TSTP Solution File: SET083-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET083-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n028.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 22:46:46 EDT 2022
% Result : Unsatisfiable 2.20s 2.61s
% Output : Refutation 2.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.15 % Problem : SET083-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.02/0.16 % Command : bliksem %s
% 0.12/0.35 % Computer : n028.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % DateTime : Sun Jul 10 16:39:12 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.53/0.93 *** allocated 10000 integers for termspace/termends
% 0.53/0.93 *** allocated 10000 integers for clauses
% 0.53/0.93 *** allocated 10000 integers for justifications
% 0.53/0.93 Bliksem 1.12
% 0.53/0.93
% 0.53/0.93
% 0.53/0.93 Automatic Strategy Selection
% 0.53/0.93
% 0.53/0.93 Clauses:
% 0.53/0.93 [
% 0.53/0.93 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.53/0.93 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.53/0.93 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.53/0.93 ,
% 0.53/0.93 [ subclass( X, 'universal_class' ) ],
% 0.53/0.93 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.53/0.93 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.53/0.93 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.53/0.93 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.53/0.93 ,
% 0.53/0.93 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.53/0.93 ) ) ],
% 0.53/0.93 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.53/0.93 ) ) ],
% 0.53/0.93 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.53/0.93 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.53/0.93 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.53/0.93 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.53/0.93 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.53/0.93 X, Z ) ],
% 0.53/0.93 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.53/0.93 Y, T ) ],
% 0.53/0.93 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.53/0.93 ), 'cross_product'( Y, T ) ) ],
% 0.53/0.93 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.53/0.93 ), second( X ) ), X ) ],
% 0.53/0.93 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.53/0.93 'universal_class' ) ) ],
% 0.53/0.93 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.53/0.93 Y ) ],
% 0.53/0.93 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.53/0.93 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.53/0.93 , Y ), 'element_relation' ) ],
% 0.53/0.93 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.53/0.93 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.53/0.93 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.53/0.93 Z ) ) ],
% 0.53/0.93 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.53/0.93 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.53/0.93 member( X, Y ) ],
% 0.53/0.93 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.53/0.93 union( X, Y ) ) ],
% 0.53/0.93 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.53/0.93 intersection( complement( X ), complement( Y ) ) ) ),
% 0.53/0.93 'symmetric_difference'( X, Y ) ) ],
% 0.53/0.93 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.53/0.93 ,
% 0.53/0.93 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.53/0.93 ,
% 0.53/0.93 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.53/0.93 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.53/0.93 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.53/0.93 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.53/0.93 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.53/0.93 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.53/0.93 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.53/0.93 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.53/0.93 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.53/0.93 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.53/0.93 'cross_product'( 'universal_class', 'universal_class' ),
% 0.53/0.93 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.53/0.93 Y ), rotate( T ) ) ],
% 0.53/0.93 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.53/0.93 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.53/0.93 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.53/0.93 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.53/0.93 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.53/0.93 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.53/0.93 'cross_product'( 'universal_class', 'universal_class' ),
% 0.53/0.93 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.53/0.93 Z ), flip( T ) ) ],
% 0.53/0.93 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.53/0.93 inverse( X ) ) ],
% 0.53/0.93 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.53/0.93 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.53/0.93 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.53/0.93 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.53/0.93 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.53/0.93 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.53/0.93 ],
% 0.53/0.93 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.53/0.93 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.53/0.93 'universal_class' ) ) ],
% 0.53/0.93 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.53/0.93 successor( X ), Y ) ],
% 0.53/0.93 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.53/0.93 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.53/0.93 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.53/0.93 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.53/0.93 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.53/0.93 ,
% 0.53/0.93 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.53/0.93 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.53/0.93 [ inductive( omega ) ],
% 0.53/0.93 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.53/0.93 [ member( omega, 'universal_class' ) ],
% 0.53/0.93 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.53/0.93 , 'sum_class'( X ) ) ],
% 0.53/0.93 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.53/0.93 'universal_class' ) ],
% 0.53/0.93 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.53/0.93 'power_class'( X ) ) ],
% 0.53/0.93 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.53/0.93 'universal_class' ) ],
% 0.53/0.93 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.53/0.93 'universal_class' ) ) ],
% 0.53/0.93 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.53/0.93 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.53/0.93 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.53/0.93 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.53/0.93 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.53/0.93 ) ],
