%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET083-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.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 22:46:46 EDT 2022
% Result : Unsatisfiable 1.10s 1.47s
% Output : Refutation 1.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET083-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.00/0.10 % Command : bliksem %s
% 0.09/0.30 % Computer : n025.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % DateTime : Sun Jul 10 14:24:16 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.65/1.02 *** allocated 10000 integers for termspace/termends
% 0.65/1.02 *** allocated 10000 integers for clauses
% 0.65/1.02 *** allocated 10000 integers for justifications
% 0.65/1.02 Bliksem 1.12
% 0.65/1.02
% 0.65/1.02
% 0.65/1.02 Automatic Strategy Selection
% 0.65/1.02
% 0.65/1.02 Clauses:
% 0.65/1.02 [
% 0.65/1.02 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.65/1.02 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.65/1.02 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.65/1.02 ,
% 0.65/1.02 [ subclass( X, 'universal_class' ) ],
% 0.65/1.02 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.65/1.02 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.65/1.02 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.65/1.02 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.65/1.02 ,
% 0.65/1.02 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.65/1.02 ) ) ],
% 0.65/1.02 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.65/1.02 ) ) ],
% 0.65/1.02 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.65/1.02 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.65/1.02 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.65/1.02 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.65/1.02 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.65/1.02 X, Z ) ],
% 0.65/1.02 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.65/1.02 Y, T ) ],
% 0.65/1.02 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.65/1.02 ), 'cross_product'( Y, T ) ) ],
% 0.65/1.02 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.65/1.02 ), second( X ) ), X ) ],
% 0.65/1.02 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.65/1.02 'universal_class' ) ) ],
% 0.65/1.02 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.65/1.02 Y ) ],
% 0.65/1.02 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.65/1.02 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.65/1.02 , Y ), 'element_relation' ) ],
% 0.65/1.02 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.65/1.02 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.65/1.02 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.65/1.02 Z ) ) ],
% 0.65/1.02 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.65/1.02 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.65/1.02 member( X, Y ) ],
% 0.65/1.02 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.65/1.02 union( X, Y ) ) ],
% 0.65/1.02 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.65/1.02 intersection( complement( X ), complement( Y ) ) ) ),
% 0.65/1.02 'symmetric_difference'( X, Y ) ) ],
% 0.65/1.02 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.65/1.02 ,
% 0.65/1.02 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.65/1.02 ,
% 0.65/1.02 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.65/1.02 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.65/1.02 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.65/1.02 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.65/1.02 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.65/1.02 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.65/1.02 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.65/1.02 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.65/1.02 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.65/1.02 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.65/1.02 'cross_product'( 'universal_class', 'universal_class' ),
% 0.65/1.02 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.65/1.02 Y ), rotate( T ) ) ],
% 0.65/1.02 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.65/1.02 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.65/1.02 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.65/1.02 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.65/1.02 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.65/1.02 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.65/1.02 'cross_product'( 'universal_class', 'universal_class' ),
% 0.65/1.02 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.65/1.02 Z ), flip( T ) ) ],
% 0.65/1.02 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.65/1.02 inverse( X ) ) ],
% 0.65/1.02 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.65/1.02 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.65/1.02 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.65/1.02 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.65/1.02 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.65/1.02 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.65/1.02 ],
