TSTP Solution File: SET081-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET081-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Mon Jul 18 22:46:44 EDT 2022
% Result : Unsatisfiable 2.24s 2.52s
% Output : Refutation 2.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET081-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n024.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 19:15:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.43/1.08 *** allocated 10000 integers for termspace/termends
% 0.43/1.08 *** allocated 10000 integers for clauses
% 0.43/1.08 *** allocated 10000 integers for justifications
% 0.43/1.08 Bliksem 1.12
% 0.43/1.08
% 0.43/1.08
% 0.43/1.08 Automatic Strategy Selection
% 0.43/1.08
% 0.43/1.08 Clauses:
% 0.43/1.08 [
% 0.43/1.08 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.43/1.08 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.43/1.08 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.43/1.08 ,
% 0.43/1.08 [ subclass( X, 'universal_class' ) ],
% 0.43/1.08 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.43/1.08 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.43/1.08 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.43/1.08 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.43/1.08 ,
% 0.43/1.08 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.43/1.08 ) ) ],
% 0.43/1.08 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.43/1.08 ) ) ],
% 0.43/1.08 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.43/1.08 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.43/1.08 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.43/1.08 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.08 X, Z ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.08 Y, T ) ],
% 0.43/1.08 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.43/1.08 ), 'cross_product'( Y, T ) ) ],
% 0.43/1.08 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.43/1.08 ), second( X ) ), X ) ],
% 0.43/1.08 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.43/1.08 'universal_class' ) ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.43/1.08 Y ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.43/1.08 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.43/1.08 , Y ), 'element_relation' ) ],
% 0.43/1.08 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.43/1.08 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.43/1.08 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.43/1.08 Z ) ) ],
% 0.43/1.08 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.43/1.08 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.43/1.08 member( X, Y ) ],
% 0.43/1.08 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.43/1.08 union( X, Y ) ) ],
% 0.43/1.08 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.43/1.08 intersection( complement( X ), complement( Y ) ) ) ),
% 0.43/1.08 'symmetric_difference'( X, Y ) ) ],
% 0.43/1.08 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.43/1.08 ,
% 0.43/1.08 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.43/1.08 ,
% 0.43/1.08 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.43/1.08 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.43/1.08 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.43/1.08 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.43/1.08 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.43/1.08 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.43/1.08 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.43/1.08 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.43/1.08 'cross_product'( 'universal_class', 'universal_class' ),
% 0.43/1.08 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.43/1.08 Y ), rotate( T ) ) ],
% 0.43/1.08 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.43/1.08 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.43/1.08 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.43/1.08 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.43/1.08 'cross_product'( 'universal_class', 'universal_class' ),
% 0.43/1.08 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.43/1.08 Z ), flip( T ) ) ],
% 0.43/1.08 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.43/1.08 inverse( X ) ) ],
% 0.43/1.08 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.43/1.08 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.43/1.08 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.43/1.08 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.43/1.08 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.43/1.08 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.43/1.08 ],
% 0.43/1.08 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.43/1.08 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.43/1.08 'universal_class' ) ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.43/1.08 successor( X ), Y ) ],
% 0.43/1.08 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.43/1.08 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.43/1.08 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.43/1.08 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.43/1.08 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.43/1.08 ,
% 0.43/1.08 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.43/1.08 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.43/1.08 [ inductive( omega ) ],
% 0.43/1.08 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.43/1.08 [ member( omega, 'universal_class' ) ],
% 0.43/1.08 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.43/1.08 , 'sum_class'( X ) ) ],
% 0.43/1.08 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.43/1.08 'universal_class' ) ],
% 0.43/1.08 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.43/1.08 'power_class'( X ) ) ],
% 0.43/1.08 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.43/1.08 'universal_class' ) ],
% 0.43/1.08 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.43/1.08 'universal_class' ) ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.43/1.08 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.43/1.08 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.43/1.08 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.43/1.08 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.43/1.08 ) ],
% 0.43/1.08 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.43/1.08 , 'identity_relation' ) ],
