TSTP Solution File: SET078-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET078-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 22:46:41 EDT 2022
% Result : Unsatisfiable 1.92s 2.35s
% Output : Refutation 1.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET078-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Sat Jul 9 19:08:55 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.69/1.11 *** allocated 10000 integers for termspace/termends
% 0.69/1.11 *** allocated 10000 integers for clauses
% 0.69/1.11 *** allocated 10000 integers for justifications
% 0.69/1.11 Bliksem 1.12
% 0.69/1.11
% 0.69/1.11
% 0.69/1.11 Automatic Strategy Selection
% 0.69/1.11
% 0.69/1.11 Clauses:
% 0.69/1.11 [
% 0.69/1.11 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.69/1.11 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.69/1.11 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.69/1.11 ,
% 0.69/1.11 [ subclass( X, 'universal_class' ) ],
% 0.69/1.11 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.69/1.11 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.69/1.11 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.69/1.11 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.69/1.11 ,
% 0.69/1.11 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.69/1.11 ) ) ],
% 0.69/1.11 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.69/1.11 ) ) ],
% 0.69/1.11 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.69/1.11 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.69/1.11 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.69/1.11 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.69/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.69/1.11 X, Z ) ],
% 0.69/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.69/1.11 Y, T ) ],
% 0.69/1.11 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.69/1.11 ), 'cross_product'( Y, T ) ) ],
% 0.69/1.11 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.69/1.11 ), second( X ) ), X ) ],
% 0.69/1.11 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.69/1.11 'universal_class' ) ) ],
% 0.69/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.69/1.11 Y ) ],
% 0.69/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.69/1.11 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.69/1.11 , Y ), 'element_relation' ) ],
% 0.69/1.11 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.69/1.11 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.69/1.11 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.69/1.11 Z ) ) ],
% 0.69/1.11 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.69/1.11 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.69/1.11 member( X, Y ) ],
% 0.69/1.11 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.69/1.11 union( X, Y ) ) ],
% 0.69/1.11 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.69/1.11 intersection( complement( X ), complement( Y ) ) ) ),
% 0.69/1.11 'symmetric_difference'( X, Y ) ) ],
% 0.69/1.11 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.69/1.11 ,
% 0.69/1.11 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.69/1.11 ,
% 0.69/1.11 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.69/1.11 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.69/1.11 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.69/1.11 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.69/1.11 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.69/1.11 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.69/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.69/1.11 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.69/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.69/1.11 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.69/1.11 'cross_product'( 'universal_class', 'universal_class' ),
% 0.69/1.11 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.69/1.11 Y ), rotate( T ) ) ],
% 0.69/1.11 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.69/1.11 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.69/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.69/1.11 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.69/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.69/1.11 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.69/1.11 'cross_product'( 'universal_class', 'universal_class' ),
% 0.69/1.11 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.69/1.11 Z ), flip( T ) ) ],
% 0.69/1.11 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.69/1.11 inverse( X ) ) ],
% 0.69/1.11 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.69/1.11 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.69/1.11 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.69/1.11 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.69/1.11 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.69/1.11 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.69/1.11 ],
% 0.69/1.11 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.69/1.11 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.69/1.11 'universal_class' ) ) ],
% 0.69/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.69/1.11 successor( X ), Y ) ],
% 0.69/1.11 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.69/1.11 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.69/1.11 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.69/1.11 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.69/1.11 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.69/1.11 ,
% 0.69/1.11 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.69/1.11 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.69/1.11 [ inductive( omega ) ],
% 0.69/1.11 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.69/1.11 [ member( omega, 'universal_class' ) ],
% 0.69/1.11 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.69/1.11 , 'sum_class'( X ) ) ],
% 0.69/1.11 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.69/1.11 'universal_class' ) ],
% 0.69/1.11 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.69/1.11 'power_class'( X ) ) ],
% 0.69/1.11 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.69/1.11 'universal_class' ) ],
% 0.69/1.11 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.69/1.11 'universal_class' ) ) ],
% 0.69/1.11 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.69/1.11 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.69/1.11 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.69/1.11 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.69/1.11 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.69/1.11 ) ],
