TSTP Solution File: SET098-7 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET098-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Mon Jul 18 22:47:03 EDT 2022
% Result : Unsatisfiable 5.01s 5.39s
% Output : Refutation 5.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET098-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.11 % Command : bliksem %s
% 0.12/0.32 % Computer : n003.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Sun Jul 10 02:57:29 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.41/1.07 *** allocated 10000 integers for termspace/termends
% 0.41/1.07 *** allocated 10000 integers for clauses
% 0.41/1.07 *** allocated 10000 integers for justifications
% 0.41/1.07 Bliksem 1.12
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 Automatic Strategy Selection
% 0.41/1.07
% 0.41/1.07 Clauses:
% 0.41/1.07 [
% 0.41/1.07 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.41/1.07 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.41/1.07 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.41/1.07 ,
% 0.41/1.07 [ subclass( X, 'universal_class' ) ],
% 0.41/1.07 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.41/1.07 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.41/1.07 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.41/1.07 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.41/1.07 ,
% 0.41/1.07 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.41/1.07 ) ) ],
% 0.41/1.07 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.41/1.07 ) ) ],
% 0.41/1.07 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.41/1.07 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.41/1.07 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.41/1.07 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.41/1.07 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.41/1.07 X, Z ) ],
% 0.41/1.07 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.41/1.07 Y, T ) ],
% 0.41/1.07 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.41/1.07 ), 'cross_product'( Y, T ) ) ],
% 0.41/1.07 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.41/1.07 ), second( X ) ), X ) ],
% 0.41/1.07 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.41/1.07 'universal_class' ) ) ],
% 0.41/1.07 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.41/1.07 Y ) ],
% 0.41/1.07 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.41/1.07 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.41/1.07 , Y ), 'element_relation' ) ],
% 0.41/1.07 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.41/1.07 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.41/1.07 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.41/1.07 Z ) ) ],
% 0.41/1.07 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.41/1.07 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.41/1.07 member( X, Y ) ],
% 0.41/1.07 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.41/1.07 union( X, Y ) ) ],
% 0.41/1.07 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.41/1.07 intersection( complement( X ), complement( Y ) ) ) ),
% 0.41/1.07 'symmetric_difference'( X, Y ) ) ],
% 0.41/1.07 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.41/1.07 ,
% 0.41/1.07 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.41/1.07 ,
% 0.41/1.07 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.41/1.07 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.41/1.07 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.41/1.07 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.41/1.07 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.41/1.07 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.41/1.07 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.41/1.07 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.41/1.07 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.41/1.07 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.41/1.07 'cross_product'( 'universal_class', 'universal_class' ),
% 0.41/1.07 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.41/1.07 Y ), rotate( T ) ) ],
% 0.41/1.07 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.41/1.07 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.41/1.07 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.41/1.07 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.41/1.07 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.41/1.07 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.41/1.07 'cross_product'( 'universal_class', 'universal_class' ),
% 0.41/1.07 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.41/1.07 Z ), flip( T ) ) ],
% 0.41/1.07 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.41/1.07 inverse( X ) ) ],
% 0.41/1.07 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.41/1.07 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.41/1.07 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.41/1.07 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.41/1.07 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.41/1.07 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.41/1.07 ],
% 0.41/1.07 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.41/1.07 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.41/1.07 'universal_class' ) ) ],
% 0.41/1.07 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.41/1.07 successor( X ), Y ) ],
% 0.41/1.07 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.41/1.07 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.41/1.07 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.41/1.07 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.41/1.07 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.41/1.07 ,
% 0.41/1.07 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.41/1.07 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.41/1.07 [ inductive( omega ) ],
% 0.41/1.07 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.41/1.07 [ member( omega, 'universal_class' ) ],
% 0.41/1.07 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.41/1.07 , 'sum_class'( X ) ) ],
% 0.41/1.07 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.41/1.07 'universal_class' ) ],
% 0.41/1.07 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.41/1.07 'power_class'( X ) ) ],
% 0.41/1.07 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.41/1.07 'universal_class' ) ],
% 0.41/1.07 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.41/1.07 'universal_class' ) ) ],
% 0.41/1.07 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.41/1.07 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.41/1.07 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.41/1.07 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.41/1.07 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.41/1.07 ) ],
% 0.41/1.07 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.41/1.07 , 'identity_relation' ) ],
% 0.41/1.07 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.41/1.07 'single_valued_class'( X ) ],
% 0.41/1.07 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.41/1.07 'universal_class' ) ) ],
% 0.41/1.07 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.41/1.07 'identity_relation' ) ],
% 0.41/1.07 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.41/1.07 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.41/1.07 , function( X ) ],
% 0.41/1.07 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.41/1.07 X, Y ), 'universal_class' ) ],
% 0.41/1.07 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.41/1.07 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.41/1.07 ) ],
% 0.41/1.07 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.41/1.07 [ function( choice ) ],
% 0.41/1.07 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.41/1.07 apply( choice, X ), X ) ],