% 0.43/1.08 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.43/1.08 'single_valued_class'( X ) ],
% 0.43/1.08 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.43/1.08 'universal_class' ) ) ],
% 0.43/1.08 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.43/1.08 'identity_relation' ) ],
% 0.43/1.08 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.43/1.08 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.43/1.08 , function( X ) ],
% 0.43/1.08 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.43/1.08 X, Y ), 'universal_class' ) ],
% 0.43/1.08 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.43/1.08 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.43/1.08 ) ],
% 0.43/1.08 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.43/1.08 [ function( choice ) ],
% 0.43/1.08 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.43/1.08 apply( choice, X ), X ) ],
% 0.43/1.08 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.43/1.08 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.43/1.08 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.43/1.08 ,
% 0.43/1.08 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.43/1.08 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.43/1.08 , complement( compose( complement( 'element_relation' ), inverse(
% 0.43/1.08 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.43/1.08 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.43/1.08 'identity_relation' ) ],
% 0.43/1.08 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.43/1.08 , diagonalise( X ) ) ],
% 0.43/1.08 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.43/1.08 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.43/1.08 [ ~( operation( X ) ), function( X ) ],
% 0.43/1.08 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.43/1.08 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.43/1.08 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.43/1.08 'domain_of'( X ) ) ) ],
% 0.43/1.08 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.43/1.08 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.43/1.08 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.43/1.08 X ) ],
% 0.43/1.08 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.43/1.08 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.43/1.08 'domain_of'( X ) ) ],
% 0.43/1.08 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.43/1.08 'domain_of'( Z ) ) ) ],
% 0.43/1.08 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.43/1.08 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.43/1.08 ), compatible( X, Y, Z ) ],
% 0.43/1.08 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.43/1.08 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.43/1.08 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.43/1.08 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.43/1.08 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.43/1.08 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.43/1.08 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.43/1.08 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.43/1.08 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.43/1.08 , Y ) ],
% 0.43/1.08 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.43/1.08 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.43/1.08 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.43/1.08 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.43/1.08 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.08 X, 'unordered_pair'( X, Y ) ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.08 Y, 'unordered_pair'( X, Y ) ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.08 X, 'universal_class' ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.43/1.08 Y, 'universal_class' ) ],
% 0.43/1.08 [ subclass( X, X ) ],
% 0.43/1.08 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.43/1.08 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.43/1.08 'not_subclass_element'( Y, X ), Y ) ],
% 0.43/1.08 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.43/1.08 'not_subclass_element'( Y, X ), Y ) ],
% 0.43/1.08 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.43/1.08 'not_subclass_element'( Y, X ), Y ) ],
% 0.43/1.08 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.43/1.08 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.43/1.08 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.43/1.08 [ ~( member( X, 'null_class' ) ) ],
% 0.43/1.08 [ subclass( 'null_class', X ) ],
% 0.43/1.08 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.43/1.08 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.43/1.08 ), X ) ],
% 0.43/1.08 [ member( 'null_class', 'universal_class' ) ],
% 0.43/1.08 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.43/1.08 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.43/1.08 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.43/1.08 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.43/1.08 Y ) ) ],
% 0.43/1.08 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.43/1.08 Y ) ) ],
% 0.43/1.08 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.43/1.08 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.43/1.08 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.43/1.08 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.43/1.08 'universal_class' ) ) ), =( Y, Z ) ],
% 0.43/1.08 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.43/1.08 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.43/1.08 'universal_class' ) ) ), =( X, Z ) ],
% 0.43/1.08 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.43/1.08 'null_class' ) ) ],
% 0.43/1.08 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.43/1.08 'null_class' ) ) ],
% 0.43/1.08 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.43/1.08 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 2.24/2.52 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 2.24/2.52 X, Z ), Y ) ],
% 2.24/2.52 [ member( singleton( X ), 'universal_class' ) ],
% 2.24/2.52 [ member( singleton( X ), 'unordered_pair'( Y, singleton( X ) ) ) ],
% 2.24/2.52 [ ~( member( X, 'universal_class' ) ), member( X, singleton( X ) ) ]
% 2.24/2.52 ,
% 2.24/2.52 [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X ),
% 2.24/2.52 'null_class' ) ) ],
% 2.24/2.52 [ member( 'null_class', singleton( 'null_class' ) ) ],
% 2.24/2.52 [ member( y, singleton( x ) ) ],
% 2.24/2.52 [ ~( =( y, x ) ) ]
% 2.24/2.52 ] .