% 0.69/1.11 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.69/1.11 , 'identity_relation' ) ],
% 0.69/1.11 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.69/1.11 'single_valued_class'( X ) ],
% 0.69/1.11 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.69/1.11 'universal_class' ) ) ],
% 0.69/1.11 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.69/1.11 'identity_relation' ) ],
% 0.69/1.11 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.69/1.11 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.69/1.11 , function( X ) ],
% 0.69/1.11 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.69/1.11 X, Y ), 'universal_class' ) ],
% 0.69/1.11 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.69/1.11 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.69/1.11 ) ],
% 0.69/1.11 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.69/1.11 [ function( choice ) ],
% 0.69/1.11 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.69/1.11 apply( choice, X ), X ) ],
% 0.69/1.11 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.69/1.11 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.69/1.11 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.69/1.11 ,
% 0.69/1.11 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.69/1.11 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.69/1.11 , complement( compose( complement( 'element_relation' ), inverse(
% 0.69/1.11 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.69/1.11 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.69/1.11 'identity_relation' ) ],
% 0.69/1.11 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.69/1.11 , diagonalise( X ) ) ],
% 0.69/1.11 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.69/1.11 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.69/1.11 [ ~( operation( X ) ), function( X ) ],
% 0.69/1.11 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.69/1.11 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.69/1.11 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.69/1.11 'domain_of'( X ) ) ) ],
% 0.69/1.11 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.69/1.11 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.69/1.11 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.69/1.11 X ) ],
% 0.69/1.11 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.69/1.11 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.69/1.11 'domain_of'( X ) ) ],
% 0.69/1.11 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.69/1.11 'domain_of'( Z ) ) ) ],
% 0.69/1.11 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.69/1.11 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.69/1.11 ), compatible( X, Y, Z ) ],
% 0.69/1.11 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.69/1.11 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.69/1.11 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.69/1.11 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.69/1.11 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.69/1.11 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.69/1.11 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.69/1.11 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.69/1.11 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.69/1.11 , Y ) ],
% 0.69/1.11 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.69/1.11 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.69/1.11 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.69/1.11 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.69/1.11 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.69/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.69/1.11 X, 'unordered_pair'( X, Y ) ) ],
% 0.69/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.69/1.11 Y, 'unordered_pair'( X, Y ) ) ],
% 0.69/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.69/1.11 X, 'universal_class' ) ],
% 0.69/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.69/1.11 Y, 'universal_class' ) ],
% 0.69/1.11 [ subclass( X, X ) ],
% 0.69/1.11 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.69/1.11 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.69/1.11 'not_subclass_element'( Y, X ), Y ) ],
% 0.69/1.11 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.69/1.11 'not_subclass_element'( Y, X ), Y ) ],
% 0.69/1.11 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.69/1.11 'not_subclass_element'( Y, X ), Y ) ],
% 0.69/1.11 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.69/1.11 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.69/1.11 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.69/1.11 [ ~( member( X, 'null_class' ) ) ],
% 0.69/1.11 [ subclass( 'null_class', X ) ],
% 0.69/1.11 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.69/1.11 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.69/1.11 ), X ) ],
% 0.69/1.11 [ member( 'null_class', 'universal_class' ) ],
% 0.69/1.11 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.69/1.11 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.69/1.11 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.69/1.11 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.69/1.11 Y ) ) ],
% 0.69/1.11 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.69/1.11 Y ) ) ],
% 0.69/1.11 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.69/1.11 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.69/1.11 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.69/1.11 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.69/1.11 'universal_class' ) ) ), =( Y, Z ) ],
% 0.69/1.11 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.69/1.11 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.69/1.11 'universal_class' ) ) ), =( X, Z ) ],
% 0.69/1.11 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.69/1.11 'null_class' ) ) ],
% 0.69/1.11 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.69/1.11 'null_class' ) ) ],
% 0.69/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.69/1.11 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 1.92/2.35 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 1.92/2.35 X, Z ), Y ) ],
% 1.92/2.35 [ member( singleton( X ), 'universal_class' ) ],
% 1.92/2.35 [ ~( member( singleton( y ), 'unordered_pair'( x, singleton( y ) ) ) ) ]
% 1.92/2.35
% 1.92/2.35 ] .
