TSTP Solution File: SET239-6 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET239-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 22:48:20 EDT 2022
% Result : Unsatisfiable 0.74s 1.18s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET239-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n017.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 : Sun Jul 10 08:54:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.08 *** allocated 10000 integers for termspace/termends
% 0.44/1.08 *** allocated 10000 integers for clauses
% 0.44/1.08 *** allocated 10000 integers for justifications
% 0.44/1.08 Bliksem 1.12
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 Automatic Strategy Selection
% 0.44/1.08
% 0.44/1.08 Clauses:
% 0.44/1.08 [
% 0.44/1.08 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.44/1.08 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.44/1.08 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.44/1.08 ,
% 0.44/1.08 [ subclass( X, 'universal_class' ) ],
% 0.44/1.08 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.44/1.08 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.44/1.08 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.44/1.08 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.44/1.08 ,
% 0.44/1.08 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.44/1.08 ) ) ],
% 0.44/1.08 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.44/1.08 ) ) ],
% 0.44/1.08 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.44/1.08 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.44/1.08 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.44/1.08 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.44/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.44/1.08 X, Z ) ],
% 0.44/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.44/1.08 Y, T ) ],
% 0.44/1.08 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.44/1.08 ), 'cross_product'( Y, T ) ) ],
% 0.44/1.08 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.44/1.08 ), second( X ) ), X ) ],
% 0.44/1.08 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.44/1.08 'universal_class' ) ) ],
% 0.44/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.44/1.08 Y ) ],
% 0.44/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.44/1.08 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.44/1.08 , Y ), 'element_relation' ) ],
% 0.44/1.08 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.44/1.08 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.44/1.08 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.44/1.08 Z ) ) ],
% 0.44/1.09 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.44/1.09 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.44/1.09 member( X, Y ) ],
% 0.44/1.09 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.44/1.09 union( X, Y ) ) ],
% 0.44/1.09 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.44/1.09 intersection( complement( X ), complement( Y ) ) ) ),
% 0.44/1.09 'symmetric_difference'( X, Y ) ) ],
% 0.44/1.09 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.44/1.09 ,
% 0.44/1.09 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.44/1.09 ,
% 0.44/1.09 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.44/1.09 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.44/1.09 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.44/1.09 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.44/1.09 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.44/1.09 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.44/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.44/1.09 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.44/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.44/1.09 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.44/1.09 'cross_product'( 'universal_class', 'universal_class' ),
% 0.44/1.09 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.44/1.09 Y ), rotate( T ) ) ],
% 0.44/1.09 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.44/1.09 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.44/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.44/1.09 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.44/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.44/1.09 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.44/1.09 'cross_product'( 'universal_class', 'universal_class' ),
% 0.44/1.09 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.44/1.09 Z ), flip( T ) ) ],
% 0.44/1.09 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.44/1.09 inverse( X ) ) ],
% 0.44/1.09 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.44/1.09 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.44/1.09 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.44/1.09 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.44/1.09 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.44/1.09 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.44/1.09 ],
% 0.44/1.09 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.44/1.09 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.44/1.09 'universal_class' ) ) ],
% 0.44/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.44/1.09 successor( X ), Y ) ],
% 0.44/1.09 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.44/1.09 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.44/1.09 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.44/1.09 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.44/1.09 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.44/1.09 ,
% 0.44/1.09 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.44/1.09 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.44/1.09 [ inductive( omega ) ],
% 0.44/1.09 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.44/1.09 [ member( omega, 'universal_class' ) ],
% 0.44/1.09 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.44/1.09 , 'sum_class'( X ) ) ],
% 0.44/1.09 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.44/1.09 'universal_class' ) ],
% 0.44/1.09 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.44/1.09 'power_class'( X ) ) ],
% 0.44/1.09 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.44/1.09 'universal_class' ) ],
% 0.44/1.09 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.44/1.09 'universal_class' ) ) ],
% 0.44/1.09 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.44/1.09 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.44/1.09 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.44/1.09 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.44/1.09 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.44/1.09 ) ],
