TSTP Solution File: SET108-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET108-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 22:47:12 EDT 2022
% Result : Unsatisfiable 6.74s 7.12s
% Output : Refutation 6.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : SET108-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.05/0.13 % Command : bliksem %s
% 0.12/0.33 % Computer : n023.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 14:44:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.85/1.22 *** allocated 10000 integers for termspace/termends
% 0.85/1.22 *** allocated 10000 integers for clauses
% 0.85/1.22 *** allocated 10000 integers for justifications
% 0.85/1.22 Bliksem 1.12
% 0.85/1.22
% 0.85/1.22
% 0.85/1.22 Automatic Strategy Selection
% 0.85/1.22
% 0.85/1.22 Clauses:
% 0.85/1.22 [
% 0.85/1.22 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.85/1.22 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.85/1.22 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.85/1.22 ,
% 0.85/1.22 [ subclass( X, 'universal_class' ) ],
% 0.85/1.22 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.85/1.22 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.85/1.22 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.85/1.22 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.85/1.22 ,
% 0.85/1.22 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.85/1.22 ) ) ],
% 0.85/1.22 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.85/1.22 ) ) ],
% 0.85/1.22 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.85/1.22 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.85/1.22 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.85/1.22 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.85/1.22 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.85/1.22 X, Z ) ],
% 0.85/1.22 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.85/1.22 Y, T ) ],
% 0.85/1.22 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.85/1.22 ), 'cross_product'( Y, T ) ) ],
% 0.85/1.22 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.85/1.22 ), second( X ) ), X ) ],
% 0.85/1.22 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.85/1.22 'universal_class' ) ) ],
% 0.85/1.22 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.85/1.22 Y ) ],
% 0.85/1.22 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.85/1.22 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.85/1.22 , Y ), 'element_relation' ) ],
% 0.85/1.22 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.85/1.22 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.85/1.22 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.85/1.22 Z ) ) ],
% 0.85/1.22 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.85/1.22 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.85/1.22 member( X, Y ) ],
% 0.85/1.22 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.85/1.22 union( X, Y ) ) ],
% 0.85/1.22 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.85/1.22 intersection( complement( X ), complement( Y ) ) ) ),
% 0.85/1.22 'symmetric_difference'( X, Y ) ) ],
% 0.85/1.22 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.85/1.22 ,
% 0.85/1.22 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.85/1.22 ,
% 0.85/1.22 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.85/1.22 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.85/1.22 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.85/1.22 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.85/1.22 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.85/1.22 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.85/1.22 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.85/1.22 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.85/1.22 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.85/1.22 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.85/1.22 'cross_product'( 'universal_class', 'universal_class' ),
% 0.85/1.22 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.85/1.22 Y ), rotate( T ) ) ],
% 0.85/1.22 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.85/1.22 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.85/1.22 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.85/1.22 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.85/1.22 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.85/1.22 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.85/1.22 'cross_product'( 'universal_class', 'universal_class' ),
% 0.85/1.22 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.85/1.22 Z ), flip( T ) ) ],
% 0.85/1.22 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.85/1.22 inverse( X ) ) ],
% 0.85/1.22 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.85/1.22 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.85/1.22 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.85/1.22 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.85/1.22 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.85/1.22 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.85/1.22 ],
% 0.85/1.22 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.85/1.22 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.85/1.22 'universal_class' ) ) ],
% 0.85/1.22 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.85/1.22 successor( X ), Y ) ],
% 0.85/1.22 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.85/1.22 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.85/1.22 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.85/1.22 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.85/1.22 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.85/1.22 ,
% 0.85/1.22 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.85/1.22 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.85/1.22 [ inductive( omega ) ],
% 0.85/1.22 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.85/1.22 [ member( omega, 'universal_class' ) ],
% 0.85/1.22 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.85/1.22 , 'sum_class'( X ) ) ],
% 0.85/1.22 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.85/1.22 'universal_class' ) ],
% 0.85/1.22 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.85/1.22 'power_class'( X ) ) ],
% 0.85/1.22 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.85/1.22 'universal_class' ) ],
% 0.85/1.22 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.85/1.22 'universal_class' ) ) ],
% 0.85/1.22 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.85/1.22 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.85/1.22 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.85/1.22 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.85/1.22 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.85/1.22 ) ],
% 0.85/1.22 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.85/1.22 , 'identity_relation' ) ],
% 0.85/1.22 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.85/1.22 'single_valued_class'( X ) ],
% 0.85/1.22 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.85/1.22 'universal_class' ) ) ],
% 0.85/1.22 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.85/1.22 'identity_relation' ) ],
% 0.85/1.22 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.85/1.22 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.85/1.22 , function( X ) ],
% 0.85/1.22 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.85/1.22 X, Y ), 'universal_class' ) ],
% 0.85/1.22 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.85/1.22 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.85/1.22 ) ],
% 0.85/1.22 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.85/1.22 [ function( choice ) ],
% 0.85/1.22 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.85/1.22 apply( choice, X ), X ) ],
% 0.85/1.22 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.85/1.22 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.85/1.22 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.85/1.22 ,
% 0.85/1.22 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.85/1.22 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.85/1.22 , complement( compose( complement( 'element_relation' ), inverse(
% 0.85/1.22 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.85/1.22 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.85/1.22 'identity_relation' ) ],
% 0.85/1.22 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.85/1.22 , diagonalise( X ) ) ],
% 0.85/1.22 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.85/1.22 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.85/1.22 [ ~( operation( X ) ), function( X ) ],
