TSTP Solution File: SET082-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET082-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.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 22:46:45 EDT 2022
% Result : Unsatisfiable 2.20s 2.57s
% Output : Refutation 2.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET082-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n020.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 : Mon Jul 11 05:18:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.71/1.10 *** allocated 10000 integers for termspace/termends
% 0.71/1.10 *** allocated 10000 integers for clauses
% 0.71/1.10 *** allocated 10000 integers for justifications
% 0.71/1.10 Bliksem 1.12
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 Automatic Strategy Selection
% 0.71/1.10
% 0.71/1.10 Clauses:
% 0.71/1.10 [
% 0.71/1.10 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.71/1.10 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.71/1.10 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ subclass( X, 'universal_class' ) ],
% 0.71/1.10 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.71/1.10 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.71/1.10 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.71/1.10 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.71/1.10 ) ) ],
% 0.71/1.10 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.71/1.10 ) ) ],
% 0.71/1.10 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.71/1.10 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.71/1.10 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.71/1.10 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.71/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.71/1.10 X, Z ) ],
% 0.71/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.71/1.10 Y, T ) ],
% 0.71/1.10 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.71/1.10 ), 'cross_product'( Y, T ) ) ],
% 0.71/1.10 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.71/1.10 ), second( X ) ), X ) ],
% 0.71/1.10 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.71/1.10 'universal_class' ) ) ],
% 0.71/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.71/1.10 Y ) ],
% 0.71/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.71/1.10 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.71/1.10 , Y ), 'element_relation' ) ],
% 0.71/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.71/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.71/1.10 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.71/1.10 Z ) ) ],
% 0.71/1.10 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.71/1.10 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.71/1.10 member( X, Y ) ],
% 0.71/1.10 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.71/1.10 union( X, Y ) ) ],
% 0.71/1.10 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.71/1.10 intersection( complement( X ), complement( Y ) ) ) ),
% 0.71/1.10 'symmetric_difference'( X, Y ) ) ],
% 0.71/1.10 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.71/1.10 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.71/1.10 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.71/1.10 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.71/1.10 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.71/1.10 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.71/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.71/1.10 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.71/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.71/1.10 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.71/1.10 'cross_product'( 'universal_class', 'universal_class' ),
% 0.71/1.10 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.71/1.10 Y ), rotate( T ) ) ],
% 0.71/1.10 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.71/1.10 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.71/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.71/1.10 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.71/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.71/1.10 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.71/1.10 'cross_product'( 'universal_class', 'universal_class' ),
% 0.71/1.10 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.71/1.10 Z ), flip( T ) ) ],
% 0.71/1.10 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.71/1.10 inverse( X ) ) ],
% 0.71/1.10 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.71/1.10 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.71/1.10 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.71/1.10 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.71/1.10 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.71/1.10 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.71/1.10 ],
% 0.71/1.10 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.71/1.10 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.71/1.10 'universal_class' ) ) ],
% 0.71/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.71/1.10 successor( X ), Y ) ],
% 0.71/1.10 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.71/1.10 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.71/1.10 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.71/1.10 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.71/1.10 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.71/1.10 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.71/1.10 [ inductive( omega ) ],
% 0.71/1.10 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.71/1.10 [ member( omega, 'universal_class' ) ],
% 0.71/1.10 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.71/1.10 , 'sum_class'( X ) ) ],
% 0.71/1.10 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.71/1.10 'universal_class' ) ],
% 0.71/1.10 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.71/1.10 'power_class'( X ) ) ],
% 0.71/1.10 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.71/1.10 'universal_class' ) ],
% 0.71/1.10 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.71/1.10 'universal_class' ) ) ],
% 0.71/1.10 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.71/1.10 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.71/1.10 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.71/1.10 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.71/1.10 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.71/1.10 ) ],
% 0.71/1.10 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.71/1.10 , 'identity_relation' ) ],