% 0.44/1.09 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.44/1.09 , 'identity_relation' ) ],
% 0.44/1.09 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.44/1.09 'single_valued_class'( X ) ],
% 0.44/1.09 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.44/1.09 'universal_class' ) ) ],
% 0.44/1.09 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.44/1.09 'identity_relation' ) ],
% 0.44/1.09 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.44/1.09 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.44/1.09 , function( X ) ],
% 0.44/1.09 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.44/1.09 X, Y ), 'universal_class' ) ],
% 0.44/1.09 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.44/1.09 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.44/1.09 ) ],
% 0.44/1.09 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.44/1.09 [ function( choice ) ],
% 0.44/1.09 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.44/1.09 apply( choice, X ), X ) ],
% 0.44/1.09 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.44/1.09 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.44/1.09 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.44/1.09 ,
% 0.44/1.09 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.44/1.09 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.44/1.09 , complement( compose( complement( 'element_relation' ), inverse(
% 0.44/1.09 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.44/1.09 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.44/1.09 'identity_relation' ) ],
% 0.44/1.09 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.44/1.09 , diagonalise( X ) ) ],
% 0.44/1.09 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.44/1.09 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.44/1.09 [ ~( operation( X ) ), function( X ) ],
% 0.44/1.09 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.44/1.09 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.44/1.09 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.44/1.09 'domain_of'( X ) ) ) ],
% 0.44/1.09 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.44/1.09 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.44/1.09 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.44/1.09 X ) ],
% 0.44/1.09 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.44/1.09 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.44/1.09 'domain_of'( X ) ) ],
% 0.44/1.09 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.44/1.09 'domain_of'( Z ) ) ) ],
% 0.44/1.09 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.44/1.09 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.44/1.09 ), compatible( X, Y, Z ) ],
% 0.44/1.09 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.44/1.09 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.44/1.09 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.44/1.09 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.44/1.09 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.44/1.09 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.44/1.09 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.44/1.09 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.44/1.09 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.44/1.09 , Y ) ],
% 0.44/1.09 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.44/1.09 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.44/1.09 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.44/1.09 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.44/1.09 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.44/1.09 [ subclass( 'compose_class'( X ), 'cross_product'( 'universal_class',
% 0.44/1.09 'universal_class' ) ) ],
% 0.44/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ), =(
% 0.44/1.09 compose( Z, X ), Y ) ],
% 0.44/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.44/1.09 , 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) ), member(
% 0.44/1.09 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ],
% 0.44/1.09 [ subclass( 'composition_function', 'cross_product'( 'universal_class',
% 0.44/1.09 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.44/1.09 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.44/1.09 'composition_function' ) ), =( compose( X, Y ), Z ) ],
% 0.44/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.44/1.09 , 'universal_class' ) ) ), member( 'ordered_pair'( X, 'ordered_pair'( Y,
% 0.44/1.09 compose( X, Y ) ) ), 'composition_function' ) ],
% 0.44/1.09 [ subclass( 'domain_relation', 'cross_product'( 'universal_class',
% 0.44/1.09 'universal_class' ) ) ],
% 0.44/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) ), =(
% 0.44/1.09 'domain_of'( X ), Y ) ],
% 0.44/1.09 [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X,
% 0.44/1.09 'domain_of'( X ) ), 'domain_relation' ) ],
% 0.44/1.09 [ =( first( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.44/1.09 'identity_relation' ) ), 'single_valued1'( X ) ) ],
% 0.44/1.09 [ =( second( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.44/1.09 'identity_relation' ) ), 'single_valued2'( X ) ) ],
% 0.44/1.09 [ =( domain( X, image( inverse( X ), singleton( 'single_valued1'( X ) )
% 0.44/1.09 ), 'single_valued2'( X ) ), 'single_valued3'( X ) ) ],
% 0.44/1.09 [ =( intersection( complement( compose( 'element_relation', complement(
% 0.44/1.09 'identity_relation' ) ) ), 'element_relation' ), 'singleton_relation' ) ]
% 0.44/1.09 ,
% 0.44/1.09 [ subclass( 'application_function', 'cross_product'( 'universal_class',
% 0.44/1.09 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.44/1.09 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.44/1.09 'application_function' ) ), member( Y, 'domain_of'( X ) ) ],
% 0.44/1.09 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.44/1.09 'application_function' ) ), =( apply( X, Y ), Z ) ],
% 0.44/1.09 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.44/1.09 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 0.44/1.09 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 0.44/1.09 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 0.44/1.09 'application_function' ) ],
% 0.44/1.09 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.44/1.09 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 0.74/1.18 [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ],
% 0.74/1.18 [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ), maps( X,
% 0.74/1.18 'domain_of'( X ), Y ) ],
% 0.74/1.18 [ member( z, restrict( xr, x, y ) ) ],
% 0.74/1.18 [ ~( member( z, xr ) ) ]
% 0.74/1.18 ] .
