TSTP Solution File: SET050-6 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET050-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n019.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 22:46:07 EDT 2022
% Result : Unsatisfiable 0.74s 1.54s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET050-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Sun Jul 10 03:12:53 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.43/1.08 *** allocated 10000 integers for termspace/termends
% 0.43/1.08 *** allocated 10000 integers for clauses
% 0.43/1.08 *** allocated 10000 integers for justifications
% 0.43/1.08 Bliksem 1.12
% 0.43/1.08
% 0.43/1.08
% 0.43/1.08 Automatic Strategy Selection
% 0.43/1.08
% 0.43/1.08 Clauses:
% 0.43/1.08 [
% 0.43/1.08 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.43/1.08 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.43/1.08 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.43/1.08 ,
% 0.43/1.08 [ subclass( X, 'universal_class' ) ],
% 0.43/1.08 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.43/1.08 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.43/1.08 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.43/1.08 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.43/1.08 ,
% 0.43/1.08 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.43/1.08 ) ) ],
% 0.43/1.08 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.43/1.08 ) ) ],
% 0.43/1.08 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.43/1.08 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.43/1.08 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.43/1.08 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.08 X, Z ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.08 Y, T ) ],
% 0.43/1.08 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.43/1.08 ), 'cross_product'( Y, T ) ) ],
% 0.43/1.08 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.43/1.08 ), second( X ) ), X ) ],
% 0.43/1.08 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.43/1.08 'universal_class' ) ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.43/1.08 Y ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.43/1.08 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.43/1.08 , Y ), 'element_relation' ) ],
% 0.43/1.08 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.43/1.08 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.43/1.08 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.43/1.08 Z ) ) ],
% 0.43/1.08 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.43/1.08 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.43/1.08 member( X, Y ) ],
% 0.43/1.08 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.43/1.08 union( X, Y ) ) ],
% 0.43/1.08 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.43/1.08 intersection( complement( X ), complement( Y ) ) ) ),
% 0.43/1.08 'symmetric_difference'( X, Y ) ) ],
% 0.43/1.08 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.43/1.08 ,
% 0.43/1.08 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.43/1.08 ,
% 0.43/1.08 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.43/1.08 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.43/1.08 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.43/1.08 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.43/1.08 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.43/1.08 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.43/1.08 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.43/1.08 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.43/1.08 'cross_product'( 'universal_class', 'universal_class' ),
% 0.43/1.08 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.43/1.08 Y ), rotate( T ) ) ],
% 0.43/1.08 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.43/1.08 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.43/1.08 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.43/1.08 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.43/1.08 'cross_product'( 'universal_class', 'universal_class' ),
% 0.43/1.08 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.43/1.08 Z ), flip( T ) ) ],
% 0.43/1.08 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.43/1.08 inverse( X ) ) ],
% 0.43/1.08 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.43/1.08 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.43/1.08 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.43/1.08 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.43/1.08 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.43/1.08 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.43/1.08 ],
