TSTP Solution File: SET096-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET096-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Mon Jul 18 22:47:01 EDT 2022
% Result : Unsatisfiable 4.76s 5.15s
% Output : Refutation 4.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET096-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n003.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 08:58:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.65/1.04 *** allocated 10000 integers for termspace/termends
% 0.65/1.04 *** allocated 10000 integers for clauses
% 0.65/1.04 *** allocated 10000 integers for justifications
% 0.65/1.04 Bliksem 1.12
% 0.65/1.04
% 0.65/1.04
% 0.65/1.04 Automatic Strategy Selection
% 0.65/1.04
% 0.65/1.04 Clauses:
% 0.65/1.04 [
% 0.65/1.04 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.65/1.04 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.65/1.04 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.65/1.04 ,
% 0.65/1.04 [ subclass( X, 'universal_class' ) ],
% 0.65/1.04 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.65/1.04 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.65/1.04 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.65/1.04 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.65/1.04 ,
% 0.65/1.04 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.65/1.04 ) ) ],
% 0.65/1.04 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.65/1.04 ) ) ],
% 0.65/1.04 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.65/1.04 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.65/1.04 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.65/1.04 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.65/1.04 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.65/1.04 X, Z ) ],
% 0.65/1.04 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.65/1.04 Y, T ) ],
% 0.65/1.04 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.65/1.04 ), 'cross_product'( Y, T ) ) ],
% 0.65/1.04 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.65/1.04 ), second( X ) ), X ) ],
% 0.65/1.04 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.65/1.04 'universal_class' ) ) ],
% 0.65/1.04 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.65/1.04 Y ) ],
% 0.65/1.04 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.65/1.04 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.65/1.04 , Y ), 'element_relation' ) ],
% 0.65/1.04 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.65/1.04 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.65/1.04 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.65/1.04 Z ) ) ],
% 0.65/1.04 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.65/1.04 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.65/1.04 member( X, Y ) ],
% 0.65/1.04 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.65/1.04 union( X, Y ) ) ],
% 0.65/1.04 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.65/1.04 intersection( complement( X ), complement( Y ) ) ) ),
% 0.65/1.04 'symmetric_difference'( X, Y ) ) ],
% 0.65/1.04 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.65/1.04 ,
% 0.65/1.04 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.65/1.04 ,
% 0.65/1.04 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.65/1.04 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.65/1.04 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.65/1.04 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.65/1.04 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.65/1.04 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.65/1.04 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.65/1.04 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.65/1.04 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.65/1.04 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.65/1.04 'cross_product'( 'universal_class', 'universal_class' ),
% 0.65/1.04 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.65/1.04 Y ), rotate( T ) ) ],
% 0.65/1.04 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.65/1.04 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.65/1.04 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.65/1.04 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.65/1.04 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.65/1.04 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.65/1.04 'cross_product'( 'universal_class', 'universal_class' ),
% 0.65/1.04 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.65/1.04 Z ), flip( T ) ) ],
% 0.65/1.04 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.65/1.04 inverse( X ) ) ],
% 0.65/1.04 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.65/1.04 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.65/1.04 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.65/1.04 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.65/1.04 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.65/1.04 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.65/1.04 ],
% 0.65/1.04 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.65/1.04 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.65/1.04 'universal_class' ) ) ],
% 0.65/1.04 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.65/1.04 successor( X ), Y ) ],
% 0.65/1.04 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.65/1.04 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.65/1.04 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.65/1.04 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.65/1.04 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.65/1.04 ,
% 0.65/1.04 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.65/1.04 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.65/1.04 [ inductive( omega ) ],
% 0.65/1.04 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.65/1.04 [ member( omega, 'universal_class' ) ],
% 0.65/1.04 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.65/1.04 , 'sum_class'( X ) ) ],
% 0.65/1.04 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.65/1.04 'universal_class' ) ],
% 0.65/1.04 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.65/1.04 'power_class'( X ) ) ],
% 0.65/1.04 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.65/1.04 'universal_class' ) ],
% 0.65/1.04 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.65/1.04 'universal_class' ) ) ],
% 0.65/1.04 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.65/1.04 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.65/1.04 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.65/1.04 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.65/1.04 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.65/1.04 ) ],
% 0.65/1.04 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.65/1.04 , 'identity_relation' ) ],
% 0.65/1.04 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.65/1.04 'single_valued_class'( X ) ],
% 0.65/1.04 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.65/1.04 'universal_class' ) ) ],
% 0.65/1.04 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.65/1.04 'identity_relation' ) ],
% 0.65/1.04 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.65/1.04 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.65/1.04 , function( X ) ],
% 0.65/1.04 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.65/1.04 X, Y ), 'universal_class' ) ],
% 0.65/1.04 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.65/1.04 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.65/1.04 ) ],
