TSTP Solution File: SET116-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET116-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n014.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 22:47:18 EDT 2022
% Result : Unsatisfiable 6.48s 6.88s
% Output : Refutation 6.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET116-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sun Jul 10 18:37:35 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.72/1.10 *** allocated 10000 integers for termspace/termends
% 0.72/1.10 *** allocated 10000 integers for clauses
% 0.72/1.10 *** allocated 10000 integers for justifications
% 0.72/1.10 Bliksem 1.12
% 0.72/1.10
% 0.72/1.10
% 0.72/1.10 Automatic Strategy Selection
% 0.72/1.10
% 0.72/1.10 Clauses:
% 0.72/1.10 [
% 0.72/1.10 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.72/1.10 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.72/1.10 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.72/1.10 ,
% 0.72/1.10 [ subclass( X, 'universal_class' ) ],
% 0.72/1.10 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.72/1.10 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.72/1.10 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.72/1.10 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.72/1.10 ,
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.72/1.10 ) ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.72/1.10 ) ) ],
% 0.72/1.10 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.72/1.10 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.72/1.10 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.72/1.10 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.72/1.10 X, Z ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.72/1.10 Y, T ) ],
% 0.72/1.10 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.72/1.10 ), 'cross_product'( Y, T ) ) ],
% 0.72/1.10 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.72/1.10 ), second( X ) ), X ) ],
% 0.72/1.10 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.72/1.10 'universal_class' ) ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.72/1.10 Y ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.72/1.10 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.72/1.10 , Y ), 'element_relation' ) ],
% 0.72/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.72/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.72/1.10 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.72/1.10 Z ) ) ],
% 0.72/1.10 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.72/1.10 member( X, Y ) ],
% 0.72/1.10 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.72/1.10 union( X, Y ) ) ],
% 0.72/1.10 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.72/1.10 intersection( complement( X ), complement( Y ) ) ) ),
% 0.72/1.10 'symmetric_difference'( X, Y ) ) ],
% 0.72/1.10 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.72/1.10 ,
% 0.72/1.10 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.72/1.10 ,
% 0.72/1.10 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.72/1.10 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.72/1.10 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.72/1.10 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.72/1.10 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.72/1.10 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.72/1.10 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.72/1.10 'cross_product'( 'universal_class', 'universal_class' ),
% 0.72/1.10 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.72/1.10 Y ), rotate( T ) ) ],
% 0.72/1.10 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.72/1.10 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.72/1.10 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.72/1.10 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.72/1.10 'cross_product'( 'universal_class', 'universal_class' ),
% 0.72/1.10 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.72/1.10 Z ), flip( T ) ) ],
% 0.72/1.10 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.72/1.10 inverse( X ) ) ],
% 0.72/1.10 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.72/1.10 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.72/1.10 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.72/1.10 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.72/1.10 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.72/1.10 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.72/1.10 ],
% 0.72/1.10 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.72/1.10 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.72/1.10 'universal_class' ) ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.72/1.10 successor( X ), Y ) ],
% 0.72/1.10 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.72/1.10 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.72/1.10 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.72/1.10 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.72/1.10 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.72/1.10 ,
% 0.72/1.10 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.72/1.10 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.72/1.10 [ inductive( omega ) ],
% 0.72/1.10 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.72/1.10 [ member( omega, 'universal_class' ) ],
% 0.72/1.10 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.72/1.10 , 'sum_class'( X ) ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.72/1.10 'universal_class' ) ],
% 0.72/1.10 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.72/1.10 'power_class'( X ) ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.72/1.10 'universal_class' ) ],
% 0.72/1.10 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.72/1.10 'universal_class' ) ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.72/1.10 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.72/1.10 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.72/1.10 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.72/1.10 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.72/1.10 ) ],
% 0.72/1.10 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.72/1.10 , 'identity_relation' ) ],
% 0.72/1.10 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.72/1.10 'single_valued_class'( X ) ],
% 0.72/1.10 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.72/1.10 'universal_class' ) ) ],
% 0.72/1.10 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.72/1.10 'identity_relation' ) ],
% 0.72/1.10 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.72/1.10 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.72/1.10 , function( X ) ],
% 0.72/1.10 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.72/1.10 X, Y ), 'universal_class' ) ],
% 0.72/1.10 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.72/1.10 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.72/1.10 ) ],
% 0.72/1.10 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.72/1.10 [ function( choice ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.72/1.10 apply( choice, X ), X ) ],
% 0.72/1.10 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.72/1.10 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.72/1.10 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.72/1.10 ,
% 0.72/1.10 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.72/1.10 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.72/1.10 , complement( compose( complement( 'element_relation' ), inverse(
% 0.72/1.10 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.72/1.10 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.72/1.10 'identity_relation' ) ],
% 0.72/1.10 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.72/1.10 , diagonalise( X ) ) ],
% 0.72/1.10 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.72/1.10 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.72/1.10 [ ~( operation( X ) ), function( X ) ],
% 0.72/1.10 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.72/1.10 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.72/1.10 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.72/1.10 'domain_of'( X ) ) ) ],
% 0.72/1.10 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.72/1.10 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.72/1.10 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.72/1.10 X ) ],
% 0.72/1.10 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.72/1.10 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.72/1.10 'domain_of'( X ) ) ],
% 0.72/1.10 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.72/1.10 'domain_of'( Z ) ) ) ],
% 0.72/1.10 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.72/1.10 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.72/1.10 ), compatible( X, Y, Z ) ],