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 percentage equality = 0.233333, percentage horn = 0.876033
% 1.92/2.35 This is a problem with some equality
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 Options Used:
% 1.92/2.35
% 1.92/2.35 useres = 1
% 1.92/2.35 useparamod = 1
% 1.92/2.35 useeqrefl = 1
% 1.92/2.35 useeqfact = 1
% 1.92/2.35 usefactor = 1
% 1.92/2.35 usesimpsplitting = 0
% 1.92/2.35 usesimpdemod = 5
% 1.92/2.35 usesimpres = 3
% 1.92/2.35
% 1.92/2.35 resimpinuse = 1000
% 1.92/2.35 resimpclauses = 20000
% 1.92/2.35 substype = eqrewr
% 1.92/2.35 backwardsubs = 1
% 1.92/2.35 selectoldest = 5
% 1.92/2.35
% 1.92/2.35 litorderings [0] = split
% 1.92/2.35 litorderings [1] = extend the termordering, first sorting on arguments
% 1.92/2.35
% 1.92/2.35 termordering = kbo
% 1.92/2.35
% 1.92/2.35 litapriori = 0
% 1.92/2.35 termapriori = 1
% 1.92/2.35 litaposteriori = 0
% 1.92/2.35 termaposteriori = 0
% 1.92/2.35 demodaposteriori = 0
% 1.92/2.35 ordereqreflfact = 0
% 1.92/2.35
% 1.92/2.35 litselect = negord
% 1.92/2.35
% 1.92/2.35 maxweight = 15
% 1.92/2.35 maxdepth = 30000
% 1.92/2.35 maxlength = 115
% 1.92/2.35 maxnrvars = 195
% 1.92/2.35 excuselevel = 1
% 1.92/2.35 increasemaxweight = 1
% 1.92/2.35
% 1.92/2.35 maxselected = 10000000
% 1.92/2.35 maxnrclauses = 10000000
% 1.92/2.35
% 1.92/2.35 showgenerated = 0
% 1.92/2.35 showkept = 0
% 1.92/2.35 showselected = 0
% 1.92/2.35 showdeleted = 0
% 1.92/2.35 showresimp = 1
% 1.92/2.35 showstatus = 2000
% 1.92/2.35
% 1.92/2.35 prologoutput = 1
% 1.92/2.35 nrgoals = 5000000
% 1.92/2.35 totalproof = 1
% 1.92/2.35
% 1.92/2.35 Symbols occurring in the translation:
% 1.92/2.35
% 1.92/2.35 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.92/2.35 . [1, 2] (w:1, o:56, a:1, s:1, b:0),
% 1.92/2.35 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 1.92/2.35 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.92/2.35 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.92/2.35 subclass [41, 2] (w:1, o:81, a:1, s:1, b:0),
% 1.92/2.35 member [43, 2] (w:1, o:82, a:1, s:1, b:0),
% 1.92/2.35 'not_subclass_element' [44, 2] (w:1, o:83, a:1, s:1, b:0),
% 1.92/2.35 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 1.92/2.35 'unordered_pair' [46, 2] (w:1, o:84, a:1, s:1, b:0),
% 1.92/2.35 singleton [47, 1] (w:1, o:39, a:1, s:1, b:0),
% 1.92/2.35 'ordered_pair' [48, 2] (w:1, o:85, a:1, s:1, b:0),
% 1.92/2.35 'cross_product' [50, 2] (w:1, o:86, a:1, s:1, b:0),
% 1.92/2.35 first [52, 1] (w:1, o:40, a:1, s:1, b:0),
% 1.92/2.35 second [53, 1] (w:1, o:41, a:1, s:1, b:0),
% 1.92/2.35 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 1.92/2.35 intersection [55, 2] (w:1, o:88, a:1, s:1, b:0),
% 1.92/2.35 complement [56, 1] (w:1, o:42, a:1, s:1, b:0),
% 1.92/2.35 union [57, 2] (w:1, o:89, a:1, s:1, b:0),
% 1.92/2.35 'symmetric_difference' [58, 2] (w:1, o:90, a:1, s:1, b:0),
% 1.92/2.35 restrict [60, 3] (w:1, o:93, a:1, s:1, b:0),
% 1.92/2.35 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.92/2.35 'domain_of' [62, 1] (w:1, o:44, a:1, s:1, b:0),
% 1.92/2.35 rotate [63, 1] (w:1, o:36, a:1, s:1, b:0),
% 1.92/2.35 flip [65, 1] (w:1, o:45, a:1, s:1, b:0),
% 1.92/2.35 inverse [66, 1] (w:1, o:46, a:1, s:1, b:0),
% 1.92/2.35 'range_of' [67, 1] (w:1, o:37, a:1, s:1, b:0),
% 1.92/2.35 domain [68, 3] (w:1, o:95, a:1, s:1, b:0),
% 1.92/2.35 range [69, 3] (w:1, o:96, a:1, s:1, b:0),
% 1.92/2.35 image [70, 2] (w:1, o:87, a:1, s:1, b:0),
% 1.92/2.35 successor [71, 1] (w:1, o:47, a:1, s:1, b:0),
% 1.92/2.35 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 1.92/2.35 inductive [73, 1] (w:1, o:48, a:1, s:1, b:0),
