TSTP Solution File: SET075-6 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET075-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n007.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 22:46:37 EDT 2022
% Result : Unsatisfiable 0.76s 1.56s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET075-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Sun Jul 10 15:04:32 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.72/1.10 *** allocated 10000 integers for termspace/termends
% 0.72/1.10 *** allocated 10000 integers for clauses
% 0.72/1.10 *** allocated 10000 integers for justifications
% 0.72/1.10 Bliksem 1.12
% 0.72/1.10
% 0.72/1.10
% 0.72/1.10 Automatic Strategy Selection
% 0.72/1.10
% 0.72/1.10 Clauses:
% 0.72/1.10 [
% 0.72/1.10 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.72/1.10 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.72/1.10 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.72/1.10 ,
% 0.72/1.10 [ subclass( X, 'universal_class' ) ],
% 0.72/1.10 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.72/1.10 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.72/1.10 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.72/1.10 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.72/1.10 ,
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.72/1.10 ) ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.72/1.10 ) ) ],
% 0.72/1.10 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.72/1.10 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.72/1.10 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.72/1.10 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.72/1.10 X, Z ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.72/1.10 Y, T ) ],
% 0.72/1.10 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.72/1.10 ), 'cross_product'( Y, T ) ) ],
% 0.72/1.10 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.72/1.10 ), second( X ) ), X ) ],
% 0.72/1.10 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.72/1.10 'universal_class' ) ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.72/1.10 Y ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.72/1.10 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.72/1.10 , Y ), 'element_relation' ) ],
% 0.72/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.72/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.72/1.10 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.72/1.10 Z ) ) ],
% 0.72/1.10 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.72/1.10 member( X, Y ) ],
% 0.72/1.10 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.72/1.10 union( X, Y ) ) ],
% 0.72/1.10 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.72/1.10 intersection( complement( X ), complement( Y ) ) ) ),
% 0.72/1.10 'symmetric_difference'( X, Y ) ) ],
% 0.72/1.10 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.72/1.10 ,
% 0.72/1.10 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.72/1.10 ,
% 0.72/1.10 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.72/1.10 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.72/1.10 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.72/1.10 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.72/1.10 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.72/1.10 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.72/1.10 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.72/1.10 'cross_product'( 'universal_class', 'universal_class' ),
% 0.72/1.10 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.72/1.10 Y ), rotate( T ) ) ],
% 0.72/1.10 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.72/1.10 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.72/1.10 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.72/1.10 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.72/1.10 'cross_product'( 'universal_class', 'universal_class' ),
% 0.72/1.10 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.72/1.10 Z ), flip( T ) ) ],
% 0.72/1.10 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.72/1.10 inverse( X ) ) ],
% 0.72/1.10 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.72/1.10 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.72/1.10 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.72/1.10 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.72/1.10 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.72/1.10 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.72/1.10 ],
% 0.72/1.10 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.72/1.10 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.72/1.10 'universal_class' ) ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.72/1.10 successor( X ), Y ) ],
% 0.72/1.10 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.72/1.10 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.72/1.10 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.72/1.10 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.72/1.10 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.72/1.10 ,
% 0.72/1.10 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.72/1.10 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.72/1.10 [ inductive( omega ) ],
% 0.72/1.10 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.72/1.10 [ member( omega, 'universal_class' ) ],
% 0.72/1.10 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.72/1.10 , 'sum_class'( X ) ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.72/1.10 'universal_class' ) ],
% 0.72/1.10 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.72/1.10 'power_class'( X ) ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.72/1.10 'universal_class' ) ],
% 0.72/1.10 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.72/1.10 'universal_class' ) ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.72/1.10 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.72/1.10 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.72/1.10 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.72/1.10 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.72/1.10 ) ],
% 0.72/1.10 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.72/1.10 , 'identity_relation' ) ],
% 0.72/1.10 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.72/1.10 'single_valued_class'( X ) ],
% 0.72/1.10 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.72/1.10 'universal_class' ) ) ],
% 0.72/1.10 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.72/1.10 'identity_relation' ) ],
% 0.72/1.10 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.72/1.10 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.72/1.10 , function( X ) ],
% 0.72/1.10 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.72/1.10 X, Y ), 'universal_class' ) ],
% 0.72/1.10 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.72/1.10 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.72/1.10 ) ],
% 0.72/1.10 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.72/1.10 [ function( choice ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.72/1.10 apply( choice, X ), X ) ],
% 0.72/1.10 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.72/1.10 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.72/1.10 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.72/1.10 ,
% 0.72/1.10 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.72/1.10 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.72/1.10 , complement( compose( complement( 'element_relation' ), inverse(
% 0.72/1.10 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.72/1.10 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.72/1.10 'identity_relation' ) ],
% 0.72/1.10 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.72/1.10 , diagonalise( X ) ) ],
% 0.72/1.10 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.72/1.10 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.72/1.10 [ ~( operation( X ) ), function( X ) ],
% 0.72/1.10 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.72/1.10 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.72/1.10 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.76/1.56 'domain_of'( X ) ) ) ],
% 0.76/1.56 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.76/1.56 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.76/1.56 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.76/1.56 X ) ],
% 0.76/1.56 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.76/1.56 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.76/1.56 'domain_of'( X ) ) ],
% 0.76/1.56 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.76/1.56 'domain_of'( Z ) ) ) ],
% 0.76/1.56 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.76/1.56 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.76/1.56 ), compatible( X, Y, Z ) ],
% 0.76/1.56 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.76/1.56 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.76/1.56 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.76/1.56 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.76/1.56 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.76/1.56 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.76/1.56 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.76/1.56 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.76/1.56 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.76/1.56 , Y ) ],
% 0.76/1.56 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.76/1.56 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.76/1.56 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.76/1.56 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.76/1.56 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.76/1.56 [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v ) ) ],
% 0.76/1.56 [ =( 'unordered_pair'( x, y ), 'null_class' ) ]
% 0.76/1.56 ] .
