TSTP Solution File: SET120-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET120-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n027.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 22:47:23 EDT 2022
% Result : Unsatisfiable 6.69s 7.09s
% Output : Refutation 6.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET120-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.04/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n027.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Mon Jul 11 08:17:18 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.77/1.16 *** allocated 10000 integers for termspace/termends
% 0.77/1.16 *** allocated 10000 integers for clauses
% 0.77/1.16 *** allocated 10000 integers for justifications
% 0.77/1.16 Bliksem 1.12
% 0.77/1.16
% 0.77/1.16
% 0.77/1.16 Automatic Strategy Selection
% 0.77/1.16
% 0.77/1.16 Clauses:
% 0.77/1.16 [
% 0.77/1.16 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.77/1.16 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.77/1.16 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.77/1.16 ,
% 0.77/1.16 [ subclass( X, 'universal_class' ) ],
% 0.77/1.16 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.77/1.16 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.77/1.16 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.77/1.16 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.77/1.16 ,
% 0.77/1.16 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.77/1.16 ) ) ],
% 0.77/1.16 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.77/1.16 ) ) ],
% 0.77/1.16 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.77/1.16 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.77/1.16 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.77/1.16 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.77/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.77/1.16 X, Z ) ],
% 0.77/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.77/1.16 Y, T ) ],
% 0.77/1.16 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.77/1.16 ), 'cross_product'( Y, T ) ) ],
% 0.77/1.16 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.77/1.16 ), second( X ) ), X ) ],
% 0.77/1.16 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.77/1.16 'universal_class' ) ) ],
% 0.77/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.77/1.16 Y ) ],
% 0.77/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.77/1.16 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.77/1.16 , Y ), 'element_relation' ) ],
% 0.77/1.16 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.77/1.16 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.77/1.16 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.77/1.16 Z ) ) ],
% 0.77/1.16 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.77/1.16 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.77/1.16 member( X, Y ) ],
% 0.77/1.16 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.77/1.16 union( X, Y ) ) ],
% 0.77/1.16 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.77/1.16 intersection( complement( X ), complement( Y ) ) ) ),
% 0.77/1.16 'symmetric_difference'( X, Y ) ) ],
% 0.77/1.16 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.77/1.16 ,
% 0.77/1.16 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.77/1.16 ,
% 0.77/1.16 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.77/1.16 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.77/1.16 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.77/1.16 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.77/1.16 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.77/1.16 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.77/1.16 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.77/1.16 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.77/1.16 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.77/1.16 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.77/1.16 'cross_product'( 'universal_class', 'universal_class' ),
% 0.77/1.16 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.77/1.16 Y ), rotate( T ) ) ],
% 0.77/1.16 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.77/1.16 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.77/1.16 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.77/1.16 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.77/1.16 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.77/1.16 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.77/1.16 'cross_product'( 'universal_class', 'universal_class' ),
% 0.77/1.16 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.77/1.16 Z ), flip( T ) ) ],
% 0.77/1.16 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.77/1.16 inverse( X ) ) ],
% 0.77/1.16 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.77/1.16 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.77/1.16 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.77/1.16 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.77/1.16 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.77/1.16 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.77/1.16 ],
% 0.77/1.16 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.77/1.16 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.77/1.16 'universal_class' ) ) ],
% 0.77/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.77/1.16 successor( X ), Y ) ],
% 0.77/1.16 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.77/1.16 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.77/1.16 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.77/1.16 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.77/1.16 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.77/1.16 ,
% 0.77/1.16 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.77/1.16 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.77/1.16 [ inductive( omega ) ],
% 0.77/1.16 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.77/1.16 [ member( omega, 'universal_class' ) ],
% 0.77/1.16 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.77/1.16 , 'sum_class'( X ) ) ],
% 0.77/1.16 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.77/1.16 'universal_class' ) ],
% 0.77/1.16 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.77/1.16 'power_class'( X ) ) ],
% 0.77/1.16 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.77/1.16 'universal_class' ) ],
% 0.77/1.16 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.77/1.16 'universal_class' ) ) ],
% 0.77/1.16 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.77/1.16 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.77/1.16 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.77/1.16 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.77/1.16 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.77/1.16 ) ],
% 0.77/1.16 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.77/1.16 , 'identity_relation' ) ],
% 0.77/1.16 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.77/1.16 'single_valued_class'( X ) ],
% 0.77/1.16 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.77/1.16 'universal_class' ) ) ],
% 0.77/1.16 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.77/1.16 'identity_relation' ) ],
% 0.77/1.16 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.77/1.16 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.77/1.16 , function( X ) ],
% 0.77/1.16 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.77/1.16 X, Y ), 'universal_class' ) ],
% 0.77/1.16 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.77/1.16 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.77/1.16 ) ],
% 0.77/1.16 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.77/1.16 [ function( choice ) ],
% 0.77/1.16 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.77/1.16 apply( choice, X ), X ) ],
% 0.77/1.16 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.77/1.16 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.77/1.16 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.77/1.16 ,
% 0.77/1.16 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.77/1.16 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.77/1.16 , complement( compose( complement( 'element_relation' ), inverse(
% 0.77/1.16 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.77/1.16 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.77/1.16 'identity_relation' ) ],
% 0.77/1.16 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.77/1.16 , diagonalise( X ) ) ],
% 0.77/1.16 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.77/1.16 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.77/1.16 [ ~( operation( X ) ), function( X ) ],
% 0.77/1.16 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.77/1.16 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.77/1.16 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.77/1.16 'domain_of'( X ) ) ) ],
% 0.77/1.16 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.77/1.16 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.77/1.16 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.77/1.16 X ) ],
% 0.77/1.16 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.77/1.16 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.77/1.16 'domain_of'( X ) ) ],
% 0.77/1.16 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.77/1.16 'domain_of'( Z ) ) ) ],
% 0.77/1.16 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.77/1.16 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.77/1.16 ), compatible( X, Y, Z ) ],
