TSTP Solution File: SET102-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET102-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 22:47:07 EDT 2022
% Result : Unsatisfiable 4.57s 4.96s
% Output : Refutation 4.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET102-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : bliksem %s
% 0.11/0.33 % Computer : n018.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % DateTime : Sun Jul 10 12:34:57 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.68/1.07 *** allocated 10000 integers for termspace/termends
% 0.68/1.07 *** allocated 10000 integers for clauses
% 0.68/1.07 *** allocated 10000 integers for justifications
% 0.68/1.07 Bliksem 1.12
% 0.68/1.07
% 0.68/1.07
% 0.68/1.07 Automatic Strategy Selection
% 0.68/1.07
% 0.68/1.07 Clauses:
% 0.68/1.07 [
% 0.68/1.07 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.68/1.07 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.68/1.07 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.68/1.07 ,
% 0.68/1.07 [ subclass( X, 'universal_class' ) ],
% 0.68/1.07 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.68/1.07 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.68/1.07 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.68/1.07 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.68/1.07 ,
% 0.68/1.07 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.68/1.07 ) ) ],
% 0.68/1.07 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.68/1.07 ) ) ],
% 0.68/1.07 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.68/1.07 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.68/1.07 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.68/1.07 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.68/1.07 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.68/1.07 X, Z ) ],
% 0.68/1.07 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.68/1.07 Y, T ) ],
% 0.68/1.07 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.68/1.07 ), 'cross_product'( Y, T ) ) ],
% 0.68/1.07 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.68/1.07 ), second( X ) ), X ) ],
% 0.68/1.07 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.68/1.07 'universal_class' ) ) ],
% 0.68/1.07 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.68/1.07 Y ) ],
% 0.68/1.07 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.68/1.07 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.68/1.07 , Y ), 'element_relation' ) ],
% 0.68/1.07 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.68/1.07 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.68/1.07 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.68/1.07 Z ) ) ],
% 0.68/1.07 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.68/1.07 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.68/1.07 member( X, Y ) ],
% 0.68/1.07 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.68/1.07 union( X, Y ) ) ],
% 0.68/1.07 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.68/1.07 intersection( complement( X ), complement( Y ) ) ) ),
% 0.68/1.07 'symmetric_difference'( X, Y ) ) ],
% 0.68/1.07 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.68/1.07 ,
% 0.68/1.07 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.68/1.07 ,
% 0.68/1.07 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.68/1.07 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.68/1.07 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.68/1.07 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.68/1.07 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.68/1.07 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.68/1.07 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.68/1.07 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.68/1.07 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.68/1.07 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.68/1.07 'cross_product'( 'universal_class', 'universal_class' ),
% 0.68/1.07 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.68/1.07 Y ), rotate( T ) ) ],
% 0.68/1.07 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.68/1.07 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.68/1.07 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.68/1.07 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.68/1.07 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.68/1.07 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.68/1.07 'cross_product'( 'universal_class', 'universal_class' ),
% 0.68/1.07 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.68/1.07 Z ), flip( T ) ) ],
% 0.68/1.07 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.68/1.07 inverse( X ) ) ],
% 0.68/1.07 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.68/1.07 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.68/1.07 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.68/1.07 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.68/1.07 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.68/1.07 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.68/1.07 ],
% 0.68/1.07 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.68/1.07 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.68/1.07 'universal_class' ) ) ],
% 0.68/1.07 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.68/1.07 successor( X ), Y ) ],
% 0.68/1.07 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.68/1.07 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.68/1.07 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.68/1.07 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.68/1.07 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.68/1.07 ,
% 0.68/1.07 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.68/1.08 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.68/1.08 [ inductive( omega ) ],
% 0.68/1.08 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.68/1.08 [ member( omega, 'universal_class' ) ],
% 0.68/1.08 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.68/1.08 , 'sum_class'( X ) ) ],
% 0.68/1.08 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.68/1.08 'universal_class' ) ],
% 0.68/1.08 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.68/1.08 'power_class'( X ) ) ],
% 0.68/1.08 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.68/1.08 'universal_class' ) ],
% 0.68/1.08 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.68/1.08 'universal_class' ) ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.68/1.08 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.68/1.08 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.68/1.08 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.68/1.08 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.68/1.08 ) ],
% 0.68/1.08 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.68/1.08 , 'identity_relation' ) ],
% 0.68/1.08 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.68/1.08 'single_valued_class'( X ) ],
% 0.68/1.08 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.68/1.08 'universal_class' ) ) ],
% 0.68/1.08 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.68/1.08 'identity_relation' ) ],
% 0.68/1.08 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.68/1.08 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.68/1.08 , function( X ) ],
% 0.68/1.08 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.68/1.08 X, Y ), 'universal_class' ) ],
% 0.68/1.08 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.68/1.08 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.68/1.08 ) ],
% 0.68/1.08 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.68/1.08 [ function( choice ) ],
% 0.68/1.08 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.68/1.08 apply( choice, X ), X ) ],
% 0.68/1.08 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.68/1.08 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.68/1.08 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.68/1.08 ,