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 percentage equality = 0.218579, percentage horn = 0.913978
% 0.76/1.56 This is a problem with some equality
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 Options Used:
% 0.76/1.56
% 0.76/1.56 useres = 1
% 0.76/1.56 useparamod = 1
% 0.76/1.56 useeqrefl = 1
% 0.76/1.56 useeqfact = 1
% 0.76/1.56 usefactor = 1
% 0.76/1.56 usesimpsplitting = 0
% 0.76/1.56 usesimpdemod = 5
% 0.76/1.56 usesimpres = 3
% 0.76/1.56
% 0.76/1.56 resimpinuse = 1000
% 0.76/1.56 resimpclauses = 20000
% 0.76/1.56 substype = eqrewr
% 0.76/1.56 backwardsubs = 1
% 0.76/1.56 selectoldest = 5
% 0.76/1.56
% 0.76/1.56 litorderings [0] = split
% 0.76/1.56 litorderings [1] = extend the termordering, first sorting on arguments
% 0.76/1.56
% 0.76/1.56 termordering = kbo
% 0.76/1.56
% 0.76/1.56 litapriori = 0
% 0.76/1.56 termapriori = 1
% 0.76/1.56 litaposteriori = 0
% 0.76/1.56 termaposteriori = 0
% 0.76/1.56 demodaposteriori = 0
% 0.76/1.56 ordereqreflfact = 0
% 0.76/1.56
% 0.76/1.56 litselect = negord
% 0.76/1.56
% 0.76/1.56 maxweight = 15
% 0.76/1.56 maxdepth = 30000
% 0.76/1.56 maxlength = 115
% 0.76/1.56 maxnrvars = 195
% 0.76/1.56 excuselevel = 1
% 0.76/1.56 increasemaxweight = 1
% 0.76/1.56
% 0.76/1.56 maxselected = 10000000
% 0.76/1.56 maxnrclauses = 10000000
% 0.76/1.56
% 0.76/1.56 showgenerated = 0
% 0.76/1.56 showkept = 0
% 0.76/1.56 showselected = 0
% 0.76/1.56 showdeleted = 0
% 0.76/1.56 showresimp = 1
% 0.76/1.56 showstatus = 2000
% 0.76/1.56
% 0.76/1.56 prologoutput = 1
% 0.76/1.56 nrgoals = 5000000
% 0.76/1.56 totalproof = 1
% 0.76/1.56
% 0.76/1.56 Symbols occurring in the translation:
% 0.76/1.56
% 0.76/1.56 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.76/1.56 . [1, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.76/1.56 ! [4, 1] (w:0, o:33, a:1, s:1, b:0),
% 0.76/1.56 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.76/1.56 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.76/1.56 subclass [41, 2] (w:1, o:83, a:1, s:1, b:0),
% 0.76/1.56 member [43, 2] (w:1, o:84, a:1, s:1, b:0),
% 0.76/1.56 'not_subclass_element' [44, 2] (w:1, o:85, a:1, s:1, b:0),
% 0.76/1.56 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.76/1.56 'unordered_pair' [46, 2] (w:1, o:86, a:1, s:1, b:0),
% 0.76/1.56 singleton [47, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.76/1.56 'ordered_pair' [48, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.76/1.56 'cross_product' [50, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.76/1.56 first [52, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.76/1.56 second [53, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.76/1.56 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.76/1.56 intersection [55, 2] (w:1, o:90, a:1, s:1, b:0),
% 0.76/1.56 complement [56, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.76/1.56 union [57, 2] (w:1, o:91, a:1, s:1, b:0),
% 0.76/1.56 'symmetric_difference' [58, 2] (w:1, o:92, a:1, s:1, b:0),
% 0.76/1.56 restrict [60, 3] (w:1, o:95, a:1, s:1, b:0),
% 0.76/1.56 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.76/1.56 'domain_of' [62, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.76/1.56 rotate [63, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.76/1.56 flip [65, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.76/1.56 inverse [66, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.76/1.56 'range_of' [67, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.76/1.56 domain [68, 3] (w:1, o:97, a:1, s:1, b:0),
% 0.76/1.56 range [69, 3] (w:1, o:98, a:1, s:1, b:0),
