TSTP Solution File: SET094-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET094-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.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 22:46:57 EDT 2022
% Result : Unsatisfiable 2.33s 2.73s
% Output : Refutation 2.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET094-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Sat Jul 9 18:15:58 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.74/1.13 *** allocated 10000 integers for termspace/termends
% 0.74/1.13 *** allocated 10000 integers for clauses
% 0.74/1.13 *** allocated 10000 integers for justifications
% 0.74/1.13 Bliksem 1.12
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Automatic Strategy Selection
% 0.74/1.13
% 0.74/1.13 Clauses:
% 0.74/1.13 [
% 0.74/1.13 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.74/1.13 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.74/1.13 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.74/1.13 ,
% 0.74/1.13 [ subclass( X, 'universal_class' ) ],
% 0.74/1.13 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.74/1.13 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.74/1.13 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.74/1.13 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.74/1.13 ,
% 0.74/1.13 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.74/1.13 ) ) ],
% 0.74/1.13 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.74/1.13 ) ) ],
% 0.74/1.13 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.74/1.13 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.74/1.13 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.74/1.13 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.13 X, Z ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.13 Y, T ) ],
% 0.74/1.13 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.74/1.13 ), 'cross_product'( Y, T ) ) ],
% 0.74/1.13 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.74/1.13 ), second( X ) ), X ) ],
% 0.74/1.13 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.74/1.13 'universal_class' ) ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.74/1.13 Y ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.74/1.13 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.74/1.13 , Y ), 'element_relation' ) ],
% 0.74/1.13 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.74/1.13 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.74/1.13 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.74/1.13 Z ) ) ],
% 0.74/1.13 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.74/1.13 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.74/1.13 member( X, Y ) ],
% 0.74/1.13 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.74/1.13 union( X, Y ) ) ],
% 0.74/1.13 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.74/1.13 intersection( complement( X ), complement( Y ) ) ) ),
% 0.74/1.13 'symmetric_difference'( X, Y ) ) ],
% 0.74/1.13 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.74/1.13 ,
% 0.74/1.13 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.74/1.13 ,
% 0.74/1.13 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.74/1.13 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.74/1.13 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.74/1.13 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.74/1.13 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.74/1.13 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.74/1.13 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.74/1.13 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.74/1.13 'cross_product'( 'universal_class', 'universal_class' ),
% 0.74/1.13 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.74/1.13 Y ), rotate( T ) ) ],
% 0.74/1.13 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.74/1.13 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.74/1.13 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.74/1.13 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.74/1.13 'cross_product'( 'universal_class', 'universal_class' ),
% 0.74/1.13 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.74/1.13 Z ), flip( T ) ) ],
% 0.74/1.13 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.74/1.13 inverse( X ) ) ],
% 0.74/1.13 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.74/1.13 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.74/1.13 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.74/1.13 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.74/1.13 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.74/1.13 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.74/1.13 ],
% 0.74/1.13 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.74/1.13 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.74/1.13 'universal_class' ) ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.74/1.13 successor( X ), Y ) ],
% 0.74/1.13 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.74/1.13 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.74/1.13 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.74/1.13 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.74/1.13 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.74/1.13 ,
% 0.74/1.13 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.74/1.13 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.74/1.13 [ inductive( omega ) ],
% 0.74/1.13 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.74/1.13 [ member( omega, 'universal_class' ) ],
% 0.74/1.13 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.74/1.13 , 'sum_class'( X ) ) ],
% 0.74/1.13 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.74/1.13 'universal_class' ) ],
% 0.74/1.13 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.74/1.13 'power_class'( X ) ) ],
% 0.74/1.13 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.74/1.13 'universal_class' ) ],
% 0.74/1.13 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.74/1.13 'universal_class' ) ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.74/1.13 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.74/1.13 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.74/1.13 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.74/1.13 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.74/1.13 ) ],
% 0.74/1.13 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.74/1.13 , 'identity_relation' ) ],
% 0.74/1.13 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.74/1.13 'single_valued_class'( X ) ],
% 0.74/1.13 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.74/1.13 'universal_class' ) ) ],
% 0.74/1.13 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.74/1.13 'identity_relation' ) ],
% 0.74/1.13 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.74/1.13 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.74/1.13 , function( X ) ],
% 0.74/1.13 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.74/1.13 X, Y ), 'universal_class' ) ],
% 0.74/1.13 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.74/1.13 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.74/1.13 ) ],