% 0.68/1.08 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.68/1.08 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.68/1.08 , complement( compose( complement( 'element_relation' ), inverse(
% 0.68/1.08 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.68/1.08 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.68/1.08 'identity_relation' ) ],
% 0.68/1.08 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.68/1.08 , diagonalise( X ) ) ],
% 0.68/1.08 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.68/1.08 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.68/1.08 [ ~( operation( X ) ), function( X ) ],
% 0.68/1.08 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.68/1.08 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.68/1.08 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.68/1.08 'domain_of'( X ) ) ) ],
% 0.68/1.08 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.68/1.08 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.68/1.08 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.68/1.08 X ) ],
% 0.68/1.08 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.68/1.08 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.68/1.08 'domain_of'( X ) ) ],
% 0.68/1.08 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.68/1.08 'domain_of'( Z ) ) ) ],
% 0.68/1.08 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.68/1.08 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.68/1.08 ), compatible( X, Y, Z ) ],
% 0.68/1.08 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.68/1.08 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.68/1.08 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.68/1.08 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.68/1.08 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.68/1.08 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.68/1.08 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.68/1.08 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.68/1.08 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.68/1.08 , Y ) ],
% 0.68/1.08 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.68/1.08 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.68/1.08 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.68/1.08 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.68/1.08 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.68/1.08 X, 'unordered_pair'( X, Y ) ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.68/1.08 Y, 'unordered_pair'( X, Y ) ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.68/1.08 X, 'universal_class' ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.68/1.08 Y, 'universal_class' ) ],
% 0.68/1.08 [ subclass( X, X ) ],
% 0.68/1.08 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.68/1.08 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.68/1.08 'not_subclass_element'( Y, X ), Y ) ],
% 0.68/1.08 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.68/1.08 'not_subclass_element'( Y, X ), Y ) ],
% 0.68/1.08 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.68/1.08 'not_subclass_element'( Y, X ), Y ) ],
% 0.68/1.08 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.68/1.08 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.68/1.08 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.68/1.08 [ ~( member( X, 'null_class' ) ) ],
% 0.68/1.08 [ subclass( 'null_class', X ) ],
% 0.68/1.08 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.68/1.08 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.68/1.08 ), X ) ],
% 0.68/1.08 [ member( 'null_class', 'universal_class' ) ],
% 0.68/1.08 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.68/1.08 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.68/1.08 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.68/1.08 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.68/1.08 Y ) ) ],
% 0.68/1.08 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.68/1.08 Y ) ) ],
% 0.68/1.08 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.68/1.08 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.68/1.08 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.68/1.08 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.68/1.08 'universal_class' ) ) ), =( Y, Z ) ],
% 0.68/1.08 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.68/1.08 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.68/1.08 'universal_class' ) ) ), =( X, Z ) ],
% 0.68/1.08 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.68/1.08 'null_class' ) ) ],
% 0.68/1.08 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.68/1.08 'null_class' ) ) ],
% 0.68/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.68/1.08 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 2.06/2.44 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 2.06/2.44 X, Z ), Y ) ],
% 2.06/2.44 [ member( singleton( X ), 'universal_class' ) ],
% 2.06/2.44 [ member( singleton( X ), 'unordered_pair'( Y, singleton( X ) ) ) ],
% 2.06/2.44 [ ~( member( X, 'universal_class' ) ), member( X, singleton( X ) ) ]
% 2.06/2.44 ,
% 2.06/2.44 [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X ),
% 2.06/2.44 'null_class' ) ) ],
% 2.06/2.44 [ member( 'null_class', singleton( 'null_class' ) ) ],
% 2.06/2.44 [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ],
% 2.06/2.44 [ member( X, 'universal_class' ), =( singleton( X ), 'null_class' ) ]
% 2.06/2.44 ,
% 2.06/2.44 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 2.06/2.44 'universal_class' ) ), =( X, Y ) ],
% 2.06/2.44 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 2.06/2.44 'universal_class' ) ), =( X, Y ) ],
% 2.06/2.44 [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~( member( Z,
% 2.06/2.44 'universal_class' ) ), =( Z, X ), =( Z, Y ) ],
% 2.06/2.44 [ ~( member( X, 'universal_class' ) ), member( 'member_of'( singleton( X
% 2.06/2.44 ) ), 'universal_class' ) ],
% 2.06/2.44 [ ~( member( X, 'universal_class' ) ), =( singleton( 'member_of'(
% 2.06/2.44 singleton( X ) ) ), singleton( X ) ) ],
% 2.06/2.44 [ member( 'member_of'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 2.06/2.44 ) ],
% 2.06/2.44 [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X ), X ) ],
% 2.06/2.44 [ ~( member( X, 'universal_class' ) ), =( 'member_of'( singleton( X ) )
% 2.06/2.44 , X ) ],
% 2.06/2.44 [ member( 'member_of1'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 2.06/2.44 ) ],
% 2.06/2.44 [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'( X ), X ) ]
% 2.06/2.44 ,
% 2.06/2.44 [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 2.06/2.44 'universal_class' ) ],
% 2.06/2.44 [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y, X ) ), =(
% 2.06/2.44 'member_of'( X ), Y ) ],
% 2.06/2.44 [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ],
% 2.06/2.44 [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' ), =( singleton(
% 2.06/2.44 Y ), X ) ],
% 2.06/2.44 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 2.06/2.44 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 2.06/2.44 intersection( complement( singleton( 'not_subclass_element'( X,
% 2.06/2.44 'null_class' ) ) ), X ) ), =( singleton( 'not_subclass_element'( X,
% 2.06/2.44 'null_class' ) ), X ), =( X, 'null_class' ) ],
% 2.06/2.44 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 2.06/2.44 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ), X ),
% 2.06/2.44 =( singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 2.06/2.44 'null_class' ) ],
% 2.06/2.44 [ ~( =( 'not_subclass_element'( intersection( complement( singleton(
% 2.06/2.44 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 2.06/2.44 'not_subclass_element'( X, 'null_class' ) ) ), =( singleton(
% 2.06/2.44 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 2.06/2.44 ,
% 2.06/2.44 [ =( 'unordered_pair'( X, Y ), union( singleton( X ), singleton( Y ) ) )
% 2.06/2.44 ],
% 2.06/2.44 [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ],
% 2.06/2.44 [ ~( member( 'unordered_pair'( x, singleton( y ) ), 'ordered_pair'( x, y
% 2.06/2.44 ) ) ) ]
% 2.06/2.44 ] .
