TSTP Solution File: NUM139-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM139-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 06:20:05 EDT 2022
% Result : Unsatisfiable 2.55s 3.01s
% Output : Refutation 2.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM139-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Thu Jul 7 07:04:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.13 *** allocated 10000 integers for termspace/termends
% 0.43/1.13 *** allocated 10000 integers for clauses
% 0.43/1.13 *** allocated 10000 integers for justifications
% 0.43/1.13 Bliksem 1.12
% 0.43/1.13
% 0.43/1.13
% 0.43/1.13 Automatic Strategy Selection
% 0.43/1.13
% 0.43/1.13 Clauses:
% 0.43/1.13 [
% 0.43/1.13 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.43/1.13 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.43/1.13 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.43/1.13 ,
% 0.43/1.13 [ subclass( X, 'universal_class' ) ],
% 0.43/1.13 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.43/1.13 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.43/1.13 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.43/1.13 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.43/1.13 ,
% 0.43/1.13 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.43/1.13 ) ) ],
% 0.43/1.13 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.43/1.13 ) ) ],
% 0.43/1.13 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.43/1.13 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.43/1.13 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.43/1.13 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.13 X, Z ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.13 Y, T ) ],
% 0.43/1.13 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.43/1.13 ), 'cross_product'( Y, T ) ) ],
% 0.43/1.13 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.43/1.13 ), second( X ) ), X ) ],
% 0.43/1.13 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.43/1.13 'universal_class' ) ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.43/1.13 Y ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.43/1.13 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.43/1.13 , Y ), 'element_relation' ) ],
% 0.43/1.13 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.43/1.13 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.43/1.13 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.43/1.13 Z ) ) ],
% 0.43/1.13 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.43/1.13 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.43/1.13 member( X, Y ) ],
% 0.43/1.13 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.43/1.13 union( X, Y ) ) ],
% 0.43/1.13 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.43/1.13 intersection( complement( X ), complement( Y ) ) ) ),
% 0.43/1.13 'symmetric_difference'( X, Y ) ) ],
% 0.43/1.13 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.43/1.13 ,
% 0.43/1.13 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.43/1.13 ,
% 0.43/1.13 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.43/1.13 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.43/1.13 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.43/1.13 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.43/1.13 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.43/1.13 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.43/1.13 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.43/1.13 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.43/1.13 'cross_product'( 'universal_class', 'universal_class' ),
% 0.43/1.13 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.43/1.13 Y ), rotate( T ) ) ],
% 0.43/1.13 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.43/1.13 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.43/1.13 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.43/1.13 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.43/1.13 'cross_product'( 'universal_class', 'universal_class' ),
% 0.43/1.13 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.43/1.13 Z ), flip( T ) ) ],
% 0.43/1.13 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.43/1.13 inverse( X ) ) ],
% 0.43/1.13 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.43/1.13 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.43/1.13 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.43/1.13 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.43/1.13 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.43/1.13 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.43/1.13 ],
% 0.43/1.13 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.43/1.13 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.43/1.13 'universal_class' ) ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.43/1.13 successor( X ), Y ) ],
% 0.43/1.13 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.43/1.13 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.43/1.13 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.43/1.13 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.43/1.13 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.43/1.13 ,
% 0.43/1.13 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.43/1.13 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.43/1.13 [ inductive( omega ) ],
% 0.43/1.13 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.43/1.13 [ member( omega, 'universal_class' ) ],
% 0.43/1.13 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.43/1.13 , 'sum_class'( X ) ) ],
% 0.43/1.13 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.43/1.13 'universal_class' ) ],
% 0.43/1.13 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.43/1.13 'power_class'( X ) ) ],
% 0.43/1.13 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.43/1.13 'universal_class' ) ],
% 0.43/1.13 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.43/1.13 'universal_class' ) ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.43/1.13 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.43/1.13 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.43/1.13 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.43/1.13 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.43/1.13 ) ],
% 0.43/1.13 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.43/1.13 , 'identity_relation' ) ],
% 0.43/1.13 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.43/1.13 'single_valued_class'( X ) ],
% 0.43/1.13 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.43/1.13 'universal_class' ) ) ],
% 0.43/1.13 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.43/1.13 'identity_relation' ) ],
% 0.43/1.13 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.43/1.13 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.43/1.13 , function( X ) ],
% 0.43/1.13 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.43/1.13 X, Y ), 'universal_class' ) ],
% 0.43/1.13 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.43/1.13 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.43/1.13 ) ],
% 0.43/1.13 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.43/1.13 [ function( choice ) ],
% 0.43/1.13 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.43/1.13 apply( choice, X ), X ) ],
% 0.43/1.13 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.43/1.13 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.43/1.13 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.43/1.13 ,
% 0.43/1.13 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.43/1.13 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.43/1.13 , complement( compose( complement( 'element_relation' ), inverse(
% 0.43/1.13 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.43/1.13 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.43/1.13 'identity_relation' ) ],
% 0.43/1.13 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.43/1.13 , diagonalise( X ) ) ],
% 0.43/1.13 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.43/1.13 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.43/1.13 [ ~( operation( X ) ), function( X ) ],
% 0.43/1.13 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.43/1.13 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.43/1.13 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.43/1.13 'domain_of'( X ) ) ) ],
% 0.43/1.13 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.43/1.13 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.43/1.13 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.43/1.13 X ) ],
% 0.43/1.13 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.43/1.13 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.43/1.13 'domain_of'( X ) ) ],
% 0.43/1.13 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.43/1.13 'domain_of'( Z ) ) ) ],
% 0.43/1.13 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.43/1.13 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.43/1.13 ), compatible( X, Y, Z ) ],
% 0.43/1.13 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.43/1.13 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.43/1.13 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.43/1.13 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.43/1.13 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.43/1.13 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.43/1.13 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.43/1.13 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.43/1.13 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.43/1.13 , Y ) ],
