TSTP Solution File: SET558-6 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET558-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.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 22:50:15 EDT 2022
% Result : Unsatisfiable 2.33s 2.75s
% Output : Refutation 2.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET558-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.14 % Command : bliksem %s
% 0.14/0.35 % Computer : n006.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
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Sun Jul 10 19:29:50 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.48/1.17 *** allocated 10000 integers for termspace/termends
% 0.48/1.17 *** allocated 10000 integers for clauses
% 0.48/1.17 *** allocated 10000 integers for justifications
% 0.48/1.17 Bliksem 1.12
% 0.48/1.17
% 0.48/1.17
% 0.48/1.17 Automatic Strategy Selection
% 0.48/1.17
% 0.48/1.17 Clauses:
% 0.48/1.17 [
% 0.48/1.17 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.48/1.17 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.48/1.17 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.48/1.17 ,
% 0.48/1.17 [ subclass( X, 'universal_class' ) ],
% 0.48/1.17 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.48/1.17 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.48/1.17 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.48/1.17 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.48/1.17 ,
% 0.48/1.17 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.48/1.17 ) ) ],
% 0.48/1.17 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.48/1.17 ) ) ],
% 0.48/1.17 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.48/1.17 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.48/1.17 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.48/1.17 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.48/1.17 X, Z ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.48/1.17 Y, T ) ],
% 0.48/1.17 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.48/1.17 ), 'cross_product'( Y, T ) ) ],
% 0.48/1.17 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.48/1.17 ), second( X ) ), X ) ],
% 0.48/1.17 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.48/1.17 'universal_class' ) ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.48/1.17 Y ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.48/1.17 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.48/1.17 , Y ), 'element_relation' ) ],
% 0.48/1.17 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.48/1.17 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.48/1.17 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.48/1.17 Z ) ) ],
% 0.48/1.17 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.48/1.17 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.48/1.17 member( X, Y ) ],
% 0.48/1.17 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.48/1.17 union( X, Y ) ) ],
% 0.48/1.17 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.48/1.17 intersection( complement( X ), complement( Y ) ) ) ),
% 0.48/1.17 'symmetric_difference'( X, Y ) ) ],
% 0.48/1.17 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.48/1.17 ,
% 0.48/1.17 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.48/1.17 ,
% 0.48/1.17 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.48/1.17 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.48/1.17 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.48/1.17 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.48/1.17 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.48/1.17 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.48/1.17 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.48/1.17 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.48/1.17 'cross_product'( 'universal_class', 'universal_class' ),
% 0.48/1.17 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.48/1.17 Y ), rotate( T ) ) ],
% 0.48/1.17 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.48/1.17 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.48/1.17 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.48/1.17 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.48/1.17 'cross_product'( 'universal_class', 'universal_class' ),
% 0.48/1.17 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.48/1.17 Z ), flip( T ) ) ],
% 0.48/1.17 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.48/1.17 inverse( X ) ) ],
% 0.48/1.17 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.48/1.17 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.48/1.17 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.48/1.17 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.48/1.17 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.48/1.17 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.48/1.17 ],
% 0.48/1.17 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.48/1.17 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.48/1.17 'universal_class' ) ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.48/1.17 successor( X ), Y ) ],
% 0.48/1.17 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.48/1.17 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.48/1.17 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.48/1.17 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.48/1.17 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.48/1.17 ,
% 0.48/1.17 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.48/1.17 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.48/1.17 [ inductive( omega ) ],
% 0.48/1.17 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.48/1.17 [ member( omega, 'universal_class' ) ],
% 0.48/1.17 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.48/1.17 , 'sum_class'( X ) ) ],
% 0.48/1.17 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.48/1.17 'universal_class' ) ],
% 0.48/1.17 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.48/1.17 'power_class'( X ) ) ],
% 0.48/1.17 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.48/1.17 'universal_class' ) ],
