TSTP Solution File: SET103-7 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET103-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.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 22:47:09 EDT 2022
% Result : Unsatisfiable 4.66s 5.08s
% Output : Refutation 4.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET103-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Mon Jul 11 09:16:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.71/1.09 *** allocated 10000 integers for termspace/termends
% 0.71/1.09 *** allocated 10000 integers for clauses
% 0.71/1.09 *** allocated 10000 integers for justifications
% 0.71/1.09 Bliksem 1.12
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 Automatic Strategy Selection
% 0.71/1.09
% 0.71/1.09 Clauses:
% 0.71/1.09 [
% 0.71/1.09 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.71/1.09 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.71/1.09 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.71/1.09 ,
% 0.71/1.09 [ subclass( X, 'universal_class' ) ],
% 0.71/1.09 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.71/1.09 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.71/1.09 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.71/1.09 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.71/1.09 ,
% 0.71/1.09 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.71/1.09 ) ) ],
% 0.71/1.09 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.71/1.09 ) ) ],
% 0.71/1.09 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.71/1.09 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.71/1.09 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.71/1.09 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.71/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.71/1.09 X, Z ) ],
% 0.71/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.71/1.09 Y, T ) ],
% 0.71/1.09 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.71/1.09 ), 'cross_product'( Y, T ) ) ],
% 0.71/1.09 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.71/1.09 ), second( X ) ), X ) ],
% 0.71/1.09 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.71/1.09 'universal_class' ) ) ],
% 0.71/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.71/1.09 Y ) ],
% 0.71/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.71/1.09 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.71/1.09 , Y ), 'element_relation' ) ],
% 0.71/1.09 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.71/1.09 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.71/1.09 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.71/1.09 Z ) ) ],
% 0.71/1.09 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.71/1.09 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.71/1.09 member( X, Y ) ],
% 0.71/1.09 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.71/1.09 union( X, Y ) ) ],
% 0.71/1.09 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.71/1.09 intersection( complement( X ), complement( Y ) ) ) ),
% 0.71/1.09 'symmetric_difference'( X, Y ) ) ],
% 0.71/1.09 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.71/1.09 ,
% 0.71/1.09 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.71/1.09 ,
% 0.71/1.09 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.71/1.09 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.71/1.09 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.71/1.09 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.71/1.09 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.71/1.09 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.71/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.71/1.09 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.71/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.71/1.09 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.71/1.09 'cross_product'( 'universal_class', 'universal_class' ),
% 0.71/1.09 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.71/1.09 Y ), rotate( T ) ) ],
% 0.71/1.09 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.71/1.09 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.71/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.71/1.09 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.71/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.71/1.09 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.71/1.09 'cross_product'( 'universal_class', 'universal_class' ),
% 0.71/1.09 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.71/1.09 Z ), flip( T ) ) ],
% 0.71/1.09 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.71/1.09 inverse( X ) ) ],
% 0.71/1.09 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.71/1.09 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.71/1.09 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.71/1.09 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.71/1.09 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.71/1.09 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.71/1.09 ],
% 0.71/1.09 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.71/1.09 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.71/1.09 'universal_class' ) ) ],
% 0.71/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.71/1.09 successor( X ), Y ) ],
% 0.71/1.09 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.71/1.09 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.71/1.09 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.71/1.09 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.71/1.09 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.71/1.09 ,
% 0.71/1.09 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.71/1.09 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.71/1.09 [ inductive( omega ) ],
% 0.71/1.09 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.71/1.09 [ member( omega, 'universal_class' ) ],
% 0.71/1.09 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.71/1.09 , 'sum_class'( X ) ) ],
% 0.71/1.09 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.71/1.09 'universal_class' ) ],
% 0.71/1.09 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.71/1.09 'power_class'( X ) ) ],
% 0.71/1.09 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.71/1.09 'universal_class' ) ],
% 0.71/1.09 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.71/1.09 'universal_class' ) ) ],
% 0.71/1.09 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.71/1.09 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.71/1.09 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.71/1.09 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.71/1.09 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.71/1.09 ) ],
% 0.71/1.09 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.71/1.09 , 'identity_relation' ) ],
% 0.71/1.09 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.71/1.09 'single_valued_class'( X ) ],
% 0.71/1.09 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.71/1.09 'universal_class' ) ) ],
% 0.71/1.09 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.71/1.09 'identity_relation' ) ],
% 0.71/1.09 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.71/1.09 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.71/1.09 , function( X ) ],
% 0.71/1.09 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.71/1.09 X, Y ), 'universal_class' ) ],
% 0.71/1.09 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.71/1.09 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.71/1.09 ) ],
% 0.71/1.09 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.71/1.09 [ function( choice ) ],
% 0.71/1.09 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.71/1.09 apply( choice, X ), X ) ],
% 0.71/1.09 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.71/1.09 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.71/1.09 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.71/1.09 ,
% 0.71/1.09 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.71/1.09 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.71/1.09 , complement( compose( complement( 'element_relation' ), inverse(
