%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM228-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n015.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 06:20:38 EDT 2022
% Result : Unsatisfiable 1.04s 1.42s
% Output : Refutation 1.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM228-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Thu Jul 7 07:41:49 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.45/1.12 *** allocated 10000 integers for termspace/termends
% 0.45/1.12 *** allocated 10000 integers for clauses
% 0.45/1.12 *** allocated 10000 integers for justifications
% 0.45/1.12 Bliksem 1.12
% 0.45/1.12
% 0.45/1.12
% 0.45/1.12 Automatic Strategy Selection
% 0.45/1.12
% 0.45/1.12 Clauses:
% 0.45/1.12 [
% 0.45/1.12 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.45/1.12 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.45/1.12 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.45/1.12 ,
% 0.45/1.12 [ subclass( X, 'universal_class' ) ],
% 0.45/1.12 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.45/1.12 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.45/1.12 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.45/1.12 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.45/1.12 ,
% 0.45/1.12 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.45/1.12 ) ) ],
% 0.45/1.12 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.45/1.12 ) ) ],
% 0.45/1.12 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.45/1.12 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.45/1.12 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.45/1.12 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.45/1.12 X, Z ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.45/1.12 Y, T ) ],
% 0.45/1.12 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.45/1.12 ), 'cross_product'( Y, T ) ) ],
% 0.45/1.12 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.45/1.12 ), second( X ) ), X ) ],
% 0.45/1.12 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.45/1.12 'universal_class' ) ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.45/1.12 Y ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.45/1.12 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.45/1.12 , Y ), 'element_relation' ) ],
% 0.45/1.12 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.45/1.12 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.45/1.12 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.45/1.12 Z ) ) ],
% 0.45/1.12 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.45/1.12 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.45/1.12 member( X, Y ) ],
% 0.45/1.12 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.45/1.12 union( X, Y ) ) ],
% 0.45/1.12 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.45/1.12 intersection( complement( X ), complement( Y ) ) ) ),
% 0.45/1.12 'symmetric_difference'( X, Y ) ) ],
% 0.45/1.12 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.45/1.12 ,
% 0.45/1.12 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.45/1.12 ,
% 0.45/1.12 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.45/1.12 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.45/1.12 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.45/1.12 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.45/1.12 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.45/1.12 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.45/1.12 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.45/1.12 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.45/1.12 'cross_product'( 'universal_class', 'universal_class' ),
% 0.45/1.12 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.45/1.12 Y ), rotate( T ) ) ],
% 0.45/1.12 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.45/1.12 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.45/1.12 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.45/1.12 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.45/1.12 'cross_product'( 'universal_class', 'universal_class' ),
% 0.45/1.12 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.45/1.12 Z ), flip( T ) ) ],
% 0.45/1.12 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.45/1.12 inverse( X ) ) ],
% 0.45/1.12 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.45/1.12 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.45/1.12 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.45/1.12 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.45/1.12 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.45/1.12 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.45/1.12 ],
% 0.45/1.12 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.45/1.12 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.45/1.12 'universal_class' ) ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.45/1.12 successor( X ), Y ) ],
% 0.45/1.12 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.45/1.12 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.45/1.12 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.45/1.12 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.45/1.12 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.45/1.12 ,
% 0.45/1.12 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.45/1.12 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.45/1.12 [ inductive( omega ) ],
% 0.45/1.12 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.45/1.12 [ member( omega, 'universal_class' ) ],
% 0.45/1.12 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.45/1.12 , 'sum_class'( X ) ) ],
% 0.45/1.12 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.45/1.12 'universal_class' ) ],
% 0.45/1.12 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.45/1.12 'power_class'( X ) ) ],
% 0.45/1.12 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.45/1.12 'universal_class' ) ],
% 0.45/1.12 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.45/1.12 'universal_class' ) ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.45/1.12 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.45/1.12 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.45/1.12 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.45/1.12 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.45/1.12 ) ],
% 0.45/1.12 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.45/1.12 , 'identity_relation' ) ],
% 0.45/1.12 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.45/1.12 'single_valued_class'( X ) ],
% 0.45/1.12 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.45/1.12 'universal_class' ) ) ],
% 0.45/1.12 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.45/1.12 'identity_relation' ) ],
% 0.45/1.12 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.45/1.12 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.45/1.12 , function( X ) ],
% 0.45/1.12 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.45/1.12 X, Y ), 'universal_class' ) ],
% 0.45/1.12 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.45/1.12 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.45/1.12 ) ],
% 0.45/1.12 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.45/1.12 [ function( choice ) ],
% 0.45/1.12 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.45/1.12 apply( choice, X ), X ) ],
% 0.45/1.12 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.45/1.12 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.45/1.12 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.45/1.12 ,
% 0.45/1.12 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.45/1.12 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.45/1.12 , complement( compose( complement( 'element_relation' ), inverse(
% 0.45/1.12 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.45/1.12 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.45/1.12 'identity_relation' ) ],
% 0.45/1.12 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.45/1.12 , diagonalise( X ) ) ],
% 0.45/1.12 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.45/1.12 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.45/1.12 [ ~( operation( X ) ), function( X ) ],
% 0.45/1.12 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.45/1.12 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.45/1.12 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.45/1.12 'domain_of'( X ) ) ) ],
% 0.45/1.12 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.45/1.12 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.45/1.12 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.45/1.12 X ) ],
% 0.45/1.12 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.45/1.12 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.45/1.12 'domain_of'( X ) ) ],
% 0.45/1.12 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.45/1.12 'domain_of'( Z ) ) ) ],
% 0.45/1.12 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.45/1.12 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.45/1.12 ), compatible( X, Y, Z ) ],
% 0.45/1.12 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.45/1.12 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.45/1.12 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.45/1.12 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.45/1.12 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.45/1.12 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.45/1.12 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.45/1.12 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.45/1.12 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.45/1.12 , Y ) ],