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 percentage equality = 0.234818, percentage horn = 0.880952
% 2.24/2.52 This is a problem with some equality
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 Options Used:
% 2.24/2.52
% 2.24/2.52 useres = 1
% 2.24/2.52 useparamod = 1
% 2.24/2.52 useeqrefl = 1
% 2.24/2.52 useeqfact = 1
% 2.24/2.52 usefactor = 1
% 2.24/2.52 usesimpsplitting = 0
% 2.24/2.52 usesimpdemod = 5
% 2.24/2.52 usesimpres = 3
% 2.24/2.52
% 2.24/2.52 resimpinuse = 1000
% 2.24/2.52 resimpclauses = 20000
% 2.24/2.52 substype = eqrewr
% 2.24/2.52 backwardsubs = 1
% 2.24/2.52 selectoldest = 5
% 2.24/2.52
% 2.24/2.52 litorderings [0] = split
% 2.24/2.52 litorderings [1] = extend the termordering, first sorting on arguments
% 2.24/2.52
% 2.24/2.52 termordering = kbo
% 2.24/2.52
% 2.24/2.52 litapriori = 0
% 2.24/2.52 termapriori = 1
% 2.24/2.52 litaposteriori = 0
% 2.24/2.52 termaposteriori = 0
% 2.24/2.52 demodaposteriori = 0
% 2.24/2.52 ordereqreflfact = 0
% 2.24/2.52
% 2.24/2.52 litselect = negord
% 2.24/2.52
% 2.24/2.52 maxweight = 15
% 2.24/2.52 maxdepth = 30000
% 2.24/2.52 maxlength = 115
% 2.24/2.52 maxnrvars = 195
% 2.24/2.52 excuselevel = 1
% 2.24/2.52 increasemaxweight = 1
% 2.24/2.52
% 2.24/2.52 maxselected = 10000000
% 2.24/2.52 maxnrclauses = 10000000
% 2.24/2.52
% 2.24/2.52 showgenerated = 0
% 2.24/2.52 showkept = 0
% 2.24/2.52 showselected = 0
% 2.24/2.52 showdeleted = 0
% 2.24/2.52 showresimp = 1
% 2.24/2.52 showstatus = 2000
% 2.24/2.52
% 2.24/2.52 prologoutput = 1
% 2.24/2.52 nrgoals = 5000000
% 2.24/2.52 totalproof = 1
% 2.24/2.52
% 2.24/2.52 Symbols occurring in the translation:
% 2.24/2.52
% 2.24/2.52 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.24/2.52 . [1, 2] (w:1, o:56, a:1, s:1, b:0),
% 2.24/2.52 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 2.24/2.52 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.24/2.52 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.24/2.52 subclass [41, 2] (w:1, o:81, a:1, s:1, b:0),
% 2.24/2.52 member [43, 2] (w:1, o:82, a:1, s:1, b:0),
% 2.24/2.52 'not_subclass_element' [44, 2] (w:1, o:83, a:1, s:1, b:0),
% 2.24/2.52 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 2.24/2.52 'unordered_pair' [46, 2] (w:1, o:84, a:1, s:1, b:0),
% 2.24/2.52 singleton [47, 1] (w:1, o:39, a:1, s:1, b:0),
% 2.24/2.52 'ordered_pair' [48, 2] (w:1, o:85, a:1, s:1, b:0),
% 2.24/2.52 'cross_product' [50, 2] (w:1, o:86, a:1, s:1, b:0),
% 2.24/2.52 first [52, 1] (w:1, o:40, a:1, s:1, b:0),
% 2.24/2.52 second [53, 1] (w:1, o:41, a:1, s:1, b:0),
% 2.24/2.52 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 2.24/2.52 intersection [55, 2] (w:1, o:88, a:1, s:1, b:0),
% 2.24/2.52 complement [56, 1] (w:1, o:42, a:1, s:1, b:0),
% 2.24/2.52 union [57, 2] (w:1, o:89, a:1, s:1, b:0),
% 2.24/2.52 'symmetric_difference' [58, 2] (w:1, o:90, a:1, s:1, b:0),
% 2.24/2.52 restrict [60, 3] (w:1, o:93, a:1, s:1, b:0),
% 2.24/2.52 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 2.24/2.52 'domain_of' [62, 1] (w:1, o:44, a:1, s:1, b:0),
% 2.24/2.52 rotate [63, 1] (w:1, o:36, a:1, s:1, b:0),
% 2.24/2.52 flip [65, 1] (w:1, o:45, a:1, s:1, b:0),
% 2.24/2.52 inverse [66, 1] (w:1, o:46, a:1, s:1, b:0),
% 2.24/2.52 'range_of' [67, 1] (w:1, o:37, a:1, s:1, b:0),
% 2.24/2.52 domain [68, 3] (w:1, o:95, a:1, s:1, b:0),
% 2.24/2.52 range [69, 3] (w:1, o:96, a:1, s:1, b:0),
% 2.24/2.52 image [70, 2] (w:1, o:87, a:1, s:1, b:0),
% 2.24/2.52 successor [71, 1] (w:1, o:47, a:1, s:1, b:0),
% 2.24/2.52 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 2.24/2.52 inductive [73, 1] (w:1, o:48, a:1, s:1, b:0),
