TSTP Solution File: SET197-6 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET197-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n012.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 22:48:03 EDT 2022
% Result : Unsatisfiable 3.06s 3.47s
% Output : Refutation 3.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET197-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.15 % Command : bliksem %s
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Mon Jul 11 03:03:28 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.49/1.17 *** allocated 10000 integers for termspace/termends
% 0.49/1.17 *** allocated 10000 integers for clauses
% 0.49/1.17 *** allocated 10000 integers for justifications
% 0.49/1.17 Bliksem 1.12
% 0.49/1.17
% 0.49/1.17
% 0.49/1.17 Automatic Strategy Selection
% 0.49/1.17
% 0.49/1.17 Clauses:
% 0.49/1.17 [
% 0.49/1.17 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.49/1.17 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.49/1.17 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.49/1.17 ,
% 0.49/1.17 [ subclass( X, 'universal_class' ) ],
% 0.49/1.17 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.49/1.17 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.49/1.17 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.49/1.17 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.49/1.17 ,
% 0.49/1.17 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.49/1.17 ) ) ],
% 0.49/1.17 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.49/1.17 ) ) ],
% 0.49/1.17 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.49/1.17 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.49/1.17 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.49/1.17 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.49/1.17 X, Z ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.49/1.17 Y, T ) ],
% 0.49/1.17 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.49/1.17 ), 'cross_product'( Y, T ) ) ],
% 0.49/1.17 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.49/1.17 ), second( X ) ), X ) ],
% 0.49/1.17 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.49/1.17 'universal_class' ) ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.49/1.17 Y ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.49/1.17 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.49/1.17 , Y ), 'element_relation' ) ],
% 0.49/1.17 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.49/1.17 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.49/1.17 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.49/1.17 Z ) ) ],
% 0.49/1.17 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.49/1.17 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.49/1.17 member( X, Y ) ],
% 0.49/1.17 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.49/1.17 union( X, Y ) ) ],
% 0.49/1.17 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.49/1.17 intersection( complement( X ), complement( Y ) ) ) ),
% 0.49/1.17 'symmetric_difference'( X, Y ) ) ],
% 0.49/1.17 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.49/1.17 ,
% 0.49/1.17 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.49/1.17 ,
% 0.49/1.17 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.49/1.17 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.49/1.17 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.49/1.17 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.49/1.17 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.49/1.17 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.49/1.17 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.49/1.17 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.49/1.17 'cross_product'( 'universal_class', 'universal_class' ),
% 0.49/1.17 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.49/1.17 Y ), rotate( T ) ) ],
% 0.49/1.17 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.49/1.17 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.49/1.17 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.49/1.17 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.49/1.17 'cross_product'( 'universal_class', 'universal_class' ),
% 0.49/1.17 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.49/1.17 Z ), flip( T ) ) ],
% 0.49/1.17 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.49/1.17 inverse( X ) ) ],
% 0.49/1.17 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.49/1.17 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.49/1.17 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.49/1.17 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.49/1.17 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.49/1.17 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.49/1.17 ],
% 0.49/1.17 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.49/1.17 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.49/1.17 'universal_class' ) ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.49/1.17 successor( X ), Y ) ],
% 0.49/1.17 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.49/1.17 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.49/1.17 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.49/1.17 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.49/1.17 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.49/1.17 ,
% 0.49/1.17 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.49/1.17 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.49/1.17 [ inductive( omega ) ],
% 0.49/1.17 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.49/1.17 [ member( omega, 'universal_class' ) ],
% 0.49/1.17 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.49/1.17 , 'sum_class'( X ) ) ],
% 0.49/1.17 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.49/1.17 'universal_class' ) ],
% 0.49/1.17 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.49/1.17 'power_class'( X ) ) ],
% 0.49/1.17 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.49/1.17 'universal_class' ) ],
% 0.49/1.17 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.49/1.17 'universal_class' ) ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.49/1.17 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.49/1.17 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.49/1.17 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.49/1.17 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.49/1.17 ) ],
