TSTP Solution File: SET060-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET060-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 22:46:17 EDT 2022
% Result : Unsatisfiable 1.44s 1.79s
% Output : Refutation 1.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET060-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sun Jul 10 01:57:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.75/1.13 *** allocated 10000 integers for termspace/termends
% 0.75/1.13 *** allocated 10000 integers for clauses
% 0.75/1.13 *** allocated 10000 integers for justifications
% 0.75/1.13 Bliksem 1.12
% 0.75/1.13
% 0.75/1.13
% 0.75/1.13 Automatic Strategy Selection
% 0.75/1.13
% 0.75/1.13 Clauses:
% 0.75/1.13 [
% 0.75/1.13 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.75/1.13 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.75/1.13 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.75/1.13 ,
% 0.75/1.13 [ subclass( X, 'universal_class' ) ],
% 0.75/1.13 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.75/1.13 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.75/1.13 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.75/1.13 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.75/1.13 ,
% 0.75/1.13 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.75/1.13 ) ) ],
% 0.75/1.13 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.75/1.13 ) ) ],
% 0.75/1.13 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.75/1.13 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.75/1.13 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.75/1.13 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.75/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.75/1.13 X, Z ) ],
% 0.75/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.75/1.13 Y, T ) ],
% 0.75/1.13 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.75/1.13 ), 'cross_product'( Y, T ) ) ],
% 0.75/1.13 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.75/1.13 ), second( X ) ), X ) ],
% 0.75/1.13 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.75/1.13 'universal_class' ) ) ],
% 0.75/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.75/1.13 Y ) ],
% 0.75/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.75/1.13 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.75/1.13 , Y ), 'element_relation' ) ],
% 0.75/1.13 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.75/1.13 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.75/1.13 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.75/1.13 Z ) ) ],
% 0.75/1.13 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.75/1.13 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.75/1.13 member( X, Y ) ],
% 0.75/1.13 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.75/1.13 union( X, Y ) ) ],
% 0.75/1.13 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.75/1.13 intersection( complement( X ), complement( Y ) ) ) ),
% 0.75/1.13 'symmetric_difference'( X, Y ) ) ],
% 0.75/1.13 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.75/1.13 ,
% 0.75/1.13 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.75/1.13 ,
% 0.75/1.13 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.75/1.13 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.75/1.13 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.75/1.13 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.75/1.13 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.75/1.13 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.75/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.75/1.13 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.75/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.75/1.13 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.75/1.13 'cross_product'( 'universal_class', 'universal_class' ),
% 0.75/1.13 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.75/1.13 Y ), rotate( T ) ) ],
% 0.75/1.13 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.75/1.13 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.75/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.75/1.13 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.75/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.75/1.13 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.75/1.13 'cross_product'( 'universal_class', 'universal_class' ),
% 0.75/1.13 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.75/1.13 Z ), flip( T ) ) ],
% 0.75/1.13 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.75/1.13 inverse( X ) ) ],
% 0.75/1.13 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.75/1.13 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.75/1.13 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.75/1.13 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.75/1.13 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.75/1.13 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.75/1.13 ],
% 0.75/1.13 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.75/1.13 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.75/1.13 'universal_class' ) ) ],
% 0.75/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.75/1.13 successor( X ), Y ) ],
% 0.75/1.13 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.75/1.13 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.75/1.13 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.75/1.13 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.75/1.13 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.75/1.13 ,
% 0.75/1.13 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.75/1.13 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.75/1.13 [ inductive( omega ) ],