% 0.43/1.13 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.43/1.13 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.43/1.13 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.43/1.13 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.43/1.13 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.43/1.13 [ subclass( 'compose_class'( X ), 'cross_product'( 'universal_class',
% 0.43/1.13 'universal_class' ) ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ), =(
% 0.43/1.13 compose( Z, X ), Y ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.43/1.13 , 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) ), member(
% 0.43/1.13 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ],
% 0.43/1.13 [ subclass( 'composition_function', 'cross_product'( 'universal_class',
% 0.43/1.13 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.43/1.13 'composition_function' ) ), =( compose( X, Y ), Z ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.43/1.13 , 'universal_class' ) ) ), member( 'ordered_pair'( X, 'ordered_pair'( Y,
% 0.43/1.13 compose( X, Y ) ) ), 'composition_function' ) ],
% 0.43/1.13 [ subclass( 'domain_relation', 'cross_product'( 'universal_class',
% 0.43/1.13 'universal_class' ) ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) ), =(
% 0.43/1.13 'domain_of'( X ), Y ) ],
% 0.43/1.13 [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X,
% 0.43/1.13 'domain_of'( X ) ), 'domain_relation' ) ],
% 0.43/1.13 [ =( first( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.43/1.13 'identity_relation' ) ), 'single_valued1'( X ) ) ],
% 0.43/1.13 [ =( second( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.43/1.13 'identity_relation' ) ), 'single_valued2'( X ) ) ],
% 0.43/1.13 [ =( domain( X, image( inverse( X ), singleton( 'single_valued1'( X ) )
% 0.43/1.13 ), 'single_valued2'( X ) ), 'single_valued3'( X ) ) ],
% 0.43/1.13 [ =( intersection( complement( compose( 'element_relation', complement(
% 0.43/1.13 'identity_relation' ) ) ), 'element_relation' ), 'singleton_relation' ) ]
% 0.43/1.13 ,
% 0.43/1.13 [ subclass( 'application_function', 'cross_product'( 'universal_class',
% 0.43/1.13 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.43/1.13 'application_function' ) ), member( Y, 'domain_of'( X ) ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.43/1.13 'application_function' ) ), =( apply( X, Y ), Z ) ],
% 0.43/1.13 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.43/1.13 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 0.43/1.13 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 0.43/1.13 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 0.43/1.13 'application_function' ) ],
% 0.43/1.13 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.43/1.13 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 0.77/1.13 [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ],
% 0.77/1.13 [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ), maps( X,
% 0.77/1.13 'domain_of'( X ), Y ) ],
% 0.77/1.13 [ =( union( X, inverse( X ) ), 'symmetrization_of'( X ) ) ],
% 0.77/1.13 [ ~( irreflexive( X, Y ) ), subclass( restrict( X, Y, Y ), complement(
% 0.77/1.13 'identity_relation' ) ) ],
% 0.77/1.13 [ ~( subclass( restrict( X, Y, Y ), complement( 'identity_relation' ) )
% 0.77/1.13 ), irreflexive( X, Y ) ],
% 0.77/1.13 [ ~( connected( X, Y ) ), subclass( 'cross_product'( Y, Y ), union(
% 0.77/1.13 'identity_relation', 'symmetrization_of'( X ) ) ) ],
% 0.77/1.13 [ ~( subclass( 'cross_product'( X, X ), union( 'identity_relation',
% 0.77/1.13 'symmetrization_of'( Y ) ) ) ), connected( Y, X ) ],
% 0.77/1.13 [ ~( transitive( X, Y ) ), subclass( compose( restrict( X, Y, Y ),
% 0.77/1.13 restrict( X, Y, Y ) ), restrict( X, Y, Y ) ) ],
% 0.77/1.13 [ ~( subclass( compose( restrict( X, Y, Y ), restrict( X, Y, Y ) ),
% 0.77/1.13 restrict( X, Y, Y ) ) ), transitive( X, Y ) ],
% 0.77/1.13 [ ~( asymmetric( X, Y ) ), =( restrict( intersection( X, inverse( X ) )
% 0.77/1.13 , Y, Y ), 'null_class' ) ],
% 0.77/1.13 [ ~( =( restrict( intersection( X, inverse( X ) ), Y, Y ), 'null_class'
% 0.77/1.13 ) ), asymmetric( X, Y ) ],
% 0.77/1.13 [ =( segment( X, Y, Z ), 'domain_of'( restrict( X, Y, singleton( Z ) ) )
% 0.77/1.13 ) ],
% 0.77/1.13 [ ~( 'well_ordering'( X, Y ) ), connected( X, Y ) ],
% 0.77/1.13 [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), =( Z,
% 0.77/1.13 'null_class' ), member( least( X, Z ), Z ) ],
% 0.77/1.13 [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), ~( member( T, Z )
% 0.77/1.13 ), member( least( X, Z ), Z ) ],
% 0.77/1.13 [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), =( segment( X, Z
% 0.77/1.13 , least( X, Z ) ), 'null_class' ) ],
% 0.77/1.13 [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), ~( member( T, Z )
% 0.77/1.13 ), ~( member( 'ordered_pair'( T, least( X, Z ) ), X ) ) ],
% 0.77/1.13 [ ~( connected( X, Y ) ), ~( =( 'not_well_ordering'( X, Y ),
% 0.77/1.13 'null_class' ) ), 'well_ordering'( X, Y ) ],
% 0.77/1.13 [ ~( connected( X, Y ) ), subclass( 'not_well_ordering'( X, Y ), Y ),
% 0.77/1.13 'well_ordering'( X, Y ) ],
% 0.77/1.13 [ ~( member( X, 'not_well_ordering'( Y, Z ) ) ), ~( =( segment( Y,
% 0.77/1.13 'not_well_ordering'( Y, Z ), X ), 'null_class' ) ), ~( connected( Y, Z )
% 0.77/1.13 ), 'well_ordering'( Y, Z ) ],
% 0.77/1.13 [ ~( section( X, Y, Z ) ), subclass( Y, Z ) ],
% 0.77/1.13 [ ~( section( X, Y, Z ) ), subclass( 'domain_of'( restrict( X, Z, Y ) )
% 0.77/1.13 , Y ) ],
% 0.77/1.13 [ ~( subclass( X, Y ) ), ~( subclass( 'domain_of'( restrict( Z, Y, X ) )
% 0.77/1.13 , X ) ), section( Z, X, Y ) ],
% 0.77/1.13 [ ~( member( X, 'ordinal_numbers' ) ), 'well_ordering'(
% 0.77/1.13 'element_relation', X ) ],
% 0.77/1.13 [ ~( member( X, 'ordinal_numbers' ) ), subclass( 'sum_class'( X ), X ) ]
% 0.77/1.13 ,
% 0.77/1.13 [ ~( 'well_ordering'( 'element_relation', X ) ), ~( subclass(
% 0.77/1.13 'sum_class'( X ), X ) ), ~( member( X, 'universal_class' ) ), member( X,
% 0.77/1.13 'ordinal_numbers' ) ],
% 0.77/1.13 [ ~( 'well_ordering'( 'element_relation', X ) ), ~( subclass(
% 0.77/1.13 'sum_class'( X ), X ) ), member( X, 'ordinal_numbers' ), =( X,
% 0.77/1.13 'ordinal_numbers' ) ],
% 0.77/1.13 [ =( union( singleton( 'null_class' ), image( 'successor_relation',
% 0.77/1.13 'ordinal_numbers' ) ), 'kind_1_ordinals' ) ],
% 0.77/1.13 [ =( intersection( complement( 'kind_1_ordinals' ), 'ordinal_numbers' )
% 0.77/1.13 , 'limit_ordinals' ) ],
% 0.77/1.13 [ subclass( 'rest_of'( X ), 'cross_product'( 'universal_class',
% 0.77/1.13 'universal_class' ) ) ],
% 0.77/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'rest_of'( Z ) ) ), member( X,
% 0.77/1.13 'domain_of'( Z ) ) ],
% 0.77/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'rest_of'( Z ) ) ), =( restrict( Z
% 0.77/1.13 , X, 'universal_class' ), Y ) ],
% 0.77/1.13 [ ~( member( X, 'domain_of'( Y ) ) ), ~( =( restrict( Y, X,
% 0.77/1.13 'universal_class' ), Z ) ), member( 'ordered_pair'( X, Z ), 'rest_of'( Y
% 0.77/1.13 ) ) ],
% 0.77/1.13 [ subclass( 'rest_relation', 'cross_product'( 'universal_class',
% 0.77/1.13 'universal_class' ) ) ],
% 0.77/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'rest_relation' ) ), =( 'rest_of'(
% 0.77/1.13 X ), Y ) ],
% 0.77/1.13 [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X,
% 0.77/1.13 'rest_of'( X ) ), 'rest_relation' ) ],
% 0.77/1.13 [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), function( Y ) ]
% 0.77/1.13 ,
% 0.77/1.13 [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), function( X ) ]
% 0.77/1.13 ,
% 0.77/1.13 [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), member(
% 1.32/1.69 'domain_of'( X ), 'ordinal_numbers' ) ],
% 1.32/1.69 [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), =( compose( Y,
% 1.32/1.69 'rest_of'( X ) ), X ) ],
% 1.32/1.69 [ ~( function( X ) ), ~( function( Y ) ), ~( member( 'domain_of'( Y ),
% 1.32/1.69 'ordinal_numbers' ) ), ~( =( compose( X, 'rest_of'( Y ) ), Y ) ), member(
% 1.32/1.69 Y, 'recursion_equation_functions'( X ) ) ],
% 1.32/1.69 [ subclass( 'union_of_range_map', 'cross_product'( 'universal_class',
% 1.32/1.69 'universal_class' ) ) ],
% 1.32/1.69 [ ~( member( 'ordered_pair'( X, Y ), 'union_of_range_map' ) ), =(
% 1.32/1.69 'sum_class'( 'range_of'( X ) ), Y ) ],
% 1.32/1.69 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 1.32/1.69 , 'universal_class' ) ) ), ~( =( 'sum_class'( 'range_of'( X ) ), Y ) ),
% 1.32/1.69 member( 'ordered_pair'( X, Y ), 'union_of_range_map' ) ],
% 1.32/1.69 [ =( apply( recursion( X, 'successor_relation', 'union_of_range_map' ),
% 1.32/1.69 Y ), 'ordinal_add'( X, Y ) ) ],
% 1.32/1.69 [ =( recursion( 'null_class', apply( 'add_relation', X ),
% 1.32/1.69 'union_of_range_map' ), 'ordinal_multiply'( X, Y ) ) ],
% 1.32/1.69 [ ~( member( X, omega ) ), =( 'integer_of'( X ), X ) ],
% 1.32/1.69 [ member( X, omega ), =( 'integer_of'( X ), 'null_class' ) ],
% 1.32/1.69 [ ~( member( 'not_subclass_element'( intersection( 'power_class'( x ), z
% 1.32/1.69 ), x ), z ) ) ],
% 1.32/1.69 [ ~( subclass( intersection( 'power_class'( x ), z ), x ) ) ]
% 1.32/1.69 ] .
