TSTP Solution File: SET061-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET061-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n019.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 22:46:18 EDT 2022
% Result : Unsatisfiable 1.01s 1.41s
% Output : Refutation 1.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET061-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.10/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n019.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sun Jul 10 16:18:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.10 *** allocated 10000 integers for termspace/termends
% 0.43/1.10 *** allocated 10000 integers for clauses
% 0.43/1.10 *** allocated 10000 integers for justifications
% 0.43/1.10 Bliksem 1.12
% 0.43/1.10
% 0.43/1.10
% 0.43/1.10 Automatic Strategy Selection
% 0.43/1.10
% 0.43/1.10 Clauses:
% 0.43/1.10 [
% 0.43/1.10 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.43/1.10 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.43/1.10 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.43/1.10 ,
% 0.43/1.10 [ subclass( X, 'universal_class' ) ],
% 0.43/1.10 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.43/1.10 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.43/1.10 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.43/1.10 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.43/1.10 ,
% 0.43/1.10 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.43/1.10 ) ) ],
% 0.43/1.10 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.43/1.10 ) ) ],
% 0.43/1.10 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.43/1.10 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.43/1.10 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.43/1.10 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.10 X, Z ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.10 Y, T ) ],
% 0.43/1.10 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.43/1.10 ), 'cross_product'( Y, T ) ) ],
% 0.43/1.10 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.43/1.10 ), second( X ) ), X ) ],
% 0.43/1.10 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.43/1.10 'universal_class' ) ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.43/1.10 Y ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.43/1.10 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.43/1.10 , Y ), 'element_relation' ) ],
% 0.43/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.43/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.43/1.10 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.43/1.10 Z ) ) ],
% 0.43/1.10 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.43/1.10 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.43/1.10 member( X, Y ) ],
% 0.43/1.10 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.43/1.10 union( X, Y ) ) ],
% 0.43/1.10 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.43/1.10 intersection( complement( X ), complement( Y ) ) ) ),
% 0.43/1.10 'symmetric_difference'( X, Y ) ) ],
% 0.43/1.10 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.43/1.10 ,
% 0.43/1.10 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.43/1.10 ,
% 0.43/1.10 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.43/1.10 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.43/1.10 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.43/1.10 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.43/1.10 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.43/1.10 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.43/1.10 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.43/1.10 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.43/1.10 'cross_product'( 'universal_class', 'universal_class' ),
% 0.43/1.10 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.43/1.10 Y ), rotate( T ) ) ],
% 0.43/1.10 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.43/1.10 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.43/1.10 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.43/1.10 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.43/1.10 'cross_product'( 'universal_class', 'universal_class' ),
% 0.43/1.10 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.43/1.10 Z ), flip( T ) ) ],
% 0.43/1.10 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.43/1.10 inverse( X ) ) ],
% 0.43/1.10 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.43/1.10 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.43/1.10 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.43/1.10 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.43/1.10 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.43/1.10 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.43/1.10 ],
% 0.43/1.10 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.43/1.10 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.43/1.10 'universal_class' ) ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.43/1.10 successor( X ), Y ) ],
% 0.43/1.10 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.43/1.10 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.43/1.10 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.43/1.10 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.43/1.10 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.43/1.10 ,
% 0.43/1.10 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.43/1.10 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.43/1.10 [ inductive( omega ) ],
% 0.43/1.10 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.43/1.10 [ member( omega, 'universal_class' ) ],