% 0.65/1.02 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.65/1.02 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.65/1.02 'universal_class' ) ) ],
% 0.65/1.02 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.65/1.02 successor( X ), Y ) ],
% 0.65/1.02 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.65/1.02 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.65/1.02 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.65/1.02 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.65/1.02 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.65/1.02 ,
% 0.65/1.02 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.65/1.02 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.65/1.02 [ inductive( omega ) ],
% 0.65/1.02 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.65/1.02 [ member( omega, 'universal_class' ) ],
% 0.65/1.02 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.65/1.02 , 'sum_class'( X ) ) ],
% 0.65/1.02 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.65/1.02 'universal_class' ) ],
% 0.65/1.02 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.65/1.02 'power_class'( X ) ) ],
% 0.65/1.02 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.65/1.02 'universal_class' ) ],
% 0.65/1.02 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.65/1.02 'universal_class' ) ) ],
% 0.65/1.02 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.65/1.02 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.65/1.02 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.65/1.02 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.65/1.02 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.65/1.02 ) ],
% 0.65/1.02 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.65/1.02 , 'identity_relation' ) ],
% 0.65/1.02 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.65/1.02 'single_valued_class'( X ) ],
% 0.65/1.02 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.65/1.02 'universal_class' ) ) ],
% 0.65/1.02 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.65/1.02 'identity_relation' ) ],
% 0.65/1.02 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.65/1.02 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.65/1.02 , function( X ) ],
% 0.65/1.02 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.65/1.02 X, Y ), 'universal_class' ) ],
% 0.65/1.02 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.65/1.02 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.65/1.02 ) ],
% 0.65/1.02 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.65/1.02 [ function( choice ) ],
% 0.65/1.02 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.65/1.02 apply( choice, X ), X ) ],
% 0.65/1.02 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.65/1.02 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.65/1.02 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.65/1.02 ,
% 0.65/1.02 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.65/1.02 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.65/1.02 , complement( compose( complement( 'element_relation' ), inverse(
% 0.65/1.02 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.65/1.02 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.65/1.02 'identity_relation' ) ],
% 0.65/1.02 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.65/1.02 , diagonalise( X ) ) ],
% 0.65/1.02 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.65/1.02 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.65/1.02 [ ~( operation( X ) ), function( X ) ],
% 0.65/1.02 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.65/1.02 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.65/1.02 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 1.10/1.47 'domain_of'( X ) ) ) ],
% 1.10/1.47 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 1.10/1.47 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 1.10/1.47 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 1.10/1.47 X ) ],
% 1.10/1.47 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 1.10/1.47 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 1.10/1.47 'domain_of'( X ) ) ],
% 1.10/1.47 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 1.10/1.47 'domain_of'( Z ) ) ) ],
% 1.10/1.47 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 1.10/1.47 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 1.10/1.47 ), compatible( X, Y, Z ) ],
% 1.10/1.47 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 1.10/1.47 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 1.10/1.47 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 1.10/1.47 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 1.10/1.47 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 1.10/1.47 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 1.10/1.47 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 1.10/1.47 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.10/1.47 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.10/1.47 , Y ) ],
% 1.10/1.47 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 1.10/1.47 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 1.10/1.47 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 1.10/1.47 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 1.10/1.47 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 1.10/1.47 [ =( singleton( x ), singleton( y ) ) ],
