TSTP Solution File: SET101-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET101-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.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 22:47:06 EDT 2022
% Result : Unsatisfiable 1.97s 2.39s
% Output : Refutation 1.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET101-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n021.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 : Sat Jul 9 16:49:06 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.10 *** allocated 10000 integers for termspace/termends
% 0.43/1.10 *** allocated 10000 integers for clauses
% 0.43/1.10 *** allocated 10000 integers for justifications
% 0.43/1.10 Bliksem 1.12
% 0.43/1.10
% 0.43/1.10
% 0.43/1.10 Automatic Strategy Selection
% 0.43/1.10
% 0.43/1.10 Clauses:
% 0.43/1.10 [
% 0.43/1.10 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.43/1.10 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.43/1.10 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.43/1.10 ,
% 0.43/1.10 [ subclass( X, 'universal_class' ) ],
% 0.43/1.10 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.43/1.10 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.43/1.10 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.43/1.10 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.43/1.10 ,
% 0.43/1.10 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.43/1.10 ) ) ],
% 0.43/1.10 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.43/1.10 ) ) ],
% 0.43/1.10 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.43/1.10 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.43/1.10 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.43/1.10 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.10 X, Z ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.10 Y, T ) ],
% 0.43/1.10 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.43/1.10 ), 'cross_product'( Y, T ) ) ],
% 0.43/1.10 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.43/1.10 ), second( X ) ), X ) ],
% 0.43/1.10 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.43/1.10 'universal_class' ) ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.43/1.10 Y ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.43/1.10 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.43/1.10 , Y ), 'element_relation' ) ],
% 0.43/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.43/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.43/1.10 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.43/1.10 Z ) ) ],
% 0.43/1.10 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.43/1.10 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.43/1.10 member( X, Y ) ],
% 0.43/1.10 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.43/1.10 union( X, Y ) ) ],
% 0.43/1.10 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.43/1.10 intersection( complement( X ), complement( Y ) ) ) ),
% 0.43/1.10 'symmetric_difference'( X, Y ) ) ],
% 0.43/1.10 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.43/1.10 ,
% 0.43/1.10 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.43/1.10 ,
% 0.43/1.10 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.43/1.10 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.43/1.10 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.43/1.10 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.43/1.10 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.43/1.10 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.43/1.10 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.43/1.10 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.43/1.10 'cross_product'( 'universal_class', 'universal_class' ),
% 0.43/1.10 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.43/1.10 Y ), rotate( T ) ) ],
% 0.43/1.10 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.43/1.10 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.43/1.10 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.43/1.10 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.43/1.10 'cross_product'( 'universal_class', 'universal_class' ),
% 0.43/1.10 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.43/1.10 Z ), flip( T ) ) ],
% 0.43/1.10 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.43/1.10 inverse( X ) ) ],
% 0.43/1.10 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.43/1.10 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.43/1.10 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.43/1.10 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.43/1.10 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.43/1.10 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.43/1.10 ],
% 0.43/1.10 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.43/1.10 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.43/1.10 'universal_class' ) ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.43/1.10 successor( X ), Y ) ],
% 0.43/1.10 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.43/1.10 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.43/1.10 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.43/1.10 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.43/1.10 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.43/1.10 ,
% 0.43/1.10 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.43/1.10 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.43/1.10 [ inductive( omega ) ],
% 0.43/1.10 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.43/1.10 [ member( omega, 'universal_class' ) ],
% 0.43/1.10 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.43/1.10 , 'sum_class'( X ) ) ],
% 0.43/1.10 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.43/1.10 'universal_class' ) ],
% 0.43/1.10 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.43/1.10 'power_class'( X ) ) ],
% 0.43/1.10 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.43/1.10 'universal_class' ) ],
% 0.43/1.10 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.43/1.10 'universal_class' ) ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.43/1.10 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.43/1.10 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.43/1.10 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.43/1.10 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.43/1.10 ) ],
% 0.43/1.10 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.43/1.10 , 'identity_relation' ) ],
% 0.43/1.10 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.43/1.10 'single_valued_class'( X ) ],
% 0.43/1.10 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.43/1.10 'universal_class' ) ) ],
% 0.43/1.10 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.43/1.10 'identity_relation' ) ],
% 0.43/1.10 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.43/1.10 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.43/1.10 , function( X ) ],
% 0.43/1.10 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.43/1.10 X, Y ), 'universal_class' ) ],
% 0.43/1.10 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.43/1.10 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.43/1.10 ) ],
% 0.43/1.10 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.43/1.10 [ function( choice ) ],
% 0.43/1.10 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.43/1.10 apply( choice, X ), X ) ],
% 0.43/1.10 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.43/1.10 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.43/1.10 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.43/1.10 ,
% 0.43/1.10 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.43/1.10 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.43/1.10 , complement( compose( complement( 'element_relation' ), inverse(
