TSTP Solution File: SET204-6 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET204-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n014.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 22:48:08 EDT 2022
% Result : Unsatisfiable 1.42s 1.80s
% Output : Refutation 1.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET204-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Mon Jul 11 03:38:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.68/1.08 *** allocated 10000 integers for termspace/termends
% 0.68/1.08 *** allocated 10000 integers for clauses
% 0.68/1.08 *** allocated 10000 integers for justifications
% 0.68/1.08 Bliksem 1.12
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 Automatic Strategy Selection
% 0.68/1.08
% 0.68/1.08 Clauses:
% 0.68/1.08 [
% 0.68/1.08 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.68/1.08 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.68/1.08 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.68/1.08 ,
% 0.68/1.08 [ subclass( X, 'universal_class' ) ],
% 0.68/1.08 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.68/1.08 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.68/1.08 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.68/1.08 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.68/1.08 ,
% 0.68/1.08 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.68/1.08 ) ) ],
% 0.68/1.08 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.68/1.08 ) ) ],
% 0.68/1.08 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.68/1.08 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.68/1.08 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.68/1.08 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.68/1.08 X, Z ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.68/1.08 Y, T ) ],
% 0.68/1.08 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.68/1.08 ), 'cross_product'( Y, T ) ) ],
% 0.68/1.08 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.68/1.08 ), second( X ) ), X ) ],
% 0.68/1.08 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.68/1.08 'universal_class' ) ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.68/1.08 Y ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.68/1.08 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.68/1.08 , Y ), 'element_relation' ) ],
% 0.68/1.08 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.68/1.08 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.68/1.08 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.68/1.08 Z ) ) ],
% 0.68/1.08 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.68/1.08 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.68/1.08 member( X, Y ) ],
% 0.68/1.08 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.68/1.08 union( X, Y ) ) ],
% 0.68/1.08 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.68/1.08 intersection( complement( X ), complement( Y ) ) ) ),
% 0.68/1.08 'symmetric_difference'( X, Y ) ) ],
% 0.68/1.08 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.68/1.08 ,
% 0.68/1.08 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.68/1.08 ,
% 0.68/1.08 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.68/1.08 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.68/1.08 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.68/1.08 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.68/1.08 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.68/1.08 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.68/1.08 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.68/1.08 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.68/1.08 'cross_product'( 'universal_class', 'universal_class' ),
% 0.68/1.08 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.68/1.08 Y ), rotate( T ) ) ],
% 0.68/1.08 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.68/1.08 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.68/1.08 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.68/1.08 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.68/1.08 'cross_product'( 'universal_class', 'universal_class' ),
% 0.68/1.08 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.68/1.08 Z ), flip( T ) ) ],
% 0.68/1.08 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.68/1.08 inverse( X ) ) ],
% 0.68/1.08 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.68/1.08 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.68/1.08 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.68/1.08 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.68/1.08 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.68/1.08 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.68/1.08 ],
% 0.68/1.08 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.68/1.08 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.68/1.08 'universal_class' ) ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.68/1.08 successor( X ), Y ) ],
% 0.68/1.08 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.68/1.08 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.68/1.08 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.68/1.08 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.68/1.08 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.68/1.08 ,
% 0.68/1.08 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.68/1.08 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.68/1.08 [ inductive( omega ) ],