% 1.10/1.47 [ member( x, 'universal_class' ) ],
% 1.10/1.47 [ ~( =( x, y ) ) ]
% 1.10/1.47 ] .
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 percentage equality = 0.222826, percentage horn = 0.914894
% 1.10/1.47 This is a problem with some equality
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 Options Used:
% 1.10/1.47
% 1.10/1.47 useres = 1
% 1.10/1.47 useparamod = 1
% 1.10/1.47 useeqrefl = 1
% 1.10/1.47 useeqfact = 1
% 1.10/1.47 usefactor = 1
% 1.10/1.47 usesimpsplitting = 0
% 1.10/1.47 usesimpdemod = 5
% 1.10/1.47 usesimpres = 3
% 1.10/1.47
% 1.10/1.47 resimpinuse = 1000
% 1.10/1.47 resimpclauses = 20000
% 1.10/1.47 substype = eqrewr
% 1.10/1.47 backwardsubs = 1
% 1.10/1.47 selectoldest = 5
% 1.10/1.47
% 1.10/1.47 litorderings [0] = split
% 1.10/1.47 litorderings [1] = extend the termordering, first sorting on arguments
% 1.10/1.47
% 1.10/1.47 termordering = kbo
% 1.10/1.47
% 1.10/1.47 litapriori = 0
% 1.10/1.47 termapriori = 1
% 1.10/1.47 litaposteriori = 0
% 1.10/1.47 termaposteriori = 0
% 1.10/1.47 demodaposteriori = 0
% 1.10/1.47 ordereqreflfact = 0
% 1.10/1.47
% 1.10/1.47 litselect = negord
% 1.10/1.47
% 1.10/1.47 maxweight = 15
% 1.10/1.47 maxdepth = 30000
% 1.10/1.47 maxlength = 115
% 1.10/1.47 maxnrvars = 195
% 1.10/1.47 excuselevel = 1
% 1.10/1.47 increasemaxweight = 1
% 1.10/1.47
% 1.10/1.47 maxselected = 10000000
% 1.10/1.47 maxnrclauses = 10000000
% 1.10/1.47
% 1.10/1.47 showgenerated = 0
% 1.10/1.47 showkept = 0
% 1.10/1.47 showselected = 0
% 1.10/1.47 showdeleted = 0
% 1.10/1.47 showresimp = 1
% 1.10/1.47 showstatus = 2000
% 1.10/1.47
% 1.10/1.47 prologoutput = 1
% 1.10/1.47 nrgoals = 5000000
% 1.10/1.47 totalproof = 1
% 1.10/1.47
% 1.10/1.47 Symbols occurring in the translation:
% 1.10/1.47
% 1.10/1.47 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.10/1.47 . [1, 2] (w:1, o:56, a:1, s:1, b:0),
% 1.10/1.47 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 1.10/1.47 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.10/1.47 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.10/1.47 subclass [41, 2] (w:1, o:81, a:1, s:1, b:0),
% 1.10/1.47 member [43, 2] (w:1, o:82, a:1, s:1, b:0),
% 1.10/1.47 'not_subclass_element' [44, 2] (w:1, o:83, a:1, s:1, b:0),
% 1.10/1.47 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 1.10/1.47 'unordered_pair' [46, 2] (w:1, o:84, a:1, s:1, b:0),
% 1.10/1.47 singleton [47, 1] (w:1, o:39, a:1, s:1, b:0),
% 1.10/1.47 'ordered_pair' [48, 2] (w:1, o:85, a:1, s:1, b:0),
% 1.10/1.47 'cross_product' [50, 2] (w:1, o:86, a:1, s:1, b:0),
% 1.10/1.47 first [52, 1] (w:1, o:40, a:1, s:1, b:0),
% 1.10/1.47 second [53, 1] (w:1, o:41, a:1, s:1, b:0),
% 1.10/1.47 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 1.10/1.47 intersection [55, 2] (w:1, o:88, a:1, s:1, b:0),
% 1.10/1.47 complement [56, 1] (w:1, o:42, a:1, s:1, b:0),
% 1.10/1.47 union [57, 2] (w:1, o:89, a:1, s:1, b:0),
% 1.10/1.47 'symmetric_difference' [58, 2] (w:1, o:90, a:1, s:1, b:0),
% 1.10/1.47 restrict [60, 3] (w:1, o:93, a:1, s:1, b:0),
% 1.10/1.47 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.10/1.47 'domain_of' [62, 1] (w:1, o:44, a:1, s:1, b:0),
% 1.10/1.47 rotate [63, 1] (w:1, o:36, a:1, s:1, b:0),
% 1.10/1.47 flip [65, 1] (w:1, o:45, a:1, s:1, b:0),
% 1.10/1.47 inverse [66, 1] (w:1, o:46, a:1, s:1, b:0),
% 1.10/1.47 'range_of' [67, 1] (w:1, o:37, a:1, s:1, b:0),
% 1.10/1.47 domain [68, 3] (w:1, o:95, a:1, s:1, b:0),
% 1.10/1.47 range [69, 3] (w:1, o:96, a:1, s:1, b:0),
% 1.10/1.47 image [70, 2] (w:1, o:87, a:1, s:1, b:0),
% 1.10/1.47 successor [71, 1] (w:1, o:47, a:1, s:1, b:0),
% 1.10/1.47 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 1.10/1.47 inductive [73, 1] (w:1, o:48, a:1, s:1, b:0),
% 1.10/1.47 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.10/1.47 'sum_class' [75, 1] (w:1, o:49, a:1, s:1, b:0),
% 1.10/1.47 'power_class' [76, 1] (w:1, o:52, a:1, s:1, b:0),
% 1.10/1.47 compose [78, 2] (w:1, o:91, a:1, s:1, b:0),
% 1.10/1.47 'single_valued_class' [79, 1] (w:1, o:53, a:1, s:1, b:0),
% 1.10/1.47 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 1.10/1.47 function [82, 1] (w:1, o:54, a:1, s:1, b:0),
% 1.10/1.47 regular [83, 1] (w:1, o:38, a:1, s:1, b:0),
% 1.10/1.47 apply [84, 2] (w:1, o:92, a:1, s:1, b:0),
% 1.10/1.47 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.10/1.47 'one_to_one' [86, 1] (w:1, o:50, a:1, s:1, b:0),
% 1.10/1.47 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 1.10/1.47 diagonalise [88, 1] (w:1, o:55, a:1, s:1, b:0),
% 1.10/1.47 cantor [89, 1] (w:1, o:43, a:1, s:1, b:0),
% 1.10/1.47 operation [90, 1] (w:1, o:51, a:1, s:1, b:0),
% 1.10/1.47 compatible [94, 3] (w:1, o:94, a:1, s:1, b:0),
% 1.10/1.47 homomorphism [95, 3] (w:1, o:97, a:1, s:1, b:0),
% 1.10/1.47 'not_homomorphism1' [96, 3] (w:1, o:98, a:1, s:1, b:0),
% 1.10/1.47 'not_homomorphism2' [97, 3] (w:1, o:99, a:1, s:1, b:0),
% 1.10/1.47 x [98, 0] (w:1, o:29, a:1, s:1, b:0),
% 1.10/1.47 y [99, 0] (w:1, o:30, a:1, s:1, b:0).