% 0.48/1.17 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.48/1.17 'universal_class' ) ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.48/1.17 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.48/1.17 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.48/1.17 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.48/1.17 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.48/1.17 ) ],
% 0.48/1.17 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.48/1.17 , 'identity_relation' ) ],
% 0.48/1.17 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.48/1.17 'single_valued_class'( X ) ],
% 0.48/1.17 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.48/1.17 'universal_class' ) ) ],
% 0.48/1.17 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.48/1.17 'identity_relation' ) ],
% 0.48/1.17 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.48/1.17 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.48/1.17 , function( X ) ],
% 0.48/1.17 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.48/1.17 X, Y ), 'universal_class' ) ],
% 0.48/1.17 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.48/1.17 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.48/1.17 ) ],
% 0.48/1.17 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.48/1.17 [ function( choice ) ],
% 0.48/1.17 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.48/1.17 apply( choice, X ), X ) ],
% 0.48/1.17 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.48/1.17 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.48/1.17 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.48/1.17 ,
% 0.48/1.17 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.48/1.17 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.48/1.17 , complement( compose( complement( 'element_relation' ), inverse(
% 0.48/1.17 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.48/1.17 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.48/1.17 'identity_relation' ) ],
% 0.48/1.17 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.48/1.17 , diagonalise( X ) ) ],
% 0.48/1.17 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.48/1.17 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.48/1.17 [ ~( operation( X ) ), function( X ) ],
% 0.48/1.17 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.48/1.17 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.48/1.17 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.48/1.17 'domain_of'( X ) ) ) ],
% 0.48/1.17 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.48/1.17 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.48/1.17 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.48/1.17 X ) ],
% 0.48/1.17 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.48/1.17 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.48/1.17 'domain_of'( X ) ) ],
% 0.48/1.17 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.48/1.17 'domain_of'( Z ) ) ) ],
% 0.48/1.17 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.48/1.17 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.48/1.17 ), compatible( X, Y, Z ) ],
% 0.48/1.17 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.48/1.17 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.48/1.17 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.48/1.17 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.48/1.17 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.48/1.17 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.48/1.17 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.48/1.17 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.48/1.17 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.48/1.17 , Y ) ],
% 0.48/1.17 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.48/1.17 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.48/1.17 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.48/1.17 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.48/1.17 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.48/1.17 [ subclass( 'compose_class'( X ), 'cross_product'( 'universal_class',
% 0.48/1.17 'universal_class' ) ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ), =(
% 0.48/1.17 compose( Z, X ), Y ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.48/1.17 , 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) ), member(
% 0.48/1.17 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ],
% 0.48/1.17 [ subclass( 'composition_function', 'cross_product'( 'universal_class',
% 0.48/1.17 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.48/1.17 'composition_function' ) ), =( compose( X, Y ), Z ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.48/1.17 , 'universal_class' ) ) ), member( 'ordered_pair'( X, 'ordered_pair'( Y,
% 0.48/1.17 compose( X, Y ) ) ), 'composition_function' ) ],
% 0.48/1.17 [ subclass( 'domain_relation', 'cross_product'( 'universal_class',
% 0.48/1.17 'universal_class' ) ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) ), =(
% 0.48/1.17 'domain_of'( X ), Y ) ],
% 0.48/1.17 [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X,
% 0.48/1.17 'domain_of'( X ) ), 'domain_relation' ) ],
% 0.48/1.17 [ =( first( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.48/1.17 'identity_relation' ) ), 'single_valued1'( X ) ) ],
% 0.48/1.17 [ =( second( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.48/1.17 'identity_relation' ) ), 'single_valued2'( X ) ) ],
% 0.48/1.17 [ =( domain( X, image( inverse( X ), singleton( 'single_valued1'( X ) )
% 0.48/1.17 ), 'single_valued2'( X ) ), 'single_valued3'( X ) ) ],
% 0.48/1.17 [ =( intersection( complement( compose( 'element_relation', complement(
% 0.48/1.17 'identity_relation' ) ) ), 'element_relation' ), 'singleton_relation' ) ]
% 0.48/1.17 ,
% 0.48/1.17 [ subclass( 'application_function', 'cross_product'( 'universal_class',
% 0.48/1.17 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.48/1.17 'application_function' ) ), member( Y, 'domain_of'( X ) ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.48/1.17 'application_function' ) ), =( apply( X, Y ), Z ) ],
% 0.48/1.17 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.48/1.17 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 0.48/1.17 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 0.48/1.17 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 0.48/1.17 'application_function' ) ],