% 0.49/1.17 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.49/1.17 , 'identity_relation' ) ],
% 0.49/1.17 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.49/1.17 'single_valued_class'( X ) ],
% 0.49/1.17 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.49/1.17 'universal_class' ) ) ],
% 0.49/1.17 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.49/1.17 'identity_relation' ) ],
% 0.49/1.17 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.49/1.17 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.49/1.17 , function( X ) ],
% 0.49/1.17 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.49/1.17 X, Y ), 'universal_class' ) ],
% 0.49/1.17 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.49/1.17 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.49/1.17 ) ],
% 0.49/1.17 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.49/1.17 [ function( choice ) ],
% 0.49/1.17 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.49/1.17 apply( choice, X ), X ) ],
% 0.49/1.17 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.49/1.17 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.49/1.17 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.49/1.17 ,
% 0.49/1.17 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.49/1.17 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.49/1.17 , complement( compose( complement( 'element_relation' ), inverse(
% 0.49/1.17 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.49/1.17 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.49/1.17 'identity_relation' ) ],
% 0.49/1.17 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.49/1.17 , diagonalise( X ) ) ],
% 0.49/1.17 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.49/1.17 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.49/1.17 [ ~( operation( X ) ), function( X ) ],
% 0.49/1.17 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.49/1.17 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.49/1.17 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.49/1.17 'domain_of'( X ) ) ) ],
% 0.49/1.17 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.49/1.17 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.49/1.17 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.49/1.17 X ) ],
% 0.49/1.17 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.49/1.17 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.49/1.17 'domain_of'( X ) ) ],
% 0.49/1.17 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.49/1.17 'domain_of'( Z ) ) ) ],
% 0.49/1.17 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.49/1.17 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.49/1.17 ), compatible( X, Y, Z ) ],
% 0.49/1.17 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.49/1.17 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.49/1.17 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.49/1.17 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.49/1.17 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.49/1.17 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.49/1.17 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.49/1.17 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.49/1.17 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.49/1.17 , Y ) ],
% 0.49/1.17 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.49/1.17 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.49/1.17 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.49/1.17 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.49/1.17 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.49/1.17 [ subclass( 'compose_class'( X ), 'cross_product'( 'universal_class',
% 0.49/1.17 'universal_class' ) ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ), =(
% 0.49/1.17 compose( Z, X ), Y ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.49/1.17 , 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) ), member(
% 0.49/1.17 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ],
% 0.49/1.17 [ subclass( 'composition_function', 'cross_product'( 'universal_class',
% 0.49/1.17 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.49/1.17 'composition_function' ) ), =( compose( X, Y ), Z ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.49/1.17 , 'universal_class' ) ) ), member( 'ordered_pair'( X, 'ordered_pair'( Y,
% 0.49/1.17 compose( X, Y ) ) ), 'composition_function' ) ],
% 0.49/1.17 [ subclass( 'domain_relation', 'cross_product'( 'universal_class',
% 0.49/1.17 'universal_class' ) ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) ), =(
% 0.49/1.17 'domain_of'( X ), Y ) ],
% 0.49/1.17 [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X,
% 0.49/1.17 'domain_of'( X ) ), 'domain_relation' ) ],
% 0.49/1.17 [ =( first( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.49/1.17 'identity_relation' ) ), 'single_valued1'( X ) ) ],
% 0.49/1.17 [ =( second( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.49/1.17 'identity_relation' ) ), 'single_valued2'( X ) ) ],
% 0.49/1.17 [ =( domain( X, image( inverse( X ), singleton( 'single_valued1'( X ) )
% 0.49/1.17 ), 'single_valued2'( X ) ), 'single_valued3'( X ) ) ],
% 0.49/1.17 [ =( intersection( complement( compose( 'element_relation', complement(
% 0.49/1.17 'identity_relation' ) ) ), 'element_relation' ), 'singleton_relation' ) ]
% 0.49/1.17 ,
% 0.49/1.17 [ subclass( 'application_function', 'cross_product'( 'universal_class',
% 0.49/1.17 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.49/1.17 'application_function' ) ), member( Y, 'domain_of'( X ) ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.49/1.17 'application_function' ) ), =( apply( X, Y ), Z ) ],
% 0.49/1.17 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.49/1.17 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 0.49/1.17 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 0.49/1.17 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 0.49/1.17 'application_function' ) ],
% 0.49/1.17 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.49/1.17 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 3.06/3.47 [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ],
% 3.06/3.47 [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ), maps( X,
% 3.06/3.47 'domain_of'( X ), Y ) ],
% 3.06/3.47 [ ~( subclass( intersection( x, y ), y ) ) ]
% 3.06/3.47 ] .