% 0.45/1.12 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.45/1.12 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.45/1.12 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.45/1.12 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.45/1.12 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.45/1.12 [ subclass( 'compose_class'( X ), 'cross_product'( 'universal_class',
% 0.45/1.12 'universal_class' ) ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ), =(
% 0.45/1.12 compose( Z, X ), Y ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.45/1.12 , 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) ), member(
% 0.45/1.12 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ],
% 0.45/1.12 [ subclass( 'composition_function', 'cross_product'( 'universal_class',
% 0.45/1.12 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.45/1.12 'composition_function' ) ), =( compose( X, Y ), Z ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.45/1.12 , 'universal_class' ) ) ), member( 'ordered_pair'( X, 'ordered_pair'( Y,
% 0.45/1.12 compose( X, Y ) ) ), 'composition_function' ) ],
% 0.45/1.12 [ subclass( 'domain_relation', 'cross_product'( 'universal_class',
% 0.45/1.12 'universal_class' ) ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) ), =(
% 0.45/1.12 'domain_of'( X ), Y ) ],
% 0.45/1.12 [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X,
% 0.45/1.12 'domain_of'( X ) ), 'domain_relation' ) ],
% 0.45/1.12 [ =( first( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.45/1.12 'identity_relation' ) ), 'single_valued1'( X ) ) ],
% 0.45/1.12 [ =( second( 'not_subclass_element'( compose( X, inverse( X ) ),
% 0.45/1.12 'identity_relation' ) ), 'single_valued2'( X ) ) ],
% 0.45/1.12 [ =( domain( X, image( inverse( X ), singleton( 'single_valued1'( X ) )
% 0.45/1.12 ), 'single_valued2'( X ) ), 'single_valued3'( X ) ) ],
% 0.45/1.12 [ =( intersection( complement( compose( 'element_relation', complement(
% 0.45/1.12 'identity_relation' ) ) ), 'element_relation' ), 'singleton_relation' ) ]
% 0.45/1.12 ,
% 0.45/1.12 [ subclass( 'application_function', 'cross_product'( 'universal_class',
% 0.45/1.12 'cross_product'( 'universal_class', 'universal_class' ) ) ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.45/1.12 'application_function' ) ), member( Y, 'domain_of'( X ) ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.45/1.12 'application_function' ) ), =( apply( X, Y ), Z ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 0.45/1.12 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 0.45/1.12 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 0.45/1.12 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 0.45/1.12 'application_function' ) ],
% 0.45/1.12 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.45/1.12 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 0.45/1.12 [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ],
% 0.45/1.12 [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ), maps( X,
% 0.45/1.12 'domain_of'( X ), Y ) ],
% 0.45/1.12 [ =( union( X, inverse( X ) ), 'symmetrization_of'( X ) ) ],
% 0.45/1.12 [ ~( irreflexive( X, Y ) ), subclass( restrict( X, Y, Y ), complement(
% 0.45/1.12 'identity_relation' ) ) ],
% 0.45/1.12 [ ~( subclass( restrict( X, Y, Y ), complement( 'identity_relation' ) )
% 0.45/1.12 ), irreflexive( X, Y ) ],
% 0.45/1.12 [ ~( connected( X, Y ) ), subclass( 'cross_product'( Y, Y ), union(
% 0.45/1.12 'identity_relation', 'symmetrization_of'( X ) ) ) ],
% 0.45/1.12 [ ~( subclass( 'cross_product'( X, X ), union( 'identity_relation',
% 0.45/1.12 'symmetrization_of'( Y ) ) ) ), connected( Y, X ) ],
% 0.45/1.12 [ ~( transitive( X, Y ) ), subclass( compose( restrict( X, Y, Y ),
% 0.45/1.12 restrict( X, Y, Y ) ), restrict( X, Y, Y ) ) ],
% 0.45/1.12 [ ~( subclass( compose( restrict( X, Y, Y ), restrict( X, Y, Y ) ),
% 0.45/1.12 restrict( X, Y, Y ) ) ), transitive( X, Y ) ],
% 0.45/1.12 [ ~( asymmetric( X, Y ) ), =( restrict( intersection( X, inverse( X ) )
% 0.45/1.12 , Y, Y ), 'null_class' ) ],
% 0.45/1.12 [ ~( =( restrict( intersection( X, inverse( X ) ), Y, Y ), 'null_class'
% 0.45/1.12 ) ), asymmetric( X, Y ) ],
% 0.45/1.12 [ =( segment( X, Y, Z ), 'domain_of'( restrict( X, Y, singleton( Z ) ) )
% 0.45/1.12 ) ],
% 0.45/1.12 [ ~( 'well_ordering'( X, Y ) ), connected( X, Y ) ],
% 0.45/1.12 [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), =( Z,
% 0.45/1.12 'null_class' ), member( least( X, Z ), Z ) ],
% 0.45/1.12 [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), ~( member( T, Z )
% 0.45/1.12 ), member( least( X, Z ), Z ) ],
% 0.45/1.12 [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), =( segment( X, Z
% 0.45/1.12 , least( X, Z ) ), 'null_class' ) ],
% 0.45/1.12 [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), ~( member( T, Z )
% 0.45/1.12 ), ~( member( 'ordered_pair'( T, least( X, Z ) ), X ) ) ],
% 0.45/1.12 [ ~( connected( X, Y ) ), ~( =( 'not_well_ordering'( X, Y ),
% 0.45/1.12 'null_class' ) ), 'well_ordering'( X, Y ) ],
% 0.45/1.12 [ ~( connected( X, Y ) ), subclass( 'not_well_ordering'( X, Y ), Y ),
% 0.45/1.12 'well_ordering'( X, Y ) ],
% 0.45/1.12 [ ~( member( X, 'not_well_ordering'( Y, Z ) ) ), ~( =( segment( Y,
% 0.45/1.12 'not_well_ordering'( Y, Z ), X ), 'null_class' ) ), ~( connected( Y, Z )
% 0.45/1.12 ), 'well_ordering'( Y, Z ) ],
% 0.45/1.12 [ ~( section( X, Y, Z ) ), subclass( Y, Z ) ],
% 0.45/1.12 [ ~( section( X, Y, Z ) ), subclass( 'domain_of'( restrict( X, Z, Y ) )
% 0.45/1.12 , Y ) ],
% 0.45/1.12 [ ~( subclass( X, Y ) ), ~( subclass( 'domain_of'( restrict( Z, Y, X ) )
% 0.45/1.12 , X ) ), section( Z, X, Y ) ],
% 0.45/1.12 [ ~( member( X, 'ordinal_numbers' ) ), 'well_ordering'(
% 0.45/1.12 'element_relation', X ) ],
% 0.45/1.12 [ ~( member( X, 'ordinal_numbers' ) ), subclass( 'sum_class'( X ), X ) ]
% 0.45/1.12 ,
% 0.45/1.12 [ ~( 'well_ordering'( 'element_relation', X ) ), ~( subclass(
% 0.45/1.12 'sum_class'( X ), X ) ), ~( member( X, 'universal_class' ) ), member( X,
% 0.45/1.12 'ordinal_numbers' ) ],
% 0.45/1.12 [ ~( 'well_ordering'( 'element_relation', X ) ), ~( subclass(
% 0.45/1.12 'sum_class'( X ), X ) ), member( X, 'ordinal_numbers' ), =( X,
% 0.45/1.12 'ordinal_numbers' ) ],
% 0.45/1.12 [ =( union( singleton( 'null_class' ), image( 'successor_relation',
% 0.45/1.12 'ordinal_numbers' ) ), 'kind_1_ordinals' ) ],
% 0.45/1.12 [ =( intersection( complement( 'kind_1_ordinals' ), 'ordinal_numbers' )
% 0.45/1.12 , 'limit_ordinals' ) ],
% 0.45/1.12 [ subclass( 'rest_of'( X ), 'cross_product'( 'universal_class',
% 0.45/1.12 'universal_class' ) ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'rest_of'( Z ) ) ), member( X,
% 0.45/1.12 'domain_of'( Z ) ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'rest_of'( Z ) ) ), =( restrict( Z
% 0.45/1.12 , X, 'universal_class' ), Y ) ],
% 0.45/1.12 [ ~( member( X, 'domain_of'( Y ) ) ), ~( =( restrict( Y, X,
% 0.45/1.12 'universal_class' ), Z ) ), member( 'ordered_pair'( X, Z ), 'rest_of'( Y
% 0.45/1.12 ) ) ],
% 0.45/1.12 [ subclass( 'rest_relation', 'cross_product'( 'universal_class',
% 0.45/1.12 'universal_class' ) ) ],
% 0.45/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'rest_relation' ) ), =( 'rest_of'(
% 0.45/1.12 X ), Y ) ],
% 0.45/1.12 [ ~( member( X, 'universal_class' ) ), member( 'ordered_pair'( X,
% 0.45/1.12 'rest_of'( X ) ), 'rest_relation' ) ],
% 0.45/1.12 [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), function( Y ) ]
% 0.45/1.12 ,
% 0.45/1.12 [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), function( X ) ]
% 0.45/1.12 ,
% 0.45/1.12 [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), member(
% 1.04/1.42 'domain_of'( X ), 'ordinal_numbers' ) ],
% 1.04/1.42 [ ~( member( X, 'recursion_equation_functions'( Y ) ) ), =( compose( Y,
% 1.04/1.42 'rest_of'( X ) ), X ) ],
% 1.04/1.42 [ ~( function( X ) ), ~( function( Y ) ), ~( member( 'domain_of'( Y ),
% 1.04/1.42 'ordinal_numbers' ) ), ~( =( compose( X, 'rest_of'( Y ) ), Y ) ), member(
% 1.04/1.42 Y, 'recursion_equation_functions'( X ) ) ],
% 1.04/1.42 [ subclass( 'union_of_range_map', 'cross_product'( 'universal_class',
% 1.04/1.42 'universal_class' ) ) ],
% 1.04/1.42 [ ~( member( 'ordered_pair'( X, Y ), 'union_of_range_map' ) ), =(
% 1.04/1.42 'sum_class'( 'range_of'( X ) ), Y ) ],
% 1.04/1.42 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 1.04/1.42 , 'universal_class' ) ) ), ~( =( 'sum_class'( 'range_of'( X ) ), Y ) ),
% 1.04/1.42 member( 'ordered_pair'( X, Y ), 'union_of_range_map' ) ],
% 1.04/1.42 [ =( apply( recursion( X, 'successor_relation', 'union_of_range_map' ),
% 1.04/1.42 Y ), 'ordinal_add'( X, Y ) ) ],
% 1.04/1.42 [ =( recursion( 'null_class', apply( 'add_relation', X ),
% 1.04/1.42 'union_of_range_map' ), 'ordinal_multiply'( X, Y ) ) ],
% 1.04/1.42 [ ~( member( X, omega ) ), =( 'integer_of'( X ), X ) ],
% 1.04/1.42 [ member( X, omega ), =( 'integer_of'( X ), 'null_class' ) ],
% 1.04/1.42 [ ~( function( z ) ) ],
% 1.04/1.42 [ ~( =( 'recursion_equation_functions'( z ), 'null_class' ) ) ]
% 1.04/1.42 ] .