% 0.77/1.16 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.77/1.16 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.77/1.16 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.77/1.16 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.77/1.16 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.77/1.16 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.77/1.16 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.77/1.16 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.77/1.16 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.77/1.16 , Y ) ],
% 0.77/1.16 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.77/1.16 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.77/1.16 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.77/1.16 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.77/1.16 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.77/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.77/1.16 X, 'unordered_pair'( X, Y ) ) ],
% 0.77/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.77/1.16 Y, 'unordered_pair'( X, Y ) ) ],
% 0.77/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.77/1.16 X, 'universal_class' ) ],
% 0.77/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.77/1.16 Y, 'universal_class' ) ],
% 0.77/1.16 [ subclass( X, X ) ],
% 0.77/1.16 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.77/1.16 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.77/1.16 'not_subclass_element'( Y, X ), Y ) ],
% 0.77/1.16 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.77/1.16 'not_subclass_element'( Y, X ), Y ) ],
% 0.77/1.16 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.77/1.16 'not_subclass_element'( Y, X ), Y ) ],
% 0.77/1.16 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.77/1.16 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.77/1.16 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.77/1.16 [ ~( member( X, 'null_class' ) ) ],
% 0.77/1.16 [ subclass( 'null_class', X ) ],
% 0.77/1.16 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.77/1.16 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.77/1.16 ), X ) ],
% 0.77/1.16 [ member( 'null_class', 'universal_class' ) ],
% 0.77/1.16 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.77/1.16 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.77/1.16 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.77/1.16 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.77/1.16 Y ) ) ],
% 0.77/1.16 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.77/1.16 Y ) ) ],
% 0.77/1.16 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.77/1.16 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.77/1.16 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.77/1.16 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.77/1.16 'universal_class' ) ) ), =( Y, Z ) ],
% 0.77/1.16 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.77/1.16 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.77/1.16 'universal_class' ) ) ), =( X, Z ) ],
% 0.77/1.16 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.77/1.16 'null_class' ) ) ],
% 0.77/1.16 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.77/1.16 'null_class' ) ) ],
% 0.77/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.77/1.16 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 0.77/1.16 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 0.77/1.16 X, Z ), Y ) ],
% 0.77/1.16 [ member( singleton( X ), 'universal_class' ) ],
% 0.77/1.16 [ member( singleton( X ), 'unordered_pair'( Y, singleton( X ) ) ) ],
% 0.77/1.16 [ ~( member( X, 'universal_class' ) ), member( X, singleton( X ) ) ]
% 0.77/1.16 ,
% 0.77/1.16 [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X ),
% 0.77/1.16 'null_class' ) ) ],
% 0.77/1.16 [ member( 'null_class', singleton( 'null_class' ) ) ],
% 0.77/1.16 [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ],
% 0.77/1.16 [ member( X, 'universal_class' ), =( singleton( X ), 'null_class' ) ]
% 0.77/1.16 ,
% 0.77/1.16 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 0.77/1.16 'universal_class' ) ), =( X, Y ) ],
% 0.77/1.16 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 0.77/1.16 'universal_class' ) ), =( X, Y ) ],
% 0.77/1.16 [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~( member( Z,
% 0.77/1.16 'universal_class' ) ), =( Z, X ), =( Z, Y ) ],
% 0.77/1.16 [ ~( member( X, 'universal_class' ) ), member( 'member_of'( singleton( X
% 0.77/1.16 ) ), 'universal_class' ) ],
% 0.77/1.16 [ ~( member( X, 'universal_class' ) ), =( singleton( 'member_of'(
% 0.77/1.16 singleton( X ) ) ), singleton( X ) ) ],
% 0.77/1.16 [ member( 'member_of'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 0.77/1.16 ) ],
% 0.77/1.16 [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X ), X ) ],
% 0.77/1.16 [ ~( member( X, 'universal_class' ) ), =( 'member_of'( singleton( X ) )
% 0.77/1.16 , X ) ],
% 0.77/1.16 [ member( 'member_of1'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 0.77/1.16 ) ],
% 0.77/1.16 [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'( X ), X ) ]
% 0.77/1.16 ,
% 0.77/1.16 [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 0.77/1.16 'universal_class' ) ],
% 0.77/1.16 [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y, X ) ), =(
% 0.77/1.16 'member_of'( X ), Y ) ],
% 0.77/1.16 [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ],
% 0.77/1.16 [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' ), =( singleton(
% 0.77/1.16 Y ), X ) ],
% 0.77/1.16 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 0.77/1.16 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 0.77/1.16 intersection( complement( singleton( 'not_subclass_element'( X,
% 0.77/1.16 'null_class' ) ) ), X ) ), =( singleton( 'not_subclass_element'( X,
% 0.77/1.16 'null_class' ) ), X ), =( X, 'null_class' ) ],
% 0.77/1.16 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 0.77/1.16 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ), X ),
% 0.77/1.16 =( singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 0.77/1.16 'null_class' ) ],
% 0.77/1.16 [ ~( =( 'not_subclass_element'( intersection( complement( singleton(
% 0.77/1.16 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 0.77/1.16 'not_subclass_element'( X, 'null_class' ) ) ), =( singleton(
% 0.77/1.16 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 0.77/1.16 ,
% 0.77/1.16 [ =( 'unordered_pair'( X, Y ), union( singleton( X ), singleton( Y ) ) )
% 0.77/1.16 ],
% 0.77/1.16 [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ],
% 0.77/1.16 [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ],
% 0.77/1.16 [ member( 'unordered_pair'( X, singleton( Y ) ), 'ordered_pair'( X, Y )
% 0.77/1.16 ) ],
% 0.77/1.16 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, 'null_class'
% 0.77/1.16 ) ), 'ordered_pair'( X, Y ) ), member( Y, 'universal_class' ) ],
% 0.77/1.16 [ ~( member( X, 'universal_class' ) ), =( 'unordered_pair'( 'null_class'
% 0.77/1.16 , singleton( singleton( X ) ) ), 'ordered_pair'( Y, X ) ), member( Y,
% 0.77/1.16 'universal_class' ) ],
% 0.77/1.16 [ =( 'unordered_pair'( 'null_class', singleton( 'null_class' ) ),
% 0.77/1.16 'ordered_pair'( X, Y ) ), member( X, 'universal_class' ), member( Y,
% 0.77/1.16 'universal_class' ) ],
% 0.77/1.16 [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) ), ~( member( X
% 0.77/1.16 , 'universal_class' ) ), =( X, Z ) ],
% 0.77/1.16 [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) ), ~( member( Y
% 0.77/1.16 , 'universal_class' ) ), =( Y, T ) ],
% 0.77/1.16 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.77/1.16 , 'universal_class' ) ) ), member( 'ordered_pair'( first( 'ordered_pair'(
% 0.77/1.16 X, Y ) ), second( 'ordered_pair'( X, Y ) ) ), 'cross_product'(
% 0.77/1.16 'universal_class', 'universal_class' ) ) ],
% 0.77/1.16 [ member( 'ordered_pair'( first( X ), second( X ) ), 'cross_product'(
% 0.77/1.16 'universal_class', 'universal_class' ) ), =( first( X ), X ) ],
% 6.69/7.09 [ member( 'ordered_pair'( first( X ), second( X ) ), 'cross_product'(
% 6.69/7.09 'universal_class', 'universal_class' ) ), =( second( X ), X ) ],
% 6.69/7.09 [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( first( X ), X )
% 6.69/7.09 ],
% 6.69/7.09 [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( second( X ), X )
% 6.69/7.09 ],
% 6.69/7.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 6.69/7.09 , 'universal_class' ) ) ), =( first( 'ordered_pair'( X, Y ) ), X ) ],
% 6.69/7.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 6.69/7.09 , 'universal_class' ) ) ), =( second( 'ordered_pair'( X, Y ) ), Y ) ]
% 6.69/7.09 ,
% 6.69/7.09 [ member( 'ordered_pair'( first( X ), second( X ) ), 'cross_product'(
% 6.69/7.09 'universal_class', 'universal_class' ) ), =( first( X ), X ) ],
% 6.69/7.09 [ member( 'ordered_pair'( first( X ), second( X ) ), 'cross_product'(
% 6.69/7.09 'universal_class', 'universal_class' ) ), =( second( X ), X ) ],
% 6.69/7.09 [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( first( X ), X )
% 6.69/7.09 ],
% 6.69/7.09 [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( second( X ), X )
% 6.69/7.09 ],
% 6.69/7.09 [ ~( =( 'ordered_pair'( first( X ), second( X ) ), X ) ), member( X,
% 6.69/7.09 'universal_class' ) ],
% 6.69/7.09 [ ~( member( X, 'cross_product'( 'universal_class', 'universal_class' )
% 6.69/7.09 ) ), member( X, 'universal_class' ) ],
% 6.69/7.09 [ ~( member( x, 'universal_class' ) ) ],
% 6.69/7.09 [ ~( =( second( 'ordered_pair'( x, y ) ), 'ordered_pair'( x, y ) ) ) ]
% 6.69/7.09 ] .
