%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET082-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n016.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 22:46:44 EDT 2022
% Result : Unsatisfiable 0.77s 1.54s
% Output : Refutation 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET082-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.14 % Command : bliksem %s
% 0.13/0.36 % Computer : n016.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % DateTime : Sun Jul 10 10:33:56 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.72/1.12 *** allocated 10000 integers for termspace/termends
% 0.72/1.12 *** allocated 10000 integers for clauses
% 0.72/1.12 *** allocated 10000 integers for justifications
% 0.72/1.12 Bliksem 1.12
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 Automatic Strategy Selection
% 0.72/1.12
% 0.72/1.12 Clauses:
% 0.72/1.12 [
% 0.72/1.12 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.72/1.12 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.72/1.12 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.72/1.12 ,
% 0.72/1.12 [ subclass( X, 'universal_class' ) ],
% 0.72/1.12 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.72/1.12 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.72/1.12 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.72/1.12 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.72/1.12 ,
% 0.72/1.12 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.72/1.12 ) ) ],
% 0.72/1.12 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.72/1.12 ) ) ],
% 0.72/1.12 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.72/1.12 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.72/1.12 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.72/1.12 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.72/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.72/1.12 X, Z ) ],
% 0.72/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.72/1.12 Y, T ) ],
% 0.72/1.12 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.72/1.12 ), 'cross_product'( Y, T ) ) ],
% 0.72/1.12 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.72/1.12 ), second( X ) ), X ) ],
% 0.72/1.12 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.72/1.12 'universal_class' ) ) ],
% 0.72/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.72/1.12 Y ) ],
% 0.72/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.72/1.12 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.72/1.12 , Y ), 'element_relation' ) ],
% 0.72/1.12 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.72/1.12 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.72/1.12 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.72/1.12 Z ) ) ],
% 0.72/1.12 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.72/1.12 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.72/1.12 member( X, Y ) ],
% 0.72/1.12 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.72/1.12 union( X, Y ) ) ],
% 0.72/1.12 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.72/1.12 intersection( complement( X ), complement( Y ) ) ) ),
% 0.72/1.12 'symmetric_difference'( X, Y ) ) ],
% 0.72/1.12 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.72/1.12 ,
% 0.72/1.12 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.72/1.12 ,
% 0.72/1.12 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.72/1.12 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.72/1.12 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.72/1.12 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.72/1.12 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.72/1.12 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.72/1.12 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.72/1.12 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.72/1.12 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.72/1.12 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.72/1.12 'cross_product'( 'universal_class', 'universal_class' ),
% 0.72/1.12 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.72/1.12 Y ), rotate( T ) ) ],
% 0.72/1.12 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.72/1.12 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.72/1.12 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.72/1.12 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.72/1.12 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.72/1.12 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.72/1.12 'cross_product'( 'universal_class', 'universal_class' ),
% 0.72/1.12 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.72/1.12 Z ), flip( T ) ) ],
% 0.72/1.12 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.72/1.12 inverse( X ) ) ],
% 0.72/1.12 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.72/1.12 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.72/1.12 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.72/1.12 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.72/1.12 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.72/1.12 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.72/1.12 ],
% 0.72/1.12 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.72/1.12 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.72/1.12 'universal_class' ) ) ],