% 0.74/1.13 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.74/1.13 [ function( choice ) ],
% 0.74/1.13 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.74/1.13 apply( choice, X ), X ) ],
% 0.74/1.13 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.74/1.13 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.74/1.13 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.74/1.13 ,
% 0.74/1.13 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.74/1.13 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.74/1.13 , complement( compose( complement( 'element_relation' ), inverse(
% 0.74/1.13 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.74/1.13 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.74/1.13 'identity_relation' ) ],
% 0.74/1.13 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.74/1.13 , diagonalise( X ) ) ],
% 0.74/1.13 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.74/1.13 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.74/1.13 [ ~( operation( X ) ), function( X ) ],
% 0.74/1.13 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.74/1.13 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.74/1.13 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.74/1.13 'domain_of'( X ) ) ) ],
% 0.74/1.13 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.74/1.13 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.74/1.13 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.74/1.13 X ) ],
% 0.74/1.13 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.74/1.13 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.74/1.13 'domain_of'( X ) ) ],
% 0.74/1.13 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.74/1.13 'domain_of'( Z ) ) ) ],
% 0.74/1.13 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.74/1.13 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.74/1.13 ), compatible( X, Y, Z ) ],
% 0.74/1.13 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.74/1.13 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.74/1.13 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.74/1.13 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.74/1.13 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.74/1.13 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.74/1.13 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.74/1.13 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.74/1.13 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.74/1.13 , Y ) ],
% 0.74/1.13 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.74/1.13 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.74/1.13 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.74/1.13 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.74/1.13 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.13 X, 'unordered_pair'( X, Y ) ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.13 Y, 'unordered_pair'( X, Y ) ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.13 X, 'universal_class' ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.74/1.13 Y, 'universal_class' ) ],
% 0.74/1.13 [ subclass( X, X ) ],
% 0.74/1.13 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.74/1.13 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.74/1.13 'not_subclass_element'( Y, X ), Y ) ],
% 0.74/1.13 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.74/1.13 'not_subclass_element'( Y, X ), Y ) ],
% 0.74/1.13 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.74/1.13 'not_subclass_element'( Y, X ), Y ) ],
% 0.74/1.13 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.74/1.13 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.74/1.13 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.74/1.13 [ ~( member( X, 'null_class' ) ) ],
% 0.74/1.13 [ subclass( 'null_class', X ) ],
% 0.74/1.13 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.74/1.13 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.74/1.13 ), X ) ],
% 0.74/1.13 [ member( 'null_class', 'universal_class' ) ],
% 0.74/1.13 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.74/1.13 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.74/1.13 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.74/1.13 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.74/1.13 Y ) ) ],
% 0.74/1.13 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.74/1.13 Y ) ) ],
% 0.74/1.13 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.74/1.13 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.74/1.13 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.74/1.13 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.74/1.13 'universal_class' ) ) ), =( Y, Z ) ],
% 0.74/1.13 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.74/1.13 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.74/1.13 'universal_class' ) ) ), =( X, Z ) ],
% 0.74/1.13 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.74/1.13 'null_class' ) ) ],
% 0.74/1.13 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.74/1.13 'null_class' ) ) ],
% 0.74/1.13 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.74/1.13 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 2.33/2.73 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 2.33/2.73 X, Z ), Y ) ],
% 2.33/2.73 [ member( singleton( X ), 'universal_class' ) ],
% 2.33/2.73 [ member( singleton( X ), 'unordered_pair'( Y, singleton( X ) ) ) ],
% 2.33/2.73 [ ~( member( X, 'universal_class' ) ), member( X, singleton( X ) ) ]
% 2.33/2.73 ,
% 2.33/2.73 [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X ),
% 2.33/2.73 'null_class' ) ) ],
% 2.33/2.73 [ member( 'null_class', singleton( 'null_class' ) ) ],
% 2.33/2.73 [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ],
% 2.33/2.73 [ member( X, 'universal_class' ), =( singleton( X ), 'null_class' ) ]
% 2.33/2.73 ,
% 2.33/2.73 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 2.33/2.73 'universal_class' ) ), =( X, Y ) ],
% 2.33/2.73 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 2.33/2.73 'universal_class' ) ), =( X, Y ) ],
% 2.33/2.73 [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~( member( Z,
% 2.33/2.73 'universal_class' ) ), =( Z, X ), =( Z, Y ) ],
% 2.33/2.73 [ ~( member( X, 'universal_class' ) ), member( 'member_of'( singleton( X
% 2.33/2.73 ) ), 'universal_class' ) ],
% 2.33/2.73 [ ~( member( X, 'universal_class' ) ), =( singleton( 'member_of'(
% 2.33/2.73 singleton( X ) ) ), singleton( X ) ) ],
% 2.33/2.73 [ member( 'member_of'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 2.33/2.73 ) ],
% 2.33/2.73 [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X ), X ) ],
% 2.33/2.73 [ ~( member( X, 'universal_class' ) ), =( 'member_of'( singleton( X ) )
% 2.33/2.73 , X ) ],
% 2.33/2.73 [ member( 'member_of1'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 2.33/2.73 ) ],
% 2.33/2.73 [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'( X ), X ) ]
% 2.33/2.73 ,
% 2.33/2.73 [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 2.33/2.73 'universal_class' ) ],
% 2.33/2.73 [ =( singleton( 'member_of'( x ) ), x ) ],
% 2.33/2.73 [ member( y, x ) ],
% 2.33/2.73 [ ~( =( 'member_of'( x ), y ) ) ]
% 2.33/2.73 ] .