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 percentage equality = 0.223744, percentage horn = 0.929204
% 3.06/3.47 This is a problem with some equality
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 Options Used:
% 3.06/3.47
% 3.06/3.47 useres = 1
% 3.06/3.47 useparamod = 1
% 3.06/3.47 useeqrefl = 1
% 3.06/3.47 useeqfact = 1
% 3.06/3.47 usefactor = 1
% 3.06/3.47 usesimpsplitting = 0
% 3.06/3.47 usesimpdemod = 5
% 3.06/3.47 usesimpres = 3
% 3.06/3.47
% 3.06/3.47 resimpinuse = 1000
% 3.06/3.47 resimpclauses = 20000
% 3.06/3.47 substype = eqrewr
% 3.06/3.47 backwardsubs = 1
% 3.06/3.47 selectoldest = 5
% 3.06/3.47
% 3.06/3.47 litorderings [0] = split
% 3.06/3.47 litorderings [1] = extend the termordering, first sorting on arguments
% 3.06/3.47
% 3.06/3.47 termordering = kbo
% 3.06/3.47
% 3.06/3.47 litapriori = 0
% 3.06/3.47 termapriori = 1
% 3.06/3.47 litaposteriori = 0
% 3.06/3.47 termaposteriori = 0
% 3.06/3.47 demodaposteriori = 0
% 3.06/3.47 ordereqreflfact = 0
% 3.06/3.47
% 3.06/3.47 litselect = negord
% 3.06/3.47
% 3.06/3.47 maxweight = 15
% 3.06/3.47 maxdepth = 30000
% 3.06/3.47 maxlength = 115
% 3.06/3.47 maxnrvars = 195
% 3.06/3.47 excuselevel = 1
% 3.06/3.47 increasemaxweight = 1
% 3.06/3.47
% 3.06/3.47 maxselected = 10000000
% 3.06/3.47 maxnrclauses = 10000000
% 3.06/3.47
% 3.06/3.47 showgenerated = 0
% 3.06/3.47 showkept = 0
% 3.06/3.47 showselected = 0
% 3.06/3.47 showdeleted = 0
% 3.06/3.47 showresimp = 1
% 3.06/3.47 showstatus = 2000
% 3.06/3.47
% 3.06/3.47 prologoutput = 1
% 3.06/3.47 nrgoals = 5000000
% 3.06/3.47 totalproof = 1
% 3.06/3.47
% 3.06/3.47 Symbols occurring in the translation:
% 3.06/3.47
% 3.06/3.47 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 3.06/3.47 . [1, 2] (w:1, o:64, a:1, s:1, b:0),
% 3.06/3.47 ! [4, 1] (w:0, o:35, a:1, s:1, b:0),
% 3.06/3.47 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.06/3.47 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.06/3.47 subclass [41, 2] (w:1, o:89, a:1, s:1, b:0),
% 3.06/3.47 member [43, 2] (w:1, o:90, a:1, s:1, b:0),
% 3.06/3.47 'not_subclass_element' [44, 2] (w:1, o:91, a:1, s:1, b:0),
% 3.06/3.47 'universal_class' [45, 0] (w:1, o:22, a:1, s:1, b:0),
% 3.06/3.47 'unordered_pair' [46, 2] (w:1, o:92, a:1, s:1, b:0),
% 3.06/3.47 singleton [47, 1] (w:1, o:43, a:1, s:1, b:0),
% 3.06/3.47 'ordered_pair' [48, 2] (w:1, o:93, a:1, s:1, b:0),
% 3.06/3.47 'cross_product' [50, 2] (w:1, o:94, a:1, s:1, b:0),
% 3.06/3.47 first [52, 1] (w:1, o:44, a:1, s:1, b:0),
% 3.06/3.47 second [53, 1] (w:1, o:45, a:1, s:1, b:0),
% 3.06/3.47 'element_relation' [54, 0] (w:1, o:27, a:1, s:1, b:0),
% 3.06/3.47 intersection [55, 2] (w:1, o:96, a:1, s:1, b:0),
% 3.06/3.47 complement [56, 1] (w:1, o:46, a:1, s:1, b:0),
% 3.06/3.47 union [57, 2] (w:1, o:97, a:1, s:1, b:0),
% 3.06/3.47 'symmetric_difference' [58, 2] (w:1, o:98, a:1, s:1, b:0),
% 3.06/3.47 restrict [60, 3] (w:1, o:101, a:1, s:1, b:0),
% 3.06/3.47 'null_class' [61, 0] (w:1, o:28, a:1, s:1, b:0),
% 3.06/3.47 'domain_of' [62, 1] (w:1, o:49, a:1, s:1, b:0),
% 3.06/3.47 rotate [63, 1] (w:1, o:40, a:1, s:1, b:0),
% 3.06/3.47 flip [65, 1] (w:1, o:50, a:1, s:1, b:0),
% 3.06/3.47 inverse [66, 1] (w:1, o:51, a:1, s:1, b:0),
% 3.06/3.47 'range_of' [67, 1] (w:1, o:41, a:1, s:1, b:0),
% 3.06/3.47 domain [68, 3] (w:1, o:103, a:1, s:1, b:0),
% 3.06/3.47 range [69, 3] (w:1, o:104, a:1, s:1, b:0),
% 3.06/3.47 image [70, 2] (w:1, o:95, a:1, s:1, b:0),
% 3.06/3.47 successor [71, 1] (w:1, o:52, a:1, s:1, b:0),
% 3.06/3.47 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 3.06/3.47 inductive [73, 1] (w:1, o:53, a:1, s:1, b:0),
% 3.06/3.47 omega [74, 0] (w:1, o:10, a:1, s:1, b:0),
% 3.06/3.47 'sum_class' [75, 1] (w:1, o:54, a:1, s:1, b:0),
% 3.06/3.47 'power_class' [76, 1] (w:1, o:57, a:1, s:1, b:0),
% 3.06/3.47 compose [78, 2] (w:1, o:99, a:1, s:1, b:0),
% 3.06/3.47 'single_valued_class' [79, 1] (w:1, o:58, a:1, s:1, b:0),
% 3.06/3.47 'identity_relation' [80, 0] (w:1, o:29, a:1, s:1, b:0),
