TSTP Solution File: SET103-6 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET103-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n028.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 22:47:08 EDT 2022
% Result : Unsatisfiable 1.25s 1.66s
% Output : Refutation 1.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET103-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.10/0.10 % Command : bliksem %s
% 0.10/0.29 % Computer : n028.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % DateTime : Sun Jul 10 04:46:12 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.67/1.02 *** allocated 10000 integers for termspace/termends
% 0.67/1.02 *** allocated 10000 integers for clauses
% 0.67/1.02 *** allocated 10000 integers for justifications
% 0.67/1.02 Bliksem 1.12
% 0.67/1.02
% 0.67/1.02
% 0.67/1.02 Automatic Strategy Selection
% 0.67/1.02
% 0.67/1.02 Clauses:
% 0.67/1.02 [
% 0.67/1.02 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.67/1.02 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.67/1.02 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.67/1.02 ,
% 0.67/1.02 [ subclass( X, 'universal_class' ) ],
% 0.67/1.02 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.67/1.02 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.67/1.02 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.67/1.02 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.67/1.02 ,
% 0.67/1.02 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.67/1.02 ) ) ],
% 0.67/1.02 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.67/1.02 ) ) ],
% 0.67/1.02 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.67/1.02 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.67/1.02 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.67/1.02 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.67/1.02 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.67/1.02 X, Z ) ],
% 0.67/1.02 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.67/1.02 Y, T ) ],
% 0.67/1.02 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.67/1.02 ), 'cross_product'( Y, T ) ) ],
% 0.67/1.02 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.67/1.02 ), second( X ) ), X ) ],
% 0.67/1.02 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.67/1.02 'universal_class' ) ) ],
% 0.67/1.02 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.67/1.02 Y ) ],
% 0.67/1.02 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.67/1.02 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.67/1.02 , Y ), 'element_relation' ) ],
% 0.67/1.02 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.67/1.02 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.67/1.02 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.67/1.02 Z ) ) ],
% 0.67/1.02 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.67/1.02 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.67/1.02 member( X, Y ) ],
% 0.67/1.02 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.67/1.02 union( X, Y ) ) ],
% 0.67/1.02 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.67/1.02 intersection( complement( X ), complement( Y ) ) ) ),
% 0.67/1.02 'symmetric_difference'( X, Y ) ) ],
% 0.67/1.02 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.67/1.02 ,
% 0.67/1.02 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.67/1.02 ,
% 0.67/1.02 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.67/1.02 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.67/1.02 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.67/1.02 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.67/1.02 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.67/1.02 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.67/1.02 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.67/1.02 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.67/1.02 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.67/1.02 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.67/1.02 'cross_product'( 'universal_class', 'universal_class' ),
% 0.67/1.02 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.67/1.02 Y ), rotate( T ) ) ],
% 0.67/1.02 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.67/1.02 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.67/1.02 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.67/1.02 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.67/1.02 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.67/1.02 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.67/1.02 'cross_product'( 'universal_class', 'universal_class' ),