% 0.71/1.09 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.71/1.09 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.71/1.09 'identity_relation' ) ],
% 0.71/1.09 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.71/1.09 , diagonalise( X ) ) ],
% 0.71/1.09 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.71/1.09 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.71/1.09 [ ~( operation( X ) ), function( X ) ],
% 0.71/1.09 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.71/1.09 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.71/1.09 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.71/1.09 'domain_of'( X ) ) ) ],
% 0.71/1.09 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.71/1.09 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.71/1.09 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.71/1.09 X ) ],
% 0.71/1.09 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.71/1.09 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.71/1.09 'domain_of'( X ) ) ],
% 0.71/1.09 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.71/1.09 'domain_of'( Z ) ) ) ],
% 0.71/1.09 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.71/1.09 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.71/1.09 ), compatible( X, Y, Z ) ],
% 0.71/1.09 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.71/1.09 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.71/1.09 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.71/1.09 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.71/1.09 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.71/1.09 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.71/1.09 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.71/1.09 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.71/1.09 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.71/1.09 , Y ) ],
% 0.71/1.09 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.71/1.09 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.71/1.09 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.71/1.09 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.71/1.09 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.71/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.71/1.09 X, 'unordered_pair'( X, Y ) ) ],
% 0.71/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.71/1.09 Y, 'unordered_pair'( X, Y ) ) ],
% 0.71/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.71/1.09 X, 'universal_class' ) ],
% 0.71/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.71/1.09 Y, 'universal_class' ) ],
% 0.71/1.09 [ subclass( X, X ) ],
% 0.71/1.09 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.71/1.09 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.71/1.09 'not_subclass_element'( Y, X ), Y ) ],
% 0.71/1.09 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.71/1.09 'not_subclass_element'( Y, X ), Y ) ],
% 0.71/1.09 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.71/1.09 'not_subclass_element'( Y, X ), Y ) ],
% 0.71/1.09 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.71/1.09 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.71/1.09 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.71/1.09 [ ~( member( X, 'null_class' ) ) ],
% 0.71/1.09 [ subclass( 'null_class', X ) ],
% 0.71/1.09 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.71/1.09 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.71/1.09 ), X ) ],
% 0.71/1.09 [ member( 'null_class', 'universal_class' ) ],
% 0.71/1.09 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.71/1.09 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.71/1.09 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.71/1.09 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.71/1.09 Y ) ) ],
% 0.71/1.09 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.71/1.09 Y ) ) ],
% 0.71/1.09 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.71/1.09 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.71/1.09 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.71/1.09 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.71/1.09 'universal_class' ) ) ), =( Y, Z ) ],
% 0.71/1.09 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.71/1.09 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.71/1.09 'universal_class' ) ) ), =( X, Z ) ],
% 0.71/1.09 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.71/1.09 'null_class' ) ) ],
% 0.71/1.09 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.71/1.09 'null_class' ) ) ],
% 0.71/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.71/1.09 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 1.43/1.79 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 1.43/1.79 X, Z ), Y ) ],
% 1.43/1.79 [ member( singleton( X ), 'universal_class' ) ],
% 1.43/1.79 [ member( singleton( X ), 'unordered_pair'( Y, singleton( X ) ) ) ],
% 1.43/1.79 [ ~( member( X, 'universal_class' ) ), member( X, singleton( X ) ) ]
% 1.43/1.79 ,
% 1.43/1.79 [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X ),
% 1.43/1.79 'null_class' ) ) ],
% 1.43/1.79 [ member( 'null_class', singleton( 'null_class' ) ) ],
% 1.43/1.79 [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ],
% 1.43/1.79 [ member( X, 'universal_class' ), =( singleton( X ), 'null_class' ) ]
% 1.43/1.79 ,
% 1.43/1.79 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 1.43/1.79 'universal_class' ) ), =( X, Y ) ],
% 1.43/1.79 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 1.43/1.79 'universal_class' ) ), =( X, Y ) ],
% 1.43/1.79 [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~( member( Z,
% 1.43/1.79 'universal_class' ) ), =( Z, X ), =( Z, Y ) ],
% 1.43/1.79 [ ~( member( X, 'universal_class' ) ), member( 'member_of'( singleton( X
% 1.43/1.79 ) ), 'universal_class' ) ],
% 1.43/1.79 [ ~( member( X, 'universal_class' ) ), =( singleton( 'member_of'(
% 1.43/1.79 singleton( X ) ) ), singleton( X ) ) ],
% 1.43/1.79 [ member( 'member_of'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 1.43/1.79 ) ],
% 1.43/1.79 [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X ), X ) ],
% 1.43/1.79 [ ~( member( X, 'universal_class' ) ), =( 'member_of'( singleton( X ) )
% 1.43/1.79 , X ) ],
% 1.43/1.79 [ member( 'member_of1'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 1.43/1.79 ) ],
% 1.43/1.79 [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'( X ), X ) ]
% 1.43/1.79 ,
% 1.43/1.79 [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 1.43/1.79 'universal_class' ) ],
% 1.43/1.79 [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y, X ) ), =(
% 1.43/1.79 'member_of'( X ), Y ) ],
% 1.43/1.79 [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ],
% 1.43/1.79 [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' ), =( singleton(
% 1.43/1.79 Y ), X ) ],
% 1.43/1.79 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 1.43/1.79 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 1.43/1.79 intersection( complement( singleton( 'not_subclass_element'( X,
% 1.43/1.79 'null_class' ) ) ), X ) ), =( singleton( 'not_subclass_element'( X,
% 1.43/1.79 'null_class' ) ), X ), =( X, 'null_class' ) ],
% 1.43/1.79 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 1.43/1.79 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ), X ),
% 1.43/1.79 =( singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 1.43/1.79 'null_class' ) ],
% 1.43/1.79 [ ~( =( 'not_subclass_element'( intersection( complement( singleton(
% 1.43/1.79 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 1.43/1.79 'not_subclass_element'( X, 'null_class' ) ) ), =( singleton(
% 1.43/1.79 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 1.43/1.79 ,
% 1.43/1.79 [ =( 'unordered_pair'( X, Y ), union( singleton( X ), singleton( Y ) ) )
% 1.43/1.79 ],
% 1.43/1.79 [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ],
% 1.43/1.79 [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ],
% 1.43/1.79 [ member( 'unordered_pair'( X, singleton( Y ) ), 'ordered_pair'( X, Y )
% 1.43/1.79 ) ],
% 1.43/1.79 [ ~( =( 'unordered_pair'( singleton( x ), 'unordered_pair'( x,
% 1.43/1.79 'null_class' ) ), 'ordered_pair'( x, y ) ) ) ],
% 1.43/1.79 [ ~( member( y, 'universal_class' ) ) ]
% 1.43/1.79 ] .