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 percentage equality = 0.222222, percentage horn = 0.925000
% 1.04/1.42 This is a problem with some equality
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 Options Used:
% 1.04/1.42
% 1.04/1.42 useres = 1
% 1.04/1.42 useparamod = 1
% 1.04/1.42 useeqrefl = 1
% 1.04/1.42 useeqfact = 1
% 1.04/1.42 usefactor = 1
% 1.04/1.42 usesimpsplitting = 0
% 1.04/1.42 usesimpdemod = 5
% 1.04/1.42 usesimpres = 3
% 1.04/1.42
% 1.04/1.42 resimpinuse = 1000
% 1.04/1.42 resimpclauses = 20000
% 1.04/1.42 substype = eqrewr
% 1.04/1.42 backwardsubs = 1
% 1.04/1.42 selectoldest = 5
% 1.04/1.42
% 1.04/1.42 litorderings [0] = split
% 1.04/1.42 litorderings [1] = extend the termordering, first sorting on arguments
% 1.04/1.42
% 1.04/1.42 termordering = kbo
% 1.04/1.42
% 1.04/1.42 litapriori = 0
% 1.04/1.42 termapriori = 1
% 1.04/1.42 litaposteriori = 0
% 1.04/1.42 termaposteriori = 0
% 1.04/1.42 demodaposteriori = 0
% 1.04/1.42 ordereqreflfact = 0
% 1.04/1.42
% 1.04/1.42 litselect = negord
% 1.04/1.42
% 1.04/1.42 maxweight = 15
% 1.04/1.42 maxdepth = 30000
% 1.04/1.42 maxlength = 115
% 1.04/1.42 maxnrvars = 195
% 1.04/1.42 excuselevel = 1
% 1.04/1.42 increasemaxweight = 1
% 1.04/1.42
% 1.04/1.42 maxselected = 10000000
% 1.04/1.42 maxnrclauses = 10000000
% 1.04/1.42
% 1.04/1.42 showgenerated = 0
% 1.04/1.42 showkept = 0
% 1.04/1.42 showselected = 0
% 1.04/1.42 showdeleted = 0
% 1.04/1.42 showresimp = 1
% 1.04/1.42 showstatus = 2000
% 1.04/1.42
% 1.04/1.42 prologoutput = 1
% 1.04/1.42 nrgoals = 5000000
% 1.04/1.42 totalproof = 1
% 1.04/1.42
% 1.04/1.42 Symbols occurring in the translation:
% 1.04/1.42
% 1.04/1.42 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.04/1.42 . [1, 2] (w:1, o:73, a:1, s:1, b:0),
% 1.04/1.42 ! [4, 1] (w:0, o:40, a:1, s:1, b:0),
% 1.04/1.42 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.04/1.42 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.04/1.42 subclass [41, 2] (w:1, o:98, a:1, s:1, b:0),
% 1.04/1.42 member [43, 2] (w:1, o:100, a:1, s:1, b:0),
% 1.04/1.42 'not_subclass_element' [44, 2] (w:1, o:101, a:1, s:1, b:0),
% 1.04/1.42 'universal_class' [45, 0] (w:1, o:24, a:1, s:1, b:0),
% 1.04/1.42 'unordered_pair' [46, 2] (w:1, o:103, a:1, s:1, b:0),
% 1.04/1.42 singleton [47, 1] (w:1, o:50, a:1, s:1, b:0),
% 1.04/1.42 'ordered_pair' [48, 2] (w:1, o:105, a:1, s:1, b:0),
% 1.04/1.42 'cross_product' [50, 2] (w:1, o:106, a:1, s:1, b:0),
% 1.04/1.42 first [52, 1] (w:1, o:51, a:1, s:1, b:0),
% 1.04/1.42 second [53, 1] (w:1, o:52, a:1, s:1, b:0),
% 1.04/1.42 'element_relation' [54, 0] (w:1, o:29, a:1, s:1, b:0),
% 1.04/1.42 intersection [55, 2] (w:1, o:108, a:1, s:1, b:0),
% 1.04/1.42 complement [56, 1] (w:1, o:53, a:1, s:1, b:0),
% 1.04/1.42 union [57, 2] (w:1, o:109, a:1, s:1, b:0),
% 1.04/1.42 'symmetric_difference' [58, 2] (w:1, o:110, a:1, s:1, b:0),
% 1.04/1.42 restrict [60, 3] (w:1, o:119, a:1, s:1, b:0),
% 1.04/1.42 'null_class' [61, 0] (w:1, o:30, a:1, s:1, b:0),
% 1.04/1.42 'domain_of' [62, 1] (w:1, o:56, a:1, s:1, b:0),
% 1.04/1.42 rotate [63, 1] (w:1, o:45, a:1, s:1, b:0),
% 1.04/1.42 flip [65, 1] (w:1, o:57, a:1, s:1, b:0),
% 1.04/1.42 inverse [66, 1] (w:1, o:58, a:1, s:1, b:0),
% 1.04/1.42 'range_of' [67, 1] (w:1, o:46, a:1, s:1, b:0),
% 1.04/1.42 domain [68, 3] (w:1, o:121, a:1, s:1, b:0),
% 1.04/1.42 range [69, 3] (w:1, o:122, a:1, s:1, b:0),
% 1.04/1.42 image [70, 2] (w:1, o:107, a:1, s:1, b:0),
% 1.04/1.42 successor [71, 1] (w:1, o:59, a:1, s:1, b:0),
% 1.04/1.42 'successor_relation' [72, 0] (w:1, o:7, a:1, s:1, b:0),
% 1.04/1.42 inductive [73, 1] (w:1, o:60, a:1, s:1, b:0),
% 1.04/1.42 omega [74, 0] (w:1, o:11, a:1, s:1, b:0),
% 1.04/1.42 'sum_class' [75, 1] (w:1, o:61, a:1, s:1, b:0),
% 1.04/1.42 'power_class' [76, 1] (w:1, o:64, a:1, s:1, b:0),
% 1.04/1.42 compose [78, 2] (w:1, o:111, a:1, s:1, b:0),
% 1.04/1.42 'single_valued_class' [79, 1] (w:1, o:65, a:1, s:1, b:0),
% 1.04/1.42 'identity_relation' [80, 0] (w:1, o:31, a:1, s:1, b:0),
% 1.04/1.42 function [82, 1] (w:1, o:66, a:1, s:1, b:0),
% 1.04/1.42 regular [83, 1] (w:1, o:47, a:1, s:1, b:0),
% 1.04/1.42 apply [84, 2] (w:1, o:112, a:1, s:1, b:0),