% 3.06/3.47 function [82, 1] (w:1, o:59, a:1, s:1, b:0),
% 3.06/3.47 regular [83, 1] (w:1, o:42, a:1, s:1, b:0),
% 3.06/3.47 apply [84, 2] (w:1, o:100, a:1, s:1, b:0),
% 3.06/3.47 choice [85, 0] (w:1, o:30, a:1, s:1, b:0),
% 3.06/3.47 'one_to_one' [86, 1] (w:1, o:55, a:1, s:1, b:0),
% 3.06/3.47 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 3.06/3.47 diagonalise [88, 1] (w:1, o:60, a:1, s:1, b:0),
% 3.06/3.47 cantor [89, 1] (w:1, o:47, a:1, s:1, b:0),
% 3.06/3.47 operation [90, 1] (w:1, o:56, a:1, s:1, b:0),
% 3.06/3.47 compatible [94, 3] (w:1, o:102, a:1, s:1, b:0),
% 3.06/3.47 homomorphism [95, 3] (w:1, o:105, a:1, s:1, b:0),
% 3.06/3.47 'not_homomorphism1' [96, 3] (w:1, o:107, a:1, s:1, b:0),
% 3.06/3.47 'not_homomorphism2' [97, 3] (w:1, o:108, a:1, s:1, b:0),
% 3.06/3.47 'compose_class' [98, 1] (w:1, o:48, a:1, s:1, b:0),
% 3.06/3.47 'composition_function' [99, 0] (w:1, o:31, a:1, s:1, b:0),
% 3.06/3.47 'domain_relation' [100, 0] (w:1, o:26, a:1, s:1, b:0),
% 3.06/3.47 'single_valued1' [101, 1] (w:1, o:61, a:1, s:1, b:0),
% 3.06/3.47 'single_valued2' [102, 1] (w:1, o:62, a:1, s:1, b:0),
% 3.06/3.47 'single_valued3' [103, 1] (w:1, o:63, a:1, s:1, b:0),
% 3.06/3.47 'singleton_relation' [104, 0] (w:1, o:7, a:1, s:1, b:0),
% 3.06/3.47 'application_function' [105, 0] (w:1, o:32, a:1, s:1, b:0),
% 3.06/3.47 maps [106, 3] (w:1, o:106, a:1, s:1, b:0),
% 3.06/3.47 x [107, 0] (w:1, o:33, a:1, s:1, b:0),
% 3.06/3.47 y [108, 0] (w:1, o:34, a:1, s:1, b:0).
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 Starting Search:
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 Intermediate Status:
% 3.06/3.47 Generated: 4597
% 3.06/3.47 Kept: 2005
% 3.06/3.47 Inuse: 111
% 3.06/3.47 Deleted: 4
% 3.06/3.47 Deletedinuse: 2
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 Intermediate Status:
% 3.06/3.47 Generated: 9166
% 3.06/3.47 Kept: 4017
% 3.06/3.47 Inuse: 183
% 3.06/3.47 Deleted: 13
% 3.06/3.47 Deletedinuse: 5
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 Intermediate Status:
% 3.06/3.47 Generated: 13053
% 3.06/3.47 Kept: 6064
% 3.06/3.47 Inuse: 236
% 3.06/3.47 Deleted: 20
% 3.06/3.47 Deletedinuse: 10
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 Intermediate Status:
% 3.06/3.47 Generated: 18118
% 3.06/3.47 Kept: 8239
% 3.06/3.47 Inuse: 289
% 3.06/3.47 Deleted: 80
% 3.06/3.47 Deletedinuse: 68
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 Intermediate Status:
% 3.06/3.47 Generated: 23961
% 3.06/3.47 Kept: 10765
% 3.06/3.47 Inuse: 366
% 3.06/3.47 Deleted: 89
% 3.06/3.47 Deletedinuse: 74
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 Intermediate Status:
% 3.06/3.47 Generated: 27500
% 3.06/3.47 Kept: 12768
% 3.06/3.47 Inuse: 394
% 3.06/3.47 Deleted: 94
% 3.06/3.47 Deletedinuse: 79
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 Intermediate Status:
% 3.06/3.47 Generated: 31513
% 3.06/3.47 Kept: 14909
% 3.06/3.47 Inuse: 431
% 3.06/3.47 Deleted: 95
% 3.06/3.47 Deletedinuse: 80
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 Intermediate Status:
% 3.06/3.47 Generated: 36690
% 3.06/3.47 Kept: 18218
% 3.06/3.47 Inuse: 456
% 3.06/3.47 Deleted: 95
% 3.06/3.47 Deletedinuse: 80
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 Intermediate Status:
% 3.06/3.47 Generated: 44843
% 3.06/3.47 Kept: 21171
% 3.06/3.47 Inuse: 466
% 3.06/3.47 Deleted: 96
% 3.06/3.47 Deletedinuse: 81
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47 Resimplifying clauses:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 Intermediate Status:
% 3.06/3.47 Generated: 50112
% 3.06/3.47 Kept: 23191
% 3.06/3.47 Inuse: 510
% 3.06/3.47 Deleted: 3338
% 3.06/3.47 Deletedinuse: 81
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47 Resimplifying inuse:
% 3.06/3.47 Done
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 Bliksems!, er is een bewijs:
% 3.06/3.47 % SZS status Unsatisfiable
% 3.06/3.47 % SZS output start Refutation
% 3.06/3.47
% 3.06/3.47 clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y )
% 3.06/3.47 ] )
% 3.06/3.47 .