% 1.43/1.79
% 1.43/1.79
% 1.43/1.79 percentage equality = 0.295302, percentage horn = 0.832215
% 1.43/1.79 This is a problem with some equality
% 1.43/1.79
% 1.43/1.79
% 1.43/1.79
% 1.43/1.79 Options Used:
% 1.43/1.79
% 1.43/1.79 useres = 1
% 1.43/1.79 useparamod = 1
% 1.43/1.79 useeqrefl = 1
% 1.43/1.79 useeqfact = 1
% 1.43/1.79 usefactor = 1
% 1.43/1.79 usesimpsplitting = 0
% 1.43/1.79 usesimpdemod = 5
% 1.43/1.79 usesimpres = 3
% 1.43/1.79
% 1.43/1.79 resimpinuse = 1000
% 1.43/1.79 resimpclauses = 20000
% 1.43/1.79 substype = eqrewr
% 1.43/1.79 backwardsubs = 1
% 1.43/1.79 selectoldest = 5
% 1.43/1.79
% 1.43/1.79 litorderings [0] = split
% 1.43/1.79 litorderings [1] = extend the termordering, first sorting on arguments
% 1.43/1.79
% 1.43/1.79 termordering = kbo
% 1.43/1.79
% 1.43/1.79 litapriori = 0
% 1.43/1.79 termapriori = 1
% 1.43/1.79 litaposteriori = 0
% 1.43/1.79 termaposteriori = 0
% 1.43/1.79 demodaposteriori = 0
% 1.43/1.79 ordereqreflfact = 0
% 1.43/1.79
% 1.43/1.79 litselect = negord
% 1.43/1.79
% 1.43/1.79 maxweight = 15
% 1.43/1.79 maxdepth = 30000
% 1.43/1.79 maxlength = 115
% 1.43/1.79 maxnrvars = 195
% 1.43/1.79 excuselevel = 1
% 1.43/1.79 increasemaxweight = 1
% 1.43/1.79
% 1.43/1.79 maxselected = 10000000
% 1.43/1.79 maxnrclauses = 10000000
% 4.66/5.08
% 4.66/5.08 showgenerated = 0
% 4.66/5.08 showkept = 0
% 4.66/5.08 showselected = 0
% 4.66/5.08 showdeleted = 0
% 4.66/5.08 showresimp = 1
% 4.66/5.08 showstatus = 2000
% 4.66/5.08
% 4.66/5.08 prologoutput = 1
% 4.66/5.08 nrgoals = 5000000
% 4.66/5.08 totalproof = 1
% 4.66/5.08
% 4.66/5.08 Symbols occurring in the translation:
% 4.66/5.08
% 4.66/5.08 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 4.66/5.08 . [1, 2] (w:1, o:58, a:1, s:1, b:0),
% 4.66/5.08 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 4.66/5.08 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 4.66/5.08 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 4.66/5.08 subclass [41, 2] (w:1, o:83, a:1, s:1, b:0),
% 4.66/5.08 member [43, 2] (w:1, o:84, a:1, s:1, b:0),
% 4.66/5.08 'not_subclass_element' [44, 2] (w:1, o:85, a:1, s:1, b:0),
% 4.66/5.08 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 4.66/5.08 'unordered_pair' [46, 2] (w:1, o:86, a:1, s:1, b:0),
% 4.66/5.08 singleton [47, 1] (w:1, o:39, a:1, s:1, b:0),
% 4.66/5.08 'ordered_pair' [48, 2] (w:1, o:87, a:1, s:1, b:0),
% 4.66/5.08 'cross_product' [50, 2] (w:1, o:88, a:1, s:1, b:0),
% 4.66/5.08 first [52, 1] (w:1, o:40, a:1, s:1, b:0),
% 4.66/5.08 second [53, 1] (w:1, o:41, a:1, s:1, b:0),
% 4.66/5.08 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 4.66/5.08 intersection [55, 2] (w:1, o:90, a:1, s:1, b:0),
% 4.66/5.08 complement [56, 1] (w:1, o:42, a:1, s:1, b:0),
% 4.66/5.08 union [57, 2] (w:1, o:91, a:1, s:1, b:0),
% 4.66/5.08 'symmetric_difference' [58, 2] (w:1, o:92, a:1, s:1, b:0),
% 4.66/5.08 restrict [60, 3] (w:1, o:95, a:1, s:1, b:0),
% 4.66/5.08 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 4.66/5.08 'domain_of' [62, 1] (w:1, o:44, a:1, s:1, b:0),
% 4.66/5.08 rotate [63, 1] (w:1, o:36, a:1, s:1, b:0),
% 4.66/5.08 flip [65, 1] (w:1, o:45, a:1, s:1, b:0),
