TSTP Solution File: SET238-6 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET238-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n014.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 22:48:20 EDT 2022
% Result : Unsatisfiable 1.45s 1.88s
% Output : Refutation 1.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET238-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Mon Jul 11 01:14:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.70/1.09 *** allocated 10000 integers for termspace/termends
% 0.70/1.09 *** allocated 10000 integers for clauses
% 0.70/1.09 *** allocated 10000 integers for justifications
% 0.70/1.09 Bliksem 1.12
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 Automatic Strategy Selection
% 0.70/1.09
% 0.70/1.09 Clauses:
% 0.70/1.09 [
% 0.70/1.09 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.70/1.09 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.70/1.09 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.70/1.09 ,
% 0.70/1.09 [ subclass( X, 'universal_class' ) ],
% 0.70/1.09 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.70/1.09 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.70/1.09 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.70/1.09 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.70/1.09 ,
% 0.70/1.09 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.70/1.09 ) ) ],
% 0.70/1.09 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.70/1.09 ) ) ],
% 0.70/1.09 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.70/1.09 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.70/1.09 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.70/1.09 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.70/1.09 X, Z ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.70/1.09 Y, T ) ],
% 0.70/1.09 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.70/1.09 ), 'cross_product'( Y, T ) ) ],
% 0.70/1.09 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.70/1.09 ), second( X ) ), X ) ],
% 0.70/1.09 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.70/1.09 'universal_class' ) ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.70/1.09 Y ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.70/1.09 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.70/1.09 , Y ), 'element_relation' ) ],
% 0.70/1.09 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.70/1.09 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.70/1.09 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.70/1.09 Z ) ) ],
% 0.70/1.09 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.70/1.09 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.70/1.09 member( X, Y ) ],
% 0.70/1.09 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.70/1.09 union( X, Y ) ) ],
% 0.70/1.09 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.70/1.09 intersection( complement( X ), complement( Y ) ) ) ),
% 0.70/1.09 'symmetric_difference'( X, Y ) ) ],
% 0.70/1.09 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.70/1.09 ,
% 0.70/1.09 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.70/1.09 ,
% 0.70/1.09 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.70/1.09 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.70/1.09 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.70/1.09 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.70/1.09 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.70/1.09 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.70/1.09 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.70/1.09 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.70/1.09 'cross_product'( 'universal_class', 'universal_class' ),
% 0.70/1.09 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.70/1.09 Y ), rotate( T ) ) ],
% 0.70/1.09 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.70/1.09 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.70/1.09 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.70/1.09 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.70/1.09 'cross_product'( 'universal_class', 'universal_class' ),
% 0.70/1.09 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.70/1.09 Z ), flip( T ) ) ],
% 0.70/1.09 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.70/1.09 inverse( X ) ) ],
% 0.70/1.09 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.70/1.09 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.70/1.09 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.70/1.09 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.70/1.09 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.70/1.09 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.70/1.09 ],
% 0.70/1.09 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.70/1.09 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.70/1.09 'universal_class' ) ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.70/1.09 successor( X ), Y ) ],
% 0.70/1.09 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.70/1.09 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.70/1.09 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.70/1.09 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.70/1.09 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.70/1.09 ,
% 0.70/1.09 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.70/1.09 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.70/1.09 [ inductive( omega ) ],