% 0.43/1.10 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.43/1.10 , 'sum_class'( X ) ) ],
% 0.43/1.10 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.43/1.10 'universal_class' ) ],
% 0.43/1.10 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.43/1.10 'power_class'( X ) ) ],
% 0.43/1.10 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.43/1.10 'universal_class' ) ],
% 0.43/1.10 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.43/1.10 'universal_class' ) ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.43/1.10 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.43/1.10 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.43/1.10 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.43/1.10 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.43/1.10 ) ],
% 0.43/1.10 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.43/1.10 , 'identity_relation' ) ],
% 0.43/1.10 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.43/1.10 'single_valued_class'( X ) ],
% 0.43/1.10 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.43/1.10 'universal_class' ) ) ],
% 0.43/1.10 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.43/1.10 'identity_relation' ) ],
% 0.43/1.10 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.43/1.10 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.43/1.10 , function( X ) ],
% 0.43/1.10 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.43/1.10 X, Y ), 'universal_class' ) ],
% 0.43/1.10 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.43/1.10 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.43/1.10 ) ],
% 0.43/1.10 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.43/1.10 [ function( choice ) ],
% 0.43/1.10 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.43/1.10 apply( choice, X ), X ) ],
% 0.43/1.10 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.43/1.10 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.43/1.10 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.43/1.10 ,
% 0.43/1.10 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.43/1.10 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.43/1.10 , complement( compose( complement( 'element_relation' ), inverse(
% 0.43/1.10 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.43/1.10 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.43/1.10 'identity_relation' ) ],
% 0.43/1.10 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.43/1.10 , diagonalise( X ) ) ],
% 0.43/1.10 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.43/1.10 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.43/1.10 [ ~( operation( X ) ), function( X ) ],
% 0.43/1.10 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.43/1.10 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.43/1.10 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 1.01/1.41 'domain_of'( X ) ) ) ],
% 1.01/1.41 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 1.01/1.41 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 1.01/1.41 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 1.01/1.41 X ) ],
% 1.01/1.41 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 1.01/1.41 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 1.01/1.41 'domain_of'( X ) ) ],
% 1.01/1.41 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 1.01/1.41 'domain_of'( Z ) ) ) ],
% 1.01/1.41 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 1.01/1.41 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 1.01/1.41 ), compatible( X, Y, Z ) ],
% 1.01/1.41 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 1.01/1.41 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 1.01/1.41 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 1.01/1.41 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 1.01/1.41 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 1.01/1.41 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 1.01/1.41 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 1.01/1.41 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.01/1.41 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.01/1.41 , Y ) ],
% 1.01/1.41 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 1.01/1.41 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 1.01/1.41 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 1.01/1.41 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 1.01/1.41 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 1.01/1.41 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 1.01/1.41 X, 'unordered_pair'( X, Y ) ) ],
% 1.01/1.41 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 1.01/1.41 Y, 'unordered_pair'( X, Y ) ) ],
% 1.01/1.41 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 1.01/1.41 X, 'universal_class' ) ],
% 1.01/1.41 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 1.01/1.41 Y, 'universal_class' ) ],
% 1.01/1.41 [ subclass( X, X ) ],
% 1.01/1.41 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 1.01/1.41 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 1.01/1.41 'not_subclass_element'( Y, X ), Y ) ],
% 1.01/1.41 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 1.01/1.41 'not_subclass_element'( Y, X ), Y ) ],
% 1.01/1.41 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 1.01/1.41 'not_subclass_element'( Y, X ), Y ) ],
% 1.01/1.41 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 1.01/1.41 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 1.01/1.41 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 1.01/1.41 [ member( z, 'null_class' ) ]
% 1.01/1.41 ] .