% 0.68/1.08 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.68/1.08 [ member( omega, 'universal_class' ) ],
% 0.68/1.08 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.68/1.08 , 'sum_class'( X ) ) ],
% 0.68/1.08 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.68/1.08 'universal_class' ) ],
% 0.68/1.08 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.68/1.08 'power_class'( X ) ) ],
% 0.68/1.08 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.68/1.08 'universal_class' ) ],
% 0.68/1.08 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.68/1.08 'universal_class' ) ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.68/1.08 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.68/1.08 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.68/1.08 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.68/1.08 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.68/1.08 ) ],
% 0.68/1.08 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.68/1.08 , 'identity_relation' ) ],
% 0.68/1.08 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.68/1.08 'single_valued_class'( X ) ],
% 0.68/1.08 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.68/1.08 'universal_class' ) ) ],
% 0.68/1.08 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.68/1.08 'identity_relation' ) ],
% 0.68/1.08 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.68/1.08 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.68/1.08 , function( X ) ],
% 0.68/1.08 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.68/1.08 X, Y ), 'universal_class' ) ],
% 0.68/1.08 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.68/1.08 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.68/1.08 ) ],
% 0.68/1.08 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.68/1.08 [ function( choice ) ],
% 0.68/1.08 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.68/1.08 apply( choice, X ), X ) ],
% 0.68/1.08 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.68/1.08 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.68/1.08 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.68/1.08 ,
% 0.68/1.08 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.68/1.08 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.68/1.08 , complement( compose( complement( 'element_relation' ), inverse(
% 0.68/1.08 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.68/1.08 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.68/1.08 'identity_relation' ) ],
% 0.68/1.08 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.68/1.08 , diagonalise( X ) ) ],
% 0.68/1.08 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.68/1.08 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.68/1.08 [ ~( operation( X ) ), function( X ) ],
% 0.68/1.08 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.68/1.08 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.68/1.08 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.68/1.08 'domain_of'( X ) ) ) ],
% 0.68/1.08 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.68/1.08 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.68/1.08 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.68/1.08 X ) ],
% 0.68/1.08 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.68/1.08 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.68/1.08 'domain_of'( X ) ) ],
% 0.68/1.08 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.68/1.08 'domain_of'( Z ) ) ) ],
% 0.68/1.08 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.68/1.08 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.68/1.08 ), compatible( X, Y, Z ) ],
% 0.68/1.08 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.68/1.08 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.68/1.08 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.68/1.08 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.68/1.08 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.68/1.08 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.68/1.08 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.68/1.08 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.68/1.08 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.68/1.08 , Y ) ],
% 0.68/1.08 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.68/1.08 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.68/1.08 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.68/1.08 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.68/1.08 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.68/1.08 [ subclass( 'compose_class'( X ), 'cross_product'( 'universal_class',
% 0.68/1.08 'universal_class' ) ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ), =(
% 0.68/1.08 compose( Z, X ), Y ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.68/1.08 , 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) ), member(
% 0.68/1.08 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ],
% 0.68/1.08 [ subclass( 'composition_function', 'cross_product'( 'universal_class',
% 0.68/1.08 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.68/1.08 'composition_function' ) ), =( compose( X, Y ), Z ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.68/1.08 , 'universal_class' ) ) ), member( 'ordered_pair'( X, 'ordered_pair'( Y,