% 0.70/1.09 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.70/1.09 [ member( omega, 'universal_class' ) ],
% 0.70/1.09 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.70/1.09 , 'sum_class'( X ) ) ],
% 0.70/1.09 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.70/1.09 'universal_class' ) ],
% 0.70/1.09 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.70/1.09 'power_class'( X ) ) ],
% 0.70/1.09 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.70/1.09 'universal_class' ) ],
% 0.70/1.09 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.70/1.09 'universal_class' ) ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.70/1.09 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.70/1.09 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.70/1.09 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.70/1.09 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.70/1.09 ) ],
% 0.70/1.09 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.70/1.09 , 'identity_relation' ) ],
% 0.70/1.09 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.70/1.09 'single_valued_class'( X ) ],
% 0.70/1.09 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.70/1.09 'universal_class' ) ) ],
% 0.70/1.09 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.70/1.09 'identity_relation' ) ],
% 0.70/1.09 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.70/1.09 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.70/1.09 , function( X ) ],
% 0.70/1.09 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.70/1.09 X, Y ), 'universal_class' ) ],
% 0.70/1.09 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.70/1.09 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.70/1.09 ) ],
% 0.70/1.09 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.70/1.09 [ function( choice ) ],
% 0.70/1.09 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.70/1.09 apply( choice, X ), X ) ],
% 0.70/1.09 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.70/1.10 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.70/1.10 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.70/1.10 ,
% 0.70/1.10 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.70/1.10 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.70/1.10 , complement( compose( complement( 'element_relation' ), inverse(
% 0.70/1.10 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.70/1.10 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.70/1.10 'identity_relation' ) ],
% 0.70/1.10 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.70/1.10 , diagonalise( X ) ) ],
% 0.70/1.10 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.70/1.10 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.70/1.10 [ ~( operation( X ) ), function( X ) ],
% 0.70/1.10 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.70/1.10 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.70/1.10 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.70/1.10 'domain_of'( X ) ) ) ],
% 0.70/1.10 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.70/1.10 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.70/1.10 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.70/1.10 X ) ],
% 0.70/1.10 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.70/1.10 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.70/1.10 'domain_of'( X ) ) ],
% 0.70/1.10 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.70/1.10 'domain_of'( Z ) ) ) ],
% 0.70/1.10 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.70/1.10 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.70/1.10 ), compatible( X, Y, Z ) ],
% 0.70/1.10 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.70/1.10 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.70/1.10 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.70/1.10 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.70/1.10 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.70/1.10 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.70/1.10 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.70/1.10 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.70/1.10 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.70/1.10 , Y ) ],
% 0.70/1.10 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.70/1.10 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.70/1.10 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.70/1.10 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.70/1.10 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.70/1.10 [ subclass( 'compose_class'( X ), 'cross_product'( 'universal_class',
% 0.70/1.10 'universal_class' ) ) ],
% 0.70/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ), =(
% 0.70/1.10 compose( Z, X ), Y ) ],
% 0.70/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.70/1.10 , 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) ), member(
% 0.70/1.10 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ],
% 0.70/1.10 [ subclass( 'composition_function', 'cross_product'( 'universal_class',
% 0.70/1.10 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.70/1.10 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.70/1.10 'composition_function' ) ), =( compose( X, Y ), Z ) ],
% 0.70/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.70/1.10 , 'universal_class' ) ) ), member( 'ordered_pair'( X, 'ordered_pair'( Y,
