TSTP Solution File: SET085-6 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET085-6 : 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 22:46:48 EDT 2022
% Result : Unsatisfiable 3.05s 3.46s
% Output : Refutation 3.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET085-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sun Jul 10 11:26:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/1.09 *** allocated 10000 integers for termspace/termends
% 0.42/1.09 *** allocated 10000 integers for clauses
% 0.42/1.09 *** allocated 10000 integers for justifications
% 0.42/1.09 Bliksem 1.12
% 0.42/1.09
% 0.42/1.09
% 0.42/1.09 Automatic Strategy Selection
% 0.42/1.09
% 0.42/1.09 Clauses:
% 0.42/1.09 [
% 0.42/1.09 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.42/1.09 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.42/1.09 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.42/1.09 ,
% 0.42/1.09 [ subclass( X, 'universal_class' ) ],
% 0.42/1.09 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.42/1.09 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.42/1.09 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.42/1.09 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.42/1.09 ,
% 0.42/1.09 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.42/1.09 ) ) ],
% 0.42/1.09 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.42/1.09 ) ) ],
% 0.42/1.09 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.42/1.09 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.42/1.09 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.42/1.09 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.42/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.42/1.09 X, Z ) ],
% 0.42/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.42/1.09 Y, T ) ],
% 0.42/1.09 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.42/1.09 ), 'cross_product'( Y, T ) ) ],
% 0.42/1.09 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.42/1.09 ), second( X ) ), X ) ],
% 0.42/1.09 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.42/1.09 'universal_class' ) ) ],
% 0.42/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.42/1.09 Y ) ],
% 0.42/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.42/1.09 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.42/1.09 , Y ), 'element_relation' ) ],
% 0.42/1.09 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.42/1.09 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.42/1.09 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.42/1.09 Z ) ) ],
% 0.42/1.09 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.42/1.09 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.42/1.09 member( X, Y ) ],
% 0.42/1.09 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.42/1.09 union( X, Y ) ) ],
% 0.42/1.09 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.42/1.09 intersection( complement( X ), complement( Y ) ) ) ),
% 0.42/1.09 'symmetric_difference'( X, Y ) ) ],
% 0.42/1.09 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.42/1.09 ,
% 0.42/1.09 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.42/1.09 ,
% 0.42/1.09 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.42/1.09 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.42/1.09 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.42/1.09 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.42/1.09 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.42/1.09 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.42/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.42/1.09 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.42/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.42/1.09 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.42/1.09 'cross_product'( 'universal_class', 'universal_class' ),
% 0.42/1.09 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.42/1.09 Y ), rotate( T ) ) ],