% 0.53/0.93 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.53/0.93 , 'identity_relation' ) ],
% 0.53/0.93 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.53/0.93 'single_valued_class'( X ) ],
% 0.53/0.93 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.53/0.93 'universal_class' ) ) ],
% 0.53/0.93 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.53/0.93 'identity_relation' ) ],
% 0.53/0.93 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.53/0.93 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.53/0.93 , function( X ) ],
% 0.53/0.93 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.53/0.93 X, Y ), 'universal_class' ) ],
% 0.53/0.93 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.53/0.93 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.53/0.93 ) ],
% 0.53/0.93 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.53/0.93 [ function( choice ) ],
% 0.53/0.93 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.53/0.93 apply( choice, X ), X ) ],
% 0.53/0.93 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.53/0.93 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.53/0.93 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.53/0.93 ,
% 0.53/0.93 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.53/0.93 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.53/0.93 , complement( compose( complement( 'element_relation' ), inverse(
% 0.53/0.93 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.53/0.93 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.53/0.93 'identity_relation' ) ],
% 0.53/0.93 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.53/0.93 , diagonalise( X ) ) ],
% 0.53/0.93 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.53/0.93 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.53/0.93 [ ~( operation( X ) ), function( X ) ],
% 0.53/0.93 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.53/0.93 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.53/0.93 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.53/0.93 'domain_of'( X ) ) ) ],
% 0.53/0.93 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.53/0.93 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.53/0.93 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.53/0.93 X ) ],
% 0.53/0.93 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.53/0.93 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.53/0.93 'domain_of'( X ) ) ],
% 0.53/0.93 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.53/0.93 'domain_of'( Z ) ) ) ],
% 0.53/0.93 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.53/0.93 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.53/0.93 ), compatible( X, Y, Z ) ],
% 0.53/0.93 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.53/0.93 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.53/0.93 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.53/0.93 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.53/0.93 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.53/0.93 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.53/0.93 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.53/0.93 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.53/0.93 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.53/0.93 , Y ) ],
% 0.53/0.93 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.53/0.93 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.53/0.93 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.53/0.93 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.53/0.93 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.53/0.93 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.53/0.93 X, 'unordered_pair'( X, Y ) ) ],
% 0.53/0.93 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.53/0.93 Y, 'unordered_pair'( X, Y ) ) ],
% 0.53/0.93 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.53/0.93 X, 'universal_class' ) ],
% 0.53/0.93 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.53/0.93 Y, 'universal_class' ) ],
% 0.53/0.93 [ subclass( X, X ) ],
% 0.53/0.93 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.53/0.93 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.53/0.93 'not_subclass_element'( Y, X ), Y ) ],
% 0.53/0.93 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.53/0.93 'not_subclass_element'( Y, X ), Y ) ],
% 0.53/0.93 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.53/0.93 'not_subclass_element'( Y, X ), Y ) ],
% 0.53/0.93 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.53/0.93 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.53/0.93 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.53/0.93 [ ~( member( X, 'null_class' ) ) ],
% 0.53/0.93 [ subclass( 'null_class', X ) ],
% 0.53/0.93 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.53/0.93 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.53/0.93 ), X ) ],
% 0.53/0.93 [ member( 'null_class', 'universal_class' ) ],
% 0.53/0.93 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.53/0.93 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.53/0.93 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.53/0.93 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.53/0.93 Y ) ) ],
% 0.53/0.93 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.53/0.93 Y ) ) ],
% 0.53/0.93 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.53/0.93 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.53/0.93 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.53/0.93 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.53/0.93 'universal_class' ) ) ), =( Y, Z ) ],
% 0.53/0.93 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.53/0.93 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.53/0.93 'universal_class' ) ) ), =( X, Z ) ],
% 0.53/0.93 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.53/0.93 'null_class' ) ) ],
% 0.53/0.93 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.53/0.93 'null_class' ) ) ],
% 0.53/0.93 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.53/0.93 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 2.20/2.61 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 2.20/2.61 X, Z ), Y ) ],
% 2.20/2.61 [ member( singleton( X ), 'universal_class' ) ],
% 2.20/2.61 [ member( singleton( X ), 'unordered_pair'( Y, singleton( X ) ) ) ],
% 2.20/2.61 [ ~( member( X, 'universal_class' ) ), member( X, singleton( X ) ) ]
% 2.20/2.61 ,
% 2.20/2.61 [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X ),
% 2.20/2.61 'null_class' ) ) ],
% 2.20/2.61 [ member( 'null_class', singleton( 'null_class' ) ) ],
% 2.20/2.61 [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ],
% 2.20/2.61 [ member( X, 'universal_class' ), =( singleton( X ), 'null_class' ) ]
% 2.20/2.61 ,
% 2.20/2.61 [ =( singleton( x ), singleton( y ) ) ],
% 2.20/2.61 [ member( x, 'universal_class' ) ],
% 2.20/2.61 [ ~( =( x, y ) ) ]
% 2.20/2.61 ] .
