TSTP Solution File: SET071-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET071-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n012.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 22:46:33 EDT 2022
% Result : Unsatisfiable 1.62s 2.04s
% Output : Refutation 1.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET071-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.14 % Command : bliksem %s
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % DateTime : Sat Jul 9 23:31:58 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.44/1.11 *** allocated 10000 integers for termspace/termends
% 0.44/1.11 *** allocated 10000 integers for clauses
% 0.44/1.11 *** allocated 10000 integers for justifications
% 0.44/1.11 Bliksem 1.12
% 0.44/1.11
% 0.44/1.11
% 0.44/1.11 Automatic Strategy Selection
% 0.44/1.11
% 0.44/1.11 Clauses:
% 0.44/1.11 [
% 0.44/1.11 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.44/1.11 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.44/1.11 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.44/1.11 ,
% 0.44/1.11 [ subclass( X, 'universal_class' ) ],
% 0.44/1.11 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.44/1.11 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.44/1.11 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.44/1.11 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.44/1.11 ,
% 0.44/1.11 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.44/1.11 ) ) ],
% 0.44/1.11 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.44/1.11 ) ) ],
% 0.44/1.11 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.44/1.11 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.44/1.11 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.44/1.11 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.44/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.44/1.11 X, Z ) ],
% 0.44/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.44/1.11 Y, T ) ],
% 0.44/1.11 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.44/1.11 ), 'cross_product'( Y, T ) ) ],
% 0.44/1.11 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.44/1.11 ), second( X ) ), X ) ],
% 0.44/1.11 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.44/1.11 'universal_class' ) ) ],
% 0.44/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.44/1.11 Y ) ],
% 0.44/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.44/1.11 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.44/1.11 , Y ), 'element_relation' ) ],
% 0.44/1.11 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.44/1.11 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.44/1.11 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.44/1.11 Z ) ) ],
% 0.44/1.11 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.44/1.11 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.44/1.11 member( X, Y ) ],
% 0.44/1.11 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.44/1.11 union( X, Y ) ) ],
% 0.44/1.11 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.44/1.11 intersection( complement( X ), complement( Y ) ) ) ),
% 0.44/1.11 'symmetric_difference'( X, Y ) ) ],
% 0.44/1.11 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.44/1.11 ,
% 0.44/1.11 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.44/1.11 ,
% 0.44/1.11 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.44/1.11 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.44/1.11 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.44/1.11 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.44/1.11 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.44/1.11 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.44/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.44/1.11 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.44/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.44/1.11 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.44/1.11 'cross_product'( 'universal_class', 'universal_class' ),
% 0.44/1.11 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.44/1.11 Y ), rotate( T ) ) ],
% 0.44/1.11 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.44/1.11 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.44/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.44/1.11 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.44/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.44/1.11 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.44/1.11 'cross_product'( 'universal_class', 'universal_class' ),
% 0.44/1.11 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.44/1.11 Z ), flip( T ) ) ],
% 0.44/1.11 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.44/1.11 inverse( X ) ) ],
% 0.44/1.11 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.44/1.11 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.44/1.11 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.44/1.11 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.44/1.11 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.44/1.11 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.44/1.11 ],
% 0.44/1.11 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.44/1.11 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.44/1.11 'universal_class' ) ) ],
% 0.44/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.44/1.11 successor( X ), Y ) ],
% 0.44/1.11 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.44/1.11 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.44/1.11 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.44/1.11 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.44/1.11 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.44/1.11 ,
% 0.44/1.11 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.44/1.11 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.44/1.11 [ inductive( omega ) ],
% 0.44/1.11 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.44/1.11 [ member( omega, 'universal_class' ) ],
% 0.44/1.11 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.44/1.11 , 'sum_class'( X ) ) ],
% 0.44/1.11 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.44/1.11 'universal_class' ) ],
