TSTP Solution File: SET563-6 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET563-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n011.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 22:50:17 EDT 2022
% Result : Unsatisfiable 0.79s 1.56s
% Output : Refutation 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET563-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.14 % Command : bliksem %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Mon Jul 11 04:58:57 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.75/1.16 *** allocated 10000 integers for termspace/termends
% 0.75/1.16 *** allocated 10000 integers for clauses
% 0.75/1.16 *** allocated 10000 integers for justifications
% 0.75/1.16 Bliksem 1.12
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 Automatic Strategy Selection
% 0.75/1.16
% 0.75/1.16 Clauses:
% 0.75/1.16 [
% 0.75/1.16 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.75/1.16 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.75/1.16 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.75/1.16 ,
% 0.75/1.16 [ subclass( X, 'universal_class' ) ],
% 0.75/1.16 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.75/1.16 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.75/1.16 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.75/1.16 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.75/1.16 ,
% 0.75/1.16 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.75/1.16 ) ) ],
% 0.75/1.16 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.75/1.16 ) ) ],
% 0.75/1.16 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.75/1.16 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.75/1.16 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.75/1.16 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.75/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.75/1.16 X, Z ) ],
% 0.75/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.75/1.16 Y, T ) ],
% 0.75/1.16 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.75/1.16 ), 'cross_product'( Y, T ) ) ],
% 0.75/1.16 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.75/1.16 ), second( X ) ), X ) ],
% 0.75/1.16 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.75/1.16 'universal_class' ) ) ],
% 0.75/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.75/1.16 Y ) ],
% 0.75/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.75/1.16 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.75/1.16 , Y ), 'element_relation' ) ],
% 0.75/1.16 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.75/1.16 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.75/1.16 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.75/1.16 Z ) ) ],
% 0.75/1.16 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.75/1.16 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.75/1.16 member( X, Y ) ],
% 0.75/1.16 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.75/1.16 union( X, Y ) ) ],
% 0.75/1.16 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.75/1.16 intersection( complement( X ), complement( Y ) ) ) ),
% 0.75/1.16 'symmetric_difference'( X, Y ) ) ],
% 0.75/1.16 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.75/1.16 ,
% 0.75/1.16 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.75/1.16 ,
% 0.75/1.16 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.75/1.16 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.75/1.16 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.75/1.16 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.75/1.16 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.75/1.16 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.75/1.16 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.75/1.16 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.75/1.16 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.75/1.16 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.75/1.16 'cross_product'( 'universal_class', 'universal_class' ),
% 0.75/1.16 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.75/1.16 Y ), rotate( T ) ) ],
% 0.75/1.16 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.75/1.16 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.75/1.16 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.75/1.16 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.75/1.16 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.75/1.16 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.75/1.16 'cross_product'( 'universal_class', 'universal_class' ),
% 0.75/1.16 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.75/1.16 Z ), flip( T ) ) ],
% 0.75/1.16 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.79/1.16 inverse( X ) ) ],
% 0.79/1.16 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.79/1.16 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.79/1.16 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.79/1.16 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.79/1.16 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.79/1.16 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.79/1.16 ],
% 0.79/1.16 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.79/1.16 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.79/1.16 'universal_class' ) ) ],
% 0.79/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.79/1.16 successor( X ), Y ) ],
% 0.79/1.16 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.79/1.16 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.79/1.16 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.79/1.16 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.79/1.16 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.79/1.16 ,
% 0.79/1.16 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.79/1.16 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.79/1.16 [ inductive( omega ) ],
% 0.79/1.16 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.79/1.16 [ member( omega, 'universal_class' ) ],
% 0.79/1.16 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.79/1.16 , 'sum_class'( X ) ) ],
% 0.79/1.16 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.79/1.16 'universal_class' ) ],
% 0.79/1.16 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.79/1.16 'power_class'( X ) ) ],
% 0.79/1.16 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.79/1.16 'universal_class' ) ],
% 0.79/1.16 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.79/1.16 'universal_class' ) ) ],
% 0.79/1.16 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.79/1.16 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.79/1.16 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.79/1.16 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.79/1.16 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.79/1.16 ) ],