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 percentage equality = 0.222727, percentage horn = 0.929825
% 0.74/1.18 This is a problem with some equality
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 Options Used:
% 0.74/1.18
% 0.74/1.18 useres = 1
% 0.74/1.18 useparamod = 1
% 0.74/1.18 useeqrefl = 1
% 0.74/1.18 useeqfact = 1
% 0.74/1.18 usefactor = 1
% 0.74/1.18 usesimpsplitting = 0
% 0.74/1.18 usesimpdemod = 5
% 0.74/1.18 usesimpres = 3
% 0.74/1.18
% 0.74/1.18 resimpinuse = 1000
% 0.74/1.18 resimpclauses = 20000
% 0.74/1.18 substype = eqrewr
% 0.74/1.18 backwardsubs = 1
% 0.74/1.18 selectoldest = 5
% 0.74/1.18
% 0.74/1.18 litorderings [0] = split
% 0.74/1.18 litorderings [1] = extend the termordering, first sorting on arguments
% 0.74/1.18
% 0.74/1.18 termordering = kbo
% 0.74/1.18
% 0.74/1.18 litapriori = 0
% 0.74/1.18 termapriori = 1
% 0.74/1.18 litaposteriori = 0
% 0.74/1.18 termaposteriori = 0
% 0.74/1.18 demodaposteriori = 0
% 0.74/1.18 ordereqreflfact = 0
% 0.74/1.18
% 0.74/1.18 litselect = negord
% 0.74/1.18
% 0.74/1.18 maxweight = 15
% 0.74/1.18 maxdepth = 30000
% 0.74/1.18 maxlength = 115
% 0.74/1.18 maxnrvars = 195
% 0.74/1.18 excuselevel = 1
% 0.74/1.18 increasemaxweight = 1
% 0.74/1.18
% 0.74/1.18 maxselected = 10000000
% 0.74/1.18 maxnrclauses = 10000000
% 0.74/1.18
% 0.74/1.18 showgenerated = 0
% 0.74/1.18 showkept = 0
% 0.74/1.18 showselected = 0
% 0.74/1.18 showdeleted = 0
% 0.74/1.18 showresimp = 1
% 0.74/1.18 showstatus = 2000
% 0.74/1.18
% 0.74/1.18 prologoutput = 1
% 0.74/1.18 nrgoals = 5000000
% 0.74/1.18 totalproof = 1
% 0.74/1.18
% 0.74/1.18 Symbols occurring in the translation:
% 0.74/1.18
% 0.74/1.18 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.74/1.18 . [1, 2] (w:1, o:66, a:1, s:1, b:0),
% 0.74/1.18 ! [4, 1] (w:0, o:37, a:1, s:1, b:0),
% 0.74/1.18 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.18 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.18 subclass [41, 2] (w:1, o:91, a:1, s:1, b:0),
% 0.74/1.18 member [43, 2] (w:1, o:92, a:1, s:1, b:0),
% 0.74/1.18 'not_subclass_element' [44, 2] (w:1, o:93, a:1, s:1, b:0),
% 0.74/1.18 'universal_class' [45, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.74/1.18 'unordered_pair' [46, 2] (w:1, o:94, a:1, s:1, b:0),
% 0.74/1.18 singleton [47, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.74/1.18 'ordered_pair' [48, 2] (w:1, o:95, a:1, s:1, b:0),
% 0.74/1.18 'cross_product' [50, 2] (w:1, o:96, a:1, s:1, b:0),
% 0.74/1.18 first [52, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.74/1.18 second [53, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.74/1.18 'element_relation' [54, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.74/1.18 intersection [55, 2] (w:1, o:98, a:1, s:1, b:0),
% 0.74/1.18 complement [56, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.74/1.18 union [57, 2] (w:1, o:99, a:1, s:1, b:0),
% 0.74/1.18 'symmetric_difference' [58, 2] (w:1, o:100, a:1, s:1, b:0),
% 0.74/1.18 restrict [60, 3] (w:1, o:103, a:1, s:1, b:0),
% 0.74/1.18 'null_class' [61, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.74/1.18 'domain_of' [62, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.74/1.18 rotate [63, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.74/1.18 flip [65, 1] (w:1, o:52, a:1, s:1, b:0),
% 0.74/1.18 inverse [66, 1] (w:1, o:53, a:1, s:1, b:0),
% 0.74/1.18 'range_of' [67, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.74/1.18 domain [68, 3] (w:1, o:105, a:1, s:1, b:0),