% 0.85/1.22 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.85/1.22 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.85/1.22 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.85/1.22 'domain_of'( X ) ) ) ],
% 0.85/1.22 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.85/1.22 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.85/1.22 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.85/1.22 X ) ],
% 0.85/1.22 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.85/1.22 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.85/1.22 'domain_of'( X ) ) ],
% 0.85/1.22 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.85/1.22 'domain_of'( Z ) ) ) ],
% 0.85/1.22 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.85/1.22 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.85/1.22 ), compatible( X, Y, Z ) ],
% 0.85/1.22 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.85/1.22 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.85/1.22 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.85/1.22 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.85/1.22 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.85/1.22 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.85/1.22 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.85/1.22 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.85/1.22 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.85/1.22 , Y ) ],
% 0.85/1.22 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.85/1.22 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.85/1.22 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.85/1.22 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.85/1.22 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.85/1.22 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.85/1.22 X, 'unordered_pair'( X, Y ) ) ],
% 0.85/1.22 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.85/1.22 Y, 'unordered_pair'( X, Y ) ) ],
% 0.85/1.22 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.85/1.22 X, 'universal_class' ) ],
% 0.85/1.22 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.85/1.22 Y, 'universal_class' ) ],
% 0.85/1.22 [ subclass( X, X ) ],
% 0.85/1.22 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.85/1.22 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.85/1.22 'not_subclass_element'( Y, X ), Y ) ],
% 0.85/1.22 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.85/1.22 'not_subclass_element'( Y, X ), Y ) ],
% 0.85/1.22 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.85/1.22 'not_subclass_element'( Y, X ), Y ) ],
% 0.85/1.22 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.85/1.22 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.85/1.22 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.85/1.22 [ ~( member( X, 'null_class' ) ) ],
% 0.85/1.22 [ subclass( 'null_class', X ) ],
% 0.85/1.22 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.85/1.22 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.85/1.22 ), X ) ],
% 0.85/1.22 [ member( 'null_class', 'universal_class' ) ],
% 0.85/1.22 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.85/1.22 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.85/1.22 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.85/1.22 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.85/1.22 Y ) ) ],
% 0.85/1.22 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.85/1.22 Y ) ) ],
% 0.85/1.22 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.85/1.22 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.85/1.22 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.85/1.22 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.85/1.22 'universal_class' ) ) ), =( Y, Z ) ],
% 0.85/1.22 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.85/1.22 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.85/1.22 'universal_class' ) ) ), =( X, Z ) ],
% 0.85/1.22 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.85/1.22 'null_class' ) ) ],
% 0.85/1.22 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.85/1.22 'null_class' ) ) ],
% 0.85/1.22 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.85/1.22 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 0.85/1.22 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 0.85/1.22 X, Z ), Y ) ],
% 0.85/1.22 [ member( singleton( X ), 'universal_class' ) ],
% 0.85/1.22 [ member( singleton( X ), 'unordered_pair'( Y, singleton( X ) ) ) ],
% 0.85/1.22 [ ~( member( X, 'universal_class' ) ), member( X, singleton( X ) ) ]
% 0.85/1.22 ,
% 0.85/1.22 [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X ),
% 0.85/1.22 'null_class' ) ) ],
% 0.85/1.22 [ member( 'null_class', singleton( 'null_class' ) ) ],
% 0.85/1.22 [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ],
% 0.85/1.22 [ member( X, 'universal_class' ), =( singleton( X ), 'null_class' ) ]
% 0.85/1.22 ,
% 0.85/1.22 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 0.85/1.22 'universal_class' ) ), =( X, Y ) ],
% 0.85/1.22 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 0.85/1.22 'universal_class' ) ), =( X, Y ) ],
% 0.85/1.22 [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~( member( Z,
% 0.85/1.22 'universal_class' ) ), =( Z, X ), =( Z, Y ) ],
% 0.85/1.22 [ ~( member( X, 'universal_class' ) ), member( 'member_of'( singleton( X
% 0.85/1.22 ) ), 'universal_class' ) ],
% 0.85/1.22 [ ~( member( X, 'universal_class' ) ), =( singleton( 'member_of'(
% 0.85/1.22 singleton( X ) ) ), singleton( X ) ) ],
% 0.85/1.22 [ member( 'member_of'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 0.85/1.22 ) ],
% 0.85/1.22 [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X ), X ) ],
% 0.85/1.22 [ ~( member( X, 'universal_class' ) ), =( 'member_of'( singleton( X ) )
% 0.85/1.22 , X ) ],
% 0.85/1.22 [ member( 'member_of1'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 0.85/1.22 ) ],
% 0.85/1.22 [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'( X ), X ) ]
% 0.85/1.22 ,
% 0.85/1.22 [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 0.85/1.22 'universal_class' ) ],
% 0.85/1.22 [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y, X ) ), =(
% 0.85/1.22 'member_of'( X ), Y ) ],
% 0.85/1.22 [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ],
% 0.85/1.22 [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' ), =( singleton(
% 0.85/1.22 Y ), X ) ],
% 0.85/1.22 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 0.85/1.22 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 0.85/1.22 intersection( complement( singleton( 'not_subclass_element'( X,
% 0.85/1.22 'null_class' ) ) ), X ) ), =( singleton( 'not_subclass_element'( X,
% 0.85/1.22 'null_class' ) ), X ), =( X, 'null_class' ) ],
% 0.85/1.22 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 0.85/1.22 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ), X ),
% 0.85/1.22 =( singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 0.85/1.22 'null_class' ) ],
% 0.85/1.22 [ ~( =( 'not_subclass_element'( intersection( complement( singleton(
% 0.85/1.22 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 0.85/1.22 'not_subclass_element'( X, 'null_class' ) ) ), =( singleton(
% 0.85/1.22 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 0.85/1.22 ,
% 0.85/1.22 [ =( 'unordered_pair'( X, Y ), union( singleton( X ), singleton( Y ) ) )
% 0.85/1.22 ],
% 0.85/1.22 [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ],
% 0.85/1.22 [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ],
% 0.85/1.22 [ member( 'unordered_pair'( X, singleton( Y ) ), 'ordered_pair'( X, Y )
% 0.85/1.22 ) ],
% 0.85/1.22 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, 'null_class'
% 0.85/1.22 ) ), 'ordered_pair'( X, Y ) ), member( Y, 'universal_class' ) ],
% 0.85/1.22 [ ~( member( X, 'universal_class' ) ), =( 'unordered_pair'( 'null_class'
% 0.85/1.22 , singleton( singleton( X ) ) ), 'ordered_pair'( Y, X ) ), member( Y,
% 0.85/1.22 'universal_class' ) ],
% 0.85/1.22 [ =( 'unordered_pair'( 'null_class', singleton( 'null_class' ) ),
% 0.85/1.22 'ordered_pair'( X, Y ) ), member( X, 'universal_class' ), member( Y,
% 0.85/1.22 'universal_class' ) ],
% 0.85/1.22 [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) ), ~( member( X
% 0.85/1.22 , 'universal_class' ) ), =( X, Z ) ],
% 0.85/1.22 [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) ), ~( member( Y
% 0.85/1.22 , 'universal_class' ) ), =( Y, T ) ],
% 0.85/1.22 [ member( 'ordered_pair'( y, z ), 'cross_product'( 'universal_class',
% 0.85/1.22 'universal_class' ) ) ],
% 0.85/1.22 [ ~( member( 'ordered_pair'( first( 'ordered_pair'( y, z ) ), second(
% 0.85/1.22 'ordered_pair'( y, z ) ) ), 'cross_product'( 'universal_class',
% 0.85/1.22 'universal_class' ) ) ) ]
% 0.85/1.22 ] .
