TSTP Solution File: SET090-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET090-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.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 22:46:53 EDT 2022
% Result : Unsatisfiable 4.75s 5.20s
% Output : Refutation 4.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET090-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n025.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 09:51:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.70/1.09 *** allocated 10000 integers for termspace/termends
% 0.70/1.09 *** allocated 10000 integers for clauses
% 0.70/1.09 *** allocated 10000 integers for justifications
% 0.70/1.09 Bliksem 1.12
% 0.70/1.09
% 0.70/1.09
% 0.70/1.09 Automatic Strategy Selection
% 0.70/1.09
% 0.70/1.09 Clauses:
% 0.70/1.09 [
% 0.70/1.09 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.70/1.09 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.70/1.09 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.70/1.09 ,
% 0.70/1.09 [ subclass( X, 'universal_class' ) ],
% 0.70/1.09 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.70/1.09 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.70/1.09 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.70/1.09 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.70/1.09 ,
% 0.70/1.09 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.70/1.09 ) ) ],
% 0.70/1.09 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.70/1.09 ) ) ],
% 0.70/1.09 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.70/1.09 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.70/1.09 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.70/1.09 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.70/1.09 X, Z ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.70/1.09 Y, T ) ],
% 0.70/1.09 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.70/1.09 ), 'cross_product'( Y, T ) ) ],
% 0.70/1.09 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.70/1.09 ), second( X ) ), X ) ],
% 0.70/1.09 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.70/1.09 'universal_class' ) ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.70/1.09 Y ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.70/1.09 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.70/1.09 , Y ), 'element_relation' ) ],
% 0.70/1.09 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.70/1.09 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.70/1.09 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.70/1.09 Z ) ) ],
% 0.70/1.09 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.70/1.09 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.70/1.09 member( X, Y ) ],
% 0.70/1.09 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.70/1.09 union( X, Y ) ) ],
% 0.70/1.09 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.70/1.09 intersection( complement( X ), complement( Y ) ) ) ),
% 0.70/1.09 'symmetric_difference'( X, Y ) ) ],
% 0.70/1.09 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.70/1.09 ,
% 0.70/1.09 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.70/1.09 ,
% 0.70/1.09 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.70/1.09 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.70/1.09 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.70/1.09 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.70/1.09 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.70/1.09 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.70/1.09 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.70/1.09 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.70/1.09 'cross_product'( 'universal_class', 'universal_class' ),
% 0.70/1.09 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.70/1.09 Y ), rotate( T ) ) ],
% 0.70/1.09 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.70/1.09 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.70/1.09 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.70/1.09 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.70/1.09 'cross_product'( 'universal_class', 'universal_class' ),
% 0.70/1.09 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.70/1.09 Z ), flip( T ) ) ],
% 0.70/1.09 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.70/1.09 inverse( X ) ) ],
% 0.70/1.09 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.70/1.09 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.70/1.09 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.70/1.09 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.70/1.09 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.70/1.09 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.70/1.09 ],
% 0.70/1.09 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.70/1.09 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.70/1.09 'universal_class' ) ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.70/1.09 successor( X ), Y ) ],
% 0.70/1.09 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.70/1.09 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.70/1.09 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.70/1.09 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.70/1.09 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.70/1.09 ,
% 0.70/1.09 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.70/1.09 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.70/1.09 [ inductive( omega ) ],
% 0.70/1.09 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.70/1.09 [ member( omega, 'universal_class' ) ],
% 0.70/1.09 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.70/1.09 , 'sum_class'( X ) ) ],
% 0.70/1.09 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.70/1.09 'universal_class' ) ],
% 0.70/1.09 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.70/1.09 'power_class'( X ) ) ],
% 0.70/1.09 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.70/1.09 'universal_class' ) ],
% 0.70/1.09 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.70/1.09 'universal_class' ) ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.70/1.09 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.70/1.09 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.70/1.09 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.70/1.09 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.70/1.09 ) ],
% 0.70/1.09 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.70/1.09 , 'identity_relation' ) ],
% 0.70/1.09 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.70/1.09 'single_valued_class'( X ) ],
% 0.70/1.09 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.70/1.09 'universal_class' ) ) ],
% 0.70/1.09 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.70/1.09 'identity_relation' ) ],
% 0.70/1.09 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.70/1.09 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.70/1.09 , function( X ) ],