% 0.75/1.13 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.75/1.13 [ member( omega, 'universal_class' ) ],
% 0.75/1.13 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.75/1.13 , 'sum_class'( X ) ) ],
% 0.75/1.13 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.75/1.13 'universal_class' ) ],
% 0.75/1.13 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.75/1.13 'power_class'( X ) ) ],
% 0.75/1.13 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.75/1.13 'universal_class' ) ],
% 0.75/1.13 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.75/1.13 'universal_class' ) ) ],
% 0.75/1.13 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.75/1.13 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.75/1.13 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.75/1.13 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.75/1.13 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.75/1.13 ) ],
% 0.75/1.13 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.75/1.13 , 'identity_relation' ) ],
% 0.75/1.13 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.75/1.13 'single_valued_class'( X ) ],
% 0.75/1.13 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.75/1.13 'universal_class' ) ) ],
% 0.75/1.13 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.75/1.13 'identity_relation' ) ],
% 0.75/1.13 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.75/1.13 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.75/1.13 , function( X ) ],
% 0.75/1.13 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.75/1.13 X, Y ), 'universal_class' ) ],
% 0.75/1.13 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.75/1.13 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.75/1.13 ) ],
% 0.75/1.13 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.75/1.13 [ function( choice ) ],
% 0.75/1.13 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.75/1.13 apply( choice, X ), X ) ],
% 0.75/1.13 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.75/1.13 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.75/1.13 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.75/1.13 ,
% 0.75/1.13 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.75/1.13 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.75/1.13 , complement( compose( complement( 'element_relation' ), inverse(
% 0.75/1.13 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.75/1.13 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.75/1.13 'identity_relation' ) ],
% 0.75/1.13 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.75/1.13 , diagonalise( X ) ) ],
% 0.75/1.13 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.75/1.13 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.75/1.13 [ ~( operation( X ) ), function( X ) ],
% 0.75/1.13 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.75/1.13 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.75/1.13 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 1.44/1.79 'domain_of'( X ) ) ) ],
% 1.44/1.79 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 1.44/1.79 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 1.44/1.79 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 1.44/1.79 X ) ],
% 1.44/1.79 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 1.44/1.79 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 1.44/1.79 'domain_of'( X ) ) ],
% 1.44/1.79 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 1.44/1.79 'domain_of'( Z ) ) ) ],
% 1.44/1.79 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 1.44/1.79 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 1.44/1.79 ), compatible( X, Y, Z ) ],
% 1.44/1.79 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 1.44/1.79 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 1.44/1.79 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 1.44/1.79 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 1.44/1.79 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 1.44/1.79 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 1.44/1.79 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 1.44/1.79 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.44/1.79 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.44/1.79 , Y ) ],
% 1.44/1.79 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 1.44/1.79 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 1.44/1.79 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 1.44/1.79 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 1.44/1.79 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 1.44/1.79 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 1.44/1.79 X, 'unordered_pair'( X, Y ) ) ],
% 1.44/1.79 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 1.44/1.79 Y, 'unordered_pair'( X, Y ) ) ],
% 1.44/1.79 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 1.44/1.79 X, 'universal_class' ) ],
% 1.44/1.79 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 1.44/1.79 Y, 'universal_class' ) ],
% 1.44/1.79 [ subclass( X, X ) ],
% 1.44/1.79 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 1.44/1.79 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 1.44/1.79 'not_subclass_element'( Y, X ), Y ) ],
% 1.44/1.79 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 1.44/1.79 'not_subclass_element'( Y, X ), Y ) ],
% 1.44/1.79 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 1.44/1.79 'not_subclass_element'( Y, X ), Y ) ],
% 1.44/1.79 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 1.44/1.79 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 1.44/1.79 [ member( y, intersection( complement( x ), x ) ) ]
% 1.44/1.79 ] .