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73 percentage equality = 0.276978, percentage horn = 0.850000
% 2.33/2.73 This is a problem with some equality
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73 Options Used:
% 2.33/2.73
% 2.33/2.73 useres = 1
% 2.33/2.73 useparamod = 1
% 2.33/2.73 useeqrefl = 1
% 2.33/2.73 useeqfact = 1
% 2.33/2.73 usefactor = 1
% 2.33/2.73 usesimpsplitting = 0
% 2.33/2.73 usesimpdemod = 5
% 2.33/2.73 usesimpres = 3
% 2.33/2.73
% 2.33/2.73 resimpinuse = 1000
% 2.33/2.73 resimpclauses = 20000
% 2.33/2.73 substype = eqrewr
% 2.33/2.73 backwardsubs = 1
% 2.33/2.73 selectoldest = 5
% 2.33/2.73
% 2.33/2.73 litorderings [0] = split
% 2.33/2.73 litorderings [1] = extend the termordering, first sorting on arguments
% 2.33/2.73
% 2.33/2.73 termordering = kbo
% 2.33/2.73
% 2.33/2.73 litapriori = 0
% 2.33/2.73 termapriori = 1
% 2.33/2.73 litaposteriori = 0
% 2.33/2.73 termaposteriori = 0
% 2.33/2.73 demodaposteriori = 0
% 2.33/2.73 ordereqreflfact = 0
% 2.33/2.73
% 2.33/2.73 litselect = negord
% 2.33/2.73
% 2.33/2.73 maxweight = 15
% 2.33/2.73 maxdepth = 30000
% 2.33/2.73 maxlength = 115
% 2.33/2.73 maxnrvars = 195
% 2.33/2.73 excuselevel = 1
% 2.33/2.73 increasemaxweight = 1
% 2.33/2.73
% 2.33/2.73 maxselected = 10000000
% 2.33/2.73 maxnrclauses = 10000000
% 2.33/2.73
% 2.33/2.73 showgenerated = 0
% 2.33/2.73 showkept = 0
% 2.33/2.73 showselected = 0
% 2.33/2.73 showdeleted = 0
% 2.33/2.73 showresimp = 1
% 2.33/2.73 showstatus = 2000
% 2.33/2.73
% 2.33/2.73 prologoutput = 1
% 2.33/2.73 nrgoals = 5000000
% 2.33/2.73 totalproof = 1
% 2.33/2.73
% 2.33/2.73 Symbols occurring in the translation:
% 2.33/2.73
% 2.33/2.73 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.33/2.73 . [1, 2] (w:1, o:58, a:1, s:1, b:0),
% 2.33/2.73 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 2.33/2.73 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.33/2.73 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.33/2.73 subclass [41, 2] (w:1, o:83, a:1, s:1, b:0),
% 2.33/2.73 member [43, 2] (w:1, o:84, a:1, s:1, b:0),
% 2.33/2.73 'not_subclass_element' [44, 2] (w:1, o:85, a:1, s:1, b:0),
% 2.33/2.73 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 2.33/2.73 'unordered_pair' [46, 2] (w:1, o:86, a:1, s:1, b:0),
% 2.33/2.73 singleton [47, 1] (w:1, o:39, a:1, s:1, b:0),
% 2.33/2.73 'ordered_pair' [48, 2] (w:1, o:87, a:1, s:1, b:0),
% 2.33/2.73 'cross_product' [50, 2] (w:1, o:88, a:1, s:1, b:0),
% 2.33/2.73 first [52, 1] (w:1, o:40, a:1, s:1, b:0),
% 2.33/2.73 second [53, 1] (w:1, o:41, a:1, s:1, b:0),
% 2.33/2.73 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 2.33/2.73 intersection [55, 2] (w:1, o:90, a:1, s:1, b:0),
% 2.33/2.73 complement [56, 1] (w:1, o:42, a:1, s:1, b:0),
% 2.33/2.73 union [57, 2] (w:1, o:91, a:1, s:1, b:0),
% 2.33/2.73 'symmetric_difference' [58, 2] (w:1, o:92, a:1, s:1, b:0),
% 2.33/2.73 restrict [60, 3] (w:1, o:95, a:1, s:1, b:0),
% 2.33/2.73 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 2.33/2.73 'domain_of' [62, 1] (w:1, o:44, a:1, s:1, b:0),
% 2.33/2.73 rotate [63, 1] (w:1, o:36, a:1, s:1, b:0),
% 2.33/2.73 flip [65, 1] (w:1, o:45, a:1, s:1, b:0),
% 2.33/2.73 inverse [66, 1] (w:1, o:46, a:1, s:1, b:0),
% 2.33/2.73 'range_of' [67, 1] (w:1, o:37, a:1, s:1, b:0),
% 2.33/2.73 domain [68, 3] (w:1, o:97, a:1, s:1, b:0),
% 2.33/2.73 range [69, 3] (w:1, o:98, a:1, s:1, b:0),
% 2.33/2.73 image [70, 2] (w:1, o:89, a:1, s:1, b:0),
% 2.33/2.73 successor [71, 1] (w:1, o:47, a:1, s:1, b:0),
% 2.33/2.73 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 2.33/2.73 inductive [73, 1] (w:1, o:48, a:1, s:1, b:0),
% 2.33/2.73 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 2.33/2.73 'sum_class' [75, 1] (w:1, o:49, a:1, s:1, b:0),
% 2.33/2.73 'power_class' [76, 1] (w:1, o:52, a:1, s:1, b:0),
% 2.33/2.73 compose [78, 2] (w:1, o:93, a:1, s:1, b:0),
% 2.33/2.73 'single_valued_class' [79, 1] (w:1, o:53, a:1, s:1, b:0),
% 2.33/2.73 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 2.33/2.73 function [82, 1] (w:1, o:54, a:1, s:1, b:0),
% 2.33/2.73 regular [83, 1] (w:1, o:38, a:1, s:1, b:0),
% 2.33/2.73 apply [84, 2] (w:1, o:94, a:1, s:1, b:0),
% 2.33/2.73 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 2.33/2.73 'one_to_one' [86, 1] (w:1, o:50, a:1, s:1, b:0),
% 2.33/2.73 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 2.33/2.73 diagonalise [88, 1] (w:1, o:55, a:1, s:1, b:0),
% 2.33/2.73 cantor [89, 1] (w:1, o:43, a:1, s:1, b:0),
% 2.33/2.73 operation [90, 1] (w:1, o:51, a:1, s:1, b:0),
% 2.33/2.73 compatible [94, 3] (w:1, o:96, a:1, s:1, b:0),