% 0.43/1.10 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.43/1.10 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.43/1.10 'identity_relation' ) ],
% 0.43/1.10 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.43/1.10 , diagonalise( X ) ) ],
% 0.43/1.10 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.43/1.10 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.43/1.10 [ ~( operation( X ) ), function( X ) ],
% 0.43/1.10 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.43/1.10 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.43/1.10 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.43/1.10 'domain_of'( X ) ) ) ],
% 0.43/1.10 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.43/1.10 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.43/1.10 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.43/1.10 X ) ],
% 0.43/1.10 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.43/1.10 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.43/1.10 'domain_of'( X ) ) ],
% 0.43/1.10 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.43/1.10 'domain_of'( Z ) ) ) ],
% 0.43/1.10 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.43/1.10 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.43/1.10 ), compatible( X, Y, Z ) ],
% 0.43/1.10 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.43/1.10 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.43/1.10 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.43/1.10 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.43/1.10 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.43/1.10 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.43/1.10 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.43/1.10 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.43/1.10 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.43/1.10 , Y ) ],
% 0.43/1.10 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.43/1.10 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.43/1.10 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.43/1.10 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.43/1.10 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.10 X, 'unordered_pair'( X, Y ) ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.10 Y, 'unordered_pair'( X, Y ) ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.10 X, 'universal_class' ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.10 Y, 'universal_class' ) ],
% 0.43/1.10 [ subclass( X, X ) ],
% 0.43/1.10 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.43/1.10 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.43/1.10 'not_subclass_element'( Y, X ), Y ) ],
% 0.43/1.10 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.43/1.10 'not_subclass_element'( Y, X ), Y ) ],
% 0.43/1.10 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.43/1.10 'not_subclass_element'( Y, X ), Y ) ],
% 0.43/1.10 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.43/1.10 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.43/1.10 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.43/1.10 [ ~( member( X, 'null_class' ) ) ],
% 0.43/1.10 [ subclass( 'null_class', X ) ],
% 0.43/1.10 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.43/1.10 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.43/1.10 ), X ) ],
% 0.43/1.10 [ member( 'null_class', 'universal_class' ) ],
% 0.43/1.10 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.43/1.10 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.43/1.10 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.43/1.10 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.43/1.10 Y ) ) ],
% 0.43/1.10 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.43/1.10 Y ) ) ],
% 0.43/1.10 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.43/1.10 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.43/1.10 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.43/1.10 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.43/1.10 'universal_class' ) ) ), =( Y, Z ) ],
% 0.43/1.10 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.43/1.10 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.43/1.10 'universal_class' ) ) ), =( X, Z ) ],
% 0.43/1.10 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.43/1.10 'null_class' ) ) ],
% 0.43/1.10 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.43/1.10 'null_class' ) ) ],
% 0.43/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.43/1.10 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 1.97/2.39 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 1.97/2.39 X, Z ), Y ) ],
% 1.97/2.39 [ member( singleton( X ), 'universal_class' ) ],
% 1.97/2.39 [ member( singleton( X ), 'unordered_pair'( Y, singleton( X ) ) ) ],
% 1.97/2.39 [ ~( member( X, 'universal_class' ) ), member( X, singleton( X ) ) ]
% 1.97/2.39 ,
% 1.97/2.39 [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X ),
% 1.97/2.39 'null_class' ) ) ],
% 1.97/2.39 [ member( 'null_class', singleton( 'null_class' ) ) ],
% 1.97/2.39 [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ],
% 1.97/2.39 [ member( X, 'universal_class' ), =( singleton( X ), 'null_class' ) ]
% 1.97/2.39 ,
% 1.97/2.39 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 1.97/2.39 'universal_class' ) ), =( X, Y ) ],
% 1.97/2.39 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 1.97/2.39 'universal_class' ) ), =( X, Y ) ],
% 1.97/2.39 [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~( member( Z,
% 1.97/2.39 'universal_class' ) ), =( Z, X ), =( Z, Y ) ],
% 1.97/2.39 [ ~( member( X, 'universal_class' ) ), member( 'member_of'( singleton( X
% 1.97/2.39 ) ), 'universal_class' ) ],
% 1.97/2.39 [ ~( member( X, 'universal_class' ) ), =( singleton( 'member_of'(
% 1.97/2.39 singleton( X ) ) ), singleton( X ) ) ],
% 1.97/2.39 [ member( 'member_of'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 1.97/2.39 ) ],
% 1.97/2.39 [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X ), X ) ],
% 1.97/2.39 [ ~( member( X, 'universal_class' ) ), =( 'member_of'( singleton( X ) )
% 1.97/2.39 , X ) ],
% 1.97/2.39 [ member( 'member_of1'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 1.97/2.39 ) ],
% 1.97/2.39 [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'( X ), X ) ]
% 1.97/2.39 ,
% 1.97/2.39 [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 1.97/2.39 'universal_class' ) ],
% 1.97/2.39 [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y, X ) ), =(
% 1.97/2.39 'member_of'( X ), Y ) ],
% 1.97/2.39 [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ],
% 1.97/2.39 [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' ), =( singleton(
% 1.97/2.39 Y ), X ) ],
% 1.97/2.39 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 1.97/2.39 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 1.97/2.39 intersection( complement( singleton( 'not_subclass_element'( X,
% 1.97/2.39 'null_class' ) ) ), X ) ), =( singleton( 'not_subclass_element'( X,
% 1.97/2.39 'null_class' ) ), X ), =( X, 'null_class' ) ],
% 1.97/2.39 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 1.97/2.39 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ), X ),
% 1.97/2.39 =( singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 1.97/2.39 'null_class' ) ],
% 1.97/2.39 [ ~( =( 'not_subclass_element'( intersection( complement( singleton(
% 1.97/2.39 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 1.97/2.39 'not_subclass_element'( X, 'null_class' ) ) ), =( singleton(
% 1.97/2.39 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 1.97/2.39 ,
% 1.97/2.39 [ =( 'unordered_pair'( X, Y ), union( singleton( X ), singleton( Y ) ) )
% 1.97/2.39 ],
% 1.97/2.39 [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ],
% 1.97/2.39 [ ~( member( singleton( x ), 'ordered_pair'( x, y ) ) ) ]
% 1.97/2.39 ] .
