TSTP Solution File: SET122-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET122-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n027.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 22:47:25 EDT 2022
% Result : Unsatisfiable 6.43s 6.79s
% Output : Refutation 6.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET122-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.12/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sat Jul 9 20:00:17 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.74/1.14 *** allocated 10000 integers for termspace/termends
% 0.74/1.14 *** allocated 10000 integers for clauses
% 0.74/1.14 *** allocated 10000 integers for justifications
% 0.74/1.14 Bliksem 1.12
% 0.74/1.14
% 0.74/1.14
% 0.74/1.14 Automatic Strategy Selection
% 0.74/1.14
% 0.74/1.14 Clauses:
% 0.74/1.14 [
% 0.74/1.14 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.74/1.14 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.74/1.14 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.74/1.14 ,
% 0.74/1.14 [ subclass( X, 'universal_class' ) ],
% 0.74/1.14 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.74/1.14 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.74/1.14 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.74/1.14 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.74/1.14 ,
% 0.74/1.14 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.74/1.14 ) ) ],
% 0.74/1.14 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.74/1.14 ) ) ],
% 0.74/1.14 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.74/1.14 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.74/1.14 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.74/1.14 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.74/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.14 X, Z ) ],
% 0.74/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.14 Y, T ) ],
% 0.74/1.14 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.74/1.14 ), 'cross_product'( Y, T ) ) ],
% 0.74/1.14 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.74/1.14 ), second( X ) ), X ) ],
% 0.74/1.14 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.74/1.14 'universal_class' ) ) ],
% 0.74/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.74/1.14 Y ) ],
% 0.74/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.74/1.14 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.74/1.14 , Y ), 'element_relation' ) ],
% 0.74/1.14 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.74/1.14 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.74/1.14 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.74/1.14 Z ) ) ],
% 0.74/1.14 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.74/1.14 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.74/1.14 member( X, Y ) ],
% 0.74/1.14 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.74/1.14 union( X, Y ) ) ],
% 0.74/1.14 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.74/1.14 intersection( complement( X ), complement( Y ) ) ) ),
% 0.74/1.14 'symmetric_difference'( X, Y ) ) ],
% 0.74/1.14 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.74/1.14 ,
% 0.74/1.14 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.74/1.14 ,
% 0.74/1.14 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.74/1.14 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.74/1.14 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.74/1.14 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.74/1.14 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.74/1.14 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.74/1.14 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.74/1.14 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.74/1.14 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.74/1.14 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.74/1.14 'cross_product'( 'universal_class', 'universal_class' ),
% 0.74/1.14 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.74/1.14 Y ), rotate( T ) ) ],
% 0.74/1.14 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.74/1.14 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.74/1.14 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.74/1.14 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.74/1.14 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.74/1.14 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.74/1.14 'cross_product'( 'universal_class', 'universal_class' ),
% 0.74/1.14 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.74/1.14 Z ), flip( T ) ) ],
% 0.74/1.14 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.74/1.14 inverse( X ) ) ],
% 0.74/1.14 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.74/1.14 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.74/1.14 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.74/1.14 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.74/1.14 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.74/1.14 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.74/1.14 ],
% 0.74/1.14 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.74/1.14 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.74/1.14 'universal_class' ) ) ],
% 0.74/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.74/1.14 successor( X ), Y ) ],
% 0.74/1.14 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.74/1.14 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.74/1.14 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.74/1.14 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.74/1.14 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.74/1.14 ,
% 0.74/1.14 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.74/1.14 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.74/1.14 [ inductive( omega ) ],
% 0.74/1.14 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.74/1.14 [ member( omega, 'universal_class' ) ],
% 0.74/1.14 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.74/1.14 , 'sum_class'( X ) ) ],
% 0.74/1.14 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.74/1.14 'universal_class' ) ],
% 0.74/1.14 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.74/1.14 'power_class'( X ) ) ],
% 0.74/1.14 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.74/1.14 'universal_class' ) ],
% 0.74/1.14 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.74/1.14 'universal_class' ) ) ],
% 0.74/1.14 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.74/1.14 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.74/1.14 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.74/1.14 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.74/1.14 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.74/1.14 ) ],
% 0.74/1.14 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.74/1.14 , 'identity_relation' ) ],
% 0.74/1.14 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.74/1.14 'single_valued_class'( X ) ],
% 0.74/1.14 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.74/1.14 'universal_class' ) ) ],
% 0.74/1.14 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.74/1.14 'identity_relation' ) ],
% 0.74/1.14 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.74/1.14 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.74/1.14 , function( X ) ],
% 0.74/1.14 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.74/1.14 X, Y ), 'universal_class' ) ],
% 0.74/1.14 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.74/1.14 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.74/1.14 ) ],
% 0.74/1.14 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.74/1.14 [ function( choice ) ],
% 0.74/1.14 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.74/1.14 apply( choice, X ), X ) ],
% 0.74/1.14 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.74/1.14 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.74/1.14 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.74/1.14 ,
% 0.74/1.14 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.74/1.14 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.74/1.14 , complement( compose( complement( 'element_relation' ), inverse(
% 0.74/1.14 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.74/1.14 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.74/1.14 'identity_relation' ) ],
% 0.74/1.14 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.74/1.14 , diagonalise( X ) ) ],
% 0.74/1.14 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.74/1.14 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.74/1.14 [ ~( operation( X ) ), function( X ) ],
% 0.74/1.14 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.74/1.14 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.74/1.14 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.74/1.14 'domain_of'( X ) ) ) ],
% 0.74/1.14 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.74/1.14 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.74/1.14 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.74/1.14 X ) ],
% 0.74/1.14 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.74/1.14 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.74/1.14 'domain_of'( X ) ) ],
% 0.74/1.14 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.74/1.14 'domain_of'( Z ) ) ) ],
% 0.74/1.14 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.74/1.14 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.74/1.14 ), compatible( X, Y, Z ) ],