% 0.43/1.08 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.43/1.08 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.43/1.08 'universal_class' ) ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.43/1.08 successor( X ), Y ) ],
% 0.43/1.08 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.43/1.08 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.43/1.08 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.43/1.08 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.43/1.08 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.43/1.08 ,
% 0.43/1.08 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.43/1.08 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.43/1.08 [ inductive( omega ) ],
% 0.43/1.08 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.43/1.08 [ member( omega, 'universal_class' ) ],
% 0.43/1.08 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.43/1.08 , 'sum_class'( X ) ) ],
% 0.43/1.08 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.43/1.08 'universal_class' ) ],
% 0.43/1.08 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.43/1.08 'power_class'( X ) ) ],
% 0.43/1.08 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.43/1.08 'universal_class' ) ],
% 0.43/1.08 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.43/1.08 'universal_class' ) ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.43/1.08 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.43/1.08 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.43/1.08 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.43/1.08 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.43/1.08 ) ],
% 0.43/1.08 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.43/1.08 , 'identity_relation' ) ],
% 0.43/1.08 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.43/1.08 'single_valued_class'( X ) ],
% 0.43/1.08 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.43/1.08 'universal_class' ) ) ],
% 0.43/1.08 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.43/1.08 'identity_relation' ) ],
% 0.43/1.08 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.43/1.08 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.43/1.08 , function( X ) ],
% 0.43/1.08 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.43/1.08 X, Y ), 'universal_class' ) ],
% 0.43/1.08 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.43/1.08 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.43/1.08 ) ],
% 0.43/1.08 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.43/1.08 [ function( choice ) ],
% 0.43/1.08 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.43/1.08 apply( choice, X ), X ) ],
% 0.43/1.08 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.43/1.08 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.43/1.08 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.43/1.08 ,
% 0.43/1.08 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.43/1.08 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.43/1.08 , complement( compose( complement( 'element_relation' ), inverse(
% 0.43/1.08 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.43/1.08 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.43/1.08 'identity_relation' ) ],
% 0.43/1.08 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.43/1.08 , diagonalise( X ) ) ],
% 0.43/1.08 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.43/1.08 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.43/1.08 [ ~( operation( X ) ), function( X ) ],
% 0.43/1.08 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.43/1.08 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.43/1.08 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.74/1.54 'domain_of'( X ) ) ) ],
% 0.74/1.54 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.74/1.54 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.74/1.54 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.74/1.54 X ) ],
% 0.74/1.54 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.74/1.54 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.74/1.54 'domain_of'( X ) ) ],
% 0.74/1.54 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.74/1.54 'domain_of'( Z ) ) ) ],
% 0.74/1.54 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.74/1.54 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.74/1.54 ), compatible( X, Y, Z ) ],