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 percentage equality = 0.208738, percentage horn = 0.892157
% 1.44/1.79 This is a problem with some equality
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 Options Used:
% 1.44/1.79
% 1.44/1.79 useres = 1
% 1.44/1.79 useparamod = 1
% 1.44/1.79 useeqrefl = 1
% 1.44/1.79 useeqfact = 1
% 1.44/1.79 usefactor = 1
% 1.44/1.79 usesimpsplitting = 0
% 1.44/1.79 usesimpdemod = 5
% 1.44/1.79 usesimpres = 3
% 1.44/1.79
% 1.44/1.79 resimpinuse = 1000
% 1.44/1.79 resimpclauses = 20000
% 1.44/1.79 substype = eqrewr
% 1.44/1.79 backwardsubs = 1
% 1.44/1.79 selectoldest = 5
% 1.44/1.79
% 1.44/1.79 litorderings [0] = split
% 1.44/1.79 litorderings [1] = extend the termordering, first sorting on arguments
% 1.44/1.79
% 1.44/1.79 termordering = kbo
% 1.44/1.79
% 1.44/1.79 litapriori = 0
% 1.44/1.79 termapriori = 1
% 1.44/1.79 litaposteriori = 0
% 1.44/1.79 termaposteriori = 0
% 1.44/1.79 demodaposteriori = 0
% 1.44/1.79 ordereqreflfact = 0
% 1.44/1.79
% 1.44/1.79 litselect = negord
% 1.44/1.79
% 1.44/1.79 maxweight = 15
% 1.44/1.79 maxdepth = 30000
% 1.44/1.79 maxlength = 115
% 1.44/1.79 maxnrvars = 195
% 1.44/1.79 excuselevel = 1
% 1.44/1.79 increasemaxweight = 1
% 1.44/1.79
% 1.44/1.79 maxselected = 10000000
% 1.44/1.79 maxnrclauses = 10000000
% 1.44/1.79
% 1.44/1.79 showgenerated = 0
% 1.44/1.79 showkept = 0
% 1.44/1.79 showselected = 0
% 1.44/1.79 showdeleted = 0
% 1.44/1.79 showresimp = 1
% 1.44/1.79 showstatus = 2000
% 1.44/1.79
% 1.44/1.79 prologoutput = 1
% 1.44/1.79 nrgoals = 5000000
% 1.44/1.79 totalproof = 1
% 1.44/1.79
% 1.44/1.79 Symbols occurring in the translation:
% 1.44/1.79
% 1.44/1.79 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.44/1.79 . [1, 2] (w:1, o:56, a:1, s:1, b:0),
% 1.44/1.79 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 1.44/1.79 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.44/1.79 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.44/1.79 subclass [41, 2] (w:1, o:81, a:1, s:1, b:0),
% 1.44/1.79 member [43, 2] (w:1, o:82, a:1, s:1, b:0),
% 1.44/1.79 'not_subclass_element' [44, 2] (w:1, o:83, a:1, s:1, b:0),
% 1.44/1.79 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 1.44/1.79 'unordered_pair' [46, 2] (w:1, o:84, a:1, s:1, b:0),
% 1.44/1.79 singleton [47, 1] (w:1, o:39, a:1, s:1, b:0),
% 1.44/1.79 'ordered_pair' [48, 2] (w:1, o:85, a:1, s:1, b:0),
% 1.44/1.79 'cross_product' [50, 2] (w:1, o:86, a:1, s:1, b:0),
% 1.44/1.79 first [52, 1] (w:1, o:40, a:1, s:1, b:0),
% 1.44/1.79 second [53, 1] (w:1, o:41, a:1, s:1, b:0),
% 1.44/1.79 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 1.44/1.79 intersection [55, 2] (w:1, o:88, a:1, s:1, b:0),
% 1.44/1.79 complement [56, 1] (w:1, o:42, a:1, s:1, b:0),
% 1.44/1.79 union [57, 2] (w:1, o:89, a:1, s:1, b:0),
% 1.44/1.79 'symmetric_difference' [58, 2] (w:1, o:90, a:1, s:1, b:0),
% 1.44/1.79 restrict [60, 3] (w:1, o:93, a:1, s:1, b:0),
% 1.44/1.79 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.44/1.79 'domain_of' [62, 1] (w:1, o:44, a:1, s:1, b:0),
% 1.44/1.79 rotate [63, 1] (w:1, o:36, a:1, s:1, b:0),
% 1.44/1.79 flip [65, 1] (w:1, o:45, a:1, s:1, b:0),
% 1.44/1.79 inverse [66, 1] (w:1, o:46, a:1, s:1, b:0),
% 1.44/1.79 'range_of' [67, 1] (w:1, o:37, a:1, s:1, b:0),
% 1.44/1.79 domain [68, 3] (w:1, o:95, a:1, s:1, b:0),
% 1.44/1.79 range [69, 3] (w:1, o:96, a:1, s:1, b:0),
% 1.44/1.79 image [70, 2] (w:1, o:87, a:1, s:1, b:0),
% 1.44/1.79 successor [71, 1] (w:1, o:47, a:1, s:1, b:0),
% 1.44/1.79 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 1.44/1.79 inductive [73, 1] (w:1, o:48, a:1, s:1, b:0),