% 2.06/2.44
% 2.06/2.44
% 2.06/2.44 percentage equality = 0.294915, percentage horn = 0.828767
% 2.06/2.44 This is a problem with some equality
% 2.06/2.44
% 2.06/2.44
% 2.06/2.44
% 2.06/2.44 Options Used:
% 2.06/2.44
% 2.06/2.44 useres = 1
% 2.06/2.44 useparamod = 1
% 2.06/2.44 useeqrefl = 1
% 2.06/2.44 useeqfact = 1
% 2.06/2.44 usefactor = 1
% 2.06/2.44 usesimpsplitting = 0
% 2.06/2.44 usesimpdemod = 5
% 2.06/2.44 usesimpres = 3
% 2.06/2.44
% 2.06/2.44 resimpinuse = 1000
% 2.06/2.44 resimpclauses = 20000
% 2.06/2.44 substype = eqrewr
% 2.06/2.44 backwardsubs = 1
% 2.06/2.44 selectoldest = 5
% 2.06/2.44
% 2.06/2.44 litorderings [0] = split
% 2.06/2.44 litorderings [1] = extend the termordering, first sorting on arguments
% 2.06/2.44
% 2.06/2.44 termordering = kbo
% 2.06/2.44
% 2.06/2.44 litapriori = 0
% 2.06/2.44 termapriori = 1
% 2.06/2.44 litaposteriori = 0
% 2.06/2.44 termaposteriori = 0
% 2.06/2.44 demodaposteriori = 0
% 2.06/2.44 ordereqreflfact = 0
% 2.06/2.44
% 2.06/2.44 litselect = negord
% 2.06/2.44
% 2.06/2.44 maxweight = 15
% 2.06/2.44 maxdepth = 30000
% 2.06/2.44 maxlength = 115
% 2.06/2.44 maxnrvars = 195
% 2.06/2.44 excuselevel = 1
% 2.06/2.44 increasemaxweight = 1
% 2.06/2.44
% 2.06/2.44 maxselected = 10000000
% 2.06/2.44 maxnrclauses = 10000000
% 2.06/2.44
% 2.06/2.44 showgenerated = 0
% 2.06/2.44 showkept = 0
% 2.06/2.44 showselected = 0
% 2.06/2.44 showdeleted = 0
% 2.06/2.44 showresimp = 1
% 2.06/2.44 showstatus = 2000
% 2.06/2.44
% 2.06/2.44 prologoutput = 1
% 2.06/2.44 nrgoals = 5000000
% 2.06/2.44 totalproof = 1
% 2.06/2.44
% 2.06/2.44 Symbols occurring in the translation:
% 4.57/4.95
% 4.57/4.95 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 4.57/4.95 . [1, 2] (w:1, o:58, a:1, s:1, b:0),
% 4.57/4.95 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 4.57/4.95 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 4.57/4.95 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 4.57/4.95 subclass [41, 2] (w:1, o:83, a:1, s:1, b:0),
% 4.57/4.95 member [43, 2] (w:1, o:84, a:1, s:1, b:0),
% 4.57/4.95 'not_subclass_element' [44, 2] (w:1, o:85, a:1, s:1, b:0),
% 4.57/4.95 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 4.57/4.95 'unordered_pair' [46, 2] (w:1, o:86, a:1, s:1, b:0),
% 4.57/4.95 singleton [47, 1] (w:1, o:39, a:1, s:1, b:0),
% 4.57/4.95 'ordered_pair' [48, 2] (w:1, o:87, a:1, s:1, b:0),
% 4.57/4.95 'cross_product' [50, 2] (w:1, o:88, a:1, s:1, b:0),
% 4.57/4.95 first [52, 1] (w:1, o:40, a:1, s:1, b:0),
% 4.57/4.95 second [53, 1] (w:1, o:41, a:1, s:1, b:0),
% 4.57/4.95 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 4.57/4.95 intersection [55, 2] (w:1, o:90, a:1, s:1, b:0),
% 4.57/4.95 complement [56, 1] (w:1, o:42, a:1, s:1, b:0),
% 4.57/4.95 union [57, 2] (w:1, o:91, a:1, s:1, b:0),
% 4.57/4.96 'symmetric_difference' [58, 2] (w:1, o:92, a:1, s:1, b:0),
% 4.57/4.96 restrict [60, 3] (w:1, o:95, a:1, s:1, b:0),
% 4.57/4.96 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 4.57/4.96 'domain_of' [62, 1] (w:1, o:44, a:1, s:1, b:0),
% 4.57/4.96 rotate [63, 1] (w:1, o:36, a:1, s:1, b:0),
% 4.57/4.96 flip [65, 1] (w:1, o:45, a:1, s:1, b:0),
% 4.57/4.96 inverse [66, 1] (w:1, o:46, a:1, s:1, b:0),
% 4.57/4.96 'range_of' [67, 1] (w:1, o:37, a:1, s:1, b:0),
% 4.57/4.96 domain [68, 3] (w:1, o:97, a:1, s:1, b:0),
% 4.57/4.96 range [69, 3] (w:1, o:98, a:1, s:1, b:0),
% 4.57/4.96 image [70, 2] (w:1, o:89, a:1, s:1, b:0),
% 4.57/4.96 successor [71, 1] (w:1, o:47, a:1, s:1, b:0),
% 4.57/4.96 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 4.57/4.96 inductive [73, 1] (w:1, o:48, a:1, s:1, b:0),
% 4.57/4.96 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 4.57/4.96 'sum_class' [75, 1] (w:1, o:49, a:1, s:1, b:0),
% 4.57/4.96 'power_class' [76, 1] (w:1, o:52, a:1, s:1, b:0),
% 4.57/4.96 compose [78, 2] (w:1, o:93, a:1, s:1, b:0),
% 4.57/4.96 'single_valued_class' [79, 1] (w:1, o:53, a:1, s:1, b:0),
% 4.57/4.96 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 4.57/4.96 function [82, 1] (w:1, o:54, a:1, s:1, b:0),
% 4.57/4.96 regular [83, 1] (w:1, o:38, a:1, s:1, b:0),