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 Starting Search:
% 1.10/1.47
% 1.10/1.47 Resimplifying inuse:
% 1.10/1.47 Done
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 Intermediate Status:
% 1.10/1.47 Generated: 5110
% 1.10/1.47 Kept: 2009
% 1.10/1.47 Inuse: 108
% 1.10/1.47 Deleted: 6
% 1.10/1.47 Deletedinuse: 2
% 1.10/1.47
% 1.10/1.47 Resimplifying inuse:
% 1.10/1.47 Done
% 1.10/1.47
% 1.10/1.47 Resimplifying inuse:
% 1.10/1.47 Done
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 Intermediate Status:
% 1.10/1.47 Generated: 9959
% 1.10/1.47 Kept: 4045
% 1.10/1.47 Inuse: 188
% 1.10/1.47 Deleted: 17
% 1.10/1.47 Deletedinuse: 7
% 1.10/1.47
% 1.10/1.47 Resimplifying inuse:
% 1.10/1.47 Done
% 1.10/1.47
% 1.10/1.47 Resimplifying inuse:
% 1.10/1.47 Done
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 Intermediate Status:
% 1.10/1.47 Generated: 14121
% 1.10/1.47 Kept: 6048
% 1.10/1.47 Inuse: 246
% 1.10/1.47 Deleted: 25
% 1.10/1.47 Deletedinuse: 10
% 1.10/1.47
% 1.10/1.47 Resimplifying inuse:
% 1.10/1.47 Done
% 1.10/1.47
% 1.10/1.47 Resimplifying inuse:
% 1.10/1.47 Done
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 Intermediate Status:
% 1.10/1.47 Generated: 19336
% 1.10/1.47 Kept: 8067
% 1.10/1.47 Inuse: 298
% 1.10/1.47 Deleted: 45
% 1.10/1.47 Deletedinuse: 27
% 1.10/1.47
% 1.10/1.47 Resimplifying inuse:
% 1.10/1.47 Done
% 1.10/1.47
% 1.10/1.47 Resimplifying inuse:
% 1.10/1.47 Done
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 Bliksems!, er is een bewijs:
% 1.10/1.47 % SZS status Unsatisfiable
% 1.10/1.47 % SZS output start Refutation
% 1.10/1.47
% 1.10/1.47 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.10/1.47 .
% 1.10/1.47 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 1.10/1.47 .
% 1.10/1.47 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z
% 1.10/1.47 ) ] )
% 1.10/1.47 .
% 1.10/1.47 clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.10/1.47 'unordered_pair'( Y, X ) ) ] )
% 1.10/1.47 .
% 1.10/1.47 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.10/1.47 .
% 1.10/1.47 clause( 90, [ =( singleton( y ), singleton( x ) ) ] )
% 1.10/1.47 .
% 1.10/1.47 clause( 91, [ member( x, 'universal_class' ) ] )
% 1.10/1.47 .
% 1.10/1.47 clause( 92, [ ~( =( y, x ) ) ] )
% 1.10/1.47 .
% 1.10/1.47 clause( 94, [ =( X, Y ), ~( member( X, singleton( Y ) ) ) ] )
% 1.10/1.47 .