% 0.72/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.72/1.12 successor( X ), Y ) ],
% 0.72/1.12 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.72/1.12 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.72/1.12 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.72/1.12 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.72/1.12 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.72/1.12 ,
% 0.72/1.12 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.72/1.12 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.72/1.12 [ inductive( omega ) ],
% 0.72/1.12 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.72/1.12 [ member( omega, 'universal_class' ) ],
% 0.72/1.12 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.72/1.12 , 'sum_class'( X ) ) ],
% 0.72/1.12 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.72/1.12 'universal_class' ) ],
% 0.72/1.12 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.72/1.12 'power_class'( X ) ) ],
% 0.72/1.12 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.72/1.12 'universal_class' ) ],
% 0.72/1.12 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.72/1.12 'universal_class' ) ) ],
% 0.72/1.12 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.72/1.12 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.72/1.12 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.72/1.12 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.72/1.12 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.72/1.12 ) ],
% 0.72/1.12 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.72/1.12 , 'identity_relation' ) ],
% 0.72/1.12 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.72/1.12 'single_valued_class'( X ) ],
% 0.72/1.12 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.72/1.12 'universal_class' ) ) ],
% 0.72/1.12 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.72/1.12 'identity_relation' ) ],
% 0.72/1.12 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.72/1.12 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.72/1.12 , function( X ) ],
% 0.72/1.12 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.72/1.12 X, Y ), 'universal_class' ) ],
% 0.72/1.12 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.72/1.12 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.72/1.12 ) ],
% 0.72/1.12 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.72/1.12 [ function( choice ) ],
% 0.72/1.12 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.72/1.12 apply( choice, X ), X ) ],
% 0.72/1.12 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.72/1.12 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.72/1.12 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.72/1.12 ,
% 0.72/1.12 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.72/1.12 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.72/1.12 , complement( compose( complement( 'element_relation' ), inverse(
% 0.72/1.12 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.72/1.12 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.72/1.12 'identity_relation' ) ],
% 0.72/1.12 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.72/1.12 , diagonalise( X ) ) ],
% 0.72/1.12 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.72/1.12 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.72/1.12 [ ~( operation( X ) ), function( X ) ],
% 0.72/1.12 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.72/1.12 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.72/1.12 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.77/1.54 'domain_of'( X ) ) ) ],
% 0.77/1.54 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.77/1.54 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.77/1.54 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.77/1.54 X ) ],
% 0.77/1.54 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.77/1.54 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.77/1.54 'domain_of'( X ) ) ],
% 0.77/1.54 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.77/1.54 'domain_of'( Z ) ) ) ],
% 0.77/1.54 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.77/1.54 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.77/1.54 ), compatible( X, Y, Z ) ],
% 0.77/1.54 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.77/1.54 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.77/1.54 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.77/1.54 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.77/1.54 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.77/1.54 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.77/1.54 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.77/1.54 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.77/1.54 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.77/1.54 , Y ) ],
% 0.77/1.54 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.77/1.54 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.77/1.54 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.77/1.54 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.77/1.54 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.77/1.54 [ ~( member( x, 'universal_class' ) ) ],