% 0.67/1.02 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.67/1.02 Z ), flip( T ) ) ],
% 0.67/1.02 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.67/1.02 inverse( X ) ) ],
% 0.67/1.02 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.67/1.02 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.67/1.02 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.67/1.02 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.67/1.02 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.67/1.02 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.67/1.02 ],
% 0.67/1.02 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.67/1.02 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.67/1.02 'universal_class' ) ) ],
% 0.67/1.02 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.67/1.02 successor( X ), Y ) ],
% 0.67/1.02 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.67/1.02 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.67/1.02 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.67/1.02 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.67/1.02 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.67/1.02 ,
% 0.67/1.02 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.67/1.02 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.67/1.02 [ inductive( omega ) ],
% 0.67/1.02 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.67/1.02 [ member( omega, 'universal_class' ) ],
% 0.67/1.02 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.67/1.02 , 'sum_class'( X ) ) ],
% 0.67/1.02 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.67/1.02 'universal_class' ) ],
% 0.67/1.02 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.67/1.02 'power_class'( X ) ) ],
% 0.67/1.02 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.67/1.02 'universal_class' ) ],
% 0.67/1.02 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.67/1.02 'universal_class' ) ) ],
% 0.67/1.02 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.67/1.02 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.67/1.02 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.67/1.02 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.67/1.02 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.67/1.02 ) ],
% 0.67/1.02 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.67/1.02 , 'identity_relation' ) ],
% 0.67/1.02 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.67/1.02 'single_valued_class'( X ) ],
% 0.67/1.02 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.67/1.02 'universal_class' ) ) ],
% 0.67/1.02 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.67/1.02 'identity_relation' ) ],
% 0.67/1.02 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.67/1.02 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.67/1.02 , function( X ) ],
% 0.67/1.02 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.67/1.02 X, Y ), 'universal_class' ) ],
% 0.67/1.02 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.67/1.02 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.67/1.02 ) ],
% 0.67/1.02 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.67/1.02 [ function( choice ) ],
% 0.67/1.02 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.67/1.02 apply( choice, X ), X ) ],
% 0.67/1.02 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.67/1.02 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.67/1.02 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.67/1.02 ,
% 0.67/1.02 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.67/1.02 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.67/1.02 , complement( compose( complement( 'element_relation' ), inverse(
% 0.67/1.02 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.67/1.02 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.67/1.02 'identity_relation' ) ],
% 0.67/1.02 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.67/1.02 , diagonalise( X ) ) ],
% 0.67/1.02 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.67/1.02 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.67/1.02 [ ~( operation( X ) ), function( X ) ],