% 0.71/1.10 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.71/1.10 'single_valued_class'( X ) ],
% 0.71/1.10 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.71/1.10 'universal_class' ) ) ],
% 0.71/1.10 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.71/1.10 'identity_relation' ) ],
% 0.71/1.10 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.71/1.10 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.71/1.10 , function( X ) ],
% 0.71/1.10 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.71/1.10 X, Y ), 'universal_class' ) ],
% 0.71/1.10 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.71/1.10 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.71/1.10 ) ],
% 0.71/1.10 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.71/1.10 [ function( choice ) ],
% 0.71/1.10 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.71/1.10 apply( choice, X ), X ) ],
% 0.71/1.10 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.71/1.10 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.71/1.10 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.71/1.10 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.71/1.10 , complement( compose( complement( 'element_relation' ), inverse(
% 0.71/1.10 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.71/1.10 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.71/1.10 'identity_relation' ) ],
% 0.71/1.10 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.71/1.10 , diagonalise( X ) ) ],
% 0.71/1.10 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.71/1.10 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.71/1.10 [ ~( operation( X ) ), function( X ) ],
% 0.71/1.10 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.71/1.10 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.71/1.10 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.71/1.10 'domain_of'( X ) ) ) ],
% 0.71/1.10 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.71/1.10 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.71/1.10 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.71/1.10 X ) ],
% 0.71/1.10 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.71/1.10 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.71/1.10 'domain_of'( X ) ) ],
% 0.71/1.10 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.71/1.10 'domain_of'( Z ) ) ) ],
% 0.71/1.10 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.71/1.10 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.71/1.10 ), compatible( X, Y, Z ) ],
% 0.71/1.10 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.71/1.10 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.71/1.10 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.71/1.10 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.71/1.10 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.71/1.10 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.71/1.10 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.71/1.10 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.71/1.10 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.71/1.10 , Y ) ],
% 0.71/1.10 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.71/1.10 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.71/1.10 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.71/1.10 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.71/1.10 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.71/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.71/1.10 X, 'unordered_pair'( X, Y ) ) ],
% 0.71/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.71/1.10 Y, 'unordered_pair'( X, Y ) ) ],
% 0.71/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.71/1.10 X, 'universal_class' ) ],
% 0.71/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.71/1.10 Y, 'universal_class' ) ],
% 0.71/1.10 [ subclass( X, X ) ],
% 0.71/1.10 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.71/1.10 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.71/1.10 'not_subclass_element'( Y, X ), Y ) ],
% 0.71/1.10 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.71/1.10 'not_subclass_element'( Y, X ), Y ) ],
% 0.71/1.10 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.71/1.10 'not_subclass_element'( Y, X ), Y ) ],
% 0.71/1.10 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.71/1.10 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.71/1.10 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.71/1.10 [ ~( member( X, 'null_class' ) ) ],
% 0.71/1.10 [ subclass( 'null_class', X ) ],
% 0.71/1.10 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.71/1.10 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.71/1.10 ), X ) ],
% 0.71/1.10 [ member( 'null_class', 'universal_class' ) ],
% 0.71/1.10 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.71/1.10 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.71/1.10 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.71/1.10 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.71/1.10 Y ) ) ],
% 0.71/1.10 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.71/1.10 Y ) ) ],
% 0.71/1.10 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.71/1.10 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.71/1.10 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.71/1.10 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.71/1.10 'universal_class' ) ) ), =( Y, Z ) ],
% 0.71/1.10 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.71/1.10 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.71/1.10 'universal_class' ) ) ), =( X, Z ) ],
% 0.71/1.10 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.71/1.10 'null_class' ) ) ],
% 0.71/1.10 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.71/1.10 'null_class' ) ) ],
% 0.71/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.71/1.10 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 2.13/2.57 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 2.13/2.57 X, Z ), Y ) ],
% 2.13/2.57 [ member( singleton( X ), 'universal_class' ) ],
% 2.13/2.57 [ member( singleton( X ), 'unordered_pair'( Y, singleton( X ) ) ) ],
% 2.13/2.57 [ ~( member( X, 'universal_class' ) ), member( X, singleton( X ) ) ]
% 2.13/2.57 ,
% 2.13/2.57 [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X ),
% 2.13/2.57 'null_class' ) ) ],
% 2.13/2.57 [ member( 'null_class', singleton( 'null_class' ) ) ],
% 2.13/2.57 [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ],
% 2.13/2.57 [ ~( member( x, 'universal_class' ) ) ],
% 2.13/2.57 [ ~( =( singleton( x ), 'null_class' ) ) ]
% 2.13/2.57 ] .