% 0.74/1.18 range [69, 3] (w:1, o:106, a:1, s:1, b:0),
% 0.74/1.18 image [70, 2] (w:1, o:97, a:1, s:1, b:0),
% 0.74/1.18 successor [71, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.74/1.18 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.74/1.18 inductive [73, 1] (w:1, o:55, a:1, s:1, b:0),
% 0.74/1.18 omega [74, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.74/1.18 'sum_class' [75, 1] (w:1, o:56, a:1, s:1, b:0),
% 0.74/1.18 'power_class' [76, 1] (w:1, o:59, a:1, s:1, b:0),
% 0.74/1.18 compose [78, 2] (w:1, o:101, a:1, s:1, b:0),
% 0.74/1.18 'single_valued_class' [79, 1] (w:1, o:60, a:1, s:1, b:0),
% 0.74/1.18 'identity_relation' [80, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.74/1.18 function [82, 1] (w:1, o:61, a:1, s:1, b:0),
% 0.74/1.18 regular [83, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.74/1.18 apply [84, 2] (w:1, o:102, a:1, s:1, b:0),
% 0.74/1.18 choice [85, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.74/1.18 'one_to_one' [86, 1] (w:1, o:57, a:1, s:1, b:0),
% 0.74/1.18 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 0.74/1.18 diagonalise [88, 1] (w:1, o:62, a:1, s:1, b:0),
% 0.74/1.18 cantor [89, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.74/1.18 operation [90, 1] (w:1, o:58, a:1, s:1, b:0),
% 0.74/1.18 compatible [94, 3] (w:1, o:104, a:1, s:1, b:0),
% 0.74/1.18 homomorphism [95, 3] (w:1, o:107, a:1, s:1, b:0),
% 0.74/1.18 'not_homomorphism1' [96, 3] (w:1, o:109, a:1, s:1, b:0),
% 0.74/1.18 'not_homomorphism2' [97, 3] (w:1, o:110, a:1, s:1, b:0),
% 0.74/1.18 'compose_class' [98, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.74/1.18 'composition_function' [99, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.74/1.18 'domain_relation' [100, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.74/1.18 'single_valued1' [101, 1] (w:1, o:63, a:1, s:1, b:0),
% 0.74/1.18 'single_valued2' [102, 1] (w:1, o:64, a:1, s:1, b:0),
% 0.74/1.18 'single_valued3' [103, 1] (w:1, o:65, a:1, s:1, b:0),
% 0.74/1.18 'singleton_relation' [104, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.74/1.18 'application_function' [105, 0] (w:1, o:32, a:1, s:1, b:0),
% 0.74/1.18 maps [106, 3] (w:1, o:108, a:1, s:1, b:0),
% 0.74/1.18 z [107, 0] (w:1, o:34, a:1, s:1, b:0),
% 0.74/1.18 xr [108, 0] (w:1, o:35, a:1, s:1, b:0),
% 0.74/1.18 x [109, 0] (w:1, o:36, a:1, s:1, b:0),
% 0.74/1.18 y [110, 0] (w:1, o:33, a:1, s:1, b:0).
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 Starting Search:
% 0.74/1.18
% 0.74/1.18 Resimplifying inuse:
% 0.74/1.18 Done
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 Intermediate Status:
% 0.74/1.18 Generated: 4382
% 0.74/1.18 Kept: 2009
% 0.74/1.18 Inuse: 107
% 0.74/1.18 Deleted: 3
% 0.74/1.18 Deletedinuse: 2
% 0.74/1.18
% 0.74/1.18 Resimplifying inuse:
% 0.74/1.18 Done
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 Bliksems!, er is een bewijs:
% 0.74/1.18 % SZS status Unsatisfiable
% 0.74/1.18 % SZS output start Refutation
% 0.74/1.18
% 0.74/1.18 clause( 19, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ] )
% 0.74/1.18 .
% 0.74/1.18 clause( 26, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y
% 0.74/1.18 , Z ) ) ] )
% 0.74/1.18 .
% 0.74/1.18 clause( 111, [ member( z, restrict( xr, x, y ) ) ] )
% 0.74/1.18 .
% 0.74/1.18 clause( 112, [ ~( member( z, xr ) ) ] )
% 0.74/1.18 .
% 0.74/1.18 clause( 1407, [ ~( member( z, intersection( xr, X ) ) ) ] )
% 0.74/1.18 .
% 0.74/1.18 clause( 2160, [ ~( member( z, restrict( xr, X, Y ) ) ) ] )
% 0.74/1.18 .