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 percentage equality = 0.242063, percentage horn = 0.875969
% 2.20/2.61 This is a problem with some equality
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 Options Used:
% 2.20/2.61
% 2.20/2.61 useres = 1
% 2.20/2.61 useparamod = 1
% 2.20/2.61 useeqrefl = 1
% 2.20/2.61 useeqfact = 1
% 2.20/2.61 usefactor = 1
% 2.20/2.61 usesimpsplitting = 0
% 2.20/2.61 usesimpdemod = 5
% 2.20/2.61 usesimpres = 3
% 2.20/2.61
% 2.20/2.61 resimpinuse = 1000
% 2.20/2.61 resimpclauses = 20000
% 2.20/2.61 substype = eqrewr
% 2.20/2.61 backwardsubs = 1
% 2.20/2.61 selectoldest = 5
% 2.20/2.61
% 2.20/2.61 litorderings [0] = split
% 2.20/2.61 litorderings [1] = extend the termordering, first sorting on arguments
% 2.20/2.61
% 2.20/2.61 termordering = kbo
% 2.20/2.61
% 2.20/2.61 litapriori = 0
% 2.20/2.61 termapriori = 1
% 2.20/2.61 litaposteriori = 0
% 2.20/2.61 termaposteriori = 0
% 2.20/2.61 demodaposteriori = 0
% 2.20/2.61 ordereqreflfact = 0
% 2.20/2.61
% 2.20/2.61 litselect = negord
% 2.20/2.61
% 2.20/2.61 maxweight = 15
% 2.20/2.61 maxdepth = 30000
% 2.20/2.61 maxlength = 115
% 2.20/2.61 maxnrvars = 195
% 2.20/2.61 excuselevel = 1
% 2.20/2.61 increasemaxweight = 1
% 2.20/2.61
% 2.20/2.61 maxselected = 10000000
% 2.20/2.61 maxnrclauses = 10000000
% 2.20/2.61
% 2.20/2.61 showgenerated = 0
% 2.20/2.61 showkept = 0
% 2.20/2.61 showselected = 0
% 2.20/2.61 showdeleted = 0
% 2.20/2.61 showresimp = 1
% 2.20/2.61 showstatus = 2000
% 2.20/2.61
% 2.20/2.61 prologoutput = 1
% 2.20/2.61 nrgoals = 5000000
% 2.20/2.61 totalproof = 1
% 2.20/2.61
% 2.20/2.61 Symbols occurring in the translation:
% 2.20/2.61
% 2.20/2.61 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.20/2.61 . [1, 2] (w:1, o:56, a:1, s:1, b:0),
% 2.20/2.61 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 2.20/2.61 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.20/2.61 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.20/2.61 subclass [41, 2] (w:1, o:81, a:1, s:1, b:0),
% 2.20/2.61 member [43, 2] (w:1, o:82, a:1, s:1, b:0),
% 2.20/2.61 'not_subclass_element' [44, 2] (w:1, o:83, a:1, s:1, b:0),
% 2.20/2.61 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 2.20/2.61 'unordered_pair' [46, 2] (w:1, o:84, a:1, s:1, b:0),
% 2.20/2.61 singleton [47, 1] (w:1, o:39, a:1, s:1, b:0),
% 2.20/2.61 'ordered_pair' [48, 2] (w:1, o:85, a:1, s:1, b:0),
% 2.20/2.61 'cross_product' [50, 2] (w:1, o:86, a:1, s:1, b:0),
% 2.20/2.61 first [52, 1] (w:1, o:40, a:1, s:1, b:0),
% 2.20/2.61 second [53, 1] (w:1, o:41, a:1, s:1, b:0),
% 2.20/2.61 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 2.20/2.61 intersection [55, 2] (w:1, o:88, a:1, s:1, b:0),
% 2.20/2.61 complement [56, 1] (w:1, o:42, a:1, s:1, b:0),
% 2.20/2.61 union [57, 2] (w:1, o:89, a:1, s:1, b:0),
% 2.20/2.61 'symmetric_difference' [58, 2] (w:1, o:90, a:1, s:1, b:0),
% 2.20/2.61 restrict [60, 3] (w:1, o:93, a:1, s:1, b:0),
% 2.20/2.61 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 2.20/2.61 'domain_of' [62, 1] (w:1, o:44, a:1, s:1, b:0),
% 2.20/2.61 rotate [63, 1] (w:1, o:36, a:1, s:1, b:0),
% 2.20/2.61 flip [65, 1] (w:1, o:45, a:1, s:1, b:0),
% 2.20/2.61 inverse [66, 1] (w:1, o:46, a:1, s:1, b:0),
% 2.20/2.61 'range_of' [67, 1] (w:1, o:37, a:1, s:1, b:0),
% 2.20/2.61 domain [68, 3] (w:1, o:95, a:1, s:1, b:0),
% 2.20/2.61 range [69, 3] (w:1, o:96, a:1, s:1, b:0),
% 2.20/2.61 image [70, 2] (w:1, o:87, a:1, s:1, b:0),
% 2.20/2.61 successor [71, 1] (w:1, o:47, a:1, s:1, b:0),
% 2.20/2.61 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 2.20/2.61 inductive [73, 1] (w:1, o:48, a:1, s:1, b:0),
% 2.20/2.61 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 2.20/2.61 'sum_class' [75, 1] (w:1, o:49, a:1, s:1, b:0),