% 0.76/1.56 image [70, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.76/1.56 successor [71, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.76/1.56 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.76/1.56 inductive [73, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.76/1.56 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.76/1.56 'sum_class' [75, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.76/1.56 'power_class' [76, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.76/1.56 compose [78, 2] (w:1, o:93, a:1, s:1, b:0),
% 0.76/1.56 'single_valued_class' [79, 1] (w:1, o:55, a:1, s:1, b:0),
% 0.76/1.56 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.76/1.56 function [82, 1] (w:1, o:56, a:1, s:1, b:0),
% 0.76/1.56 regular [83, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.76/1.56 apply [84, 2] (w:1, o:94, a:1, s:1, b:0),
% 0.76/1.56 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.76/1.56 'one_to_one' [86, 1] (w:1, o:52, a:1, s:1, b:0),
% 0.76/1.56 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 0.76/1.56 diagonalise [88, 1] (w:1, o:57, a:1, s:1, b:0),
% 0.76/1.56 cantor [89, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.76/1.56 operation [90, 1] (w:1, o:53, a:1, s:1, b:0),
% 0.76/1.56 compatible [94, 3] (w:1, o:96, a:1, s:1, b:0),
% 0.76/1.56 homomorphism [95, 3] (w:1, o:99, a:1, s:1, b:0),
% 0.76/1.56 'not_homomorphism1' [96, 3] (w:1, o:100, a:1, s:1, b:0),
% 0.76/1.56 'not_homomorphism2' [97, 3] (w:1, o:101, a:1, s:1, b:0),
% 0.76/1.56 x [98, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.76/1.56 y [99, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.76/1.56 u [100, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.76/1.56 v [101, 0] (w:1, o:32, a:1, s:1, b:0).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 Starting Search:
% 0.76/1.56
% 0.76/1.56 Resimplifying inuse:
% 0.76/1.56 Done
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 Intermediate Status:
% 0.76/1.56 Generated: 5705
% 0.76/1.56 Kept: 2020
% 0.76/1.56 Inuse: 110
% 0.76/1.56 Deleted: 4
% 0.76/1.56 Deletedinuse: 3
% 0.76/1.56
% 0.76/1.56 Resimplifying inuse:
% 0.76/1.56 Done
% 0.76/1.56
% 0.76/1.56 Resimplifying inuse:
% 0.76/1.56 Done
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 Intermediate Status:
% 0.76/1.56 Generated: 10380
% 0.76/1.56 Kept: 4023
% 0.76/1.56 Inuse: 187
% 0.76/1.56 Deleted: 23
% 0.76/1.56 Deletedinuse: 16
% 0.76/1.56
% 0.76/1.56 Resimplifying inuse:
% 0.76/1.56 Done
% 0.76/1.56
% 0.76/1.56 Resimplifying inuse:
% 0.76/1.56 Done
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 Intermediate Status:
% 0.76/1.56 Generated: 14238
% 0.76/1.56 Kept: 6049
% 0.76/1.56 Inuse: 237
% 0.76/1.56 Deleted: 25
% 0.76/1.56 Deletedinuse: 16
% 0.76/1.56
% 0.76/1.56 Resimplifying inuse:
% 0.76/1.56 Done
% 0.76/1.56
% 0.76/1.56 Resimplifying inuse:
% 0.76/1.56 Done
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 Intermediate Status:
% 0.76/1.56 Generated: 19060
% 0.76/1.56 Kept: 8114
% 0.76/1.56 Inuse: 290
% 0.76/1.56 Deleted: 86
% 0.76/1.56 Deletedinuse: 75
% 0.76/1.56
% 0.76/1.56 Resimplifying inuse:
% 0.76/1.56 Done
% 0.76/1.56
% 0.76/1.56 Resimplifying inuse:
% 0.76/1.56 Done
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 Bliksems!, er is een bewijs:
% 0.76/1.56 % SZS status Unsatisfiable
% 0.76/1.56 % SZS output start Refutation
% 0.76/1.56
% 0.76/1.56 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.76/1.56 )
% 0.76/1.56 .
% 0.76/1.56 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 0.76/1.56 .
% 0.76/1.56 clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.76/1.56 'unordered_pair'( Y, X ) ) ] )
% 0.76/1.56 .
% 0.76/1.56 clause( 13, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) )
% 0.76/1.56 ), member( Y, T ) ] )
% 0.76/1.56 .
% 0.76/1.56 clause( 19, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ] )
% 0.76/1.56 .