% 0.70/1.09 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.70/1.09 X, Y ), 'universal_class' ) ],
% 0.70/1.09 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.70/1.09 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.70/1.09 ) ],
% 0.70/1.09 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.70/1.09 [ function( choice ) ],
% 0.70/1.09 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.70/1.09 apply( choice, X ), X ) ],
% 0.70/1.09 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.70/1.09 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.70/1.09 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.70/1.09 ,
% 0.70/1.09 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.70/1.09 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.70/1.09 , complement( compose( complement( 'element_relation' ), inverse(
% 0.70/1.09 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.70/1.09 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.70/1.09 'identity_relation' ) ],
% 0.70/1.09 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.70/1.09 , diagonalise( X ) ) ],
% 0.70/1.09 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.70/1.09 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.70/1.09 [ ~( operation( X ) ), function( X ) ],
% 0.70/1.09 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.70/1.09 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.70/1.09 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.70/1.09 'domain_of'( X ) ) ) ],
% 0.70/1.09 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.70/1.09 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.70/1.09 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.70/1.09 X ) ],
% 0.70/1.09 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.70/1.09 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.70/1.09 'domain_of'( X ) ) ],
% 0.70/1.09 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.70/1.09 'domain_of'( Z ) ) ) ],
% 0.70/1.09 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.70/1.09 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.70/1.09 ), compatible( X, Y, Z ) ],
% 0.70/1.09 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.70/1.09 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.70/1.09 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.70/1.09 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.70/1.09 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.70/1.09 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.70/1.09 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.70/1.09 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.70/1.09 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.70/1.09 , Y ) ],
% 0.70/1.09 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.70/1.09 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.70/1.09 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.70/1.09 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.70/1.09 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.70/1.09 X, 'unordered_pair'( X, Y ) ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.70/1.09 Y, 'unordered_pair'( X, Y ) ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.70/1.09 X, 'universal_class' ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.70/1.09 Y, 'universal_class' ) ],
% 0.70/1.09 [ subclass( X, X ) ],
% 0.70/1.09 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.70/1.09 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.70/1.09 'not_subclass_element'( Y, X ), Y ) ],
% 0.70/1.09 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.70/1.09 'not_subclass_element'( Y, X ), Y ) ],
% 0.70/1.09 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.70/1.09 'not_subclass_element'( Y, X ), Y ) ],
% 0.70/1.09 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.70/1.09 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.70/1.09 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.70/1.09 [ ~( member( X, 'null_class' ) ) ],
% 0.70/1.09 [ subclass( 'null_class', X ) ],
% 0.70/1.09 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.70/1.09 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.70/1.09 ), X ) ],
% 0.70/1.09 [ member( 'null_class', 'universal_class' ) ],
% 0.70/1.09 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.70/1.09 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.70/1.09 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.70/1.09 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.70/1.09 Y ) ) ],
% 0.70/1.09 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.70/1.09 Y ) ) ],
% 0.70/1.09 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.70/1.09 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.70/1.09 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.70/1.09 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.70/1.09 'universal_class' ) ) ), =( Y, Z ) ],
% 0.70/1.09 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.70/1.09 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.70/1.09 'universal_class' ) ) ), =( X, Z ) ],
% 0.70/1.09 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.70/1.09 'null_class' ) ) ],
% 0.70/1.09 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.70/1.09 'null_class' ) ) ],
% 0.70/1.09 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.70/1.09 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 4.75/5.20 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 4.75/5.20 X, Z ), Y ) ],
% 4.75/5.20 [ member( singleton( X ), 'universal_class' ) ],
% 4.75/5.20 [ member( singleton( X ), 'unordered_pair'( Y, singleton( X ) ) ) ],
% 4.75/5.20 [ ~( member( X, 'universal_class' ) ), member( X, singleton( X ) ) ]
% 4.75/5.20 ,
% 4.75/5.20 [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X ),
% 4.75/5.20 'null_class' ) ) ],
% 4.75/5.20 [ member( 'null_class', singleton( 'null_class' ) ) ],
% 4.75/5.20 [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ],
% 4.75/5.20 [ member( X, 'universal_class' ), =( singleton( X ), 'null_class' ) ]
% 4.75/5.20 ,
% 4.75/5.20 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 4.75/5.20 'universal_class' ) ), =( X, Y ) ],
% 4.75/5.20 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 4.75/5.20 'universal_class' ) ), =( X, Y ) ],
% 4.75/5.20 [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~( member( Z,
% 4.75/5.20 'universal_class' ) ), =( Z, X ), =( Z, Y ) ],
% 4.75/5.20 [ ~( member( X, 'universal_class' ) ), member( 'member_of'( singleton( X
% 4.75/5.20 ) ), 'universal_class' ) ],
% 4.75/5.20 [ ~( member( X, 'universal_class' ) ), =( singleton( 'member_of'(
% 4.75/5.20 singleton( X ) ) ), singleton( X ) ) ],
% 4.75/5.20 [ member( 'member_of'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 4.75/5.20 ) ],
% 4.75/5.20 [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X ), X ) ],
% 4.75/5.20 [ member( u, 'universal_class' ) ],
% 4.75/5.20 [ ~( =( 'member_of'( singleton( u ) ), u ) ) ]
% 4.75/5.20 ] .