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 percentage equality = 0.294915, percentage horn = 0.828767
% 1.97/2.39 This is a problem with some equality
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Options Used:
% 1.97/2.39
% 1.97/2.39 useres = 1
% 1.97/2.39 useparamod = 1
% 1.97/2.39 useeqrefl = 1
% 1.97/2.39 useeqfact = 1
% 1.97/2.39 usefactor = 1
% 1.97/2.39 usesimpsplitting = 0
% 1.97/2.39 usesimpdemod = 5
% 1.97/2.39 usesimpres = 3
% 1.97/2.39
% 1.97/2.39 resimpinuse = 1000
% 1.97/2.39 resimpclauses = 20000
% 1.97/2.39 substype = eqrewr
% 1.97/2.39 backwardsubs = 1
% 1.97/2.39 selectoldest = 5
% 1.97/2.39
% 1.97/2.39 litorderings [0] = split
% 1.97/2.39 litorderings [1] = extend the termordering, first sorting on arguments
% 1.97/2.39
% 1.97/2.39 termordering = kbo
% 1.97/2.39
% 1.97/2.39 litapriori = 0
% 1.97/2.39 termapriori = 1
% 1.97/2.39 litaposteriori = 0
% 1.97/2.39 termaposteriori = 0
% 1.97/2.39 demodaposteriori = 0
% 1.97/2.39 ordereqreflfact = 0
% 1.97/2.39
% 1.97/2.39 litselect = negord
% 1.97/2.39
% 1.97/2.39 maxweight = 15
% 1.97/2.39 maxdepth = 30000
% 1.97/2.39 maxlength = 115
% 1.97/2.39 maxnrvars = 195
% 1.97/2.39 excuselevel = 1
% 1.97/2.39 increasemaxweight = 1
% 1.97/2.39
% 1.97/2.39 maxselected = 10000000
% 1.97/2.39 maxnrclauses = 10000000
% 1.97/2.39
% 1.97/2.39 showgenerated = 0
% 1.97/2.39 showkept = 0
% 1.97/2.39 showselected = 0
% 1.97/2.39 showdeleted = 0
% 1.97/2.39 showresimp = 1
% 1.97/2.39 showstatus = 2000
% 1.97/2.39
% 1.97/2.39 prologoutput = 1
% 1.97/2.39 nrgoals = 5000000
% 1.97/2.39 totalproof = 1
% 1.97/2.39
% 1.97/2.39 Symbols occurring in the translation:
% 1.97/2.39
% 1.97/2.39 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.97/2.39 . [1, 2] (w:1, o:58, a:1, s:1, b:0),
% 1.97/2.39 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 1.97/2.39 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.97/2.39 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.97/2.39 subclass [41, 2] (w:1, o:83, a:1, s:1, b:0),
% 1.97/2.39 member [43, 2] (w:1, o:84, a:1, s:1, b:0),
% 1.97/2.39 'not_subclass_element' [44, 2] (w:1, o:85, a:1, s:1, b:0),
% 1.97/2.39 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 1.97/2.39 'unordered_pair' [46, 2] (w:1, o:86, a:1, s:1, b:0),
% 1.97/2.39 singleton [47, 1] (w:1, o:39, a:1, s:1, b:0),
% 1.97/2.39 'ordered_pair' [48, 2] (w:1, o:87, a:1, s:1, b:0),
% 1.97/2.39 'cross_product' [50, 2] (w:1, o:88, a:1, s:1, b:0),
% 1.97/2.39 first [52, 1] (w:1, o:40, a:1, s:1, b:0),
% 1.97/2.39 second [53, 1] (w:1, o:41, a:1, s:1, b:0),
% 1.97/2.39 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 1.97/2.39 intersection [55, 2] (w:1, o:90, a:1, s:1, b:0),
% 1.97/2.39 complement [56, 1] (w:1, o:42, a:1, s:1, b:0),
% 1.97/2.39 union [57, 2] (w:1, o:91, a:1, s:1, b:0),
% 1.97/2.39 'symmetric_difference' [58, 2] (w:1, o:92, a:1, s:1, b:0),
% 1.97/2.39 restrict [60, 3] (w:1, o:95, a:1, s:1, b:0),
% 1.97/2.39 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.97/2.39 'domain_of' [62, 1] (w:1, o:44, a:1, s:1, b:0),
% 1.97/2.39 rotate [63, 1] (w:1, o:36, a:1, s:1, b:0),
% 1.97/2.39 flip [65, 1] (w:1, o:45, a:1, s:1, b:0),
% 1.97/2.39 inverse [66, 1] (w:1, o:46, a:1, s:1, b:0),
% 1.97/2.39 'range_of' [67, 1] (w:1, o:37, a:1, s:1, b:0),
% 1.97/2.39 domain [68, 3] (w:1, o:97, a:1, s:1, b:0),
% 1.97/2.39 range [69, 3] (w:1, o:98, a:1, s:1, b:0),
% 1.97/2.39 image [70, 2] (w:1, o:89, a:1, s:1, b:0),
