TSTP Solution File: SET076-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET076-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n029.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 22:46:39 EDT 2022
% Result : Unsatisfiable 9.43s 9.79s
% Output : Refutation 9.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET076-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : bliksem %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Mon Jul 11 10:53:02 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.76/1.12 *** allocated 10000 integers for termspace/termends
% 0.76/1.12 *** allocated 10000 integers for clauses
% 0.76/1.12 *** allocated 10000 integers for justifications
% 0.76/1.12 Bliksem 1.12
% 0.76/1.12
% 0.76/1.12
% 0.76/1.12 Automatic Strategy Selection
% 0.76/1.12
% 0.76/1.12 Clauses:
% 0.76/1.12 [
% 0.76/1.12 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.76/1.12 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.76/1.12 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.76/1.12 ,
% 0.76/1.12 [ subclass( X, 'universal_class' ) ],
% 0.76/1.12 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.76/1.12 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.76/1.12 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.76/1.12 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.76/1.12 ,
% 0.76/1.12 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.76/1.12 ) ) ],
% 0.76/1.12 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.76/1.12 ) ) ],
% 0.76/1.12 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.76/1.12 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.76/1.12 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.76/1.12 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.76/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.76/1.12 X, Z ) ],
% 0.76/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.76/1.12 Y, T ) ],
% 0.76/1.12 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.76/1.12 ), 'cross_product'( Y, T ) ) ],
% 0.76/1.12 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.76/1.12 ), second( X ) ), X ) ],
% 0.76/1.12 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.76/1.12 'universal_class' ) ) ],
% 0.76/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.76/1.12 Y ) ],
% 0.76/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.76/1.12 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.76/1.12 , Y ), 'element_relation' ) ],
% 0.76/1.12 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.76/1.12 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.76/1.12 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.76/1.12 Z ) ) ],
% 0.76/1.12 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.76/1.12 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.76/1.12 member( X, Y ) ],
% 0.76/1.12 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.76/1.12 union( X, Y ) ) ],
% 0.76/1.12 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.76/1.12 intersection( complement( X ), complement( Y ) ) ) ),
% 0.76/1.12 'symmetric_difference'( X, Y ) ) ],
% 0.76/1.12 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.76/1.12 ,
% 0.76/1.12 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.76/1.12 ,
% 0.76/1.12 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.76/1.12 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.76/1.12 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.76/1.12 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.76/1.12 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.76/1.12 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.76/1.12 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.76/1.12 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.76/1.12 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.76/1.12 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.76/1.12 'cross_product'( 'universal_class', 'universal_class' ),
% 0.76/1.12 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.76/1.12 Y ), rotate( T ) ) ],
% 0.76/1.12 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.76/1.12 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.76/1.12 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.76/1.12 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.76/1.12 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.76/1.12 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.76/1.12 'cross_product'( 'universal_class', 'universal_class' ),
% 0.76/1.12 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.76/1.12 Z ), flip( T ) ) ],
% 0.76/1.12 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.76/1.12 inverse( X ) ) ],
% 0.76/1.12 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.76/1.12 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.76/1.12 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.76/1.12 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.76/1.12 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.76/1.12 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.76/1.12 ],
% 0.76/1.12 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.76/1.12 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.76/1.12 'universal_class' ) ) ],
% 0.76/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.76/1.12 successor( X ), Y ) ],
% 0.76/1.12 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.76/1.12 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.76/1.12 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.76/1.12 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.76/1.12 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.76/1.12 ,
% 0.76/1.12 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.76/1.12 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.76/1.12 [ inductive( omega ) ],
% 0.76/1.12 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.76/1.12 [ member( omega, 'universal_class' ) ],
% 0.76/1.12 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.76/1.12 , 'sum_class'( X ) ) ],
% 0.76/1.12 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.76/1.12 'universal_class' ) ],
% 0.76/1.12 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.76/1.12 'power_class'( X ) ) ],
% 0.76/1.12 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.76/1.12 'universal_class' ) ],
% 0.76/1.12 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.76/1.12 'universal_class' ) ) ],