% 0.77/1.54 [ ~( =( singleton( x ), 'null_class' ) ) ]
% 0.77/1.54 ] .
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54 percentage equality = 0.218579, percentage horn = 0.913978
% 0.77/1.54 This is a problem with some equality
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54 Options Used:
% 0.77/1.54
% 0.77/1.54 useres = 1
% 0.77/1.54 useparamod = 1
% 0.77/1.54 useeqrefl = 1
% 0.77/1.54 useeqfact = 1
% 0.77/1.54 usefactor = 1
% 0.77/1.54 usesimpsplitting = 0
% 0.77/1.54 usesimpdemod = 5
% 0.77/1.54 usesimpres = 3
% 0.77/1.54
% 0.77/1.54 resimpinuse = 1000
% 0.77/1.54 resimpclauses = 20000
% 0.77/1.54 substype = eqrewr
% 0.77/1.54 backwardsubs = 1
% 0.77/1.54 selectoldest = 5
% 0.77/1.54
% 0.77/1.54 litorderings [0] = split
% 0.77/1.54 litorderings [1] = extend the termordering, first sorting on arguments
% 0.77/1.54
% 0.77/1.54 termordering = kbo
% 0.77/1.54
% 0.77/1.54 litapriori = 0
% 0.77/1.54 termapriori = 1
% 0.77/1.54 litaposteriori = 0
% 0.77/1.54 termaposteriori = 0
% 0.77/1.54 demodaposteriori = 0
% 0.77/1.54 ordereqreflfact = 0
% 0.77/1.54
% 0.77/1.54 litselect = negord
% 0.77/1.54
% 0.77/1.54 maxweight = 15
% 0.77/1.54 maxdepth = 30000
% 0.77/1.54 maxlength = 115
% 0.77/1.54 maxnrvars = 195
% 0.77/1.54 excuselevel = 1
% 0.77/1.54 increasemaxweight = 1
% 0.77/1.54
% 0.77/1.54 maxselected = 10000000
% 0.77/1.54 maxnrclauses = 10000000
% 0.77/1.54
% 0.77/1.54 showgenerated = 0
% 0.77/1.54 showkept = 0
% 0.77/1.54 showselected = 0
% 0.77/1.54 showdeleted = 0
% 0.77/1.54 showresimp = 1
% 0.77/1.54 showstatus = 2000
% 0.77/1.54
% 0.77/1.54 prologoutput = 1
% 0.77/1.54 nrgoals = 5000000
% 0.77/1.54 totalproof = 1
% 0.77/1.54
% 0.77/1.54 Symbols occurring in the translation:
% 0.77/1.54
% 0.77/1.54 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.77/1.54 . [1, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.77/1.54 ! [4, 1] (w:0, o:30, a:1, s:1, b:0),
% 0.77/1.54 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.77/1.54 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.77/1.54 subclass [41, 2] (w:1, o:80, a:1, s:1, b:0),
% 0.77/1.54 member [43, 2] (w:1, o:81, a:1, s:1, b:0),
% 0.77/1.54 'not_subclass_element' [44, 2] (w:1, o:82, a:1, s:1, b:0),
% 0.77/1.54 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.77/1.54 'unordered_pair' [46, 2] (w:1, o:83, a:1, s:1, b:0),
% 0.77/1.54 singleton [47, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.77/1.54 'ordered_pair' [48, 2] (w:1, o:84, a:1, s:1, b:0),
% 0.77/1.54 'cross_product' [50, 2] (w:1, o:85, a:1, s:1, b:0),
% 0.77/1.54 first [52, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.77/1.54 second [53, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.77/1.54 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.77/1.54 intersection [55, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.77/1.54 complement [56, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.77/1.54 union [57, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.77/1.54 'symmetric_difference' [58, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.77/1.54 restrict [60, 3] (w:1, o:92, a:1, s:1, b:0),
% 0.77/1.54 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.77/1.54 'domain_of' [62, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.77/1.54 rotate [63, 1] (w:1, o:35, a:1, s:1, b:0),
% 0.77/1.54 flip [65, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.77/1.54 inverse [66, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.77/1.54 'range_of' [67, 1] (w:1, o:36, a:1, s:1, b:0),
% 0.77/1.54 domain [68, 3] (w:1, o:94, a:1, s:1, b:0),
% 0.77/1.54 range [69, 3] (w:1, o:95, a:1, s:1, b:0),
% 0.77/1.54 image [70, 2] (w:1, o:86, a:1, s:1, b:0),
% 0.77/1.54 successor [71, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.77/1.54 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.77/1.54 inductive [73, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.77/1.54 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.77/1.54 'sum_class' [75, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.77/1.54 'power_class' [76, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.77/1.54 compose [78, 2] (w:1, o:90, a:1, s:1, b:0),
% 0.77/1.54 'single_valued_class' [79, 1] (w:1, o:52, a:1, s:1, b:0),
% 0.77/1.54 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.77/1.54 function [82, 1] (w:1, o:53, a:1, s:1, b:0),
% 0.77/1.54 regular [83, 1] (w:1, o:37, a:1, s:1, b:0),
% 0.77/1.54 apply [84, 2] (w:1, o:91, a:1, s:1, b:0),
% 0.77/1.54 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.77/1.54 'one_to_one' [86, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.77/1.54 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 0.77/1.54 diagonalise [88, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.77/1.54 cantor [89, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.77/1.54 operation [90, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.77/1.54 compatible [94, 3] (w:1, o:93, a:1, s:1, b:0),
% 0.77/1.54 homomorphism [95, 3] (w:1, o:96, a:1, s:1, b:0),
% 0.77/1.54 'not_homomorphism1' [96, 3] (w:1, o:97, a:1, s:1, b:0),
% 0.77/1.54 'not_homomorphism2' [97, 3] (w:1, o:98, a:1, s:1, b:0),
% 0.77/1.54 x [98, 0] (w:1, o:29, a:1, s:1, b:0).