% 0.67/1.02 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.67/1.02 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.67/1.02 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 1.25/1.66 'domain_of'( X ) ) ) ],
% 1.25/1.66 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 1.25/1.66 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 1.25/1.66 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 1.25/1.66 X ) ],
% 1.25/1.66 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 1.25/1.66 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 1.25/1.66 'domain_of'( X ) ) ],
% 1.25/1.66 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 1.25/1.66 'domain_of'( Z ) ) ) ],
% 1.25/1.66 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 1.25/1.66 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 1.25/1.66 ), compatible( X, Y, Z ) ],
% 1.25/1.66 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 1.25/1.66 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 1.25/1.66 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 1.25/1.66 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 1.25/1.66 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 1.25/1.66 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 1.25/1.66 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 1.25/1.66 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.25/1.66 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.25/1.66 , Y ) ],
% 1.25/1.66 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 1.25/1.66 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 1.25/1.66 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 1.25/1.66 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 1.25/1.66 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 1.25/1.66 [ ~( =( 'unordered_pair'( singleton( x ), 'unordered_pair'( x,
% 1.25/1.66 'null_class' ) ), 'ordered_pair'( x, y ) ) ) ],
% 1.25/1.66 [ ~( member( y, 'universal_class' ) ) ]
% 1.25/1.66 ] .
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 percentage equality = 0.218579, percentage horn = 0.913978
% 1.25/1.66 This is a problem with some equality
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 Options Used:
% 1.25/1.66
% 1.25/1.66 useres = 1
% 1.25/1.66 useparamod = 1
% 1.25/1.66 useeqrefl = 1
% 1.25/1.66 useeqfact = 1
% 1.25/1.66 usefactor = 1
% 1.25/1.66 usesimpsplitting = 0
% 1.25/1.66 usesimpdemod = 5
% 1.25/1.66 usesimpres = 3
% 1.25/1.66
% 1.25/1.66 resimpinuse = 1000
% 1.25/1.66 resimpclauses = 20000
% 1.25/1.66 substype = eqrewr
% 1.25/1.66 backwardsubs = 1
% 1.25/1.66 selectoldest = 5
% 1.25/1.66
% 1.25/1.66 litorderings [0] = split
% 1.25/1.66 litorderings [1] = extend the termordering, first sorting on arguments
% 1.25/1.66
% 1.25/1.66 termordering = kbo
% 1.25/1.66
% 1.25/1.66 litapriori = 0
% 1.25/1.66 termapriori = 1
% 1.25/1.66 litaposteriori = 0
% 1.25/1.66 termaposteriori = 0
% 1.25/1.66 demodaposteriori = 0
% 1.25/1.66 ordereqreflfact = 0
% 1.25/1.66
% 1.25/1.66 litselect = negord
% 1.25/1.66
% 1.25/1.66 maxweight = 15
% 1.25/1.66 maxdepth = 30000
% 1.25/1.66 maxlength = 115
% 1.25/1.66 maxnrvars = 195
% 1.25/1.66 excuselevel = 1
% 1.25/1.66 increasemaxweight = 1
% 1.25/1.66
% 1.25/1.66 maxselected = 10000000
% 1.25/1.66 maxnrclauses = 10000000
% 1.25/1.66
% 1.25/1.66 showgenerated = 0
% 1.25/1.66 showkept = 0
% 1.25/1.66 showselected = 0
% 1.25/1.66 showdeleted = 0
% 1.25/1.66 showresimp = 1
% 1.25/1.66 showstatus = 2000
% 1.25/1.66
% 1.25/1.66 prologoutput = 1
% 1.25/1.66 nrgoals = 5000000
% 1.25/1.66 totalproof = 1
% 1.25/1.66
% 1.25/1.66 Symbols occurring in the translation:
% 1.25/1.66
% 1.25/1.66 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.25/1.66 . [1, 2] (w:1, o:56, a:1, s:1, b:0),
% 1.25/1.66 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 1.25/1.66 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.25/1.66 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.25/1.66 subclass [41, 2] (w:1, o:81, a:1, s:1, b:0),
% 1.25/1.66 member [43, 2] (w:1, o:82, a:1, s:1, b:0),
% 1.25/1.66 'not_subclass_element' [44, 2] (w:1, o:83, a:1, s:1, b:0),
% 1.25/1.66 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 1.25/1.66 'unordered_pair' [46, 2] (w:1, o:84, a:1, s:1, b:0),
% 1.25/1.66 singleton [47, 1] (w:1, o:39, a:1, s:1, b:0),
% 1.25/1.66 'ordered_pair' [48, 2] (w:1, o:85, a:1, s:1, b:0),
% 1.25/1.66 'cross_product' [50, 2] (w:1, o:86, a:1, s:1, b:0),