% 1.44/1.79 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.44/1.79 'sum_class' [75, 1] (w:1, o:49, a:1, s:1, b:0),
% 1.44/1.79 'power_class' [76, 1] (w:1, o:52, a:1, s:1, b:0),
% 1.44/1.79 compose [78, 2] (w:1, o:91, a:1, s:1, b:0),
% 1.44/1.79 'single_valued_class' [79, 1] (w:1, o:53, a:1, s:1, b:0),
% 1.44/1.79 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 1.44/1.79 function [82, 1] (w:1, o:54, a:1, s:1, b:0),
% 1.44/1.79 regular [83, 1] (w:1, o:38, a:1, s:1, b:0),
% 1.44/1.79 apply [84, 2] (w:1, o:92, a:1, s:1, b:0),
% 1.44/1.79 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.44/1.79 'one_to_one' [86, 1] (w:1, o:50, a:1, s:1, b:0),
% 1.44/1.79 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 1.44/1.79 diagonalise [88, 1] (w:1, o:55, a:1, s:1, b:0),
% 1.44/1.79 cantor [89, 1] (w:1, o:43, a:1, s:1, b:0),
% 1.44/1.79 operation [90, 1] (w:1, o:51, a:1, s:1, b:0),
% 1.44/1.79 compatible [94, 3] (w:1, o:94, a:1, s:1, b:0),
% 1.44/1.79 homomorphism [95, 3] (w:1, o:97, a:1, s:1, b:0),
% 1.44/1.79 'not_homomorphism1' [96, 3] (w:1, o:98, a:1, s:1, b:0),
% 1.44/1.79 'not_homomorphism2' [97, 3] (w:1, o:99, a:1, s:1, b:0),
% 1.44/1.79 y [98, 0] (w:1, o:30, a:1, s:1, b:0),
% 1.44/1.79 x [99, 0] (w:1, o:29, a:1, s:1, b:0).
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 Starting Search:
% 1.44/1.79
% 1.44/1.79 Resimplifying inuse:
% 1.44/1.79 Done
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 Intermediate Status:
% 1.44/1.79 Generated: 5509
% 1.44/1.79 Kept: 2046
% 1.44/1.79 Inuse: 103
% 1.44/1.79 Deleted: 5
% 1.44/1.79 Deletedinuse: 2
% 1.44/1.79
% 1.44/1.79 Resimplifying inuse:
% 1.44/1.79 Done
% 1.44/1.79
% 1.44/1.79 Resimplifying inuse:
% 1.44/1.79 Done
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 Intermediate Status:
% 1.44/1.79 Generated: 10265
% 1.44/1.79 Kept: 4054
% 1.44/1.79 Inuse: 188
% 1.44/1.79 Deleted: 23
% 1.44/1.79 Deletedinuse: 14
% 1.44/1.79
% 1.44/1.79 Resimplifying inuse:
% 1.44/1.79 Done
% 1.44/1.79
% 1.44/1.79 Resimplifying inuse:
% 1.44/1.79 Done
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 Intermediate Status:
% 1.44/1.79 Generated: 14138
% 1.44/1.79 Kept: 6086
% 1.44/1.79 Inuse: 239
% 1.44/1.79 Deleted: 27
% 1.44/1.79 Deletedinuse: 15
% 1.44/1.79
% 1.44/1.79 Resimplifying inuse:
% 1.44/1.79 Done
% 1.44/1.79
% 1.44/1.79 Resimplifying inuse:
% 1.44/1.79 Done
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 Intermediate Status:
% 1.44/1.79 Generated: 18836
% 1.44/1.79 Kept: 8095
% 1.44/1.79 Inuse: 291
% 1.44/1.79 Deleted: 84
% 1.44/1.79 Deletedinuse: 71
% 1.44/1.79
% 1.44/1.79 Resimplifying inuse:
% 1.44/1.79 Done
% 1.44/1.79
% 1.44/1.79 Resimplifying inuse:
% 1.44/1.79 Done
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 Intermediate Status:
% 1.44/1.79 Generated: 24101
% 1.44/1.79 Kept: 10123
% 1.44/1.79 Inuse: 381
% 1.44/1.79 Deleted: 95
% 1.44/1.79 Deletedinuse: 80
% 1.44/1.79
% 1.44/1.79 Resimplifying inuse:
% 1.44/1.79 Done
% 1.44/1.79
% 1.44/1.79 Resimplifying inuse:
% 1.44/1.79 Done
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 Intermediate Status:
% 1.44/1.79 Generated: 31744
% 1.44/1.79 Kept: 12123
% 1.44/1.79 Inuse: 405
% 1.44/1.79 Deleted: 100
% 1.44/1.79 Deletedinuse: 85
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 Bliksems!, er is een bewijs:
% 1.44/1.79 % SZS status Unsatisfiable
% 1.44/1.79 % SZS output start Refutation
% 1.44/1.79
% 1.44/1.79 clause( 19, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ] )
% 1.44/1.79 .