% 0.76/1.12 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.76/1.12 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.76/1.12 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.76/1.12 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.76/1.12 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.76/1.12 ) ],
% 0.76/1.12 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.76/1.12 , 'identity_relation' ) ],
% 0.76/1.12 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.76/1.12 'single_valued_class'( X ) ],
% 0.76/1.12 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.76/1.12 'universal_class' ) ) ],
% 0.76/1.12 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.76/1.12 'identity_relation' ) ],
% 0.76/1.12 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.76/1.12 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.76/1.12 , function( X ) ],
% 0.76/1.12 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.76/1.12 X, Y ), 'universal_class' ) ],
% 0.76/1.12 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.76/1.12 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.76/1.12 ) ],
% 0.76/1.12 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.76/1.12 [ function( choice ) ],
% 0.76/1.12 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.76/1.12 apply( choice, X ), X ) ],
% 0.76/1.12 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.76/1.12 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.76/1.12 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.76/1.12 ,
% 0.76/1.12 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.76/1.12 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.76/1.12 , complement( compose( complement( 'element_relation' ), inverse(
% 0.76/1.12 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.76/1.12 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.76/1.12 'identity_relation' ) ],
% 0.76/1.12 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.76/1.12 , diagonalise( X ) ) ],
% 0.76/1.12 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.76/1.12 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.76/1.12 [ ~( operation( X ) ), function( X ) ],
% 0.76/1.12 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.76/1.12 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.76/1.12 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.76/1.12 'domain_of'( X ) ) ) ],
% 0.76/1.12 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.76/1.12 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.76/1.12 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.76/1.12 X ) ],
% 0.76/1.12 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.76/1.12 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.76/1.12 'domain_of'( X ) ) ],
% 0.76/1.12 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.76/1.12 'domain_of'( Z ) ) ) ],
% 0.76/1.12 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.76/1.12 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.76/1.12 ), compatible( X, Y, Z ) ],
% 0.76/1.12 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.76/1.12 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.76/1.12 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.76/1.12 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.76/1.12 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.76/1.12 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.76/1.12 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.76/1.12 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.76/1.12 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.76/1.12 , Y ) ],
% 0.76/1.12 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.76/1.12 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.76/1.12 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.76/1.12 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.76/1.12 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.76/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.76/1.12 X, 'unordered_pair'( X, Y ) ) ],
% 0.76/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.76/1.12 Y, 'unordered_pair'( X, Y ) ) ],
% 0.76/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.76/1.12 X, 'universal_class' ) ],
% 0.76/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.76/1.12 Y, 'universal_class' ) ],
% 0.76/1.12 [ subclass( X, X ) ],
% 0.76/1.12 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.76/1.12 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.76/1.12 'not_subclass_element'( Y, X ), Y ) ],
% 0.76/1.12 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.76/1.12 'not_subclass_element'( Y, X ), Y ) ],
% 0.76/1.12 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.76/1.12 'not_subclass_element'( Y, X ), Y ) ],
% 0.76/1.12 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.76/1.12 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.76/1.12 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.76/1.12 [ ~( member( X, 'null_class' ) ) ],
% 0.76/1.12 [ subclass( 'null_class', X ) ],
% 0.76/1.12 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.76/1.12 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.76/1.12 ), X ) ],
% 0.76/1.12 [ member( 'null_class', 'universal_class' ) ],
% 0.76/1.12 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.76/1.12 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.76/1.12 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.76/1.12 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.76/1.12 Y ) ) ],
% 0.76/1.12 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.76/1.12 Y ) ) ],
% 0.76/1.12 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.76/1.12 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.76/1.12 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.76/1.12 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.76/1.12 'universal_class' ) ) ), =( Y, Z ) ],
% 0.76/1.12 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.76/1.12 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.76/1.12 'universal_class' ) ) ), =( X, Z ) ],
% 0.76/1.12 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.76/1.12 'null_class' ) ) ],
% 0.76/1.12 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.76/1.12 'null_class' ) ) ],
% 0.76/1.12 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.76/1.12 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 9.43/9.79 [ member( x, z ) ],
% 9.43/9.79 [ member( y, z ) ],
% 9.43/9.79 [ ~( subclass( 'unordered_pair'( x, y ), z ) ) ]
% 9.43/9.79 ] .