% 0.68/1.08 compose( X, Y ) ) ), 'composition_function' ) ],
% 0.68/1.08 [ subclass( 'domain_relation', 'cross_product'( 'universal_class',
% 0.68/1.08 'universal_class' ) ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) ), =(
% 0.68/1.08 'domain_of'( X ), Y ) ],
% 0.68/1.08 [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X,
% 0.68/1.08 'domain_of'( X ) ), 'domain_relation' ) ],
% 0.68/1.08 [ =( first( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.68/1.08 'identity_relation' ) ), 'single_valued1'( X ) ) ],
% 0.68/1.08 [ =( second( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.68/1.08 'identity_relation' ) ), 'single_valued2'( X ) ) ],
% 0.68/1.08 [ =( domain( X, image( inverse( X ), singleton( 'single_valued1'( X ) )
% 0.68/1.08 ), 'single_valued2'( X ) ), 'single_valued3'( X ) ) ],
% 0.68/1.08 [ =( intersection( complement( compose( 'element_relation', complement(
% 0.68/1.08 'identity_relation' ) ) ), 'element_relation' ), 'singleton_relation' ) ]
% 0.68/1.08 ,
% 0.68/1.08 [ subclass( 'application_function', 'cross_product'( 'universal_class',
% 0.68/1.08 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.68/1.08 'application_function' ) ), member( Y, 'domain_of'( X ) ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.68/1.08 'application_function' ) ), =( apply( X, Y ), Z ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.68/1.08 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 0.68/1.08 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 0.68/1.08 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 0.68/1.08 'application_function' ) ],
% 0.68/1.08 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.68/1.08 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 1.42/1.80 [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ],
% 1.42/1.80 [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ), maps( X,
% 1.42/1.80 'domain_of'( X ), Y ) ],
% 1.42/1.80 [ member( 'ordered_pair'( u, v ), 'cross_product'( x, y ) ) ],
% 1.42/1.80 [ ~( member( 'ordered_pair'( v, u ), 'cross_product'( y, x ) ) ) ]
% 1.42/1.80 ] .
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 percentage equality = 0.222727, percentage horn = 0.929825
% 1.42/1.80 This is a problem with some equality
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 Options Used:
% 1.42/1.80
% 1.42/1.80 useres = 1
% 1.42/1.80 useparamod = 1
% 1.42/1.80 useeqrefl = 1
% 1.42/1.80 useeqfact = 1
% 1.42/1.80 usefactor = 1
% 1.42/1.80 usesimpsplitting = 0
% 1.42/1.80 usesimpdemod = 5
% 1.42/1.80 usesimpres = 3
% 1.42/1.80
% 1.42/1.80 resimpinuse = 1000
% 1.42/1.80 resimpclauses = 20000
% 1.42/1.80 substype = eqrewr
% 1.42/1.80 backwardsubs = 1
% 1.42/1.80 selectoldest = 5
% 1.42/1.80
% 1.42/1.80 litorderings [0] = split
% 1.42/1.80 litorderings [1] = extend the termordering, first sorting on arguments
% 1.42/1.80
% 1.42/1.80 termordering = kbo
% 1.42/1.80
% 1.42/1.80 litapriori = 0
% 1.42/1.80 termapriori = 1
% 1.42/1.80 litaposteriori = 0
% 1.42/1.80 termaposteriori = 0
% 1.42/1.80 demodaposteriori = 0
% 1.42/1.80 ordereqreflfact = 0
% 1.42/1.80
% 1.42/1.80 litselect = negord
% 1.42/1.80
% 1.42/1.80 maxweight = 15
% 1.42/1.80 maxdepth = 30000
% 1.42/1.80 maxlength = 115
% 1.42/1.80 maxnrvars = 195
% 1.42/1.80 excuselevel = 1
% 1.42/1.80 increasemaxweight = 1
% 1.42/1.80
% 1.42/1.80 maxselected = 10000000
% 1.42/1.80 maxnrclauses = 10000000
% 1.42/1.80
% 1.42/1.80 showgenerated = 0
% 1.42/1.80 showkept = 0
% 1.42/1.80 showselected = 0
% 1.42/1.80 showdeleted = 0
% 1.42/1.80 showresimp = 1
% 1.42/1.80 showstatus = 2000
% 1.42/1.80
% 1.42/1.80 prologoutput = 1
% 1.42/1.80 nrgoals = 5000000
% 1.42/1.80 totalproof = 1
% 1.42/1.80
% 1.42/1.80 Symbols occurring in the translation:
% 1.42/1.80
% 1.42/1.80 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.42/1.80 . [1, 2] (w:1, o:66, a:1, s:1, b:0),
% 1.42/1.80 ! [4, 1] (w:0, o:37, a:1, s:1, b:0),
% 1.42/1.80 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.42/1.80 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.42/1.80 subclass [41, 2] (w:1, o:91, a:1, s:1, b:0),
% 1.42/1.80 member [43, 2] (w:1, o:92, a:1, s:1, b:0),
% 1.42/1.80 'not_subclass_element' [44, 2] (w:1, o:93, a:1, s:1, b:0),
% 1.42/1.80 'universal_class' [45, 0] (w:1, o:22, a:1, s:1, b:0),
% 1.42/1.80 'unordered_pair' [46, 2] (w:1, o:94, a:1, s:1, b:0),
% 1.42/1.80 singleton [47, 1] (w:1, o:45, a:1, s:1, b:0),
% 1.42/1.80 'ordered_pair' [48, 2] (w:1, o:95, a:1, s:1, b:0),
% 1.42/1.80 'cross_product' [50, 2] (w:1, o:96, a:1, s:1, b:0),
% 1.42/1.80 first [52, 1] (w:1, o:46, a:1, s:1, b:0),
% 1.42/1.80 second [53, 1] (w:1, o:47, a:1, s:1, b:0),
% 1.42/1.80 'element_relation' [54, 0] (w:1, o:27, a:1, s:1, b:0),
% 1.42/1.80 intersection [55, 2] (w:1, o:98, a:1, s:1, b:0),
% 1.42/1.80 complement [56, 1] (w:1, o:48, a:1, s:1, b:0),
% 1.42/1.80 union [57, 2] (w:1, o:99, a:1, s:1, b:0),
% 1.42/1.80 'symmetric_difference' [58, 2] (w:1, o:100, a:1, s:1, b:0),
% 1.42/1.80 restrict [60, 3] (w:1, o:103, a:1, s:1, b:0),
% 1.42/1.80 'null_class' [61, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.42/1.80 'domain_of' [62, 1] (w:1, o:51, a:1, s:1, b:0),
% 1.42/1.80 rotate [63, 1] (w:1, o:42, a:1, s:1, b:0),
% 1.42/1.80 flip [65, 1] (w:1, o:52, a:1, s:1, b:0),
% 1.42/1.80 inverse [66, 1] (w:1, o:53, a:1, s:1, b:0),