% 0.74/1.14 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.74/1.14 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.74/1.14 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.74/1.14 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.74/1.14 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.74/1.14 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.74/1.14 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.74/1.14 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.74/1.14 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.74/1.14 , Y ) ],
% 0.74/1.14 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.74/1.14 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.74/1.14 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.74/1.14 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.74/1.14 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.74/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.14 X, 'unordered_pair'( X, Y ) ) ],
% 0.74/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.14 Y, 'unordered_pair'( X, Y ) ) ],
% 0.74/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.14 X, 'universal_class' ) ],
% 0.74/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.14 Y, 'universal_class' ) ],
% 0.74/1.14 [ subclass( X, X ) ],
% 0.74/1.14 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.74/1.14 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.74/1.14 'not_subclass_element'( Y, X ), Y ) ],
% 0.74/1.14 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.74/1.14 'not_subclass_element'( Y, X ), Y ) ],
% 0.74/1.14 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.74/1.14 'not_subclass_element'( Y, X ), Y ) ],
% 0.74/1.14 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.74/1.14 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.74/1.14 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.74/1.14 [ ~( member( X, 'null_class' ) ) ],
% 0.74/1.14 [ subclass( 'null_class', X ) ],
% 0.74/1.14 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.74/1.14 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.74/1.14 ), X ) ],
% 0.74/1.14 [ member( 'null_class', 'universal_class' ) ],
% 0.74/1.14 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.74/1.14 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.74/1.14 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.74/1.14 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.74/1.14 Y ) ) ],
% 0.74/1.14 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.74/1.14 Y ) ) ],
% 0.74/1.14 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.74/1.14 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.74/1.14 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.74/1.14 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.74/1.14 'universal_class' ) ) ), =( Y, Z ) ],
% 0.74/1.14 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.74/1.14 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.74/1.14 'universal_class' ) ) ), =( X, Z ) ],
% 0.74/1.14 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.74/1.14 'null_class' ) ) ],
% 0.74/1.14 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.74/1.14 'null_class' ) ) ],
% 0.74/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.74/1.14 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 0.74/1.14 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 0.74/1.14 X, Z ), Y ) ],
% 0.74/1.14 [ member( singleton( X ), 'universal_class' ) ],
% 0.74/1.14 [ member( singleton( X ), 'unordered_pair'( Y, singleton( X ) ) ) ],
% 0.74/1.14 [ ~( member( X, 'universal_class' ) ), member( X, singleton( X ) ) ]
% 0.74/1.14 ,
% 0.74/1.14 [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X ),
% 0.74/1.14 'null_class' ) ) ],
% 0.74/1.14 [ member( 'null_class', singleton( 'null_class' ) ) ],
% 0.74/1.14 [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ],
% 0.74/1.14 [ member( X, 'universal_class' ), =( singleton( X ), 'null_class' ) ]
% 0.74/1.14 ,
% 0.74/1.14 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 0.74/1.14 'universal_class' ) ), =( X, Y ) ],
% 0.74/1.14 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 0.74/1.14 'universal_class' ) ), =( X, Y ) ],
% 0.74/1.14 [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~( member( Z,
% 0.74/1.14 'universal_class' ) ), =( Z, X ), =( Z, Y ) ],
% 0.74/1.14 [ ~( member( X, 'universal_class' ) ), member( 'member_of'( singleton( X
% 0.74/1.14 ) ), 'universal_class' ) ],
% 0.74/1.14 [ ~( member( X, 'universal_class' ) ), =( singleton( 'member_of'(
% 0.74/1.14 singleton( X ) ) ), singleton( X ) ) ],
% 0.74/1.14 [ member( 'member_of'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 0.74/1.14 ) ],
% 0.74/1.14 [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X ), X ) ],
% 0.74/1.14 [ ~( member( X, 'universal_class' ) ), =( 'member_of'( singleton( X ) )
% 0.74/1.14 , X ) ],
% 0.74/1.14 [ member( 'member_of1'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 0.74/1.14 ) ],
% 0.74/1.14 [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'( X ), X ) ]
% 0.74/1.14 ,
% 0.74/1.14 [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 0.74/1.14 'universal_class' ) ],
% 0.74/1.14 [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y, X ) ), =(
% 0.74/1.14 'member_of'( X ), Y ) ],
% 0.74/1.14 [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ],
% 0.74/1.14 [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' ), =( singleton(
% 0.74/1.14 Y ), X ) ],
% 0.74/1.14 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 0.74/1.14 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 0.74/1.14 intersection( complement( singleton( 'not_subclass_element'( X,
% 0.74/1.14 'null_class' ) ) ), X ) ), =( singleton( 'not_subclass_element'( X,
% 0.74/1.14 'null_class' ) ), X ), =( X, 'null_class' ) ],
% 0.74/1.14 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 0.74/1.14 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ), X ),
% 0.74/1.14 =( singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 0.74/1.14 'null_class' ) ],
% 0.74/1.14 [ ~( =( 'not_subclass_element'( intersection( complement( singleton(
% 0.74/1.14 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 0.74/1.14 'not_subclass_element'( X, 'null_class' ) ) ), =( singleton(
% 0.74/1.14 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 0.74/1.14 ,
% 0.74/1.14 [ =( 'unordered_pair'( X, Y ), union( singleton( X ), singleton( Y ) ) )
% 0.74/1.14 ],
% 0.74/1.14 [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ],
% 0.74/1.14 [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ],
% 0.74/1.14 [ member( 'unordered_pair'( X, singleton( Y ) ), 'ordered_pair'( X, Y )
% 0.74/1.14 ) ],
% 0.74/1.14 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, 'null_class'
% 0.74/1.14 ) ), 'ordered_pair'( X, Y ) ), member( Y, 'universal_class' ) ],
% 0.74/1.14 [ ~( member( X, 'universal_class' ) ), =( 'unordered_pair'( 'null_class'
% 0.74/1.14 , singleton( singleton( X ) ) ), 'ordered_pair'( Y, X ) ), member( Y,
% 0.74/1.14 'universal_class' ) ],
% 0.74/1.14 [ =( 'unordered_pair'( 'null_class', singleton( 'null_class' ) ),
% 0.74/1.14 'ordered_pair'( X, Y ) ), member( X, 'universal_class' ), member( Y,
% 0.74/1.14 'universal_class' ) ],
% 0.74/1.14 [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) ), ~( member( X
% 0.74/1.14 , 'universal_class' ) ), =( X, Z ) ],
% 0.74/1.14 [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) ), ~( member( Y
% 0.74/1.14 , 'universal_class' ) ), =( Y, T ) ],
% 0.74/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.74/1.14 , 'universal_class' ) ) ), member( 'ordered_pair'( first( 'ordered_pair'(
% 0.74/1.14 X, Y ) ), second( 'ordered_pair'( X, Y ) ) ), 'cross_product'(
% 0.74/1.14 'universal_class', 'universal_class' ) ) ],
% 0.74/1.14 [ member( 'ordered_pair'( first( X ), second( X ) ), 'cross_product'(
% 0.74/1.14 'universal_class', 'universal_class' ) ), =( first( X ), X ) ],
% 6.41/6.79 [ member( 'ordered_pair'( first( X ), second( X ) ), 'cross_product'(
% 6.41/6.79 'universal_class', 'universal_class' ) ), =( second( X ), X ) ],
% 6.41/6.79 [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( first( X ), X )
% 6.41/6.79 ],
% 6.41/6.79 [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( second( X ), X )
% 6.41/6.79 ],
% 6.41/6.79 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 6.41/6.79 , 'universal_class' ) ) ), =( first( 'ordered_pair'( X, Y ) ), X ) ],
% 6.41/6.79 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 6.41/6.79 , 'universal_class' ) ) ), =( second( 'ordered_pair'( X, Y ) ), Y ) ]
% 6.41/6.79 ,
% 6.41/6.79 [ member( 'ordered_pair'( first( X ), second( X ) ), 'cross_product'(
% 6.41/6.79 'universal_class', 'universal_class' ) ), =( first( X ), X ) ],
% 6.41/6.79 [ member( 'ordered_pair'( first( X ), second( X ) ), 'cross_product'(
% 6.41/6.79 'universal_class', 'universal_class' ) ), =( second( X ), X ) ],
% 6.41/6.79 [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( first( X ), X )
% 6.41/6.79 ],
% 6.41/6.79 [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( second( X ), X )
% 6.41/6.79 ],
% 6.41/6.79 [ ~( =( 'ordered_pair'( first( X ), second( X ) ), X ) ), member( X,
% 6.41/6.79 'universal_class' ) ],
% 6.41/6.79 [ ~( member( X, 'cross_product'( 'universal_class', 'universal_class' )
% 6.41/6.79 ) ), member( X, 'universal_class' ) ],
% 6.41/6.79 [ member( X, 'universal_class' ), =( first( 'ordered_pair'( X, Y ) ),
% 6.41/6.79 'ordered_pair'( X, Y ) ) ],
% 6.41/6.79 [ member( X, 'universal_class' ), =( second( 'ordered_pair'( X, Y ) ),
% 6.41/6.79 'ordered_pair'( X, Y ) ) ],
% 6.41/6.79 [ ~( member( y, 'universal_class' ) ) ],
% 6.41/6.79 [ ~( =( second( 'ordered_pair'( x, y ) ), 'ordered_pair'( x, y ) ) ) ]
% 6.41/6.79 ] .