% 4.57/4.96 apply [84, 2] (w:1, o:94, a:1, s:1, b:0),
% 4.57/4.96 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 4.57/4.96 'one_to_one' [86, 1] (w:1, o:50, a:1, s:1, b:0),
% 4.57/4.96 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 4.57/4.96 diagonalise [88, 1] (w:1, o:55, a:1, s:1, b:0),
% 4.57/4.96 cantor [89, 1] (w:1, o:43, a:1, s:1, b:0),
% 4.57/4.96 operation [90, 1] (w:1, o:51, a:1, s:1, b:0),
% 4.57/4.96 compatible [94, 3] (w:1, o:96, a:1, s:1, b:0),
% 4.57/4.96 homomorphism [95, 3] (w:1, o:99, a:1, s:1, b:0),
% 4.57/4.96 'not_homomorphism1' [96, 3] (w:1, o:100, a:1, s:1, b:0),
% 4.57/4.96 'not_homomorphism2' [97, 3] (w:1, o:101, a:1, s:1, b:0),
% 4.57/4.96 'member_of' [98, 1] (w:1, o:56, a:1, s:1, b:0),
% 4.57/4.96 'member_of1' [99, 1] (w:1, o:57, a:1, s:1, b:0),
% 4.57/4.96 x [100, 0] (w:1, o:29, a:1, s:1, b:0),
% 4.57/4.96 y [101, 0] (w:1, o:30, a:1, s:1, b:0).
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 Starting Search:
% 4.57/4.96
% 4.57/4.96 Resimplifying inuse:
% 4.57/4.96 Done
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 Intermediate Status:
% 4.57/4.96 Generated: 4171
% 4.57/4.96 Kept: 2009
% 4.57/4.96 Inuse: 121
% 4.57/4.96 Deleted: 5
% 4.57/4.96 Deletedinuse: 2
% 4.57/4.96
% 4.57/4.96 Resimplifying inuse:
% 4.57/4.96 Done
% 4.57/4.96
% 4.57/4.96 Resimplifying inuse:
% 4.57/4.96 Done
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 Intermediate Status:
% 4.57/4.96 Generated: 9978
% 4.57/4.96 Kept: 4012
% 4.57/4.96 Inuse: 195
% 4.57/4.96 Deleted: 10
% 4.57/4.96 Deletedinuse: 4
% 4.57/4.96
% 4.57/4.96 Resimplifying inuse:
% 4.57/4.96 Done
% 4.57/4.96
% 4.57/4.96 Resimplifying inuse:
% 4.57/4.96 Done
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 Intermediate Status:
% 4.57/4.96 Generated: 15176
% 4.57/4.96 Kept: 6016
% 4.57/4.96 Inuse: 275
% 4.57/4.96 Deleted: 57
% 4.57/4.96 Deletedinuse: 39
% 4.57/4.96
% 4.57/4.96 Resimplifying inuse:
% 4.57/4.96 Done
% 4.57/4.96
% 4.57/4.96 Resimplifying inuse:
% 4.57/4.96 Done
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 Intermediate Status:
% 4.57/4.96 Generated: 20704
% 4.57/4.96 Kept: 8035
% 4.57/4.96 Inuse: 355
% 4.57/4.96 Deleted: 65
% 4.57/4.96 Deletedinuse: 45
% 4.57/4.96
% 4.57/4.96 Resimplifying inuse:
% 4.57/4.96 Done
% 4.57/4.96
% 4.57/4.96 Resimplifying inuse:
% 4.57/4.96 Done
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 Intermediate Status:
% 4.57/4.96 Generated: 27139
% 4.57/4.96 Kept: 10119
% 4.57/4.96 Inuse: 391
% 4.57/4.96 Deleted: 65
% 4.57/4.96 Deletedinuse: 45
% 4.57/4.96
% 4.57/4.96 Resimplifying inuse:
% 4.57/4.96 Done
% 4.57/4.96
% 4.57/4.96 Resimplifying inuse:
% 4.57/4.96 Done
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 Intermediate Status:
% 4.57/4.96 Generated: 36642
% 4.57/4.96 Kept: 12189
% 4.57/4.96 Inuse: 430
% 4.57/4.96 Deleted: 67
% 4.57/4.96 Deletedinuse: 46
% 4.57/4.96
% 4.57/4.96 Resimplifying inuse:
% 4.57/4.96 Done
% 4.57/4.96
% 4.57/4.96 Resimplifying inuse:
% 4.57/4.96 Done
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 Intermediate Status:
% 4.57/4.96 Generated: 46682
% 4.57/4.96 Kept: 15863
% 4.57/4.96 Inuse: 470
% 4.57/4.96 Deleted: 77
% 4.57/4.96 Deletedinuse: 51
% 4.57/4.96
% 4.57/4.96 Resimplifying inuse:
% 4.57/4.96 Done
% 4.57/4.96
% 4.57/4.96 Resimplifying inuse:
% 4.57/4.96 Done
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 Intermediate Status:
% 4.57/4.96 Generated: 52344
% 4.57/4.96 Kept: 17879
% 4.57/4.96 Inuse: 484
% 4.57/4.96 Deleted: 78
% 4.57/4.96 Deletedinuse: 52
% 4.57/4.96
% 4.57/4.96 Resimplifying inuse:
% 4.57/4.96 Done
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 Intermediate Status:
% 4.57/4.96 Generated: 60799
% 4.57/4.96 Kept: 19892
% 4.57/4.96 Inuse: 486
% 4.57/4.96 Deleted: 79
% 4.57/4.96 Deletedinuse: 53
% 4.57/4.96
% 4.57/4.96 Resimplifying clauses:
% 4.57/4.96
% 4.57/4.96 Bliksems!, er is een bewijs:
% 4.57/4.96 % SZS status Unsatisfiable
% 4.57/4.96 % SZS output start Refutation
% 4.57/4.96
% 4.57/4.96 clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.57/4.96 'unordered_pair'( Y, X ) ) ] )
% 4.57/4.96 .