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 percentage equality = 0.207729, percentage horn = 0.893204
% 1.01/1.41 This is a problem with some equality
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 Options Used:
% 1.01/1.41
% 1.01/1.41 useres = 1
% 1.01/1.41 useparamod = 1
% 1.01/1.41 useeqrefl = 1
% 1.01/1.41 useeqfact = 1
% 1.01/1.41 usefactor = 1
% 1.01/1.41 usesimpsplitting = 0
% 1.01/1.41 usesimpdemod = 5
% 1.01/1.41 usesimpres = 3
% 1.01/1.41
% 1.01/1.41 resimpinuse = 1000
% 1.01/1.41 resimpclauses = 20000
% 1.01/1.41 substype = eqrewr
% 1.01/1.41 backwardsubs = 1
% 1.01/1.41 selectoldest = 5
% 1.01/1.41
% 1.01/1.41 litorderings [0] = split
% 1.01/1.41 litorderings [1] = extend the termordering, first sorting on arguments
% 1.01/1.41
% 1.01/1.41 termordering = kbo
% 1.01/1.41
% 1.01/1.41 litapriori = 0
% 1.01/1.41 termapriori = 1
% 1.01/1.41 litaposteriori = 0
% 1.01/1.41 termaposteriori = 0
% 1.01/1.41 demodaposteriori = 0
% 1.01/1.41 ordereqreflfact = 0
% 1.01/1.41
% 1.01/1.41 litselect = negord
% 1.01/1.41
% 1.01/1.41 maxweight = 15
% 1.01/1.41 maxdepth = 30000
% 1.01/1.41 maxlength = 115
% 1.01/1.41 maxnrvars = 195
% 1.01/1.41 excuselevel = 1
% 1.01/1.41 increasemaxweight = 1
% 1.01/1.41
% 1.01/1.41 maxselected = 10000000
% 1.01/1.41 maxnrclauses = 10000000
% 1.01/1.41
% 1.01/1.41 showgenerated = 0
% 1.01/1.41 showkept = 0
% 1.01/1.41 showselected = 0
% 1.01/1.41 showdeleted = 0
% 1.01/1.41 showresimp = 1
% 1.01/1.41 showstatus = 2000
% 1.01/1.41
% 1.01/1.41 prologoutput = 1
% 1.01/1.41 nrgoals = 5000000
% 1.01/1.41 totalproof = 1
% 1.01/1.41
% 1.01/1.41 Symbols occurring in the translation:
% 1.01/1.41
% 1.01/1.41 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.01/1.41 . [1, 2] (w:1, o:55, a:1, s:1, b:0),
% 1.01/1.41 ! [4, 1] (w:0, o:30, a:1, s:1, b:0),
% 1.01/1.41 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.01/1.41 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.01/1.41 subclass [41, 2] (w:1, o:80, a:1, s:1, b:0),
% 1.01/1.41 member [43, 2] (w:1, o:81, a:1, s:1, b:0),
% 1.01/1.41 'not_subclass_element' [44, 2] (w:1, o:82, a:1, s:1, b:0),
% 1.01/1.41 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 1.01/1.41 'unordered_pair' [46, 2] (w:1, o:83, a:1, s:1, b:0),
% 1.01/1.41 singleton [47, 1] (w:1, o:38, a:1, s:1, b:0),
% 1.01/1.41 'ordered_pair' [48, 2] (w:1, o:84, a:1, s:1, b:0),
% 1.01/1.41 'cross_product' [50, 2] (w:1, o:85, a:1, s:1, b:0),
% 1.01/1.41 first [52, 1] (w:1, o:39, a:1, s:1, b:0),
% 1.01/1.41 second [53, 1] (w:1, o:40, a:1, s:1, b:0),
% 1.01/1.41 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 1.01/1.41 intersection [55, 2] (w:1, o:87, a:1, s:1, b:0),
% 1.01/1.41 complement [56, 1] (w:1, o:41, a:1, s:1, b:0),
% 1.01/1.41 union [57, 2] (w:1, o:88, a:1, s:1, b:0),
% 1.01/1.41 'symmetric_difference' [58, 2] (w:1, o:89, a:1, s:1, b:0),
% 1.01/1.41 restrict [60, 3] (w:1, o:92, a:1, s:1, b:0),
% 1.01/1.41 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.01/1.41 'domain_of' [62, 1] (w:1, o:43, a:1, s:1, b:0),