% 0.65/1.04 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.65/1.04 [ function( choice ) ],
% 0.65/1.04 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.65/1.04 apply( choice, X ), X ) ],
% 0.65/1.04 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.65/1.04 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.65/1.04 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.65/1.04 ,
% 0.65/1.04 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.65/1.04 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.65/1.04 , complement( compose( complement( 'element_relation' ), inverse(
% 0.65/1.04 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.65/1.04 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.65/1.04 'identity_relation' ) ],
% 0.65/1.04 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.65/1.04 , diagonalise( X ) ) ],
% 0.65/1.04 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.65/1.04 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.65/1.04 [ ~( operation( X ) ), function( X ) ],
% 0.65/1.04 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.65/1.04 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.65/1.04 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.65/1.04 'domain_of'( X ) ) ) ],
% 0.65/1.04 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.65/1.04 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.65/1.04 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.65/1.04 X ) ],
% 0.65/1.04 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.65/1.04 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.65/1.04 'domain_of'( X ) ) ],
% 0.65/1.04 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.65/1.04 'domain_of'( Z ) ) ) ],
% 0.65/1.04 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.65/1.04 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.65/1.04 ), compatible( X, Y, Z ) ],
% 0.65/1.04 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.65/1.04 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.65/1.04 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.65/1.04 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.65/1.04 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.65/1.04 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.65/1.04 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.65/1.04 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.65/1.04 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.65/1.04 , Y ) ],
% 0.65/1.04 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.65/1.04 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.65/1.04 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.65/1.04 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.65/1.04 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.65/1.04 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.65/1.04 X, 'unordered_pair'( X, Y ) ) ],
% 0.65/1.04 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.65/1.04 Y, 'unordered_pair'( X, Y ) ) ],
% 0.65/1.04 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.65/1.04 X, 'universal_class' ) ],
% 0.65/1.04 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.65/1.04 Y, 'universal_class' ) ],
% 0.65/1.04 [ subclass( X, X ) ],
% 0.65/1.04 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.65/1.04 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.65/1.04 'not_subclass_element'( Y, X ), Y ) ],
% 0.65/1.04 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.65/1.04 'not_subclass_element'( Y, X ), Y ) ],
% 0.65/1.04 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.65/1.04 'not_subclass_element'( Y, X ), Y ) ],
% 0.65/1.04 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.65/1.04 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.65/1.04 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.65/1.04 [ ~( member( X, 'null_class' ) ) ],
% 0.65/1.04 [ subclass( 'null_class', X ) ],
% 0.65/1.04 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.65/1.04 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.65/1.04 ), X ) ],
% 0.65/1.04 [ member( 'null_class', 'universal_class' ) ],
% 0.65/1.04 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.65/1.04 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.65/1.04 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.65/1.04 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.65/1.04 Y ) ) ],
% 0.65/1.04 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.65/1.04 Y ) ) ],
% 0.65/1.04 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.65/1.04 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.65/1.04 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.65/1.04 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.65/1.04 'universal_class' ) ) ), =( Y, Z ) ],
% 0.65/1.04 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.65/1.04 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.65/1.04 'universal_class' ) ) ), =( X, Z ) ],
% 0.65/1.04 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.65/1.04 'null_class' ) ) ],
% 0.65/1.04 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.65/1.04 'null_class' ) ) ],
% 0.65/1.04 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.65/1.04 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 4.76/5.15 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 4.76/5.15 X, Z ), Y ) ],
% 4.76/5.15 [ member( singleton( X ), 'universal_class' ) ],
% 4.76/5.15 [ member( singleton( X ), 'unordered_pair'( Y, singleton( X ) ) ) ],
% 4.76/5.15 [ ~( member( X, 'universal_class' ) ), member( X, singleton( X ) ) ]
% 4.76/5.15 ,
% 4.76/5.15 [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X ),
% 4.76/5.15 'null_class' ) ) ],
% 4.76/5.15 [ member( 'null_class', singleton( 'null_class' ) ) ],
% 4.76/5.15 [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ],
% 4.76/5.15 [ member( X, 'universal_class' ), =( singleton( X ), 'null_class' ) ]
% 4.76/5.15 ,
% 4.76/5.15 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 4.76/5.15 'universal_class' ) ), =( X, Y ) ],
% 4.76/5.15 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 4.76/5.15 'universal_class' ) ), =( X, Y ) ],
% 4.76/5.15 [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~( member( Z,
% 4.76/5.15 'universal_class' ) ), =( Z, X ), =( Z, Y ) ],
% 4.76/5.15 [ ~( member( X, 'universal_class' ) ), member( 'member_of'( singleton( X
% 4.76/5.15 ) ), 'universal_class' ) ],
% 4.76/5.15 [ ~( member( X, 'universal_class' ) ), =( singleton( 'member_of'(
% 4.76/5.15 singleton( X ) ) ), singleton( X ) ) ],
% 4.76/5.15 [ member( 'member_of'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 4.76/5.15 ) ],
% 4.76/5.15 [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X ), X ) ],
% 4.76/5.15 [ ~( member( X, 'universal_class' ) ), =( 'member_of'( singleton( X ) )
% 4.76/5.15 , X ) ],
% 4.76/5.15 [ member( 'member_of1'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 4.76/5.15 ) ],
% 4.76/5.15 [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'( X ), X ) ]
% 4.76/5.15 ,
% 4.76/5.15 [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 4.76/5.15 'universal_class' ) ],
% 4.76/5.15 [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y, X ) ), =(
% 4.76/5.15 'member_of'( X ), Y ) ],
% 4.76/5.15 [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ],
% 4.76/5.15 [ subclass( x, singleton( y ) ) ],
% 4.76/5.15 [ ~( =( x, 'null_class' ) ) ],
% 4.76/5.15 [ ~( =( singleton( y ), x ) ) ]
% 4.76/5.15 ] .