% 0.74/1.54 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.74/1.54 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.74/1.54 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.74/1.54 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.74/1.54 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.74/1.54 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.74/1.54 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.74/1.54 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.74/1.54 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.74/1.54 , Y ) ],
% 0.74/1.54 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.74/1.54 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.74/1.54 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.74/1.54 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.74/1.54 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.74/1.54 [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v ) ) ],
% 0.74/1.54 [ ~( member( x, 'unordered_pair'( x, y ) ) ) ]
% 0.74/1.54 ] .
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 percentage equality = 0.213115, percentage horn = 0.913978
% 0.74/1.54 This is a problem with some equality
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 Options Used:
% 0.74/1.54
% 0.74/1.54 useres = 1
% 0.74/1.54 useparamod = 1
% 0.74/1.54 useeqrefl = 1
% 0.74/1.54 useeqfact = 1
% 0.74/1.54 usefactor = 1
% 0.74/1.54 usesimpsplitting = 0
% 0.74/1.54 usesimpdemod = 5
% 0.74/1.54 usesimpres = 3
% 0.74/1.54
% 0.74/1.54 resimpinuse = 1000
% 0.74/1.54 resimpclauses = 20000
% 0.74/1.54 substype = eqrewr
% 0.74/1.54 backwardsubs = 1
% 0.74/1.54 selectoldest = 5
% 0.74/1.54
% 0.74/1.54 litorderings [0] = split
% 0.74/1.54 litorderings [1] = extend the termordering, first sorting on arguments
% 0.74/1.54
% 0.74/1.54 termordering = kbo
% 0.74/1.54
% 0.74/1.54 litapriori = 0
% 0.74/1.54 termapriori = 1
% 0.74/1.54 litaposteriori = 0
% 0.74/1.54 termaposteriori = 0
% 0.74/1.54 demodaposteriori = 0
% 0.74/1.54 ordereqreflfact = 0
% 0.74/1.54
% 0.74/1.54 litselect = negord
% 0.74/1.54
% 0.74/1.54 maxweight = 15
% 0.74/1.54 maxdepth = 30000
% 0.74/1.54 maxlength = 115
% 0.74/1.54 maxnrvars = 195
% 0.74/1.54 excuselevel = 1
% 0.74/1.54 increasemaxweight = 1
% 0.74/1.54
% 0.74/1.54 maxselected = 10000000
% 0.74/1.54 maxnrclauses = 10000000
% 0.74/1.54
% 0.74/1.54 showgenerated = 0
% 0.74/1.54 showkept = 0
% 0.74/1.54 showselected = 0
% 0.74/1.54 showdeleted = 0
% 0.74/1.54 showresimp = 1
% 0.74/1.54 showstatus = 2000
% 0.74/1.54
% 0.74/1.54 prologoutput = 1
% 0.74/1.54 nrgoals = 5000000
% 0.74/1.54 totalproof = 1
% 0.74/1.54
% 0.74/1.54 Symbols occurring in the translation:
% 0.74/1.54
% 0.74/1.54 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.74/1.54 . [1, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.74/1.54 ! [4, 1] (w:0, o:33, a:1, s:1, b:0),
% 0.74/1.54 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.54 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.54 subclass [41, 2] (w:1, o:83, a:1, s:1, b:0),
% 0.74/1.54 member [43, 2] (w:1, o:84, a:1, s:1, b:0),
% 0.74/1.54 'not_subclass_element' [44, 2] (w:1, o:85, a:1, s:1, b:0),
% 0.74/1.54 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.74/1.54 'unordered_pair' [46, 2] (w:1, o:86, a:1, s:1, b:0),
% 0.74/1.54 singleton [47, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.74/1.54 'ordered_pair' [48, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.74/1.54 'cross_product' [50, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.74/1.54 first [52, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.74/1.54 second [53, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.74/1.54 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.74/1.54 intersection [55, 2] (w:1, o:90, a:1, s:1, b:0),
% 0.74/1.54 complement [56, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.74/1.54 union [57, 2] (w:1, o:91, a:1, s:1, b:0),
% 0.74/1.54 'symmetric_difference' [58, 2] (w:1, o:92, a:1, s:1, b:0),
% 0.74/1.54 restrict [60, 3] (w:1, o:95, a:1, s:1, b:0),
% 0.74/1.54 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.74/1.54 'domain_of' [62, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.74/1.54 rotate [63, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.74/1.54 flip [65, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.74/1.54 inverse [66, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.74/1.54 'range_of' [67, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.74/1.54 domain [68, 3] (w:1, o:97, a:1, s:1, b:0),
% 0.74/1.54 range [69, 3] (w:1, o:98, a:1, s:1, b:0),