% 2.24/2.52 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 2.24/2.52 'sum_class' [75, 1] (w:1, o:49, a:1, s:1, b:0),
% 2.24/2.52 'power_class' [76, 1] (w:1, o:52, a:1, s:1, b:0),
% 2.24/2.52 compose [78, 2] (w:1, o:91, a:1, s:1, b:0),
% 2.24/2.52 'single_valued_class' [79, 1] (w:1, o:53, a:1, s:1, b:0),
% 2.24/2.52 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 2.24/2.52 function [82, 1] (w:1, o:54, a:1, s:1, b:0),
% 2.24/2.52 regular [83, 1] (w:1, o:38, a:1, s:1, b:0),
% 2.24/2.52 apply [84, 2] (w:1, o:92, a:1, s:1, b:0),
% 2.24/2.52 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 2.24/2.52 'one_to_one' [86, 1] (w:1, o:50, a:1, s:1, b:0),
% 2.24/2.52 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 2.24/2.52 diagonalise [88, 1] (w:1, o:55, a:1, s:1, b:0),
% 2.24/2.52 cantor [89, 1] (w:1, o:43, a:1, s:1, b:0),
% 2.24/2.52 operation [90, 1] (w:1, o:51, a:1, s:1, b:0),
% 2.24/2.52 compatible [94, 3] (w:1, o:94, a:1, s:1, b:0),
% 2.24/2.52 homomorphism [95, 3] (w:1, o:97, a:1, s:1, b:0),
% 2.24/2.52 'not_homomorphism1' [96, 3] (w:1, o:98, a:1, s:1, b:0),
% 2.24/2.52 'not_homomorphism2' [97, 3] (w:1, o:99, a:1, s:1, b:0),
% 2.24/2.52 y [98, 0] (w:1, o:30, a:1, s:1, b:0),
% 2.24/2.52 x [99, 0] (w:1, o:29, a:1, s:1, b:0).
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 Starting Search:
% 2.24/2.52
% 2.24/2.52 Resimplifying inuse:
% 2.24/2.52 Done
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 Intermediate Status:
% 2.24/2.52 Generated: 3989
% 2.24/2.52 Kept: 2008
% 2.24/2.52 Inuse: 120
% 2.24/2.52 Deleted: 6
% 2.24/2.52 Deletedinuse: 2
% 2.24/2.52
% 2.24/2.52 Resimplifying inuse:
% 2.24/2.52 Done
% 2.24/2.52
% 2.24/2.52 Resimplifying inuse:
% 2.24/2.52 Done
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 Intermediate Status:
% 2.24/2.52 Generated: 10080
% 2.24/2.52 Kept: 4156
% 2.24/2.52 Inuse: 197
% 2.24/2.52 Deleted: 8
% 2.24/2.52 Deletedinuse: 4
% 2.24/2.52
% 2.24/2.52 Resimplifying inuse:
% 2.24/2.52 Done
% 2.24/2.52
% 2.24/2.52 Resimplifying inuse:
% 2.24/2.52 Done
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 Intermediate Status:
% 2.24/2.52 Generated: 15477
% 2.24/2.52 Kept: 6300
% 2.24/2.52 Inuse: 275
% 2.24/2.52 Deleted: 47
% 2.24/2.52 Deletedinuse: 36
% 2.24/2.52
% 2.24/2.52 Resimplifying inuse:
% 2.24/2.52 Done
% 2.24/2.52
% 2.24/2.52 Resimplifying inuse:
% 2.24/2.52 Done
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 Intermediate Status:
% 2.24/2.52 Generated: 21699
% 2.24/2.52 Kept: 8318
% 2.24/2.52 Inuse: 356
% 2.24/2.52 Deleted: 62
% 2.24/2.52 Deletedinuse: 43
% 2.24/2.52
% 2.24/2.52 Resimplifying inuse:
% 2.24/2.52 Done
% 2.24/2.52
% 2.24/2.52 Resimplifying inuse:
% 2.24/2.52 Done
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 Intermediate Status:
% 2.24/2.52 Generated: 28245
% 2.24/2.52 Kept: 10513
% 2.24/2.52 Inuse: 389
% 2.24/2.52 Deleted: 79
% 2.24/2.52 Deletedinuse: 57
% 2.24/2.52
% 2.24/2.52 Resimplifying inuse:
% 2.24/2.52 Done
% 2.24/2.52
% 2.24/2.52 Resimplifying inuse:
% 2.24/2.52 Done
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 Intermediate Status:
% 2.24/2.52 Generated: 38137
% 2.24/2.52 Kept: 12886
% 2.24/2.52 Inuse: 438
% 2.24/2.52 Deleted: 81
% 2.24/2.52 Deletedinuse: 58
% 2.24/2.52
% 2.24/2.52 Resimplifying inuse:
% 2.24/2.52 Done
% 2.24/2.52
% 2.24/2.52 Resimplifying inuse:
% 2.24/2.52 Done
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 Bliksems!, er is een bewijs:
% 2.24/2.52 % SZS status Unsatisfiable
% 2.24/2.52 % SZS output start Refutation
% 2.24/2.52
% 2.24/2.52 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.24/2.52 .