% 0.41/1.07 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.41/1.07 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.41/1.07 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.41/1.07 ,
% 0.41/1.07 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.41/1.07 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.41/1.07 , complement( compose( complement( 'element_relation' ), inverse(
% 0.41/1.07 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.41/1.07 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.41/1.07 'identity_relation' ) ],
% 0.41/1.07 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.41/1.07 , diagonalise( X ) ) ],
% 0.41/1.07 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.41/1.07 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.41/1.07 [ ~( operation( X ) ), function( X ) ],
% 0.41/1.07 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.41/1.07 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.41/1.07 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.41/1.07 'domain_of'( X ) ) ) ],
% 0.41/1.07 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.41/1.07 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.41/1.07 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.41/1.07 X ) ],
% 0.41/1.07 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.41/1.07 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.41/1.07 'domain_of'( X ) ) ],
% 0.41/1.07 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.41/1.07 'domain_of'( Z ) ) ) ],
% 0.41/1.07 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.41/1.07 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.41/1.07 ), compatible( X, Y, Z ) ],
% 0.41/1.07 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.41/1.07 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.41/1.07 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.41/1.07 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.41/1.07 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.41/1.07 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.41/1.07 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.41/1.07 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.41/1.07 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.41/1.07 , Y ) ],
% 0.41/1.07 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.41/1.07 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.41/1.07 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.41/1.07 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.41/1.07 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.41/1.07 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.41/1.07 X, 'unordered_pair'( X, Y ) ) ],
% 0.41/1.07 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.41/1.07 Y, 'unordered_pair'( X, Y ) ) ],
% 0.41/1.07 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.41/1.07 X, 'universal_class' ) ],
% 0.41/1.07 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.41/1.07 Y, 'universal_class' ) ],
% 0.41/1.07 [ subclass( X, X ) ],
% 0.41/1.07 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.41/1.07 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.41/1.07 'not_subclass_element'( Y, X ), Y ) ],
% 0.41/1.07 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.41/1.07 'not_subclass_element'( Y, X ), Y ) ],
% 0.41/1.07 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.41/1.07 'not_subclass_element'( Y, X ), Y ) ],
% 0.41/1.07 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.41/1.07 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.41/1.07 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.41/1.07 [ ~( member( X, 'null_class' ) ) ],
% 0.41/1.07 [ subclass( 'null_class', X ) ],
% 0.41/1.07 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.41/1.07 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.41/1.07 ), X ) ],
% 0.41/1.07 [ member( 'null_class', 'universal_class' ) ],
% 0.41/1.07 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.41/1.07 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.41/1.07 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.41/1.07 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.41/1.07 Y ) ) ],
% 0.41/1.07 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.41/1.07 Y ) ) ],
% 0.41/1.07 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.41/1.07 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.41/1.07 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.41/1.07 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.41/1.07 'universal_class' ) ) ), =( Y, Z ) ],
% 0.41/1.07 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.41/1.07 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.41/1.07 'universal_class' ) ) ), =( X, Z ) ],
% 0.41/1.07 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.41/1.07 'null_class' ) ) ],
% 0.41/1.07 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.41/1.07 'null_class' ) ) ],
% 0.41/1.07 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.41/1.07 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 5.01/5.39 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 5.01/5.39 X, Z ), Y ) ],
% 5.01/5.39 [ member( singleton( X ), 'universal_class' ) ],
% 5.01/5.39 [ member( singleton( X ), 'unordered_pair'( Y, singleton( X ) ) ) ],
% 5.01/5.39 [ ~( member( X, 'universal_class' ) ), member( X, singleton( X ) ) ]
% 5.01/5.39 ,
% 5.01/5.39 [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X ),
% 5.01/5.39 'null_class' ) ) ],
% 5.01/5.39 [ member( 'null_class', singleton( 'null_class' ) ) ],
% 5.01/5.39 [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ],
% 5.01/5.39 [ member( X, 'universal_class' ), =( singleton( X ), 'null_class' ) ]
% 5.01/5.39 ,
% 5.01/5.39 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 5.01/5.39 'universal_class' ) ), =( X, Y ) ],
% 5.01/5.39 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 5.01/5.39 'universal_class' ) ), =( X, Y ) ],
% 5.01/5.39 [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~( member( Z,
% 5.01/5.39 'universal_class' ) ), =( Z, X ), =( Z, Y ) ],
% 5.01/5.39 [ ~( member( X, 'universal_class' ) ), member( 'member_of'( singleton( X
% 5.01/5.39 ) ), 'universal_class' ) ],
% 5.01/5.39 [ ~( member( X, 'universal_class' ) ), =( singleton( 'member_of'(
% 5.01/5.39 singleton( X ) ) ), singleton( X ) ) ],
% 5.01/5.39 [ member( 'member_of'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 5.01/5.39 ) ],
% 5.01/5.39 [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X ), X ) ],
% 5.01/5.39 [ ~( member( X, 'universal_class' ) ), =( 'member_of'( singleton( X ) )
% 5.01/5.39 , X ) ],
% 5.01/5.39 [ member( 'member_of1'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 5.01/5.39 ) ],
% 5.01/5.39 [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'( X ), X ) ]
% 5.01/5.39 ,
% 5.01/5.39 [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 5.01/5.39 'universal_class' ) ],
% 5.01/5.39 [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y, X ) ), =(
% 5.01/5.39 'member_of'( X ), Y ) ],
% 5.01/5.39 [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ],
% 5.01/5.39 [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' ), =( singleton(
% 5.01/5.39 Y ), X ) ],
% 5.01/5.39 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 5.01/5.39 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 5.01/5.39 intersection( complement( singleton( 'not_subclass_element'( X,
% 5.01/5.39 'null_class' ) ) ), X ) ), =( singleton( 'not_subclass_element'( X,
% 5.01/5.39 'null_class' ) ), X ), =( X, 'null_class' ) ],
% 5.01/5.39 [ ~( member( 'not_subclass_element'( intersection( complement( singleton(
% 5.01/5.39 'not_subclass_element'( x, 'null_class' ) ) ), x ), 'null_class' ), x ) )
% 5.01/5.39 ],
% 5.01/5.39 [ ~( =( singleton( 'not_subclass_element'( x, 'null_class' ) ), x ) ) ]
% 5.01/5.39 ,
% 5.01/5.39 [ ~( =( x, 'null_class' ) ) ]
% 5.01/5.39 ] .