% 1.01/1.41 rotate [63, 1] (w:1, o:35, a:1, s:1, b:0),
% 1.01/1.41 flip [65, 1] (w:1, o:44, a:1, s:1, b:0),
% 1.01/1.41 inverse [66, 1] (w:1, o:45, a:1, s:1, b:0),
% 1.01/1.41 'range_of' [67, 1] (w:1, o:36, a:1, s:1, b:0),
% 1.01/1.41 domain [68, 3] (w:1, o:94, a:1, s:1, b:0),
% 1.01/1.41 range [69, 3] (w:1, o:95, a:1, s:1, b:0),
% 1.01/1.41 image [70, 2] (w:1, o:86, a:1, s:1, b:0),
% 1.01/1.41 successor [71, 1] (w:1, o:46, a:1, s:1, b:0),
% 1.01/1.41 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 1.01/1.41 inductive [73, 1] (w:1, o:47, a:1, s:1, b:0),
% 1.01/1.41 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.01/1.41 'sum_class' [75, 1] (w:1, o:48, a:1, s:1, b:0),
% 1.01/1.41 'power_class' [76, 1] (w:1, o:51, a:1, s:1, b:0),
% 1.01/1.41 compose [78, 2] (w:1, o:90, a:1, s:1, b:0),
% 1.01/1.41 'single_valued_class' [79, 1] (w:1, o:52, a:1, s:1, b:0),
% 1.01/1.41 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 1.01/1.41 function [82, 1] (w:1, o:53, a:1, s:1, b:0),
% 1.01/1.41 regular [83, 1] (w:1, o:37, a:1, s:1, b:0),
% 1.01/1.41 apply [84, 2] (w:1, o:91, a:1, s:1, b:0),
% 1.01/1.41 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.01/1.41 'one_to_one' [86, 1] (w:1, o:49, a:1, s:1, b:0),
% 1.01/1.41 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 1.01/1.41 diagonalise [88, 1] (w:1, o:54, a:1, s:1, b:0),
% 1.01/1.41 cantor [89, 1] (w:1, o:42, a:1, s:1, b:0),
% 1.01/1.41 operation [90, 1] (w:1, o:50, a:1, s:1, b:0),
% 1.01/1.41 compatible [94, 3] (w:1, o:93, a:1, s:1, b:0),
% 1.01/1.41 homomorphism [95, 3] (w:1, o:96, a:1, s:1, b:0),
% 1.01/1.41 'not_homomorphism1' [96, 3] (w:1, o:97, a:1, s:1, b:0),
% 1.01/1.41 'not_homomorphism2' [97, 3] (w:1, o:98, a:1, s:1, b:0),
% 1.01/1.41 z [98, 0] (w:1, o:29, a:1, s:1, b:0).
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 Starting Search:
% 1.01/1.41
% 1.01/1.41 Resimplifying inuse:
% 1.01/1.41 Done
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 Intermediate Status:
% 1.01/1.41 Generated: 5639
% 1.01/1.41 Kept: 2016
% 1.01/1.41 Inuse: 104
% 1.01/1.41 Deleted: 2
% 1.01/1.41 Deletedinuse: 2
% 1.01/1.41
% 1.01/1.41 Resimplifying inuse:
% 1.01/1.41 Done
% 1.01/1.41
% 1.01/1.41 Resimplifying inuse:
% 1.01/1.41 Done
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 Intermediate Status:
% 1.01/1.41 Generated: 10402
% 1.01/1.41 Kept: 4035
% 1.01/1.41 Inuse: 192
% 1.01/1.41 Deleted: 21
% 1.01/1.41 Deletedinuse: 14
% 1.01/1.41
% 1.01/1.41 Resimplifying inuse:
% 1.01/1.41 Done
% 1.01/1.41
% 1.01/1.41 Resimplifying inuse:
% 1.01/1.41 Done
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 Intermediate Status:
% 1.01/1.41 Generated: 14365
% 1.01/1.41 Kept: 6058
% 1.01/1.41 Inuse: 243
% 1.01/1.41 Deleted: 25
% 1.01/1.41 Deletedinuse: 16
% 1.01/1.41
% 1.01/1.41 Resimplifying inuse:
% 1.01/1.41 Done
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 Bliksems!, er is een bewijs:
% 1.01/1.41 % SZS status Unsatisfiable
% 1.01/1.41 % SZS output start Refutation
% 1.01/1.41
% 1.01/1.41 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 1.01/1.41 )
% 1.01/1.41 .