% 4.57/4.96 clause( 9, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ] )
% 4.57/4.96 .
% 4.57/4.96 clause( 11, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 4.57/4.96 singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 4.57/4.96 .
% 4.57/4.96 clause( 142, [ ~( member( 'unordered_pair'( x, singleton( y ) ),
% 4.57/4.96 'ordered_pair'( x, y ) ) ) ] )
% 4.57/4.96 .
% 4.57/4.96 clause( 563, [ member( 'unordered_pair'( X, singleton( Y ) ),
% 4.57/4.96 'ordered_pair'( X, Y ) ) ] )
% 4.57/4.96 .
% 4.57/4.96 clause( 20032, [] )
% 4.57/4.96 .
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 % SZS output end Refutation
% 4.57/4.96 found a proof!
% 4.57/4.96
% 4.57/4.96 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 4.57/4.96
% 4.57/4.96 initialclauses(
% 4.57/4.96 [ clause( 20034, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 4.57/4.96 ) ] )
% 4.57/4.96 , clause( 20035, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 4.57/4.96 , Y ) ] )
% 4.57/4.96 , clause( 20036, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 4.57/4.96 subclass( X, Y ) ] )
% 4.57/4.96 , clause( 20037, [ subclass( X, 'universal_class' ) ] )
% 4.57/4.96 , clause( 20038, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 4.57/4.96 , clause( 20039, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 4.57/4.96 , clause( 20040, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 4.57/4.96 ] )
% 4.57/4.96 , clause( 20041, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 4.57/4.96 =( X, Z ) ] )
% 4.57/4.96 , clause( 20042, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.57/4.96 'unordered_pair'( X, Y ) ) ] )
% 4.57/4.96 , clause( 20043, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.57/4.96 'unordered_pair'( Y, X ) ) ] )
% 4.57/4.96 , clause( 20044, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 4.57/4.96 )
% 4.57/4.96 , clause( 20045, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 4.57/4.96 , clause( 20046, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 4.57/4.96 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 4.57/4.96 , clause( 20047, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.57/4.96 ) ) ), member( X, Z ) ] )
% 4.57/4.96 , clause( 20048, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.57/4.96 ) ) ), member( Y, T ) ] )
% 4.57/4.96 , clause( 20049, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 4.57/4.96 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 4.57/4.96 , clause( 20050, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 4.57/4.96 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 4.57/4.96 , clause( 20051, [ subclass( 'element_relation', 'cross_product'(
% 4.57/4.96 'universal_class', 'universal_class' ) ) ] )
% 4.57/4.96 , clause( 20052, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 4.57/4.96 ), member( X, Y ) ] )
% 4.57/4.96 , clause( 20053, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 4.57/4.96 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 4.57/4.96 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 4.57/4.96 , clause( 20054, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 4.57/4.96 )
% 4.57/4.96 , clause( 20055, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 4.57/4.96 )
% 4.57/4.96 , clause( 20056, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 4.57/4.96 intersection( Y, Z ) ) ] )
% 4.57/4.96 , clause( 20057, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 4.57/4.96 )
% 4.57/4.96 , clause( 20058, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.57/4.96 complement( Y ) ), member( X, Y ) ] )
% 4.57/4.96 , clause( 20059, [ =( complement( intersection( complement( X ), complement(
% 4.57/4.96 Y ) ) ), union( X, Y ) ) ] )
% 4.57/4.96 , clause( 20060, [ =( intersection( complement( intersection( X, Y ) ),
% 4.57/4.96 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 4.57/4.96 'symmetric_difference'( X, Y ) ) ] )
% 4.57/4.96 , clause( 20061, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 4.57/4.96 X, Y, Z ) ) ] )
% 4.57/4.96 , clause( 20062, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 4.57/4.96 Z, X, Y ) ) ] )
% 4.57/4.96 , clause( 20063, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 4.57/4.96 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 4.57/4.96 , clause( 20064, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 4.57/4.96 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 4.57/4.96 'domain_of'( Y ) ) ] )
% 4.57/4.96 , clause( 20065, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 4.57/4.96 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 4.57/4.96 , clause( 20066, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 4.57/4.96 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 4.57/4.96 ] )
% 4.57/4.96 , clause( 20067, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 4.57/4.96 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 4.57/4.96 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 4.57/4.96 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 4.57/4.96 , Y ), rotate( T ) ) ] )
% 4.57/4.96 , clause( 20068, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 4.57/4.96 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 4.57/4.96 , clause( 20069, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 4.57/4.96 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 4.57/4.96 )
% 4.57/4.96 , clause( 20070, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 4.57/4.96 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 4.57/4.96 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 4.57/4.96 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 4.57/4.96 , Z ), flip( T ) ) ] )
% 4.57/4.96 , clause( 20071, [ =( 'domain_of'( flip( 'cross_product'( X,
% 4.57/4.96 'universal_class' ) ) ), inverse( X ) ) ] )
% 4.57/4.96 , clause( 20072, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 4.57/4.96 , clause( 20073, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 4.57/4.96 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 4.57/4.96 , clause( 20074, [ =( second( 'not_subclass_element'( restrict( X,
% 4.57/4.96 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 4.57/4.96 , clause( 20075, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 4.57/4.96 image( X, Y ) ) ] )
% 4.57/4.96 , clause( 20076, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 4.57/4.96 , clause( 20077, [ subclass( 'successor_relation', 'cross_product'(
% 4.57/4.96 'universal_class', 'universal_class' ) ) ] )
% 4.57/4.96 , clause( 20078, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 4.57/4.96 ) ), =( successor( X ), Y ) ] )
