/1.39 rotate [63, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.75/1.39 flip [65, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.75/1.39 inverse [66, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.75/1.39 'range_of' [67, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.75/1.39 domain [68, 3] (w:1, o:101, a:1, s:1, b:0),
% 0.75/1.39 range [69, 3] (w:1, o:102, a:1, s:1, b:0),
% 0.75/1.39 image [70, 2] (w:1, o:93, a:1, s:1, b:0),
% 0.75/1.39 successor [71, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.75/1.39 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.75/1.39 inductive [73, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.75/1.39 omega [74, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.75/1.39 'sum_class' [75, 1] (w:1, o:52, a:1, s:1, b:0),
% 0.75/1.39 'power_class' [76, 1] (w:1, o:55, a:1, s:1, b:0),
% 0.75/1.39 compose [78, 2] (w:1, o:97, a:1, s:1, b:0),
% 0.75/1.39 'single_valued_class' [79, 1] (w:1, o:56, a:1, s:1, b:0),
% 0.75/1.39 'identity_relation' [80, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.75/1.39 function [82, 1] (w:1, o:57, a:1, s:1, b:0),
% 0.75/1.39 regular [83, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.75/1.39 apply [84, 2] (w:1, o:98, a:1, s:1, b:0),
% 0.75/1.39 choice [85, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.75/1.39 'one_to_one' [86, 1] (w:1, o:53, a:1, s:1, b:0),
% 0.75/1.39 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 0.75/1.39 diagonalise [88, 1] (w:1, o:58, a:1, s:1, b:0),
% 0.75/1.39 cantor [89, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.75/1.39 operation [90, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.75/1.39 compatible [94, 3] (w:1, o:100, a:1, s:1, b:0),
% 0.75/1.39 homomorphism [95, 3] (w:1, o:103, a:1, s:1, b:0),
% 0.75/1.39 'not_homomorphism1' [96, 3] (w:1, o:105, a:1, s:1, b:0),
% 0.75/1.39 'not_homomorphism2' [97, 3] (w:1, o:106, a:1, s:1, b:0),
% 0.75/1.39 'compose_class' [98, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.75/1.39 'composition_function' [99, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.75/1.39 'domain_relation' [100, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.75/1.39 'single_valued1' [101, 1] (w:1, o:59, a:1, s:1, b:0),
% 0.75/1.39 'single_valued2' [102, 1] (w:1, o:60, a:1, s:1, b:0),
% 0.75/1.39 'single_valued3' [103, 1] (w:1, o:61, a:1, s:1, b:0),
% 0.75/1.39 'singleton_relation' [104, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.75/1.39 'application_function' [105, 0] (w:1, o:32, a:1, s:1, b:0),
% 0.75/1.39 maps [106, 3] (w:1, o:104, a:1, s:1, b:0).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 Starting Search:
% 0.75/1.39
% 0.75/1.39 Resimplifying inuse:
% 0.75/1.39 Done
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 Intermediate Status:
% 0.75/1.39 Generated: 4959
% 0.75/1.39 Kept: 2038
% 0.75/1.39 Inuse: 101
% 0.75/1.39 Deleted: 7
% 0.75/1.39 Deletedinuse: 2
% 0.75/1.39
% 0.75/1.39 Resimplifying inuse:
% 0.75/1.39 Done
% 0.75/1.39
% 0.75/1.39 Resimplifying inuse:
% 0.75/1.39 Done
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 Intermediate Status:
% 0.75/1.39 Generated: 9632
% 0.75/1.39 Kept: 4040
% 0.75/1.39 Inuse: 184
% 0.75/1.39 Deleted: 19
% 0.75/1.39 Deletedinuse: 7
% 0.75/1.39
% 0.75/1.39 Resimplifying inuse:
% 0.75/1.39 Done
% 0.75/1.39
% 0.75/1.39 Resimplifying inuse:
% 0.75/1.39 Done
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 Intermediate Status:
% 0.75/1.39 Generated: 13593
% 0.75/1.39 Kept: 6100
% 0.75/1.39 Inuse: 237
% 0.75/1.39 Deleted: 22
% 0.75/1.39 Deletedinuse: 8
% 0.75/1.39
% 0.75/1.39 Resimplifying inuse:
% 0.75/1.39 Done
% 0.75/1.39
% 0.75/1.39 Resimplifying inuse:
% 0.75/1.39
% 0.75/1.39 Bliksems!, er is een bewijs:
% 0.75/1.39 % SZS status Unsatisfiable
% 0.75/1.39 % SZS output start Refutation
% 0.75/1.39
% 0.75/1.39 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.75/1.39 )
% 0.75/1.39 .