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 percentage equality = 0.287197, percentage horn = 0.840278
% 5.01/5.39 This is a problem with some equality
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 Options Used:
% 5.01/5.39
% 5.01/5.39 useres = 1
% 5.01/5.39 useparamod = 1
% 5.01/5.39 useeqrefl = 1
% 5.01/5.39 useeqfact = 1
% 5.01/5.39 usefactor = 1
% 5.01/5.39 usesimpsplitting = 0
% 5.01/5.39 usesimpdemod = 5
% 5.01/5.39 usesimpres = 3
% 5.01/5.39
% 5.01/5.39 resimpinuse = 1000
% 5.01/5.39 resimpclauses = 20000
% 5.01/5.39 substype = eqrewr
% 5.01/5.39 backwardsubs = 1
% 5.01/5.39 selectoldest = 5
% 5.01/5.39
% 5.01/5.39 litorderings [0] = split
% 5.01/5.39 litorderings [1] = extend the termordering, first sorting on arguments
% 5.01/5.39
% 5.01/5.39 termordering = kbo
% 5.01/5.39
% 5.01/5.39 litapriori = 0
% 5.01/5.39 termapriori = 1
% 5.01/5.39 litaposteriori = 0
% 5.01/5.39 termaposteriori = 0
% 5.01/5.39 demodaposteriori = 0
% 5.01/5.39 ordereqreflfact = 0
% 5.01/5.39
% 5.01/5.39 litselect = negord
% 5.01/5.39
% 5.01/5.39 maxweight = 15
% 5.01/5.39 maxdepth = 30000
% 5.01/5.39 maxlength = 115
% 5.01/5.39 maxnrvars = 195
% 5.01/5.39 excuselevel = 1
% 5.01/5.39 increasemaxweight = 1
% 5.01/5.39
% 5.01/5.39 maxselected = 10000000
% 5.01/5.39 maxnrclauses = 10000000
% 5.01/5.39
% 5.01/5.39 showgenerated = 0
% 5.01/5.39 showkept = 0
% 5.01/5.39 showselected = 0
% 5.01/5.39 showdeleted = 0
% 5.01/5.39 showresimp = 1
% 5.01/5.39 showstatus = 2000
% 5.01/5.39
% 5.01/5.39 prologoutput = 1
% 5.01/5.39 nrgoals = 5000000
% 5.01/5.39 totalproof = 1
% 5.01/5.39
% 5.01/5.39 Symbols occurring in the translation:
% 5.01/5.39
% 5.01/5.39 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 5.01/5.39 . [1, 2] (w:1, o:57, a:1, s:1, b:0),
% 5.01/5.39 ! [4, 1] (w:0, o:30, a:1, s:1, b:0),
% 5.01/5.39 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.01/5.39 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.01/5.39 subclass [41, 2] (w:1, o:82, a:1, s:1, b:0),
% 5.01/5.39 member [43, 2] (w:1, o:83, a:1, s:1, b:0),
% 5.01/5.39 'not_subclass_element' [44, 2] (w:1, o:84, a:1, s:1, b:0),
% 5.01/5.39 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 5.01/5.39 'unordered_pair' [46, 2] (w:1, o:85, a:1, s:1, b:0),
% 5.01/5.39 singleton [47, 1] (w:1, o:38, a:1, s:1, b:0),
% 5.01/5.39 'ordered_pair' [48, 2] (w:1, o:86, a:1, s:1, b:0),
% 5.01/5.39 'cross_product' [50, 2] (w:1, o:87, a:1, s:1, b:0),
% 5.01/5.39 first [52, 1] (w:1, o:39, a:1, s:1, b:0),
% 5.01/5.39 second [53, 1] (w:1, o:40, a:1, s:1, b:0),
% 5.01/5.39 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 5.01/5.39 intersection [55, 2] (w:1, o:89, a:1, s:1, b:0),
% 5.01/5.39 complement [56, 1] (w:1, o:41, a:1, s:1, b:0),
% 5.01/5.39 union [57, 2] (w:1, o:90, a:1, s:1, b:0),
% 5.01/5.39 'symmetric_difference' [58, 2] (w:1, o:91, a:1, s:1, b:0),
% 5.01/5.39 restrict [60, 3] (w:1, o:94, a:1, s:1, b:0),
% 5.01/5.39 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 5.01/5.39 'domain_of' [62, 1] (w:1, o:43, a:1, s:1, b:0),
% 5.01/5.39 rotate [63, 1] (w:1, o:35, a:1, s:1, b:0),
% 5.01/5.39 flip [65, 1] (w:1, o:44, a:1, s:1, b:0),
% 5.01/5.39 inverse [66, 1] (w:1, o:45, a:1, s:1, b:0),
% 5.01/5.39 'range_of' [67, 1] (w:1, o:36, a:1, s:1, b:0),
% 5.01/5.39 domain [68, 3] (w:1, o:96, a:1, s:1, b:0),
% 5.01/5.39 range [69, 3] (w:1, o:97, a:1, s:1, b:0),
% 5.01/5.39 image [70, 2] (w:1, o:88, a:1, s:1, b:0),
% 5.01/5.39 successor [71, 1] (w:1, o:46, a:1, s:1, b:0),
% 5.01/5.39 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 5.01/5.39 inductive [73, 1] (w:1, o:47, a:1, s:1, b:0),
% 5.01/5.39 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 5.01/5.39 'sum_class' [75, 1] (w:1, o:48, a:1, s:1, b:0),
% 5.01/5.39 'power_class' [76, 1] (w:1, o:51, a:1, s:1, b:0),
% 5.01/5.39 compose [78, 2] (w:1, o:92, a:1, s:1, b:0),
% 5.01/5.39 'single_valued_class' [79, 1] (w:1, o:52, a:1, s:1, b:0),
% 5.01/5.39 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 5.01/5.39 function [82, 1] (w:1, o:53, a:1, s:1, b:0),
% 5.01/5.39 regular [83, 1] (w:1, o:37, a:1, s:1, b:0),
% 5.01/5.39 apply [84, 2] (w:1, o:93, a:1, s:1, b:0),
% 5.01/5.39 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 5.01/5.39 'one_to_one' [86, 1] (w:1, o:49, a:1, s:1, b:0),
% 5.01/5.39 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 5.01/5.39 diagonalise [88, 1] (w:1, o:54, a:1, s:1, b:0),
% 5.01/5.39 cantor [89, 1] (w:1, o:42, a:1, s:1, b:0),
% 5.01/5.39 operation [90, 1] (w:1, o:50, a:1, s:1, b:0),
% 5.01/5.39 compatible [94, 3] (w:1, o:95, a:1, s:1, b:0),
% 5.01/5.39 homomorphism [95, 3] (w:1, o:98, a:1, s:1, b:0),
% 5.01/5.39 'not_homomorphism1' [96, 3] (w:1, o:99, a:1, s:1, b:0),
% 5.01/5.39 'not_homomorphism2' [97, 3] (w:1, o:100, a:1, s:1, b:0),
% 5.01/5.39 'member_of' [98, 1] (w:1, o:55, a:1, s:1, b:0),
% 5.01/5.39 'member_of1' [99, 1] (w:1, o:56, a:1, s:1, b:0),
% 5.01/5.39 x [100, 0] (w:1, o:29, a:1, s:1, b:0).