% 6.41/6.79
% 6.41/6.79
% 6.41/6.79 percentage equality = 0.317365, percentage horn = 0.793939
% 6.41/6.79 This is a problem with some equality
% 6.41/6.79
% 6.41/6.79
% 6.41/6.79
% 6.41/6.79 Options Used:
% 6.41/6.79
% 6.41/6.79 useres = 1
% 6.41/6.79 useparamod = 1
% 6.41/6.79 useeqrefl = 1
% 6.41/6.79 useeqfact = 1
% 6.41/6.79 usefactor = 1
% 6.41/6.79 usesimpsplitting = 0
% 6.41/6.79 usesimpdemod = 5
% 6.41/6.79 usesimpres = 3
% 6.41/6.79
% 6.41/6.79 resimpinuse = 1000
% 6.41/6.79 resimpclauses = 20000
% 6.41/6.79 substype = eqrewr
% 6.41/6.79 backwardsubs = 1
% 6.41/6.79 selectoldest = 5
% 6.41/6.79
% 6.41/6.79 litorderings [0] = split
% 6.41/6.79 litorderings [1] = extend the termordering, first sorting on arguments
% 6.41/6.79
% 6.41/6.79 termordering = kbo
% 6.41/6.79
% 6.41/6.79 litapriori = 0
% 6.41/6.79 termapriori = 1
% 6.41/6.79 litaposteriori = 0
% 6.41/6.79 termaposteriori = 0
% 6.41/6.79 demodaposteriori = 0
% 6.41/6.79 ordereqreflfact = 0
% 6.41/6.79
% 6.41/6.79 litselect = negord
% 6.41/6.79
% 6.41/6.79 maxweight = 15
% 6.41/6.79 maxdepth = 30000
% 6.41/6.79 maxlength = 115
% 6.41/6.79 maxnrvars = 195
% 6.41/6.79 excuselevel = 1
% 6.41/6.79 increasemaxweight = 1
% 6.41/6.79
% 6.41/6.79 maxselected = 10000000
% 6.41/6.79 maxnrclauses = 10000000
% 6.41/6.79
% 6.41/6.79 showgenerated = 0
% 6.41/6.79 showkept = 0
% 6.41/6.79 showselected = 0
% 6.41/6.79 showdeleted = 0
% 6.41/6.79 showresimp = 1
% 6.41/6.79 showstatus = 2000
% 6.41/6.79
% 6.41/6.79 prologoutput = 1
% 6.41/6.79 nrgoals = 5000000
% 6.41/6.79 totalproof = 1
% 6.41/6.79
% 6.41/6.79 Symbols occurring in the translation:
% 6.41/6.79
% 6.41/6.79 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 6.41/6.79 . [1, 2] (w:1, o:58, a:1, s:1, b:0),
% 6.41/6.79 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 6.41/6.79 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.41/6.79 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.41/6.79 subclass [41, 2] (w:1, o:83, a:1, s:1, b:0),
% 6.41/6.79 member [43, 2] (w:1, o:84, a:1, s:1, b:0),
% 6.41/6.79 'not_subclass_element' [44, 2] (w:1, o:85, a:1, s:1, b:0),
% 6.41/6.79 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 6.41/6.79 'unordered_pair' [46, 2] (w:1, o:86, a:1, s:1, b:0),
% 6.41/6.79 singleton [47, 1] (w:1, o:39, a:1, s:1, b:0),
% 6.41/6.79 'ordered_pair' [48, 2] (w:1, o:87, a:1, s:1, b:0),
% 6.41/6.79 'cross_product' [50, 2] (w:1, o:88, a:1, s:1, b:0),
% 6.41/6.79 first [52, 1] (w:1, o:40, a:1, s:1, b:0),
% 6.41/6.79 second [53, 1] (w:1, o:41, a:1, s:1, b:0),
% 6.41/6.79 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 6.41/6.79 intersection [55, 2] (w:1, o:90, a:1, s:1, b:0),
% 6.41/6.79 complement [56, 1] (w:1, o:42, a:1, s:1, b:0),
% 6.41/6.79 union [57, 2] (w:1, o:91, a:1, s:1, b:0),
% 6.41/6.79 'symmetric_difference' [58, 2] (w:1, o:92, a:1, s:1, b:0),
% 6.41/6.79 restrict [60, 3] (w:1, o:95, a:1, s:1, b:0),
% 6.41/6.79 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 6.41/6.79 'domain_of' [62, 1] (w:1, o:44, a:1, s:1, b:0),
% 6.41/6.79 rotate [63, 1] (w:1, o:36, a:1, s:1, b:0),
% 6.41/6.79 flip [65, 1] (w:1, o:45, a:1, s:1, b:0),
% 6.41/6.79 inverse [66, 1] (w:1, o:46, a:1, s:1, b:0),
% 6.41/6.79 'range_of' [67, 1] (w:1, o:37, a:1, s:1, b:0),
% 6.41/6.79 domain [68, 3] (w:1, o:97, a:1, s:1, b:0),
% 6.41/6.79 range [69, 3] (w:1, o:98, a:1, s:1, b:0),
% 6.41/6.79 image [70, 2] (w:1, o:89, a:1, s:1, b:0),
% 6.41/6.79 successor [71, 1] (w:1, o:47, a:1, s:1, b:0),
% 6.41/6.79 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 6.41/6.79 inductive [73, 1] (w:1, o:48, a:1, s:1, b:0),
% 6.41/6.79 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 6.41/6.79 'sum_class' [75, 1] (w:1, o:49, a:1, s:1, b:0),
% 6.41/6.79 'power_class' [76, 1] (w:1, o:52, a:1, s:1, b:0),
% 6.41/6.79 compose [78, 2] (w:1, o:93, a:1, s:1, b:0),
% 6.41/6.79 'single_valued_class' [79, 1] (w:1, o:53, a:1, s:1, b:0),
% 6.41/6.79 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 6.41/6.79 function [82, 1] (w:1, o:54, a:1, s:1, b:0),
% 6.41/6.79 regular [83, 1] (w:1, o:38, a:1, s:1, b:0),
% 6.41/6.79 apply [84, 2] (w:1, o:94, a:1, s:1, b:0),
% 6.41/6.79 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 6.41/6.79 'one_to_one' [86, 1] (w:1, o:50, a:1, s:1, b:0),
% 6.41/6.79 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 6.41/6.79 diagonalise [88, 1] (w:1, o:55, a:1, s:1, b:0),
% 6.41/6.79 cantor [89, 1] (w:1, o:43, a:1, s:1, b:0),
% 6.41/6.79 operation [90, 1] (w:1, o:51, a:1, s:1, b:0),
% 6.41/6.79 compatible [94, 3] (w:1, o:96, a:1, s:1, b:0),
% 6.41/6.79 homomorphism [95, 3] (w:1, o:99, a:1, s:1, b:0),
% 6.41/6.79 'not_homomorphism1' [96, 3] (w:1, o:100, a:1, s:1, b:0),
% 6.41/6.79 'not_homomorphism2' [97, 3] (w:1, o:101, a:1, s:1, b:0),
% 6.41/6.79 'member_of' [98, 1] (w:1, o:56, a:1, s:1, b:0),
% 6.41/6.79 'member_of1' [99, 1] (w:1, o:57, a:1, s:1, b:0),
% 6.41/6.79 y [100, 0] (w:1, o:30, a:1, s:1, b:0),
% 6.41/6.79 x [101, 0] (w:1, o:29, a:1, s:1, b:0).
