TSTP Solution File: SET065-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET065-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n008.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 22:46:26 EDT 2022
% Result : Unsatisfiable 0.74s 1.13s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET065-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n008.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 19:39:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.74/1.13 *** allocated 10000 integers for termspace/termends
% 0.74/1.13 *** allocated 10000 integers for clauses
% 0.74/1.13 *** allocated 10000 integers for justifications
% 0.74/1.13 Bliksem 1.12
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Automatic Strategy Selection
% 0.74/1.13
% 0.74/1.13 Clauses:
% 0.74/1.13 [
% 0.74/1.13 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.74/1.13 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.74/1.13 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.74/1.13 ,
% 0.74/1.13 [ subclass( X, 'universal_class' ) ],
% 0.74/1.13 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.74/1.13 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.74/1.13 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.74/1.13 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.74/1.13 ,
% 0.74/1.13 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.74/1.13 ) ) ],
% 0.74/1.13 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.74/1.13 ) ) ],
% 0.74/1.13 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.74/1.13 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.74/1.13 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.74/1.13 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.13 X, Z ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.13 Y, T ) ],
% 0.74/1.13 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.74/1.13 ), 'cross_product'( Y, T ) ) ],
% 0.74/1.13 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.74/1.13 ), second( X ) ), X ) ],
% 0.74/1.13 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.74/1.13 'universal_class' ) ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.74/1.13 Y ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.74/1.13 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.74/1.13 , Y ), 'element_relation' ) ],
% 0.74/1.13 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.74/1.13 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.74/1.13 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.74/1.13 Z ) ) ],
% 0.74/1.13 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.74/1.13 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.74/1.13 member( X, Y ) ],
% 0.74/1.13 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.74/1.13 union( X, Y ) ) ],
% 0.74/1.13 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.74/1.13 intersection( complement( X ), complement( Y ) ) ) ),
% 0.74/1.13 'symmetric_difference'( X, Y ) ) ],
% 0.74/1.13 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.74/1.13 ,
% 0.74/1.13 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.74/1.13 ,
% 0.74/1.13 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.74/1.13 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.74/1.13 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.74/1.13 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.74/1.13 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.74/1.13 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.74/1.13 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.74/1.13 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.74/1.13 'cross_product'( 'universal_class', 'universal_class' ),
% 0.74/1.13 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.74/1.13 Y ), rotate( T ) ) ],
% 0.74/1.13 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.74/1.13 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.74/1.13 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.74/1.13 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.74/1.13 'cross_product'( 'universal_class', 'universal_class' ),
% 0.74/1.13 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.74/1.13 Z ), flip( T ) ) ],
% 0.74/1.13 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.74/1.13 inverse( X ) ) ],
% 0.74/1.13 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.74/1.13 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.74/1.13 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.74/1.13 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.74/1.13 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.74/1.13 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.74/1.13 ],
% 0.74/1.13 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.74/1.13 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.74/1.13 'universal_class' ) ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.74/1.13 successor( X ), Y ) ],
% 0.74/1.13 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.74/1.13 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.74/1.13 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.74/1.13 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.74/1.13 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.74/1.13 ,
% 0.74/1.13 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.74/1.13 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.74/1.13 [ inductive( omega ) ],