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 Starting Search:
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 Intermediate Status:
% 5.01/5.39 Generated: 4054
% 5.01/5.39 Kept: 2010
% 5.01/5.39 Inuse: 120
% 5.01/5.39 Deleted: 5
% 5.01/5.39 Deletedinuse: 2
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 Intermediate Status:
% 5.01/5.39 Generated: 10082
% 5.01/5.39 Kept: 4117
% 5.01/5.39 Inuse: 198
% 5.01/5.39 Deleted: 7
% 5.01/5.39 Deletedinuse: 4
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 Intermediate Status:
% 5.01/5.39 Generated: 15421
% 5.01/5.39 Kept: 6127
% 5.01/5.39 Inuse: 274
% 5.01/5.39 Deleted: 65
% 5.01/5.39 Deletedinuse: 45
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 Intermediate Status:
% 5.01/5.39 Generated: 21167
% 5.01/5.39 Kept: 8131
% 5.01/5.39 Inuse: 352
% 5.01/5.39 Deleted: 72
% 5.01/5.39 Deletedinuse: 49
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 Intermediate Status:
% 5.01/5.39 Generated: 27176
% 5.01/5.39 Kept: 10205
% 5.01/5.39 Inuse: 388
% 5.01/5.39 Deleted: 83
% 5.01/5.39 Deletedinuse: 60
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 Intermediate Status:
% 5.01/5.39 Generated: 37282
% 5.01/5.39 Kept: 12577
% 5.01/5.39 Inuse: 437
% 5.01/5.39 Deleted: 85
% 5.01/5.39 Deletedinuse: 61
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 Intermediate Status:
% 5.01/5.39 Generated: 47284
% 5.01/5.39 Kept: 16263
% 5.01/5.39 Inuse: 481
% 5.01/5.39 Deleted: 88
% 5.01/5.39 Deletedinuse: 63
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 Intermediate Status:
% 5.01/5.39 Generated: 61205
% 5.01/5.39 Kept: 20180
% 5.01/5.39 Inuse: 496
% 5.01/5.39 Deleted: 91
% 5.01/5.39 Deletedinuse: 66
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39 Resimplifying clauses:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 Intermediate Status:
% 5.01/5.39 Generated: 71207
% 5.01/5.39 Kept: 22387
% 5.01/5.39 Inuse: 534
% 5.01/5.39 Deleted: 1643
% 5.01/5.39 Deletedinuse: 78
% 5.01/5.39
% 5.01/5.39 Resimplifying inuse:
% 5.01/5.39 Done
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 Bliksems!, er is een bewijs:
% 5.01/5.39 % SZS status Unsatisfiable
% 5.01/5.39 % SZS output start Refutation
% 5.01/5.39
% 5.01/5.39 clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 5.01/5.39 .
% 5.01/5.39 clause( 137, [ member( 'not_subclass_element'( intersection( complement(
% 5.01/5.39 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 5.01/5.39 'null_class' ), intersection( complement( singleton(
% 5.01/5.39 'not_subclass_element'( X, 'null_class' ) ) ), X ) ), =( singleton(
% 5.01/5.39 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 5.01/5.39 )
% 5.01/5.39 .
% 5.01/5.39 clause( 138, [ ~( member( 'not_subclass_element'( intersection( complement(
% 5.01/5.39 singleton( 'not_subclass_element'( x, 'null_class' ) ) ), x ),
% 5.01/5.39 'null_class' ), x ) ) ] )
% 5.01/5.39 .
% 5.01/5.39 clause( 139, [ ~( =( singleton( 'not_subclass_element'( x, 'null_class' ) )
% 5.01/5.39 , x ) ) ] )
% 5.01/5.39 .
% 5.01/5.39 clause( 140, [ ~( =( x, 'null_class' ) ) ] )
% 5.01/5.39 .
% 5.01/5.39 clause( 22515, [ ~( member( 'not_subclass_element'( intersection(
% 5.01/5.39 complement( singleton( 'not_subclass_element'( x, 'null_class' ) ) ), x )
% 5.01/5.39 , 'null_class' ), intersection( X, x ) ) ) ] )
% 5.01/5.39 .
% 5.01/5.39 clause( 22739, [ =( x, 'null_class' ) ] )
% 5.01/5.39 .
% 5.01/5.39 clause( 22785, [] )
% 5.01/5.39 .
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 % SZS output end Refutation
% 5.01/5.39 found a proof!
