TSTP Solution File: SET115-7 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET115-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n007.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 6.83s 7.19s
% Output : Refutation 6.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET115-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.14/0.13 % Command : bliksem %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Sun Jul 10 07:22:31 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.76/1.13 *** allocated 10000 integers for termspace/termends
% 0.76/1.13 *** allocated 10000 integers for clauses
% 0.76/1.13 *** allocated 10000 integers for justifications
% 0.76/1.13 Bliksem 1.12
% 0.76/1.13
% 0.76/1.13
% 0.76/1.13 Automatic Strategy Selection
% 0.76/1.13
% 0.76/1.13 Clauses:
% 0.76/1.13 [
% 0.76/1.13 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.76/1.13 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.76/1.13 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ subclass( X, 'universal_class' ) ],
% 0.76/1.13 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.76/1.13 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.76/1.13 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.76/1.13 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.76/1.13 ) ) ],
% 0.76/1.13 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.76/1.13 ) ) ],
% 0.76/1.13 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.76/1.13 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.76/1.13 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.76/1.13 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.76/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.76/1.13 X, Z ) ],
% 0.76/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.76/1.13 Y, T ) ],
% 0.76/1.13 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.76/1.13 ), 'cross_product'( Y, T ) ) ],
% 0.76/1.13 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.76/1.13 ), second( X ) ), X ) ],
% 0.76/1.13 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.76/1.13 'universal_class' ) ) ],
% 0.76/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.76/1.13 Y ) ],
% 0.76/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.76/1.13 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.76/1.13 , Y ), 'element_relation' ) ],
% 0.76/1.13 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.76/1.13 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.76/1.13 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.76/1.13 Z ) ) ],
% 0.76/1.13 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.76/1.13 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.76/1.13 member( X, Y ) ],
% 0.76/1.13 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.76/1.13 union( X, Y ) ) ],
% 0.76/1.13 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.76/1.13 intersection( complement( X ), complement( Y ) ) ) ),
% 0.76/1.13 'symmetric_difference'( X, Y ) ) ],
% 0.76/1.13 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.76/1.13 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.76/1.13 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.76/1.13 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.76/1.13 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.76/1.13 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.76/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.76/1.13 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.76/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.76/1.13 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.76/1.13 'cross_product'( 'universal_class', 'universal_class' ),
% 0.76/1.13 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.76/1.13 Y ), rotate( T ) ) ],
% 0.76/1.13 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.76/1.13 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.76/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.76/1.13 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.76/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.76/1.13 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.76/1.13 'cross_product'( 'universal_class', 'universal_class' ),
% 0.76/1.13 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.76/1.13 Z ), flip( T ) ) ],
% 0.76/1.13 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.76/1.13 inverse( X ) ) ],
% 0.76/1.13 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.76/1.13 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.76/1.13 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.76/1.13 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.76/1.13 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.76/1.13 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.76/1.13 ],
% 0.76/1.13 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.76/1.13 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.76/1.13 'universal_class' ) ) ],
% 0.76/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.76/1.13 successor( X ), Y ) ],
% 0.76/1.13 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.76/1.13 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.76/1.13 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.76/1.13 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.76/1.13 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.76/1.13 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.76/1.13 [ inductive( omega ) ],
% 0.76/1.13 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.76/1.13 [ member( omega, 'universal_class' ) ],
% 0.76/1.13 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.76/1.13 , 'sum_class'( X ) ) ],
% 0.76/1.13 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.76/1.13 'universal_class' ) ],
% 0.76/1.13 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.76/1.13 'power_class'( X ) ) ],
% 0.76/1.13 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.76/1.13 'universal_class' ) ],
% 0.76/1.13 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.76/1.13 'universal_class' ) ) ],
% 0.76/1.13 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.76/1.13 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.76/1.13 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.76/1.13 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.76/1.13 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.76/1.13 ) ],
% 0.76/1.13 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.76/1.13 , 'identity_relation' ) ],
% 0.76/1.13 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.76/1.13 'single_valued_class'( X ) ],
% 0.76/1.13 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.76/1.13 'universal_class' ) ) ],
% 0.76/1.13 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.76/1.13 'identity_relation' ) ],
% 0.76/1.13 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.76/1.13 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.76/1.13 , function( X ) ],
% 0.76/1.13 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.76/1.13 X, Y ), 'universal_class' ) ],
% 0.76/1.13 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.76/1.13 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.76/1.13 ) ],
% 0.76/1.13 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.76/1.13 [ function( choice ) ],
% 0.76/1.13 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.76/1.13 apply( choice, X ), X ) ],
% 0.76/1.13 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.76/1.13 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.76/1.13 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.76/1.13 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.76/1.13 , complement( compose( complement( 'element_relation' ), inverse(
% 0.76/1.13 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.76/1.13 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.76/1.13 'identity_relation' ) ],
% 0.76/1.13 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.76/1.13 , diagonalise( X ) ) ],
% 0.76/1.13 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.76/1.13 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.76/1.13 [ ~( operation( X ) ), function( X ) ],
% 0.76/1.13 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.76/1.13 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.76/1.13 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.76/1.13 'domain_of'( X ) ) ) ],
% 0.76/1.13 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.76/1.13 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.76/1.13 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.76/1.13 X ) ],
% 0.76/1.13 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.76/1.13 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.76/1.13 'domain_of'( X ) ) ],
% 0.76/1.13 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.76/1.13 'domain_of'( Z ) ) ) ],
