TSTP Solution File: NUM180-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM180-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n016.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 06:20:20 EDT 2022
% Result : Unsatisfiable 2.81s 3.18s
% Output : Refutation 2.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM180-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Wed Jul 6 05:56:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.75/1.14 *** allocated 10000 integers for termspace/termends
% 0.75/1.14 *** allocated 10000 integers for clauses
% 0.75/1.14 *** allocated 10000 integers for justifications
% 0.75/1.14 Bliksem 1.12
% 0.75/1.14
% 0.75/1.14
% 0.75/1.14 Automatic Strategy Selection
% 0.75/1.14
% 0.75/1.14 Clauses:
% 0.75/1.14 [
% 0.75/1.14 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.75/1.14 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.75/1.14 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.75/1.14 ,
% 0.75/1.14 [ subclass( X, 'universal_class' ) ],
% 0.75/1.14 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.75/1.14 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.75/1.14 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.75/1.14 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.75/1.14 ,
% 0.75/1.14 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.75/1.14 ) ) ],
% 0.75/1.14 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.75/1.14 ) ) ],
% 0.75/1.14 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.75/1.14 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.75/1.14 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.75/1.14 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.75/1.14 X, Z ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.75/1.14 Y, T ) ],
% 0.75/1.14 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.75/1.14 ), 'cross_product'( Y, T ) ) ],
% 0.75/1.14 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.75/1.14 ), second( X ) ), X ) ],
% 0.75/1.14 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.75/1.14 'universal_class' ) ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.75/1.14 Y ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.75/1.14 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.75/1.14 , Y ), 'element_relation' ) ],
% 0.75/1.14 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.75/1.14 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.75/1.14 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.75/1.14 Z ) ) ],
% 0.75/1.14 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.75/1.14 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.75/1.14 member( X, Y ) ],
% 0.75/1.14 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.75/1.14 union( X, Y ) ) ],
% 0.75/1.14 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.75/1.14 intersection( complement( X ), complement( Y ) ) ) ),
% 0.75/1.14 'symmetric_difference'( X, Y ) ) ],
% 0.75/1.14 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.75/1.14 ,
% 0.75/1.14 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.75/1.14 ,
% 0.75/1.14 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.75/1.14 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.75/1.14 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.75/1.14 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.75/1.14 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.75/1.14 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.75/1.14 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.75/1.14 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.75/1.14 'cross_product'( 'universal_class', 'universal_class' ),
% 0.75/1.14 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.75/1.14 Y ), rotate( T ) ) ],
% 0.75/1.14 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.75/1.14 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.75/1.14 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.75/1.14 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.75/1.14 'cross_product'( 'universal_class', 'universal_class' ),
% 0.75/1.14 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.75/1.14 Z ), flip( T ) ) ],
% 0.75/1.14 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.75/1.14 inverse( X ) ) ],
% 0.75/1.14 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.75/1.14 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.75/1.14 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.75/1.14 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.75/1.14 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.75/1.14 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.75/1.14 ],
% 0.75/1.14 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.75/1.14 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.75/1.14 'universal_class' ) ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.75/1.14 successor( X ), Y ) ],
% 0.75/1.14 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.75/1.14 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.75/1.14 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.75/1.14 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.75/1.14 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.75/1.14 ,
% 0.75/1.14 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.75/1.14 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.75/1.14 [ inductive( omega ) ],
% 0.75/1.14 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.75/1.14 [ member( omega, 'universal_class' ) ],
% 0.75/1.14 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.75/1.14 , 'sum_class'( X ) ) ],
% 0.75/1.14 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.75/1.14 'universal_class' ) ],
% 0.75/1.14 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.75/1.14 'power_class'( X ) ) ],
% 0.75/1.14 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.75/1.14 'universal_class' ) ],
% 0.75/1.14 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.75/1.14 'universal_class' ) ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.75/1.14 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.75/1.14 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.75/1.14 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.75/1.14 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.75/1.14 ) ],
% 0.75/1.14 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.75/1.14 , 'identity_relation' ) ],
% 0.75/1.14 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.75/1.14 'single_valued_class'( X ) ],
% 0.75/1.14 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.75/1.14 'universal_class' ) ) ],
% 0.75/1.14 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.75/1.14 'identity_relation' ) ],
% 0.75/1.14 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.75/1.14 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.75/1.14 , function( X ) ],
% 0.75/1.14 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.75/1.14 X, Y ), 'universal_class' ) ],
% 0.75/1.14 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.75/1.14 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.75/1.14 ) ],
% 0.75/1.14 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.75/1.14 [ function( choice ) ],
% 0.75/1.14 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.75/1.14 apply( choice, X ), X ) ],
% 0.75/1.14 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.75/1.14 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.75/1.14 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.75/1.14 ,
% 0.75/1.14 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.75/1.14 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.75/1.14 , complement( compose( complement( 'element_relation' ), inverse(
% 0.75/1.14 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.75/1.14 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.75/1.14 'identity_relation' ) ],
% 0.75/1.14 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.75/1.14 , diagonalise( X ) ) ],
% 0.75/1.14 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.75/1.14 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.75/1.14 [ ~( operation( X ) ), function( X ) ],
% 0.75/1.14 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.75/1.14 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.75/1.14 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.75/1.14 'domain_of'( X ) ) ) ],
% 0.75/1.14 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.75/1.14 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.75/1.14 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.75/1.14 X ) ],
% 0.75/1.14 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.75/1.14 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.75/1.14 'domain_of'( X ) ) ],
% 0.75/1.14 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.75/1.14 'domain_of'( Z ) ) ) ],
% 0.75/1.14 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.75/1.14 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.75/1.14 ), compatible( X, Y, Z ) ],