% 0.75/1.39 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 0.75/1.39 .
% 0.75/1.39 clause( 22, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ] )
% 0.75/1.39 .
% 0.75/1.39 clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.75/1.39 .
% 0.75/1.39 clause( 111, [ ~( =( complement( 'universal_class' ), 'null_class' ) ) ] )
% 0.75/1.39 .
% 0.75/1.39 clause( 127, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ] )
% 0.75/1.39 .
% 0.75/1.39 clause( 1878, [ ~( member( X, complement( 'universal_class' ) ) ), ~(
% 0.75/1.39 member( X, Y ) ) ] )
% 0.75/1.39 .
% 0.75/1.39 clause( 1902, [ ~( member( X, complement( 'universal_class' ) ) ) ] )
% 0.75/1.39 .
% 0.75/1.39 clause( 6807, [ =( complement( 'universal_class' ), 'null_class' ) ] )
% 0.75/1.39 .
% 0.75/1.39 clause( 7395, [] )
% 0.75/1.39 .
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 % SZS output end Refutation
% 0.75/1.39 found a proof!
% 0.75/1.39
% 0.75/1.39 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.75/1.39
% 0.75/1.39 initialclauses(
% 0.75/1.39 [ clause( 7397, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 0.75/1.39 ) ] )
% 0.75/1.39 , clause( 7398, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 0.75/1.39 , Y ) ] )
% 0.75/1.39 , clause( 7399, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 0.75/1.39 subclass( X, Y ) ] )
% 0.75/1.39 , clause( 7400, [ subclass( X, 'universal_class' ) ] )
% 0.75/1.39 , clause( 7401, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 0.75/1.39 , clause( 7402, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 0.75/1.39 , clause( 7403, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ]
% 0.75/1.39 )
% 0.75/1.39 , clause( 7404, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 0.75/1.39 =( X, Z ) ] )
% 0.75/1.39 , clause( 7405, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.75/1.39 'unordered_pair'( X, Y ) ) ] )
% 0.75/1.39 , clause( 7406, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.75/1.39 'unordered_pair'( Y, X ) ) ] )
% 0.75/1.39 , clause( 7407, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 0.75/1.39 )
% 0.75/1.39 , clause( 7408, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 0.75/1.39 , clause( 7409, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 0.75/1.39 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.75/1.39 , clause( 7410, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.75/1.39 ) ) ), member( X, Z ) ] )
% 0.75/1.39 , clause( 7411, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.75/1.39 ) ) ), member( Y, T ) ] )
% 0.75/1.39 , clause( 7412, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 0.75/1.39 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 0.75/1.39 , clause( 7413, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 0.75/1.39 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 0.75/1.39 , clause( 7414, [ subclass( 'element_relation', 'cross_product'(
% 0.75/1.39 'universal_class', 'universal_class' ) ) ] )
% 0.75/1.39 , clause( 7415, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) )
% 0.75/1.39 , member( X, Y ) ] )
% 0.75/1.39 , clause( 7416, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.75/1.39 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 0.75/1.39 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 0.75/1.39 , clause( 7417, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.75/1.39 )
% 0.75/1.39 , clause( 7418, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 0.75/1.39 )
% 0.75/1.39 , clause( 7419, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 0.75/1.39 intersection( Y, Z ) ) ] )
% 0.75/1.39 , clause( 7420, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 0.75/1.39 )
% 0.75/1.39 , clause( 7421, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.75/1.39 complement( Y ) ), member( X, Y ) ] )
% 0.75/1.39 , clause( 7422, [ =( complement( intersection( complement( X ), complement(
% 0.75/1.39 Y ) ) ), union( X, Y ) ) ] )
% 0.75/1.39 , clause( 7423, [ =( intersection( complement( intersection( X, Y ) ),
% 0.75/1.39 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 0.75/1.39 'symmetric_difference'( X, Y ) ) ] )
% 0.75/1.39 , clause( 7424, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 0.75/1.39 X, Y, Z ) ) ] )
% 0.75/1.39 , clause( 7425, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 0.75/1.39 Z, X, Y ) ) ] )
% 0.75/1.39 , clause( 7426, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 0.75/1.39 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 0.75/1.39 , clause( 7427, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 0.75/1.39 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 0.75/1.39 'domain_of'( Y ) ) ] )