% 0.79/1.16 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.79/1.16 , 'identity_relation' ) ],
% 0.79/1.16 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.79/1.16 'single_valued_class'( X ) ],
% 0.79/1.16 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.79/1.16 'universal_class' ) ) ],
% 0.79/1.16 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.79/1.16 'identity_relation' ) ],
% 0.79/1.16 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.79/1.16 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.79/1.16 , function( X ) ],
% 0.79/1.16 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.79/1.16 X, Y ), 'universal_class' ) ],
% 0.79/1.16 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.79/1.16 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.79/1.16 ) ],
% 0.79/1.16 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.79/1.16 [ function( choice ) ],
% 0.79/1.16 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.79/1.16 apply( choice, X ), X ) ],
% 0.79/1.16 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.79/1.16 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.79/1.16 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.79/1.16 ,
% 0.79/1.16 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.79/1.16 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.79/1.16 , complement( compose( complement( 'element_relation' ), inverse(
% 0.79/1.16 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.79/1.16 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.79/1.16 'identity_relation' ) ],
% 0.79/1.16 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.79/1.16 , diagonalise( X ) ) ],
% 0.79/1.16 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.79/1.16 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.79/1.16 [ ~( operation( X ) ), function( X ) ],
% 0.79/1.16 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.79/1.16 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.79/1.16 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.79/1.16 'domain_of'( X ) ) ) ],
% 0.79/1.16 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.79/1.16 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.79/1.16 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.79/1.16 X ) ],
% 0.79/1.16 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.79/1.16 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.79/1.16 'domain_of'( X ) ) ],
% 0.79/1.16 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.79/1.16 'domain_of'( Z ) ) ) ],
% 0.79/1.16 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.79/1.16 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.79/1.16 ), compatible( X, Y, Z ) ],
% 0.79/1.16 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.79/1.16 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.79/1.16 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.79/1.16 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.79/1.16 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.79/1.16 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.79/1.16 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.79/1.16 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.79/1.16 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.79/1.16 , Y ) ],
% 0.79/1.16 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.79/1.16 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.79/1.16 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.79/1.16 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.79/1.16 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.79/1.16 [ subclass( 'compose_class'( X ), 'cross_product'( 'universal_class',
% 0.79/1.16 'universal_class' ) ) ],
% 0.79/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ), =(
% 0.79/1.16 compose( Z, X ), Y ) ],
% 0.79/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.79/1.16 , 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) ), member(
% 0.79/1.16 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ],
% 0.79/1.16 [ subclass( 'composition_function', 'cross_product'( 'universal_class',
% 0.79/1.16 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.79/1.16 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.79/1.16 'composition_function' ) ), =( compose( X, Y ), Z ) ],
% 0.79/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.79/1.16 , 'universal_class' ) ) ), member( 'ordered_pair'( X, 'ordered_pair'( Y,
% 0.79/1.16 compose( X, Y ) ) ), 'composition_function' ) ],
% 0.79/1.16 [ subclass( 'domain_relation', 'cross_product'( 'universal_class',
% 0.79/1.16 'universal_class' ) ) ],
% 0.79/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) ), =(
% 0.79/1.16 'domain_of'( X ), Y ) ],
% 0.79/1.16 [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X,
% 0.79/1.16 'domain_of'( X ) ), 'domain_relation' ) ],
% 0.79/1.16 [ =( first( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.79/1.16 'identity_relation' ) ), 'single_valued1'( X ) ) ],
% 0.79/1.16 [ =( second( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.79/1.16 'identity_relation' ) ), 'single_valued2'( X ) ) ],
% 0.79/1.16 [ =( domain( X, image( inverse( X ), singleton( 'single_valued1'( X ) )
% 0.79/1.16 ), 'single_valued2'( X ) ), 'single_valued3'( X ) ) ],
% 0.79/1.16 [ =( intersection( complement( compose( 'element_relation', complement(
% 0.79/1.16 'identity_relation' ) ) ), 'element_relation' ), 'singleton_relation' ) ]
% 0.79/1.16 ,
% 0.79/1.16 [ subclass( 'application_function', 'cross_product'( 'universal_class',
% 0.79/1.16 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.79/1.16 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.79/1.16 'application_function' ) ), member( Y, 'domain_of'( X ) ) ],
% 0.79/1.16 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.79/1.16 'application_function' ) ), =( apply( X, Y ), Z ) ],
% 0.79/1.16 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.79/1.16 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 0.79/1.16 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 0.79/1.16 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 0.79/1.16 'application_function' ) ],
% 0.79/1.16 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.79/1.16 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 0.79/1.56 [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ],
% 0.79/1.56 [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ), maps( X,
% 0.79/1.56 'domain_of'( X ), Y ) ],
% 0.79/1.56 [ compatible( xh1, xf1, xf2 ) ],
% 0.79/1.56 [ compatible( xh2, xf2, xf3 ) ],
% 0.79/1.56 [ ~( subclass( 'range_of'( xh1 ), 'domain_of'( xh2 ) ) ) ]
% 0.79/1.56 ] .