% 0.75/1.14 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.75/1.14 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.75/1.14 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.75/1.14 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.75/1.14 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.75/1.14 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.75/1.14 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.75/1.14 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.75/1.14 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.75/1.14 , Y ) ],
% 0.75/1.14 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.75/1.14 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.75/1.14 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.75/1.14 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.75/1.14 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.75/1.14 [ subclass( 'compose_class'( X ), 'cross_product'( 'universal_class',
% 0.75/1.14 'universal_class' ) ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ), =(
% 0.75/1.14 compose( Z, X ), Y ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.75/1.14 , 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) ), member(
% 0.75/1.14 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ],
% 0.75/1.14 [ subclass( 'composition_function', 'cross_product'( 'universal_class',
% 0.75/1.14 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.75/1.14 'composition_function' ) ), =( compose( X, Y ), Z ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.75/1.14 , 'universal_class' ) ) ), member( 'ordered_pair'( X, 'ordered_pair'( Y,
% 0.75/1.14 compose( X, Y ) ) ), 'composition_function' ) ],
% 0.75/1.14 [ subclass( 'domain_relation', 'cross_product'( 'universal_class',
% 0.75/1.14 'universal_class' ) ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) ), =(
% 0.75/1.14 'domain_of'( X ), Y ) ],
% 0.75/1.14 [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X,
% 0.75/1.14 'domain_of'( X ) ), 'domain_relation' ) ],
% 0.75/1.14 [ =( first( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.75/1.14 'identity_relation' ) ), 'single_valued1'( X ) ) ],
% 0.75/1.14 [ =( second( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.75/1.14 'identity_relation' ) ), 'single_valued2'( X ) ) ],
% 0.75/1.14 [ =( domain( X, image( inverse( X ), singleton( 'single_valued1'( X ) )
% 0.75/1.14 ), 'single_valued2'( X ) ), 'single_valued3'( X ) ) ],
% 0.75/1.14 [ =( intersection( complement( compose( 'element_relation', complement(
% 0.75/1.14 'identity_relation' ) ) ), 'element_relation' ), 'singleton_relation' ) ]
% 0.75/1.14 ,
% 0.75/1.14 [ subclass( 'application_function', 'cross_product'( 'universal_class',
% 0.75/1.14 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.75/1.14 'application_function' ) ), member( Y, 'domain_of'( X ) ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.75/1.14 'application_function' ) ), =( apply( X, Y ), Z ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.75/1.14 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 0.75/1.14 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 0.75/1.14 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 0.75/1.14 'application_function' ) ],
% 0.75/1.14 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.75/1.14 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 0.75/1.14 [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ],
% 0.75/1.14 [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ), maps( X,
% 0.75/1.14 'domain_of'( X ), Y ) ],
% 0.75/1.14 [ =( union( X, inverse( X ) ), 'symmetrization_of'( X ) ) ],
% 0.75/1.14 [ ~( irreflexive( X, Y ) ), subclass( restrict( X, Y, Y ), complement(
% 0.75/1.14 'identity_relation' ) ) ],
% 0.75/1.14 [ ~( subclass( restrict( X, Y, Y ), complement( 'identity_relation' ) )
% 0.75/1.14 ), irreflexive( X, Y ) ],
% 0.75/1.14 [ ~( connected( X, Y ) ), subclass( 'cross_product'( Y, Y ), union(
% 0.75/1.14 'identity_relation', 'symmetrization_of'( X ) ) ) ],
% 0.75/1.14 [ ~( subclass( 'cross_product'( X, X ), union( 'identity_relation',
% 0.75/1.14 'symmetrization_of'( Y ) ) ) ), connected( Y, X ) ],
% 0.75/1.14 [ ~( transitive( X, Y ) ), subclass( compose( restrict( X, Y, Y ),
% 0.75/1.14 restrict( X, Y, Y ) ), restrict( X, Y, Y ) ) ],
% 0.75/1.14 [ ~( subclass( compose( restrict( X, Y, Y ), restrict( X, Y, Y ) ),
% 0.75/1.14 restrict( X, Y, Y ) ) ), transitive( X, Y ) ],
% 0.75/1.14 [ ~( asymmetric( X, Y ) ), =( restrict( intersection( X, inverse( X ) )
% 0.75/1.14 , Y, Y ), 'null_class' ) ],
% 0.75/1.14 [ ~( =( restrict( intersection( X, inverse( X ) ), Y, Y ), 'null_class'
% 0.75/1.14 ) ), asymmetric( X, Y ) ],
% 0.75/1.14 [ =( segment( X, Y, Z ), 'domain_of'( restrict( X, Y, singleton( Z ) ) )
% 0.75/1.14 ) ],
% 0.75/1.14 [ ~( 'well_ordering'( X, Y ) ), connected( X, Y ) ],
% 0.75/1.14 [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), =( Z,
% 0.75/1.14 'null_class' ), member( least( X, Z ), Z ) ],
% 0.75/1.14 [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), ~( member( T, Z )
% 0.75/1.14 ), member( least( X, Z ), Z ) ],
% 0.75/1.14 [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), =( segment( X, Z
% 0.75/1.14 , least( X, Z ) ), 'null_class' ) ],
% 0.75/1.14 [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), ~( member( T, Z )
% 0.75/1.14 ), ~( member( 'ordered_pair'( T, least( X, Z ) ), X ) ) ],
% 0.75/1.14 [ ~( connected( X, Y ) ), ~( =( 'not_well_ordering'( X, Y ),
% 0.75/1.14 'null_class' ) ), 'well_ordering'( X, Y ) ],
% 0.75/1.14 [ ~( connected( X, Y ) ), subclass( 'not_well_ordering'( X, Y ), Y ),
% 0.75/1.14 'well_ordering'( X, Y ) ],
% 0.75/1.14 [ ~( member( X, 'not_well_ordering'( Y, Z ) ) ), ~( =( segment( Y,
% 0.75/1.14 'not_well_ordering'( Y, Z ), X ), 'null_class' ) ), ~( connected( Y, Z )
% 0.75/1.14 ), 'well_ordering'( Y, Z ) ],
% 0.75/1.14 [ ~( section( X, Y, Z ) ), subclass( Y, Z ) ],
% 0.75/1.14 [ ~( section( X, Y, Z ) ), subclass( 'domain_of'( restrict( X, Z, Y ) )
% 0.75/1.14 , Y ) ],
% 0.75/1.14 [ ~( subclass( X, Y ) ), ~( subclass( 'domain_of'( restrict( Z, Y, X ) )
% 0.75/1.14 , X ) ), section( Z, X, Y ) ],
% 0.75/1.14 [ ~( member( X, 'ordinal_numbers' ) ), 'well_ordering'(
% 0.75/1.14 'element_relation', X ) ],
% 0.75/1.14 [ ~( member( X, 'ordinal_numbers' ) ), subclass( 'sum_class'( X ), X ) ]
% 0.75/1.14 ,
% 0.75/1.14 [ ~( 'well_ordering'( 'element_relation', X ) ), ~( subclass(
% 0.75/1.14 'sum_class'( X ), X ) ), ~( member( X, 'universal_class' ) ), member( X,
% 0.75/1.14 'ordinal_numbers' ) ],
% 0.75/1.14 [ ~( 'well_ordering'( 'element_relation', X ) ), ~( subclass(
% 0.75/1.14 'sum_class'( X ), X ) ), member( X, 'ordinal_numbers' ), =( X,
% 0.75/1.14 'ordinal_numbers' ) ],
% 0.75/1.14 [ =( union( singleton( 'null_class' ), image( 'successor_relation',
% 0.75/1.14 'ordinal_numbers' ) ), 'kind_1_ordinals' ) ],
% 0.75/1.14 [ =( intersection( complement( 'kind_1_ordinals' ), 'ordinal_numbers' )
% 0.75/1.14 , 'limit_ordinals' ) ],
% 0.75/1.14 [ subclass( 'rest_of'( X ), 'cross_product'( 'universal_class',
% 0.75/1.14 'universal_class' ) ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'rest_of'( Z ) ) ), member( X,
% 0.75/1.14 'domain_of'( Z ) ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'rest_of'( Z ) ) ), =( restrict( Z
% 0.75/1.14 , X, 'universal_class' ), Y ) ],
% 0.75/1.14 [ ~( member( X, 'domain_of'( Y ) ) ), ~( =( restrict( Y, X,
% 0.75/1.14 'universal_class' ), Z ) ), member( 'ordered_pair'( X, Z ), 'rest_of'( Y
% 0.75/1.14 ) ) ],
% 0.75/1.14 [ subclass( 'rest_relation', 'cross_product'( 'universal_class',
% 0.75/1.14 'universal_class' ) ) ],
% 0.75/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'rest_relation' ) ), =( 'rest_of'(
% 0.75/1.14 X ), Y ) ],
% 0.75/1.14 [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X,
% 0.75/1.14 'rest_of'( X ) ), 'rest_relation' ) ],
% 0.75/1.14 [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), function( Y ) ]
% 0.75/1.14 ,
% 0.75/1.14 [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), function( X ) ]
% 0.75/1.14 ,
% 0.75/1.14 [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), member(
% 1.51/1.92 'domain_of'( X ), 'ordinal_numbers' ) ],
% 1.51/1.92 [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), =( compose( Y,
% 1.51/1.92 'rest_of'( X ) ), X ) ],
% 1.51/1.92 [ ~( function( X ) ), ~( function( Y ) ), ~( member( 'domain_of'( Y ),
% 1.51/1.92 'ordinal_numbers' ) ), ~( =( compose( X, 'rest_of'( Y ) ), Y ) ), member(
% 1.51/1.92 Y, 'recursion_equation_functions'( X ) ) ],
% 1.51/1.92 [ subclass( 'union_of_range_map', 'cross_product'( 'universal_class',
% 1.51/1.92 'universal_class' ) ) ],
% 1.51/1.92 [ ~( member( 'ordered_pair'( X, Y ), 'union_of_range_map' ) ), =(
% 1.51/1.92 'sum_class'( 'range_of'( X ) ), Y ) ],
% 1.51/1.92 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 1.51/1.92 , 'universal_class' ) ) ), ~( =( 'sum_class'( 'range_of'( X ) ), Y ) ),
% 1.51/1.92 member( 'ordered_pair'( X, Y ), 'union_of_range_map' ) ],
% 1.51/1.92 [ =( apply( recursion( X, 'successor_relation', 'union_of_range_map' ),
% 1.51/1.92 Y ), 'ordinal_add'( X, Y ) ) ],
% 1.51/1.92 [ =( recursion( 'null_class', apply( 'add_relation', X ),
% 1.51/1.92 'union_of_range_map' ), 'ordinal_multiply'( X, Y ) ) ],
% 1.51/1.92 [ ~( member( X, omega ) ), =( 'integer_of'( X ), X ) ],
% 1.51/1.92 [ member( X, omega ), =( 'integer_of'( X ), 'null_class' ) ],
% 1.51/1.92 [ ~( subclass( 'limit_ordinals', 'ordinal_numbers' ) ) ]
% 1.51/1.92 ] .