% 0.42/1.09 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.42/1.09 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.42/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.42/1.09 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.42/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.42/1.09 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.42/1.09 'cross_product'( 'universal_class', 'universal_class' ),
% 0.42/1.09 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.42/1.09 Z ), flip( T ) ) ],
% 0.42/1.09 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.42/1.09 inverse( X ) ) ],
% 0.42/1.09 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.42/1.09 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.42/1.09 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.42/1.09 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.42/1.09 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.42/1.09 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.42/1.09 ],
% 0.42/1.09 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.42/1.09 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.42/1.09 'universal_class' ) ) ],
% 0.42/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.42/1.09 successor( X ), Y ) ],
% 0.42/1.09 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.42/1.09 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.42/1.09 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.42/1.09 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.42/1.09 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.42/1.09 ,
% 0.42/1.09 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.42/1.09 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.42/1.09 [ inductive( omega ) ],
% 0.42/1.09 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.42/1.09 [ member( omega, 'universal_class' ) ],
% 0.42/1.09 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.42/1.09 , 'sum_class'( X ) ) ],
% 0.42/1.09 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.42/1.09 'universal_class' ) ],
% 0.42/1.09 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.42/1.09 'power_class'( X ) ) ],
% 0.42/1.09 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.42/1.09 'universal_class' ) ],
% 0.42/1.09 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.42/1.09 'universal_class' ) ) ],
% 0.42/1.09 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.42/1.09 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.42/1.09 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.42/1.09 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.42/1.09 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.42/1.09 ) ],
% 0.42/1.09 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.42/1.09 , 'identity_relation' ) ],
% 0.42/1.09 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.42/1.09 'single_valued_class'( X ) ],
% 0.42/1.09 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.42/1.09 'universal_class' ) ) ],
% 0.42/1.09 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.42/1.09 'identity_relation' ) ],
% 0.42/1.09 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.42/1.09 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.42/1.09 , function( X ) ],
% 0.42/1.09 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.42/1.09 X, Y ), 'universal_class' ) ],
% 0.42/1.09 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.42/1.09 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.42/1.09 ) ],
% 0.42/1.09 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.42/1.09 [ function( choice ) ],
% 0.42/1.09 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.42/1.09 apply( choice, X ), X ) ],
% 0.42/1.09 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.42/1.09 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.42/1.09 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.42/1.09 ,