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09 percentage equality = 0.315152, percentage horn = 0.803681
% 6.69/7.09 This is a problem with some equality
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09 Options Used:
% 6.69/7.09
% 6.69/7.09 useres = 1
% 6.69/7.09 useparamod = 1
% 6.69/7.09 useeqrefl = 1
% 6.69/7.09 useeqfact = 1
% 6.69/7.09 usefactor = 1
% 6.69/7.09 usesimpsplitting = 0
% 6.69/7.09 usesimpdemod = 5
% 6.69/7.09 usesimpres = 3
% 6.69/7.09
% 6.69/7.09 resimpinuse = 1000
% 6.69/7.09 resimpclauses = 20000
% 6.69/7.09 substype = eqrewr
% 6.69/7.09 backwardsubs = 1
% 6.69/7.09 selectoldest = 5
% 6.69/7.09
% 6.69/7.09 litorderings [0] = split
% 6.69/7.09 litorderings [1] = extend the termordering, first sorting on arguments
% 6.69/7.09
% 6.69/7.09 termordering = kbo
% 6.69/7.09
% 6.69/7.09 litapriori = 0
% 6.69/7.09 termapriori = 1
% 6.69/7.09 litaposteriori = 0
% 6.69/7.09 termaposteriori = 0
% 6.69/7.09 demodaposteriori = 0
% 6.69/7.09 ordereqreflfact = 0
% 6.69/7.09
% 6.69/7.09 litselect = negord
% 6.69/7.09
% 6.69/7.09 maxweight = 15
% 6.69/7.09 maxdepth = 30000
% 6.69/7.09 maxlength = 115
% 6.69/7.09 maxnrvars = 195
% 6.69/7.09 excuselevel = 1
% 6.69/7.09 increasemaxweight = 1
% 6.69/7.09
% 6.69/7.09 maxselected = 10000000
% 6.69/7.09 maxnrclauses = 10000000
% 6.69/7.09
% 6.69/7.09 showgenerated = 0
% 6.69/7.09 showkept = 0
% 6.69/7.09 showselected = 0
% 6.69/7.09 showdeleted = 0
% 6.69/7.09 showresimp = 1
% 6.69/7.09 showstatus = 2000
% 6.69/7.09
% 6.69/7.09 prologoutput = 1
% 6.69/7.09 nrgoals = 5000000
% 6.69/7.09 totalproof = 1
% 6.69/7.09
% 6.69/7.09 Symbols occurring in the translation:
% 6.69/7.09
% 6.69/7.09 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 6.69/7.09 . [1, 2] (w:1, o:58, a:1, s:1, b:0),
% 6.69/7.09 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 6.69/7.09 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.69/7.09 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.69/7.09 subclass [41, 2] (w:1, o:83, a:1, s:1, b:0),
% 6.69/7.09 member [43, 2] (w:1, o:84, a:1, s:1, b:0),
% 6.69/7.09 'not_subclass_element' [44, 2] (w:1, o:85, a:1, s:1, b:0),
% 6.69/7.09 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 6.69/7.09 'unordered_pair' [46, 2] (w:1, o:86, a:1, s:1, b:0),
% 6.69/7.09 singleton [47, 1] (w:1, o:39, a:1, s:1, b:0),
% 6.69/7.09 'ordered_pair' [48, 2] (w:1, o:87, a:1, s:1, b:0),
% 6.69/7.09 'cross_product' [50, 2] (w:1, o:88, a:1, s:1, b:0),
% 6.69/7.09 first [52, 1] (w:1, o:40, a:1, s:1, b:0),
% 6.69/7.09 second [53, 1] (w:1, o:41, a:1, s:1, b:0),
% 6.69/7.09 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 6.69/7.09 intersection [55, 2] (w:1, o:90, a:1, s:1, b:0),
% 6.69/7.09 complement [56, 1] (w:1, o:42, a:1, s:1, b:0),
% 6.69/7.09 union [57, 2] (w:1, o:91, a:1, s:1, b:0),
% 6.69/7.09 'symmetric_difference' [58, 2] (w:1, o:92, a:1, s:1, b:0),
% 6.69/7.09 restrict [60, 3] (w:1, o:95, a:1, s:1, b:0),
% 6.69/7.09 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 6.69/7.09 'domain_of' [62, 1] (w:1, o:44, a:1, s:1, b:0),
% 6.69/7.09 rotate [63, 1] (w:1, o:36, a:1, s:1, b:0),
% 6.69/7.09 flip [65, 1] (w:1, o:45, a:1, s:1, b:0),
% 6.69/7.09 inverse [66, 1] (w:1, o:46, a:1, s:1, b:0),
% 6.69/7.09 'range_of' [67, 1] (w:1, o:37, a:1, s:1, b:0),
% 6.69/7.09 domain [68, 3] (w:1, o:97, a:1, s:1, b:0),
% 6.69/7.09 range [69, 3] (w:1, o:98, a:1, s:1, b:0),
% 6.69/7.09 image [70, 2] (w:1, o:89, a:1, s:1, b:0),
% 6.69/7.09 successor [71, 1] (w:1, o:47, a:1, s:1, b:0),
% 6.69/7.09 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 6.69/7.09 inductive [73, 1] (w:1, o:48, a:1, s:1, b:0),
% 6.69/7.09 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 6.69/7.09 'sum_class' [75, 1] (w:1, o:49, a:1, s:1, b:0),
% 6.69/7.09 'power_class' [76, 1] (w:1, o:52, a:1, s:1, b:0),
% 6.69/7.09 compose [78, 2] (w:1, o:93, a:1, s:1, b:0),
% 6.69/7.09 'single_valued_class' [79, 1] (w:1, o:53, a:1, s:1, b:0),
% 6.69/7.09 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 6.69/7.09 function [82, 1] (w:1, o:54, a:1, s:1, b:0),
% 6.69/7.09 regular [83, 1] (w:1, o:38, a:1, s:1, b:0),
% 6.69/7.09 apply [84, 2] (w:1, o:94, a:1, s:1, b:0),
% 6.69/7.09 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 6.69/7.09 'one_to_one' [86, 1] (w:1, o:50, a:1, s:1, b:0),
% 6.69/7.09 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 6.69/7.09 diagonalise [88, 1] (w:1, o:55, a:1, s:1, b:0),
% 6.69/7.09 cantor [89, 1] (w:1, o:43, a:1, s:1, b:0),
% 6.69/7.09 operation [90, 1] (w:1, o:51, a:1, s:1, b:0),
% 6.69/7.09 compatible [94, 3] (w:1, o:96, a:1, s:1, b:0),
% 6.69/7.09 homomorphism [95, 3] (w:1, o:99, a:1, s:1, b:0),
% 6.69/7.09 'not_homomorphism1' [96, 3] (w:1, o:100, a:1, s:1, b:0),
% 6.69/7.09 'not_homomorphism2' [97, 3] (w:1, o:101, a:1, s:1, b:0),
% 6.69/7.09 'member_of' [98, 1] (w:1, o:56, a:1, s:1, b:0),
% 6.69/7.09 'member_of1' [99, 1] (w:1, o:57, a:1, s:1, b:0),
% 6.69/7.09 x [100, 0] (w:1, o:29, a:1, s:1, b:0),
% 6.69/7.09 y [101, 0] (w:1, o:30, a:1, s:1, b:0).