% 0.70/1.10 compose( X, Y ) ) ), 'composition_function' ) ],
% 0.70/1.10 [ subclass( 'domain_relation', 'cross_product'( 'universal_class',
% 0.70/1.10 'universal_class' ) ) ],
% 0.70/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) ), =(
% 0.70/1.10 'domain_of'( X ), Y ) ],
% 0.70/1.10 [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X,
% 0.70/1.10 'domain_of'( X ) ), 'domain_relation' ) ],
% 0.70/1.10 [ =( first( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.70/1.10 'identity_relation' ) ), 'single_valued1'( X ) ) ],
% 0.70/1.10 [ =( second( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.70/1.10 'identity_relation' ) ), 'single_valued2'( X ) ) ],
% 0.70/1.10 [ =( domain( X, image( inverse( X ), singleton( 'single_valued1'( X ) )
% 0.70/1.10 ), 'single_valued2'( X ) ), 'single_valued3'( X ) ) ],
% 0.70/1.10 [ =( intersection( complement( compose( 'element_relation', complement(
% 0.70/1.10 'identity_relation' ) ) ), 'element_relation' ), 'singleton_relation' ) ]
% 0.70/1.10 ,
% 0.70/1.10 [ subclass( 'application_function', 'cross_product'( 'universal_class',
% 0.70/1.10 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.70/1.10 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.70/1.10 'application_function' ) ), member( Y, 'domain_of'( X ) ) ],
% 0.70/1.10 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.70/1.10 'application_function' ) ), =( apply( X, Y ), Z ) ],
% 0.70/1.10 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.70/1.10 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 0.70/1.10 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 0.70/1.10 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 0.70/1.10 'application_function' ) ],
% 0.70/1.10 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.70/1.10 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 1.45/1.88 [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ],
% 1.45/1.88 [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ), maps( X,
% 1.45/1.88 'domain_of'( X ), Y ) ],
% 1.45/1.88 [ member( z, restrict( xr, x, y ) ) ],
% 1.45/1.88 [ ~( member( 'ordered_pair'( first( z ), second( z ) ), restrict( xr, x
% 1.45/1.88 , y ) ) ) ]
% 1.45/1.88 ] .
% 1.45/1.88
% 1.45/1.88
% 1.45/1.88 percentage equality = 0.222727, percentage horn = 0.929825
% 1.45/1.88 This is a problem with some equality
% 1.45/1.88
% 1.45/1.88
% 1.45/1.88
% 1.45/1.88 Options Used:
% 1.45/1.88
% 1.45/1.88 useres = 1
% 1.45/1.88 useparamod = 1
% 1.45/1.88 useeqrefl = 1
% 1.45/1.88 useeqfact = 1
% 1.45/1.88 usefactor = 1
% 1.45/1.88 usesimpsplitting = 0
% 1.45/1.88 usesimpdemod = 5
% 1.45/1.88 usesimpres = 3
% 1.45/1.88
% 1.45/1.88 resimpinuse = 1000
% 1.45/1.88 resimpclauses = 20000
% 1.45/1.88 substype = eqrewr
% 1.45/1.88 backwardsubs = 1
% 1.45/1.88 selectoldest = 5
% 1.45/1.88
% 1.45/1.88 litorderings [0] = split
% 1.45/1.88 litorderings [1] = extend the termordering, first sorting on arguments
% 1.45/1.88
% 1.45/1.88 termordering = kbo
% 1.45/1.88
% 1.45/1.88 litapriori = 0
% 1.45/1.88 termapriori = 1
% 1.45/1.88 litaposteriori = 0
% 1.45/1.88 termaposteriori = 0
% 1.45/1.88 demodaposteriori = 0
% 1.45/1.88 ordereqreflfact = 0
% 1.45/1.88
% 1.45/1.88 litselect = negord
% 1.45/1.88
% 1.45/1.88 maxweight = 15
% 1.45/1.88 maxdepth = 30000
% 1.45/1.88 maxlength = 115
% 1.45/1.88 maxnrvars = 195
% 1.45/1.88 excuselevel = 1
% 1.45/1.88 increasemaxweight = 1
% 1.45/1.88
% 1.45/1.88 maxselected = 10000000
% 1.45/1.88 maxnrclauses = 10000000
% 1.45/1.88
% 1.45/1.88 showgenerated = 0
% 1.45/1.88 showkept = 0
% 1.45/1.88 showselected = 0
% 1.45/1.88 showdeleted = 0
% 1.45/1.88 showresimp = 1
% 1.45/1.88 showstatus = 2000
% 1.45/1.88
% 1.45/1.88 prologoutput = 1
% 1.45/1.88 nrgoals = 5000000
% 1.45/1.88 totalproof = 1
% 1.45/1.88
% 1.45/1.88 Symbols occurring in the translation:
% 1.45/1.88
% 1.45/1.88 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.45/1.88 . [1, 2] (w:1, o:66, a:1, s:1, b:0),
% 1.45/1.88 ! [4, 1] (w:0, o:37, a:1, s:1, b:0),
% 1.45/1.88 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.45/1.88 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.45/1.88 subclass [41, 2] (w:1, o:91, a:1, s:1, b:0),
% 1.45/1.88 member [43, 2] (w:1, o:92, a:1, s:1, b:0),
% 1.45/1.88 'not_subclass_element' [44, 2] (w:1, o:93, a:1, s:1, b:0),
% 1.45/1.88 'universal_class' [45, 0] (w:1, o:22, a:1, s:1, b:0),
% 1.45/1.88 'unordered_pair' [46, 2] (w:1, o:94, a:1, s:1, b:0),
% 1.45/1.88 singleton [47, 1] (w:1, o:45, a:1, s:1, b:0),
% 1.45/1.88 'ordered_pair' [48, 2] (w:1, o:95, a:1, s:1, b:0),
% 1.45/1.88 'cross_product' [50, 2] (w:1, o:96, a:1, s:1, b:0),
% 1.45/1.88 first [52, 1] (w:1, o:46, a:1, s:1, b:0),
% 1.45/1.88 second [53, 1] (w:1, o:47, a:1, s:1, b:0),
% 1.45/1.88 'element_relation' [54, 0] (w:1, o:27, a:1, s:1, b:0),
% 1.45/1.88 intersection [55, 2] (w:1, o:98, a:1, s:1, b:0),
% 1.45/1.88 complement [56, 1] (w:1, o:48, a:1, s:1, b:0),
% 1.45/1.88 union [57, 2] (w:1, o:99, a:1, s:1, b:0),
% 1.45/1.88 'symmetric_difference' [58, 2] (w:1, o:100, a:1, s:1, b:0),
% 1.45/1.88 restrict [60, 3] (w:1, o:103, a:1, s:1, b:0),
% 1.45/1.88 'null_class' [61, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.45/1.88 'domain_of' [62, 1] (w:1, o:51, a:1, s:1, b:0),