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54 Starting Search:
% 0.77/1.54
% 0.77/1.54 Resimplifying inuse:
% 0.77/1.54 Done
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54 Intermediate Status:
% 0.77/1.54 Generated: 4773
% 0.77/1.54 Kept: 2012
% 0.77/1.54 Inuse: 119
% 0.77/1.54 Deleted: 7
% 0.77/1.54 Deletedinuse: 3
% 0.77/1.54
% 0.77/1.54 Resimplifying inuse:
% 0.77/1.54 Done
% 0.77/1.54
% 0.77/1.54 Resimplifying inuse:
% 0.77/1.54 Done
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54 Intermediate Status:
% 0.77/1.54 Generated: 10096
% 0.77/1.54 Kept: 4235
% 0.77/1.54 Inuse: 194
% 0.77/1.54 Deleted: 12
% 0.77/1.54 Deletedinuse: 5
% 0.77/1.54
% 0.77/1.54 Resimplifying inuse:
% 0.77/1.54 Done
% 0.77/1.54
% 0.77/1.54 Resimplifying inuse:
% 0.77/1.54 Done
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54 Intermediate Status:
% 0.77/1.54 Generated: 14011
% 0.77/1.54 Kept: 6236
% 0.77/1.54 Inuse: 262
% 0.77/1.54 Deleted: 19
% 0.77/1.54 Deletedinuse: 9
% 0.77/1.54
% 0.77/1.54 Resimplifying inuse:
% 0.77/1.54 Done
% 0.77/1.54
% 0.77/1.54 Resimplifying inuse:
% 0.77/1.54 Done
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54 Intermediate Status:
% 0.77/1.54 Generated: 19393
% 0.77/1.54 Kept: 8254
% 0.77/1.54 Inuse: 315
% 0.77/1.54 Deleted: 66
% 0.77/1.54 Deletedinuse: 54
% 0.77/1.54
% 0.77/1.54 Resimplifying inuse:
% 0.77/1.54 Done
% 0.77/1.54
% 0.77/1.54 Resimplifying inuse:
% 0.77/1.54 Done
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54 Intermediate Status:
% 0.77/1.54 Generated: 24746
% 0.77/1.54 Kept: 10780
% 0.77/1.54 Inuse: 368
% 0.77/1.54 Deleted: 74
% 0.77/1.54 Deletedinuse: 61
% 0.77/1.54
% 0.77/1.54 Resimplifying inuse:
% 0.77/1.54 Done
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54 Bliksems!, er is een bewijs:
% 0.77/1.54 % SZS status Unsatisfiable
% 0.77/1.54 % SZS output start Refutation
% 0.77/1.54
% 0.77/1.54 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.77/1.54 )
% 0.77/1.54 .
% 0.77/1.54 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 0.77/1.54 .
% 0.77/1.54 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 0.77/1.54 .
% 0.77/1.54 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 0.77/1.54 .
% 0.77/1.54 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z
% 0.77/1.54 ) ] )
% 0.77/1.54 .
% 0.77/1.54 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 0.77/1.54 .
% 0.77/1.54 clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.77/1.54 .
% 0.77/1.54 clause( 90, [ ~( member( x, 'universal_class' ) ) ] )
% 0.77/1.54 .
% 0.77/1.54 clause( 91, [ ~( =( singleton( x ), 'null_class' ) ) ] )
% 0.77/1.54 .
% 0.77/1.54 clause( 93, [ =( X, Y ), ~( member( X, singleton( Y ) ) ) ] )
% 0.77/1.54 .
% 0.77/1.54 clause( 105, [ ~( member( x, X ) ) ] )
% 0.77/1.54 .
% 0.77/1.54 clause( 122, [ =( X, Y ), ~( =( Y, X ) ) ] )
% 0.77/1.54 .