% 4.57/4.96 , clause( 20079, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 4.57/4.96 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 4.57/4.96 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 4.57/4.96 , clause( 20080, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 4.57/4.96 , clause( 20081, [ ~( inductive( X ) ), subclass( image(
% 4.57/4.96 'successor_relation', X ), X ) ] )
% 4.57/4.96 , clause( 20082, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 4.57/4.96 'successor_relation', X ), X ) ), inductive( X ) ] )
% 4.57/4.96 , clause( 20083, [ inductive( omega ) ] )
% 4.57/4.96 , clause( 20084, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 4.57/4.96 , clause( 20085, [ member( omega, 'universal_class' ) ] )
% 4.57/4.96 , clause( 20086, [ =( 'domain_of'( restrict( 'element_relation',
% 4.57/4.96 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 4.57/4.96 , clause( 20087, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 4.57/4.96 X ), 'universal_class' ) ] )
% 4.57/4.96 , clause( 20088, [ =( complement( image( 'element_relation', complement( X
% 4.57/4.96 ) ) ), 'power_class'( X ) ) ] )
% 4.57/4.96 , clause( 20089, [ ~( member( X, 'universal_class' ) ), member(
% 4.57/4.96 'power_class'( X ), 'universal_class' ) ] )
% 4.57/4.96 , clause( 20090, [ subclass( compose( X, Y ), 'cross_product'(
% 4.57/4.96 'universal_class', 'universal_class' ) ) ] )
% 4.57/4.96 , clause( 20091, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 4.57/4.96 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 4.57/4.96 , clause( 20092, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 4.57/4.96 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 4.57/4.96 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 4.57/4.96 ) ] )
% 4.57/4.96 , clause( 20093, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 4.57/4.96 inverse( X ) ), 'identity_relation' ) ] )
% 4.57/4.96 , clause( 20094, [ ~( subclass( compose( X, inverse( X ) ),
% 4.57/4.96 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 4.57/4.96 , clause( 20095, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 4.57/4.96 'universal_class', 'universal_class' ) ) ] )
% 4.57/4.96 , clause( 20096, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 4.57/4.96 , 'identity_relation' ) ] )
% 4.57/4.96 , clause( 20097, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 4.57/4.96 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 4.57/4.96 'identity_relation' ) ), function( X ) ] )
% 4.57/4.96 , clause( 20098, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 4.57/4.96 , member( image( X, Y ), 'universal_class' ) ] )
% 4.57/4.96 , clause( 20099, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 4.57/4.96 , clause( 20100, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 4.57/4.96 , 'null_class' ) ] )
% 4.57/4.96 , clause( 20101, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 4.57/4.96 Y ) ) ] )
% 4.57/4.96 , clause( 20102, [ function( choice ) ] )
% 4.57/4.96 , clause( 20103, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 4.57/4.96 ), member( apply( choice, X ), X ) ] )
% 4.57/4.96 , clause( 20104, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 4.57/4.96 , clause( 20105, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 4.57/4.96 , clause( 20106, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 4.57/4.96 'one_to_one'( X ) ] )
% 4.57/4.96 , clause( 20107, [ =( intersection( 'cross_product'( 'universal_class',
% 4.57/4.96 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 4.57/4.96 'universal_class' ), complement( compose( complement( 'element_relation'
% 4.57/4.96 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 4.57/4.96 , clause( 20108, [ =( intersection( inverse( 'subset_relation' ),
% 4.57/4.96 'subset_relation' ), 'identity_relation' ) ] )
% 4.57/4.96 , clause( 20109, [ =( complement( 'domain_of'( intersection( X,
% 4.57/4.96 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 4.57/4.96 , clause( 20110, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 4.57/4.96 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 4.57/4.96 , clause( 20111, [ ~( operation( X ) ), function( X ) ] )
% 4.57/4.96 , clause( 20112, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 4.57/4.96 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 4.57/4.96 ] )
% 4.57/4.96 , clause( 20113, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 4.57/4.96 'domain_of'( 'domain_of'( X ) ) ) ] )
% 4.57/4.96 , clause( 20114, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 4.57/4.96 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 4.57/4.96 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 4.57/4.96 operation( X ) ] )
% 4.57/4.96 , clause( 20115, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 4.57/4.96 , clause( 20116, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 4.57/4.96 Y ) ), 'domain_of'( X ) ) ] )
% 4.57/4.96 , clause( 20117, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 4.57/4.96 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 4.57/4.96 , clause( 20118, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 4.57/4.96 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 4.57/4.96 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 4.57/4.96 , clause( 20119, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 4.57/4.96 , clause( 20120, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 4.57/4.96 , clause( 20121, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 4.57/4.96 , clause( 20122, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 4.57/4.96 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 4.57/4.96 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 4.57/4.96 )
% 4.57/4.96 , clause( 20123, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 4.57/4.96 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 4.57/4.96 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 4.57/4.96 , Y ) ] )
% 4.57/4.96 , clause( 20124, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 4.57/4.96 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 4.57/4.96 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 4.57/4.96 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 4.57/4.96 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 4.57/4.96 )
% 4.57/4.96 , clause( 20125, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.57/4.96 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 4.57/4.96 , clause( 20126, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.57/4.96 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 4.57/4.96 , clause( 20127, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.57/4.96 ) ) ), member( X, 'universal_class' ) ] )
% 4.57/4.96 , clause( 20128, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.57/4.96 ) ) ), member( Y, 'universal_class' ) ] )