% 1.45/1.88 rotate [63, 1] (w:1, o:42, a:1, s:1, b:0),
% 1.45/1.88 flip [65, 1] (w:1, o:52, a:1, s:1, b:0),
% 1.45/1.88 inverse [66, 1] (w:1, o:53, a:1, s:1, b:0),
% 1.45/1.88 'range_of' [67, 1] (w:1, o:43, a:1, s:1, b:0),
% 1.45/1.88 domain [68, 3] (w:1, o:105, a:1, s:1, b:0),
% 1.45/1.88 range [69, 3] (w:1, o:106, a:1, s:1, b:0),
% 1.45/1.88 image [70, 2] (w:1, o:97, a:1, s:1, b:0),
% 1.45/1.88 successor [71, 1] (w:1, o:54, a:1, s:1, b:0),
% 1.45/1.88 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 1.45/1.88 inductive [73, 1] (w:1, o:55, a:1, s:1, b:0),
% 1.45/1.88 omega [74, 0] (w:1, o:10, a:1, s:1, b:0),
% 1.45/1.88 'sum_class' [75, 1] (w:1, o:56, a:1, s:1, b:0),
% 1.45/1.88 'power_class' [76, 1] (w:1, o:59, a:1, s:1, b:0),
% 1.45/1.88 compose [78, 2] (w:1, o:101, a:1, s:1, b:0),
% 1.45/1.88 'single_valued_class' [79, 1] (w:1, o:60, a:1, s:1, b:0),
% 1.45/1.88 'identity_relation' [80, 0] (w:1, o:29, a:1, s:1, b:0),
% 1.45/1.88 function [82, 1] (w:1, o:61, a:1, s:1, b:0),
% 1.45/1.88 regular [83, 1] (w:1, o:44, a:1, s:1, b:0),
% 1.45/1.88 apply [84, 2] (w:1, o:102, a:1, s:1, b:0),
% 1.45/1.88 choice [85, 0] (w:1, o:30, a:1, s:1, b:0),
% 1.45/1.88 'one_to_one' [86, 1] (w:1, o:57, a:1, s:1, b:0),
% 1.45/1.88 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 1.45/1.88 diagonalise [88, 1] (w:1, o:62, a:1, s:1, b:0),
% 1.45/1.88 cantor [89, 1] (w:1, o:49, a:1, s:1, b:0),
% 1.45/1.88 operation [90, 1] (w:1, o:58, a:1, s:1, b:0),
% 1.45/1.88 compatible [94, 3] (w:1, o:104, a:1, s:1, b:0),
% 1.45/1.88 homomorphism [95, 3] (w:1, o:107, a:1, s:1, b:0),
% 1.45/1.88 'not_homomorphism1' [96, 3] (w:1, o:109, a:1, s:1, b:0),
% 1.45/1.88 'not_homomorphism2' [97, 3] (w:1, o:110, a:1, s:1, b:0),
% 1.45/1.88 'compose_class' [98, 1] (w:1, o:50, a:1, s:1, b:0),
% 1.45/1.88 'composition_function' [99, 0] (w:1, o:31, a:1, s:1, b:0),
% 1.45/1.88 'domain_relation' [100, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.45/1.88 'single_valued1' [101, 1] (w:1, o:63, a:1, s:1, b:0),
% 1.45/1.88 'single_valued2' [102, 1] (w:1, o:64, a:1, s:1, b:0),
% 1.45/1.88 'single_valued3' [103, 1] (w:1, o:65, a:1, s:1, b:0),
% 1.45/1.88 'singleton_relation' [104, 0] (w:1, o:7, a:1, s:1, b:0),
% 1.45/1.88 'application_function' [105, 0] (w:1, o:32, a:1, s:1, b:0),
% 1.45/1.88 maps [106, 3] (w:1, o:108, a:1, s:1, b:0),
% 1.45/1.88 z [107, 0] (w:1, o:34, a:1, s:1, b:0),
% 1.45/1.88 xr [108, 0] (w:1, o:35, a:1, s:1, b:0),
% 1.45/1.88 x [109, 0] (w:1, o:36, a:1, s:1, b:0),
% 1.45/1.88 y [110, 0] (w:1, o:33, a:1, s:1, b:0).
% 1.45/1.88
% 1.45/1.88
% 1.45/1.88 Starting Search:
% 1.45/1.88
% 1.45/1.88 Resimplifying inuse:
% 1.45/1.88 Done
% 1.45/1.88
% 1.45/1.88
% 1.45/1.88 Intermediate Status:
% 1.45/1.88 Generated: 5524
% 1.45/1.88 Kept: 2003
% 1.45/1.88 Inuse: 103
% 1.45/1.88 Deleted: 3
% 1.45/1.88 Deletedinuse: 2
% 1.45/1.88
% 1.45/1.88 Resimplifying inuse:
% 1.45/1.88 Done
% 1.45/1.88
% 1.45/1.88 Resimplifying inuse:
% 1.45/1.88 Done
% 1.45/1.88
% 1.45/1.88
% 1.45/1.88 Intermediate Status:
% 1.45/1.88 Generated: 10235
% 1.45/1.88 Kept: 4006
% 1.45/1.88 Inuse: 185
% 1.45/1.88 Deleted: 22
% 1.45/1.88 Deletedinuse: 14
% 1.45/1.88
% 1.45/1.88 Resimplifying inuse:
% 1.45/1.88 Done
% 1.45/1.88
% 1.45/1.88 Resimplifying inuse:
% 1.45/1.88 Done
% 1.45/1.88
% 1.45/1.88
% 1.45/1.88 Intermediate Status:
% 1.45/1.88 Generated: 14273
% 1.45/1.88 Kept: 6070
% 1.45/1.88 Inuse: 240
% 1.45/1.88 Deleted: 26
% 1.45/1.88 Deletedinuse: 15
% 1.45/1.88
% 1.45/1.88 Resimplifying inuse:
% 1.45/1.88 Done
% 1.45/1.88
% 1.45/1.88 Resimplifying inuse:
% 1.45/1.88 Done
% 1.45/1.88
% 1.45/1.88
% 1.45/1.88 Intermediate Status:
% 1.45/1.88 Generated: 19006
% 1.45/1.88 Kept: 8089
% 1.45/1.88 Inuse: 293
% 1.45/1.88 Deleted: 84
% 1.45/1.88 Deletedinuse: 71
% 1.45/1.88
% 1.45/1.88 Resimplifying inuse:
% 1.45/1.88 Done
% 1.45/1.88
% 1.45/1.88 Resimplifying inuse:
% 1.45/1.88 Done
% 1.45/1.88
% 1.45/1.88
% 1.45/1.88 Intermediate Status:
% 1.45/1.88 Generated: 24415
% 1.45/1.88 Kept: 10362
% 1.45/1.88 Inuse: 366
% 1.45/1.88 Deleted: 94
% 1.45/1.88 Deletedinuse: 79
% 1.45/1.88
% 1.45/1.88 Resimplifying inuse:
% 1.45/1.88 Done
% 1.45/1.88
% 1.45/1.88 Resimplifying inuse:
% 1.45/1.88 Done
% 1.45/1.88
% 1.45/1.88
% 1.45/1.88 Intermediate Status:
% 1.45/1.88 Generated: 28080
% 1.45/1.88 Kept: 12392
% 1.45/1.88 Inuse: 392
% 1.45/1.88 Deleted: 99
% 1.45/1.88 Deletedinuse: 84
% 1.45/1.88
% 1.45/1.88 Resimplifying inuse:
% 1.45/1.88 Done
% 1.45/1.88
% 1.45/1.88 Resimplifying inuse:
% 1.45/1.88 Done
% 1.45/1.88
% 1.45/1.88
% 1.45/1.88 Intermediate Status:
% 1.45/1.88 Generated: 32266
% 1.45/1.88 Kept: 14472
% 1.45/1.88 Inuse: 431
% 1.45/1.88 Deleted: 101
% 1.45/1.88 Deletedinuse: 86
% 1.45/1.88
% 1.45/1.88 Resimplifying inuse:
% 1.45/1.88 Done
% 1.45/1.88
% 1.45/1.88 Resimplifying inuse:
% 1.45/1.88 Done
% 1.45/1.88
% 1.45/1.88
% 1.45/1.88 Intermediate Status:
% 1.45/1.88 Generated: 35582
% 1.45/1.88 Kept: 16477
% 1.45/1.88 Inuse: 458
% 1.45/1.88 Deleted: 101
% 1.45/1.88 Deletedinuse: 86
% 1.45/1.88
% 1.45/1.88 Resimplifying inuse:
% 1.45/1.88
% 1.45/1.88 Bliksems!, er is een bewijs:
% 1.45/1.88 % SZS status Unsatisfiable
% 1.45/1.88 % SZS output start Refutation
% 1.45/1.88
% 1.45/1.88 clause( 15, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'(
% 1.45/1.88 first( X ), second( X ) ), X ) ] )
% 1.45/1.88 .