% 0.74/1.13 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.74/1.13 [ member( omega, 'universal_class' ) ],
% 0.74/1.13 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.74/1.13 , 'sum_class'( X ) ) ],
% 0.74/1.13 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.74/1.13 'universal_class' ) ],
% 0.74/1.13 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.74/1.13 'power_class'( X ) ) ],
% 0.74/1.13 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.74/1.13 'universal_class' ) ],
% 0.74/1.13 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.74/1.13 'universal_class' ) ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.74/1.13 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.74/1.13 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.74/1.13 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.74/1.13 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.74/1.13 ) ],
% 0.74/1.13 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.74/1.13 , 'identity_relation' ) ],
% 0.74/1.13 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.74/1.13 'single_valued_class'( X ) ],
% 0.74/1.13 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.74/1.13 'universal_class' ) ) ],
% 0.74/1.13 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.74/1.13 'identity_relation' ) ],
% 0.74/1.13 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.74/1.13 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.74/1.13 , function( X ) ],
% 0.74/1.13 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.74/1.13 X, Y ), 'universal_class' ) ],
% 0.74/1.13 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.74/1.13 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.74/1.13 ) ],
% 0.74/1.13 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.74/1.13 [ function( choice ) ],
% 0.74/1.13 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.74/1.13 apply( choice, X ), X ) ],
% 0.74/1.13 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.74/1.13 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.74/1.13 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.74/1.13 ,
% 0.74/1.13 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.74/1.13 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.74/1.13 , complement( compose( complement( 'element_relation' ), inverse(
% 0.74/1.13 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.74/1.13 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.74/1.13 'identity_relation' ) ],
% 0.74/1.13 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.74/1.13 , diagonalise( X ) ) ],
% 0.74/1.13 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.74/1.13 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.74/1.13 [ ~( operation( X ) ), function( X ) ],
% 0.74/1.13 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.74/1.13 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.74/1.13 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.74/1.13 'domain_of'( X ) ) ) ],
% 0.74/1.13 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.74/1.13 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.74/1.13 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.74/1.13 X ) ],
% 0.74/1.13 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.74/1.13 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.74/1.13 'domain_of'( X ) ) ],
% 0.74/1.13 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.74/1.13 'domain_of'( Z ) ) ) ],
% 0.74/1.13 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.74/1.13 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.74/1.13 ), compatible( X, Y, Z ) ],
% 0.74/1.13 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.74/1.13 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.74/1.13 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.74/1.13 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.74/1.13 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.74/1.13 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.74/1.13 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.74/1.13 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.74/1.13 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.74/1.13 , Y ) ],
% 0.74/1.13 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.74/1.13 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.74/1.13 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.74/1.13 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.74/1.13 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.13 X, 'unordered_pair'( X, Y ) ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.13 Y, 'unordered_pair'( X, Y ) ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.13 X, 'universal_class' ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.13 Y, 'universal_class' ) ],
% 0.74/1.13 [ subclass( X, X ) ],
% 0.74/1.13 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.74/1.13 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.74/1.13 'not_subclass_element'( Y, X ), Y ) ],
% 0.74/1.13 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.74/1.13 'not_subclass_element'( Y, X ), Y ) ],
% 0.74/1.13 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.74/1.13 'not_subclass_element'( Y, X ), Y ) ],
% 0.74/1.13 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.74/1.13 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.74/1.13 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.74/1.13 [ ~( member( X, 'null_class' ) ) ],