% 0.72/1.10 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.72/1.10 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.72/1.10 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.72/1.10 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.72/1.10 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.72/1.10 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.72/1.10 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.72/1.10 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.72/1.10 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.72/1.10 , Y ) ],
% 0.72/1.10 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.72/1.10 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.72/1.10 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.72/1.10 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.72/1.10 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.72/1.10 X, 'unordered_pair'( X, Y ) ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.72/1.10 Y, 'unordered_pair'( X, Y ) ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.72/1.10 X, 'universal_class' ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.72/1.10 Y, 'universal_class' ) ],
% 0.72/1.10 [ subclass( X, X ) ],
% 0.72/1.10 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.72/1.10 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.72/1.10 'not_subclass_element'( Y, X ), Y ) ],
% 0.72/1.10 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.72/1.10 'not_subclass_element'( Y, X ), Y ) ],
% 0.72/1.10 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.72/1.10 'not_subclass_element'( Y, X ), Y ) ],
% 0.72/1.10 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.72/1.10 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.72/1.10 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.72/1.10 [ ~( member( X, 'null_class' ) ) ],
% 0.72/1.10 [ subclass( 'null_class', X ) ],
% 0.72/1.10 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.72/1.10 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.72/1.10 ), X ) ],
% 0.72/1.10 [ member( 'null_class', 'universal_class' ) ],
% 0.72/1.10 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.72/1.10 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.72/1.10 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.72/1.10 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.72/1.10 Y ) ) ],
% 0.72/1.10 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.72/1.10 Y ) ) ],
% 0.72/1.10 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.72/1.10 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.72/1.10 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.72/1.10 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.72/1.10 'universal_class' ) ) ), =( Y, Z ) ],
% 0.72/1.10 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.72/1.10 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.72/1.10 'universal_class' ) ) ), =( X, Z ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.72/1.10 'null_class' ) ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.72/1.10 'null_class' ) ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.72/1.10 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 0.72/1.10 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 0.72/1.10 X, Z ), Y ) ],
% 0.72/1.10 [ member( singleton( X ), 'universal_class' ) ],
% 0.72/1.10 [ member( singleton( X ), 'unordered_pair'( Y, singleton( X ) ) ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), member( X, singleton( X ) ) ]
% 0.72/1.10 ,
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X ),
% 0.72/1.10 'null_class' ) ) ],
% 0.72/1.10 [ member( 'null_class', singleton( 'null_class' ) ) ],
% 0.72/1.10 [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ],
% 0.72/1.10 [ member( X, 'universal_class' ), =( singleton( X ), 'null_class' ) ]
% 0.72/1.10 ,
% 0.72/1.10 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 0.72/1.10 'universal_class' ) ), =( X, Y ) ],
% 0.72/1.10 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 0.72/1.10 'universal_class' ) ), =( X, Y ) ],
% 0.72/1.10 [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~( member( Z,
% 0.72/1.10 'universal_class' ) ), =( Z, X ), =( Z, Y ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), member( 'member_of'( singleton( X
% 0.72/1.10 ) ), 'universal_class' ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), =( singleton( 'member_of'(
% 0.72/1.10 singleton( X ) ) ), singleton( X ) ) ],
% 0.72/1.10 [ member( 'member_of'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 0.72/1.10 ) ],
% 0.72/1.10 [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X ), X ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), =( 'member_of'( singleton( X ) )
% 0.72/1.10 , X ) ],
% 0.72/1.10 [ member( 'member_of1'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 0.72/1.10 ) ],
% 0.72/1.10 [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'( X ), X ) ]
% 0.72/1.10 ,
% 0.72/1.10 [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 0.72/1.10 'universal_class' ) ],
% 0.72/1.10 [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y, X ) ), =(
% 0.72/1.10 'member_of'( X ), Y ) ],
% 0.72/1.10 [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ],
% 0.72/1.10 [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' ), =( singleton(
% 0.72/1.10 Y ), X ) ],
% 0.72/1.10 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 0.72/1.10 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 0.72/1.10 intersection( complement( singleton( 'not_subclass_element'( X,
% 0.72/1.10 'null_class' ) ) ), X ) ), =( singleton( 'not_subclass_element'( X,
% 0.72/1.10 'null_class' ) ), X ), =( X, 'null_class' ) ],
% 0.72/1.10 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 0.72/1.10 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ), X ),
% 0.72/1.10 =( singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 0.72/1.10 'null_class' ) ],
% 0.72/1.10 [ ~( =( 'not_subclass_element'( intersection( complement( singleton(
% 0.72/1.10 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 0.72/1.10 'not_subclass_element'( X, 'null_class' ) ) ), =( singleton(
% 0.72/1.10 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 0.72/1.10 ,
% 0.72/1.10 [ =( 'unordered_pair'( X, Y ), union( singleton( X ), singleton( Y ) ) )
% 0.72/1.10 ],
% 0.72/1.10 [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ],
% 0.72/1.10 [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ],
% 0.72/1.10 [ member( 'unordered_pair'( X, singleton( Y ) ), 'ordered_pair'( X, Y )
% 0.72/1.10 ) ],
% 0.72/1.10 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, 'null_class'
% 0.72/1.10 ) ), 'ordered_pair'( X, Y ) ), member( Y, 'universal_class' ) ],
% 0.72/1.10 [ ~( member( X, 'universal_class' ) ), =( 'unordered_pair'( 'null_class'
% 0.72/1.10 , singleton( singleton( X ) ) ), 'ordered_pair'( Y, X ) ), member( Y,
% 0.72/1.10 'universal_class' ) ],
% 0.72/1.10 [ =( 'unordered_pair'( 'null_class', singleton( 'null_class' ) ),
% 0.72/1.10 'ordered_pair'( X, Y ) ), member( X, 'universal_class' ), member( Y,
% 0.72/1.10 'universal_class' ) ],
% 0.72/1.10 [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) ), ~( member( X
% 0.72/1.10 , 'universal_class' ) ), =( X, Z ) ],
% 0.72/1.10 [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) ), ~( member( Y
% 0.72/1.10 , 'universal_class' ) ), =( Y, T ) ],
% 0.72/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.72/1.10 , 'universal_class' ) ) ), member( 'ordered_pair'( first( 'ordered_pair'(
% 0.72/1.10 X, Y ) ), second( 'ordered_pair'( X, Y ) ) ), 'cross_product'(
% 0.72/1.10 'universal_class', 'universal_class' ) ) ],
% 0.72/1.10 [ member( 'ordered_pair'( first( X ), second( X ) ), 'cross_product'(
% 0.72/1.10 'universal_class', 'universal_class' ) ), =( first( X ), X ) ],
% 6.48/6.88 [ member( 'ordered_pair'( first( X ), second( X ) ), 'cross_product'(
% 6.48/6.88 'universal_class', 'universal_class' ) ), =( second( X ), X ) ],
% 6.48/6.88 [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( first( X ), X )
% 6.48/6.88 ],
% 6.48/6.88 [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( second( X ), X )
% 6.48/6.88 ],
% 6.48/6.88 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 6.48/6.88 , 'universal_class' ) ) ), =( first( 'ordered_pair'( X, Y ) ), X ) ],
% 6.48/6.88 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 6.48/6.88 , 'universal_class' ) ) ), =( second( 'ordered_pair'( X, Y ) ), Y ) ]
% 6.48/6.88 ,
% 6.48/6.88 [ ~( =( 'ordered_pair'( first( x ), second( x ) ), x ) ) ],
% 6.48/6.88 [ ~( =( second( x ), x ) ) ]
% 6.48/6.88 ] .