% 1.32/1.69
% 1.32/1.69
% 1.32/1.69 percentage equality = 0.219136, percentage horn = 0.925000
% 1.32/1.69 This is a problem with some equality
% 1.32/1.69
% 1.32/1.69
% 1.32/1.69
% 1.32/1.69 Options Used:
% 1.32/1.69
% 1.32/1.69 useres = 1
% 1.32/1.69 useparamod = 1
% 1.32/1.69 useeqrefl = 1
% 1.32/1.69 useeqfact = 1
% 1.32/1.69 usefactor = 1
% 1.32/1.69 usesimpsplitting = 0
% 1.32/1.69 usesimpdemod = 5
% 1.32/1.69 usesimpres = 3
% 1.32/1.69
% 1.32/1.69 resimpinuse = 1000
% 1.32/1.69 resimpclauses = 20000
% 1.32/1.69 substype = eqrewr
% 1.32/1.69 backwardsubs = 1
% 1.32/1.69 selectoldest = 5
% 1.32/1.69
% 1.32/1.69 litorderings [0] = split
% 1.32/1.69 litorderings [1] = extend the termordering, first sorting on arguments
% 1.32/1.69
% 1.32/1.69 termordering = kbo
% 1.32/1.69
% 1.32/1.69 litapriori = 0
% 1.32/1.69 termapriori = 1
% 1.32/1.69 litaposteriori = 0
% 1.32/1.69 termaposteriori = 0
% 1.32/1.69 demodaposteriori = 0
% 1.32/1.69 ordereqreflfact = 0
% 1.32/1.69
% 1.32/1.69 litselect = negord
% 1.32/1.69
% 1.32/1.69 maxweight = 15
% 1.32/1.69 maxdepth = 30000
% 1.32/1.69 maxlength = 115
% 1.32/1.69 maxnrvars = 195
% 1.32/1.69 excuselevel = 1
% 1.32/1.69 increasemaxweight = 1
% 1.32/1.69
% 1.32/1.69 maxselected = 10000000
% 1.32/1.69 maxnrclauses = 10000000
% 1.32/1.69
% 1.32/1.69 showgenerated = 0
% 1.32/1.69 showkept = 0
% 1.32/1.69 showselected = 0
% 1.32/1.69 showdeleted = 0
% 1.32/1.69 showresimp = 1
% 1.32/1.69 showstatus = 2000
% 1.32/1.69
% 1.32/1.69 prologoutput = 1
% 1.32/1.69 nrgoals = 5000000
% 1.32/1.69 totalproof = 1
% 1.32/1.69
% 1.32/1.69 Symbols occurring in the translation:
% 1.32/1.69
% 1.32/1.69 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.32/1.69 . [1, 2] (w:1, o:74, a:1, s:1, b:0),
% 1.32/1.69 ! [4, 1] (w:0, o:41, a:1, s:1, b:0),
% 1.32/1.69 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.32/1.69 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.32/1.69 subclass [41, 2] (w:1, o:99, a:1, s:1, b:0),
% 1.32/1.69 member [43, 2] (w:1, o:101, a:1, s:1, b:0),
% 1.32/1.69 'not_subclass_element' [44, 2] (w:1, o:102, a:1, s:1, b:0),
% 1.32/1.69 'universal_class' [45, 0] (w:1, o:24, a:1, s:1, b:0),
% 1.32/1.69 'unordered_pair' [46, 2] (w:1, o:104, a:1, s:1, b:0),
% 1.32/1.69 singleton [47, 1] (w:1, o:51, a:1, s:1, b:0),
% 1.32/1.69 'ordered_pair' [48, 2] (w:1, o:106, a:1, s:1, b:0),
% 1.32/1.69 'cross_product' [50, 2] (w:1, o:107, a:1, s:1, b:0),
% 1.32/1.69 first [52, 1] (w:1, o:52, a:1, s:1, b:0),
% 1.32/1.69 second [53, 1] (w:1, o:53, a:1, s:1, b:0),
% 1.32/1.69 'element_relation' [54, 0] (w:1, o:29, a:1, s:1, b:0),
% 1.32/1.69 intersection [55, 2] (w:1, o:109, a:1, s:1, b:0),
% 1.32/1.69 complement [56, 1] (w:1, o:54, a:1, s:1, b:0),
% 1.32/1.69 union [57, 2] (w:1, o:110, a:1, s:1, b:0),
% 1.32/1.69 'symmetric_difference' [58, 2] (w:1, o:111, a:1, s:1, b:0),
% 1.32/1.69 restrict [60, 3] (w:1, o:120, a:1, s:1, b:0),
% 1.32/1.69 'null_class' [61, 0] (w:1, o:30, a:1, s:1, b:0),
% 1.32/1.69 'domain_of' [62, 1] (w:1, o:57, a:1, s:1, b:0),
% 1.32/1.69 rotate [63, 1] (w:1, o:46, a:1, s:1, b:0),
% 1.32/1.69 flip [65, 1] (w:1, o:58, a:1, s:1, b:0),
% 1.32/1.69 inverse [66, 1] (w:1, o:59, a:1, s:1, b:0),
% 1.32/1.69 'range_of' [67, 1] (w:1, o:47, a:1, s:1, b:0),
% 1.32/1.69 domain [68, 3] (w:1, o:122, a:1, s:1, b:0),
% 1.32/1.69 range [69, 3] (w:1, o:123, a:1, s:1, b:0),
% 1.32/1.69 image [70, 2] (w:1, o:108, a:1, s:1, b:0),
% 1.32/1.69 successor [71, 1] (w:1, o:60, a:1, s:1, b:0),
% 1.32/1.69 'successor_relation' [72, 0] (w:1, o:7, a:1, s:1, b:0),
% 2.55/3.01 inductive [73, 1] (w:1, o:61, a:1, s:1, b:0),
% 2.55/3.01 omega [74, 0] (w:1, o:11, a:1, s:1, b:0),
% 2.55/3.01 'sum_class' [75, 1] (w:1, o:62, a:1, s:1, b:0),
% 2.55/3.01 'power_class' [76, 1] (w:1, o:65, a:1, s:1, b:0),
% 2.55/3.01 compose [78, 2] (w:1, o:112, a:1, s:1, b:0),
% 2.55/3.01 'single_valued_class' [79, 1] (w:1, o:66, a:1, s:1, b:0),
% 2.55/3.01 'identity_relation' [80, 0] (w:1, o:31, a:1, s:1, b:0),
% 2.55/3.01 function [82, 1] (w:1, o:67, a:1, s:1, b:0),
% 2.55/3.01 regular [83, 1] (w:1, o:48, a:1, s:1, b:0),
% 2.55/3.01 apply [84, 2] (w:1, o:113, a:1, s:1, b:0),
% 2.55/3.01 choice [85, 0] (w:1, o:32, a:1, s:1, b:0),
% 2.55/3.01 'one_to_one' [86, 1] (w:1, o:63, a:1, s:1, b:0),
% 2.55/3.01 'subset_relation' [87, 0] (w:1, o:6, a:1, s:1, b:0),
% 2.55/3.01 diagonalise [88, 1] (w:1, o:68, a:1, s:1, b:0),
% 2.55/3.01 cantor [89, 1] (w:1, o:55, a:1, s:1, b:0),
% 2.55/3.01 operation [90, 1] (w:1, o:64, a:1, s:1, b:0),
% 2.55/3.01 compatible [94, 3] (w:1, o:121, a:1, s:1, b:0),
% 2.55/3.01 homomorphism [95, 3] (w:1, o:124, a:1, s:1, b:0),
% 2.55/3.01 'not_homomorphism1' [96, 3] (w:1, o:126, a:1, s:1, b:0),
% 2.55/3.01 'not_homomorphism2' [97, 3] (w:1, o:127, a:1, s:1, b:0),
% 2.55/3.01 'compose_class' [98, 1] (w:1, o:56, a:1, s:1, b:0),
% 2.55/3.01 'composition_function' [99, 0] (w:1, o:33, a:1, s:1, b:0),
% 2.55/3.01 'domain_relation' [100, 0] (w:1, o:28, a:1, s:1, b:0),
% 2.55/3.01 'single_valued1' [101, 1] (w:1, o:69, a:1, s:1, b:0),