% 0.44/1.11 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.44/1.11 'power_class'( X ) ) ],
% 0.44/1.11 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.44/1.11 'universal_class' ) ],
% 0.44/1.11 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.44/1.11 'universal_class' ) ) ],
% 0.44/1.11 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.44/1.11 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.44/1.11 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.44/1.11 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.44/1.11 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.44/1.11 ) ],
% 0.44/1.11 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.44/1.11 , 'identity_relation' ) ],
% 0.44/1.11 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.44/1.11 'single_valued_class'( X ) ],
% 0.44/1.11 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.44/1.11 'universal_class' ) ) ],
% 0.44/1.11 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.44/1.11 'identity_relation' ) ],
% 0.44/1.11 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.44/1.11 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.44/1.11 , function( X ) ],
% 0.44/1.11 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.44/1.11 X, Y ), 'universal_class' ) ],
% 0.44/1.11 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.44/1.11 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.44/1.11 ) ],
% 0.44/1.11 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.44/1.11 [ function( choice ) ],
% 0.44/1.11 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.44/1.11 apply( choice, X ), X ) ],
% 0.44/1.11 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.44/1.11 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.44/1.11 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.44/1.11 ,
% 0.44/1.11 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.44/1.11 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.44/1.11 , complement( compose( complement( 'element_relation' ), inverse(
% 0.44/1.11 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.44/1.11 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.44/1.11 'identity_relation' ) ],
% 0.44/1.11 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.44/1.11 , diagonalise( X ) ) ],
% 0.44/1.11 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.44/1.11 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.44/1.11 [ ~( operation( X ) ), function( X ) ],
% 0.44/1.11 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.44/1.11 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.44/1.11 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 1.14/1.53 'domain_of'( X ) ) ) ],
% 1.14/1.53 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 1.14/1.53 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 1.14/1.53 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 1.14/1.53 X ) ],
% 1.14/1.53 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 1.14/1.53 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 1.14/1.53 'domain_of'( X ) ) ],
% 1.14/1.53 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 1.14/1.53 'domain_of'( Z ) ) ) ],
% 1.14/1.53 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 1.14/1.53 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 1.14/1.53 ), compatible( X, Y, Z ) ],
% 1.14/1.53 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 1.14/1.53 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 1.14/1.53 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 1.14/1.53 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 1.14/1.53 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 1.14/1.53 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 1.14/1.53 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 1.14/1.53 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.14/1.53 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.14/1.53 , Y ) ],
% 1.14/1.53 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 1.14/1.53 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 1.14/1.53 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 1.14/1.53 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 1.14/1.53 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 1.14/1.53 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 1.14/1.53 X, 'unordered_pair'( X, Y ) ) ],
% 1.14/1.53 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 1.14/1.53 Y, 'unordered_pair'( X, Y ) ) ],
% 1.14/1.53 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 1.14/1.53 X, 'universal_class' ) ],
% 1.14/1.53 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 1.14/1.53 Y, 'universal_class' ) ],
% 1.14/1.53 [ subclass( X, X ) ],
% 1.14/1.53 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 1.14/1.53 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 1.14/1.53 'not_subclass_element'( Y, X ), Y ) ],
% 1.14/1.53 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 1.14/1.53 'not_subclass_element'( Y, X ), Y ) ],
% 1.14/1.53 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 1.14/1.53 'not_subclass_element'( Y, X ), Y ) ],
% 1.14/1.53 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 1.14/1.53 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 1.14/1.53 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 1.14/1.53 [ ~( member( X, 'null_class' ) ) ],
% 1.14/1.53 [ subclass( 'null_class', X ) ],
% 1.14/1.53 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 1.14/1.53 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 1.14/1.53 ), X ) ],
% 1.14/1.53 [ member( 'null_class', 'universal_class' ) ],
% 1.14/1.53 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 1.14/1.53 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 1.14/1.53 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 1.14/1.53 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 1.14/1.53 Y ) ) ],
% 1.14/1.53 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 1.14/1.53 Y ) ) ],
% 1.14/1.53 [ ~( =( 'unordered_pair'( x, y ), 'null_class' ) ) ],
% 1.14/1.53 [ ~( member( x, 'universal_class' ) ) ],
% 1.14/1.53 [ ~( member( y, 'universal_class' ) ) ]
% 1.14/1.53 ] .