% 4.76/5.15
% 4.76/5.15
% 4.76/5.15 percentage equality = 0.279152, percentage horn = 0.852113
% 4.76/5.15 This is a problem with some equality
% 4.76/5.15
% 4.76/5.15
% 4.76/5.15
% 4.76/5.15 Options Used:
% 4.76/5.15
% 4.76/5.15 useres = 1
% 4.76/5.15 useparamod = 1
% 4.76/5.15 useeqrefl = 1
% 4.76/5.15 useeqfact = 1
% 4.76/5.15 usefactor = 1
% 4.76/5.15 usesimpsplitting = 0
% 4.76/5.15 usesimpdemod = 5
% 4.76/5.15 usesimpres = 3
% 4.76/5.15
% 4.76/5.15 resimpinuse = 1000
% 4.76/5.15 resimpclauses = 20000
% 4.76/5.15 substype = eqrewr
% 4.76/5.15 backwardsubs = 1
% 4.76/5.15 selectoldest = 5
% 4.76/5.15
% 4.76/5.15 litorderings [0] = split
% 4.76/5.15 litorderings [1] = extend the termordering, first sorting on arguments
% 4.76/5.15
% 4.76/5.15 termordering = kbo
% 4.76/5.15
% 4.76/5.15 litapriori = 0
% 4.76/5.15 termapriori = 1
% 4.76/5.15 litaposteriori = 0
% 4.76/5.15 termaposteriori = 0
% 4.76/5.15 demodaposteriori = 0
% 4.76/5.15 ordereqreflfact = 0
% 4.76/5.15
% 4.76/5.15 litselect = negord
% 4.76/5.15
% 4.76/5.15 maxweight = 15
% 4.76/5.15 maxdepth = 30000
% 4.76/5.15 maxlength = 115
% 4.76/5.15 maxnrvars = 195
% 4.76/5.15 excuselevel = 1
% 4.76/5.15 increasemaxweight = 1
% 4.76/5.15
% 4.76/5.15 maxselected = 10000000
% 4.76/5.15 maxnrclauses = 10000000
% 4.76/5.15
% 4.76/5.15 showgenerated = 0
% 4.76/5.15 showkept = 0
% 4.76/5.15 showselected = 0
% 4.76/5.15 showdeleted = 0
% 4.76/5.15 showresimp = 1
% 4.76/5.15 showstatus = 2000
% 4.76/5.15
% 4.76/5.15 prologoutput = 1
% 4.76/5.15 nrgoals = 5000000
% 4.76/5.15 totalproof = 1
% 4.76/5.15
% 4.76/5.15 Symbols occurring in the translation:
% 4.76/5.15
% 4.76/5.15 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 4.76/5.15 . [1, 2] (w:1, o:58, a:1, s:1, b:0),
% 4.76/5.15 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 4.76/5.15 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 4.76/5.15 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 4.76/5.15 subclass [41, 2] (w:1, o:83, a:1, s:1, b:0),
% 4.76/5.15 member [43, 2] (w:1, o:84, a:1, s:1, b:0),
% 4.76/5.15 'not_subclass_element' [44, 2] (w:1, o:85, a:1, s:1, b:0),
% 4.76/5.15 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 4.76/5.15 'unordered_pair' [46, 2] (w:1, o:86, a:1, s:1, b:0),
% 4.76/5.15 singleton [47, 1] (w:1, o:39, a:1, s:1, b:0),
% 4.76/5.15 'ordered_pair' [48, 2] (w:1, o:87, a:1, s:1, b:0),
% 4.76/5.15 'cross_product' [50, 2] (w:1, o:88, a:1, s:1, b:0),
% 4.76/5.15 first [52, 1] (w:1, o:40, a:1, s:1, b:0),
% 4.76/5.15 second [53, 1] (w:1, o:41, a:1, s:1, b:0),
% 4.76/5.15 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 4.76/5.15 intersection [55, 2] (w:1, o:90, a:1, s:1, b:0),
% 4.76/5.15 complement [56, 1] (w:1, o:42, a:1, s:1, b:0),
% 4.76/5.15 union [57, 2] (w:1, o:91, a:1, s:1, b:0),
% 4.76/5.15 'symmetric_difference' [58, 2] (w:1, o:92, a:1, s:1, b:0),
% 4.76/5.15 restrict [60, 3] (w:1, o:95, a:1, s:1, b:0),
% 4.76/5.15 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 4.76/5.15 'domain_of' [62, 1] (w:1, o:44, a:1, s:1, b:0),
% 4.76/5.15 rotate [63, 1] (w:1, o:36, a:1, s:1, b:0),
% 4.76/5.15 flip [65, 1] (w:1, o:45, a:1, s:1, b:0),
% 4.76/5.15 inverse [66, 1] (w:1, o:46, a:1, s:1, b:0),
% 4.76/5.15 'range_of' [67, 1] (w:1, o:37, a:1, s:1, b:0),
% 4.76/5.15 domain [68, 3] (w:1, o:97, a:1, s:1, b:0),
% 4.76/5.15 range [69, 3] (w:1, o:98, a:1, s:1, b:0),
% 4.76/5.15 image [70, 2] (w:1, o:89, a:1, s:1, b:0),
% 4.76/5.15 successor [71, 1] (w:1, o:47, a:1, s:1, b:0),
% 4.76/5.15 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 4.76/5.15 inductive [73, 1] (w:1, o:48, a:1, s:1, b:0),
% 4.76/5.15 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 4.76/5.15 'sum_class' [75, 1] (w:1, o:49, a:1, s:1, b:0),
% 4.76/5.15 'power_class' [76, 1] (w:1, o:52, a:1, s:1, b:0),
% 4.76/5.15 compose [78, 2] (w:1, o:93, a:1, s:1, b:0),
% 4.76/5.15 'single_valued_class' [79, 1] (w:1, o:53, a:1, s:1, b:0),
% 4.76/5.15 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 4.76/5.15 function [82, 1] (w:1, o:54, a:1, s:1, b:0),
% 4.76/5.15 regular [83, 1] (w:1, o:38, a:1, s:1, b:0),
% 4.76/5.15 apply [84, 2] (w:1, o:94, a:1, s:1, b:0),
% 4.76/5.15 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 4.76/5.15 'one_to_one' [86, 1] (w:1, o:50, a:1, s:1, b:0),
% 4.76/5.15 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 4.76/5.15 diagonalise [88, 1] (w:1, o:55, a:1, s:1, b:0),
% 4.76/5.15 cantor [89, 1] (w:1, o:43, a:1, s:1, b:0),
% 4.76/5.15 operation [90, 1] (w:1, o:51, a:1, s:1, b:0),
% 4.76/5.15 compatible [94, 3] (w:1, o:96, a:1, s:1, b:0),
% 4.76/5.15 homomorphism [95, 3] (w:1, o:99, a:1, s:1, b:0),
% 4.76/5.15 'not_homomorphism1' [96, 3] (w:1, o:100, a:1, s:1, b:0),
% 4.76/5.15 'not_homomorphism2' [97, 3] (w:1, o:101, a:1, s:1, b:0),
% 4.76/5.15 'member_of' [98, 1] (w:1, o:56, a:1, s:1, b:0),
% 4.76/5.15 'member_of1' [99, 1] (w:1, o:57, a:1, s:1, b:0),
% 4.76/5.15 x [100, 0] (w:1, o:29, a:1, s:1, b:0),
% 4.76/5.15 y [101, 0] (w:1, o:30, a:1, s:1, b:0).