% 2.55/3.01 'single_valued2' [102, 1] (w:1, o:70, a:1, s:1, b:0),
% 2.55/3.01 'single_valued3' [103, 1] (w:1, o:71, a:1, s:1, b:0),
% 2.55/3.01 'singleton_relation' [104, 0] (w:1, o:8, a:1, s:1, b:0),
% 2.55/3.01 'application_function' [105, 0] (w:1, o:34, a:1, s:1, b:0),
% 2.55/3.01 maps [106, 3] (w:1, o:125, a:1, s:1, b:0),
% 2.55/3.01 'symmetrization_of' [107, 1] (w:1, o:72, a:1, s:1, b:0),
% 2.55/3.01 irreflexive [108, 2] (w:1, o:114, a:1, s:1, b:0),
% 2.55/3.01 connected [109, 2] (w:1, o:115, a:1, s:1, b:0),
% 2.55/3.01 transitive [110, 2] (w:1, o:103, a:1, s:1, b:0),
% 2.55/3.01 asymmetric [111, 2] (w:1, o:116, a:1, s:1, b:0),
% 2.55/3.01 segment [112, 3] (w:1, o:129, a:1, s:1, b:0),
% 2.55/3.01 'well_ordering' [113, 2] (w:1, o:117, a:1, s:1, b:0),
% 2.55/3.01 least [114, 2] (w:1, o:100, a:1, s:1, b:0),
% 2.55/3.01 'not_well_ordering' [115, 2] (w:1, o:105, a:1, s:1, b:0),
% 2.55/3.01 section [116, 3] (w:1, o:130, a:1, s:1, b:0),
% 2.55/3.01 'ordinal_numbers' [117, 0] (w:1, o:12, a:1, s:1, b:0),
% 2.55/3.01 'kind_1_ordinals' [118, 0] (w:1, o:35, a:1, s:1, b:0),
% 2.55/3.01 'limit_ordinals' [119, 0] (w:1, o:36, a:1, s:1, b:0),
% 2.55/3.01 'rest_of' [120, 1] (w:1, o:49, a:1, s:1, b:0),
% 2.55/3.01 'rest_relation' [121, 0] (w:1, o:5, a:1, s:1, b:0),
% 2.55/3.01 'recursion_equation_functions' [122, 1] (w:1, o:50, a:1, s:1, b:0),
% 2.55/3.01 'union_of_range_map' [123, 0] (w:1, o:37, a:1, s:1, b:0),
% 2.55/3.01 recursion [124, 3] (w:1, o:128, a:1, s:1, b:0),
% 2.55/3.01 'ordinal_add' [125, 2] (w:1, o:118, a:1, s:1, b:0),
% 2.55/3.01 'add_relation' [126, 0] (w:1, o:38, a:1, s:1, b:0),
% 2.55/3.01 'ordinal_multiply' [127, 2] (w:1, o:119, a:1, s:1, b:0),
% 2.55/3.01 'integer_of' [128, 1] (w:1, o:73, a:1, s:1, b:0),
% 2.55/3.01 x [129, 0] (w:1, o:39, a:1, s:1, b:0),
% 2.55/3.01 z [130, 0] (w:1, o:40, a:1, s:1, b:0).
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 Starting Search:
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 Intermediate Status:
% 2.55/3.01 Generated: 5321
% 2.55/3.01 Kept: 2006
% 2.55/3.01 Inuse: 110
% 2.55/3.01 Deleted: 8
% 2.55/3.01 Deletedinuse: 2
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 Intermediate Status:
% 2.55/3.01 Generated: 9915
% 2.55/3.01 Kept: 4013
% 2.55/3.01 Inuse: 188
% 2.55/3.01 Deleted: 31
% 2.55/3.01 Deletedinuse: 18
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 Intermediate Status:
% 2.55/3.01 Generated: 13892
% 2.55/3.01 Kept: 6033
% 2.55/3.01 Inuse: 247
% 2.55/3.01 Deleted: 37
% 2.55/3.01 Deletedinuse: 20
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 Intermediate Status:
% 2.55/3.01 Generated: 18866
% 2.55/3.01 Kept: 8062
% 2.55/3.01 Inuse: 294
% 2.55/3.01 Deleted: 72
% 2.55/3.01 Deletedinuse: 45
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 Intermediate Status:
% 2.55/3.01 Generated: 23564
% 2.55/3.01 Kept: 10146
% 2.55/3.01 Inuse: 354
% 2.55/3.01 Deleted: 96
% 2.55/3.01 Deletedinuse: 69
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 Intermediate Status:
% 2.55/3.01 Generated: 27124
% 2.55/3.01 Kept: 12173
% 2.55/3.01 Inuse: 384
% 2.55/3.01 Deleted: 101
% 2.55/3.01 Deletedinuse: 74
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 Intermediate Status:
% 2.55/3.01 Generated: 31112
% 2.55/3.01 Kept: 14198
% 2.55/3.01 Inuse: 421
% 2.55/3.01 Deleted: 102
% 2.55/3.01 Deletedinuse: 75
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 Intermediate Status:
% 2.55/3.01 Generated: 34520
% 2.55/3.01 Kept: 16206
% 2.55/3.01 Inuse: 451
% 2.55/3.01 Deleted: 102
% 2.55/3.01 Deletedinuse: 75
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 Intermediate Status:
% 2.55/3.01 Generated: 39756
% 2.55/3.01 Kept: 18212
% 2.55/3.01 Inuse: 500
% 2.55/3.01 Deleted: 104
% 2.55/3.01 Deletedinuse: 76
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01 Resimplifying clauses:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 Intermediate Status:
% 2.55/3.01 Generated: 45172
% 2.55/3.01 Kept: 20228
% 2.55/3.01 Inuse: 544
% 2.55/3.01 Deleted: 2650
% 2.55/3.01 Deletedinuse: 80
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 Intermediate Status:
% 2.55/3.01 Generated: 49881
% 2.55/3.01 Kept: 22527
% 2.55/3.01 Inuse: 573
% 2.55/3.01 Deleted: 2653
% 2.55/3.01 Deletedinuse: 83
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 Intermediate Status:
% 2.55/3.01 Generated: 53928
% 2.55/3.01 Kept: 24533
% 2.55/3.01 Inuse: 601
% 2.55/3.01 Deleted: 2653
% 2.55/3.01 Deletedinuse: 83
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 Intermediate Status:
% 2.55/3.01 Generated: 57386
% 2.55/3.01 Kept: 26578
% 2.55/3.01 Inuse: 617
% 2.55/3.01 Deleted: 2655
% 2.55/3.01 Deletedinuse: 85
% 2.55/3.01
% 2.55/3.01 Resimplifying inuse:
% 2.55/3.01 Done
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 Bliksems!, er is een bewijs:
% 2.55/3.01 % SZS status Unsatisfiable
% 2.55/3.01 % SZS output start Refutation
% 2.55/3.01
% 2.55/3.01 clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y )
% 2.55/3.01 ] )
% 2.55/3.01 .