% 0.74/1.13 [ subclass( 'null_class', X ) ],
% 0.74/1.13 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.74/1.13 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.74/1.13 ), X ) ],
% 0.74/1.13 [ ~( member( 'null_class', 'universal_class' ) ) ]
% 0.74/1.13 ] .
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 percentage equality = 0.211268, percentage horn = 0.887850
% 0.74/1.13 This is a problem with some equality
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Options Used:
% 0.74/1.13
% 0.74/1.13 useres = 1
% 0.74/1.13 useparamod = 1
% 0.74/1.13 useeqrefl = 1
% 0.74/1.13 useeqfact = 1
% 0.74/1.13 usefactor = 1
% 0.74/1.13 usesimpsplitting = 0
% 0.74/1.13 usesimpdemod = 5
% 0.74/1.13 usesimpres = 3
% 0.74/1.13
% 0.74/1.13 resimpinuse = 1000
% 0.74/1.13 resimpclauses = 20000
% 0.74/1.13 substype = eqrewr
% 0.74/1.13 backwardsubs = 1
% 0.74/1.13 selectoldest = 5
% 0.74/1.13
% 0.74/1.13 litorderings [0] = split
% 0.74/1.13 litorderings [1] = extend the termordering, first sorting on arguments
% 0.74/1.13
% 0.74/1.13 termordering = kbo
% 0.74/1.13
% 0.74/1.13 litapriori = 0
% 0.74/1.13 termapriori = 1
% 0.74/1.13 litaposteriori = 0
% 0.74/1.13 termaposteriori = 0
% 0.74/1.13 demodaposteriori = 0
% 0.74/1.13 ordereqreflfact = 0
% 0.74/1.13
% 0.74/1.13 litselect = negord
% 0.74/1.13
% 0.74/1.13 maxweight = 15
% 0.74/1.13 maxdepth = 30000
% 0.74/1.13 maxlength = 115
% 0.74/1.13 maxnrvars = 195
% 0.74/1.13 excuselevel = 1
% 0.74/1.13 increasemaxweight = 1
% 0.74/1.13
% 0.74/1.13 maxselected = 10000000
% 0.74/1.13 maxnrclauses = 10000000
% 0.74/1.13
% 0.74/1.13 showgenerated = 0
% 0.74/1.13 showkept = 0
% 0.74/1.13 showselected = 0
% 0.74/1.13 showdeleted = 0
% 0.74/1.13 showresimp = 1
% 0.74/1.13 showstatus = 2000
% 0.74/1.13
% 0.74/1.13 prologoutput = 1
% 0.74/1.13 nrgoals = 5000000
% 0.74/1.13 totalproof = 1
% 0.74/1.13
% 0.74/1.13 Symbols occurring in the translation:
% 0.74/1.13
% 0.74/1.13 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.74/1.13 . [1, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.74/1.13 ! [4, 1] (w:0, o:29, a:1, s:1, b:0),
% 0.74/1.13 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.13 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.13 subclass [41, 2] (w:1, o:79, a:1, s:1, b:0),
% 0.74/1.13 member [43, 2] (w:1, o:80, a:1, s:1, b:0),
% 0.74/1.13 'not_subclass_element' [44, 2] (w:1, o:81, a:1, s:1, b:0),
% 0.74/1.13 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.74/1.13 'unordered_pair' [46, 2] (w:1, o:82, a:1, s:1, b:0),
% 0.74/1.13 singleton [47, 1] (w:1, o:37, a:1, s:1, b:0),
% 0.74/1.13 'ordered_pair' [48, 2] (w:1, o:83, a:1, s:1, b:0),
% 0.74/1.13 'cross_product' [50, 2] (w:1, o:84, a:1, s:1, b:0),
% 0.74/1.13 first [52, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.74/1.13 second [53, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.74/1.13 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.74/1.13 intersection [55, 2] (w:1, o:86, a:1, s:1, b:0),
% 0.74/1.13 complement [56, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.74/1.13 union [57, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.74/1.13 'symmetric_difference' [58, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.74/1.13 restrict [60, 3] (w:1, o:91, a:1, s:1, b:0),
% 0.74/1.13 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.74/1.13 'domain_of' [62, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.74/1.13 rotate [63, 1] (w:1, o:34, a:1, s:1, b:0),
% 0.74/1.13 flip [65, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.74/1.13 inverse [66, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.74/1.13 'range_of' [67, 1] (w:1, o:35, a:1, s:1, b:0),
% 0.74/1.13 domain [68, 3] (w:1, o:93, a:1, s:1, b:0),
% 0.74/1.13 range [69, 3] (w:1, o:94, a:1, s:1, b:0),
% 0.74/1.13 image [70, 2] (w:1, o:85, a:1, s:1, b:0),
% 0.74/1.13 successor [71, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.74/1.13 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.74/1.13 inductive [73, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.74/1.13 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.74/1.13 'sum_class' [75, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.74/1.13 'power_class' [76, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.74/1.13 compose [78, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.74/1.13 'single_valued_class' [79, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.74/1.13 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.74/1.13 function [82, 1] (w:1, o:52, a:1, s:1, b:0),
% 0.74/1.13 regular [83, 1] (w:1, o:36, a:1, s:1, b:0),
% 0.74/1.13 apply [84, 2] (w:1, o:90, a:1, s:1, b:0),
% 0.74/1.13 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.74/1.13 'one_to_one' [86, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.74/1.13 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 0.74/1.13 diagonalise [88, 1] (w:1, o:53, a:1, s:1, b:0),
% 0.74/1.13 cantor [89, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.74/1.13 operation [90, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.74/1.13 compatible [94, 3] (w:1, o:92, a:1, s:1, b:0),
% 0.74/1.13 homomorphism [95, 3] (w:1, o:95, a:1, s:1, b:0),
% 0.74/1.13 'not_homomorphism1' [96, 3] (w:1, o:96, a:1, s:1, b:0),
% 0.74/1.13 'not_homomorphism2' [97, 3] (w:1, o:97, a:1, s:1, b:0).