% 2.33/2.73 homomorphism [95, 3] (w:1, o:99, a:1, s:1, b:0),
% 2.33/2.73 'not_homomorphism1' [96, 3] (w:1, o:100, a:1, s:1, b:0),
% 2.33/2.73 'not_homomorphism2' [97, 3] (w:1, o:101, a:1, s:1, b:0),
% 2.33/2.73 'member_of' [98, 1] (w:1, o:56, a:1, s:1, b:0),
% 2.33/2.73 'member_of1' [99, 1] (w:1, o:57, a:1, s:1, b:0),
% 2.33/2.73 x [100, 0] (w:1, o:29, a:1, s:1, b:0),
% 2.33/2.73 y [101, 0] (w:1, o:30, a:1, s:1, b:0).
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73 Starting Search:
% 2.33/2.73
% 2.33/2.73 Resimplifying inuse:
% 2.33/2.73 Done
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73 Intermediate Status:
% 2.33/2.73 Generated: 3831
% 2.33/2.73 Kept: 2013
% 2.33/2.73 Inuse: 118
% 2.33/2.73 Deleted: 2
% 2.33/2.73 Deletedinuse: 2
% 2.33/2.73
% 2.33/2.73 Resimplifying inuse:
% 2.33/2.73 Done
% 2.33/2.73
% 2.33/2.73 Resimplifying inuse:
% 2.33/2.73 Done
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73 Intermediate Status:
% 2.33/2.73 Generated: 8927
% 2.33/2.73 Kept: 4204
% 2.33/2.73 Inuse: 201
% 2.33/2.73 Deleted: 8
% 2.33/2.73 Deletedinuse: 8
% 2.33/2.73
% 2.33/2.73 Resimplifying inuse:
% 2.33/2.73 Done
% 2.33/2.73
% 2.33/2.73 Resimplifying inuse:
% 2.33/2.73 Done
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73 Intermediate Status:
% 2.33/2.73 Generated: 13809
% 2.33/2.73 Kept: 6206
% 2.33/2.73 Inuse: 281
% 2.33/2.73 Deleted: 11
% 2.33/2.73 Deletedinuse: 11
% 2.33/2.73
% 2.33/2.73 Resimplifying inuse:
% 2.33/2.73 Done
% 2.33/2.73
% 2.33/2.73 Resimplifying inuse:
% 2.33/2.73 Done
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73 Intermediate Status:
% 2.33/2.73 Generated: 19787
% 2.33/2.73 Kept: 8232
% 2.33/2.73 Inuse: 331
% 2.33/2.73 Deleted: 55
% 2.33/2.73 Deletedinuse: 55
% 2.33/2.73
% 2.33/2.73 Resimplifying inuse:
% 2.33/2.73 Done
% 2.33/2.73
% 2.33/2.73 Resimplifying inuse:
% 2.33/2.73 Done
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73 Intermediate Status:
% 2.33/2.73 Generated: 28041
% 2.33/2.73 Kept: 10741
% 2.33/2.73 Inuse: 391
% 2.33/2.73 Deleted: 75
% 2.33/2.73 Deletedinuse: 60
% 2.33/2.73
% 2.33/2.73 Resimplifying inuse:
% 2.33/2.73 Done
% 2.33/2.73
% 2.33/2.73 Resimplifying inuse:
% 2.33/2.73 Done
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73 Intermediate Status:
% 2.33/2.73 Generated: 35710
% 2.33/2.73 Kept: 12743
% 2.33/2.73 Inuse: 431
% 2.33/2.73 Deleted: 82
% 2.33/2.73 Deletedinuse: 61
% 2.33/2.73
% 2.33/2.73 Resimplifying inuse:
% 2.33/2.73 Done
% 2.33/2.73
% 2.33/2.73 Resimplifying inuse:
% 2.33/2.73 Done
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73 Intermediate Status:
% 2.33/2.73 Generated: 44893
% 2.33/2.73 Kept: 14824
% 2.33/2.73 Inuse: 463
% 2.33/2.73 Deleted: 89
% 2.33/2.73 Deletedinuse: 66
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73 Bliksems!, er is een bewijs:
% 2.33/2.73 % SZS status Unsatisfiable
% 2.33/2.73 % SZS output start Refutation
% 2.33/2.73
% 2.33/2.73 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.33/2.73 .
% 2.33/2.73 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 2.33/2.73 .
% 2.33/2.73 clause( 122, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 2.33/2.73 .
% 2.33/2.73 clause( 134, [ =( singleton( 'member_of'( x ) ), x ) ] )
% 2.33/2.73 .
% 2.33/2.73 clause( 135, [ member( y, x ) ] )
% 2.33/2.73 .
% 2.33/2.73 clause( 136, [ ~( =( 'member_of'( x ), y ) ) ] )
% 2.33/2.73 .
% 2.33/2.73 clause( 173, [ =( X, Y ), ~( =( Y, X ) ) ] )
% 2.33/2.73 .
% 2.33/2.73 clause( 630, [ member( X, x ), ~( =( X, y ) ) ] )
% 2.33/2.73 .
% 2.33/2.73 clause( 16959, [ ~( =( X, y ) ) ] )
% 2.33/2.73 .
% 2.33/2.73 clause( 16973, [] )
% 2.33/2.73 .
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73 % SZS output end Refutation
% 2.33/2.73 found a proof!
% 2.33/2.73
% 2.33/2.73 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.33/2.73
% 2.33/2.73 initialclauses(
% 2.33/2.73 [ clause( 16975, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 2.33/2.73 ) ] )
% 2.33/2.73 , clause( 16976, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 2.33/2.73 , Y ) ] )
% 2.33/2.73 , clause( 16977, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 2.33/2.73 subclass( X, Y ) ] )
% 2.33/2.73 , clause( 16978, [ subclass( X, 'universal_class' ) ] )
% 2.33/2.73 , clause( 16979, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.33/2.73 , clause( 16980, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 2.33/2.73 , clause( 16981, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 2.33/2.73 ] )
% 2.33/2.73 , clause( 16982, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 2.33/2.73 =( X, Z ) ] )