% 4.75/5.20
% 4.75/5.20
% 4.75/5.20 percentage equality = 0.263941, percentage horn = 0.859259
% 4.75/5.20 This is a problem with some equality
% 4.75/5.20
% 4.75/5.20
% 4.75/5.20
% 4.75/5.20 Options Used:
% 4.75/5.20
% 4.75/5.20 useres = 1
% 4.75/5.20 useparamod = 1
% 4.75/5.20 useeqrefl = 1
% 4.75/5.20 useeqfact = 1
% 4.75/5.20 usefactor = 1
% 4.75/5.20 usesimpsplitting = 0
% 4.75/5.20 usesimpdemod = 5
% 4.75/5.20 usesimpres = 3
% 4.75/5.20
% 4.75/5.20 resimpinuse = 1000
% 4.75/5.20 resimpclauses = 20000
% 4.75/5.20 substype = eqrewr
% 4.75/5.20 backwardsubs = 1
% 4.75/5.20 selectoldest = 5
% 4.75/5.20
% 4.75/5.20 litorderings [0] = split
% 4.75/5.20 litorderings [1] = extend the termordering, first sorting on arguments
% 4.75/5.20
% 4.75/5.20 termordering = kbo
% 4.75/5.20
% 4.75/5.20 litapriori = 0
% 4.75/5.20 termapriori = 1
% 4.75/5.20 litaposteriori = 0
% 4.75/5.20 termaposteriori = 0
% 4.75/5.20 demodaposteriori = 0
% 4.75/5.20 ordereqreflfact = 0
% 4.75/5.20
% 4.75/5.20 litselect = negord
% 4.75/5.20
% 4.75/5.20 maxweight = 15
% 4.75/5.20 maxdepth = 30000
% 4.75/5.20 maxlength = 115
% 4.75/5.20 maxnrvars = 195
% 4.75/5.20 excuselevel = 1
% 4.75/5.20 increasemaxweight = 1
% 4.75/5.20
% 4.75/5.20 maxselected = 10000000
% 4.75/5.20 maxnrclauses = 10000000
% 4.75/5.20
% 4.75/5.20 showgenerated = 0
% 4.75/5.20 showkept = 0
% 4.75/5.20 showselected = 0
% 4.75/5.20 showdeleted = 0
% 4.75/5.20 showresimp = 1
% 4.75/5.20 showstatus = 2000
% 4.75/5.20
% 4.75/5.20 prologoutput = 1
% 4.75/5.20 nrgoals = 5000000
% 4.75/5.20 totalproof = 1
% 4.75/5.20
% 4.75/5.20 Symbols occurring in the translation:
% 4.75/5.20
% 4.75/5.20 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 4.75/5.20 . [1, 2] (w:1, o:56, a:1, s:1, b:0),
% 4.75/5.20 ! [4, 1] (w:0, o:30, a:1, s:1, b:0),
% 4.75/5.20 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 4.75/5.20 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 4.75/5.20 subclass [41, 2] (w:1, o:81, a:1, s:1, b:0),
% 4.75/5.20 member [43, 2] (w:1, o:82, a:1, s:1, b:0),
% 4.75/5.20 'not_subclass_element' [44, 2] (w:1, o:83, a:1, s:1, b:0),
% 4.75/5.20 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 4.75/5.20 'unordered_pair' [46, 2] (w:1, o:84, a:1, s:1, b:0),
% 4.75/5.20 singleton [47, 1] (w:1, o:38, a:1, s:1, b:0),
% 4.75/5.20 'ordered_pair' [48, 2] (w:1, o:85, a:1, s:1, b:0),
% 4.75/5.20 'cross_product' [50, 2] (w:1, o:86, a:1, s:1, b:0),
% 4.75/5.20 first [52, 1] (w:1, o:39, a:1, s:1, b:0),
% 4.75/5.20 second [53, 1] (w:1, o:40, a:1, s:1, b:0),
% 4.75/5.20 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 4.75/5.20 intersection [55, 2] (w:1, o:88, a:1, s:1, b:0),
% 4.75/5.20 complement [56, 1] (w:1, o:41, a:1, s:1, b:0),
% 4.75/5.20 union [57, 2] (w:1, o:89, a:1, s:1, b:0),
% 4.75/5.20 'symmetric_difference' [58, 2] (w:1, o:90, a:1, s:1, b:0),
% 4.75/5.20 restrict [60, 3] (w:1, o:93, a:1, s:1, b:0),
% 4.75/5.20 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 4.75/5.20 'domain_of' [62, 1] (w:1, o:43, a:1, s:1, b:0),