% 3.06/3.47 clause( 2, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X
% 3.06/3.47 , Y ) ] )
% 3.06/3.47 .
% 3.06/3.47 clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 3.06/3.47 .
% 3.06/3.47 clause( 111, [ ~( subclass( intersection( x, y ), y ) ) ] )
% 3.06/3.47 .
% 3.06/3.47 clause( 135, [ member( 'not_subclass_element'( intersection( x, y ), y ),
% 3.06/3.47 intersection( x, y ) ) ] )
% 3.06/3.47 .
% 3.06/3.47 clause( 137, [ ~( member( 'not_subclass_element'( intersection( x, y ), y )
% 3.06/3.47 , y ) ) ] )
% 3.06/3.47 .
% 3.06/3.47 clause( 24773, [] )
% 3.06/3.47 .
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 % SZS output end Refutation
% 3.06/3.47 found a proof!
% 3.06/3.47
% 3.06/3.47 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 3.06/3.47
% 3.06/3.47 initialclauses(
% 3.06/3.47 [ clause( 24775, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 3.06/3.47 ) ] )
% 3.06/3.47 , clause( 24776, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 3.06/3.47 , Y ) ] )
% 3.06/3.47 , clause( 24777, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 3.06/3.47 subclass( X, Y ) ] )
% 3.06/3.47 , clause( 24778, [ subclass( X, 'universal_class' ) ] )
% 3.06/3.47 , clause( 24779, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 3.06/3.47 , clause( 24780, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 3.06/3.47 , clause( 24781, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 3.06/3.47 ] )
% 3.06/3.47 , clause( 24782, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 3.06/3.47 =( X, Z ) ] )
% 3.06/3.47 , clause( 24783, [ ~( member( X, 'universal_class' ) ), member( X,
% 3.06/3.47 'unordered_pair'( X, Y ) ) ] )
% 3.06/3.47 , clause( 24784, [ ~( member( X, 'universal_class' ) ), member( X,
% 3.06/3.47 'unordered_pair'( Y, X ) ) ] )
% 3.06/3.47 , clause( 24785, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 3.06/3.47 )
% 3.06/3.47 , clause( 24786, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 3.06/3.47 , clause( 24787, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 3.06/3.47 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 3.06/3.47 , clause( 24788, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 3.06/3.47 ) ) ), member( X, Z ) ] )
% 3.06/3.47 , clause( 24789, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 3.06/3.47 ) ) ), member( Y, T ) ] )
% 3.06/3.47 , clause( 24790, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 3.06/3.47 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 3.06/3.47 , clause( 24791, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 3.06/3.47 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 3.06/3.47 , clause( 24792, [ subclass( 'element_relation', 'cross_product'(
% 3.06/3.47 'universal_class', 'universal_class' ) ) ] )
% 3.06/3.47 , clause( 24793, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 3.06/3.47 ), member( X, Y ) ] )
% 3.06/3.47 , clause( 24794, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 3.06/3.47 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 3.06/3.47 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 3.06/3.47 , clause( 24795, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 3.06/3.47 )
% 3.06/3.47 , clause( 24796, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 3.06/3.47 )
% 3.06/3.47 , clause( 24797, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 3.06/3.47 intersection( Y, Z ) ) ] )
% 3.06/3.47 , clause( 24798, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 3.06/3.47 )
% 3.06/3.47 , clause( 24799, [ ~( member( X, 'universal_class' ) ), member( X,
% 3.06/3.47 complement( Y ) ), member( X, Y ) ] )
% 3.06/3.47 , clause( 24800, [ =( complement( intersection( complement( X ), complement(
% 3.06/3.47 Y ) ) ), union( X, Y ) ) ] )
% 3.06/3.47 , clause( 24801, [ =( intersection( complement( intersection( X, Y ) ),
% 3.06/3.47 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 3.06/3.47 'symmetric_difference'( X, Y ) ) ] )
% 3.06/3.47 , clause( 24802, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 3.06/3.47 X, Y, Z ) ) ] )
% 3.06/3.47 , clause( 24803, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 3.06/3.47 Z, X, Y ) ) ] )
% 3.06/3.47 , clause( 24804, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 3.06/3.47 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 3.06/3.47 , clause( 24805, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 3.06/3.47 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 3.06/3.47 'domain_of'( Y ) ) ] )
% 3.06/3.47 , clause( 24806, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 3.06/3.47 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 3.06/3.47 , clause( 24807, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 3.06/3.47 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 3.06/3.47 ] )
% 3.06/3.47 , clause( 24808, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 3.06/3.47 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 3.06/3.47 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 3.06/3.47 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 3.06/3.47 , Y ), rotate( T ) ) ] )
% 3.06/3.47 , clause( 24809, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 3.06/3.47 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 3.06/3.47 , clause( 24810, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 3.06/3.47 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 3.06/3.47 )