% 0.42/1.09 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.42/1.09 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.42/1.09 , complement( compose( complement( 'element_relation' ), inverse(
% 0.42/1.09 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.42/1.09 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.42/1.09 'identity_relation' ) ],
% 0.42/1.09 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.42/1.09 , diagonalise( X ) ) ],
% 0.42/1.09 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.42/1.09 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.42/1.09 [ ~( operation( X ) ), function( X ) ],
% 0.42/1.09 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.42/1.09 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.42/1.09 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 3.05/3.45 'domain_of'( X ) ) ) ],
% 3.05/3.45 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 3.05/3.45 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 3.05/3.45 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 3.05/3.45 X ) ],
% 3.05/3.45 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 3.05/3.45 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 3.05/3.45 'domain_of'( X ) ) ],
% 3.05/3.45 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 3.05/3.45 'domain_of'( Z ) ) ) ],
% 3.05/3.45 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 3.05/3.45 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 3.05/3.45 ), compatible( X, Y, Z ) ],
% 3.05/3.45 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 3.05/3.45 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 3.05/3.45 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 3.05/3.45 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 3.05/3.45 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 3.05/3.45 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 3.05/3.45 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 3.05/3.45 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 3.05/3.45 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 3.05/3.45 , Y ) ],
% 3.05/3.45 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 3.05/3.45 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 3.05/3.45 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 3.05/3.45 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 3.05/3.45 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 3.05/3.45 [ =( 'unordered_pair'( y, z ), singleton( x ) ) ],
% 3.05/3.45 [ member( x, 'universal_class' ) ],
% 3.05/3.45 [ ~( =( x, y ) ) ],
% 3.05/3.45 [ ~( =( x, z ) ) ]
% 3.05/3.45 ] .
% 3.05/3.45
% 3.05/3.45
% 3.05/3.45 percentage equality = 0.227027, percentage horn = 0.915789
% 3.05/3.45 This is a problem with some equality
% 3.05/3.45
% 3.05/3.45
% 3.05/3.45
% 3.05/3.45 Options Used:
% 3.05/3.45
% 3.05/3.45 useres = 1
% 3.05/3.45 useparamod = 1
% 3.05/3.45 useeqrefl = 1
% 3.05/3.45 useeqfact = 1
% 3.05/3.45 usefactor = 1
% 3.05/3.45 usesimpsplitting = 0
% 3.05/3.45 usesimpdemod = 5
% 3.05/3.45 usesimpres = 3
% 3.05/3.45
% 3.05/3.45 resimpinuse = 1000
% 3.05/3.45 resimpclauses = 20000
% 3.05/3.45 substype = eqrewr
% 3.05/3.45 backwardsubs = 1
% 3.05/3.45 selectoldest = 5
% 3.05/3.45
% 3.05/3.45 litorderings [0] = split
% 3.05/3.45 litorderings [1] = extend the termordering, first sorting on arguments
% 3.05/3.45
% 3.05/3.45 termordering = kbo
% 3.05/3.45
% 3.05/3.45 litapriori = 0
% 3.05/3.45 termapriori = 1
% 3.05/3.45 litaposteriori = 0
% 3.05/3.45 termaposteriori = 0
% 3.05/3.45 demodaposteriori = 0
% 3.05/3.45 ordereqreflfact = 0
% 3.05/3.45
% 3.05/3.45 litselect = negord
% 3.05/3.45
% 3.05/3.45 maxweight = 15
% 3.05/3.45 maxdepth = 30000
% 3.05/3.45 maxlength = 115
% 3.05/3.45 maxnrvars = 195
% 3.05/3.45 excuselevel = 1
% 3.05/3.45 increasemaxweight = 1
% 3.05/3.45
% 3.05/3.45 maxselected = 10000000
% 3.05/3.45 maxnrclauses = 10000000
% 3.05/3.45
% 3.05/3.45 showgenerated = 0
% 3.05/3.45 showkept = 0
% 3.05/3.45 showselected = 0