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 percentage equality = 0.235294, percentage horn = 0.876033
% 9.43/9.79 This is a problem with some equality
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Options Used:
% 9.43/9.79
% 9.43/9.79 useres = 1
% 9.43/9.79 useparamod = 1
% 9.43/9.79 useeqrefl = 1
% 9.43/9.79 useeqfact = 1
% 9.43/9.79 usefactor = 1
% 9.43/9.79 usesimpsplitting = 0
% 9.43/9.79 usesimpdemod = 5
% 9.43/9.79 usesimpres = 3
% 9.43/9.79
% 9.43/9.79 resimpinuse = 1000
% 9.43/9.79 resimpclauses = 20000
% 9.43/9.79 substype = eqrewr
% 9.43/9.79 backwardsubs = 1
% 9.43/9.79 selectoldest = 5
% 9.43/9.79
% 9.43/9.79 litorderings [0] = split
% 9.43/9.79 litorderings [1] = extend the termordering, first sorting on arguments
% 9.43/9.79
% 9.43/9.79 termordering = kbo
% 9.43/9.79
% 9.43/9.79 litapriori = 0
% 9.43/9.79 termapriori = 1
% 9.43/9.79 litaposteriori = 0
% 9.43/9.79 termaposteriori = 0
% 9.43/9.79 demodaposteriori = 0
% 9.43/9.79 ordereqreflfact = 0
% 9.43/9.79
% 9.43/9.79 litselect = negord
% 9.43/9.79
% 9.43/9.79 maxweight = 15
% 9.43/9.79 maxdepth = 30000
% 9.43/9.79 maxlength = 115
% 9.43/9.79 maxnrvars = 195
% 9.43/9.79 excuselevel = 1
% 9.43/9.79 increasemaxweight = 1
% 9.43/9.79
% 9.43/9.79 maxselected = 10000000
% 9.43/9.79 maxnrclauses = 10000000
% 9.43/9.79
% 9.43/9.79 showgenerated = 0
% 9.43/9.79 showkept = 0
% 9.43/9.79 showselected = 0
% 9.43/9.79 showdeleted = 0
% 9.43/9.79 showresimp = 1
% 9.43/9.79 showstatus = 2000
% 9.43/9.79
% 9.43/9.79 prologoutput = 1
% 9.43/9.79 nrgoals = 5000000
% 9.43/9.79 totalproof = 1
% 9.43/9.79
% 9.43/9.79 Symbols occurring in the translation:
% 9.43/9.79
% 9.43/9.79 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 9.43/9.79 . [1, 2] (w:1, o:57, a:1, s:1, b:0),
% 9.43/9.79 ! [4, 1] (w:0, o:32, a:1, s:1, b:0),
% 9.43/9.79 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 9.43/9.79 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 9.43/9.79 subclass [41, 2] (w:1, o:82, a:1, s:1, b:0),
% 9.43/9.79 member [43, 2] (w:1, o:83, a:1, s:1, b:0),
% 9.43/9.79 'not_subclass_element' [44, 2] (w:1, o:84, a:1, s:1, b:0),
% 9.43/9.79 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 9.43/9.79 'unordered_pair' [46, 2] (w:1, o:85, a:1, s:1, b:0),
% 9.43/9.79 singleton [47, 1] (w:1, o:40, a:1, s:1, b:0),
% 9.43/9.79 'ordered_pair' [48, 2] (w:1, o:86, a:1, s:1, b:0),
% 9.43/9.79 'cross_product' [50, 2] (w:1, o:87, a:1, s:1, b:0),
% 9.43/9.79 first [52, 1] (w:1, o:41, a:1, s:1, b:0),
% 9.43/9.79 second [53, 1] (w:1, o:42, a:1, s:1, b:0),
% 9.43/9.79 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 9.43/9.79 intersection [55, 2] (w:1, o:89, a:1, s:1, b:0),
% 9.43/9.79 complement [56, 1] (w:1, o:43, a:1, s:1, b:0),
% 9.43/9.79 union [57, 2] (w:1, o:90, a:1, s:1, b:0),
% 9.43/9.79 'symmetric_difference' [58, 2] (w:1, o:91, a:1, s:1, b:0),
% 9.43/9.79 restrict [60, 3] (w:1, o:94, a:1, s:1, b:0),
% 9.43/9.79 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 9.43/9.79 'domain_of' [62, 1] (w:1, o:45, a:1, s:1, b:0),
% 9.43/9.79 rotate [63, 1] (w:1, o:37, a:1, s:1, b:0),
% 9.43/9.79 flip [65, 1] (w:1, o:46, a:1, s:1, b:0),
% 9.43/9.79 inverse [66, 1] (w:1, o:47, a:1, s:1, b:0),