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88 percentage equality = 0.319018, percentage horn = 0.801242
% 6.48/6.88 This is a problem with some equality
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88 Options Used:
% 6.48/6.88
% 6.48/6.88 useres = 1
% 6.48/6.88 useparamod = 1
% 6.48/6.88 useeqrefl = 1
% 6.48/6.88 useeqfact = 1
% 6.48/6.88 usefactor = 1
% 6.48/6.88 usesimpsplitting = 0
% 6.48/6.88 usesimpdemod = 5
% 6.48/6.88 usesimpres = 3
% 6.48/6.88
% 6.48/6.88 resimpinuse = 1000
% 6.48/6.88 resimpclauses = 20000
% 6.48/6.88 substype = eqrewr
% 6.48/6.88 backwardsubs = 1
% 6.48/6.88 selectoldest = 5
% 6.48/6.88
% 6.48/6.88 litorderings [0] = split
% 6.48/6.88 litorderings [1] = extend the termordering, first sorting on arguments
% 6.48/6.88
% 6.48/6.88 termordering = kbo
% 6.48/6.88
% 6.48/6.88 litapriori = 0
% 6.48/6.88 termapriori = 1
% 6.48/6.88 litaposteriori = 0
% 6.48/6.88 termaposteriori = 0
% 6.48/6.88 demodaposteriori = 0
% 6.48/6.88 ordereqreflfact = 0
% 6.48/6.88
% 6.48/6.88 litselect = negord
% 6.48/6.88
% 6.48/6.88 maxweight = 15
% 6.48/6.88 maxdepth = 30000
% 6.48/6.88 maxlength = 115
% 6.48/6.88 maxnrvars = 195
% 6.48/6.88 excuselevel = 1
% 6.48/6.88 increasemaxweight = 1
% 6.48/6.88
% 6.48/6.88 maxselected = 10000000
% 6.48/6.88 maxnrclauses = 10000000
% 6.48/6.88
% 6.48/6.88 showgenerated = 0
% 6.48/6.88 showkept = 0
% 6.48/6.88 showselected = 0
% 6.48/6.88 showdeleted = 0
% 6.48/6.88 showresimp = 1
% 6.48/6.88 showstatus = 2000
% 6.48/6.88
% 6.48/6.88 prologoutput = 1
% 6.48/6.88 nrgoals = 5000000
% 6.48/6.88 totalproof = 1
% 6.48/6.88
% 6.48/6.88 Symbols occurring in the translation:
% 6.48/6.88
% 6.48/6.88 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 6.48/6.88 . [1, 2] (w:1, o:57, a:1, s:1, b:0),
% 6.48/6.88 ! [4, 1] (w:0, o:30, a:1, s:1, b:0),
% 6.48/6.88 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.48/6.88 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.48/6.88 subclass [41, 2] (w:1, o:82, a:1, s:1, b:0),
% 6.48/6.88 member [43, 2] (w:1, o:83, a:1, s:1, b:0),
% 6.48/6.88 'not_subclass_element' [44, 2] (w:1, o:84, a:1, s:1, b:0),
% 6.48/6.88 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 6.48/6.88 'unordered_pair' [46, 2] (w:1, o:85, a:1, s:1, b:0),
% 6.48/6.88 singleton [47, 1] (w:1, o:38, a:1, s:1, b:0),
% 6.48/6.88 'ordered_pair' [48, 2] (w:1, o:86, a:1, s:1, b:0),
% 6.48/6.88 'cross_product' [50, 2] (w:1, o:87, a:1, s:1, b:0),
% 6.48/6.88 first [52, 1] (w:1, o:39, a:1, s:1, b:0),
% 6.48/6.88 second [53, 1] (w:1, o:40, a:1, s:1, b:0),
% 6.48/6.88 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 6.48/6.88 intersection [55, 2] (w:1, o:89, a:1, s:1, b:0),
% 6.48/6.88 complement [56, 1] (w:1, o:41, a:1, s:1, b:0),
% 6.48/6.88 union [57, 2] (w:1, o:90, a:1, s:1, b:0),
% 6.48/6.88 'symmetric_difference' [58, 2] (w:1, o:91, a:1, s:1, b:0),
% 6.48/6.88 restrict [60, 3] (w:1, o:94, a:1, s:1, b:0),
% 6.48/6.88 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 6.48/6.88 'domain_of' [62, 1] (w:1, o:43, a:1, s:1, b:0),
% 6.48/6.88 rotate [63, 1] (w:1, o:35, a:1, s:1, b:0),
% 6.48/6.88 flip [65, 1] (w:1, o:44, a:1, s:1, b:0),
% 6.48/6.88 inverse [66, 1] (w:1, o:45, a:1, s:1, b:0),
% 6.48/6.88 'range_of' [67, 1] (w:1, o:36, a:1, s:1, b:0),
% 6.48/6.88 domain [68, 3] (w:1, o:96, a:1, s:1, b:0),
% 6.48/6.88 range [69, 3] (w:1, o:97, a:1, s:1, b:0),
% 6.48/6.88 image [70, 2] (w:1, o:88, a:1, s:1, b:0),
% 6.48/6.88 successor [71, 1] (w:1, o:46, a:1, s:1, b:0),
% 6.48/6.88 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 6.48/6.88 inductive [73, 1] (w:1, o:47, a:1, s:1, b:0),
% 6.48/6.88 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 6.48/6.88 'sum_class' [75, 1] (w:1, o:48, a:1, s:1, b:0),
% 6.48/6.88 'power_class' [76, 1] (w:1, o:51, a:1, s:1, b:0),
% 6.48/6.88 compose [78, 2] (w:1, o:92, a:1, s:1, b:0),
% 6.48/6.88 'single_valued_class' [79, 1] (w:1, o:52, a:1, s:1, b:0),
% 6.48/6.88 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 6.48/6.88 function [82, 1] (w:1, o:53, a:1, s:1, b:0),