% 1.14/1.53
% 1.14/1.53
% 1.14/1.53 percentage equality = 0.219731, percentage horn = 0.878261
% 1.14/1.53 This is a problem with some equality
% 1.14/1.53
% 1.14/1.53
% 1.14/1.53
% 1.14/1.53 Options Used:
% 1.14/1.53
% 1.14/1.53 useres = 1
% 1.14/1.53 useparamod = 1
% 1.14/1.53 useeqrefl = 1
% 1.14/1.53 useeqfact = 1
% 1.14/1.53 usefactor = 1
% 1.14/1.53 usesimpsplitting = 0
% 1.14/1.53 usesimpdemod = 5
% 1.14/1.53 usesimpres = 3
% 1.14/1.53
% 1.14/1.53 resimpinuse = 1000
% 1.14/1.53 resimpclauses = 20000
% 1.14/1.53 substype = eqrewr
% 1.14/1.53 backwardsubs = 1
% 1.14/1.53 selectoldest = 5
% 1.14/1.53
% 1.14/1.53 litorderings [0] = split
% 1.14/1.53 litorderings [1] = extend the termordering, first sorting on arguments
% 1.14/1.53
% 1.14/1.53 termordering = kbo
% 1.14/1.53
% 1.14/1.53 litapriori = 0
% 1.14/1.53 termapriori = 1
% 1.14/1.53 litaposteriori = 0
% 1.14/1.53 termaposteriori = 0
% 1.62/2.04 demodaposteriori = 0
% 1.62/2.04 ordereqreflfact = 0
% 1.62/2.04
% 1.62/2.04 litselect = negord
% 1.62/2.04
% 1.62/2.04 maxweight = 15
% 1.62/2.04 maxdepth = 30000
% 1.62/2.04 maxlength = 115
% 1.62/2.04 maxnrvars = 195
% 1.62/2.04 excuselevel = 1
% 1.62/2.04 increasemaxweight = 1
% 1.62/2.04
% 1.62/2.04 maxselected = 10000000
% 1.62/2.04 maxnrclauses = 10000000
% 1.62/2.04
% 1.62/2.04 showgenerated = 0
% 1.62/2.04 showkept = 0
% 1.62/2.04 showselected = 0
% 1.62/2.04 showdeleted = 0
% 1.62/2.04 showresimp = 1
% 1.62/2.04 showstatus = 2000
% 1.62/2.04
% 1.62/2.04 prologoutput = 1
% 1.62/2.04 nrgoals = 5000000
% 1.62/2.04 totalproof = 1
% 1.62/2.04
% 1.62/2.04 Symbols occurring in the translation:
% 1.62/2.04
% 1.62/2.04 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.62/2.04 . [1, 2] (w:1, o:56, a:1, s:1, b:0),
% 1.62/2.04 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 1.62/2.04 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.62/2.04 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.62/2.04 subclass [41, 2] (w:1, o:81, a:1, s:1, b:0),
% 1.62/2.04 member [43, 2] (w:1, o:82, a:1, s:1, b:0),
% 1.62/2.04 'not_subclass_element' [44, 2] (w:1, o:83, a:1, s:1, b:0),
% 1.62/2.04 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 1.62/2.04 'unordered_pair' [46, 2] (w:1, o:84, a:1, s:1, b:0),
% 1.62/2.04 singleton [47, 1] (w:1, o:39, a:1, s:1, b:0),
% 1.62/2.04 'ordered_pair' [48, 2] (w:1, o:85, a:1, s:1, b:0),
% 1.62/2.04 'cross_product' [50, 2] (w:1, o:86, a:1, s:1, b:0),
% 1.62/2.04 first [52, 1] (w:1, o:40, a:1, s:1, b:0),
% 1.62/2.04 second [53, 1] (w:1, o:41, a:1, s:1, b:0),
% 1.62/2.04 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 1.62/2.04 intersection [55, 2] (w:1, o:88, a:1, s:1, b:0),
% 1.62/2.04 complement [56, 1] (w:1, o:42, a:1, s:1, b:0),
% 1.62/2.04 union [57, 2] (w:1, o:89, a:1, s:1, b:0),
% 1.62/2.04 'symmetric_difference' [58, 2] (w:1, o:90, a:1, s:1, b:0),
% 1.62/2.04 restrict [60, 3] (w:1, o:93, a:1, s:1, b:0),
% 1.62/2.04 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.62/2.04 'domain_of' [62, 1] (w:1, o:44, a:1, s:1, b:0),
% 1.62/2.04 rotate [63, 1] (w:1, o:36, a:1, s:1, b:0),
% 1.62/2.04 flip [65, 1] (w:1, o:45, a:1, s:1, b:0),
% 1.62/2.04 inverse [66, 1] (w:1, o:46, a:1, s:1, b:0),
% 1.62/2.04 'range_of' [67, 1] (w:1, o:37, a:1, s:1, b:0),
% 1.62/2.04 domain [68, 3] (w:1, o:95, a:1, s:1, b:0),
% 1.62/2.04 range [69, 3] (w:1, o:96, a:1, s:1, b:0),
% 1.62/2.04 image [70, 2] (w:1, o:87, a:1, s:1, b:0),
% 1.62/2.04 successor [71, 1] (w:1, o:47, a:1, s:1, b:0),
% 1.62/2.04 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 1.62/2.04 inductive [73, 1] (w:1, o:48, a:1, s:1, b:0),