% 1.92/2.35 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.92/2.35 'sum_class' [75, 1] (w:1, o:49, a:1, s:1, b:0),
% 1.92/2.35 'power_class' [76, 1] (w:1, o:52, a:1, s:1, b:0),
% 1.92/2.35 compose [78, 2] (w:1, o:91, a:1, s:1, b:0),
% 1.92/2.35 'single_valued_class' [79, 1] (w:1, o:53, a:1, s:1, b:0),
% 1.92/2.35 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 1.92/2.35 function [82, 1] (w:1, o:54, a:1, s:1, b:0),
% 1.92/2.35 regular [83, 1] (w:1, o:38, a:1, s:1, b:0),
% 1.92/2.35 apply [84, 2] (w:1, o:92, a:1, s:1, b:0),
% 1.92/2.35 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.92/2.35 'one_to_one' [86, 1] (w:1, o:50, a:1, s:1, b:0),
% 1.92/2.35 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 1.92/2.35 diagonalise [88, 1] (w:1, o:55, a:1, s:1, b:0),
% 1.92/2.35 cantor [89, 1] (w:1, o:43, a:1, s:1, b:0),
% 1.92/2.35 operation [90, 1] (w:1, o:51, a:1, s:1, b:0),
% 1.92/2.35 compatible [94, 3] (w:1, o:94, a:1, s:1, b:0),
% 1.92/2.35 homomorphism [95, 3] (w:1, o:97, a:1, s:1, b:0),
% 1.92/2.35 'not_homomorphism1' [96, 3] (w:1, o:98, a:1, s:1, b:0),
% 1.92/2.35 'not_homomorphism2' [97, 3] (w:1, o:99, a:1, s:1, b:0),
% 1.92/2.35 y [98, 0] (w:1, o:30, a:1, s:1, b:0),
% 1.92/2.35 x [99, 0] (w:1, o:29, a:1, s:1, b:0).
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 Starting Search:
% 1.92/2.35
% 1.92/2.35 Resimplifying inuse:
% 1.92/2.35 Done
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 Intermediate Status:
% 1.92/2.35 Generated: 4175
% 1.92/2.35 Kept: 2012
% 1.92/2.35 Inuse: 122
% 1.92/2.35 Deleted: 5
% 1.92/2.35 Deletedinuse: 2
% 1.92/2.35
% 1.92/2.35 Resimplifying inuse:
% 1.92/2.35 Done
% 1.92/2.35
% 1.92/2.35 Resimplifying inuse:
% 1.92/2.35 Done
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 Intermediate Status:
% 1.92/2.35 Generated: 10114
% 1.92/2.35 Kept: 4053
% 1.92/2.35 Inuse: 196
% 1.92/2.35 Deleted: 14
% 1.92/2.35 Deletedinuse: 4
% 1.92/2.35
% 1.92/2.35 Resimplifying inuse:
% 1.92/2.35 Done
% 1.92/2.35
% 1.92/2.35 Resimplifying inuse:
% 1.92/2.35 Done
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 Intermediate Status:
% 1.92/2.35 Generated: 15368
% 1.92/2.35 Kept: 6054
% 1.92/2.35 Inuse: 281
% 1.92/2.35 Deleted: 57
% 1.92/2.35 Deletedinuse: 39
% 1.92/2.35
% 1.92/2.35 Resimplifying inuse:
% 1.92/2.35 Done
% 1.92/2.35
% 1.92/2.35 Resimplifying inuse:
% 1.92/2.35 Done
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 Intermediate Status:
% 1.92/2.35 Generated: 20931
% 1.92/2.35 Kept: 8092
% 1.92/2.35 Inuse: 356
% 1.92/2.35 Deleted: 65
% 1.92/2.35 Deletedinuse: 45
% 1.92/2.35
% 1.92/2.35 Resimplifying inuse:
% 1.92/2.35 Done
% 1.92/2.35
% 1.92/2.35 Resimplifying inuse:
% 1.92/2.35 Done
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 Intermediate Status:
% 1.92/2.35 Generated: 27098
% 1.92/2.35 Kept: 10094
% 1.92/2.35 Inuse: 391
% 1.92/2.35 Deleted: 65
% 1.92/2.35 Deletedinuse: 45
% 1.92/2.35
% 1.92/2.35 Resimplifying inuse:
% 1.92/2.35 Done
% 1.92/2.35
% 1.92/2.35 Resimplifying inuse:
% 1.92/2.35 Done
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 Intermediate Status:
% 1.92/2.35 Generated: 36593
% 1.92/2.35 Kept: 12160
% 1.92/2.35 Inuse: 430
% 1.92/2.35 Deleted: 67
% 1.92/2.35 Deletedinuse: 46
% 1.92/2.35
% 1.92/2.35 Resimplifying inuse:
% 1.92/2.35 Done
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 Bliksems!, er is een bewijs:
% 1.92/2.35 % SZS status Unsatisfiable
% 1.92/2.35 % SZS output start Refutation
% 1.92/2.35
% 1.92/2.35 clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.92/2.35 'unordered_pair'( Y, X ) ) ] )
% 1.92/2.35 .