% 0.74/1.18 clause( 2737, [] )
% 0.74/1.18 .
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 % SZS output end Refutation
% 0.74/1.18 found a proof!
% 0.74/1.18
% 0.74/1.18 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.74/1.18
% 0.74/1.18 initialclauses(
% 0.74/1.18 [ clause( 2739, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 0.74/1.18 ) ] )
% 0.74/1.18 , clause( 2740, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 0.74/1.18 , Y ) ] )
% 0.74/1.18 , clause( 2741, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 0.74/1.18 subclass( X, Y ) ] )
% 0.74/1.18 , clause( 2742, [ subclass( X, 'universal_class' ) ] )
% 0.74/1.18 , clause( 2743, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 0.74/1.18 , clause( 2744, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 0.74/1.18 , clause( 2745, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ]
% 0.74/1.18 )
% 0.74/1.18 , clause( 2746, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 0.74/1.18 =( X, Z ) ] )
% 0.74/1.18 , clause( 2747, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.74/1.18 'unordered_pair'( X, Y ) ) ] )
% 0.74/1.18 , clause( 2748, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.74/1.18 'unordered_pair'( Y, X ) ) ] )
% 0.74/1.18 , clause( 2749, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 0.74/1.18 )
% 0.74/1.18 , clause( 2750, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 0.74/1.18 , clause( 2751, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 0.74/1.18 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.74/1.18 , clause( 2752, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.74/1.18 ) ) ), member( X, Z ) ] )
% 0.74/1.18 , clause( 2753, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.74/1.18 ) ) ), member( Y, T ) ] )
% 0.74/1.18 , clause( 2754, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 0.74/1.18 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 0.74/1.18 , clause( 2755, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 0.74/1.18 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 0.74/1.18 , clause( 2756, [ subclass( 'element_relation', 'cross_product'(
% 0.74/1.18 'universal_class', 'universal_class' ) ) ] )
% 0.74/1.18 , clause( 2757, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) )
% 0.74/1.18 , member( X, Y ) ] )
% 0.74/1.18 , clause( 2758, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.74/1.18 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 0.74/1.18 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 0.74/1.18 , clause( 2759, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.74/1.18 )
% 0.74/1.18 , clause( 2760, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 0.74/1.18 )
% 0.74/1.18 , clause( 2761, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 0.74/1.18 intersection( Y, Z ) ) ] )
% 0.74/1.18 , clause( 2762, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 0.74/1.18 )
% 0.74/1.18 , clause( 2763, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.74/1.18 complement( Y ) ), member( X, Y ) ] )
% 0.74/1.18 , clause( 2764, [ =( complement( intersection( complement( X ), complement(
% 0.74/1.18 Y ) ) ), union( X, Y ) ) ] )
% 0.74/1.18 , clause( 2765, [ =( intersection( complement( intersection( X, Y ) ),
% 0.74/1.18 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 0.74/1.18 'symmetric_difference'( X, Y ) ) ] )
% 0.74/1.18 , clause( 2766, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 0.74/1.18 X, Y, Z ) ) ] )
% 0.74/1.18 , clause( 2767, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 0.74/1.18 Z, X, Y ) ) ] )
% 0.74/1.18 , clause( 2768, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 0.74/1.18 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 0.74/1.18 , clause( 2769, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 0.74/1.18 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 0.74/1.18 'domain_of'( Y ) ) ] )
% 0.74/1.18 , clause( 2770, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.74/1.18 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.74/1.18 , clause( 2771, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.74/1.18 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 0.74/1.18 ] )
% 0.74/1.18 , clause( 2772, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.74/1.18 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 0.74/1.18 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.74/1.18 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 0.74/1.18 , Y ), rotate( T ) ) ] )
% 0.74/1.18 , clause( 2773, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.74/1.18 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.74/1.18 , clause( 2774, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.74/1.18 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 0.74/1.18 )
% 0.74/1.18 , clause( 2775, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.74/1.18 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 0.74/1.18 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.74/1.18 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 0.74/1.18 , Z ), flip( T ) ) ] )
% 0.74/1.18 , clause( 2776, [ =( 'domain_of'( flip( 'cross_product'( X,
% 0.74/1.18 'universal_class' ) ) ), inverse( X ) ) ] )