% 2.24/2.52 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 2.24/2.52 .
% 2.24/2.52 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z
% 2.24/2.52 ) ] )
% 2.24/2.52 .
% 2.24/2.52 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.24/2.52 .
% 2.24/2.52 clause( 122, [ member( y, singleton( x ) ) ] )
% 2.24/2.52 .
% 2.24/2.52 clause( 123, [ ~( =( y, x ) ) ] )
% 2.24/2.52 .
% 2.24/2.52 clause( 124, [ =( X, Y ), ~( member( X, singleton( Y ) ) ) ] )
% 2.24/2.52 .
% 2.24/2.52 clause( 160, [ =( X, Y ), ~( =( Y, X ) ) ] )
% 2.24/2.52 .
% 2.24/2.52 clause( 494, [ member( X, singleton( x ) ), ~( =( X, y ) ) ] )
% 2.24/2.52 .
% 2.24/2.52 clause( 504, [ ~( =( X, x ) ), ~( =( X, y ) ) ] )
% 2.24/2.52 .
% 2.24/2.52 clause( 14897, [ ~( =( X, y ) ) ] )
% 2.24/2.52 .
% 2.24/2.52 clause( 16404, [] )
% 2.24/2.52 .
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 % SZS output end Refutation
% 2.24/2.52 found a proof!
% 2.24/2.52
% 2.24/2.52 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.24/2.52
% 2.24/2.52 initialclauses(
% 2.24/2.52 [ clause( 16406, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 2.24/2.52 ) ] )
% 2.24/2.52 , clause( 16407, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 2.24/2.52 , Y ) ] )
% 2.24/2.52 , clause( 16408, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 2.24/2.52 subclass( X, Y ) ] )
% 2.24/2.52 , clause( 16409, [ subclass( X, 'universal_class' ) ] )
% 2.24/2.52 , clause( 16410, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.24/2.52 , clause( 16411, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 2.24/2.52 , clause( 16412, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 2.24/2.52 ] )
% 2.24/2.52 , clause( 16413, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 2.24/2.52 =( X, Z ) ] )
% 2.24/2.52 , clause( 16414, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.24/2.52 'unordered_pair'( X, Y ) ) ] )
% 2.24/2.52 , clause( 16415, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.24/2.52 'unordered_pair'( Y, X ) ) ] )
% 2.24/2.52 , clause( 16416, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 2.24/2.52 )
% 2.24/2.52 , clause( 16417, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.24/2.52 , clause( 16418, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 2.24/2.52 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 2.24/2.52 , clause( 16419, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.24/2.52 ) ) ), member( X, Z ) ] )
% 2.24/2.52 , clause( 16420, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.24/2.52 ) ) ), member( Y, T ) ] )
% 2.24/2.52 , clause( 16421, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 2.24/2.52 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 2.24/2.52 , clause( 16422, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 2.24/2.52 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 2.24/2.52 , clause( 16423, [ subclass( 'element_relation', 'cross_product'(
% 2.24/2.52 'universal_class', 'universal_class' ) ) ] )
% 2.24/2.52 , clause( 16424, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 2.24/2.52 ), member( X, Y ) ] )
% 2.24/2.52 , clause( 16425, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 2.24/2.52 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 2.24/2.52 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 2.24/2.52 , clause( 16426, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 2.24/2.52 )
% 2.24/2.52 , clause( 16427, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 2.24/2.52 )
% 2.24/2.52 , clause( 16428, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 2.24/2.52 intersection( Y, Z ) ) ] )
% 2.24/2.52 , clause( 16429, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 2.24/2.52 )
% 2.24/2.52 , clause( 16430, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.24/2.52 complement( Y ) ), member( X, Y ) ] )
% 2.24/2.52 , clause( 16431, [ =( complement( intersection( complement( X ), complement(
% 2.24/2.52 Y ) ) ), union( X, Y ) ) ] )
% 2.24/2.52 , clause( 16432, [ =( intersection( complement( intersection( X, Y ) ),
% 2.24/2.52 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 2.24/2.52 'symmetric_difference'( X, Y ) ) ] )
% 2.24/2.52 , clause( 16433, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 2.24/2.52 X, Y, Z ) ) ] )
% 2.24/2.52 , clause( 16434, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 2.24/2.52 Z, X, Y ) ) ] )
% 2.24/2.52 , clause( 16435, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 2.24/2.52 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 2.24/2.52 , clause( 16436, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 2.24/2.52 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 2.24/2.52 'domain_of'( Y ) ) ] )
% 2.24/2.52 , clause( 16437, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 2.24/2.52 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.24/2.52 , clause( 16438, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.24/2.52 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 2.24/2.52 ] )
% 2.24/2.52 , clause( 16439, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.24/2.52 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 2.24/2.52 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.24/2.52 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 2.24/2.52 , Y ), rotate( T ) ) ] )
% 2.24/2.52 , clause( 16440, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 2.24/2.52 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.24/2.52 , clause( 16441, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.24/2.52 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 2.24/2.52 )