% 0.85/1.22
% 0.85/1.22
% 0.85/1.22 percentage equality = 0.301282, percentage horn = 0.818182
% 0.85/1.22 This is a problem with some equality
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 Options Used:
% 6.74/7.12
% 6.74/7.12 useres = 1
% 6.74/7.12 useparamod = 1
% 6.74/7.12 useeqrefl = 1
% 6.74/7.12 useeqfact = 1
% 6.74/7.12 usefactor = 1
% 6.74/7.12 usesimpsplitting = 0
% 6.74/7.12 usesimpdemod = 5
% 6.74/7.12 usesimpres = 3
% 6.74/7.12
% 6.74/7.12 resimpinuse = 1000
% 6.74/7.12 resimpclauses = 20000
% 6.74/7.12 substype = eqrewr
% 6.74/7.12 backwardsubs = 1
% 6.74/7.12 selectoldest = 5
% 6.74/7.12
% 6.74/7.12 litorderings [0] = split
% 6.74/7.12 litorderings [1] = extend the termordering, first sorting on arguments
% 6.74/7.12
% 6.74/7.12 termordering = kbo
% 6.74/7.12
% 6.74/7.12 litapriori = 0
% 6.74/7.12 termapriori = 1
% 6.74/7.12 litaposteriori = 0
% 6.74/7.12 termaposteriori = 0
% 6.74/7.12 demodaposteriori = 0
% 6.74/7.12 ordereqreflfact = 0
% 6.74/7.12
% 6.74/7.12 litselect = negord
% 6.74/7.12
% 6.74/7.12 maxweight = 15
% 6.74/7.12 maxdepth = 30000
% 6.74/7.12 maxlength = 115
% 6.74/7.12 maxnrvars = 195
% 6.74/7.12 excuselevel = 1
% 6.74/7.12 increasemaxweight = 1
% 6.74/7.12
% 6.74/7.12 maxselected = 10000000
% 6.74/7.12 maxnrclauses = 10000000
% 6.74/7.12
% 6.74/7.12 showgenerated = 0
% 6.74/7.12 showkept = 0
% 6.74/7.12 showselected = 0
% 6.74/7.12 showdeleted = 0
% 6.74/7.12 showresimp = 1
% 6.74/7.12 showstatus = 2000
% 6.74/7.12
% 6.74/7.12 prologoutput = 1
% 6.74/7.12 nrgoals = 5000000
% 6.74/7.12 totalproof = 1
% 6.74/7.12
% 6.74/7.12 Symbols occurring in the translation:
% 6.74/7.12
% 6.74/7.12 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 6.74/7.12 . [1, 2] (w:1, o:58, a:1, s:1, b:0),
% 6.74/7.12 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 6.74/7.12 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.74/7.12 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.74/7.12 subclass [41, 2] (w:1, o:83, a:1, s:1, b:0),
% 6.74/7.12 member [43, 2] (w:1, o:84, a:1, s:1, b:0),
% 6.74/7.12 'not_subclass_element' [44, 2] (w:1, o:85, a:1, s:1, b:0),
% 6.74/7.12 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 6.74/7.12 'unordered_pair' [46, 2] (w:1, o:86, a:1, s:1, b:0),
% 6.74/7.12 singleton [47, 1] (w:1, o:39, a:1, s:1, b:0),
% 6.74/7.12 'ordered_pair' [48, 2] (w:1, o:87, a:1, s:1, b:0),
% 6.74/7.12 'cross_product' [50, 2] (w:1, o:88, a:1, s:1, b:0),
% 6.74/7.12 first [52, 1] (w:1, o:40, a:1, s:1, b:0),
% 6.74/7.12 second [53, 1] (w:1, o:41, a:1, s:1, b:0),
% 6.74/7.12 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 6.74/7.12 intersection [55, 2] (w:1, o:90, a:1, s:1, b:0),
% 6.74/7.12 complement [56, 1] (w:1, o:42, a:1, s:1, b:0),
% 6.74/7.12 union [57, 2] (w:1, o:91, a:1, s:1, b:0),
% 6.74/7.12 'symmetric_difference' [58, 2] (w:1, o:92, a:1, s:1, b:0),
% 6.74/7.12 restrict [60, 3] (w:1, o:95, a:1, s:1, b:0),
% 6.74/7.12 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 6.74/7.12 'domain_of' [62, 1] (w:1, o:44, a:1, s:1, b:0),
% 6.74/7.12 rotate [63, 1] (w:1, o:36, a:1, s:1, b:0),
% 6.74/7.12 flip [65, 1] (w:1, o:45, a:1, s:1, b:0),
% 6.74/7.12 inverse [66, 1] (w:1, o:46, a:1, s:1, b:0),
% 6.74/7.12 'range_of' [67, 1] (w:1, o:37, a:1, s:1, b:0),
% 6.74/7.12 domain [68, 3] (w:1, o:97, a:1, s:1, b:0),
% 6.74/7.12 range [69, 3] (w:1, o:98, a:1, s:1, b:0),
% 6.74/7.12 image [70, 2] (w:1, o:89, a:1, s:1, b:0),
% 6.74/7.12 successor [71, 1] (w:1, o:47, a:1, s:1, b:0),
% 6.74/7.12 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 6.74/7.12 inductive [73, 1] (w:1, o:48, a:1, s:1, b:0),
% 6.74/7.12 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 6.74/7.12 'sum_class' [75, 1] (w:1, o:49, a:1, s:1, b:0),
% 6.74/7.12 'power_class' [76, 1] (w:1, o:52, a:1, s:1, b:0),
% 6.74/7.12 compose [78, 2] (w:1, o:93, a:1, s:1, b:0),
% 6.74/7.12 'single_valued_class' [79, 1] (w:1, o:53, a:1, s:1, b:0),
% 6.74/7.12 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 6.74/7.12 function [82, 1] (w:1, o:54, a:1, s:1, b:0),
% 6.74/7.12 regular [83, 1] (w:1, o:38, a:1, s:1, b:0),
% 6.74/7.12 apply [84, 2] (w:1, o:94, a:1, s:1, b:0),
% 6.74/7.12 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 6.74/7.12 'one_to_one' [86, 1] (w:1, o:50, a:1, s:1, b:0),
% 6.74/7.12 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 6.74/7.12 diagonalise [88, 1] (w:1, o:55, a:1, s:1, b:0),
% 6.74/7.12 cantor [89, 1] (w:1, o:43, a:1, s:1, b:0),
% 6.74/7.12 operation [90, 1] (w:1, o:51, a:1, s:1, b:0),
% 6.74/7.12 compatible [94, 3] (w:1, o:96, a:1, s:1, b:0),
% 6.74/7.12 homomorphism [95, 3] (w:1, o:99, a:1, s:1, b:0),
% 6.74/7.12 'not_homomorphism1' [96, 3] (w:1, o:100, a:1, s:1, b:0),
% 6.74/7.12 'not_homomorphism2' [97, 3] (w:1, o:101, a:1, s:1, b:0),
% 6.74/7.12 'member_of' [98, 1] (w:1, o:56, a:1, s:1, b:0),
% 6.74/7.12 'member_of1' [99, 1] (w:1, o:57, a:1, s:1, b:0),
% 6.74/7.12 y [100, 0] (w:1, o:29, a:1, s:1, b:0),
% 6.74/7.12 z [101, 0] (w:1, o:30, a:1, s:1, b:0).