% 0.76/1.13 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.76/1.13 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.76/1.13 ), compatible( X, Y, Z ) ],
% 0.76/1.13 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.76/1.13 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.76/1.13 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.76/1.13 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.76/1.13 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.76/1.13 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.76/1.13 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.76/1.13 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.76/1.13 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.76/1.13 , Y ) ],
% 0.76/1.13 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.76/1.13 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.76/1.13 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.76/1.13 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.76/1.13 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.76/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.76/1.13 X, 'unordered_pair'( X, Y ) ) ],
% 0.76/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.76/1.13 Y, 'unordered_pair'( X, Y ) ) ],
% 0.76/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.76/1.13 X, 'universal_class' ) ],
% 0.76/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.76/1.13 Y, 'universal_class' ) ],
% 0.76/1.13 [ subclass( X, X ) ],
% 0.76/1.13 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.76/1.13 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.76/1.13 'not_subclass_element'( Y, X ), Y ) ],
% 0.76/1.13 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.76/1.13 'not_subclass_element'( Y, X ), Y ) ],
% 0.76/1.13 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.76/1.13 'not_subclass_element'( Y, X ), Y ) ],
% 0.76/1.13 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.76/1.13 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.76/1.13 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.76/1.13 [ ~( member( X, 'null_class' ) ) ],
% 0.76/1.13 [ subclass( 'null_class', X ) ],
% 0.76/1.13 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.76/1.13 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.76/1.13 ), X ) ],
% 0.76/1.13 [ member( 'null_class', 'universal_class' ) ],
% 0.76/1.13 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.76/1.13 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.76/1.13 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.76/1.13 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.76/1.13 Y ) ) ],
% 0.76/1.13 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.76/1.13 Y ) ) ],
% 0.76/1.13 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.76/1.13 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.76/1.13 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.76/1.13 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.76/1.13 'universal_class' ) ) ), =( Y, Z ) ],
% 0.76/1.13 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.76/1.13 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.76/1.13 'universal_class' ) ) ), =( X, Z ) ],
% 0.76/1.13 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.76/1.13 'null_class' ) ) ],
% 0.76/1.13 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.76/1.13 'null_class' ) ) ],
% 0.76/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.76/1.13 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 0.76/1.13 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 0.76/1.13 X, Z ), Y ) ],
% 0.76/1.13 [ member( singleton( X ), 'universal_class' ) ],
% 0.76/1.13 [ member( singleton( X ), 'unordered_pair'( Y, singleton( X ) ) ) ],
% 0.76/1.13 [ ~( member( X, 'universal_class' ) ), member( X, singleton( X ) ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X ),
% 0.76/1.13 'null_class' ) ) ],
% 0.76/1.13 [ member( 'null_class', singleton( 'null_class' ) ) ],
% 0.76/1.13 [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ],
% 0.76/1.13 [ member( X, 'universal_class' ), =( singleton( X ), 'null_class' ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 0.76/1.13 'universal_class' ) ), =( X, Y ) ],
% 0.76/1.13 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 0.76/1.13 'universal_class' ) ), =( X, Y ) ],
% 0.76/1.13 [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~( member( Z,
% 0.76/1.13 'universal_class' ) ), =( Z, X ), =( Z, Y ) ],
% 0.76/1.13 [ ~( member( X, 'universal_class' ) ), member( 'member_of'( singleton( X
% 0.76/1.13 ) ), 'universal_class' ) ],
% 0.76/1.13 [ ~( member( X, 'universal_class' ) ), =( singleton( 'member_of'(
% 0.76/1.13 singleton( X ) ) ), singleton( X ) ) ],
% 0.76/1.13 [ member( 'member_of'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 0.76/1.13 ) ],
% 0.76/1.13 [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X ), X ) ],
% 0.76/1.13 [ ~( member( X, 'universal_class' ) ), =( 'member_of'( singleton( X ) )
% 0.76/1.13 , X ) ],
% 0.76/1.13 [ member( 'member_of1'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 0.76/1.13 ) ],
% 0.76/1.13 [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'( X ), X ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 0.76/1.13 'universal_class' ) ],
% 0.76/1.13 [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y, X ) ), =(
% 0.76/1.13 'member_of'( X ), Y ) ],
% 0.76/1.13 [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ],
% 0.76/1.13 [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' ), =( singleton(
% 0.76/1.13 Y ), X ) ],
% 0.76/1.13 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 0.76/1.13 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 0.76/1.13 intersection( complement( singleton( 'not_subclass_element'( X,
% 0.76/1.13 'null_class' ) ) ), X ) ), =( singleton( 'not_subclass_element'( X,
% 0.76/1.13 'null_class' ) ), X ), =( X, 'null_class' ) ],
% 0.76/1.13 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 0.76/1.13 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ), X ),
% 0.76/1.13 =( singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 0.76/1.13 'null_class' ) ],
% 0.76/1.13 [ ~( =( 'not_subclass_element'( intersection( complement( singleton(
% 0.76/1.13 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 0.76/1.13 'not_subclass_element'( X, 'null_class' ) ) ), =( singleton(
% 0.76/1.13 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ =( 'unordered_pair'( X, Y ), union( singleton( X ), singleton( Y ) ) )
% 0.76/1.13 ],
% 0.76/1.13 [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ],
% 0.76/1.13 [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ],
% 0.76/1.13 [ member( 'unordered_pair'( X, singleton( Y ) ), 'ordered_pair'( X, Y )
% 0.76/1.13 ) ],
% 0.76/1.13 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, 'null_class'
% 0.76/1.13 ) ), 'ordered_pair'( X, Y ) ), member( Y, 'universal_class' ) ],
% 0.76/1.13 [ ~( member( X, 'universal_class' ) ), =( 'unordered_pair'( 'null_class'
% 0.76/1.13 , singleton( singleton( X ) ) ), 'ordered_pair'( Y, X ) ), member( Y,
% 0.76/1.13 'universal_class' ) ],
% 0.76/1.13 [ =( 'unordered_pair'( 'null_class', singleton( 'null_class' ) ),
% 0.76/1.13 'ordered_pair'( X, Y ) ), member( X, 'universal_class' ), member( Y,
% 0.76/1.13 'universal_class' ) ],
% 0.76/1.13 [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) ), ~( member( X
% 0.76/1.13 , 'universal_class' ) ), =( X, Z ) ],
% 0.76/1.13 [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) ), ~( member( Y
% 0.76/1.13 , 'universal_class' ) ), =( Y, T ) ],
% 0.76/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.76/1.13 , 'universal_class' ) ) ), member( 'ordered_pair'( first( 'ordered_pair'(
% 0.76/1.13 X, Y ) ), second( 'ordered_pair'( X, Y ) ) ), 'cross_product'(
% 0.76/1.13 'universal_class', 'universal_class' ) ) ],
% 0.76/1.13 [ member( 'ordered_pair'( first( X ), second( X ) ), 'cross_product'(
% 0.76/1.13 'universal_class', 'universal_class' ) ), =( first( X ), X ) ],
% 6.83/7.19 [ member( 'ordered_pair'( first( X ), second( X ) ), 'cross_product'(
% 6.83/7.19 'universal_class', 'universal_class' ) ), =( second( X ), X ) ],
% 6.83/7.19 [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( first( X ), X )
% 6.83/7.19 ],
% 6.83/7.19 [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( second( X ), X )
% 6.83/7.19 ],
% 6.83/7.19 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 6.83/7.19 , 'universal_class' ) ) ), =( first( 'ordered_pair'( X, Y ) ), X ) ],
% 6.83/7.19 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 6.83/7.19 , 'universal_class' ) ) ), =( second( 'ordered_pair'( X, Y ) ), Y ) ]
% 6.83/7.19 ,
% 6.83/7.19 [ ~( =( 'ordered_pair'( first( x ), second( x ) ), x ) ) ],
% 6.83/7.19 [ ~( =( first( x ), x ) ) ]
% 6.83/7.19 ] .