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Starting Search:
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Bliksems!, er is een bewijs:
% 0.74/1.13 % SZS status Unsatisfiable
% 0.74/1.13 % SZS output start Refutation
% 0.74/1.13
% 0.74/1.13 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.74/1.13 )
% 0.74/1.13 .
% 0.74/1.13 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 0.74/1.13 .
% 0.74/1.13 clause( 45, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 0.74/1.13 .
% 0.74/1.13 clause( 48, [ inductive( omega ) ] )
% 0.74/1.13 .
% 0.74/1.13 clause( 104, [ ~( member( 'null_class', 'universal_class' ) ) ] )
% 0.74/1.13 .
% 0.74/1.13 clause( 119, [ ~( member( 'null_class', X ) ) ] )
% 0.74/1.13 .
% 0.74/1.13 clause( 124, [ ~( inductive( X ) ) ] )
% 0.74/1.13 .
% 0.74/1.13 clause( 127, [] )
% 0.74/1.13 .
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 % SZS output end Refutation
% 0.74/1.13 found a proof!
% 0.74/1.13
% 0.74/1.13 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.74/1.13
% 0.74/1.13 initialclauses(
% 0.74/1.13 [ clause( 129, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y )
% 0.74/1.13 ] )
% 0.74/1.13 , clause( 130, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X,
% 0.74/1.13 Y ) ] )
% 0.74/1.13 , clause( 131, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass(
% 0.74/1.13 X, Y ) ] )
% 0.74/1.13 , clause( 132, [ subclass( X, 'universal_class' ) ] )
% 0.74/1.13 , clause( 133, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 0.74/1.13 , clause( 134, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 0.74/1.13 , clause( 135, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ]
% 0.74/1.13 )
% 0.74/1.13 , clause( 136, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =(
% 0.74/1.13 X, Z ) ] )
% 0.74/1.13 , clause( 137, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.74/1.13 'unordered_pair'( X, Y ) ) ] )
% 0.74/1.13 , clause( 138, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.74/1.13 'unordered_pair'( Y, X ) ) ] )
% 0.74/1.13 , clause( 139, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ] )
% 0.74/1.13 , clause( 140, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 0.74/1.13 , clause( 141, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 0.74/1.13 singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.74/1.13 , clause( 142, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T )
% 0.74/1.13 ) ), member( X, Z ) ] )
% 0.74/1.13 , clause( 143, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T )
% 0.74/1.13 ) ), member( Y, T ) ] )
% 0.74/1.13 , clause( 144, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 0.74/1.13 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 0.74/1.13 , clause( 145, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 0.74/1.13 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 0.74/1.13 , clause( 146, [ subclass( 'element_relation', 'cross_product'(
% 0.74/1.13 'universal_class', 'universal_class' ) ) ] )
% 0.74/1.13 , clause( 147, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) )
% 0.74/1.13 , member( X, Y ) ] )
% 0.74/1.13 , clause( 148, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.74/1.13 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 0.74/1.13 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 0.74/1.13 , clause( 149, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.74/1.13 )
% 0.74/1.13 , clause( 150, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 0.74/1.13 )
% 0.74/1.13 , clause( 151, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 0.74/1.13 intersection( Y, Z ) ) ] )
% 0.74/1.13 , clause( 152, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 0.74/1.13 )
% 0.74/1.13 , clause( 153, [ ~( member( X, 'universal_class' ) ), member( X, complement(
% 0.74/1.13 Y ) ), member( X, Y ) ] )
% 0.74/1.13 , clause( 154, [ =( complement( intersection( complement( X ), complement(
% 0.74/1.13 Y ) ) ), union( X, Y ) ) ] )
% 0.74/1.13 , clause( 155, [ =( intersection( complement( intersection( X, Y ) ),
% 0.74/1.13 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 0.74/1.13 'symmetric_difference'( X, Y ) ) ] )
% 0.74/1.13 , clause( 156, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X
% 0.74/1.13 , Y, Z ) ) ] )
% 0.74/1.13 , clause( 157, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z
% 0.74/1.13 , X, Y ) ) ] )
% 0.74/1.13 , clause( 158, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 0.74/1.13 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 0.74/1.13 , clause( 159, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 0.74/1.13 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 0.74/1.13 'domain_of'( Y ) ) ] )
% 0.74/1.13 , clause( 160, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.74/1.13 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.74/1.13 , clause( 161, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.74/1.13 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 0.74/1.13 ] )