% 9.43/9.79 'range_of' [67, 1] (w:1, o:38, a:1, s:1, b:0),
% 9.43/9.79 domain [68, 3] (w:1, o:96, a:1, s:1, b:0),
% 9.43/9.79 range [69, 3] (w:1, o:97, a:1, s:1, b:0),
% 9.43/9.79 image [70, 2] (w:1, o:88, a:1, s:1, b:0),
% 9.43/9.79 successor [71, 1] (w:1, o:48, a:1, s:1, b:0),
% 9.43/9.79 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 9.43/9.79 inductive [73, 1] (w:1, o:49, a:1, s:1, b:0),
% 9.43/9.79 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 9.43/9.79 'sum_class' [75, 1] (w:1, o:50, a:1, s:1, b:0),
% 9.43/9.79 'power_class' [76, 1] (w:1, o:53, a:1, s:1, b:0),
% 9.43/9.79 compose [78, 2] (w:1, o:92, a:1, s:1, b:0),
% 9.43/9.79 'single_valued_class' [79, 1] (w:1, o:54, a:1, s:1, b:0),
% 9.43/9.79 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 9.43/9.79 function [82, 1] (w:1, o:55, a:1, s:1, b:0),
% 9.43/9.79 regular [83, 1] (w:1, o:39, a:1, s:1, b:0),
% 9.43/9.79 apply [84, 2] (w:1, o:93, a:1, s:1, b:0),
% 9.43/9.79 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 9.43/9.79 'one_to_one' [86, 1] (w:1, o:51, a:1, s:1, b:0),
% 9.43/9.79 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 9.43/9.79 diagonalise [88, 1] (w:1, o:56, a:1, s:1, b:0),
% 9.43/9.79 cantor [89, 1] (w:1, o:44, a:1, s:1, b:0),
% 9.43/9.79 operation [90, 1] (w:1, o:52, a:1, s:1, b:0),
% 9.43/9.79 compatible [94, 3] (w:1, o:95, a:1, s:1, b:0),
% 9.43/9.79 homomorphism [95, 3] (w:1, o:98, a:1, s:1, b:0),
% 9.43/9.79 'not_homomorphism1' [96, 3] (w:1, o:99, a:1, s:1, b:0),
% 9.43/9.79 'not_homomorphism2' [97, 3] (w:1, o:100, a:1, s:1, b:0),
% 9.43/9.79 x [98, 0] (w:1, o:29, a:1, s:1, b:0),
% 9.43/9.79 z [99, 0] (w:1, o:31, a:1, s:1, b:0),
% 9.43/9.79 y [100, 0] (w:1, o:30, a:1, s:1, b:0).
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Starting Search:
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 3838
% 9.43/9.79 Kept: 2019
% 9.43/9.79 Inuse: 118
% 9.43/9.79 Deleted: 2
% 9.43/9.79 Deletedinuse: 2
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 8955
% 9.43/9.79 Kept: 4165
% 9.43/9.79 Inuse: 201
% 9.43/9.79 Deleted: 7
% 9.43/9.79 Deletedinuse: 7
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 13881
% 9.43/9.79 Kept: 6167
% 9.43/9.79 Inuse: 284
% 9.43/9.79 Deleted: 10
% 9.43/9.79 Deletedinuse: 9
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 19745
% 9.43/9.79 Kept: 8175
% 9.43/9.79 Inuse: 332
% 9.43/9.79 Deleted: 52
% 9.43/9.79 Deletedinuse: 47
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 27934
% 9.43/9.79 Kept: 10650
% 9.43/9.79 Inuse: 389
% 9.43/9.79 Deleted: 68
% 9.43/9.79 Deletedinuse: 51
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 35638
% 9.43/9.79 Kept: 12650
% 9.43/9.79 Inuse: 428
% 9.43/9.79 Deleted: 76
% 9.43/9.79 Deletedinuse: 52
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 44474
% 9.43/9.79 Kept: 14651
% 9.43/9.79 Inuse: 457
% 9.43/9.79 Deleted: 85
% 9.43/9.79 Deletedinuse: 59
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 51950
% 9.43/9.79 Kept: 17907
% 9.43/9.79 Inuse: 465
% 9.43/9.79 Deleted: 87
% 9.43/9.79 Deletedinuse: 61
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 57645
% 9.43/9.79 Kept: 19926
% 9.43/9.79 Inuse: 479
% 9.43/9.79 Deleted: 89
% 9.43/9.79 Deletedinuse: 62
% 9.43/9.79