% 1.45/1.88 clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 1.45/1.88 .
% 1.45/1.88 clause( 26, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y
% 1.45/1.88 , Z ) ) ] )
% 1.45/1.88 .
% 1.45/1.88 clause( 111, [ member( z, restrict( xr, x, y ) ) ] )
% 1.45/1.88 .
% 1.45/1.88 clause( 112, [ ~( member( 'ordered_pair'( first( z ), second( z ) ),
% 1.45/1.88 restrict( xr, x, y ) ) ) ] )
% 1.45/1.88 .
% 1.45/1.88 clause( 16366, [ ~( member( z, 'cross_product'( X, Y ) ) ) ] )
% 1.45/1.88 .
% 1.45/1.88 clause( 16422, [ ~( member( z, restrict( X, Y, Z ) ) ) ] )
% 1.45/1.88 .
% 1.45/1.88 clause( 18015, [] )
% 1.45/1.88 .
% 1.45/1.88
% 1.45/1.88
% 1.45/1.88 % SZS output end Refutation
% 1.45/1.88 found a proof!
% 1.45/1.88
% 1.45/1.88 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.45/1.88
% 1.45/1.88 initialclauses(
% 1.45/1.88 [ clause( 18017, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.45/1.88 ) ] )
% 1.45/1.88 , clause( 18018, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 1.45/1.88 , Y ) ] )
% 1.45/1.88 , clause( 18019, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 1.45/1.88 subclass( X, Y ) ] )
% 1.45/1.88 , clause( 18020, [ subclass( X, 'universal_class' ) ] )
% 1.45/1.88 , clause( 18021, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.45/1.88 , clause( 18022, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 1.45/1.88 , clause( 18023, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 1.45/1.88 ] )
% 1.45/1.88 , clause( 18024, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 1.45/1.88 =( X, Z ) ] )
% 1.45/1.88 , clause( 18025, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.45/1.88 'unordered_pair'( X, Y ) ) ] )
% 1.45/1.88 , clause( 18026, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.45/1.88 'unordered_pair'( Y, X ) ) ] )
% 1.45/1.88 , clause( 18027, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 1.45/1.88 )
% 1.45/1.88 , clause( 18028, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.45/1.88 , clause( 18029, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 1.45/1.88 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.45/1.88 , clause( 18030, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.45/1.88 ) ) ), member( X, Z ) ] )
% 1.45/1.88 , clause( 18031, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.45/1.88 ) ) ), member( Y, T ) ] )
% 1.45/1.88 , clause( 18032, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.45/1.88 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.45/1.88 , clause( 18033, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 1.45/1.88 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 1.45/1.88 , clause( 18034, [ subclass( 'element_relation', 'cross_product'(
% 1.45/1.88 'universal_class', 'universal_class' ) ) ] )
% 1.45/1.88 , clause( 18035, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 1.45/1.88 ), member( X, Y ) ] )
% 1.45/1.88 , clause( 18036, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.45/1.88 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 1.45/1.88 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 1.45/1.88 , clause( 18037, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.45/1.88 )
% 1.45/1.88 , clause( 18038, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 1.45/1.88 )
% 1.45/1.88 , clause( 18039, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 1.45/1.88 intersection( Y, Z ) ) ] )
% 1.45/1.88 , clause( 18040, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 1.45/1.88 )
% 1.45/1.88 , clause( 18041, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.45/1.88 complement( Y ) ), member( X, Y ) ] )
% 1.45/1.88 , clause( 18042, [ =( complement( intersection( complement( X ), complement(
% 1.45/1.88 Y ) ) ), union( X, Y ) ) ] )
% 1.45/1.88 , clause( 18043, [ =( intersection( complement( intersection( X, Y ) ),
% 1.45/1.88 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 1.45/1.88 'symmetric_difference'( X, Y ) ) ] )
% 1.45/1.88 , clause( 18044, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 1.45/1.88 X, Y, Z ) ) ] )
% 1.45/1.88 , clause( 18045, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 1.45/1.88 Z, X, Y ) ) ] )
% 1.45/1.88 , clause( 18046, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 1.45/1.88 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 1.45/1.88 , clause( 18047, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 1.45/1.88 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 1.45/1.88 'domain_of'( Y ) ) ] )
% 1.45/1.88 , clause( 18048, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 1.45/1.88 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.45/1.88 , clause( 18049, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.45/1.88 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 1.45/1.88 ] )
% 1.45/1.88 , clause( 18050, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.45/1.88 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 1.45/1.88 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.45/1.88 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 1.45/1.88 , Y ), rotate( T ) ) ] )
% 1.45/1.88 , clause( 18051, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 1.45/1.88 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.45/1.88 , clause( 18052, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.45/1.88 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 1.45/1.88 )
