TSTP Solution File: SET027-7 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET027-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.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 22:45:47 EDT 2022
% Result : Unsatisfiable 0.87s 1.25s
% Output : Refutation 0.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET027-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.13 % Command : bliksem %s
% 0.13/0.33 % Computer : n006.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 14:41:36 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.73/1.09 *** allocated 10000 integers for termspace/termends
% 0.73/1.09 *** allocated 10000 integers for clauses
% 0.73/1.09 *** allocated 10000 integers for justifications
% 0.73/1.09 Bliksem 1.12
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 Automatic Strategy Selection
% 0.73/1.09
% 0.73/1.09 Clauses:
% 0.73/1.09 [
% 0.73/1.09 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.73/1.09 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.73/1.09 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.73/1.09 ,
% 0.73/1.09 [ subclass( X, 'universal_class' ) ],
% 0.73/1.09 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.73/1.09 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.73/1.09 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.73/1.09 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.73/1.09 ,
% 0.73/1.09 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.73/1.09 ) ) ],
% 0.73/1.09 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.73/1.09 ) ) ],
% 0.73/1.09 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.73/1.09 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.73/1.09 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.73/1.09 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.73/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.73/1.09 X, Z ) ],
% 0.73/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.73/1.09 Y, T ) ],
% 0.73/1.09 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.73/1.09 ), 'cross_product'( Y, T ) ) ],
% 0.73/1.09 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.73/1.09 ), second( X ) ), X ) ],
% 0.73/1.09 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.73/1.09 'universal_class' ) ) ],
% 0.73/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.73/1.09 Y ) ],
% 0.73/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.73/1.09 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.73/1.09 , Y ), 'element_relation' ) ],
% 0.73/1.09 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.73/1.09 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.73/1.09 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.73/1.09 Z ) ) ],
% 0.73/1.09 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.73/1.09 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.73/1.09 member( X, Y ) ],
% 0.73/1.09 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.73/1.09 union( X, Y ) ) ],
% 0.73/1.09 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.73/1.09 intersection( complement( X ), complement( Y ) ) ) ),
% 0.73/1.09 'symmetric_difference'( X, Y ) ) ],
% 0.73/1.09 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.73/1.09 ,
% 0.73/1.09 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.73/1.09 ,
% 0.73/1.09 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.73/1.09 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.73/1.09 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.73/1.09 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.73/1.09 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.73/1.09 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.73/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.73/1.09 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.73/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.73/1.09 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.73/1.09 'cross_product'( 'universal_class', 'universal_class' ),
% 0.73/1.09 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.73/1.09 Y ), rotate( T ) ) ],
% 0.73/1.09 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.73/1.09 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.73/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.73/1.09 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.73/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.73/1.09 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.73/1.09 'cross_product'( 'universal_class', 'universal_class' ),
% 0.73/1.09 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.73/1.09 Z ), flip( T ) ) ],
% 0.73/1.09 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.73/1.09 inverse( X ) ) ],
% 0.73/1.09 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.73/1.09 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.73/1.09 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.73/1.09 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.73/1.09 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.73/1.09 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.73/1.09 ],
% 0.73/1.09 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.73/1.09 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.73/1.09 'universal_class' ) ) ],
% 0.73/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.73/1.09 successor( X ), Y ) ],