% 2.13/2.57
% 2.13/2.57
% 2.13/2.57 percentage equality = 0.236948, percentage horn = 0.881890
% 2.13/2.57 This is a problem with some equality
% 2.13/2.57
% 2.13/2.57
% 2.13/2.57
% 2.13/2.57 Options Used:
% 2.13/2.57
% 2.13/2.57 useres = 1
% 2.13/2.57 useparamod = 1
% 2.13/2.57 useeqrefl = 1
% 2.13/2.57 useeqfact = 1
% 2.13/2.57 usefactor = 1
% 2.13/2.57 usesimpsplitting = 0
% 2.13/2.57 usesimpdemod = 5
% 2.13/2.57 usesimpres = 3
% 2.13/2.57
% 2.13/2.57 resimpinuse = 1000
% 2.13/2.57 resimpclauses = 20000
% 2.13/2.57 substype = eqrewr
% 2.13/2.57 backwardsubs = 1
% 2.13/2.57 selectoldest = 5
% 2.13/2.57
% 2.13/2.57 litorderings [0] = split
% 2.13/2.57 litorderings [1] = extend the termordering, first sorting on arguments
% 2.13/2.57
% 2.13/2.57 termordering = kbo
% 2.13/2.57
% 2.13/2.57 litapriori = 0
% 2.13/2.57 termapriori = 1
% 2.13/2.57 litaposteriori = 0
% 2.13/2.57 termaposteriori = 0
% 2.13/2.57 demodaposteriori = 0
% 2.13/2.57 ordereqreflfact = 0
% 2.13/2.57
% 2.13/2.57 litselect = negord
% 2.13/2.57
% 2.13/2.57 maxweight = 15
% 2.13/2.57 maxdepth = 30000
% 2.13/2.57 maxlength = 115
% 2.13/2.57 maxnrvars = 195
% 2.13/2.57 excuselevel = 1
% 2.13/2.57 increasemaxweight = 1
% 2.13/2.57
% 2.13/2.57 maxselected = 10000000
% 2.13/2.57 maxnrclauses = 10000000
% 2.13/2.57
% 2.13/2.57 showgenerated = 0
% 2.13/2.57 showkept = 0
% 2.13/2.57 showselected = 0
% 2.13/2.57 showdeleted = 0
% 2.13/2.57 showresimp = 1
% 2.13/2.57 showstatus = 2000
% 2.13/2.57
% 2.13/2.57 prologoutput = 1
% 2.13/2.57 nrgoals = 5000000
% 2.13/2.57 totalproof = 1
% 2.13/2.57
% 2.13/2.57 Symbols occurring in the translation:
% 2.13/2.57
% 2.13/2.57 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.13/2.57 . [1, 2] (w:1, o:55, a:1, s:1, b:0),
% 2.13/2.57 ! [4, 1] (w:0, o:30, a:1, s:1, b:0),
% 2.13/2.57 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.13/2.57 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.13/2.57 subclass [41, 2] (w:1, o:80, a:1, s:1, b:0),
% 2.13/2.57 member [43, 2] (w:1, o:81, a:1, s:1, b:0),
% 2.20/2.57 'not_subclass_element' [44, 2] (w:1, o:82, a:1, s:1, b:0),
% 2.20/2.57 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 2.20/2.57 'unordered_pair' [46, 2] (w:1, o:83, a:1, s:1, b:0),
% 2.20/2.57 singleton [47, 1] (w:1, o:38, a:1, s:1, b:0),
% 2.20/2.57 'ordered_pair' [48, 2] (w:1, o:84, a:1, s:1, b:0),
% 2.20/2.57 'cross_product' [50, 2] (w:1, o:85, a:1, s:1, b:0),
% 2.20/2.57 first [52, 1] (w:1, o:39, a:1, s:1, b:0),
% 2.20/2.57 second [53, 1] (w:1, o:40, a:1, s:1, b:0),
% 2.20/2.57 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 2.20/2.57 intersection [55, 2] (w:1, o:87, a:1, s:1, b:0),
% 2.20/2.57 complement [56, 1] (w:1, o:41, a:1, s:1, b:0),
% 2.20/2.57 union [57, 2] (w:1, o:88, a:1, s:1, b:0),
% 2.20/2.57 'symmetric_difference' [58, 2] (w:1, o:89, a:1, s:1, b:0),
% 2.20/2.57 restrict [60, 3] (w:1, o:92, a:1, s:1, b:0),
% 2.20/2.57 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 2.20/2.57 'domain_of' [62, 1] (w:1, o:43, a:1, s:1, b:0),
% 2.20/2.57 rotate [63, 1] (w:1, o:35, a:1, s:1, b:0),
% 2.20/2.57 flip [65, 1] (w:1, o:44, a:1, s:1, b:0),
% 2.20/2.57 inverse [66, 1] (w:1, o:45, a:1, s:1, b:0),
% 2.20/2.57 'range_of' [67, 1] (w:1, o:36, a:1, s:1, b:0),
% 2.20/2.57 domain [68, 3] (w:1, o:94, a:1, s:1, b:0),
% 2.20/2.57 range [69, 3] (w:1, o:95, a:1, s:1, b:0),
% 2.20/2.57 image [70, 2] (w:1, o:86, a:1, s:1, b:0),
% 2.20/2.57 successor [71, 1] (w:1, o:46, a:1, s:1, b:0),
% 2.20/2.57 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 2.20/2.57 inductive [73, 1] (w:1, o:47, a:1, s:1, b:0),
% 2.20/2.57 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 2.20/2.57 'sum_class' [75, 1] (w:1, o:48, a:1, s:1, b:0),