% 1.04/1.42 choice [85, 0] (w:1, o:32, a:1, s:1, b:0),
% 1.04/1.42 'one_to_one' [86, 1] (w:1, o:62, a:1, s:1, b:0),
% 1.04/1.42 'subset_relation' [87, 0] (w:1, o:6, a:1, s:1, b:0),
% 1.04/1.42 diagonalise [88, 1] (w:1, o:67, a:1, s:1, b:0),
% 1.04/1.42 cantor [89, 1] (w:1, o:54, a:1, s:1, b:0),
% 1.04/1.42 operation [90, 1] (w:1, o:63, a:1, s:1, b:0),
% 1.04/1.42 compatible [94, 3] (w:1, o:120, a:1, s:1, b:0),
% 1.04/1.42 homomorphism [95, 3] (w:1, o:123, a:1, s:1, b:0),
% 1.04/1.42 'not_homomorphism1' [96, 3] (w:1, o:125, a:1, s:1, b:0),
% 1.04/1.42 'not_homomorphism2' [97, 3] (w:1, o:126, a:1, s:1, b:0),
% 1.04/1.42 'compose_class' [98, 1] (w:1, o:55, a:1, s:1, b:0),
% 1.04/1.42 'composition_function' [99, 0] (w:1, o:33, a:1, s:1, b:0),
% 1.04/1.42 'domain_relation' [100, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.04/1.42 'single_valued1' [101, 1] (w:1, o:68, a:1, s:1, b:0),
% 1.04/1.42 'single_valued2' [102, 1] (w:1, o:69, a:1, s:1, b:0),
% 1.04/1.42 'single_valued3' [103, 1] (w:1, o:70, a:1, s:1, b:0),
% 1.04/1.42 'singleton_relation' [104, 0] (w:1, o:8, a:1, s:1, b:0),
% 1.04/1.42 'application_function' [105, 0] (w:1, o:34, a:1, s:1, b:0),
% 1.04/1.42 maps [106, 3] (w:1, o:124, a:1, s:1, b:0),
% 1.04/1.42 'symmetrization_of' [107, 1] (w:1, o:71, a:1, s:1, b:0),
% 1.04/1.42 irreflexive [108, 2] (w:1, o:113, a:1, s:1, b:0),
% 1.04/1.42 connected [109, 2] (w:1, o:114, a:1, s:1, b:0),
% 1.04/1.42 transitive [110, 2] (w:1, o:102, a:1, s:1, b:0),
% 1.04/1.42 asymmetric [111, 2] (w:1, o:115, a:1, s:1, b:0),
% 1.04/1.42 segment [112, 3] (w:1, o:128, a:1, s:1, b:0),
% 1.04/1.42 'well_ordering' [113, 2] (w:1, o:116, a:1, s:1, b:0),
% 1.04/1.42 least [114, 2] (w:1, o:99, a:1, s:1, b:0),
% 1.04/1.42 'not_well_ordering' [115, 2] (w:1, o:104, a:1, s:1, b:0),
% 1.04/1.42 section [116, 3] (w:1, o:129, a:1, s:1, b:0),
% 1.04/1.42 'ordinal_numbers' [117, 0] (w:1, o:12, a:1, s:1, b:0),
% 1.04/1.42 'kind_1_ordinals' [118, 0] (w:1, o:35, a:1, s:1, b:0),
% 1.04/1.42 'limit_ordinals' [119, 0] (w:1, o:36, a:1, s:1, b:0),
% 1.04/1.42 'rest_of' [120, 1] (w:1, o:48, a:1, s:1, b:0),
% 1.04/1.42 'rest_relation' [121, 0] (w:1, o:5, a:1, s:1, b:0),
% 1.04/1.42 'recursion_equation_functions' [122, 1] (w:1, o:49, a:1, s:1, b:0),
% 1.04/1.42 'union_of_range_map' [123, 0] (w:1, o:37, a:1, s:1, b:0),
% 1.04/1.42 recursion [124, 3] (w:1, o:127, a:1, s:1, b:0),
% 1.04/1.42 'ordinal_add' [125, 2] (w:1, o:117, a:1, s:1, b:0),
% 1.04/1.42 'add_relation' [126, 0] (w:1, o:38, a:1, s:1, b:0),
% 1.04/1.42 'ordinal_multiply' [127, 2] (w:1, o:118, a:1, s:1, b:0),
% 1.04/1.42 'integer_of' [128, 1] (w:1, o:72, a:1, s:1, b:0),
% 1.04/1.42 z [129, 0] (w:1, o:39, a:1, s:1, b:0).
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 Starting Search:
% 1.04/1.42
% 1.04/1.42 Resimplifying inuse:
% 1.04/1.42 Done
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 Intermediate Status:
% 1.04/1.42 Generated: 4996
% 1.04/1.42 Kept: 2022
% 1.04/1.42 Inuse: 116
% 1.04/1.42 Deleted: 8
% 1.04/1.42 Deletedinuse: 2
% 1.04/1.42
% 1.04/1.42 Resimplifying inuse:
% 1.04/1.42 Done
% 1.04/1.42
% 1.04/1.42 Resimplifying inuse:
% 1.04/1.42 Done
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 Intermediate Status:
% 1.04/1.42 Generated: 9717
% 1.04/1.42 Kept: 4172
% 1.04/1.42 Inuse: 192
% 1.04/1.42 Deleted: 16
% 1.04/1.42 Deletedinuse: 7
% 1.04/1.42
% 1.04/1.42 Resimplifying inuse:
% 1.04/1.42 Done
% 1.04/1.42
% 1.04/1.42 Resimplifying inuse:
% 1.04/1.42 Done
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 Intermediate Status:
% 1.04/1.42 Generated: 13889
% 1.04/1.42 Kept: 6234
% 1.04/1.42 Inuse: 260
% 1.04/1.42 Deleted: 20
% 1.04/1.42 Deletedinuse: 10
% 1.04/1.42
% 1.04/1.42 Resimplifying inuse:
% 1.04/1.42 Done
% 1.04/1.42
% 1.04/1.42 Resimplifying inuse:
% 1.04/1.42
% 1.04/1.42 Bliksems!, er is een bewijs:
% 1.04/1.42 % SZS status Unsatisfiable
% 1.04/1.42 % SZS output start Refutation
% 1.04/1.42
% 1.04/1.42 clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.04/1.42 .
% 1.04/1.42 clause( 145, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ),
% 1.04/1.42 function( Y ) ] )
% 1.04/1.42 .