% 0.73/1.09 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.73/1.09 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.73/1.09 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.73/1.09 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.73/1.09 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.73/1.09 ,
% 0.73/1.09 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.73/1.09 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.73/1.09 [ inductive( omega ) ],
% 0.73/1.09 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.73/1.09 [ member( omega, 'universal_class' ) ],
% 0.73/1.09 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.73/1.09 , 'sum_class'( X ) ) ],
% 0.73/1.09 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.73/1.09 'universal_class' ) ],
% 0.73/1.09 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.73/1.09 'power_class'( X ) ) ],
% 0.73/1.09 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.73/1.09 'universal_class' ) ],
% 0.73/1.09 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.73/1.09 'universal_class' ) ) ],
% 0.73/1.09 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.73/1.09 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.73/1.09 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.73/1.09 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.73/1.09 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.73/1.09 ) ],
% 0.73/1.09 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.73/1.09 , 'identity_relation' ) ],
% 0.73/1.09 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.73/1.09 'single_valued_class'( X ) ],
% 0.73/1.09 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.73/1.09 'universal_class' ) ) ],
% 0.73/1.09 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.73/1.09 'identity_relation' ) ],
% 0.73/1.09 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.73/1.09 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.73/1.09 , function( X ) ],
% 0.73/1.09 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.73/1.09 X, Y ), 'universal_class' ) ],
% 0.73/1.09 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.73/1.09 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.73/1.09 ) ],
% 0.73/1.09 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.73/1.09 [ function( choice ) ],
% 0.73/1.09 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.73/1.09 apply( choice, X ), X ) ],
% 0.73/1.09 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.73/1.09 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.73/1.09 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.73/1.09 ,
% 0.73/1.09 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.73/1.09 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.73/1.09 , complement( compose( complement( 'element_relation' ), inverse(
% 0.73/1.09 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.73/1.09 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.73/1.09 'identity_relation' ) ],
% 0.73/1.09 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.73/1.09 , diagonalise( X ) ) ],
% 0.73/1.09 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.73/1.09 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.73/1.09 [ ~( operation( X ) ), function( X ) ],
% 0.73/1.09 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.73/1.09 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.73/1.09 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.87/1.25 'domain_of'( X ) ) ) ],
% 0.87/1.25 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.87/1.25 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.87/1.25 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.87/1.25 X ) ],
% 0.87/1.25 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.87/1.25 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.87/1.25 'domain_of'( X ) ) ],
% 0.87/1.25 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.87/1.25 'domain_of'( Z ) ) ) ],
% 0.87/1.25 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.87/1.25 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.87/1.25 ), compatible( X, Y, Z ) ],
% 0.87/1.25 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.87/1.25 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.87/1.25 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.87/1.25 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.87/1.25 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.87/1.25 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.87/1.25 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.87/1.25 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.87/1.25 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.87/1.25 , Y ) ],
% 0.87/1.25 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.87/1.25 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.87/1.25 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.87/1.25 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.87/1.25 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.87/1.25 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.87/1.25 X, 'unordered_pair'( X, Y ) ) ],
% 0.87/1.25 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.87/1.25 Y, 'unordered_pair'( X, Y ) ) ],
% 0.87/1.25 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.87/1.25 X, 'universal_class' ) ],
% 0.87/1.25 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.87/1.25 Y, 'universal_class' ) ],
% 0.87/1.25 [ subclass( X, X ) ],
% 0.87/1.25 [ subclass( x, y ) ],
% 0.87/1.25 [ subclass( y, z ) ],
% 0.87/1.25 [ ~( subclass( x, z ) ) ]
% 0.87/1.25 ] .