% 1.92/2.35 clause( 117, [ member( singleton( X ), 'universal_class' ) ] )
% 1.92/2.35 .
% 1.92/2.35 clause( 118, [ ~( member( singleton( y ), 'unordered_pair'( x, singleton( y
% 1.92/2.35 ) ) ) ) ] )
% 1.92/2.35 .
% 1.92/2.35 clause( 443, [ member( singleton( X ), 'unordered_pair'( Y, singleton( X )
% 1.92/2.35 ) ) ] )
% 1.92/2.35 .
% 1.92/2.35 clause( 13524, [] )
% 1.92/2.35 .
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 % SZS output end Refutation
% 1.92/2.35 found a proof!
% 1.92/2.35
% 1.92/2.35 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.92/2.35
% 1.92/2.35 initialclauses(
% 1.92/2.35 [ clause( 13526, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.92/2.35 ) ] )
% 1.92/2.35 , clause( 13527, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 1.92/2.35 , Y ) ] )
% 1.92/2.35 , clause( 13528, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 1.92/2.35 subclass( X, Y ) ] )
% 1.92/2.35 , clause( 13529, [ subclass( X, 'universal_class' ) ] )
% 1.92/2.35 , clause( 13530, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.92/2.35 , clause( 13531, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 1.92/2.35 , clause( 13532, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 1.92/2.35 ] )
% 1.92/2.35 , clause( 13533, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 1.92/2.35 =( X, Z ) ] )
% 1.92/2.35 , clause( 13534, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.92/2.35 'unordered_pair'( X, Y ) ) ] )
% 1.92/2.35 , clause( 13535, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.92/2.35 'unordered_pair'( Y, X ) ) ] )
% 1.92/2.35 , clause( 13536, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 1.92/2.35 )
% 1.92/2.35 , clause( 13537, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.92/2.35 , clause( 13538, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 1.92/2.35 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.92/2.35 , clause( 13539, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.92/2.35 ) ) ), member( X, Z ) ] )
% 1.92/2.35 , clause( 13540, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.92/2.35 ) ) ), member( Y, T ) ] )
% 1.92/2.35 , clause( 13541, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.92/2.35 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.92/2.35 , clause( 13542, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 1.92/2.35 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 1.92/2.35 , clause( 13543, [ subclass( 'element_relation', 'cross_product'(
% 1.92/2.35 'universal_class', 'universal_class' ) ) ] )
% 1.92/2.35 , clause( 13544, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 1.92/2.35 ), member( X, Y ) ] )
% 1.92/2.35 , clause( 13545, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.92/2.35 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 1.92/2.35 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 1.92/2.35 , clause( 13546, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.92/2.35 )
% 1.92/2.35 , clause( 13547, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 1.92/2.35 )
% 1.92/2.35 , clause( 13548, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 1.92/2.35 intersection( Y, Z ) ) ] )
% 1.92/2.35 , clause( 13549, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 1.92/2.35 )
% 1.92/2.35 , clause( 13550, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.92/2.35 complement( Y ) ), member( X, Y ) ] )
% 1.92/2.35 , clause( 13551, [ =( complement( intersection( complement( X ), complement(
% 1.92/2.35 Y ) ) ), union( X, Y ) ) ] )
% 1.92/2.35 , clause( 13552, [ =( intersection( complement( intersection( X, Y ) ),
% 1.92/2.35 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 1.92/2.35 'symmetric_difference'( X, Y ) ) ] )
% 1.92/2.35 , clause( 13553, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 1.92/2.35 X, Y, Z ) ) ] )
% 1.92/2.35 , clause( 13554, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 1.92/2.35 Z, X, Y ) ) ] )
% 1.92/2.35 , clause( 13555, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 1.92/2.35 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 1.92/2.35 , clause( 13556, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 1.92/2.35 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 1.92/2.35 'domain_of'( Y ) ) ] )
% 1.92/2.35 , clause( 13557, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 1.92/2.35 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.92/2.35 , clause( 13558, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.92/2.35 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 1.92/2.35 ] )
% 1.92/2.35 , clause( 13559, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.92/2.35 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 1.92/2.35 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.92/2.35 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 1.92/2.35 , Y ), rotate( T ) ) ] )
% 1.92/2.35 , clause( 13560, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 1.92/2.35 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.92/2.35 , clause( 13561, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.92/2.35 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 1.92/2.35 )
% 1.92/2.35 , clause( 13562, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.92/2.35 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 1.92/2.35 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.92/2.35 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 1.92/2.35 , Z ), flip( T ) ) ] )