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 Starting Search:
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 Intermediate Status:
% 6.74/7.12 Generated: 4182
% 6.74/7.12 Kept: 2016
% 6.74/7.12 Inuse: 121
% 6.74/7.12 Deleted: 5
% 6.74/7.12 Deletedinuse: 2
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 Intermediate Status:
% 6.74/7.12 Generated: 9989
% 6.74/7.12 Kept: 4019
% 6.74/7.12 Inuse: 195
% 6.74/7.12 Deleted: 10
% 6.74/7.12 Deletedinuse: 4
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 Intermediate Status:
% 6.74/7.12 Generated: 15187
% 6.74/7.12 Kept: 6026
% 6.74/7.12 Inuse: 275
% 6.74/7.12 Deleted: 57
% 6.74/7.12 Deletedinuse: 39
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 Intermediate Status:
% 6.74/7.12 Generated: 20715
% 6.74/7.12 Kept: 8045
% 6.74/7.12 Inuse: 355
% 6.74/7.12 Deleted: 65
% 6.74/7.12 Deletedinuse: 45
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 Intermediate Status:
% 6.74/7.12 Generated: 27152
% 6.74/7.12 Kept: 10135
% 6.74/7.12 Inuse: 391
% 6.74/7.12 Deleted: 65
% 6.74/7.12 Deletedinuse: 45
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 Intermediate Status:
% 6.74/7.12 Generated: 36661
% 6.74/7.12 Kept: 12211
% 6.74/7.12 Inuse: 430
% 6.74/7.12 Deleted: 67
% 6.74/7.12 Deletedinuse: 46
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 Intermediate Status:
% 6.74/7.12 Generated: 46712
% 6.74/7.12 Kept: 15895
% 6.74/7.12 Inuse: 470
% 6.74/7.12 Deleted: 75
% 6.74/7.12 Deletedinuse: 49
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 Intermediate Status:
% 6.74/7.12 Generated: 52374
% 6.74/7.12 Kept: 17910
% 6.74/7.12 Inuse: 484
% 6.74/7.12 Deleted: 78
% 6.74/7.12 Deletedinuse: 52
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 Intermediate Status:
% 6.74/7.12 Generated: 60829
% 6.74/7.12 Kept: 19931
% 6.74/7.12 Inuse: 486
% 6.74/7.12 Deleted: 79
% 6.74/7.12 Deletedinuse: 53
% 6.74/7.12
% 6.74/7.12 Resimplifying clauses:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 Intermediate Status:
% 6.74/7.12 Generated: 70648
% 6.74/7.12 Kept: 22051
% 6.74/7.12 Inuse: 521
% 6.74/7.12 Deleted: 1191
% 6.74/7.12 Deletedinuse: 62
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 Intermediate Status:
% 6.74/7.12 Generated: 84529
% 6.74/7.12 Kept: 25486
% 6.74/7.12 Inuse: 551
% 6.74/7.12 Deleted: 1196
% 6.74/7.12 Deletedinuse: 62
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12 Resimplifying inuse:
% 6.74/7.12 Done
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 Intermediate Status:
% 6.74/7.12 Generated: 90789
% 6.74/7.12 Kept: 27597
% 6.74/7.12 Inuse: 561
% 6.74/7.12 Deleted: 1198
% 6.74/7.12 Deletedinuse: 64
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 Bliksems!, er is een bewijs:
% 6.74/7.12 % SZS status Unsatisfiable
% 6.74/7.12 % SZS output start Refutation
% 6.74/7.12
% 6.74/7.12 clause( 15, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'(
% 6.74/7.12 first( X ), second( X ) ), X ) ] )
% 6.74/7.12 .
% 6.74/7.12 clause( 149, [ member( 'ordered_pair'( y, z ), 'cross_product'(
% 6.74/7.12 'universal_class', 'universal_class' ) ) ] )
% 6.74/7.12 .
% 6.74/7.12 clause( 150, [ ~( member( 'ordered_pair'( first( 'ordered_pair'( y, z ) ),
% 6.74/7.12 second( 'ordered_pair'( y, z ) ) ), 'cross_product'( 'universal_class',
% 6.74/7.12 'universal_class' ) ) ) ] )
% 6.74/7.12 .
% 6.74/7.12 clause( 27482, [ =( 'ordered_pair'( first( 'ordered_pair'( y, z ) ), second(
% 6.74/7.12 'ordered_pair'( y, z ) ) ), 'ordered_pair'( y, z ) ) ] )
% 6.74/7.12 .
% 6.74/7.12 clause( 27746, [] )
% 6.74/7.12 .
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 % SZS output end Refutation
% 6.74/7.12 found a proof!