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 percentage equality = 0.221719, percentage horn = 0.930435
% 0.79/1.56 This is a problem with some equality
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 Options Used:
% 0.79/1.56
% 0.79/1.56 useres = 1
% 0.79/1.56 useparamod = 1
% 0.79/1.56 useeqrefl = 1
% 0.79/1.56 useeqfact = 1
% 0.79/1.56 usefactor = 1
% 0.79/1.56 usesimpsplitting = 0
% 0.79/1.56 usesimpdemod = 5
% 0.79/1.56 usesimpres = 3
% 0.79/1.56
% 0.79/1.56 resimpinuse = 1000
% 0.79/1.56 resimpclauses = 20000
% 0.79/1.56 substype = eqrewr
% 0.79/1.56 backwardsubs = 1
% 0.79/1.56 selectoldest = 5
% 0.79/1.56
% 0.79/1.56 litorderings [0] = split
% 0.79/1.56 litorderings [1] = extend the termordering, first sorting on arguments
% 0.79/1.56
% 0.79/1.56 termordering = kbo
% 0.79/1.56
% 0.79/1.56 litapriori = 0
% 0.79/1.56 termapriori = 1
% 0.79/1.56 litaposteriori = 0
% 0.79/1.56 termaposteriori = 0
% 0.79/1.56 demodaposteriori = 0
% 0.79/1.56 ordereqreflfact = 0
% 0.79/1.56
% 0.79/1.56 litselect = negord
% 0.79/1.56
% 0.79/1.56 maxweight = 15
% 0.79/1.56 maxdepth = 30000
% 0.79/1.56 maxlength = 115
% 0.79/1.56 maxnrvars = 195
% 0.79/1.56 excuselevel = 1
% 0.79/1.56 increasemaxweight = 1
% 0.79/1.56
% 0.79/1.56 maxselected = 10000000
% 0.79/1.56 maxnrclauses = 10000000
% 0.79/1.56
% 0.79/1.56 showgenerated = 0
% 0.79/1.56 showkept = 0
% 0.79/1.56 showselected = 0
% 0.79/1.56 showdeleted = 0
% 0.79/1.56 showresimp = 1
% 0.79/1.56 showstatus = 2000
% 0.79/1.56
% 0.79/1.56 prologoutput = 1
% 0.79/1.56 nrgoals = 5000000
% 0.79/1.56 totalproof = 1
% 0.79/1.56
% 0.79/1.56 Symbols occurring in the translation:
% 0.79/1.56
% 0.79/1.56 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.79/1.56 . [1, 2] (w:1, o:67, a:1, s:1, b:0),
% 0.79/1.56 ! [4, 1] (w:0, o:38, a:1, s:1, b:0),
% 0.79/1.56 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.79/1.56 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.79/1.56 subclass [41, 2] (w:1, o:92, a:1, s:1, b:0),
% 0.79/1.56 member [43, 2] (w:1, o:93, a:1, s:1, b:0),
% 0.79/1.56 'not_subclass_element' [44, 2] (w:1, o:94, a:1, s:1, b:0),
% 0.79/1.56 'universal_class' [45, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.79/1.56 'unordered_pair' [46, 2] (w:1, o:95, a:1, s:1, b:0),
% 0.79/1.56 singleton [47, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.79/1.56 'ordered_pair' [48, 2] (w:1, o:96, a:1, s:1, b:0),
% 0.79/1.56 'cross_product' [50, 2] (w:1, o:97, a:1, s:1, b:0),
% 0.79/1.56 first [52, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.79/1.56 second [53, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.79/1.56 'element_relation' [54, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.79/1.56 intersection [55, 2] (w:1, o:99, a:1, s:1, b:0),
% 0.79/1.56 complement [56, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.79/1.56 union [57, 2] (w:1, o:100, a:1, s:1, b:0),
% 0.79/1.56 'symmetric_difference' [58, 2] (w:1, o:101, a:1, s:1, b:0),
% 0.79/1.56 restrict [60, 3] (w:1, o:104, a:1, s:1, b:0),
% 0.79/1.56 'null_class' [61, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.79/1.56 'domain_of' [62, 1] (w:1, o:52, a:1, s:1, b:0),
% 0.79/1.56 rotate [63, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.79/1.56 flip [65, 1] (w:1, o:53, a:1, s:1, b:0),
% 0.79/1.56 inverse [66, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.79/1.56 'range_of' [67, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.79/1.56 domain [68, 3] (w:1, o:106, a:1, s:1, b:0),
% 0.79/1.56 range [69, 3] (w:1, o:107, a:1, s:1, b:0),
% 0.79/1.56 image [70, 2] (w:1, o:98, a:1, s:1, b:0),
% 0.79/1.56 successor [71, 1] (w:1, o:55, a:1, s:1, b:0),
% 0.79/1.56 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.79/1.56 inductive [73, 1] (w:1, o:56, a:1, s:1, b:0),
% 0.79/1.56 omega [74, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.79/1.56 'sum_class' [75, 1] (w:1, o:57, a:1, s:1, b:0),
% 0.79/1.56 'power_class' [76, 1] (w:1, o:60, a:1, s:1, b:0),
% 0.79/1.56 compose [78, 2] (w:1, o:102, a:1, s:1, b:0),
% 0.79/1.56 'single_valued_class' [79, 1] (w:1, o:61, a:1, s:1, b:0),