% 6.48/6.88 regular [83, 1] (w:1, o:37, a:1, s:1, b:0),
% 6.48/6.88 apply [84, 2] (w:1, o:93, a:1, s:1, b:0),
% 6.48/6.88 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 6.48/6.88 'one_to_one' [86, 1] (w:1, o:49, a:1, s:1, b:0),
% 6.48/6.88 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 6.48/6.88 diagonalise [88, 1] (w:1, o:54, a:1, s:1, b:0),
% 6.48/6.88 cantor [89, 1] (w:1, o:42, a:1, s:1, b:0),
% 6.48/6.88 operation [90, 1] (w:1, o:50, a:1, s:1, b:0),
% 6.48/6.88 compatible [94, 3] (w:1, o:95, a:1, s:1, b:0),
% 6.48/6.88 homomorphism [95, 3] (w:1, o:98, a:1, s:1, b:0),
% 6.48/6.88 'not_homomorphism1' [96, 3] (w:1, o:99, a:1, s:1, b:0),
% 6.48/6.88 'not_homomorphism2' [97, 3] (w:1, o:100, a:1, s:1, b:0),
% 6.48/6.88 'member_of' [98, 1] (w:1, o:55, a:1, s:1, b:0),
% 6.48/6.88 'member_of1' [99, 1] (w:1, o:56, a:1, s:1, b:0),
% 6.48/6.88 x [100, 0] (w:1, o:29, a:1, s:1, b:0).
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88 Starting Search:
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88 Intermediate Status:
% 6.48/6.88 Generated: 4128
% 6.48/6.88 Kept: 2007
% 6.48/6.88 Inuse: 120
% 6.48/6.88 Deleted: 5
% 6.48/6.88 Deletedinuse: 2
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88 Intermediate Status:
% 6.48/6.88 Generated: 10023
% 6.48/6.88 Kept: 4049
% 6.48/6.88 Inuse: 196
% 6.48/6.88 Deleted: 9
% 6.48/6.88 Deletedinuse: 4
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88 Intermediate Status:
% 6.48/6.88 Generated: 15212
% 6.48/6.88 Kept: 6057
% 6.48/6.88 Inuse: 276
% 6.48/6.88 Deleted: 57
% 6.48/6.88 Deletedinuse: 39
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88 Intermediate Status:
% 6.48/6.88 Generated: 20882
% 6.48/6.88 Kept: 8129
% 6.48/6.88 Inuse: 356
% 6.48/6.88 Deleted: 65
% 6.48/6.88 Deletedinuse: 45
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88 Intermediate Status:
% 6.48/6.88 Generated: 27058
% 6.48/6.88 Kept: 10146
% 6.48/6.88 Inuse: 391
% 6.48/6.88 Deleted: 65
% 6.48/6.88 Deletedinuse: 45
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88 Intermediate Status:
% 6.48/6.88 Generated: 36575
% 6.48/6.88 Kept: 12231
% 6.48/6.88 Inuse: 430
% 6.48/6.88 Deleted: 67
% 6.48/6.88 Deletedinuse: 46
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88 Intermediate Status:
% 6.48/6.88 Generated: 46659
% 6.48/6.88 Kept: 15916
% 6.48/6.88 Inuse: 470
% 6.48/6.88 Deleted: 75
% 6.48/6.88 Deletedinuse: 49
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88 Intermediate Status:
% 6.48/6.88 Generated: 52325
% 6.48/6.88 Kept: 17934
% 6.48/6.88 Inuse: 484
% 6.48/6.88 Deleted: 78
% 6.48/6.88 Deletedinuse: 52
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88 Intermediate Status:
% 6.48/6.88 Generated: 60702
% 6.48/6.88 Kept: 19937
% 6.48/6.88 Inuse: 485
% 6.48/6.88 Deleted: 78
% 6.48/6.88 Deletedinuse: 52
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88 Resimplifying clauses:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88 Intermediate Status:
% 6.48/6.88 Generated: 70612
% 6.48/6.88 Kept: 22091
% 6.48/6.88 Inuse: 521
% 6.48/6.88 Deleted: 1193
% 6.48/6.88 Deletedinuse: 62
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88 Intermediate Status:
% 6.48/6.88 Generated: 84494
% 6.48/6.88 Kept: 25530
% 6.48/6.88 Inuse: 551
% 6.48/6.88 Deleted: 1198
% 6.48/6.88 Deletedinuse: 62
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88 Resimplifying inuse:
% 6.48/6.88 Done
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88 Intermediate Status:
% 6.48/6.88 Generated: 90756
% 6.48/6.88 Kept: 27597
% 6.48/6.88 Inuse: 561
% 6.48/6.88 Deleted: 1200
% 6.48/6.88 Deletedinuse: 64
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88 Bliksems!, er is een bewijs:
% 6.48/6.88 % SZS status Unsatisfiable
% 6.48/6.88 % SZS output start Refutation
% 6.48/6.88
% 6.48/6.88 clause( 153, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( second(
% 6.48/6.88 X ), X ) ] )
% 6.48/6.88 .
% 6.48/6.88 clause( 156, [ ~( =( 'ordered_pair'( first( x ), second( x ) ), x ) ) ] )
% 6.48/6.88 .
% 6.48/6.88 clause( 157, [ ~( =( second( x ), x ) ) ] )
% 6.48/6.88 .