% 4.75/5.20 rotate [63, 1] (w:1, o:35, a:1, s:1, b:0),
% 4.75/5.20 flip [65, 1] (w:1, o:44, a:1, s:1, b:0),
% 4.75/5.20 inverse [66, 1] (w:1, o:45, a:1, s:1, b:0),
% 4.75/5.20 'range_of' [67, 1] (w:1, o:36, a:1, s:1, b:0),
% 4.75/5.20 domain [68, 3] (w:1, o:95, a:1, s:1, b:0),
% 4.75/5.20 range [69, 3] (w:1, o:96, a:1, s:1, b:0),
% 4.75/5.20 image [70, 2] (w:1, o:87, a:1, s:1, b:0),
% 4.75/5.20 successor [71, 1] (w:1, o:46, a:1, s:1, b:0),
% 4.75/5.20 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 4.75/5.20 inductive [73, 1] (w:1, o:47, a:1, s:1, b:0),
% 4.75/5.20 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 4.75/5.20 'sum_class' [75, 1] (w:1, o:48, a:1, s:1, b:0),
% 4.75/5.20 'power_class' [76, 1] (w:1, o:51, a:1, s:1, b:0),
% 4.75/5.20 compose [78, 2] (w:1, o:91, a:1, s:1, b:0),
% 4.75/5.20 'single_valued_class' [79, 1] (w:1, o:52, a:1, s:1, b:0),
% 4.75/5.20 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 4.75/5.20 function [82, 1] (w:1, o:53, a:1, s:1, b:0),
% 4.75/5.20 regular [83, 1] (w:1, o:37, a:1, s:1, b:0),
% 4.75/5.20 apply [84, 2] (w:1, o:92, a:1, s:1, b:0),
% 4.75/5.20 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 4.75/5.20 'one_to_one' [86, 1] (w:1, o:49, a:1, s:1, b:0),
% 4.75/5.20 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 4.75/5.20 diagonalise [88, 1] (w:1, o:54, a:1, s:1, b:0),
% 4.75/5.20 cantor [89, 1] (w:1, o:42, a:1, s:1, b:0),
% 4.75/5.20 operation [90, 1] (w:1, o:50, a:1, s:1, b:0),
% 4.75/5.20 compatible [94, 3] (w:1, o:94, a:1, s:1, b:0),
% 4.75/5.20 homomorphism [95, 3] (w:1, o:97, a:1, s:1, b:0),
% 4.75/5.20 'not_homomorphism1' [96, 3] (w:1, o:98, a:1, s:1, b:0),
% 4.75/5.20 'not_homomorphism2' [97, 3] (w:1, o:99, a:1, s:1, b:0),
% 4.75/5.20 'member_of' [98, 1] (w:1, o:55, a:1, s:1, b:0),
% 4.75/5.20 u [99, 0] (w:1, o:29, a:1, s:1, b:0).
% 4.75/5.20
% 4.75/5.20
% 4.75/5.20 Starting Search:
% 4.75/5.20
% 4.75/5.20 Resimplifying inuse:
% 4.75/5.20 Done
% 4.75/5.20
% 4.75/5.20
% 4.75/5.20 Intermediate Status:
% 4.75/5.20 Generated: 3835
% 4.75/5.20 Kept: 2001
% 4.75/5.20 Inuse: 117
% 4.75/5.20 Deleted: 2
% 4.75/5.20 Deletedinuse: 2
% 4.75/5.20
% 4.75/5.20 Resimplifying inuse:
% 4.75/5.20 Done
% 4.75/5.20
% 4.75/5.20 Resimplifying inuse:
% 4.75/5.20 Done
% 4.75/5.20
% 4.75/5.20
% 4.75/5.20 Intermediate Status:
% 4.75/5.20 Generated: 9523
% 4.75/5.20 Kept: 4261
% 4.75/5.20 Inuse: 201
% 4.75/5.20 Deleted: 8
% 4.75/5.20 Deletedinuse: 8
% 4.75/5.20
% 4.75/5.20 Resimplifying inuse:
% 4.75/5.20 Done
% 4.75/5.20
% 4.75/5.20 Resimplifying inuse:
% 4.75/5.20 Done
% 4.75/5.20
% 4.75/5.20
% 4.75/5.20 Intermediate Status:
% 4.75/5.20 Generated: 14631
% 4.75/5.20 Kept: 6276
% 4.75/5.20 Inuse: 279
% 4.75/5.20 Deleted: 47
% 4.75/5.20 Deletedinuse: 45
% 4.75/5.20
% 4.75/5.20 Resimplifying inuse:
% 4.75/5.20 Done
% 4.75/5.20
% 4.75/5.20 Resimplifying inuse:
% 4.75/5.20 Done
% 4.75/5.20
% 4.75/5.20
% 4.75/5.20 Intermediate Status:
% 4.75/5.20 Generated: 20833
% 4.75/5.20 Kept: 8294
% 4.75/5.20 Inuse: 331
% 4.75/5.20 Deleted: 66