% 1.42/1.80 'range_of' [67, 1] (w:1, o:43, a:1, s:1, b:0),
% 1.42/1.80 domain [68, 3] (w:1, o:105, a:1, s:1, b:0),
% 1.42/1.80 range [69, 3] (w:1, o:106, a:1, s:1, b:0),
% 1.42/1.80 image [70, 2] (w:1, o:97, a:1, s:1, b:0),
% 1.42/1.80 successor [71, 1] (w:1, o:54, a:1, s:1, b:0),
% 1.42/1.80 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 1.42/1.80 inductive [73, 1] (w:1, o:55, a:1, s:1, b:0),
% 1.42/1.80 omega [74, 0] (w:1, o:10, a:1, s:1, b:0),
% 1.42/1.80 'sum_class' [75, 1] (w:1, o:56, a:1, s:1, b:0),
% 1.42/1.80 'power_class' [76, 1] (w:1, o:59, a:1, s:1, b:0),
% 1.42/1.80 compose [78, 2] (w:1, o:101, a:1, s:1, b:0),
% 1.42/1.80 'single_valued_class' [79, 1] (w:1, o:60, a:1, s:1, b:0),
% 1.42/1.80 'identity_relation' [80, 0] (w:1, o:29, a:1, s:1, b:0),
% 1.42/1.80 function [82, 1] (w:1, o:61, a:1, s:1, b:0),
% 1.42/1.80 regular [83, 1] (w:1, o:44, a:1, s:1, b:0),
% 1.42/1.80 apply [84, 2] (w:1, o:102, a:1, s:1, b:0),
% 1.42/1.80 choice [85, 0] (w:1, o:30, a:1, s:1, b:0),
% 1.42/1.80 'one_to_one' [86, 1] (w:1, o:57, a:1, s:1, b:0),
% 1.42/1.80 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 1.42/1.80 diagonalise [88, 1] (w:1, o:62, a:1, s:1, b:0),
% 1.42/1.80 cantor [89, 1] (w:1, o:49, a:1, s:1, b:0),
% 1.42/1.80 operation [90, 1] (w:1, o:58, a:1, s:1, b:0),
% 1.42/1.80 compatible [94, 3] (w:1, o:104, a:1, s:1, b:0),
% 1.42/1.80 homomorphism [95, 3] (w:1, o:107, a:1, s:1, b:0),
% 1.42/1.80 'not_homomorphism1' [96, 3] (w:1, o:109, a:1, s:1, b:0),
% 1.42/1.80 'not_homomorphism2' [97, 3] (w:1, o:110, a:1, s:1, b:0),
% 1.42/1.80 'compose_class' [98, 1] (w:1, o:50, a:1, s:1, b:0),
% 1.42/1.80 'composition_function' [99, 0] (w:1, o:31, a:1, s:1, b:0),
% 1.42/1.80 'domain_relation' [100, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.42/1.80 'single_valued1' [101, 1] (w:1, o:63, a:1, s:1, b:0),
% 1.42/1.80 'single_valued2' [102, 1] (w:1, o:64, a:1, s:1, b:0),
% 1.42/1.80 'single_valued3' [103, 1] (w:1, o:65, a:1, s:1, b:0),
% 1.42/1.80 'singleton_relation' [104, 0] (w:1, o:7, a:1, s:1, b:0),
% 1.42/1.80 'application_function' [105, 0] (w:1, o:32, a:1, s:1, b:0),
% 1.42/1.80 maps [106, 3] (w:1, o:108, a:1, s:1, b:0),
% 1.42/1.80 u [107, 0] (w:1, o:33, a:1, s:1, b:0),
% 1.42/1.80 v [108, 0] (w:1, o:34, a:1, s:1, b:0),
% 1.42/1.80 x [109, 0] (w:1, o:35, a:1, s:1, b:0),
% 1.42/1.80 y [110, 0] (w:1, o:36, a:1, s:1, b:0).
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 Starting Search:
% 1.42/1.80
% 1.42/1.80 Resimplifying inuse:
% 1.42/1.80 Done
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 Intermediate Status:
% 1.42/1.80 Generated: 5518
% 1.42/1.80 Kept: 2049
% 1.42/1.80 Inuse: 104
% 1.42/1.80 Deleted: 4
% 1.42/1.80 Deletedinuse: 2
% 1.42/1.80
% 1.42/1.80 Resimplifying inuse:
% 1.42/1.80 Done
% 1.42/1.80
% 1.42/1.80 Resimplifying inuse:
% 1.42/1.80 Done
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 Intermediate Status:
% 1.42/1.80 Generated: 10259
% 1.42/1.80 Kept: 4065
% 1.42/1.80 Inuse: 189
% 1.42/1.80 Deleted: 22
% 1.42/1.80 Deletedinuse: 14
% 1.42/1.80
% 1.42/1.80 Resimplifying inuse:
% 1.42/1.80 Done
% 1.42/1.80
% 1.42/1.80 Resimplifying inuse:
% 1.42/1.80 Done
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 Intermediate Status:
% 1.42/1.80 Generated: 14142
% 1.42/1.80 Kept: 6105
% 1.42/1.80 Inuse: 240
% 1.42/1.80 Deleted: 26
% 1.42/1.80 Deletedinuse: 15
% 1.42/1.80
% 1.42/1.80 Resimplifying inuse:
% 1.42/1.80 Done
% 1.42/1.80
% 1.42/1.80 Resimplifying inuse:
% 1.42/1.80 Done
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 Intermediate Status:
% 1.42/1.80 Generated: 18876
% 1.42/1.80 Kept: 8128
% 1.42/1.80 Inuse: 294
% 1.42/1.80 Deleted: 82
% 1.42/1.80 Deletedinuse: 70
% 1.42/1.80
% 1.42/1.80 Resimplifying inuse:
% 1.42/1.80 Done
% 1.42/1.80
% 1.42/1.80 Resimplifying inuse:
% 1.42/1.80 Done
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 Intermediate Status:
% 1.42/1.80 Generated: 24281
% 1.42/1.80 Kept: 10413
% 1.42/1.80 Inuse: 367
% 1.42/1.80 Deleted: 92
% 1.42/1.80 Deletedinuse: 78
% 1.42/1.80
% 1.42/1.80 Resimplifying inuse:
% 1.42/1.80 Done
% 1.42/1.80
% 1.42/1.80 Resimplifying inuse:
% 1.42/1.80 Done
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 Intermediate Status:
% 1.42/1.80 Generated: 27873
% 1.42/1.80 Kept: 12437
% 1.42/1.80 Inuse: 392
% 1.42/1.80 Deleted: 97
% 1.42/1.80 Deletedinuse: 83
% 1.42/1.80
% 1.42/1.80 Resimplifying inuse:
% 1.42/1.80 Done
% 1.42/1.80
% 1.42/1.80 Resimplifying inuse:
% 1.42/1.80 Done
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 Intermediate Status:
% 1.42/1.80 Generated: 32108
% 1.42/1.80 Kept: 14551
% 1.42/1.80 Inuse: 432
% 1.42/1.80 Deleted: 99
% 1.42/1.80 Deletedinuse: 85
% 1.42/1.80
% 1.42/1.80 Resimplifying inuse:
% 1.42/1.80 Done
% 1.42/1.80
% 1.42/1.80 Resimplifying inuse:
% 1.42/1.80 Done
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 Intermediate Status:
% 1.42/1.80 Generated: 35356
% 1.42/1.80 Kept: 16567
% 1.42/1.80 Inuse: 460
% 1.42/1.80 Deleted: 99
% 1.42/1.80 Deletedinuse: 85
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 Bliksems!, er is een bewijs:
% 1.42/1.80 % SZS status Unsatisfiable
% 1.42/1.80 % SZS output start Refutation
% 1.42/1.80
% 1.42/1.80 clause( 12, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) )
% 1.42/1.80 ), member( X, Z ) ] )
% 1.42/1.80 .