% 1.45/1.88 , clause( 18053, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.45/1.88 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 1.45/1.88 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.45/1.88 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 1.45/1.88 , Z ), flip( T ) ) ] )
% 1.45/1.88 , clause( 18054, [ =( 'domain_of'( flip( 'cross_product'( X,
% 1.45/1.88 'universal_class' ) ) ), inverse( X ) ) ] )
% 1.45/1.88 , clause( 18055, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 1.45/1.88 , clause( 18056, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 1.45/1.88 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 1.45/1.88 , clause( 18057, [ =( second( 'not_subclass_element'( restrict( X,
% 1.45/1.88 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 1.45/1.88 , clause( 18058, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 1.45/1.88 image( X, Y ) ) ] )
% 1.45/1.88 , clause( 18059, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 1.45/1.88 , clause( 18060, [ subclass( 'successor_relation', 'cross_product'(
% 1.45/1.88 'universal_class', 'universal_class' ) ) ] )
% 1.45/1.88 , clause( 18061, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 1.45/1.88 ) ), =( successor( X ), Y ) ] )
% 1.45/1.88 , clause( 18062, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 1.45/1.88 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 1.45/1.88 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 1.45/1.88 , clause( 18063, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 1.45/1.88 , clause( 18064, [ ~( inductive( X ) ), subclass( image(
% 1.45/1.88 'successor_relation', X ), X ) ] )
% 1.45/1.88 , clause( 18065, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 1.45/1.88 'successor_relation', X ), X ) ), inductive( X ) ] )
% 1.45/1.88 , clause( 18066, [ inductive( omega ) ] )
% 1.45/1.88 , clause( 18067, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 1.45/1.88 , clause( 18068, [ member( omega, 'universal_class' ) ] )
% 1.45/1.88 , clause( 18069, [ =( 'domain_of'( restrict( 'element_relation',
% 1.45/1.88 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 1.45/1.88 , clause( 18070, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 1.45/1.88 X ), 'universal_class' ) ] )
% 1.45/1.88 , clause( 18071, [ =( complement( image( 'element_relation', complement( X
% 1.45/1.88 ) ) ), 'power_class'( X ) ) ] )
% 1.45/1.88 , clause( 18072, [ ~( member( X, 'universal_class' ) ), member(
% 1.45/1.88 'power_class'( X ), 'universal_class' ) ] )
% 1.45/1.88 , clause( 18073, [ subclass( compose( X, Y ), 'cross_product'(
% 1.45/1.88 'universal_class', 'universal_class' ) ) ] )
% 1.45/1.88 , clause( 18074, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 1.45/1.88 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 1.45/1.88 , clause( 18075, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 1.45/1.88 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 1.45/1.88 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 1.45/1.88 ) ] )
% 1.45/1.88 , clause( 18076, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 1.45/1.88 inverse( X ) ), 'identity_relation' ) ] )
% 1.45/1.88 , clause( 18077, [ ~( subclass( compose( X, inverse( X ) ),
% 1.45/1.88 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 1.45/1.88 , clause( 18078, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 1.45/1.88 'universal_class', 'universal_class' ) ) ] )
% 1.45/1.88 , clause( 18079, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 1.45/1.88 , 'identity_relation' ) ] )
% 1.45/1.88 , clause( 18080, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 1.45/1.88 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 1.45/1.88 'identity_relation' ) ), function( X ) ] )
% 1.45/1.88 , clause( 18081, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 1.45/1.88 , member( image( X, Y ), 'universal_class' ) ] )
% 1.45/1.88 , clause( 18082, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.45/1.88 , clause( 18083, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 1.45/1.88 , 'null_class' ) ] )
% 1.45/1.88 , clause( 18084, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 1.45/1.88 Y ) ) ] )
% 1.45/1.88 , clause( 18085, [ function( choice ) ] )
% 1.45/1.88 , clause( 18086, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 1.45/1.88 ), member( apply( choice, X ), X ) ] )
% 1.45/1.88 , clause( 18087, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 1.45/1.88 , clause( 18088, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 1.45/1.88 , clause( 18089, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 1.45/1.88 'one_to_one'( X ) ] )
% 1.45/1.88 , clause( 18090, [ =( intersection( 'cross_product'( 'universal_class',
% 1.45/1.88 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 1.45/1.88 'universal_class' ), complement( compose( complement( 'element_relation'
% 1.45/1.88 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 1.45/1.88 , clause( 18091, [ =( intersection( inverse( 'subset_relation' ),
% 1.45/1.88 'subset_relation' ), 'identity_relation' ) ] )
% 1.45/1.88 , clause( 18092, [ =( complement( 'domain_of'( intersection( X,
% 1.45/1.88 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 1.45/1.88 , clause( 18093, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 1.45/1.88 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 1.45/1.88 , clause( 18094, [ ~( operation( X ) ), function( X ) ] )