% 0.76/1.56 clause( 22, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ] )
% 0.76/1.56 .
% 0.76/1.56 clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.76/1.56 .
% 0.76/1.56 clause( 90, [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v ) ) ]
% 0.76/1.56 )
% 0.76/1.56 .
% 0.76/1.56 clause( 91, [ =( 'unordered_pair'( x, y ), 'null_class' ) ] )
% 0.76/1.56 .
% 0.76/1.56 clause( 106, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ] )
% 0.76/1.56 .
% 0.76/1.56 clause( 463, [ ~( member( y, 'universal_class' ) ), member( y, 'null_class'
% 0.76/1.56 ) ] )
% 0.76/1.56 .
% 0.76/1.56 clause( 960, [ member( y, 'null_class' ), ~( member( y, X ) ) ] )
% 0.76/1.56 .
% 0.76/1.56 clause( 1803, [ ~( member( X, complement( 'universal_class' ) ) ), ~(
% 0.76/1.56 member( X, Y ) ) ] )
% 0.76/1.56 .
% 0.76/1.56 clause( 1826, [ ~( member( X, complement( 'universal_class' ) ) ) ] )
% 0.76/1.56 .
% 0.76/1.56 clause( 1837, [ ~( member( X, intersection( complement( 'universal_class' )
% 0.76/1.56 , Y ) ) ) ] )
% 0.76/1.56 .
% 0.76/1.56 clause( 6927, [ =( intersection( complement( 'universal_class' ), X ),
% 0.76/1.56 'null_class' ) ] )
% 0.76/1.56 .
% 0.76/1.56 clause( 7493, [ ~( member( X, 'null_class' ) ) ] )
% 0.76/1.56 .
% 0.76/1.56 clause( 7515, [ ~( member( y, X ) ) ] )
% 0.76/1.56 .
% 0.76/1.56 clause( 7789, [ ~( member( 'ordered_pair'( X, y ), 'cross_product'( Y, Z )
% 0.76/1.56 ) ) ] )
% 0.76/1.56 .
% 0.76/1.56 clause( 9974, [] )
% 0.76/1.56 .
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 % SZS output end Refutation
% 0.76/1.56 found a proof!
% 0.76/1.56
% 0.76/1.56 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.76/1.56
% 0.76/1.56 initialclauses(
% 0.76/1.56 [ clause( 9976, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 0.76/1.56 ) ] )
% 0.76/1.56 , clause( 9977, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 0.76/1.56 , Y ) ] )
% 0.76/1.56 , clause( 9978, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 0.76/1.56 subclass( X, Y ) ] )
% 0.76/1.56 , clause( 9979, [ subclass( X, 'universal_class' ) ] )
% 0.76/1.56 , clause( 9980, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 0.76/1.56 , clause( 9981, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 0.76/1.56 , clause( 9982, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ]
% 0.76/1.56 )
% 0.76/1.56 , clause( 9983, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 0.76/1.56 =( X, Z ) ] )
% 0.76/1.56 , clause( 9984, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.76/1.56 'unordered_pair'( X, Y ) ) ] )
% 0.76/1.56 , clause( 9985, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.76/1.56 'unordered_pair'( Y, X ) ) ] )
% 0.76/1.56 , clause( 9986, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 0.76/1.56 )
% 0.76/1.56 , clause( 9987, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 0.76/1.56 , clause( 9988, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 0.76/1.56 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.76/1.56 , clause( 9989, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.76/1.56 ) ) ), member( X, Z ) ] )
% 0.76/1.56 , clause( 9990, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.76/1.56 ) ) ), member( Y, T ) ] )
% 0.76/1.56 , clause( 9991, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 0.76/1.56 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 0.76/1.56 , clause( 9992, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 0.76/1.56 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 0.76/1.56 , clause( 9993, [ subclass( 'element_relation', 'cross_product'(
% 0.76/1.56 'universal_class', 'universal_class' ) ) ] )
% 0.76/1.56 , clause( 9994, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) )
% 0.76/1.56 , member( X, Y ) ] )
% 0.76/1.56 , clause( 9995, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.76/1.56 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 0.76/1.56 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 0.76/1.56 , clause( 9996, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.76/1.56 )
% 0.76/1.56 , clause( 9997, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 0.76/1.56 )
% 0.76/1.56 , clause( 9998, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 0.76/1.56 intersection( Y, Z ) ) ] )
% 0.76/1.56 , clause( 9999, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 0.76/1.56 )
% 0.76/1.56 , clause( 10000, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.76/1.56 complement( Y ) ), member( X, Y ) ] )
% 0.76/1.56 , clause( 10001, [ =( complement( intersection( complement( X ), complement(
% 0.76/1.56 Y ) ) ), union( X, Y ) ) ] )
% 0.76/1.56 , clause( 10002, [ =( intersection( complement( intersection( X, Y ) ),
% 0.76/1.56 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 0.76/1.56 'symmetric_difference'( X, Y ) ) ] )
% 0.76/1.56 , clause( 10003, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 0.76/1.56 X, Y, Z ) ) ] )
% 0.76/1.56 , clause( 10004, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 0.76/1.56 Z, X, Y ) ) ] )