% 6.41/6.79
% 6.41/6.79
% 6.41/6.79 Starting Search:
% 6.41/6.79
% 6.41/6.79 Resimplifying inuse:
% 6.41/6.79 Done
% 6.41/6.79
% 6.41/6.79
% 6.41/6.79 Intermediate Status:
% 6.41/6.79 Generated: 3907
% 6.41/6.79 Kept: 2001
% 6.41/6.79 Inuse: 120
% 6.41/6.79 Deleted: 3
% 6.41/6.79 Deletedinuse: 3
% 6.41/6.79
% 6.41/6.79 Resimplifying inuse:
% 6.41/6.79 Done
% 6.41/6.79
% 6.41/6.79 Resimplifying inuse:
% 6.41/6.79 Done
% 6.41/6.79
% 6.41/6.79
% 6.41/6.79 Intermediate Status:
% 6.41/6.79 Generated: 9359
% 6.41/6.79 Kept: 4046
% 6.41/6.79 Inuse: 201
% 6.41/6.79 Deleted: 8
% 6.41/6.79 Deletedinuse: 8
% 6.41/6.79
% 6.41/6.79 Resimplifying inuse:
% 6.41/6.79 Done
% 6.41/6.79
% 6.41/6.79 Resimplifying inuse:
% 6.41/6.79 Done
% 6.41/6.79
% 6.41/6.79
% 6.41/6.79 Intermediate Status:
% 6.41/6.79 Generated: 15278
% 6.41/6.79 Kept: 6341
% 6.41/6.79 Inuse: 285
% 6.41/6.79 Deleted: 12
% 6.41/6.79 Deletedinuse: 11
% 6.41/6.79
% 6.41/6.79 Resimplifying inuse:
% 6.41/6.79 Done
% 6.41/6.79
% 6.41/6.79 Resimplifying inuse:
% 6.41/6.79 Done
% 6.41/6.79
% 6.41/6.79
% 6.41/6.79 Intermediate Status:
% 6.41/6.79 Generated: 21183
% 6.41/6.79 Kept: 8376
% 6.41/6.79 Inuse: 343
% 6.41/6.79 Deleted: 62
% 6.41/6.79 Deletedinuse: 58
% 6.41/6.79
% 6.41/6.79 Resimplifying inuse:
% 6.41/6.79 Done
% 6.41/6.79
% 6.41/6.79 Resimplifying inuse:
% 6.41/6.79 Done
% 6.41/6.79
% 6.41/6.79
% 6.41/6.79 Intermediate Status:
% 6.41/6.79 Generated: 28793
% 6.41/6.79 Kept: 10802
% 6.41/6.79 Inuse: 395
% 6.41/6.79 Deleted: 79
% 6.41/6.79 Deletedinuse: 63
% 6.41/6.79
% 6.41/6.79 Resimplifying inuse:
% 6.41/6.79 Done
% 6.41/6.79
% 6.41/6.79 Resimplifying inuse:
% 6.41/6.79 Done
% 6.41/6.79
% 6.41/6.79
% 6.41/6.79 Intermediate Status:
% 6.41/6.79 Generated: 38207
% 6.41/6.79 Kept: 12827
% 6.41/6.79 Inuse: 444
% 6.41/6.79 Deleted: 81
% 6.41/6.79 Deletedinuse: 64
% 6.41/6.79
% 6.41/6.79 Resimplifying inuse:
% 6.41/6.79 Done
% 6.41/6.79
% 6.41/6.79 Resimplifying inuse:
% 6.41/6.79 Done
% 6.41/6.79
% 6.41/6.79
% 6.41/6.79 Intermediate Status:
% 6.41/6.79 Generated: 47917
% 6.41/6.79 Kept: 16583
% 6.41/6.79 Inuse: 488
% 6.41/6.79 Deleted: 93
% 6.41/6.79 Deletedinuse: 75
% 6.41/6.79
% 6.41/6.79 Resimplifying inuse:
% 6.41/6.79 Done
% 6.41/6.79
% 6.41/6.79 Resimplifying inuse:
% 6.41/6.79 Done
% 6.41/6.79
% 6.41/6.79
% 6.41/6.79 Intermediate Status:
% 6.41/6.79 Generated: 61708
% 6.41/6.79 Kept: 20423
% 6.41/6.79 Inuse: 503
% 6.41/6.79 Deleted: 97
% 6.41/6.79 Deletedinuse: 79
% 6.41/6.79
% 6.41/6.79 Resimplifying inuse:
% 6.41/6.79 Done
% 6.41/6.79
% 6.41/6.79 Resimplifying clauses:
% 6.43/6.79 Done
% 6.43/6.79
% 6.43/6.79 Resimplifying inuse:
% 6.43/6.79 Done
% 6.43/6.79
% 6.43/6.79
% 6.43/6.79 Intermediate Status:
% 6.43/6.79 Generated: 72191
% 6.43/6.79 Kept: 22615
% 6.43/6.79 Inuse: 541
% 6.43/6.79 Deleted: 2234
% 6.43/6.79 Deletedinuse: 90
% 6.43/6.79
% 6.43/6.79 Resimplifying inuse:
% 6.43/6.79 Done
% 6.43/6.79
% 6.43/6.79 Resimplifying inuse:
% 6.43/6.79 Done
% 6.43/6.79
% 6.43/6.79
% 6.43/6.79 Intermediate Status:
% 6.43/6.79 Generated: 84940
% 6.43/6.79 Kept: 25712
% 6.43/6.79 Inuse: 567
% 6.43/6.79 Deleted: 2238
% 6.43/6.79 Deletedinuse: 90
% 6.43/6.79
% 6.43/6.79 Resimplifying inuse:
% 6.43/6.79 Done
% 6.43/6.79
% 6.43/6.79 Resimplifying inuse:
% 6.43/6.79 Done
% 6.43/6.79
% 6.43/6.79
% 6.43/6.79 Intermediate Status:
% 6.43/6.79 Generated: 91093
% 6.43/6.79 Kept: 27761
% 6.43/6.79 Inuse: 577
% 6.43/6.79 Deleted: 2240
% 6.43/6.79 Deletedinuse: 92
% 6.43/6.79
% 6.43/6.79 Resimplifying inuse:
% 6.43/6.79 Done
% 6.43/6.79
% 6.43/6.79
% 6.43/6.79 Bliksems!, er is een bewijs:
% 6.43/6.79 % SZS status Unsatisfiable
% 6.43/6.79 % SZS output start Refutation
% 6.43/6.79
% 6.43/6.79 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 6.43/6.79 )
% 6.43/6.79 .
% 6.43/6.79 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 6.43/6.79 .
% 6.43/6.79 clause( 13, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) )
% 6.43/6.79 ), member( Y, T ) ] )
% 6.43/6.79 .
% 6.43/6.79 clause( 153, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( second(
% 6.43/6.79 X ), X ) ] )
% 6.43/6.79 .
% 6.43/6.79 clause( 157, [ =( second( X ), X ), member( X, 'cross_product'(
% 6.43/6.79 'universal_class', 'universal_class' ) ) ] )
% 6.43/6.79 .
% 6.43/6.79 clause( 162, [ ~( member( y, 'universal_class' ) ) ] )
% 6.43/6.79 .
% 6.43/6.79 clause( 163, [ ~( =( second( 'ordered_pair'( x, y ) ), 'ordered_pair'( x, y
% 6.43/6.79 ) ) ) ] )
% 6.43/6.79 .
% 6.43/6.79 clause( 182, [ ~( member( y, X ) ) ] )
% 6.43/6.79 .
% 6.43/6.79 clause( 673, [ ~( member( 'ordered_pair'( X, y ), 'cross_product'( Y, Z ) )
% 6.43/6.79 ) ] )
% 6.43/6.79 .
% 6.43/6.79 clause( 29052, [] )
% 6.43/6.79 .
% 6.43/6.79
% 6.43/6.79
% 6.43/6.79 % SZS output end Refutation
% 6.43/6.79 found a proof!