% 0.77/1.54 clause( 169, [ ~( member( X, Y ) ), ~( =( X, x ) ) ] )
% 0.77/1.54 .
% 0.77/1.54 clause( 9675, [ ~( member( X, singleton( x ) ) ), ~( member( X, Y ) ) ] )
% 0.77/1.54 .
% 0.77/1.54 clause( 10779, [ ~( member( X, singleton( x ) ) ) ] )
% 0.77/1.54 .
% 0.77/1.54 clause( 10780, [ =( singleton( x ), 'null_class' ) ] )
% 0.77/1.54 .
% 0.77/1.54 clause( 10785, [] )
% 0.77/1.54 .
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54 % SZS output end Refutation
% 0.77/1.54 found a proof!
% 0.77/1.54
% 0.77/1.54 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.77/1.54
% 0.77/1.54 initialclauses(
% 0.77/1.54 [ clause( 10787, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 0.77/1.54 ) ] )
% 0.77/1.54 , clause( 10788, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 0.77/1.54 , Y ) ] )
% 0.77/1.54 , clause( 10789, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 0.77/1.54 subclass( X, Y ) ] )
% 0.77/1.54 , clause( 10790, [ subclass( X, 'universal_class' ) ] )
% 0.77/1.54 , clause( 10791, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 0.77/1.54 , clause( 10792, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 0.77/1.54 , clause( 10793, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 0.77/1.54 ] )
% 0.77/1.54 , clause( 10794, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 0.77/1.54 =( X, Z ) ] )
% 0.77/1.54 , clause( 10795, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.77/1.54 'unordered_pair'( X, Y ) ) ] )
% 0.77/1.54 , clause( 10796, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.77/1.54 'unordered_pair'( Y, X ) ) ] )
% 0.77/1.54 , clause( 10797, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 0.77/1.54 )
% 0.77/1.54 , clause( 10798, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 0.77/1.54 , clause( 10799, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 0.77/1.54 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.77/1.54 , clause( 10800, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.77/1.54 ) ) ), member( X, Z ) ] )
% 0.77/1.54 , clause( 10801, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.77/1.54 ) ) ), member( Y, T ) ] )
% 0.77/1.54 , clause( 10802, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 0.77/1.54 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 0.77/1.54 , clause( 10803, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 0.77/1.54 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 0.77/1.54 , clause( 10804, [ subclass( 'element_relation', 'cross_product'(
% 0.77/1.54 'universal_class', 'universal_class' ) ) ] )
% 0.77/1.54 , clause( 10805, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 0.77/1.54 ), member( X, Y ) ] )
% 0.77/1.54 , clause( 10806, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.77/1.54 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 0.77/1.54 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 0.77/1.54 , clause( 10807, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.77/1.54 )
% 0.77/1.54 , clause( 10808, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 0.77/1.54 )
% 0.77/1.54 , clause( 10809, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 0.77/1.54 intersection( Y, Z ) ) ] )
% 0.77/1.54 , clause( 10810, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 0.77/1.54 )
% 0.77/1.54 , clause( 10811, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.77/1.54 complement( Y ) ), member( X, Y ) ] )
% 0.77/1.54 , clause( 10812, [ =( complement( intersection( complement( X ), complement(
% 0.77/1.54 Y ) ) ), union( X, Y ) ) ] )
% 0.77/1.54 , clause( 10813, [ =( intersection( complement( intersection( X, Y ) ),
% 0.77/1.54 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 0.77/1.54 'symmetric_difference'( X, Y ) ) ] )
% 0.77/1.54 , clause( 10814, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 0.77/1.54 X, Y, Z ) ) ] )
% 0.77/1.54 , clause( 10815, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 0.77/1.54 Z, X, Y ) ) ] )
% 0.77/1.54 , clause( 10816, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 0.77/1.54 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 0.77/1.54 , clause( 10817, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 0.77/1.54 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 0.77/1.54 'domain_of'( Y ) ) ] )
% 0.77/1.54 , clause( 10818, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.77/1.54 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.77/1.54 , clause( 10819, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.77/1.54 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 0.77/1.54 ] )
% 0.77/1.54 , clause( 10820, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.77/1.54 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 0.77/1.54 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.77/1.54 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 0.77/1.54 , Y ), rotate( T ) ) ] )