% 0.48/1.17 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.48/1.17 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 2.33/2.75 [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ],
% 2.33/2.75 [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ), maps( X,
% 2.33/2.75 'domain_of'( X ), Y ) ],
% 2.33/2.75 [ operation( xf1 ) ],
% 2.33/2.75 [ compatible( xh, xf1, xf2 ) ],
% 2.33/2.75 [ ~( =( 'cross_product'( 'domain_of'( xh ), 'domain_of'( xh ) ),
% 2.33/2.75 'domain_of'( xf1 ) ) ) ]
% 2.33/2.75 ] .
% 2.33/2.75
% 2.33/2.75
% 2.33/2.75 percentage equality = 0.226244, percentage horn = 0.930435
% 2.33/2.75 This is a problem with some equality
% 2.33/2.75
% 2.33/2.75
% 2.33/2.75
% 2.33/2.75 Options Used:
% 2.33/2.75
% 2.33/2.75 useres = 1
% 2.33/2.75 useparamod = 1
% 2.33/2.75 useeqrefl = 1
% 2.33/2.75 useeqfact = 1
% 2.33/2.75 usefactor = 1
% 2.33/2.75 usesimpsplitting = 0
% 2.33/2.75 usesimpdemod = 5
% 2.33/2.75 usesimpres = 3
% 2.33/2.75
% 2.33/2.75 resimpinuse = 1000
% 2.33/2.75 resimpclauses = 20000
% 2.33/2.75 substype = eqrewr
% 2.33/2.75 backwardsubs = 1
% 2.33/2.75 selectoldest = 5
% 2.33/2.75
% 2.33/2.75 litorderings [0] = split
% 2.33/2.75 litorderings [1] = extend the termordering, first sorting on arguments
% 2.33/2.75
% 2.33/2.75 termordering = kbo
% 2.33/2.75
% 2.33/2.75 litapriori = 0
% 2.33/2.75 termapriori = 1
% 2.33/2.75 litaposteriori = 0
% 2.33/2.75 termaposteriori = 0
% 2.33/2.75 demodaposteriori = 0
% 2.33/2.75 ordereqreflfact = 0
% 2.33/2.75
% 2.33/2.75 litselect = negord
% 2.33/2.75
% 2.33/2.75 maxweight = 15
% 2.33/2.75 maxdepth = 30000
% 2.33/2.75 maxlength = 115
% 2.33/2.75 maxnrvars = 195
% 2.33/2.75 excuselevel = 1
% 2.33/2.75 increasemaxweight = 1
% 2.33/2.75
% 2.33/2.75 maxselected = 10000000
% 2.33/2.75 maxnrclauses = 10000000
% 2.33/2.75
% 2.33/2.75 showgenerated = 0
% 2.33/2.75 showkept = 0
% 2.33/2.75 showselected = 0
% 2.33/2.75 showdeleted = 0
% 2.33/2.75 showresimp = 1
% 2.33/2.75 showstatus = 2000
% 2.33/2.75
% 2.33/2.75 prologoutput = 1
% 2.33/2.75 nrgoals = 5000000
% 2.33/2.75 totalproof = 1
% 2.33/2.75
% 2.33/2.75 Symbols occurring in the translation:
% 2.33/2.75
% 2.33/2.75 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.33/2.75 . [1, 2] (w:1, o:65, a:1, s:1, b:0),
% 2.33/2.75 ! [4, 1] (w:0, o:36, a:1, s:1, b:0),
% 2.33/2.75 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.33/2.75 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.33/2.75 subclass [41, 2] (w:1, o:90, a:1, s:1, b:0),
% 2.33/2.75 member [43, 2] (w:1, o:91, a:1, s:1, b:0),
% 2.33/2.75 'not_subclass_element' [44, 2] (w:1, o:92, a:1, s:1, b:0),
% 2.33/2.75 'universal_class' [45, 0] (w:1, o:22, a:1, s:1, b:0),
% 2.33/2.75 'unordered_pair' [46, 2] (w:1, o:93, a:1, s:1, b:0),
% 2.33/2.75 singleton [47, 1] (w:1, o:44, a:1, s:1, b:0),
% 2.33/2.75 'ordered_pair' [48, 2] (w:1, o:94, a:1, s:1, b:0),
% 2.33/2.75 'cross_product' [50, 2] (w:1, o:95, a:1, s:1, b:0),
% 2.33/2.75 first [52, 1] (w:1, o:45, a:1, s:1, b:0),
% 2.33/2.75 second [53, 1] (w:1, o:46, a:1, s:1, b:0),
% 2.33/2.75 'element_relation' [54, 0] (w:1, o:27, a:1, s:1, b:0),
% 2.33/2.75 intersection [55, 2] (w:1, o:97, a:1, s:1, b:0),
% 2.33/2.75 complement [56, 1] (w:1, o:47, a:1, s:1, b:0),
% 2.33/2.75 union [57, 2] (w:1, o:98, a:1, s:1, b:0),
% 2.33/2.75 'symmetric_difference' [58, 2] (w:1, o:99, a:1, s:1, b:0),
% 2.33/2.75 restrict [60, 3] (w:1, o:102, a:1, s:1, b:0),
% 2.33/2.75 'null_class' [61, 0] (w:1, o:28, a:1, s:1, b:0),
% 2.33/2.75 'domain_of' [62, 1] (w:1, o:50, a:1, s:1, b:0),
% 2.33/2.75 rotate [63, 1] (w:1, o:41, a:1, s:1, b:0),
% 2.33/2.75 flip [65, 1] (w:1, o:51, a:1, s:1, b:0),
% 2.33/2.75 inverse [66, 1] (w:1, o:52, a:1, s:1, b:0),
% 2.33/2.75 'range_of' [67, 1] (w:1, o:42, a:1, s:1, b:0),
% 2.33/2.75 domain [68, 3] (w:1, o:104, a:1, s:1, b:0),
% 2.33/2.75 range [69, 3] (w:1, o:105, a:1, s:1, b:0),
% 2.33/2.75 image [70, 2] (w:1, o:96, a:1, s:1, b:0),
% 2.33/2.75 successor [71, 1] (w:1, o:53, a:1, s:1, b:0),
% 2.33/2.75 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 2.33/2.75 inductive [73, 1] (w:1, o:54, a:1, s:1, b:0),
% 2.33/2.75 omega [74, 0] (w:1, o:10, a:1, s:1, b:0),
% 2.33/2.75 'sum_class' [75, 1] (w:1, o:55, a:1, s:1, b:0),
% 2.33/2.75 'power_class' [76, 1] (w:1, o:58, a:1, s:1, b:0),
% 2.33/2.75 compose [78, 2] (w:1, o:100, a:1, s:1, b:0),
% 2.33/2.75 'single_valued_class' [79, 1] (w:1, o:59, a:1, s:1, b:0),
% 2.33/2.75 'identity_relation' [80, 0] (w:1, o:29, a:1, s:1, b:0),
% 2.33/2.75 function [82, 1] (w:1, o:60, a:1, s:1, b:0),
% 2.33/2.75 regular [83, 1] (w:1, o:43, a:1, s:1, b:0),
% 2.33/2.75 apply [84, 2] (w:1, o:101, a:1, s:1, b:0),
% 2.33/2.75 choice [85, 0] (w:1, o:30, a:1, s:1, b:0),
% 2.33/2.75 'one_to_one' [86, 1] (w:1, o:56, a:1, s:1, b:0),
% 2.33/2.75 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 2.33/2.75 diagonalise [88, 1] (w:1, o:61, a:1, s:1, b:0),
% 2.33/2.75 cantor [89, 1] (w:1, o:48, a:1, s:1, b:0),
% 2.33/2.75 operation [90, 1] (w:1, o:57, a:1, s:1, b:0),
% 2.33/2.75 compatible [94, 3] (w:1, o:103, a:1, s:1, b:0),
% 2.33/2.75 homomorphism [95, 3] (w:1, o:106, a:1, s:1, b:0),
% 2.33/2.75 'not_homomorphism1' [96, 3] (w:1, o:108, a:1, s:1, b:0),
% 2.33/2.75 'not_homomorphism2' [97, 3] (w:1, o:109, a:1, s:1, b:0),
% 2.33/2.75 'compose_class' [98, 1] (w:1, o:49, a:1, s:1, b:0),
% 2.33/2.75 'composition_function' [99, 0] (w:1, o:31, a:1, s:1, b:0),
% 2.33/2.75 'domain_relation' [100, 0] (w:1, o:26, a:1, s:1, b:0),
% 2.33/2.75 'single_valued1' [101, 1] (w:1, o:62, a:1, s:1, b:0),
% 2.33/2.75 'single_valued2' [102, 1] (w:1, o:63, a:1, s:1, b:0),
% 2.33/2.75 'single_valued3' [103, 1] (w:1, o:64, a:1, s:1, b:0),
% 2.33/2.75 'singleton_relation' [104, 0] (w:1, o:7, a:1, s:1, b:0),
% 2.33/2.75 'application_function' [105, 0] (w:1, o:32, a:1, s:1, b:0),
% 2.33/2.75 maps [106, 3] (w:1, o:107, a:1, s:1, b:0),
% 2.33/2.75 xf1 [107, 0] (w:1, o:33, a:1, s:1, b:0),
% 2.33/2.75 xh [108, 0] (w:1, o:34, a:1, s:1, b:0),
% 2.33/2.75 xf2 [109, 0] (w:1, o:35, a:1, s:1, b:0).