% 1.10/1.47 clause( 123, [ =( X, Y ), ~( =( Y, X ) ) ] )
% 1.10/1.47 .
% 1.10/1.47 clause( 171, [ ~( =( X, x ) ), ~( =( X, y ) ) ] )
% 1.10/1.47 .
% 1.10/1.47 clause( 444, [ member( x, 'unordered_pair'( X, x ) ) ] )
% 1.10/1.47 .
% 1.10/1.47 clause( 492, [ member( x, singleton( x ) ) ] )
% 1.10/1.47 .
% 1.10/1.47 clause( 10524, [ ~( =( Y, X ) ), ~( =( Y, y ) ), ~( member( x, singleton( X
% 1.10/1.47 ) ) ) ] )
% 1.10/1.47 .
% 1.10/1.47 clause( 10662, [ ~( =( X, y ) ) ] )
% 1.10/1.47 .
% 1.10/1.47 clause( 10663, [] )
% 1.10/1.47 .
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 % SZS output end Refutation
% 1.10/1.47 found a proof!
% 1.10/1.47
% 1.10/1.47 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.10/1.47
% 1.10/1.47 initialclauses(
% 1.10/1.47 [ clause( 10665, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.10/1.47 ) ] )
% 1.10/1.47 , clause( 10666, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 1.10/1.47 , Y ) ] )
% 1.10/1.47 , clause( 10667, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 1.10/1.47 subclass( X, Y ) ] )
% 1.10/1.47 , clause( 10668, [ subclass( X, 'universal_class' ) ] )
% 1.10/1.47 , clause( 10669, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.10/1.47 , clause( 10670, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 1.10/1.47 , clause( 10671, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 1.10/1.47 ] )
% 1.10/1.47 , clause( 10672, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 1.10/1.47 =( X, Z ) ] )
% 1.10/1.47 , clause( 10673, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.10/1.47 'unordered_pair'( X, Y ) ) ] )
% 1.10/1.47 , clause( 10674, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.10/1.47 'unordered_pair'( Y, X ) ) ] )
% 1.10/1.47 , clause( 10675, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 1.10/1.47 )
% 1.10/1.47 , clause( 10676, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.10/1.47 , clause( 10677, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 1.10/1.47 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.10/1.47 , clause( 10678, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.10/1.47 ) ) ), member( X, Z ) ] )
% 1.10/1.47 , clause( 10679, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.10/1.47 ) ) ), member( Y, T ) ] )
% 1.10/1.47 , clause( 10680, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.10/1.47 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.10/1.47 , clause( 10681, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 1.10/1.47 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 1.10/1.47 , clause( 10682, [ subclass( 'element_relation', 'cross_product'(
% 1.10/1.47 'universal_class', 'universal_class' ) ) ] )
% 1.10/1.47 , clause( 10683, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 1.10/1.47 ), member( X, Y ) ] )
% 1.10/1.47 , clause( 10684, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.10/1.47 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 1.10/1.47 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 1.10/1.47 , clause( 10685, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.10/1.47 )
% 1.10/1.47 , clause( 10686, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 1.10/1.47 )
% 1.10/1.47 , clause( 10687, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 1.10/1.47 intersection( Y, Z ) ) ] )
% 1.10/1.47 , clause( 10688, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 1.10/1.47 )
% 1.10/1.47 , clause( 10689, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.10/1.47 complement( Y ) ), member( X, Y ) ] )
% 1.10/1.47 , clause( 10690, [ =( complement( intersection( complement( X ), complement(
% 1.10/1.47 Y ) ) ), union( X, Y ) ) ] )
% 1.10/1.47 , clause( 10691, [ =( intersection( complement( intersection( X, Y ) ),
% 1.10/1.47 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 1.10/1.47 'symmetric_difference'( X, Y ) ) ] )
% 1.10/1.47 , clause( 10692, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 1.10/1.47 X, Y, Z ) ) ] )
% 1.10/1.47 , clause( 10693, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 1.10/1.47 Z, X, Y ) ) ] )
% 1.10/1.47 , clause( 10694, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 1.10/1.47 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 1.10/1.47 , clause( 10695, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 1.10/1.47 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 1.10/1.47 'domain_of'( Y ) ) ] )
% 1.10/1.47 , clause( 10696, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 1.10/1.47 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.10/1.47 , clause( 10697, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.10/1.47 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 1.10/1.47 ] )
% 1.10/1.47 , clause( 10698, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.10/1.47 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 1.10/1.47 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.10/1.47 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 1.10/1.47 , Y ), rotate( T ) ) ] )