% 4.76/5.15
% 4.76/5.15
% 4.76/5.15 Starting Search:
% 4.76/5.15
% 4.76/5.15 Resimplifying inuse:
% 4.76/5.15 Done
% 4.76/5.15
% 4.76/5.15
% 4.76/5.15 Intermediate Status:
% 4.76/5.15 Generated: 3819
% 4.76/5.15 Kept: 2000
% 4.76/5.15 Inuse: 117
% 4.76/5.15 Deleted: 2
% 4.76/5.15 Deletedinuse: 2
% 4.76/5.15
% 4.76/5.15 Resimplifying inuse:
% 4.76/5.15 Done
% 4.76/5.15
% 4.76/5.15 Resimplifying inuse:
% 4.76/5.15 Done
% 4.76/5.15
% 4.76/5.15
% 4.76/5.15 Intermediate Status:
% 4.76/5.15 Generated: 9481
% 4.76/5.15 Kept: 4170
% 4.76/5.15 Inuse: 201
% 4.76/5.15 Deleted: 7
% 4.76/5.15 Deletedinuse: 7
% 4.76/5.15
% 4.76/5.15 Resimplifying inuse:
% 4.76/5.15 Done
% 4.76/5.15
% 4.76/5.15 Resimplifying inuse:
% 4.76/5.15 Done
% 4.76/5.15
% 4.76/5.15
% 4.76/5.15 Intermediate Status:
% 4.76/5.15 Generated: 14564
% 4.76/5.15 Kept: 6177
% 4.76/5.15 Inuse: 281
% 4.76/5.15 Deleted: 49
% 4.76/5.15 Deletedinuse: 49
% 4.76/5.15
% 4.76/5.15 Resimplifying inuse:
% 4.76/5.15 Done
% 4.76/5.15
% 4.76/5.15 Resimplifying inuse:
% 4.76/5.15 Done
% 4.76/5.15
% 4.76/5.15
% 4.76/5.15 Intermediate Status:
% 4.76/5.15 Generated: 20641
% 4.76/5.15 Kept: 8185
% 4.76/5.15 Inuse: 332
% 4.76/5.15 Deleted: 70
% 4.76/5.15 Deletedinuse: 55
% 4.76/5.15
% 4.76/5.15 Resimplifying inuse:
% 4.76/5.15 Done
% 4.76/5.15
% 4.76/5.15 Resimplifying inuse:
% 4.76/5.15 Done
% 4.76/5.15
% 4.76/5.15
% 4.76/5.15 Intermediate Status:
% 4.76/5.15 Generated: 28193
% 4.76/5.15 Kept: 10682
% 4.76/5.15 Inuse: 396
% 4.76/5.15 Deleted: 75
% 4.76/5.15 Deletedinuse: 60
% 4.76/5.15
% 4.76/5.15 Resimplifying inuse:
% 4.76/5.15 Done
% 4.76/5.15
% 4.76/5.15 Resimplifying inuse:
% 4.76/5.15 Done
% 4.76/5.15
% 4.76/5.15
% 4.76/5.15 Intermediate Status:
% 4.76/5.15 Generated: 37646
% 4.76/5.15 Kept: 12917
% 4.76/5.15 Inuse: 445
% 4.76/5.15 Deleted: 86
% 4.76/5.15 Deletedinuse: 70
% 4.76/5.15
% 4.76/5.15 Resimplifying inuse:
% 4.76/5.15 Done
% 4.76/5.15
% 4.76/5.15 Resimplifying inuse:
% 4.76/5.15 Done
% 4.76/5.15
% 4.76/5.15
% 4.76/5.15 Intermediate Status:
% 4.76/5.15 Generated: 45061
% 4.76/5.15 Kept: 14938
% 4.76/5.15 Inuse: 488
% 4.76/5.15 Deleted: 90
% 4.76/5.15 Deletedinuse: 73
% 4.76/5.15
% 4.76/5.15 Resimplifying inuse:
% 4.76/5.15 Done
% 4.76/5.15
% 4.76/5.15
% 4.76/5.15 Intermediate Status:
% 4.76/5.15 Generated: 48394
% 4.76/5.15 Kept: 16964
% 4.76/5.15 Inuse: 494
% 4.76/5.15 Deleted: 91
% 4.76/5.15 Deletedinuse: 74
% 4.76/5.15
% 4.76/5.15 Resimplifying inuse:
% 4.76/5.15 Done
% 4.76/5.15
% 4.76/5.15
% 4.76/5.15 Intermediate Status:
% 4.76/5.15 Generated: 61848
% 4.76/5.15 Kept: 20783
% 4.76/5.15 Inuse: 504
% 4.76/5.15 Deleted: 92
% 4.76/5.15 Deletedinuse: 75
% 4.76/5.15
% 4.76/5.15 Resimplifying inuse:
% 4.76/5.15 Done
% 4.76/5.15
% 4.76/5.15 Resimplifying clauses:
% 4.76/5.15 Done
% 4.76/5.15
% 4.76/5.15
% 4.76/5.15 Bliksems!, er is een bewijs:
% 4.76/5.15 % SZS status Unsatisfiable
% 4.76/5.15 % SZS output start Refutation
% 4.76/5.15
% 4.76/5.15 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 4.76/5.15 )
% 4.76/5.15 .