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 percentage equality = 0.319018, percentage horn = 0.801242
% 6.83/7.19 This is a problem with some equality
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 Options Used:
% 6.83/7.19
% 6.83/7.19 useres = 1
% 6.83/7.19 useparamod = 1
% 6.83/7.19 useeqrefl = 1
% 6.83/7.19 useeqfact = 1
% 6.83/7.19 usefactor = 1
% 6.83/7.19 usesimpsplitting = 0
% 6.83/7.19 usesimpdemod = 5
% 6.83/7.19 usesimpres = 3
% 6.83/7.19
% 6.83/7.19 resimpinuse = 1000
% 6.83/7.19 resimpclauses = 20000
% 6.83/7.19 substype = eqrewr
% 6.83/7.19 backwardsubs = 1
% 6.83/7.19 selectoldest = 5
% 6.83/7.19
% 6.83/7.19 litorderings [0] = split
% 6.83/7.19 litorderings [1] = extend the termordering, first sorting on arguments
% 6.83/7.19
% 6.83/7.19 termordering = kbo
% 6.83/7.19
% 6.83/7.19 litapriori = 0
% 6.83/7.19 termapriori = 1
% 6.83/7.19 litaposteriori = 0
% 6.83/7.19 termaposteriori = 0
% 6.83/7.19 demodaposteriori = 0
% 6.83/7.19 ordereqreflfact = 0
% 6.83/7.19
% 6.83/7.19 litselect = negord
% 6.83/7.19
% 6.83/7.19 maxweight = 15
% 6.83/7.19 maxdepth = 30000
% 6.83/7.19 maxlength = 115
% 6.83/7.19 maxnrvars = 195
% 6.83/7.19 excuselevel = 1
% 6.83/7.19 increasemaxweight = 1
% 6.83/7.19
% 6.83/7.19 maxselected = 10000000
% 6.83/7.19 maxnrclauses = 10000000
% 6.83/7.19
% 6.83/7.19 showgenerated = 0
% 6.83/7.19 showkept = 0
% 6.83/7.19 showselected = 0
% 6.83/7.19 showdeleted = 0
% 6.83/7.19 showresimp = 1
% 6.83/7.19 showstatus = 2000
% 6.83/7.19
% 6.83/7.19 prologoutput = 1
% 6.83/7.19 nrgoals = 5000000
% 6.83/7.19 totalproof = 1
% 6.83/7.19
% 6.83/7.19 Symbols occurring in the translation:
% 6.83/7.19
% 6.83/7.19 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 6.83/7.19 . [1, 2] (w:1, o:57, a:1, s:1, b:0),
% 6.83/7.19 ! [4, 1] (w:0, o:30, a:1, s:1, b:0),
% 6.83/7.19 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.83/7.19 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.83/7.19 subclass [41, 2] (w:1, o:82, a:1, s:1, b:0),
% 6.83/7.19 member [43, 2] (w:1, o:83, a:1, s:1, b:0),
% 6.83/7.19 'not_subclass_element' [44, 2] (w:1, o:84, a:1, s:1, b:0),
% 6.83/7.19 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 6.83/7.19 'unordered_pair' [46, 2] (w:1, o:85, a:1, s:1, b:0),
% 6.83/7.19 singleton [47, 1] (w:1, o:38, a:1, s:1, b:0),
% 6.83/7.19 'ordered_pair' [48, 2] (w:1, o:86, a:1, s:1, b:0),
% 6.83/7.19 'cross_product' [50, 2] (w:1, o:87, a:1, s:1, b:0),
% 6.83/7.19 first [52, 1] (w:1, o:39, a:1, s:1, b:0),
% 6.83/7.19 second [53, 1] (w:1, o:40, a:1, s:1, b:0),
% 6.83/7.19 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 6.83/7.19 intersection [55, 2] (w:1, o:89, a:1, s:1, b:0),
% 6.83/7.19 complement [56, 1] (w:1, o:41, a:1, s:1, b:0),
% 6.83/7.19 union [57, 2] (w:1, o:90, a:1, s:1, b:0),
% 6.83/7.19 'symmetric_difference' [58, 2] (w:1, o:91, a:1, s:1, b:0),
% 6.83/7.19 restrict [60, 3] (w:1, o:94, a:1, s:1, b:0),
% 6.83/7.19 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 6.83/7.19 'domain_of' [62, 1] (w:1, o:43, a:1, s:1, b:0),
% 6.83/7.19 rotate [63, 1] (w:1, o:35, a:1, s:1, b:0),
% 6.83/7.19 flip [65, 1] (w:1, o:44, a:1, s:1, b:0),
% 6.83/7.19 inverse [66, 1] (w:1, o:45, a:1, s:1, b:0),
% 6.83/7.19 'range_of' [67, 1] (w:1, o:36, a:1, s:1, b:0),
% 6.83/7.19 domain [68, 3] (w:1, o:96, a:1, s:1, b:0),
% 6.83/7.19 range [69, 3] (w:1, o:97, a:1, s:1, b:0),
% 6.83/7.19 image [70, 2] (w:1, o:88, a:1, s:1, b:0),
% 6.83/7.19 successor [71, 1] (w:1, o:46, a:1, s:1, b:0),
% 6.83/7.19 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 6.83/7.19 inductive [73, 1] (w:1, o:47, a:1, s:1, b:0),
% 6.83/7.19 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 6.83/7.19 'sum_class' [75, 1] (w:1, o:48, a:1, s:1, b:0),
% 6.83/7.19 'power_class' [76, 1] (w:1, o:51, a:1, s:1, b:0),
% 6.83/7.19 compose [78, 2] (w:1, o:92, a:1, s:1, b:0),