% 1.01/1.41 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.01/1.41 'unordered_pair'( Y, X ) ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 19, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 22, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 65, [ =( X, 'null_class' ), =( intersection( X, regular( X ) ),
% 1.01/1.41 'null_class' ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 100, [ member( z, 'null_class' ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 114, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 133, [ member( z, 'universal_class' ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 134, [ =( X, Y ), ~( =( Y, X ) ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 164, [ member( z, X ), ~( =( X, 'universal_class' ) ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 186, [ member( z, X ), ~( =( X, 'null_class' ) ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 435, [ member( z, 'unordered_pair'( X, z ) ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 491, [ member( z, singleton( z ) ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 1337, [ member( z, X ), ~( =( intersection( X, Y ), 'null_class' )
% 1.01/1.41 ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 1935, [ ~( member( z, complement( singleton( z ) ) ) ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 7270, [ member( z, X ) ] )
% 1.01/1.41 .
% 1.01/1.41 clause( 7470, [] )
% 1.01/1.41 .
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 % SZS output end Refutation
% 1.01/1.41 found a proof!
% 1.01/1.41
% 1.01/1.41 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.01/1.41
% 1.01/1.41 initialclauses(
% 1.01/1.41 [ clause( 7472, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.01/1.41 ) ] )
% 1.01/1.41 , clause( 7473, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 1.01/1.41 , Y ) ] )
% 1.01/1.41 , clause( 7474, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 1.01/1.41 subclass( X, Y ) ] )
% 1.01/1.41 , clause( 7475, [ subclass( X, 'universal_class' ) ] )
% 1.01/1.41 , clause( 7476, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.01/1.41 , clause( 7477, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 1.01/1.41 , clause( 7478, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ]
% 1.01/1.41 )
% 1.01/1.41 , clause( 7479, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 1.01/1.41 =( X, Z ) ] )
% 1.01/1.41 , clause( 7480, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.01/1.41 'unordered_pair'( X, Y ) ) ] )
% 1.01/1.41 , clause( 7481, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.01/1.41 'unordered_pair'( Y, X ) ) ] )
% 1.01/1.41 , clause( 7482, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 1.01/1.41 )
% 1.01/1.41 , clause( 7483, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.01/1.41 , clause( 7484, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 1.01/1.41 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.01/1.41 , clause( 7485, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.01/1.41 ) ) ), member( X, Z ) ] )
% 1.01/1.41 , clause( 7486, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.01/1.41 ) ) ), member( Y, T ) ] )
% 1.01/1.41 , clause( 7487, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.01/1.41 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.01/1.41 , clause( 7488, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 1.01/1.41 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 1.01/1.41 , clause( 7489, [ subclass( 'element_relation', 'cross_product'(
% 1.01/1.41 'universal_class', 'universal_class' ) ) ] )
% 1.01/1.41 , clause( 7490, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) )
% 1.01/1.41 , member( X, Y ) ] )
% 1.01/1.41 , clause( 7491, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.01/1.41 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 1.01/1.41 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 1.01/1.41 , clause( 7492, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.01/1.41 )
% 1.01/1.41 , clause( 7493, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 1.01/1.41 )
% 1.01/1.41 , clause( 7494, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 1.01/1.41 intersection( Y, Z ) ) ] )
% 1.01/1.41 , clause( 7495, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 1.01/1.41 )
% 1.01/1.41 , clause( 7496, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.01/1.41 complement( Y ) ), member( X, Y ) ] )
% 1.01/1.41 , clause( 7497, [ =( complement( intersection( complement( X ), complement(
% 1.01/1.41 Y ) ) ), union( X, Y ) ) ] )
% 1.01/1.41 , clause( 7498, [ =( intersection( complement( intersection( X, Y ) ),
% 1.01/1.41 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 1.01/1.41 'symmetric_difference'( X, Y ) ) ] )
% 1.01/1.41 , clause( 7499, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 1.01/1.41 X, Y, Z ) ) ] )
% 1.01/1.41 , clause( 7500, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 1.01/1.41 Z, X, Y ) ) ] )