% 0.77/1.54 , clause( 10821, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.77/1.54 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.77/1.54 , clause( 10822, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.77/1.54 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 0.77/1.54 )
% 0.77/1.54 , clause( 10823, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.77/1.54 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 0.77/1.54 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.77/1.54 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 0.77/1.54 , Z ), flip( T ) ) ] )
% 0.77/1.54 , clause( 10824, [ =( 'domain_of'( flip( 'cross_product'( X,
% 0.77/1.54 'universal_class' ) ) ), inverse( X ) ) ] )
% 0.77/1.54 , clause( 10825, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 0.77/1.54 , clause( 10826, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 0.77/1.54 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 0.77/1.54 , clause( 10827, [ =( second( 'not_subclass_element'( restrict( X,
% 0.77/1.54 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 0.77/1.54 , clause( 10828, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 0.77/1.54 image( X, Y ) ) ] )
% 0.77/1.54 , clause( 10829, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 0.77/1.54 , clause( 10830, [ subclass( 'successor_relation', 'cross_product'(
% 0.77/1.54 'universal_class', 'universal_class' ) ) ] )
% 0.77/1.54 , clause( 10831, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 0.77/1.54 ) ), =( successor( X ), Y ) ] )
% 0.77/1.54 , clause( 10832, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 0.77/1.54 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 0.77/1.54 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 0.77/1.54 , clause( 10833, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 0.77/1.54 , clause( 10834, [ ~( inductive( X ) ), subclass( image(
% 0.77/1.54 'successor_relation', X ), X ) ] )
% 0.77/1.54 , clause( 10835, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.77/1.54 'successor_relation', X ), X ) ), inductive( X ) ] )
% 0.77/1.54 , clause( 10836, [ inductive( omega ) ] )
% 0.77/1.54 , clause( 10837, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 0.77/1.54 , clause( 10838, [ member( omega, 'universal_class' ) ] )
% 0.77/1.54 , clause( 10839, [ =( 'domain_of'( restrict( 'element_relation',
% 0.77/1.54 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 0.77/1.54 , clause( 10840, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 0.77/1.54 X ), 'universal_class' ) ] )
% 0.77/1.54 , clause( 10841, [ =( complement( image( 'element_relation', complement( X
% 0.77/1.54 ) ) ), 'power_class'( X ) ) ] )
% 0.77/1.54 , clause( 10842, [ ~( member( X, 'universal_class' ) ), member(
% 0.77/1.54 'power_class'( X ), 'universal_class' ) ] )
% 0.77/1.54 , clause( 10843, [ subclass( compose( X, Y ), 'cross_product'(
% 0.77/1.54 'universal_class', 'universal_class' ) ) ] )
% 0.77/1.54 , clause( 10844, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 0.77/1.54 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 0.77/1.54 , clause( 10845, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 0.77/1.54 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.77/1.54 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.77/1.54 ) ] )
% 0.77/1.54 , clause( 10846, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 0.77/1.54 inverse( X ) ), 'identity_relation' ) ] )
% 0.77/1.54 , clause( 10847, [ ~( subclass( compose( X, inverse( X ) ),
% 0.77/1.54 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 0.77/1.54 , clause( 10848, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 0.77/1.54 'universal_class', 'universal_class' ) ) ] )
% 0.77/1.54 , clause( 10849, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 0.77/1.54 , 'identity_relation' ) ] )
% 0.77/1.54 , clause( 10850, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 0.77/1.54 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 0.77/1.54 'identity_relation' ) ), function( X ) ] )
% 0.77/1.54 , clause( 10851, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 0.77/1.54 , member( image( X, Y ), 'universal_class' ) ] )
% 0.77/1.54 , clause( 10852, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.77/1.54 , clause( 10853, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 0.77/1.54 , 'null_class' ) ] )
% 0.77/1.54 , clause( 10854, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 0.77/1.54 Y ) ) ] )
% 0.77/1.54 , clause( 10855, [ function( choice ) ] )
% 0.77/1.54 , clause( 10856, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 0.77/1.54 ), member( apply( choice, X ), X ) ] )
% 0.77/1.54 , clause( 10857, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 0.77/1.54 , clause( 10858, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 0.77/1.54 , clause( 10859, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 0.77/1.54 'one_to_one'( X ) ] )