% 1.04/1.42 clause( 157, [ ~( function( z ) ) ] )
% 1.04/1.42 .
% 1.04/1.42 clause( 158, [ ~( =( 'recursion_equation_functions'( z ), 'null_class' ) )
% 1.04/1.42 ] )
% 1.04/1.42 .
% 1.04/1.42 clause( 3575, [ ~( member( X, 'recursion_equation_functions'( z ) ) ) ] )
% 1.04/1.42 .
% 1.04/1.42 clause( 6608, [ =( 'recursion_equation_functions'( z ), 'null_class' ) ] )
% 1.04/1.42 .
% 1.04/1.42 clause( 7521, [] )
% 1.04/1.42 .
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 % SZS output end Refutation
% 1.04/1.42 found a proof!
% 1.04/1.42
% 1.04/1.42 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.04/1.42
% 1.04/1.42 initialclauses(
% 1.04/1.42 [ clause( 7523, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.04/1.42 ) ] )
% 1.04/1.42 , clause( 7524, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 1.04/1.42 , Y ) ] )
% 1.04/1.42 , clause( 7525, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 1.04/1.42 subclass( X, Y ) ] )
% 1.04/1.42 , clause( 7526, [ subclass( X, 'universal_class' ) ] )
% 1.04/1.42 , clause( 7527, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.04/1.42 , clause( 7528, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 1.04/1.42 , clause( 7529, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ]
% 1.04/1.42 )
% 1.04/1.42 , clause( 7530, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 1.04/1.42 =( X, Z ) ] )
% 1.04/1.42 , clause( 7531, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.04/1.42 'unordered_pair'( X, Y ) ) ] )
% 1.04/1.42 , clause( 7532, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.04/1.42 'unordered_pair'( Y, X ) ) ] )
% 1.04/1.42 , clause( 7533, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 1.04/1.42 )
% 1.04/1.42 , clause( 7534, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.04/1.42 , clause( 7535, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 1.04/1.42 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.04/1.42 , clause( 7536, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.04/1.42 ) ) ), member( X, Z ) ] )
% 1.04/1.42 , clause( 7537, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.04/1.42 ) ) ), member( Y, T ) ] )
% 1.04/1.42 , clause( 7538, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.04/1.42 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.04/1.42 , clause( 7539, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 1.04/1.42 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 1.04/1.42 , clause( 7540, [ subclass( 'element_relation', 'cross_product'(
% 1.04/1.42 'universal_class', 'universal_class' ) ) ] )
% 1.04/1.42 , clause( 7541, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) )
% 1.04/1.42 , member( X, Y ) ] )
% 1.04/1.42 , clause( 7542, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.04/1.42 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 1.04/1.42 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 1.04/1.42 , clause( 7543, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.04/1.42 )
% 1.04/1.42 , clause( 7544, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 1.04/1.42 )
% 1.04/1.42 , clause( 7545, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 1.04/1.42 intersection( Y, Z ) ) ] )
% 1.04/1.42 , clause( 7546, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 1.04/1.42 )
% 1.04/1.42 , clause( 7547, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.04/1.42 complement( Y ) ), member( X, Y ) ] )
% 1.04/1.42 , clause( 7548, [ =( complement( intersection( complement( X ), complement(
% 1.04/1.42 Y ) ) ), union( X, Y ) ) ] )
% 1.04/1.42 , clause( 7549, [ =( intersection( complement( intersection( X, Y ) ),
% 1.04/1.42 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 1.04/1.42 'symmetric_difference'( X, Y ) ) ] )
% 1.04/1.42 , clause( 7550, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 1.04/1.42 X, Y, Z ) ) ] )
% 1.04/1.42 , clause( 7551, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 1.04/1.42 Z, X, Y ) ) ] )
% 1.04/1.42 , clause( 7552, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 1.04/1.42 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 1.04/1.42 , clause( 7553, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 1.04/1.42 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 1.04/1.42 'domain_of'( Y ) ) ] )
% 1.04/1.42 , clause( 7554, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 1.04/1.42 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.04/1.42 , clause( 7555, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.04/1.42 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 1.04/1.42 ] )
% 1.04/1.42 , clause( 7556, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 1.04/1.42 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 1.04/1.42 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.04/1.42 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 1.04/1.42 , Y ), rotate( T ) ) ] )
% 1.04/1.42 , clause( 7557, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 1.04/1.42 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.04/1.42 , clause( 7558, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.04/1.42 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 1.04/1.42 )
% 1.04/1.42 , clause( 7559, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 1.04/1.42 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 1.04/1.42 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.04/1.42 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 1.04/1.42 , Z ), flip( T ) ) ] )
% 1.04/1.42 , clause( 7560, [ =( 'domain_of'( flip( 'cross_product'( X,
% 1.04/1.42 'universal_class' ) ) ), inverse( X ) ) ] )
% 1.04/1.42 , clause( 7561, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 1.04/1.42 , clause( 7562, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 1.04/1.42 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 1.04/1.42 , clause( 7563, [ =( second( 'not_subclass_element'( restrict( X, singleton(
% 1.04/1.42 Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 1.04/1.42 , clause( 7564, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 1.04/1.42 image( X, Y ) ) ] )
% 1.04/1.42 , clause( 7565, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 1.04/1.42 , clause( 7566, [ subclass( 'successor_relation', 'cross_product'(
% 1.04/1.42 'universal_class', 'universal_class' ) ) ] )
% 1.04/1.42 , clause( 7567, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' )
% 1.04/1.42 ), =( successor( X ), Y ) ] )
% 1.04/1.42 , clause( 7568, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X
% 1.04/1.42 , Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 1.04/1.42 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 1.04/1.42 , clause( 7569, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 1.04/1.42 , clause( 7570, [ ~( inductive( X ) ), subclass( image(
% 1.04/1.42 'successor_relation', X ), X ) ] )
% 1.04/1.42 , clause( 7571, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 1.04/1.42 'successor_relation', X ), X ) ), inductive( X ) ] )
% 1.04/1.42 , clause( 7572, [ inductive( omega ) ] )
% 1.04/1.42 , clause( 7573, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 1.04/1.42 , clause( 7574, [ member( omega, 'universal_class' ) ] )
% 1.04/1.42 , clause( 7575, [ =( 'domain_of'( restrict( 'element_relation',
% 1.04/1.42 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 1.04/1.42 , clause( 7576, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 1.04/1.42 X ), 'universal_class' ) ] )
% 1.04/1.42 , clause( 7577, [ =( complement( image( 'element_relation', complement( X )
% 1.04/1.42 ) ), 'power_class'( X ) ) ] )
% 1.04/1.42 , clause( 7578, [ ~( member( X, 'universal_class' ) ), member(