% 0.74/1.54 image [70, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.74/1.54 successor [71, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.74/1.54 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.74/1.54 inductive [73, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.74/1.54 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.74/1.54 'sum_class' [75, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.74/1.54 'power_class' [76, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.74/1.54 compose [78, 2] (w:1, o:93, a:1, s:1, b:0),
% 0.74/1.54 'single_valued_class' [79, 1] (w:1, o:55, a:1, s:1, b:0),
% 0.74/1.54 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.74/1.54 function [82, 1] (w:1, o:56, a:1, s:1, b:0),
% 0.74/1.54 regular [83, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.74/1.54 apply [84, 2] (w:1, o:94, a:1, s:1, b:0),
% 0.74/1.54 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.74/1.54 'one_to_one' [86, 1] (w:1, o:52, a:1, s:1, b:0),
% 0.74/1.54 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 0.74/1.54 diagonalise [88, 1] (w:1, o:57, a:1, s:1, b:0),
% 0.74/1.54 cantor [89, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.74/1.54 operation [90, 1] (w:1, o:53, a:1, s:1, b:0),
% 0.74/1.54 compatible [94, 3] (w:1, o:96, a:1, s:1, b:0),
% 0.74/1.54 homomorphism [95, 3] (w:1, o:99, a:1, s:1, b:0),
% 0.74/1.54 'not_homomorphism1' [96, 3] (w:1, o:100, a:1, s:1, b:0),
% 0.74/1.54 'not_homomorphism2' [97, 3] (w:1, o:101, a:1, s:1, b:0),
% 0.74/1.54 x [98, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.74/1.54 y [99, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.74/1.54 u [100, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.74/1.54 v [101, 0] (w:1, o:32, a:1, s:1, b:0).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 Starting Search:
% 0.74/1.54
% 0.74/1.54 Resimplifying inuse:
% 0.74/1.54 Done
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 Intermediate Status:
% 0.74/1.54 Generated: 4758
% 0.74/1.54 Kept: 2002
% 0.74/1.54 Inuse: 118
% 0.74/1.54 Deleted: 9
% 0.74/1.54 Deletedinuse: 4
% 0.74/1.54
% 0.74/1.54 Resimplifying inuse:
% 0.74/1.54 Done
% 0.74/1.54
% 0.74/1.54 Resimplifying inuse:
% 0.74/1.54 Done
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 Intermediate Status:
% 0.74/1.54 Generated: 10098
% 0.74/1.54 Kept: 4226
% 0.74/1.54 Inuse: 193
% 0.74/1.54 Deleted: 14
% 0.74/1.54 Deletedinuse: 6
% 0.74/1.54
% 0.74/1.54 Resimplifying inuse:
% 0.74/1.54 Done
% 0.74/1.54
% 0.74/1.54 Resimplifying inuse:
% 0.74/1.54 Done
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 Intermediate Status:
% 0.74/1.54 Generated: 14048
% 0.74/1.54 Kept: 6268
% 0.74/1.54 Inuse: 264
% 0.74/1.54 Deleted: 22
% 0.74/1.54 Deletedinuse: 10
% 0.74/1.54
% 0.74/1.54 Resimplifying inuse:
% 0.74/1.54 Done
% 0.74/1.54
% 0.74/1.54 Resimplifying inuse:
% 0.74/1.54 Done
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 Intermediate Status:
% 0.74/1.54 Generated: 19447
% 0.74/1.54 Kept: 8274
% 0.74/1.54 Inuse: 316
% 0.74/1.54 Deleted: 69
% 0.74/1.54 Deletedinuse: 55
% 0.74/1.54
% 0.74/1.54 Resimplifying inuse:
% 0.74/1.54 Done
% 0.74/1.54
% 0.74/1.54 Resimplifying inuse:
% 0.74/1.54 Done
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 Bliksems!, er is een bewijs:
% 0.74/1.54 % SZS status Unsatisfiable
% 0.74/1.54 % SZS output start Refutation
% 0.74/1.54
% 0.74/1.54 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.74/1.54 )
% 0.74/1.54 .
% 0.74/1.54 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 0.74/1.54 .
% 0.74/1.54 clause( 7, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.74/1.54 'unordered_pair'( X, Y ) ) ] )
% 0.74/1.54 .
% 0.74/1.54 clause( 12, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) )
% 0.74/1.54 ), member( X, Z ) ] )
% 0.74/1.54 .
% 0.74/1.54 clause( 90, [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v ) ) ]
% 0.74/1.54 )
% 0.74/1.54 .
% 0.74/1.54 clause( 91, [ ~( member( x, 'unordered_pair'( x, y ) ) ) ] )
% 0.74/1.54 .
% 0.74/1.54 clause( 106, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ] )
% 0.74/1.54 .
% 0.74/1.54 clause( 383, [ ~( member( x, 'universal_class' ) ) ] )
% 0.74/1.54 .
% 0.74/1.54 clause( 394, [ ~( member( x, X ) ) ] )
% 0.74/1.54 .
% 0.74/1.54 clause( 561, [ ~( member( 'ordered_pair'( x, X ), 'cross_product'( Y, Z ) )
% 0.74/1.54 ) ] )
% 0.74/1.54 .
% 0.74/1.54 clause( 9616, [] )
% 0.74/1.54 .
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 % SZS output end Refutation
% 0.74/1.54 found a proof!