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09 Starting Search:
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09 Intermediate Status:
% 6.69/7.09 Generated: 3957
% 6.69/7.09 Kept: 2016
% 6.69/7.09 Inuse: 121
% 6.69/7.09 Deleted: 3
% 6.69/7.09 Deletedinuse: 3
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09 Intermediate Status:
% 6.69/7.09 Generated: 9357
% 6.69/7.09 Kept: 4044
% 6.69/7.09 Inuse: 201
% 6.69/7.09 Deleted: 8
% 6.69/7.09 Deletedinuse: 8
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09 Intermediate Status:
% 6.69/7.09 Generated: 15276
% 6.69/7.09 Kept: 6339
% 6.69/7.09 Inuse: 285
% 6.69/7.09 Deleted: 12
% 6.69/7.09 Deletedinuse: 11
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09 Intermediate Status:
% 6.69/7.09 Generated: 21181
% 6.69/7.09 Kept: 8374
% 6.69/7.09 Inuse: 343
% 6.69/7.09 Deleted: 62
% 6.69/7.09 Deletedinuse: 58
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09 Intermediate Status:
% 6.69/7.09 Generated: 28791
% 6.69/7.09 Kept: 10800
% 6.69/7.09 Inuse: 395
% 6.69/7.09 Deleted: 79
% 6.69/7.09 Deletedinuse: 63
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09 Intermediate Status:
% 6.69/7.09 Generated: 38205
% 6.69/7.09 Kept: 12825
% 6.69/7.09 Inuse: 444
% 6.69/7.09 Deleted: 81
% 6.69/7.09 Deletedinuse: 64
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09 Intermediate Status:
% 6.69/7.09 Generated: 47915
% 6.69/7.09 Kept: 16581
% 6.69/7.09 Inuse: 488
% 6.69/7.09 Deleted: 93
% 6.69/7.09 Deletedinuse: 75
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09 Intermediate Status:
% 6.69/7.09 Generated: 61706
% 6.69/7.09 Kept: 20421
% 6.69/7.09 Inuse: 503
% 6.69/7.09 Deleted: 97
% 6.69/7.09 Deletedinuse: 79
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09 Resimplifying clauses:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09 Intermediate Status:
% 6.69/7.09 Generated: 72189
% 6.69/7.09 Kept: 22613
% 6.69/7.09 Inuse: 541
% 6.69/7.09 Deleted: 2234
% 6.69/7.09 Deletedinuse: 90
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09 Intermediate Status:
% 6.69/7.09 Generated: 84938
% 6.69/7.09 Kept: 25710
% 6.69/7.09 Inuse: 567
% 6.69/7.09 Deleted: 2238
% 6.69/7.09 Deletedinuse: 90
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09 Intermediate Status:
% 6.69/7.09 Generated: 91091
% 6.69/7.09 Kept: 27759
% 6.69/7.09 Inuse: 577
% 6.69/7.09 Deleted: 2240
% 6.69/7.09 Deletedinuse: 92
% 6.69/7.09
% 6.69/7.09 Resimplifying inuse:
% 6.69/7.09 Done
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09 Bliksems!, er is een bewijs:
% 6.69/7.09 % SZS status Unsatisfiable
% 6.69/7.09 % SZS output start Refutation
% 6.69/7.09
% 6.69/7.09 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 6.69/7.09 )
% 6.69/7.09 .
% 6.69/7.09 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 6.69/7.09 .
% 6.69/7.09 clause( 12, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) )
% 6.69/7.09 ), member( X, Z ) ] )
% 6.69/7.09 .
% 6.69/7.09 clause( 153, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( second(
% 6.69/7.09 X ), X ) ] )
% 6.69/7.09 .
% 6.69/7.09 clause( 157, [ =( second( X ), X ), member( X, 'cross_product'(
% 6.69/7.09 'universal_class', 'universal_class' ) ) ] )
% 6.69/7.09 .
% 6.69/7.09 clause( 160, [ ~( member( x, 'universal_class' ) ) ] )
% 6.69/7.09 .
% 6.69/7.09 clause( 161, [ ~( =( second( 'ordered_pair'( x, y ) ), 'ordered_pair'( x, y
% 6.69/7.09 ) ) ) ] )
% 6.69/7.09 .
% 6.69/7.09 clause( 180, [ ~( member( x, X ) ) ] )
% 6.69/7.09 .
% 6.69/7.09 clause( 614, [ ~( member( 'ordered_pair'( x, X ), 'cross_product'( Y, Z ) )
% 6.69/7.09 ) ] )
% 6.69/7.09 .
% 6.69/7.09 clause( 28649, [] )
% 6.69/7.09 .
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09 % SZS output end Refutation
% 6.69/7.09 found a proof!