% 2.24/2.52 , clause( 16442, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.24/2.52 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 2.24/2.52 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.24/2.52 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 2.24/2.52 , Z ), flip( T ) ) ] )
% 2.24/2.52 , clause( 16443, [ =( 'domain_of'( flip( 'cross_product'( X,
% 2.24/2.52 'universal_class' ) ) ), inverse( X ) ) ] )
% 2.24/2.52 , clause( 16444, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 2.24/2.52 , clause( 16445, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 2.24/2.52 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 2.24/2.52 , clause( 16446, [ =( second( 'not_subclass_element'( restrict( X,
% 2.24/2.52 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 2.24/2.52 , clause( 16447, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 2.24/2.52 image( X, Y ) ) ] )
% 2.24/2.52 , clause( 16448, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 2.24/2.52 , clause( 16449, [ subclass( 'successor_relation', 'cross_product'(
% 2.24/2.52 'universal_class', 'universal_class' ) ) ] )
% 2.24/2.52 , clause( 16450, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 2.24/2.52 ) ), =( successor( X ), Y ) ] )
% 2.24/2.52 , clause( 16451, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 2.24/2.52 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 2.24/2.52 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 2.24/2.52 , clause( 16452, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 2.24/2.52 , clause( 16453, [ ~( inductive( X ) ), subclass( image(
% 2.24/2.52 'successor_relation', X ), X ) ] )
% 2.24/2.52 , clause( 16454, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 2.24/2.52 'successor_relation', X ), X ) ), inductive( X ) ] )
% 2.24/2.52 , clause( 16455, [ inductive( omega ) ] )
% 2.24/2.52 , clause( 16456, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 2.24/2.52 , clause( 16457, [ member( omega, 'universal_class' ) ] )
% 2.24/2.52 , clause( 16458, [ =( 'domain_of'( restrict( 'element_relation',
% 2.24/2.52 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 2.24/2.52 , clause( 16459, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 2.24/2.52 X ), 'universal_class' ) ] )
% 2.24/2.52 , clause( 16460, [ =( complement( image( 'element_relation', complement( X
% 2.24/2.52 ) ) ), 'power_class'( X ) ) ] )
% 2.24/2.52 , clause( 16461, [ ~( member( X, 'universal_class' ) ), member(
% 2.24/2.52 'power_class'( X ), 'universal_class' ) ] )
% 2.24/2.52 , clause( 16462, [ subclass( compose( X, Y ), 'cross_product'(
% 2.24/2.52 'universal_class', 'universal_class' ) ) ] )
% 2.24/2.52 , clause( 16463, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 2.24/2.52 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 2.24/2.52 , clause( 16464, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 2.24/2.52 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 2.24/2.52 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 2.24/2.52 ) ] )
% 2.24/2.52 , clause( 16465, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 2.24/2.52 inverse( X ) ), 'identity_relation' ) ] )
% 2.24/2.52 , clause( 16466, [ ~( subclass( compose( X, inverse( X ) ),
% 2.24/2.52 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 2.24/2.52 , clause( 16467, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 2.24/2.52 'universal_class', 'universal_class' ) ) ] )
% 2.24/2.52 , clause( 16468, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 2.24/2.52 , 'identity_relation' ) ] )
% 2.24/2.52 , clause( 16469, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 2.24/2.52 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 2.24/2.52 'identity_relation' ) ), function( X ) ] )
% 2.24/2.52 , clause( 16470, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 2.24/2.52 , member( image( X, Y ), 'universal_class' ) ] )
% 2.24/2.52 , clause( 16471, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 2.24/2.52 , clause( 16472, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 2.24/2.52 , 'null_class' ) ] )
% 2.24/2.52 , clause( 16473, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 2.24/2.52 Y ) ) ] )
% 2.24/2.52 , clause( 16474, [ function( choice ) ] )
% 2.24/2.52 , clause( 16475, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 2.24/2.52 ), member( apply( choice, X ), X ) ] )
% 2.24/2.52 , clause( 16476, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 2.24/2.52 , clause( 16477, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 2.24/2.52 , clause( 16478, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 2.24/2.52 'one_to_one'( X ) ] )
% 2.24/2.52 , clause( 16479, [ =( intersection( 'cross_product'( 'universal_class',
% 2.24/2.52 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 2.24/2.52 'universal_class' ), complement( compose( complement( 'element_relation'
% 2.24/2.52 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 2.24/2.52 , clause( 16480, [ =( intersection( inverse( 'subset_relation' ),
% 2.24/2.52 'subset_relation' ), 'identity_relation' ) ] )
% 2.24/2.52 , clause( 16481, [ =( complement( 'domain_of'( intersection( X,
% 2.24/2.52 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 2.24/2.52 , clause( 16482, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 2.24/2.52 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 2.24/2.52 , clause( 16483, [ ~( operation( X ) ), function( X ) ] )
% 2.24/2.52 , clause( 16484, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 2.24/2.52 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.24/2.52 ] )
% 2.24/2.52 , clause( 16485, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 2.24/2.52 'domain_of'( 'domain_of'( X ) ) ) ] )
% 2.24/2.52 , clause( 16486, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 2.24/2.52 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.24/2.52 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 2.24/2.52 operation( X ) ] )