% 5.01/5.39
% 5.01/5.39 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 5.01/5.39
% 5.01/5.39 initialclauses(
% 5.01/5.39 [ clause( 22787, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 5.01/5.39 ) ] )
% 5.01/5.39 , clause( 22788, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 5.01/5.39 , Y ) ] )
% 5.01/5.39 , clause( 22789, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 5.01/5.39 subclass( X, Y ) ] )
% 5.01/5.39 , clause( 22790, [ subclass( X, 'universal_class' ) ] )
% 5.01/5.39 , clause( 22791, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 5.01/5.39 , clause( 22792, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 5.01/5.39 , clause( 22793, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 5.01/5.39 ] )
% 5.01/5.39 , clause( 22794, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 5.01/5.39 =( X, Z ) ] )
% 5.01/5.39 , clause( 22795, [ ~( member( X, 'universal_class' ) ), member( X,
% 5.01/5.39 'unordered_pair'( X, Y ) ) ] )
% 5.01/5.39 , clause( 22796, [ ~( member( X, 'universal_class' ) ), member( X,
% 5.01/5.39 'unordered_pair'( Y, X ) ) ] )
% 5.01/5.39 , clause( 22797, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 5.01/5.39 )
% 5.01/5.39 , clause( 22798, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 5.01/5.39 , clause( 22799, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 5.01/5.39 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 5.01/5.39 , clause( 22800, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 5.01/5.39 ) ) ), member( X, Z ) ] )
% 5.01/5.39 , clause( 22801, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 5.01/5.39 ) ) ), member( Y, T ) ] )
% 5.01/5.39 , clause( 22802, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 5.01/5.39 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 5.01/5.39 , clause( 22803, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 5.01/5.39 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 5.01/5.39 , clause( 22804, [ subclass( 'element_relation', 'cross_product'(
% 5.01/5.39 'universal_class', 'universal_class' ) ) ] )
% 5.01/5.39 , clause( 22805, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 5.01/5.39 ), member( X, Y ) ] )
% 5.01/5.39 , clause( 22806, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 5.01/5.39 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 5.01/5.39 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 5.01/5.39 , clause( 22807, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 5.01/5.39 )
% 5.01/5.39 , clause( 22808, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 5.01/5.39 )
% 5.01/5.39 , clause( 22809, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 5.01/5.39 intersection( Y, Z ) ) ] )
% 5.01/5.39 , clause( 22810, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 5.01/5.39 )
% 5.01/5.39 , clause( 22811, [ ~( member( X, 'universal_class' ) ), member( X,
% 5.01/5.39 complement( Y ) ), member( X, Y ) ] )
% 5.01/5.39 , clause( 22812, [ =( complement( intersection( complement( X ), complement(
% 5.01/5.39 Y ) ) ), union( X, Y ) ) ] )
% 5.01/5.39 , clause( 22813, [ =( intersection( complement( intersection( X, Y ) ),
% 5.01/5.39 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 5.01/5.39 'symmetric_difference'( X, Y ) ) ] )
% 5.01/5.39 , clause( 22814, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 5.01/5.39 X, Y, Z ) ) ] )
% 5.01/5.39 , clause( 22815, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 5.01/5.39 Z, X, Y ) ) ] )
% 5.01/5.39 , clause( 22816, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 5.01/5.39 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 5.01/5.39 , clause( 22817, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 5.01/5.39 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 5.01/5.39 'domain_of'( Y ) ) ] )
% 5.01/5.39 , clause( 22818, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 5.01/5.39 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 5.01/5.39 , clause( 22819, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 5.01/5.39 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 5.01/5.39 ] )
% 5.01/5.39 , clause( 22820, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 5.01/5.39 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 5.01/5.39 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 5.01/5.39 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 5.01/5.39 , Y ), rotate( T ) ) ] )
% 5.01/5.39 , clause( 22821, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 5.01/5.39 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 5.01/5.39 , clause( 22822, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 5.01/5.39 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 5.01/5.39 )
% 5.01/5.39 , clause( 22823, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 5.01/5.39 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 5.01/5.39 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 5.01/5.39 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 5.01/5.39 , Z ), flip( T ) ) ] )
% 5.01/5.39 , clause( 22824, [ =( 'domain_of'( flip( 'cross_product'( X,
% 5.01/5.39 'universal_class' ) ) ), inverse( X ) ) ] )
% 5.01/5.39 , clause( 22825, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 5.01/5.39 , clause( 22826, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 5.01/5.39 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 5.01/5.39 , clause( 22827, [ =( second( 'not_subclass_element'( restrict( X,
% 5.01/5.39 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 5.01/5.39 , clause( 22828, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 5.01/5.39 image( X, Y ) ) ] )
% 5.01/5.39 , clause( 22829, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 5.01/5.39 , clause( 22830, [ subclass( 'successor_relation', 'cross_product'(
% 5.01/5.39 'universal_class', 'universal_class' ) ) ] )
% 5.01/5.39 , clause( 22831, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 5.01/5.39 ) ), =( successor( X ), Y ) ] )
% 5.01/5.39 , clause( 22832, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 5.01/5.39 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 5.01/5.39 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 5.01/5.39 , clause( 22833, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 5.01/5.39 , clause( 22834, [ ~( inductive( X ) ), subclass( image(
% 5.01/5.39 'successor_relation', X ), X ) ] )
% 5.01/5.39 , clause( 22835, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 5.01/5.39 'successor_relation', X ), X ) ), inductive( X ) ] )
% 5.01/5.39 , clause( 22836, [ inductive( omega ) ] )
% 5.01/5.39 , clause( 22837, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 5.01/5.39 , clause( 22838, [ member( omega, 'universal_class' ) ] )
% 5.01/5.39 , clause( 22839, [ =( 'domain_of'( restrict( 'element_relation',
% 5.01/5.39 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 5.01/5.39 , clause( 22840, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 5.01/5.39 X ), 'universal_class' ) ] )
% 5.01/5.39 , clause( 22841, [ =( complement( image( 'element_relation', complement( X
% 5.01/5.39 ) ) ), 'power_class'( X ) ) ] )
% 5.01/5.39 , clause( 22842, [ ~( member( X, 'universal_class' ) ), member(
% 5.01/5.39 'power_class'( X ), 'universal_class' ) ] )
% 5.01/5.39 , clause( 22843, [ subclass( compose( X, Y ), 'cross_product'(