% 3.06/3.47 , clause( 24811, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 3.06/3.47 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 3.06/3.47 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 3.06/3.47 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 3.06/3.47 , Z ), flip( T ) ) ] )
% 3.06/3.47 , clause( 24812, [ =( 'domain_of'( flip( 'cross_product'( X,
% 3.06/3.47 'universal_class' ) ) ), inverse( X ) ) ] )
% 3.06/3.47 , clause( 24813, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 3.06/3.47 , clause( 24814, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 3.06/3.47 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 3.06/3.47 , clause( 24815, [ =( second( 'not_subclass_element'( restrict( X,
% 3.06/3.47 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 3.06/3.47 , clause( 24816, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 3.06/3.47 image( X, Y ) ) ] )
% 3.06/3.47 , clause( 24817, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 3.06/3.47 , clause( 24818, [ subclass( 'successor_relation', 'cross_product'(
% 3.06/3.47 'universal_class', 'universal_class' ) ) ] )
% 3.06/3.47 , clause( 24819, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 3.06/3.47 ) ), =( successor( X ), Y ) ] )
% 3.06/3.47 , clause( 24820, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 3.06/3.47 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 3.06/3.47 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 3.06/3.47 , clause( 24821, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 3.06/3.47 , clause( 24822, [ ~( inductive( X ) ), subclass( image(
% 3.06/3.47 'successor_relation', X ), X ) ] )
% 3.06/3.47 , clause( 24823, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 3.06/3.47 'successor_relation', X ), X ) ), inductive( X ) ] )
% 3.06/3.47 , clause( 24824, [ inductive( omega ) ] )
% 3.06/3.47 , clause( 24825, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 3.06/3.47 , clause( 24826, [ member( omega, 'universal_class' ) ] )
% 3.06/3.47 , clause( 24827, [ =( 'domain_of'( restrict( 'element_relation',
% 3.06/3.47 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 3.06/3.47 , clause( 24828, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 3.06/3.47 X ), 'universal_class' ) ] )
% 3.06/3.47 , clause( 24829, [ =( complement( image( 'element_relation', complement( X
% 3.06/3.47 ) ) ), 'power_class'( X ) ) ] )
% 3.06/3.47 , clause( 24830, [ ~( member( X, 'universal_class' ) ), member(
% 3.06/3.47 'power_class'( X ), 'universal_class' ) ] )
% 3.06/3.47 , clause( 24831, [ subclass( compose( X, Y ), 'cross_product'(
% 3.06/3.47 'universal_class', 'universal_class' ) ) ] )
% 3.06/3.47 , clause( 24832, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 3.06/3.47 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 3.06/3.47 , clause( 24833, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 3.06/3.47 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 3.06/3.47 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 3.06/3.47 ) ] )
% 3.06/3.47 , clause( 24834, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 3.06/3.47 inverse( X ) ), 'identity_relation' ) ] )
% 3.06/3.47 , clause( 24835, [ ~( subclass( compose( X, inverse( X ) ),
% 3.06/3.47 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 3.06/3.47 , clause( 24836, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 3.06/3.47 'universal_class', 'universal_class' ) ) ] )
% 3.06/3.47 , clause( 24837, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 3.06/3.47 , 'identity_relation' ) ] )
% 3.06/3.47 , clause( 24838, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 3.06/3.47 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 3.06/3.47 'identity_relation' ) ), function( X ) ] )
% 3.06/3.47 , clause( 24839, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 3.06/3.47 , member( image( X, Y ), 'universal_class' ) ] )
% 3.06/3.47 , clause( 24840, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 3.06/3.47 , clause( 24841, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 3.06/3.47 , 'null_class' ) ] )
% 3.06/3.47 , clause( 24842, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 3.06/3.47 Y ) ) ] )
% 3.06/3.47 , clause( 24843, [ function( choice ) ] )
% 3.06/3.47 , clause( 24844, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 3.06/3.47 ), member( apply( choice, X ), X ) ] )
% 3.06/3.47 , clause( 24845, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 3.06/3.47 , clause( 24846, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 3.06/3.47 , clause( 24847, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 3.06/3.47 'one_to_one'( X ) ] )
% 3.06/3.47 , clause( 24848, [ =( intersection( 'cross_product'( 'universal_class',
% 3.06/3.47 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 3.06/3.47 'universal_class' ), complement( compose( complement( 'element_relation'
% 3.06/3.47 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 3.06/3.47 , clause( 24849, [ =( intersection( inverse( 'subset_relation' ),
% 3.06/3.47 'subset_relation' ), 'identity_relation' ) ] )
% 3.06/3.47 , clause( 24850, [ =( complement( 'domain_of'( intersection( X,
% 3.06/3.47 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 3.06/3.47 , clause( 24851, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 3.06/3.47 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 3.06/3.47 , clause( 24852, [ ~( operation( X ) ), function( X ) ] )
% 3.06/3.47 , clause( 24853, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 3.06/3.47 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 3.06/3.47 ] )