% 2.24/2.52 , clause( 16487, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 2.24/2.52 , clause( 16488, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 2.24/2.52 Y ) ), 'domain_of'( X ) ) ] )
% 2.24/2.52 , clause( 16489, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 2.24/2.52 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 2.24/2.52 , clause( 16490, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 2.24/2.52 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 2.24/2.52 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 2.24/2.52 , clause( 16491, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 2.24/2.52 , clause( 16492, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 2.24/2.52 , clause( 16493, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 2.24/2.52 , clause( 16494, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 2.24/2.52 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 2.24/2.52 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 2.24/2.52 )
% 2.24/2.52 , clause( 16495, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.24/2.52 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 2.24/2.52 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 2.24/2.52 , Y ) ] )
% 2.24/2.52 , clause( 16496, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.24/2.52 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 2.24/2.52 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 2.24/2.52 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 2.24/2.52 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 2.24/2.52 )
% 2.24/2.52 , clause( 16497, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.24/2.52 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 2.24/2.52 , clause( 16498, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.24/2.52 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 2.24/2.52 , clause( 16499, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.24/2.52 ) ) ), member( X, 'universal_class' ) ] )
% 2.24/2.52 , clause( 16500, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.24/2.52 ) ) ), member( Y, 'universal_class' ) ] )
% 2.24/2.52 , clause( 16501, [ subclass( X, X ) ] )
% 2.24/2.52 , clause( 16502, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 2.24/2.52 X, Z ) ] )
% 2.24/2.52 , clause( 16503, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 2.24/2.52 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.24/2.52 , clause( 16504, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 2.24/2.52 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.24/2.52 , clause( 16505, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 2.24/2.52 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.24/2.52 , clause( 16506, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 2.24/2.52 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 2.24/2.52 , clause( 16507, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 2.24/2.52 )
% 2.24/2.52 , clause( 16508, [ ~( member( X, 'null_class' ) ) ] )
% 2.24/2.52 , clause( 16509, [ subclass( 'null_class', X ) ] )
% 2.24/2.52 , clause( 16510, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 2.24/2.52 )
% 2.24/2.52 , clause( 16511, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 2.24/2.52 , 'null_class' ), X ) ] )
% 2.24/2.52 , clause( 16512, [ member( 'null_class', 'universal_class' ) ] )
% 2.24/2.52 , clause( 16513, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 2.24/2.52 ] )
% 2.24/2.52 , clause( 16514, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 2.24/2.52 )
% 2.24/2.52 , clause( 16515, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 2.24/2.52 )
% 2.24/2.52 , clause( 16516, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 2.24/2.52 X ), singleton( Y ) ) ] )
% 2.24/2.52 , clause( 16517, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 2.24/2.52 Y ), singleton( Y ) ) ] )
% 2.24/2.52 , clause( 16518, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 2.24/2.52 'universal_class' ), member( Y, 'universal_class' ) ] )
% 2.24/2.52 , clause( 16519, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 2.24/2.52 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 2.24/2.52 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 2.24/2.52 , clause( 16520, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 2.24/2.52 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 2.24/2.52 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 2.24/2.52 , clause( 16521, [ ~( member( X, 'universal_class' ) ), ~( =(
% 2.24/2.52 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 2.24/2.52 , clause( 16522, [ ~( member( X, 'universal_class' ) ), ~( =(
% 2.24/2.52 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 2.24/2.52 , clause( 16523, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.24/2.52 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 2.24/2.52 , clause( 16524, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 2.24/2.52 'unordered_pair'( X, Z ), Y ) ] )
% 2.24/2.52 , clause( 16525, [ member( singleton( X ), 'universal_class' ) ] )
% 2.24/2.52 , clause( 16526, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 2.24/2.52 X ) ) ) ] )
% 2.24/2.52 , clause( 16527, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.24/2.52 singleton( X ) ) ] )
% 2.24/2.52 , clause( 16528, [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X
% 2.24/2.52 ), 'null_class' ) ) ] )
% 2.24/2.52 , clause( 16529, [ member( 'null_class', singleton( 'null_class' ) ) ] )
% 2.24/2.52 , clause( 16530, [ member( y, singleton( x ) ) ] )
% 2.24/2.52 , clause( 16531, [ ~( =( y, x ) ) ] )
% 2.24/2.52 ] ).