% 2.20/2.61 'power_class' [76, 1] (w:1, o:52, a:1, s:1, b:0),
% 2.20/2.61 compose [78, 2] (w:1, o:91, a:1, s:1, b:0),
% 2.20/2.61 'single_valued_class' [79, 1] (w:1, o:53, a:1, s:1, b:0),
% 2.20/2.61 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 2.20/2.61 function [82, 1] (w:1, o:54, a:1, s:1, b:0),
% 2.20/2.61 regular [83, 1] (w:1, o:38, a:1, s:1, b:0),
% 2.20/2.61 apply [84, 2] (w:1, o:92, a:1, s:1, b:0),
% 2.20/2.61 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 2.20/2.61 'one_to_one' [86, 1] (w:1, o:50, a:1, s:1, b:0),
% 2.20/2.61 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 2.20/2.61 diagonalise [88, 1] (w:1, o:55, a:1, s:1, b:0),
% 2.20/2.61 cantor [89, 1] (w:1, o:43, a:1, s:1, b:0),
% 2.20/2.61 operation [90, 1] (w:1, o:51, a:1, s:1, b:0),
% 2.20/2.61 compatible [94, 3] (w:1, o:94, a:1, s:1, b:0),
% 2.20/2.61 homomorphism [95, 3] (w:1, o:97, a:1, s:1, b:0),
% 2.20/2.61 'not_homomorphism1' [96, 3] (w:1, o:98, a:1, s:1, b:0),
% 2.20/2.61 'not_homomorphism2' [97, 3] (w:1, o:99, a:1, s:1, b:0),
% 2.20/2.61 x [98, 0] (w:1, o:29, a:1, s:1, b:0),
% 2.20/2.61 y [99, 0] (w:1, o:30, a:1, s:1, b:0).
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 Starting Search:
% 2.20/2.61
% 2.20/2.61 Resimplifying inuse:
% 2.20/2.61 Done
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 Intermediate Status:
% 2.20/2.61 Generated: 3845
% 2.20/2.61 Kept: 2022
% 2.20/2.61 Inuse: 118
% 2.20/2.61 Deleted: 2
% 2.20/2.61 Deletedinuse: 2
% 2.20/2.61
% 2.20/2.61 Resimplifying inuse:
% 2.20/2.61 Done
% 2.20/2.61
% 2.20/2.61 Resimplifying inuse:
% 2.20/2.61 Done
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 Intermediate Status:
% 2.20/2.61 Generated: 9516
% 2.20/2.61 Kept: 4222
% 2.20/2.61 Inuse: 201
% 2.20/2.61 Deleted: 8
% 2.20/2.61 Deletedinuse: 8
% 2.20/2.61
% 2.20/2.61 Resimplifying inuse:
% 2.20/2.61 Done
% 2.20/2.61
% 2.20/2.61 Resimplifying inuse:
% 2.20/2.61 Done
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 Intermediate Status:
% 2.20/2.61 Generated: 14632
% 2.20/2.61 Kept: 6225
% 2.20/2.61 Inuse: 280
% 2.20/2.61 Deleted: 12
% 2.20/2.61 Deletedinuse: 11
% 2.20/2.61
% 2.20/2.61 Resimplifying inuse:
% 2.20/2.61 Done
% 2.20/2.61
% 2.20/2.61 Resimplifying inuse:
% 2.20/2.61 Done
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 Intermediate Status:
% 2.20/2.61 Generated: 20598
% 2.20/2.61 Kept: 8250
% 2.20/2.61 Inuse: 331
% 2.20/2.61 Deleted: 56
% 2.20/2.61 Deletedinuse: 52
% 2.20/2.61
% 2.20/2.61 Resimplifying inuse:
% 2.20/2.61 Done
% 2.20/2.61
% 2.20/2.61 Resimplifying inuse:
% 2.20/2.61 Done
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 Intermediate Status:
% 2.20/2.61 Generated: 29178
% 2.20/2.61 Kept: 10998
% 2.20/2.61 Inuse: 397
% 2.20/2.61 Deleted: 71
% 2.20/2.61 Deletedinuse: 57
% 2.20/2.61
% 2.20/2.61 Resimplifying inuse:
% 2.20/2.61 Done
% 2.20/2.61
% 2.20/2.61 Resimplifying inuse:
% 2.20/2.61 Done
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 Intermediate Status:
% 2.20/2.61 Generated: 38701
% 2.20/2.61 Kept: 13007
% 2.20/2.61 Inuse: 446
% 2.20/2.61 Deleted: 73
% 2.20/2.61 Deletedinuse: 58
% 2.20/2.61
% 2.20/2.61 Resimplifying inuse:
% 2.20/2.61 Done
% 2.20/2.61
% 2.20/2.61 Resimplifying inuse:
% 2.20/2.61 Done
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 Intermediate Status:
% 2.20/2.61 Generated: 45776
% 2.20/2.61 Kept: 15040
% 2.20/2.61 Inuse: 486
% 2.20/2.61 Deleted: 87
% 2.20/2.61 Deletedinuse: 71
% 2.20/2.61
% 2.20/2.61 Resimplifying inuse:
% 2.20/2.61 Done
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 Bliksems!, er is een bewijs:
% 2.20/2.61 % SZS status Unsatisfiable
% 2.20/2.61 % SZS output start Refutation
% 2.20/2.61
% 2.20/2.61 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.20/2.61 .