% 6.83/7.19 'single_valued_class' [79, 1] (w:1, o:52, a:1, s:1, b:0),
% 6.83/7.19 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 6.83/7.19 function [82, 1] (w:1, o:53, a:1, s:1, b:0),
% 6.83/7.19 regular [83, 1] (w:1, o:37, a:1, s:1, b:0),
% 6.83/7.19 apply [84, 2] (w:1, o:93, a:1, s:1, b:0),
% 6.83/7.19 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 6.83/7.19 'one_to_one' [86, 1] (w:1, o:49, a:1, s:1, b:0),
% 6.83/7.19 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 6.83/7.19 diagonalise [88, 1] (w:1, o:54, a:1, s:1, b:0),
% 6.83/7.19 cantor [89, 1] (w:1, o:42, a:1, s:1, b:0),
% 6.83/7.19 operation [90, 1] (w:1, o:50, a:1, s:1, b:0),
% 6.83/7.19 compatible [94, 3] (w:1, o:95, a:1, s:1, b:0),
% 6.83/7.19 homomorphism [95, 3] (w:1, o:98, a:1, s:1, b:0),
% 6.83/7.19 'not_homomorphism1' [96, 3] (w:1, o:99, a:1, s:1, b:0),
% 6.83/7.19 'not_homomorphism2' [97, 3] (w:1, o:100, a:1, s:1, b:0),
% 6.83/7.19 'member_of' [98, 1] (w:1, o:55, a:1, s:1, b:0),
% 6.83/7.19 'member_of1' [99, 1] (w:1, o:56, a:1, s:1, b:0),
% 6.83/7.19 x [100, 0] (w:1, o:29, a:1, s:1, b:0).
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 Starting Search:
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 Intermediate Status:
% 6.83/7.19 Generated: 4128
% 6.83/7.19 Kept: 2007
% 6.83/7.19 Inuse: 120
% 6.83/7.19 Deleted: 5
% 6.83/7.19 Deletedinuse: 2
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 Intermediate Status:
% 6.83/7.19 Generated: 10023
% 6.83/7.19 Kept: 4049
% 6.83/7.19 Inuse: 196
% 6.83/7.19 Deleted: 9
% 6.83/7.19 Deletedinuse: 4
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 Intermediate Status:
% 6.83/7.19 Generated: 15212
% 6.83/7.19 Kept: 6057
% 6.83/7.19 Inuse: 276
% 6.83/7.19 Deleted: 57
% 6.83/7.19 Deletedinuse: 39
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 Intermediate Status:
% 6.83/7.19 Generated: 20882
% 6.83/7.19 Kept: 8129
% 6.83/7.19 Inuse: 356
% 6.83/7.19 Deleted: 65
% 6.83/7.19 Deletedinuse: 45
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 Intermediate Status:
% 6.83/7.19 Generated: 27058
% 6.83/7.19 Kept: 10146
% 6.83/7.19 Inuse: 391
% 6.83/7.19 Deleted: 65
% 6.83/7.19 Deletedinuse: 45
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 Intermediate Status:
% 6.83/7.19 Generated: 36575
% 6.83/7.19 Kept: 12231
% 6.83/7.19 Inuse: 430
% 6.83/7.19 Deleted: 67
% 6.83/7.19 Deletedinuse: 46
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 Intermediate Status:
% 6.83/7.19 Generated: 46659
% 6.83/7.19 Kept: 15916
% 6.83/7.19 Inuse: 470
% 6.83/7.19 Deleted: 75
% 6.83/7.19 Deletedinuse: 49
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 Intermediate Status:
% 6.83/7.19 Generated: 52325
% 6.83/7.19 Kept: 17934
% 6.83/7.19 Inuse: 484
% 6.83/7.19 Deleted: 78
% 6.83/7.19 Deletedinuse: 52
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 Intermediate Status:
% 6.83/7.19 Generated: 60702
% 6.83/7.19 Kept: 19937
% 6.83/7.19 Inuse: 485
% 6.83/7.19 Deleted: 78
% 6.83/7.19 Deletedinuse: 52
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19 Resimplifying clauses:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 Intermediate Status:
% 6.83/7.19 Generated: 70612
% 6.83/7.19 Kept: 22091
% 6.83/7.19 Inuse: 521
% 6.83/7.19 Deleted: 1193
% 6.83/7.19 Deletedinuse: 62
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 Intermediate Status:
% 6.83/7.19 Generated: 84494
% 6.83/7.19 Kept: 25530
% 6.83/7.19 Inuse: 551
% 6.83/7.19 Deleted: 1198
% 6.83/7.19 Deletedinuse: 62
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19 Resimplifying inuse:
% 6.83/7.19 Done
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 Bliksems!, er is een bewijs:
% 6.83/7.19 % SZS status Unsatisfiable
% 6.83/7.19 % SZS output start Refutation
% 6.83/7.19
% 6.83/7.19 clause( 152, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( first(
% 6.83/7.19 X ), X ) ] )
% 6.83/7.19 .