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 subsumption(
% 2.24/2.52 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.24/2.52 , clause( 16410, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.24/2.52 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.24/2.52 ), ==>( 1, 1 )] ) ).
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 subsumption(
% 2.24/2.52 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 2.24/2.52 , clause( 16412, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 2.24/2.52 ] )
% 2.24/2.52 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.24/2.52 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 subsumption(
% 2.24/2.52 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z
% 2.24/2.52 ) ] )
% 2.24/2.52 , clause( 16413, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 2.24/2.52 =( X, Z ) ] )
% 2.24/2.52 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.24/2.52 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 subsumption(
% 2.24/2.52 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.24/2.52 , clause( 16417, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.24/2.52 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 subsumption(
% 2.24/2.52 clause( 122, [ member( y, singleton( x ) ) ] )
% 2.24/2.52 , clause( 16530, [ member( y, singleton( x ) ) ] )
% 2.24/2.52 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 subsumption(
% 2.24/2.52 clause( 123, [ ~( =( y, x ) ) ] )
% 2.24/2.52 , clause( 16531, [ ~( =( y, x ) ) ] )
% 2.24/2.52 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 factor(
% 2.24/2.52 clause( 16706, [ ~( member( X, 'unordered_pair'( Y, Y ) ) ), =( X, Y ) ] )
% 2.24/2.52 , clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X
% 2.24/2.52 , Z ) ] )
% 2.24/2.52 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y )] )).
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 paramod(
% 2.24/2.52 clause( 16707, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 2.24/2.52 , clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.24/2.52 , 0, clause( 16706, [ ~( member( X, 'unordered_pair'( Y, Y ) ) ), =( X, Y )
% 2.24/2.52 ] )
% 2.24/2.52 , 0, 3, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 2.24/2.52 :=( Y, Y )] )).
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 subsumption(
% 2.24/2.52 clause( 124, [ =( X, Y ), ~( member( X, singleton( Y ) ) ) ] )
% 2.24/2.52 , clause( 16707, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 2.24/2.52 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 2.24/2.52 ), ==>( 1, 0 )] ) ).
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 eqswap(
% 2.24/2.52 clause( 16709, [ ~( =( Y, X ) ), subclass( X, Y ) ] )
% 2.24/2.52 , clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.24/2.52 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 eqswap(
% 2.24/2.52 clause( 16710, [ ~( =( Y, X ) ), subclass( X, Y ) ] )
% 2.24/2.52 , clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.24/2.52 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 resolution(
% 2.24/2.52 clause( 16711, [ ~( subclass( Y, X ) ), =( X, Y ), ~( =( Y, X ) ) ] )
% 2.24/2.52 , clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 2.24/2.52 , 0, clause( 16709, [ ~( =( Y, X ) ), subclass( X, Y ) ] )
% 2.24/2.52 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 2.24/2.52 , X ), :=( Y, Y )] )).
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 resolution(
% 2.24/2.52 clause( 16713, [ =( Y, X ), ~( =( X, Y ) ), ~( =( Y, X ) ) ] )
% 2.24/2.52 , clause( 16711, [ ~( subclass( Y, X ) ), =( X, Y ), ~( =( Y, X ) ) ] )
% 2.24/2.52 , 0, clause( 16710, [ ~( =( Y, X ) ), subclass( X, Y ) ] )
% 2.24/2.52 , 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [ :=( X
% 2.24/2.52 , X ), :=( Y, Y )] )).
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 eqswap(
% 2.24/2.52 clause( 16715, [ ~( =( Y, X ) ), =( X, Y ), ~( =( Y, X ) ) ] )
% 2.24/2.52 , clause( 16713, [ =( Y, X ), ~( =( X, Y ) ), ~( =( Y, X ) ) ] )
% 2.24/2.52 , 2, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 factor(
% 2.24/2.52 clause( 16717, [ ~( =( X, Y ) ), =( Y, X ) ] )
% 2.24/2.52 , clause( 16715, [ ~( =( Y, X ) ), =( X, Y ), ~( =( Y, X ) ) ] )
% 2.24/2.52 , 0, 2, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 2.24/2.52
% 2.24/2.52
% 2.24/2.52 subsumption(
% 2.24/2.52 clause( 160, Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------