% 1.44/1.79 clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 1.44/1.79 .
% 1.44/1.79 clause( 22, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ] )
% 1.44/1.79 .
% 1.44/1.79 clause( 99, [ member( y, intersection( complement( x ), x ) ) ] )
% 1.44/1.79 .
% 1.44/1.79 clause( 12128, [ member( y, x ) ] )
% 1.44/1.79 .
% 1.44/1.79 clause( 12129, [ member( y, complement( x ) ) ] )
% 1.44/1.79 .
% 1.44/1.79 clause( 12195, [] )
% 1.44/1.79 .
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 % SZS output end Refutation
% 1.44/1.79 found a proof!
% 1.44/1.79
% 1.44/1.79 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.44/1.79
% 1.44/1.79 initialclauses(
% 1.44/1.79 [ clause( 12197, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.44/1.79 ) ] )
% 1.44/1.79 , clause( 12198, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 1.44/1.79 , Y ) ] )
% 1.44/1.79 , clause( 12199, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 1.44/1.79 subclass( X, Y ) ] )
% 1.44/1.79 , clause( 12200, [ subclass( X, 'universal_class' ) ] )
% 1.44/1.79 , clause( 12201, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.44/1.79 , clause( 12202, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 1.44/1.79 , clause( 12203, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 1.44/1.79 ] )
% 1.44/1.79 , clause( 12204, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 1.44/1.79 =( X, Z ) ] )
% 1.44/1.79 , clause( 12205, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.44/1.79 'unordered_pair'( X, Y ) ) ] )
% 1.44/1.79 , clause( 12206, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.44/1.79 'unordered_pair'( Y, X ) ) ] )
% 1.44/1.79 , clause( 12207, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 1.44/1.79 )
% 1.44/1.79 , clause( 12208, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.44/1.79 , clause( 12209, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 1.44/1.79 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.44/1.79 , clause( 12210, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.44/1.79 ) ) ), member( X, Z ) ] )
% 1.44/1.79 , clause( 12211, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.44/1.79 ) ) ), member( Y, T ) ] )
% 1.44/1.79 , clause( 12212, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.44/1.79 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.44/1.79 , clause( 12213, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 1.44/1.79 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 1.44/1.79 , clause( 12214, [ subclass( 'element_relation', 'cross_product'(
% 1.44/1.79 'universal_class', 'universal_class' ) ) ] )
% 1.44/1.79 , clause( 12215, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 1.44/1.79 ), member( X, Y ) ] )
% 1.44/1.79 , clause( 12216, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.44/1.79 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 1.44/1.79 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 1.44/1.79 , clause( 12217, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.44/1.79 )
% 1.44/1.79 , clause( 12218, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 1.44/1.79 )
% 1.44/1.79 , clause( 12219, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 1.44/1.79 intersection( Y, Z ) ) ] )
% 1.44/1.79 , clause( 12220, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 1.44/1.79 )
% 1.44/1.79 , clause( 12221, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.44/1.79 complement( Y ) ), member( X, Y ) ] )
% 1.44/1.79 , clause( 12222, [ =( complement( intersection( complement( X ), complement(
% 1.44/1.79 Y ) ) ), union( X, Y ) ) ] )
% 1.44/1.79 , clause( 12223, [ =( intersection( complement( intersection( X, Y ) ),
% 1.44/1.79 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 1.44/1.79 'symmetric_difference'( X, Y ) ) ] )
% 1.44/1.79 , clause( 12224, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 1.44/1.79 X, Y, Z ) ) ] )
% 1.44/1.79 , clause( 12225, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 1.44/1.79 Z, X, Y ) ) ] )
% 1.44/1.79 , clause( 12226, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 1.44/1.79 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 1.44/1.79 , clause( 12227, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 1.44/1.79 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 1.44/1.79 'domain_of'( Y ) ) ] )
% 1.44/1.79 , clause( 12228, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 1.44/1.79 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.44/1.79 , clause( 12229, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.44/1.79 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 1.44/1.79 ] )