% 9.43/9.79 Resimplifying clauses:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 65511
% 9.43/9.79 Kept: 21986
% 9.43/9.79 Inuse: 525
% 9.43/9.79 Deleted: 2025
% 9.43/9.79 Deletedinuse: 65
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 70405
% 9.43/9.79 Kept: 24024
% 9.43/9.79 Inuse: 559
% 9.43/9.79 Deleted: 2025
% 9.43/9.79 Deletedinuse: 65
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 77224
% 9.43/9.79 Kept: 26062
% 9.43/9.79 Inuse: 596
% 9.43/9.79 Deleted: 2029
% 9.43/9.79 Deletedinuse: 69
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 84718
% 9.43/9.79 Kept: 28088
% 9.43/9.79 Inuse: 620
% 9.43/9.79 Deleted: 2029
% 9.43/9.79 Deletedinuse: 69
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 91012
% 9.43/9.79 Kept: 30106
% 9.43/9.79 Inuse: 658
% 9.43/9.79 Deleted: 2029
% 9.43/9.79 Deletedinuse: 69
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 100648
% 9.43/9.79 Kept: 33327
% 9.43/9.79 Inuse: 699
% 9.43/9.79 Deleted: 2029
% 9.43/9.79 Deletedinuse: 69
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 106007
% 9.43/9.79 Kept: 35351
% 9.43/9.79 Inuse: 708
% 9.43/9.79 Deleted: 2029
% 9.43/9.79 Deletedinuse: 69
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 110231
% 9.43/9.79 Kept: 37413
% 9.43/9.79 Inuse: 709
% 9.43/9.79 Deleted: 2029
% 9.43/9.79 Deletedinuse: 69
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 Intermediate Status:
% 9.43/9.79 Generated: 115269
% 9.43/9.79 Kept: 39798
% 9.43/9.79 Inuse: 714
% 9.43/9.79 Deleted: 2029
% 9.43/9.79 Deletedinuse: 69
% 9.43/9.79
% 9.43/9.79 Resimplifying inuse:
% 9.43/9.79 Done
% 9.43/9.79
% 9.43/9.79 Resimplifying clauses:
% 9.43/9.79
% 9.43/9.79 Bliksems!, er is een bewijs:
% 9.43/9.79 % SZS status Unsatisfiable
% 9.43/9.79 % SZS output start Refutation
% 9.43/9.79
% 9.43/9.79 clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y )
% 9.43/9.79 ] )
% 9.43/9.79 .
% 9.43/9.79 clause( 2, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X
% 9.43/9.79 , Y ) ] )
% 9.43/9.79 .
% 9.43/9.79 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 9.43/9.79 .
% 9.43/9.79 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 9.43/9.79 .
% 9.43/9.79 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z
% 9.43/9.79 ) ] )
% 9.43/9.79 .
% 9.43/9.79 clause( 116, [ member( x, z ) ] )
% 9.43/9.79 .
% 9.43/9.79 clause( 117, [ member( y, z ) ] )
% 9.43/9.79 .
% 9.43/9.79 clause( 118, [ ~( subclass( 'unordered_pair'( x, y ), z ) ) ] )
% 9.43/9.79 .
% 9.43/9.79 clause( 150, [ ~( member( 'not_subclass_element'( 'unordered_pair'( x, y )
% 9.43/9.79 , z ), z ) ) ] )
% 9.43/9.79 .
% 9.43/9.79 clause( 151, [ member( 'not_subclass_element'( 'unordered_pair'( x, y ), z
% 9.43/9.79 ), 'unordered_pair'( x, y ) ) ] )
% 9.43/9.79 .
% 9.43/9.79 clause( 156, [ =( X, Y ), ~( =( Y, X ) ) ] )
% 9.43/9.79 .
% 9.43/9.79 clause( 518, [ member( X, z ), ~( =( X, x ) ) ] )
% 9.43/9.79 .
% 9.43/9.79 clause( 520, [ member( X, z ), ~( =( X, y ) ) ] )
% 9.43/9.79 .
% 9.43/9.79 clause( 24059, [ ~( =( 'not_subclass_element'( 'unordered_pair'( x, y ), z
% 9.43/9.79 ), y ) ) ] )
% 9.43/9.79 .
% 9.43/9.79 clause( 24060, [ ~( =( 'not_subclass_element'( 'unordered_pair'( x, y ), z
% 9.43/9.79 ), x ) ) ] )
% 9.43/9.79 .