% 0.76/1.56 , clause( 10005, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 0.76/1.56 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 0.76/1.56 , clause( 10006, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 0.76/1.56 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 0.76/1.56 'domain_of'( Y ) ) ] )
% 0.76/1.56 , clause( 10007, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.76/1.56 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.76/1.56 , clause( 10008, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.76/1.56 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 0.76/1.56 ] )
% 0.76/1.56 , clause( 10009, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.76/1.56 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 0.76/1.56 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.76/1.56 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 0.76/1.56 , Y ), rotate( T ) ) ] )
% 0.76/1.56 , clause( 10010, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.76/1.56 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.76/1.56 , clause( 10011, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.76/1.56 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 0.76/1.56 )
% 0.76/1.56 , clause( 10012, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.76/1.56 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 0.76/1.56 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.76/1.56 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 0.76/1.56 , Z ), flip( T ) ) ] )
% 0.76/1.56 , clause( 10013, [ =( 'domain_of'( flip( 'cross_product'( X,
% 0.76/1.56 'universal_class' ) ) ), inverse( X ) ) ] )
% 0.76/1.56 , clause( 10014, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 0.76/1.56 , clause( 10015, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 0.76/1.56 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 0.76/1.56 , clause( 10016, [ =( second( 'not_subclass_element'( restrict( X,
% 0.76/1.56 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 0.76/1.56 , clause( 10017, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 0.76/1.56 image( X, Y ) ) ] )
% 0.76/1.56 , clause( 10018, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 0.76/1.56 , clause( 10019, [ subclass( 'successor_relation', 'cross_product'(
% 0.76/1.56 'universal_class', 'universal_class' ) ) ] )
% 0.76/1.56 , clause( 10020, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 0.76/1.56 ) ), =( successor( X ), Y ) ] )
% 0.76/1.56 , clause( 10021, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 0.76/1.56 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 0.76/1.56 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 0.76/1.56 , clause( 10022, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 0.76/1.56 , clause( 10023, [ ~( inductive( X ) ), subclass( image(
% 0.76/1.56 'successor_relation', X ), X ) ] )
% 0.76/1.56 , clause( 10024, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.76/1.56 'successor_relation', X ), X ) ), inductive( X ) ] )
% 0.76/1.56 , clause( 10025, [ inductive( omega ) ] )
% 0.76/1.56 , clause( 10026, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 0.76/1.56 , clause( 10027, [ member( omega, 'universal_class' ) ] )
% 0.76/1.56 , clause( 10028, [ =( 'domain_of'( restrict( 'element_relation',
% 0.76/1.56 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 0.76/1.56 , clause( 10029, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 0.76/1.56 X ), 'universal_class' ) ] )
% 0.76/1.56 , clause( 10030, [ =( complement( image( 'element_relation', complement( X
% 0.76/1.56 ) ) ), 'power_class'( X ) ) ] )
% 0.76/1.56 , clause( 10031, [ ~( member( X, 'universal_class' ) ), member(
% 0.76/1.56 'power_class'( X ), 'universal_class' ) ] )
% 0.76/1.56 , clause( 10032, [ subclass( compose( X, Y ), 'cross_product'(
% 0.76/1.56 'universal_class', 'universal_class' ) ) ] )
% 0.76/1.56 , clause( 10033, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 0.76/1.56 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 0.76/1.56 , clause( 10034, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 0.76/1.56 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.76/1.56 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.76/1.56 ) ] )
% 0.76/1.56 , clause( 10035, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 0.76/1.56 inverse( X ) ), 'identity_relation' ) ] )
% 0.76/1.56 , clause( 10036, [ ~( subclass( compose( X, inverse( X ) ),
% 0.76/1.56 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 0.76/1.56 , clause( 10037, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 0.76/1.56 'universal_class', 'universal_class' ) ) ] )
% 0.76/1.56 , clause( 10038, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 0.76/1.56 , 'identity_relation' ) ] )
% 0.76/1.56 , clause( 10039, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 0.76/1.56 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 0.76/1.56 'identity_relation' ) ), function( X ) ] )
% 0.76/1.56 , clause( 10040, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 0.76/1.56 , member( image( X, Y ), 'universal_class' ) ] )