% 1.04/1.42 'power_class'( X ), 'universal_class' ) ] )
% 1.04/1.42 , clause( 7579, [ subclass( compose( X, Y ), 'cross_product'(
% 1.04/1.42 'universal_class', 'universal_class' ) ) ] )
% 1.04/1.42 , clause( 7580, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 1.04/1.42 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 1.04/1.42 , clause( 7581, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 1.04/1.42 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 1.04/1.42 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 1.04/1.42 ) ] )
% 1.04/1.42 , clause( 7582, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 1.04/1.42 inverse( X ) ), 'identity_relation' ) ] )
% 1.04/1.42 , clause( 7583, [ ~( subclass( compose( X, inverse( X ) ),
% 1.04/1.42 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 1.04/1.42 , clause( 7584, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 1.04/1.42 'universal_class', 'universal_class' ) ) ] )
% 1.04/1.42 , clause( 7585, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 1.04/1.42 , 'identity_relation' ) ] )
% 1.04/1.42 , clause( 7586, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 1.04/1.42 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 1.04/1.42 'identity_relation' ) ), function( X ) ] )
% 1.04/1.42 , clause( 7587, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ),
% 1.04/1.42 member( image( X, Y ), 'universal_class' ) ] )
% 1.04/1.42 , clause( 7588, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.04/1.42 , clause( 7589, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 1.04/1.42 , 'null_class' ) ] )
% 1.04/1.42 , clause( 7590, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y
% 1.04/1.42 ) ) ] )
% 1.04/1.42 , clause( 7591, [ function( choice ) ] )
% 1.04/1.42 , clause( 7592, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' )
% 1.04/1.42 , member( apply( choice, X ), X ) ] )
% 1.04/1.42 , clause( 7593, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 1.04/1.42 , clause( 7594, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 1.04/1.42 , clause( 7595, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 1.04/1.42 'one_to_one'( X ) ] )
% 1.04/1.42 , clause( 7596, [ =( intersection( 'cross_product'( 'universal_class',
% 1.04/1.42 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 1.04/1.42 'universal_class' ), complement( compose( complement( 'element_relation'
% 1.04/1.42 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 1.04/1.42 , clause( 7597, [ =( intersection( inverse( 'subset_relation' ),
% 1.04/1.42 'subset_relation' ), 'identity_relation' ) ] )
% 1.04/1.42 , clause( 7598, [ =( complement( 'domain_of'( intersection( X,
% 1.04/1.42 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 1.04/1.42 , clause( 7599, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 1.04/1.42 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 1.04/1.42 , clause( 7600, [ ~( operation( X ) ), function( X ) ] )
% 1.04/1.42 , clause( 7601, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 1.04/1.42 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.04/1.42 ] )
% 1.04/1.42 , clause( 7602, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 1.04/1.42 'domain_of'( 'domain_of'( X ) ) ) ] )
% 1.04/1.42 , clause( 7603, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 1.04/1.42 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.04/1.42 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 1.04/1.42 operation( X ) ] )
% 1.04/1.42 , clause( 7604, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 1.04/1.42 , clause( 7605, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 1.04/1.42 Y ) ), 'domain_of'( X ) ) ] )
% 1.04/1.42 , clause( 7606, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 1.04/1.42 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 1.04/1.42 , clause( 7607, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) )
% 1.04/1.42 , 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 1.04/1.42 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 1.04/1.42 , clause( 7608, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 1.04/1.42 , clause( 7609, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 1.04/1.42 , clause( 7610, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 1.04/1.42 , clause( 7611, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 1.04/1.42 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 1.04/1.42 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 1.04/1.42 )
% 1.04/1.42 , clause( 7612, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.04/1.42 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.04/1.42 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.04/1.42 , Y ) ] )
% 1.04/1.42 , clause( 7613, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.04/1.42 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 1.04/1.42 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 1.04/1.42 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 1.04/1.42 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 1.04/1.42 )
% 1.04/1.42 , clause( 7614, [ subclass( 'compose_class'( X ), 'cross_product'(
% 1.04/1.42 'universal_class', 'universal_class' ) ) ] )
% 1.04/1.42 , clause( 7615, [ ~( member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) )
% 1.04/1.42 ), =( compose( Z, X ), Y ) ] )
% 1.04/1.42 , clause( 7616, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.04/1.42 'universal_class', 'universal_class' ) ) ), ~( =( compose( Z, X ), Y ) )
% 1.04/1.42 , member( 'ordered_pair'( X, Y ), 'compose_class'( Z ) ) ] )
% 1.04/1.42 , clause( 7617, [ subclass( 'composition_function', 'cross_product'(
% 1.04/1.42 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 1.04/1.42 ) ) ) ] )
% 1.04/1.42 , clause( 7618, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.04/1.42 'composition_function' ) ), =( compose( X, Y ), Z ) ] )
% 1.04/1.42 , clause( 7619, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.04/1.42 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( X,
% 1.04/1.42 'ordered_pair'( Y, compose( X, Y ) ) ), 'composition_function' ) ] )
% 1.04/1.42 , clause( 7620, [ subclass( 'domain_relation', 'cross_product'(
% 1.04/1.42 'universal_class', 'universal_class' ) ) ] )
% 1.04/1.42 , clause( 7621, [ ~( member( 'ordered_pair'( X, Y ), 'domain_relation' ) )
% 1.04/1.42 , =( 'domain_of'( X ), Y ) ] )
% 1.04/1.42 , clause( 7622, [ ~( member( X, 'universal_class' ) ), member(
% 1.04/1.42 'ordered_pair'( X, 'domain_of'( X ) ), 'domain_relation' ) ] )
% 1.04/1.42 , clause( 7623, [ =( first( 'not_subclass_element'( compose( X, inverse( X
% 1.04/1.42 ) ), 'identity_relation' ) ), 'single_valued1'( X ) ) ] )
% 1.04/1.42 , clause( 7624, [ =( second( 'not_subclass_element'( compose( X, inverse( X
% 1.04/1.42 ) ), 'identity_relation' ) ), 'single_valued2'( X ) ) ] )
% 1.04/1.42 , clause( 7625, [ =( domain( X, image( inverse( X ), singleton(
% 1.04/1.42 'single_valued1'( X ) ) ), 'single_valued2'( X ) ), 'single_valued3'( X )
% 1.04/1.42 ) ] )
% 1.04/1.42 , clause( 7626, [ =( intersection( complement( compose( 'element_relation'
% 1.04/1.42 , complement( 'identity_relation' ) ) ), 'element_relation' ),
% 1.04/1.42 'singleton_relation' ) ] )
% 1.04/1.42 , clause( 7627, [ subclass( 'application_function', 'cross_product'(
% 1.04/1.42 'universal_class', 'cross_product'( 'universal_class', 'universal_class'
% 1.04/1.42 ) ) ) ] )
% 1.04/1.42 , clause( 7628, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.04/1.42 'application_function' ) ), member( Y, 'domain_of'( X ) ) ] )
% 1.04/1.42 , clause( 7629, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.04/1.42 'application_function' ) ), =( apply( X, Y ), Z ) ] )