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 percentage equality = 0.202073, percentage horn = 0.919192
% 0.87/1.25 This is a problem with some equality
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 Options Used:
% 0.87/1.25
% 0.87/1.25 useres = 1
% 0.87/1.25 useparamod = 1
% 0.87/1.25 useeqrefl = 1
% 0.87/1.25 useeqfact = 1
% 0.87/1.25 usefactor = 1
% 0.87/1.25 usesimpsplitting = 0
% 0.87/1.25 usesimpdemod = 5
% 0.87/1.25 usesimpres = 3
% 0.87/1.25
% 0.87/1.25 resimpinuse = 1000
% 0.87/1.25 resimpclauses = 20000
% 0.87/1.25 substype = eqrewr
% 0.87/1.25 backwardsubs = 1
% 0.87/1.25 selectoldest = 5
% 0.87/1.25
% 0.87/1.25 litorderings [0] = split
% 0.87/1.25 litorderings [1] = extend the termordering, first sorting on arguments
% 0.87/1.25
% 0.87/1.25 termordering = kbo
% 0.87/1.25
% 0.87/1.25 litapriori = 0
% 0.87/1.25 termapriori = 1
% 0.87/1.25 litaposteriori = 0
% 0.87/1.25 termaposteriori = 0
% 0.87/1.25 demodaposteriori = 0
% 0.87/1.25 ordereqreflfact = 0
% 0.87/1.25
% 0.87/1.25 litselect = negord
% 0.87/1.25
% 0.87/1.25 maxweight = 15
% 0.87/1.25 maxdepth = 30000
% 0.87/1.25 maxlength = 115
% 0.87/1.25 maxnrvars = 195
% 0.87/1.25 excuselevel = 1
% 0.87/1.25 increasemaxweight = 1
% 0.87/1.25
% 0.87/1.25 maxselected = 10000000
% 0.87/1.25 maxnrclauses = 10000000
% 0.87/1.25
% 0.87/1.25 showgenerated = 0
% 0.87/1.25 showkept = 0
% 0.87/1.25 showselected = 0
% 0.87/1.25 showdeleted = 0
% 0.87/1.25 showresimp = 1
% 0.87/1.25 showstatus = 2000
% 0.87/1.25
% 0.87/1.25 prologoutput = 1
% 0.87/1.25 nrgoals = 5000000
% 0.87/1.25 totalproof = 1
% 0.87/1.25
% 0.87/1.25 Symbols occurring in the translation:
% 0.87/1.25
% 0.87/1.25 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.87/1.25 . [1, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.87/1.25 ! [4, 1] (w:0, o:32, a:1, s:1, b:0),
% 0.87/1.25 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.87/1.25 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.87/1.25 subclass [41, 2] (w:1, o:82, a:1, s:1, b:0),
% 0.87/1.25 member [43, 2] (w:1, o:83, a:1, s:1, b:0),
% 0.87/1.25 'not_subclass_element' [44, 2] (w:1, o:84, a:1, s:1, b:0),
% 0.87/1.25 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.87/1.25 'unordered_pair' [46, 2] (w:1, o:85, a:1, s:1, b:0),
% 0.87/1.25 singleton [47, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.87/1.25 'ordered_pair' [48, 2] (w:1, o:86, a:1, s:1, b:0),
% 0.87/1.25 'cross_product' [50, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.87/1.25 first [52, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.87/1.25 second [53, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.87/1.25 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.87/1.25 intersection [55, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.87/1.25 complement [56, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.87/1.25 union [57, 2] (w:1, o:90, a:1, s:1, b:0),
% 0.87/1.25 'symmetric_difference' [58, 2] (w:1, o:91, a:1, s:1, b:0),
% 0.87/1.25 restrict [60, 3] (w:1, o:94, a:1, s:1, b:0),
% 0.87/1.25 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.87/1.25 'domain_of' [62, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.87/1.25 rotate [63, 1] (w:1, o:37, a:1, s:1, b:0),
% 0.87/1.25 flip [65, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.87/1.25 inverse [66, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.87/1.25 'range_of' [67, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.87/1.25 domain [68, 3] (w:1, o:96, a:1, s:1, b:0),