% 6.83/7.19 clause( 156, [ ~( =( 'ordered_pair'( first( x ), second( x ) ), x ) ) ] )
% 6.83/7.19 .
% 6.83/7.19 clause( 157, [ ~( =( first( x ), x ) ) ] )
% 6.83/7.19 .
% 6.83/7.19 clause( 27520, [] )
% 6.83/7.19 .
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 % SZS output end Refutation
% 6.83/7.19 found a proof!
% 6.83/7.19
% 6.83/7.19 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 6.83/7.19
% 6.83/7.19 initialclauses(
% 6.83/7.19 [ clause( 27522, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 6.83/7.19 ) ] )
% 6.83/7.19 , clause( 27523, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 6.83/7.19 , Y ) ] )
% 6.83/7.19 , clause( 27524, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 6.83/7.19 subclass( X, Y ) ] )
% 6.83/7.19 , clause( 27525, [ subclass( X, 'universal_class' ) ] )
% 6.83/7.19 , clause( 27526, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 6.83/7.19 , clause( 27527, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 6.83/7.19 , clause( 27528, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 6.83/7.19 ] )
% 6.83/7.19 , clause( 27529, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 6.83/7.19 =( X, Z ) ] )
% 6.83/7.19 , clause( 27530, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.83/7.19 'unordered_pair'( X, Y ) ) ] )
% 6.83/7.19 , clause( 27531, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.83/7.19 'unordered_pair'( Y, X ) ) ] )
% 6.83/7.19 , clause( 27532, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 6.83/7.19 )
% 6.83/7.19 , clause( 27533, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 6.83/7.19 , clause( 27534, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 6.83/7.19 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 6.83/7.19 , clause( 27535, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.83/7.19 ) ) ), member( X, Z ) ] )
% 6.83/7.19 , clause( 27536, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.83/7.19 ) ) ), member( Y, T ) ] )
% 6.83/7.19 , clause( 27537, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 6.83/7.19 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 6.83/7.19 , clause( 27538, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 6.83/7.19 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 6.83/7.19 , clause( 27539, [ subclass( 'element_relation', 'cross_product'(
% 6.83/7.19 'universal_class', 'universal_class' ) ) ] )
% 6.83/7.19 , clause( 27540, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 6.83/7.19 ), member( X, Y ) ] )
% 6.83/7.19 , clause( 27541, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 6.83/7.19 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 6.83/7.19 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 6.83/7.19 , clause( 27542, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 6.83/7.19 )
% 6.83/7.19 , clause( 27543, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 6.83/7.19 )
% 6.83/7.19 , clause( 27544, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 6.83/7.19 intersection( Y, Z ) ) ] )
% 6.83/7.19 , clause( 27545, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 6.83/7.19 )
% 6.83/7.19 , clause( 27546, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.83/7.19 complement( Y ) ), member( X, Y ) ] )
% 6.83/7.19 , clause( 27547, [ =( complement( intersection( complement( X ), complement(
% 6.83/7.19 Y ) ) ), union( X, Y ) ) ] )
% 6.83/7.19 , clause( 27548, [ =( intersection( complement( intersection( X, Y ) ),
% 6.83/7.19 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 6.83/7.19 'symmetric_difference'( X, Y ) ) ] )
% 6.83/7.19 , clause( 27549, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 6.83/7.19 X, Y, Z ) ) ] )
% 6.83/7.19 , clause( 27550, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 6.83/7.19 Z, X, Y ) ) ] )
% 6.83/7.19 , clause( 27551, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 6.83/7.19 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 6.83/7.19 , clause( 27552, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 6.83/7.19 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 6.83/7.19 'domain_of'( Y ) ) ] )
% 6.83/7.19 , clause( 27553, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 6.83/7.19 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 6.83/7.19 , clause( 27554, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.83/7.19 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 6.83/7.19 ] )
% 6.83/7.19 , clause( 27555, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.83/7.19 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 6.83/7.19 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 6.83/7.19 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 6.83/7.19 , Y ), rotate( T ) ) ] )
% 6.83/7.19 , clause( 27556, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 6.83/7.19 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 6.83/7.19 , clause( 27557, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.83/7.19 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 6.83/7.19 )
% 6.83/7.19 , clause( 27558, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.83/7.19 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 6.83/7.19 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 6.83/7.19 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 6.83/7.19 , Z ), flip( T ) ) ] )
% 6.83/7.19 , clause( 27559, [ =( 'domain_of'( flip( 'cross_product'( X,
% 6.83/7.19 'universal_class' ) ) ), inverse( X ) ) ] )
% 6.83/7.19 , clause( 27560, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 6.83/7.19 , clause( 27561, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 6.83/7.19 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 6.83/7.19 , clause( 27562, [ =( second( 'not_subclass_element'( restrict( X,
% 6.83/7.19 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 6.83/7.19 , clause( 27563, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 6.83/7.19 image( X, Y ) ) ] )
% 6.83/7.19 , clause( 27564, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 6.83/7.19 , clause( 27565, [ subclass( 'successor_relation', 'cross_product'(
% 6.83/7.19 'universal_class', 'universal_class' ) ) ] )
% 6.83/7.19 , clause( 27566, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 6.83/7.19 ) ), =( successor( X ), Y ) ] )