% 0.79/1.56 'identity_relation' [80, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.79/1.56 function [82, 1] (w:1, o:62, a:1, s:1, b:0),
% 0.79/1.56 regular [83, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.79/1.56 apply [84, 2] (w:1, o:103, a:1, s:1, b:0),
% 0.79/1.56 choice [85, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.79/1.56 'one_to_one' [86, 1] (w:1, o:58, a:1, s:1, b:0),
% 0.79/1.56 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 0.79/1.56 diagonalise [88, 1] (w:1, o:63, a:1, s:1, b:0),
% 0.79/1.56 cantor [89, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.79/1.56 operation [90, 1] (w:1, o:59, a:1, s:1, b:0),
% 0.79/1.56 compatible [94, 3] (w:1, o:105, a:1, s:1, b:0),
% 0.79/1.56 homomorphism [95, 3] (w:1, o:108, a:1, s:1, b:0),
% 0.79/1.56 'not_homomorphism1' [96, 3] (w:1, o:110, a:1, s:1, b:0),
% 0.79/1.56 'not_homomorphism2' [97, 3] (w:1, o:111, a:1, s:1, b:0),
% 0.79/1.56 'compose_class' [98, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.79/1.56 'composition_function' [99, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.79/1.56 'domain_relation' [100, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.79/1.56 'single_valued1' [101, 1] (w:1, o:64, a:1, s:1, b:0),
% 0.79/1.56 'single_valued2' [102, 1] (w:1, o:65, a:1, s:1, b:0),
% 0.79/1.56 'single_valued3' [103, 1] (w:1, o:66, a:1, s:1, b:0),
% 0.79/1.56 'singleton_relation' [104, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.79/1.56 'application_function' [105, 0] (w:1, o:32, a:1, s:1, b:0),
% 0.79/1.56 maps [106, 3] (w:1, o:109, a:1, s:1, b:0),
% 0.79/1.56 xh1 [107, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.79/1.56 xf1 [108, 0] (w:1, o:34, a:1, s:1, b:0),
% 0.79/1.56 xf2 [109, 0] (w:1, o:35, a:1, s:1, b:0),
% 0.79/1.56 xh2 [110, 0] (w:1, o:36, a:1, s:1, b:0),
% 0.79/1.56 xf3 [111, 0] (w:1, o:37, a:1, s:1, b:0).
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 Starting Search:
% 0.79/1.56
% 0.79/1.56 Resimplifying inuse:
% 0.79/1.56 Done
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 Intermediate Status:
% 0.79/1.56 Generated: 4995
% 0.79/1.56 Kept: 2004
% 0.79/1.56 Inuse: 113
% 0.79/1.56 Deleted: 10
% 0.79/1.56 Deletedinuse: 2
% 0.79/1.56
% 0.79/1.56 Resimplifying inuse:
% 0.79/1.56 Done
% 0.79/1.56
% 0.79/1.56 Resimplifying inuse:
% 0.79/1.56 Done
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 Intermediate Status:
% 0.79/1.56 Generated: 9540
% 0.79/1.56 Kept: 4012
% 0.79/1.56 Inuse: 185
% 0.79/1.56 Deleted: 18
% 0.79/1.56 Deletedinuse: 7
% 0.79/1.56
% 0.79/1.56 Resimplifying inuse:
% 0.79/1.56 Done
% 0.79/1.56
% 0.79/1.56 Resimplifying inuse:
% 0.79/1.56 Done
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 Intermediate Status:
% 0.79/1.56 Generated: 13361
% 0.79/1.56 Kept: 6014
% 0.79/1.56 Inuse: 236
% 0.79/1.56 Deleted: 21
% 0.79/1.56 Deletedinuse: 8
% 0.79/1.56
% 0.79/1.56 Resimplifying inuse:
% 0.79/1.56 Done
% 0.79/1.56
% 0.79/1.56 Resimplifying inuse:
% 0.79/1.56 Done
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 Intermediate Status:
% 0.79/1.56 Generated: 18211
% 0.79/1.56 Kept: 8146
% 0.79/1.56 Inuse: 286
% 0.79/1.56 Deleted: 75
% 0.79/1.56 Deletedinuse: 60
% 0.79/1.56
% 0.79/1.56 Resimplifying inuse:
% 0.79/1.56 Done
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 Bliksems!, er is een bewijs:
% 0.79/1.56 % SZS status Unsatisfiable
% 0.79/1.56 % SZS output start Refutation
% 0.79/1.56
% 0.79/1.56 clause( 81, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y )
% 0.79/1.56 ), 'domain_of'( X ) ) ] )
% 0.79/1.56 .
% 0.79/1.56 clause( 82, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 0.79/1.56 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 0.79/1.56 .
% 0.79/1.56 clause( 111, [ compatible( xh1, xf1, xf2 ) ] )
% 0.79/1.56 .
% 0.79/1.56 clause( 112, [ compatible( xh2, xf2, xf3 ) ] )
% 0.79/1.56 .
% 0.79/1.56 clause( 113, [ ~( subclass( 'range_of'( xh1 ), 'domain_of'( xh2 ) ) ) ] )
% 0.79/1.56 .
% 0.79/1.56 clause( 9180, [ =( 'domain_of'( 'domain_of'( xf2 ) ), 'domain_of'( xh2 ) )
% 0.79/1.56 ] )
% 0.79/1.56 .
% 0.79/1.56 clause( 9286, [] )
% 0.79/1.56 .