% 1.45/1.88 , clause( 18095, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 1.45/1.88 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.45/1.88 ] )
% 1.45/1.88 , clause( 18096, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 1.45/1.88 'domain_of'( 'domain_of'( X ) ) ) ] )
% 1.45/1.88 , clause( 18097, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 1.45/1.88 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.45/1.88 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 1.45/1.88 operation( X ) ] )
% 1.45/1.88 , clause( 18098, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 1.45/1.88 , clause( 18099, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 1.45/1.88 Y ) ), 'domain_of'( X ) ) ] )
% 1.45/1.88 , clause( 18100, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 1.45/1.88 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 1.45/1.88 , clause( 18101, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 1.45/1.88 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 1.45/1.88 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 1.45/1.88 , clause( 18102, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 1.45/1.88 , clause( 18103, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 1.45/1.88 , clause( 18104, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 1.45/1.88 , clause( 18105, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 1.45/1.89 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 1.45/1.89 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 1.45/1.89 )
% 1.45/1.89 , clause( 18106, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.45/1.89 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.45/1.89 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.45/1.89 , Y ) ] )
% 1.45/1.89 , clause( 18107, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.45/1.89 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 1.45/1.89 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 1.45/1.89 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 1.45/1.89 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 1.45/1.89 )
% 1.45/1.89 , clause( 18108, [ subclass( 'compose_class'( X ), 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ] )
% 1.45/1.89 , clause( 18109, [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z )
% 1.45/1.89 ) ), =( compose( Z, X ), Y ) ] )
% 1.45/1.89 , clause( 18110, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) )
% 1.45/1.89 , member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ] )
% 1.45/1.89 , clause( 18111, [ subclass( 'composition_function', 'cross_product'(
% 1.45/1.89 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 1.45/1.89 ) ) ) ] )
% 1.45/1.89 , clause( 18112, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.45/1.89 'composition_function' ) ), =( compose( X, Y ), Z ) ] )
% 1.45/1.89 , clause( 18113, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( X,
% 1.45/1.89 'ordered_pair'( Y, compose( X, Y ) ) ), 'composition_function' ) ] )
% 1.45/1.89 , clause( 18114, [ subclass( 'domain_relation', 'cross_product'(
% 1.45/1.89 'universal_class', 'universal_class' ) ) ] )
% 1.45/1.89 , clause( 18115, [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) )
% 1.45/1.89 , =( 'domain_of'( X ), Y ) ] )
% 1.45/1.89 , clause( 18116, [ ~( member( X, 'universal_class' ) ), member(
% 1.45/1.89 'ordered_pair'( X, 'domain_of'( X ) ), 'domain_relation' ) ] )
% 1.45/1.89 , clause( 18117, [ =( first( 'not_subclass_element'( compose( X, inverse( X
% 1.45/1.89 ) ), 'identity_relation' ) ), 'single_valued1'( X ) ) ] )
% 1.45/1.89 , clause( 18118, [ =( second( 'not_subclass_element'( compose( X, inverse(
% 1.45/1.89 X ) ), 'identity_relation' ) ), 'single_valued2'( X ) ) ] )
% 1.45/1.89 , clause( 18119, [ =( domain( X, image( inverse( X ), singleton(
% 1.45/1.89 'single_valued1'( X ) ) ), 'single_valued2'( X ) ), 'single_valued3'( X )
% 1.45/1.89 ) ] )
% 1.45/1.89 , clause( 18120, [ =( intersection( complement( compose( 'element_relation'
% 1.45/1.89 , complement( 'identity_relation' ) ) ), 'element_relation' ),
% 1.45/1.89 'singleton_relation' ) ] )
% 1.45/1.89 , clause( 18121, [ subclass( 'application_function', 'cross_product'(
% 1.45/1.89 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 1.45/1.89 ) ) ) ] )
% 1.45/1.89 , clause( 18122, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.45/1.89 'application_function' ) ), member( Y, 'domain_of'( X ) ) ] )
% 1.45/1.89 , clause( 18123, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.45/1.89 'application_function' ) ), =( apply( X, Y ), Z ) ] )
% 1.45/1.89 , clause( 18124, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.45/1.89 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 1.45/1.89 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 1.45/1.89 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 1.45/1.89 'application_function' ) ] )
% 1.45/1.89 , clause( 18125, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 1.45/1.89 , clause( 18126, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 1.45/1.89 , clause( 18127, [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ]
% 1.45/1.89 )
% 1.45/1.89 , clause( 18128, [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) )