% 4.75/5.20 Deletedinuse: 51
% 4.75/5.20
% 4.75/5.20 Resimplifying inuse:
% 4.75/5.20 Done
% 4.75/5.20
% 4.75/5.20 Resimplifying inuse:
% 4.75/5.20 Done
% 4.75/5.20
% 4.75/5.20
% 4.75/5.20 Intermediate Status:
% 4.75/5.20 Generated: 28457
% 4.75/5.20 Kept: 10808
% 4.75/5.20 Inuse: 396
% 4.75/5.20 Deleted: 70
% 4.75/5.20 Deletedinuse: 55
% 4.75/5.20
% 4.75/5.20 Resimplifying inuse:
% 4.75/5.20 Done
% 4.75/5.20
% 4.75/5.20 Resimplifying inuse:
% 4.75/5.20 Done
% 4.75/5.20
% 4.75/5.20
% 4.75/5.20 Intermediate Status:
% 4.75/5.20 Generated: 38171
% 4.75/5.20 Kept: 13118
% 4.75/5.20 Inuse: 445
% 4.75/5.20 Deleted: 83
% 4.75/5.20 Deletedinuse: 67
% 4.75/5.20
% 4.75/5.20 Resimplifying inuse:
% 4.75/5.20 Done
% 4.75/5.20
% 4.75/5.20 Resimplifying inuse:
% 4.75/5.20 Done
% 4.75/5.20
% 4.75/5.20
% 4.75/5.20 Intermediate Status:
% 4.75/5.20 Generated: 48527
% 4.75/5.20 Kept: 16969
% 4.75/5.20 Inuse: 489
% 4.75/5.20 Deleted: 85
% 4.75/5.20 Deletedinuse: 68
% 4.75/5.20
% 4.75/5.20 Resimplifying inuse:
% 4.75/5.20 Done
% 4.75/5.20
% 4.75/5.20 Resimplifying inuse:
% 4.75/5.20 Done
% 4.75/5.20
% 4.75/5.20
% 4.75/5.20 Intermediate Status:
% 4.75/5.20 Generated: 54205
% 4.75/5.20 Kept: 18981
% 4.75/5.20 Inuse: 503
% 4.75/5.20 Deleted: 89
% 4.75/5.20 Deletedinuse: 72
% 4.75/5.20
% 4.75/5.20 Resimplifying inuse:
% 4.75/5.20 Done
% 4.75/5.20
% 4.75/5.20 Resimplifying clauses:
% 4.75/5.20 Done
% 4.75/5.20
% 4.75/5.20
% 4.75/5.20 Intermediate Status:
% 4.75/5.20 Generated: 63285
% 4.75/5.20 Kept: 21027
% 4.75/5.20 Inuse: 504
% 4.75/5.20 Deleted: 1977
% 4.75/5.20 Deletedinuse: 73
% 4.75/5.20
% 4.75/5.20
% 4.75/5.20 Bliksems!, er is een bewijs:
% 4.75/5.20 % SZS status Unsatisfiable
% 4.75/5.20 % SZS output start Refutation
% 4.75/5.20
% 4.75/5.20 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 4.75/5.20 .
% 4.75/5.20 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 4.75/5.20 .
% 4.75/5.20 clause( 124, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 4.75/5.20 'universal_class' ) ), =( X, Y ) ] )
% 4.75/5.20 .
% 4.75/5.20 clause( 127, [ ~( member( X, 'universal_class' ) ), =( singleton(
% 4.75/5.20 'member_of'( singleton( X ) ) ), singleton( X ) ) ] )
% 4.75/5.20 .
% 4.75/5.20 clause( 130, [ member( u, 'universal_class' ) ] )
% 4.75/5.20 .
% 4.75/5.20 clause( 131, [ ~( =( 'member_of'( singleton( u ) ), u ) ) ] )
% 4.75/5.20 .
% 4.75/5.20 clause( 168, [ =( X, Y ), ~( =( Y, X ) ) ] )
% 4.75/5.20 .
% 4.75/5.20 clause( 561, [ member( X, 'universal_class' ), ~( =( X, u ) ) ] )
% 4.75/5.20 .
% 4.75/5.20 clause( 562, [ member( u, X ), ~( =( X, 'universal_class' ) ) ] )
% 4.75/5.20 .
% 4.75/5.20 clause( 18675, [ ~( =( X, u ) ), ~( =( singleton( X ), singleton(
% 4.75/5.20 'member_of'( singleton( u ) ) ) ) ) ] )
% 4.75/5.20 .
% 4.75/5.20 clause( 18734, [ ~( =( singleton( 'member_of'( singleton( u ) ) ),
% 4.75/5.20 singleton( u ) ) ) ] )
% 4.75/5.20 .
% 4.75/5.20 clause( 21426, [] )
% 4.75/5.20 .
% 4.75/5.20
% 4.75/5.20
% 4.75/5.20 % SZS output end Refutation
% 4.75/5.20 found a proof!