% 1.44/1.79 , clause( 12230, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.44/1.79 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 1.44/1.79 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.44/1.79 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 1.44/1.79 , Y ), rotate( T ) ) ] )
% 1.44/1.79 , clause( 12231, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 1.44/1.79 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.44/1.79 , clause( 12232, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.44/1.79 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 1.44/1.79 )
% 1.44/1.79 , clause( 12233, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.44/1.79 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 1.44/1.79 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.44/1.79 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 1.44/1.79 , Z ), flip( T ) ) ] )
% 1.44/1.79 , clause( 12234, [ =( 'domain_of'( flip( 'cross_product'( X,
% 1.44/1.79 'universal_class' ) ) ), inverse( X ) ) ] )
% 1.44/1.79 , clause( 12235, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 1.44/1.79 , clause( 12236, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 1.44/1.79 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 1.44/1.79 , clause( 12237, [ =( second( 'not_subclass_element'( restrict( X,
% 1.44/1.79 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 1.44/1.79 , clause( 12238, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 1.44/1.79 image( X, Y ) ) ] )
% 1.44/1.79 , clause( 12239, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 1.44/1.79 , clause( 12240, [ subclass( 'successor_relation', 'cross_product'(
% 1.44/1.79 'universal_class', 'universal_class' ) ) ] )
% 1.44/1.79 , clause( 12241, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 1.44/1.79 ) ), =( successor( X ), Y ) ] )
% 1.44/1.79 , clause( 12242, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 1.44/1.79 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 1.44/1.79 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 1.44/1.79 , clause( 12243, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 1.44/1.79 , clause( 12244, [ ~( inductive( X ) ), subclass( image(
% 1.44/1.79 'successor_relation', X ), X ) ] )
% 1.44/1.79 , clause( 12245, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 1.44/1.79 'successor_relation', X ), X ) ), inductive( X ) ] )
% 1.44/1.79 , clause( 12246, [ inductive( omega ) ] )
% 1.44/1.79 , clause( 12247, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 1.44/1.79 , clause( 12248, [ member( omega, 'universal_class' ) ] )
% 1.44/1.79 , clause( 12249, [ =( 'domain_of'( restrict( 'element_relation',
% 1.44/1.79 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 1.44/1.79 , clause( 12250, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 1.44/1.79 X ), 'universal_class' ) ] )
% 1.44/1.79 , clause( 12251, [ =( complement( image( 'element_relation', complement( X
% 1.44/1.79 ) ) ), 'power_class'( X ) ) ] )
% 1.44/1.79 , clause( 12252, [ ~( member( X, 'universal_class' ) ), member(
% 1.44/1.79 'power_class'( X ), 'universal_class' ) ] )
% 1.44/1.79 , clause( 12253, [ subclass( compose( X, Y ), 'cross_product'(
% 1.44/1.79 'universal_class', 'universal_class' ) ) ] )
% 1.44/1.79 , clause( 12254, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 1.44/1.79 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 1.44/1.79 , clause( 12255, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 1.44/1.79 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 1.44/1.79 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 1.44/1.79 ) ] )
% 1.44/1.79 , clause( 12256, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 1.44/1.79 inverse( X ) ), 'identity_relation' ) ] )
% 1.44/1.79 , clause( 12257, [ ~( subclass( compose( X, inverse( X ) ),
% 1.44/1.79 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 1.44/1.79 , clause( 12258, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 1.44/1.79 'universal_class', 'universal_class' ) ) ] )
% 1.44/1.79 , clause( 12259, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 1.44/1.79 , 'identity_relation' ) ] )
% 1.44/1.79 , clause( 12260, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 1.44/1.79 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 1.44/1.79 'identity_relation' ) ), function( X ) ] )
% 1.44/1.79 , clause( 12261, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 1.44/1.79 , member( image( X, Y ), 'universal_class' ) ] )
% 1.44/1.79 , clause( 12262, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.44/1.79 , clause( 12263, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 1.44/1.79 , 'null_class' ) ] )
% 1.44/1.79 , clause( 12264, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 1.44/1.79 Y ) ) ] )