% 4.76/5.15 clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y )
% 4.76/5.15 ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 94, [ subclass( X, X ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 100, [ ~( member( X, 'null_class' ) ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 101, [ subclass( 'null_class', X ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 122, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 135, [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 136, [ subclass( x, singleton( y ) ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 137, [ ~( =( x, 'null_class' ) ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 138, [ ~( =( singleton( y ), x ) ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 161, [ ~( member( X, x ) ), member( X, singleton( y ) ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 174, [ ~( subclass( singleton( y ), x ) ), =( singleton( y ), x ) ]
% 4.76/5.15 )
% 4.76/5.15 .
% 4.76/5.15 clause( 191, [ ~( =( X, x ) ), ~( subclass( singleton( y ), X ) ), ~(
% 4.76/5.15 subclass( X, singleton( y ) ) ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 197, [ ~( =( X, 'null_class' ) ), ~( subclass( x, X ) ), ~(
% 4.76/5.15 subclass( X, x ) ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 202, [ ~( subclass( x, 'null_class' ) ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 203, [ ~( subclass( singleton( y ), x ) ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 204, [ member( 'not_subclass_element'( x, 'null_class' ), x ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 6429, [ member( regular( x ), x ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 21713, [ ~( member( y, x ) ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 21738, [ ~( member( X, x ) ) ] )
% 4.76/5.15 .
% 4.76/5.15 clause( 21750, [] )
% 4.76/5.15 .
% 4.76/5.15
% 4.76/5.15
% 4.76/5.15 % SZS output end Refutation
% 4.76/5.15 found a proof!
% 4.76/5.15
% 4.76/5.15 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 4.76/5.15
% 4.76/5.15 initialclauses(
% 4.76/5.15 [ clause( 21752, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 4.76/5.15 ) ] )
% 4.76/5.15 , clause( 21753, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 4.76/5.15 , Y ) ] )
% 4.76/5.15 , clause( 21754, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 4.76/5.15 subclass( X, Y ) ] )
% 4.76/5.15 , clause( 21755, [ subclass( X, 'universal_class' ) ] )
% 4.76/5.15 , clause( 21756, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 4.76/5.15 , clause( 21757, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 4.76/5.15 , clause( 21758, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 4.76/5.15 ] )
% 4.76/5.15 , clause( 21759, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 4.76/5.15 =( X, Z ) ] )
% 4.76/5.15 , clause( 21760, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.76/5.15 'unordered_pair'( X, Y ) ) ] )
% 4.76/5.15 , clause( 21761, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.76/5.15 'unordered_pair'( Y, X ) ) ] )
% 4.76/5.15 , clause( 21762, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 4.76/5.15 )
% 4.76/5.15 , clause( 21763, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 4.76/5.15 , clause( 21764, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 4.76/5.15 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 4.76/5.15 , clause( 21765, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.76/5.15 ) ) ), member( X, Z ) ] )
% 4.76/5.15 , clause( 21766, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.76/5.15 ) ) ), member( Y, T ) ] )
% 4.76/5.15 , clause( 21767, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 4.76/5.15 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 4.76/5.15 , clause( 21768, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 4.76/5.15 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 4.76/5.15 , clause( 21769, [ subclass( 'element_relation', 'cross_product'(
% 4.76/5.15 'universal_class', 'universal_class' ) ) ] )
% 4.76/5.15 , clause( 21770, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 4.76/5.15 ), member( X, Y ) ] )
% 4.76/5.15 , clause( 21771, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 4.76/5.15 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 4.76/5.15 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 4.76/5.15 , clause( 21772, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 4.76/5.15 )
% 4.76/5.15 , clause( 21773, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 4.76/5.15 )
% 4.76/5.15 , clause( 21774, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 4.76/5.15 intersection( Y, Z ) ) ] )
% 4.76/5.15 , clause( 21775, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 4.76/5.15 )
% 4.76/5.15 , clause( 21776, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.76/5.15 complement( Y ) ), member( X, Y ) ] )
% 4.76/5.15 , clause( 21777, [ =( complement( intersection( complement( X ), complement(
% 4.76/5.15 Y ) ) ), union( X, Y ) ) ] )
% 4.76/5.15 , clause( 21778, [ =( intersection( complement( intersection( X, Y ) ),
% 4.76/5.15 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 4.76/5.15 'symmetric_difference'( X, Y ) ) ] )
% 4.76/5.15 , clause( 21779, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 4.76/5.15 X, Y, Z ) ) ] )
% 4.76/5.15 , clause( 21780, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 4.76/5.15 Z, X, Y ) ) ] )
% 4.76/5.15 , clause( 21781, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 4.76/5.15 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 4.76/5.15 , clause( 21782, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 4.76/5.15 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 4.76/5.15 'domain_of'( Y ) ) ] )
% 4.76/5.15 , clause( 21783, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 4.76/5.15 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 4.76/5.15 , clause( 21784, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 4.76/5.15 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 4.76/5.15 ] )
% 4.76/5.15 , clause( 21785, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 4.76/5.15 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 4.76/5.15 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 4.76/5.15 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 4.76/5.15 , Y ), rotate( T ) ) ] )
% 4.76/5.15 , clause( 21786, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 4.76/5.15 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 4.76/5.15 , clause( 21787, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 4.76/5.15 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 4.76/5.15 )