% 1.62/2.04 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.62/2.04 'sum_class' [75, 1] (w:1, o:49, a:1, s:1, b:0),
% 1.62/2.04 'power_class' [76, 1] (w:1, o:52, a:1, s:1, b:0),
% 1.62/2.04 compose [78, 2] (w:1, o:91, a:1, s:1, b:0),
% 1.62/2.04 'single_valued_class' [79, 1] (w:1, o:53, a:1, s:1, b:0),
% 1.62/2.04 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 1.62/2.04 function [82, 1] (w:1, o:54, a:1, s:1, b:0),
% 1.62/2.04 regular [83, 1] (w:1, o:38, a:1, s:1, b:0),
% 1.62/2.04 apply [84, 2] (w:1, o:92, a:1, s:1, b:0),
% 1.62/2.04 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.62/2.04 'one_to_one' [86, 1] (w:1, o:50, a:1, s:1, b:0),
% 1.62/2.04 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 1.62/2.04 diagonalise [88, 1] (w:1, o:55, a:1, s:1, b:0),
% 1.62/2.04 cantor [89, 1] (w:1, o:43, a:1, s:1, b:0),
% 1.62/2.04 operation [90, 1] (w:1, o:51, a:1, s:1, b:0),
% 1.62/2.04 compatible [94, 3] (w:1, o:94, a:1, s:1, b:0),
% 1.62/2.04 homomorphism [95, 3] (w:1, o:97, a:1, s:1, b:0),
% 1.62/2.04 'not_homomorphism1' [96, 3] (w:1, o:98, a:1, s:1, b:0),
% 1.62/2.04 'not_homomorphism2' [97, 3] (w:1, o:99, a:1, s:1, b:0),
% 1.62/2.04 x [98, 0] (w:1, o:29, a:1, s:1, b:0),
% 1.62/2.04 y [99, 0] (w:1, o:30, a:1, s:1, b:0).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 Starting Search:
% 1.62/2.04
% 1.62/2.04 Resimplifying inuse:
% 1.62/2.04 Done
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 Intermediate Status:
% 1.62/2.04 Generated: 4124
% 1.62/2.04 Kept: 2000
% 1.62/2.04 Inuse: 129
% 1.62/2.04 Deleted: 4
% 1.62/2.04 Deletedinuse: 4
% 1.62/2.04
% 1.62/2.04 Resimplifying inuse:
% 1.62/2.04 Done
% 1.62/2.04
% 1.62/2.04 Resimplifying inuse:
% 1.62/2.04 Done
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 Intermediate Status:
% 1.62/2.04 Generated: 9028
% 1.62/2.04 Kept: 4001
% 1.62/2.04 Inuse: 212
% 1.62/2.04 Deleted: 9
% 1.62/2.04 Deletedinuse: 9
% 1.62/2.04
% 1.62/2.04 Resimplifying inuse:
% 1.62/2.04 Done
% 1.62/2.04
% 1.62/2.04 Resimplifying inuse:
% 1.62/2.04 Done
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 Intermediate Status:
% 1.62/2.04 Generated: 14448
% 1.62/2.04 Kept: 6211
% 1.62/2.04 Inuse: 291
% 1.62/2.04 Deleted: 11
% 1.62/2.04 Deletedinuse: 11
% 1.62/2.04
% 1.62/2.04 Resimplifying inuse:
% 1.62/2.04 Done
% 1.62/2.04
% 1.62/2.04 Resimplifying inuse:
% 1.62/2.04 Done
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 Intermediate Status:
% 1.62/2.04 Generated: 20075
% 1.62/2.04 Kept: 8259
% 1.62/2.04 Inuse: 356
% 1.62/2.04 Deleted: 53
% 1.62/2.04 Deletedinuse: 53
% 1.62/2.04
% 1.62/2.04 Resimplifying inuse:
% 1.62/2.04 Done
% 1.62/2.04
% 1.62/2.04 Resimplifying inuse:
% 1.62/2.04 Done
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 Intermediate Status:
% 1.62/2.04 Generated: 27439
% 1.62/2.04 Kept: 10264
% 1.62/2.04 Inuse: 410
% 1.62/2.04 Deleted: 57
% 1.62/2.04 Deletedinuse: 57
% 1.62/2.04
% 1.62/2.04 Resimplifying inuse:
% 1.62/2.04 Done
% 1.62/2.04
% 1.62/2.04 Resimplifying inuse:
% 1.62/2.04 Done
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 Intermediate Status:
% 1.62/2.04 Generated: 35371
% 1.62/2.04 Kept: 12296
% 1.62/2.04 Inuse: 433
% 1.62/2.04 Deleted: 64
% 1.62/2.04 Deletedinuse: 58
% 1.62/2.04
% 1.62/2.04 Resimplifying inuse:
% 1.62/2.04 Done
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 Bliksems!, er is een bewijs:
% 1.62/2.04 % SZS status Unsatisfiable
% 1.62/2.04 % SZS output start Refutation
% 1.62/2.04
% 1.62/2.04 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 1.62/2.04 )
% 1.62/2.04 .