% 3.05/3.45 showdeleted = 0
% 3.05/3.45 showresimp = 1
% 3.05/3.45 showstatus = 2000
% 3.05/3.45
% 3.05/3.45 prologoutput = 1
% 3.05/3.45 nrgoals = 5000000
% 3.05/3.45 totalproof = 1
% 3.05/3.45
% 3.05/3.45 Symbols occurring in the translation:
% 3.05/3.45
% 3.05/3.45 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 3.05/3.45 . [1, 2] (w:1, o:57, a:1, s:1, b:0),
% 3.05/3.45 ! [4, 1] (w:0, o:32, a:1, s:1, b:0),
% 3.05/3.45 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.05/3.45 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.05/3.45 subclass [41, 2] (w:1, o:82, a:1, s:1, b:0),
% 3.05/3.45 member [43, 2] (w:1, o:83, a:1, s:1, b:0),
% 3.05/3.45 'not_subclass_element' [44, 2] (w:1, o:84, a:1, s:1, b:0),
% 3.05/3.45 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 3.05/3.45 'unordered_pair' [46, 2] (w:1, o:85, a:1, s:1, b:0),
% 3.05/3.45 singleton [47, 1] (w:1, o:40, a:1, s:1, b:0),
% 3.05/3.45 'ordered_pair' [48, 2] (w:1, o:86, a:1, s:1, b:0),
% 3.05/3.45 'cross_product' [50, 2] (w:1, o:87, a:1, s:1, b:0),
% 3.05/3.45 first [52, 1] (w:1, o:41, a:1, s:1, b:0),
% 3.05/3.45 second [53, 1] (w:1, o:42, a:1, s:1, b:0),
% 3.05/3.45 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 3.05/3.45 intersection [55, 2] (w:1, o:89, a:1, s:1, b:0),
% 3.05/3.45 complement [56, 1] (w:1, o:43, a:1, s:1, b:0),
% 3.05/3.45 union [57, 2] (w:1, o:90, a:1, s:1, b:0),
% 3.05/3.45 'symmetric_difference' [58, 2] (w:1, o:91, a:1, s:1, b:0),
% 3.05/3.45 restrict [60, 3] (w:1, o:94, a:1, s:1, b:0),
% 3.05/3.45 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 3.05/3.45 'domain_of' [62, 1] (w:1, o:45, a:1, s:1, b:0),
% 3.05/3.45 rotate [63, 1] (w:1, o:37, a:1, s:1, b:0),
% 3.05/3.45 flip [65, 1] (w:1, o:46, a:1, s:1, b:0),
% 3.05/3.45 inverse [66, 1] (w:1, o:47, a:1, s:1, b:0),
% 3.05/3.45 'range_of' [67, 1] (w:1, o:38, a:1, s:1, b:0),
% 3.05/3.45 domain [68, 3] (w:1, o:96, a:1, s:1, b:0),
% 3.05/3.45 range [69, 3] (w:1, o:97, a:1, s:1, b:0),
% 3.05/3.45 image [70, 2] (w:1, o:88, a:1, s:1, b:0),
% 3.05/3.45 successor [71, 1] (w:1, o:48, a:1, s:1, b:0),
% 3.05/3.45 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 3.05/3.45 inductive [73, 1] (w:1, o:49, a:1, s:1, b:0),
% 3.05/3.45 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 3.05/3.45 'sum_class' [75, 1] (w:1, o:50, a:1, s:1, b:0),
% 3.05/3.45 'power_class' [76, 1] (w:1, o:53, a:1, s:1, b:0),
% 3.05/3.45 compose [78, 2] (w:1, o:92, a:1, s:1, b:0),
% 3.05/3.45 'single_valued_class' [79, 1] (w:1, o:54, a:1, s:1, b:0),
% 3.05/3.45 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 3.05/3.45 function [82, 1] (w:1, o:55, a:1, s:1, b:0),
% 3.05/3.45 regular [83, 1] (w:1, o:39, a:1, s:1, b:0),
% 3.05/3.45 apply [84, 2] (w:1, o:93, a:1, s:1, b:0),
% 3.05/3.45 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 3.05/3.45 'one_to_one' [86, 1] (w:1, o:51, a:1, s:1, b:0),
% 3.05/3.45 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 3.05/3.45 diagonalise [88, 1] (w:1, o:56, a:1, s:1, b:0),
% 3.05/3.45 cantor [89, 1] (w:1, o:44, a:1, s:1, b:0),
% 3.05/3.45 operation [90, 1] (w:1, o:52, a:1, s:1, b:0),
% 3.05/3.45 compatible [94, 3] (w:1, o:95, a:1, s:1, b:0),
% 3.05/3.45 homomorphism [95, 3] (w:1, o:98, a:1, s:1, b:0),
% 3.05/3.45 'not_homomorphism1' [96, 3] (w:1, o:99, a:1, s:1, b:0),
% 3.05/3.45 'not_homomorphism2' [97, 3] (w:1, o:100, a:1, s:1, b:0),
% 3.05/3.45 y [98, 0] (w:1, o:30, a:1, s:1, b:0),
% 3.05/3.45 z [99, 0] (w:1, o:31, a:1, s:1, b:0),
% 3.05/3.45 x [100, 0] (w:1, o:29, a:1, s:1, b:0).
% 3.05/3.45
% 3.05/3.45
% 3.05/3.45 Starting Search:
% 3.05/3.45
% 3.05/3.45 Resimplifying inuse:
% 3.05/3.45 Done
% 3.05/3.45
% 3.05/3.45
% 3.05/3.45 Intermediate Status:
% 3.05/3.45 Generated: 5137
% 3.05/3.45 Kept: 2011
% 3.05/3.45 Inuse: 109
% 3.05/3.45 Deleted: 6
% 3.05/3.45 Deletedinuse: 2
% 3.05/3.45
% 3.05/3.45 Resimplifying inuse:
% 3.05/3.45 Done
% 3.05/3.45
% 3.05/3.45 Resimplifying inuse:
% 3.05/3.45 Done
% 3.05/3.45
% 3.05/3.45
% 3.05/3.45 Intermediate Status:
% 3.05/3.45 Generated: 9991
% 3.05/3.45 Kept: 4016
% 3.05/3.45 Inuse: 187
% 3.05/3.45 Deleted: 17
% 3.05/3.45 Deletedinuse: 7
% 3.05/3.45
% 3.05/3.45 Resimplifying inuse:
% 3.05/3.45 Done
% 3.05/3.45
% 3.05/3.45 Resimplifying inuse:
% 3.05/3.45 Done
% 3.05/3.45
% 3.05/3.45
% 3.05/3.45 Intermediate Status:
% 3.05/3.45 Generated: 13945
% 3.05/3.45 Kept: 6048
% 3.05/3.45 Inuse: 238
% 3.05/3.45 Deleted: 21
% 3.05/3.45 Deletedinuse: 8
% 3.05/3.45
% 3.05/3.45 Resimplifying inuse:
% 3.05/3.45 Done
% 3.05/3.45
% 3.05/3.45 Resimplifying inuse:
% 3.05/3.45 Done
% 3.05/3.45
% 3.05/3.45
% 3.05/3.45 Intermediate Status:
% 3.05/3.45 Generated: 18779
% 3.05/3.45 Kept: 8127
% 3.05/3.45 Inuse: 286
% 3.05/3.45 Deleted: 50
% 3.05/3.45 Deletedinuse: 35
% 3.05/3.45
% 3.05/3.45 Resimplifying inuse:
% 3.05/3.45 Done
% 3.05/3.45
% 3.05/3.45 Resimplifying inuse:
% 3.05/3.45 Done
% 3.05/3.45
% 3.05/3.45
% 3.05/3.45 Intermediate Status:
% 3.05/3.45 Generated: 25559
% 3.05/3.45 Kept: 11147
% 3.05/3.45 Inuse: 364
% 3.05/3.45 Deleted: 70
% 3.05/3.45 Deletedinuse: 53
% 3.05/3.45
% 3.05/3.45 Resimplifying inuse:
% 3.05/3.45 Done
% 3.05/3.45
% 3.05/3.45 Resimplifying inuse:
% 3.05/3.45 Done
% 3.05/3.45
% 3.05/3.45
% 3.05/3.45 Intermediate Status:
% 3.05/3.45 Generated: 32203
% 3.05/3.45 Kept: 13449
% 3.05/3.45 Inuse: 374
% 3.05/3.45 Deleted: 76
% 3.05/3.45 Deletedinuse: 59
% 3.05/3.45
% 3.05/3.45 Resimplifying inuse:
% 3.05/3.45 Done
% 3.05/3.45
% 3.05/3.45 Resimplifying inuse:
% 3.05/3.45 Done
% 3.05/3.45
% 3.05/3.45
% 3.05/3.45 Intermediate Status:
% 3.05/3.45 Generated: 37512
% 3.05/3.45 Kept: 15493
% 3.05/3.45 Inuse: 427
% 3.05/3.45 Deleted: 76
% 3.05/3.45 Deletedinuse: 59
% 3.05/3.45
% 3.05/3.45 Resimplifying inuse:
% 3.05/3.45 Done
% 3.05/3.45
% 3.05/3.45 Resimplifying inuse:
% 3.05/3.45 Done
% 3.05/3.45
% 3.05/3.45
% 3.05/3.45 Intermediate Status:
% 3.05/3.45 Generated: 44518
% 3.05/3.45 Kept: 18127
% 3.05/3.45 Inuse: 484
% 3.05/3.45 Deleted: 78
% 3.05/3.46 Deletedinuse: 61
% 3.05/3.46
% 3.05/3.46 Resimplifying inuse:
% 3.05/3.46 Done
% 3.05/3.46
% 3.05/3.46 Resimplifying inuse:
% 3.05/3.46 Done
% 3.05/3.46
% 3.05/3.46 Resimplifying clauses:
% 3.05/3.46 Done
% 3.05/3.46
% 3.05/3.46
% 3.05/3.46 Bliksems!, er is een bewijs:
% 3.05/3.46 % SZS status Unsatisfiable
% 3.05/3.46 % SZS output start Refutation
% 3.05/3.46
% 3.05/3.46 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z
% 3.05/3.46 ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 3.05/3.46 'unordered_pair'( Y, X ) ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 90, [ =( 'unordered_pair'( y, z ), singleton( x ) ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 91, [ member( x, 'universal_class' ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 92, [ ~( =( y, x ) ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 93, [ ~( =( z, x ) ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 95, [ =( X, Y ), ~( member( X, singleton( Y ) ) ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 124, [ =( X, Y ), ~( =( Y, X ) ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 172, [ ~( =( X, x ) ), ~( =( X, y ) ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 173, [ ~( =( X, x ) ), ~( =( X, z ) ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 434, [ member( x, 'unordered_pair'( X, x ) ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 482, [ member( x, singleton( x ) ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 3196, [ ~( member( X, singleton( x ) ) ), =( X, y ), =( X, z ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 9958, [ ~( member( X, singleton( x ) ) ), ~( =( X, z ) ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 9960, [ ~( member( X, singleton( x ) ) ), ~( =( X, y ) ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 20086, [ ~( member( X, singleton( x ) ) ) ] )
% 3.05/3.46 .