% 0.74/1.13 , clause( 162, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.74/1.13 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 0.74/1.13 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.74/1.13 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 0.74/1.13 , Y ), rotate( T ) ) ] )
% 0.74/1.13 , clause( 163, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.74/1.13 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.74/1.13 , clause( 164, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.74/1.13 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 0.74/1.13 )
% 0.74/1.13 , clause( 165, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.74/1.13 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 0.74/1.13 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.74/1.13 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 0.74/1.13 , Z ), flip( T ) ) ] )
% 0.74/1.13 , clause( 166, [ =( 'domain_of'( flip( 'cross_product'( X,
% 0.74/1.13 'universal_class' ) ) ), inverse( X ) ) ] )
% 0.74/1.13 , clause( 167, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 0.74/1.13 , clause( 168, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 0.74/1.13 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 0.74/1.13 , clause( 169, [ =( second( 'not_subclass_element'( restrict( X, singleton(
% 0.74/1.13 Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 0.74/1.13 , clause( 170, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 0.74/1.13 image( X, Y ) ) ] )
% 0.74/1.13 , clause( 171, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 0.74/1.13 , clause( 172, [ subclass( 'successor_relation', 'cross_product'(
% 0.74/1.13 'universal_class', 'universal_class' ) ) ] )
% 0.74/1.13 , clause( 173, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' )
% 0.74/1.13 ), =( successor( X ), Y ) ] )
% 0.74/1.13 , clause( 174, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X
% 0.74/1.13 , Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 0.74/1.13 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 0.74/1.13 , clause( 175, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 0.74/1.13 , clause( 176, [ ~( inductive( X ) ), subclass( image( 'successor_relation'
% 0.74/1.13 , X ), X ) ] )
% 0.74/1.13 , clause( 177, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.74/1.13 'successor_relation', X ), X ) ), inductive( X ) ] )
% 0.74/1.13 , clause( 178, [ inductive( omega ) ] )
% 0.74/1.13 , clause( 179, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 0.74/1.13 , clause( 180, [ member( omega, 'universal_class' ) ] )
% 0.74/1.13 , clause( 181, [ =( 'domain_of'( restrict( 'element_relation',
% 0.74/1.13 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 0.74/1.13 , clause( 182, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 0.74/1.13 X ), 'universal_class' ) ] )
% 0.74/1.13 , clause( 183, [ =( complement( image( 'element_relation', complement( X )
% 0.74/1.13 ) ), 'power_class'( X ) ) ] )
% 0.74/1.13 , clause( 184, [ ~( member( X, 'universal_class' ) ), member( 'power_class'(
% 0.74/1.13 X ), 'universal_class' ) ] )
% 0.74/1.13 , clause( 185, [ subclass( compose( X, Y ), 'cross_product'(
% 0.74/1.13 'universal_class', 'universal_class' ) ) ] )
% 0.74/1.13 , clause( 186, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 0.74/1.13 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 0.74/1.13 , clause( 187, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ),
% 0.74/1.13 ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.74/1.13 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.74/1.13 ) ] )
% 0.74/1.13 , clause( 188, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 0.74/1.13 inverse( X ) ), 'identity_relation' ) ] )
% 0.74/1.13 , clause( 189, [ ~( subclass( compose( X, inverse( X ) ),
% 0.74/1.13 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 0.74/1.13 , clause( 190, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 0.74/1.13 'universal_class', 'universal_class' ) ) ] )
% 0.74/1.13 , clause( 191, [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.74/1.13 'identity_relation' ) ] )
% 0.74/1.13 , clause( 192, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 0.74/1.13 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 0.74/1.13 'identity_relation' ) ), function( X ) ] )
% 0.74/1.13 , clause( 193, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ),
% 0.74/1.13 member( image( X, Y ), 'universal_class' ) ] )
% 0.74/1.13 , clause( 194, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.74/1.13 , clause( 195, [ =( X, 'null_class' ), =( intersection( X, regular( X ) ),
% 0.74/1.13 'null_class' ) ] )
% 0.74/1.13 , clause( 196, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y
% 0.74/1.13 ) ) ] )
% 0.74/1.13 , clause( 197, [ function( choice ) ] )
% 0.74/1.13 , clause( 198, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' )
% 0.74/1.13 , member( apply( choice, X ), X ) ] )