% 2.33/2.75
% 2.33/2.75
% 2.33/2.75 Starting Search:
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75
% 2.33/2.75 Intermediate Status:
% 2.33/2.75 Generated: 5446
% 2.33/2.75 Kept: 2006
% 2.33/2.75 Inuse: 108
% 2.33/2.75 Deleted: 2
% 2.33/2.75 Deletedinuse: 2
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75
% 2.33/2.75 Intermediate Status:
% 2.33/2.75 Generated: 10096
% 2.33/2.75 Kept: 4009
% 2.33/2.75 Inuse: 192
% 2.33/2.75 Deleted: 22
% 2.33/2.75 Deletedinuse: 16
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75
% 2.33/2.75 Intermediate Status:
% 2.33/2.75 Generated: 14003
% 2.33/2.75 Kept: 6046
% 2.33/2.75 Inuse: 243
% 2.33/2.75 Deleted: 25
% 2.33/2.75 Deletedinuse: 17
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75
% 2.33/2.75 Intermediate Status:
% 2.33/2.75 Generated: 18647
% 2.33/2.75 Kept: 8064
% 2.33/2.75 Inuse: 292
% 2.33/2.75 Deleted: 79
% 2.33/2.75 Deletedinuse: 69
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75
% 2.33/2.75 Intermediate Status:
% 2.33/2.75 Generated: 24424
% 2.33/2.75 Kept: 10543
% 2.33/2.75 Inuse: 369
% 2.33/2.75 Deleted: 93
% 2.33/2.75 Deletedinuse: 81
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75
% 2.33/2.75 Intermediate Status:
% 2.33/2.75 Generated: 28036
% 2.33/2.75 Kept: 12544
% 2.33/2.75 Inuse: 400
% 2.33/2.75 Deleted: 103
% 2.33/2.75 Deletedinuse: 91
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75
% 2.33/2.75 Intermediate Status:
% 2.33/2.75 Generated: 31912
% 2.33/2.75 Kept: 14567
% 2.33/2.75 Inuse: 438
% 2.33/2.75 Deleted: 104
% 2.33/2.75 Deletedinuse: 92
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75
% 2.33/2.75 Intermediate Status:
% 2.33/2.75 Generated: 37021
% 2.33/2.75 Kept: 17779
% 2.33/2.75 Inuse: 464
% 2.33/2.75 Deleted: 104
% 2.33/2.75 Deletedinuse: 92
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75
% 2.33/2.75 Intermediate Status:
% 2.33/2.75 Generated: 44807
% 2.33/2.75 Kept: 20585
% 2.33/2.75 Inuse: 474
% 2.33/2.75 Deleted: 105
% 2.33/2.75 Deletedinuse: 93
% 2.33/2.75
% 2.33/2.75 Resimplifying inuse:
% 2.33/2.75 Done
% 2.33/2.75
% 2.33/2.75 Resimplifying clauses:
% 2.33/2.75
% 2.33/2.75 Bliksems!, er is een bewijs:
% 2.33/2.75 % SZS status Unsatisfiable
% 2.33/2.75 % SZS output start Refutation
% 2.33/2.75
% 2.33/2.75 clause( 77, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 2.33/2.75 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.33/2.75 ] )
% 2.33/2.75 .
% 2.33/2.75 clause( 81, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y )
% 2.33/2.75 ), 'domain_of'( X ) ) ] )
% 2.33/2.75 .
% 2.33/2.75 clause( 111, [ operation( xf1 ) ] )
% 2.33/2.75 .
% 2.33/2.75 clause( 112, [ compatible( xh, xf1, xf2 ) ] )
% 2.33/2.75 .
% 2.33/2.75 clause( 113, [ ~( =( 'cross_product'( 'domain_of'( xh ), 'domain_of'( xh )
% 2.33/2.75 ), 'domain_of'( xf1 ) ) ) ] )
% 2.33/2.75 .
% 2.33/2.75 clause( 8711, [ =( 'cross_product'( 'domain_of'( 'domain_of'( xf1 ) ),
% 2.33/2.75 'domain_of'( 'domain_of'( xf1 ) ) ), 'domain_of'( xf1 ) ) ] )
% 2.33/2.75 .
% 2.33/2.75 clause( 9092, [ =( 'domain_of'( 'domain_of'( xf1 ) ), 'domain_of'( xh ) ) ]
% 2.33/2.75 )
% 2.33/2.75 .
% 2.33/2.75 clause( 20590, [] )
% 2.33/2.75 .
% 2.33/2.75
% 2.33/2.75
% 2.33/2.75 % SZS output end Refutation
% 2.33/2.75 found a proof!