% 6.48/6.88 clause( 27740, [] )
% 6.48/6.88 .
% 6.48/6.88
% 6.48/6.88
% 6.48/6.88 % SZS output end Refutation
% 6.48/6.88 found a proof!
% 6.48/6.89
% 6.48/6.89 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 6.48/6.89
% 6.48/6.89 initialclauses(
% 6.48/6.89 [ clause( 27742, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 6.48/6.89 ) ] )
% 6.48/6.89 , clause( 27743, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 6.48/6.89 , Y ) ] )
% 6.48/6.89 , clause( 27744, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 6.48/6.89 subclass( X, Y ) ] )
% 6.48/6.89 , clause( 27745, [ subclass( X, 'universal_class' ) ] )
% 6.48/6.89 , clause( 27746, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 6.48/6.89 , clause( 27747, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 6.48/6.89 , clause( 27748, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 6.48/6.89 ] )
% 6.48/6.89 , clause( 27749, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 6.48/6.89 =( X, Z ) ] )
% 6.48/6.89 , clause( 27750, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.48/6.89 'unordered_pair'( X, Y ) ) ] )
% 6.48/6.89 , clause( 27751, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.48/6.89 'unordered_pair'( Y, X ) ) ] )
% 6.48/6.89 , clause( 27752, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 6.48/6.89 )
% 6.48/6.89 , clause( 27753, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 6.48/6.89 , clause( 27754, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 6.48/6.89 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 6.48/6.89 , clause( 27755, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.48/6.89 ) ) ), member( X, Z ) ] )
% 6.48/6.89 , clause( 27756, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.48/6.89 ) ) ), member( Y, T ) ] )
% 6.48/6.89 , clause( 27757, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 6.48/6.89 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 6.48/6.89 , clause( 27758, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 6.48/6.89 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 6.48/6.89 , clause( 27759, [ subclass( 'element_relation', 'cross_product'(
% 6.48/6.89 'universal_class', 'universal_class' ) ) ] )
% 6.48/6.89 , clause( 27760, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 6.48/6.89 ), member( X, Y ) ] )
% 6.48/6.89 , clause( 27761, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 6.48/6.89 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 6.48/6.89 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 6.48/6.89 , clause( 27762, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 6.48/6.89 )
% 6.48/6.89 , clause( 27763, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 6.48/6.89 )
% 6.48/6.89 , clause( 27764, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 6.48/6.89 intersection( Y, Z ) ) ] )
% 6.48/6.89 , clause( 27765, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 6.48/6.89 )
% 6.48/6.89 , clause( 27766, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.48/6.89 complement( Y ) ), member( X, Y ) ] )
% 6.48/6.89 , clause( 27767, [ =( complement( intersection( complement( X ), complement(
% 6.48/6.89 Y ) ) ), union( X, Y ) ) ] )
% 6.48/6.89 , clause( 27768, [ =( intersection( complement( intersection( X, Y ) ),
% 6.48/6.89 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 6.48/6.89 'symmetric_difference'( X, Y ) ) ] )
% 6.48/6.89 , clause( 27769, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 6.48/6.89 X, Y, Z ) ) ] )
% 6.48/6.89 , clause( 27770, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 6.48/6.89 Z, X, Y ) ) ] )
% 6.48/6.89 , clause( 27771, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 6.48/6.89 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 6.48/6.89 , clause( 27772, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 6.48/6.89 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 6.48/6.89 'domain_of'( Y ) ) ] )
% 6.48/6.89 , clause( 27773, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 6.48/6.89 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 6.48/6.89 , clause( 27774, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.48/6.89 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 6.48/6.89 ] )
% 6.48/6.89 , clause( 27775, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.48/6.89 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 6.48/6.89 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 6.48/6.89 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 6.48/6.89 , Y ), rotate( T ) ) ] )
% 6.48/6.89 , clause( 27776, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 6.48/6.89 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 6.48/6.89 , clause( 27777, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.48/6.89 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 6.48/6.89 )
% 6.48/6.89 , clause( 27778, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.48/6.89 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 6.48/6.89 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 6.48/6.89 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 6.48/6.89 , Z ), flip( T ) ) ] )
% 6.48/6.89 , clause( 27779, [ =( 'domain_of'( flip( 'cross_product'( X,
% 6.48/6.89 'universal_class' ) ) ), inverse( X ) ) ] )
% 6.48/6.89 , clause( 27780, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 6.48/6.89 , clause( 27781, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 6.48/6.89 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 6.48/6.89 , clause( 27782, [ =( second( 'not_subclass_element'( restrict( X,
% 6.48/6.89 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 6.48/6.89 , clause( 27783, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 6.48/6.89 image( X, Y ) ) ] )
% 6.48/6.89 , clause( 27784, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 6.48/6.89 , clause( 27785, [ subclass( 'successor_relation', 'cross_product'(
% 6.48/6.89 'universal_class', 'universal_class' ) ) ] )
% 6.48/6.89 , clause( 27786, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 6.48/6.89 ) ), =( successor( X ), Y ) ] )
% 6.48/6.89 , clause( 27787, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 6.48/6.89 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 6.48/6.89 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 6.48/6.89 , clause( 27788, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 6.48/6.89 , clause( 27789, [ ~( inductive( X ) ), subclass( image(
% 6.48/6.89 'successor_relation', X ), X ) ] )
% 6.48/6.89 , clause( 27790, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 6.48/6.89 'successor_relation', X ), X ) ), inductive( X ) ] )
% 6.48/6.89 , clause( 27791, [ inductive( omega ) ] )
% 6.48/6.89 , clause( 27792, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 6.48/6.89 , clause( 27793, [ member( omega, 'universal_class' ) ] )
% 6.48/6.89 , clause( 27794, [ =( 'domain_of'( restrict( 'element_relation',
% 6.48/6.89 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 6.48/6.89 , clause( 27795, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 6.48/6.89 X ), 'universal_class' ) ] )
% 6.48/6.89 , clause( 27796, [ =( complement( image( 'element_relation', complement( X
% 6.48/6.89 ) ) ), 'power_class'( X ) ) ] )
% 6.48/6.89 , clause( 27797, [ ~( member( X, 'universal_class' ) ), member(
% 6.48/6.89 'power_class'( X ), 'universal_class' ) ] )