% 1.97/2.39 successor [71, 1] (w:1, o:47, a:1, s:1, b:0),
% 1.97/2.39 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 1.97/2.39 inductive [73, 1] (w:1, o:48, a:1, s:1, b:0),
% 1.97/2.39 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.97/2.39 'sum_class' [75, 1] (w:1, o:49, a:1, s:1, b:0),
% 1.97/2.39 'power_class' [76, 1] (w:1, o:52, a:1, s:1, b:0),
% 1.97/2.39 compose [78, 2] (w:1, o:93, a:1, s:1, b:0),
% 1.97/2.39 'single_valued_class' [79, 1] (w:1, o:53, a:1, s:1, b:0),
% 1.97/2.39 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 1.97/2.39 function [82, 1] (w:1, o:54, a:1, s:1, b:0),
% 1.97/2.39 regular [83, 1] (w:1, o:38, a:1, s:1, b:0),
% 1.97/2.39 apply [84, 2] (w:1, o:94, a:1, s:1, b:0),
% 1.97/2.39 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.97/2.39 'one_to_one' [86, 1] (w:1, o:50, a:1, s:1, b:0),
% 1.97/2.39 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 1.97/2.39 diagonalise [88, 1] (w:1, o:55, a:1, s:1, b:0),
% 1.97/2.39 cantor [89, 1] (w:1, o:43, a:1, s:1, b:0),
% 1.97/2.39 operation [90, 1] (w:1, o:51, a:1, s:1, b:0),
% 1.97/2.39 compatible [94, 3] (w:1, o:96, a:1, s:1, b:0),
% 1.97/2.39 homomorphism [95, 3] (w:1, o:99, a:1, s:1, b:0),
% 1.97/2.39 'not_homomorphism1' [96, 3] (w:1, o:100, a:1, s:1, b:0),
% 1.97/2.39 'not_homomorphism2' [97, 3] (w:1, o:101, a:1, s:1, b:0),
% 1.97/2.39 'member_of' [98, 1] (w:1, o:56, a:1, s:1, b:0),
% 1.97/2.39 'member_of1' [99, 1] (w:1, o:57, a:1, s:1, b:0),
% 1.97/2.39 x [100, 0] (w:1, o:29, a:1, s:1, b:0),
% 1.97/2.39 y [101, 0] (w:1, o:30, a:1, s:1, b:0).
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Starting Search:
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Intermediate Status:
% 1.97/2.39 Generated: 4171
% 1.97/2.39 Kept: 2009
% 1.97/2.39 Inuse: 121
% 1.97/2.39 Deleted: 5
% 1.97/2.39 Deletedinuse: 2
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Intermediate Status:
% 1.97/2.39 Generated: 9978
% 1.97/2.39 Kept: 4012
% 1.97/2.39 Inuse: 195
% 1.97/2.39 Deleted: 10
% 1.97/2.39 Deletedinuse: 4
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Intermediate Status:
% 1.97/2.39 Generated: 15176
% 1.97/2.39 Kept: 6016
% 1.97/2.39 Inuse: 275
% 1.97/2.39 Deleted: 57
% 1.97/2.39 Deletedinuse: 39
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Intermediate Status:
% 1.97/2.39 Generated: 20704
% 1.97/2.39 Kept: 8035
% 1.97/2.39 Inuse: 355
% 1.97/2.39 Deleted: 65
% 1.97/2.39 Deletedinuse: 45
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Intermediate Status:
% 1.97/2.39 Generated: 27139
% 1.97/2.39 Kept: 10119
% 1.97/2.39 Inuse: 391
% 1.97/2.39 Deleted: 65
% 1.97/2.39 Deletedinuse: 45
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Intermediate Status:
% 1.97/2.39 Generated: 36642
% 1.97/2.39 Kept: 12189
% 1.97/2.39 Inuse: 430
% 1.97/2.39 Deleted: 67
% 1.97/2.39 Deletedinuse: 46
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Bliksems!, er is een bewijs:
% 1.97/2.39 % SZS status Unsatisfiable
% 1.97/2.39 % SZS output start Refutation
% 1.97/2.39
% 1.97/2.39 clause( 7, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.97/2.39 'unordered_pair'( X, Y ) ) ] )
% 1.97/2.39 .
% 1.97/2.39 clause( 11, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 1.97/2.39 singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.97/2.39 .
% 1.97/2.39 clause( 117, [ member( singleton( X ), 'universal_class' ) ] )
% 1.97/2.39 .
% 1.97/2.39 clause( 142, [ ~( member( singleton( x ), 'ordered_pair'( x, y ) ) ) ] )
% 1.97/2.39 .