% 1.92/2.35 , clause( 13563, [ =( 'domain_of'( flip( 'cross_product'( X,
% 1.92/2.35 'universal_class' ) ) ), inverse( X ) ) ] )
% 1.92/2.35 , clause( 13564, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 1.92/2.35 , clause( 13565, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 1.92/2.35 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 1.92/2.35 , clause( 13566, [ =( second( 'not_subclass_element'( restrict( X,
% 1.92/2.35 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 1.92/2.35 , clause( 13567, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 1.92/2.35 image( X, Y ) ) ] )
% 1.92/2.35 , clause( 13568, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 1.92/2.35 , clause( 13569, [ subclass( 'successor_relation', 'cross_product'(
% 1.92/2.35 'universal_class', 'universal_class' ) ) ] )
% 1.92/2.35 , clause( 13570, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 1.92/2.35 ) ), =( successor( X ), Y ) ] )
% 1.92/2.35 , clause( 13571, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 1.92/2.35 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 1.92/2.35 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 1.92/2.35 , clause( 13572, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 1.92/2.35 , clause( 13573, [ ~( inductive( X ) ), subclass( image(
% 1.92/2.35 'successor_relation', X ), X ) ] )
% 1.92/2.35 , clause( 13574, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 1.92/2.35 'successor_relation', X ), X ) ), inductive( X ) ] )
% 1.92/2.35 , clause( 13575, [ inductive( omega ) ] )
% 1.92/2.35 , clause( 13576, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 1.92/2.35 , clause( 13577, [ member( omega, 'universal_class' ) ] )
% 1.92/2.35 , clause( 13578, [ =( 'domain_of'( restrict( 'element_relation',
% 1.92/2.35 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 1.92/2.35 , clause( 13579, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 1.92/2.35 X ), 'universal_class' ) ] )
% 1.92/2.35 , clause( 13580, [ =( complement( image( 'element_relation', complement( X
% 1.92/2.35 ) ) ), 'power_class'( X ) ) ] )
% 1.92/2.35 , clause( 13581, [ ~( member( X, 'universal_class' ) ), member(
% 1.92/2.35 'power_class'( X ), 'universal_class' ) ] )
% 1.92/2.35 , clause( 13582, [ subclass( compose( X, Y ), 'cross_product'(
% 1.92/2.35 'universal_class', 'universal_class' ) ) ] )
% 1.92/2.35 , clause( 13583, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 1.92/2.35 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 1.92/2.35 , clause( 13584, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 1.92/2.35 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 1.92/2.35 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 1.92/2.35 ) ] )
% 1.92/2.35 , clause( 13585, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 1.92/2.35 inverse( X ) ), 'identity_relation' ) ] )
% 1.92/2.35 , clause( 13586, [ ~( subclass( compose( X, inverse( X ) ),
% 1.92/2.35 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 1.92/2.35 , clause( 13587, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 1.92/2.35 'universal_class', 'universal_class' ) ) ] )
% 1.92/2.35 , clause( 13588, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 1.92/2.35 , 'identity_relation' ) ] )
% 1.92/2.35 , clause( 13589, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 1.92/2.35 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 1.92/2.35 'identity_relation' ) ), function( X ) ] )
% 1.92/2.35 , clause( 13590, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 1.92/2.35 , member( image( X, Y ), 'universal_class' ) ] )
% 1.92/2.35 , clause( 13591, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.92/2.35 , clause( 13592, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 1.92/2.35 , 'null_class' ) ] )
% 1.92/2.35 , clause( 13593, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 1.92/2.35 Y ) ) ] )
% 1.92/2.35 , clause( 13594, [ function( choice ) ] )
% 1.92/2.35 , clause( 13595, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 1.92/2.35 ), member( apply( choice, X ), X ) ] )
% 1.92/2.35 , clause( 13596, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 1.92/2.35 , clause( 13597, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 1.92/2.35 , clause( 13598, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 1.92/2.35 'one_to_one'( X ) ] )
% 1.92/2.35 , clause( 13599, [ =( intersection( 'cross_product'( 'universal_class',
% 1.92/2.35 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 1.92/2.35 'universal_class' ), complement( compose( complement( 'element_relation'
% 1.92/2.35 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 1.92/2.35 , clause( 13600, [ =( intersection( inverse( 'subset_relation' ),
% 1.92/2.35 'subset_relation' ), 'identity_relation' ) ] )
% 1.92/2.35 , clause( 13601, [ =( complement( 'domain_of'( intersection( X,
% 1.92/2.35 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 1.92/2.35 , clause( 13602, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 1.92/2.35 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 1.92/2.35 , clause( 13603, [ ~( operation( X ) ), function( X ) ] )
% 1.92/2.35 , clause( 13604, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 1.92/2.35 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.92/2.35 ] )
% 1.92/2.35 , clause( 13605, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 1.92/2.35 'domain_of'( 'domain_of'( X ) ) ) ] )