% 6.83/7.19 , clause( 27567, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 6.83/7.19 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 6.83/7.19 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 6.83/7.19 , clause( 27568, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 6.83/7.19 , clause( 27569, [ ~( inductive( X ) ), subclass( image(
% 6.83/7.19 'successor_relation', X ), X ) ] )
% 6.83/7.19 , clause( 27570, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 6.83/7.19 'successor_relation', X ), X ) ), inductive( X ) ] )
% 6.83/7.19 , clause( 27571, [ inductive( omega ) ] )
% 6.83/7.19 , clause( 27572, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 6.83/7.19 , clause( 27573, [ member( omega, 'universal_class' ) ] )
% 6.83/7.19 , clause( 27574, [ =( 'domain_of'( restrict( 'element_relation',
% 6.83/7.19 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 6.83/7.19 , clause( 27575, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 6.83/7.19 X ), 'universal_class' ) ] )
% 6.83/7.19 , clause( 27576, [ =( complement( image( 'element_relation', complement( X
% 6.83/7.19 ) ) ), 'power_class'( X ) ) ] )
% 6.83/7.19 , clause( 27577, [ ~( member( X, 'universal_class' ) ), member(
% 6.83/7.19 'power_class'( X ), 'universal_class' ) ] )
% 6.83/7.19 , clause( 27578, [ subclass( compose( X, Y ), 'cross_product'(
% 6.83/7.19 'universal_class', 'universal_class' ) ) ] )
% 6.83/7.19 , clause( 27579, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 6.83/7.19 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 6.83/7.19 , clause( 27580, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 6.83/7.19 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 6.83/7.19 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 6.83/7.19 ) ] )
% 6.83/7.19 , clause( 27581, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 6.83/7.19 inverse( X ) ), 'identity_relation' ) ] )
% 6.83/7.19 , clause( 27582, [ ~( subclass( compose( X, inverse( X ) ),
% 6.83/7.19 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 6.83/7.19 , clause( 27583, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 6.83/7.19 'universal_class', 'universal_class' ) ) ] )
% 6.83/7.19 , clause( 27584, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 6.83/7.19 , 'identity_relation' ) ] )
% 6.83/7.19 , clause( 27585, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 6.83/7.19 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 6.83/7.19 'identity_relation' ) ), function( X ) ] )
% 6.83/7.19 , clause( 27586, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 6.83/7.19 , member( image( X, Y ), 'universal_class' ) ] )
% 6.83/7.19 , clause( 27587, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 6.83/7.19 , clause( 27588, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 6.83/7.19 , 'null_class' ) ] )
% 6.83/7.19 , clause( 27589, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 6.83/7.19 Y ) ) ] )
% 6.83/7.19 , clause( 27590, [ function( choice ) ] )
% 6.83/7.19 , clause( 27591, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 6.83/7.19 ), member( apply( choice, X ), X ) ] )
% 6.83/7.19 , clause( 27592, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 6.83/7.19 , clause( 27593, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 6.83/7.19 , clause( 27594, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 6.83/7.19 'one_to_one'( X ) ] )
% 6.83/7.19 , clause( 27595, [ =( intersection( 'cross_product'( 'universal_class',
% 6.83/7.19 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 6.83/7.19 'universal_class' ), complement( compose( complement( 'element_relation'
% 6.83/7.19 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 6.83/7.19 , clause( 27596, [ =( intersection( inverse( 'subset_relation' ),
% 6.83/7.19 'subset_relation' ), 'identity_relation' ) ] )
% 6.83/7.19 , clause( 27597, [ =( complement( 'domain_of'( intersection( X,
% 6.83/7.19 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 6.83/7.19 , clause( 27598, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 6.83/7.19 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 6.83/7.19 , clause( 27599, [ ~( operation( X ) ), function( X ) ] )
% 6.83/7.19 , clause( 27600, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 6.83/7.19 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 6.83/7.19 ] )
% 6.83/7.19 , clause( 27601, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 6.83/7.19 'domain_of'( 'domain_of'( X ) ) ) ] )
% 6.83/7.19 , clause( 27602, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 6.83/7.19 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 6.83/7.19 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 6.83/7.19 operation( X ) ] )
% 6.83/7.19 , clause( 27603, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 6.83/7.19 , clause( 27604, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 6.83/7.19 Y ) ), 'domain_of'( X ) ) ] )
% 6.83/7.19 , clause( 27605, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 6.83/7.19 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 6.83/7.19 , clause( 27606, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 6.83/7.19 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 6.83/7.19 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 6.83/7.19 , clause( 27607, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 6.83/7.19 , clause( 27608, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 6.83/7.19 , clause( 27609, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 6.83/7.19 , clause( 27610, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 6.83/7.19 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 6.83/7.19 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 6.83/7.19 )
% 6.83/7.19 , clause( 27611, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 6.83/7.19 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 6.83/7.19 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 6.83/7.19 , Y ) ] )
% 6.83/7.19 , clause( 27612, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 6.83/7.19 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 6.83/7.19 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 6.83/7.19 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 6.83/7.19 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 6.83/7.19 )