% 5.01/5.39 'universal_class', 'universal_class' ) ) ] )
% 5.01/5.39 , clause( 22844, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 5.01/5.39 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 5.01/5.39 , clause( 22845, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 5.01/5.39 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 5.01/5.39 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 5.01/5.39 ) ] )
% 5.01/5.39 , clause( 22846, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 5.01/5.39 inverse( X ) ), 'identity_relation' ) ] )
% 5.01/5.39 , clause( 22847, [ ~( subclass( compose( X, inverse( X ) ),
% 5.01/5.39 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 5.01/5.39 , clause( 22848, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 5.01/5.39 'universal_class', 'universal_class' ) ) ] )
% 5.01/5.39 , clause( 22849, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 5.01/5.39 , 'identity_relation' ) ] )
% 5.01/5.39 , clause( 22850, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 5.01/5.39 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 5.01/5.39 'identity_relation' ) ), function( X ) ] )
% 5.01/5.39 , clause( 22851, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 5.01/5.39 , member( image( X, Y ), 'universal_class' ) ] )
% 5.01/5.39 , clause( 22852, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 5.01/5.39 , clause( 22853, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 5.01/5.39 , 'null_class' ) ] )
% 5.01/5.39 , clause( 22854, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 5.01/5.39 Y ) ) ] )
% 5.01/5.39 , clause( 22855, [ function( choice ) ] )
% 5.01/5.39 , clause( 22856, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 5.01/5.39 ), member( apply( choice, X ), X ) ] )
% 5.01/5.39 , clause( 22857, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 5.01/5.39 , clause( 22858, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 5.01/5.39 , clause( 22859, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 5.01/5.39 'one_to_one'( X ) ] )
% 5.01/5.39 , clause( 22860, [ =( intersection( 'cross_product'( 'universal_class',
% 5.01/5.39 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 5.01/5.39 'universal_class' ), complement( compose( complement( 'element_relation'
% 5.01/5.39 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 5.01/5.39 , clause( 22861, [ =( intersection( inverse( 'subset_relation' ),
% 5.01/5.39 'subset_relation' ), 'identity_relation' ) ] )
% 5.01/5.39 , clause( 22862, [ =( complement( 'domain_of'( intersection( X,
% 5.01/5.39 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 5.01/5.39 , clause( 22863, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 5.01/5.39 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 5.01/5.39 , clause( 22864, [ ~( operation( X ) ), function( X ) ] )
% 5.01/5.39 , clause( 22865, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 5.01/5.39 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 5.01/5.39 ] )
% 5.01/5.39 , clause( 22866, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 5.01/5.39 'domain_of'( 'domain_of'( X ) ) ) ] )
% 5.01/5.39 , clause( 22867, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 5.01/5.39 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 5.01/5.39 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 5.01/5.39 operation( X ) ] )
% 5.01/5.39 , clause( 22868, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 5.01/5.39 , clause( 22869, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 5.01/5.39 Y ) ), 'domain_of'( X ) ) ] )
% 5.01/5.39 , clause( 22870, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 5.01/5.39 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 5.01/5.39 , clause( 22871, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 5.01/5.39 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 5.01/5.39 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 5.01/5.39 , clause( 22872, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 5.01/5.39 , clause( 22873, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 5.01/5.39 , clause( 22874, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 5.01/5.39 , clause( 22875, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 5.01/5.39 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 5.01/5.39 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 5.01/5.39 )
% 5.01/5.39 , clause( 22876, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 5.01/5.39 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 5.01/5.39 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 5.01/5.39 , Y ) ] )
% 5.01/5.39 , clause( 22877, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 5.01/5.39 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 5.01/5.39 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 5.01/5.39 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 5.01/5.39 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 5.01/5.39 )
% 5.01/5.39 , clause( 22878, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 5.01/5.39 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 5.01/5.39 , clause( 22879, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 5.01/5.39 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 5.01/5.39 , clause( 22880, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 5.01/5.39 ) ) ), member( X, 'universal_class' ) ] )
% 5.01/5.39 , clause( 22881, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 5.01/5.39 ) ) ), member( Y, 'universal_class' ) ] )
% 5.01/5.39 , clause( 22882, [ subclass( X, X ) ] )
% 5.01/5.39 , clause( 22883, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 5.01/5.39 X, Z ) ] )
% 5.01/5.39 , clause( 22884, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 5.01/5.39 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 5.01/5.39 , clause( 22885, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 5.01/5.39 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 5.01/5.39 , clause( 22886, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 5.01/5.39 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 5.01/5.39 , clause( 22887, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 5.01/5.39 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 5.01/5.39 , clause( 22888, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 5.01/5.39 )
% 5.01/5.39 , clause( 22889, [ ~( member( X, 'null_class' ) ) ] )
% 5.01/5.39 , clause( 22890, [ subclass( 'null_class', X ) ] )
% 5.01/5.39 , clause( 22891, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 5.01/5.39 )
% 5.01/5.39 , clause( 22892, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 5.01/5.39 , 'null_class' ), X ) ] )
% 5.01/5.39 , clause( 22893, [ member( 'null_class', 'universal_class' ) ] )
% 5.01/5.39 , clause( 22894, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 5.01/5.39 ] )
% 5.01/5.39 , clause( 22895, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 5.01/5.39 )
% 5.01/5.39 , clause( 22896, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 5.01/5.39 )
% 5.01/5.39 , clause( 22897, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 5.01/5.39 X ), singleton( Y ) ) ] )
% 5.01/5.39 , clause( 22898, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 5.01/5.39 Y ), singleton( Y ) ) ] )