% 6.43/6.79
% 6.43/6.79 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 6.43/6.79
% 6.43/6.79 initialclauses(
% 6.43/6.79 [ clause( 29054, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 6.43/6.79 ) ] )
% 6.43/6.79 , clause( 29055, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 6.43/6.79 , Y ) ] )
% 6.43/6.79 , clause( 29056, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 6.43/6.79 subclass( X, Y ) ] )
% 6.43/6.79 , clause( 29057, [ subclass( X, 'universal_class' ) ] )
% 6.43/6.79 , clause( 29058, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 6.43/6.79 , clause( 29059, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 6.43/6.79 , clause( 29060, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 6.43/6.79 ] )
% 6.43/6.79 , clause( 29061, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 6.43/6.79 =( X, Z ) ] )
% 6.43/6.79 , clause( 29062, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.43/6.79 'unordered_pair'( X, Y ) ) ] )
% 6.43/6.79 , clause( 29063, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.43/6.79 'unordered_pair'( Y, X ) ) ] )
% 6.43/6.79 , clause( 29064, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 6.43/6.79 )
% 6.43/6.79 , clause( 29065, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 6.43/6.79 , clause( 29066, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 6.43/6.79 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 6.43/6.79 , clause( 29067, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.43/6.79 ) ) ), member( X, Z ) ] )
% 6.43/6.79 , clause( 29068, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.43/6.79 ) ) ), member( Y, T ) ] )
% 6.43/6.79 , clause( 29069, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 6.43/6.79 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 6.43/6.79 , clause( 29070, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 6.43/6.79 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 6.43/6.79 , clause( 29071, [ subclass( 'element_relation', 'cross_product'(
% 6.43/6.79 'universal_class', 'universal_class' ) ) ] )
% 6.43/6.79 , clause( 29072, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 6.43/6.79 ), member( X, Y ) ] )
% 6.43/6.79 , clause( 29073, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 6.43/6.79 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 6.43/6.79 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 6.43/6.79 , clause( 29074, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 6.43/6.79 )
% 6.43/6.79 , clause( 29075, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 6.43/6.79 )
% 6.43/6.79 , clause( 29076, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 6.43/6.79 intersection( Y, Z ) ) ] )
% 6.43/6.79 , clause( 29077, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 6.43/6.79 )
% 6.43/6.79 , clause( 29078, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.43/6.79 complement( Y ) ), member( X, Y ) ] )
% 6.43/6.79 , clause( 29079, [ =( complement( intersection( complement( X ), complement(
% 6.43/6.79 Y ) ) ), union( X, Y ) ) ] )
% 6.43/6.79 , clause( 29080, [ =( intersection( complement( intersection( X, Y ) ),
% 6.43/6.79 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 6.43/6.79 'symmetric_difference'( X, Y ) ) ] )
% 6.43/6.79 , clause( 29081, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 6.43/6.79 X, Y, Z ) ) ] )
% 6.43/6.79 , clause( 29082, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 6.43/6.79 Z, X, Y ) ) ] )
% 6.43/6.79 , clause( 29083, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 6.43/6.79 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 6.43/6.79 , clause( 29084, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 6.43/6.79 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 6.43/6.79 'domain_of'( Y ) ) ] )
% 6.43/6.79 , clause( 29085, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 6.43/6.79 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 6.43/6.79 , clause( 29086, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.43/6.79 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 6.43/6.79 ] )
% 6.43/6.79 , clause( 29087, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.43/6.79 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 6.43/6.79 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 6.43/6.79 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 6.43/6.79 , Y ), rotate( T ) ) ] )
% 6.43/6.79 , clause( 29088, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 6.43/6.79 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 6.43/6.79 , clause( 29089, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.43/6.79 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 6.43/6.79 )
% 6.43/6.79 , clause( 29090, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.43/6.79 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 6.43/6.79 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 6.43/6.79 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 6.43/6.79 , Z ), flip( T ) ) ] )
% 6.43/6.79 , clause( 29091, [ =( 'domain_of'( flip( 'cross_product'( X,
% 6.43/6.79 'universal_class' ) ) ), inverse( X ) ) ] )
% 6.43/6.79 , clause( 29092, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 6.43/6.79 , clause( 29093, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 6.43/6.79 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 6.43/6.79 , clause( 29094, [ =( second( 'not_subclass_element'( restrict( X,
% 6.43/6.79 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 6.43/6.79 , clause( 29095, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 6.43/6.79 image( X, Y ) ) ] )
% 6.43/6.79 , clause( 29096, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 6.43/6.79 , clause( 29097, [ subclass( 'successor_relation', 'cross_product'(
% 6.43/6.79 'universal_class', 'universal_class' ) ) ] )
% 6.43/6.79 , clause( 29098, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 6.43/6.79 ) ), =( successor( X ), Y ) ] )
% 6.43/6.79 , clause( 29099, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 6.43/6.79 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 6.43/6.79 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 6.43/6.79 , clause( 29100, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 6.43/6.79 , clause( 29101, [ ~( inductive( X ) ), subclass( image(
% 6.43/6.79 'successor_relation', X ), X ) ] )
% 6.43/6.79 , clause( 29102, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 6.43/6.79 'successor_relation', X ), X ) ), inductive( X ) ] )
% 6.43/6.79 , clause( 29103, [ inductive( omega ) ] )
% 6.43/6.79 , clause( 29104, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 6.43/6.79 , clause( 29105, [ member( omega, 'universal_class' ) ] )
% 6.43/6.79 , clause( 29106, [ =( 'domain_of'( restrict( 'element_relation',
% 6.43/6.79 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 6.43/6.79 , clause( 29107, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 6.43/6.79 X ), 'universal_class' ) ] )
% 6.43/6.79 , clause( 29108, [ =( complement( image( 'element_relation', complement( X
% 6.43/6.79 ) ) ), 'power_class'( X ) ) ] )
% 6.43/6.79 , clause( 29109, [ ~( member( X, 'universal_class' ) ), member(
% 6.43/6.79 'power_class'( X ), 'universal_class' ) ] )
% 6.43/6.79 , clause( 29110, [ subclass( compose( X, Y ), 'cross_product'(
% 6.43/6.79 'universal_class', 'universal_class' ) ) ] )
% 6.43/6.79 , clause( 29111, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 6.43/6.79 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 6.43/6.79 , clause( 29112, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 6.43/6.79 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 6.43/6.79 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 6.43/6.79 ) ] )
% 6.43/6.79 , clause( 29113, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 6.43/6.79 inverse( X ) ), 'identity_relation' ) ] )
% 6.43/6.79 , clause( 29114, [ ~( subclass( compose( X, inverse( X ) ),
% 6.43/6.79 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 6.43/6.79 , clause( 29115, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 6.43/6.79 'universal_class', 'universal_class' ) ) ] )
% 6.43/6.79 , clause( 29116, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 6.43/6.79 , 'identity_relation' ) ] )
% 6.43/6.79 , clause( 29117, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 6.43/6.79 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 6.43/6.79 'identity_relation' ) ), function( X ) ] )