% 1.97/2.39 clause( 564, [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ] )
% 1.97/2.39 .
% 1.97/2.39 clause( 13737, [] )
% 1.97/2.39 .
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 % SZS output end Refutation
% 1.97/2.39 found a proof!
% 1.97/2.39
% 1.97/2.39 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.97/2.39
% 1.97/2.39 initialclauses(
% 1.97/2.39 [ clause( 13739, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.97/2.39 ) ] )
% 1.97/2.39 , clause( 13740, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 1.97/2.39 , Y ) ] )
% 1.97/2.39 , clause( 13741, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 1.97/2.39 subclass( X, Y ) ] )
% 1.97/2.39 , clause( 13742, [ subclass( X, 'universal_class' ) ] )
% 1.97/2.39 , clause( 13743, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.97/2.39 , clause( 13744, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 1.97/2.39 , clause( 13745, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 1.97/2.39 ] )
% 1.97/2.39 , clause( 13746, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 1.97/2.39 =( X, Z ) ] )
% 1.97/2.39 , clause( 13747, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.97/2.39 'unordered_pair'( X, Y ) ) ] )
% 1.97/2.39 , clause( 13748, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.97/2.39 'unordered_pair'( Y, X ) ) ] )
% 1.97/2.39 , clause( 13749, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 1.97/2.39 )
% 1.97/2.39 , clause( 13750, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.97/2.39 , clause( 13751, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 1.97/2.39 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.97/2.39 , clause( 13752, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.97/2.39 ) ) ), member( X, Z ) ] )
% 1.97/2.39 , clause( 13753, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.97/2.39 ) ) ), member( Y, T ) ] )
% 1.97/2.39 , clause( 13754, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.97/2.39 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.97/2.39 , clause( 13755, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 1.97/2.39 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 1.97/2.39 , clause( 13756, [ subclass( 'element_relation', 'cross_product'(
% 1.97/2.39 'universal_class', 'universal_class' ) ) ] )
% 1.97/2.39 , clause( 13757, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 1.97/2.39 ), member( X, Y ) ] )
% 1.97/2.39 , clause( 13758, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.97/2.39 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 1.97/2.39 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 1.97/2.39 , clause( 13759, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.97/2.39 )
% 1.97/2.39 , clause( 13760, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 1.97/2.39 )
% 1.97/2.39 , clause( 13761, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 1.97/2.39 intersection( Y, Z ) ) ] )
% 1.97/2.39 , clause( 13762, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 1.97/2.39 )
% 1.97/2.39 , clause( 13763, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.97/2.39 complement( Y ) ), member( X, Y ) ] )
% 1.97/2.39 , clause( 13764, [ =( complement( intersection( complement( X ), complement(
% 1.97/2.39 Y ) ) ), union( X, Y ) ) ] )
% 1.97/2.39 , clause( 13765, [ =( intersection( complement( intersection( X, Y ) ),
% 1.97/2.39 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 1.97/2.39 'symmetric_difference'( X, Y ) ) ] )
% 1.97/2.39 , clause( 13766, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 1.97/2.39 X, Y, Z ) ) ] )
% 1.97/2.39 , clause( 13767, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 1.97/2.39 Z, X, Y ) ) ] )
% 1.97/2.39 , clause( 13768, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 1.97/2.39 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 1.97/2.39 , clause( 13769, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 1.97/2.39 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 1.97/2.39 'domain_of'( Y ) ) ] )
% 1.97/2.39 , clause( 13770, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 1.97/2.39 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.97/2.39 , clause( 13771, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.97/2.39 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 1.97/2.39 ] )
% 1.97/2.39 , clause( 13772, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.97/2.39 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 1.97/2.39 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.97/2.39 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 1.97/2.39 , Y ), rotate( T ) ) ] )
% 1.97/2.39 , clause( 13773, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 1.97/2.39 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.97/2.39 , clause( 13774, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.97/2.39 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 1.97/2.39 )
% 1.97/2.39 , clause( 13775, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.97/2.39 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 1.97/2.39 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.97/2.39 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 1.97/2.39 , Z ), flip( T ) ) ] )
% 1.97/2.39 , clause( 13776, [ =( 'domain_of'( flip( 'cross_product'( X,
% 1.97/2.39 'universal_class' ) ) ), inverse( X ) ) ] )
% 1.97/2.39 , clause( 13777, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 1.97/2.39 , clause( 13778, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 1.97/2.39 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 1.97/2.39 , clause( 13779, [ =( second( 'not_subclass_element'( restrict( X,
% 1.97/2.39 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 1.97/2.39 , clause( 13780, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 1.97/2.39 image( X, Y ) ) ] )
% 1.97/2.39 , clause( 13781, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 1.97/2.39 , clause( 13782, [ subclass( 'successor_relation', 'cross_product'(
% 1.97/2.39 'universal_class', 'universal_class' ) ) ] )
% 1.97/2.39 , clause( 13783, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 1.97/2.39 ) ), =( successor( X ), Y ) ] )
% 1.97/2.39 , clause( 13784, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 1.97/2.39 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 1.97/2.39 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 1.97/2.39 , clause( 13785, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 1.97/2.39 , clause( 13786, [ ~( inductive( X ) ), subclass( image(