% 6.74/7.12
% 6.74/7.12 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 6.74/7.12
% 6.74/7.12 initialclauses(
% 6.74/7.12 [ clause( 27748, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 6.74/7.12 ) ] )
% 6.74/7.12 , clause( 27749, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 6.74/7.12 , Y ) ] )
% 6.74/7.12 , clause( 27750, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 6.74/7.12 subclass( X, Y ) ] )
% 6.74/7.12 , clause( 27751, [ subclass( X, 'universal_class' ) ] )
% 6.74/7.12 , clause( 27752, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 6.74/7.12 , clause( 27753, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 6.74/7.12 , clause( 27754, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 6.74/7.12 ] )
% 6.74/7.12 , clause( 27755, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 6.74/7.12 =( X, Z ) ] )
% 6.74/7.12 , clause( 27756, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.74/7.12 'unordered_pair'( X, Y ) ) ] )
% 6.74/7.12 , clause( 27757, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.74/7.12 'unordered_pair'( Y, X ) ) ] )
% 6.74/7.12 , clause( 27758, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 6.74/7.12 )
% 6.74/7.12 , clause( 27759, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 6.74/7.12 , clause( 27760, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 6.74/7.12 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 6.74/7.12 , clause( 27761, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.74/7.12 ) ) ), member( X, Z ) ] )
% 6.74/7.12 , clause( 27762, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.74/7.12 ) ) ), member( Y, T ) ] )
% 6.74/7.12 , clause( 27763, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 6.74/7.12 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 6.74/7.12 , clause( 27764, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 6.74/7.12 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 6.74/7.12 , clause( 27765, [ subclass( 'element_relation', 'cross_product'(
% 6.74/7.12 'universal_class', 'universal_class' ) ) ] )
% 6.74/7.12 , clause( 27766, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 6.74/7.12 ), member( X, Y ) ] )
% 6.74/7.12 , clause( 27767, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 6.74/7.12 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 6.74/7.12 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 6.74/7.12 , clause( 27768, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 6.74/7.12 )
% 6.74/7.12 , clause( 27769, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 6.74/7.12 )
% 6.74/7.12 , clause( 27770, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 6.74/7.12 intersection( Y, Z ) ) ] )
% 6.74/7.12 , clause( 27771, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 6.74/7.12 )
% 6.74/7.12 , clause( 27772, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.74/7.12 complement( Y ) ), member( X, Y ) ] )
% 6.74/7.12 , clause( 27773, [ =( complement( intersection( complement( X ), complement(
% 6.74/7.12 Y ) ) ), union( X, Y ) ) ] )
% 6.74/7.12 , clause( 27774, [ =( intersection( complement( intersection( X, Y ) ),
% 6.74/7.12 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 6.74/7.12 'symmetric_difference'( X, Y ) ) ] )
% 6.74/7.12 , clause( 27775, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 6.74/7.12 X, Y, Z ) ) ] )
% 6.74/7.12 , clause( 27776, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 6.74/7.12 Z, X, Y ) ) ] )
% 6.74/7.12 , clause( 27777, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 6.74/7.12 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 6.74/7.12 , clause( 27778, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 6.74/7.12 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 6.74/7.12 'domain_of'( Y ) ) ] )
% 6.74/7.12 , clause( 27779, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 6.74/7.12 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 6.74/7.12 , clause( 27780, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.74/7.12 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 6.74/7.12 ] )
% 6.74/7.12 , clause( 27781, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.74/7.12 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 6.74/7.12 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 6.74/7.12 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 6.74/7.12 , Y ), rotate( T ) ) ] )
% 6.74/7.12 , clause( 27782, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 6.74/7.12 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 6.74/7.12 , clause( 27783, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.74/7.12 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 6.74/7.12 )
% 6.74/7.12 , clause( 27784, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 6.74/7.12 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 6.74/7.12 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 6.74/7.12 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 6.74/7.12 , Z ), flip( T ) ) ] )
% 6.74/7.12 , clause( 27785, [ =( 'domain_of'( flip( 'cross_product'( X,
% 6.74/7.12 'universal_class' ) ) ), inverse( X ) ) ] )
% 6.74/7.12 , clause( 27786, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 6.74/7.12 , clause( 27787, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 6.74/7.12 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 6.74/7.12 , clause( 27788, [ =( second( 'not_subclass_element'( restrict( X,
% 6.74/7.12 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 6.74/7.12 , clause( 27789, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 6.74/7.12 image( X, Y ) ) ] )
% 6.74/7.12 , clause( 27790, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 6.74/7.12 , clause( 27791, [ subclass( 'successor_relation', 'cross_product'(
% 6.74/7.12 'universal_class', 'universal_class' ) ) ] )
% 6.74/7.12 , clause( 27792, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 6.74/7.12 ) ), =( successor( X ), Y ) ] )
% 6.74/7.12 , clause( 27793, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 6.74/7.12 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 6.74/7.12 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 6.74/7.12 , clause( 27794, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 6.74/7.12 , clause( 27795, [ ~( inductive( X ) ), subclass( image(
% 6.74/7.12 'successor_relation', X ), X ) ] )
% 6.74/7.12 , clause( 27796, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 6.74/7.12 'successor_relation', X ), X ) ), inductive( X ) ] )
% 6.74/7.12 , clause( 27797, [ inductive( omega ) ] )
% 6.74/7.12 , clause( 27798, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 6.74/7.12 , clause( 27799, [ member( omega, 'universal_class' ) ] )
% 6.74/7.12 , clause( 27800, [ =( 'domain_of'( restrict( 'element_relation',
% 6.74/7.12 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 6.74/7.12 , clause( 27801, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 6.74/7.12 X ), 'universal_class' ) ] )