% 0.87/1.25 range [69, 3] (w:1, o:97, a:1, s:1, b:0),
% 0.87/1.25 image [70, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.87/1.25 successor [71, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.87/1.25 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.87/1.25 inductive [73, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.87/1.25 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.87/1.25 'sum_class' [75, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.87/1.25 'power_class' [76, 1] (w:1, o:53, a:1, s:1, b:0),
% 0.87/1.25 compose [78, 2] (w:1, o:92, a:1, s:1, b:0),
% 0.87/1.25 'single_valued_class' [79, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.87/1.25 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.87/1.25 function [82, 1] (w:1, o:55, a:1, s:1, b:0),
% 0.87/1.25 regular [83, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.87/1.25 apply [84, 2] (w:1, o:93, a:1, s:1, b:0),
% 0.87/1.25 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.87/1.25 'one_to_one' [86, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.87/1.25 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 0.87/1.25 diagonalise [88, 1] (w:1, o:56, a:1, s:1, b:0),
% 0.87/1.25 cantor [89, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.87/1.25 operation [90, 1] (w:1, o:52, a:1, s:1, b:0),
% 0.87/1.25 compatible [94, 3] (w:1, o:95, a:1, s:1, b:0),
% 0.87/1.25 homomorphism [95, 3] (w:1, o:98, a:1, s:1, b:0),
% 0.87/1.25 'not_homomorphism1' [96, 3] (w:1, o:99, a:1, s:1, b:0),
% 0.87/1.25 'not_homomorphism2' [97, 3] (w:1, o:100, a:1, s:1, b:0),
% 0.87/1.25 x [98, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.87/1.25 y [99, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.87/1.25 z [100, 0] (w:1, o:31, a:1, s:1, b:0).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 Starting Search:
% 0.87/1.25
% 0.87/1.25 Resimplifying inuse:
% 0.87/1.25 Done
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 Intermediate Status:
% 0.87/1.25 Generated: 4444
% 0.87/1.25 Kept: 2003
% 0.87/1.25 Inuse: 119
% 0.87/1.25 Deleted: 4
% 0.87/1.25 Deletedinuse: 2
% 0.87/1.25
% 0.87/1.25 Resimplifying inuse:
% 0.87/1.25 Done
% 0.87/1.25
% 0.87/1.25 Resimplifying inuse:
% 0.87/1.25 Done
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 Bliksems!, er is een bewijs:
% 0.87/1.25 % SZS status Unsatisfiable
% 0.87/1.25 % SZS output start Refutation
% 0.87/1.25
% 0.87/1.25 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.87/1.25 )
% 0.87/1.25 .
% 0.87/1.25 clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y )
% 0.87/1.25 ] )
% 0.87/1.25 .
% 0.87/1.25 clause( 2, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X
% 0.87/1.25 , Y ) ] )
% 0.87/1.25 .
% 0.87/1.25 clause( 95, [ subclass( x, y ) ] )
% 0.87/1.25 .
% 0.87/1.25 clause( 96, [ subclass( y, z ) ] )
% 0.87/1.25 .
% 0.87/1.25 clause( 97, [ ~( subclass( x, z ) ) ] )
% 0.87/1.25 .
% 0.87/1.25 clause( 111, [ ~( member( X, y ) ), member( X, z ) ] )
% 0.87/1.25 .
% 0.87/1.25 clause( 112, [ ~( member( X, x ) ), member( X, y ) ] )
% 0.87/1.25 .
% 0.87/1.25 clause( 116, [ member( 'not_subclass_element'( x, z ), x ) ] )
% 0.87/1.25 .
% 0.87/1.25 clause( 123, [ ~( member( 'not_subclass_element'( x, z ), z ) ) ] )
% 0.87/1.25 .
% 0.87/1.25 clause( 3541, [ member( 'not_subclass_element'( x, z ), y ) ] )
% 0.87/1.25 .
% 0.87/1.25 clause( 3682, [] )
% 0.87/1.25 .
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 % SZS output end Refutation
% 0.87/1.25 found a proof!