% 4.66/5.08 inverse [66, 1] (w:1, o:46, a:1, s:1, b:0),
% 4.66/5.08 'range_of' [67, 1] (w:1, o:37, a:1, s:1, b:0),
% 4.66/5.08 domain [68, 3] (w:1, o:97, a:1, s:1, b:0),
% 4.66/5.08 range [69, 3] (w:1, o:98, a:1, s:1, b:0),
% 4.66/5.08 image [70, 2] (w:1, o:89, a:1, s:1, b:0),
% 4.66/5.08 successor [71, 1] (w:1, o:47, a:1, s:1, b:0),
% 4.66/5.08 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 4.66/5.08 inductive [73, 1] (w:1, o:48, a:1, s:1, b:0),
% 4.66/5.08 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 4.66/5.08 'sum_class' [75, 1] (w:1, o:49, a:1, s:1, b:0),
% 4.66/5.08 'power_class' [76, 1] (w:1, o:52, a:1, s:1, b:0),
% 4.66/5.08 compose [78, 2] (w:1, o:93, a:1, s:1, b:0),
% 4.66/5.08 'single_valued_class' [79, 1] (w:1, o:53, a:1, s:1, b:0),
% 4.66/5.08 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 4.66/5.08 function [82, 1] (w:1, o:54, a:1, s:1, b:0),
% 4.66/5.08 regular [83, 1] (w:1, o:38, a:1, s:1, b:0),
% 4.66/5.08 apply [84, 2] (w:1, o:94, a:1, s:1, b:0),
% 4.66/5.08 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 4.66/5.08 'one_to_one' [86, 1] (w:1, o:50, a:1, s:1, b:0),
% 4.66/5.08 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 4.66/5.08 diagonalise [88, 1] (w:1, o:55, a:1, s:1, b:0),
% 4.66/5.08 cantor [89, 1] (w:1, o:43, a:1, s:1, b:0),
% 4.66/5.08 operation [90, 1] (w:1, o:51, a:1, s:1, b:0),
% 4.66/5.08 compatible [94, 3] (w:1, o:96, a:1, s:1, b:0),
% 4.66/5.08 homomorphism [95, 3] (w:1, o:99, a:1, s:1, b:0),
% 4.66/5.08 'not_homomorphism1' [96, 3] (w:1, o:100, a:1, s:1, b:0),
% 4.66/5.08 'not_homomorphism2' [97, 3] (w:1, o:101, a:1, s:1, b:0),
% 4.66/5.08 'member_of' [98, 1] (w:1, o:56, a:1, s:1, b:0),
% 4.66/5.08 'member_of1' [99, 1] (w:1, o:57, a:1, s:1, b:0),
% 4.66/5.08 x [100, 0] (w:1, o:29, a:1, s:1, b:0),
% 4.66/5.08 y [101, 0] (w:1, o:30, a:1, s:1, b:0).
% 4.66/5.08
% 4.66/5.08
% 4.66/5.08 Starting Search:
% 4.66/5.08
% 4.66/5.08 Resimplifying inuse:
% 4.66/5.08 Done
% 4.66/5.08
% 4.66/5.08
% 4.66/5.08 Intermediate Status:
% 4.66/5.08 Generated: 3955
% 4.66/5.08 Kept: 2009
% 4.66/5.08 Inuse: 122
% 4.66/5.08 Deleted: 3
% 4.66/5.08 Deletedinuse: 3
% 4.66/5.08
% 4.66/5.08 Resimplifying inuse:
% 4.66/5.08 Done
% 4.66/5.08
% 4.66/5.08 Resimplifying inuse:
% 4.66/5.08 Done
% 4.66/5.08
% 4.66/5.08
% 4.66/5.08 Intermediate Status:
% 4.66/5.08 Generated: 9336
% 4.66/5.08 Kept: 4027
% 4.66/5.08 Inuse: 201
% 4.66/5.08 Deleted: 8
% 4.66/5.08 Deletedinuse: 8
% 4.66/5.08
% 4.66/5.08 Resimplifying inuse:
% 4.66/5.08 Done
% 4.66/5.08
% 4.66/5.08 Resimplifying inuse:
% 4.66/5.08 Done
% 4.66/5.08
% 4.66/5.08
% 4.66/5.08 Intermediate Status:
% 4.66/5.08 Generated: 15255
% 4.66/5.08 Kept: 6322
% 4.66/5.08 Inuse: 285
% 4.66/5.08 Deleted: 12
% 4.66/5.08 Deletedinuse: 11
% 4.66/5.08
% 4.66/5.08 Resimplifying inuse:
% 4.66/5.08 Done
% 4.66/5.08
% 4.66/5.08 Resimplifying inuse:
% 4.66/5.08 Done
% 4.66/5.08
% 4.66/5.08
% 4.66/5.08 Intermediate Status:
% 4.66/5.08 Generated: 21160
% 4.66/5.08 Kept: 8357
% 4.66/5.08 Inuse: 343
% 4.66/5.08 Deleted: 62
% 4.66/5.08 Deletedinuse: 58
% 4.66/5.08
% 4.66/5.08 Resimplifying inuse:
% 4.66/5.08 Done
% 4.66/5.08