% 1.04/1.42 , clause( 7630, [ ~( member( 'ordered_pair'( X, 'ordered_pair'( Y, Z ) ),
% 1.04/1.42 'cross_product'( 'universal_class', 'cross_product'( 'universal_class',
% 1.04/1.42 'universal_class' ) ) ) ), ~( member( Y, 'domain_of'( X ) ) ), member(
% 1.04/1.42 'ordered_pair'( X, 'ordered_pair'( Y, apply( X, Y ) ) ),
% 1.04/1.42 'application_function' ) ] )
% 1.04/1.42 , clause( 7631, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 1.04/1.42 , clause( 7632, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 1.04/1.42 , clause( 7633, [ ~( maps( X, Y, Z ) ), subclass( 'range_of'( X ), Z ) ] )
% 1.04/1.42 , clause( 7634, [ ~( function( X ) ), ~( subclass( 'range_of'( X ), Y ) ),
% 1.04/1.42 maps( X, 'domain_of'( X ), Y ) ] )
% 1.04/1.42 , clause( 7635, [ =( union( X, inverse( X ) ), 'symmetrization_of'( X ) ) ]
% 1.04/1.42 )
% 1.04/1.42 , clause( 7636, [ ~( irreflexive( X, Y ) ), subclass( restrict( X, Y, Y ),
% 1.04/1.42 complement( 'identity_relation' ) ) ] )
% 1.04/1.42 , clause( 7637, [ ~( subclass( restrict( X, Y, Y ), complement(
% 1.04/1.42 'identity_relation' ) ) ), irreflexive( X, Y ) ] )
% 1.04/1.42 , clause( 7638, [ ~( connected( X, Y ) ), subclass( 'cross_product'( Y, Y )
% 1.04/1.42 , union( 'identity_relation', 'symmetrization_of'( X ) ) ) ] )
% 1.04/1.42 , clause( 7639, [ ~( subclass( 'cross_product'( X, X ), union(
% 1.04/1.42 'identity_relation', 'symmetrization_of'( Y ) ) ) ), connected( Y, X ) ]
% 1.04/1.42 )
% 1.04/1.42 , clause( 7640, [ ~( transitive( X, Y ) ), subclass( compose( restrict( X,
% 1.04/1.42 Y, Y ), restrict( X, Y, Y ) ), restrict( X, Y, Y ) ) ] )
% 1.04/1.42 , clause( 7641, [ ~( subclass( compose( restrict( X, Y, Y ), restrict( X, Y
% 1.04/1.42 , Y ) ), restrict( X, Y, Y ) ) ), transitive( X, Y ) ] )
% 1.04/1.42 , clause( 7642, [ ~( asymmetric( X, Y ) ), =( restrict( intersection( X,
% 1.04/1.42 inverse( X ) ), Y, Y ), 'null_class' ) ] )
% 1.04/1.42 , clause( 7643, [ ~( =( restrict( intersection( X, inverse( X ) ), Y, Y ),
% 1.04/1.42 'null_class' ) ), asymmetric( X, Y ) ] )
% 1.04/1.42 , clause( 7644, [ =( segment( X, Y, Z ), 'domain_of'( restrict( X, Y,
% 1.04/1.42 singleton( Z ) ) ) ) ] )
% 1.04/1.42 , clause( 7645, [ ~( 'well_ordering'( X, Y ) ), connected( X, Y ) ] )
% 1.04/1.42 , clause( 7646, [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), =( Z
% 1.04/1.42 , 'null_class' ), member( least( X, Z ), Z ) ] )
% 1.04/1.42 , clause( 7647, [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), ~(
% 1.04/1.42 member( T, Z ) ), member( least( X, Z ), Z ) ] )
% 1.04/1.42 , clause( 7648, [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), =(
% 1.04/1.42 segment( X, Z, least( X, Z ) ), 'null_class' ) ] )
% 1.04/1.42 , clause( 7649, [ ~( 'well_ordering'( X, Y ) ), ~( subclass( Z, Y ) ), ~(
% 1.04/1.42 member( T, Z ) ), ~( member( 'ordered_pair'( T, least( X, Z ) ), X ) ) ]
% 1.04/1.42 )
% 1.04/1.42 , clause( 7650, [ ~( connected( X, Y ) ), ~( =( 'not_well_ordering'( X, Y )
% 1.04/1.42 , 'null_class' ) ), 'well_ordering'( X, Y ) ] )
% 1.04/1.42 , clause( 7651, [ ~( connected( X, Y ) ), subclass( 'not_well_ordering'( X
% 1.04/1.42 , Y ), Y ), 'well_ordering'( X, Y ) ] )
% 1.04/1.42 , clause( 7652, [ ~( member( X, 'not_well_ordering'( Y, Z ) ) ), ~( =(
% 1.04/1.42 segment( Y, 'not_well_ordering'( Y, Z ), X ), 'null_class' ) ), ~(
% 1.04/1.42 connected( Y, Z ) ), 'well_ordering'( Y, Z ) ] )
% 1.04/1.42 , clause( 7653, [ ~( section( X, Y, Z ) ), subclass( Y, Z ) ] )
% 1.04/1.42 , clause( 7654, [ ~( section( X, Y, Z ) ), subclass( 'domain_of'( restrict(
% 1.04/1.42 X, Z, Y ) ), Y ) ] )
% 1.04/1.42 , clause( 7655, [ ~( subclass( X, Y ) ), ~( subclass( 'domain_of'( restrict(
% 1.04/1.42 Z, Y, X ) ), X ) ), section( Z, X, Y ) ] )
% 1.04/1.42 , clause( 7656, [ ~( member( X, 'ordinal_numbers' ) ), 'well_ordering'(
% 1.04/1.42 'element_relation', X ) ] )
% 1.04/1.42 , clause( 7657, [ ~( member( X, 'ordinal_numbers' ) ), subclass(
% 1.04/1.42 'sum_class'( X ), X ) ] )
% 1.04/1.42 , clause( 7658, [ ~( 'well_ordering'( 'element_relation', X ) ), ~(
% 1.04/1.42 subclass( 'sum_class'( X ), X ) ), ~( member( X, 'universal_class' ) ),
% 1.04/1.42 member( X, 'ordinal_numbers' ) ] )
% 1.04/1.42 , clause( 7659, [ ~( 'well_ordering'( 'element_relation', X ) ), ~(
% 1.04/1.42 subclass( 'sum_class'( X ), X ) ), member( X, 'ordinal_numbers' ), =( X,
% 1.04/1.42 'ordinal_numbers' ) ] )
% 1.04/1.42 , clause( 7660, [ =( union( singleton( 'null_class' ), image(
% 1.04/1.42 'successor_relation', 'ordinal_numbers' ) ), 'kind_1_ordinals' ) ] )
% 1.04/1.42 , clause( 7661, [ =( intersection( complement( 'kind_1_ordinals' ),
% 1.04/1.42 'ordinal_numbers' ), 'limit_ordinals' ) ] )
% 1.04/1.42 , clause( 7662, [ subclass( 'rest_of'( X ), 'cross_product'(
% 1.04/1.42 'universal_class', 'universal_class' ) ) ] )
% 1.04/1.42 , clause( 7663, [ ~( member( 'ordered_pair'( X, Y ), 'rest_of'( Z ) ) ),
% 1.04/1.42 member( X, 'domain_of'( Z ) ) ] )
% 1.04/1.42 , clause( 7664, [ ~( member( 'ordered_pair'( X, Y ), 'rest_of'( Z ) ) ),
% 1.04/1.42 =( restrict( Z, X, 'universal_class' ), Y ) ] )
% 1.04/1.42 , clause( 7665, [ ~( member( X, 'domain_of'( Y ) ) ), ~( =( restrict( Y, X
% 1.04/1.42 , 'universal_class' ), Z ) ), member( 'ordered_pair'( X, Z ), 'rest_of'(
% 1.04/1.42 Y ) ) ] )
% 1.04/1.42 , clause( 7666, [ subclass( 'rest_relation', 'cross_product'(
% 1.04/1.42 'universal_class', 'universal_class' ) ) ] )
% 1.04/1.42 , clause( 7667, [ ~( member( 'ordered_pair'( X, Y ), 'rest_relation' ) ),
% 1.04/1.42 =( 'rest_of'( X ), Y ) ] )
% 1.04/1.42 , clause( 7668, [ ~( member( X, 'universal_class' ) ), member(
% 1.04/1.42 'ordered_pair'( X, 'rest_of'( X ) ), 'rest_relation' ) ] )
% 1.04/1.42 , clause( 7669, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ),
% 1.04/1.42 function( Y ) ] )
% 1.04/1.42 , clause( 7670, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ),
% 1.04/1.42 function( X ) ] )
% 1.04/1.42 , clause( 7671, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ),
% 1.04/1.42 member( 'domain_of'( X ), 'ordinal_numbers' ) ] )
% 1.04/1.42 , clause( 7672, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ),
% 1.04/1.42 =( compose( Y, 'rest_of'( X ) ), X ) ] )
% 1.04/1.42 , clause( 7673, [ ~( function( X ) ), ~( function( Y ) ), ~( member(
% 1.04/1.42 'domain_of'( Y ), 'ordinal_numbers' ) ), ~( =( compose( X, 'rest_of'( Y )
% 1.04/1.42 ), Y ) ), member( Y, 'recursion_equation_functions'( X ) ) ] )
% 1.04/1.42 , clause( 7674, [ subclass( 'union_of_range_map', 'cross_product'(
% 1.04/1.42 'universal_class', 'universal_class' ) ) ] )
% 1.04/1.42 , clause( 7675, [ ~( member( 'ordered_pair'( X, Y ), 'union_of_range_map' )
% 1.04/1.42 ), =( 'sum_class'( 'range_of'( X ) ), Y ) ] )
% 1.04/1.42 , clause( 7676, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.04/1.42 'universal_class', 'universal_class' ) ) ), ~( =( 'sum_class'( 'range_of'(
% 1.04/1.42 X ) ), Y ) ), member( 'ordered_pair'( X, Y ), 'union_of_range_map' ) ] )
% 1.04/1.42 , clause( 7677, [ =( apply( recursion( X, 'successor_relation',
% 1.04/1.42 'union_of_range_map' ), Y ), 'ordinal_add'( X, Y ) ) ] )
% 1.04/1.42 , clause( 7678, [ =( recursion( 'null_class', apply( 'add_relation', X ),
% 1.04/1.42 'union_of_range_map' ), 'ordinal_multiply'( X, Y ) ) ] )
% 1.04/1.42 , clause( 7679, [ ~( member( X, omega ) ), =( 'integer_of'( X ), X ) ] )
% 1.04/1.42 , clause( 7680, [ member( X, omega ), =( 'integer_of'( X ), 'null_class' )
% 1.04/1.42 ] )
% 1.04/1.42 , clause( 7681, [ ~( function( z ) ) ] )
% 1.04/1.42 , clause( 7682, [ ~( =( 'recursion_equation_functions'( z ), 'null_class' )
% 1.04/1.42 ) ] )
% 1.04/1.42 ] ).