% 9.43/9.79 clause( 24240, [ =( 'not_subclass_element'( 'unordered_pair'( x, y ), z ),
% 9.43/9.79 x ), =( 'not_subclass_element'( 'unordered_pair'( x, y ), z ), y ) ] )
% 9.43/9.79 .
% 9.43/9.79 clause( 40147, [] )
% 9.43/9.79 .
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 % SZS output end Refutation
% 9.43/9.79 found a proof!
% 9.43/9.79
% 9.43/9.79 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 9.43/9.79
% 9.43/9.79 initialclauses(
% 9.43/9.79 [ clause( 40149, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 9.43/9.79 ) ] )
% 9.43/9.79 , clause( 40150, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 9.43/9.79 , Y ) ] )
% 9.43/9.79 , clause( 40151, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 9.43/9.79 subclass( X, Y ) ] )
% 9.43/9.79 , clause( 40152, [ subclass( X, 'universal_class' ) ] )
% 9.43/9.79 , clause( 40153, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 9.43/9.79 , clause( 40154, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 9.43/9.79 , clause( 40155, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 9.43/9.79 ] )
% 9.43/9.79 , clause( 40156, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 9.43/9.79 =( X, Z ) ] )
% 9.43/9.79 , clause( 40157, [ ~( member( X, 'universal_class' ) ), member( X,
% 9.43/9.79 'unordered_pair'( X, Y ) ) ] )
% 9.43/9.79 , clause( 40158, [ ~( member( X, 'universal_class' ) ), member( X,
% 9.43/9.79 'unordered_pair'( Y, X ) ) ] )
% 9.43/9.79 , clause( 40159, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 9.43/9.79 )
% 9.43/9.79 , clause( 40160, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 9.43/9.79 , clause( 40161, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 9.43/9.79 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 9.43/9.79 , clause( 40162, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 9.43/9.79 ) ) ), member( X, Z ) ] )
% 9.43/9.79 , clause( 40163, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 9.43/9.79 ) ) ), member( Y, T ) ] )
% 9.43/9.79 , clause( 40164, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 9.43/9.79 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 9.43/9.79 , clause( 40165, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 9.43/9.79 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 9.43/9.79 , clause( 40166, [ subclass( 'element_relation', 'cross_product'(
% 9.43/9.79 'universal_class', 'universal_class' ) ) ] )
% 9.43/9.79 , clause( 40167, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 9.43/9.79 ), member( X, Y ) ] )
% 9.43/9.79 , clause( 40168, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 9.43/9.79 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 9.43/9.79 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 9.43/9.79 , clause( 40169, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 9.43/9.79 )
% 9.43/9.79 , clause( 40170, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 9.43/9.79 )
% 9.43/9.79 , clause( 40171, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 9.43/9.79 intersection( Y, Z ) ) ] )
% 9.43/9.79 , clause( 40172, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 9.43/9.79 )
% 9.43/9.79 , clause( 40173, [ ~( member( X, 'universal_class' ) ), member( X,
% 9.43/9.79 complement( Y ) ), member( X, Y ) ] )
% 9.43/9.79 , clause( 40174, [ =( complement( intersection( complement( X ), complement(
% 9.43/9.79 Y ) ) ), union( X, Y ) ) ] )
% 9.43/9.79 , clause( 40175, [ =( intersection( complement( intersection( X, Y ) ),
% 9.43/9.79 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 9.43/9.79 'symmetric_difference'( X, Y ) ) ] )
% 9.43/9.79 , clause( 40176, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 9.43/9.79 X, Y, Z ) ) ] )
% 9.43/9.79 , clause( 40177, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 9.43/9.79 Z, X, Y ) ) ] )
% 9.43/9.79 , clause( 40178, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 9.43/9.79 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 9.43/9.79 , clause( 40179, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 9.43/9.79 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 9.43/9.79 'domain_of'( Y ) ) ] )
% 9.43/9.79 , clause( 40180, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 9.43/9.79 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 9.43/9.79 , clause( 40181, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 9.43/9.79 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 9.43/9.79 ] )
% 9.43/9.79 , clause( 40182, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 9.43/9.79 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 9.43/9.79 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 9.43/9.79 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 9.43/9.79 , Y ), rotate( T ) ) ] )
% 9.43/9.79 , clause( 40183, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 9.43/9.79 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 9.43/9.79 , clause( 40184, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 9.43/9.79 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 9.43/9.79 )
% 9.43/9.79 , clause( 40185, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 9.43/9.79 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 9.43/9.79 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 9.43/9.79 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 9.43/9.79 , Z ), flip( T ) ) ] )