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 % SZS output end Refutation
% 0.79/1.56 found a proof!
% 0.79/1.56
% 0.79/1.56 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.79/1.56
% 0.79/1.56 initialclauses(
% 0.79/1.56 [ clause( 9288, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 0.79/1.56 ) ] )
% 0.79/1.56 , clause( 9289, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 0.79/1.56 , Y ) ] )
% 0.79/1.56 , clause( 9290, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 0.79/1.56 subclass( X, Y ) ] )
% 0.79/1.56 , clause( 9291, [ subclass( X, 'universal_class' ) ] )
% 0.79/1.56 , clause( 9292, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 0.79/1.56 , clause( 9293, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 0.79/1.56 , clause( 9294, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ]
% 0.79/1.56 )
% 0.79/1.56 , clause( 9295, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 0.79/1.56 =( X, Z ) ] )
% 0.79/1.56 , clause( 9296, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.79/1.56 'unordered_pair'( X, Y ) ) ] )
% 0.79/1.56 , clause( 9297, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.79/1.56 'unordered_pair'( Y, X ) ) ] )
% 0.79/1.56 , clause( 9298, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 0.79/1.56 )
% 0.79/1.56 , clause( 9299, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 0.79/1.56 , clause( 9300, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 0.79/1.56 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.79/1.56 , clause( 9301, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.79/1.56 ) ) ), member( X, Z ) ] )
% 0.79/1.56 , clause( 9302, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 0.79/1.56 ) ) ), member( Y, T ) ] )
% 0.79/1.56 , clause( 9303, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 0.79/1.56 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 0.79/1.56 , clause( 9304, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 0.79/1.56 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 0.79/1.56 , clause( 9305, [ subclass( 'element_relation', 'cross_product'(
% 0.79/1.56 'universal_class', 'universal_class' ) ) ] )
% 0.79/1.56 , clause( 9306, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) )
% 0.79/1.56 , member( X, Y ) ] )
% 0.79/1.56 , clause( 9307, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.79/1.56 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 0.79/1.56 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 0.79/1.56 , clause( 9308, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.79/1.56 )
% 0.79/1.56 , clause( 9309, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 0.79/1.56 )
% 0.79/1.56 , clause( 9310, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 0.79/1.56 intersection( Y, Z ) ) ] )
% 0.79/1.56 , clause( 9311, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 0.79/1.56 )
% 0.79/1.56 , clause( 9312, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.79/1.56 complement( Y ) ), member( X, Y ) ] )
% 0.79/1.56 , clause( 9313, [ =( complement( intersection( complement( X ), complement(
% 0.79/1.56 Y ) ) ), union( X, Y ) ) ] )
% 0.79/1.56 , clause( 9314, [ =( intersection( complement( intersection( X, Y ) ),
% 0.79/1.56 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 0.79/1.56 'symmetric_difference'( X, Y ) ) ] )
% 0.79/1.56 , clause( 9315, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 0.79/1.56 X, Y, Z ) ) ] )
% 0.79/1.56 , clause( 9316, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 0.79/1.56 Z, X, Y ) ) ] )
% 0.79/1.56 , clause( 9317, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 0.79/1.56 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 0.79/1.56 , clause( 9318, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 0.79/1.56 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 0.79/1.56 'domain_of'( Y ) ) ] )
% 0.79/1.56 , clause( 9319, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.79/1.56 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.79/1.56 , clause( 9320, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.79/1.56 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 0.79/1.56 ] )
% 0.79/1.56 , clause( 9321, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.79/1.56 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 0.79/1.56 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.79/1.56 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 0.79/1.56 , Y ), rotate( T ) ) ] )
% 0.79/1.56 , clause( 9322, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.79/1.56 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.79/1.56 , clause( 9323, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.79/1.56 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 0.79/1.56 )
% 0.79/1.56 , clause( 9324, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.79/1.56 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 0.79/1.56 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.79/1.56 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 0.79/1.56 , Z ), flip( T ) ) ] )
% 0.79/1.56 , clause( 9325, [ =( 'domain_of'( flip( 'cross_product'( X,
% 0.79/1.56 'universal_class' ) ) ), inverse( X ) ) ] )
% 0.79/1.56 , clause( 9326, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 0.79/1.56 , clause( 9327, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 0.79/1.56 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 0.79/1.56 , clause( 9328, [ =( second( 'not_subclass_element'( restrict( X, singleton(
% 0.79/1.56 Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 0.79/1.56 , clause( 9329, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 0.79/1.56 image( X, Y ) ) ] )
% 0.79/1.56 , clause( 9330, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 0.79/1.56 , clause( 9331, [ subclass( 'successor_relation', 'cross_product'(
% 0.79/1.56 'universal_class', 'universal_class' ) ) ] )