% 0.76/1.56 , clause( 10041, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.76/1.56 , clause( 10042, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 0.76/1.56 , 'null_class' ) ] )
% 0.76/1.56 , clause( 10043, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 0.76/1.56 Y ) ) ] )
% 0.76/1.56 , clause( 10044, [ function( choice ) ] )
% 0.76/1.56 , clause( 10045, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 0.76/1.56 ), member( apply( choice, X ), X ) ] )
% 0.76/1.56 , clause( 10046, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 0.76/1.56 , clause( 10047, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 0.76/1.56 , clause( 10048, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 0.76/1.56 'one_to_one'( X ) ] )
% 0.76/1.56 , clause( 10049, [ =( intersection( 'cross_product'( 'universal_class',
% 0.76/1.56 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 0.76/1.56 'universal_class' ), complement( compose( complement( 'element_relation'
% 0.76/1.56 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 0.76/1.56 , clause( 10050, [ =( intersection( inverse( 'subset_relation' ),
% 0.76/1.56 'subset_relation' ), 'identity_relation' ) ] )
% 0.76/1.56 , clause( 10051, [ =( complement( 'domain_of'( intersection( X,
% 0.76/1.56 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 0.76/1.56 , clause( 10052, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 0.76/1.56 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 0.76/1.56 , clause( 10053, [ ~( operation( X ) ), function( X ) ] )
% 0.76/1.56 , clause( 10054, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 0.76/1.56 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.76/1.56 ] )
% 0.76/1.56 , clause( 10055, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 0.76/1.56 'domain_of'( 'domain_of'( X ) ) ) ] )
% 0.76/1.56 , clause( 10056, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 0.76/1.56 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.76/1.56 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 0.76/1.56 operation( X ) ] )
% 0.76/1.56 , clause( 10057, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 0.76/1.56 , clause( 10058, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 0.76/1.56 Y ) ), 'domain_of'( X ) ) ] )
% 0.76/1.56 , clause( 10059, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 0.76/1.56 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 0.76/1.56 , clause( 10060, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 0.76/1.56 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 0.76/1.56 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 0.76/1.56 , clause( 10061, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 0.76/1.56 , clause( 10062, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 0.76/1.56 , clause( 10063, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 0.76/1.56 , clause( 10064, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 0.76/1.56 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 0.76/1.56 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 0.76/1.56 )
% 0.76/1.56 , clause( 10065, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 0.76/1.56 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.76/1.56 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.76/1.56 , Y ) ] )
% 0.76/1.56 , clause( 10066, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 0.76/1.56 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 0.76/1.56 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 0.76/1.56 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 0.76/1.56 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 0.76/1.56 )
% 0.76/1.56 , clause( 10067, [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v )
% 0.76/1.56 ) ] )
% 0.76/1.56 , clause( 10068, [ =( 'unordered_pair'( x, y ), 'null_class' ) ] )
% 0.76/1.56 ] ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.76/1.56 )
% 0.76/1.56 , clause( 9976, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 0.76/1.56 ) ] )
% 0.76/1.56 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.76/1.56 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 0.76/1.56 , clause( 9979, [ subclass( X, 'universal_class' ) ] )
% 0.76/1.56 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.76/1.56 'unordered_pair'( Y, X ) ) ] )
% 0.76/1.56 , clause( 9985, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.76/1.56 'unordered_pair'( Y, X ) ) ] )
% 0.76/1.56 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.56 ), ==>( 1, 1 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 13, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) )
% 0.76/1.56 ), member( Y, T ) ] )
% 0.76/1.56 , clause( 9990, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.76/1.56 ) ) ), member( Y, T ) ] )
% 0.76/1.56 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.76/1.56 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 19, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ] )
% 0.76/1.56 , clause( 9996, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.76/1.56 )
% 0.76/1.56 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.76/1.56 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 22, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ] )