% 1.97/2.39 'successor_relation', X ), X ) ] )
% 1.97/2.39 , clause( 13787, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 1.97/2.39 'successor_relation', X ), X ) ), inductive( X ) ] )
% 1.97/2.39 , clause( 13788, [ inductive( omega ) ] )
% 1.97/2.39 , clause( 13789, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 1.97/2.39 , clause( 13790, [ member( omega, 'universal_class' ) ] )
% 1.97/2.39 , clause( 13791, [ =( 'domain_of'( restrict( 'element_relation',
% 1.97/2.39 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 1.97/2.39 , clause( 13792, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 1.97/2.39 X ), 'universal_class' ) ] )
% 1.97/2.39 , clause( 13793, [ =( complement( image( 'element_relation', complement( X
% 1.97/2.39 ) ) ), 'power_class'( X ) ) ] )
% 1.97/2.39 , clause( 13794, [ ~( member( X, 'universal_class' ) ), member(
% 1.97/2.39 'power_class'( X ), 'universal_class' ) ] )
% 1.97/2.39 , clause( 13795, [ subclass( compose( X, Y ), 'cross_product'(
% 1.97/2.39 'universal_class', 'universal_class' ) ) ] )
% 1.97/2.39 , clause( 13796, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 1.97/2.39 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 1.97/2.39 , clause( 13797, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 1.97/2.39 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 1.97/2.39 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 1.97/2.39 ) ] )
% 1.97/2.39 , clause( 13798, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 1.97/2.39 inverse( X ) ), 'identity_relation' ) ] )
% 1.97/2.39 , clause( 13799, [ ~( subclass( compose( X, inverse( X ) ),
% 1.97/2.39 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 1.97/2.39 , clause( 13800, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 1.97/2.39 'universal_class', 'universal_class' ) ) ] )
% 1.97/2.39 , clause( 13801, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 1.97/2.39 , 'identity_relation' ) ] )
% 1.97/2.39 , clause( 13802, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 1.97/2.39 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 1.97/2.39 'identity_relation' ) ), function( X ) ] )
% 1.97/2.39 , clause( 13803, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 1.97/2.39 , member( image( X, Y ), 'universal_class' ) ] )
% 1.97/2.39 , clause( 13804, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.97/2.39 , clause( 13805, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 1.97/2.39 , 'null_class' ) ] )
% 1.97/2.39 , clause( 13806, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 1.97/2.39 Y ) ) ] )
% 1.97/2.39 , clause( 13807, [ function( choice ) ] )
% 1.97/2.39 , clause( 13808, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 1.97/2.39 ), member( apply( choice, X ), X ) ] )
% 1.97/2.39 , clause( 13809, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 1.97/2.39 , clause( 13810, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 1.97/2.39 , clause( 13811, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 1.97/2.39 'one_to_one'( X ) ] )
% 1.97/2.39 , clause( 13812, [ =( intersection( 'cross_product'( 'universal_class',
% 1.97/2.39 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 1.97/2.39 'universal_class' ), complement( compose( complement( 'element_relation'
% 1.97/2.39 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 1.97/2.39 , clause( 13813, [ =( intersection( inverse( 'subset_relation' ),
% 1.97/2.39 'subset_relation' ), 'identity_relation' ) ] )
% 1.97/2.39 , clause( 13814, [ =( complement( 'domain_of'( intersection( X,
% 1.97/2.39 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 1.97/2.39 , clause( 13815, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 1.97/2.39 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 1.97/2.39 , clause( 13816, [ ~( operation( X ) ), function( X ) ] )
% 1.97/2.39 , clause( 13817, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 1.97/2.39 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.97/2.39 ] )
% 1.97/2.39 , clause( 13818, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 1.97/2.39 'domain_of'( 'domain_of'( X ) ) ) ] )
% 1.97/2.39 , clause( 13819, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 1.97/2.39 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.97/2.39 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 1.97/2.39 operation( X ) ] )
% 1.97/2.39 , clause( 13820, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 1.97/2.39 , clause( 13821, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 1.97/2.39 Y ) ), 'domain_of'( X ) ) ] )
% 1.97/2.39 , clause( 13822, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 1.97/2.39 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 1.97/2.39 , clause( 13823, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 1.97/2.39 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 1.97/2.39 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 1.97/2.39 , clause( 13824, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 1.97/2.39 , clause( 13825, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 1.97/2.39 , clause( 13826, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 1.97/2.39 , clause( 13827, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 1.97/2.39 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 1.97/2.39 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 1.97/2.39 )
% 1.97/2.39 , clause( 13828, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.97/2.39 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.97/2.39 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.97/2.39 , Y ) ] )
% 1.97/2.39 , clause( 13829, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.97/2.39 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 1.97/2.39 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 1.97/2.39 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 1.97/2.39 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 1.97/2.39 )
% 1.97/2.39 , clause( 13830, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.97/2.39 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 1.97/2.39 , clause( 13831, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.97/2.39 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 1.97/2.39 , clause( 13832, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.97/2.39 ) ) ), member( X, 'universal_class' ) ] )
% 1.97/2.39 , clause( 13833, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.97/2.39 ) ) ), member( Y, 'universal_class' ) ] )
% 1.97/2.39 , clause( 13834, [ subclass( X, X ) ] )