% 6.74/7.12 , clause( 27802, [ =( complement( image( 'element_relation', complement( X
% 6.74/7.12 ) ) ), 'power_class'( X ) ) ] )
% 6.74/7.12 , clause( 27803, [ ~( member( X, 'universal_class' ) ), member(
% 6.74/7.12 'power_class'( X ), 'universal_class' ) ] )
% 6.74/7.12 , clause( 27804, [ subclass( compose( X, Y ), 'cross_product'(
% 6.74/7.12 'universal_class', 'universal_class' ) ) ] )
% 6.74/7.12 , clause( 27805, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 6.74/7.12 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 6.74/7.12 , clause( 27806, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 6.74/7.12 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 6.74/7.12 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 6.74/7.12 ) ] )
% 6.74/7.12 , clause( 27807, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 6.74/7.12 inverse( X ) ), 'identity_relation' ) ] )
% 6.74/7.12 , clause( 27808, [ ~( subclass( compose( X, inverse( X ) ),
% 6.74/7.12 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 6.74/7.12 , clause( 27809, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 6.74/7.12 'universal_class', 'universal_class' ) ) ] )
% 6.74/7.12 , clause( 27810, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 6.74/7.12 , 'identity_relation' ) ] )
% 6.74/7.12 , clause( 27811, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 6.74/7.12 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 6.74/7.12 'identity_relation' ) ), function( X ) ] )
% 6.74/7.12 , clause( 27812, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 6.74/7.12 , member( image( X, Y ), 'universal_class' ) ] )
% 6.74/7.12 , clause( 27813, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 6.74/7.12 , clause( 27814, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 6.74/7.12 , 'null_class' ) ] )
% 6.74/7.12 , clause( 27815, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 6.74/7.12 Y ) ) ] )
% 6.74/7.12 , clause( 27816, [ function( choice ) ] )
% 6.74/7.12 , clause( 27817, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 6.74/7.12 ), member( apply( choice, X ), X ) ] )
% 6.74/7.12 , clause( 27818, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 6.74/7.12 , clause( 27819, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 6.74/7.12 , clause( 27820, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 6.74/7.12 'one_to_one'( X ) ] )
% 6.74/7.12 , clause( 27821, [ =( intersection( 'cross_product'( 'universal_class',
% 6.74/7.12 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 6.74/7.12 'universal_class' ), complement( compose( complement( 'element_relation'
% 6.74/7.12 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 6.74/7.12 , clause( 27822, [ =( intersection( inverse( 'subset_relation' ),
% 6.74/7.12 'subset_relation' ), 'identity_relation' ) ] )
% 6.74/7.12 , clause( 27823, [ =( complement( 'domain_of'( intersection( X,
% 6.74/7.12 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 6.74/7.12 , clause( 27824, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 6.74/7.12 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 6.74/7.12 , clause( 27825, [ ~( operation( X ) ), function( X ) ] )
% 6.74/7.12 , clause( 27826, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 6.74/7.12 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 6.74/7.12 ] )
% 6.74/7.12 , clause( 27827, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 6.74/7.12 'domain_of'( 'domain_of'( X ) ) ) ] )
% 6.74/7.12 , clause( 27828, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 6.74/7.12 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 6.74/7.12 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 6.74/7.12 operation( X ) ] )
% 6.74/7.12 , clause( 27829, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 6.74/7.12 , clause( 27830, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 6.74/7.12 Y ) ), 'domain_of'( X ) ) ] )
% 6.74/7.12 , clause( 27831, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 6.74/7.12 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 6.74/7.12 , clause( 27832, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 6.74/7.12 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 6.74/7.12 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 6.74/7.12 , clause( 27833, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 6.74/7.12 , clause( 27834, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 6.74/7.12 , clause( 27835, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 6.74/7.12 , clause( 27836, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 6.74/7.12 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 6.74/7.12 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 6.74/7.12 )
% 6.74/7.12 , clause( 27837, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 6.74/7.12 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 6.74/7.12 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 6.74/7.12 , Y ) ] )
% 6.74/7.12 , clause( 27838, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 6.74/7.12 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 6.74/7.12 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 6.74/7.12 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 6.74/7.12 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 6.74/7.12 )
% 6.74/7.12 , clause( 27839, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.74/7.12 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 6.74/7.12 , clause( 27840, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.74/7.12 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 6.74/7.12 , clause( 27841, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.74/7.12 ) ) ), member( X, 'universal_class' ) ] )
% 6.74/7.12 , clause( 27842, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.74/7.12 ) ) ), member( Y, 'universal_class' ) ] )
% 6.74/7.12 , clause( 27843, [ subclass( X, X ) ] )
% 6.74/7.12 , clause( 27844, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 6.74/7.12 X, Z ) ] )
% 6.74/7.12 , clause( 27845, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 6.74/7.12 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 6.74/7.12 , clause( 27846, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 6.74/7.12 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 6.74/7.12 , clause( 27847, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 6.74/7.12 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 6.74/7.12 , clause( 27848, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 6.74/7.12 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 6.74/7.12 , clause( 27849, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 6.74/7.12 )
% 6.74/7.12 , clause( 27850, [ ~( member( X, 'null_class' ) ) ] )
% 6.74/7.12 , clause( 27851, [ subclass( 'null_class', X ) ] )
% 6.74/7.12 , clause( 27852, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 6.74/7.12 )