% 2.20/2.61 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 2.20/2.61 .
% 2.20/2.61 clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.20/2.61 'unordered_pair'( Y, X ) ) ] )
% 2.20/2.61 .
% 2.20/2.61 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.20/2.61 .
% 2.20/2.61 clause( 122, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 2.20/2.61 .
% 2.20/2.61 clause( 124, [ =( singleton( y ), singleton( x ) ) ] )
% 2.20/2.61 .
% 2.20/2.61 clause( 125, [ member( x, 'universal_class' ) ] )
% 2.20/2.61 .
% 2.20/2.61 clause( 126, [ ~( =( y, x ) ) ] )
% 2.20/2.61 .
% 2.20/2.61 clause( 159, [ =( X, Y ), ~( =( Y, X ) ) ] )
% 2.20/2.61 .
% 2.20/2.61 clause( 459, [ member( x, 'unordered_pair'( X, x ) ) ] )
% 2.20/2.61 .
% 2.20/2.61 clause( 491, [ member( x, singleton( x ) ) ] )
% 2.20/2.61 .
% 2.20/2.61 clause( 600, [ ~( =( X, x ) ), ~( =( X, y ) ) ] )
% 2.20/2.61 .
% 2.20/2.61 clause( 16362, [ ~( =( Y, X ) ), ~( =( Y, y ) ), ~( member( x, singleton( X
% 2.20/2.61 ) ) ) ] )
% 2.20/2.61 .
% 2.20/2.61 clause( 16912, [ ~( =( X, y ) ) ] )
% 2.20/2.61 .
% 2.20/2.61 clause( 16913, [] )
% 2.20/2.61 .
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 % SZS output end Refutation
% 2.20/2.61 found a proof!
% 2.20/2.61
% 2.20/2.61 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.20/2.61
% 2.20/2.61 initialclauses(
% 2.20/2.61 [ clause( 16915, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 2.20/2.61 ) ] )
% 2.20/2.61 , clause( 16916, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 2.20/2.61 , Y ) ] )
% 2.20/2.61 , clause( 16917, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 2.20/2.61 subclass( X, Y ) ] )
% 2.20/2.61 , clause( 16918, [ subclass( X, 'universal_class' ) ] )
% 2.20/2.61 , clause( 16919, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.20/2.61 , clause( 16920, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 2.20/2.61 , clause( 16921, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 2.20/2.61 ] )
% 2.20/2.61 , clause( 16922, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 2.20/2.61 =( X, Z ) ] )
% 2.20/2.61 , clause( 16923, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.20/2.61 'unordered_pair'( X, Y ) ) ] )
% 2.20/2.61 , clause( 16924, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.20/2.61 'unordered_pair'( Y, X ) ) ] )
% 2.20/2.61 , clause( 16925, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 2.20/2.61 )
% 2.20/2.61 , clause( 16926, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.20/2.61 , clause( 16927, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 2.20/2.61 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 2.20/2.61 , clause( 16928, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.20/2.61 ) ) ), member( X, Z ) ] )
% 2.20/2.61 , clause( 16929, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.20/2.61 ) ) ), member( Y, T ) ] )
% 2.20/2.61 , clause( 16930, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 2.20/2.61 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 2.20/2.61 , clause( 16931, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 2.20/2.61 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 2.20/2.61 , clause( 16932, [ subclass( 'element_relation', 'cross_product'(
% 2.20/2.61 'universal_class', 'universal_class' ) ) ] )
% 2.20/2.61 , clause( 16933, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 2.20/2.61 ), member( X, Y ) ] )
% 2.20/2.61 , clause( 16934, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 2.20/2.61 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 2.20/2.61 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 2.20/2.61 , clause( 16935, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 2.20/2.61 )
% 2.20/2.61 , clause( 16936, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 2.20/2.61 )
% 2.20/2.61 , clause( 16937, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 2.20/2.61 intersection( Y, Z ) ) ] )
% 2.20/2.61 , clause( 16938, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 2.20/2.61 )
% 2.20/2.61 , clause( 16939, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.20/2.61 complement( Y ) ), member( X, Y ) ] )
% 2.20/2.61 , clause( 16940, [ =( complement( intersection( complement( X ), complement(
% 2.20/2.61 Y ) ) ), union( X, Y ) ) ] )
% 2.20/2.61 , clause( 16941, [ =( intersection( complement( intersection( X, Y ) ),
% 2.20/2.61 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 2.20/2.61 'symmetric_difference'( X, Y ) ) ] )
% 2.20/2.61 , clause( 16942, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 2.20/2.61 X, Y, Z ) ) ] )
% 2.20/2.61 , clause( 16943, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 2.20/2.61 Z, X, Y ) ) ] )
% 2.20/2.61 , clause( 16944, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 2.20/2.61 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 2.20/2.61 , clause( 16945, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 2.20/2.61 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 2.20/2.61 'domain_of'( Y ) ) ] )
% 2.20/2.61 , clause( 16946, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 2.20/2.61 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.20/2.61 , clause( 16947, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.20/2.61 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 2.20/2.61 ] )