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 subsumption(
% 1.04/1.42 clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.04/1.42 , clause( 7588, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.04/1.42 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.04/1.42 1 )] ) ).
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 subsumption(
% 1.04/1.42 clause( 145, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ),
% 1.04/1.42 function( Y ) ] )
% 1.04/1.42 , clause( 7669, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ),
% 1.04/1.42 function( Y ) ] )
% 1.04/1.42 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.04/1.42 ), ==>( 1, 1 )] ) ).
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 subsumption(
% 1.04/1.42 clause( 157, [ ~( function( z ) ) ] )
% 1.04/1.42 , clause( 7681, [ ~( function( z ) ) ] )
% 1.04/1.42 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 subsumption(
% 1.04/1.42 clause( 158, [ ~( =( 'recursion_equation_functions'( z ), 'null_class' ) )
% 1.04/1.42 ] )
% 1.04/1.42 , clause( 7682, [ ~( =( 'recursion_equation_functions'( z ), 'null_class' )
% 1.04/1.42 ) ] )
% 1.04/1.42 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 resolution(
% 1.04/1.42 clause( 7958, [ ~( member( X, 'recursion_equation_functions'( z ) ) ) ] )
% 1.04/1.42 , clause( 157, [ ~( function( z ) ) ] )
% 1.04/1.42 , 0, clause( 145, [ ~( member( X, 'recursion_equation_functions'( Y ) ) ),
% 1.04/1.42 function( Y ) ] )
% 1.04/1.42 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, z )] )
% 1.04/1.42 ).
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 subsumption(
% 1.04/1.42 clause( 3575, [ ~( member( X, 'recursion_equation_functions'( z ) ) ) ] )
% 1.04/1.42 , clause( 7958, [ ~( member( X, 'recursion_equation_functions'( z ) ) ) ]
% 1.04/1.42 )
% 1.04/1.42 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 eqswap(
% 1.04/1.42 clause( 7959, [ =( 'null_class', X ), member( regular( X ), X ) ] )
% 1.04/1.42 , clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.04/1.42 , 0, substitution( 0, [ :=( X, X )] )).
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 resolution(
% 1.04/1.42 clause( 7960, [ =( 'null_class', 'recursion_equation_functions'( z ) ) ] )
% 1.04/1.42 , clause( 3575, [ ~( member( X, 'recursion_equation_functions'( z ) ) ) ]
% 1.04/1.42 )
% 1.04/1.42 , 0, clause( 7959, [ =( 'null_class', X ), member( regular( X ), X ) ] )
% 1.04/1.42 , 1, substitution( 0, [ :=( X, regular( 'recursion_equation_functions'( z )
% 1.04/1.42 ) )] ), substitution( 1, [ :=( X, 'recursion_equation_functions'( z ) )] )
% 1.04/1.42 ).
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 eqswap(
% 1.04/1.42 clause( 7961, [ =( 'recursion_equation_functions'( z ), 'null_class' ) ] )
% 1.04/1.42 , clause( 7960, [ =( 'null_class', 'recursion_equation_functions'( z ) ) ]
% 1.04/1.42 )
% 1.04/1.42 , 0, substitution( 0, [] )).
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 subsumption(
% 1.04/1.42 clause( 6608, [ =( 'recursion_equation_functions'( z ), 'null_class' ) ] )
% 1.04/1.42 , clause( 7961, [ =( 'recursion_equation_functions'( z ), 'null_class' ) ]
% 1.04/1.42 )
% 1.04/1.42 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 paramod(
% 1.04/1.42 clause( 7964, [ ~( =( 'null_class', 'null_class' ) ) ] )
% 1.04/1.42 , clause( 6608, [ =( 'recursion_equation_functions'( z ), 'null_class' ) ]
% 1.04/1.42 )
% 1.04/1.42 , 0, clause( 158, [ ~( =( 'recursion_equation_functions'( z ), 'null_class'
% 1.04/1.42 ) ) ] )
% 1.04/1.42 , 0, 2, substitution( 0, [] ), substitution( 1, [] )).
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 eqrefl(
% 1.04/1.42 clause( 7965, [] )
% 1.04/1.42 , clause( 7964, [ ~( =( 'null_class', 'null_class' ) ) ] )
% 1.04/1.42 , 0, substitution( 0, [] )).
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 subsumption(
% 1.04/1.42 clause( 7521, [] )
% 1.04/1.42 , clause( 7965, [] )
% 1.04/1.42 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 end.
% 1.04/1.42
% 1.04/1.42 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.04/1.42
% 1.04/1.42 Memory use:
% 1.04/1.42
% 1.04/1.42 space for terms: 113045
% 1.04/1.42 space for clauses: 356807
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 clauses generated: 16635
% 1.04/1.42 clauses kept: 7522
% 1.04/1.42 clauses selected: 281
% 1.04/1.42 clauses deleted: 53
% 1.04/1.42 clauses inuse deleted: 43
% 1.04/1.42
% 1.04/1.42 subsentry: 38713
% 1.04/1.42 literals s-matched: 29623
% 1.04/1.42 literals matched: 29286
% 1.04/1.42 full subsumption: 13764
% 1.04/1.42
% 1.04/1.42 checksum: 1562233390
% 1.04/1.42
% 1.04/1.42
% 1.04/1.42 Bliksem ended
%------------------------------------------------------------------------------