% 1.01/1.41 , clause( 7501, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 1.01/1.41 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 1.01/1.41 , clause( 7502, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 1.01/1.41 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 1.01/1.41 'domain_of'( Y ) ) ] )
% 1.01/1.41 , clause( 7503, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 1.01/1.41 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.01/1.41 , clause( 7504, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.01/1.41 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 1.01/1.41 ] )
% 1.01/1.41 , clause( 7505, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 1.01/1.41 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 1.01/1.41 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.01/1.41 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 1.01/1.41 , Y ), rotate( T ) ) ] )
% 1.01/1.41 , clause( 7506, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 1.01/1.41 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.01/1.41 , clause( 7507, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.01/1.41 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 1.01/1.41 )
% 1.01/1.41 , clause( 7508, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 1.01/1.41 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 1.01/1.41 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.01/1.41 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 1.01/1.41 , Z ), flip( T ) ) ] )
% 1.01/1.41 , clause( 7509, [ =( 'domain_of'( flip( 'cross_product'( X,
% 1.01/1.41 'universal_class' ) ) ), inverse( X ) ) ] )
% 1.01/1.41 , clause( 7510, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 1.01/1.41 , clause( 7511, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 1.01/1.41 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 1.01/1.41 , clause( 7512, [ =( second( 'not_subclass_element'( restrict( X, singleton(
% 1.01/1.41 Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 1.01/1.41 , clause( 7513, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 1.01/1.41 image( X, Y ) ) ] )
% 1.01/1.41 , clause( 7514, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 1.01/1.41 , clause( 7515, [ subclass( 'successor_relation', 'cross_product'(
% 1.01/1.41 'universal_class', 'universal_class' ) ) ] )
% 1.01/1.41 , clause( 7516, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' )
% 1.01/1.41 ), =( successor( X ), Y ) ] )
% 1.01/1.41 , clause( 7517, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X
% 1.01/1.41 , Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 1.01/1.41 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 1.01/1.41 , clause( 7518, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 1.01/1.41 , clause( 7519, [ ~( inductive( X ) ), subclass( image(
% 1.01/1.41 'successor_relation', X ), X ) ] )
% 1.01/1.41 , clause( 7520, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 1.01/1.41 'successor_relation', X ), X ) ), inductive( X ) ] )
% 1.01/1.41 , clause( 7521, [ inductive( omega ) ] )
% 1.01/1.41 , clause( 7522, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 1.01/1.41 , clause( 7523, [ member( omega, 'universal_class' ) ] )
% 1.01/1.41 , clause( 7524, [ =( 'domain_of'( restrict( 'element_relation',
% 1.01/1.41 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 1.01/1.41 , clause( 7525, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 1.01/1.41 X ), 'universal_class' ) ] )
% 1.01/1.41 , clause( 7526, [ =( complement( image( 'element_relation', complement( X )
% 1.01/1.41 ) ), 'power_class'( X ) ) ] )
% 1.01/1.41 , clause( 7527, [ ~( member( X, 'universal_class' ) ), member(
% 1.01/1.41 'power_class'( X ), 'universal_class' ) ] )
% 1.01/1.41 , clause( 7528, [ subclass( compose( X, Y ), 'cross_product'(
% 1.01/1.41 'universal_class', 'universal_class' ) ) ] )
% 1.01/1.41 , clause( 7529, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 1.01/1.41 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 1.01/1.41 , clause( 7530, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 1.01/1.41 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 1.01/1.41 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 1.01/1.41 ) ] )
% 1.01/1.41 , clause( 7531, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 1.01/1.41 inverse( X ) ), 'identity_relation' ) ] )
% 1.01/1.41 , clause( 7532, [ ~( subclass( compose( X, inverse( X ) ),
% 1.01/1.41 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 1.01/1.41 , clause( 7533, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 1.01/1.41 'universal_class', 'universal_class' ) ) ] )
% 1.01/1.41 , clause( 7534, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 1.01/1.41 , 'identity_relation' ) ] )
% 1.01/1.41 , clause( 7535, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 1.01/1.41 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 1.01/1.41 'identity_relation' ) ), function( X ) ] )
% 1.01/1.41 , clause( 7536, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ),
% 1.01/1.41 member( image( X, Y ), 'universal_class' ) ] )