% 2.33/2.75
% 2.33/2.75 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.33/2.75
% 2.33/2.75 initialclauses(
% 2.33/2.75 [ clause( 20592, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 2.33/2.75 ) ] )
% 2.33/2.75 , clause( 20593, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 2.33/2.75 , Y ) ] )
% 2.33/2.75 , clause( 20594, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 2.33/2.75 subclass( X, Y ) ] )
% 2.33/2.75 , clause( 20595, [ subclass( X, 'universal_class' ) ] )
% 2.33/2.75 , clause( 20596, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.33/2.75 , clause( 20597, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 2.33/2.75 , clause( 20598, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 2.33/2.75 ] )
% 2.33/2.75 , clause( 20599, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 2.33/2.75 =( X, Z ) ] )
% 2.33/2.75 , clause( 20600, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.33/2.75 'unordered_pair'( X, Y ) ) ] )
% 2.33/2.75 , clause( 20601, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.33/2.75 'unordered_pair'( Y, X ) ) ] )
% 2.33/2.75 , clause( 20602, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 2.33/2.75 )
% 2.33/2.75 , clause( 20603, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.33/2.75 , clause( 20604, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 2.33/2.75 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 2.33/2.75 , clause( 20605, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.33/2.75 ) ) ), member( X, Z ) ] )
% 2.33/2.75 , clause( 20606, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.33/2.75 ) ) ), member( Y, T ) ] )
% 2.33/2.75 , clause( 20607, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 2.33/2.75 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 2.33/2.75 , clause( 20608, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 2.33/2.75 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 2.33/2.75 , clause( 20609, [ subclass( 'element_relation', 'cross_product'(
% 2.33/2.75 'universal_class', 'universal_class' ) ) ] )
% 2.33/2.75 , clause( 20610, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 2.33/2.75 ), member( X, Y ) ] )
% 2.33/2.75 , clause( 20611, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 2.33/2.75 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 2.33/2.75 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 2.33/2.75 , clause( 20612, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 2.33/2.75 )
% 2.33/2.75 , clause( 20613, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 2.33/2.75 )
% 2.33/2.75 , clause( 20614, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 2.33/2.75 intersection( Y, Z ) ) ] )
% 2.33/2.75 , clause( 20615, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 2.33/2.75 )
% 2.33/2.75 , clause( 20616, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.33/2.75 complement( Y ) ), member( X, Y ) ] )
% 2.33/2.75 , clause( 20617, [ =( complement( intersection( complement( X ), complement(
% 2.33/2.75 Y ) ) ), union( X, Y ) ) ] )
% 2.33/2.75 , clause( 20618, [ =( intersection( complement( intersection( X, Y ) ),
% 2.33/2.75 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 2.33/2.75 'symmetric_difference'( X, Y ) ) ] )
% 2.33/2.75 , clause( 20619, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 2.33/2.75 X, Y, Z ) ) ] )
% 2.33/2.75 , clause( 20620, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 2.33/2.76 Z, X, Y ) ) ] )
% 2.33/2.76 , clause( 20621, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 2.33/2.76 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 2.33/2.76 , clause( 20622, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 2.33/2.76 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 2.33/2.76 'domain_of'( Y ) ) ] )
% 2.33/2.76 , clause( 20623, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 2.33/2.76 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.33/2.76 , clause( 20624, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.33/2.76 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 2.33/2.76 ] )
% 2.33/2.76 , clause( 20625, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.33/2.76 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 2.33/2.76 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.33/2.76 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 2.33/2.76 , Y ), rotate( T ) ) ] )
% 2.33/2.76 , clause( 20626, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 2.33/2.76 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.33/2.76 , clause( 20627, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.33/2.76 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 2.33/2.76 )
% 2.33/2.76 , clause( 20628, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.33/2.76 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 2.33/2.76 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.33/2.76 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 2.33/2.76 , Z ), flip( T ) ) ] )
% 2.33/2.76 , clause( 20629, [ =( 'domain_of'( flip( 'cross_product'( X,
% 2.33/2.76 'universal_class' ) ) ), inverse( X ) ) ] )
% 2.33/2.76 , clause( 20630, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 2.33/2.76 , clause( 20631, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 2.33/2.76 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 2.33/2.76 , clause( 20632, [ =( second( 'not_subclass_element'( restrict( X,
% 2.33/2.76 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 2.33/2.76 , clause( 20633, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 2.33/2.76 image( X, Y ) ) ] )
% 2.33/2.76 , clause( 20634, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 2.33/2.76 , clause( 20635, [ subclass( 'successor_relation', 'cross_product'(