% 6.74/7.12 , clause( 27853, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 6.74/7.12 , 'null_class' ), X ) ] )
% 6.74/7.12 , clause( 27854, [ member( 'null_class', 'universal_class' ) ] )
% 6.74/7.12 , clause( 27855, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 6.74/7.12 ] )
% 6.74/7.12 , clause( 27856, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 6.74/7.12 )
% 6.74/7.12 , clause( 27857, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 6.74/7.12 )
% 6.74/7.12 , clause( 27858, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 6.74/7.12 X ), singleton( Y ) ) ] )
% 6.74/7.12 , clause( 27859, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 6.74/7.12 Y ), singleton( Y ) ) ] )
% 6.74/7.12 , clause( 27860, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 6.74/7.12 'universal_class' ), member( Y, 'universal_class' ) ] )
% 6.74/7.12 , clause( 27861, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 6.74/7.12 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 6.74/7.12 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 6.74/7.12 , clause( 27862, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 6.74/7.12 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 6.74/7.12 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 6.74/7.12 , clause( 27863, [ ~( member( X, 'universal_class' ) ), ~( =(
% 6.74/7.12 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 6.74/7.12 , clause( 27864, [ ~( member( X, 'universal_class' ) ), ~( =(
% 6.74/7.12 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 6.74/7.12 , clause( 27865, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 6.74/7.12 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 6.74/7.12 , clause( 27866, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 6.74/7.12 'unordered_pair'( X, Z ), Y ) ] )
% 6.74/7.12 , clause( 27867, [ member( singleton( X ), 'universal_class' ) ] )
% 6.74/7.12 , clause( 27868, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 6.74/7.12 X ) ) ) ] )
% 6.74/7.12 , clause( 27869, [ ~( member( X, 'universal_class' ) ), member( X,
% 6.74/7.12 singleton( X ) ) ] )
% 6.74/7.12 , clause( 27870, [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X
% 6.74/7.12 ), 'null_class' ) ) ] )
% 6.74/7.12 , clause( 27871, [ member( 'null_class', singleton( 'null_class' ) ) ] )
% 6.74/7.12 , clause( 27872, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 6.74/7.12 , clause( 27873, [ member( X, 'universal_class' ), =( singleton( X ),
% 6.74/7.12 'null_class' ) ] )
% 6.74/7.12 , clause( 27874, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 6.74/7.12 'universal_class' ) ), =( X, Y ) ] )
% 6.74/7.12 , clause( 27875, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 6.74/7.12 'universal_class' ) ), =( X, Y ) ] )
% 6.74/7.12 , clause( 27876, [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~(
% 6.74/7.12 member( Z, 'universal_class' ) ), =( Z, X ), =( Z, Y ) ] )
% 6.74/7.12 , clause( 27877, [ ~( member( X, 'universal_class' ) ), member( 'member_of'(
% 6.74/7.12 singleton( X ) ), 'universal_class' ) ] )
% 6.74/7.12 , clause( 27878, [ ~( member( X, 'universal_class' ) ), =( singleton(
% 6.74/7.12 'member_of'( singleton( X ) ) ), singleton( X ) ) ] )
% 6.74/7.12 , clause( 27879, [ member( 'member_of'( X ), 'universal_class' ), =(
% 6.74/7.12 'member_of'( X ), X ) ] )
% 6.74/7.12 , clause( 27880, [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X
% 6.74/7.12 ), X ) ] )
% 6.74/7.12 , clause( 27881, [ ~( member( X, 'universal_class' ) ), =( 'member_of'(
% 6.74/7.12 singleton( X ) ), X ) ] )
% 6.74/7.12 , clause( 27882, [ member( 'member_of1'( X ), 'universal_class' ), =(
% 6.74/7.12 'member_of'( X ), X ) ] )
% 6.74/7.12 , clause( 27883, [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'(
% 6.74/7.12 X ), X ) ] )
% 6.74/7.12 , clause( 27884, [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 6.74/7.12 'universal_class' ) ] )
% 6.74/7.12 , clause( 27885, [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y
% 6.74/7.12 , X ) ), =( 'member_of'( X ), Y ) ] )
% 6.74/7.12 , clause( 27886, [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ] )
% 6.74/7.12 , clause( 27887, [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' )
% 6.74/7.12 , =( singleton( Y ), X ) ] )
% 6.74/7.12 , clause( 27888, [ member( 'not_subclass_element'( intersection( complement(
% 6.74/7.12 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 6.74/7.12 'null_class' ), intersection( complement( singleton(
% 6.74/7.12 'not_subclass_element'( X, 'null_class' ) ) ), X ) ), =( singleton(
% 6.74/7.12 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 6.74/7.12 )
% 6.74/7.12 , clause( 27889, [ member( 'not_subclass_element'( intersection( complement(
% 6.74/7.12 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 6.74/7.12 'null_class' ), X ), =( singleton( 'not_subclass_element'( X,
% 6.74/7.12 'null_class' ) ), X ), =( X, 'null_class' ) ] )
% 6.74/7.12 , clause( 27890, [ ~( =( 'not_subclass_element'( intersection( complement(
% 6.74/7.12 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 6.74/7.12 'null_class' ), 'not_subclass_element'( X, 'null_class' ) ) ), =(
% 6.74/7.12 singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 6.74/7.12 'null_class' ) ] )
% 6.74/7.12 , clause( 27891, [ =( 'unordered_pair'( X, Y ), union( singleton( X ),
% 6.74/7.12 singleton( Y ) ) ) ] )
% 6.74/7.12 , clause( 27892, [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ] )
% 6.74/7.12 , clause( 27893, [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ] )
% 6.74/7.12 , clause( 27894, [ member( 'unordered_pair'( X, singleton( Y ) ),
% 6.74/7.12 'ordered_pair'( X, Y ) ) ] )
% 6.74/7.12 , clause( 27895, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 6.74/7.12 , 'null_class' ) ), 'ordered_pair'( X, Y ) ), member( Y,
% 6.74/7.12 'universal_class' ) ] )
% 6.74/7.12 , clause( 27896, [ ~( member( X, 'universal_class' ) ), =( 'unordered_pair'(
% 6.74/7.12 'null_class', singleton( singleton( X ) ) ), 'ordered_pair'( Y, X ) ),
% 6.74/7.12 member( Y, 'universal_class' ) ] )
% 6.74/7.12 , clause( 27897, [ =( 'unordered_pair'( 'null_class', singleton(
% 6.74/7.12 'null_class' ) ), 'ordered_pair'( X, Y ) ), member( X, 'universal_class'
% 6.74/7.12 ), member( Y, 'universal_class' ) ] )
% 6.74/7.12 , clause( 27898, [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) )
% 6.74/7.12 , ~( member( X, 'universal_class' ) ), =( X, Z ) ] )
% 6.74/7.12 , clause( 27899, [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) )
% 6.74/7.12 , ~( member( Y, 'universal_class' ) ), =( Y, T ) ] )
% 6.74/7.12 , clause( 27900, [ member( 'ordered_pair'( y, z ), 'cross_product'(
% 6.74/7.12 'universal_class', 'universal_class' ) ) ] )
% 6.74/7.12 , clause( 27901, [ ~( member( 'ordered_pair'( first( 'ordered_pair'( y, z )
% 6.74/7.12 ), second( 'ordered_pair'( y, z ) ) ), 'cross_product'(
% 6.74/7.12 'universal_class', 'universal_class' ) ) ) ] )
% 6.74/7.12 ] ).