% 9.43/9.79 , clause( 40186, [ =( 'domain_of'( flip( 'cross_product'( X,
% 9.43/9.79 'universal_class' ) ) ), inverse( X ) ) ] )
% 9.43/9.79 , clause( 40187, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 9.43/9.79 , clause( 40188, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 9.43/9.79 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 9.43/9.79 , clause( 40189, [ =( second( 'not_subclass_element'( restrict( X,
% 9.43/9.79 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 9.43/9.79 , clause( 40190, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 9.43/9.79 image( X, Y ) ) ] )
% 9.43/9.79 , clause( 40191, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 9.43/9.79 , clause( 40192, [ subclass( 'successor_relation', 'cross_product'(
% 9.43/9.79 'universal_class', 'universal_class' ) ) ] )
% 9.43/9.79 , clause( 40193, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 9.43/9.79 ) ), =( successor( X ), Y ) ] )
% 9.43/9.79 , clause( 40194, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 9.43/9.79 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 9.43/9.79 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 9.43/9.79 , clause( 40195, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 9.43/9.79 , clause( 40196, [ ~( inductive( X ) ), subclass( image(
% 9.43/9.79 'successor_relation', X ), X ) ] )
% 9.43/9.79 , clause( 40197, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 9.43/9.79 'successor_relation', X ), X ) ), inductive( X ) ] )
% 9.43/9.79 , clause( 40198, [ inductive( omega ) ] )
% 9.43/9.79 , clause( 40199, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 9.43/9.79 , clause( 40200, [ member( omega, 'universal_class' ) ] )
% 9.43/9.79 , clause( 40201, [ =( 'domain_of'( restrict( 'element_relation',
% 9.43/9.79 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 9.43/9.79 , clause( 40202, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 9.43/9.79 X ), 'universal_class' ) ] )
% 9.43/9.79 , clause( 40203, [ =( complement( image( 'element_relation', complement( X
% 9.43/9.79 ) ) ), 'power_class'( X ) ) ] )
% 9.43/9.79 , clause( 40204, [ ~( member( X, 'universal_class' ) ), member(
% 9.43/9.79 'power_class'( X ), 'universal_class' ) ] )
% 9.43/9.79 , clause( 40205, [ subclass( compose( X, Y ), 'cross_product'(
% 9.43/9.79 'universal_class', 'universal_class' ) ) ] )
% 9.43/9.79 , clause( 40206, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 9.43/9.79 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 9.43/9.79 , clause( 40207, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 9.43/9.79 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 9.43/9.79 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 9.43/9.79 ) ] )
% 9.43/9.79 , clause( 40208, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 9.43/9.79 inverse( X ) ), 'identity_relation' ) ] )
% 9.43/9.79 , clause( 40209, [ ~( subclass( compose( X, inverse( X ) ),
% 9.43/9.79 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 9.43/9.79 , clause( 40210, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 9.43/9.79 'universal_class', 'universal_class' ) ) ] )
% 9.43/9.79 , clause( 40211, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 9.43/9.79 , 'identity_relation' ) ] )
% 9.43/9.79 , clause( 40212, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 9.43/9.79 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 9.43/9.79 'identity_relation' ) ), function( X ) ] )
% 9.43/9.79 , clause( 40213, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 9.43/9.79 , member( image( X, Y ), 'universal_class' ) ] )
% 9.43/9.79 , clause( 40214, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 9.43/9.79 , clause( 40215, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 9.43/9.79 , 'null_class' ) ] )
% 9.43/9.79 , clause( 40216, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 9.43/9.79 Y ) ) ] )
% 9.43/9.79 , clause( 40217, [ function( choice ) ] )
% 9.43/9.79 , clause( 40218, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 9.43/9.79 ), member( apply( choice, X ), X ) ] )
% 9.43/9.79 , clause( 40219, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 9.43/9.79 , clause( 40220, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 9.43/9.79 , clause( 40221, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 9.43/9.79 'one_to_one'( X ) ] )
% 9.43/9.79 , clause( 40222, [ =( intersection( 'cross_product'( 'universal_class',
% 9.43/9.79 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 9.43/9.79 'universal_class' ), complement( compose( complement( 'element_relation'
% 9.43/9.79 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 9.43/9.79 , clause( 40223, [ =( intersection( inverse( 'subset_relation' ),
% 9.43/9.79 'subset_relation' ), 'identity_relation' ) ] )
% 9.43/9.79 , clause( 40224, [ =( complement( 'domain_of'( intersection( X,
% 9.43/9.79 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 9.43/9.79 , clause( 40225, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 9.43/9.79 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 9.43/9.79 , clause( 40226, [ ~( operation( X ) ), function( X ) ] )