% 0.79/1.56 , clause( 9332, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' )
% 0.79/1.56 ), =( successor( X ), Y ) ] )
% 0.79/1.56 , clause( 9333, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X
% 0.79/1.56 , Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 0.79/1.56 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 0.79/1.56 , clause( 9334, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 0.79/1.56 , clause( 9335, [ ~( inductive( X ) ), subclass( image(
% 0.79/1.56 'successor_relation', X ), X ) ] )
% 0.79/1.56 , clause( 9336, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.79/1.56 'successor_relation', X ), X ) ), inductive( X ) ] )
% 0.79/1.56 , clause( 9337, [ inductive( omega ) ] )
% 0.79/1.56 , clause( 9338, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 0.79/1.56 , clause( 9339, [ member( omega, 'universal_class' ) ] )
% 0.79/1.56 , clause( 9340, [ =( 'domain_of'( restrict( 'element_relation',
% 0.79/1.56 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 0.79/1.56 , clause( 9341, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 0.79/1.56 X ), 'universal_class' ) ] )
% 0.79/1.56 , clause( 9342, [ =( complement( image( 'element_relation', complement( X )
% 0.79/1.56 ) ), 'power_class'( X ) ) ] )
% 0.79/1.56 , clause( 9343, [ ~( member( X, 'universal_class' ) ), member(
% 0.79/1.56 'power_class'( X ), 'universal_class' ) ] )
% 0.79/1.56 , clause( 9344, [ subclass( compose( X, Y ), 'cross_product'(
% 0.79/1.56 'universal_class', 'universal_class' ) ) ] )
% 0.79/1.56 , clause( 9345, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 0.79/1.56 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 0.79/1.56 , clause( 9346, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 0.79/1.56 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.79/1.56 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.79/1.56 ) ] )
% 0.79/1.56 , clause( 9347, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 0.79/1.56 inverse( X ) ), 'identity_relation' ) ] )
% 0.79/1.56 , clause( 9348, [ ~( subclass( compose( X, inverse( X ) ),
% 0.79/1.56 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 0.79/1.56 , clause( 9349, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 0.79/1.56 'universal_class', 'universal_class' ) ) ] )
% 0.79/1.56 , clause( 9350, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 0.79/1.56 , 'identity_relation' ) ] )
% 0.79/1.56 , clause( 9351, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 0.79/1.56 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 0.79/1.56 'identity_relation' ) ), function( X ) ] )
% 0.79/1.56 , clause( 9352, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ),
% 0.79/1.56 member( image( X, Y ), 'universal_class' ) ] )
% 0.79/1.56 , clause( 9353, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.79/1.56 , clause( 9354, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 0.79/1.56 , 'null_class' ) ] )
% 0.79/1.56 , clause( 9355, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y
% 0.79/1.56 ) ) ] )
% 0.79/1.56 , clause( 9356, [ function( choice ) ] )
% 0.79/1.56 , clause( 9357, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' )
% 0.79/1.56 , member( apply( choice, X ), X ) ] )
% 0.79/1.56 , clause( 9358, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 0.79/1.56 , clause( 9359, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 0.79/1.56 , clause( 9360, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 0.79/1.56 'one_to_one'( X ) ] )
% 0.79/1.56 , clause( 9361, [ =( intersection( 'cross_product'( 'universal_class',
% 0.79/1.56 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 0.79/1.56 'universal_class' ), complement( compose( complement( 'element_relation'
% 0.79/1.56 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 0.79/1.56 , clause( 9362, [ =( intersection( inverse( 'subset_relation' ),
% 0.79/1.56 'subset_relation' ), 'identity_relation' ) ] )
% 0.79/1.56 , clause( 9363, [ =( complement( 'domain_of'( intersection( X,
% 0.79/1.56 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 0.79/1.56 , clause( 9364, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 0.79/1.56 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 0.79/1.56 , clause( 9365, [ ~( operation( X ) ), function( X ) ] )
% 0.79/1.56 , clause( 9366, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 0.79/1.56 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.79/1.56 ] )
% 0.79/1.56 , clause( 9367, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 0.79/1.56 'domain_of'( 'domain_of'( X ) ) ) ] )
% 0.79/1.56 , clause( 9368, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 0.79/1.56 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.79/1.56 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 0.79/1.56 operation( X ) ] )
% 0.79/1.56 , clause( 9369, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 0.79/1.56 , clause( 9370, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 0.79/1.56 Y ) ), 'domain_of'( X ) ) ] )
% 0.79/1.56 , clause( 9371, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 0.79/1.56 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 0.79/1.56 , clause( 9372, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) )
% 0.79/1.56 , 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 0.79/1.56 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 0.79/1.56 , clause( 9373, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 0.79/1.56 , clause( 9374, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 0.79/1.56 , clause( 9375, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 0.79/1.56 , clause( 9376, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 0.79/1.56 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 0.79/1.56 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 0.79/1.56 )