% 2.55/3.01 clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 2.55/3.01 .
% 2.55/3.01 clause( 157, [ ~( member( 'not_subclass_element'( intersection(
% 2.55/3.01 'power_class'( x ), z ), x ), z ) ) ] )
% 2.55/3.01 .
% 2.55/3.01 clause( 158, [ ~( subclass( intersection( 'power_class'( x ), z ), x ) ) ]
% 2.55/3.01 )
% 2.55/3.01 .
% 2.55/3.01 clause( 27500, [ ~( member( 'not_subclass_element'( intersection(
% 2.55/3.01 'power_class'( x ), z ), x ), intersection( X, z ) ) ) ] )
% 2.55/3.01 .
% 2.55/3.01 clause( 27755, [] )
% 2.55/3.01 .
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 % SZS output end Refutation
% 2.55/3.01 found a proof!
% 2.55/3.01
% 2.55/3.01 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.55/3.01
% 2.55/3.01 initialclauses(
% 2.55/3.01 [ clause( 27757, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 2.55/3.01 ) ] )
% 2.55/3.01 , clause( 27758, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 2.55/3.01 , Y ) ] )
% 2.55/3.01 , clause( 27759, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 2.55/3.01 subclass( X, Y ) ] )
% 2.55/3.01 , clause( 27760, [ subclass( X, 'universal_class' ) ] )
% 2.55/3.01 , clause( 27761, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.55/3.01 , clause( 27762, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 2.55/3.01 , clause( 27763, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 2.55/3.01 ] )
% 2.55/3.01 , clause( 27764, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 2.55/3.01 =( X, Z ) ] )
% 2.55/3.01 , clause( 27765, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.55/3.01 'unordered_pair'( X, Y ) ) ] )
% 2.55/3.01 , clause( 27766, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.55/3.01 'unordered_pair'( Y, X ) ) ] )
% 2.55/3.01 , clause( 27767, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 2.55/3.01 )
% 2.55/3.01 , clause( 27768, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.55/3.01 , clause( 27769, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 2.55/3.01 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 2.55/3.01 , clause( 27770, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.55/3.01 ) ) ), member( X, Z ) ] )
% 2.55/3.01 , clause( 27771, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.55/3.01 ) ) ), member( Y, T ) ] )
% 2.55/3.01 , clause( 27772, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 2.55/3.01 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 2.55/3.01 , clause( 27773, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 2.55/3.01 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 2.55/3.01 , clause( 27774, [ subclass( 'element_relation', 'cross_product'(
% 2.55/3.01 'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01 , clause( 27775, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 2.55/3.01 ), member( X, Y ) ] )
% 2.55/3.01 , clause( 27776, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 2.55/3.01 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 2.55/3.01 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 2.55/3.01 , clause( 27777, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 2.55/3.01 )
% 2.55/3.01 , clause( 27778, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 2.55/3.01 )
% 2.55/3.01 , clause( 27779, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 2.55/3.01 intersection( Y, Z ) ) ] )
% 2.55/3.01 , clause( 27780, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 2.55/3.01 )
% 2.55/3.01 , clause( 27781, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.55/3.01 complement( Y ) ), member( X, Y ) ] )
% 2.55/3.01 , clause( 27782, [ =( complement( intersection( complement( X ), complement(
% 2.55/3.01 Y ) ) ), union( X, Y ) ) ] )
% 2.55/3.01 , clause( 27783, [ =( intersection( complement( intersection( X, Y ) ),
% 2.55/3.01 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 2.55/3.01 'symmetric_difference'( X, Y ) ) ] )
% 2.55/3.01 , clause( 27784, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 2.55/3.01 X, Y, Z ) ) ] )
% 2.55/3.01 , clause( 27785, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 2.55/3.01 Z, X, Y ) ) ] )
% 2.55/3.01 , clause( 27786, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 2.55/3.01 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 2.55/3.01 , clause( 27787, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 2.55/3.01 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 2.55/3.01 'domain_of'( Y ) ) ] )
% 2.55/3.01 , clause( 27788, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 2.55/3.01 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.55/3.01 , clause( 27789, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.55/3.01 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 2.55/3.01 ] )
% 2.55/3.01 , clause( 27790, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.55/3.01 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 2.55/3.01 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.55/3.01 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 2.55/3.01 , Y ), rotate( T ) ) ] )
% 2.55/3.01 , clause( 27791, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 2.55/3.01 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.55/3.01 , clause( 27792, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.55/3.01 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 2.55/3.01 )
% 2.55/3.01 , clause( 27793, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.55/3.01 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 2.55/3.01 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.55/3.01 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 2.55/3.01 , Z ), flip( T ) ) ] )
% 2.55/3.01 , clause( 27794, [ =( 'domain_of'( flip( 'cross_product'( X,
% 2.55/3.01 'universal_class' ) ) ), inverse( X ) ) ] )
% 2.55/3.01 , clause( 27795, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 2.55/3.01 , clause( 27796, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 2.55/3.01 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 2.55/3.01 , clause( 27797, [ =( second( 'not_subclass_element'( restrict( X,
% 2.55/3.01 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 2.55/3.01 , clause( 27798, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 2.55/3.01 image( X, Y ) ) ] )
% 2.55/3.01 , clause( 27799, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 2.55/3.01 , clause( 27800, [ subclass( 'successor_relation', 'cross_product'(
% 2.55/3.01 'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01 , clause( 27801, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 2.55/3.01 ) ), =( successor( X ), Y ) ] )
% 2.55/3.01 , clause( 27802, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 2.55/3.01 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 2.55/3.01 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 2.55/3.01 , clause( 27803, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 2.55/3.01 , clause( 27804, [ ~( inductive( X ) ), subclass( image(