% 0.74/1.54
% 0.74/1.54 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.74/1.54
% 0.74/1.54 initialclauses(
% 0.74/1.54 [ clause( 9618, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 0.74/1.54 ) ] )
% 0.74/1.54 , clause( 9619, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 0.74/1.54 , Y ) ] )
% 0.74/1.54 , clause( 9620, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 0.74/1.54 subclass( X, Y ) ] )
% 0.74/1.54 , clause( 9621, [ subclass( X, 'universal_class' ) ] )
% 0.74/1.54 , clause( 9622, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 0.74/1.54 , clause( 9623, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 0.74/1.54 , clause( 9624, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ]
% 0.74/1.54 )
% 0.74/1.54 , clause( 9625, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 0.74/1.54 =( X, Z ) ] )
% 0.74/1.54 , clause( 9626, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.74/1.54 'unordered_pair'( X, Y ) ) ] )
% 0.74/1.54 , clause( 9627, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.74/1.54 'unordered_pair'( Y, X ) ) ] )
% 0.74/1.54 , clause( 9628, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 0.74/1.54 )
% 0.74/1.54 , clause( 9629, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 0.74/1.54 , clause( 9630, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 0.74/1.54 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.74/1.54 , clause( 9631, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.74/1.54 ) ) ), member( X, Z ) ] )
% 0.74/1.54 , clause( 9632, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.74/1.54 ) ) ), member( Y, T ) ] )
% 0.74/1.54 , clause( 9633, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 0.74/1.54 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 0.74/1.54 , clause( 9634, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 0.74/1.54 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 0.74/1.54 , clause( 9635, [ subclass( 'element_relation', 'cross_product'(
% 0.74/1.54 'universal_class', 'universal_class' ) ) ] )
% 0.74/1.54 , clause( 9636, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) )
% 0.74/1.54 , member( X, Y ) ] )
% 0.74/1.54 , clause( 9637, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.74/1.54 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 0.74/1.54 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 0.74/1.54 , clause( 9638, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.74/1.54 )
% 0.74/1.54 , clause( 9639, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 0.74/1.54 )
% 0.74/1.54 , clause( 9640, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 0.74/1.54 intersection( Y, Z ) ) ] )
% 0.74/1.54 , clause( 9641, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 0.74/1.54 )
% 0.74/1.54 , clause( 9642, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.74/1.54 complement( Y ) ), member( X, Y ) ] )
% 0.74/1.54 , clause( 9643, [ =( complement( intersection( complement( X ), complement(
% 0.74/1.54 Y ) ) ), union( X, Y ) ) ] )
% 0.74/1.54 , clause( 9644, [ =( intersection( complement( intersection( X, Y ) ),
% 0.74/1.54 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 0.74/1.54 'symmetric_difference'( X, Y ) ) ] )
% 0.74/1.54 , clause( 9645, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 0.74/1.54 X, Y, Z ) ) ] )
% 0.74/1.54 , clause( 9646, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 0.74/1.54 Z, X, Y ) ) ] )
% 0.74/1.54 , clause( 9647, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 0.74/1.54 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 0.74/1.54 , clause( 9648, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 0.74/1.54 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 0.74/1.54 'domain_of'( Y ) ) ] )
% 0.74/1.54 , clause( 9649, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.74/1.54 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.74/1.54 , clause( 9650, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.74/1.54 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 0.74/1.54 ] )
% 0.74/1.54 , clause( 9651, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.74/1.54 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 0.74/1.54 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.74/1.54 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 0.74/1.54 , Y ), rotate( T ) ) ] )
% 0.74/1.54 , clause( 9652, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.74/1.54 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.74/1.54 , clause( 9653, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.74/1.54 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 0.74/1.54 )