% 4.66/5.08 Resimplifying inuse:
% 4.66/5.08 Done
% 4.66/5.08
% 4.66/5.08
% 4.66/5.08 Intermediate Status:
% 4.66/5.08 Generated: 28770
% 4.66/5.08 Kept: 10783
% 4.66/5.08 Inuse: 395
% 4.66/5.08 Deleted: 79
% 4.66/5.08 Deletedinuse: 63
% 4.66/5.08
% 4.66/5.08 Resimplifying inuse:
% 4.66/5.08 Done
% 4.66/5.08
% 4.66/5.08 Resimplifying inuse:
% 4.66/5.08 Done
% 4.66/5.08
% 4.66/5.08
% 4.66/5.08 Intermediate Status:
% 4.66/5.08 Generated: 38184
% 4.66/5.08 Kept: 12808
% 4.66/5.08 Inuse: 444
% 4.66/5.08 Deleted: 81
% 4.66/5.08 Deletedinuse: 64
% 4.66/5.08
% 4.66/5.08 Resimplifying inuse:
% 4.66/5.08 Done
% 4.66/5.08
% 4.66/5.08 Resimplifying inuse:
% 4.66/5.08 Done
% 4.66/5.08
% 4.66/5.08
% 4.66/5.08 Intermediate Status:
% 4.66/5.08 Generated: 47894
% 4.66/5.08 Kept: 16564
% 4.66/5.08 Inuse: 488
% 4.66/5.08 Deleted: 93
% 4.66/5.08 Deletedinuse: 75
% 4.66/5.08
% 4.66/5.08 Resimplifying inuse:
% 4.66/5.08 Done
% 4.66/5.08
% 4.66/5.08 Resimplifying inuse:
% 4.66/5.08 Done
% 4.66/5.08
% 4.66/5.08
% 4.66/5.08 Intermediate Status:
% 4.66/5.08 Generated: 61687
% 4.66/5.08 Kept: 20404
% 4.66/5.08 Inuse: 503
% 4.66/5.08 Deleted: 97
% 4.66/5.08 Deletedinuse: 79
% 4.66/5.08
% 4.66/5.08 Resimplifying inuse:
% 4.66/5.08 Done
% 4.66/5.08
% 4.66/5.08 Resimplifying clauses:
% 4.66/5.08
% 4.66/5.08 Bliksems!, er is een bewijs:
% 4.66/5.08 % SZS status Unsatisfiable
% 4.66/5.08 % SZS output start Refutation
% 4.66/5.08
% 4.66/5.08 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 4.66/5.08 )
% 4.66/5.08 .
% 4.66/5.08 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 4.66/5.08 .
% 4.66/5.08 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 4.66/5.08 .
% 4.66/5.08 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 4.66/5.08 .
% 4.66/5.08 clause( 11, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 4.66/5.08 singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 4.66/5.08 .
% 4.66/5.08 clause( 103, [ =( X, 'null_class' ), member( 'not_subclass_element'( X,
% 4.66/5.08 'null_class' ), X ) ] )
% 4.66/5.08 .
% 4.66/5.08 clause( 122, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 4.66/5.08 .
% 4.66/5.08 clause( 144, [ ~( =( 'unordered_pair'( singleton( x ), 'unordered_pair'( x
% 4.66/5.08 , 'null_class' ) ), 'ordered_pair'( x, y ) ) ) ] )
% 4.66/5.08 .
% 4.66/5.08 clause( 145, [ ~( member( y, 'universal_class' ) ) ] )
% 4.66/5.08 .
% 4.66/5.08 clause( 163, [ ~( member( y, X ) ) ] )
% 4.66/5.08 .
% 4.66/5.08 clause( 182, [ =( X, Y ), ~( =( Y, X ) ) ] )
% 4.66/5.08 .
% 4.66/5.08 clause( 528, [ ~( member( X, Y ) ), ~( =( X, y ) ) ] )
% 4.66/5.08 .
% 4.66/5.08 clause( 14838, [ ~( member( X, singleton( y ) ) ), ~( member( X, Y ) ) ] )
% 4.66/5.08 .
% 4.66/5.08 clause( 16563, [ ~( member( X, singleton( y ) ) ) ] )
% 4.66/5.08 .
% 4.66/5.08 clause( 16564, [ =( singleton( y ), 'null_class' ) ] )
% 4.66/5.08 .
% 4.66/5.08 clause( 16586, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 4.66/5.08 'null_class' ) ), 'ordered_pair'( X, y ) ) ] )
% 4.66/5.08 .
% 4.66/5.08 clause( 20500, [] )
% 4.66/5.08 .
% 4.66/5.08
% 4.66/5.08
% 4.66/5.08 % SZS output end Refutation
% 4.66/5.08 found a proof!