% 0.75/1.39 , clause( 7428, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.75/1.39 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.75/1.39 , clause( 7429, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.75/1.39 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 0.75/1.39 ] )
% 0.75/1.39 , clause( 7430, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.75/1.39 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 0.75/1.39 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.75/1.39 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 0.75/1.39 , Y ), rotate( T ) ) ] )
% 0.75/1.39 , clause( 7431, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.75/1.39 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.75/1.39 , clause( 7432, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.75/1.39 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 0.75/1.39 )
% 0.75/1.39 , clause( 7433, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.75/1.39 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 0.75/1.39 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.75/1.39 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 0.75/1.39 , Z ), flip( T ) ) ] )
% 0.75/1.39 , clause( 7434, [ =( 'domain_of'( flip( 'cross_product'( X,
% 0.75/1.39 'universal_class' ) ) ), inverse( X ) ) ] )
% 0.75/1.39 , clause( 7435, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 0.75/1.39 , clause( 7436, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 0.75/1.39 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 0.75/1.39 , clause( 7437, [ =( second( 'not_subclass_element'( restrict( X, singleton(
% 0.75/1.39 Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 0.75/1.39 , clause( 7438, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 0.75/1.39 image( X, Y ) ) ] )
% 0.75/1.39 , clause( 7439, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 0.75/1.39 , clause( 7440, [ subclass( 'successor_relation', 'cross_product'(
% 0.75/1.39 'universal_class', 'universal_class' ) ) ] )
% 0.75/1.39 , clause( 7441, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' )
% 0.75/1.39 ), =( successor( X ), Y ) ] )
% 0.75/1.39 , clause( 7442, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X
% 0.75/1.39 , Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 0.75/1.39 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 0.75/1.39 , clause( 7443, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 0.75/1.39 , clause( 7444, [ ~( inductive( X ) ), subclass( image(
% 0.75/1.39 'successor_relation', X ), X ) ] )
% 0.75/1.39 , clause( 7445, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.75/1.39 'successor_relation', X ), X ) ), inductive( X ) ] )
% 0.75/1.39 , clause( 7446, [ inductive( omega ) ] )
% 0.75/1.39 , clause( 7447, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 0.75/1.39 , clause( 7448, [ member( omega, 'universal_class' ) ] )
% 0.75/1.39 , clause( 7449, [ =( 'domain_of'( restrict( 'element_relation',
% 0.75/1.39 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 0.75/1.39 , clause( 7450, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 0.75/1.39 X ), 'universal_class' ) ] )
% 0.75/1.39 , clause( 7451, [ =( complement( image( 'element_relation', complement( X )
% 0.75/1.39 ) ), 'power_class'( X ) ) ] )
% 0.75/1.39 , clause( 7452, [ ~( member( X, 'universal_class' ) ), member(
% 0.75/1.39 'power_class'( X ), 'universal_class' ) ] )
% 0.75/1.39 , clause( 7453, [ subclass( compose( X, Y ), 'cross_product'(
% 0.75/1.39 'universal_class', 'universal_class' ) ) ] )
% 0.75/1.39 , clause( 7454, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 0.75/1.39 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 0.75/1.39 , clause( 7455, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 0.75/1.39 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.75/1.39 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.75/1.39 ) ] )
% 0.75/1.39 , clause( 7456, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 0.75/1.39 inverse( X ) ), 'identity_relation' ) ] )
% 0.75/1.39 , clause( 7457, [ ~( subclass( compose( X, inverse( X ) ),
% 0.75/1.39 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 0.75/1.39 , clause( 7458, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 0.75/1.39 'universal_class', 'universal_class' ) ) ] )
% 0.75/1.39 , clause( 7459, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 0.75/1.39 , 'identity_relation' ) ] )
% 0.75/1.39 , clause( 7460, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 0.75/1.39 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 0.75/1.39 'identity_relation' ) ), function( X ) ] )