% 1.44/1.79 , clause( 12265, [ function( choice ) ] )
% 1.44/1.79 , clause( 12266, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 1.44/1.79 ), member( apply( choice, X ), X ) ] )
% 1.44/1.79 , clause( 12267, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 1.44/1.79 , clause( 12268, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 1.44/1.79 , clause( 12269, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 1.44/1.79 'one_to_one'( X ) ] )
% 1.44/1.79 , clause( 12270, [ =( intersection( 'cross_product'( 'universal_class',
% 1.44/1.79 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 1.44/1.79 'universal_class' ), complement( compose( complement( 'element_relation'
% 1.44/1.79 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 1.44/1.79 , clause( 12271, [ =( intersection( inverse( 'subset_relation' ),
% 1.44/1.79 'subset_relation' ), 'identity_relation' ) ] )
% 1.44/1.79 , clause( 12272, [ =( complement( 'domain_of'( intersection( X,
% 1.44/1.79 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 1.44/1.79 , clause( 12273, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 1.44/1.79 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 1.44/1.79 , clause( 12274, [ ~( operation( X ) ), function( X ) ] )
% 1.44/1.79 , clause( 12275, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 1.44/1.79 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.44/1.79 ] )
% 1.44/1.79 , clause( 12276, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 1.44/1.79 'domain_of'( 'domain_of'( X ) ) ) ] )
% 1.44/1.79 , clause( 12277, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 1.44/1.79 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.44/1.79 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 1.44/1.79 operation( X ) ] )
% 1.44/1.79 , clause( 12278, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 1.44/1.79 , clause( 12279, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 1.44/1.79 Y ) ), 'domain_of'( X ) ) ] )
% 1.44/1.79 , clause( 12280, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 1.44/1.79 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 1.44/1.79 , clause( 12281, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 1.44/1.79 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 1.44/1.79 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 1.44/1.79 , clause( 12282, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 1.44/1.79 , clause( 12283, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 1.44/1.79 , clause( 12284, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 1.44/1.79 , clause( 12285, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 1.44/1.79 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 1.44/1.79 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 1.44/1.79 )
% 1.44/1.79 , clause( 12286, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.44/1.79 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.44/1.79 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.44/1.79 , Y ) ] )
% 1.44/1.79 , clause( 12287, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.44/1.79 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 1.44/1.79 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 1.44/1.79 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 1.44/1.79 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 1.44/1.79 )
% 1.44/1.79 , clause( 12288, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.44/1.79 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 1.44/1.79 , clause( 12289, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.44/1.79 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 1.44/1.79 , clause( 12290, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.44/1.79 ) ) ), member( X, 'universal_class' ) ] )
% 1.44/1.79 , clause( 12291, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.44/1.79 ) ) ), member( Y, 'universal_class' ) ] )
% 1.44/1.79 , clause( 12292, [ subclass( X, X ) ] )
% 1.44/1.79 , clause( 12293, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 1.44/1.79 X, Z ) ] )
% 1.44/1.79 , clause( 12294, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 1.44/1.79 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 1.44/1.79 , clause( 12295, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 1.44/1.79 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 1.44/1.79 , clause( 12296, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 1.44/1.79 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 1.44/1.79 , clause( 12297, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 1.44/1.79 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 1.44/1.79 , clause( 12298, [ member( y, intersection( complement( x ), x ) ) ] )
% 1.44/1.79 ] ).