% 2.33/2.73 , clause( 16983, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.33/2.73 'unordered_pair'( X, Y ) ) ] )
% 2.33/2.73 , clause( 16984, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.33/2.73 'unordered_pair'( Y, X ) ) ] )
% 2.33/2.73 , clause( 16985, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 2.33/2.73 )
% 2.33/2.73 , clause( 16986, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.33/2.73 , clause( 16987, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 2.33/2.73 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 2.33/2.73 , clause( 16988, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.33/2.73 ) ) ), member( X, Z ) ] )
% 2.33/2.73 , clause( 16989, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.33/2.73 ) ) ), member( Y, T ) ] )
% 2.33/2.73 , clause( 16990, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 2.33/2.73 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 2.33/2.73 , clause( 16991, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 2.33/2.73 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 2.33/2.73 , clause( 16992, [ subclass( 'element_relation', 'cross_product'(
% 2.33/2.73 'universal_class', 'universal_class' ) ) ] )
% 2.33/2.73 , clause( 16993, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 2.33/2.73 ), member( X, Y ) ] )
% 2.33/2.73 , clause( 16994, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 2.33/2.73 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 2.33/2.73 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 2.33/2.73 , clause( 16995, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 2.33/2.73 )
% 2.33/2.73 , clause( 16996, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 2.33/2.73 )
% 2.33/2.73 , clause( 16997, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 2.33/2.73 intersection( Y, Z ) ) ] )
% 2.33/2.73 , clause( 16998, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 2.33/2.73 )
% 2.33/2.73 , clause( 16999, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.33/2.73 complement( Y ) ), member( X, Y ) ] )
% 2.33/2.73 , clause( 17000, [ =( complement( intersection( complement( X ), complement(
% 2.33/2.73 Y ) ) ), union( X, Y ) ) ] )
% 2.33/2.73 , clause( 17001, [ =( intersection( complement( intersection( X, Y ) ),
% 2.33/2.73 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 2.33/2.73 'symmetric_difference'( X, Y ) ) ] )
% 2.33/2.73 , clause( 17002, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 2.33/2.73 X, Y, Z ) ) ] )
% 2.33/2.73 , clause( 17003, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 2.33/2.73 Z, X, Y ) ) ] )
% 2.33/2.73 , clause( 17004, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 2.33/2.73 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 2.33/2.73 , clause( 17005, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 2.33/2.73 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 2.33/2.73 'domain_of'( Y ) ) ] )
% 2.33/2.73 , clause( 17006, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 2.33/2.73 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.33/2.73 , clause( 17007, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.33/2.73 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 2.33/2.73 ] )
% 2.33/2.73 , clause( 17008, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.33/2.73 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 2.33/2.73 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.33/2.73 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 2.33/2.73 , Y ), rotate( T ) ) ] )
% 2.33/2.73 , clause( 17009, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 2.33/2.73 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.33/2.73 , clause( 17010, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.33/2.73 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 2.33/2.73 )
% 2.33/2.73 , clause( 17011, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.33/2.73 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 2.33/2.73 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.33/2.73 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 2.33/2.73 , Z ), flip( T ) ) ] )
% 2.33/2.73 , clause( 17012, [ =( 'domain_of'( flip( 'cross_product'( X,
% 2.33/2.73 'universal_class' ) ) ), inverse( X ) ) ] )
% 2.33/2.73 , clause( 17013, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 2.33/2.73 , clause( 17014, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 2.33/2.73 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 2.33/2.73 , clause( 17015, [ =( second( 'not_subclass_element'( restrict( X,