% 1.25/1.66 first [52, 1] (w:1, o:40, a:1, s:1, b:0),
% 1.25/1.66 second [53, 1] (w:1, o:41, a:1, s:1, b:0),
% 1.25/1.66 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 1.25/1.66 intersection [55, 2] (w:1, o:88, a:1, s:1, b:0),
% 1.25/1.66 complement [56, 1] (w:1, o:42, a:1, s:1, b:0),
% 1.25/1.66 union [57, 2] (w:1, o:89, a:1, s:1, b:0),
% 1.25/1.66 'symmetric_difference' [58, 2] (w:1, o:90, a:1, s:1, b:0),
% 1.25/1.66 restrict [60, 3] (w:1, o:93, a:1, s:1, b:0),
% 1.25/1.66 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.25/1.66 'domain_of' [62, 1] (w:1, o:44, a:1, s:1, b:0),
% 1.25/1.66 rotate [63, 1] (w:1, o:36, a:1, s:1, b:0),
% 1.25/1.66 flip [65, 1] (w:1, o:45, a:1, s:1, b:0),
% 1.25/1.66 inverse [66, 1] (w:1, o:46, a:1, s:1, b:0),
% 1.25/1.66 'range_of' [67, 1] (w:1, o:37, a:1, s:1, b:0),
% 1.25/1.66 domain [68, 3] (w:1, o:95, a:1, s:1, b:0),
% 1.25/1.66 range [69, 3] (w:1, o:96, a:1, s:1, b:0),
% 1.25/1.66 image [70, 2] (w:1, o:87, a:1, s:1, b:0),
% 1.25/1.66 successor [71, 1] (w:1, o:47, a:1, s:1, b:0),
% 1.25/1.66 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 1.25/1.66 inductive [73, 1] (w:1, o:48, a:1, s:1, b:0),
% 1.25/1.66 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.25/1.66 'sum_class' [75, 1] (w:1, o:49, a:1, s:1, b:0),
% 1.25/1.66 'power_class' [76, 1] (w:1, o:52, a:1, s:1, b:0),
% 1.25/1.66 compose [78, 2] (w:1, o:91, a:1, s:1, b:0),
% 1.25/1.66 'single_valued_class' [79, 1] (w:1, o:53, a:1, s:1, b:0),
% 1.25/1.66 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 1.25/1.66 function [82, 1] (w:1, o:54, a:1, s:1, b:0),
% 1.25/1.66 regular [83, 1] (w:1, o:38, a:1, s:1, b:0),
% 1.25/1.66 apply [84, 2] (w:1, o:92, a:1, s:1, b:0),
% 1.25/1.66 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.25/1.66 'one_to_one' [86, 1] (w:1, o:50, a:1, s:1, b:0),
% 1.25/1.66 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 1.25/1.66 diagonalise [88, 1] (w:1, o:55, a:1, s:1, b:0),
% 1.25/1.66 cantor [89, 1] (w:1, o:43, a:1, s:1, b:0),
% 1.25/1.66 operation [90, 1] (w:1, o:51, a:1, s:1, b:0),
% 1.25/1.66 compatible [94, 3] (w:1, o:94, a:1, s:1, b:0),
% 1.25/1.66 homomorphism [95, 3] (w:1, o:97, a:1, s:1, b:0),
% 1.25/1.66 'not_homomorphism1' [96, 3] (w:1, o:98, a:1, s:1, b:0),
% 1.25/1.66 'not_homomorphism2' [97, 3] (w:1, o:99, a:1, s:1, b:0),
% 1.25/1.66 x [98, 0] (w:1, o:29, a:1, s:1, b:0),
% 1.25/1.66 y [99, 0] (w:1, o:30, a:1, s:1, b:0).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 Starting Search:
% 1.25/1.66
% 1.25/1.66 Resimplifying inuse:
% 1.25/1.66 Done
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 Intermediate Status:
% 1.25/1.66 Generated: 4804
% 1.25/1.66 Kept: 2010
% 1.25/1.66 Inuse: 119
% 1.25/1.66 Deleted: 7
% 1.25/1.66 Deletedinuse: 3
% 1.25/1.66
% 1.25/1.66 Resimplifying inuse:
% 1.25/1.66 Done
% 1.25/1.66
% 1.25/1.66 Resimplifying inuse:
% 1.25/1.66 Done
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 Intermediate Status:
% 1.25/1.66 Generated: 10164
% 1.25/1.66 Kept: 4270
% 1.25/1.66 Inuse: 194
% 1.25/1.66 Deleted: 12
% 1.25/1.66 Deletedinuse: 5
% 1.25/1.66
% 1.25/1.66 Resimplifying inuse:
% 1.25/1.66 Done
% 1.25/1.66
% 1.25/1.66 Resimplifying inuse:
% 1.25/1.66 Done
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 Intermediate Status:
% 1.25/1.66 Generated: 14049
% 1.25/1.66 Kept: 6270
% 1.25/1.66 Inuse: 262
% 1.25/1.66 Deleted: 20
% 1.25/1.66 Deletedinuse: 9
% 1.25/1.66
% 1.25/1.66 Resimplifying inuse:
% 1.25/1.66 Done
% 1.25/1.66
% 1.25/1.66 Resimplifying inuse:
% 1.25/1.66 Done
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 Intermediate Status:
% 1.25/1.66 Generated: 19475
% 1.25/1.66 Kept: 8293
% 1.25/1.66 Inuse: 315
% 1.25/1.66 Deleted: 69
% 1.25/1.66 Deletedinuse: 56
% 1.25/1.66
% 1.25/1.66 Resimplifying inuse:
% 1.25/1.66 Done
% 1.25/1.66
% 1.25/1.66 Resimplifying inuse:
% 1.25/1.66 Done
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 Intermediate Status:
% 1.25/1.66 Generated: 25049
% 1.25/1.66 Kept: 10900
% 1.25/1.66 Inuse: 372
% 1.25/1.66 Deleted: 77
% 1.25/1.66 Deletedinuse: 63
% 1.25/1.66
% 1.25/1.66 Resimplifying inuse:
% 1.25/1.66 Done
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 Bliksems!, er is een bewijs:
% 1.25/1.66 % SZS status Unsatisfiable
% 1.25/1.66 % SZS output start Refutation
% 1.25/1.66
% 1.25/1.66 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 1.25/1.66 )
% 1.25/1.66 .