% 0.74/1.54 , clause( 9654, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.74/1.54 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 0.74/1.54 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.74/1.54 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 0.74/1.54 , Z ), flip( T ) ) ] )
% 0.74/1.54 , clause( 9655, [ =( 'domain_of'( flip( 'cross_product'( X,
% 0.74/1.54 'universal_class' ) ) ), inverse( X ) ) ] )
% 0.74/1.54 , clause( 9656, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 0.74/1.54 , clause( 9657, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 0.74/1.54 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 0.74/1.54 , clause( 9658, [ =( second( 'not_subclass_element'( restrict( X, singleton(
% 0.74/1.54 Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 0.74/1.54 , clause( 9659, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 0.74/1.54 image( X, Y ) ) ] )
% 0.74/1.54 , clause( 9660, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 0.74/1.54 , clause( 9661, [ subclass( 'successor_relation', 'cross_product'(
% 0.74/1.54 'universal_class', 'universal_class' ) ) ] )
% 0.74/1.54 , clause( 9662, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' )
% 0.74/1.54 ), =( successor( X ), Y ) ] )
% 0.74/1.54 , clause( 9663, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X
% 0.74/1.54 , Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 0.74/1.54 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 0.74/1.54 , clause( 9664, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 0.74/1.54 , clause( 9665, [ ~( inductive( X ) ), subclass( image(
% 0.74/1.54 'successor_relation', X ), X ) ] )
% 0.74/1.54 , clause( 9666, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.74/1.54 'successor_relation', X ), X ) ), inductive( X ) ] )
% 0.74/1.54 , clause( 9667, [ inductive( omega ) ] )
% 0.74/1.54 , clause( 9668, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 0.74/1.54 , clause( 9669, [ member( omega, 'universal_class' ) ] )
% 0.74/1.54 , clause( 9670, [ =( 'domain_of'( restrict( 'element_relation',
% 0.74/1.54 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 0.74/1.54 , clause( 9671, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 0.74/1.54 X ), 'universal_class' ) ] )
% 0.74/1.54 , clause( 9672, [ =( complement( image( 'element_relation', complement( X )
% 0.74/1.54 ) ), 'power_class'( X ) ) ] )
% 0.74/1.54 , clause( 9673, [ ~( member( X, 'universal_class' ) ), member(
% 0.74/1.54 'power_class'( X ), 'universal_class' ) ] )
% 0.74/1.54 , clause( 9674, [ subclass( compose( X, Y ), 'cross_product'(
% 0.74/1.54 'universal_class', 'universal_class' ) ) ] )
% 0.74/1.54 , clause( 9675, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 0.74/1.54 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 0.74/1.54 , clause( 9676, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 0.74/1.54 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.74/1.54 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.74/1.54 ) ] )
% 0.74/1.54 , clause( 9677, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 0.74/1.54 inverse( X ) ), 'identity_relation' ) ] )
% 0.74/1.54 , clause( 9678, [ ~( subclass( compose( X, inverse( X ) ),
% 0.74/1.54 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 0.74/1.54 , clause( 9679, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 0.74/1.54 'universal_class', 'universal_class' ) ) ] )
% 0.74/1.54 , clause( 9680, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 0.74/1.54 , 'identity_relation' ) ] )
% 0.74/1.54 , clause( 9681, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 0.74/1.54 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 0.74/1.54 'identity_relation' ) ), function( X ) ] )
% 0.74/1.54 , clause( 9682, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ),
% 0.74/1.54 member( image( X, Y ), 'universal_class' ) ] )
% 0.74/1.54 , clause( 9683, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.74/1.54 , clause( 9684, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 0.74/1.54 , 'null_class' ) ] )
% 0.74/1.54 , clause( 9685, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y
% 0.74/1.54 ) ) ] )
% 0.74/1.54 , clause( 9686, [ function( choice ) ] )
% 0.74/1.54 , clause( 9687, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' )
% 0.74/1.54 , member( apply( choice, X ), X ) ] )
% 0.74/1.54 , clause( 9688, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 0.74/1.54 , clause( 9689, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 0.74/1.54 , clause( 9690, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 0.74/1.54 'one_to_one'( X ) ] )