% 1.62/2.04 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z
% 1.62/2.04 ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 103, [ =( X, 'null_class' ), member( 'not_subclass_element'( X,
% 1.62/2.04 'null_class' ), X ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 108, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X )
% 1.62/2.04 , singleton( Y ) ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 110, [ ~( =( 'unordered_pair'( x, y ), 'null_class' ) ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 111, [ ~( member( x, 'universal_class' ) ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 112, [ ~( member( y, 'universal_class' ) ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 113, [ =( X, Y ), ~( member( X, singleton( Y ) ) ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 127, [ ~( member( y, X ) ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 128, [ ~( member( x, X ) ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 144, [ =( X, Y ), ~( =( Y, X ) ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 559, [ ~( member( X, Y ) ), ~( =( X, x ) ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 12416, [ ~( =( singleton( x ), 'null_class' ) ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 12613, [ ~( member( X, singleton( x ) ) ), ~( member( X, Y ) ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 14018, [ ~( member( X, singleton( x ) ) ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 14029, [ =( singleton( x ), 'null_class' ) ] )
% 1.62/2.04 .
% 1.62/2.04 clause( 14038, [] )
% 1.62/2.04 .
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 % SZS output end Refutation
% 1.62/2.04 found a proof!
% 1.62/2.04
% 1.62/2.04 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.62/2.04
% 1.62/2.04 initialclauses(
% 1.62/2.04 [ clause( 14040, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.62/2.04 ) ] )
% 1.62/2.04 , clause( 14041, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 1.62/2.04 , Y ) ] )
% 1.62/2.04 , clause( 14042, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 1.62/2.04 subclass( X, Y ) ] )
% 1.62/2.04 , clause( 14043, [ subclass( X, 'universal_class' ) ] )
% 1.62/2.04 , clause( 14044, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.62/2.04 , clause( 14045, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 1.62/2.04 , clause( 14046, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 1.62/2.04 ] )
% 1.62/2.04 , clause( 14047, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 1.62/2.04 =( X, Z ) ] )
% 1.62/2.04 , clause( 14048, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.62/2.04 'unordered_pair'( X, Y ) ) ] )
% 1.62/2.04 , clause( 14049, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.62/2.04 'unordered_pair'( Y, X ) ) ] )
% 1.62/2.04 , clause( 14050, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 1.62/2.04 )
% 1.62/2.04 , clause( 14051, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.62/2.04 , clause( 14052, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 1.62/2.04 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.62/2.04 , clause( 14053, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.62/2.04 ) ) ), member( X, Z ) ] )
% 1.62/2.04 , clause( 14054, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.62/2.04 ) ) ), member( Y, T ) ] )
% 1.62/2.04 , clause( 14055, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.62/2.04 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.62/2.04 , clause( 14056, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 1.62/2.04 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 1.62/2.04 , clause( 14057, [ subclass( 'element_relation', 'cross_product'(
% 1.62/2.04 'universal_class', 'universal_class' ) ) ] )
% 1.62/2.04 , clause( 14058, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 1.62/2.04 ), member( X, Y ) ] )
% 1.62/2.04 , clause( 14059, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.62/2.04 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 1.62/2.04 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 1.62/2.04 , clause( 14060, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.62/2.04 )
% 1.62/2.04 , clause( 14061, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 1.62/2.04 )
% 1.62/2.04 , clause( 14062, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 1.62/2.04 intersection( Y, Z ) ) ] )
% 1.62/2.04 , clause( 14063, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 1.62/2.04 )
% 1.62/2.04 , clause( 14064, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.62/2.04 complement( Y ) ), member( X, Y ) ] )
% 1.62/2.04 , clause( 14065, [ =( complement( intersection( complement( X ), complement(
% 1.62/2.04 Y ) ) ), union( X, Y ) ) ] )
% 1.62/2.04 , clause( 14066, [ =( intersection( complement( intersection( X, Y ) ),
% 1.62/2.04 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 1.62/2.04 'symmetric_difference'( X, Y ) ) ] )
% 1.62/2.04 , clause( 14067, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 1.62/2.04 X, Y, Z ) ) ] )
% 1.62/2.04 , clause( 14068, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 1.62/2.04 Z, X, Y ) ) ] )
% 1.62/2.04 , clause( 14069, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 1.62/2.04 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 1.62/2.04 , clause( 14070, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 1.62/2.04 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 1.62/2.04 'domain_of'( Y ) ) ] )
% 1.62/2.04 , clause( 14071, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 1.62/2.04 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.62/2.04 , clause( 14072, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.62/2.04 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 1.62/2.04 ] )