% 1.97/2.39 , clause( 13835, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 1.97/2.39 X, Z ) ] )
% 1.97/2.39 , clause( 13836, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 1.97/2.39 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 1.97/2.39 , clause( 13837, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 1.97/2.39 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 1.97/2.39 , clause( 13838, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 1.97/2.39 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 1.97/2.39 , clause( 13839, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 1.97/2.39 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 1.97/2.39 , clause( 13840, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 1.97/2.39 )
% 1.97/2.39 , clause( 13841, [ ~( member( X, 'null_class' ) ) ] )
% 1.97/2.39 , clause( 13842, [ subclass( 'null_class', X ) ] )
% 1.97/2.39 , clause( 13843, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 1.97/2.39 )
% 1.97/2.39 , clause( 13844, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 1.97/2.39 , 'null_class' ), X ) ] )
% 1.97/2.39 , clause( 13845, [ member( 'null_class', 'universal_class' ) ] )
% 1.97/2.39 , clause( 13846, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 1.97/2.39 ] )
% 1.97/2.39 , clause( 13847, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 1.97/2.39 )
% 1.97/2.39 , clause( 13848, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 1.97/2.39 )
% 1.97/2.39 , clause( 13849, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 1.97/2.39 X ), singleton( Y ) ) ] )
% 1.97/2.39 , clause( 13850, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 1.97/2.39 Y ), singleton( Y ) ) ] )
% 1.97/2.39 , clause( 13851, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 1.97/2.39 'universal_class' ), member( Y, 'universal_class' ) ] )
% 1.97/2.39 , clause( 13852, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 1.97/2.39 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 1.97/2.39 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 1.97/2.39 , clause( 13853, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 1.97/2.39 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 1.97/2.39 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 1.97/2.39 , clause( 13854, [ ~( member( X, 'universal_class' ) ), ~( =(
% 1.97/2.39 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 1.97/2.39 , clause( 13855, [ ~( member( X, 'universal_class' ) ), ~( =(
% 1.97/2.39 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 1.97/2.39 , clause( 13856, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.97/2.39 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 1.97/2.39 , clause( 13857, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 1.97/2.39 'unordered_pair'( X, Z ), Y ) ] )
% 1.97/2.39 , clause( 13858, [ member( singleton( X ), 'universal_class' ) ] )
% 1.97/2.39 , clause( 13859, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 1.97/2.39 X ) ) ) ] )
% 1.97/2.39 , clause( 13860, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.97/2.39 singleton( X ) ) ] )
% 1.97/2.39 , clause( 13861, [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X
% 1.97/2.39 ), 'null_class' ) ) ] )
% 1.97/2.39 , clause( 13862, [ member( 'null_class', singleton( 'null_class' ) ) ] )
% 1.97/2.39 , clause( 13863, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 1.97/2.39 , clause( 13864, [ member( X, 'universal_class' ), =( singleton( X ),
% 1.97/2.39 'null_class' ) ] )
% 1.97/2.39 , clause( 13865, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 1.97/2.39 'universal_class' ) ), =( X, Y ) ] )
% 1.97/2.39 , clause( 13866, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 1.97/2.39 'universal_class' ) ), =( X, Y ) ] )
% 1.97/2.39 , clause( 13867, [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~(
% 1.97/2.39 member( Z, 'universal_class' ) ), =( Z, X ), =( Z, Y ) ] )
% 1.97/2.39 , clause( 13868, [ ~( member( X, 'universal_class' ) ), member( 'member_of'(
% 1.97/2.39 singleton( X ) ), 'universal_class' ) ] )
% 1.97/2.39 , clause( 13869, [ ~( member( X, 'universal_class' ) ), =( singleton(
% 1.97/2.39 'member_of'( singleton( X ) ) ), singleton( X ) ) ] )
% 1.97/2.39 , clause( 13870, [ member( 'member_of'( X ), 'universal_class' ), =(
% 1.97/2.39 'member_of'( X ), X ) ] )
% 1.97/2.39 , clause( 13871, [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X
% 1.97/2.39 ), X ) ] )
% 1.97/2.39 , clause( 13872, [ ~( member( X, 'universal_class' ) ), =( 'member_of'(
% 1.97/2.39 singleton( X ) ), X ) ] )
% 1.97/2.39 , clause( 13873, [ member( 'member_of1'( X ), 'universal_class' ), =(
% 1.97/2.39 'member_of'( X ), X ) ] )
% 1.97/2.39 , clause( 13874, [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'(
% 1.97/2.39 X ), X ) ] )
% 1.97/2.39 , clause( 13875, [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 1.97/2.39 'universal_class' ) ] )
% 1.97/2.39 , clause( 13876, [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y
% 1.97/2.39 , X ) ), =( 'member_of'( X ), Y ) ] )
% 1.97/2.39 , clause( 13877, [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ] )
% 1.97/2.39 , clause( 13878, [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' )
% 1.97/2.39 , =( singleton( Y ), X ) ] )
% 1.97/2.39 , clause( 13879, [ member( 'not_subclass_element'( intersection( complement(
% 1.97/2.39 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 1.97/2.39 'null_class' ), intersection( complement( singleton(
% 1.97/2.39 'not_subclass_element'( X, 'null_class' ) ) ), X ) ), =( singleton(
% 1.97/2.39 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 1.97/2.39 )
% 1.97/2.39 , clause( 13880, [ member( 'not_subclass_element'( intersection( complement(
% 1.97/2.39 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 1.97/2.39 'null_class' ), X ), =( singleton( 'not_subclass_element'( X,
% 1.97/2.39 'null_class' ) ), X ), =( X, 'null_class' ) ] )
% 1.97/2.39 , clause( 13881, [ ~( =( 'not_subclass_element'( intersection( complement(
% 1.97/2.39 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 1.97/2.39 'null_class' ), 'not_subclass_element'( X, 'null_class' ) ) ), =(
% 1.97/2.39 singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 1.97/2.39 'null_class' ) ] )
% 1.97/2.39 , clause( 13882, [ =( 'unordered_pair'( X, Y ), union( singleton( X ),
% 1.97/2.39 singleton( Y ) ) ) ] )
% 1.97/2.39 , clause( 13883, [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ] )
% 1.97/2.39 , clause( 13884, [ ~( member( singleton( x ), 'ordered_pair'( x, y ) ) ) ]
% 1.97/2.39 )
% 1.97/2.39 ] ).