% 4.76/5.15 , clause( 21788, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 4.76/5.15 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 4.76/5.15 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 4.76/5.15 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 4.76/5.15 , Z ), flip( T ) ) ] )
% 4.76/5.15 , clause( 21789, [ =( 'domain_of'( flip( 'cross_product'( X,
% 4.76/5.15 'universal_class' ) ) ), inverse( X ) ) ] )
% 4.76/5.15 , clause( 21790, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 4.76/5.15 , clause( 21791, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 4.76/5.15 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 4.76/5.15 , clause( 21792, [ =( second( 'not_subclass_element'( restrict( X,
% 4.76/5.15 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 4.76/5.15 , clause( 21793, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 4.76/5.15 image( X, Y ) ) ] )
% 4.76/5.15 , clause( 21794, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 4.76/5.15 , clause( 21795, [ subclass( 'successor_relation', 'cross_product'(
% 4.76/5.15 'universal_class', 'universal_class' ) ) ] )
% 4.76/5.15 , clause( 21796, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 4.76/5.15 ) ), =( successor( X ), Y ) ] )
% 4.76/5.15 , clause( 21797, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 4.76/5.15 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 4.76/5.15 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 4.76/5.15 , clause( 21798, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 4.76/5.15 , clause( 21799, [ ~( inductive( X ) ), subclass( image(
% 4.76/5.15 'successor_relation', X ), X ) ] )
% 4.76/5.15 , clause( 21800, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 4.76/5.15 'successor_relation', X ), X ) ), inductive( X ) ] )
% 4.76/5.15 , clause( 21801, [ inductive( omega ) ] )
% 4.76/5.15 , clause( 21802, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 4.76/5.15 , clause( 21803, [ member( omega, 'universal_class' ) ] )
% 4.76/5.15 , clause( 21804, [ =( 'domain_of'( restrict( 'element_relation',
% 4.76/5.15 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 4.76/5.15 , clause( 21805, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 4.76/5.15 X ), 'universal_class' ) ] )
% 4.76/5.15 , clause( 21806, [ =( complement( image( 'element_relation', complement( X
% 4.76/5.15 ) ) ), 'power_class'( X ) ) ] )
% 4.76/5.15 , clause( 21807, [ ~( member( X, 'universal_class' ) ), member(
% 4.76/5.15 'power_class'( X ), 'universal_class' ) ] )
% 4.76/5.15 , clause( 21808, [ subclass( compose( X, Y ), 'cross_product'(
% 4.76/5.15 'universal_class', 'universal_class' ) ) ] )
% 4.76/5.15 , clause( 21809, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 4.76/5.15 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 4.76/5.15 , clause( 21810, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 4.76/5.15 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 4.76/5.15 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 4.76/5.15 ) ] )
% 4.76/5.15 , clause( 21811, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 4.76/5.15 inverse( X ) ), 'identity_relation' ) ] )
% 4.76/5.15 , clause( 21812, [ ~( subclass( compose( X, inverse( X ) ),
% 4.76/5.15 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 4.76/5.15 , clause( 21813, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 4.76/5.15 'universal_class', 'universal_class' ) ) ] )
% 4.76/5.15 , clause( 21814, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 4.76/5.15 , 'identity_relation' ) ] )
% 4.76/5.15 , clause( 21815, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 4.76/5.15 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 4.76/5.15 'identity_relation' ) ), function( X ) ] )
% 4.76/5.15 , clause( 21816, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 4.76/5.15 , member( image( X, Y ), 'universal_class' ) ] )
% 4.76/5.15 , clause( 21817, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 4.76/5.15 , clause( 21818, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 4.76/5.15 , 'null_class' ) ] )
% 4.76/5.15 , clause( 21819, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 4.76/5.15 Y ) ) ] )
% 4.76/5.15 , clause( 21820, [ function( choice ) ] )
% 4.76/5.15 , clause( 21821, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 4.76/5.15 ), member( apply( choice, X ), X ) ] )
% 4.76/5.15 , clause( 21822, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 4.76/5.15 , clause( 21823, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 4.76/5.15 , clause( 21824, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 4.76/5.15 'one_to_one'( X ) ] )
% 4.76/5.15 , clause( 21825, [ =( intersection( 'cross_product'( 'universal_class',
% 4.76/5.15 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 4.76/5.15 'universal_class' ), complement( compose( complement( 'element_relation'
% 4.76/5.15 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 4.76/5.15 , clause( 21826, [ =( intersection( inverse( 'subset_relation' ),
% 4.76/5.15 'subset_relation' ), 'identity_relation' ) ] )
% 4.76/5.15 , clause( 21827, [ =( complement( 'domain_of'( intersection( X,
% 4.76/5.15 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 4.76/5.15 , clause( 21828, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 4.76/5.15 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 4.76/5.15 , clause( 21829, [ ~( operation( X ) ), function( X ) ] )
% 4.76/5.15 , clause( 21830, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 4.76/5.15 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 4.76/5.15 ] )
% 4.76/5.15 , clause( 21831, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 4.76/5.15 'domain_of'( 'domain_of'( X ) ) ) ] )
% 4.76/5.15 , clause( 21832, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 4.76/5.15 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 4.76/5.15 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 4.76/5.15 operation( X ) ] )
% 4.76/5.15 , clause( 21833, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 4.76/5.15 , clause( 21834, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 4.76/5.15 Y ) ), 'domain_of'( X ) ) ] )
% 4.76/5.15 , clause( 21835, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 4.76/5.15 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 4.76/5.15 , clause( 21836, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 4.76/5.15 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 4.76/5.15 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 4.76/5.15 , clause( 21837, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 4.76/5.15 , clause( 21838, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 4.76/5.15 , clause( 21839, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 4.76/5.15 , clause( 21840, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 4.76/5.15 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 4.76/5.15 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 4.76/5.15 )