% 2.20/2.61 , clause( 16948, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.20/2.61 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 2.20/2.61 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.20/2.61 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 2.20/2.61 , Y ), rotate( T ) ) ] )
% 2.20/2.61 , clause( 16949, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 2.20/2.61 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.20/2.61 , clause( 16950, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.20/2.61 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 2.20/2.61 )
% 2.20/2.61 , clause( 16951, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.20/2.61 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 2.20/2.61 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.20/2.61 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 2.20/2.61 , Z ), flip( T ) ) ] )
% 2.20/2.61 , clause( 16952, [ =( 'domain_of'( flip( 'cross_product'( X,
% 2.20/2.61 'universal_class' ) ) ), inverse( X ) ) ] )
% 2.20/2.61 , clause( 16953, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 2.20/2.61 , clause( 16954, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 2.20/2.61 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 2.20/2.61 , clause( 16955, [ =( second( 'not_subclass_element'( restrict( X,
% 2.20/2.61 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 2.20/2.61 , clause( 16956, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 2.20/2.61 image( X, Y ) ) ] )
% 2.20/2.61 , clause( 16957, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 2.20/2.61 , clause( 16958, [ subclass( 'successor_relation', 'cross_product'(
% 2.20/2.61 'universal_class', 'universal_class' ) ) ] )
% 2.20/2.61 , clause( 16959, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 2.20/2.61 ) ), =( successor( X ), Y ) ] )
% 2.20/2.61 , clause( 16960, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 2.20/2.61 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 2.20/2.61 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 2.20/2.61 , clause( 16961, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 2.20/2.61 , clause( 16962, [ ~( inductive( X ) ), subclass( image(
% 2.20/2.61 'successor_relation', X ), X ) ] )
% 2.20/2.61 , clause( 16963, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 2.20/2.61 'successor_relation', X ), X ) ), inductive( X ) ] )
% 2.20/2.61 , clause( 16964, [ inductive( omega ) ] )
% 2.20/2.61 , clause( 16965, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 2.20/2.61 , clause( 16966, [ member( omega, 'universal_class' ) ] )
% 2.20/2.61 , clause( 16967, [ =( 'domain_of'( restrict( 'element_relation',
% 2.20/2.61 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 2.20/2.61 , clause( 16968, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 2.20/2.61 X ), 'universal_class' ) ] )
% 2.20/2.61 , clause( 16969, [ =( complement( image( 'element_relation', complement( X
% 2.20/2.61 ) ) ), 'power_class'( X ) ) ] )
% 2.20/2.61 , clause( 16970, [ ~( member( X, 'universal_class' ) ), member(
% 2.20/2.61 'power_class'( X ), 'universal_class' ) ] )
% 2.20/2.61 , clause( 16971, [ subclass( compose( X, Y ), 'cross_product'(
% 2.20/2.61 'universal_class', 'universal_class' ) ) ] )
% 2.20/2.61 , clause( 16972, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 2.20/2.61 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 2.20/2.61 , clause( 16973, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 2.20/2.61 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 2.20/2.61 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 2.20/2.61 ) ] )
% 2.20/2.61 , clause( 16974, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 2.20/2.61 inverse( X ) ), 'identity_relation' ) ] )
% 2.20/2.61 , clause( 16975, [ ~( subclass( compose( X, inverse( X ) ),
% 2.20/2.61 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 2.20/2.61 , clause( 16976, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 2.20/2.61 'universal_class', 'universal_class' ) ) ] )
% 2.20/2.61 , clause( 16977, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 2.20/2.61 , 'identity_relation' ) ] )
% 2.20/2.61 , clause( 16978, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 2.20/2.61 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 2.20/2.61 'identity_relation' ) ), function( X ) ] )
% 2.20/2.61 , clause( 16979, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 2.20/2.61 , member( image( X, Y ), 'universal_class' ) ] )
% 2.20/2.61 , clause( 16980, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 2.20/2.61 , clause( 16981, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 2.20/2.61 , 'null_class' ) ] )
% 2.20/2.61 , clause( 16982, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 2.20/2.61 Y ) ) ] )
% 2.20/2.61 , clause( 16983, [ function( choice ) ] )
% 2.20/2.61 , clause( 16984, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 2.20/2.61 ), member( apply( choice, X ), X ) ] )
% 2.20/2.61 , clause( 16985, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 2.20/2.61 , clause( 16986, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 2.20/2.61 , clause( 16987, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 2.20/2.61 'one_to_one'( X ) ] )
% 2.20/2.61 , clause( 16988, [ =( intersection( 'cross_product'( 'universal_class',