% 1.10/1.47 , clause( 10699, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 1.10/1.47 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.10/1.47 , clause( 10700, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.10/1.47 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 1.10/1.47 )
% 1.10/1.47 , clause( 10701, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.10/1.47 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 1.10/1.47 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.10/1.47 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 1.10/1.47 , Z ), flip( T ) ) ] )
% 1.10/1.47 , clause( 10702, [ =( 'domain_of'( flip( 'cross_product'( X,
% 1.10/1.47 'universal_class' ) ) ), inverse( X ) ) ] )
% 1.10/1.47 , clause( 10703, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 1.10/1.47 , clause( 10704, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 1.10/1.47 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 1.10/1.47 , clause( 10705, [ =( second( 'not_subclass_element'( restrict( X,
% 1.10/1.47 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 1.10/1.47 , clause( 10706, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 1.10/1.47 image( X, Y ) ) ] )
% 1.10/1.47 , clause( 10707, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 1.10/1.47 , clause( 10708, [ subclass( 'successor_relation', 'cross_product'(
% 1.10/1.47 'universal_class', 'universal_class' ) ) ] )
% 1.10/1.47 , clause( 10709, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 1.10/1.47 ) ), =( successor( X ), Y ) ] )
% 1.10/1.47 , clause( 10710, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 1.10/1.47 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 1.10/1.47 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 1.10/1.47 , clause( 10711, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 1.10/1.47 , clause( 10712, [ ~( inductive( X ) ), subclass( image(
% 1.10/1.47 'successor_relation', X ), X ) ] )
% 1.10/1.47 , clause( 10713, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 1.10/1.47 'successor_relation', X ), X ) ), inductive( X ) ] )
% 1.10/1.47 , clause( 10714, [ inductive( omega ) ] )
% 1.10/1.47 , clause( 10715, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 1.10/1.47 , clause( 10716, [ member( omega, 'universal_class' ) ] )
% 1.10/1.47 , clause( 10717, [ =( 'domain_of'( restrict( 'element_relation',
% 1.10/1.47 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 1.10/1.47 , clause( 10718, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 1.10/1.47 X ), 'universal_class' ) ] )
% 1.10/1.47 , clause( 10719, [ =( complement( image( 'element_relation', complement( X
% 1.10/1.47 ) ) ), 'power_class'( X ) ) ] )
% 1.10/1.47 , clause( 10720, [ ~( member( X, 'universal_class' ) ), member(
% 1.10/1.47 'power_class'( X ), 'universal_class' ) ] )
% 1.10/1.47 , clause( 10721, [ subclass( compose( X, Y ), 'cross_product'(
% 1.10/1.47 'universal_class', 'universal_class' ) ) ] )
% 1.10/1.47 , clause( 10722, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 1.10/1.47 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 1.10/1.47 , clause( 10723, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 1.10/1.47 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 1.10/1.47 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 1.10/1.47 ) ] )
% 1.10/1.47 , clause( 10724, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 1.10/1.47 inverse( X ) ), 'identity_relation' ) ] )
% 1.10/1.47 , clause( 10725, [ ~( subclass( compose( X, inverse( X ) ),
% 1.10/1.47 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 1.10/1.47 , clause( 10726, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 1.10/1.47 'universal_class', 'universal_class' ) ) ] )
% 1.10/1.47 , clause( 10727, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 1.10/1.47 , 'identity_relation' ) ] )
% 1.10/1.47 , clause( 10728, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 1.10/1.47 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 1.10/1.47 'identity_relation' ) ), function( X ) ] )
% 1.10/1.47 , clause( 10729, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 1.10/1.47 , member( image( X, Y ), 'universal_class' ) ] )
% 1.10/1.47 , clause( 10730, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.10/1.47 , clause( 10731, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 1.10/1.47 , 'null_class' ) ] )
% 1.10/1.47 , clause( 10732, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 1.10/1.47 Y ) ) ] )
% 1.10/1.47 , clause( 10733, [ function( choice ) ] )
% 1.10/1.47 , clause( 10734, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 1.10/1.47 ), member( apply( choice, X ), X ) ] )
% 1.10/1.47 , clause( 10735, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 1.10/1.47 , clause( 10736, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 1.10/1.47 , clause( 10737, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 1.10/1.47 'one_to_one'( X ) ] )
% 1.10/1.47 , clause( 10738, [ =( intersection( 'cross_product'( 'universal_class',