% 2.20/2.57 'power_class' [76, 1] (w:1, o:51, a:1, s:1, b:0),
% 2.20/2.57 compose [78, 2] (w:1, o:90, a:1, s:1, b:0),
% 2.20/2.57 'single_valued_class' [79, 1] (w:1, o:52, a:1, s:1, b:0),
% 2.20/2.57 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 2.20/2.57 function [82, 1] (w:1, o:53, a:1, s:1, b:0),
% 2.20/2.57 regular [83, 1] (w:1, o:37, a:1, s:1, b:0),
% 2.20/2.57 apply [84, 2] (w:1, o:91, a:1, s:1, b:0),
% 2.20/2.57 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 2.20/2.57 'one_to_one' [86, 1] (w:1, o:49, a:1, s:1, b:0),
% 2.20/2.57 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 2.20/2.57 diagonalise [88, 1] (w:1, o:54, a:1, s:1, b:0),
% 2.20/2.57 cantor [89, 1] (w:1, o:42, a:1, s:1, b:0),
% 2.20/2.57 operation [90, 1] (w:1, o:50, a:1, s:1, b:0),
% 2.20/2.57 compatible [94, 3] (w:1, o:93, a:1, s:1, b:0),
% 2.20/2.57 homomorphism [95, 3] (w:1, o:96, a:1, s:1, b:0),
% 2.20/2.57 'not_homomorphism1' [96, 3] (w:1, o:97, a:1, s:1, b:0),
% 2.20/2.57 'not_homomorphism2' [97, 3] (w:1, o:98, a:1, s:1, b:0),
% 2.20/2.57 x [98, 0] (w:1, o:29, a:1, s:1, b:0).
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 Starting Search:
% 2.20/2.57
% 2.20/2.57 Resimplifying inuse:
% 2.20/2.57 Done
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 Intermediate Status:
% 2.20/2.57 Generated: 3973
% 2.20/2.57 Kept: 2018
% 2.20/2.57 Inuse: 124
% 2.20/2.57 Deleted: 3
% 2.20/2.57 Deletedinuse: 3
% 2.20/2.57
% 2.20/2.57 Resimplifying inuse:
% 2.20/2.57 Done
% 2.20/2.57
% 2.20/2.57 Resimplifying inuse:
% 2.20/2.57 Done
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 Intermediate Status:
% 2.20/2.57 Generated: 9310
% 2.20/2.57 Kept: 4028
% 2.20/2.57 Inuse: 202
% 2.20/2.57 Deleted: 8
% 2.20/2.57 Deletedinuse: 8
% 2.20/2.57
% 2.20/2.57 Resimplifying inuse:
% 2.20/2.57 Done
% 2.20/2.57
% 2.20/2.57 Resimplifying inuse:
% 2.20/2.57 Done
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 Intermediate Status:
% 2.20/2.57 Generated: 15234
% 2.20/2.57 Kept: 6327
% 2.20/2.57 Inuse: 286
% 2.20/2.57 Deleted: 11
% 2.20/2.57 Deletedinuse: 11
% 2.20/2.57
% 2.20/2.57 Resimplifying inuse:
% 2.20/2.57 Done
% 2.20/2.57
% 2.20/2.57 Resimplifying inuse:
% 2.20/2.57 Done
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 Intermediate Status:
% 2.20/2.57 Generated: 21069
% 2.20/2.57 Kept: 8345
% 2.20/2.57 Inuse: 344
% 2.20/2.57 Deleted: 61
% 2.20/2.57 Deletedinuse: 58
% 2.20/2.57
% 2.20/2.57 Resimplifying inuse:
% 2.20/2.57 Done
% 2.20/2.57
% 2.20/2.57 Resimplifying inuse:
% 2.20/2.57 Done
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 Intermediate Status:
% 2.20/2.57 Generated: 28781
% 2.20/2.57 Kept: 10798
% 2.20/2.57 Inuse: 396
% 2.20/2.57 Deleted: 78
% 2.20/2.57 Deletedinuse: 63
% 2.20/2.57
% 2.20/2.57 Resimplifying inuse:
% 2.20/2.57 Done
% 2.20/2.57
% 2.20/2.57 Resimplifying inuse:
% 2.20/2.57 Done
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 Intermediate Status:
% 2.20/2.57 Generated: 38202
% 2.20/2.57 Kept: 12809
% 2.20/2.57 Inuse: 445
% 2.20/2.57 Deleted: 80
% 2.20/2.57 Deletedinuse: 64
% 2.20/2.57
% 2.20/2.57 Resimplifying inuse:
% 2.20/2.57 Done
% 2.20/2.57
% 2.20/2.57 Resimplifying inuse:
% 2.20/2.57 Done
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 Intermediate Status:
% 2.20/2.57 Generated: 47866
% 2.20/2.57 Kept: 16536
% 2.20/2.57 Inuse: 489
% 2.20/2.57 Deleted: 92
% 2.20/2.57 Deletedinuse: 75
% 2.20/2.57
% 2.20/2.57 Resimplifying inuse:
% 2.20/2.57 Done
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 Bliksems!, er is een bewijs:
% 2.20/2.57 % SZS status Unsatisfiable
% 2.20/2.57 % SZS output start Refutation
% 2.20/2.57
% 2.20/2.57 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 2.20/2.57 )
% 2.20/2.57 .