% 0.74/1.13 , clause( 199, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 0.74/1.13 , clause( 200, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 0.74/1.13 , clause( 201, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 0.74/1.13 'one_to_one'( X ) ] )
% 0.74/1.13 , clause( 202, [ =( intersection( 'cross_product'( 'universal_class',
% 0.74/1.13 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 0.74/1.13 'universal_class' ), complement( compose( complement( 'element_relation'
% 0.74/1.13 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 0.74/1.13 , clause( 203, [ =( intersection( inverse( 'subset_relation' ),
% 0.74/1.13 'subset_relation' ), 'identity_relation' ) ] )
% 0.74/1.13 , clause( 204, [ =( complement( 'domain_of'( intersection( X,
% 0.74/1.13 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 0.74/1.13 , clause( 205, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 0.74/1.13 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 0.74/1.13 , clause( 206, [ ~( operation( X ) ), function( X ) ] )
% 0.74/1.13 , clause( 207, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 0.74/1.13 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.74/1.13 ] )
% 0.74/1.13 , clause( 208, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 0.74/1.13 'domain_of'( 'domain_of'( X ) ) ) ] )
% 0.74/1.13 , clause( 209, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 0.74/1.13 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.74/1.13 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 0.74/1.13 operation( X ) ] )
% 0.74/1.13 , clause( 210, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 0.74/1.13 , clause( 211, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y
% 0.74/1.13 ) ), 'domain_of'( X ) ) ] )
% 0.74/1.13 , clause( 212, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 0.74/1.13 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 0.74/1.13 , clause( 213, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) )
% 0.74/1.13 , 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 0.74/1.13 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 0.74/1.13 , clause( 214, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 0.74/1.13 , clause( 215, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 0.74/1.13 , clause( 216, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 0.74/1.13 , clause( 217, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T
% 0.74/1.13 , U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ),
% 0.74/1.13 apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ] )
% 0.74/1.13 , clause( 218, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z
% 0.74/1.13 , X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.74/1.13 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.74/1.13 , Y ) ] )
% 0.74/1.13 , clause( 219, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z
% 0.74/1.13 , X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'(
% 0.74/1.13 Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z,
% 0.74/1.13 apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.74/1.13 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ] )
% 0.74/1.13 , clause( 220, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T )
% 0.74/1.13 ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 0.74/1.13 , clause( 221, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T )
% 0.74/1.13 ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 0.74/1.13 , clause( 222, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T )
% 0.74/1.13 ) ), member( X, 'universal_class' ) ] )
% 0.74/1.13 , clause( 223, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T )
% 0.74/1.13 ) ), member( Y, 'universal_class' ) ] )
% 0.74/1.13 , clause( 224, [ subclass( X, X ) ] )
% 0.74/1.13 , clause( 225, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X
% 0.74/1.13 , Z ) ] )
% 0.74/1.13 , clause( 226, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 0.74/1.13 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 0.74/1.13 , clause( 227, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y
% 0.74/1.13 ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 0.74/1.13 , clause( 228, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X
% 0.74/1.13 ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 0.74/1.13 , clause( 229, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 0.74/1.13 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 0.74/1.13 , clause( 230, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ] )
% 0.74/1.13 , clause( 231, [ ~( member( X, 'null_class' ) ) ] )
% 0.74/1.13 , clause( 232, [ subclass( 'null_class', X ) ] )
% 0.74/1.13 , clause( 233, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 0.74/1.13 )
% 0.74/1.13 , clause( 234, [ =( X, 'null_class' ), member( 'not_subclass_element'( X,
% 0.74/1.13 'null_class' ), X ) ] )
% 0.74/1.13 , clause( 235, [ ~( member( 'null_class', 'universal_class' ) ) ] )
% 0.74/1.13 ] ).