% 1.51/1.92
% 1.51/1.92
% 1.51/1.92 percentage equality = 0.219814, percentage horn = 0.924528
% 1.51/1.92 This is a problem with some equality
% 1.51/1.92
% 1.51/1.92
% 1.51/1.92
% 1.51/1.92 Options Used:
% 1.51/1.92
% 1.51/1.92 useres = 1
% 1.51/1.92 useparamod = 1
% 1.51/1.92 useeqrefl = 1
% 1.51/1.92 useeqfact = 1
% 1.51/1.92 usefactor = 1
% 1.51/1.92 usesimpsplitting = 0
% 1.51/1.92 usesimpdemod = 5
% 1.51/1.92 usesimpres = 3
% 1.51/1.92
% 1.51/1.92 resimpinuse = 1000
% 1.51/1.92 resimpclauses = 20000
% 1.51/1.92 substype = eqrewr
% 1.51/1.92 backwardsubs = 1
% 1.51/1.92 selectoldest = 5
% 1.51/1.92
% 1.51/1.92 litorderings [0] = split
% 1.51/1.92 litorderings [1] = extend the termordering, first sorting on arguments
% 1.51/1.92
% 1.51/1.92 termordering = kbo
% 1.51/1.92
% 1.51/1.92 litapriori = 0
% 1.51/1.92 termapriori = 1
% 1.51/1.92 litaposteriori = 0
% 1.51/1.92 termaposteriori = 0
% 1.51/1.92 demodaposteriori = 0
% 1.51/1.92 ordereqreflfact = 0
% 1.51/1.92
% 1.51/1.92 litselect = negord
% 1.51/1.92
% 1.51/1.92 maxweight = 15
% 1.51/1.92 maxdepth = 30000
% 1.51/1.92 maxlength = 115
% 1.51/1.92 maxnrvars = 195
% 1.51/1.92 excuselevel = 1
% 1.51/1.92 increasemaxweight = 1
% 1.51/1.92
% 1.51/1.92 maxselected = 10000000
% 1.51/1.92 maxnrclauses = 10000000
% 1.51/1.92
% 1.51/1.92 showgenerated = 0
% 1.51/1.92 showkept = 0
% 1.51/1.92 showselected = 0
% 1.51/1.92 showdeleted = 0
% 1.51/1.92 showresimp = 1
% 1.51/1.92 showstatus = 2000
% 1.51/1.92
% 1.51/1.92 prologoutput = 1
% 1.51/1.92 nrgoals = 5000000
% 1.51/1.92 totalproof = 1
% 1.51/1.92
% 1.51/1.92 Symbols occurring in the translation:
% 1.51/1.92
% 1.51/1.92 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.51/1.92 . [1, 2] (w:1, o:72, a:1, s:1, b:0),
% 1.51/1.92 ! [4, 1] (w:0, o:39, a:1, s:1, b:0),
% 1.51/1.92 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.51/1.92 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.51/1.92 subclass [41, 2] (w:1, o:97, a:1, s:1, b:0),
% 1.51/1.92 member [43, 2] (w:1, o:99, a:1, s:1, b:0),
% 1.51/1.92 'not_subclass_element' [44, 2] (w:1, o:100, a:1, s:1, b:0),
% 1.51/1.92 'universal_class' [45, 0] (w:1, o:24, a:1, s:1, b:0),
% 1.51/1.92 'unordered_pair' [46, 2] (w:1, o:102, a:1, s:1, b:0),
% 1.51/1.92 singleton [47, 1] (w:1, o:49, a:1, s:1, b:0),
% 1.51/1.92 'ordered_pair' [48, 2] (w:1, o:104, a:1, s:1, b:0),
% 1.51/1.92 'cross_product' [50, 2] (w:1, o:105, a:1, s:1, b:0),
% 1.51/1.92 first [52, 1] (w:1, o:50, a:1, s:1, b:0),
% 1.51/1.92 second [53, 1] (w:1, o:51, a:1, s:1, b:0),
% 1.51/1.92 'element_relation' [54, 0] (w:1, o:29, a:1, s:1, b:0),
% 1.51/1.92 intersection [55, 2] (w:1, o:107, a:1, s:1, b:0),
% 1.51/1.92 complement [56, 1] (w:1, o:52, a:1, s:1, b:0),
% 1.51/1.92 union [57, 2] (w:1, o:108, a:1, s:1, b:0),
% 1.51/1.92 'symmetric_difference' [58, 2] (w:1, o:109, a:1, s:1, b:0),
% 1.51/1.92 restrict [60, 3] (w:1, o:118, a:1, s:1, b:0),
% 1.51/1.92 'null_class' [61, 0] (w:1, o:30, a:1, s:1, b:0),
% 1.51/1.92 'domain_of' [62, 1] (w:1, o:55, a:1, s:1, b:0),
% 1.51/1.92 rotate [63, 1] (w:1, o:44, a:1, s:1, b:0),
% 1.51/1.92 flip [65, 1] (w:1, o:56, a:1, s:1, b:0),
% 1.51/1.92 inverse [66, 1] (w:1, o:57, a:1, s:1, b:0),
% 1.51/1.92 'range_of' [67, 1] (w:1, o:45, a:1, s:1, b:0),
% 1.51/1.92 domain [68, 3] (w:1, o:120, a:1, s:1, b:0),
% 1.51/1.92 range [69, 3] (w:1, o:121, a:1, s:1, b:0),
% 1.51/1.92 image [70, 2] (w:1, o:106, a:1, s:1, b:0),
% 1.51/1.92 successor [71, 1] (w:1, o:58, a:1, s:1, b:0),
% 1.51/1.92 'successor_relation' [72, 0] (w:1, o:7, a:1, s:1, b:0),
% 1.51/1.92 inductive [73, 1] (w:1, o:59, a:1, s:1, b:0),
% 2.81/3.18 omega [74, 0] (w:1, o:11, a:1, s:1, b:0),
% 2.81/3.18 'sum_class' [75, 1] (w:1, o:60, a:1, s:1, b:0),
% 2.81/3.18 'power_class' [76, 1] (w:1, o:63, a:1, s:1, b:0),
% 2.81/3.18 compose [78, 2] (w:1, o:110, a:1, s:1, b:0),
% 2.81/3.18 'single_valued_class' [79, 1] (w:1, o:64, a:1, s:1, b:0),
% 2.81/3.18 'identity_relation' [80, 0] (w:1, o:31, a:1, s:1, b:0),
% 2.81/3.18 function [82, 1] (w:1, o:65, a:1, s:1, b:0),
% 2.81/3.18 regular [83, 1] (w:1, o:46, a:1, s:1, b:0),
% 2.81/3.18 apply [84, 2] (w:1, o:111, a:1, s:1, b:0),
% 2.81/3.18 choice [85, 0] (w:1, o:32, a:1, s:1, b:0),
% 2.81/3.18 'one_to_one' [86, 1] (w:1, o:61, a:1, s:1, b:0),
% 2.81/3.18 'subset_relation' [87, 0] (w:1, o:6, a:1, s:1, b:0),
% 2.81/3.18 diagonalise [88, 1] (w:1, o:66, a:1, s:1, b:0),
% 2.81/3.18 cantor [89, 1] (w:1, o:53, a:1, s:1, b:0),
% 2.81/3.18 operation [90, 1] (w:1, o:62, a:1, s:1, b:0),
% 2.81/3.18 compatible [94, 3] (w:1, o:119, a:1, s:1, b:0),
% 2.81/3.18 homomorphism [95, 3] (w:1, o:122, a:1, s:1, b:0),
% 2.81/3.18 'not_homomorphism1' [96, 3] (w:1, o:124, a:1, s:1, b:0),
% 2.81/3.18 'not_homomorphism2' [97, 3] (w:1, o:125, a:1, s:1, b:0),
% 2.81/3.18 'compose_class' [98, 1] (w:1, o:54, a:1, s:1, b:0),
% 2.81/3.18 'composition_function' [99, 0] (w:1, o:33, a:1, s:1, b:0),
% 2.81/3.18 'domain_relation' [100, 0] (w:1, o:28, a:1, s:1, b:0),