% 0.75/1.39 , clause( 7461, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ),
% 0.75/1.39 member( image( X, Y ), 'universal_class' ) ] )
% 0.75/1.39 , clause( 7462, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.75/1.39 , clause( 7463, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 0.75/1.39 , 'null_class' ) ] )
% 0.75/1.39 , clause( 7464, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y
% 0.75/1.39 ) ) ] )
% 0.75/1.39 , clause( 7465, [ function( choice ) ] )
% 0.75/1.39 , clause( 7466, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' )
% 0.75/1.39 , member( apply( choice, X ), X ) ] )
% 0.75/1.39 , clause( 7467, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 0.75/1.39 , clause( 7468, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 0.75/1.39 , clause( 7469, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 0.75/1.39 'one_to_one'( X ) ] )
% 0.75/1.39 , clause( 7470, [ =( intersection( 'cross_product'( 'universal_class',
% 0.75/1.39 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 0.75/1.39 'universal_class' ), complement( compose( complement( 'element_relation'
% 0.75/1.39 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 0.75/1.39 , clause( 7471, [ =( intersection( inverse( 'subset_relation' ),
% 0.75/1.39 'subset_relation' ), 'identity_relation' ) ] )
% 0.75/1.39 , clause( 7472, [ =( complement( 'domain_of'( intersection( X,
% 0.75/1.39 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 0.75/1.39 , clause( 7473, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 0.75/1.39 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 0.75/1.39 , clause( 7474, [ ~( operation( X ) ), function( X ) ] )
% 0.75/1.39 , clause( 7475, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 0.75/1.39 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.75/1.39 ] )
% 0.75/1.39 , clause( 7476, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 0.75/1.39 'domain_of'( 'domain_of'( X ) ) ) ] )
% 0.75/1.39 , clause( 7477, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 0.75/1.39 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.75/1.39 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 0.75/1.39 operation( X ) ] )
% 0.75/1.39 , clause( 7478, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 0.75/1.39 , clause( 7479, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 0.75/1.39 Y ) ), 'domain_of'( X ) ) ] )
% 0.75/1.39 , clause( 7480, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 0.75/1.39 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 0.75/1.39 , clause( 7481, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) )
% 0.75/1.39 , 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 0.75/1.39 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 0.75/1.39 , clause( 7482, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 0.75/1.39 , clause( 7483, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 0.75/1.39 , clause( 7484, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 0.75/1.39 , clause( 7485, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 0.75/1.39 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 0.75/1.39 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 0.75/1.39 )
% 0.75/1.39 , clause( 7486, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 0.75/1.39 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.75/1.39 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.75/1.39 , Y ) ] )
% 0.75/1.39 , clause( 7487, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 0.75/1.39 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 0.75/1.39 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 0.75/1.39 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 0.75/1.39 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 0.75/1.39 )
% 0.75/1.39 , clause( 7488, [ subclass( 'compose_class'( X ), 'cross_product'(
% 0.75/1.39 'universal_class', 'universal_class' ) ) ] )
% 0.75/1.39 , clause( 7489, [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) )
% 0.75/1.39 ), =( compose( Z, X ), Y ) ] )
% 0.75/1.39 , clause( 7490, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.75/1.39 'universal_class', 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) )
% 0.75/1.39 , member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ] )
% 0.75/1.39 , clause( 7491, [ subclass( 'composition_function', 'cross_product'(
% 0.75/1.39 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 0.75/1.39 ) ) ) ] )