% 3.05/3.46 clause( 20105, [] )
% 3.05/3.46 .
% 3.05/3.46
% 3.05/3.46
% 3.05/3.46 % SZS output end Refutation
% 3.05/3.46 found a proof!
% 3.05/3.46
% 3.05/3.46 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 3.05/3.46
% 3.05/3.46 initialclauses(
% 3.05/3.46 [ clause( 20107, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 3.05/3.46 ) ] )
% 3.05/3.46 , clause( 20108, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 3.05/3.46 , Y ) ] )
% 3.05/3.46 , clause( 20109, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 3.05/3.46 subclass( X, Y ) ] )
% 3.05/3.46 , clause( 20110, [ subclass( X, 'universal_class' ) ] )
% 3.05/3.46 , clause( 20111, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 3.05/3.46 , clause( 20112, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 3.05/3.46 , clause( 20113, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 3.05/3.46 ] )
% 3.05/3.46 , clause( 20114, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 3.05/3.46 =( X, Z ) ] )
% 3.05/3.46 , clause( 20115, [ ~( member( X, 'universal_class' ) ), member( X,
% 3.05/3.46 'unordered_pair'( X, Y ) ) ] )
% 3.05/3.46 , clause( 20116, [ ~( member( X, 'universal_class' ) ), member( X,
% 3.05/3.46 'unordered_pair'( Y, X ) ) ] )
% 3.05/3.46 , clause( 20117, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 3.05/3.46 )
% 3.05/3.46 , clause( 20118, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 3.05/3.46 , clause( 20119, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 3.05/3.46 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 3.05/3.46 , clause( 20120, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 3.05/3.46 ) ) ), member( X, Z ) ] )
% 3.05/3.46 , clause( 20121, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 3.05/3.46 ) ) ), member( Y, T ) ] )
% 3.05/3.46 , clause( 20122, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 3.05/3.46 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 3.05/3.46 , clause( 20123, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 3.05/3.46 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 3.05/3.46 , clause( 20124, [ subclass( 'element_relation', 'cross_product'(
% 3.05/3.46 'universal_class', 'universal_class' ) ) ] )
% 3.05/3.46 , clause( 20125, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 3.05/3.46 ), member( X, Y ) ] )
% 3.05/3.46 , clause( 20126, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 3.05/3.46 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 3.05/3.46 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 3.05/3.46 , clause( 20127, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 3.05/3.46 )
% 3.05/3.46 , clause( 20128, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 3.05/3.46 )
% 3.05/3.46 , clause( 20129, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 3.05/3.46 intersection( Y, Z ) ) ] )
% 3.05/3.46 , clause( 20130, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 3.05/3.46 )
% 3.05/3.46 , clause( 20131, [ ~( member( X, 'universal_class' ) ), member( X,
% 3.05/3.46 complement( Y ) ), member( X, Y ) ] )
% 3.05/3.46 , clause( 20132, [ =( complement( intersection( complement( X ), complement(
% 3.05/3.46 Y ) ) ), union( X, Y ) ) ] )
% 3.05/3.46 , clause( 20133, [ =( intersection( complement( intersection( X, Y ) ),
% 3.05/3.46 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 3.05/3.46 'symmetric_difference'( X, Y ) ) ] )
% 3.05/3.46 , clause( 20134, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 3.05/3.46 X, Y, Z ) ) ] )
% 3.05/3.46 , clause( 20135, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 3.05/3.46 Z, X, Y ) ) ] )
% 3.05/3.46 , clause( 20136, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 3.05/3.46 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 3.05/3.46 , clause( 20137, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 3.05/3.46 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 3.05/3.46 'domain_of'( Y ) ) ] )
% 3.05/3.46 , clause( 20138, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 3.05/3.46 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 3.05/3.46 , clause( 20139, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 3.05/3.46 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 3.05/3.46 ] )
% 3.05/3.46 , clause( 20140, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 3.05/3.46 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 3.05/3.46 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 3.05/3.46 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 3.05/3.46 , Y ), rotate( T ) ) ] )