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 subsumption(
% 1.44/1.79 clause( 19, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ] )
% 1.44/1.79 , clause( 12217, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.44/1.79 )
% 1.44/1.79 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.44/1.79 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 subsumption(
% 1.44/1.79 clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 1.44/1.79 , clause( 12218, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 1.44/1.79 )
% 1.44/1.79 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.44/1.79 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 subsumption(
% 1.44/1.79 clause( 22, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ] )
% 1.44/1.79 , clause( 12220, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 1.44/1.79 )
% 1.44/1.79 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.44/1.79 ), ==>( 1, 1 )] ) ).
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 subsumption(
% 1.44/1.79 clause( 99, [ member( y, intersection( complement( x ), x ) ) ] )
% 1.44/1.79 , clause( 12298, [ member( y, intersection( complement( x ), x ) ) ] )
% 1.44/1.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 resolution(
% 1.44/1.79 clause( 12391, [ member( y, x ) ] )
% 1.44/1.79 , clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 1.44/1.79 , 0, clause( 99, [ member( y, intersection( complement( x ), x ) ) ] )
% 1.44/1.79 , 0, substitution( 0, [ :=( X, y ), :=( Y, complement( x ) ), :=( Z, x )] )
% 1.44/1.79 , substitution( 1, [] )).
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 subsumption(
% 1.44/1.79 clause( 12128, [ member( y, x ) ] )
% 1.44/1.79 , clause( 12391, [ member( y, x ) ] )
% 1.44/1.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 resolution(
% 1.44/1.79 clause( 12392, [ member( y, complement( x ) ) ] )
% 1.44/1.79 , clause( 19, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ] )
% 1.44/1.79 , 0, clause( 99, [ member( y, intersection( complement( x ), x ) ) ] )
% 1.44/1.79 , 0, substitution( 0, [ :=( X, y ), :=( Y, complement( x ) ), :=( Z, x )] )
% 1.44/1.79 , substitution( 1, [] )).
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 subsumption(
% 1.44/1.79 clause( 12129, [ member( y, complement( x ) ) ] )
% 1.44/1.79 , clause( 12392, [ member( y, complement( x ) ) ] )
% 1.44/1.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 resolution(
% 1.44/1.79 clause( 12393, [ ~( member( y, complement( x ) ) ) ] )
% 1.44/1.79 , clause( 22, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ] )
% 1.44/1.79 , 1, clause( 12128, [ member( y, x ) ] )
% 1.44/1.79 , 0, substitution( 0, [ :=( X, y ), :=( Y, x )] ), substitution( 1, [] )
% 1.44/1.79 ).
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 resolution(
% 1.44/1.79 clause( 12394, [] )
% 1.44/1.79 , clause( 12393, [ ~( member( y, complement( x ) ) ) ] )
% 1.44/1.79 , 0, clause( 12129, [ member( y, complement( x ) ) ] )
% 1.44/1.79 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 subsumption(
% 1.44/1.79 clause( 12195, [] )
% 1.44/1.79 , clause( 12394, [] )
% 1.44/1.79 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 end.
% 1.44/1.79
% 1.44/1.79 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.44/1.79
% 1.44/1.79 Memory use:
% 1.44/1.79
% 1.44/1.79 space for terms: 201324
% 1.44/1.79 space for clauses: 572987
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 clauses generated: 31869
% 1.44/1.79 clauses kept: 12196
% 1.44/1.79 clauses selected: 407
% 1.44/1.79 clauses deleted: 100
% 1.44/1.79 clauses inuse deleted: 85
% 1.44/1.79
% 1.44/1.79 subsentry: 69918
% 1.44/1.79 literals s-matched: 55173
% 1.44/1.79 literals matched: 54347
% 1.44/1.79 full subsumption: 24763
% 1.44/1.79
% 1.44/1.79 checksum: 830431337
% 1.44/1.79
% 1.44/1.79
% 1.44/1.79 Bliksem ended
%------------------------------------------------------------------------------