% 0.79/1.56 , clause( 9377, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 0.79/1.56 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.79/1.56 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.79/1.56 , Y ) ] )
% 0.79/1.56 , clause( 9378, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 0.79/1.56 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 0.79/1.56 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 0.79/1.56 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 0.79/1.56 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 0.79/1.56 )
% 0.79/1.56 , clause( 9379, [ subclass( 'compose_class'( X ), 'cross_product'(
% 0.79/1.56 'universal_class', 'universal_class' ) ) ] )
% 0.79/1.56 , clause( 9380, [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) )
% 0.79/1.56 ), =( compose( Z, X ), Y ) ] )
% 0.79/1.56 , clause( 9381, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.79/1.56 'universal_class', 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) )
% 0.79/1.56 , member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ] )
% 0.79/1.56 , clause( 9382, [ subclass( 'composition_function', 'cross_product'(
% 0.79/1.56 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 0.79/1.56 ) ) ) ] )
% 0.79/1.56 , clause( 9383, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.79/1.56 'composition_function' ) ), =( compose( X, Y ), Z ) ] )
% 0.79/1.56 , clause( 9384, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.79/1.56 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( X,
% 0.79/1.56 'ordered_pair'( Y, compose( X, Y ) ) ), 'composition_function' ) ] )
% 0.79/1.56 , clause( 9385, [ subclass( 'domain_relation', 'cross_product'(
% 0.79/1.56 'universal_class', 'universal_class' ) ) ] )
% 0.79/1.56 , clause( 9386, [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) )
% 0.79/1.56 , =( 'domain_of'( X ), Y ) ] )
% 0.79/1.56 , clause( 9387, [ ~( member( X, 'universal_class' ) ), member(
% 0.79/1.56 'ordered_pair'( X, 'domain_of'( X ) ), 'domain_relation' ) ] )
% 0.79/1.56 , clause( 9388, [ =( first( 'not_subclass_element'( compose( X, inverse( X
% 0.79/1.56 ) ), 'identity_relation' ) ), 'single_valued1'( X ) ) ] )
% 0.79/1.56 , clause( 9389, [ =( second( 'not_subclass_element'( compose( X, inverse( X
% 0.79/1.56 ) ), 'identity_relation' ) ), 'single_valued2'( X ) ) ] )
% 0.79/1.56 , clause( 9390, [ =( domain( X, image( inverse( X ), singleton(
% 0.79/1.56 'single_valued1'( X ) ) ), 'single_valued2'( X ) ), 'single_valued3'( X )
% 0.79/1.56 ) ] )
% 0.79/1.56 , clause( 9391, [ =( intersection( complement( compose( 'element_relation'
% 0.79/1.56 , complement( 'identity_relation' ) ) ), 'element_relation' ),
% 0.79/1.56 'singleton_relation' ) ] )
% 0.79/1.56 , clause( 9392, [ subclass( 'application_function', 'cross_product'(
% 0.79/1.56 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 0.79/1.56 ) ) ) ] )
% 0.79/1.56 , clause( 9393, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.79/1.56 'application_function' ) ), member( Y, 'domain_of'( X ) ) ] )
% 0.79/1.56 , clause( 9394, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.79/1.56 'application_function' ) ), =( apply( X, Y ), Z ) ] )
% 0.79/1.56 , clause( 9395, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.79/1.56 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 0.79/1.56 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 0.79/1.56 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 0.79/1.56 'application_function' ) ] )
% 0.79/1.56 , clause( 9396, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 0.79/1.56 , clause( 9397, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 0.79/1.56 , clause( 9398, [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ] )
% 0.79/1.56 , clause( 9399, [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ),
% 0.79/1.56 maps( X, 'domain_of'( X ), Y ) ] )
% 0.79/1.56 , clause( 9400, [ compatible( xh1, xf1, xf2 ) ] )
% 0.79/1.56 , clause( 9401, [ compatible( xh2, xf2, xf3 ) ] )
% 0.79/1.56 , clause( 9402, [ ~( subclass( 'range_of'( xh1 ), 'domain_of'( xh2 ) ) ) ]
% 0.79/1.56 )
% 0.79/1.56 ] ).
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 subsumption(
% 0.79/1.56 clause( 81, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y )
% 0.79/1.56 ), 'domain_of'( X ) ) ] )
% 0.79/1.56 , clause( 9370, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 0.79/1.56 Y ) ), 'domain_of'( X ) ) ] )
% 0.79/1.56 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.79/1.56 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 subsumption(
% 0.79/1.56 clause( 82, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 0.79/1.56 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 0.79/1.56 , clause( 9371, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 0.79/1.56 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 0.79/1.56 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.79/1.56 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 subsumption(
% 0.79/1.56 clause( 111, [ compatible( xh1, xf1, xf2 ) ] )
% 0.79/1.56 , clause( 9400, [ compatible( xh1, xf1, xf2 ) ] )
% 0.79/1.56 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 subsumption(
% 0.79/1.56 clause( 112, [ compatible( xh2, xf2, xf3 ) ] )
% 0.79/1.56 , clause( 9401, [ compatible( xh2, xf2, xf3 ) ] )
% 0.79/1.56 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 subsumption(
% 0.79/1.56 clause( 113, [ ~( subclass( 'range_of'( xh1 ), 'domain_of'( xh2 ) ) ) ] )
% 0.79/1.56 , clause( 9402, [ ~( subclass( 'range_of'( xh1 ), 'domain_of'( xh2 ) ) ) ]
% 0.79/1.56 )
% 0.79/1.56 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 eqswap(
% 0.79/1.56 clause( 9671, [ =( 'domain_of'( Y ), 'domain_of'( 'domain_of'( X ) ) ), ~(
% 0.79/1.56 compatible( Y, X, Z ) ) ] )
% 0.79/1.56 , clause( 81, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y
% 0.79/1.56 ) ), 'domain_of'( X ) ) ] )
% 0.79/1.56 , 1, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] )).