% 4.66/5.08
% 4.66/5.08 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 4.66/5.08
% 4.66/5.08 initialclauses(
% 4.66/5.08 [ clause( 20502, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 4.66/5.08 ) ] )
% 4.66/5.08 , clause( 20503, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 4.66/5.08 , Y ) ] )
% 4.66/5.08 , clause( 20504, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 4.66/5.08 subclass( X, Y ) ] )
% 4.66/5.08 , clause( 20505, [ subclass( X, 'universal_class' ) ] )
% 4.66/5.08 , clause( 20506, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 4.66/5.08 , clause( 20507, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 4.66/5.08 , clause( 20508, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 4.66/5.08 ] )
% 4.66/5.08 , clause( 20509, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 4.66/5.08 =( X, Z ) ] )
% 4.66/5.08 , clause( 20510, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.66/5.08 'unordered_pair'( X, Y ) ) ] )
% 4.66/5.08 , clause( 20511, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.66/5.08 'unordered_pair'( Y, X ) ) ] )
% 4.66/5.08 , clause( 20512, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 4.66/5.08 )
% 4.66/5.08 , clause( 20513, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 4.66/5.08 , clause( 20514, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 4.66/5.08 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 4.66/5.08 , clause( 20515, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.66/5.08 ) ) ), member( X, Z ) ] )
% 4.66/5.08 , clause( 20516, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.66/5.08 ) ) ), member( Y, T ) ] )
% 4.66/5.08 , clause( 20517, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 4.66/5.08 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 4.66/5.08 , clause( 20518, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 4.66/5.08 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 4.66/5.08 , clause( 20519, [ subclass( 'element_relation', 'cross_product'(
% 4.66/5.08 'universal_class', 'universal_class' ) ) ] )
% 4.66/5.08 , clause( 20520, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 4.66/5.08 ), member( X, Y ) ] )
% 4.66/5.08 , clause( 20521, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 4.66/5.08 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 4.66/5.08 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 4.66/5.08 , clause( 20522, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 4.66/5.08 )
% 4.66/5.08 , clause( 20523, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 4.66/5.08 )
% 4.66/5.08 , clause( 20524, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 4.66/5.08 intersection( Y, Z ) ) ] )
% 4.66/5.08 , clause( 20525, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 4.66/5.08 )
% 4.66/5.08 , clause( 20526, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.66/5.08 complement( Y ) ), member( X, Y ) ] )
% 4.66/5.08 , clause( 20527, [ =( complement( intersection( complement( X ), complement(
% 4.66/5.08 Y ) ) ), union( X, Y ) ) ] )
% 4.66/5.08 , clause( 20528, [ =( intersection( complement( intersection( X, Y ) ),
% 4.66/5.08 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 4.66/5.08 'symmetric_difference'( X, Y ) ) ] )
% 4.66/5.08 , clause( 20529, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 4.66/5.08 X, Y, Z ) ) ] )
% 4.66/5.08 , clause( 20530, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 4.66/5.08 Z, X, Y ) ) ] )
% 4.66/5.08 , clause( 20531, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 4.66/5.08 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 4.66/5.08 , clause( 20532, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 4.66/5.08 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 4.66/5.08 'domain_of'( Y ) ) ] )
% 4.66/5.08 , clause( 20533, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 4.66/5.08 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 4.66/5.08 , clause( 20534, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 4.66/5.08 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 4.66/5.08 ] )
% 4.66/5.08 , clause( 20535, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 4.66/5.08 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 4.66/5.08 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 4.66/5.08 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 4.66/5.08 , Y ), rotate( T ) ) ] )
% 4.66/5.08 , clause( 20536, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 4.66/5.08 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 4.66/5.08 , clause( 20537, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 4.66/5.08 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 4.66/5.08 )
% 4.66/5.08 , clause( 20538, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 4.66/5.08 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 4.66/5.08 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 4.66/5.08 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 4.66/5.08 , Z ), flip( T ) ) ] )
% 4.66/5.08 , clause( 20539, [ =( 'domain_of'( flip( 'cross_product'( X,
% 4.66/5.08 'universal_class' ) ) ), inverse( X ) ) ] )
% 4.66/5.08 , clause( 20540, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 4.66/5.08 , clause( 20541, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 4.66/5.08 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 4.66/5.08 , clause( 20542, [ =( second( 'not_subclass_element'( restrict( X,
% 4.66/5.08 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 4.66/5.08 , clause( 20543, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 4.66/5.08 image( X, Y ) ) ] )
% 4.66/5.08 , clause( 20544, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 4.66/5.08 , clause( 20545, [ subclass( 'successor_relation', 'cross_product'(
% 4.66/5.08 'universal_class', 'universal_class' ) ) ] )
% 4.66/5.08 , clause( 20546, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 4.66/5.08 ) ), =( successor( X ), Y ) ] )
% 4.66/5.08 , clause( 20547, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 4.66/5.08 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 4.66/5.08 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 4.66/5.08 , clause( 20548, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 4.66/5.08 , clause( 20549, [ ~( inductive( X ) ), subclass( image(
% 4.66/5.08 'successor_relation', X ), X ) ] )
% 4.66/5.08 , clause( 20550, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 4.66/5.08 'successor_relation', X ), X ) ), inductive( X ) ] )
% 4.66/5.08 , clause( 20551, [ inductive( omega ) ] )
% 4.66/5.08 , clause( 20552, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 4.66/5.08 , clause( 20553, [ member( omega, 'universal_class' ) ] )
% 4.66/5.08 , clause( 20554, [ =( 'domain_of'( restrict( 'element_relation',
% 4.66/5.08 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 4.66/5.08 , clause( 20555, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 4.66/5.08 X ), 'universal_class' ) ] )