% 1.01/1.41 , clause( 7537, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.01/1.41 , clause( 7538, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 1.01/1.41 , 'null_class' ) ] )
% 1.01/1.41 , clause( 7539, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y
% 1.01/1.41 ) ) ] )
% 1.01/1.41 , clause( 7540, [ function( choice ) ] )
% 1.01/1.41 , clause( 7541, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' )
% 1.01/1.41 , member( apply( choice, X ), X ) ] )
% 1.01/1.41 , clause( 7542, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 1.01/1.41 , clause( 7543, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 1.01/1.41 , clause( 7544, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 1.01/1.41 'one_to_one'( X ) ] )
% 1.01/1.41 , clause( 7545, [ =( intersection( 'cross_product'( 'universal_class',
% 1.01/1.41 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 1.01/1.41 'universal_class' ), complement( compose( complement( 'element_relation'
% 1.01/1.41 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 1.01/1.41 , clause( 7546, [ =( intersection( inverse( 'subset_relation' ),
% 1.01/1.41 'subset_relation' ), 'identity_relation' ) ] )
% 1.01/1.41 , clause( 7547, [ =( complement( 'domain_of'( intersection( X,
% 1.01/1.41 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 1.01/1.41 , clause( 7548, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 1.01/1.41 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 1.01/1.41 , clause( 7549, [ ~( operation( X ) ), function( X ) ] )
% 1.01/1.41 , clause( 7550, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 1.01/1.41 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.01/1.41 ] )
% 1.01/1.41 , clause( 7551, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 1.01/1.41 'domain_of'( 'domain_of'( X ) ) ) ] )
% 1.01/1.41 , clause( 7552, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 1.01/1.41 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.01/1.41 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 1.01/1.41 operation( X ) ] )
% 1.01/1.41 , clause( 7553, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 1.01/1.41 , clause( 7554, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 1.01/1.41 Y ) ), 'domain_of'( X ) ) ] )
% 1.01/1.41 , clause( 7555, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 1.01/1.41 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 1.01/1.41 , clause( 7556, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) )
% 1.01/1.41 , 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 1.01/1.41 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 1.01/1.41 , clause( 7557, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 1.01/1.41 , clause( 7558, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 1.01/1.41 , clause( 7559, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 1.01/1.41 , clause( 7560, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 1.01/1.41 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 1.01/1.41 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 1.01/1.41 )
% 1.01/1.41 , clause( 7561, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.01/1.41 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.01/1.41 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.01/1.41 , Y ) ] )
% 1.01/1.41 , clause( 7562, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.01/1.41 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 1.01/1.41 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 1.01/1.41 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 1.01/1.41 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 1.01/1.41 )
% 1.01/1.41 , clause( 7563, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.01/1.41 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 1.01/1.41 , clause( 7564, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.01/1.41 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 1.01/1.41 , clause( 7565, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.01/1.41 ) ) ), member( X, 'universal_class' ) ] )
% 1.01/1.41 , clause( 7566, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.01/1.41 ) ) ), member( Y, 'universal_class' ) ] )
% 1.01/1.41 , clause( 7567, [ subclass( X, X ) ] )
% 1.01/1.41 , clause( 7568, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X
% 1.01/1.41 , Z ) ] )
% 1.01/1.41 , clause( 7569, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 1.01/1.41 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 1.01/1.41 , clause( 7570, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y
% 1.01/1.41 ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 1.01/1.41 , clause( 7571, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X
% 1.01/1.41 ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 1.01/1.41 , clause( 7572, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 1.01/1.41 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 1.01/1.41 , clause( 7573, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ] )
% 1.01/1.41 , clause( 7574, [ member( z, 'null_class' ) ] )
% 1.01/1.41 ] ).