% 2.81/3.18 'single_valued1' [101, 1] (w:1, o:67, a:1, s:1, b:0),
% 2.81/3.18 'single_valued2' [102, 1] (w:1, o:68, a:1, s:1, b:0),
% 2.81/3.18 'single_valued3' [103, 1] (w:1, o:69, a:1, s:1, b:0),
% 2.81/3.18 'singleton_relation' [104, 0] (w:1, o:8, a:1, s:1, b:0),
% 2.81/3.18 'application_function' [105, 0] (w:1, o:34, a:1, s:1, b:0),
% 2.81/3.18 maps [106, 3] (w:1, o:123, a:1, s:1, b:0),
% 2.81/3.18 'symmetrization_of' [107, 1] (w:1, o:70, a:1, s:1, b:0),
% 2.81/3.18 irreflexive [108, 2] (w:1, o:112, a:1, s:1, b:0),
% 2.81/3.18 connected [109, 2] (w:1, o:113, a:1, s:1, b:0),
% 2.81/3.18 transitive [110, 2] (w:1, o:101, a:1, s:1, b:0),
% 2.81/3.18 asymmetric [111, 2] (w:1, o:114, a:1, s:1, b:0),
% 2.81/3.18 segment [112, 3] (w:1, o:127, a:1, s:1, b:0),
% 2.81/3.18 'well_ordering' [113, 2] (w:1, o:115, a:1, s:1, b:0),
% 2.81/3.18 least [114, 2] (w:1, o:98, a:1, s:1, b:0),
% 2.81/3.18 'not_well_ordering' [115, 2] (w:1, o:103, a:1, s:1, b:0),
% 2.81/3.18 section [116, 3] (w:1, o:128, a:1, s:1, b:0),
% 2.81/3.18 'ordinal_numbers' [117, 0] (w:1, o:12, a:1, s:1, b:0),
% 2.81/3.18 'kind_1_ordinals' [118, 0] (w:1, o:35, a:1, s:1, b:0),
% 2.81/3.18 'limit_ordinals' [119, 0] (w:1, o:36, a:1, s:1, b:0),
% 2.81/3.18 'rest_of' [120, 1] (w:1, o:47, a:1, s:1, b:0),
% 2.81/3.18 'rest_relation' [121, 0] (w:1, o:5, a:1, s:1, b:0),
% 2.81/3.18 'recursion_equation_functions' [122, 1] (w:1, o:48, a:1, s:1, b:0),
% 2.81/3.18 'union_of_range_map' [123, 0] (w:1, o:37, a:1, s:1, b:0),
% 2.81/3.18 recursion [124, 3] (w:1, o:126, a:1, s:1, b:0),
% 2.81/3.18 'ordinal_add' [125, 2] (w:1, o:116, a:1, s:1, b:0),
% 2.81/3.18 'add_relation' [126, 0] (w:1, o:38, a:1, s:1, b:0),
% 2.81/3.18 'ordinal_multiply' [127, 2] (w:1, o:117, a:1, s:1, b:0),
% 2.81/3.18 'integer_of' [128, 1] (w:1, o:71, a:1, s:1, b:0).
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 Starting Search:
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 Intermediate Status:
% 2.81/3.18 Generated: 4524
% 2.81/3.18 Kept: 2005
% 2.81/3.18 Inuse: 111
% 2.81/3.18 Deleted: 3
% 2.81/3.18 Deletedinuse: 2
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 Intermediate Status:
% 2.81/3.18 Generated: 9260
% 2.81/3.18 Kept: 4128
% 2.81/3.18 Inuse: 192
% 2.81/3.18 Deleted: 14
% 2.81/3.18 Deletedinuse: 5
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 Intermediate Status:
% 2.81/3.18 Generated: 13237
% 2.81/3.18 Kept: 6138
% 2.81/3.18 Inuse: 250
% 2.81/3.18 Deleted: 19
% 2.81/3.18 Deletedinuse: 7
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 Intermediate Status:
% 2.81/3.18 Generated: 18104
% 2.81/3.18 Kept: 8154
% 2.81/3.18 Inuse: 297
% 2.81/3.18 Deleted: 51
% 2.81/3.18 Deletedinuse: 36
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 Intermediate Status:
% 2.81/3.18 Generated: 23293
% 2.81/3.18 Kept: 10509
% 2.81/3.18 Inuse: 356
% 2.81/3.18 Deleted: 79
% 2.81/3.18 Deletedinuse: 54
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 Intermediate Status:
% 2.81/3.18 Generated: 26834
% 2.81/3.18 Kept: 12516
% 2.81/3.18 Inuse: 383
% 2.81/3.18 Deleted: 83
% 2.81/3.18 Deletedinuse: 58
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 Intermediate Status:
% 2.81/3.18 Generated: 30631
% 2.81/3.18 Kept: 14516
% 2.81/3.18 Inuse: 425
% 2.81/3.18 Deleted: 89
% 2.81/3.18 Deletedinuse: 64
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 Intermediate Status:
% 2.81/3.18 Generated: 34181
% 2.81/3.18 Kept: 16545
% 2.81/3.18 Inuse: 456
% 2.81/3.18 Deleted: 89
% 2.81/3.18 Deletedinuse: 64
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 Intermediate Status:
% 2.81/3.18 Generated: 39242
% 2.81/3.18 Kept: 18580
% 2.81/3.18 Inuse: 504
% 2.81/3.18 Deleted: 90
% 2.81/3.18 Deletedinuse: 65
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18 Resimplifying clauses:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 Intermediate Status:
% 2.81/3.18 Generated: 43329
% 2.81/3.18 Kept: 20585
% 2.81/3.18 Inuse: 551
% 2.81/3.18 Deleted: 2539
% 2.81/3.18 Deletedinuse: 65
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 Intermediate Status:
% 2.81/3.18 Generated: 47776
% 2.81/3.18 Kept: 22659
% 2.81/3.18 Inuse: 575
% 2.81/3.18 Deleted: 2541
% 2.81/3.18 Deletedinuse: 67
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 Intermediate Status:
% 2.81/3.18 Generated: 51515
% 2.81/3.18 Kept: 24676
% 2.81/3.18 Inuse: 600
% 2.81/3.18 Deleted: 2541
% 2.81/3.18 Deletedinuse: 67
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18 Resimplifying inuse:
% 2.81/3.18 Done
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 Intermediate Status:
% 2.81/3.18 Generated: 54972
% 2.81/3.18 Kept: 26720
% 2.81/3.18 Inuse: 615
% 2.81/3.18 Deleted: 2542
% 2.81/3.18 Deletedinuse: 68
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 Bliksems!, er is een bewijs:
% 2.81/3.18 % SZS status Unsatisfiable
% 2.81/3.18 % SZS output start Refutation
% 2.81/3.18
% 2.81/3.18 clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y )
% 2.81/3.18 ] )
% 2.81/3.18 .