% 1.62/2.04 , clause( 14073, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.62/2.04 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 1.62/2.04 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.62/2.04 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 1.62/2.04 , Y ), rotate( T ) ) ] )
% 1.62/2.04 , clause( 14074, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 1.62/2.04 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.62/2.04 , clause( 14075, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.62/2.04 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 1.62/2.04 )
% 1.62/2.04 , clause( 14076, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.62/2.04 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 1.62/2.04 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.62/2.04 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 1.62/2.04 , Z ), flip( T ) ) ] )
% 1.62/2.04 , clause( 14077, [ =( 'domain_of'( flip( 'cross_product'( X,
% 1.62/2.04 'universal_class' ) ) ), inverse( X ) ) ] )
% 1.62/2.04 , clause( 14078, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 1.62/2.04 , clause( 14079, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 1.62/2.04 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 1.62/2.04 , clause( 14080, [ =( second( 'not_subclass_element'( restrict( X,
% 1.62/2.04 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 1.62/2.04 , clause( 14081, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 1.62/2.04 image( X, Y ) ) ] )
% 1.62/2.04 , clause( 14082, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 1.62/2.04 , clause( 14083, [ subclass( 'successor_relation', 'cross_product'(
% 1.62/2.04 'universal_class', 'universal_class' ) ) ] )
% 1.62/2.04 , clause( 14084, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 1.62/2.04 ) ), =( successor( X ), Y ) ] )
% 1.62/2.04 , clause( 14085, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 1.62/2.04 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 1.62/2.04 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 1.62/2.04 , clause( 14086, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 1.62/2.04 , clause( 14087, [ ~( inductive( X ) ), subclass( image(
% 1.62/2.04 'successor_relation', X ), X ) ] )
% 1.62/2.04 , clause( 14088, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 1.62/2.04 'successor_relation', X ), X ) ), inductive( X ) ] )
% 1.62/2.04 , clause( 14089, [ inductive( omega ) ] )
% 1.62/2.04 , clause( 14090, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 1.62/2.04 , clause( 14091, [ member( omega, 'universal_class' ) ] )
% 1.62/2.04 , clause( 14092, [ =( 'domain_of'( restrict( 'element_relation',
% 1.62/2.04 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 1.62/2.04 , clause( 14093, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 1.62/2.04 X ), 'universal_class' ) ] )
% 1.62/2.04 , clause( 14094, [ =( complement( image( 'element_relation', complement( X
% 1.62/2.04 ) ) ), 'power_class'( X ) ) ] )
% 1.62/2.04 , clause( 14095, [ ~( member( X, 'universal_class' ) ), member(
% 1.62/2.04 'power_class'( X ), 'universal_class' ) ] )
% 1.62/2.04 , clause( 14096, [ subclass( compose( X, Y ), 'cross_product'(
% 1.62/2.04 'universal_class', 'universal_class' ) ) ] )
% 1.62/2.04 , clause( 14097, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 1.62/2.04 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 1.62/2.04 , clause( 14098, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 1.62/2.04 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 1.62/2.04 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 1.62/2.04 ) ] )
% 1.62/2.04 , clause( 14099, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 1.62/2.04 inverse( X ) ), 'identity_relation' ) ] )
% 1.62/2.04 , clause( 14100, [ ~( subclass( compose( X, inverse( X ) ),
% 1.62/2.04 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 1.62/2.04 , clause( 14101, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 1.62/2.04 'universal_class', 'universal_class' ) ) ] )
% 1.62/2.04 , clause( 14102, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 1.62/2.04 , 'identity_relation' ) ] )
% 1.62/2.04 , clause( 14103, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 1.62/2.04 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 1.62/2.04 'identity_relation' ) ), function( X ) ] )
% 1.62/2.04 , clause( 14104, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 1.62/2.04 , member( image( X, Y ), 'universal_class' ) ] )
% 1.62/2.04 , clause( 14105, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.62/2.04 , clause( 14106, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 1.62/2.04 , 'null_class' ) ] )
% 1.62/2.04 , clause( 14107, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 1.62/2.04 Y ) ) ] )
% 1.62/2.04 , clause( 14108, [ function( choice ) ] )
% 1.62/2.04 , clause( 14109, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 1.62/2.04 ), member( apply( choice, X ), X ) ] )
% 1.62/2.04 , clause( 14110, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 1.62/2.04 , clause( 14111, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 1.62/2.04 , clause( 14112, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 1.62/2.04 'one_to_one'( X ) ] )
% 1.62/2.04 , clause( 14113, [ =( intersection( 'cross_product'( 'universal_class',
% 1.62/2.04 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 1.62/2.04 'universal_class' ), complement( compose( complement( 'element_relation'
% 1.62/2.04 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 1.62/2.04 , clause( 14114, [ =( intersection( inverse( 'subset_relation' ),
% 1.62/2.04 'subset_relation' ), 'identity_relation' ) ] )
% 1.62/2.04 , clause( 14115, [ =( complement( 'domain_of'( intersection( X,