% 2.33/2.76 'universal_class', 'universal_class' ) ) ] )
% 2.33/2.76 , clause( 20636, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 2.33/2.76 ) ), =( successor( X ), Y ) ] )
% 2.33/2.76 , clause( 20637, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 2.33/2.76 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 2.33/2.76 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 2.33/2.76 , clause( 20638, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 2.33/2.76 , clause( 20639, [ ~( inductive( X ) ), subclass( image(
% 2.33/2.76 'successor_relation', X ), X ) ] )
% 2.33/2.76 , clause( 20640, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 2.33/2.76 'successor_relation', X ), X ) ), inductive( X ) ] )
% 2.33/2.76 , clause( 20641, [ inductive( omega ) ] )
% 2.33/2.76 , clause( 20642, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 2.33/2.76 , clause( 20643, [ member( omega, 'universal_class' ) ] )
% 2.33/2.76 , clause( 20644, [ =( 'domain_of'( restrict( 'element_relation',
% 2.33/2.76 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 2.33/2.76 , clause( 20645, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 2.33/2.76 X ), 'universal_class' ) ] )
% 2.33/2.76 , clause( 20646, [ =( complement( image( 'element_relation', complement( X
% 2.33/2.76 ) ) ), 'power_class'( X ) ) ] )
% 2.33/2.76 , clause( 20647, [ ~( member( X, 'universal_class' ) ), member(
% 2.33/2.76 'power_class'( X ), 'universal_class' ) ] )
% 2.33/2.76 , clause( 20648, [ subclass( compose( X, Y ), 'cross_product'(
% 2.33/2.76 'universal_class', 'universal_class' ) ) ] )
% 2.33/2.76 , clause( 20649, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 2.33/2.76 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 2.33/2.76 , clause( 20650, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 2.33/2.76 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 2.33/2.76 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 2.33/2.76 ) ] )
% 2.33/2.76 , clause( 20651, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 2.33/2.76 inverse( X ) ), 'identity_relation' ) ] )
% 2.33/2.76 , clause( 20652, [ ~( subclass( compose( X, inverse( X ) ),
% 2.33/2.76 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 2.33/2.76 , clause( 20653, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 2.33/2.76 'universal_class', 'universal_class' ) ) ] )
% 2.33/2.76 , clause( 20654, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 2.33/2.76 , 'identity_relation' ) ] )
% 2.33/2.76 , clause( 20655, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 2.33/2.76 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 2.33/2.76 'identity_relation' ) ), function( X ) ] )
% 2.33/2.76 , clause( 20656, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 2.33/2.76 , member( image( X, Y ), 'universal_class' ) ] )
% 2.33/2.76 , clause( 20657, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 2.33/2.76 , clause( 20658, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 2.33/2.76 , 'null_class' ) ] )
% 2.33/2.76 , clause( 20659, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 2.33/2.76 Y ) ) ] )
% 2.33/2.76 , clause( 20660, [ function( choice ) ] )
% 2.33/2.76 , clause( 20661, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 2.33/2.76 ), member( apply( choice, X ), X ) ] )
% 2.33/2.76 , clause( 20662, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 2.33/2.76 , clause( 20663, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 2.33/2.76 , clause( 20664, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 2.33/2.76 'one_to_one'( X ) ] )
% 2.33/2.76 , clause( 20665, [ =( intersection( 'cross_product'( 'universal_class',
% 2.33/2.76 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 2.33/2.76 'universal_class' ), complement( compose( complement( 'element_relation'
% 2.33/2.76 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 2.33/2.76 , clause( 20666, [ =( intersection( inverse( 'subset_relation' ),
% 2.33/2.76 'subset_relation' ), 'identity_relation' ) ] )
% 2.33/2.76 , clause( 20667, [ =( complement( 'domain_of'( intersection( X,
% 2.33/2.76 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 2.33/2.76 , clause( 20668, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 2.33/2.76 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 2.33/2.76 , clause( 20669, [ ~( operation( X ) ), function( X ) ] )
% 2.33/2.76 , clause( 20670, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 2.33/2.76 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.33/2.76 ] )
% 2.33/2.76 , clause( 20671, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 2.33/2.76 'domain_of'( 'domain_of'( X ) ) ) ] )
% 2.33/2.76 , clause( 20672, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 2.33/2.76 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.33/2.76 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 2.33/2.76 operation( X ) ] )
% 2.33/2.76 , clause( 20673, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 2.33/2.76 , clause( 20674, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 2.33/2.76 Y ) ), 'domain_of'( X ) ) ] )
% 2.33/2.76 , clause( 20675, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 2.33/2.76 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 2.33/2.76 , clause( 20676, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 2.33/2.76 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 2.33/2.76 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 2.33/2.76 , clause( 20677, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 2.33/2.76 , clause( 20678, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 2.33/2.76 , clause( 20679, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 2.33/2.76 , clause( 20680, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 2.33/2.76 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 2.33/2.76 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 2.33/2.76 )