% 0.87/1.25
% 0.87/1.25 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.87/1.25
% 0.87/1.25 initialclauses(
% 0.87/1.25 [ clause( 3684, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 0.87/1.25 ) ] )
% 0.87/1.25 , clause( 3685, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 0.87/1.25 , Y ) ] )
% 0.87/1.25 , clause( 3686, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 0.87/1.25 subclass( X, Y ) ] )
% 0.87/1.25 , clause( 3687, [ subclass( X, 'universal_class' ) ] )
% 0.87/1.25 , clause( 3688, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 0.87/1.25 , clause( 3689, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 0.87/1.25 , clause( 3690, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 3691, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 0.87/1.25 =( X, Z ) ] )
% 0.87/1.25 , clause( 3692, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.87/1.25 'unordered_pair'( X, Y ) ) ] )
% 0.87/1.25 , clause( 3693, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.87/1.25 'unordered_pair'( Y, X ) ) ] )
% 0.87/1.25 , clause( 3694, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 3695, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 0.87/1.25 , clause( 3696, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 0.87/1.25 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.87/1.25 , clause( 3697, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.87/1.25 ) ) ), member( X, Z ) ] )
% 0.87/1.25 , clause( 3698, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.87/1.25 ) ) ), member( Y, T ) ] )
% 0.87/1.25 , clause( 3699, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 0.87/1.25 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 0.87/1.25 , clause( 3700, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 0.87/1.25 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 0.87/1.25 , clause( 3701, [ subclass( 'element_relation', 'cross_product'(
% 0.87/1.25 'universal_class', 'universal_class' ) ) ] )
% 0.87/1.25 , clause( 3702, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) )
% 0.87/1.25 , member( X, Y ) ] )
% 0.87/1.25 , clause( 3703, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.87/1.25 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 0.87/1.25 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 0.87/1.25 , clause( 3704, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 3705, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 3706, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 0.87/1.25 intersection( Y, Z ) ) ] )
% 0.87/1.25 , clause( 3707, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 3708, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.87/1.25 complement( Y ) ), member( X, Y ) ] )
% 0.87/1.25 , clause( 3709, [ =( complement( intersection( complement( X ), complement(
% 0.87/1.25 Y ) ) ), union( X, Y ) ) ] )
% 0.87/1.25 , clause( 3710, [ =( intersection( complement( intersection( X, Y ) ),
% 0.87/1.25 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 0.87/1.25 'symmetric_difference'( X, Y ) ) ] )
% 0.87/1.25 , clause( 3711, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 0.87/1.25 X, Y, Z ) ) ] )
% 0.87/1.25 , clause( 3712, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 0.87/1.25 Z, X, Y ) ) ] )
% 0.87/1.25 , clause( 3713, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 0.87/1.25 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 0.87/1.25 , clause( 3714, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 0.87/1.25 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 0.87/1.25 'domain_of'( Y ) ) ] )
% 0.87/1.25 , clause( 3715, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.87/1.25 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.87/1.25 , clause( 3716, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.87/1.25 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 3717, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.87/1.25 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 0.87/1.25 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.87/1.25 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 0.87/1.25 , Y ), rotate( T ) ) ] )
% 0.87/1.25 , clause( 3718, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.87/1.25 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.87/1.25 , clause( 3719, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.87/1.25 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 3720, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.87/1.25 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 0.87/1.25 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.87/1.25 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 0.87/1.25 , Z ), flip( T ) ) ] )
% 0.87/1.25 , clause( 3721, [ =( 'domain_of'( flip( 'cross_product'( X,