% 6.48/6.89 , clause( 27798, [ subclass( compose( X, Y ), 'cross_product'(
% 6.48/6.89 'universal_class', 'universal_class' ) ) ] )
% 6.48/6.89 , clause( 27799, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 6.48/6.89 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 6.48/6.89 , clause( 27800, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 6.48/6.89 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 6.48/6.89 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 6.48/6.89 ) ] )
% 6.48/6.89 , clause( 27801, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 6.48/6.89 inverse( X ) ), 'identity_relation' ) ] )
% 6.48/6.89 , clause( 27802, [ ~( subclass( compose( X, inverse( X ) ),
% 6.48/6.89 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 6.48/6.89 , clause( 27803, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 6.48/6.89 'universal_class', 'universal_class' ) ) ] )
% 6.48/6.89 , clause( 27804, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 6.48/6.89 , 'identity_relation' ) ] )
% 6.48/6.89 , clause( 27805, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 6.48/6.89 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 6.48/6.89 'identity_relation' ) ), function( X ) ] )
% 6.48/6.89 , clause( 27806, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 6.48/6.89 , member( image( X, Y ), 'universal_class' ) ] )
% 6.48/6.89 , clause( 27807, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 6.48/6.89 , clause( 27808, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 6.48/6.89 , 'null_class' ) ] )
% 6.48/6.89 , clause( 27809, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 6.48/6.89 Y ) ) ] )
% 6.48/6.89 , clause( 27810, [ function( choice ) ] )
% 6.48/6.89 , clause( 27811, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 6.48/6.89 ), member( apply( choice, X ), X ) ] )
% 6.48/6.89 , clause( 27812, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 6.48/6.89 , clause( 27813, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 6.48/6.89 , clause( 27814, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 6.48/6.89 'one_to_one'( X ) ] )
% 6.48/6.89 , clause( 27815, [ =( intersection( 'cross_product'( 'universal_class',
% 6.48/6.89 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 6.48/6.89 'universal_class' ), complement( compose( complement( 'element_relation'
% 6.48/6.89 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 6.48/6.89 , clause( 27816, [ =( intersection( inverse( 'subset_relation' ),
% 6.48/6.89 'subset_relation' ), 'identity_relation' ) ] )
% 6.48/6.89 , clause( 27817, [ =( complement( 'domain_of'( intersection( X,
% 6.48/6.89 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 6.48/6.89 , clause( 27818, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 6.48/6.89 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 6.48/6.89 , clause( 27819, [ ~( operation( X ) ), function( X ) ] )
% 6.48/6.89 , clause( 27820, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 6.48/6.89 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 6.48/6.89 ] )
% 6.48/6.89 , clause( 27821, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 6.48/6.89 'domain_of'( 'domain_of'( X ) ) ) ] )
% 6.48/6.89 , clause( 27822, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 6.48/6.89 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 6.48/6.89 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 6.48/6.89 operation( X ) ] )
% 6.48/6.89 , clause( 27823, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 6.48/6.89 , clause( 27824, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 6.48/6.89 Y ) ), 'domain_of'( X ) ) ] )
% 6.48/6.89 , clause( 27825, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 6.48/6.89 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 6.48/6.89 , clause( 27826, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 6.48/6.89 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 6.48/6.89 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 6.48/6.89 , clause( 27827, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 6.48/6.89 , clause( 27828, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 6.48/6.89 , clause( 27829, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 6.48/6.89 , clause( 27830, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 6.48/6.89 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 6.48/6.89 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 6.48/6.89 )
% 6.48/6.89 , clause( 27831, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 6.48/6.89 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 6.48/6.89 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 6.48/6.89 , Y ) ] )
% 6.48/6.89 , clause( 27832, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 6.48/6.89 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 6.48/6.89 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 6.48/6.89 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 6.48/6.89 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 6.48/6.89 )
% 6.48/6.89 , clause( 27833, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.48/6.89 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 6.48/6.89 , clause( 27834, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.48/6.89 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 6.48/6.89 , clause( 27835, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.48/6.89 ) ) ), member( X, 'universal_class' ) ] )
% 6.48/6.89 , clause( 27836, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.48/6.89 ) ) ), member( Y, 'universal_class' ) ] )
% 6.48/6.89 , clause( 27837, [ subclass( X, X ) ] )
% 6.48/6.89 , clause( 27838, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 6.48/6.89 X, Z ) ] )
% 6.48/6.89 , clause( 27839, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 6.48/6.89 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 6.48/6.89 , clause( 27840, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 6.48/6.89 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 6.48/6.89 , clause( 27841, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 6.48/6.89 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 6.48/6.89 , clause( 27842, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 6.48/6.89 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 6.48/6.89 , clause( 27843, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 6.48/6.89 )
% 6.48/6.89 , clause( 27844, [ ~( member( X, 'null_class' ) ) ] )
% 6.48/6.89 , clause( 27845, [ subclass( 'null_class', X ) ] )
% 6.48/6.89 , clause( 27846, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 6.48/6.89 )
% 6.48/6.89 , clause( 27847, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 6.48/6.89 , 'null_class' ), X ) ] )
% 6.48/6.89 , clause( 27848, [ member( 'null_class', 'universal_class' ) ] )
% 6.48/6.89 , clause( 27849, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 6.48/6.89 ] )
% 6.48/6.89 , clause( 27850, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 6.48/6.89 )
% 6.48/6.89 , clause( 27851, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 6.48/6.89 )
% 6.48/6.89 , clause( 27852, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 6.48/6.89 X ), singleton( Y ) ) ] )
% 6.48/6.89 , clause( 27853, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 6.48/6.89 Y ), singleton( Y ) ) ] )