% 2.81/3.18 clause( 2, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X
% 2.81/3.18 , Y ) ] )
% 2.81/3.18 .
% 2.81/3.18 clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 2.81/3.18 .
% 2.81/3.18 clause( 137, [ =( intersection( complement( 'kind_1_ordinals' ),
% 2.81/3.18 'ordinal_numbers' ), 'limit_ordinals' ) ] )
% 2.81/3.18 .
% 2.81/3.18 clause( 157, [ ~( subclass( 'limit_ordinals', 'ordinal_numbers' ) ) ] )
% 2.81/3.18 .
% 2.81/3.18 clause( 180, [ member( 'not_subclass_element'( 'limit_ordinals',
% 2.81/3.18 'ordinal_numbers' ), 'limit_ordinals' ) ] )
% 2.81/3.18 .
% 2.81/3.18 clause( 188, [ ~( member( 'not_subclass_element'( 'limit_ordinals',
% 2.81/3.18 'ordinal_numbers' ), 'ordinal_numbers' ) ) ] )
% 2.81/3.18 .
% 2.81/3.18 clause( 21454, [ ~( member( X, 'limit_ordinals' ) ), member( X,
% 2.81/3.18 'ordinal_numbers' ) ] )
% 2.81/3.18 .
% 2.81/3.18 clause( 27372, [] )
% 2.81/3.18 .
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 % SZS output end Refutation
% 2.81/3.18 found a proof!
% 2.81/3.18
% 2.81/3.18 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.81/3.18
% 2.81/3.18 initialclauses(
% 2.81/3.18 [ clause( 27374, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 2.81/3.18 ) ] )
% 2.81/3.18 , clause( 27375, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 2.81/3.18 , Y ) ] )
% 2.81/3.18 , clause( 27376, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 2.81/3.18 subclass( X, Y ) ] )
% 2.81/3.18 , clause( 27377, [ subclass( X, 'universal_class' ) ] )
% 2.81/3.18 , clause( 27378, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.81/3.18 , clause( 27379, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 2.81/3.18 , clause( 27380, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 2.81/3.18 ] )
% 2.81/3.18 , clause( 27381, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 2.81/3.18 =( X, Z ) ] )
% 2.81/3.18 , clause( 27382, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.81/3.18 'unordered_pair'( X, Y ) ) ] )
% 2.81/3.18 , clause( 27383, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.81/3.18 'unordered_pair'( Y, X ) ) ] )
% 2.81/3.18 , clause( 27384, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 2.81/3.18 )
% 2.81/3.18 , clause( 27385, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.81/3.18 , clause( 27386, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 2.81/3.18 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 2.81/3.18 , clause( 27387, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.81/3.18 ) ) ), member( X, Z ) ] )
% 2.81/3.18 , clause( 27388, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.81/3.18 ) ) ), member( Y, T ) ] )
% 2.81/3.18 , clause( 27389, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 2.81/3.18 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 2.81/3.18 , clause( 27390, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 2.81/3.18 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 2.81/3.18 , clause( 27391, [ subclass( 'element_relation', 'cross_product'(
% 2.81/3.18 'universal_class', 'universal_class' ) ) ] )
% 2.81/3.18 , clause( 27392, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 2.81/3.18 ), member( X, Y ) ] )
% 2.81/3.18 , clause( 27393, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 2.81/3.18 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 2.81/3.18 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 2.81/3.18 , clause( 27394, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 2.81/3.18 )
% 2.81/3.18 , clause( 27395, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 2.81/3.18 )
% 2.81/3.18 , clause( 27396, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 2.81/3.18 intersection( Y, Z ) ) ] )
% 2.81/3.18 , clause( 27397, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 2.81/3.18 )
% 2.81/3.18 , clause( 27398, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.81/3.18 complement( Y ) ), member( X, Y ) ] )
% 2.81/3.18 , clause( 27399, [ =( complement( intersection( complement( X ), complement(
% 2.81/3.18 Y ) ) ), union( X, Y ) ) ] )
% 2.81/3.18 , clause( 27400, [ =( intersection( complement( intersection( X, Y ) ),
% 2.81/3.18 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 2.81/3.18 'symmetric_difference'( X, Y ) ) ] )
% 2.81/3.18 , clause( 27401, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 2.81/3.18 X, Y, Z ) ) ] )
% 2.81/3.18 , clause( 27402, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 2.81/3.18 Z, X, Y ) ) ] )
% 2.81/3.18 , clause( 27403, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 2.81/3.18 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 2.81/3.18 , clause( 27404, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 2.81/3.18 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 2.81/3.18 'domain_of'( Y ) ) ] )
% 2.81/3.18 , clause( 27405, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 2.81/3.18 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.81/3.18 , clause( 27406, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.81/3.18 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 2.81/3.18 ] )
% 2.81/3.18 , clause( 27407, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.81/3.18 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 2.81/3.18 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.81/3.18 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 2.81/3.18 , Y ), rotate( T ) ) ] )
% 2.81/3.18 , clause( 27408, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 2.81/3.18 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.81/3.18 , clause( 27409, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.81/3.18 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 2.81/3.18 )
% 2.81/3.18 , clause( 27410, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.81/3.18 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 2.81/3.18 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.81/3.18 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 2.81/3.18 , Z ), flip( T ) ) ] )
% 2.81/3.18 , clause( 27411, [ =( 'domain_of'( flip( 'cross_product'( X,
% 2.81/3.18 'universal_class' ) ) ), inverse( X ) ) ] )
% 2.81/3.18 , clause( 27412, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 2.81/3.18 , clause( 27413, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 2.81/3.18 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 2.81/3.18 , clause( 27414, [ =( second( 'not_subclass_element'( restrict( X,
% 2.81/3.18 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 2.81/3.18 , clause( 27415, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 2.81/3.18 image( X, Y ) ) ] )
% 2.81/3.18 , clause( 27416, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 2.81/3.18 , clause( 27417, [ subclass( 'successor_relation', 'cross_product'(
% 2.81/3.18 'universal_class', 'universal_class' ) ) ] )
% 2.81/3.18 , clause( 27418, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 2.81/3.18 ) ), =( successor( X ), Y ) ] )
% 2.81/3.18 , clause( 27419, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 2.81/3.18 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 2.81/3.18 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 2.81/3.18 , clause( 27420, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 2.81/3.18 , clause( 27421, [ ~( inductive( X ) ), subclass( image(
% 2.81/3.18 'successor_relation', X ), X ) ] )
% 2.81/3.18 , clause( 27422, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 2.81/3.18 'successor_relation', X ), X ) ), inductive( X ) ] )
% 2.81/3.18 , clause( 27423, [ inductive( omega ) ] )
% 2.81/3.18 , clause( 27424, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 2.81/3.18 , clause( 27425, [ member( omega, 'universal_class' ) ] )
% 2.81/3.18 , clause( 27426, [ =( 'domain_of'( restrict( 'element_relation',