% 2.20/2.57 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 2.20/2.57 .
% 2.20/2.57 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.20/2.57 .
% 2.20/2.57 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 2.20/2.57 .
% 2.20/2.57 clause( 103, [ =( X, 'null_class' ), member( 'not_subclass_element'( X,
% 2.20/2.57 'null_class' ), X ) ] )
% 2.20/2.57 .
% 2.20/2.57 clause( 122, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 2.20/2.57 .
% 2.20/2.57 clause( 123, [ ~( member( x, 'universal_class' ) ) ] )
% 2.20/2.57 .
% 2.20/2.57 clause( 124, [ ~( =( singleton( x ), 'null_class' ) ) ] )
% 2.20/2.57 .
% 2.20/2.57 clause( 140, [ ~( member( x, X ) ) ] )
% 2.20/2.57 .
% 2.20/2.57 clause( 158, [ =( X, Y ), ~( =( Y, X ) ) ] )
% 2.20/2.57 .
% 2.20/2.57 clause( 526, [ ~( member( X, Y ) ), ~( =( X, x ) ) ] )
% 2.20/2.57 .
% 2.20/2.57 clause( 14810, [ ~( member( X, singleton( x ) ) ), ~( member( X, Y ) ) ] )
% 2.20/2.57 .
% 2.20/2.57 clause( 16535, [ ~( member( X, singleton( x ) ) ) ] )
% 2.20/2.57 .
% 2.20/2.57 clause( 16536, [ =( singleton( x ), 'null_class' ) ] )
% 2.20/2.57 .
% 2.20/2.57 clause( 16545, [] )
% 2.20/2.57 .
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 % SZS output end Refutation
% 2.20/2.57 found a proof!
% 2.20/2.57
% 2.20/2.57 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.20/2.57
% 2.20/2.57 initialclauses(
% 2.20/2.57 [ clause( 16547, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 2.20/2.57 ) ] )
% 2.20/2.57 , clause( 16548, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 2.20/2.57 , Y ) ] )
% 2.20/2.57 , clause( 16549, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 2.20/2.57 subclass( X, Y ) ] )
% 2.20/2.57 , clause( 16550, [ subclass( X, 'universal_class' ) ] )
% 2.20/2.57 , clause( 16551, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.20/2.57 , clause( 16552, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 2.20/2.57 , clause( 16553, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 2.20/2.57 ] )
% 2.20/2.57 , clause( 16554, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 2.20/2.57 =( X, Z ) ] )
% 2.20/2.57 , clause( 16555, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.20/2.57 'unordered_pair'( X, Y ) ) ] )
% 2.20/2.57 , clause( 16556, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.20/2.57 'unordered_pair'( Y, X ) ) ] )
% 2.20/2.57 , clause( 16557, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 2.20/2.57 )
% 2.20/2.57 , clause( 16558, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.20/2.57 , clause( 16559, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 2.20/2.57 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 2.20/2.57 , clause( 16560, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.20/2.57 ) ) ), member( X, Z ) ] )
% 2.20/2.57 , clause( 16561, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.20/2.57 ) ) ), member( Y, T ) ] )
% 2.20/2.57 , clause( 16562, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 2.20/2.57 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 2.20/2.57 , clause( 16563, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 2.20/2.57 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 2.20/2.57 , clause( 16564, [ subclass( 'element_relation', 'cross_product'(
% 2.20/2.57 'universal_class', 'universal_class' ) ) ] )
% 2.20/2.57 , clause( 16565, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 2.20/2.57 ), member( X, Y ) ] )
% 2.20/2.57 , clause( 16566, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 2.20/2.57 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 2.20/2.57 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 2.20/2.57 , clause( 16567, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 2.20/2.57 )
% 2.20/2.57 , clause( 16568, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 2.20/2.57 )
% 2.20/2.57 , clause( 16569, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 2.20/2.57 intersection( Y, Z ) ) ] )
% 2.20/2.57 , clause( 16570, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 2.20/2.57 )
% 2.20/2.57 , clause( 16571, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.20/2.57 complement( Y ) ), member( X, Y ) ] )
% 2.20/2.57 , clause( 16572, [ =( complement( intersection( complement( X ), complement(
% 2.20/2.57 Y ) ) ), union( X, Y ) ) ] )
% 2.20/2.57 , clause( 16573, [ =( intersection( complement( intersection( X, Y ) ),
% 2.20/2.57 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 2.20/2.57 'symmetric_difference'( X, Y ) ) ] )
% 2.20/2.57 , clause( 16574, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 2.20/2.57 X, Y, Z ) ) ] )
% 2.20/2.57 , clause( 16575, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 2.20/2.57 Z, X, Y ) ) ] )
% 2.20/2.57 , clause( 16576, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 2.20/2.57 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 2.20/2.57 , clause( 16577, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 2.20/2.57 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 2.20/2.57 'domain_of'( Y ) ) ] )
% 2.20/2.57 , clause( 16578, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 2.20/2.57 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.20/2.57 , clause( 16579, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.20/2.57 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 2.20/2.57 ] )
% 2.20/2.57 , clause( 16580, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.20/2.57 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 2.20/2.57 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.20/2.57 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 2.20/2.57 , Y ), rotate( T ) ) ] )
% 2.20/2.57 , clause( 16581, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 2.20/2.57 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.20/2.57 , clause( 16582, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.20/2.57 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 2.20/2.57 )