% 4.66/5.08 , clause( 20556, [ =( complement( image( 'element_relation', complement( X
% 4.66/5.08 ) ) ), 'power_class'( X ) ) ] )
% 4.66/5.08 , clause( 20557, [ ~( member( X, 'universal_class' ) ), member(
% 4.66/5.08 'power_class'( X ), 'universal_class' ) ] )
% 4.66/5.08 , clause( 20558, [ subclass( compose( X, Y ), 'cross_product'(
% 4.66/5.08 'universal_class', 'universal_class' ) ) ] )
% 4.66/5.08 , clause( 20559, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 4.66/5.08 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 4.66/5.08 , clause( 20560, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 4.66/5.08 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 4.66/5.08 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 4.66/5.08 ) ] )
% 4.66/5.08 , clause( 20561, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 4.66/5.08 inverse( X ) ), 'identity_relation' ) ] )
% 4.66/5.08 , clause( 20562, [ ~( subclass( compose( X, inverse( X ) ),
% 4.66/5.08 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 4.66/5.08 , clause( 20563, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 4.66/5.08 'universal_class', 'universal_class' ) ) ] )
% 4.66/5.08 , clause( 20564, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 4.66/5.08 , 'identity_relation' ) ] )
% 4.66/5.08 , clause( 20565, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 4.66/5.08 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 4.66/5.08 'identity_relation' ) ), function( X ) ] )
% 4.66/5.08 , clause( 20566, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 4.66/5.08 , member( image( X, Y ), 'universal_class' ) ] )
% 4.66/5.08 , clause( 20567, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 4.66/5.08 , clause( 20568, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 4.66/5.08 , 'null_class' ) ] )
% 4.66/5.08 , clause( 20569, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 4.66/5.08 Y ) ) ] )
% 4.66/5.08 , clause( 20570, [ function( choice ) ] )
% 4.66/5.08 , clause( 20571, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 4.66/5.08 ), member( apply( choice, X ), X ) ] )
% 4.66/5.08 , clause( 20572, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 4.66/5.08 , clause( 20573, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 4.66/5.08 , clause( 20574, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 4.66/5.08 'one_to_one'( X ) ] )
% 4.66/5.08 , clause( 20575, [ =( intersection( 'cross_product'( 'universal_class',
% 4.66/5.08 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 4.66/5.08 'universal_class' ), complement( compose( complement( 'element_relation'
% 4.66/5.08 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 4.66/5.08 , clause( 20576, [ =( intersection( inverse( 'subset_relation' ),
% 4.66/5.08 'subset_relation' ), 'identity_relation' ) ] )
% 4.66/5.08 , clause( 20577, [ =( complement( 'domain_of'( intersection( X,
% 4.66/5.08 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 4.66/5.08 , clause( 20578, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 4.66/5.08 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 4.66/5.08 , clause( 20579, [ ~( operation( X ) ), function( X ) ] )
% 4.66/5.08 , clause( 20580, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 4.66/5.08 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 4.66/5.08 ] )
% 4.66/5.08 , clause( 20581, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 4.66/5.08 'domain_of'( 'domain_of'( X ) ) ) ] )
% 4.66/5.08 , clause( 20582, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 4.66/5.08 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 4.66/5.08 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 4.66/5.08 operation( X ) ] )
% 4.66/5.08 , clause( 20583, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 4.66/5.08 , clause( 20584, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 4.66/5.08 Y ) ), 'domain_of'( X ) ) ] )
% 4.66/5.08 , clause( 20585, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 4.66/5.08 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 4.66/5.08 , clause( 20586, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 4.66/5.08 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 4.66/5.08 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 4.66/5.08 , clause( 20587, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 4.66/5.08 , clause( 20588, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 4.66/5.08 , clause( 20589, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 4.66/5.08 , clause( 20590, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 4.66/5.08 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 4.66/5.08 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 4.66/5.08 )
% 4.66/5.08 , clause( 20591, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 4.66/5.08 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 4.66/5.08 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 4.66/5.08 , Y ) ] )
% 4.66/5.08 , clause( 20592, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 4.66/5.08 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 4.66/5.08 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 4.66/5.08 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 4.66/5.08 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 4.66/5.08 )
% 4.66/5.08 , clause( 20593, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.66/5.08 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 4.66/5.08 , clause( 20594, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.66/5.08 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 4.66/5.08 , clause( 20595, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.66/5.08 ) ) ), member( X, 'universal_class' ) ] )
% 4.66/5.08 , clause( 20596, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.66/5.08 ) ) ), member( Y, 'universal_class' ) ] )
% 4.66/5.08 , clause( 20597, [ subclass( X, X ) ] )
% 4.66/5.08 , clause( 20598, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 4.66/5.08 X, Z ) ] )
% 4.66/5.08 , clause( 20599, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 4.66/5.08 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 4.66/5.08 , clause( 20600, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 4.66/5.08 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 4.66/5.08 , clause( 20601, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 4.66/5.08 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 4.66/5.08 , clause( 20602, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 4.66/5.08 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 4.66/5.08 , clause( 20603, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 4.66/5.08 )
% 4.66/5.08 , clause( 20604, [ ~( member( X, 'null_class' ) ) ] )
% 4.66/5.08 , clause( 20605, [ subclass( 'null_class', X ) ] )
% 4.66/5.08 , clause( 20606, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 4.66/5.08 )
% 4.66/5.08 , clause( 20607, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 4.66/5.08 , 'null_class' ), X ) ] )