% 2.33/2.73 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 2.33/2.73 , clause( 17016, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 2.33/2.73 image( X, Y ) ) ] )
% 2.33/2.73 , clause( 17017, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 2.33/2.73 , clause( 17018, [ subclass( 'successor_relation', 'cross_product'(
% 2.33/2.73 'universal_class', 'universal_class' ) ) ] )
% 2.33/2.73 , clause( 17019, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 2.33/2.73 ) ), =( successor( X ), Y ) ] )
% 2.33/2.73 , clause( 17020, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 2.33/2.73 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 2.33/2.73 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 2.33/2.73 , clause( 17021, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 2.33/2.73 , clause( 17022, [ ~( inductive( X ) ), subclass( image(
% 2.33/2.73 'successor_relation', X ), X ) ] )
% 2.33/2.73 , clause( 17023, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 2.33/2.73 'successor_relation', X ), X ) ), inductive( X ) ] )
% 2.33/2.73 , clause( 17024, [ inductive( omega ) ] )
% 2.33/2.73 , clause( 17025, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 2.33/2.73 , clause( 17026, [ member( omega, 'universal_class' ) ] )
% 2.33/2.73 , clause( 17027, [ =( 'domain_of'( restrict( 'element_relation',
% 2.33/2.73 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 2.33/2.73 , clause( 17028, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 2.33/2.73 X ), 'universal_class' ) ] )
% 2.33/2.73 , clause( 17029, [ =( complement( image( 'element_relation', complement( X
% 2.33/2.73 ) ) ), 'power_class'( X ) ) ] )
% 2.33/2.73 , clause( 17030, [ ~( member( X, 'universal_class' ) ), member(
% 2.33/2.73 'power_class'( X ), 'universal_class' ) ] )
% 2.33/2.73 , clause( 17031, [ subclass( compose( X, Y ), 'cross_product'(
% 2.33/2.73 'universal_class', 'universal_class' ) ) ] )
% 2.33/2.73 , clause( 17032, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 2.33/2.73 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 2.33/2.73 , clause( 17033, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 2.33/2.73 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 2.33/2.73 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 2.33/2.73 ) ] )
% 2.33/2.73 , clause( 17034, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 2.33/2.73 inverse( X ) ), 'identity_relation' ) ] )
% 2.33/2.73 , clause( 17035, [ ~( subclass( compose( X, inverse( X ) ),
% 2.33/2.73 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 2.33/2.73 , clause( 17036, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 2.33/2.73 'universal_class', 'universal_class' ) ) ] )
% 2.33/2.73 , clause( 17037, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 2.33/2.73 , 'identity_relation' ) ] )
% 2.33/2.73 , clause( 17038, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 2.33/2.73 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 2.33/2.73 'identity_relation' ) ), function( X ) ] )
% 2.33/2.73 , clause( 17039, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 2.33/2.73 , member( image( X, Y ), 'universal_class' ) ] )
% 2.33/2.73 , clause( 17040, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 2.33/2.73 , clause( 17041, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 2.33/2.73 , 'null_class' ) ] )
% 2.33/2.73 , clause( 17042, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 2.33/2.73 Y ) ) ] )
% 2.33/2.73 , clause( 17043, [ function( choice ) ] )
% 2.33/2.73 , clause( 17044, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 2.33/2.73 ), member( apply( choice, X ), X ) ] )
% 2.33/2.73 , clause( 17045, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 2.33/2.73 , clause( 17046, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 2.33/2.73 , clause( 17047, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 2.33/2.73 'one_to_one'( X ) ] )
% 2.33/2.73 , clause( 17048, [ =( intersection( 'cross_product'( 'universal_class',
% 2.33/2.73 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 2.33/2.73 'universal_class' ), complement( compose( complement( 'element_relation'
% 2.33/2.73 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 2.33/2.73 , clause( 17049, [ =( intersection( inverse( 'subset_relation' ),
% 2.33/2.73 'subset_relation' ), 'identity_relation' ) ] )
% 2.33/2.73 , clause( 17050, [ =( complement( 'domain_of'( intersection( X,