% 5.01/5.39 , clause( 22899, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 5.01/5.39 'universal_class' ), member( Y, 'universal_class' ) ] )
% 5.01/5.39 , clause( 22900, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 5.01/5.39 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 5.01/5.39 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 5.01/5.39 , clause( 22901, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 5.01/5.39 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 5.01/5.39 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 5.01/5.39 , clause( 22902, [ ~( member( X, 'universal_class' ) ), ~( =(
% 5.01/5.39 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 5.01/5.39 , clause( 22903, [ ~( member( X, 'universal_class' ) ), ~( =(
% 5.01/5.39 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 5.01/5.39 , clause( 22904, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 5.01/5.39 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 5.01/5.39 , clause( 22905, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 5.01/5.39 'unordered_pair'( X, Z ), Y ) ] )
% 5.01/5.39 , clause( 22906, [ member( singleton( X ), 'universal_class' ) ] )
% 5.01/5.39 , clause( 22907, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 5.01/5.39 X ) ) ) ] )
% 5.01/5.39 , clause( 22908, [ ~( member( X, 'universal_class' ) ), member( X,
% 5.01/5.39 singleton( X ) ) ] )
% 5.01/5.39 , clause( 22909, [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X
% 5.01/5.39 ), 'null_class' ) ) ] )
% 5.01/5.39 , clause( 22910, [ member( 'null_class', singleton( 'null_class' ) ) ] )
% 5.01/5.39 , clause( 22911, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 5.01/5.39 , clause( 22912, [ member( X, 'universal_class' ), =( singleton( X ),
% 5.01/5.39 'null_class' ) ] )
% 5.01/5.39 , clause( 22913, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 5.01/5.39 'universal_class' ) ), =( X, Y ) ] )
% 5.01/5.39 , clause( 22914, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 5.01/5.39 'universal_class' ) ), =( X, Y ) ] )
% 5.01/5.39 , clause( 22915, [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~(
% 5.01/5.39 member( Z, 'universal_class' ) ), =( Z, X ), =( Z, Y ) ] )
% 5.01/5.39 , clause( 22916, [ ~( member( X, 'universal_class' ) ), member( 'member_of'(
% 5.01/5.39 singleton( X ) ), 'universal_class' ) ] )
% 5.01/5.39 , clause( 22917, [ ~( member( X, 'universal_class' ) ), =( singleton(
% 5.01/5.39 'member_of'( singleton( X ) ) ), singleton( X ) ) ] )
% 5.01/5.39 , clause( 22918, [ member( 'member_of'( X ), 'universal_class' ), =(
% 5.01/5.39 'member_of'( X ), X ) ] )
% 5.01/5.39 , clause( 22919, [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X
% 5.01/5.39 ), X ) ] )
% 5.01/5.39 , clause( 22920, [ ~( member( X, 'universal_class' ) ), =( 'member_of'(
% 5.01/5.39 singleton( X ) ), X ) ] )
% 5.01/5.39 , clause( 22921, [ member( 'member_of1'( X ), 'universal_class' ), =(
% 5.01/5.39 'member_of'( X ), X ) ] )
% 5.01/5.39 , clause( 22922, [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'(
% 5.01/5.39 X ), X ) ] )
% 5.01/5.39 , clause( 22923, [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 5.01/5.39 'universal_class' ) ] )
% 5.01/5.39 , clause( 22924, [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y
% 5.01/5.39 , X ) ), =( 'member_of'( X ), Y ) ] )
% 5.01/5.39 , clause( 22925, [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ] )
% 5.01/5.39 , clause( 22926, [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' )
% 5.01/5.39 , =( singleton( Y ), X ) ] )
% 5.01/5.39 , clause( 22927, [ member( 'not_subclass_element'( intersection( complement(
% 5.01/5.39 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 5.01/5.39 'null_class' ), intersection( complement( singleton(
% 5.01/5.39 'not_subclass_element'( X, 'null_class' ) ) ), X ) ), =( singleton(
% 5.01/5.39 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 5.01/5.39 )
% 5.01/5.39 , clause( 22928, [ ~( member( 'not_subclass_element'( intersection(
% 5.01/5.39 complement( singleton( 'not_subclass_element'( x, 'null_class' ) ) ), x )
% 5.01/5.39 , 'null_class' ), x ) ) ] )
% 5.01/5.39 , clause( 22929, [ ~( =( singleton( 'not_subclass_element'( x, 'null_class'
% 5.01/5.39 ) ), x ) ) ] )
% 5.01/5.39 , clause( 22930, [ ~( =( x, 'null_class' ) ) ] )
% 5.01/5.39 ] ).
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 subsumption(
% 5.01/5.39 clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ] )
% 5.01/5.39 , clause( 22808, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 5.01/5.39 )
% 5.01/5.39 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 5.01/5.39 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 subsumption(
% 5.01/5.39 clause( 137, [ member( 'not_subclass_element'( intersection( complement(
% 5.01/5.39 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 5.01/5.39 'null_class' ), intersection( complement( singleton(
% 5.01/5.39 'not_subclass_element'( X, 'null_class' ) ) ), X ) ), =( singleton(
% 5.01/5.39 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 5.01/5.39 )
% 5.01/5.39 , clause( 22927, [ member( 'not_subclass_element'( intersection( complement(
% 5.01/5.39 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 5.01/5.39 'null_class' ), intersection( complement( singleton(
% 5.01/5.39 'not_subclass_element'( X, 'null_class' ) ) ), X ) ), =( singleton(
% 5.01/5.39 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 5.01/5.39 )
% 5.01/5.39 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 5.01/5.39 1 ), ==>( 2, 2 )] ) ).
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 subsumption(
% 5.01/5.39 clause( 138, [ ~( member( 'not_subclass_element'( intersection( complement(
% 5.01/5.39 singleton( 'not_subclass_element'( x, 'null_class' ) ) ), x ),
% 5.01/5.39 'null_class' ), x ) ) ] )
% 5.01/5.39 , clause( 22928, [ ~( member( 'not_subclass_element'( intersection(
% 5.01/5.39 complement( singleton( 'not_subclass_element'( x, 'null_class' ) ) ), x )
% 5.01/5.39 , 'null_class' ), x ) ) ] )
% 5.01/5.39 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 subsumption(
% 5.01/5.39 clause( 139, [ ~( =( singleton( 'not_subclass_element'( x, 'null_class' ) )
% 5.01/5.39 , x ) ) ] )
% 5.01/5.39 , clause( 22929, [ ~( =( singleton( 'not_subclass_element'( x, 'null_class'
% 5.01/5.39 ) ), x ) ) ] )
% 5.01/5.39 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 subsumption(
% 5.01/5.39 clause( 140, [ ~( =( x, 'null_class' ) ) ] )
% 5.01/5.39 , clause( 22930, [ ~( =( x, 'null_class' ) ) ] )
% 5.01/5.39 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 resolution(
% 5.01/5.39 clause( 23394, [ ~( member( 'not_subclass_element'( intersection(
% 5.01/5.39 complement( singleton( 'not_subclass_element'( x, 'null_class' ) ) ), x )
% 5.01/5.39 , 'null_class' ), intersection( X, x ) ) ) ] )
% 5.01/5.39 , clause( 138, [ ~( member( 'not_subclass_element'( intersection(
% 5.01/5.39 complement( singleton( 'not_subclass_element'( x, 'null_class' ) ) ), x )
% 5.01/5.39 , 'null_class' ), x ) ) ] )
% 5.01/5.39 , 0, clause( 20, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 5.01/5.39 )
% 5.01/5.39 , 1, substitution( 0, [] ), substitution( 1, [ :=( X,
% 5.01/5.39 'not_subclass_element'( intersection( complement( singleton(
% 5.01/5.39 'not_subclass_element'( x, 'null_class' ) ) ), x ), 'null_class' ) ),
% 5.01/5.39 :=( Y, X ), :=( Z, x )] )).