% 1.45/1.89 , maps( X, 'domain_of'( X ), Y ) ] )
% 1.45/1.89 , clause( 18129, [ member( z, restrict( xr, x, y ) ) ] )
% 1.45/1.89 , clause( 18130, [ ~( member( 'ordered_pair'( first( z ), second( z ) ),
% 1.45/1.89 restrict( xr, x, y ) ) ) ] )
% 1.45/1.89 ] ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 15, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'(
% 1.45/1.89 first( X ), second( X ) ), X ) ] )
% 1.45/1.89 , clause( 18033, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 1.45/1.89 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 1.45/1.89 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.45/1.89 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 1.45/1.89 , clause( 18038, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 1.45/1.89 )
% 1.45/1.89 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.45/1.89 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 26, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y
% 1.45/1.89 , Z ) ) ] )
% 1.45/1.89 , clause( 18044, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 1.45/1.89 X, Y, Z ) ) ] )
% 1.45/1.89 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.45/1.89 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 111, [ member( z, restrict( xr, x, y ) ) ] )
% 1.45/1.89 , clause( 18129, [ member( z, restrict( xr, x, y ) ) ] )
% 1.45/1.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 112, [ ~( member( 'ordered_pair'( first( z ), second( z ) ),
% 1.45/1.89 restrict( xr, x, y ) ) ) ] )
% 1.45/1.89 , clause( 18130, [ ~( member( 'ordered_pair'( first( z ), second( z ) ),
% 1.45/1.89 restrict( xr, x, y ) ) ) ] )
% 1.45/1.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 paramod(
% 1.45/1.89 clause( 18292, [ ~( member( z, restrict( xr, x, y ) ) ), ~( member( z,
% 1.45/1.89 'cross_product'( X, Y ) ) ) ] )
% 1.45/1.89 , clause( 15, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 1.45/1.89 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 1.45/1.89 , 1, clause( 112, [ ~( member( 'ordered_pair'( first( z ), second( z ) ),
% 1.45/1.89 restrict( xr, x, y ) ) ) ] )
% 1.45/1.89 , 0, 2, substitution( 0, [ :=( X, z ), :=( Y, X ), :=( Z, Y )] ),
% 1.45/1.89 substitution( 1, [] )).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 resolution(
% 1.45/1.89 clause( 18293, [ ~( member( z, 'cross_product'( X, Y ) ) ) ] )
% 1.45/1.89 , clause( 18292, [ ~( member( z, restrict( xr, x, y ) ) ), ~( member( z,
% 1.45/1.89 'cross_product'( X, Y ) ) ) ] )
% 1.45/1.89 , 0, clause( 111, [ member( z, restrict( xr, x, y ) ) ] )
% 1.45/1.89 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [] )
% 1.45/1.89 ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 16366, [ ~( member( z, 'cross_product'( X, Y ) ) ) ] )
% 1.45/1.89 , clause( 18293, [ ~( member( z, 'cross_product'( X, Y ) ) ) ] )
% 1.45/1.89 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.45/1.89 )] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 resolution(
% 1.45/1.89 clause( 18295, [ ~( member( z, intersection( Z, 'cross_product'( X, Y ) ) )
% 1.45/1.89 ) ] )
% 1.45/1.89 , clause( 16366, [ ~( member( z, 'cross_product'( X, Y ) ) ) ] )
% 1.45/1.89 , 0, clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 1.45/1.89 )
% 1.45/1.89 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 1.45/1.89 , z ), :=( Y, Z ), :=( Z, 'cross_product'( X, Y ) )] )).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 paramod(
% 1.45/1.89 clause( 18296, [ ~( member( z, restrict( X, Y, Z ) ) ) ] )
% 1.45/1.89 , clause( 26, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X
% 1.45/1.89 , Y, Z ) ) ] )
% 1.45/1.89 , 0, clause( 18295, [ ~( member( z, intersection( Z, 'cross_product'( X, Y
% 1.45/1.89 ) ) ) ) ] )
% 1.45/1.89 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.45/1.89 substitution( 1, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 16422, [ ~( member( z, restrict( X, Y, Z ) ) ) ] )
% 1.45/1.89 , clause( 18296, [ ~( member( z, restrict( X, Y, Z ) ) ) ] )
% 1.45/1.89 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.45/1.89 permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 resolution(
% 1.45/1.89 clause( 18297, [] )
% 1.45/1.89 , clause( 16422, [ ~( member( z, restrict( X, Y, Z ) ) ) ] )
% 1.45/1.89 , 0, clause( 111, [ member( z, restrict( xr, x, y ) ) ] )
% 1.45/1.89 , 0, substitution( 0, [ :=( X, xr ), :=( Y, x ), :=( Z, y )] ),
% 1.45/1.89 substitution( 1, [] )).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 subsumption(
% 1.45/1.89 clause( 18015, [] )
% 1.45/1.89 , clause( 18297, [] )
% 1.45/1.89 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 end.
% 1.45/1.89
% 1.45/1.89 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.45/1.89
% 1.45/1.89 Memory use:
% 1.45/1.89
% 1.45/1.89 space for terms: 280430
% 1.45/1.89 space for clauses: 860901
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 clauses generated: 38101
% 1.45/1.89 clauses kept: 18016
% 1.45/1.89 clauses selected: 461
% 1.45/1.89 clauses deleted: 102
% 1.45/1.89 clauses inuse deleted: 87
% 1.45/1.89
% 1.45/1.89 subsentry: 78790
% 1.45/1.89 literals s-matched: 58453
% 1.45/1.89 literals matched: 57498
% 1.45/1.89 full subsumption: 23748
% 1.45/1.89
% 1.45/1.89 checksum: 231297255
% 1.45/1.89
% 1.45/1.89
% 1.45/1.89 Bliksem ended
%------------------------------------------------------------------------------