% 4.76/5.15 , clause( 21841, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 4.76/5.15 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 4.76/5.15 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 4.76/5.15 , Y ) ] )
% 4.76/5.15 , clause( 21842, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 4.76/5.15 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 4.76/5.15 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 4.76/5.15 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 4.76/5.15 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 4.76/5.15 )
% 4.76/5.15 , clause( 21843, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.76/5.15 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 4.76/5.15 , clause( 21844, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.76/5.15 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 4.76/5.15 , clause( 21845, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.76/5.15 ) ) ), member( X, 'universal_class' ) ] )
% 4.76/5.15 , clause( 21846, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.76/5.15 ) ) ), member( Y, 'universal_class' ) ] )
% 4.76/5.15 , clause( 21847, [ subclass( X, X ) ] )
% 4.76/5.15 , clause( 21848, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 4.76/5.15 X, Z ) ] )
% 4.76/5.15 , clause( 21849, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 4.76/5.15 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 4.76/5.15 , clause( 21850, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 4.76/5.15 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 4.76/5.15 , clause( 21851, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 4.76/5.15 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 4.76/5.15 , clause( 21852, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 4.76/5.15 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 4.76/5.15 , clause( 21853, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 4.76/5.15 )
% 4.76/5.15 , clause( 21854, [ ~( member( X, 'null_class' ) ) ] )
% 4.76/5.15 , clause( 21855, [ subclass( 'null_class', X ) ] )
% 4.76/5.15 , clause( 21856, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 4.76/5.15 )
% 4.76/5.15 , clause( 21857, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 4.76/5.15 , 'null_class' ), X ) ] )
% 4.76/5.15 , clause( 21858, [ member( 'null_class', 'universal_class' ) ] )
% 4.76/5.15 , clause( 21859, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 4.76/5.15 ] )
% 4.76/5.15 , clause( 21860, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 4.76/5.15 )
% 4.76/5.15 , clause( 21861, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 4.76/5.15 )
% 4.76/5.15 , clause( 21862, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 4.76/5.15 X ), singleton( Y ) ) ] )
% 4.76/5.15 , clause( 21863, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 4.76/5.15 Y ), singleton( Y ) ) ] )
% 4.76/5.15 , clause( 21864, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 4.76/5.15 'universal_class' ), member( Y, 'universal_class' ) ] )
% 4.76/5.15 , clause( 21865, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 4.76/5.15 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 4.76/5.15 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 4.76/5.15 , clause( 21866, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 4.76/5.15 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 4.76/5.15 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 4.76/5.15 , clause( 21867, [ ~( member( X, 'universal_class' ) ), ~( =(
% 4.76/5.15 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 4.76/5.15 , clause( 21868, [ ~( member( X, 'universal_class' ) ), ~( =(
% 4.76/5.15 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 4.76/5.15 , clause( 21869, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.76/5.15 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 4.76/5.15 , clause( 21870, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 4.76/5.15 'unordered_pair'( X, Z ), Y ) ] )
% 4.76/5.15 , clause( 21871, [ member( singleton( X ), 'universal_class' ) ] )
% 4.76/5.15 , clause( 21872, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 4.76/5.15 X ) ) ) ] )
% 4.76/5.15 , clause( 21873, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.76/5.15 singleton( X ) ) ] )
% 4.76/5.15 , clause( 21874, [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X
% 4.76/5.15 ), 'null_class' ) ) ] )
% 4.76/5.15 , clause( 21875, [ member( 'null_class', singleton( 'null_class' ) ) ] )
% 4.76/5.15 , clause( 21876, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 4.76/5.15 , clause( 21877, [ member( X, 'universal_class' ), =( singleton( X ),
% 4.76/5.15 'null_class' ) ] )
% 4.76/5.15 , clause( 21878, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 4.76/5.15 'universal_class' ) ), =( X, Y ) ] )
% 4.76/5.15 , clause( 21879, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 4.76/5.15 'universal_class' ) ), =( X, Y ) ] )
% 4.76/5.15 , clause( 21880, [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~(
% 4.76/5.15 member( Z, 'universal_class' ) ), =( Z, X ), =( Z, Y ) ] )
% 4.76/5.15 , clause( 21881, [ ~( member( X, 'universal_class' ) ), member( 'member_of'(
% 4.76/5.15 singleton( X ) ), 'universal_class' ) ] )
% 4.76/5.15 , clause( 21882, [ ~( member( X, 'universal_class' ) ), =( singleton(
% 4.76/5.15 'member_of'( singleton( X ) ) ), singleton( X ) ) ] )
% 4.76/5.15 , clause( 21883, [ member( 'member_of'( X ), 'universal_class' ), =(
% 4.76/5.15 'member_of'( X ), X ) ] )
% 4.76/5.15 , clause( 21884, [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X
% 4.76/5.16 ), X ) ] )
% 4.76/5.16 , clause( 21885, [ ~( member( X, 'universal_class' ) ), =( 'member_of'(
% 4.76/5.16 singleton( X ) ), X ) ] )
% 4.76/5.16 , clause( 21886, [ member( 'member_of1'( X ), 'universal_class' ), =(
% 4.76/5.16 'member_of'( X ), X ) ] )
% 4.76/5.16 , clause( 21887, [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'(
% 4.76/5.16 X ), X ) ] )
% 4.76/5.16 , clause( 21888, [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 4.76/5.16 'universal_class' ) ] )
% 4.76/5.16 , clause( 21889, [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y
% 4.76/5.16 , X ) ), =( 'member_of'( X ), Y ) ] )
% 4.76/5.16 , clause( 21890, [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ] )
% 4.76/5.16 , clause( 21891, [ subclass( x, singleton( y ) ) ] )
% 4.76/5.16 , clause( 21892, [ ~( =( x, 'null_class' ) ) ] )
% 4.76/5.16 , clause( 21893, [ ~( =( singleton( y ), x ) ) ] )
% 4.76/5.16 ] ).