% 6.43/6.79 , clause( 29118, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 6.43/6.79 , member( image( X, Y ), 'universal_class' ) ] )
% 6.43/6.79 , clause( 29119, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 6.43/6.79 , clause( 29120, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 6.43/6.79 , 'null_class' ) ] )
% 6.43/6.79 , clause( 29121, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 6.43/6.79 Y ) ) ] )
% 6.43/6.79 , clause( 29122, [ function( choice ) ] )
% 6.43/6.79 , clause( 29123, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 6.43/6.79 ), member( apply( choice, X ), X ) ] )
% 6.43/6.79 , clause( 29124, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 6.43/6.79 , clause( 29125, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 6.43/6.79 , clause( 29126, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 6.43/6.79 'one_to_one'( X ) ] )
% 6.43/6.79 , clause( 29127, [ =( intersection( 'cross_product'( 'universal_class',
% 6.43/6.79 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 6.43/6.79 'universal_class' ), complement( compose( complement( 'element_relation'
% 6.43/6.79 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 6.43/6.79 , clause( 29128, [ =( intersection( inverse( 'subset_relation' ),
% 6.43/6.79 'subset_relation' ), 'identity_relation' ) ] )
% 6.43/6.79 , clause( 29129, [ =( complement( 'domain_of'( intersection( X,
% 6.43/6.79 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 6.43/6.79 , clause( 29130, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 6.43/6.79 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 6.43/6.79 , clause( 29131, [ ~( operation( X ) ), function( X ) ] )
% 6.43/6.79 , clause( 29132, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 6.43/6.79 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 6.43/6.79 ] )
% 6.43/6.79 , clause( 29133, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 6.43/6.79 'domain_of'( 'domain_of'( X ) ) ) ] )
% 6.43/6.79 , clause( 29134, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 6.43/6.79 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 6.43/6.79 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 6.43/6.79 operation( X ) ] )
% 6.43/6.79 , clause( 29135, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 6.43/6.79 , clause( 29136, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 6.43/6.79 Y ) ), 'domain_of'( X ) ) ] )
% 6.43/6.79 , clause( 29137, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 6.43/6.79 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 6.43/6.79 , clause( 29138, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 6.43/6.79 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 6.43/6.79 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 6.43/6.79 , clause( 29139, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 6.43/6.79 , clause( 29140, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 6.43/6.79 , clause( 29141, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 6.43/6.79 , clause( 29142, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 6.43/6.79 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 6.43/6.79 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 6.43/6.79 )
% 6.43/6.79 , clause( 29143, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 6.43/6.79 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 6.43/6.79 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 6.43/6.79 , Y ) ] )
% 6.43/6.79 , clause( 29144, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 6.43/6.79 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 6.43/6.79 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 6.43/6.79 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 6.43/6.79 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 6.43/6.79 )
% 6.43/6.79 , clause( 29145, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.43/6.79 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 6.43/6.79 , clause( 29146, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.43/6.79 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 6.43/6.79 , clause( 29147, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.43/6.79 ) ) ), member( X, 'universal_class' ) ] )
% 6.43/6.79 , clause( 29148, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.43/6.79 ) ) ), member( Y, 'universal_class' ) ] )
% 6.43/6.79 , clause( 29149, [ subclass( X, X ) ] )
% 6.43/6.79 , clause( 29150, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 6.43/6.79 X, Z ) ] )
% 6.43/6.79 , clause( 29151, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 6.43/6.79 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 6.43/6.79 , clause( 29152, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 6.43/6.79 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 6.43/6.79 , clause( 29153, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 6.43/6.79 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 6.43/6.79 , clause( 29154, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 6.43/6.79 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 6.43/6.79 , clause( 29155, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 6.43/6.79 )
% 6.43/6.79 , clause( 29156, [ ~( member( X, 'null_class' ) ) ] )
% 6.43/6.79 , clause( 29157, [ subclass( 'null_class', X ) ] )
% 6.43/6.79 , clause( 29158, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 6.43/6.79 )
% 6.43/6.79 , clause( 29159, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 6.43/6.79 , 'null_class' ), X ) ] )
% 6.43/6.79 , clause( 29160, [ member( 'null_class', 'universal_class' ) ] )
% 6.43/6.79 , clause( 29161, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 6.43/6.79 ] )
% 6.43/6.79 , clause( 29162, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 6.43/6.79 )
% 6.43/6.79 , clause( 29163, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 6.43/6.79 )
% 6.43/6.79 , clause( 29164, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 6.43/6.79 X ), singleton( Y ) ) ] )
% 6.43/6.79 , clause( 29165, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 6.43/6.79 Y ), singleton( Y ) ) ] )
% 6.43/6.79 , clause( 29166, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 6.43/6.79 'universal_class' ), member( Y, 'universal_class' ) ] )
% 6.43/6.79 , clause( 29167, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 6.43/6.79 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 6.43/6.79 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 6.43/6.79 , clause( 29168, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 6.43/6.79 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 6.43/6.79 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 6.43/6.79 , clause( 29169, [ ~( member( X, 'universal_class' ) ), ~( =(
% 6.43/6.79 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 6.43/6.79 , clause( 29170, [ ~( member( X, 'universal_class' ) ), ~( =(
% 6.43/6.79 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 6.43/6.79 , clause( 29171, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.43/6.79 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 6.43/6.79 , clause( 29172, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 6.43/6.79 'unordered_pair'( X, Z ), Y ) ] )
% 6.43/6.79 , clause( 29173, [ member( singleton( X ), 'universal_class' ) ] )
% 6.43/6.79 , clause( 29174, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 6.43/6.79 X ) ) ) ] )
% 6.43/6.79 , clause( 29175, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.43/6.79 singleton( X ) ) ] )
% 6.43/6.79 , clause( 29176, [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X
% 6.43/6.79 ), 'null_class' ) ) ] )
% 6.43/6.79 , clause( 29177, [ member( 'null_class', singleton( 'null_class' ) ) ] )
% 6.43/6.79 , clause( 29178, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 6.43/6.79 , clause( 29179, [ member( X, 'universal_class' ), =( singleton( X ),
% 6.43/6.79 'null_class' ) ] )
% 6.43/6.79 , clause( 29180, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 6.43/6.79 'universal_class' ) ), =( X, Y ) ] )
% 6.43/6.79 , clause( 29181, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 6.43/6.79 'universal_class' ) ), =( X, Y ) ] )
% 6.43/6.79 , clause( 29182, [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~(
% 6.43/6.79 member( Z, 'universal_class' ) ), =( Z, X ), =( Z, Y ) ] )
% 6.43/6.79 , clause( 29183, [ ~( member( X, 'universal_class' ) ), member( 'member_of'(
% 6.43/6.79 singleton( X ) ), 'universal_class' ) ] )