% 1.42/1.80 clause( 13, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) )
% 1.42/1.80 ), member( Y, T ) ] )
% 1.42/1.80 .
% 1.42/1.80 clause( 14, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.42/1.80 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.42/1.80 .
% 1.42/1.80 clause( 111, [ member( 'ordered_pair'( u, v ), 'cross_product'( x, y ) ) ]
% 1.42/1.80 )
% 1.42/1.80 .
% 1.42/1.80 clause( 112, [ ~( member( 'ordered_pair'( v, u ), 'cross_product'( y, x ) )
% 1.42/1.80 ) ] )
% 1.42/1.80 .
% 1.42/1.80 clause( 16394, [ member( v, y ) ] )
% 1.42/1.80 .
% 1.42/1.80 clause( 16395, [ member( u, x ) ] )
% 1.42/1.80 .
% 1.42/1.80 clause( 16594, [ ~( member( u, x ) ) ] )
% 1.42/1.80 .
% 1.42/1.80 clause( 16680, [] )
% 1.42/1.80 .
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 % SZS output end Refutation
% 1.42/1.80 found a proof!
% 1.42/1.80
% 1.42/1.80 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.42/1.80
% 1.42/1.80 initialclauses(
% 1.42/1.80 [ clause( 16682, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.42/1.80 ) ] )
% 1.42/1.80 , clause( 16683, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 1.42/1.80 , Y ) ] )
% 1.42/1.80 , clause( 16684, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 1.42/1.80 subclass( X, Y ) ] )
% 1.42/1.80 , clause( 16685, [ subclass( X, 'universal_class' ) ] )
% 1.42/1.80 , clause( 16686, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.42/1.80 , clause( 16687, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 1.42/1.80 , clause( 16688, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 1.42/1.80 ] )
% 1.42/1.80 , clause( 16689, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 1.42/1.80 =( X, Z ) ] )
% 1.42/1.80 , clause( 16690, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.42/1.80 'unordered_pair'( X, Y ) ) ] )
% 1.42/1.80 , clause( 16691, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.42/1.80 'unordered_pair'( Y, X ) ) ] )
% 1.42/1.80 , clause( 16692, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 1.42/1.80 )
% 1.42/1.80 , clause( 16693, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.42/1.80 , clause( 16694, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 1.42/1.80 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.42/1.80 , clause( 16695, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.42/1.80 ) ) ), member( X, Z ) ] )
% 1.42/1.80 , clause( 16696, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.42/1.80 ) ) ), member( Y, T ) ] )
% 1.42/1.80 , clause( 16697, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.42/1.80 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.42/1.80 , clause( 16698, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 1.42/1.80 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 1.42/1.80 , clause( 16699, [ subclass( 'element_relation', 'cross_product'(
% 1.42/1.80 'universal_class', 'universal_class' ) ) ] )
% 1.42/1.80 , clause( 16700, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 1.42/1.80 ), member( X, Y ) ] )
% 1.42/1.80 , clause( 16701, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.42/1.80 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 1.42/1.80 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 1.42/1.80 , clause( 16702, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.42/1.80 )
% 1.42/1.80 , clause( 16703, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 1.42/1.80 )
% 1.42/1.80 , clause( 16704, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 1.42/1.80 intersection( Y, Z ) ) ] )
% 1.42/1.80 , clause( 16705, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 1.42/1.80 )
% 1.42/1.80 , clause( 16706, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.42/1.80 complement( Y ) ), member( X, Y ) ] )
% 1.42/1.80 , clause( 16707, [ =( complement( intersection( complement( X ), complement(
% 1.42/1.80 Y ) ) ), union( X, Y ) ) ] )
% 1.42/1.80 , clause( 16708, [ =( intersection( complement( intersection( X, Y ) ),
% 1.42/1.80 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 1.42/1.80 'symmetric_difference'( X, Y ) ) ] )
% 1.42/1.80 , clause( 16709, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 1.42/1.80 X, Y, Z ) ) ] )
% 1.42/1.80 , clause( 16710, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 1.42/1.80 Z, X, Y ) ) ] )
% 1.42/1.80 , clause( 16711, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 1.42/1.80 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 1.42/1.80 , clause( 16712, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 1.42/1.80 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 1.42/1.80 'domain_of'( Y ) ) ] )
% 1.42/1.80 , clause( 16713, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 1.42/1.80 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.42/1.80 , clause( 16714, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.42/1.80 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 1.42/1.80 ] )
% 1.42/1.80 , clause( 16715, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.42/1.80 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 1.42/1.80 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.42/1.80 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 1.42/1.80 , Y ), rotate( T ) ) ] )
% 1.42/1.80 , clause( 16716, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 1.42/1.80 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.42/1.80 , clause( 16717, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.42/1.80 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 1.42/1.80 )