% 4.75/5.20
% 4.75/5.20 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 4.75/5.20
% 4.75/5.20 initialclauses(
% 4.75/5.20 [ clause( 21428, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 4.75/5.20 ) ] )
% 4.75/5.20 , clause( 21429, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 4.75/5.20 , Y ) ] )
% 4.75/5.20 , clause( 21430, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 4.75/5.20 subclass( X, Y ) ] )
% 4.75/5.20 , clause( 21431, [ subclass( X, 'universal_class' ) ] )
% 4.75/5.20 , clause( 21432, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 4.75/5.20 , clause( 21433, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 4.75/5.20 , clause( 21434, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 4.75/5.20 ] )
% 4.75/5.20 , clause( 21435, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 4.75/5.20 =( X, Z ) ] )
% 4.75/5.20 , clause( 21436, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.75/5.20 'unordered_pair'( X, Y ) ) ] )
% 4.75/5.20 , clause( 21437, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.75/5.20 'unordered_pair'( Y, X ) ) ] )
% 4.75/5.20 , clause( 21438, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 4.75/5.20 )
% 4.75/5.20 , clause( 21439, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 4.75/5.20 , clause( 21440, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 4.75/5.20 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 4.75/5.20 , clause( 21441, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.75/5.20 ) ) ), member( X, Z ) ] )
% 4.75/5.20 , clause( 21442, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.75/5.20 ) ) ), member( Y, T ) ] )
% 4.75/5.20 , clause( 21443, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 4.75/5.20 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 4.75/5.20 , clause( 21444, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 4.75/5.20 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 4.75/5.20 , clause( 21445, [ subclass( 'element_relation', 'cross_product'(
% 4.75/5.20 'universal_class', 'universal_class' ) ) ] )
% 4.75/5.20 , clause( 21446, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 4.75/5.20 ), member( X, Y ) ] )
% 4.75/5.20 , clause( 21447, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 4.75/5.20 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 4.75/5.20 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 4.75/5.20 , clause( 21448, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 4.75/5.20 )
% 4.75/5.20 , clause( 21449, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 4.75/5.20 )
% 4.75/5.20 , clause( 21450, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 4.75/5.20 intersection( Y, Z ) ) ] )
% 4.75/5.20 , clause( 21451, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 4.75/5.20 )
% 4.75/5.20 , clause( 21452, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.75/5.20 complement( Y ) ), member( X, Y ) ] )
% 4.75/5.20 , clause( 21453, [ =( complement( intersection( complement( X ), complement(
% 4.75/5.20 Y ) ) ), union( X, Y ) ) ] )
% 4.75/5.20 , clause( 21454, [ =( intersection( complement( intersection( X, Y ) ),
% 4.75/5.20 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 4.75/5.20 'symmetric_difference'( X, Y ) ) ] )
% 4.75/5.20 , clause( 21455, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 4.75/5.20 X, Y, Z ) ) ] )
% 4.75/5.20 , clause( 21456, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 4.75/5.20 Z, X, Y ) ) ] )
% 4.75/5.20 , clause( 21457, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 4.75/5.20 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 4.75/5.20 , clause( 21458, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 4.75/5.20 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 4.75/5.20 'domain_of'( Y ) ) ] )
% 4.75/5.20 , clause( 21459, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 4.75/5.20 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 4.75/5.20 , clause( 21460, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 4.75/5.20 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 4.75/5.20 ] )
% 4.75/5.20 , clause( 21461, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 4.75/5.20 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 4.75/5.20 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 4.75/5.20 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 4.75/5.20 , Y ), rotate( T ) ) ] )
% 4.75/5.20 , clause( 21462, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 4.75/5.20 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 4.75/5.20 , clause( 21463, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 4.75/5.20 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 4.75/5.20 )
% 4.75/5.20 , clause( 21464, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 4.75/5.20 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 4.75/5.20 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 4.75/5.20 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 4.75/5.20 , Z ), flip( T ) ) ] )
% 4.75/5.20 , clause( 21465, [ =( 'domain_of'( flip( 'cross_product'( X,
% 4.75/5.20 'universal_class' ) ) ), inverse( X ) ) ] )
% 4.75/5.20 , clause( 21466, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 4.75/5.20 , clause( 21467, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 4.75/5.20 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 4.75/5.20 , clause( 21468, [ =( second( 'not_subclass_element'( restrict( X,
% 4.75/5.20 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 4.75/5.20 , clause( 21469, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 4.75/5.20 image( X, Y ) ) ] )
% 4.75/5.20 , clause( 21470, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 4.75/5.20 , clause( 21471, [ subclass( 'successor_relation', 'cross_product'(
% 4.75/5.20 'universal_class', 'universal_class' ) ) ] )
% 4.75/5.20 , clause( 21472, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 4.75/5.20 ) ), =( successor( X ), Y ) ] )
% 4.75/5.20 , clause( 21473, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 4.75/5.20 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 4.75/5.20 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 4.75/5.20 , clause( 21474, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 4.75/5.20 , clause( 21475, [ ~( inductive( X ) ), subclass( image(