% 2.20/2.57 , clause( 16583, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.20/2.57 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 2.20/2.57 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.20/2.57 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 2.20/2.57 , Z ), flip( T ) ) ] )
% 2.20/2.57 , clause( 16584, [ =( 'domain_of'( flip( 'cross_product'( X,
% 2.20/2.57 'universal_class' ) ) ), inverse( X ) ) ] )
% 2.20/2.57 , clause( 16585, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 2.20/2.57 , clause( 16586, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 2.20/2.57 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 2.20/2.57 , clause( 16587, [ =( second( 'not_subclass_element'( restrict( X,
% 2.20/2.57 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 2.20/2.57 , clause( 16588, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 2.20/2.57 image( X, Y ) ) ] )
% 2.20/2.57 , clause( 16589, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 2.20/2.57 , clause( 16590, [ subclass( 'successor_relation', 'cross_product'(
% 2.20/2.57 'universal_class', 'universal_class' ) ) ] )
% 2.20/2.57 , clause( 16591, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 2.20/2.57 ) ), =( successor( X ), Y ) ] )
% 2.20/2.57 , clause( 16592, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 2.20/2.57 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 2.20/2.57 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 2.20/2.57 , clause( 16593, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 2.20/2.57 , clause( 16594, [ ~( inductive( X ) ), subclass( image(
% 2.20/2.57 'successor_relation', X ), X ) ] )
% 2.20/2.57 , clause( 16595, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 2.20/2.57 'successor_relation', X ), X ) ), inductive( X ) ] )
% 2.20/2.57 , clause( 16596, [ inductive( omega ) ] )
% 2.20/2.57 , clause( 16597, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 2.20/2.57 , clause( 16598, [ member( omega, 'universal_class' ) ] )
% 2.20/2.57 , clause( 16599, [ =( 'domain_of'( restrict( 'element_relation',
% 2.20/2.57 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 2.20/2.57 , clause( 16600, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 2.20/2.57 X ), 'universal_class' ) ] )
% 2.20/2.57 , clause( 16601, [ =( complement( image( 'element_relation', complement( X
% 2.20/2.57 ) ) ), 'power_class'( X ) ) ] )
% 2.20/2.57 , clause( 16602, [ ~( member( X, 'universal_class' ) ), member(
% 2.20/2.57 'power_class'( X ), 'universal_class' ) ] )
% 2.20/2.57 , clause( 16603, [ subclass( compose( X, Y ), 'cross_product'(
% 2.20/2.57 'universal_class', 'universal_class' ) ) ] )
% 2.20/2.57 , clause( 16604, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 2.20/2.57 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 2.20/2.57 , clause( 16605, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 2.20/2.57 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 2.20/2.57 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 2.20/2.57 ) ] )
% 2.20/2.57 , clause( 16606, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 2.20/2.57 inverse( X ) ), 'identity_relation' ) ] )
% 2.20/2.57 , clause( 16607, [ ~( subclass( compose( X, inverse( X ) ),
% 2.20/2.57 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 2.20/2.57 , clause( 16608, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 2.20/2.57 'universal_class', 'universal_class' ) ) ] )
% 2.20/2.57 , clause( 16609, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 2.20/2.57 , 'identity_relation' ) ] )
% 2.20/2.57 , clause( 16610, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 2.20/2.57 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 2.20/2.57 'identity_relation' ) ), function( X ) ] )
% 2.20/2.57 , clause( 16611, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 2.20/2.57 , member( image( X, Y ), 'universal_class' ) ] )
% 2.20/2.57 , clause( 16612, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 2.20/2.57 , clause( 16613, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 2.20/2.57 , 'null_class' ) ] )
% 2.20/2.57 , clause( 16614, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 2.20/2.57 Y ) ) ] )
% 2.20/2.57 , clause( 16615, [ function( choice ) ] )
% 2.20/2.57 , clause( 16616, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 2.20/2.57 ), member( apply( choice, X ), X ) ] )
% 2.20/2.57 , clause( 16617, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 2.20/2.57 , clause( 16618, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 2.20/2.57 , clause( 16619, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 2.20/2.57 'one_to_one'( X ) ] )
% 2.20/2.57 , clause( 16620, [ =( intersection( 'cross_product'( 'universal_class',
% 2.20/2.57 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 2.20/2.57 'universal_class' ), complement( compose( complement( 'element_relation'
% 2.20/2.57 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 2.20/2.57 , clause( 16621, [ =( intersection( inverse( 'subset_relation' ),
% 2.20/2.57 'subset_relation' ), 'identity_relation' ) ] )
% 2.20/2.57 , clause( 16622, [ =( complement( 'domain_of'( intersection( X,
% 2.20/2.57 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 2.20/2.57 , clause( 16623, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 2.20/2.57 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 2.20/2.57 , clause( 16624, [ ~( operation( X ) ), function( X ) ] )
% 2.20/2.57 , clause( 16625, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 2.20/2.57 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.20/2.57 ] )
% 2.20/2.57 , clause( 16626, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 2.20/2.57 'domain_of'( 'domain_of'( X ) ) ) ] )