% 2.33/2.76 , clause( 20681, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.33/2.76 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 2.33/2.76 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 2.33/2.76 , Y ) ] )
% 2.33/2.76 , clause( 20682, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.33/2.76 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 2.33/2.76 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 2.33/2.76 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 2.33/2.76 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 2.33/2.76 )
% 2.33/2.76 , clause( 20683, [ subclass( 'compose_class'( X ), 'cross_product'(
% 2.33/2.76 'universal_class', 'universal_class' ) ) ] )
% 2.33/2.76 , clause( 20684, [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z )
% 2.33/2.76 ) ), =( compose( Z, X ), Y ) ] )
% 2.33/2.76 , clause( 20685, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 2.33/2.76 'universal_class', 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) )
% 2.33/2.76 , member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ] )
% 2.33/2.76 , clause( 20686, [ subclass( 'composition_function', 'cross_product'(
% 2.33/2.76 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 2.33/2.76 ) ) ) ] )
% 2.33/2.76 , clause( 20687, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 2.33/2.76 'composition_function' ) ), =( compose( X, Y ), Z ) ] )
% 2.33/2.76 , clause( 20688, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 2.33/2.76 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( X,
% 2.33/2.76 'ordered_pair'( Y, compose( X, Y ) ) ), 'composition_function' ) ] )
% 2.33/2.76 , clause( 20689, [ subclass( 'domain_relation', 'cross_product'(
% 2.33/2.76 'universal_class', 'universal_class' ) ) ] )
% 2.33/2.76 , clause( 20690, [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) )
% 2.33/2.76 , =( 'domain_of'( X ), Y ) ] )
% 2.33/2.76 , clause( 20691, [ ~( member( X, 'universal_class' ) ), member(
% 2.33/2.76 'ordered_pair'( X, 'domain_of'( X ) ), 'domain_relation' ) ] )
% 2.33/2.76 , clause( 20692, [ =( first( 'not_subclass_element'( compose( X, inverse( X
% 2.33/2.76 ) ), 'identity_relation' ) ), 'single_valued1'( X ) ) ] )
% 2.33/2.76 , clause( 20693, [ =( second( 'not_subclass_element'( compose( X, inverse(
% 2.33/2.76 X ) ), 'identity_relation' ) ), 'single_valued2'( X ) ) ] )
% 2.33/2.76 , clause( 20694, [ =( domain( X, image( inverse( X ), singleton(
% 2.33/2.76 'single_valued1'( X ) ) ), 'single_valued2'( X ) ), 'single_valued3'( X )
% 2.33/2.76 ) ] )
% 2.33/2.76 , clause( 20695, [ =( intersection( complement( compose( 'element_relation'
% 2.33/2.76 , complement( 'identity_relation' ) ) ), 'element_relation' ),
% 2.33/2.76 'singleton_relation' ) ] )
% 2.33/2.76 , clause( 20696, [ subclass( 'application_function', 'cross_product'(
% 2.33/2.76 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 2.33/2.76 ) ) ) ] )
% 2.33/2.76 , clause( 20697, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 2.33/2.76 'application_function' ) ), member( Y, 'domain_of'( X ) ) ] )
% 2.33/2.76 , clause( 20698, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 2.33/2.76 'application_function' ) ), =( apply( X, Y ), Z ) ] )
% 2.33/2.76 , clause( 20699, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 2.33/2.76 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 2.33/2.76 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 2.33/2.76 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 2.33/2.76 'application_function' ) ] )
% 2.33/2.76 , clause( 20700, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 2.33/2.76 , clause( 20701, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 2.33/2.76 , clause( 20702, [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ]
% 2.33/2.76 )
% 2.33/2.76 , clause( 20703, [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) )
% 2.33/2.76 , maps( X, 'domain_of'( X ), Y ) ] )
% 2.33/2.76 , clause( 20704, [ operation( xf1 ) ] )
% 2.33/2.76 , clause( 20705, [ compatible( xh, xf1, xf2 ) ] )
% 2.33/2.76 , clause( 20706, [ ~( =( 'cross_product'( 'domain_of'( xh ), 'domain_of'(
% 2.33/2.76 xh ) ), 'domain_of'( xf1 ) ) ) ] )
% 2.33/2.76 ] ).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 subsumption(
% 2.33/2.76 clause( 77, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 2.33/2.76 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.33/2.76 ] )
% 2.33/2.76 , clause( 20670, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 2.33/2.76 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.33/2.76 ] )
% 2.33/2.76 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 2.33/2.76 1 )] ) ).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 subsumption(
% 2.33/2.76 clause( 81, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y )
% 2.33/2.76 ), 'domain_of'( X ) ) ] )
% 2.33/2.76 , clause( 20674, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 2.33/2.76 Y ) ), 'domain_of'( X ) ) ] )
% 2.33/2.76 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.33/2.76 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 subsumption(
% 2.33/2.76 clause( 111, [ operation( xf1 ) ] )
% 2.33/2.76 , clause( 20704, [ operation( xf1 ) ] )
% 2.33/2.76 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 subsumption(
% 2.33/2.76 clause( 112, [ compatible( xh, xf1, xf2 ) ] )
% 2.33/2.76 , clause( 20705, [ compatible( xh, xf1, xf2 ) ] )
% 2.33/2.76 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 subsumption(
% 2.33/2.76 clause( 113, [ ~( =( 'cross_product'( 'domain_of'( xh ), 'domain_of'( xh )
% 2.33/2.76 ), 'domain_of'( xf1 ) ) ) ] )
% 2.33/2.76 , clause( 20706, [ ~( =( 'cross_product'( 'domain_of'( xh ), 'domain_of'(