% 4.57/4.96 , clause( 20129, [ subclass( X, X ) ] )
% 4.57/4.96 , clause( 20130, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 4.57/4.96 X, Z ) ] )
% 4.57/4.96 , clause( 20131, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 4.57/4.96 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 4.57/4.96 , clause( 20132, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 4.57/4.96 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 4.57/4.96 , clause( 20133, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 4.57/4.96 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 4.57/4.96 , clause( 20134, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 4.57/4.96 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 4.57/4.96 , clause( 20135, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 4.57/4.96 )
% 4.57/4.96 , clause( 20136, [ ~( member( X, 'null_class' ) ) ] )
% 4.57/4.96 , clause( 20137, [ subclass( 'null_class', X ) ] )
% 4.57/4.96 , clause( 20138, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 4.57/4.96 )
% 4.57/4.96 , clause( 20139, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 4.57/4.96 , 'null_class' ), X ) ] )
% 4.57/4.96 , clause( 20140, [ member( 'null_class', 'universal_class' ) ] )
% 4.57/4.96 , clause( 20141, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 4.57/4.96 ] )
% 4.57/4.96 , clause( 20142, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 4.57/4.96 )
% 4.57/4.96 , clause( 20143, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 4.57/4.96 )
% 4.57/4.96 , clause( 20144, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 4.57/4.96 X ), singleton( Y ) ) ] )
% 4.57/4.96 , clause( 20145, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 4.57/4.96 Y ), singleton( Y ) ) ] )
% 4.57/4.96 , clause( 20146, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 4.57/4.96 'universal_class' ), member( Y, 'universal_class' ) ] )
% 4.57/4.96 , clause( 20147, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 4.57/4.96 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 4.57/4.96 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 4.57/4.96 , clause( 20148, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 4.57/4.96 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 4.57/4.96 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 4.57/4.96 , clause( 20149, [ ~( member( X, 'universal_class' ) ), ~( =(
% 4.57/4.96 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 4.57/4.96 , clause( 20150, [ ~( member( X, 'universal_class' ) ), ~( =(
% 4.57/4.96 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 4.57/4.96 , clause( 20151, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 4.57/4.96 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 4.57/4.96 , clause( 20152, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 4.57/4.96 'unordered_pair'( X, Z ), Y ) ] )
% 4.57/4.96 , clause( 20153, [ member( singleton( X ), 'universal_class' ) ] )
% 4.57/4.96 , clause( 20154, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 4.57/4.96 X ) ) ) ] )
% 4.57/4.96 , clause( 20155, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.57/4.96 singleton( X ) ) ] )
% 4.57/4.96 , clause( 20156, [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X
% 4.57/4.96 ), 'null_class' ) ) ] )
% 4.57/4.96 , clause( 20157, [ member( 'null_class', singleton( 'null_class' ) ) ] )
% 4.57/4.96 , clause( 20158, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 4.57/4.96 , clause( 20159, [ member( X, 'universal_class' ), =( singleton( X ),
% 4.57/4.96 'null_class' ) ] )
% 4.57/4.96 , clause( 20160, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 4.57/4.96 'universal_class' ) ), =( X, Y ) ] )
% 4.57/4.96 , clause( 20161, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 4.57/4.96 'universal_class' ) ), =( X, Y ) ] )
% 4.57/4.96 , clause( 20162, [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~(
% 4.57/4.96 member( Z, 'universal_class' ) ), =( Z, X ), =( Z, Y ) ] )
% 4.57/4.96 , clause( 20163, [ ~( member( X, 'universal_class' ) ), member( 'member_of'(
% 4.57/4.96 singleton( X ) ), 'universal_class' ) ] )
% 4.57/4.96 , clause( 20164, [ ~( member( X, 'universal_class' ) ), =( singleton(
% 4.57/4.96 'member_of'( singleton( X ) ) ), singleton( X ) ) ] )
% 4.57/4.96 , clause( 20165, [ member( 'member_of'( X ), 'universal_class' ), =(
% 4.57/4.96 'member_of'( X ), X ) ] )
% 4.57/4.96 , clause( 20166, [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X
% 4.57/4.96 ), X ) ] )
% 4.57/4.96 , clause( 20167, [ ~( member( X, 'universal_class' ) ), =( 'member_of'(
% 4.57/4.96 singleton( X ) ), X ) ] )
% 4.57/4.96 , clause( 20168, [ member( 'member_of1'( X ), 'universal_class' ), =(
% 4.57/4.96 'member_of'( X ), X ) ] )
% 4.57/4.96 , clause( 20169, [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'(
% 4.57/4.96 X ), X ) ] )
% 4.57/4.96 , clause( 20170, [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 4.57/4.96 'universal_class' ) ] )
% 4.57/4.96 , clause( 20171, [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y
% 4.57/4.96 , X ) ), =( 'member_of'( X ), Y ) ] )
% 4.57/4.96 , clause( 20172, [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ] )
% 4.57/4.96 , clause( 20173, [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' )
% 4.57/4.96 , =( singleton( Y ), X ) ] )
% 4.57/4.96 , clause( 20174, [ member( 'not_subclass_element'( intersection( complement(
% 4.57/4.96 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 4.57/4.96 'null_class' ), intersection( complement( singleton(
% 4.57/4.96 'not_subclass_element'( X, 'null_class' ) ) ), X ) ), =( singleton(
% 4.57/4.96 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 4.57/4.96 )
% 4.57/4.96 , clause( 20175, [ member( 'not_subclass_element'( intersection( complement(
% 4.57/4.96 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 4.57/4.96 'null_class' ), X ), =( singleton( 'not_subclass_element'( X,
% 4.57/4.96 'null_class' ) ), X ), =( X, 'null_class' ) ] )
% 4.57/4.96 , clause( 20176, [ ~( =( 'not_subclass_element'( intersection( complement(
% 4.57/4.96 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 4.57/4.96 'null_class' ), 'not_subclass_element'( X, 'null_class' ) ) ), =(
% 4.57/4.96 singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 4.57/4.96 'null_class' ) ] )
% 4.57/4.96 , clause( 20177, [ =( 'unordered_pair'( X, Y ), union( singleton( X ),
% 4.57/4.96 singleton( Y ) ) ) ] )
% 4.57/4.96 , clause( 20178, [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ] )
% 4.57/4.96 , clause( 20179, [ ~( member( 'unordered_pair'( x, singleton( y ) ),
% 4.57/4.96 'ordered_pair'( x, y ) ) ) ] )
% 4.57/4.96 ] ).