% 2.55/3.01 'successor_relation', X ), X ) ] )
% 2.55/3.01 , clause( 27805, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 2.55/3.01 'successor_relation', X ), X ) ), inductive( X ) ] )
% 2.55/3.01 , clause( 27806, [ inductive( omega ) ] )
% 2.55/3.01 , clause( 27807, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 2.55/3.01 , clause( 27808, [ member( omega, 'universal_class' ) ] )
% 2.55/3.01 , clause( 27809, [ =( 'domain_of'( restrict( 'element_relation',
% 2.55/3.01 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 2.55/3.01 , clause( 27810, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 2.55/3.01 X ), 'universal_class' ) ] )
% 2.55/3.01 , clause( 27811, [ =( complement( image( 'element_relation', complement( X
% 2.55/3.01 ) ) ), 'power_class'( X ) ) ] )
% 2.55/3.01 , clause( 27812, [ ~( member( X, 'universal_class' ) ), member(
% 2.55/3.01 'power_class'( X ), 'universal_class' ) ] )
% 2.55/3.01 , clause( 27813, [ subclass( compose( X, Y ), 'cross_product'(
% 2.55/3.01 'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01 , clause( 27814, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 2.55/3.01 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 2.55/3.01 , clause( 27815, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 2.55/3.01 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 2.55/3.01 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 2.55/3.01 ) ] )
% 2.55/3.01 , clause( 27816, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 2.55/3.01 inverse( X ) ), 'identity_relation' ) ] )
% 2.55/3.01 , clause( 27817, [ ~( subclass( compose( X, inverse( X ) ),
% 2.55/3.01 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 2.55/3.01 , clause( 27818, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 2.55/3.01 'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01 , clause( 27819, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 2.55/3.01 , 'identity_relation' ) ] )
% 2.55/3.01 , clause( 27820, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 2.55/3.01 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 2.55/3.01 'identity_relation' ) ), function( X ) ] )
% 2.55/3.01 , clause( 27821, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 2.55/3.01 , member( image( X, Y ), 'universal_class' ) ] )
% 2.55/3.01 , clause( 27822, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 2.55/3.01 , clause( 27823, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 2.55/3.01 , 'null_class' ) ] )
% 2.55/3.01 , clause( 27824, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 2.55/3.01 Y ) ) ] )
% 2.55/3.01 , clause( 27825, [ function( choice ) ] )
% 2.55/3.01 , clause( 27826, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 2.55/3.01 ), member( apply( choice, X ), X ) ] )
% 2.55/3.01 , clause( 27827, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 2.55/3.01 , clause( 27828, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 2.55/3.01 , clause( 27829, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 2.55/3.01 'one_to_one'( X ) ] )
% 2.55/3.01 , clause( 27830, [ =( intersection( 'cross_product'( 'universal_class',
% 2.55/3.01 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 2.55/3.01 'universal_class' ), complement( compose( complement( 'element_relation'
% 2.55/3.01 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 2.55/3.01 , clause( 27831, [ =( intersection( inverse( 'subset_relation' ),
% 2.55/3.01 'subset_relation' ), 'identity_relation' ) ] )
% 2.55/3.01 , clause( 27832, [ =( complement( 'domain_of'( intersection( X,
% 2.55/3.01 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 2.55/3.01 , clause( 27833, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 2.55/3.01 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 2.55/3.01 , clause( 27834, [ ~( operation( X ) ), function( X ) ] )
% 2.55/3.01 , clause( 27835, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 2.55/3.01 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.55/3.01 ] )
% 2.55/3.01 , clause( 27836, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 2.55/3.01 'domain_of'( 'domain_of'( X ) ) ) ] )
% 2.55/3.01 , clause( 27837, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 2.55/3.01 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.55/3.01 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 2.55/3.01 operation( X ) ] )
% 2.55/3.01 , clause( 27838, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 2.55/3.01 , clause( 27839, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 2.55/3.01 Y ) ), 'domain_of'( X ) ) ] )
% 2.55/3.01 , clause( 27840, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 2.55/3.01 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 2.55/3.01 , clause( 27841, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 2.55/3.01 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 2.55/3.01 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 2.55/3.01 , clause( 27842, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 2.55/3.01 , clause( 27843, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 2.55/3.01 , clause( 27844, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 2.55/3.01 , clause( 27845, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 2.55/3.01 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 2.55/3.01 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 2.55/3.01 )
% 2.55/3.01 , clause( 27846, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.55/3.01 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 2.55/3.01 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 2.55/3.01 , Y ) ] )
% 2.55/3.01 , clause( 27847, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.55/3.01 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 2.55/3.01 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 2.55/3.01 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 2.55/3.01 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 2.55/3.01 )
% 2.55/3.01 , clause( 27848, [ subclass( 'compose_class'( X ), 'cross_product'(
% 2.55/3.01 'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01 , clause( 27849, [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z )
% 2.55/3.01 ) ), =( compose( Z, X ), Y ) ] )
% 2.55/3.01 , clause( 27850, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 2.55/3.01 'universal_class', 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) )
% 2.55/3.01 , member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ] )
% 2.55/3.01 , clause( 27851, [ subclass( 'composition_function', 'cross_product'(
% 2.55/3.01 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 2.55/3.01 ) ) ) ] )
% 2.55/3.01 , clause( 27852, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 2.55/3.01 'composition_function' ) ), =( compose( X, Y ), Z ) ] )
% 2.55/3.01 , clause( 27853, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 2.55/3.01 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( X,