% 1.92/2.35 , clause( 13606, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 1.92/2.35 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.92/2.35 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 1.92/2.35 operation( X ) ] )
% 1.92/2.35 , clause( 13607, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 1.92/2.35 , clause( 13608, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 1.92/2.35 Y ) ), 'domain_of'( X ) ) ] )
% 1.92/2.35 , clause( 13609, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 1.92/2.35 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 1.92/2.35 , clause( 13610, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 1.92/2.35 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 1.92/2.35 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 1.92/2.35 , clause( 13611, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 1.92/2.35 , clause( 13612, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 1.92/2.35 , clause( 13613, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 1.92/2.35 , clause( 13614, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 1.92/2.35 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 1.92/2.35 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 1.92/2.35 )
% 1.92/2.35 , clause( 13615, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.92/2.35 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.92/2.35 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.92/2.35 , Y ) ] )
% 1.92/2.35 , clause( 13616, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.92/2.35 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 1.92/2.35 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 1.92/2.35 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 1.92/2.35 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 1.92/2.35 )
% 1.92/2.35 , clause( 13617, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.92/2.35 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 1.92/2.35 , clause( 13618, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.92/2.35 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 1.92/2.35 , clause( 13619, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.92/2.35 ) ) ), member( X, 'universal_class' ) ] )
% 1.92/2.35 , clause( 13620, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.92/2.35 ) ) ), member( Y, 'universal_class' ) ] )
% 1.92/2.35 , clause( 13621, [ subclass( X, X ) ] )
% 1.92/2.35 , clause( 13622, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 1.92/2.35 X, Z ) ] )
% 1.92/2.35 , clause( 13623, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 1.92/2.35 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 1.92/2.35 , clause( 13624, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 1.92/2.35 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 1.92/2.35 , clause( 13625, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 1.92/2.35 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 1.92/2.35 , clause( 13626, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 1.92/2.35 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 1.92/2.35 , clause( 13627, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 1.92/2.35 )
% 1.92/2.35 , clause( 13628, [ ~( member( X, 'null_class' ) ) ] )
% 1.92/2.35 , clause( 13629, [ subclass( 'null_class', X ) ] )
% 1.92/2.35 , clause( 13630, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 1.92/2.35 )
% 1.92/2.35 , clause( 13631, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 1.92/2.35 , 'null_class' ), X ) ] )
% 1.92/2.35 , clause( 13632, [ member( 'null_class', 'universal_class' ) ] )
% 1.92/2.35 , clause( 13633, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 1.92/2.35 ] )
% 1.92/2.35 , clause( 13634, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 1.92/2.35 )
% 1.92/2.35 , clause( 13635, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 1.92/2.35 )
% 1.92/2.35 , clause( 13636, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 1.92/2.35 X ), singleton( Y ) ) ] )
% 1.92/2.35 , clause( 13637, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 1.92/2.35 Y ), singleton( Y ) ) ] )
% 1.92/2.35 , clause( 13638, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 1.92/2.35 'universal_class' ), member( Y, 'universal_class' ) ] )
% 1.92/2.35 , clause( 13639, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 1.92/2.35 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 1.92/2.35 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 1.92/2.35 , clause( 13640, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 1.92/2.35 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 1.92/2.35 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 1.92/2.35 , clause( 13641, [ ~( member( X, 'universal_class' ) ), ~( =(
% 1.92/2.35 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 1.92/2.35 , clause( 13642, [ ~( member( X, 'universal_class' ) ), ~( =(
% 1.92/2.35 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 1.92/2.35 , clause( 13643, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.92/2.35 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 1.92/2.35 , clause( 13644, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 1.92/2.35 'unordered_pair'( X, Z ), Y ) ] )
% 1.92/2.35 , clause( 13645, [ member( singleton( X ), 'universal_class' ) ] )
% 1.92/2.35 , clause( 13646, [ ~( member( singleton( y ), 'unordered_pair'( x,
% 1.92/2.35 singleton( y ) ) ) ) ] )
% 1.92/2.35 ] ).