% 6.69/7.09
% 6.69/7.09 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 6.69/7.09
% 6.69/7.09 initialclauses(
% 6.69/7.09 [ clause( 28651, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 6.69/7.09 ) ] )
% 6.69/7.09 , clause( 28652, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 6.69/7.09 , Y ) ] )
% 6.69/7.09 , clause( 28653, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 6.69/7.09 subclass( X, Y ) ] )
% 6.69/7.09 , clause( 28654, [ subclass( X, 'universal_class' ) ] )
% 6.69/7.09 , clause( 28655, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 6.69/7.09 , clause( 28656, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 6.69/7.09 , clause( 28657, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 6.69/7.09 ] )
% 6.69/7.09 , clause( 28658, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 6.69/7.09 =( X, Z ) ] )
% 6.69/7.09 , clause( 28659, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.69/7.09 'unordered_pair'( X, Y ) ) ] )
% 6.69/7.09 , clause( 28660, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.69/7.09 'unordered_pair'( Y, X ) ) ] )
% 6.69/7.09 , clause( 28661, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 6.69/7.09 )
% 6.69/7.09 , clause( 28662, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 6.69/7.09 , clause( 28663, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 6.69/7.09 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 6.69/7.09 , clause( 28664, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.69/7.09 ) ) ), member( X, Z ) ] )
% 6.69/7.09 , clause( 28665, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.69/7.09 ) ) ), member( Y, T ) ] )
% 6.69/7.09 , clause( 28666, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 6.69/7.09 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 6.69/7.09 , clause( 28667, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 6.69/7.09 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 6.69/7.09 , clause( 28668, [ subclass( 'element_relation', 'cross_product'(
% 6.69/7.09 'universal_class', 'universal_class' ) ) ] )
% 6.69/7.09 , clause( 28669, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 6.69/7.09 ), member( X, Y ) ] )
% 6.69/7.09 , clause( 28670, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 6.69/7.09 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 6.69/7.09 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 6.69/7.09 , clause( 28671, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 6.69/7.09 )
% 6.69/7.09 , clause( 28672, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 6.69/7.09 )
% 6.69/7.09 , clause( 28673, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 6.69/7.09 intersection( Y, Z ) ) ] )
% 6.69/7.09 , clause( 28674, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 6.69/7.09 )
% 6.69/7.09 , clause( 28675, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.69/7.09 complement( Y ) ), member( X, Y ) ] )
% 6.69/7.09 , clause( 28676, [ =( complement( intersection( complement( X ), complement(
% 6.69/7.09 Y ) ) ), union( X, Y ) ) ] )
% 6.69/7.09 , clause( 28677, [ =( intersection( complement( intersection( X, Y ) ),
% 6.69/7.09 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 6.69/7.09 'symmetric_difference'( X, Y ) ) ] )
% 6.69/7.09 , clause( 28678, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 6.69/7.09 X, Y, Z ) ) ] )
% 6.69/7.09 , clause( 28679, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 6.69/7.09 Z, X, Y ) ) ] )
% 6.69/7.09 , clause( 28680, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 6.69/7.09 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 6.69/7.09 , clause( 28681, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 6.69/7.09 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 6.69/7.09 'domain_of'( Y ) ) ] )
% 6.69/7.09 , clause( 28682, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 6.69/7.09 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 6.69/7.09 , clause( 28683, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.69/7.09 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 6.69/7.09 ] )
% 6.69/7.09 , clause( 28684, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.69/7.09 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 6.69/7.09 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 6.69/7.09 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 6.69/7.09 , Y ), rotate( T ) ) ] )
% 6.69/7.09 , clause( 28685, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 6.69/7.09 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 6.69/7.09 , clause( 28686, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.69/7.09 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 6.69/7.09 )
% 6.69/7.09 , clause( 28687, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.69/7.09 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 6.69/7.09 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 6.69/7.09 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 6.69/7.09 , Z ), flip( T ) ) ] )
% 6.69/7.09 , clause( 28688, [ =( 'domain_of'( flip( 'cross_product'( X,
% 6.69/7.09 'universal_class' ) ) ), inverse( X ) ) ] )
% 6.69/7.09 , clause( 28689, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 6.69/7.09 , clause( 28690, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 6.69/7.09 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 6.69/7.09 , clause( 28691, [ =( second( 'not_subclass_element'( restrict( X,
% 6.69/7.09 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 6.69/7.09 , clause( 28692, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 6.69/7.09 image( X, Y ) ) ] )
% 6.69/7.09 , clause( 28693, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 6.69/7.09 , clause( 28694, [ subclass( 'successor_relation', 'cross_product'(
% 6.69/7.09 'universal_class', 'universal_class' ) ) ] )
% 6.69/7.09 , clause( 28695, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 6.69/7.09 ) ), =( successor( X ), Y ) ] )
% 6.69/7.09 , clause( 28696, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 6.69/7.09 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 6.69/7.09 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 6.69/7.09 , clause( 28697, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 6.69/7.09 , clause( 28698, [ ~( inductive( X ) ), subclass( image(
% 6.69/7.09 'successor_relation', X ), X ) ] )
% 6.69/7.09 , clause( 28699, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 6.69/7.09 'successor_relation', X ), X ) ), inductive( X ) ] )
% 6.69/7.09 , clause( 28700, [ inductive( omega ) ] )
% 6.69/7.09 , clause( 28701, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 6.69/7.09 , clause( 28702, [ member( omega, 'universal_class' ) ] )
% 6.69/7.09 , clause( 28703, [ =( 'domain_of'( restrict( 'element_relation',
% 6.69/7.09 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 6.69/7.09 , clause( 28704, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 6.69/7.09 X ), 'universal_class' ) ] )
% 6.69/7.09 , clause( 28705, [ =( complement( image( 'element_relation', complement( X
% 6.69/7.09 ) ) ), 'power_class'( X ) ) ] )
% 6.69/7.09 , clause( 28706, [ ~( member( X, 'universal_class' ) ), member(
% 6.69/7.09 'power_class'( X ), 'universal_class' ) ] )
% 6.69/7.09 , clause( 28707, [ subclass( compose( X, Y ), 'cross_product'(
% 6.69/7.09 'universal_class', 'universal_class' ) ) ] )
% 6.69/7.09 , clause( 28708, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 6.69/7.09 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 6.69/7.09 , clause( 28709, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 6.69/7.09 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 6.69/7.09 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 6.69/7.09 ) ] )
% 6.69/7.09 , clause( 28710, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 6.69/7.09 inverse( X ) ), 'identity_relation' ) ] )