% 1.25/1.66 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z
% 1.25/1.66 ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.25/1.66 'unordered_pair'( Y, X ) ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 9, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 11, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 1.25/1.66 singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 90, [ ~( =( 'unordered_pair'( singleton( x ), 'unordered_pair'( x,
% 1.25/1.66 'null_class' ) ), 'ordered_pair'( x, y ) ) ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 91, [ ~( member( y, 'universal_class' ) ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 93, [ =( X, Y ), ~( member( X, singleton( Y ) ) ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 94, [ ~( =( X, Y ) ), ~( member( Z, 'unordered_pair'( X, Y ) ) ),
% 1.25/1.66 =( Z, Y ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 105, [ ~( member( y, X ) ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 122, [ =( X, Y ), ~( =( Y, X ) ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 164, [ ~( member( X, Y ) ), ~( =( X, y ) ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 509, [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 515, [ member( 'ordered_pair'( X, Y ), 'unordered_pair'( Z,
% 1.25/1.66 'ordered_pair'( X, Y ) ) ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 9787, [ ~( member( X, singleton( y ) ) ), ~( member( X, Y ) ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 10899, [ ~( member( X, singleton( y ) ) ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 10900, [ =( singleton( y ), 'null_class' ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 10914, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 1.25/1.66 'null_class' ) ), 'ordered_pair'( X, y ) ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 11035, [ ~( =( X, 'ordered_pair'( x, y ) ) ), ~( =( Y, X ) ), ~(
% 1.25/1.66 member( 'ordered_pair'( x, y ), 'unordered_pair'( Y, X ) ) ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 11964, [ ~( =( X, 'ordered_pair'( x, y ) ) ) ] )
% 1.25/1.66 .
% 1.25/1.66 clause( 11965, [] )
% 1.25/1.66 .
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 % SZS output end Refutation
% 1.25/1.66 found a proof!
% 1.25/1.66
% 1.25/1.66 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.25/1.66
% 1.25/1.66 initialclauses(
% 1.25/1.66 [ clause( 11967, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.25/1.66 ) ] )
% 1.25/1.66 , clause( 11968, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 1.25/1.66 , Y ) ] )
% 1.25/1.66 , clause( 11969, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 1.25/1.66 subclass( X, Y ) ] )
% 1.25/1.66 , clause( 11970, [ subclass( X, 'universal_class' ) ] )
% 1.25/1.66 , clause( 11971, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.25/1.66 , clause( 11972, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 1.25/1.66 , clause( 11973, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 1.25/1.66 ] )
% 1.25/1.66 , clause( 11974, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 1.25/1.66 =( X, Z ) ] )
% 1.25/1.66 , clause( 11975, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.25/1.66 'unordered_pair'( X, Y ) ) ] )
% 1.25/1.66 , clause( 11976, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.25/1.66 'unordered_pair'( Y, X ) ) ] )
% 1.25/1.66 , clause( 11977, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 1.25/1.66 )
% 1.25/1.66 , clause( 11978, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.25/1.66 , clause( 11979, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 1.25/1.66 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.25/1.66 , clause( 11980, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.25/1.66 ) ) ), member( X, Z ) ] )
% 1.25/1.66 , clause( 11981, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.25/1.66 ) ) ), member( Y, T ) ] )
% 1.25/1.66 , clause( 11982, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.25/1.66 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.25/1.66 , clause( 11983, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 1.25/1.66 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 1.25/1.66 , clause( 11984, [ subclass( 'element_relation', 'cross_product'(
% 1.25/1.66 'universal_class', 'universal_class' ) ) ] )
% 1.25/1.66 , clause( 11985, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 1.25/1.66 ), member( X, Y ) ] )
% 1.25/1.66 , clause( 11986, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.25/1.66 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 1.25/1.66 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 1.25/1.66 , clause( 11987, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.25/1.66 )
% 1.25/1.66 , clause( 11988, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 1.25/1.66 )
% 1.25/1.66 , clause( 11989, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 1.25/1.66 intersection( Y, Z ) ) ] )
% 1.25/1.66 , clause( 11990, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 1.25/1.66 )