% 2.55/3.01 'ordered_pair'( Y, compose( X, Y ) ) ), 'composition_function' ) ] )
% 2.55/3.01 , clause( 27854, [ subclass( 'domain_relation', 'cross_product'(
% 2.55/3.01 'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01 , clause( 27855, [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) )
% 2.55/3.01 , =( 'domain_of'( X ), Y ) ] )
% 2.55/3.01 , clause( 27856, [ ~( member( X, 'universal_class' ) ), member(
% 2.55/3.01 'ordered_pair'( X, 'domain_of'( X ) ), 'domain_relation' ) ] )
% 2.55/3.01 , clause( 27857, [ =( first( 'not_subclass_element'( compose( X, inverse( X
% 2.55/3.01 ) ), 'identity_relation' ) ), 'single_valued1'( X ) ) ] )
% 2.55/3.01 , clause( 27858, [ =( second( 'not_subclass_element'( compose( X, inverse(
% 2.55/3.01 X ) ), 'identity_relation' ) ), 'single_valued2'( X ) ) ] )
% 2.55/3.01 , clause( 27859, [ =( domain( X, image( inverse( X ), singleton(
% 2.55/3.01 'single_valued1'( X ) ) ), 'single_valued2'( X ) ), 'single_valued3'( X )
% 2.55/3.01 ) ] )
% 2.55/3.01 , clause( 27860, [ =( intersection( complement( compose( 'element_relation'
% 2.55/3.01 , complement( 'identity_relation' ) ) ), 'element_relation' ),
% 2.55/3.01 'singleton_relation' ) ] )
% 2.55/3.01 , clause( 27861, [ subclass( 'application_function', 'cross_product'(
% 2.55/3.01 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 2.55/3.01 ) ) ) ] )
% 2.55/3.01 , clause( 27862, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 2.55/3.01 'application_function' ) ), member( Y, 'domain_of'( X ) ) ] )
% 2.55/3.01 , clause( 27863, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 2.55/3.01 'application_function' ) ), =( apply( X, Y ), Z ) ] )
% 2.55/3.01 , clause( 27864, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 2.55/3.01 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 2.55/3.01 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 2.55/3.01 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 2.55/3.01 'application_function' ) ] )
% 2.55/3.01 , clause( 27865, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 2.55/3.01 , clause( 27866, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 2.55/3.01 , clause( 27867, [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ]
% 2.55/3.01 )
% 2.55/3.01 , clause( 27868, [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) )
% 2.55/3.01 , maps( X, 'domain_of'( X ), Y ) ] )
% 2.55/3.01 , clause( 27869, [ =( union( X, inverse( X ) ), 'symmetrization_of'( X ) )
% 2.55/3.01 ] )
% 2.55/3.01 , clause( 27870, [ ~( irreflexive( X, Y ) ), subclass( restrict( X, Y, Y )
% 2.55/3.01 , complement( 'identity_relation' ) ) ] )
% 2.55/3.01 , clause( 27871, [ ~( subclass( restrict( X, Y, Y ), complement(
% 2.55/3.01 'identity_relation' ) ) ), irreflexive( X, Y ) ] )
% 2.55/3.01 , clause( 27872, [ ~( connected( X, Y ) ), subclass( 'cross_product'( Y, Y
% 2.55/3.01 ), union( 'identity_relation', 'symmetrization_of'( X ) ) ) ] )
% 2.55/3.01 , clause( 27873, [ ~( subclass( 'cross_product'( X, X ), union(
% 2.55/3.01 'identity_relation', 'symmetrization_of'( Y ) ) ) ), connected( Y, X ) ]
% 2.55/3.01 )
% 2.55/3.01 , clause( 27874, [ ~( transitive( X, Y ) ), subclass( compose( restrict( X
% 2.55/3.01 , Y, Y ), restrict( X, Y, Y ) ), restrict( X, Y, Y ) ) ] )
% 2.55/3.01 , clause( 27875, [ ~( subclass( compose( restrict( X, Y, Y ), restrict( X,
% 2.55/3.01 Y, Y ) ), restrict( X, Y, Y ) ) ), transitive( X, Y ) ] )
% 2.55/3.01 , clause( 27876, [ ~( asymmetric( X, Y ) ), =( restrict( intersection( X,
% 2.55/3.01 inverse( X ) ), Y, Y ), 'null_class' ) ] )
% 2.55/3.01 , clause( 27877, [ ~( =( restrict( intersection( X, inverse( X ) ), Y, Y )
% 2.55/3.01 , 'null_class' ) ), asymmetric( X, Y ) ] )
% 2.55/3.01 , clause( 27878, [ =( segment( X, Y, Z ), 'domain_of'( restrict( X, Y,
% 2.55/3.01 singleton( Z ) ) ) ) ] )
% 2.55/3.01 , clause( 27879, [ ~( 'well_ordering'( X, Y ) ), connected( X, Y ) ] )
% 2.55/3.01 , clause( 27880, [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), =(
% 2.55/3.01 Z, 'null_class' ), member( least( X, Z ), Z ) ] )
% 2.55/3.01 , clause( 27881, [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), ~(
% 2.55/3.01 member( T, Z ) ), member( least( X, Z ), Z ) ] )
% 2.55/3.01 , clause( 27882, [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), =(
% 2.55/3.01 segment( X, Z, least( X, Z ) ), 'null_class' ) ] )
% 2.55/3.01 , clause( 27883, [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), ~(
% 2.55/3.01 member( T, Z ) ), ~( member( 'ordered_pair'( T, least( X, Z ) ), X ) ) ]
% 2.55/3.01 )
% 2.55/3.01 , clause( 27884, [ ~( connected( X, Y ) ), ~( =( 'not_well_ordering'( X, Y
% 2.55/3.01 ), 'null_class' ) ), 'well_ordering'( X, Y ) ] )
% 2.55/3.01 , clause( 27885, [ ~( connected( X, Y ) ), subclass( 'not_well_ordering'( X
% 2.55/3.01 , Y ), Y ), 'well_ordering'( X, Y ) ] )
% 2.55/3.01 , clause( 27886, [ ~( member( X, 'not_well_ordering'( Y, Z ) ) ), ~( =(
% 2.55/3.01 segment( Y, 'not_well_ordering'( Y, Z ), X ), 'null_class' ) ), ~(
% 2.55/3.01 connected( Y, Z ) ), 'well_ordering'( Y, Z ) ] )
% 2.55/3.01 , clause( 27887, [ ~( section( X, Y, Z ) ), subclass( Y, Z ) ] )
% 2.55/3.01 , clause( 27888, [ ~( section( X, Y, Z ) ), subclass( 'domain_of'( restrict(
% 2.55/3.01 X, Z, Y ) ), Y ) ] )
% 2.55/3.01 , clause( 27889, [ ~( subclass( X, Y ) ), ~( subclass( 'domain_of'(
% 2.55/3.01 restrict( Z, Y, X ) ), X ) ), section( Z, X, Y ) ] )
% 2.55/3.01 , clause( 27890, [ ~( member( X, 'ordinal_numbers' ) ), 'well_ordering'(
% 2.55/3.01 'element_relation', X ) ] )
% 2.55/3.01 , clause( 27891, [ ~( member( X, 'ordinal_numbers' ) ), subclass(
% 2.55/3.01 'sum_class'( X ), X ) ] )
% 2.55/3.01 , clause( 27892, [ ~( 'well_ordering'( 'element_relation', X ) ), ~(
% 2.55/3.01 subclass( 'sum_class'( X ), X ) ), ~( member( X, 'universal_class' ) ),
% 2.55/3.01 member( X, 'ordinal_numbers' ) ] )
% 2.55/3.01 , clause( 27893, [ ~( 'well_ordering'( 'element_relation', X ) ), ~(
% 2.55/3.01 subclass( 'sum_class'( X ), X ) ), member( X, 'ordinal_numbers' ), =( X,
% 2.55/3.01 'ordinal_numbers' ) ] )
% 2.55/3.01 , clause( 27894, [ =( union( singleton( 'null_class' ), image(
% 2.55/3.01 'successor_relation', 'ordinal_numbers' ) ), 'kind_1_ordinals' ) ] )
% 2.55/3.01 , clause( 27895, [ =( intersection( complement( 'kind_1_ordinals' ),
% 2.55/3.01 'ordinal_numbers' ), 'limit_ordinals' ) ] )
% 2.55/3.01 , clause( 27896, [ subclass( 'rest_of'( X ), 'cross_product'(
% 2.55/3.01 'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01 , clause( 27897, [ ~( member( 'ordered_pair'( X, Y ), 'rest_of'( Z ) ) ),
% 2.55/3.01 member( X, 'domain_of'( Z ) ) ] )
% 2.55/3.01 , clause( 27898, [ ~( member( 'ordered_pair'( X, Y ), 'rest_of'( Z ) ) ),
% 2.55/3.01 =( restrict( Z, X, 'universal_class' ), Y ) ] )
% 2.55/3.01 , clause( 27899, [ ~( member( X, 'domain_of'( Y ) ) ), ~( =( restrict( Y, X