% 6.69/7.09 , clause( 28711, [ ~( subclass( compose( X, inverse( X ) ),
% 6.69/7.09 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 6.69/7.09 , clause( 28712, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 6.69/7.09 'universal_class', 'universal_class' ) ) ] )
% 6.69/7.09 , clause( 28713, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 6.69/7.09 , 'identity_relation' ) ] )
% 6.69/7.09 , clause( 28714, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 6.69/7.09 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 6.69/7.09 'identity_relation' ) ), function( X ) ] )
% 6.69/7.09 , clause( 28715, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 6.69/7.09 , member( image( X, Y ), 'universal_class' ) ] )
% 6.69/7.09 , clause( 28716, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 6.69/7.09 , clause( 28717, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 6.69/7.09 , 'null_class' ) ] )
% 6.69/7.09 , clause( 28718, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 6.69/7.09 Y ) ) ] )
% 6.69/7.09 , clause( 28719, [ function( choice ) ] )
% 6.69/7.09 , clause( 28720, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 6.69/7.09 ), member( apply( choice, X ), X ) ] )
% 6.69/7.09 , clause( 28721, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 6.69/7.09 , clause( 28722, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 6.69/7.09 , clause( 28723, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 6.69/7.09 'one_to_one'( X ) ] )
% 6.69/7.09 , clause( 28724, [ =( intersection( 'cross_product'( 'universal_class',
% 6.69/7.09 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 6.69/7.09 'universal_class' ), complement( compose( complement( 'element_relation'
% 6.69/7.09 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 6.69/7.09 , clause( 28725, [ =( intersection( inverse( 'subset_relation' ),
% 6.69/7.09 'subset_relation' ), 'identity_relation' ) ] )
% 6.69/7.09 , clause( 28726, [ =( complement( 'domain_of'( intersection( X,
% 6.69/7.09 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 6.69/7.09 , clause( 28727, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 6.69/7.09 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 6.69/7.09 , clause( 28728, [ ~( operation( X ) ), function( X ) ] )
% 6.69/7.09 , clause( 28729, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 6.69/7.09 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 6.69/7.09 ] )
% 6.69/7.09 , clause( 28730, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 6.69/7.09 'domain_of'( 'domain_of'( X ) ) ) ] )
% 6.69/7.09 , clause( 28731, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 6.69/7.09 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 6.69/7.09 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 6.69/7.09 operation( X ) ] )
% 6.69/7.09 , clause( 28732, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 6.69/7.09 , clause( 28733, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 6.69/7.09 Y ) ), 'domain_of'( X ) ) ] )
% 6.69/7.09 , clause( 28734, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 6.69/7.09 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 6.69/7.09 , clause( 28735, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 6.69/7.09 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 6.69/7.09 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 6.69/7.09 , clause( 28736, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 6.69/7.09 , clause( 28737, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 6.69/7.09 , clause( 28738, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 6.69/7.09 , clause( 28739, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 6.69/7.09 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 6.69/7.09 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 6.69/7.09 )
% 6.69/7.09 , clause( 28740, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 6.69/7.09 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 6.69/7.09 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 6.69/7.09 , Y ) ] )
% 6.69/7.09 , clause( 28741, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 6.69/7.09 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 6.69/7.09 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 6.69/7.09 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 6.69/7.09 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 6.69/7.09 )
% 6.69/7.09 , clause( 28742, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.69/7.09 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 6.69/7.09 , clause( 28743, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.69/7.09 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 6.69/7.09 , clause( 28744, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.69/7.09 ) ) ), member( X, 'universal_class' ) ] )
% 6.69/7.09 , clause( 28745, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.69/7.09 ) ) ), member( Y, 'universal_class' ) ] )
% 6.69/7.09 , clause( 28746, [ subclass( X, X ) ] )
% 6.69/7.09 , clause( 28747, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 6.69/7.09 X, Z ) ] )
% 6.69/7.09 , clause( 28748, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 6.69/7.09 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 6.69/7.09 , clause( 28749, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 6.69/7.09 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 6.69/7.09 , clause( 28750, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 6.69/7.09 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 6.69/7.09 , clause( 28751, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 6.69/7.09 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 6.69/7.09 , clause( 28752, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 6.69/7.09 )
% 6.69/7.09 , clause( 28753, [ ~( member( X, 'null_class' ) ) ] )
% 6.69/7.09 , clause( 28754, [ subclass( 'null_class', X ) ] )
% 6.69/7.09 , clause( 28755, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 6.69/7.09 )
% 6.69/7.09 , clause( 28756, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 6.69/7.09 , 'null_class' ), X ) ] )
% 6.69/7.09 , clause( 28757, [ member( 'null_class', 'universal_class' ) ] )
% 6.69/7.09 , clause( 28758, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 6.69/7.09 ] )
% 6.69/7.09 , clause( 28759, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 6.69/7.09 )
% 6.69/7.09 , clause( 28760, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 6.69/7.09 )
% 6.69/7.09 , clause( 28761, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 6.69/7.09 X ), singleton( Y ) ) ] )
% 6.69/7.09 , clause( 28762, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 6.69/7.09 Y ), singleton( Y ) ) ] )
% 6.69/7.09 , clause( 28763, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 6.69/7.09 'universal_class' ), member( Y, 'universal_class' ) ] )
% 6.69/7.09 , clause( 28764, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 6.69/7.09 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 6.69/7.09 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 6.69/7.09 , clause( 28765, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 6.69/7.09 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 6.69/7.09 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 6.69/7.09 , clause( 28766, [ ~( member( X, 'universal_class' ) ), ~( =(
% 6.69/7.09 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 6.69/7.09 , clause( 28767, [ ~( member( X, 'universal_class' ) ), ~( =(
% 6.69/7.09 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 6.69/7.09 , clause( 28768, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.69/7.09 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 6.69/7.09 , clause( 28769, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 6.69/7.09 'unordered_pair'( X, Z ), Y ) ] )
% 6.69/7.09 , clause( 28770, [ member( singleton( X ), 'universal_class' ) ] )