% 2.33/2.73 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 2.33/2.73 , clause( 17051, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 2.33/2.73 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 2.33/2.73 , clause( 17052, [ ~( operation( X ) ), function( X ) ] )
% 2.33/2.73 , clause( 17053, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 2.33/2.73 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.33/2.73 ] )
% 2.33/2.73 , clause( 17054, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 2.33/2.73 'domain_of'( 'domain_of'( X ) ) ) ] )
% 2.33/2.73 , clause( 17055, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 2.33/2.73 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.33/2.73 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 2.33/2.73 operation( X ) ] )
% 2.33/2.73 , clause( 17056, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 2.33/2.73 , clause( 17057, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 2.33/2.73 Y ) ), 'domain_of'( X ) ) ] )
% 2.33/2.73 , clause( 17058, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 2.33/2.73 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 2.33/2.73 , clause( 17059, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 2.33/2.73 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 2.33/2.73 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 2.33/2.73 , clause( 17060, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 2.33/2.73 , clause( 17061, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 2.33/2.73 , clause( 17062, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 2.33/2.73 , clause( 17063, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 2.33/2.73 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 2.33/2.73 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 2.33/2.73 )
% 2.33/2.73 , clause( 17064, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.33/2.73 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 2.33/2.73 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 2.33/2.73 , Y ) ] )
% 2.33/2.73 , clause( 17065, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.33/2.73 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 2.33/2.73 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 2.33/2.73 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 2.33/2.73 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 2.33/2.73 )
% 2.33/2.73 , clause( 17066, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.33/2.73 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 2.33/2.73 , clause( 17067, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.33/2.73 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 2.33/2.73 , clause( 17068, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.33/2.73 ) ) ), member( X, 'universal_class' ) ] )
% 2.33/2.73 , clause( 17069, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.33/2.73 ) ) ), member( Y, 'universal_class' ) ] )
% 2.33/2.73 , clause( 17070, [ subclass( X, X ) ] )
% 2.33/2.73 , clause( 17071, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 2.33/2.73 X, Z ) ] )
% 2.33/2.73 , clause( 17072, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 2.33/2.73 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.33/2.73 , clause( 17073, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 2.33/2.73 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.33/2.73 , clause( 17074, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 2.33/2.73 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.33/2.73 , clause( 17075, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 2.33/2.73 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 2.33/2.73 , clause( 17076, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 2.33/2.73 )
% 2.33/2.73 , clause( 17077, [ ~( member( X, 'null_class' ) ) ] )
% 2.33/2.73 , clause( 17078, [ subclass( 'null_class', X ) ] )
% 2.33/2.73 , clause( 17079, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 2.33/2.73 )
% 2.33/2.73 , clause( 17080, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 2.33/2.73 , 'null_class' ), X ) ] )
% 2.33/2.73 , clause( 17081, [ member( 'null_class', 'universal_class' ) ] )
% 2.33/2.73 , clause( 17082, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 2.33/2.73 ] )
% 2.33/2.73 , clause( 17083, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 2.33/2.73 )
% 2.33/2.73 , clause( 17084, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 2.33/2.73 )
% 2.33/2.73 , clause( 17085, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 2.33/2.73 X ), singleton( Y ) ) ] )
% 2.33/2.73 , clause( 17086, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 2.33/2.73 Y ), singleton( Y ) ) ] )