% 0.75/1.39 , clause( 7492, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.75/1.39 'composition_function' ) ), =( compose( X, Y ), Z ) ] )
% 0.75/1.39 , clause( 7493, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.75/1.39 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( X,
% 0.75/1.39 'ordered_pair'( Y, compose( X, Y ) ) ), 'composition_function' ) ] )
% 0.75/1.39 , clause( 7494, [ subclass( 'domain_relation', 'cross_product'(
% 0.75/1.39 'universal_class', 'universal_class' ) ) ] )
% 0.75/1.39 , clause( 7495, [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) )
% 0.75/1.39 , =( 'domain_of'( X ), Y ) ] )
% 0.75/1.39 , clause( 7496, [ ~( member( X, 'universal_class' ) ), member(
% 0.75/1.39 'ordered_pair'( X, 'domain_of'( X ) ), 'domain_relation' ) ] )
% 0.75/1.39 , clause( 7497, [ =( first( 'not_subclass_element'( compose( X, inverse( X
% 0.75/1.39 ) ), 'identity_relation' ) ), 'single_valued1'( X ) ) ] )
% 0.75/1.39 , clause( 7498, [ =( second( 'not_subclass_element'( compose( X, inverse( X
% 0.75/1.39 ) ), 'identity_relation' ) ), 'single_valued2'( X ) ) ] )
% 0.75/1.39 , clause( 7499, [ =( domain( X, image( inverse( X ), singleton(
% 0.75/1.39 'single_valued1'( X ) ) ), 'single_valued2'( X ) ), 'single_valued3'( X )
% 0.75/1.39 ) ] )
% 0.75/1.39 , clause( 7500, [ =( intersection( complement( compose( 'element_relation'
% 0.75/1.39 , complement( 'identity_relation' ) ) ), 'element_relation' ),
% 0.75/1.39 'singleton_relation' ) ] )
% 0.75/1.39 , clause( 7501, [ subclass( 'application_function', 'cross_product'(
% 0.75/1.39 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 0.75/1.39 ) ) ) ] )
% 0.75/1.39 , clause( 7502, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.75/1.39 'application_function' ) ), member( Y, 'domain_of'( X ) ) ] )
% 0.75/1.39 , clause( 7503, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.75/1.39 'application_function' ) ), =( apply( X, Y ), Z ) ] )
% 0.75/1.39 , clause( 7504, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.75/1.39 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 0.75/1.39 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 0.75/1.39 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 0.75/1.39 'application_function' ) ] )
% 0.75/1.39 , clause( 7505, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 0.75/1.39 , clause( 7506, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 0.75/1.39 , clause( 7507, [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ] )
% 0.75/1.39 , clause( 7508, [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ),
% 0.75/1.39 maps( X, 'domain_of'( X ), Y ) ] )
% 0.75/1.39 , clause( 7509, [ ~( =( complement( 'universal_class' ), 'null_class' ) ) ]
% 0.75/1.39 )
% 0.75/1.39 ] ).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 subsumption(
% 0.75/1.39 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.75/1.39 )
% 0.75/1.39 , clause( 7397, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 0.75/1.39 ) ] )
% 0.75/1.39 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.75/1.39 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 subsumption(
% 0.75/1.39 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 0.75/1.39 , clause( 7400, [ subclass( X, 'universal_class' ) ] )
% 0.75/1.39 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 subsumption(
% 0.75/1.39 clause( 22, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ] )
% 0.75/1.39 , clause( 7420, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 0.75/1.39 )
% 0.75/1.39 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.75/1.39 ), ==>( 1, 1 )] ) ).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 subsumption(
% 0.75/1.39 clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.75/1.39 , clause( 7462, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.75/1.39 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.75/1.39 1 )] ) ).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 subsumption(
% 0.75/1.39 clause( 111, [ ~( =( complement( 'universal_class' ), 'null_class' ) ) ] )
% 0.75/1.39 , clause( 7509, [ ~( =( complement( 'universal_class' ), 'null_class' ) ) ]
% 0.75/1.39 )
% 0.75/1.39 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 resolution(
% 0.75/1.39 clause( 7616, [ ~( member( Y, X ) ), member( Y, 'universal_class' ) ] )
% 0.75/1.39 , clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.75/1.39 )
% 0.75/1.39 , 0, clause( 3, [ subclass( X, 'universal_class' ) ] )
% 0.75/1.39 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'universal_class' ), :=( Z, Y )] )
% 0.75/1.39 , substitution( 1, [ :=( X, X )] )).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 subsumption(