% 0.76/1.56 , clause( 9999, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 0.76/1.56 )
% 0.76/1.56 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.56 ), ==>( 1, 1 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.76/1.56 , clause( 10041, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.76/1.56 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.76/1.56 1 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 90, [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v ) ) ]
% 0.76/1.56 )
% 0.76/1.56 , clause( 10067, [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v )
% 0.76/1.56 ) ] )
% 0.76/1.56 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 91, [ =( 'unordered_pair'( x, y ), 'null_class' ) ] )
% 0.76/1.56 , clause( 10068, [ =( 'unordered_pair'( x, y ), 'null_class' ) ] )
% 0.76/1.56 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 resolution(
% 0.76/1.56 clause( 10245, [ ~( member( Y, X ) ), member( Y, 'universal_class' ) ] )
% 0.76/1.56 , clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.76/1.56 )
% 0.76/1.56 , 0, clause( 3, [ subclass( X, 'universal_class' ) ] )
% 0.76/1.56 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'universal_class' ), :=( Z, Y )] )
% 0.76/1.56 , substitution( 1, [ :=( X, X )] )).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 106, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ] )
% 0.76/1.56 , clause( 10245, [ ~( member( Y, X ) ), member( Y, 'universal_class' ) ] )
% 0.76/1.56 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.56 ), ==>( 1, 1 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 paramod(
% 0.76/1.56 clause( 10247, [ member( y, 'null_class' ), ~( member( y, 'universal_class'
% 0.76/1.56 ) ) ] )
% 0.76/1.56 , clause( 91, [ =( 'unordered_pair'( x, y ), 'null_class' ) ] )
% 0.76/1.56 , 0, clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.76/1.56 'unordered_pair'( Y, X ) ) ] )
% 0.76/1.56 , 1, 2, substitution( 0, [] ), substitution( 1, [ :=( X, y ), :=( Y, x )] )
% 0.76/1.56 ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 463, [ ~( member( y, 'universal_class' ) ), member( y, 'null_class'
% 0.76/1.56 ) ] )
% 0.76/1.56 , clause( 10247, [ member( y, 'null_class' ), ~( member( y,
% 0.76/1.56 'universal_class' ) ) ] )
% 0.76/1.56 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] )
% 0.76/1.56 ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 resolution(
% 0.76/1.56 clause( 10248, [ member( y, 'null_class' ), ~( member( y, X ) ) ] )
% 0.76/1.56 , clause( 463, [ ~( member( y, 'universal_class' ) ), member( y,
% 0.76/1.56 'null_class' ) ] )
% 0.76/1.56 , 0, clause( 106, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ]
% 0.76/1.56 )
% 0.76/1.56 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, y ), :=( Y, X )] )
% 0.76/1.56 ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 960, [ member( y, 'null_class' ), ~( member( y, X ) ) ] )
% 0.76/1.56 , clause( 10248, [ member( y, 'null_class' ), ~( member( y, X ) ) ] )
% 0.76/1.56 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.76/1.56 1 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 resolution(
% 0.76/1.56 clause( 10249, [ ~( member( X, complement( 'universal_class' ) ) ), ~(
% 0.76/1.56 member( X, Y ) ) ] )
% 0.76/1.56 , clause( 22, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ] )
% 0.76/1.56 , 1, clause( 106, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ]
% 0.76/1.56 )
% 0.76/1.56 , 1, substitution( 0, [ :=( X, X ), :=( Y, 'universal_class' )] ),
% 0.76/1.56 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 1803, [ ~( member( X, complement( 'universal_class' ) ) ), ~(
% 0.76/1.56 member( X, Y ) ) ] )
% 0.76/1.56 , clause( 10249, [ ~( member( X, complement( 'universal_class' ) ) ), ~(
% 0.76/1.56 member( X, Y ) ) ] )
% 0.76/1.56 , substitution( 0, [ :=( X, X ), :=( Y, complement( 'universal_class' ) )] )
% 0.76/1.56 , permutation( 0, [ ==>( 0, 0 ), ==>( 1, 0 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 factor(
% 0.76/1.56 clause( 10251, [ ~( member( X, complement( 'universal_class' ) ) ) ] )
% 0.76/1.56 , clause( 1803, [ ~( member( X, complement( 'universal_class' ) ) ), ~(
% 0.76/1.56 member( X, Y ) ) ] )
% 0.76/1.56 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, complement( 'universal_class'
% 0.76/1.56 ) )] )).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 1826, [ ~( member( X, complement( 'universal_class' ) ) ) ] )
% 0.76/1.56 , clause( 10251, [ ~( member( X, complement( 'universal_class' ) ) ) ] )
% 0.76/1.56 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 resolution(
% 0.76/1.56 clause( 10252, [ ~( member( X, intersection( complement( 'universal_class'
% 0.76/1.56 ), Y ) ) ) ] )
% 0.76/1.56 , clause( 1826, [ ~( member( X, complement( 'universal_class' ) ) ) ] )
% 0.76/1.56 , 0, clause( 19, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.76/1.56 )
% 0.76/1.56 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ), :=( Y