% 3.06/3.47 , clause( 24854, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 3.06/3.47 'domain_of'( 'domain_of'( X ) ) ) ] )
% 3.06/3.47 , clause( 24855, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 3.06/3.47 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 3.06/3.47 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 3.06/3.47 operation( X ) ] )
% 3.06/3.47 , clause( 24856, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 3.06/3.47 , clause( 24857, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 3.06/3.47 Y ) ), 'domain_of'( X ) ) ] )
% 3.06/3.47 , clause( 24858, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 3.06/3.47 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 3.06/3.47 , clause( 24859, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 3.06/3.47 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 3.06/3.47 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 3.06/3.47 , clause( 24860, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 3.06/3.47 , clause( 24861, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 3.06/3.47 , clause( 24862, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 3.06/3.47 , clause( 24863, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 3.06/3.47 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 3.06/3.47 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 3.06/3.47 )
% 3.06/3.47 , clause( 24864, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 3.06/3.47 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 3.06/3.47 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 3.06/3.47 , Y ) ] )
% 3.06/3.47 , clause( 24865, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 3.06/3.47 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 3.06/3.47 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 3.06/3.47 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 3.06/3.47 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 3.06/3.47 )
% 3.06/3.47 , clause( 24866, [ subclass( 'compose_class'( X ), 'cross_product'(
% 3.06/3.47 'universal_class', 'universal_class' ) ) ] )
% 3.06/3.47 , clause( 24867, [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z )
% 3.06/3.47 ) ), =( compose( Z, X ), Y ) ] )
% 3.06/3.47 , clause( 24868, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 3.06/3.47 'universal_class', 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) )
% 3.06/3.47 , member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ] )
% 3.06/3.47 , clause( 24869, [ subclass( 'composition_function', 'cross_product'(
% 3.06/3.47 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 3.06/3.47 ) ) ) ] )
% 3.06/3.47 , clause( 24870, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 3.06/3.47 'composition_function' ) ), =( compose( X, Y ), Z ) ] )
% 3.06/3.47 , clause( 24871, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 3.06/3.47 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( X,
% 3.06/3.47 'ordered_pair'( Y, compose( X, Y ) ) ), 'composition_function' ) ] )
% 3.06/3.47 , clause( 24872, [ subclass( 'domain_relation', 'cross_product'(
% 3.06/3.47 'universal_class', 'universal_class' ) ) ] )
% 3.06/3.47 , clause( 24873, [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) )
% 3.06/3.47 , =( 'domain_of'( X ), Y ) ] )
% 3.06/3.47 , clause( 24874, [ ~( member( X, 'universal_class' ) ), member(
% 3.06/3.47 'ordered_pair'( X, 'domain_of'( X ) ), 'domain_relation' ) ] )
% 3.06/3.47 , clause( 24875, [ =( first( 'not_subclass_element'( compose( X, inverse( X
% 3.06/3.47 ) ), 'identity_relation' ) ), 'single_valued1'( X ) ) ] )
% 3.06/3.47 , clause( 24876, [ =( second( 'not_subclass_element'( compose( X, inverse(
% 3.06/3.47 X ) ), 'identity_relation' ) ), 'single_valued2'( X ) ) ] )
% 3.06/3.47 , clause( 24877, [ =( domain( X, image( inverse( X ), singleton(
% 3.06/3.47 'single_valued1'( X ) ) ), 'single_valued2'( X ) ), 'single_valued3'( X )
% 3.06/3.47 ) ] )
% 3.06/3.47 , clause( 24878, [ =( intersection( complement( compose( 'element_relation'
% 3.06/3.47 , complement( 'identity_relation' ) ) ), 'element_relation' ),
% 3.06/3.47 'singleton_relation' ) ] )
% 3.06/3.47 , clause( 24879, [ subclass( 'application_function', 'cross_product'(
% 3.06/3.47 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 3.06/3.47 ) ) ) ] )
% 3.06/3.47 , clause( 24880, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 3.06/3.47 'application_function' ) ), member( Y, 'domain_of'( X ) ) ] )
% 3.06/3.47 , clause( 24881, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 3.06/3.47 'application_function' ) ), =( apply( X, Y ), Z ) ] )
% 3.06/3.47 , clause( 24882, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 3.06/3.47 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 3.06/3.47 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 3.06/3.47 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 3.06/3.47 'application_function' ) ] )
% 3.06/3.47 , clause( 24883, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 3.06/3.47 , clause( 24884, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 3.06/3.47 , clause( 24885, [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ]
% 3.06/3.47 )
% 3.06/3.47 , clause( 24886, [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) )
% 3.06/3.47 , maps( X, 'domain_of'( X ), Y ) ] )
% 3.06/3.47 , clause( 24887, [ ~( subclass( intersection( x, y ), y ) ) ] )
% 3.06/3.47 ] ).