% 2.81/3.18 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 2.81/3.18 , clause( 27427, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 2.81/3.18 X ), 'universal_class' ) ] )
% 2.81/3.18 , clause( 27428, [ =( complement( image( 'element_relation', complement( X
% 2.81/3.18 ) ) ), 'power_class'( X ) ) ] )
% 2.81/3.18 , clause( 27429, [ ~( member( X, 'universal_class' ) ), member(
% 2.81/3.18 'power_class'( X ), 'universal_class' ) ] )
% 2.81/3.18 , clause( 27430, [ subclass( compose( X, Y ), 'cross_product'(
% 2.81/3.18 'universal_class', 'universal_class' ) ) ] )
% 2.81/3.18 , clause( 27431, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 2.81/3.18 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 2.81/3.18 , clause( 27432, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 2.81/3.18 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 2.81/3.18 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 2.81/3.18 ) ] )
% 2.81/3.18 , clause( 27433, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 2.81/3.18 inverse( X ) ), 'identity_relation' ) ] )
% 2.81/3.18 , clause( 27434, [ ~( subclass( compose( X, inverse( X ) ),
% 2.81/3.18 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 2.81/3.18 , clause( 27435, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 2.81/3.18 'universal_class', 'universal_class' ) ) ] )
% 2.81/3.18 , clause( 27436, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 2.81/3.18 , 'identity_relation' ) ] )
% 2.81/3.18 , clause( 27437, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 2.81/3.18 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 2.81/3.18 'identity_relation' ) ), function( X ) ] )
% 2.81/3.18 , clause( 27438, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 2.81/3.18 , member( image( X, Y ), 'universal_class' ) ] )
% 2.81/3.18 , clause( 27439, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 2.81/3.18 , clause( 27440, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 2.81/3.18 , 'null_class' ) ] )
% 2.81/3.18 , clause( 27441, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 2.81/3.18 Y ) ) ] )
% 2.81/3.18 , clause( 27442, [ function( choice ) ] )
% 2.81/3.18 , clause( 27443, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 2.81/3.18 ), member( apply( choice, X ), X ) ] )
% 2.81/3.18 , clause( 27444, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 2.81/3.18 , clause( 27445, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 2.81/3.18 , clause( 27446, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 2.81/3.18 'one_to_one'( X ) ] )
% 2.81/3.18 , clause( 27447, [ =( intersection( 'cross_product'( 'universal_class',
% 2.81/3.18 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 2.81/3.18 'universal_class' ), complement( compose( complement( 'element_relation'
% 2.81/3.18 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 2.81/3.18 , clause( 27448, [ =( intersection( inverse( 'subset_relation' ),
% 2.81/3.18 'subset_relation' ), 'identity_relation' ) ] )
% 2.81/3.18 , clause( 27449, [ =( complement( 'domain_of'( intersection( X,
% 2.81/3.18 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 2.81/3.18 , clause( 27450, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 2.81/3.18 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 2.81/3.18 , clause( 27451, [ ~( operation( X ) ), function( X ) ] )
% 2.81/3.18 , clause( 27452, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 2.81/3.18 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.81/3.18 ] )
% 2.81/3.18 , clause( 27453, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 2.81/3.18 'domain_of'( 'domain_of'( X ) ) ) ] )
% 2.81/3.18 , clause( 27454, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 2.81/3.18 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.81/3.18 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 2.81/3.18 operation( X ) ] )
% 2.81/3.18 , clause( 27455, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 2.81/3.18 , clause( 27456, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 2.81/3.18 Y ) ), 'domain_of'( X ) ) ] )
% 2.81/3.18 , clause( 27457, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 2.81/3.18 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 2.81/3.18 , clause( 27458, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 2.81/3.18 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 2.81/3.18 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 2.81/3.18 , clause( 27459, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 2.81/3.18 , clause( 27460, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 2.81/3.18 , clause( 27461, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 2.81/3.18 , clause( 27462, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 2.81/3.18 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 2.81/3.18 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 2.81/3.18 )
% 2.81/3.18 , clause( 27463, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.81/3.18 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 2.81/3.18 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 2.81/3.18 , Y ) ] )
% 2.81/3.18 , clause( 27464, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.81/3.18 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 2.81/3.18 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 2.81/3.18 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 2.81/3.18 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 2.81/3.18 )
% 2.81/3.18 , clause( 27465, [ subclass( 'compose_class'( X ), 'cross_product'(
% 2.81/3.18 'universal_class', 'universal_class' ) ) ] )
% 2.81/3.18 , clause( 27466, [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z )
% 2.81/3.18 ) ), =( compose( Z, X ), Y ) ] )
% 2.81/3.18 , clause( 27467, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 2.81/3.18 'universal_class', 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) )
% 2.81/3.18 , member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ] )
% 2.81/3.18 , clause( 27468, [ subclass( 'composition_function', 'cross_product'(
% 2.81/3.18 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 2.81/3.18 ) ) ) ] )
% 2.81/3.18 , clause( 27469, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 2.81/3.18 'composition_function' ) ), =( compose( X, Y ), Z ) ] )
% 2.81/3.18 , clause( 27470, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 2.81/3.18 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( X,
% 2.81/3.18 'ordered_pair'( Y, compose( X, Y ) ) ), 'composition_function' ) ] )
% 2.81/3.18 , clause( 27471, [ subclass( 'domain_relation', 'cross_product'(
% 2.81/3.18 'universal_class', 'universal_class' ) ) ] )
% 2.81/3.18 , clause( 27472, [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) )
% 2.81/3.18 , =( 'domain_of'( X ), Y ) ] )
% 2.81/3.18 , clause( 27473, [ ~( member( X, 'universal_class' ) ), member(
% 2.81/3.18 'ordered_pair'( X, 'domain_of'( X ) ), 'domain_relation' ) ] )
% 2.81/3.18 , clause( 27474, [ =( first( 'not_subclass_element'( compose( X, inverse( X
% 2.81/3.18 ) ), 'identity_relation' ) ), 'single_valued1'( X ) ) ] )
% 2.81/3.18 , clause( 27475, [ =( second( 'not_subclass_element'( compose( X, inverse(
% 2.81/3.18 X ) ), 'identity_relation' ) ), 'single_valued2'( X ) ) ] )
% 2.81/3.18 , clause( 27476, [ =( domain( X, image( inverse( X ), singleton(
% 2.81/3.18 'single_valued1'( X ) ) ), 'single_valued2'( X ) ), 'single_valued3'( X )
% 2.81/3.18 ) ] )
% 2.81/3.18 , clause( 27477, [ =( intersection( complement( compose( 'element_relation'
% 2.81/3.18 , complement( 'identity_relation' ) ) ), 'element_relation' ),
% 2.81/3.18 'singleton_relation' ) ] )
% 2.81/3.18 , clause( 27478, [ subclass( 'application_function', 'cross_product'(
% 2.81/3.18 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 2.81/3.18 ) ) ) ] )