% 0.74/1.18 , clause( 2777, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 0.74/1.18 , clause( 2778, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 0.74/1.18 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 0.74/1.18 , clause( 2779, [ =( second( 'not_subclass_element'( restrict( X, singleton(
% 0.74/1.18 Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 0.74/1.18 , clause( 2780, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 0.74/1.18 image( X, Y ) ) ] )
% 0.74/1.18 , clause( 2781, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 0.74/1.18 , clause( 2782, [ subclass( 'successor_relation', 'cross_product'(
% 0.74/1.18 'universal_class', 'universal_class' ) ) ] )
% 0.74/1.18 , clause( 2783, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' )
% 0.74/1.18 ), =( successor( X ), Y ) ] )
% 0.74/1.18 , clause( 2784, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X
% 0.74/1.18 , Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 0.74/1.18 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 0.74/1.18 , clause( 2785, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 0.74/1.18 , clause( 2786, [ ~( inductive( X ) ), subclass( image(
% 0.74/1.18 'successor_relation', X ), X ) ] )
% 0.74/1.18 , clause( 2787, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.74/1.18 'successor_relation', X ), X ) ), inductive( X ) ] )
% 0.74/1.18 , clause( 2788, [ inductive( omega ) ] )
% 0.74/1.18 , clause( 2789, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 0.74/1.18 , clause( 2790, [ member( omega, 'universal_class' ) ] )
% 0.74/1.18 , clause( 2791, [ =( 'domain_of'( restrict( 'element_relation',
% 0.74/1.18 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 0.74/1.18 , clause( 2792, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 0.74/1.18 X ), 'universal_class' ) ] )
% 0.74/1.18 , clause( 2793, [ =( complement( image( 'element_relation', complement( X )
% 0.74/1.18 ) ), 'power_class'( X ) ) ] )
% 0.74/1.18 , clause( 2794, [ ~( member( X, 'universal_class' ) ), member(
% 0.74/1.18 'power_class'( X ), 'universal_class' ) ] )
% 0.74/1.18 , clause( 2795, [ subclass( compose( X, Y ), 'cross_product'(
% 0.74/1.18 'universal_class', 'universal_class' ) ) ] )
% 0.74/1.18 , clause( 2796, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 0.74/1.18 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 0.74/1.18 , clause( 2797, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 0.74/1.18 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.74/1.18 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.74/1.18 ) ] )
% 0.74/1.18 , clause( 2798, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 0.74/1.18 inverse( X ) ), 'identity_relation' ) ] )
% 0.74/1.18 , clause( 2799, [ ~( subclass( compose( X, inverse( X ) ),
% 0.74/1.18 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 0.74/1.18 , clause( 2800, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 0.74/1.18 'universal_class', 'universal_class' ) ) ] )
% 0.74/1.18 , clause( 2801, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 0.74/1.18 , 'identity_relation' ) ] )
% 0.74/1.18 , clause( 2802, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 0.74/1.18 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 0.74/1.18 'identity_relation' ) ), function( X ) ] )
% 0.74/1.18 , clause( 2803, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ),
% 0.74/1.18 member( image( X, Y ), 'universal_class' ) ] )
% 0.74/1.18 , clause( 2804, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.74/1.18 , clause( 2805, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 0.74/1.18 , 'null_class' ) ] )
% 0.74/1.18 , clause( 2806, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y
% 0.74/1.18 ) ) ] )
% 0.74/1.18 , clause( 2807, [ function( choice ) ] )
% 0.74/1.18 , clause( 2808, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' )
% 0.74/1.18 , member( apply( choice, X ), X ) ] )
% 0.74/1.18 , clause( 2809, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 0.74/1.18 , clause( 2810, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 0.74/1.18 , clause( 2811, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 0.74/1.18 'one_to_one'( X ) ] )
% 0.74/1.18 , clause( 2812, [ =( intersection( 'cross_product'( 'universal_class',
% 0.74/1.18 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 0.74/1.18 'universal_class' ), complement( compose( complement( 'element_relation'
% 0.74/1.18 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 0.74/1.18 , clause( 2813, [ =( intersection( inverse( 'subset_relation' ),
% 0.74/1.18 'subset_relation' ), 'identity_relation' ) ] )
% 0.74/1.18 , clause( 2814, [ =( complement( 'domain_of'( intersection( X,
% 0.74/1.18 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 0.74/1.18 , clause( 2815, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 0.74/1.18 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 0.74/1.18 , clause( 2816, [ ~( operation( X ) ), function( X ) ] )
% 0.74/1.18 , clause( 2817, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 0.74/1.18 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.74/1.18 ] )
% 0.74/1.18 , clause( 2818, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 0.74/1.18 'domain_of'( 'domain_of'( X ) ) ) ] )