% 6.48/6.89 , clause( 27854, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 6.48/6.89 'universal_class' ), member( Y, 'universal_class' ) ] )
% 6.48/6.89 , clause( 27855, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 6.48/6.89 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 6.48/6.89 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 6.48/6.89 , clause( 27856, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 6.48/6.89 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 6.48/6.89 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 6.48/6.89 , clause( 27857, [ ~( member( X, 'universal_class' ) ), ~( =(
% 6.48/6.89 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 6.48/6.89 , clause( 27858, [ ~( member( X, 'universal_class' ) ), ~( =(
% 6.48/6.89 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 6.48/6.89 , clause( 27859, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.48/6.89 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 6.48/6.89 , clause( 27860, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 6.48/6.89 'unordered_pair'( X, Z ), Y ) ] )
% 6.48/6.89 , clause( 27861, [ member( singleton( X ), 'universal_class' ) ] )
% 6.48/6.89 , clause( 27862, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 6.48/6.89 X ) ) ) ] )
% 6.48/6.89 , clause( 27863, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.48/6.89 singleton( X ) ) ] )
% 6.48/6.89 , clause( 27864, [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X
% 6.48/6.89 ), 'null_class' ) ) ] )
% 6.48/6.89 , clause( 27865, [ member( 'null_class', singleton( 'null_class' ) ) ] )
% 6.48/6.89 , clause( 27866, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 6.48/6.89 , clause( 27867, [ member( X, 'universal_class' ), =( singleton( X ),
% 6.48/6.89 'null_class' ) ] )
% 6.48/6.89 , clause( 27868, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 6.48/6.89 'universal_class' ) ), =( X, Y ) ] )
% 6.48/6.89 , clause( 27869, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 6.48/6.89 'universal_class' ) ), =( X, Y ) ] )
% 6.48/6.89 , clause( 27870, [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~(
% 6.48/6.89 member( Z, 'universal_class' ) ), =( Z, X ), =( Z, Y ) ] )
% 6.48/6.89 , clause( 27871, [ ~( member( X, 'universal_class' ) ), member( 'member_of'(
% 6.48/6.89 singleton( X ) ), 'universal_class' ) ] )
% 6.48/6.89 , clause( 27872, [ ~( member( X, 'universal_class' ) ), =( singleton(
% 6.48/6.89 'member_of'( singleton( X ) ) ), singleton( X ) ) ] )
% 6.48/6.89 , clause( 27873, [ member( 'member_of'( X ), 'universal_class' ), =(
% 6.48/6.89 'member_of'( X ), X ) ] )
% 6.48/6.89 , clause( 27874, [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X
% 6.48/6.89 ), X ) ] )
% 6.48/6.89 , clause( 27875, [ ~( member( X, 'universal_class' ) ), =( 'member_of'(
% 6.48/6.89 singleton( X ) ), X ) ] )
% 6.48/6.89 , clause( 27876, [ member( 'member_of1'( X ), 'universal_class' ), =(
% 6.48/6.89 'member_of'( X ), X ) ] )
% 6.48/6.89 , clause( 27877, [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'(
% 6.48/6.89 X ), X ) ] )
% 6.48/6.89 , clause( 27878, [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 6.48/6.89 'universal_class' ) ] )
% 6.48/6.89 , clause( 27879, [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y
% 6.48/6.89 , X ) ), =( 'member_of'( X ), Y ) ] )
% 6.48/6.89 , clause( 27880, [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ] )
% 6.48/6.89 , clause( 27881, [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' )
% 6.48/6.89 , =( singleton( Y ), X ) ] )
% 6.48/6.89 , clause( 27882, [ member( 'not_subclass_element'( intersection( complement(
% 6.48/6.89 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 6.48/6.89 'null_class' ), intersection( complement( singleton(
% 6.48/6.89 'not_subclass_element'( X, 'null_class' ) ) ), X ) ), =( singleton(
% 6.48/6.89 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 6.48/6.89 )
% 6.48/6.89 , clause( 27883, [ member( 'not_subclass_element'( intersection( complement(
% 6.48/6.89 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 6.48/6.89 'null_class' ), X ), =( singleton( 'not_subclass_element'( X,
% 6.48/6.89 'null_class' ) ), X ), =( X, 'null_class' ) ] )
% 6.48/6.89 , clause( 27884, [ ~( =( 'not_subclass_element'( intersection( complement(
% 6.48/6.89 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 6.48/6.89 'null_class' ), 'not_subclass_element'( X, 'null_class' ) ) ), =(
% 6.48/6.89 singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 6.48/6.89 'null_class' ) ] )
% 6.48/6.89 , clause( 27885, [ =( 'unordered_pair'( X, Y ), union( singleton( X ),
% 6.48/6.89 singleton( Y ) ) ) ] )
% 6.48/6.89 , clause( 27886, [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ] )
% 6.48/6.89 , clause( 27887, [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ] )
% 6.48/6.89 , clause( 27888, [ member( 'unordered_pair'( X, singleton( Y ) ),
% 6.48/6.89 'ordered_pair'( X, Y ) ) ] )
% 6.48/6.89 , clause( 27889, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 6.48/6.89 , 'null_class' ) ), 'ordered_pair'( X, Y ) ), member( Y,
% 6.48/6.89 'universal_class' ) ] )
% 6.48/6.89 , clause( 27890, [ ~( member( X, 'universal_class' ) ), =( 'unordered_pair'(
% 6.48/6.89 'null_class', singleton( singleton( X ) ) ), 'ordered_pair'( Y, X ) ),
% 6.48/6.89 member( Y, 'universal_class' ) ] )
% 6.48/6.89 , clause( 27891, [ =( 'unordered_pair'( 'null_class', singleton(
% 6.48/6.89 'null_class' ) ), 'ordered_pair'( X, Y ) ), member( X, 'universal_class'
% 6.48/6.89 ), member( Y, 'universal_class' ) ] )
% 6.48/6.89 , clause( 27892, [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) )
% 6.48/6.89 , ~( member( X, 'universal_class' ) ), =( X, Z ) ] )
% 6.48/6.89 , clause( 27893, [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) )
% 6.48/6.89 , ~( member( Y, 'universal_class' ) ), =( Y, T ) ] )
% 6.48/6.89 , clause( 27894, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 6.48/6.89 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( first(
% 6.48/6.89 'ordered_pair'( X, Y ) ), second( 'ordered_pair'( X, Y ) ) ),
% 6.48/6.89 'cross_product'( 'universal_class', 'universal_class' ) ) ] )
% 6.48/6.89 , clause( 27895, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 6.48/6.89 'cross_product'( 'universal_class', 'universal_class' ) ), =( first( X )
% 6.48/6.89 , X ) ] )
% 6.48/6.89 , clause( 27896, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 6.48/6.89 'cross_product'( 'universal_class', 'universal_class' ) ), =( second( X )
% 6.48/6.89 , X ) ] )
% 6.48/6.89 , clause( 27897, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.48/6.89 first( X ), X ) ] )
% 6.48/6.89 , clause( 27898, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.48/6.89 second( X ), X ) ] )
% 6.48/6.89 , clause( 27899, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 6.48/6.89 'universal_class', 'universal_class' ) ) ), =( first( 'ordered_pair'( X,
% 6.48/6.89 Y ) ), X ) ] )
% 6.48/6.89 , clause( 27900, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 6.48/6.89 'universal_class', 'universal_class' ) ) ), =( second( 'ordered_pair'( X
% 6.48/6.89 , Y ) ), Y ) ] )
% 6.48/6.89 , clause( 27901, [ ~( =( 'ordered_pair'( first( x ), second( x ) ), x ) ) ]
% 6.48/6.89 )
% 6.48/6.89 , clause( 27902, [ ~( =( second( x ), x ) ) ] )
% 6.48/6.89 ] ).