% 1.42/1.80 , clause( 16718, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.42/1.80 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 1.42/1.80 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.42/1.80 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 1.42/1.80 , Z ), flip( T ) ) ] )
% 1.42/1.80 , clause( 16719, [ =( 'domain_of'( flip( 'cross_product'( X,
% 1.42/1.80 'universal_class' ) ) ), inverse( X ) ) ] )
% 1.42/1.80 , clause( 16720, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 1.42/1.80 , clause( 16721, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 1.42/1.80 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 1.42/1.80 , clause( 16722, [ =( second( 'not_subclass_element'( restrict( X,
% 1.42/1.80 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 1.42/1.80 , clause( 16723, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 1.42/1.80 image( X, Y ) ) ] )
% 1.42/1.80 , clause( 16724, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 1.42/1.80 , clause( 16725, [ subclass( 'successor_relation', 'cross_product'(
% 1.42/1.80 'universal_class', 'universal_class' ) ) ] )
% 1.42/1.80 , clause( 16726, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 1.42/1.80 ) ), =( successor( X ), Y ) ] )
% 1.42/1.80 , clause( 16727, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 1.42/1.80 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 1.42/1.80 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 1.42/1.80 , clause( 16728, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 1.42/1.80 , clause( 16729, [ ~( inductive( X ) ), subclass( image(
% 1.42/1.80 'successor_relation', X ), X ) ] )
% 1.42/1.80 , clause( 16730, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 1.42/1.80 'successor_relation', X ), X ) ), inductive( X ) ] )
% 1.42/1.80 , clause( 16731, [ inductive( omega ) ] )
% 1.42/1.80 , clause( 16732, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 1.42/1.80 , clause( 16733, [ member( omega, 'universal_class' ) ] )
% 1.42/1.80 , clause( 16734, [ =( 'domain_of'( restrict( 'element_relation',
% 1.42/1.80 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 1.42/1.80 , clause( 16735, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 1.42/1.80 X ), 'universal_class' ) ] )
% 1.42/1.80 , clause( 16736, [ =( complement( image( 'element_relation', complement( X
% 1.42/1.80 ) ) ), 'power_class'( X ) ) ] )
% 1.42/1.80 , clause( 16737, [ ~( member( X, 'universal_class' ) ), member(
% 1.42/1.80 'power_class'( X ), 'universal_class' ) ] )
% 1.42/1.80 , clause( 16738, [ subclass( compose( X, Y ), 'cross_product'(
% 1.42/1.80 'universal_class', 'universal_class' ) ) ] )
% 1.42/1.80 , clause( 16739, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 1.42/1.80 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 1.42/1.80 , clause( 16740, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 1.42/1.80 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 1.42/1.80 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 1.42/1.80 ) ] )
% 1.42/1.80 , clause( 16741, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 1.42/1.80 inverse( X ) ), 'identity_relation' ) ] )
% 1.42/1.80 , clause( 16742, [ ~( subclass( compose( X, inverse( X ) ),
% 1.42/1.80 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 1.42/1.80 , clause( 16743, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 1.42/1.80 'universal_class', 'universal_class' ) ) ] )
% 1.42/1.80 , clause( 16744, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 1.42/1.80 , 'identity_relation' ) ] )
% 1.42/1.80 , clause( 16745, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 1.42/1.80 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 1.42/1.80 'identity_relation' ) ), function( X ) ] )
% 1.42/1.80 , clause( 16746, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 1.42/1.80 , member( image( X, Y ), 'universal_class' ) ] )
% 1.42/1.80 , clause( 16747, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.42/1.80 , clause( 16748, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 1.42/1.80 , 'null_class' ) ] )
% 1.42/1.80 , clause( 16749, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 1.42/1.80 Y ) ) ] )
% 1.42/1.80 , clause( 16750, [ function( choice ) ] )
% 1.42/1.80 , clause( 16751, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 1.42/1.80 ), member( apply( choice, X ), X ) ] )
% 1.42/1.80 , clause( 16752, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 1.42/1.80 , clause( 16753, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 1.42/1.80 , clause( 16754, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 1.42/1.80 'one_to_one'( X ) ] )
% 1.42/1.80 , clause( 16755, [ =( intersection( 'cross_product'( 'universal_class',
% 1.42/1.80 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 1.42/1.80 'universal_class' ), complement( compose( complement( 'element_relation'
% 1.42/1.80 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 1.42/1.80 , clause( 16756, [ =( intersection( inverse( 'subset_relation' ),
% 1.42/1.80 'subset_relation' ), 'identity_relation' ) ] )
% 1.42/1.80 , clause( 16757, [ =( complement( 'domain_of'( intersection( X,
% 1.42/1.80 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 1.42/1.80 , clause( 16758, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 1.42/1.80 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 1.42/1.80 , clause( 16759, [ ~( operation( X ) ), function( X ) ] )
% 1.42/1.80 , clause( 16760, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 1.42/1.80 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.42/1.80 ] )