% 1.62/2.04 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 1.62/2.04 , clause( 14116, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 1.62/2.04 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 1.62/2.04 , clause( 14117, [ ~( operation( X ) ), function( X ) ] )
% 1.62/2.04 , clause( 14118, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 1.62/2.04 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.62/2.04 ] )
% 1.62/2.04 , clause( 14119, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 1.62/2.04 'domain_of'( 'domain_of'( X ) ) ) ] )
% 1.62/2.04 , clause( 14120, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 1.62/2.04 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.62/2.04 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 1.62/2.04 operation( X ) ] )
% 1.62/2.04 , clause( 14121, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 1.62/2.04 , clause( 14122, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 1.62/2.04 Y ) ), 'domain_of'( X ) ) ] )
% 1.62/2.04 , clause( 14123, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 1.62/2.04 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 1.62/2.04 , clause( 14124, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 1.62/2.04 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 1.62/2.04 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 1.62/2.04 , clause( 14125, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 1.62/2.04 , clause( 14126, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 1.62/2.04 , clause( 14127, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 1.62/2.04 , clause( 14128, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 1.62/2.04 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 1.62/2.04 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 1.62/2.04 )
% 1.62/2.04 , clause( 14129, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.62/2.04 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.62/2.04 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.62/2.04 , Y ) ] )
% 1.62/2.04 , clause( 14130, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.62/2.04 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 1.62/2.04 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 1.62/2.04 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 1.62/2.04 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 1.62/2.04 )
% 1.62/2.04 , clause( 14131, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.62/2.04 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 1.62/2.04 , clause( 14132, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.62/2.04 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 1.62/2.04 , clause( 14133, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.62/2.04 ) ) ), member( X, 'universal_class' ) ] )
% 1.62/2.04 , clause( 14134, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.62/2.04 ) ) ), member( Y, 'universal_class' ) ] )
% 1.62/2.04 , clause( 14135, [ subclass( X, X ) ] )
% 1.62/2.04 , clause( 14136, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 1.62/2.04 X, Z ) ] )
% 1.62/2.04 , clause( 14137, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 1.62/2.04 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 1.62/2.04 , clause( 14138, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 1.62/2.04 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 1.62/2.04 , clause( 14139, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 1.62/2.04 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 1.62/2.04 , clause( 14140, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 1.62/2.04 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 1.62/2.04 , clause( 14141, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 1.62/2.04 )
% 1.62/2.04 , clause( 14142, [ ~( member( X, 'null_class' ) ) ] )
% 1.62/2.04 , clause( 14143, [ subclass( 'null_class', X ) ] )
% 1.62/2.04 , clause( 14144, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 1.62/2.04 )
% 1.62/2.04 , clause( 14145, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 1.62/2.04 , 'null_class' ), X ) ] )
% 1.62/2.04 , clause( 14146, [ member( 'null_class', 'universal_class' ) ] )
% 1.62/2.04 , clause( 14147, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 1.62/2.04 ] )
% 1.62/2.04 , clause( 14148, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 1.62/2.04 )
% 1.62/2.04 , clause( 14149, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 1.62/2.04 )
% 1.62/2.04 , clause( 14150, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 1.62/2.04 X ), singleton( Y ) ) ] )
% 1.62/2.04 , clause( 14151, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 1.62/2.04 Y ), singleton( Y ) ) ] )
% 1.62/2.04 , clause( 14152, [ ~( =( 'unordered_pair'( x, y ), 'null_class' ) ) ] )
% 1.62/2.04 , clause( 14153, [ ~( member( x, 'universal_class' ) ) ] )
% 1.62/2.04 , clause( 14154, [ ~( member( y, 'universal_class' ) ) ] )
% 1.62/2.04 ] ).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 subsumption(
% 1.62/2.04 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 1.62/2.04 )
% 1.62/2.04 , clause( 14040, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.62/2.04 ) ] )
% 1.62/2.04 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.62/2.04 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 subsumption(
% 1.62/2.04 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 1.62/2.04 , clause( 14043, [ subclass( X, 'universal_class' ) ] )
% 1.62/2.04 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 subsumption(
% 1.62/2.04 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.62/2.04 , clause( 14044, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.62/2.04 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.62/2.04 ), ==>( 1, 1 )] ) ).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 subsumption(