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 subsumption(
% 1.01/1.41 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 1.01/1.41 )
% 1.01/1.41 , clause( 7472, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.01/1.41 ) ] )
% 1.01/1.41 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.01/1.41 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 subsumption(
% 1.01/1.41 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 1.01/1.41 , clause( 7475, [ subclass( X, 'universal_class' ) ] )
% 1.01/1.41 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 subsumption(
% 1.01/1.41 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.01/1.41 , clause( 7476, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.01/1.41 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.01/1.41 ), ==>( 1, 1 )] ) ).
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 subsumption(
% 1.01/1.41 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 1.01/1.41 , clause( 7478, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ]
% 1.01/1.41 )
% 1.01/1.41 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.01/1.41 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 subsumption(
% 1.01/1.41 clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.01/1.41 'unordered_pair'( Y, X ) ) ] )
% 1.01/1.41 , clause( 7481, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.01/1.41 'unordered_pair'( Y, X ) ) ] )
% 1.01/1.41 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.01/1.41 ), ==>( 1, 1 )] ) ).
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 subsumption(
% 1.01/1.41 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.01/1.41 , clause( 7483, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.01/1.41 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 subsumption(
% 1.01/1.41 clause( 19, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ] )
% 1.01/1.41 , clause( 7492, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.01/1.41 )
% 1.01/1.41 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.01/1.41 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 subsumption(
% 1.01/1.41 clause( 22, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ] )
% 1.01/1.41 , clause( 7495, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 1.01/1.41 )
% 1.01/1.41 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.01/1.41 ), ==>( 1, 1 )] ) ).
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 subsumption(
% 1.01/1.41 clause( 65, [ =( X, 'null_class' ), =( intersection( X, regular( X ) ),
% 1.01/1.41 'null_class' ) ] )
% 1.01/1.41 , clause( 7538, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 1.01/1.41 , 'null_class' ) ] )
% 1.01/1.41 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.01/1.41 1 )] ) ).
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 subsumption(
% 1.01/1.41 clause( 100, [ member( z, 'null_class' ) ] )
% 1.01/1.41 , clause( 7574, [ member( z, 'null_class' ) ] )
% 1.01/1.41 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 resolution(
% 1.01/1.41 clause( 7711, [ ~( member( Y, X ) ), member( Y, 'universal_class' ) ] )
% 1.01/1.41 , clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 1.01/1.41 )
% 1.01/1.41 , 0, clause( 3, [ subclass( X, 'universal_class' ) ] )
% 1.01/1.41 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'universal_class' ), :=( Z, Y )] )
% 1.01/1.41 , substitution( 1, [ :=( X, X )] )).
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 subsumption(
% 1.01/1.41 clause( 114, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ] )
% 1.01/1.41 , clause( 7711, [ ~( member( Y, X ) ), member( Y, 'universal_class' ) ] )
% 1.01/1.41 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 1.01/1.41 ), ==>( 1, 1 )] ) ).
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 resolution(
% 1.01/1.41 clause( 7712, [ member( z, 'universal_class' ) ] )
% 1.01/1.41 , clause( 114, [ ~( member( X, Y ) ), member( X, 'universal_class' ) ] )
% 1.01/1.41 , 0, clause( 100, [ member( z, 'null_class' ) ] )
% 1.01/1.41 , 0, substitution( 0, [ :=( X, z ), :=( Y, 'null_class' )] ),
% 1.01/1.41 substitution( 1, [] )).
% 1.01/1.41
% 1.01/1.41
% 1.01/1.41 subsumption(
% 1.01/1.41 clause( 133, [ member( z, 'universal_class' ) ] )
% 1.01/1.41 , clause( 7712, [ member( z, 'universal_class' ) ] )
% 1.01/1.41 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------