% 3.05/3.46 , clause( 20141, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 3.05/3.46 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 3.05/3.46 , clause( 20142, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 3.05/3.46 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 3.05/3.46 )
% 3.05/3.46 , clause( 20143, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 3.05/3.46 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 3.05/3.46 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 3.05/3.46 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 3.05/3.46 , Z ), flip( T ) ) ] )
% 3.05/3.46 , clause( 20144, [ =( 'domain_of'( flip( 'cross_product'( X,
% 3.05/3.46 'universal_class' ) ) ), inverse( X ) ) ] )
% 3.05/3.46 , clause( 20145, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 3.05/3.46 , clause( 20146, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 3.05/3.46 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 3.05/3.46 , clause( 20147, [ =( second( 'not_subclass_element'( restrict( X,
% 3.05/3.46 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 3.05/3.46 , clause( 20148, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 3.05/3.46 image( X, Y ) ) ] )
% 3.05/3.46 , clause( 20149, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 3.05/3.46 , clause( 20150, [ subclass( 'successor_relation', 'cross_product'(
% 3.05/3.46 'universal_class', 'universal_class' ) ) ] )
% 3.05/3.46 , clause( 20151, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 3.05/3.46 ) ), =( successor( X ), Y ) ] )
% 3.05/3.46 , clause( 20152, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 3.05/3.46 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 3.05/3.46 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 3.05/3.46 , clause( 20153, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 3.05/3.46 , clause( 20154, [ ~( inductive( X ) ), subclass( image(
% 3.05/3.46 'successor_relation', X ), X ) ] )
% 3.05/3.46 , clause( 20155, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 3.05/3.46 'successor_relation', X ), X ) ), inductive( X ) ] )
% 3.05/3.46 , clause( 20156, [ inductive( omega ) ] )
% 3.05/3.46 , clause( 20157, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 3.05/3.46 , clause( 20158, [ member( omega, 'universal_class' ) ] )
% 3.05/3.46 , clause( 20159, [ =( 'domain_of'( restrict( 'element_relation',
% 3.05/3.46 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 3.05/3.46 , clause( 20160, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 3.05/3.46 X ), 'universal_class' ) ] )
% 3.05/3.46 , clause( 20161, [ =( complement( image( 'element_relation', complement( X
% 3.05/3.46 ) ) ), 'power_class'( X ) ) ] )
% 3.05/3.46 , clause( 20162, [ ~( member( X, 'universal_class' ) ), member(
% 3.05/3.46 'power_class'( X ), 'universal_class' ) ] )
% 3.05/3.46 , clause( 20163, [ subclass( compose( X, Y ), 'cross_product'(
% 3.05/3.46 'universal_class', 'universal_class' ) ) ] )
% 3.05/3.46 , clause( 20164, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 3.05/3.46 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 3.05/3.46 , clause( 20165, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 3.05/3.46 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 3.05/3.46 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 3.05/3.46 ) ] )
% 3.05/3.46 , clause( 20166, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 3.05/3.46 inverse( X ) ), 'identity_relation' ) ] )
% 3.05/3.46 , clause( 20167, [ ~( subclass( compose( X, inverse( X ) ),
% 3.05/3.46 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 3.05/3.46 , clause( 20168, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 3.05/3.46 'universal_class', 'universal_class' ) ) ] )
% 3.05/3.46 , clause( 20169, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 3.05/3.46 , 'identity_relation' ) ] )
% 3.05/3.46 , clause( 20170, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 3.05/3.46 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 3.05/3.46 'identity_relation' ) ), function( X ) ] )
% 3.05/3.46 , clause( 20171, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 3.05/3.46 , member( image( X, Y ), 'universal_class' ) ] )
% 3.05/3.46 , clause( 20172, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 3.05/3.46 , clause( 20173, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 3.05/3.46 , 'null_class' ) ] )
% 3.05/3.46 , clause( 20174, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 3.05/3.46 Y ) ) ] )