% 6.69/7.09 , clause( 28771, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 6.69/7.09 X ) ) ) ] )
% 6.69/7.09 , clause( 28772, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.69/7.09 singleton( X ) ) ] )
% 6.69/7.09 , clause( 28773, [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X
% 6.69/7.09 ), 'null_class' ) ) ] )
% 6.69/7.09 , clause( 28774, [ member( 'null_class', singleton( 'null_class' ) ) ] )
% 6.69/7.09 , clause( 28775, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 6.69/7.09 , clause( 28776, [ member( X, 'universal_class' ), =( singleton( X ),
% 6.69/7.09 'null_class' ) ] )
% 6.69/7.09 , clause( 28777, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 6.69/7.09 'universal_class' ) ), =( X, Y ) ] )
% 6.69/7.09 , clause( 28778, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 6.69/7.09 'universal_class' ) ), =( X, Y ) ] )
% 6.69/7.09 , clause( 28779, [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~(
% 6.69/7.09 member( Z, 'universal_class' ) ), =( Z, X ), =( Z, Y ) ] )
% 6.69/7.09 , clause( 28780, [ ~( member( X, 'universal_class' ) ), member( 'member_of'(
% 6.69/7.09 singleton( X ) ), 'universal_class' ) ] )
% 6.69/7.09 , clause( 28781, [ ~( member( X, 'universal_class' ) ), =( singleton(
% 6.69/7.09 'member_of'( singleton( X ) ) ), singleton( X ) ) ] )
% 6.69/7.09 , clause( 28782, [ member( 'member_of'( X ), 'universal_class' ), =(
% 6.69/7.09 'member_of'( X ), X ) ] )
% 6.69/7.09 , clause( 28783, [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X
% 6.69/7.09 ), X ) ] )
% 6.69/7.09 , clause( 28784, [ ~( member( X, 'universal_class' ) ), =( 'member_of'(
% 6.69/7.09 singleton( X ) ), X ) ] )
% 6.69/7.09 , clause( 28785, [ member( 'member_of1'( X ), 'universal_class' ), =(
% 6.69/7.09 'member_of'( X ), X ) ] )
% 6.69/7.09 , clause( 28786, [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'(
% 6.69/7.09 X ), X ) ] )
% 6.69/7.09 , clause( 28787, [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 6.69/7.09 'universal_class' ) ] )
% 6.69/7.09 , clause( 28788, [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y
% 6.69/7.09 , X ) ), =( 'member_of'( X ), Y ) ] )
% 6.69/7.09 , clause( 28789, [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ] )
% 6.69/7.09 , clause( 28790, [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' )
% 6.69/7.09 , =( singleton( Y ), X ) ] )
% 6.69/7.09 , clause( 28791, [ member( 'not_subclass_element'( intersection( complement(
% 6.69/7.09 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 6.69/7.09 'null_class' ), intersection( complement( singleton(
% 6.69/7.09 'not_subclass_element'( X, 'null_class' ) ) ), X ) ), =( singleton(
% 6.69/7.09 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 6.69/7.09 )
% 6.69/7.09 , clause( 28792, [ member( 'not_subclass_element'( intersection( complement(
% 6.69/7.09 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 6.69/7.09 'null_class' ), X ), =( singleton( 'not_subclass_element'( X,
% 6.69/7.09 'null_class' ) ), X ), =( X, 'null_class' ) ] )
% 6.69/7.09 , clause( 28793, [ ~( =( 'not_subclass_element'( intersection( complement(
% 6.69/7.09 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 6.69/7.09 'null_class' ), 'not_subclass_element'( X, 'null_class' ) ) ), =(
% 6.69/7.09 singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 6.69/7.09 'null_class' ) ] )
% 6.69/7.09 , clause( 28794, [ =( 'unordered_pair'( X, Y ), union( singleton( X ),
% 6.69/7.09 singleton( Y ) ) ) ] )
% 6.69/7.09 , clause( 28795, [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ] )
% 6.69/7.09 , clause( 28796, [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ] )
% 6.69/7.09 , clause( 28797, [ member( 'unordered_pair'( X, singleton( Y ) ),
% 6.69/7.09 'ordered_pair'( X, Y ) ) ] )
% 6.69/7.09 , clause( 28798, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 6.69/7.09 , 'null_class' ) ), 'ordered_pair'( X, Y ) ), member( Y,
% 6.69/7.09 'universal_class' ) ] )
% 6.69/7.09 , clause( 28799, [ ~( member( X, 'universal_class' ) ), =( 'unordered_pair'(
% 6.69/7.09 'null_class', singleton( singleton( X ) ) ), 'ordered_pair'( Y, X ) ),
% 6.69/7.09 member( Y, 'universal_class' ) ] )
% 6.69/7.09 , clause( 28800, [ =( 'unordered_pair'( 'null_class', singleton(
% 6.69/7.09 'null_class' ) ), 'ordered_pair'( X, Y ) ), member( X, 'universal_class'
% 6.69/7.09 ), member( Y, 'universal_class' ) ] )
% 6.69/7.09 , clause( 28801, [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) )
% 6.69/7.09 , ~( member( X, 'universal_class' ) ), =( X, Z ) ] )
% 6.69/7.09 , clause( 28802, [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) )
% 6.69/7.09 , ~( member( Y, 'universal_class' ) ), =( Y, T ) ] )
% 6.69/7.09 , clause( 28803, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 6.69/7.09 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( first(
% 6.69/7.09 'ordered_pair'( X, Y ) ), second( 'ordered_pair'( X, Y ) ) ),
% 6.69/7.09 'cross_product'( 'universal_class', 'universal_class' ) ) ] )
% 6.69/7.09 , clause( 28804, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 6.69/7.09 'cross_product'( 'universal_class', 'universal_class' ) ), =( first( X )
% 6.69/7.09 , X ) ] )
% 6.69/7.09 , clause( 28805, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 6.69/7.09 'cross_product'( 'universal_class', 'universal_class' ) ), =( second( X )
% 6.69/7.09 , X ) ] )
% 6.69/7.09 , clause( 28806, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.69/7.09 first( X ), X ) ] )
% 6.69/7.09 , clause( 28807, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.69/7.09 second( X ), X ) ] )
% 6.69/7.09 , clause( 28808, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 6.69/7.09 'universal_class', 'universal_class' ) ) ), =( first( 'ordered_pair'( X,
% 6.69/7.09 Y ) ), X ) ] )
% 6.69/7.09 , clause( 28809, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 6.69/7.09 'universal_class', 'universal_class' ) ) ), =( second( 'ordered_pair'( X
% 6.69/7.09 , Y ) ), Y ) ] )
% 6.69/7.09 , clause( 28810, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 6.69/7.09 'cross_product'( 'universal_class', 'universal_class' ) ), =( first( X )
% 6.69/7.09 , X ) ] )
% 6.69/7.09 , clause( 28811, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 6.69/7.09 'cross_product'( 'universal_class', 'universal_class' ) ), =( second( X )
% 6.69/7.09 , X ) ] )
% 6.69/7.09 , clause( 28812, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.69/7.09 first( X ), X ) ] )
% 6.69/7.09 , clause( 28813, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.69/7.09 second( X ), X ) ] )
% 6.69/7.09 , clause( 28814, [ ~( =( 'ordered_pair'( first( X ), second( X ) ), X ) ),
% 6.69/7.09 member( X, 'universal_class' ) ] )
% 6.69/7.09 , clause( 28815, [ ~( member( X, 'cross_product'( 'universal_class',
% 6.69/7.09 'universal_class' ) ) ), member( X, 'universal_class' ) ] )
% 6.69/7.09 , clause( 28816, [ ~( member( x, 'universal_class' ) ) ] )
% 6.69/7.09 , clause( 28817, [ ~( =( second( 'ordered_pair'( x, y ) ), 'ordered_pair'(
% 6.69/7.09 x, y ) ) ) ] )
% 6.69/7.09 ] ).
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09
% 6.69/7.09 subsumption(
% 6.69/7.09 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 6.69/7.12 )
% 6.69/7.12 , clause( 28651, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 6.69/7.12 ) ] )
% 6.69/7.12 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 6.69/7.12 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 subsumption(
% 6.69/7.12 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 6.69/7.12 , clause( 28654, [ subclass( X, 'universal_class' ) ] )
% 6.69/7.12 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 subsumption(
% 6.69/7.12 clause( 12, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) )
% 6.69/7.12 ), member( X, Z ) ] )