% 6.43/6.79 , clause( 29184, [ ~( member( X, 'universal_class' ) ), =( singleton(
% 6.43/6.79 'member_of'( singleton( X ) ) ), singleton( X ) ) ] )
% 6.43/6.79 , clause( 29185, [ member( 'member_of'( X ), 'universal_class' ), =(
% 6.43/6.79 'member_of'( X ), X ) ] )
% 6.43/6.79 , clause( 29186, [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X
% 6.43/6.79 ), X ) ] )
% 6.43/6.79 , clause( 29187, [ ~( member( X, 'universal_class' ) ), =( 'member_of'(
% 6.43/6.79 singleton( X ) ), X ) ] )
% 6.43/6.79 , clause( 29188, [ member( 'member_of1'( X ), 'universal_class' ), =(
% 6.43/6.79 'member_of'( X ), X ) ] )
% 6.43/6.79 , clause( 29189, [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'(
% 6.43/6.79 X ), X ) ] )
% 6.43/6.79 , clause( 29190, [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 6.43/6.79 'universal_class' ) ] )
% 6.43/6.79 , clause( 29191, [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y
% 6.43/6.79 , X ) ), =( 'member_of'( X ), Y ) ] )
% 6.43/6.79 , clause( 29192, [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ] )
% 6.43/6.79 , clause( 29193, [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' )
% 6.43/6.79 , =( singleton( Y ), X ) ] )
% 6.43/6.79 , clause( 29194, [ member( 'not_subclass_element'( intersection( complement(
% 6.43/6.79 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 6.43/6.79 'null_class' ), intersection( complement( singleton(
% 6.43/6.79 'not_subclass_element'( X, 'null_class' ) ) ), X ) ), =( singleton(
% 6.43/6.79 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 6.43/6.79 )
% 6.43/6.79 , clause( 29195, [ member( 'not_subclass_element'( intersection( complement(
% 6.43/6.79 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 6.43/6.79 'null_class' ), X ), =( singleton( 'not_subclass_element'( X,
% 6.43/6.79 'null_class' ) ), X ), =( X, 'null_class' ) ] )
% 6.43/6.79 , clause( 29196, [ ~( =( 'not_subclass_element'( intersection( complement(
% 6.43/6.79 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 6.43/6.79 'null_class' ), 'not_subclass_element'( X, 'null_class' ) ) ), =(
% 6.43/6.79 singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 6.43/6.79 'null_class' ) ] )
% 6.43/6.79 , clause( 29197, [ =( 'unordered_pair'( X, Y ), union( singleton( X ),
% 6.43/6.79 singleton( Y ) ) ) ] )
% 6.43/6.79 , clause( 29198, [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ] )
% 6.43/6.79 , clause( 29199, [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ] )
% 6.43/6.79 , clause( 29200, [ member( 'unordered_pair'( X, singleton( Y ) ),
% 6.43/6.79 'ordered_pair'( X, Y ) ) ] )
% 6.43/6.79 , clause( 29201, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 6.43/6.79 , 'null_class' ) ), 'ordered_pair'( X, Y ) ), member( Y,
% 6.43/6.79 'universal_class' ) ] )
% 6.43/6.79 , clause( 29202, [ ~( member( X, 'universal_class' ) ), =( 'unordered_pair'(
% 6.43/6.79 'null_class', singleton( singleton( X ) ) ), 'ordered_pair'( Y, X ) ),
% 6.43/6.79 member( Y, 'universal_class' ) ] )
% 6.43/6.79 , clause( 29203, [ =( 'unordered_pair'( 'null_class', singleton(
% 6.43/6.79 'null_class' ) ), 'ordered_pair'( X, Y ) ), member( X, 'universal_class'
% 6.43/6.79 ), member( Y, 'universal_class' ) ] )
% 6.43/6.79 , clause( 29204, [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) )
% 6.43/6.79 , ~( member( X, 'universal_class' ) ), =( X, Z ) ] )
% 6.43/6.79 , clause( 29205, [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) )
% 6.43/6.79 , ~( member( Y, 'universal_class' ) ), =( Y, T ) ] )
% 6.43/6.79 , clause( 29206, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 6.43/6.79 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( first(
% 6.43/6.79 'ordered_pair'( X, Y ) ), second( 'ordered_pair'( X, Y ) ) ),
% 6.43/6.79 'cross_product'( 'universal_class', 'universal_class' ) ) ] )
% 6.43/6.79 , clause( 29207, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 6.43/6.79 'cross_product'( 'universal_class', 'universal_class' ) ), =( first( X )
% 6.43/6.79 , X ) ] )
% 6.43/6.79 , clause( 29208, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 6.43/6.79 'cross_product'( 'universal_class', 'universal_class' ) ), =( second( X )
% 6.43/6.79 , X ) ] )
% 6.43/6.79 , clause( 29209, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.43/6.79 first( X ), X ) ] )
% 6.43/6.79 , clause( 29210, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.43/6.79 second( X ), X ) ] )
% 6.43/6.79 , clause( 29211, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 6.43/6.79 'universal_class', 'universal_class' ) ) ), =( first( 'ordered_pair'( X,
% 6.43/6.79 Y ) ), X ) ] )
% 6.43/6.79 , clause( 29212, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 6.43/6.79 'universal_class', 'universal_class' ) ) ), =( second( 'ordered_pair'( X
% 6.43/6.79 , Y ) ), Y ) ] )
% 6.43/6.79 , clause( 29213, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 6.43/6.79 'cross_product'( 'universal_class', 'universal_class' ) ), =( first( X )
% 6.43/6.79 , X ) ] )
% 6.43/6.79 , clause( 29214, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 6.43/6.79 'cross_product'( 'universal_class', 'universal_class' ) ), =( second( X )
% 6.43/6.79 , X ) ] )
% 6.43/6.79 , clause( 29215, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.43/6.79 first( X ), X ) ] )
% 6.43/6.79 , clause( 29216, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.43/6.79 second( X ), X ) ] )
% 6.43/6.79 , clause( 29217, [ ~( =( 'ordered_pair'( first( X ), second( X ) ), X ) ),
% 6.43/6.79 member( X, 'universal_class' ) ] )
% 6.43/6.79 , clause( 29218, [ ~( member( X, 'cross_product'( 'universal_class',
% 6.43/6.79 'universal_class' ) ) ), member( X, 'universal_class' ) ] )
% 6.43/6.82 , clause( 29219, [ member( X, 'universal_class' ), =( first( 'ordered_pair'(
% 6.43/6.82 X, Y ) ), 'ordered_pair'( X, Y ) ) ] )
% 6.43/6.82 , clause( 29220, [ member( X, 'universal_class' ), =( second(
% 6.43/6.82 'ordered_pair'( X, Y ) ), 'ordered_pair'( X, Y ) ) ] )
% 6.43/6.82 , clause( 29221, [ ~( member( y, 'universal_class' ) ) ] )
% 6.43/6.82 , clause( 29222, [ ~( =( second( 'ordered_pair'( x, y ) ), 'ordered_pair'(
% 6.43/6.82 x, y ) ) ) ] )
% 6.43/6.82 ] ).
% 6.43/6.82
% 6.43/6.82
% 6.43/6.82
% 6.43/6.82 subsumption(
% 6.43/6.82 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 6.43/6.82 )
% 6.43/6.82 , clause( 29054, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 6.43/6.82 ) ] )
% 6.43/6.82 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 6.43/6.82 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 6.43/6.82
% 6.43/6.82
% 6.43/6.82 subsumption(
% 6.43/6.82 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 6.43/6.82 , clause( 29057, [ subclass( X, 'universal_class' ) ] )
% 6.43/6.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 6.43/6.82
% 6.43/6.82
% 6.43/6.82 subsumption(
% 6.43/6.82 clause( 13, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) )
% 6.43/6.82 ), member( Y, T ) ] )
% 6.43/6.82 , clause( 29068, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.43/6.82 ) ) ), member( Y, T ) ] )
% 6.43/6.82 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 6.43/6.82 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 6.43/6.82
% 6.43/6.82
% 6.43/6.82 subsumption(
% 6.43/6.82 clause( 153, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( second(
% 6.43/6.82 X ), X ) ] )
% 6.43/6.82 , clause( 29210, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.43/6.82 second( X ), X ) ] )
% 6.43/6.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 6.43/6.82 1 )] ) ).
% 6.43/6.82
% 6.43/6.82
% 6.43/6.82 eqswap(
% 6.43/6.82 clause( 30874, [ =( X, second( X ) ), =( 'ordered_pair'( first( X ), second(
% 6.43/6.82 X ) ), X ) ] )
% 6.43/6.82 , clause( 153, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.43/6.82 second( X ), X ) ] )
% 6.43/6.82 , 1, substitution( 0, [ :=( X, X )] )).
% 6.43/6.82
% 6.43/6.82
% 6.43/6.82 paramod(
% 6.43/6.82 clause( 30909, [ member( X, 'cross_product'( 'universal_class',
% 6.43/6.82 'universal_class' ) ), =( X, second( X ) ), =( second( X ), X ) ] )
% 6.43/6.82 , clause( 30874, [ =( X, second( X ) ), =( 'ordered_pair'( first( X ),
% 6.43/6.82 second( X ) ), X ) ] )
% 6.43/6.82 , 1, clause( 29208, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 6.46/6.82 'cross_product'( 'universal_class', 'universal_class' ) ), =( second( X )
% 6.46/6.82 , X ) ] )
% 6.46/6.82 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 6.46/6.82 ).