% 2.33/2.76 xh ) ), 'domain_of'( xf1 ) ) ) ] )
% 2.33/2.76 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 eqswap(
% 2.33/2.76 clause( 20974, [ =( 'domain_of'( X ), 'cross_product'( 'domain_of'(
% 2.33/2.76 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ) ), ~( operation( X
% 2.33/2.76 ) ) ] )
% 2.33/2.76 , clause( 77, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 2.33/2.76 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.33/2.76 ] )
% 2.33/2.76 , 1, substitution( 0, [ :=( X, X )] )).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 resolution(
% 2.33/2.76 clause( 20975, [ =( 'domain_of'( xf1 ), 'cross_product'( 'domain_of'(
% 2.33/2.76 'domain_of'( xf1 ) ), 'domain_of'( 'domain_of'( xf1 ) ) ) ) ] )
% 2.33/2.76 , clause( 20974, [ =( 'domain_of'( X ), 'cross_product'( 'domain_of'(
% 2.33/2.76 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ) ), ~( operation( X
% 2.33/2.76 ) ) ] )
% 2.33/2.76 , 1, clause( 111, [ operation( xf1 ) ] )
% 2.33/2.76 , 0, substitution( 0, [ :=( X, xf1 )] ), substitution( 1, [] )).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 eqswap(
% 2.33/2.76 clause( 20976, [ =( 'cross_product'( 'domain_of'( 'domain_of'( xf1 ) ),
% 2.33/2.76 'domain_of'( 'domain_of'( xf1 ) ) ), 'domain_of'( xf1 ) ) ] )
% 2.33/2.76 , clause( 20975, [ =( 'domain_of'( xf1 ), 'cross_product'( 'domain_of'(
% 2.33/2.76 'domain_of'( xf1 ) ), 'domain_of'( 'domain_of'( xf1 ) ) ) ) ] )
% 2.33/2.76 , 0, substitution( 0, [] )).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 subsumption(
% 2.33/2.76 clause( 8711, [ =( 'cross_product'( 'domain_of'( 'domain_of'( xf1 ) ),
% 2.33/2.76 'domain_of'( 'domain_of'( xf1 ) ) ), 'domain_of'( xf1 ) ) ] )
% 2.33/2.76 , clause( 20976, [ =( 'cross_product'( 'domain_of'( 'domain_of'( xf1 ) ),
% 2.33/2.76 'domain_of'( 'domain_of'( xf1 ) ) ), 'domain_of'( xf1 ) ) ] )
% 2.33/2.76 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 eqswap(
% 2.33/2.76 clause( 20977, [ =( 'domain_of'( Y ), 'domain_of'( 'domain_of'( X ) ) ),
% 2.33/2.76 ~( compatible( Y, X, Z ) ) ] )
% 2.33/2.76 , clause( 81, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y
% 2.33/2.76 ) ), 'domain_of'( X ) ) ] )
% 2.33/2.76 , 1, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] )).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 resolution(
% 2.33/2.76 clause( 20978, [ =( 'domain_of'( xh ), 'domain_of'( 'domain_of'( xf1 ) ) )
% 2.33/2.76 ] )
% 2.33/2.76 , clause( 20977, [ =( 'domain_of'( Y ), 'domain_of'( 'domain_of'( X ) ) ),
% 2.33/2.76 ~( compatible( Y, X, Z ) ) ] )
% 2.33/2.76 , 1, clause( 112, [ compatible( xh, xf1, xf2 ) ] )
% 2.33/2.76 , 0, substitution( 0, [ :=( X, xf1 ), :=( Y, xh ), :=( Z, xf2 )] ),
% 2.33/2.76 substitution( 1, [] )).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 eqswap(
% 2.33/2.76 clause( 20979, [ =( 'domain_of'( 'domain_of'( xf1 ) ), 'domain_of'( xh ) )
% 2.33/2.76 ] )
% 2.33/2.76 , clause( 20978, [ =( 'domain_of'( xh ), 'domain_of'( 'domain_of'( xf1 ) )
% 2.33/2.76 ) ] )
% 2.33/2.76 , 0, substitution( 0, [] )).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 subsumption(
% 2.33/2.76 clause( 9092, [ =( 'domain_of'( 'domain_of'( xf1 ) ), 'domain_of'( xh ) ) ]
% 2.33/2.76 )
% 2.33/2.76 , clause( 20979, [ =( 'domain_of'( 'domain_of'( xf1 ) ), 'domain_of'( xh )
% 2.33/2.76 ) ] )
% 2.33/2.76 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 paramod(
% 2.33/2.76 clause( 20984, [ =( 'cross_product'( 'domain_of'( 'domain_of'( xf1 ) ),
% 2.33/2.76 'domain_of'( xh ) ), 'domain_of'( xf1 ) ) ] )
% 2.33/2.76 , clause( 9092, [ =( 'domain_of'( 'domain_of'( xf1 ) ), 'domain_of'( xh ) )
% 2.33/2.76 ] )
% 2.33/2.76 , 0, clause( 8711, [ =( 'cross_product'( 'domain_of'( 'domain_of'( xf1 ) )
% 2.33/2.76 , 'domain_of'( 'domain_of'( xf1 ) ) ), 'domain_of'( xf1 ) ) ] )
% 2.33/2.76 , 0, 5, substitution( 0, [] ), substitution( 1, [] )).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 paramod(
% 2.33/2.76 clause( 20985, [ =( 'cross_product'( 'domain_of'( xh ), 'domain_of'( xh ) )
% 2.33/2.76 , 'domain_of'( xf1 ) ) ] )
% 2.33/2.76 , clause( 9092, [ =( 'domain_of'( 'domain_of'( xf1 ) ), 'domain_of'( xh ) )
% 2.33/2.76 ] )
% 2.33/2.76 , 0, clause( 20984, [ =( 'cross_product'( 'domain_of'( 'domain_of'( xf1 ) )
% 2.33/2.76 , 'domain_of'( xh ) ), 'domain_of'( xf1 ) ) ] )
% 2.33/2.76 , 0, 2, substitution( 0, [] ), substitution( 1, [] )).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 resolution(
% 2.33/2.76 clause( 20986, [] )
% 2.33/2.76 , clause( 113, [ ~( =( 'cross_product'( 'domain_of'( xh ), 'domain_of'( xh
% 2.33/2.76 ) ), 'domain_of'( xf1 ) ) ) ] )
% 2.33/2.76 , 0, clause( 20985, [ =( 'cross_product'( 'domain_of'( xh ), 'domain_of'(
% 2.33/2.76 xh ) ), 'domain_of'( xf1 ) ) ] )
% 2.33/2.76 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 subsumption(
% 2.33/2.76 clause( 20590, [] )
% 2.33/2.76 , clause( 20986, [] )
% 2.33/2.76 , substitution( 0, [] ), permutation( 0, [] ) ).
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 end.
% 2.33/2.76
% 2.33/2.76 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.33/2.76
% 2.33/2.76 Memory use:
% 2.33/2.76
% 2.33/2.76 space for terms: 317240
% 2.33/2.76 space for clauses: 963510
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 clauses generated: 44820
% 2.33/2.76 clauses kept: 20591
% 2.33/2.76 clauses selected: 474
% 2.33/2.76 clauses deleted: 369
% 2.33/2.76 clauses inuse deleted: 93
% 2.33/2.76
% 2.33/2.76 subsentry: 122543
% 2.33/2.76 literals s-matched: 92413
% 2.33/2.76 literals matched: 90715
% 2.33/2.76 full subsumption: 39831
% 2.33/2.76
% 2.33/2.76 checksum: 723356339
% 2.33/2.76
% 2.33/2.76
% 2.33/2.76 Bliksem ended
%------------------------------------------------------------------------------