% 6.69/7.12 , clause( 28664, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.69/7.12 ) ) ), member( X, Z ) ] )
% 6.69/7.12 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 6.69/7.12 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 subsumption(
% 6.69/7.12 clause( 153, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( second(
% 6.69/7.12 X ), X ) ] )
% 6.69/7.12 , clause( 28807, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.69/7.12 second( X ), X ) ] )
% 6.69/7.12 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 6.69/7.12 1 )] ) ).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 eqswap(
% 6.69/7.12 clause( 30469, [ =( X, second( X ) ), =( 'ordered_pair'( first( X ), second(
% 6.69/7.12 X ) ), X ) ] )
% 6.69/7.12 , clause( 153, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.69/7.12 second( X ), X ) ] )
% 6.69/7.12 , 1, substitution( 0, [ :=( X, X )] )).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 paramod(
% 6.69/7.12 clause( 30504, [ member( X, 'cross_product'( 'universal_class',
% 6.69/7.12 'universal_class' ) ), =( X, second( X ) ), =( second( X ), X ) ] )
% 6.69/7.12 , clause( 30469, [ =( X, second( X ) ), =( 'ordered_pair'( first( X ),
% 6.69/7.12 second( X ) ), X ) ] )
% 6.69/7.12 , 1, clause( 28805, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 6.69/7.12 'cross_product'( 'universal_class', 'universal_class' ) ), =( second( X )
% 6.69/7.12 , X ) ] )
% 6.69/7.12 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 6.69/7.12 ).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 eqswap(
% 6.69/7.12 clause( 30505, [ =( second( X ), X ), member( X, 'cross_product'(
% 6.69/7.12 'universal_class', 'universal_class' ) ), =( second( X ), X ) ] )
% 6.69/7.12 , clause( 30504, [ member( X, 'cross_product'( 'universal_class',
% 6.69/7.12 'universal_class' ) ), =( X, second( X ) ), =( second( X ), X ) ] )
% 6.69/7.12 , 1, substitution( 0, [ :=( X, X )] )).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 factor(
% 6.69/7.12 clause( 30508, [ =( second( X ), X ), member( X, 'cross_product'(
% 6.69/7.12 'universal_class', 'universal_class' ) ) ] )
% 6.69/7.12 , clause( 30505, [ =( second( X ), X ), member( X, 'cross_product'(
% 6.69/7.12 'universal_class', 'universal_class' ) ), =( second( X ), X ) ] )
% 6.69/7.12 , 0, 2, substitution( 0, [ :=( X, X )] )).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 subsumption(
% 6.69/7.12 clause( 157, [ =( second( X ), X ), member( X, 'cross_product'(
% 6.69/7.12 'universal_class', 'universal_class' ) ) ] )
% 6.69/7.12 , clause( 30508, [ =( second( X ), X ), member( X, 'cross_product'(
% 6.69/7.12 'universal_class', 'universal_class' ) ) ] )
% 6.69/7.12 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 6.69/7.12 1 )] ) ).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 subsumption(
% 6.69/7.12 clause( 160, [ ~( member( x, 'universal_class' ) ) ] )
% 6.69/7.12 , clause( 28816, [ ~( member( x, 'universal_class' ) ) ] )
% 6.69/7.12 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 subsumption(
% 6.69/7.12 clause( 161, [ ~( =( second( 'ordered_pair'( x, y ) ), 'ordered_pair'( x, y
% 6.69/7.12 ) ) ) ] )
% 6.69/7.12 , clause( 28817, [ ~( =( second( 'ordered_pair'( x, y ) ), 'ordered_pair'(
% 6.69/7.12 x, y ) ) ) ] )
% 6.69/7.12 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 resolution(
% 6.69/7.12 clause( 30817, [ ~( subclass( X, 'universal_class' ) ), ~( member( x, X ) )
% 6.69/7.12 ] )
% 6.69/7.12 , clause( 160, [ ~( member( x, 'universal_class' ) ) ] )
% 6.69/7.12 , 0, clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 6.69/7.12 ) ] )
% 6.69/7.12 , 2, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y,
% 6.69/7.12 'universal_class' ), :=( Z, x )] )).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 resolution(
% 6.69/7.12 clause( 30818, [ ~( member( x, X ) ) ] )
% 6.69/7.12 , clause( 30817, [ ~( subclass( X, 'universal_class' ) ), ~( member( x, X )
% 6.69/7.12 ) ] )
% 6.69/7.12 , 0, clause( 3, [ subclass( X, 'universal_class' ) ] )
% 6.69/7.12 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 6.69/7.12 ).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 subsumption(
% 6.69/7.12 clause( 180, [ ~( member( x, X ) ) ] )
% 6.69/7.12 , clause( 30818, [ ~( member( x, X ) ) ] )
% 6.69/7.12 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 resolution(
% 6.69/7.12 clause( 30819, [ ~( member( 'ordered_pair'( x, Y ), 'cross_product'( X, Z )
% 6.69/7.12 ) ) ] )
% 6.69/7.12 , clause( 180, [ ~( member( x, X ) ) ] )
% 6.69/7.12 , 0, clause( 12, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.69/7.12 ) ) ), member( X, Z ) ] )
% 6.69/7.12 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, x ), :=( Y
% 6.69/7.12 , Y ), :=( Z, X ), :=( T, Z )] )).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 subsumption(
% 6.69/7.12 clause( 614, [ ~( member( 'ordered_pair'( x, X ), 'cross_product'( Y, Z ) )
% 6.69/7.12 ) ] )
% 6.69/7.12 , clause( 30819, [ ~( member( 'ordered_pair'( x, Y ), 'cross_product'( X, Z
% 6.69/7.12 ) ) ) ] )
% 6.69/7.12 , substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] ),
% 6.69/7.12 permutation( 0, [ ==>( 0, 0 )] ) ).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 eqswap(
% 6.69/7.12 clause( 30820, [ ~( =( 'ordered_pair'( x, y ), second( 'ordered_pair'( x, y
% 6.69/7.12 ) ) ) ) ] )
% 6.69/7.12 , clause( 161, [ ~( =( second( 'ordered_pair'( x, y ) ), 'ordered_pair'( x
% 6.69/7.12 , y ) ) ) ] )
% 6.69/7.12 , 0, substitution( 0, [] )).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 eqswap(
% 6.69/7.12 clause( 30821, [ =( X, second( X ) ), member( X, 'cross_product'(
% 6.69/7.12 'universal_class', 'universal_class' ) ) ] )
% 6.69/7.12 , clause( 157, [ =( second( X ), X ), member( X, 'cross_product'(
% 6.69/7.12 'universal_class', 'universal_class' ) ) ] )
% 6.69/7.12 , 0, substitution( 0, [ :=( X, X )] )).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 resolution(
% 6.69/7.12 clause( 30822, [ member( 'ordered_pair'( x, y ), 'cross_product'(
% 6.69/7.12 'universal_class', 'universal_class' ) ) ] )
% 6.69/7.12 , clause( 30820, [ ~( =( 'ordered_pair'( x, y ), second( 'ordered_pair'( x
% 6.69/7.12 , y ) ) ) ) ] )
% 6.69/7.12 , 0, clause( 30821, [ =( X, second( X ) ), member( X, 'cross_product'(
% 6.69/7.12 'universal_class', 'universal_class' ) ) ] )
% 6.69/7.12 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'ordered_pair'( x, y
% 6.69/7.12 ) )] )).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 resolution(
% 6.69/7.12 clause( 30823, [] )
% 6.69/7.12 , clause( 614, [ ~( member( 'ordered_pair'( x, X ), 'cross_product'( Y, Z )
% 6.69/7.12 ) ) ] )
% 6.69/7.12 , 0, clause( 30822, [ member( 'ordered_pair'( x, y ), 'cross_product'(
% 6.69/7.12 'universal_class', 'universal_class' ) ) ] )
% 6.69/7.12 , 0, substitution( 0, [ :=( X, y ), :=( Y, 'universal_class' ), :=( Z,
% 6.69/7.12 'universal_class' )] ), substitution( 1, [] )).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 subsumption(
% 6.69/7.12 clause( 28649, [] )
% 6.69/7.12 , clause( 30823, [] )
% 6.69/7.12 , substitution( 0, [] ), permutation( 0, [] ) ).
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 end.
% 6.69/7.12
% 6.69/7.12 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 6.69/7.12
% 6.69/7.12 Memory use:
% 6.69/7.12
% 6.69/7.12 space for terms: 515866
% 6.69/7.12 space for clauses: 1323427
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 clauses generated: 94631
% 6.69/7.12 clauses kept: 28650
% 6.69/7.12 clauses selected: 604
% 6.69/7.12 clauses deleted: 2243
% 6.69/7.12 clauses inuse deleted: 92
% 6.69/7.12
% 6.69/7.12 subsentry: 410059
% 6.69/7.12 literals s-matched: 289829
% 6.69/7.12 literals matched: 279390
% 6.69/7.12 full subsumption: 159800
% 6.69/7.12
% 6.69/7.12 checksum: 239000927
% 6.69/7.12
% 6.69/7.12
% 6.69/7.12 Bliksem ended
%------------------------------------------------------------------------------