% 2.33/2.73 , clause( 17087, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 2.33/2.73 'universal_class' ), member( Y, 'universal_class' ) ] )
% 2.33/2.73 , clause( 17088, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 2.33/2.73 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 2.33/2.73 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 2.33/2.73 , clause( 17089, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 2.33/2.73 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 2.33/2.73 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 2.33/2.73 , clause( 17090, [ ~( member( X, 'universal_class' ) ), ~( =(
% 2.33/2.73 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 2.33/2.73 , clause( 17091, [ ~( member( X, 'universal_class' ) ), ~( =(
% 2.33/2.73 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 2.33/2.73 , clause( 17092, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.33/2.73 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 2.33/2.73 , clause( 17093, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 2.33/2.73 'unordered_pair'( X, Z ), Y ) ] )
% 2.33/2.73 , clause( 17094, [ member( singleton( X ), 'universal_class' ) ] )
% 2.33/2.73 , clause( 17095, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 2.33/2.73 X ) ) ) ] )
% 2.33/2.73 , clause( 17096, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.33/2.73 singleton( X ) ) ] )
% 2.33/2.73 , clause( 17097, [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X
% 2.33/2.73 ), 'null_class' ) ) ] )
% 2.33/2.73 , clause( 17098, [ member( 'null_class', singleton( 'null_class' ) ) ] )
% 2.33/2.73 , clause( 17099, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 2.33/2.73 , clause( 17100, [ member( X, 'universal_class' ), =( singleton( X ),
% 2.33/2.73 'null_class' ) ] )
% 2.33/2.73 , clause( 17101, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 2.33/2.73 'universal_class' ) ), =( X, Y ) ] )
% 2.33/2.73 , clause( 17102, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 2.33/2.73 'universal_class' ) ), =( X, Y ) ] )
% 2.33/2.73 , clause( 17103, [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~(
% 2.33/2.73 member( Z, 'universal_class' ) ), =( Z, X ), =( Z, Y ) ] )
% 2.33/2.73 , clause( 17104, [ ~( member( X, 'universal_class' ) ), member( 'member_of'(
% 2.33/2.73 singleton( X ) ), 'universal_class' ) ] )
% 2.33/2.73 , clause( 17105, [ ~( member( X, 'universal_class' ) ), =( singleton(
% 2.33/2.73 'member_of'( singleton( X ) ) ), singleton( X ) ) ] )
% 2.33/2.73 , clause( 17106, [ member( 'member_of'( X ), 'universal_class' ), =(
% 2.33/2.73 'member_of'( X ), X ) ] )
% 2.33/2.73 , clause( 17107, [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X
% 2.33/2.73 ), X ) ] )
% 2.33/2.73 , clause( 17108, [ ~( member( X, 'universal_class' ) ), =( 'member_of'(
% 2.33/2.73 singleton( X ) ), X ) ] )
% 2.33/2.73 , clause( 17109, [ member( 'member_of1'( X ), 'universal_class' ), =(
% 2.33/2.73 'member_of'( X ), X ) ] )
% 2.33/2.73 , clause( 17110, [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'(
% 2.33/2.73 X ), X ) ] )
% 2.33/2.73 , clause( 17111, [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 2.33/2.73 'universal_class' ) ] )
% 2.33/2.73 , clause( 17112, [ =( singleton( 'member_of'( x ) ), x ) ] )
% 2.33/2.73 , clause( 17113, [ member( y, x ) ] )
% 2.33/2.73 , clause( 17114, [ ~( =( 'member_of'( x ), y ) ) ] )
% 2.33/2.73 ] ).
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73 subsumption(
% 2.33/2.73 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.33/2.73 , clause( 16979, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.33/2.73 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.33/2.73 ), ==>( 1, 1 )] ) ).
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73 subsumption(
% 2.33/2.73 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 2.33/2.73 , clause( 16981, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 2.33/2.73 ] )
% 2.33/2.73 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.33/2.73 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73 subsumption(
% 2.33/2.73 clause( 122, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 2.33/2.73 , clause( 17099, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 2.33/2.73 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.33/2.73 ), ==>( 1, 1 )] ) ).
% 2.33/2.73
% 2.33/2.73
% 2.33/2.73 subsumption(
% 2.33/2.73 clause( 134, [ =( singleton( 'member_of'( x ) ), x ) ] )
% 2.33/2.73 , clauseCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------