% 1.25/1.66 , clause( 11991, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.25/1.66 complement( Y ) ), member( X, Y ) ] )
% 1.25/1.66 , clause( 11992, [ =( complement( intersection( complement( X ), complement(
% 1.25/1.66 Y ) ) ), union( X, Y ) ) ] )
% 1.25/1.66 , clause( 11993, [ =( intersection( complement( intersection( X, Y ) ),
% 1.25/1.66 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 1.25/1.66 'symmetric_difference'( X, Y ) ) ] )
% 1.25/1.66 , clause( 11994, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 1.25/1.66 X, Y, Z ) ) ] )
% 1.25/1.66 , clause( 11995, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 1.25/1.66 Z, X, Y ) ) ] )
% 1.25/1.66 , clause( 11996, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 1.25/1.66 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 1.25/1.66 , clause( 11997, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 1.25/1.66 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 1.25/1.66 'domain_of'( Y ) ) ] )
% 1.25/1.66 , clause( 11998, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 1.25/1.66 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.25/1.66 , clause( 11999, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.25/1.66 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 1.25/1.66 ] )
% 1.25/1.66 , clause( 12000, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.25/1.66 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 1.25/1.66 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.25/1.66 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 1.25/1.66 , Y ), rotate( T ) ) ] )
% 1.25/1.66 , clause( 12001, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 1.25/1.66 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.25/1.66 , clause( 12002, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.25/1.66 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 1.25/1.66 )
% 1.25/1.66 , clause( 12003, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.25/1.66 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 1.25/1.66 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.25/1.66 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 1.25/1.66 , Z ), flip( T ) ) ] )
% 1.25/1.66 , clause( 12004, [ =( 'domain_of'( flip( 'cross_product'( X,
% 1.25/1.66 'universal_class' ) ) ), inverse( X ) ) ] )
% 1.25/1.66 , clause( 12005, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 1.25/1.66 , clause( 12006, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 1.25/1.66 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 1.25/1.66 , clause( 12007, [ =( second( 'not_subclass_element'( restrict( X,
% 1.25/1.66 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 1.25/1.66 , clause( 12008, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 1.25/1.66 image( X, Y ) ) ] )
% 1.25/1.66 , clause( 12009, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 1.25/1.66 , clause( 12010, [ subclass( 'successor_relation', 'cross_product'(
% 1.25/1.66 'universal_class', 'universal_class' ) ) ] )
% 1.25/1.66 , clause( 12011, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 1.25/1.66 ) ), =( successor( X ), Y ) ] )
% 1.25/1.66 , clause( 12012, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 1.25/1.66 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 1.25/1.66 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 1.25/1.66 , clause( 12013, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 1.25/1.66 , clause( 12014, [ ~( inductive( X ) ), subclass( image(
% 1.25/1.66 'successor_relation', X ), X ) ] )
% 1.25/1.66 , clause( 12015, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 1.25/1.66 'successor_relation', X ), X ) ), inductive( X ) ] )
% 1.25/1.66 , clause( 12016, [ inductive( omega ) ] )
% 1.25/1.66 , clause( 12017, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 1.25/1.66 , clause( 12018, [ member( omega, 'universal_class' ) ] )
% 1.25/1.66 , clause( 12019, [ =( 'domain_of'( restrict( 'element_relation',
% 1.25/1.66 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 1.25/1.66 , clause( 12020, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 1.25/1.66 X ), 'universal_class' ) ] )
% 1.25/1.66 , clause( 12021, [ =( complement( image( 'element_relation', complement( X
% 1.25/1.66 ) ) ), 'power_class'( X ) ) ] )
% 1.25/1.66 , clause( 12022, [ ~( member( X, 'universal_class' ) ), member(
% 1.25/1.66 'power_class'( X ), 'universal_class' ) ] )
% 1.25/1.66 , clause( 12023, [ subclass( compose( X, Y ), 'cross_product'(
% 1.25/1.66 'universal_class', 'universal_class' ) ) ] )
% 1.25/1.66 , clause( 12024, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 1.25/1.66 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 1.25/1.66 , clause( 12025, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 1.25/1.66 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 1.25/1.66 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 1.25/1.66 ) ] )
% 1.25/1.66 , clause( 12026, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 1.25/1.66 inverse( X ) ), 'identity_relation' ) ] )