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 subsumption(
% 1.92/2.35 clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.92/2.35 'unordered_pair'( Y, X ) ) ] )
% 1.92/2.35 , clause( 13535, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.92/2.35 'unordered_pair'( Y, X ) ) ] )
% 1.92/2.35 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.92/2.35 ), ==>( 1, 1 )] ) ).
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 subsumption(
% 1.92/2.35 clause( 117, [ member( singleton( X ), 'universal_class' ) ] )
% 1.92/2.35 , clause( 13645, [ member( singleton( X ), 'universal_class' ) ] )
% 1.92/2.35 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 subsumption(
% 1.92/2.35 clause( 118, [ ~( member( singleton( y ), 'unordered_pair'( x, singleton( y
% 1.92/2.35 ) ) ) ) ] )
% 1.92/2.35 , clause( 13646, [ ~( member( singleton( y ), 'unordered_pair'( x,
% 1.92/2.35 singleton( y ) ) ) ) ] )
% 1.92/2.35 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 resolution(
% 1.92/2.35 clause( 13799, [ member( singleton( X ), 'unordered_pair'( Y, singleton( X
% 1.92/2.35 ) ) ) ] )
% 1.92/2.35 , clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.92/2.35 'unordered_pair'( Y, X ) ) ] )
% 1.92/2.35 , 0, clause( 117, [ member( singleton( X ), 'universal_class' ) ] )
% 1.92/2.35 , 0, substitution( 0, [ :=( X, singleton( X ) ), :=( Y, Y )] ),
% 1.92/2.35 substitution( 1, [ :=( X, X )] )).
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 subsumption(
% 1.92/2.35 clause( 443, [ member( singleton( X ), 'unordered_pair'( Y, singleton( X )
% 1.92/2.35 ) ) ] )
% 1.92/2.35 , clause( 13799, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 1.92/2.35 X ) ) ) ] )
% 1.92/2.35 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.92/2.35 )] ) ).
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 resolution(
% 1.92/2.35 clause( 13800, [] )
% 1.92/2.35 , clause( 118, [ ~( member( singleton( y ), 'unordered_pair'( x, singleton(
% 1.92/2.35 y ) ) ) ) ] )
% 1.92/2.35 , 0, clause( 443, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 1.92/2.35 X ) ) ) ] )
% 1.92/2.35 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, y ), :=( Y, x )] )
% 1.92/2.35 ).
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 subsumption(
% 1.92/2.35 clause( 13524, [] )
% 1.92/2.35 , clause( 13800, [] )
% 1.92/2.35 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 end.
% 1.92/2.35
% 1.92/2.35 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.92/2.35
% 1.92/2.35 Memory use:
% 1.92/2.35
% 1.92/2.35 space for terms: 242771
% 1.92/2.35 space for clauses: 634133
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 clauses generated: 42564
% 1.92/2.35 clauses kept: 13525
% 1.92/2.35 clauses selected: 456
% 1.92/2.35 clauses deleted: 72
% 1.92/2.35 clauses inuse deleted: 47
% 1.92/2.35
% 1.92/2.35 subsentry: 99631
% 1.92/2.35 literals s-matched: 77592
% 1.92/2.35 literals matched: 75037
% 1.92/2.35 full subsumption: 37979
% 1.92/2.35
% 1.92/2.35 checksum: 1924380572
% 1.92/2.35
% 1.92/2.35
% 1.92/2.35 Bliksem ended
%------------------------------------------------------------------------------