% 6.83/7.19 , clause( 27613, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.83/7.19 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 6.83/7.19 , clause( 27614, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.83/7.19 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 6.83/7.19 , clause( 27615, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.83/7.19 ) ) ), member( X, 'universal_class' ) ] )
% 6.83/7.19 , clause( 27616, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.83/7.19 ) ) ), member( Y, 'universal_class' ) ] )
% 6.83/7.19 , clause( 27617, [ subclass( X, X ) ] )
% 6.83/7.19 , clause( 27618, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 6.83/7.19 X, Z ) ] )
% 6.83/7.19 , clause( 27619, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 6.83/7.19 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 6.83/7.19 , clause( 27620, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 6.83/7.19 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 6.83/7.19 , clause( 27621, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 6.83/7.19 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 6.83/7.19 , clause( 27622, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 6.83/7.19 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 6.83/7.19 , clause( 27623, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 6.83/7.19 )
% 6.83/7.19 , clause( 27624, [ ~( member( X, 'null_class' ) ) ] )
% 6.83/7.19 , clause( 27625, [ subclass( 'null_class', X ) ] )
% 6.83/7.19 , clause( 27626, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 6.83/7.19 )
% 6.83/7.19 , clause( 27627, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 6.83/7.19 , 'null_class' ), X ) ] )
% 6.83/7.19 , clause( 27628, [ member( 'null_class', 'universal_class' ) ] )
% 6.83/7.19 , clause( 27629, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 6.83/7.19 ] )
% 6.83/7.19 , clause( 27630, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 6.83/7.19 )
% 6.83/7.19 , clause( 27631, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 6.83/7.19 )
% 6.83/7.19 , clause( 27632, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 6.83/7.19 X ), singleton( Y ) ) ] )
% 6.83/7.19 , clause( 27633, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 6.83/7.19 Y ), singleton( Y ) ) ] )
% 6.83/7.19 , clause( 27634, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 6.83/7.19 'universal_class' ), member( Y, 'universal_class' ) ] )
% 6.83/7.19 , clause( 27635, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 6.83/7.19 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 6.83/7.19 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 6.83/7.19 , clause( 27636, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 6.83/7.19 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 6.83/7.19 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 6.83/7.19 , clause( 27637, [ ~( member( X, 'universal_class' ) ), ~( =(
% 6.83/7.19 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 6.83/7.19 , clause( 27638, [ ~( member( X, 'universal_class' ) ), ~( =(
% 6.83/7.19 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 6.83/7.19 , clause( 27639, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.83/7.19 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 6.83/7.19 , clause( 27640, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 6.83/7.19 'unordered_pair'( X, Z ), Y ) ] )
% 6.83/7.19 , clause( 27641, [ member( singleton( X ), 'universal_class' ) ] )
% 6.83/7.19 , clause( 27642, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 6.83/7.19 X ) ) ) ] )
% 6.83/7.19 , clause( 27643, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.83/7.19 singleton( X ) ) ] )
% 6.83/7.19 , clause( 27644, [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X
% 6.83/7.19 ), 'null_class' ) ) ] )
% 6.83/7.19 , clause( 27645, [ member( 'null_class', singleton( 'null_class' ) ) ] )
% 6.83/7.19 , clause( 27646, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 6.83/7.19 , clause( 27647, [ member( X, 'universal_class' ), =( singleton( X ),
% 6.83/7.19 'null_class' ) ] )
% 6.83/7.19 , clause( 27648, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 6.83/7.19 'universal_class' ) ), =( X, Y ) ] )
% 6.83/7.19 , clause( 27649, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 6.83/7.19 'universal_class' ) ), =( X, Y ) ] )
% 6.83/7.19 , clause( 27650, [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~(
% 6.83/7.19 member( Z, 'universal_class' ) ), =( Z, X ), =( Z, Y ) ] )
% 6.83/7.19 , clause( 27651, [ ~( member( X, 'universal_class' ) ), member( 'member_of'(
% 6.83/7.19 singleton( X ) ), 'universal_class' ) ] )
% 6.83/7.19 , clause( 27652, [ ~( member( X, 'universal_class' ) ), =( singleton(
% 6.83/7.19 'member_of'( singleton( X ) ) ), singleton( X ) ) ] )
% 6.83/7.19 , clause( 27653, [ member( 'member_of'( X ), 'universal_class' ), =(
% 6.83/7.19 'member_of'( X ), X ) ] )
% 6.83/7.19 , clause( 27654, [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X
% 6.83/7.19 ), X ) ] )
% 6.83/7.19 , clause( 27655, [ ~( member( X, 'universal_class' ) ), =( 'member_of'(
% 6.83/7.19 singleton( X ) ), X ) ] )
% 6.83/7.19 , clause( 27656, [ member( 'member_of1'( X ), 'universal_class' ), =(
% 6.83/7.19 'member_of'( X ), X ) ] )
% 6.83/7.19 , clause( 27657, [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'(
% 6.83/7.19 X ), X ) ] )
% 6.83/7.19 , clause( 27658, [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 6.83/7.19 'universal_class' ) ] )
% 6.83/7.19 , clause( 27659, [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y
% 6.83/7.19 , X ) ), =( 'member_of'( X ), Y ) ] )
% 6.83/7.19 , clause( 27660, [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ] )
% 6.83/7.19 , clause( 27661, [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' )
% 6.83/7.19 , =( singleton( Y ), X ) ] )
% 6.83/7.19 , clause( 27662, [ member( 'not_subclass_element'( intersection( complement(
% 6.83/7.19 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 6.83/7.19 'null_class' ), intersection( complement( singleton(
% 6.83/7.19 'not_subclass_element'( X, 'null_class' ) ) ), X ) ), =( singleton(
% 6.83/7.19 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 6.83/7.19 )
% 6.83/7.19 , clause( 27663, [ member( 'not_subclass_element'( intersection( complement(
% 6.83/7.19 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 6.83/7.19 'null_class' ), X ), =( singleton( 'not_subclass_element'( X,