% 1.25/1.66 , clause( 12027, [ ~( subclass( compose( X, inverse( X ) ),
% 1.25/1.66 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 1.25/1.66 , clause( 12028, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 1.25/1.66 'universal_class', 'universal_class' ) ) ] )
% 1.25/1.66 , clause( 12029, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 1.25/1.66 , 'identity_relation' ) ] )
% 1.25/1.66 , clause( 12030, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 1.25/1.66 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 1.25/1.66 'identity_relation' ) ), function( X ) ] )
% 1.25/1.66 , clause( 12031, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 1.25/1.66 , member( image( X, Y ), 'universal_class' ) ] )
% 1.25/1.66 , clause( 12032, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.25/1.66 , clause( 12033, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 1.25/1.66 , 'null_class' ) ] )
% 1.25/1.66 , clause( 12034, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 1.25/1.66 Y ) ) ] )
% 1.25/1.66 , clause( 12035, [ function( choice ) ] )
% 1.25/1.66 , clause( 12036, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 1.25/1.66 ), member( apply( choice, X ), X ) ] )
% 1.25/1.66 , clause( 12037, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 1.25/1.66 , clause( 12038, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 1.25/1.66 , clause( 12039, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 1.25/1.66 'one_to_one'( X ) ] )
% 1.25/1.66 , clause( 12040, [ =( intersection( 'cross_product'( 'universal_class',
% 1.25/1.66 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 1.25/1.66 'universal_class' ), complement( compose( complement( 'element_relation'
% 1.25/1.66 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 1.25/1.66 , clause( 12041, [ =( intersection( inverse( 'subset_relation' ),
% 1.25/1.66 'subset_relation' ), 'identity_relation' ) ] )
% 1.25/1.66 , clause( 12042, [ =( complement( 'domain_of'( intersection( X,
% 1.25/1.66 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 1.25/1.66 , clause( 12043, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 1.25/1.66 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 1.25/1.66 , clause( 12044, [ ~( operation( X ) ), function( X ) ] )
% 1.25/1.66 , clause( 12045, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 1.25/1.66 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.25/1.66 ] )
% 1.25/1.66 , clause( 12046, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 1.25/1.66 'domain_of'( 'domain_of'( X ) ) ) ] )
% 1.25/1.66 , clause( 12047, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 1.25/1.66 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.25/1.66 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 1.25/1.66 operation( X ) ] )
% 1.25/1.66 , clause( 12048, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 1.25/1.66 , clause( 12049, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 1.25/1.66 Y ) ), 'domain_of'( X ) ) ] )
% 1.25/1.66 , clause( 12050, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 1.25/1.66 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 1.25/1.66 , clause( 12051, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 1.25/1.66 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 1.25/1.66 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 1.25/1.66 , clause( 12052, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 1.25/1.66 , clause( 12053, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 1.25/1.66 , clause( 12054, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 1.25/1.66 , clause( 12055, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 1.25/1.66 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 1.25/1.66 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 1.25/1.66 )
% 1.25/1.66 , clause( 12056, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.25/1.66 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.25/1.66 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.25/1.66 , Y ) ] )
% 1.25/1.66 , clause( 12057, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.25/1.66 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 1.25/1.66 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 1.25/1.66 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 1.25/1.66 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 1.25/1.66 )
% 1.25/1.66 , clause( 12058, [ ~( =( 'unordered_pair'( singleton( x ), 'unordered_pair'(
% 1.25/1.66 x, 'null_class' ) ), 'ordered_pair'( x, y ) ) ) ] )
% 1.25/1.66 , clause( 12059, [ ~( member( y, 'universal_class' ) ) ] )
% 1.25/1.66 ] ).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 subsumption(
% 1.25/1.66 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 1.25/1.66 )
% 1.25/1.66 , clause( 11967, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.25/1.66 ) ] )
% 1.25/1.66 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.25/1.66 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 subsumption(