% 0.74/1.18 , clause( 2819, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 0.74/1.18 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.74/1.18 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 0.74/1.18 operation( X ) ] )
% 0.74/1.18 , clause( 2820, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 0.74/1.18 , clause( 2821, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 0.74/1.18 Y ) ), 'domain_of'( X ) ) ] )
% 0.74/1.18 , clause( 2822, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 0.74/1.18 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 0.74/1.18 , clause( 2823, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) )
% 0.74/1.18 , 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 0.74/1.18 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 0.74/1.18 , clause( 2824, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 0.74/1.18 , clause( 2825, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 0.74/1.18 , clause( 2826, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 0.74/1.18 , clause( 2827, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 0.74/1.18 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 0.74/1.18 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 0.74/1.18 )
% 0.74/1.18 , clause( 2828, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 0.74/1.18 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.74/1.18 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.74/1.18 , Y ) ] )
% 0.74/1.18 , clause( 2829, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 0.74/1.18 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 0.74/1.18 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 0.74/1.18 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 0.74/1.18 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 0.74/1.18 )
% 0.74/1.18 , clause( 2830, [ subclass( 'compose_class'( X ), 'cross_product'(
% 0.74/1.18 'universal_class', 'universal_class' ) ) ] )
% 0.74/1.18 , clause( 2831, [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) )
% 0.74/1.18 ), =( compose( Z, X ), Y ) ] )
% 0.74/1.18 , clause( 2832, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.74/1.18 'universal_class', 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) )
% 0.74/1.18 , member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ] )
% 0.74/1.18 , clause( 2833, [ subclass( 'composition_function', 'cross_product'(
% 0.74/1.18 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 0.74/1.18 ) ) ) ] )
% 0.74/1.18 , clause( 2834, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.74/1.18 'composition_function' ) ), =( compose( X, Y ), Z ) ] )
% 0.74/1.18 , clause( 2835, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.74/1.18 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( X,
% 0.74/1.18 'ordered_pair'( Y, compose( X, Y ) ) ), 'composition_function' ) ] )
% 0.74/1.18 , clause( 2836, [ subclass( 'domain_relation', 'cross_product'(
% 0.74/1.18 'universal_class', 'universal_class' ) ) ] )
% 0.74/1.18 , clause( 2837, [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) )
% 0.74/1.18 , =( 'domain_of'( X ), Y ) ] )
% 0.74/1.18 , clause( 2838, [ ~( member( X, 'universal_class' ) ), member(
% 0.74/1.18 'ordered_pair'( X, 'domain_of'( X ) ), 'domain_relation' ) ] )
% 0.74/1.18 , clause( 2839, [ =( first( 'not_subclass_element'( compose( X, inverse( X
% 0.74/1.18 ) ), 'identity_relation' ) ), 'single_valued1'( X ) ) ] )
% 0.74/1.18 , clause( 2840, [ =( second( 'not_subclass_element'( compose( X, inverse( X
% 0.74/1.18 ) ), 'identity_relation' ) ), 'single_valued2'( X ) ) ] )
% 0.74/1.18 , clause( 2841, [ =( domain( X, image( inverse( X ), singleton(
% 0.74/1.18 'single_valued1'( X ) ) ), 'single_valued2'( X ) ), 'single_valued3'( X )
% 0.74/1.18 ) ] )
% 0.74/1.18 , clause( 2842, [ =( intersection( complement( compose( 'element_relation'
% 0.74/1.18 , complement( 'identity_relation' ) ) ), 'element_relation' ),
% 0.74/1.18 'singleton_relation' ) ] )
% 0.74/1.18 , clause( 2843, [ subclass( 'application_function', 'cross_product'(
% 0.74/1.18 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 0.74/1.18 ) ) ) ] )
% 0.74/1.18 , clause( 2844, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.74/1.18 'application_function' ) ), member( Y, 'domain_of'( X ) ) ] )
% 0.74/1.18 , clause( 2845, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.74/1.18 'application_function' ) ), =( apply( X, Y ), Z ) ] )
% 0.74/1.18 , clause( 2846, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.74/1.18 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 0.74/1.18 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 0.74/1.18 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 0.74/1.18 'application_function' ) ] )
% 0.74/1.18 , clause( 2847, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 0.74/1.18 , clause( 2848, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 0.74/1.18 , clause( 2849, [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ] )
% 0.74/1.18 , clause( 2850, [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ),
% 0.74/1.18 maps( X, 'domain_of'( X ), Y ) ] )
% 0.74/1.18 , clause( 2851, [ member( z, restrict( xr, x, y ) ) ] )
% 0.74/1.18 , clause( 2852, [ ~( member( z, xr ) ) ] )
% 0.74/1.18 ] ).