% 0.87/1.25 'universal_class' ) ) ), inverse( X ) ) ] )
% 0.87/1.25 , clause( 3722, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 0.87/1.25 , clause( 3723, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 0.87/1.25 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 0.87/1.25 , clause( 3724, [ =( second( 'not_subclass_element'( restrict( X, singleton(
% 0.87/1.25 Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 0.87/1.25 , clause( 3725, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 0.87/1.25 image( X, Y ) ) ] )
% 0.87/1.25 , clause( 3726, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 0.87/1.25 , clause( 3727, [ subclass( 'successor_relation', 'cross_product'(
% 0.87/1.25 'universal_class', 'universal_class' ) ) ] )
% 0.87/1.25 , clause( 3728, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' )
% 0.87/1.25 ), =( successor( X ), Y ) ] )
% 0.87/1.25 , clause( 3729, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X
% 0.87/1.25 , Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 0.87/1.25 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 0.87/1.25 , clause( 3730, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 0.87/1.25 , clause( 3731, [ ~( inductive( X ) ), subclass( image(
% 0.87/1.25 'successor_relation', X ), X ) ] )
% 0.87/1.25 , clause( 3732, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.87/1.25 'successor_relation', X ), X ) ), inductive( X ) ] )
% 0.87/1.25 , clause( 3733, [ inductive( omega ) ] )
% 0.87/1.25 , clause( 3734, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 0.87/1.25 , clause( 3735, [ member( omega, 'universal_class' ) ] )
% 0.87/1.25 , clause( 3736, [ =( 'domain_of'( restrict( 'element_relation',
% 0.87/1.25 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 0.87/1.25 , clause( 3737, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 0.87/1.25 X ), 'universal_class' ) ] )
% 0.87/1.25 , clause( 3738, [ =( complement( image( 'element_relation', complement( X )
% 0.87/1.25 ) ), 'power_class'( X ) ) ] )
% 0.87/1.25 , clause( 3739, [ ~( member( X, 'universal_class' ) ), member(
% 0.87/1.25 'power_class'( X ), 'universal_class' ) ] )
% 0.87/1.25 , clause( 3740, [ subclass( compose( X, Y ), 'cross_product'(
% 0.87/1.25 'universal_class', 'universal_class' ) ) ] )
% 0.87/1.25 , clause( 3741, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 0.87/1.25 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 0.87/1.25 , clause( 3742, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 0.87/1.25 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.87/1.25 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.87/1.25 ) ] )
% 0.87/1.25 , clause( 3743, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 0.87/1.25 inverse( X ) ), 'identity_relation' ) ] )
% 0.87/1.25 , clause( 3744, [ ~( subclass( compose( X, inverse( X ) ),
% 0.87/1.25 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 0.87/1.25 , clause( 3745, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 0.87/1.25 'universal_class', 'universal_class' ) ) ] )
% 0.87/1.25 , clause( 3746, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 0.87/1.25 , 'identity_relation' ) ] )
% 0.87/1.25 , clause( 3747, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 0.87/1.25 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 0.87/1.25 'identity_relation' ) ), function( X ) ] )
% 0.87/1.25 , clause( 3748, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ),
% 0.87/1.25 member( image( X, Y ), 'universal_class' ) ] )
% 0.87/1.25 , clause( 3749, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.87/1.25 , clause( 3750, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 0.87/1.25 , 'null_class' ) ] )
% 0.87/1.25 , clause( 3751, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y
% 0.87/1.25 ) ) ] )
% 0.87/1.25 , clause( 3752, [ function( choice ) ] )
% 0.87/1.25 , clause( 3753, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' )
% 0.87/1.25 , member( apply( choice, X ), X ) ] )
% 0.87/1.25 , clause( 3754, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 0.87/1.25 , clause( 3755, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 0.87/1.25 , clause( 3756, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 0.87/1.25 'one_to_one'( X ) ] )
% 0.87/1.25 , clause( 3757, [ =( intersection( 'cross_product'( 'universal_class',
% 0.87/1.25 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 0.87/1.25 'universal_class' ), complement( compose( complement( 'element_relation'
% 0.87/1.25 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 0.87/1.25 , clause( 3758, [ =( intersection( inverse( 'subset_relation' ),
% 0.87/1.25 'subset_relation' ), 'identity_relation' ) ] )