% 1.25/1.66 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 1.25/1.66 , clause( 11970, [ subclass( X, 'universal_class' ) ] )
% 1.25/1.66 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 subsumption(
% 1.25/1.66 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.25/1.66 , clause( 11971, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.25/1.66 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.25/1.66 ), ==>( 1, 1 )] ) ).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 subsumption(
% 1.25/1.66 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 1.25/1.66 , clause( 11973, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 1.25/1.66 ] )
% 1.25/1.66 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.25/1.66 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 subsumption(
% 1.25/1.66 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z
% 1.25/1.66 ) ] )
% 1.25/1.66 , clause( 11974, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 1.25/1.66 =( X, Z ) ] )
% 1.25/1.66 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.25/1.66 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 subsumption(
% 1.25/1.66 clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.25/1.66 'unordered_pair'( Y, X ) ) ] )
% 1.25/1.66 , clause( 11976, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.25/1.66 'unordered_pair'( Y, X ) ) ] )
% 1.25/1.66 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.25/1.66 ), ==>( 1, 1 )] ) ).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 subsumption(
% 1.25/1.66 clause( 9, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ] )
% 1.25/1.66 , clause( 11977, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 1.25/1.66 )
% 1.25/1.66 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.25/1.66 )] ) ).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 subsumption(
% 1.25/1.66 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.25/1.66 , clause( 11978, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.25/1.66 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 subsumption(
% 1.25/1.66 clause( 11, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 1.25/1.66 singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.25/1.66 , clause( 11979, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 1.25/1.66 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.25/1.66 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.25/1.66 )] ) ).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 subsumption(
% 1.25/1.66 clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.25/1.66 , clause( 12032, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.25/1.66 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.25/1.66 1 )] ) ).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 subsumption(
% 1.25/1.66 clause( 90, [ ~( =( 'unordered_pair'( singleton( x ), 'unordered_pair'( x,
% 1.25/1.66 'null_class' ) ), 'ordered_pair'( x, y ) ) ) ] )
% 1.25/1.66 , clause( 12058, [ ~( =( 'unordered_pair'( singleton( x ), 'unordered_pair'(
% 1.25/1.66 x, 'null_class' ) ), 'ordered_pair'( x, y ) ) ) ] )
% 1.25/1.66 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 subsumption(
% 1.25/1.66 clause( 91, [ ~( member( y, 'universal_class' ) ) ] )
% 1.25/1.66 , clause( 12059, [ ~( member( y, 'universal_class' ) ) ] )
% 1.25/1.66 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 factor(
% 1.25/1.66 clause( 12247, [ ~( member( X, 'unordered_pair'( Y, Y ) ) ), =( X, Y ) ] )
% 1.25/1.66 , clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X
% 1.25/1.66 , Z ) ] )
% 1.25/1.66 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y )] )).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 paramod(
% 1.25/1.66 clause( 12248, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 1.25/1.66 , clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.25/1.66 , 0, clause( 12247, [ ~( member( X, 'unordered_pair'( Y, Y ) ) ), =( X, Y )
% 1.25/1.66 ] )
% 1.25/1.66 , 0, 3, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 1.25/1.66 :=( Y, Y )] )).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 subsumption(
% 1.25/1.66 clause( 93, [ =( X, Y ), ~( member( X, singleton( Y ) ) ) ] )
% 1.25/1.66 , clause( 12248, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 1.25/1.66 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 1.25/1.66 ), ==>( 1, 0 )] ) ).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 eqfact(
% 1.25/1.66 clause( 12267, [ ~( =( X, Y ) ), ~( member( Z, 'unordered_pair'( X, Y ) ) )
% 1.25/1.66 , =( Z, Y ) ] )
% 1.25/1.66 , clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X
% 1.25/1.66 , Z ) ] )
% 1.25/1.66 , 1, 2, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 1.25/1.66
% 1.25/1.66
% 1.25/1.66 subsumption(
% 1.25/1.66 clause( 94, [ ~( =( X, Y ) ), ~( member( Z, 'unordered_pair'( X, Y ) ) ),
% 1.25/1.66 =( Z, Y ) ] )
% 1.25/1.66 , clause( 12267, [ ~( =( X, Y ) ), ~( member( Z, 'unordered_pair'( X, Y ) )
% 1.25/1.66 ), =( Z, Y ) ] )
% 1.25/1.66 , sCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------