% 0.75/1.39 clause( 127, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ] )
% 0.75/1.39 , clause( 7616, [ ~( member( Y, X ) ), member( Y, 'universal_class' ) ] )
% 0.75/1.39 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.75/1.39 ), ==>( 1, 1 )] ) ).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 resolution(
% 0.75/1.39 clause( 7617, [ ~( member( X, complement( 'universal_class' ) ) ), ~(
% 0.75/1.39 member( X, Y ) ) ] )
% 0.75/1.39 , clause( 22, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ] )
% 0.75/1.39 , 1, clause( 127, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ]
% 0.75/1.39 )
% 0.75/1.39 , 1, substitution( 0, [ :=( X, X ), :=( Y, 'universal_class' )] ),
% 0.75/1.39 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 subsumption(
% 0.75/1.39 clause( 1878, [ ~( member( X, complement( 'universal_class' ) ) ), ~(
% 0.75/1.39 member( X, Y ) ) ] )
% 0.75/1.39 , clause( 7617, [ ~( member( X, complement( 'universal_class' ) ) ), ~(
% 0.75/1.39 member( X, Y ) ) ] )
% 0.75/1.39 , substitution( 0, [ :=( X, X ), :=( Y, complement( 'universal_class' ) )] )
% 0.75/1.39 , permutation( 0, [ ==>( 0, 0 ), ==>( 1, 0 )] ) ).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 factor(
% 0.75/1.39 clause( 7619, [ ~( member( X, complement( 'universal_class' ) ) ) ] )
% 0.75/1.39 , clause( 1878, [ ~( member( X, complement( 'universal_class' ) ) ), ~(
% 0.75/1.39 member( X, Y ) ) ] )
% 0.75/1.39 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, complement( 'universal_class'
% 0.75/1.39 ) )] )).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 subsumption(
% 0.75/1.39 clause( 1902, [ ~( member( X, complement( 'universal_class' ) ) ) ] )
% 0.75/1.39 , clause( 7619, [ ~( member( X, complement( 'universal_class' ) ) ) ] )
% 0.75/1.39 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 eqswap(
% 0.75/1.39 clause( 7620, [ =( 'null_class', X ), member( regular( X ), X ) ] )
% 0.75/1.39 , clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.75/1.39 , 0, substitution( 0, [ :=( X, X )] )).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 resolution(
% 0.75/1.39 clause( 7621, [ =( 'null_class', complement( 'universal_class' ) ) ] )
% 0.75/1.39 , clause( 1902, [ ~( member( X, complement( 'universal_class' ) ) ) ] )
% 0.75/1.39 , 0, clause( 7620, [ =( 'null_class', X ), member( regular( X ), X ) ] )
% 0.75/1.39 , 1, substitution( 0, [ :=( X, regular( complement( 'universal_class' ) ) )] )
% 0.75/1.39 , substitution( 1, [ :=( X, complement( 'universal_class' ) )] )).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 eqswap(
% 0.75/1.39 clause( 7622, [ =( complement( 'universal_class' ), 'null_class' ) ] )
% 0.75/1.39 , clause( 7621, [ =( 'null_class', complement( 'universal_class' ) ) ] )
% 0.75/1.39 , 0, substitution( 0, [] )).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 subsumption(
% 0.75/1.39 clause( 6807, [ =( complement( 'universal_class' ), 'null_class' ) ] )
% 0.75/1.39 , clause( 7622, [ =( complement( 'universal_class' ), 'null_class' ) ] )
% 0.75/1.39 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 paramod(
% 0.75/1.39 clause( 7625, [ ~( =( 'null_class', 'null_class' ) ) ] )
% 0.75/1.39 , clause( 6807, [ =( complement( 'universal_class' ), 'null_class' ) ] )
% 0.75/1.39 , 0, clause( 111, [ ~( =( complement( 'universal_class' ), 'null_class' ) )
% 0.75/1.39 ] )
% 0.75/1.39 , 0, 2, substitution( 0, [] ), substitution( 1, [] )).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 eqrefl(
% 0.75/1.39 clause( 7626, [] )
% 0.75/1.39 , clause( 7625, [ ~( =( 'null_class', 'null_class' ) ) ] )
% 0.75/1.39 , 0, substitution( 0, [] )).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 subsumption(
% 0.75/1.39 clause( 7395, [] )
% 0.75/1.39 , clause( 7626, [] )
% 0.75/1.39 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 end.
% 0.75/1.39
% 0.75/1.39 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.75/1.39
% 0.75/1.39 Memory use:
% 0.75/1.39
% 0.75/1.39 space for terms: 110082
% 0.75/1.39 space for clauses: 345570
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 clauses generated: 15924
% 0.75/1.39 clauses kept: 7396
% 0.75/1.39 clauses selected: 270
% 0.75/1.39 clauses deleted: 84
% 0.75/1.39 clauses inuse deleted: 68
% 0.75/1.39
% 0.75/1.39 subsentry: 37472
% 0.75/1.39 literals s-matched: 29189
% 0.75/1.39 literals matched: 28757
% 0.75/1.39 full subsumption: 13361
% 0.75/1.39
% 0.75/1.39 checksum: -1761720887
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 Bliksem ended
%------------------------------------------------------------------------------