% 3.05/3.46 , clause( 20175, [ function( choice ) ] )
% 3.05/3.46 , clause( 20176, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 3.05/3.46 ), member( apply( choice, X ), X ) ] )
% 3.05/3.46 , clause( 20177, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 3.05/3.46 , clause( 20178, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 3.05/3.46 , clause( 20179, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 3.05/3.46 'one_to_one'( X ) ] )
% 3.05/3.46 , clause( 20180, [ =( intersection( 'cross_product'( 'universal_class',
% 3.05/3.46 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 3.05/3.46 'universal_class' ), complement( compose( complement( 'element_relation'
% 3.05/3.46 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 3.05/3.46 , clause( 20181, [ =( intersection( inverse( 'subset_relation' ),
% 3.05/3.46 'subset_relation' ), 'identity_relation' ) ] )
% 3.05/3.46 , clause( 20182, [ =( complement( 'domain_of'( intersection( X,
% 3.05/3.46 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 3.05/3.46 , clause( 20183, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 3.05/3.46 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 3.05/3.46 , clause( 20184, [ ~( operation( X ) ), function( X ) ] )
% 3.05/3.46 , clause( 20185, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 3.05/3.46 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 3.05/3.46 ] )
% 3.05/3.46 , clause( 20186, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 3.05/3.46 'domain_of'( 'domain_of'( X ) ) ) ] )
% 3.05/3.46 , clause( 20187, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 3.05/3.46 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 3.05/3.46 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 3.05/3.46 operation( X ) ] )
% 3.05/3.46 , clause( 20188, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 3.05/3.46 , clause( 20189, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 3.05/3.46 Y ) ), 'domain_of'( X ) ) ] )
% 3.05/3.46 , clause( 20190, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 3.05/3.46 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 3.05/3.46 , clause( 20191, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 3.05/3.46 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 3.05/3.46 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 3.05/3.46 , clause( 20192, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 3.05/3.46 , clause( 20193, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 3.05/3.46 , clause( 20194, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 3.05/3.46 , clause( 20195, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 3.05/3.46 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 3.05/3.46 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 3.05/3.46 )
% 3.05/3.46 , clause( 20196, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 3.05/3.46 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 3.05/3.46 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 3.05/3.46 , Y ) ] )
% 3.05/3.46 , clause( 20197, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 3.05/3.46 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 3.05/3.46 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 3.05/3.46 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 3.05/3.46 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 3.05/3.46 )
% 3.05/3.46 , clause( 20198, [ =( 'unordered_pair'( y, z ), singleton( x ) ) ] )
% 3.05/3.46 , clause( 20199, [ member( x, 'universal_class' ) ] )
% 3.05/3.46 , clause( 20200, [ ~( =( x, y ) ) ] )
% 3.05/3.46 , clause( 20201, [ ~( =( x, z ) ) ] )
% 3.05/3.46 ] ).
% 3.05/3.46
% 3.05/3.46
% 3.05/3.46
% 3.05/3.46 subsumption(
% 3.05/3.46 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 3.05/3.46 , clause( 20111, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 3.05/3.46 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 3.05/3.46 ), ==>( 1, 1 )] ) ).
% 3.05/3.46
% 3.05/3.46
% 3.05/3.46 subsumption(
% 3.05/3.46 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 3.05/3.46 , clause( 20113, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 3.05/3.46 ] )
% 3.05/3.46 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 3.05/3.46 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 3.05/3.46
% 3.05/3.46
% 3.05/3.46 subsumption(
% 3.05/3.46 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =(Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------