% 2.81/3.18 , clause( 27479, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 2.81/3.18 'application_function' ) ), member( Y, 'domain_of'( X ) ) ] )
% 2.81/3.18 , clause( 27480, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 2.81/3.18 'application_function' ) ), =( apply( X, Y ), Z ) ] )
% 2.81/3.18 , clause( 27481, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 2.81/3.18 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 2.81/3.18 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 2.81/3.18 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 2.81/3.18 'application_function' ) ] )
% 2.81/3.18 , clause( 27482, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 2.81/3.18 , clause( 27483, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 2.81/3.18 , clause( 27484, [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ]
% 2.81/3.18 )
% 2.81/3.18 , clause( 27485, [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) )
% 2.81/3.18 , maps( X, 'domain_of'( X ), Y ) ] )
% 2.81/3.18 , clause( 27486, [ =( union( X, inverse( X ) ), 'symmetrization_of'( X ) )
% 2.81/3.18 ] )
% 2.81/3.18 , clause( 27487, [ ~( irreflexive( X, Y ) ), subclass( restrict( X, Y, Y )
% 2.81/3.18 , complement( 'identity_relation' ) ) ] )
% 2.81/3.18 , clause( 27488, [ ~( subclass( restrict( X, Y, Y ), complement(
% 2.81/3.18 'identity_relation' ) ) ), irreflexive( X, Y ) ] )
% 2.81/3.18 , clause( 27489, [ ~( connected( X, Y ) ), subclass( 'cross_product'( Y, Y
% 2.81/3.18 ), union( 'identity_relation', 'symmetrization_of'( X ) ) ) ] )
% 2.81/3.18 , clause( 27490, [ ~( subclass( 'cross_product'( X, X ), union(
% 2.81/3.18 'identity_relation', 'symmetrization_of'( Y ) ) ) ), connected( Y, X ) ]
% 2.81/3.18 )
% 2.81/3.18 , clause( 27491, [ ~( transitive( X, Y ) ), subclass( compose( restrict( X
% 2.81/3.18 , Y, Y ), restrict( X, Y, Y ) ), restrict( X, Y, Y ) ) ] )
% 2.81/3.18 , clause( 27492, [ ~( subclass( compose( restrict( X, Y, Y ), restrict( X,
% 2.81/3.18 Y, Y ) ), restrict( X, Y, Y ) ) ), transitive( X, Y ) ] )
% 2.81/3.18 , clause( 27493, [ ~( asymmetric( X, Y ) ), =( restrict( intersection( X,
% 2.81/3.18 inverse( X ) ), Y, Y ), 'null_class' ) ] )
% 2.81/3.18 , clause( 27494, [ ~( =( restrict( intersection( X, inverse( X ) ), Y, Y )
% 2.81/3.18 , 'null_class' ) ), asymmetric( X, Y ) ] )
% 2.81/3.18 , clause( 27495, [ =( segment( X, Y, Z ), 'domain_of'( restrict( X, Y,
% 2.81/3.18 singleton( Z ) ) ) ) ] )
% 2.81/3.18 , clause( 27496, [ ~( 'well_ordering'( X, Y ) ), connected( X, Y ) ] )
% 2.81/3.18 , clause( 27497, [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), =(
% 2.81/3.18 Z, 'null_class' ), member( least( X, Z ), Z ) ] )
% 2.81/3.18 , clause( 27498, [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), ~(
% 2.81/3.18 member( T, Z ) ), member( least( X, Z ), Z ) ] )
% 2.81/3.18 , clause( 27499, [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), =(
% 2.81/3.18 segment( X, Z, least( X, Z ) ), 'null_class' ) ] )
% 2.81/3.18 , clause( 27500, [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), ~(
% 2.81/3.18 member( T, Z ) ), ~( member( 'ordered_pair'( T, least( X, Z ) ), X ) ) ]
% 2.81/3.18 )
% 2.81/3.18 , clause( 27501, [ ~( connected( X, Y ) ), ~( =( 'not_well_ordering'( X, Y
% 2.81/3.18 ), 'null_class' ) ), 'well_ordering'( X, Y ) ] )
% 2.81/3.18 , clause( 27502, [ ~( connected( X, Y ) ), subclass( 'not_well_ordering'( X
% 2.81/3.18 , Y ), Y ), 'well_ordering'( X, Y ) ] )
% 2.81/3.18 , clause( 27503, [ ~( member( X, 'not_well_ordering'( Y, Z ) ) ), ~( =(
% 2.81/3.18 segment( Y, 'not_well_ordering'( Y, Z ), X ), 'null_class' ) ), ~(
% 2.81/3.18 connected( Y, Z ) ), 'well_ordering'( Y, Z ) ] )
% 2.81/3.18 , clause( 27504, [ ~( section( X, Y, Z ) ), subclass( Y, Z ) ] )
% 2.81/3.18 , clause( 27505, [ ~( section( X, Y, Z ) ), subclass( 'domain_of'( restrict(
% 2.81/3.18 X, Z, Y ) ), Y ) ] )
% 2.81/3.18 , clause( 27506, [ ~( subclass( X, Y ) ), ~( subclass( 'domain_of'(
% 2.81/3.18 restrict( Z, Y, X ) ), X ) ), section( Z, X, Y ) ] )
% 2.81/3.18 , clause( 27507, [ ~( member( X, 'ordinal_numbers' ) ), 'well_ordering'(
% 2.81/3.18 'element_relation', X ) ] )
% 2.81/3.18 , clause( 27508, [ ~( member( X, 'ordinal_numbers' ) ), subclass(
% 2.81/3.18 'sum_class'( X ), X ) ] )
% 2.81/3.18 , clause( 27509, [ ~( 'well_ordering'( 'element_relation', X ) ), ~(
% 2.81/3.18 subclass( 'sum_class'( X ), X ) ), ~( member( X, 'universal_class' ) ),
% 2.81/3.18 member( X, 'ordinal_numbers' ) ] )
% 2.81/3.18 , clause( 27510, [ ~( 'well_ordering'( 'element_relation', X ) ), ~(
% 2.81/3.18 subclass( 'sum_class'( X ), X ) ), member( X, 'ordinal_numbers' ), =( X,
% 2.81/3.18 'ordinal_numbers' ) ] )
% 2.81/3.18 , clause( 27511, [ =( union( singleton( 'null_class' ), image(
% 2.81/3.18 'successor_relation', 'ordinal_numbers' ) ), 'kind_1_ordinals' ) ] )
% 2.81/3.18 , clause( 27512, [ =( intersection( complement( 'kind_1_ordinals' ),
% 2.81/3.18 'ordinal_numbers' ), 'limit_ordinals' ) ] )
% 2.81/3.18 , clause( 27513, [ subclass( 'rest_of'( X ), 'cross_product'(
% 2.81/3.18 'universal_class', 'universal_class' ) ) ] )
% 2.81/3.18 , clause( 27514, [ ~( member( 'ordered_pair'( X, Y ), 'rest_of'( Z ) ) ),
% 2.81/3.18 member( X, 'domain_of'( Z ) ) ] )
% 2.81/3.18 , clause( 27515, [ ~( member( 'ordered_pair'( X, Y ), 'rest_of'( Z ) ) ),
% 2.81/3.18 =( restrict( Z, X, 'universal_class' ), Y ) ] )
% 2.81/3.18 , clause( 27516, [ ~( member( X, 'domain_of'( Y ) ) ), ~( =( restrict( Y, X
% 2.81/3.18 , 'universal_class' ), Z ) ), member( 'ordered_pair'( X, Z ), 'rest_of'(
% 2.81/3.18 Y ) ) ] )
% 2.81/3.18 , clause( 27517, [ subclass( 'rest_relation', 'cross_product'(
% 2.81/3.18 'universal_class', 'universal_class' ) ) ] )
% 2.81/3.18 , clause( 27518, [ ~( member( 'ordered_pair'( X, Y ), 'rest_relation' ) ),
% 2.81/3.18 =( 'rest_of'( X ), Y ) ] )
% 2.81/3.18 , clause( 27519, [ ~( member( X, 'universal_class' ) ), member(
% 2.81/3.18 'ordered_pair'( X, 'rest_of'( X ) ), 'rest_relation' ) ] )
% 2.81/3.18 , clause( 27520, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ),
% 2.81/3.18 function( Y ) ] )
% 2.81/3.18 , clause( 27521, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ),
% 2.81/3.18 function( X ) ] )
% 2.81/3.18 , clause( 27522, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ),
% 2.81/3.18 member( 'domain_of'( X ), 'ordinal_numbers' ) ] )
% 2.81/3.18 , clause( 27523, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ),
% 2.81/3.18 =( compose( Y, 'rest_of'( X ) ), X ) ] )
% 2.81/3.18 , clause( 27524, [ ~( function( X ) ), ~( function( Y ) ), ~( member(
% 2.81/3.18 'domain_of'( Y ), 'ordinal_numbers' ) ), ~( =( compose( X, 'rest_of'( Y )
% 2.81/3.18 ), Y ) ), member( Y, 'recursion_equation_functions'( X ) ) ] )
% 2.81/3.18 , clause( 27525, [ subclass( 'union_of_range_map', 'cross_product'(
% 2.81/3.18 'universal_class', 'universal_class' ) ) ] )
% 2.81/3.18 , clause( 27526, [ ~( member( 'ordered_pair'( X, Y ), 'union_of_range_map'
% 2.81/3.18 ) ), =( 'sum_class'( 'range_of'( X ) ), Y ) ] )
% 2.81/3.18 , clause( 27527, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 2.81/3.18 'universal_class', 'universal_class' ) ) ), ~( =( 'sum_class'( 'range_of'(
% 2.81/3.18 X ) ), Y ) ), member( 'ordered_pair'( X, Y ), 'union_of_range_map' ) ] )
% 2.81/3.18 , clause( 27528, [ =( apply( recursion( X, 'successor_relation',
% 2.81/3.18 'union_of_range_map' ), Y ), 'ordinal_add'( X, Y ) ) ] )
% 2.81/3.18 , clause( 27529, [ =( recursion( 'null_class', apply( 'add_relation', X ),
% 2.81/3.18 'union_of_range_map' ), 'ordinal_multiply'( X, Y ) ) ] )
% 2.81/3.18 , clause( 27530, [ ~( member( X, omega ) ), =( 'integer_of'( X ), X ) ] )
% 2.81/3.18 , clause( 27531, [ member( X, omega ), =( 'integer_of'( X ), 'null_class' )
% 2.81/3.18 ] )
% 2.81/3.18 , clause( 27532, [ ~( subclass( 'limit_ordinals', 'ordinal_numbers' ) ) ]
% 2.81/3.18 )
% 2.81/3.18 ] ).