% 1.62/2.04 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 1.62/2.04 , clause( 14046, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 1.62/2.04 ] )
% 1.62/2.04 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.62/2.04 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 subsumption(
% 1.62/2.04 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z
% 1.62/2.04 ) ] )
% 1.62/2.04 , clause( 14047, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 1.62/2.04 =( X, Z ) ] )
% 1.62/2.04 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.62/2.04 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 subsumption(
% 1.62/2.04 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.62/2.04 , clause( 14051, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.62/2.04 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 subsumption(
% 1.62/2.04 clause( 103, [ =( X, 'null_class' ), member( 'not_subclass_element'( X,
% 1.62/2.04 'null_class' ), X ) ] )
% 1.62/2.04 , clause( 14145, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 1.62/2.04 , 'null_class' ), X ) ] )
% 1.62/2.04 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.62/2.04 1 )] ) ).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 subsumption(
% 1.62/2.04 clause( 108, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X )
% 1.62/2.04 , singleton( Y ) ) ] )
% 1.62/2.04 , clause( 14150, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 1.62/2.04 X ), singleton( Y ) ) ] )
% 1.62/2.04 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.62/2.04 ), ==>( 1, 1 )] ) ).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 subsumption(
% 1.62/2.04 clause( 110, [ ~( =( 'unordered_pair'( x, y ), 'null_class' ) ) ] )
% 1.62/2.04 , clause( 14152, [ ~( =( 'unordered_pair'( x, y ), 'null_class' ) ) ] )
% 1.62/2.04 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 subsumption(
% 1.62/2.04 clause( 111, [ ~( member( x, 'universal_class' ) ) ] )
% 1.62/2.04 , clause( 14153, [ ~( member( x, 'universal_class' ) ) ] )
% 1.62/2.04 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 subsumption(
% 1.62/2.04 clause( 112, [ ~( member( y, 'universal_class' ) ) ] )
% 1.62/2.04 , clause( 14154, [ ~( member( y, 'universal_class' ) ) ] )
% 1.62/2.04 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 factor(
% 1.62/2.04 clause( 14477, [ ~( member( X, 'unordered_pair'( Y, Y ) ) ), =( X, Y ) ] )
% 1.62/2.04 , clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X
% 1.62/2.04 , Z ) ] )
% 1.62/2.04 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y )] )).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 paramod(
% 1.62/2.04 clause( 14478, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 1.62/2.04 , clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.62/2.04 , 0, clause( 14477, [ ~( member( X, 'unordered_pair'( Y, Y ) ) ), =( X, Y )
% 1.62/2.04 ] )
% 1.62/2.04 , 0, 3, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 1.62/2.04 :=( Y, Y )] )).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 subsumption(
% 1.62/2.04 clause( 113, [ =( X, Y ), ~( member( X, singleton( Y ) ) ) ] )
% 1.62/2.04 , clause( 14478, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 1.62/2.04 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 1.62/2.04 ), ==>( 1, 0 )] ) ).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 resolution(
% 1.62/2.04 clause( 14480, [ ~( subclass( X, 'universal_class' ) ), ~( member( y, X ) )
% 1.62/2.04 ] )
% 1.62/2.04 , clause( 112, [ ~( member( y, 'universal_class' ) ) ] )
% 1.62/2.04 , 0, clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.62/2.04 ) ] )
% 1.62/2.04 , 2, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y,
% 1.62/2.04 'universal_class' ), :=( Z, y )] )).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 resolution(
% 1.62/2.04 clause( 14481, [ ~( member( y, X ) ) ] )
% 1.62/2.04 , clause( 14480, [ ~( subclass( X, 'universal_class' ) ), ~( member( y, X )
% 1.62/2.04 ) ] )
% 1.62/2.04 , 0, clause( 3, [ subclass( X, 'universal_class' ) ] )
% 1.62/2.04 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 1.62/2.04 ).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 subsumption(
% 1.62/2.04 clause( 127, [ ~( member( y, X ) ) ] )
% 1.62/2.04 , clause( 14481, [ ~( member( y, X ) ) ] )
% 1.62/2.04 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 resolution(
% 1.62/2.04 clause( 14482, [ ~( subclass( X, 'universal_class' ) ), ~( member( x, X ) )
% 1.62/2.04 ] )
% 1.62/2.04 , clause( 111, [ ~( member( x, 'universal_class' ) ) ] )
% 1.62/2.04 , 0, clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.62/2.04 ) ] )
% 1.62/2.04 , 2, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y,
% 1.62/2.04 'universal_class' ), :=( Z, x )] )).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 resolution(
% 1.62/2.04 clause( 14483, [ ~( member( x, X ) ) ] )
% 1.62/2.04 , clause( 14482, [ ~( subclass( X, 'universal_class' ) ), ~( member( x, X )
% 1.62/2.04 ) ] )
% 1.62/2.04 , 0, clause( 3, [ subclass( X, 'universal_class' ) ] )
% 1.62/2.04 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 1.62/2.04 ).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 subsumption(
% 1.62/2.04 clause( 128, [ ~( member( x, X ) ) ] )
% 1.62/2.04 , clause( 14483, [ ~( member( x, X ) ) ] )
% 1.62/2.04 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 eqswap(
% 1.62/2.04 clause( 14484, [ ~( =( Y, X ) ), subclass( X, Y ) ] )
% 1.62/2.04 , clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.62/2.04 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.62/2.04
% 1.62/2.04
% 1.62/2.04 eqswap(
% 1.62/2.04 clause( 14485, [ ~( =( Y, X ) ), subclass( X, YCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------