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 resolution(
% 0.79/1.56 clause( 9672, [ =( 'domain_of'( xh2 ), 'domain_of'( 'domain_of'( xf2 ) ) )
% 0.79/1.56 ] )
% 0.79/1.56 , clause( 9671, [ =( 'domain_of'( Y ), 'domain_of'( 'domain_of'( X ) ) ),
% 0.79/1.56 ~( compatible( Y, X, Z ) ) ] )
% 0.79/1.56 , 1, clause( 112, [ compatible( xh2, xf2, xf3 ) ] )
% 0.79/1.56 , 0, substitution( 0, [ :=( X, xf2 ), :=( Y, xh2 ), :=( Z, xf3 )] ),
% 0.79/1.56 substitution( 1, [] )).
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 eqswap(
% 0.79/1.56 clause( 9673, [ =( 'domain_of'( 'domain_of'( xf2 ) ), 'domain_of'( xh2 ) )
% 0.79/1.56 ] )
% 0.79/1.56 , clause( 9672, [ =( 'domain_of'( xh2 ), 'domain_of'( 'domain_of'( xf2 ) )
% 0.79/1.56 ) ] )
% 0.79/1.56 , 0, substitution( 0, [] )).
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 subsumption(
% 0.79/1.56 clause( 9180, [ =( 'domain_of'( 'domain_of'( xf2 ) ), 'domain_of'( xh2 ) )
% 0.79/1.56 ] )
% 0.79/1.56 , clause( 9673, [ =( 'domain_of'( 'domain_of'( xf2 ) ), 'domain_of'( xh2 )
% 0.79/1.56 ) ] )
% 0.79/1.56 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 resolution(
% 0.79/1.56 clause( 9675, [ subclass( 'range_of'( xh1 ), 'domain_of'( 'domain_of'( xf2
% 0.79/1.56 ) ) ) ] )
% 0.79/1.56 , clause( 82, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 0.79/1.56 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 0.79/1.56 , 0, clause( 111, [ compatible( xh1, xf1, xf2 ) ] )
% 0.79/1.56 , 0, substitution( 0, [ :=( X, xh1 ), :=( Y, xf1 ), :=( Z, xf2 )] ),
% 0.79/1.56 substitution( 1, [] )).
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 paramod(
% 0.79/1.56 clause( 9676, [ subclass( 'range_of'( xh1 ), 'domain_of'( xh2 ) ) ] )
% 0.79/1.56 , clause( 9180, [ =( 'domain_of'( 'domain_of'( xf2 ) ), 'domain_of'( xh2 )
% 0.79/1.56 ) ] )
% 0.79/1.56 , 0, clause( 9675, [ subclass( 'range_of'( xh1 ), 'domain_of'( 'domain_of'(
% 0.79/1.56 xf2 ) ) ) ] )
% 0.79/1.56 , 0, 3, substitution( 0, [] ), substitution( 1, [] )).
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 resolution(
% 0.79/1.56 clause( 9677, [] )
% 0.79/1.56 , clause( 113, [ ~( subclass( 'range_of'( xh1 ), 'domain_of'( xh2 ) ) ) ]
% 0.79/1.56 )
% 0.79/1.56 , 0, clause( 9676, [ subclass( 'range_of'( xh1 ), 'domain_of'( xh2 ) ) ] )
% 0.79/1.56 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 subsumption(
% 0.79/1.56 clause( 9286, [] )
% 0.79/1.56 , clause( 9677, [] )
% 0.79/1.56 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 end.
% 0.79/1.56
% 0.79/1.56 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.79/1.56
% 0.79/1.56 Memory use:
% 0.79/1.56
% 0.79/1.56 space for terms: 136075
% 0.79/1.56 space for clauses: 445487
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 clauses generated: 21193
% 0.79/1.56 clauses kept: 9287
% 0.79/1.56 clauses selected: 334
% 0.79/1.56 clauses deleted: 87
% 0.79/1.56 clauses inuse deleted: 70
% 0.79/1.56
% 0.79/1.56 subsentry: 47283
% 0.79/1.56 literals s-matched: 36555
% 0.79/1.56 literals matched: 35958
% 0.79/1.56 full subsumption: 15840
% 0.79/1.56
% 0.79/1.56 checksum: 1562019768
% 0.79/1.56
% 0.79/1.56
% 0.79/1.56 Bliksem ended
%------------------------------------------------------------------------------