% 1.42/1.80 , clause( 16761, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 1.42/1.80 'domain_of'( 'domain_of'( X ) ) ) ] )
% 1.42/1.80 , clause( 16762, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 1.42/1.80 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.42/1.80 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 1.42/1.80 operation( X ) ] )
% 1.42/1.80 , clause( 16763, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 1.42/1.80 , clause( 16764, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 1.42/1.80 Y ) ), 'domain_of'( X ) ) ] )
% 1.42/1.80 , clause( 16765, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 1.42/1.80 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 1.42/1.80 , clause( 16766, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 1.42/1.80 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 1.42/1.80 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 1.42/1.80 , clause( 16767, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 1.42/1.80 , clause( 16768, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 1.42/1.80 , clause( 16769, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 1.42/1.80 , clause( 16770, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 1.42/1.80 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 1.42/1.80 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 1.42/1.80 )
% 1.42/1.80 , clause( 16771, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.42/1.80 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.42/1.80 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.42/1.80 , Y ) ] )
% 1.42/1.80 , clause( 16772, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.42/1.80 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 1.42/1.80 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 1.42/1.80 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 1.42/1.80 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 1.42/1.80 )
% 1.42/1.80 , clause( 16773, [ subclass( 'compose_class'( X ), 'cross_product'(
% 1.42/1.80 'universal_class', 'universal_class' ) ) ] )
% 1.42/1.80 , clause( 16774, [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z )
% 1.42/1.80 ) ), =( compose( Z, X ), Y ) ] )
% 1.42/1.80 , clause( 16775, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.42/1.80 'universal_class', 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) )
% 1.42/1.80 , member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ] )
% 1.42/1.80 , clause( 16776, [ subclass( 'composition_function', 'cross_product'(
% 1.42/1.80 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 1.42/1.80 ) ) ) ] )
% 1.42/1.80 , clause( 16777, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.42/1.80 'composition_function' ) ), =( compose( X, Y ), Z ) ] )
% 1.42/1.80 , clause( 16778, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.42/1.80 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( X,
% 1.42/1.80 'ordered_pair'( Y, compose( X, Y ) ) ), 'composition_function' ) ] )
% 1.42/1.80 , clause( 16779, [ subclass( 'domain_relation', 'cross_product'(
% 1.42/1.80 'universal_class', 'universal_class' ) ) ] )
% 1.42/1.80 , clause( 16780, [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) )
% 1.42/1.80 , =( 'domain_of'( X ), Y ) ] )
% 1.42/1.80 , clause( 16781, [ ~( member( X, 'universal_class' ) ), member(
% 1.42/1.80 'ordered_pair'( X, 'domain_of'( X ) ), 'domain_relation' ) ] )
% 1.42/1.80 , clause( 16782, [ =( first( 'not_subclass_element'( compose( X, inverse( X
% 1.42/1.80 ) ), 'identity_relation' ) ), 'single_valued1'( X ) ) ] )
% 1.42/1.80 , clause( 16783, [ =( second( 'not_subclass_element'( compose( X, inverse(
% 1.42/1.80 X ) ), 'identity_relation' ) ), 'single_valued2'( X ) ) ] )
% 1.42/1.80 , clause( 16784, [ =( domain( X, image( inverse( X ), singleton(
% 1.42/1.80 'single_valued1'( X ) ) ), 'single_valued2'( X ) ), 'single_valued3'( X )
% 1.42/1.80 ) ] )
% 1.42/1.80 , clause( 16785, [ =( intersection( complement( compose( 'element_relation'
% 1.42/1.80 , complement( 'identity_relation' ) ) ), 'element_relation' ),
% 1.42/1.80 'singleton_relation' ) ] )
% 1.42/1.80 , clause( 16786, [ subclass( 'application_function', 'cross_product'(
% 1.42/1.80 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 1.42/1.80 ) ) ) ] )
% 1.42/1.80 , clause( 16787, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.42/1.80 'application_function' ) ), member( Y, 'domain_of'( X ) ) ] )
% 1.42/1.80 , clause( 16788, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.42/1.80 'application_function' ) ), =( apply( X, Y ), Z ) ] )
% 1.42/1.80 , clause( 16789, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.42/1.80 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 1.42/1.80 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 1.42/1.80 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 1.42/1.80 'application_function' ) ] )
% 1.42/1.80 , clause( 16790, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 1.42/1.80 , clause( 16791, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 1.42/1.80 , clause( 16792, [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ]
% 1.42/1.80 )
% 1.42/1.80 , clause( 16793, [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) )
% 1.42/1.80 , maps( X, 'domain_of'( X ), Y ) ] )
% 1.42/1.80 , clause( 16794, [ member( 'ordered_pair'( u, v ), 'cross_product'( x, y )
% 1.42/1.80 ) ] )
% 1.42/1.80 , clause( 16795, [ ~( member( 'ordered_pair'( v, u ), 'cross_product'( y, x
% 1.42/1.80 ) ) ) ] )
% 1.42/1.80 ] ).