% 0.76/1.56 , complement( 'universal_class' ) ), :=( Z, Y )] )).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 1837, [ ~( member( X, intersection( complement( 'universal_class' )
% 0.76/1.56 , Y ) ) ) ] )
% 0.76/1.56 , clause( 10252, [ ~( member( X, intersection( complement(
% 0.76/1.56 'universal_class' ), Y ) ) ) ] )
% 0.76/1.56 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.56 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 eqswap(
% 0.76/1.56 clause( 10253, [ =( 'null_class', X ), member( regular( X ), X ) ] )
% 0.76/1.56 , clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.76/1.56 , 0, substitution( 0, [ :=( X, X )] )).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 resolution(
% 0.76/1.56 clause( 10254, [ =( 'null_class', intersection( complement(
% 0.76/1.56 'universal_class' ), X ) ) ] )
% 0.76/1.56 , clause( 1837, [ ~( member( X, intersection( complement( 'universal_class'
% 0.76/1.56 ), Y ) ) ) ] )
% 0.76/1.56 , 0, clause( 10253, [ =( 'null_class', X ), member( regular( X ), X ) ] )
% 0.76/1.56 , 1, substitution( 0, [ :=( X, regular( intersection( complement(
% 0.76/1.56 'universal_class' ), X ) ) ), :=( Y, X )] ), substitution( 1, [ :=( X,
% 0.76/1.56 intersection( complement( 'universal_class' ), X ) )] )).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 eqswap(
% 0.76/1.56 clause( 10255, [ =( intersection( complement( 'universal_class' ), X ),
% 0.76/1.56 'null_class' ) ] )
% 0.76/1.56 , clause( 10254, [ =( 'null_class', intersection( complement(
% 0.76/1.56 'universal_class' ), X ) ) ] )
% 0.76/1.56 , 0, substitution( 0, [ :=( X, X )] )).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 6927, [ =( intersection( complement( 'universal_class' ), X ),
% 0.76/1.56 'null_class' ) ] )
% 0.76/1.56 , clause( 10255, [ =( intersection( complement( 'universal_class' ), X ),
% 0.76/1.56 'null_class' ) ] )
% 0.76/1.56 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 paramod(
% 0.76/1.56 clause( 10257, [ ~( member( X, 'null_class' ) ) ] )
% 0.76/1.56 , clause( 6927, [ =( intersection( complement( 'universal_class' ), X ),
% 0.76/1.56 'null_class' ) ] )
% 0.76/1.56 , 0, clause( 1837, [ ~( member( X, intersection( complement(
% 0.76/1.56 'universal_class' ), Y ) ) ) ] )
% 0.76/1.56 , 0, 3, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 0.76/1.56 :=( Y, Y )] )).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 7493, [ ~( member( X, 'null_class' ) ) ] )
% 0.76/1.56 , clause( 10257, [ ~( member( X, 'null_class' ) ) ] )
% 0.76/1.56 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 resolution(
% 0.76/1.56 clause( 10258, [ ~( member( y, X ) ) ] )
% 0.76/1.56 , clause( 7493, [ ~( member( X, 'null_class' ) ) ] )
% 0.76/1.56 , 0, clause( 960, [ member( y, 'null_class' ), ~( member( y, X ) ) ] )
% 0.76/1.56 , 0, substitution( 0, [ :=( X, y )] ), substitution( 1, [ :=( X, X )] )
% 0.76/1.56 ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 7515, [ ~( member( y, X ) ) ] )
% 0.76/1.56 , clause( 10258, [ ~( member( y, X ) ) ] )
% 0.76/1.56 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 resolution(
% 0.76/1.56 clause( 10259, [ ~( member( 'ordered_pair'( Y, y ), 'cross_product'( Z, X )
% 0.76/1.56 ) ) ] )
% 0.76/1.56 , clause( 7515, [ ~( member( y, X ) ) ] )
% 0.76/1.56 , 0, clause( 13, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.76/1.56 ) ) ), member( Y, T ) ] )
% 0.76/1.56 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, Y ), :=( Y
% 0.76/1.56 , y ), :=( Z, Z ), :=( T, X )] )).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 7789, [ ~( member( 'ordered_pair'( X, y ), 'cross_product'( Y, Z )
% 0.76/1.56 ) ) ] )
% 0.76/1.56 , clause( 10259, [ ~( member( 'ordered_pair'( Y, y ), 'cross_product'( Z, X
% 0.76/1.56 ) ) ) ] )
% 0.76/1.56 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 0.76/1.56 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 resolution(
% 0.76/1.56 clause( 10260, [] )
% 0.76/1.56 , clause( 7789, [ ~( member( 'ordered_pair'( X, y ), 'cross_product'( Y, Z
% 0.76/1.56 ) ) ) ] )
% 0.76/1.56 , 0, clause( 90, [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v )
% 0.76/1.56 ) ] )
% 0.76/1.56 , 0, substitution( 0, [ :=( X, x ), :=( Y, u ), :=( Z, v )] ),
% 0.76/1.56 substitution( 1, [] )).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 subsumption(
% 0.76/1.56 clause( 9974, [] )
% 0.76/1.56 , clause( 10260, [] )
% 0.76/1.56 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 end.
% 0.76/1.56
% 0.76/1.56 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.76/1.56
% 0.76/1.56 Memory use:
% 0.76/1.56
% 0.76/1.56 space for terms: 152967
% 0.76/1.56 space for clauses: 477882
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 clauses generated: 24080
% 0.76/1.56 clauses kept: 9975
% 0.76/1.56 clauses selected: 367
% 0.76/1.56 clauses deleted: 114
% 0.76/1.56 clauses inuse deleted: 100
% 0.76/1.56
% 0.76/1.56 subsentry: 55543
% 0.76/1.56 literals s-matched: 43212
% 0.76/1.56 literals matched: 42536
% 0.76/1.56 full subsumption: 19457
% 0.76/1.56
% 0.76/1.56 checksum: -281399966
% 0.76/1.56
% 0.76/1.56
% 0.76/1.56 Bliksem ended
%------------------------------------------------------------------------------