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 eqswap(
% 6.46/6.82 clause( 30910, [ =( second( X ), X ), member( X, 'cross_product'(
% 6.46/6.82 'universal_class', 'universal_class' ) ), =( second( X ), X ) ] )
% 6.46/6.82 , clause( 30909, [ member( X, 'cross_product'( 'universal_class',
% 6.46/6.82 'universal_class' ) ), =( X, second( X ) ), =( second( X ), X ) ] )
% 6.46/6.82 , 1, substitution( 0, [ :=( X, X )] )).
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 factor(
% 6.46/6.82 clause( 30913, [ =( second( X ), X ), member( X, 'cross_product'(
% 6.46/6.82 'universal_class', 'universal_class' ) ) ] )
% 6.46/6.82 , clause( 30910, [ =( second( X ), X ), member( X, 'cross_product'(
% 6.46/6.82 'universal_class', 'universal_class' ) ), =( second( X ), X ) ] )
% 6.46/6.82 , 0, 2, substitution( 0, [ :=( X, X )] )).
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 subsumption(
% 6.46/6.82 clause( 157, [ =( second( X ), X ), member( X, 'cross_product'(
% 6.46/6.82 'universal_class', 'universal_class' ) ) ] )
% 6.46/6.82 , clause( 30913, [ =( second( X ), X ), member( X, 'cross_product'(
% 6.46/6.82 'universal_class', 'universal_class' ) ) ] )
% 6.46/6.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 6.46/6.82 1 )] ) ).
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 subsumption(
% 6.46/6.82 clause( 162, [ ~( member( y, 'universal_class' ) ) ] )
% 6.46/6.82 , clause( 29221, [ ~( member( y, 'universal_class' ) ) ] )
% 6.46/6.82 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 subsumption(
% 6.46/6.82 clause( 163, [ ~( =( second( 'ordered_pair'( x, y ) ), 'ordered_pair'( x, y
% 6.46/6.82 ) ) ) ] )
% 6.46/6.82 , clause( 29222, [ ~( =( second( 'ordered_pair'( x, y ) ), 'ordered_pair'(
% 6.46/6.82 x, y ) ) ) ] )
% 6.46/6.82 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 resolution(
% 6.46/6.82 clause( 31226, [ ~( subclass( X, 'universal_class' ) ), ~( member( y, X ) )
% 6.46/6.82 ] )
% 6.46/6.82 , clause( 162, [ ~( member( y, 'universal_class' ) ) ] )
% 6.46/6.82 , 0, clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 6.46/6.82 ) ] )
% 6.46/6.82 , 2, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y,
% 6.46/6.82 'universal_class' ), :=( Z, y )] )).
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 resolution(
% 6.46/6.82 clause( 31227, [ ~( member( y, X ) ) ] )
% 6.46/6.82 , clause( 31226, [ ~( subclass( X, 'universal_class' ) ), ~( member( y, X )
% 6.46/6.82 ) ] )
% 6.46/6.82 , 0, clause( 3, [ subclass( X, 'universal_class' ) ] )
% 6.46/6.82 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 6.46/6.82 ).
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 subsumption(
% 6.46/6.82 clause( 182, [ ~( member( y, X ) ) ] )
% 6.46/6.82 , clause( 31227, [ ~( member( y, X ) ) ] )
% 6.46/6.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 resolution(
% 6.46/6.82 clause( 31228, [ ~( member( 'ordered_pair'( Y, y ), 'cross_product'( Z, X )
% 6.46/6.82 ) ) ] )
% 6.46/6.82 , clause( 182, [ ~( member( y, X ) ) ] )
% 6.46/6.82 , 0, clause( 13, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.46/6.82 ) ) ), member( Y, T ) ] )
% 6.46/6.82 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, Y ), :=( Y
% 6.46/6.82 , y ), :=( Z, Z ), :=( T, X )] )).
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 subsumption(
% 6.46/6.82 clause( 673, [ ~( member( 'ordered_pair'( X, y ), 'cross_product'( Y, Z ) )
% 6.46/6.82 ) ] )
% 6.46/6.82 , clause( 31228, [ ~( member( 'ordered_pair'( Y, y ), 'cross_product'( Z, X
% 6.46/6.82 ) ) ) ] )
% 6.46/6.82 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 6.46/6.82 permutation( 0, [ ==>( 0, 0 )] ) ).
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 eqswap(
% 6.46/6.82 clause( 31229, [ ~( =( 'ordered_pair'( x, y ), second( 'ordered_pair'( x, y
% 6.46/6.82 ) ) ) ) ] )
% 6.46/6.82 , clause( 163, [ ~( =( second( 'ordered_pair'( x, y ) ), 'ordered_pair'( x
% 6.46/6.82 , y ) ) ) ] )
% 6.46/6.82 , 0, substitution( 0, [] )).
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 eqswap(
% 6.46/6.82 clause( 31230, [ =( X, second( X ) ), member( X, 'cross_product'(
% 6.46/6.82 'universal_class', 'universal_class' ) ) ] )
% 6.46/6.82 , clause( 157, [ =( second( X ), X ), member( X, 'cross_product'(
% 6.46/6.82 'universal_class', 'universal_class' ) ) ] )
% 6.46/6.82 , 0, substitution( 0, [ :=( X, X )] )).
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 resolution(
% 6.46/6.82 clause( 31231, [ member( 'ordered_pair'( x, y ), 'cross_product'(
% 6.46/6.82 'universal_class', 'universal_class' ) ) ] )
% 6.46/6.82 , clause( 31229, [ ~( =( 'ordered_pair'( x, y ), second( 'ordered_pair'( x
% 6.46/6.82 , y ) ) ) ) ] )
% 6.46/6.82 , 0, clause( 31230, [ =( X, second( X ) ), member( X, 'cross_product'(
% 6.46/6.82 'universal_class', 'universal_class' ) ) ] )
% 6.46/6.82 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'ordered_pair'( x, y
% 6.46/6.82 ) )] )).
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 resolution(
% 6.46/6.82 clause( 31232, [] )
% 6.46/6.82 , clause( 673, [ ~( member( 'ordered_pair'( X, y ), 'cross_product'( Y, Z )
% 6.46/6.82 ) ) ] )
% 6.46/6.82 , 0, clause( 31231, [ member( 'ordered_pair'( x, y ), 'cross_product'(
% 6.46/6.82 'universal_class', 'universal_class' ) ) ] )
% 6.46/6.82 , 0, substitution( 0, [ :=( X, x ), :=( Y, 'universal_class' ), :=( Z,
% 6.46/6.82 'universal_class' )] ), substitution( 1, [] )).
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 subsumption(
% 6.46/6.82 clause( 29052, [] )
% 6.46/6.82 , clause( 31232, [] )
% 6.46/6.82 , substitution( 0, [] ), permutation( 0, [] ) ).
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 end.
% 6.46/6.82
% 6.46/6.82 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 6.46/6.82
% 6.46/6.82 Memory use:
% 6.46/6.82
% 6.46/6.82 space for terms: 521700
% 6.46/6.82 space for clauses: 1340851
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 clauses generated: 95994
% 6.46/6.82 clauses kept: 29053
% 6.46/6.82 clauses selected: 614
% 6.46/6.82 clauses deleted: 2243
% 6.46/6.82 clauses inuse deleted: 92
% 6.46/6.82
% 6.46/6.82 subsentry: 414131
% 6.46/6.82 literals s-matched: 292602
% 6.46/6.82 literals matched: 281877
% 6.46/6.82 full subsumption: 160922
% 6.46/6.82
% 6.46/6.82 checksum: -117278892
% 6.46/6.82
% 6.46/6.82
% 6.46/6.82 Bliksem ended
%------------------------------------------------------------------------------