% 4.75/5.20 'successor_relation', X ), X ) ] )
% 4.75/5.20 , clause( 21476, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 4.75/5.20 'successor_relation', X ), X ) ), inductive( X ) ] )
% 4.75/5.20 , clause( 21477, [ inductive( omega ) ] )
% 4.75/5.20 , clause( 21478, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 4.75/5.20 , clause( 21479, [ member( omega, 'universal_class' ) ] )
% 4.75/5.20 , clause( 21480, [ =( 'domain_of'( restrict( 'element_relation',
% 4.75/5.20 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 4.75/5.20 , clause( 21481, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 4.75/5.20 X ), 'universal_class' ) ] )
% 4.75/5.20 , clause( 21482, [ =( complement( image( 'element_relation', complement( X
% 4.75/5.20 ) ) ), 'power_class'( X ) ) ] )
% 4.75/5.20 , clause( 21483, [ ~( member( X, 'universal_class' ) ), member(
% 4.75/5.20 'power_class'( X ), 'universal_class' ) ] )
% 4.75/5.20 , clause( 21484, [ subclass( compose( X, Y ), 'cross_product'(
% 4.75/5.20 'universal_class', 'universal_class' ) ) ] )
% 4.75/5.20 , clause( 21485, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 4.75/5.20 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 4.75/5.20 , clause( 21486, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 4.75/5.20 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 4.75/5.20 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 4.75/5.20 ) ] )
% 4.75/5.20 , clause( 21487, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 4.75/5.20 inverse( X ) ), 'identity_relation' ) ] )
% 4.75/5.20 , clause( 21488, [ ~( subclass( compose( X, inverse( X ) ),
% 4.75/5.20 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 4.75/5.20 , clause( 21489, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 4.75/5.20 'universal_class', 'universal_class' ) ) ] )
% 4.75/5.20 , clause( 21490, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 4.75/5.20 , 'identity_relation' ) ] )
% 4.75/5.20 , clause( 21491, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 4.75/5.21 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 4.75/5.21 'identity_relation' ) ), function( X ) ] )
% 4.75/5.21 , clause( 21492, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 4.75/5.21 , member( image( X, Y ), 'universal_class' ) ] )
% 4.75/5.21 , clause( 21493, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 4.75/5.21 , clause( 21494, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 4.75/5.21 , 'null_class' ) ] )
% 4.75/5.21 , clause( 21495, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 4.75/5.21 Y ) ) ] )
% 4.75/5.21 , clause( 21496, [ function( choice ) ] )
% 4.75/5.21 , clause( 21497, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 4.75/5.21 ), member( apply( choice, X ), X ) ] )
% 4.75/5.21 , clause( 21498, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 4.75/5.21 , clause( 21499, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 4.75/5.21 , clause( 21500, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 4.75/5.21 'one_to_one'( X ) ] )
% 4.75/5.21 , clause( 21501, [ =( intersection( 'cross_product'( 'universal_class',
% 4.75/5.21 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 4.75/5.21 'universal_class' ), complement( compose( complement( 'element_relation'
% 4.75/5.21 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 4.75/5.21 , clause( 21502, [ =( intersection( inverse( 'subset_relation' ),
% 4.75/5.21 'subset_relation' ), 'identity_relation' ) ] )
% 4.75/5.21 , clause( 21503, [ =( complement( 'domain_of'( intersection( X,
% 4.75/5.21 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 4.75/5.21 , clause( 21504, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 4.75/5.21 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 4.75/5.21 , clause( 21505, [ ~( operation( X ) ), function( X ) ] )
% 4.75/5.21 , clause( 21506, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 4.75/5.21 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 4.75/5.21 ] )
% 4.75/5.21 , clause( 21507, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 4.75/5.21 'domain_of'( 'domain_of'( X ) ) ) ] )
% 4.75/5.21 , clause( 21508, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 4.75/5.21 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 4.75/5.21 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 4.75/5.21 operation( X ) ] )
% 4.75/5.21 , clause( 21509, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 4.75/5.21 , clause( 21510, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 4.75/5.21 Y ) ), 'domain_of'( X ) ) ] )
% 4.75/5.21 , clause( 21511, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 4.75/5.21 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 4.75/5.21 , clause( 21512, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 4.75/5.21 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 4.75/5.21 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 4.75/5.21 , clause( 21513, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 4.75/5.21 , clause( 21514, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 4.75/5.21 , clause( 21515, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 4.75/5.21 , clause( 21516, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 4.75/5.21 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 4.75/5.21 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 4.75/5.21 )
% 4.75/5.21 , clause( 21517, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 4.75/5.21 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 4.75/5.21 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 4.75/5.21 , Y ) ] )
% 4.75/5.21 , clause( 21518, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 4.75/5.21 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 4.75/5.21 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 4.75/5.21 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 4.75/5.21 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 4.75/5.21 )
% 4.75/5.21 , clause( 21519, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.75/5.21 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 4.75/5.21 , clause( 21520, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.75/5.21 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 4.75/5.21 , clause( 21521, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.75/5.21 ) ) ), member( X, 'universal_class' ) ] )