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 subsumption(
% 3.06/3.47 clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y )
% 3.06/3.47 ] )
% 3.06/3.47 , clause( 24776, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 3.06/3.47 , Y ) ] )
% 3.06/3.47 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 3.06/3.47 ), ==>( 1, 1 )] ) ).
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 subsumption(
% 3.06/3.47 clause( 2, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X
% 3.06/3.47 , Y ) ] )
% 3.06/3.47 , clause( 24777, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 3.06/3.47 subclass( X, Y ) ] )
% 3.06/3.47 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 3.06/3.47 ), ==>( 1, 1 )] ) ).
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 subsumption(
% 3.06/3.47 clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 3.06/3.47 , clause( 24796, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 3.06/3.47 )
% 3.06/3.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 3.06/3.47 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 subsumption(
% 3.06/3.47 clause( 111, [ ~( subclass( intersection( x, y ), y ) ) ] )
% 3.06/3.47 , clause( 24887, [ ~( subclass( intersection( x, y ), y ) ) ] )
% 3.06/3.47 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 resolution(
% 3.06/3.47 clause( 24960, [ member( 'not_subclass_element'( intersection( x, y ), y )
% 3.06/3.47 , intersection( x, y ) ) ] )
% 3.06/3.47 , clause( 111, [ ~( subclass( intersection( x, y ), y ) ) ] )
% 3.06/3.47 , 0, clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 3.06/3.47 , Y ) ] )
% 3.06/3.47 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, intersection( x, y )
% 3.06/3.47 ), :=( Y, y )] )).
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 subsumption(
% 3.06/3.47 clause( 135, [ member( 'not_subclass_element'( intersection( x, y ), y ),
% 3.06/3.47 intersection( x, y ) ) ] )
% 3.06/3.47 , clause( 24960, [ member( 'not_subclass_element'( intersection( x, y ), y
% 3.06/3.47 ), intersection( x, y ) ) ] )
% 3.06/3.47 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 resolution(
% 3.06/3.47 clause( 24961, [ ~( member( 'not_subclass_element'( intersection( x, y ), y
% 3.06/3.47 ), y ) ) ] )
% 3.06/3.47 , clause( 111, [ ~( subclass( intersection( x, y ), y ) ) ] )
% 3.06/3.47 , 0, clause( 2, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 3.06/3.47 subclass( X, Y ) ] )
% 3.06/3.47 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, intersection( x, y )
% 3.06/3.47 ), :=( Y, y )] )).
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 subsumption(
% 3.06/3.47 clause( 137, [ ~( member( 'not_subclass_element'( intersection( x, y ), y )
% 3.06/3.47 , y ) ) ] )
% 3.06/3.47 , clause( 24961, [ ~( member( 'not_subclass_element'( intersection( x, y )
% 3.06/3.47 , y ), y ) ) ] )
% 3.06/3.47 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 resolution(
% 3.06/3.47 clause( 24962, [ member( 'not_subclass_element'( intersection( x, y ), y )
% 3.06/3.47 , y ) ] )
% 3.06/3.47 , clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 3.06/3.47 , 0, clause( 135, [ member( 'not_subclass_element'( intersection( x, y ), y
% 3.06/3.47 ), intersection( x, y ) ) ] )
% 3.06/3.47 , 0, substitution( 0, [ :=( X, 'not_subclass_element'( intersection( x, y )
% 3.06/3.47 , y ) ), :=( Y, x ), :=( Z, y )] ), substitution( 1, [] )).
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 resolution(
% 3.06/3.47 clause( 24963, [] )
% 3.06/3.47 , clause( 137, [ ~( member( 'not_subclass_element'( intersection( x, y ), y
% 3.06/3.47 ), y ) ) ] )
% 3.06/3.47 , 0, clause( 24962, [ member( 'not_subclass_element'( intersection( x, y )
% 3.06/3.47 , y ), y ) ] )
% 3.06/3.47 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 subsumption(
% 3.06/3.47 clause( 24773, [] )
% 3.06/3.47 , clause( 24963, [] )
% 3.06/3.47 , substitution( 0, [] ), permutation( 0, [] ) ).
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 end.
% 3.06/3.47
% 3.06/3.47 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 3.06/3.47
% 3.06/3.47 Memory use:
% 3.06/3.47
% 3.06/3.47 space for terms: 372052
% 3.06/3.47 space for clauses: 1153332
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 clauses generated: 53550
% 3.06/3.47 clauses kept: 24774
% 3.06/3.47 clauses selected: 546
% 3.06/3.47 clauses deleted: 3340
% 3.06/3.47 clauses inuse deleted: 83
% 3.06/3.47
% 3.06/3.47 subsentry: 178971
% 3.06/3.47 literals s-matched: 132554
% 3.06/3.47 literals matched: 130095
% 3.06/3.47 full subsumption: 58310
% 3.06/3.47
% 3.06/3.47 checksum: -2097874799
% 3.06/3.47
% 3.06/3.47
% 3.06/3.47 Bliksem ended
%------------------------------------------------------------------------------