% 6.83/7.19 'null_class' ) ), X ), =( X, 'null_class' ) ] )
% 6.83/7.19 , clause( 27664, [ ~( =( 'not_subclass_element'( intersection( complement(
% 6.83/7.19 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 6.83/7.19 'null_class' ), 'not_subclass_element'( X, 'null_class' ) ) ), =(
% 6.83/7.19 singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 6.83/7.19 'null_class' ) ] )
% 6.83/7.19 , clause( 27665, [ =( 'unordered_pair'( X, Y ), union( singleton( X ),
% 6.83/7.19 singleton( Y ) ) ) ] )
% 6.83/7.19 , clause( 27666, [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ] )
% 6.83/7.19 , clause( 27667, [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ] )
% 6.83/7.19 , clause( 27668, [ member( 'unordered_pair'( X, singleton( Y ) ),
% 6.83/7.19 'ordered_pair'( X, Y ) ) ] )
% 6.83/7.19 , clause( 27669, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 6.83/7.19 , 'null_class' ) ), 'ordered_pair'( X, Y ) ), member( Y,
% 6.83/7.19 'universal_class' ) ] )
% 6.83/7.19 , clause( 27670, [ ~( member( X, 'universal_class' ) ), =( 'unordered_pair'(
% 6.83/7.19 'null_class', singleton( singleton( X ) ) ), 'ordered_pair'( Y, X ) ),
% 6.83/7.19 member( Y, 'universal_class' ) ] )
% 6.83/7.19 , clause( 27671, [ =( 'unordered_pair'( 'null_class', singleton(
% 6.83/7.19 'null_class' ) ), 'ordered_pair'( X, Y ) ), member( X, 'universal_class'
% 6.83/7.19 ), member( Y, 'universal_class' ) ] )
% 6.83/7.19 , clause( 27672, [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) )
% 6.83/7.19 , ~( member( X, 'universal_class' ) ), =( X, Z ) ] )
% 6.83/7.19 , clause( 27673, [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) )
% 6.83/7.19 , ~( member( Y, 'universal_class' ) ), =( Y, T ) ] )
% 6.83/7.19 , clause( 27674, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 6.83/7.19 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( first(
% 6.83/7.19 'ordered_pair'( X, Y ) ), second( 'ordered_pair'( X, Y ) ) ),
% 6.83/7.19 'cross_product'( 'universal_class', 'universal_class' ) ) ] )
% 6.83/7.19 , clause( 27675, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 6.83/7.19 'cross_product'( 'universal_class', 'universal_class' ) ), =( first( X )
% 6.83/7.19 , X ) ] )
% 6.83/7.19 , clause( 27676, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 6.83/7.19 'cross_product'( 'universal_class', 'universal_class' ) ), =( second( X )
% 6.83/7.19 , X ) ] )
% 6.83/7.19 , clause( 27677, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.83/7.19 first( X ), X ) ] )
% 6.83/7.19 , clause( 27678, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.83/7.19 second( X ), X ) ] )
% 6.83/7.19 , clause( 27679, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 6.83/7.19 'universal_class', 'universal_class' ) ) ), =( first( 'ordered_pair'( X,
% 6.83/7.19 Y ) ), X ) ] )
% 6.83/7.19 , clause( 27680, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 6.83/7.19 'universal_class', 'universal_class' ) ) ), =( second( 'ordered_pair'( X
% 6.83/7.19 , Y ) ), Y ) ] )
% 6.83/7.19 , clause( 27681, [ ~( =( 'ordered_pair'( first( x ), second( x ) ), x ) ) ]
% 6.83/7.19 )
% 6.83/7.19 , clause( 27682, [ ~( =( first( x ), x ) ) ] )
% 6.83/7.19 ] ).
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 subsumption(
% 6.83/7.19 clause( 152, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( first(
% 6.83/7.19 X ), X ) ] )
% 6.83/7.19 , clause( 27677, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.83/7.19 first( X ), X ) ] )
% 6.83/7.19 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 6.83/7.19 1 )] ) ).
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 subsumption(
% 6.83/7.19 clause( 156, [ ~( =( 'ordered_pair'( first( x ), second( x ) ), x ) ) ] )
% 6.83/7.19 , clause( 27681, [ ~( =( 'ordered_pair'( first( x ), second( x ) ), x ) ) ]
% 6.83/7.19 )
% 6.83/7.19 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 subsumption(
% 6.83/7.19 clause( 157, [ ~( =( first( x ), x ) ) ] )
% 6.83/7.19 , clause( 27682, [ ~( =( first( x ), x ) ) ] )
% 6.83/7.19 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 eqswap(
% 6.83/7.19 clause( 28113, [ =( X, 'ordered_pair'( first( X ), second( X ) ) ), =(
% 6.83/7.19 first( X ), X ) ] )
% 6.83/7.19 , clause( 152, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 6.83/7.19 first( X ), X ) ] )
% 6.83/7.19 , 0, substitution( 0, [ :=( X, X )] )).
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 eqswap(
% 6.83/7.19 clause( 28117, [ ~( =( x, 'ordered_pair'( first( x ), second( x ) ) ) ) ]
% 6.83/7.19 )
% 6.83/7.19 , clause( 156, [ ~( =( 'ordered_pair'( first( x ), second( x ) ), x ) ) ]
% 6.83/7.19 )
% 6.83/7.19 , 0, substitution( 0, [] )).
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 resolution(
% 6.83/7.19 clause( 28118, [ =( x, 'ordered_pair'( first( x ), second( x ) ) ) ] )
% 6.83/7.19 , clause( 157, [ ~( =( first( x ), x ) ) ] )
% 6.83/7.19 , 0, clause( 28113, [ =( X, 'ordered_pair'( first( X ), second( X ) ) ),
% 6.83/7.19 =( first( X ), X ) ] )
% 6.83/7.19 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, x )] )).
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 resolution(
% 6.83/7.19 clause( 28119, [] )
% 6.83/7.19 , clause( 28117, [ ~( =( x, 'ordered_pair'( first( x ), second( x ) ) ) ) ]
% 6.83/7.19 )
% 6.83/7.19 , 0, clause( 28118, [ =( x, 'ordered_pair'( first( x ), second( x ) ) ) ]
% 6.83/7.19 )
% 6.83/7.19 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 subsumption(
% 6.83/7.19 clause( 27520, [] )
% 6.83/7.19 , clause( 28119, [] )
% 6.83/7.19 , substitution( 0, [] ), permutation( 0, [] ) ).
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 end.
% 6.83/7.19
% 6.83/7.19 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 6.83/7.19
% 6.83/7.19 Memory use:
% 6.83/7.19
% 6.83/7.19 space for terms: 502460
% 6.83/7.19 space for clauses: 1265191
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 clauses generated: 90508
% 6.83/7.19 clauses kept: 27521
% 6.83/7.19 clauses selected: 561
% 6.83/7.19 clauses deleted: 1200
% 6.83/7.19 clauses inuse deleted: 64
% 6.83/7.19
% 6.83/7.19 subsentry: 344425
% 6.83/7.19 literals s-matched: 262916
% 6.83/7.19 literals matched: 253105
% 6.83/7.19 full subsumption: 155683
% 6.83/7.19
% 6.83/7.19 checksum: -265266210
% 6.83/7.19
% 6.83/7.19
% 6.83/7.19 Bliksem ended
%------------------------------------------------------------------------------