% 2.20/2.61 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 2.20/2.61 'universal_class' ), complement( compose( complement( 'element_relation'
% 2.20/2.61 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 2.20/2.61 , clause( 16989, [ =( intersection( inverse( 'subset_relation' ),
% 2.20/2.61 'subset_relation' ), 'identity_relation' ) ] )
% 2.20/2.61 , clause( 16990, [ =( complement( 'domain_of'( intersection( X,
% 2.20/2.61 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 2.20/2.61 , clause( 16991, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 2.20/2.61 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 2.20/2.61 , clause( 16992, [ ~( operation( X ) ), function( X ) ] )
% 2.20/2.61 , clause( 16993, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 2.20/2.61 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.20/2.61 ] )
% 2.20/2.61 , clause( 16994, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 2.20/2.61 'domain_of'( 'domain_of'( X ) ) ) ] )
% 2.20/2.61 , clause( 16995, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 2.20/2.61 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.20/2.61 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 2.20/2.61 operation( X ) ] )
% 2.20/2.61 , clause( 16996, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 2.20/2.61 , clause( 16997, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 2.20/2.61 Y ) ), 'domain_of'( X ) ) ] )
% 2.20/2.61 , clause( 16998, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 2.20/2.61 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 2.20/2.61 , clause( 16999, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 2.20/2.61 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 2.20/2.61 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 2.20/2.61 , clause( 17000, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 2.20/2.61 , clause( 17001, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 2.20/2.61 , clause( 17002, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 2.20/2.61 , clause( 17003, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 2.20/2.61 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 2.20/2.61 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 2.20/2.61 )
% 2.20/2.61 , clause( 17004, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.20/2.61 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 2.20/2.61 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 2.20/2.61 , Y ) ] )
% 2.20/2.61 , clause( 17005, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.20/2.61 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 2.20/2.61 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 2.20/2.61 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 2.20/2.61 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 2.20/2.61 )
% 2.20/2.61 , clause( 17006, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.20/2.61 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 2.20/2.61 , clause( 17007, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.20/2.61 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 2.20/2.61 , clause( 17008, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.20/2.61 ) ) ), member( X, 'universal_class' ) ] )
% 2.20/2.61 , clause( 17009, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.20/2.61 ) ) ), member( Y, 'universal_class' ) ] )
% 2.20/2.61 , clause( 17010, [ subclass( X, X ) ] )
% 2.20/2.61 , clause( 17011, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 2.20/2.61 X, Z ) ] )
% 2.20/2.61 , clause( 17012, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 2.20/2.61 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.20/2.61 , clause( 17013, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 2.20/2.61 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.20/2.61 , clause( 17014, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 2.20/2.61 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.20/2.61 , clause( 17015, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 2.20/2.61 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 2.20/2.61 , clause( 17016, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 2.20/2.61 )
% 2.20/2.61 , clause( 17017, [ ~( member( X, 'null_class' ) ) ] )
% 2.20/2.61 , clause( 17018, [ subclass( 'null_class', X ) ] )
% 2.20/2.61 , clause( 17019, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 2.20/2.61 )
% 2.20/2.61 , clause( 17020, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 2.20/2.61 , 'null_class' ), X ) ] )
% 2.20/2.61 , clause( 17021, [ member( 'null_class', 'universal_class' ) ] )
% 2.20/2.61 , clause( 17022, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 2.20/2.61 ] )
% 2.20/2.61 , clause( 17023, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 2.20/2.61 )
% 2.20/2.61 , clause( 17024, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 2.20/2.61 )
% 2.20/2.61 , clause( 17025, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 2.20/2.61 X ), singleton( Y ) ) ] )
% 2.20/2.61 , clause( 17026, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 2.20/2.61 Y ), singleton( Y ) ) ] )
% 2.20/2.61 , clause( 17027, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 2.20/2.61 'universal_class' ), member( Y, 'universal_class' ) ] )