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 subsumption(
% 1.97/2.39 clause( 7, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.97/2.39 'unordered_pair'( X, Y ) ) ] )
% 1.97/2.39 , clause( 13747, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.97/2.39 'unordered_pair'( X, Y ) ) ] )
% 1.97/2.39 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.97/2.39 ), ==>( 1, 1 )] ) ).
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 subsumption(
% 1.97/2.39 clause( 11, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 1.97/2.39 singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.97/2.39 , clause( 13751, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 1.97/2.39 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.97/2.39 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.97/2.39 )] ) ).
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 subsumption(
% 1.97/2.39 clause( 117, [ member( singleton( X ), 'universal_class' ) ] )
% 1.97/2.39 , clause( 13858, [ member( singleton( X ), 'universal_class' ) ] )
% 1.97/2.39 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 subsumption(
% 1.97/2.39 clause( 142, [ ~( member( singleton( x ), 'ordered_pair'( x, y ) ) ) ] )
% 1.97/2.39 , clause( 13884, [ ~( member( singleton( x ), 'ordered_pair'( x, y ) ) ) ]
% 1.97/2.39 )
% 1.97/2.39 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 paramod(
% 1.97/2.39 clause( 14099, [ member( singleton( X ), 'ordered_pair'( X, Y ) ), ~(
% 1.97/2.39 member( singleton( X ), 'universal_class' ) ) ] )
% 1.97/2.39 , clause( 11, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 1.97/2.39 singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.97/2.39 , 0, clause( 7, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.97/2.39 'unordered_pair'( X, Y ) ) ] )
% 1.97/2.39 , 1, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 1.97/2.39 :=( X, singleton( X ) ), :=( Y, 'unordered_pair'( X, singleton( Y ) ) )] )
% 1.97/2.39 ).
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 resolution(
% 1.97/2.39 clause( 14100, [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ] )
% 1.97/2.39 , clause( 14099, [ member( singleton( X ), 'ordered_pair'( X, Y ) ), ~(
% 1.97/2.39 member( singleton( X ), 'universal_class' ) ) ] )
% 1.97/2.39 , 1, clause( 117, [ member( singleton( X ), 'universal_class' ) ] )
% 1.97/2.39 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 1.97/2.39 , X )] )).
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 subsumption(
% 1.97/2.39 clause( 564, [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ] )
% 1.97/2.39 , clause( 14100, [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ] )
% 1.97/2.39 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.97/2.39 )] ) ).
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 resolution(
% 1.97/2.39 clause( 14101, [] )
% 1.97/2.39 , clause( 142, [ ~( member( singleton( x ), 'ordered_pair'( x, y ) ) ) ] )
% 1.97/2.39 , 0, clause( 564, [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ] )
% 1.97/2.39 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, x ), :=( Y, y )] )
% 1.97/2.39 ).
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 subsumption(
% 1.97/2.39 clause( 13737, [] )
% 1.97/2.39 , clause( 14101, [] )
% 1.97/2.39 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 end.
% 1.97/2.39
% 1.97/2.39 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.97/2.39
% 1.97/2.39 Memory use:
% 1.97/2.39
% 1.97/2.39 space for terms: 246456
% 1.97/2.39 space for clauses: 645554
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 clauses generated: 43114
% 1.97/2.39 clauses kept: 13738
% 1.97/2.39 clauses selected: 460
% 1.97/2.39 clauses deleted: 74
% 1.97/2.39 clauses inuse deleted: 47
% 1.97/2.39
% 1.97/2.39 subsentry: 101545
% 1.97/2.39 literals s-matched: 78864
% 1.97/2.39 literals matched: 76269
% 1.97/2.39 full subsumption: 38451
% 1.97/2.39
% 1.97/2.39 checksum: -1102458299
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Bliksem ended
%------------------------------------------------------------------------------