% 0.74/1.54 , clause( 9691, [ =( intersection( 'cross_product'( 'universal_class',
% 0.74/1.54 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 0.74/1.54 'universal_class' ), complement( compose( complement( 'element_relation'
% 0.74/1.54 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 0.74/1.54 , clause( 9692, [ =( intersection( inverse( 'subset_relation' ),
% 0.74/1.54 'subset_relation' ), 'identity_relation' ) ] )
% 0.74/1.54 , clause( 9693, [ =( complement( 'domain_of'( intersection( X,
% 0.74/1.54 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 0.74/1.54 , clause( 9694, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 0.74/1.54 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 0.74/1.54 , clause( 9695, [ ~( operation( X ) ), function( X ) ] )
% 0.74/1.54 , clause( 9696, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 0.74/1.54 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.74/1.54 ] )
% 0.74/1.54 , clause( 9697, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 0.74/1.54 'domain_of'( 'domain_of'( X ) ) ) ] )
% 0.74/1.54 , clause( 9698, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 0.74/1.54 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.74/1.54 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 0.74/1.54 operation( X ) ] )
% 0.74/1.54 , clause( 9699, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 0.74/1.54 , clause( 9700, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 0.74/1.54 Y ) ), 'domain_of'( X ) ) ] )
% 0.74/1.54 , clause( 9701, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 0.74/1.54 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 0.74/1.54 , clause( 9702, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) )
% 0.74/1.54 , 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 0.74/1.54 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 0.74/1.54 , clause( 9703, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 0.74/1.54 , clause( 9704, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 0.74/1.54 , clause( 9705, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 0.74/1.54 , clause( 9706, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 0.74/1.54 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 0.74/1.54 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 0.74/1.54 )
% 0.74/1.54 , clause( 9707, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 0.74/1.54 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.74/1.54 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.74/1.54 , Y ) ] )
% 0.74/1.54 , clause( 9708, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 0.74/1.54 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 0.74/1.54 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 0.74/1.54 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 0.74/1.54 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 0.74/1.54 )
% 0.74/1.54 , clause( 9709, [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v ) )
% 0.74/1.54 ] )
% 0.74/1.54 , clause( 9710, [ ~( member( x, 'unordered_pair'( x, y ) ) ) ] )
% 0.74/1.54 ] ).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 subsumption(
% 0.74/1.54 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.74/1.54 )
% 0.74/1.54 , clause( 9618, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 0.74/1.54 ) ] )
% 0.74/1.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.74/1.54 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 subsumption(
% 0.74/1.54 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 0.74/1.54 , clause( 9621, [ subclass( X, 'universal_class' ) ] )
% 0.74/1.54 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 subsumption(
% 0.74/1.54 clause( 7, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.74/1.54 'unordered_pair'( X, Y ) ) ] )
% 0.74/1.54 , clause( 9626, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.74/1.54 'unordered_pair'( X, Y ) ) ] )
% 0.74/1.54 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.74/1.54 ), ==>( 1, 1 )] ) ).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 subsumption(
% 0.74/1.54 clause( 12, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) )
% 0.74/1.54 ), member( X, Z ) ] )
% 0.74/1.54 , clause( 9631, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.74/1.54 ) ) ), member( X, Z ) ] )
% 0.74/1.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.74/1.54 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 subsumption(