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 subsumption(
% 1.42/1.80 clause( 12, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) )
% 1.42/1.80 ), member( X, Z ) ] )
% 1.42/1.80 , clause( 16695, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.42/1.80 ) ) ), member( X, Z ) ] )
% 1.42/1.80 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.42/1.80 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 subsumption(
% 1.42/1.80 clause( 13, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) )
% 1.42/1.80 ), member( Y, T ) ] )
% 1.42/1.80 , clause( 16696, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.42/1.80 ) ) ), member( Y, T ) ] )
% 1.42/1.80 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.42/1.80 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 subsumption(
% 1.42/1.80 clause( 14, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.42/1.80 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.42/1.80 , clause( 16697, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.42/1.80 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.42/1.80 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.42/1.80 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 subsumption(
% 1.42/1.80 clause( 111, [ member( 'ordered_pair'( u, v ), 'cross_product'( x, y ) ) ]
% 1.42/1.80 )
% 1.42/1.80 , clause( 16794, [ member( 'ordered_pair'( u, v ), 'cross_product'( x, y )
% 1.42/1.80 ) ] )
% 1.42/1.80 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 subsumption(
% 1.42/1.80 clause( 112, [ ~( member( 'ordered_pair'( v, u ), 'cross_product'( y, x ) )
% 1.42/1.80 ) ] )
% 1.42/1.80 , clause( 16795, [ ~( member( 'ordered_pair'( v, u ), 'cross_product'( y, x
% 1.42/1.80 ) ) ) ] )
% 1.42/1.80 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 resolution(
% 1.42/1.80 clause( 16947, [ member( v, y ) ] )
% 1.42/1.80 , clause( 13, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T )
% 1.42/1.80 ) ), member( Y, T ) ] )
% 1.42/1.80 , 0, clause( 111, [ member( 'ordered_pair'( u, v ), 'cross_product'( x, y )
% 1.42/1.80 ) ] )
% 1.42/1.80 , 0, substitution( 0, [ :=( X, u ), :=( Y, v ), :=( Z, x ), :=( T, y )] ),
% 1.42/1.80 substitution( 1, [] )).
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 subsumption(
% 1.42/1.80 clause( 16394, [ member( v, y ) ] )
% 1.42/1.80 , clause( 16947, [ member( v, y ) ] )
% 1.42/1.80 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 resolution(
% 1.42/1.80 clause( 16948, [ member( u, x ) ] )
% 1.42/1.80 , clause( 12, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T )
% 1.42/1.80 ) ), member( X, Z ) ] )
% 1.42/1.80 , 0, clause( 111, [ member( 'ordered_pair'( u, v ), 'cross_product'( x, y )
% 1.42/1.80 ) ] )
% 1.42/1.80 , 0, substitution( 0, [ :=( X, u ), :=( Y, v ), :=( Z, x ), :=( T, y )] ),
% 1.42/1.80 substitution( 1, [] )).
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 subsumption(
% 1.42/1.80 clause( 16395, [ member( u, x ) ] )
% 1.42/1.80 , clause( 16948, [ member( u, x ) ] )
% 1.42/1.80 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 resolution(
% 1.42/1.80 clause( 16949, [ ~( member( v, y ) ), ~( member( u, x ) ) ] )
% 1.42/1.80 , clause( 112, [ ~( member( 'ordered_pair'( v, u ), 'cross_product'( y, x )
% 1.42/1.80 ) ) ] )
% 1.42/1.80 , 0, clause( 14, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.42/1.80 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.42/1.80 , 2, substitution( 0, [] ), substitution( 1, [ :=( X, v ), :=( Y, y ), :=(
% 1.42/1.80 Z, u ), :=( T, x )] )).
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 resolution(
% 1.42/1.80 clause( 16950, [ ~( member( u, x ) ) ] )
% 1.42/1.80 , clause( 16949, [ ~( member( v, y ) ), ~( member( u, x ) ) ] )
% 1.42/1.80 , 0, clause( 16394, [ member( v, y ) ] )
% 1.42/1.80 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 subsumption(
% 1.42/1.80 clause( 16594, [ ~( member( u, x ) ) ] )
% 1.42/1.80 , clause( 16950, [ ~( member( u, x ) ) ] )
% 1.42/1.80 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 resolution(
% 1.42/1.80 clause( 16951, [] )
% 1.42/1.80 , clause( 16594, [ ~( member( u, x ) ) ] )
% 1.42/1.80 , 0, clause( 16395, [ member( u, x ) ] )
% 1.42/1.80 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 subsumption(
% 1.42/1.80 clause( 16680, [] )
% 1.42/1.80 , clause( 16951, [] )
% 1.42/1.80 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 end.
% 1.42/1.80
% 1.42/1.80 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.42/1.80
% 1.42/1.80 Memory use:
% 1.42/1.80
% 1.42/1.80 space for terms: 266023
% 1.42/1.80 space for clauses: 800366
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 clauses generated: 35533
% 1.42/1.80 clauses kept: 16681
% 1.42/1.80 clauses selected: 462
% 1.42/1.80 clauses deleted: 100
% 1.42/1.80 clauses inuse deleted: 85
% 1.42/1.80
% 1.42/1.80 subsentry: 74485
% 1.42/1.80 literals s-matched: 55075
% 1.42/1.80 literals matched: 54188
% 1.42/1.80 full subsumption: 22945
% 1.42/1.80
% 1.42/1.80 checksum: -208807834
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 Bliksem ended
%------------------------------------------------------------------------------