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 subsumption(
% 0.74/1.13 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.74/1.13 )
% 0.74/1.13 , clause( 129, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y )
% 0.74/1.13 ] )
% 0.74/1.13 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.74/1.13 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 subsumption(
% 0.74/1.13 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 0.74/1.13 , clause( 132, [ subclass( X, 'universal_class' ) ] )
% 0.74/1.13 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 subsumption(
% 0.74/1.13 clause( 45, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 0.74/1.13 , clause( 175, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 0.74/1.13 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.74/1.13 1 )] ) ).
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 subsumption(
% 0.74/1.13 clause( 48, [ inductive( omega ) ] )
% 0.74/1.13 , clause( 178, [ inductive( omega ) ] )
% 0.74/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 subsumption(
% 0.74/1.13 clause( 104, [ ~( member( 'null_class', 'universal_class' ) ) ] )
% 0.74/1.13 , clause( 235, [ ~( member( 'null_class', 'universal_class' ) ) ] )
% 0.74/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 resolution(
% 0.74/1.13 clause( 351, [ ~( subclass( X, 'universal_class' ) ), ~( member(
% 0.74/1.13 'null_class', X ) ) ] )
% 0.74/1.13 , clause( 104, [ ~( member( 'null_class', 'universal_class' ) ) ] )
% 0.74/1.13 , 0, clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 0.74/1.13 ) ] )
% 0.74/1.13 , 2, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y,
% 0.74/1.13 'universal_class' ), :=( Z, 'null_class' )] )).
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 resolution(
% 0.74/1.13 clause( 352, [ ~( member( 'null_class', X ) ) ] )
% 0.74/1.13 , clause( 351, [ ~( subclass( X, 'universal_class' ) ), ~( member(
% 0.74/1.13 'null_class', X ) ) ] )
% 0.74/1.13 , 0, clause( 3, [ subclass( X, 'universal_class' ) ] )
% 0.74/1.13 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.74/1.13 ).
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 subsumption(
% 0.74/1.13 clause( 119, [ ~( member( 'null_class', X ) ) ] )
% 0.74/1.13 , clause( 352, [ ~( member( 'null_class', X ) ) ] )
% 0.74/1.13 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 resolution(
% 0.74/1.13 clause( 353, [ ~( inductive( X ) ) ] )
% 0.74/1.13 , clause( 119, [ ~( member( 'null_class', X ) ) ] )
% 0.74/1.13 , 0, clause( 45, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 0.74/1.13 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.74/1.13 ).
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 subsumption(
% 0.74/1.13 clause( 124, [ ~( inductive( X ) ) ] )
% 0.74/1.13 , clause( 353, [ ~( inductive( X ) ) ] )
% 0.74/1.13 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 resolution(
% 0.74/1.13 clause( 354, [] )
% 0.74/1.13 , clause( 124, [ ~( inductive( X ) ) ] )
% 0.74/1.13 , 0, clause( 48, [ inductive( omega ) ] )
% 0.74/1.13 , 0, substitution( 0, [ :=( X, omega )] ), substitution( 1, [] )).
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 subsumption(
% 0.74/1.13 clause( 127, [] )
% 0.74/1.13 , clause( 354, [] )
% 0.74/1.13 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 end.
% 0.74/1.13
% 0.74/1.13 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.74/1.13
% 0.74/1.13 Memory use:
% 0.74/1.13
% 0.74/1.13 space for terms: 4402
% 0.74/1.13 space for clauses: 9583
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 clauses generated: 153
% 0.74/1.13 clauses kept: 128
% 0.74/1.13 clauses selected: 16
% 0.74/1.13 clauses deleted: 1
% 0.74/1.13 clauses inuse deleted: 0
% 0.74/1.13
% 0.74/1.13 subsentry: 689
% 0.74/1.13 literals s-matched: 454
% 0.74/1.13 literals matched: 453
% 0.74/1.13 full subsumption: 141
% 0.74/1.13
% 0.74/1.13 checksum: 957160039
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Bliksem ended
%------------------------------------------------------------------------------