% 0.74/1.54 clause( 90, [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v ) ) ]
% 0.74/1.54 )
% 0.74/1.54 , clause( 9709, [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v ) )
% 0.74/1.54 ] )
% 0.74/1.54 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 subsumption(
% 0.74/1.54 clause( 91, [ ~( member( x, 'unordered_pair'( x, y ) ) ) ] )
% 0.74/1.54 , clause( 9710, [ ~( member( x, 'unordered_pair'( x, y ) ) ) ] )
% 0.74/1.54 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 resolution(
% 0.74/1.54 clause( 9829, [ ~( member( Y, X ) ), member( Y, 'universal_class' ) ] )
% 0.74/1.54 , clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.74/1.54 )
% 0.74/1.54 , 0, clause( 3, [ subclass( X, 'universal_class' ) ] )
% 0.74/1.54 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'universal_class' ), :=( Z, Y )] )
% 0.74/1.54 , substitution( 1, [ :=( X, X )] )).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 subsumption(
% 0.74/1.54 clause( 106, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ] )
% 0.74/1.54 , clause( 9829, [ ~( member( Y, X ) ), member( Y, 'universal_class' ) ] )
% 0.74/1.54 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.74/1.54 ), ==>( 1, 1 )] ) ).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 resolution(
% 0.74/1.54 clause( 9830, [ ~( member( x, 'universal_class' ) ) ] )
% 0.74/1.54 , clause( 91, [ ~( member( x, 'unordered_pair'( x, y ) ) ) ] )
% 0.74/1.54 , 0, clause( 7, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.74/1.54 'unordered_pair'( X, Y ) ) ] )
% 0.74/1.54 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, x ), :=( Y, y )] )
% 0.74/1.54 ).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 subsumption(
% 0.74/1.54 clause( 383, [ ~( member( x, 'universal_class' ) ) ] )
% 0.74/1.54 , clause( 9830, [ ~( member( x, 'universal_class' ) ) ] )
% 0.74/1.54 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 resolution(
% 0.74/1.54 clause( 9831, [ ~( member( x, X ) ) ] )
% 0.74/1.54 , clause( 383, [ ~( member( x, 'universal_class' ) ) ] )
% 0.74/1.54 , 0, clause( 106, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ]
% 0.74/1.54 )
% 0.74/1.54 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, x ), :=( Y, X )] )
% 0.74/1.54 ).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 subsumption(
% 0.74/1.54 clause( 394, [ ~( member( x, X ) ) ] )
% 0.74/1.54 , clause( 9831, [ ~( member( x, X ) ) ] )
% 0.74/1.54 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 resolution(
% 0.74/1.54 clause( 9832, [ ~( member( 'ordered_pair'( x, Y ), 'cross_product'( X, Z )
% 0.74/1.54 ) ) ] )
% 0.74/1.54 , clause( 394, [ ~( member( x, X ) ) ] )
% 0.74/1.54 , 0, clause( 12, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.74/1.54 ) ) ), member( X, Z ) ] )
% 0.74/1.54 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, x ), :=( Y
% 0.74/1.54 , Y ), :=( Z, X ), :=( T, Z )] )).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 subsumption(
% 0.74/1.54 clause( 561, [ ~( member( 'ordered_pair'( x, X ), 'cross_product'( Y, Z ) )
% 0.74/1.54 ) ] )
% 0.74/1.54 , clause( 9832, [ ~( member( 'ordered_pair'( x, Y ), 'cross_product'( X, Z
% 0.74/1.54 ) ) ) ] )
% 0.74/1.54 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 0.74/1.54 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 resolution(
% 0.74/1.54 clause( 9833, [] )
% 0.74/1.54 , clause( 561, [ ~( member( 'ordered_pair'( x, X ), 'cross_product'( Y, Z )
% 0.74/1.54 ) ) ] )
% 0.74/1.54 , 0, clause( 90, [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v )
% 0.74/1.54 ) ] )
% 0.74/1.54 , 0, substitution( 0, [ :=( X, y ), :=( Y, u ), :=( Z, v )] ),
% 0.74/1.54 substitution( 1, [] )).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 subsumption(
% 0.74/1.54 clause( 9616, [] )
% 0.74/1.54 , clause( 9833, [] )
% 0.74/1.54 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 end.
% 0.74/1.54
% 0.74/1.54 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.74/1.54
% 0.74/1.54 Memory use:
% 0.74/1.54
% 0.74/1.54 space for terms: 148435
% 0.74/1.54 space for clauses: 463166
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 clauses generated: 22745
% 0.74/1.54 clauses kept: 9617
% 0.74/1.54 clauses selected: 365
% 0.74/1.54 clauses deleted: 78
% 0.74/1.54 clauses inuse deleted: 62
% 0.74/1.54
% 0.74/1.54 subsentry: 52700
% 0.74/1.54 literals s-matched: 38946
% 0.74/1.54 literals matched: 38309
% 0.74/1.54 full subsumption: 17645
% 0.74/1.54
% 0.74/1.54 checksum: 1541248943
% 0.74/1.54
% 0.74/1.54
% 0.74/1.54 Bliksem ended
%------------------------------------------------------------------------------