% 4.76/5.16
% 4.76/5.16
% 4.76/5.16
% 4.76/5.16 subsumption(
% 4.76/5.16 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 4.76/5.16 )
% 4.76/5.16 , clause( 21752, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 4.76/5.16 ) ] )
% 4.76/5.16 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 4.76/5.16 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 4.76/5.16
% 4.76/5.16
% 4.76/5.16 subsumption(
% 4.76/5.16 clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y )
% 4.76/5.16 ] )
% 4.76/5.16 , clause( 21753, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 4.76/5.16 , Y ) ] )
% 4.76/5.16 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 4.76/5.16 ), ==>( 1, 1 )] ) ).
% 4.76/5.16
% 4.76/5.16
% 4.76/5.16 subsumption(
% 4.76/5.16 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 4.76/5.16 , clause( 21758, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 4.76/5.16 ] )
% 4.76/5.16 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 4.76/5.16 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 4.76/5.16
% 4.76/5.16
% 4.76/5.16 subsumption(
% 4.76/5.16 clause( 64, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 4.76/5.16 , clause( 21817, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 4.76/5.16 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 4.76/5.16 1 )] ) ).
% 4.76/5.16
% 4.76/5.16
% 4.76/5.16 subsumption(
% 4.76/5.16 clause( 94, [ subclass( X, X ) ] )
% 4.76/5.16 , clause( 21847, [ subclass( X, X ) ] )
% 4.76/5.16 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.76/5.16
% 4.76/5.16
% 4.76/5.16 subsumption(
% 4.76/5.16 clause( 100, [ ~( member( X, 'null_class' ) ) ] )
% 4.76/5.16 , clause( 21854, [ ~( member( X, 'null_class' ) ) ] )
% 4.76/5.16 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.76/5.16
% 4.76/5.16
% 4.76/5.16 subsumption(
% 4.76/5.16 clause( 101, [ subclass( 'null_class', X ) ] )
% 4.76/5.16 , clause( 21855, [ subclass( 'null_class', X ) ] )
% 4.76/5.16 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.76/5.16
% 4.76/5.16
% 4.76/5.16 subsumption(
% 4.76/5.16 clause( 122, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 4.76/5.16 , clause( 21876, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 4.76/5.16 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 4.76/5.16 ), ==>( 1, 1 )] ) ).
% 4.76/5.16
% 4.76/5.16
% 4.76/5.16 subsumption(
% 4.76/5.16 clause( 135, [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ] )
% 4.76/5.16 , clause( 21890, [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ] )
% 4.76/5.16 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 4.76/5.16 ), ==>( 1, 1 )] ) ).
% 4.76/5.16
% 4.76/5.16
% 4.76/5.16 subsumption(
% 4.76/5.16 clause( 136, [ subclass( x, singleton( y ) ) ] )
% 4.76/5.16 , clause( 21891, [ subclass( x, singleton( y ) ) ] )
% 4.76/5.16 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.76/5.16
% 4.76/5.16
% 4.76/5.16 subsumption(
% 4.76/5.16 clause( 137, [ ~( =( x, 'null_class' ) ) ] )
% 4.76/5.16 , clause( 21892, [ ~( =( x, 'null_class' ) ) ] )
% 4.76/5.16 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.76/5.16
% 4.76/5.16
% 4.76/5.16 subsumption(
% 4.76/5.16 clause( 138, [ ~( =( singleton( y ), x ) ) ] )
% 4.76/5.16 , clause( 21893, [ ~( =( singleton( y ), x ) ) ] )
% 4.76/5.16 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.76/5.16
% 4.76/5.16
% 4.76/5.16 resolution(
% 4.76/5.16 clause( 22590, [ ~( member( X, x ) ), member( X, singleton( y ) ) ] )
% 4.76/5.16 , clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 4.76/5.16 )
% 4.76/5.16 , 0, clause( 136, [ subclass( x, singleton( y ) ) ] )
% 4.76/5.16 , 0, substitution( 0, [ :=( X, x ), :=( Y, singleton( y ) ), :=( Z, X )] )
% 4.76/5.16 , substitution( 1, [] )).
% 4.76/5.16
% 4.76/5.16
% 4.76/5.16 subsumption(
% 4.76/5.16 clause( 161, [ ~( member( X, x ) ), member( X, singleton( y ) ) ] )
% 4.76/5.16 , clause( 22590, [ ~( member( X, x ) ), member( X, singleton( y ) ) ] )
% 4.76/5.16 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 4.76/5.16 1 )] ) ).
% 4.76/5.16
% 4.76/5.16
% 4.76/5.16 resolution(
% 4.76/5.16 clause( 22592, [ ~( subclass( singleton( y Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------