% 2.20/2.57 , clause( 16627, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 2.20/2.57 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.20/2.57 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 2.20/2.57 operation( X ) ] )
% 2.20/2.57 , clause( 16628, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 2.20/2.57 , clause( 16629, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 2.20/2.57 Y ) ), 'domain_of'( X ) ) ] )
% 2.20/2.57 , clause( 16630, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 2.20/2.57 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 2.20/2.57 , clause( 16631, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 2.20/2.57 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 2.20/2.57 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 2.20/2.57 , clause( 16632, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 2.20/2.57 , clause( 16633, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 2.20/2.57 , clause( 16634, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 2.20/2.57 , clause( 16635, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 2.20/2.57 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 2.20/2.57 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 2.20/2.57 )
% 2.20/2.57 , clause( 16636, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.20/2.57 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 2.20/2.57 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 2.20/2.57 , Y ) ] )
% 2.20/2.57 , clause( 16637, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.20/2.57 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 2.20/2.57 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 2.20/2.57 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 2.20/2.57 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 2.20/2.57 )
% 2.20/2.57 , clause( 16638, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.20/2.57 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 2.20/2.57 , clause( 16639, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.20/2.57 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 2.20/2.57 , clause( 16640, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.20/2.57 ) ) ), member( X, 'universal_class' ) ] )
% 2.20/2.57 , clause( 16641, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.20/2.57 ) ) ), member( Y, 'universal_class' ) ] )
% 2.20/2.57 , clause( 16642, [ subclass( X, X ) ] )
% 2.20/2.57 , clause( 16643, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 2.20/2.57 X, Z ) ] )
% 2.20/2.57 , clause( 16644, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 2.20/2.57 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.20/2.57 , clause( 16645, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 2.20/2.57 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.20/2.57 , clause( 16646, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 2.20/2.57 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.20/2.57 , clause( 16647, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 2.20/2.57 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 2.20/2.57 , clause( 16648, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 2.20/2.57 )
% 2.20/2.57 , clause( 16649, [ ~( member( X, 'null_class' ) ) ] )
% 2.20/2.57 , clause( 16650, [ subclass( 'null_class', X ) ] )
% 2.20/2.57 , clause( 16651, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 2.20/2.57 )
% 2.20/2.57 , clause( 16652, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 2.20/2.57 , 'null_class' ), X ) ] )
% 2.20/2.57 , clause( 16653, [ member( 'null_class', 'universal_class' ) ] )
% 2.20/2.57 , clause( 16654, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 2.20/2.57 ] )
% 2.20/2.57 , clause( 16655, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 2.20/2.57 )
% 2.20/2.57 , clause( 16656, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 2.20/2.57 )
% 2.20/2.57 , clause( 16657, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 2.20/2.57 X ), singleton( Y ) ) ] )
% 2.20/2.57 , clause( 16658, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 2.20/2.57 Y ), singleton( Y ) ) ] )
% 2.20/2.57 , clause( 16659, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 2.20/2.57 'universal_class' ), member( Y, 'universal_class' ) ] )
% 2.20/2.57 , clause( 16660, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 2.20/2.57 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 2.20/2.57 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 2.20/2.57 , clause( 16661, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 2.20/2.57 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 2.20/2.57 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 2.20/2.57 , clause( 16662, [ ~( member( X, 'universal_class' ) ), ~( =(
% 2.20/2.57 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 2.20/2.57 , clause( 16663, [ ~( member( X, 'universal_class' ) ), ~( =(
% 2.20/2.57 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 2.20/2.57 , clause( 16664, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.20/2.57 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 2.20/2.57 , clause( 16665, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 2.20/2.57 'unordered_pair'( X, Z ), Y ) ] )
% 2.20/2.57 , clause( 16666, [ member( singleton( X ), 'universal_class' ) ] )
% 2.20/2.57 , clause( 16667, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 2.20/2.57 X ) ) ) ] )
% 2.20/2.57 , clause( 16668, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.20/2.57 singleton( X ) ) ] )
% 2.20/2.57 , clause( 16669, [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X
% 2.20/2.57 ), 'null_class' ) ) ] )
% 2.20/2.57 , clause( 16670, [ member( 'null_class', singleton( 'null_class' ) ) ] )
% 2.20/2.57 , clause( 16671, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 2.20/2.57 , clause( 16672, [ ~( member( x, 'universal_class' ) ) ] )
% 2.20/2.57 , clause( 16673, [ ~( =( singleton( x ), 'null_class' ) ) ] )
% 2.20/2.57 ] ).