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 subsumption(
% 5.01/5.39 clause( 22515, [ ~( member( 'not_subclass_element'( intersection(
% 5.01/5.39 complement( singleton( 'not_subclass_element'( x, 'null_class' ) ) ), x )
% 5.01/5.39 , 'null_class' ), intersection( X, x ) ) ) ] )
% 5.01/5.39 , clause( 23394, [ ~( member( 'not_subclass_element'( intersection(
% 5.01/5.39 complement( singleton( 'not_subclass_element'( x, 'null_class' ) ) ), x )
% 5.01/5.39 , 'null_class' ), intersection( X, x ) ) ) ] )
% 5.01/5.39 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 eqswap(
% 5.01/5.39 clause( 23395, [ ~( =( x, singleton( 'not_subclass_element'( x,
% 5.01/5.39 'null_class' ) ) ) ) ] )
% 5.01/5.39 , clause( 139, [ ~( =( singleton( 'not_subclass_element'( x, 'null_class' )
% 5.01/5.39 ), x ) ) ] )
% 5.01/5.39 , 0, substitution( 0, [] )).
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 eqswap(
% 5.01/5.39 clause( 23396, [ =( X, singleton( 'not_subclass_element'( X, 'null_class' )
% 5.01/5.39 ) ), member( 'not_subclass_element'( intersection( complement( singleton(
% 5.01/5.39 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 5.01/5.39 intersection( complement( singleton( 'not_subclass_element'( X,
% 5.01/5.39 'null_class' ) ) ), X ) ), =( X, 'null_class' ) ] )
% 5.01/5.39 , clause( 137, [ member( 'not_subclass_element'( intersection( complement(
% 5.01/5.39 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 5.01/5.39 'null_class' ), intersection( complement( singleton(
% 5.01/5.39 'not_subclass_element'( X, 'null_class' ) ) ), X ) ), =( singleton(
% 5.01/5.39 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 5.01/5.39 )
% 5.01/5.39 , 1, substitution( 0, [ :=( X, X )] )).
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 resolution(
% 5.01/5.39 clause( 23399, [ member( 'not_subclass_element'( intersection( complement(
% 5.01/5.39 singleton( 'not_subclass_element'( x, 'null_class' ) ) ), x ),
% 5.01/5.39 'null_class' ), intersection( complement( singleton(
% 5.01/5.39 'not_subclass_element'( x, 'null_class' ) ) ), x ) ), =( x, 'null_class'
% 5.01/5.39 ) ] )
% 5.01/5.39 , clause( 23395, [ ~( =( x, singleton( 'not_subclass_element'( x,
% 5.01/5.39 'null_class' ) ) ) ) ] )
% 5.01/5.39 , 0, clause( 23396, [ =( X, singleton( 'not_subclass_element'( X,
% 5.01/5.39 'null_class' ) ) ), member( 'not_subclass_element'( intersection(
% 5.01/5.39 complement( singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X )
% 5.01/5.39 , 'null_class' ), intersection( complement( singleton(
% 5.01/5.39 'not_subclass_element'( X, 'null_class' ) ) ), X ) ), =( X, 'null_class'
% 5.01/5.39 ) ] )
% 5.01/5.39 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, x )] )).
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 resolution(
% 5.01/5.39 clause( 23400, [ =( x, 'null_class' ) ] )
% 5.01/5.39 , clause( 22515, [ ~( member( 'not_subclass_element'( intersection(
% 5.01/5.39 complement( singleton( 'not_subclass_element'( x, 'null_class' ) ) ), x )
% 5.01/5.39 , 'null_class' ), intersection( X, x ) ) ) ] )
% 5.01/5.39 , 0, clause( 23399, [ member( 'not_subclass_element'( intersection(
% 5.01/5.39 complement( singleton( 'not_subclass_element'( x, 'null_class' ) ) ), x )
% 5.01/5.39 , 'null_class' ), intersection( complement( singleton(
% 5.01/5.39 'not_subclass_element'( x, 'null_class' ) ) ), x ) ), =( x, 'null_class'
% 5.01/5.39 ) ] )
% 5.01/5.39 , 0, substitution( 0, [ :=( X, complement( singleton(
% 5.01/5.39 'not_subclass_element'( x, 'null_class' ) ) ) )] ), substitution( 1, [] )
% 5.01/5.39 ).
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 subsumption(
% 5.01/5.39 clause( 22739, [ =( x, 'null_class' ) ] )
% 5.01/5.39 , clause( 23400, [ =( x, 'null_class' ) ] )
% 5.01/5.39 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 resolution(
% 5.01/5.39 clause( 23404, [] )
% 5.01/5.39 , clause( 140, [ ~( =( x, 'null_class' ) ) ] )
% 5.01/5.39 , 0, clause( 22739, [ =( x, 'null_class' ) ] )
% 5.01/5.39 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 subsumption(
% 5.01/5.39 clause( 22785, [] )
% 5.01/5.39 , clause( 23404, [] )
% 5.01/5.39 , substitution( 0, [] ), permutation( 0, [] ) ).
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 end.
% 5.01/5.39
% 5.01/5.39 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 5.01/5.39
% 5.01/5.39 Memory use:
% 5.01/5.39
% 5.01/5.39 space for terms: 404212
% 5.01/5.39 space for clauses: 1053180
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 clauses generated: 72292
% 5.01/5.39 clauses kept: 22786
% 5.01/5.39 clauses selected: 541
% 5.01/5.39 clauses deleted: 1647
% 5.01/5.39 clauses inuse deleted: 78
% 5.01/5.39
% 5.01/5.39 subsentry: 307032
% 5.01/5.39 literals s-matched: 236718
% 5.01/5.39 literals matched: 228264
% 5.01/5.39 full subsumption: 139690
% 5.01/5.39
% 5.01/5.39 checksum: -1519786106
% 5.01/5.39
% 5.01/5.39
% 5.01/5.39 Bliksem ended
%------------------------------------------------------------------------------