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 subsumption(
% 6.74/7.12 clause( 15, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'(
% 6.74/7.12 first( X ), second( X ) ), X ) ] )
% 6.74/7.12 , clause( 27764, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 6.74/7.12 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 6.74/7.12 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 6.74/7.12 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 subsumption(
% 6.74/7.12 clause( 149, [ member( 'ordered_pair'( y, z ), 'cross_product'(
% 6.74/7.12 'universal_class', 'universal_class' ) ) ] )
% 6.74/7.12 , clause( 27900, [ member( 'ordered_pair'( y, z ), 'cross_product'(
% 6.74/7.12 'universal_class', 'universal_class' ) ) ] )
% 6.74/7.12 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 subsumption(
% 6.74/7.12 clause( 150, [ ~( member( 'ordered_pair'( first( 'ordered_pair'( y, z ) ),
% 6.74/7.12 second( 'ordered_pair'( y, z ) ) ), 'cross_product'( 'universal_class',
% 6.74/7.12 'universal_class' ) ) ) ] )
% 6.74/7.12 , clause( 27901, [ ~( member( 'ordered_pair'( first( 'ordered_pair'( y, z )
% 6.74/7.12 ), second( 'ordered_pair'( y, z ) ) ), 'cross_product'(
% 6.74/7.12 'universal_class', 'universal_class' ) ) ) ] )
% 6.74/7.12 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 eqswap(
% 6.74/7.12 clause( 28182, [ =( X, 'ordered_pair'( first( X ), second( X ) ) ), ~(
% 6.74/7.12 member( X, 'cross_product'( Y, Z ) ) ) ] )
% 6.74/7.12 , clause( 15, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 6.74/7.12 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 6.74/7.12 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 resolution(
% 6.74/7.12 clause( 28183, [ =( 'ordered_pair'( y, z ), 'ordered_pair'( first(
% 6.74/7.12 'ordered_pair'( y, z ) ), second( 'ordered_pair'( y, z ) ) ) ) ] )
% 6.74/7.12 , clause( 28182, [ =( X, 'ordered_pair'( first( X ), second( X ) ) ), ~(
% 6.74/7.12 member( X, 'cross_product'( Y, Z ) ) ) ] )
% 6.74/7.12 , 1, clause( 149, [ member( 'ordered_pair'( y, z ), 'cross_product'(
% 6.74/7.12 'universal_class', 'universal_class' ) ) ] )
% 6.74/7.12 , 0, substitution( 0, [ :=( X, 'ordered_pair'( y, z ) ), :=( Y,
% 6.74/7.12 'universal_class' ), :=( Z, 'universal_class' )] ), substitution( 1, [] )
% 6.74/7.12 ).
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 eqswap(
% 6.74/7.12 clause( 28184, [ =( 'ordered_pair'( first( 'ordered_pair'( y, z ) ), second(
% 6.74/7.12 'ordered_pair'( y, z ) ) ), 'ordered_pair'( y, z ) ) ] )
% 6.74/7.12 , clause( 28183, [ =( 'ordered_pair'( y, z ), 'ordered_pair'( first(
% 6.74/7.12 'ordered_pair'( y, z ) ), second( 'ordered_pair'( y, z ) ) ) ) ] )
% 6.74/7.12 , 0, substitution( 0, [] )).
% 6.74/7.12
% 6.74/7.12
% 6.74/7.12 subsumption(
% 6.74/7.12 clause( 27482, [ =( 'ordered_pair'( first( 'ordered_pair'( y, z ) ), second(
% 6.74/7.13 'ordered_pair'( y, z ) ) ), 'ordered_pair'( y, z ) ) ] )
% 6.74/7.13 , clause( 28184, [ =( 'ordered_pair'( first( 'ordered_pair'( y, z ) ),
% 6.74/7.13 second( 'ordered_pair'( y, z ) ) ), 'ordered_pair'( y, z ) ) ] )
% 6.74/7.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 6.74/7.13
% 6.74/7.13
% 6.74/7.13 paramod(
% 6.74/7.13 clause( 28186, [ ~( member( 'ordered_pair'( y, z ), 'cross_product'(
% 6.74/7.13 'universal_class', 'universal_class' ) ) ) ] )
% 6.74/7.13 , clause( 27482, [ =( 'ordered_pair'( first( 'ordered_pair'( y, z ) ),
% 6.74/7.13 second( 'ordered_pair'( y, z ) ) ), 'ordered_pair'( y, z ) ) ] )
% 6.74/7.13 , 0, clause( 150, [ ~( member( 'ordered_pair'( first( 'ordered_pair'( y, z
% 6.74/7.13 ) ), second( 'ordered_pair'( y, z ) ) ), 'cross_product'(
% 6.74/7.13 'universal_class', 'universal_class' ) ) ) ] )
% 6.74/7.13 , 0, 2, substitution( 0, [] ), substitution( 1, [] )).
% 6.74/7.13
% 6.74/7.13
% 6.74/7.13 resolution(
% 6.74/7.13 clause( 28187, [] )
% 6.74/7.13 , clause( 28186, [ ~( member( 'ordered_pair'( y, z ), 'cross_product'(
% 6.74/7.13 'universal_class', 'universal_class' ) ) ) ] )
% 6.74/7.13 , 0, clause( 149, [ member( 'ordered_pair'( y, z ), 'cross_product'(
% 6.74/7.13 'universal_class', 'universal_class' ) ) ] )
% 6.74/7.13 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 6.74/7.13
% 6.74/7.13
% 6.74/7.13 subsumption(
% 6.74/7.13 clause( 27746, [] )
% 6.74/7.13 , clause( 28187, [] )
% 6.74/7.13 , substitution( 0, [] ), permutation( 0, [] ) ).
% 6.74/7.13
% 6.74/7.13
% 6.74/7.13 end.
% 6.74/7.13
% 6.74/7.13 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 6.74/7.13
% 6.74/7.13 Memory use:
% 6.74/7.13
% 6.74/7.13 space for terms: 505473
% 6.74/7.13 space for clauses: 1276051
% 6.74/7.13
% 6.74/7.13
% 6.74/7.13 clauses generated: 91249
% 6.74/7.13 clauses kept: 27747
% 6.74/7.13 clauses selected: 565
% 6.74/7.13 clauses deleted: 1199
% 6.74/7.13 clauses inuse deleted: 64
% 6.74/7.13
% 6.74/7.13 subsentry: 345396
% 6.74/7.13 literals s-matched: 263533
% 6.74/7.13 literals matched: 253679
% 6.74/7.13 full subsumption: 155795
% 6.74/7.13
% 6.74/7.13 checksum: -1012951938
% 6.74/7.13
% 6.74/7.13
% 6.74/7.13 Bliksem ended
%------------------------------------------------------------------------------