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 subsumption(
% 2.20/2.57 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 2.20/2.57 )
% 2.20/2.57 , clause( 16547, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 2.20/2.57 ) ] )
% 2.20/2.57 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.20/2.57 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 subsumption(
% 2.20/2.57 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 2.20/2.57 , clause( 16550, [ subclass( X, 'universal_class' ) ] )
% 2.20/2.57 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 subsumption(
% 2.20/2.57 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.20/2.57 , clause( 16551, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.20/2.57 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.20/2.57 ), ==>( 1, 1 )] ) ).
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 subsumption(
% 2.20/2.57 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 2.20/2.57 , clause( 16553, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 2.20/2.57 ] )
% 2.20/2.57 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.20/2.57 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 subsumption(
% 2.20/2.57 clause( 103, [ =( X, 'null_class' ), member( 'not_subclass_element'( X,
% 2.20/2.57 'null_class' ), X ) ] )
% 2.20/2.57 , clause( 16652, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 2.20/2.57 , 'null_class' ), X ) ] )
% 2.20/2.57 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 2.20/2.57 1 )] ) ).
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 subsumption(
% 2.20/2.57 clause( 122, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 2.20/2.57 , clause( 16671, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 2.20/2.57 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.20/2.57 ), ==>( 1, 1 )] ) ).
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 subsumption(
% 2.20/2.57 clause( 123, [ ~( member( x, 'universal_class' ) ) ] )
% 2.20/2.57 , clause( 16672, [ ~( member( x, 'universal_class' ) ) ] )
% 2.20/2.57 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 subsumption(
% 2.20/2.57 clause( 124, [ ~( =( singleton( x ), 'null_class' ) ) ] )
% 2.20/2.57 , clause( 16673, [ ~( =( singleton( x ), 'null_class' ) ) ] )
% 2.20/2.57 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 resolution(
% 2.20/2.57 clause( 16958, [ ~( subclass( X, 'universal_class' ) ), ~( member( x, X ) )
% 2.20/2.57 ] )
% 2.20/2.57 , clause( 123, [ ~( member( x, 'universal_class' ) ) ] )
% 2.20/2.57 , 0, clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 2.20/2.57 ) ] )
% 2.20/2.57 , 2, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y,
% 2.20/2.57 'universal_class' ), :=( Z, x )] )).
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 resolution(
% 2.20/2.57 clause( 16959, [ ~( member( x, X ) ) ] )
% 2.20/2.57 , clause( 16958, [ ~( subclass( X, 'universal_class' ) ), ~( member( x, X )
% 2.20/2.57 ) ] )
% 2.20/2.57 , 0, clause( 3, [ subclass( X, 'universal_class' ) ] )
% 2.20/2.57 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 2.20/2.57 ).
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 subsumption(
% 2.20/2.57 clause( 140, [ ~( member( x, X ) ) ] )
% 2.20/2.57 , clause( 16959, [ ~( member( x, X ) ) ] )
% 2.20/2.57 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 eqswap(
% 2.20/2.57 clause( 16960, [ ~( =( Y, X ) ), subclass( X, Y ) ] )
% 2.20/2.57 , clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.20/2.57 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.20/2.57
% 2.20/2.57
% 2.20/2.57 eqswap(
% 2.20/2.57 clause( 16961, [ ~( =( Y, X ) ), subclass( X, Y ) ] )
% 2.20/2.57 , clause( 4, [ ~( =( X, Y ) ), subclass( X,Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------