% 6.48/6.89
% 6.48/6.89
% 6.48/6.89
% 6.48/6.89 subsumption(
% 6.48/6.89 clause( 153, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( second(
% 6.48/6.89 X ), X ) ] )
% 6.48/6.89 , clause( 27898, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.48/6.89 second( X ), X ) ] )
% 6.48/6.89 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 6.48/6.89 1 )] ) ).
% 6.48/6.89
% 6.48/6.89
% 6.48/6.89 subsumption(
% 6.48/6.89 clause( 156, [ ~( =( 'ordered_pair'( first( x ), second( x ) ), x ) ) ] )
% 6.48/6.89 , clause( 27901, [ ~( =( 'ordered_pair'( first( x ), second( x ) ), x ) ) ]
% 6.48/6.89 )
% 6.48/6.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 6.48/6.89
% 6.48/6.89
% 6.48/6.89 subsumption(
% 6.48/6.89 clause( 157, [ ~( =( second( x ), x ) ) ] )
% 6.48/6.89 , clause( 27902, [ ~( =( second( x ), x ) ) ] )
% 6.48/6.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 6.48/6.89
% 6.48/6.89
% 6.48/6.89 eqswap(
% 6.48/6.89 clause( 28336, [ =( X, 'ordered_pair'( first( X ), second( X ) ) ), =(
% 6.48/6.89 second( X ), X ) ] )
% 6.48/6.89 , clause( 153, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.48/6.89 second( X ), X ) ] )
% 6.48/6.89 , 0, substitution( 0, [ :=( X, X )] )).
% 6.48/6.89
% 6.48/6.89
% 6.48/6.89 eqswap(
% 6.48/6.89 clause( 28340, [ ~( =( x, 'ordered_pair'( first( x ), second( x ) ) ) ) ]
% 6.48/6.89 )
% 6.48/6.89 , clause( 156, [ ~( =( 'ordered_pair'( first( x ), second( x ) ), x ) ) ]
% 6.48/6.89 )
% 6.48/6.89 , 0, substitution( 0, [] )).
% 6.48/6.89
% 6.48/6.89
% 6.48/6.89 resolution(
% 6.48/6.89 clause( 28341, [ =( x, 'ordered_pair'( first( x ), second( x ) ) ) ] )
% 6.48/6.89 , clause( 157, [ ~( =( second( x ), x ) ) ] )
% 6.48/6.89 , 0, clause( 28336, [ =( X, 'ordered_pair'( first( X ), second( X ) ) ),
% 6.48/6.89 =( second( X ), X ) ] )
% 6.48/6.89 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, x )] )).
% 6.48/6.89
% 6.48/6.89
% 6.48/6.89 resolution(
% 6.48/6.89 clause( 28342, [] )
% 6.48/6.89 , clause( 28340, [ ~( =( x, 'ordered_pair'( first( x ), second( x ) ) ) ) ]
% 6.48/6.89 )
% 6.48/6.89 , 0, clause( 28341, [ =( x, 'ordered_pair'( first( x ), second( x ) ) ) ]
% 6.48/6.89 )
% 6.48/6.89 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 6.48/6.89
% 6.48/6.89
% 6.48/6.89 subsumption(
% 6.48/6.89 clause( 27740, [] )
% 6.48/6.89 , clause( 28342, [] )
% 6.48/6.89 , substitution( 0, [] ), permutation( 0, [] ) ).
% 6.48/6.89
% 6.48/6.89
% 6.48/6.89 end.
% 6.48/6.89
% 6.48/6.89 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 6.48/6.89
% 6.48/6.89 Memory use:
% 6.48/6.89
% 6.48/6.89 space for terms: 505932
% 6.48/6.89 space for clauses: 1276237
% 6.48/6.89
% 6.48/6.89
% 6.48/6.89 clauses generated: 91247
% 6.48/6.89 clauses kept: 27741
% 6.48/6.89 clauses selected: 566
% 6.48/6.89 clauses deleted: 1200
% 6.48/6.89 clauses inuse deleted: 64
% 6.48/6.89
% 6.48/6.89 subsentry: 346266
% 6.48/6.89 literals s-matched: 264074
% 6.48/6.89 literals matched: 254154
% 6.48/6.89 full subsumption: 156249
% 6.48/6.89
% 6.48/6.89 checksum: 297028618
% 6.48/6.89
% 6.48/6.89
% 6.48/6.89 Bliksem ended
%------------------------------------------------------------------------------