% 4.66/5.08 , clause( 20608, [ member( 'null_class', 'universal_class' ) ] )
% 4.66/5.08 , clause( 20609, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 4.66/5.08 ] )
% 4.66/5.08 , clause( 20610, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 4.66/5.08 )
% 4.66/5.08 , clause( 20611, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 4.66/5.08 )
% 4.66/5.08 , clause( 20612, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 4.66/5.08 X ), singleton( Y ) ) ] )
% 4.66/5.08 , clause( 20613, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 4.66/5.08 Y ), singleton( Y ) ) ] )
% 4.66/5.08 , clause( 20614, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 4.66/5.08 'universal_class' ), member( Y, 'universal_class' ) ] )
% 4.66/5.08 , clause( 20615, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 4.66/5.08 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 4.66/5.08 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 4.66/5.08 , clause( 20616, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 4.66/5.08 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 4.66/5.08 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 4.66/5.08 , clause( 20617, [ ~( member( X, 'universal_class' ) ), ~( =(
% 4.66/5.08 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 4.66/5.08 , clause( 20618, [ ~( member( X, 'universal_class' ) ), ~( =(
% 4.66/5.08 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 4.66/5.08 , clause( 20619, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.66/5.08 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 4.66/5.08 , clause( 20620, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 4.66/5.08 'unordered_pair'( X, Z ), Y ) ] )
% 4.66/5.08 , clause( 20621, [ member( singleton( X ), 'universal_class' ) ] )
% 4.66/5.08 , clause( 20622, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 4.66/5.08 X ) ) ) ] )
% 4.66/5.08 , clause( 20623, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.66/5.08 singleton( X ) ) ] )
% 4.66/5.08 , clause( 20624, [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X
% 4.66/5.08 ), 'null_class' ) ) ] )
% 4.66/5.08 , clause( 20625, [ member( 'null_class', singleton( 'null_class' ) ) ] )
% 4.66/5.08 , clause( 20626, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 4.66/5.08 , clause( 20627, [ member( X, 'universal_class' ), =( singleton( X ),
% 4.66/5.08 'null_class' ) ] )
% 4.66/5.08 , clause( 20628, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 4.66/5.08 'universal_class' ) ), =( X, Y ) ] )
% 4.66/5.08 , clause( 20629, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 4.66/5.08 'universal_class' ) ), =( X, Y ) ] )
% 4.66/5.08 , clause( 20630, [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~(
% 4.66/5.08 member( Z, 'universal_class' ) ), =( Z, X ), =( Z, Y ) ] )
% 4.66/5.08 , clause( 20631, [ ~( member( X, 'universal_class' ) ), member( 'member_of'(
% 4.66/5.08 singleton( X ) ), 'universal_class' ) ] )
% 4.66/5.08 , clause( 20632, [ ~( member( X, 'universal_class' ) ), =( singleton(
% 4.66/5.08 'member_of'( singleton( X ) ) ), singleton( X ) ) ] )
% 4.66/5.08 , clause( 20633, [ member( 'member_of'( X ), 'universal_class' ), =(
% 4.66/5.08 'member_of'( X ), X ) ] )
% 4.66/5.08 , clause( 20634, [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X
% 4.66/5.08 ), X ) ] )
% 4.66/5.08 , clause( 20635, [ ~( member( X, 'universal_class' ) ), =( 'member_of'(
% 4.66/5.08 singleton( X ) ), X ) ] )
% 4.66/5.08 , clause( 20636, [ member( 'member_of1'( X ), 'universal_class' ), =(
% 4.66/5.08 'member_of'( X ), X ) ] )
% 4.66/5.08 , clause( 20637, [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'(
% 4.66/5.08 X ), X ) ] )
% 4.66/5.08 , clause( 20638, [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 4.66/5.08 'universal_class' ) ] )
% 4.66/5.08 , clause( 20639, [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y
% 4.66/5.08 , X ) ), =( 'member_of'( X ), Y ) ] )
% 4.66/5.08 , clause( 20640, [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ] )
% 4.66/5.08 , clause( 20641, [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' )
% 4.66/5.08 , =( singleton( Y ), X ) ] )
% 4.66/5.08 , clause( 20642, [ member( 'not_subclass_element'( intersection( complement(
% 4.66/5.08 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 4.66/5.08 'null_class' ), intersection( complement( singleton(
% 4.66/5.08 'not_subclass_element'( X, 'null_class' ) ) ), X ) ), =( singleton(
% 4.66/5.08 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 4.66/5.08 )
% 4.66/5.08 , clause( 20643, [ member( 'not_subclass_element'( intersection( complement(
% 4.66/5.08 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 4.66/5.08 'null_class' ), X ), =( singleton( 'not_subclass_element'( X,
% 4.66/5.08 'null_class' ) ), X ), =( X, 'null_class' ) ] )
% 4.66/5.08 , clause( 20644, [ ~( =( 'not_subclass_element'( intersection( complement(
% 4.66/5.08 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 4.66/5.08 'null_class' ), 'not_subclass_element'( X, 'null_class' ) ) ), =(
% 4.66/5.08 singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 4.66/5.08 'null_class' ) ] )
% 4.66/5.08 , clause( 20645, [ =( 'unordered_pair'( X, Y ), union( singleton( X ),
% 4.66/5.08 singleton( Y ) ) ) ] )
% 4.66/5.08 , clause( 20646, [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ] )
% 4.66/5.08 , clause( 20647, [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ] )
% 4.66/5.08 , clause( 20648, [ member( 'unordered_pair'( X, singleton( Y ) ),
% 4.66/5.08 'ordered_pair'( X, Y ) ) ] )
% 4.66/5.08 , clause( 20649, [ ~( =( 'unordered_pair'( singleton( x ), 'unordered_pair'(
% 4.66/5.08 x, 'null_class' ) ), 'ordered_pair'( x, y ) ) ) ] )
% 4.66/5.08 , clause( 20650, [ ~( member( y, 'universal_class' ) ) ] )
% 4.66/5.08 ] ).
% 4.66/5.08
% 4.66/5.08
% 4.66/5.08
% 4.66/5.08 subsumption(
% 4.66/5.08 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 4.66/5.08 )
% 4.66/5.08 , clause( 20502, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 4.66/5.08 ) ] )
% 4.66/5.08 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 4.66/5.08 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 4.66/5.08
% 4.66/5.08
% 4.66/5.08 subsumption(
% 4.66/5.08 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 4.66/5.08 , clause( 20505, [ subclass( X, 'universal_class' ) ] )
% 4.66/5.08 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.66/5.08
% 4.66/5.08
% 4.66/5.08 subsumption(
% 4.66/5.08 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 4.66/5.08 , clause( 20506, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 4.66/5.08 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 4.66/5.08 ), ==>( 1, 1 )] ) ).
% 4.66/5.08
% 4.66/5.08
% 4.66/5.08 subsumption(
% 4.66/5.08 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 4.66/5.08 , clause( 20508, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 4.66/5.08 ] )
% 4.66/5.08 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), peCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------