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 subsumption(
% 4.57/4.96 clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.57/4.96 'unordered_pair'( Y, X ) ) ] )
% 4.57/4.96 , clause( 20043, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.57/4.96 'unordered_pair'( Y, X ) ) ] )
% 4.57/4.96 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 4.57/4.96 ), ==>( 1, 1 )] ) ).
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 subsumption(
% 4.57/4.96 clause( 9, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ] )
% 4.57/4.96 , clause( 20044, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 4.57/4.96 )
% 4.57/4.96 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 4.57/4.96 )] ) ).
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 subsumption(
% 4.57/4.96 clause( 11, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 4.57/4.96 singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 4.57/4.96 , clause( 20046, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 4.57/4.96 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 4.57/4.96 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 4.57/4.96 )] ) ).
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 subsumption(
% 4.57/4.96 clause( 142, [ ~( member( 'unordered_pair'( x, singleton( y ) ),
% 4.57/4.96 'ordered_pair'( x, y ) ) ) ] )
% 4.57/4.96 , clause( 20179, [ ~( member( 'unordered_pair'( x, singleton( y ) ),
% 4.57/4.96 'ordered_pair'( x, y ) ) ) ] )
% 4.57/4.96 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 paramod(
% 4.57/4.96 clause( 20330, [ member( 'unordered_pair'( X, singleton( Y ) ),
% 4.57/4.96 'ordered_pair'( X, Y ) ), ~( member( 'unordered_pair'( X, singleton( Y )
% 4.57/4.96 ), 'universal_class' ) ) ] )
% 4.57/4.96 , clause( 11, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 4.57/4.96 singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 4.57/4.96 , 0, clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 4.57/4.96 'unordered_pair'( Y, X ) ) ] )
% 4.57/4.96 , 1, 5, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 4.57/4.96 :=( X, 'unordered_pair'( X, singleton( Y ) ) ), :=( Y, singleton( X ) )] )
% 4.57/4.96 ).
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 resolution(
% 4.57/4.96 clause( 20331, [ member( 'unordered_pair'( X, singleton( Y ) ),
% 4.57/4.96 'ordered_pair'( X, Y ) ) ] )
% 4.57/4.96 , clause( 20330, [ member( 'unordered_pair'( X, singleton( Y ) ),
% 4.57/4.96 'ordered_pair'( X, Y ) ), ~( member( 'unordered_pair'( X, singleton( Y )
% 4.57/4.96 ), 'universal_class' ) ) ] )
% 4.57/4.96 , 1, clause( 9, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 4.57/4.96 )
% 4.57/4.96 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 4.57/4.96 , X ), :=( Y, singleton( Y ) )] )).
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 subsumption(
% 4.57/4.96 clause( 563, [ member( 'unordered_pair'( X, singleton( Y ) ),
% 4.57/4.96 'ordered_pair'( X, Y ) ) ] )
% 4.57/4.96 , clause( 20331, [ member( 'unordered_pair'( X, singleton( Y ) ),
% 4.57/4.96 'ordered_pair'( X, Y ) ) ] )
% 4.57/4.96 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 4.57/4.96 )] ) ).
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 resolution(
% 4.57/4.96 clause( 20332, [] )
% 4.57/4.96 , clause( 142, [ ~( member( 'unordered_pair'( x, singleton( y ) ),
% 4.57/4.96 'ordered_pair'( x, y ) ) ) ] )
% 4.57/4.96 , 0, clause( 563, [ member( 'unordered_pair'( X, singleton( Y ) ),
% 4.57/4.96 'ordered_pair'( X, Y ) ) ] )
% 4.57/4.96 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, x ), :=( Y, y )] )
% 4.57/4.96 ).
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 subsumption(
% 4.57/4.96 clause( 20032, [] )
% 4.57/4.96 , clause( 20332, [] )
% 4.57/4.96 , substitution( 0, [] ), permutation( 0, [] ) ).
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 end.
% 4.57/4.96
% 4.57/4.96 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 4.57/4.96
% 4.57/4.96 Memory use:
% 4.57/4.96
% 4.57/4.96 space for terms: 355507
% 4.57/4.96 space for clauses: 912598
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 clauses generated: 61545
% 4.57/4.96 clauses kept: 20033
% 4.57/4.96 clauses selected: 490
% 4.57/4.96 clauses deleted: 1171
% 4.57/4.96 clauses inuse deleted: 53
% 4.57/4.96
% 4.57/4.96 subsentry: 269094
% 4.57/4.96 literals s-matched: 209793
% 4.57/4.96 literals matched: 201926
% 4.57/4.96 full subsumption: 126469
% 4.57/4.96
% 4.57/4.96 checksum: -1323120820
% 4.57/4.96
% 4.57/4.96
% 4.57/4.96 Bliksem ended
%------------------------------------------------------------------------------