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 subsumption(
% 0.74/1.18 clause( 19, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ] )
% 0.74/1.18 , clause( 2759, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.74/1.18 )
% 0.74/1.18 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.74/1.18 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 subsumption(
% 0.74/1.18 clause( 26, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y
% 0.74/1.18 , Z ) ) ] )
% 0.74/1.18 , clause( 2766, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 0.74/1.18 X, Y, Z ) ) ] )
% 0.74/1.18 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.74/1.18 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 subsumption(
% 0.74/1.18 clause( 111, [ member( z, restrict( xr, x, y ) ) ] )
% 0.74/1.18 , clause( 2851, [ member( z, restrict( xr, x, y ) ) ] )
% 0.74/1.18 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 subsumption(
% 0.74/1.18 clause( 112, [ ~( member( z, xr ) ) ] )
% 0.74/1.18 , clause( 2852, [ ~( member( z, xr ) ) ] )
% 0.74/1.18 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 resolution(
% 0.74/1.18 clause( 3001, [ ~( member( z, intersection( xr, X ) ) ) ] )
% 0.74/1.18 , clause( 112, [ ~( member( z, xr ) ) ] )
% 0.74/1.18 , 0, clause( 19, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.74/1.18 )
% 0.74/1.18 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, z ), :=( Y, xr ),
% 0.74/1.18 :=( Z, X )] )).
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 subsumption(
% 0.74/1.18 clause( 1407, [ ~( member( z, intersection( xr, X ) ) ) ] )
% 0.74/1.18 , clause( 3001, [ ~( member( z, intersection( xr, X ) ) ) ] )
% 0.74/1.18 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 paramod(
% 0.74/1.18 clause( 3003, [ ~( member( z, restrict( xr, X, Y ) ) ) ] )
% 0.74/1.18 , clause( 26, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X
% 0.74/1.18 , Y, Z ) ) ] )
% 0.74/1.18 , 0, clause( 1407, [ ~( member( z, intersection( xr, X ) ) ) ] )
% 0.74/1.18 , 0, 3, substitution( 0, [ :=( X, xr ), :=( Y, X ), :=( Z, Y )] ),
% 0.74/1.18 substitution( 1, [ :=( X, 'cross_product'( X, Y ) )] )).
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 subsumption(
% 0.74/1.18 clause( 2160, [ ~( member( z, restrict( xr, X, Y ) ) ) ] )
% 0.74/1.18 , clause( 3003, [ ~( member( z, restrict( xr, X, Y ) ) ) ] )
% 0.74/1.18 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.74/1.18 )] ) ).
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 resolution(
% 0.74/1.18 clause( 3004, [] )
% 0.74/1.18 , clause( 2160, [ ~( member( z, restrict( xr, X, Y ) ) ) ] )
% 0.74/1.18 , 0, clause( 111, [ member( z, restrict( xr, x, y ) ) ] )
% 0.74/1.18 , 0, substitution( 0, [ :=( X, x ), :=( Y, y )] ), substitution( 1, [] )
% 0.74/1.18 ).
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 subsumption(
% 0.74/1.18 clause( 2737, [] )
% 0.74/1.18 , clause( 3004, [] )
% 0.74/1.18 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 end.
% 0.74/1.18
% 0.74/1.18 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.74/1.18
% 0.74/1.18 Memory use:
% 0.74/1.18
% 0.74/1.18 space for terms: 41248
% 0.74/1.18 space for clauses: 133186
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 clauses generated: 5989
% 0.74/1.18 clauses kept: 2738
% 0.74/1.18 clauses selected: 139
% 0.74/1.18 clauses deleted: 11
% 0.74/1.18 clauses inuse deleted: 3
% 0.74/1.18
% 0.74/1.18 subsentry: 14235
% 0.74/1.18 literals s-matched: 11517
% 0.74/1.18 literals matched: 11283
% 0.74/1.18 full subsumption: 5878
% 0.74/1.18
% 0.74/1.18 checksum: 140624893
% 0.74/1.18
% 0.74/1.18
% 0.74/1.18 Bliksem ended
%------------------------------------------------------------------------------