% 0.77/1.54 , clause( 10860, [ =( intersection( 'cross_product'( 'universal_class',
% 0.77/1.54 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 0.77/1.54 'universal_class' ), complement( compose( complement( 'element_relation'
% 0.77/1.54 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 0.77/1.54 , clause( 10861, [ =( intersection( inverse( 'subset_relation' ),
% 0.77/1.54 'subset_relation' ), 'identity_relation' ) ] )
% 0.77/1.54 , clause( 10862, [ =( complement( 'domain_of'( intersection( X,
% 0.77/1.54 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 0.77/1.54 , clause( 10863, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 0.77/1.54 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 0.77/1.54 , clause( 10864, [ ~( operation( X ) ), function( X ) ] )
% 0.77/1.54 , clause( 10865, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 0.77/1.54 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.77/1.54 ] )
% 0.77/1.54 , clause( 10866, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 0.77/1.54 'domain_of'( 'domain_of'( X ) ) ) ] )
% 0.77/1.54 , clause( 10867, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 0.77/1.54 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.77/1.54 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 0.77/1.54 operation( X ) ] )
% 0.77/1.54 , clause( 10868, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 0.77/1.54 , clause( 10869, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 0.77/1.54 Y ) ), 'domain_of'( X ) ) ] )
% 0.77/1.54 , clause( 10870, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 0.77/1.54 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 0.77/1.54 , clause( 10871, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 0.77/1.54 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 0.77/1.54 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 0.77/1.54 , clause( 10872, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 0.77/1.54 , clause( 10873, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 0.77/1.54 , clause( 10874, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 0.77/1.54 , clause( 10875, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 0.77/1.54 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 0.77/1.54 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 0.77/1.54 )
% 0.77/1.54 , clause( 10876, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 0.77/1.54 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.77/1.54 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.77/1.54 , Y ) ] )
% 0.77/1.54 , clause( 10877, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 0.77/1.54 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 0.77/1.54 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 0.77/1.54 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 0.77/1.54 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 0.77/1.54 )
% 0.77/1.54 , clause( 10878, [ ~( member( x, 'universal_class' ) ) ] )
% 0.77/1.54 , clause( 10879, [ ~( =( singleton( x ), 'null_class' ) ) ] )
% 0.77/1.54 ] ).
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54 subsumption(
% 0.77/1.54 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.77/1.54 )
% 0.77/1.54 , clause( 10787, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 0.77/1.54 ) ] )
% 0.77/1.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.77/1.54 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54 subsumption(
% 0.77/1.54 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 0.77/1.54 , clause( 10790, [ subclass( X, 'universal_class' ) ] )
% 0.77/1.54 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54 subsumption(
% 0.77/1.54 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 0.77/1.54 , clause( 10791, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 0.77/1.54 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.77/1.54 ), ==>( 1, 1 )] ) ).
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54 subsumption(
% 0.77/1.54 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 0.77/1.54 , clause( 10793, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 0.77/1.54 ] )
% 0.77/1.54 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.77/1.54 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54 subsumption(
% 0.77/1.54 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z
% 0.77/1.54 ) ] )
% 0.77/1.54 , clause( 10794, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 0.77/1.54 =( X, Z ) ] )
% 0.77/1.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.77/1.54 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.77/1.54
% 0.77/1.54
% 0.77/1.54 subsumption(
% 0.77/1.54 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 0.77/1.54 , clause( 10798, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 0.77/1.54 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 300.04/300.66 Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------