% 2.55/3.01 , 'universal_class' ), Z ) ), member( 'ordered_pair'( X, Z ), 'rest_of'(
% 2.55/3.01 Y ) ) ] )
% 2.55/3.01 , clause( 27900, [ subclass( 'rest_relation', 'cross_product'(
% 2.55/3.01 'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01 , clause( 27901, [ ~( member( 'ordered_pair'( X, Y ), 'rest_relation' ) ),
% 2.55/3.01 =( 'rest_of'( X ), Y ) ] )
% 2.55/3.01 , clause( 27902, [ ~( member( X, 'universal_class' ) ), member(
% 2.55/3.01 'ordered_pair'( X, 'rest_of'( X ) ), 'rest_relation' ) ] )
% 2.55/3.01 , clause( 27903, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ),
% 2.55/3.01 function( Y ) ] )
% 2.55/3.01 , clause( 27904, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ),
% 2.55/3.01 function( X ) ] )
% 2.55/3.01 , clause( 27905, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ),
% 2.55/3.01 member( 'domain_of'( X ), 'ordinal_numbers' ) ] )
% 2.55/3.01 , clause( 27906, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ),
% 2.55/3.01 =( compose( Y, 'rest_of'( X ) ), X ) ] )
% 2.55/3.01 , clause( 27907, [ ~( function( X ) ), ~( function( Y ) ), ~( member(
% 2.55/3.01 'domain_of'( Y ), 'ordinal_numbers' ) ), ~( =( compose( X, 'rest_of'( Y )
% 2.55/3.01 ), Y ) ), member( Y, 'recursion_equation_functions'( X ) ) ] )
% 2.55/3.01 , clause( 27908, [ subclass( 'union_of_range_map', 'cross_product'(
% 2.55/3.01 'universal_class', 'universal_class' ) ) ] )
% 2.55/3.01 , clause( 27909, [ ~( member( 'ordered_pair'( X, Y ), 'union_of_range_map'
% 2.55/3.01 ) ), =( 'sum_class'( 'range_of'( X ) ), Y ) ] )
% 2.55/3.01 , clause( 27910, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 2.55/3.01 'universal_class', 'universal_class' ) ) ), ~( =( 'sum_class'( 'range_of'(
% 2.55/3.01 X ) ), Y ) ), member( 'ordered_pair'( X, Y ), 'union_of_range_map' ) ] )
% 2.55/3.01 , clause( 27911, [ =( apply( recursion( X, 'successor_relation',
% 2.55/3.01 'union_of_range_map' ), Y ), 'ordinal_add'( X, Y ) ) ] )
% 2.55/3.01 , clause( 27912, [ =( recursion( 'null_class', apply( 'add_relation', X ),
% 2.55/3.01 'union_of_range_map' ), 'ordinal_multiply'( X, Y ) ) ] )
% 2.55/3.01 , clause( 27913, [ ~( member( X, omega ) ), =( 'integer_of'( X ), X ) ] )
% 2.55/3.01 , clause( 27914, [ member( X, omega ), =( 'integer_of'( X ), 'null_class' )
% 2.55/3.01 ] )
% 2.55/3.01 , clause( 27915, [ ~( member( 'not_subclass_element'( intersection(
% 2.55/3.01 'power_class'( x ), z ), x ), z ) ) ] )
% 2.55/3.01 , clause( 27916, [ ~( subclass( intersection( 'power_class'( x ), z ), x )
% 2.55/3.01 ) ] )
% 2.55/3.01 ] ).
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 subsumption(
% 2.55/3.01 clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y )
% 2.55/3.01 ] )
% 2.55/3.01 , clause( 27758, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 2.55/3.01 , Y ) ] )
% 2.55/3.01 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.55/3.01 ), ==>( 1, 1 )] ) ).
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 subsumption(
% 2.55/3.01 clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 2.55/3.01 , clause( 27778, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 2.55/3.01 )
% 2.55/3.01 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.55/3.01 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 subsumption(
% 2.55/3.01 clause( 157, [ ~( member( 'not_subclass_element'( intersection(
% 2.55/3.01 'power_class'( x ), z ), x ), z ) ) ] )
% 2.55/3.01 , clause( 27915, [ ~( member( 'not_subclass_element'( intersection(
% 2.55/3.01 'power_class'( x ), z ), x ), z ) ) ] )
% 2.55/3.01 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 subsumption(
% 2.55/3.01 clause( 158, [ ~( subclass( intersection( 'power_class'( x ), z ), x ) ) ]
% 2.55/3.01 )
% 2.55/3.01 , clause( 27916, [ ~( subclass( intersection( 'power_class'( x ), z ), x )
% 2.55/3.01 ) ] )
% 2.55/3.01 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 resolution(
% 2.55/3.01 clause( 28097, [ ~( member( 'not_subclass_element'( intersection(
% 2.55/3.01 'power_class'( x ), z ), x ), intersection( X, z ) ) ) ] )
% 2.55/3.01 , clause( 157, [ ~( member( 'not_subclass_element'( intersection(
% 2.55/3.01 'power_class'( x ), z ), x ), z ) ) ] )
% 2.55/3.01 , 0, clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 2.55/3.01 )
% 2.55/3.01 , 1, substitution( 0, [] ), substitution( 1, [ :=( X,
% 2.55/3.01 'not_subclass_element'( intersection( 'power_class'( x ), z ), x ) ),
% 2.55/3.01 :=( Y, X ), :=( Z, z )] )).
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 subsumption(
% 2.55/3.01 clause( 27500, [ ~( member( 'not_subclass_element'( intersection(
% 2.55/3.01 'power_class'( x ), z ), x ), intersection( X, z ) ) ) ] )
% 2.55/3.01 , clause( 28097, [ ~( member( 'not_subclass_element'( intersection(
% 2.55/3.01 'power_class'( x ), z ), x ), intersection( X, z ) ) ) ] )
% 2.55/3.01 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 resolution(
% 2.55/3.01 clause( 28098, [ member( 'not_subclass_element'( intersection(
% 2.55/3.01 'power_class'( x ), z ), x ), intersection( 'power_class'( x ), z ) ) ]
% 2.55/3.01 )
% 2.55/3.01 , clause( 158, [ ~( subclass( intersection( 'power_class'( x ), z ), x ) )
% 2.55/3.01 ] )
% 2.55/3.01 , 0, clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 2.55/3.01 , Y ) ] )
% 2.55/3.01 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, intersection(
% 2.55/3.01 'power_class'( x ), z ) ), :=( Y, x )] )).
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 resolution(
% 2.55/3.01 clause( 28099, [] )
% 2.55/3.01 , clause( 27500, [ ~( member( 'not_subclass_element'( intersection(
% 2.55/3.01 'power_class'( x ), z ), x ), intersection( X, z ) ) ) ] )
% 2.55/3.01 , 0, clause( 28098, [ member( 'not_subclass_element'( intersection(
% 2.55/3.01 'power_class'( x ), z ), x ), intersection( 'power_class'( x ), z ) ) ]
% 2.55/3.01 )
% 2.55/3.01 , 0, substitution( 0, [ :=( X, 'power_class'( x ) )] ), substitution( 1, [] )
% 2.55/3.01 ).
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 subsumption(
% 2.55/3.01 clause( 27755, [] )
% 2.55/3.01 , clause( 28099, [] )
% 2.55/3.01 , substitution( 0, [] ), permutation( 0, [] ) ).
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 end.
% 2.55/3.01
% 2.55/3.01 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.55/3.01
% 2.55/3.01 Memory use:
% 2.55/3.01
% 2.55/3.01 space for terms: 455418
% 2.55/3.01 space for clauses: 1316275
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 clauses generated: 59980
% 2.55/3.01 clauses kept: 27756
% 2.55/3.01 clauses selected: 642
% 2.55/3.01 clauses deleted: 2656
% 2.55/3.01 clauses inuse deleted: 85
% 2.55/3.01
% 2.55/3.01 subsentry: 197658
% 2.55/3.01 literals s-matched: 141935
% 2.55/3.01 literals matched: 139559
% 2.55/3.01 full subsumption: 61464
% 2.55/3.01
% 2.55/3.01 checksum: 2119345189
% 2.55/3.01
% 2.55/3.01
% 2.55/3.01 Bliksem ended
%------------------------------------------------------------------------------