% 4.75/5.21 , clause( 21522, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.75/5.21 ) ) ), member( Y, 'universal_class' ) ] )
% 4.75/5.21 , clause( 21523, [ subclass( X, X ) ] )
% 4.75/5.21 , clause( 21524, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 4.75/5.21 X, Z ) ] )
% 4.75/5.21 , clause( 21525, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 4.75/5.21 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 4.75/5.21 , clause( 21526, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 4.75/5.21 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 4.75/5.21 , clause( 21527, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 4.75/5.21 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 4.75/5.21 , clause( 21528, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 4.75/5.21 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 4.75/5.21 , clause( 21529, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 4.75/5.21 )
% 4.75/5.21 , clause( 21530, [ ~( member( X, 'null_class' ) ) ] )
% 4.75/5.21 , clause( 21531, [ subclass( 'null_class', X ) ] )
% 4.75/5.21 , clause( 21532, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 4.75/5.21 )
% 4.75/5.21 , clause( 21533, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 4.75/5.21 , 'null_class' ), X ) ] )
% 4.75/5.21 , clause( 21534, [ member( 'null_class', 'universal_class' ) ] )
% 4.75/5.21 , clause( 21535, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 4.75/5.21 ] )
% 4.75/5.21 , clause( 21536, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 4.75/5.21 )
% 4.75/5.21 , clause( 21537, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 4.75/5.21 )
% 4.75/5.21 , clause( 21538, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 4.75/5.21 X ), singleton( Y ) ) ] )
% 4.75/5.21 , clause( 21539, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 4.75/5.21 Y ), singleton( Y ) ) ] )
% 4.75/5.21 , clause( 21540, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 4.75/5.21 'universal_class' ), member( Y, 'universal_class' ) ] )
% 4.75/5.21 , clause( 21541, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 4.75/5.21 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 4.75/5.21 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 4.75/5.21 , clause( 21542, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 4.75/5.21 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 4.75/5.21 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 4.75/5.21 , clause( 21543, [ ~( member( X, 'universal_class' ) ), ~( =(
% 4.75/5.21 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 4.75/5.21 , clause( 21544, [ ~( member( X, 'universal_class' ) ), ~( =(
% 4.75/5.21 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 4.75/5.21 , clause( 21545, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.75/5.21 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 4.75/5.21 , clause( 21546, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 4.75/5.21 'unordered_pair'( X, Z ), Y ) ] )
% 4.75/5.21 , clause( 21547, [ member( singleton( X ), 'universal_class' ) ] )
% 4.75/5.21 , clause( 21548, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 4.75/5.21 X ) ) ) ] )
% 4.75/5.21 , clause( 21549, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.75/5.21 singleton( X ) ) ] )
% 4.75/5.21 , clause( 21550, [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X
% 4.75/5.21 ), 'null_class' ) ) ] )
% 4.75/5.21 , clause( 21551, [ member( 'null_class', singleton( 'null_class' ) ) ] )
% 4.75/5.21 , clause( 21552, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 4.75/5.21 , clause( 21553, [ member( X, 'universal_class' ), =( singleton( X ),
% 4.75/5.21 'null_class' ) ] )
% 4.75/5.21 , clause( 21554, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 4.75/5.21 'universal_class' ) ), =( X, Y ) ] )
% 4.75/5.21 , clause( 21555, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 4.75/5.21 'universal_class' ) ), =( X, Y ) ] )
% 4.75/5.21 , clause( 21556, [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~(
% 4.75/5.21 member( Z, 'universal_class' ) ), =( Z, X ), =( Z, Y ) ] )
% 4.75/5.21 , clause( 21557, [ ~( member( X, 'universal_class' ) ), member( 'member_of'(
% 4.75/5.21 singleton( X ) ), 'universal_class' ) ] )
% 4.75/5.21 , clause( 21558, [ ~( member( X, 'universal_class' ) ), =( singleton(
% 4.75/5.21 'member_of'( singleton( X ) ) ), singleton( X ) ) ] )
% 4.75/5.21 , clause( 21559, [ member( 'member_of'( X ), 'universal_class' ), =(
% 4.75/5.21 'member_of'( X ), X ) ] )
% 4.75/5.21 , clause( 21560, [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X
% 4.75/5.21 ), X ) ] )
% 4.75/5.21 , clause( 21561, [ member( u, 'universal_class' ) ] )
% 4.75/5.21 , clause( 21562, [ ~( =( 'member_of'( singleton( u ) ), u ) ) ] )
% 4.75/5.21 ] ).
% 4.75/5.21
% 4.75/5.21
% 4.75/5.21
% 4.75/5.21 subsumption(
% 4.75/5.21 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 4.75/5.21 , clause( 21432, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 4.75/5.21 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 4.75/5.21 ), ==>( 1, 1 )] ) ).
% 4.75/5.21
% 4.75/5.21
% 4.75/5.21 subsumption(
% 4.75/5.21 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 4.75/5.21 , clause( 21434, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 4.75/5.21 ] )
% 4.75/5.21 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 4.75/5.21 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 4.75/5.21
% 4.75/5.21
% 4.75/5.21 subsumption(
% 4.75/5.21 clause( 124, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 4.75/5.21 'universal_class' ) ), =( X, Y ) ] )
% 4.75/5.21 , clause( 21554, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 4.75/5.21 'universal_class' ) ), =( X, Y ) ] )
% 4.75/5.21 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 4.75/5.21 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 4.75/5.21
% 4.75/5.21
% 4.75/5.21 subsumption(
% 4.75/5.21 clause( 127, [ ~( member( X, 'universal_class' ) ), =( singleton(
% 4.75/5.21 'member_of'( singleton( X ) Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------