% 0.87/1.25 , clause( 3759, [ =( complement( 'domain_of'( intersection( X,
% 0.87/1.25 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 0.87/1.25 , clause( 3760, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 0.87/1.25 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 0.87/1.25 , clause( 3761, [ ~( operation( X ) ), function( X ) ] )
% 0.87/1.25 , clause( 3762, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 0.87/1.25 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 3763, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 0.87/1.25 'domain_of'( 'domain_of'( X ) ) ) ] )
% 0.87/1.25 , clause( 3764, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 0.87/1.25 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.87/1.25 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 0.87/1.25 operation( X ) ] )
% 0.87/1.25 , clause( 3765, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 0.87/1.25 , clause( 3766, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 0.87/1.25 Y ) ), 'domain_of'( X ) ) ] )
% 0.87/1.25 , clause( 3767, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 0.87/1.25 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 0.87/1.25 , clause( 3768, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) )
% 0.87/1.25 , 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 0.87/1.25 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 0.87/1.25 , clause( 3769, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 0.87/1.25 , clause( 3770, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 0.87/1.25 , clause( 3771, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 0.87/1.25 , clause( 3772, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 0.87/1.25 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 0.87/1.25 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 3773, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 0.87/1.25 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.87/1.25 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.87/1.25 , Y ) ] )
% 0.87/1.25 , clause( 3774, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 0.87/1.25 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 0.87/1.25 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 0.87/1.25 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 0.87/1.25 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 3775, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.87/1.25 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 0.87/1.25 , clause( 3776, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.87/1.25 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 0.87/1.25 , clause( 3777, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.87/1.25 ) ) ), member( X, 'universal_class' ) ] )
% 0.87/1.25 , clause( 3778, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.87/1.25 ) ) ), member( Y, 'universal_class' ) ] )
% 0.87/1.25 , clause( 3779, [ subclass( X, X ) ] )
% 0.87/1.25 , clause( 3780, [ subclass( x, y ) ] )
% 0.87/1.25 , clause( 3781, [ subclass( y, z ) ] )
% 0.87/1.25 , clause( 3782, [ ~( subclass( x, z ) ) ] )
% 0.87/1.25 ] ).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 subsumption(
% 0.87/1.25 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.87/1.25 )
% 0.87/1.25 , clause( 3684, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 0.87/1.25 ) ] )
% 0.87/1.25 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.87/1.25 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 subsumption(
% 0.87/1.25 clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y )
% 0.87/1.25 ] )
% 0.87/1.25 , clause( 3685, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 0.87/1.25 , Y ) ] )
% 0.87/1.25 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.87/1.25 ), ==>( 1, 1 )] ) ).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 subsumption(
% 0.87/1.25 clause( 2, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X
% 0.87/1.25 , Y ) ] )
% 0.87/1.25 , clause( 3686, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 0.87/1.25 subclass( X, Y ) ] )
% 0.87/1.25 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.87/1.25 ), ==>( 1, 1 )] ) ).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 subsumption(
% 0.87/1.25 clause( 95, [ subclass( x, y ) ] )
% 0.87/1.25 , clause( 3780, [ subclass( x, y ) ] )
% 0.87/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 subsumption(
% 0.87/1.25 clause( 96, [ subclass( y, z ) ] )
% 0.87/1.25 , clause( 3781, [ subclass( y, z ) ] )
% 0.87/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 subsumption(
% 0.87/1.25 clause( 97, [ ~( subclass( x, z ) ) ] )
% 0.87/1.25 , clause( 3782, [ ~( subclass( x, z ) ) ] )
% 0.87/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 resolution(