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 subsumption(
% 2.81/3.18 clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y )
% 2.81/3.18 ] )
% 2.81/3.18 , clause( 27375, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 2.81/3.18 , Y ) ] )
% 2.81/3.18 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.81/3.18 ), ==>( 1, 1 )] ) ).
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 subsumption(
% 2.81/3.18 clause( 2, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X
% 2.81/3.18 , Y ) ] )
% 2.81/3.18 , clause( 27376, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 2.81/3.18 subclass( X, Y ) ] )
% 2.81/3.18 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.81/3.18 ), ==>( 1, 1 )] ) ).
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 subsumption(
% 2.81/3.18 clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 2.81/3.18 , clause( 27395, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 2.81/3.18 )
% 2.81/3.18 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.81/3.18 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 subsumption(
% 2.81/3.18 clause( 137, [ =( intersection( complement( 'kind_1_ordinals' ),
% 2.81/3.18 'ordinal_numbers' ), 'limit_ordinals' ) ] )
% 2.81/3.18 , clause( 27512, [ =( intersection( complement( 'kind_1_ordinals' ),
% 2.81/3.18 'ordinal_numbers' ), 'limit_ordinals' ) ] )
% 2.81/3.18 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 subsumption(
% 2.81/3.18 clause( 157, [ ~( subclass( 'limit_ordinals', 'ordinal_numbers' ) ) ] )
% 2.81/3.18 , clause( 27532, [ ~( subclass( 'limit_ordinals', 'ordinal_numbers' ) ) ]
% 2.81/3.18 )
% 2.81/3.18 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 resolution(
% 2.81/3.18 clause( 27700, [ member( 'not_subclass_element'( 'limit_ordinals',
% 2.81/3.18 'ordinal_numbers' ), 'limit_ordinals' ) ] )
% 2.81/3.18 , clause( 157, [ ~( subclass( 'limit_ordinals', 'ordinal_numbers' ) ) ] )
% 2.81/3.18 , 0, clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 2.81/3.18 , Y ) ] )
% 2.81/3.18 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'limit_ordinals' ),
% 2.81/3.18 :=( Y, 'ordinal_numbers' )] )).
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 subsumption(
% 2.81/3.18 clause( 180, [ member( 'not_subclass_element'( 'limit_ordinals',
% 2.81/3.18 'ordinal_numbers' ), 'limit_ordinals' ) ] )
% 2.81/3.18 , clause( 27700, [ member( 'not_subclass_element'( 'limit_ordinals',
% 2.81/3.18 'ordinal_numbers' ), 'limit_ordinals' ) ] )
% 2.81/3.18 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 resolution(
% 2.81/3.18 clause( 27701, [ ~( member( 'not_subclass_element'( 'limit_ordinals',
% 2.81/3.18 'ordinal_numbers' ), 'ordinal_numbers' ) ) ] )
% 2.81/3.18 , clause( 157, [ ~( subclass( 'limit_ordinals', 'ordinal_numbers' ) ) ] )
% 2.81/3.18 , 0, clause( 2, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 2.81/3.18 subclass( X, Y ) ] )
% 2.81/3.18 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'limit_ordinals' ),
% 2.81/3.18 :=( Y, 'ordinal_numbers' )] )).
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 subsumption(
% 2.81/3.18 clause( 188, [ ~( member( 'not_subclass_element'( 'limit_ordinals',
% 2.81/3.18 'ordinal_numbers' ), 'ordinal_numbers' ) ) ] )
% 2.81/3.18 , clause( 27701, [ ~( member( 'not_subclass_element'( 'limit_ordinals',
% 2.81/3.18 'ordinal_numbers' ), 'ordinal_numbers' ) ) ] )
% 2.81/3.18 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 paramod(
% 2.81/3.18 clause( 27703, [ ~( member( X, 'limit_ordinals' ) ), member( X,
% 2.81/3.18 'ordinal_numbers' ) ] )
% 2.81/3.18 , clause( 137, [ =( intersection( complement( 'kind_1_ordinals' ),
% 2.81/3.18 'ordinal_numbers' ), 'limit_ordinals' ) ] )
% 2.81/3.18 , 0, clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 2.81/3.18 )
% 2.81/3.18 , 0, 3, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y,
% 2.81/3.18 complement( 'kind_1_ordinals' ) ), :=( Z, 'ordinal_numbers' )] )).
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 subsumption(
% 2.81/3.18 clause( 21454, [ ~( member( X, 'limit_ordinals' ) ), member( X,
% 2.81/3.18 'ordinal_numbers' ) ] )
% 2.81/3.18 , clause( 27703, [ ~( member( X, 'limit_ordinals' ) ), member( X,
% 2.81/3.18 'ordinal_numbers' ) ] )
% 2.81/3.18 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 2.81/3.18 1 )] ) ).
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 resolution(
% 2.81/3.18 clause( 27704, [ ~( member( 'not_subclass_element'( 'limit_ordinals',
% 2.81/3.18 'ordinal_numbers' ), 'limit_ordinals' ) ) ] )
% 2.81/3.18 , clause( 188, [ ~( member( 'not_subclass_element'( 'limit_ordinals',
% 2.81/3.18 'ordinal_numbers' ), 'ordinal_numbers' ) ) ] )
% 2.81/3.18 , 0, clause( 21454, [ ~( member( X, 'limit_ordinals' ) ), member( X,
% 2.81/3.18 'ordinal_numbers' ) ] )
% 2.81/3.18 , 1, substitution( 0, [] ), substitution( 1, [ :=( X,
% 2.81/3.18 'not_subclass_element'( 'limit_ordinals', 'ordinal_numbers' ) )] )).
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 resolution(
% 2.81/3.18 clause( 27705, [] )
% 2.81/3.18 , clause( 27704, [ ~( member( 'not_subclass_element'( 'limit_ordinals',
% 2.81/3.18 'ordinal_numbers' ), 'limit_ordinals' ) ) ] )
% 2.81/3.18 , 0, clause( 180, [ member( 'not_subclass_element'( 'limit_ordinals',
% 2.81/3.18 'ordinal_numbers' ), 'limit_ordinals' ) ] )
% 2.81/3.18 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 subsumption(
% 2.81/3.18 clause( 27372, [] )
% 2.81/3.18 , clause( 27705, [] )
% 2.81/3.18 , substitution( 0, [] ), permutation( 0, [] ) ).
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 end.
% 2.81/3.18
% 2.81/3.18 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.81/3.18
% 2.81/3.18 Memory use:
% 2.81/3.18
% 2.81/3.18 space for terms: 447836
% 2.81/3.18 space for clauses: 1307398
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 clauses generated: 56663
% 2.81/3.18 clauses kept: 27373
% 2.81/3.18 clauses selected: 633
% 2.81/3.18 clauses deleted: 2545
% 2.81/3.18 clauses inuse deleted: 68
% 2.81/3.18
% 2.81/3.18 subsentry: 175601
% 2.81/3.18 literals s-matched: 127955
% 2.81/3.18 literals matched: 125573
% 2.81/3.18 full subsumption: 55031
% 2.81/3.18
% 2.81/3.18 checksum: -515944319
% 2.81/3.18
% 2.81/3.18
% 2.81/3.18 Bliksem ended
%------------------------------------------------------------------------------