% 2.20/2.61 , clause( 17028, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 2.20/2.61 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 2.20/2.61 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 2.20/2.61 , clause( 17029, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 2.20/2.61 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 2.20/2.61 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 2.20/2.61 , clause( 17030, [ ~( member( X, 'universal_class' ) ), ~( =(
% 2.20/2.61 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 2.20/2.61 , clause( 17031, [ ~( member( X, 'universal_class' ) ), ~( =(
% 2.20/2.61 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 2.20/2.61 , clause( 17032, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.20/2.61 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 2.20/2.61 , clause( 17033, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 2.20/2.61 'unordered_pair'( X, Z ), Y ) ] )
% 2.20/2.61 , clause( 17034, [ member( singleton( X ), 'universal_class' ) ] )
% 2.20/2.61 , clause( 17035, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 2.20/2.61 X ) ) ) ] )
% 2.20/2.61 , clause( 17036, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.20/2.61 singleton( X ) ) ] )
% 2.20/2.61 , clause( 17037, [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X
% 2.20/2.61 ), 'null_class' ) ) ] )
% 2.20/2.61 , clause( 17038, [ member( 'null_class', singleton( 'null_class' ) ) ] )
% 2.20/2.61 , clause( 17039, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 2.20/2.61 , clause( 17040, [ member( X, 'universal_class' ), =( singleton( X ),
% 2.20/2.61 'null_class' ) ] )
% 2.20/2.61 , clause( 17041, [ =( singleton( x ), singleton( y ) ) ] )
% 2.20/2.61 , clause( 17042, [ member( x, 'universal_class' ) ] )
% 2.20/2.61 , clause( 17043, [ ~( =( x, y ) ) ] )
% 2.20/2.61 ] ).
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 subsumption(
% 2.20/2.61 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.20/2.61 , clause( 16919, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.20/2.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.20/2.61 ), ==>( 1, 1 )] ) ).
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 subsumption(
% 2.20/2.61 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 2.20/2.61 , clause( 16921, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 2.20/2.61 ] )
% 2.20/2.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.20/2.61 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 subsumption(
% 2.20/2.61 clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.20/2.61 'unordered_pair'( Y, X ) ) ] )
% 2.20/2.61 , clause( 16924, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.20/2.61 'unordered_pair'( Y, X ) ) ] )
% 2.20/2.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.20/2.61 ), ==>( 1, 1 )] ) ).
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 subsumption(
% 2.20/2.61 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.20/2.61 , clause( 16926, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.20/2.61 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 subsumption(
% 2.20/2.61 clause( 122, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 2.20/2.61 , clause( 17039, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 2.20/2.61 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.20/2.61 ), ==>( 1, 1 )] ) ).
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 eqswap(
% 2.20/2.61 clause( 17214, [ =( singleton( y ), singleton( x ) ) ] )
% 2.20/2.61 , clause( 17041, [ =( singleton( x ), singleton( y ) ) ] )
% 2.20/2.61 , 0, substitution( 0, [] )).
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 subsumption(
% 2.20/2.61 clause( 124, [ =( singleton( y ), singleton( x ) ) ] )
% 2.20/2.61 , clause( 17214, [ =( singleton( y ), singleton( x ) ) ] )
% 2.20/2.61 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 subsumption(
% 2.20/2.61 clause( 125, [ member( x, 'universal_class' ) ] )
% 2.20/2.61 , clause( 17042, [ member( x, 'universal_class' ) ] )
% 2.20/2.61 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 eqswap(
% 2.20/2.61 clause( 17367, [ ~( =( y, x ) ) ] )
% 2.20/2.61 , clause( 17043, [ ~( =( x, y ) ) ] )
% 2.20/2.61 , 0, substitution( 0, [] )).
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 subsumption(
% 2.20/2.61 clause( 126, [ ~( =( y, x ) ) ] )
% 2.20/2.61 , clause( 17367, [ ~( =( y, x ) ) ] )
% 2.20/2.61 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 eqswap(
% 2.20/2.61 clause( 17368, [ ~( =( Y, X ) ), subclass( X, Y ) ] )
% 2.20/2.61 , clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.20/2.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 eqswap(
% 2.20/2.61 clause( 17369, [ ~( =( Y, X ) ), subclass( X, Y ) ] )
% 2.20/2.61 , clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.20/2.61 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 resolution(
% 2.20/2.61 clause( 17370, [ ~( subclass( Y, X ) ), =( X, Y ), ~( =( Y, X ) ) ] )
% 2.20/2.61 , clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 2.20/2.61 , 0, clause( 17368, [ ~( =( Y, X ) ), subclass( X, Y ) ] )
% 2.20/2.61 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 2.20/2.61 , X ), :=( Y, Y )] )).
% 2.20/2.61
% 2.20/2.61
% 2.20/2.61 resolution(
% 2.20/2.61 clause( 17372, [ =( Y, X ), ~( =( X, Y ) ), ~Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------