% 1.10/1.47 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 1.10/1.47 'universal_class' ), complement( compose( complement( 'element_relation'
% 1.10/1.47 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 1.10/1.47 , clause( 10739, [ =( intersection( inverse( 'subset_relation' ),
% 1.10/1.47 'subset_relation' ), 'identity_relation' ) ] )
% 1.10/1.47 , clause( 10740, [ =( complement( 'domain_of'( intersection( X,
% 1.10/1.47 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 1.10/1.47 , clause( 10741, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 1.10/1.47 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 1.10/1.47 , clause( 10742, [ ~( operation( X ) ), function( X ) ] )
% 1.10/1.47 , clause( 10743, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 1.10/1.47 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.10/1.47 ] )
% 1.10/1.47 , clause( 10744, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 1.10/1.47 'domain_of'( 'domain_of'( X ) ) ) ] )
% 1.10/1.47 , clause( 10745, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 1.10/1.47 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.10/1.47 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 1.10/1.47 operation( X ) ] )
% 1.10/1.47 , clause( 10746, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 1.10/1.47 , clause( 10747, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 1.10/1.47 Y ) ), 'domain_of'( X ) ) ] )
% 1.10/1.47 , clause( 10748, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 1.10/1.47 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 1.10/1.47 , clause( 10749, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 1.10/1.47 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 1.10/1.47 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 1.10/1.47 , clause( 10750, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 1.10/1.47 , clause( 10751, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 1.10/1.47 , clause( 10752, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 1.10/1.47 , clause( 10753, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 1.10/1.47 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 1.10/1.47 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 1.10/1.47 )
% 1.10/1.47 , clause( 10754, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.10/1.47 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.10/1.47 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.10/1.47 , Y ) ] )
% 1.10/1.47 , clause( 10755, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.10/1.47 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 1.10/1.47 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 1.10/1.47 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 1.10/1.47 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 1.10/1.47 )
% 1.10/1.47 , clause( 10756, [ =( singleton( x ), singleton( y ) ) ] )
% 1.10/1.47 , clause( 10757, [ member( x, 'universal_class' ) ] )
% 1.10/1.47 , clause( 10758, [ ~( =( x, y ) ) ] )
% 1.10/1.47 ] ).
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 subsumption(
% 1.10/1.47 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.10/1.47 , clause( 10669, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.10/1.47 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.10/1.47 ), ==>( 1, 1 )] ) ).
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 subsumption(
% 1.10/1.47 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 1.10/1.47 , clause( 10671, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 1.10/1.47 ] )
% 1.10/1.47 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.10/1.47 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 subsumption(
% 1.10/1.47 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z
% 1.10/1.47 ) ] )
% 1.10/1.47 , clause( 10672, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 1.10/1.47 =( X, Z ) ] )
% 1.10/1.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.10/1.47 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 subsumption(
% 1.10/1.47 clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.10/1.47 'unordered_pair'( Y, X ) ) ] )
% 1.10/1.47 , clause( 10674, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.10/1.47 'unordered_pair'( Y, X ) ) ] )
% 1.10/1.47 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.10/1.47 ), ==>( 1, 1 )] ) ).
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 subsumption(
% 1.10/1.47 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.10/1.47 , clause( 10676, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.10/1.47 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 eqswap(
% 1.10/1.47 clause( 10838, [ =( singleton( y ), singleton( x ) ) ] )
% 1.10/1.47 , clause( 10756, [ =( singleton( x ), singleton( y ) ) ] )
% 1.10/1.47 , 0, substitution( 0, [] )).
% 1.10/1.47
% 1.10/1.47
% 1.10/1.47 subsumption(
% 1.10/1.47 clause( 90, [ =( singleton( y ), singleton( x ) ) ] )
% 1.10/1.47 , clause( 10838, [ =( singleton( y ), singleton( x ) ) ] )
% 1.10/1.47 , substitution( 0, [] ), permuCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------