% 0.87/1.25 clause( 3933, [ ~( member( X, y ) ), member( X, z ) ] )
% 0.87/1.25 , clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.87/1.25 )
% 0.87/1.25 , 0, clause( 96, [ subclass( y, z ) ] )
% 0.87/1.25 , 0, substitution( 0, [ :=( X, y ), :=( Y, z ), :=( Z, X )] ),
% 0.87/1.25 substitution( 1, [] )).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 subsumption(
% 0.87/1.25 clause( 111, [ ~( member( X, y ) ), member( X, z ) ] )
% 0.87/1.25 , clause( 3933, [ ~( member( X, y ) ), member( X, z ) ] )
% 0.87/1.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.87/1.25 1 )] ) ).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 resolution(
% 0.87/1.25 clause( 3934, [ ~( member( X, x ) ), member( X, y ) ] )
% 0.87/1.25 , clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.87/1.25 )
% 0.87/1.25 , 0, clause( 95, [ subclass( x, y ) ] )
% 0.87/1.25 , 0, substitution( 0, [ :=( X, x ), :=( Y, y ), :=( Z, X )] ),
% 0.87/1.25 substitution( 1, [] )).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 subsumption(
% 0.87/1.25 clause( 112, [ ~( member( X, x ) ), member( X, y ) ] )
% 0.87/1.25 , clause( 3934, [ ~( member( X, x ) ), member( X, y ) ] )
% 0.87/1.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.87/1.25 1 )] ) ).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 resolution(
% 0.87/1.25 clause( 3935, [ member( 'not_subclass_element'( x, z ), x ) ] )
% 0.87/1.25 , clause( 97, [ ~( subclass( x, z ) ) ] )
% 0.87/1.25 , 0, clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 0.87/1.25 , Y ) ] )
% 0.87/1.25 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, x ), :=( Y, z )] )
% 0.87/1.25 ).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 subsumption(
% 0.87/1.25 clause( 116, [ member( 'not_subclass_element'( x, z ), x ) ] )
% 0.87/1.25 , clause( 3935, [ member( 'not_subclass_element'( x, z ), x ) ] )
% 0.87/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 resolution(
% 0.87/1.25 clause( 3936, [ ~( member( 'not_subclass_element'( x, z ), z ) ) ] )
% 0.87/1.25 , clause( 97, [ ~( subclass( x, z ) ) ] )
% 0.87/1.25 , 0, clause( 2, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 0.87/1.25 subclass( X, Y ) ] )
% 0.87/1.25 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, x ), :=( Y, z )] )
% 0.87/1.25 ).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 subsumption(
% 0.87/1.25 clause( 123, [ ~( member( 'not_subclass_element'( x, z ), z ) ) ] )
% 0.87/1.25 , clause( 3936, [ ~( member( 'not_subclass_element'( x, z ), z ) ) ] )
% 0.87/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 resolution(
% 0.87/1.25 clause( 3937, [ member( 'not_subclass_element'( x, z ), y ) ] )
% 0.87/1.25 , clause( 112, [ ~( member( X, x ) ), member( X, y ) ] )
% 0.87/1.25 , 0, clause( 116, [ member( 'not_subclass_element'( x, z ), x ) ] )
% 0.87/1.25 , 0, substitution( 0, [ :=( X, 'not_subclass_element'( x, z ) )] ),
% 0.87/1.25 substitution( 1, [] )).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 subsumption(
% 0.87/1.25 clause( 3541, [ member( 'not_subclass_element'( x, z ), y ) ] )
% 0.87/1.25 , clause( 3937, [ member( 'not_subclass_element'( x, z ), y ) ] )
% 0.87/1.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 resolution(
% 0.87/1.25 clause( 3938, [ member( 'not_subclass_element'( x, z ), z ) ] )
% 0.87/1.25 , clause( 111, [ ~( member( X, y ) ), member( X, z ) ] )
% 0.87/1.25 , 0, clause( 3541, [ member( 'not_subclass_element'( x, z ), y ) ] )
% 0.87/1.25 , 0, substitution( 0, [ :=( X, 'not_subclass_element'( x, z ) )] ),
% 0.87/1.25 substitution( 1, [] )).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 resolution(
% 0.87/1.25 clause( 3939, [] )
% 0.87/1.25 , clause( 123, [ ~( member( 'not_subclass_element'( x, z ), z ) ) ] )
% 0.87/1.25 , 0, clause( 3938, [ member( 'not_subclass_element'( x, z ), z ) ] )
% 0.87/1.25 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 subsumption(
% 0.87/1.25 clause( 3682, [] )
% 0.87/1.25 , clause( 3939, [] )
% 0.87/1.25 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 end.
% 0.87/1.25
% 0.87/1.25 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.87/1.25
% 0.87/1.25 Memory use:
% 0.87/1.25
% 0.87/1.25 space for terms: 57086
% 0.87/1.25 space for clauses: 174759
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 clauses generated: 8891
% 0.87/1.25 clauses kept: 3683
% 0.87/1.25 clauses selected: 194
% 0.87/1.25 clauses deleted: 8
% 0.87/1.25 clauses inuse deleted: 4
% 0.87/1.25
% 0.87/1.25 subsentry: 21647
% 0.87/1.25 literals s-matched: 17254
% 0.87/1.25 literals matched: 17030
% 0.87/1.25 full subsumption: 9281
% 0.87/1.25
% 0.87/1.25 checksum: 1407038403
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 Bliksem ended
%------------------------------------------------------------------------------