% 9.43/9.79 , clause( 40227, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 9.43/9.79 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 9.43/9.79 ] )
% 9.43/9.79 , clause( 40228, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 9.43/9.79 'domain_of'( 'domain_of'( X ) ) ) ] )
% 9.43/9.79 , clause( 40229, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 9.43/9.79 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 9.43/9.79 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 9.43/9.79 operation( X ) ] )
% 9.43/9.79 , clause( 40230, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 9.43/9.79 , clause( 40231, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 9.43/9.79 Y ) ), 'domain_of'( X ) ) ] )
% 9.43/9.79 , clause( 40232, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 9.43/9.79 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 9.43/9.79 , clause( 40233, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 9.43/9.79 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 9.43/9.79 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 9.43/9.79 , clause( 40234, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 9.43/9.79 , clause( 40235, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 9.43/9.79 , clause( 40236, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 9.43/9.79 , clause( 40237, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 9.43/9.79 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 9.43/9.79 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 9.43/9.79 )
% 9.43/9.79 , clause( 40238, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 9.43/9.79 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 9.43/9.79 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 9.43/9.79 , Y ) ] )
% 9.43/9.79 , clause( 40239, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 9.43/9.79 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 9.43/9.79 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 9.43/9.79 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 9.43/9.79 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 9.43/9.79 )
% 9.43/9.79 , clause( 40240, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 9.43/9.79 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 9.43/9.79 , clause( 40241, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 9.43/9.79 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 9.43/9.79 , clause( 40242, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 9.43/9.79 ) ) ), member( X, 'universal_class' ) ] )
% 9.43/9.79 , clause( 40243, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 9.43/9.79 ) ) ), member( Y, 'universal_class' ) ] )
% 9.43/9.79 , clause( 40244, [ subclass( X, X ) ] )
% 9.43/9.79 , clause( 40245, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 9.43/9.79 X, Z ) ] )
% 9.43/9.79 , clause( 40246, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 9.43/9.79 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 9.43/9.79 , clause( 40247, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 9.43/9.79 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 9.43/9.79 , clause( 40248, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 9.43/9.79 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 9.43/9.79 , clause( 40249, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 9.43/9.79 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 9.43/9.79 , clause( 40250, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 9.43/9.79 )
% 9.43/9.79 , clause( 40251, [ ~( member( X, 'null_class' ) ) ] )
% 9.43/9.79 , clause( 40252, [ subclass( 'null_class', X ) ] )
% 9.43/9.79 , clause( 40253, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 9.43/9.79 )
% 9.43/9.79 , clause( 40254, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 9.43/9.79 , 'null_class' ), X ) ] )
% 9.43/9.79 , clause( 40255, [ member( 'null_class', 'universal_class' ) ] )
% 9.43/9.79 , clause( 40256, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 9.43/9.79 ] )
% 9.43/9.79 , clause( 40257, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 9.43/9.79 )
% 9.43/9.79 , clause( 40258, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 9.43/9.79 )
% 9.43/9.79 , clause( 40259, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 9.43/9.79 X ), singleton( Y ) ) ] )
% 9.43/9.79 , clause( 40260, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 9.43/9.79 Y ), singleton( Y ) ) ] )
% 9.43/9.79 , clause( 40261, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 9.43/9.79 'universal_class' ), member( Y, 'universal_class' ) ] )
% 9.43/9.79 , clause( 40262, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 9.43/9.79 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 9.43/9.79 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 9.43/9.79 , clause( 40263, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 9.43/9.79 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 9.43/9.79 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 9.43/9.79 , clause( 40264, [ ~( member( X, 'universal_class' ) ), ~( =(
% 9.43/9.79 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 9.43/9.79 , clause( 40265, [ ~( member( X, 'universal_class' ) ), ~( =(
% 9.43/9.79 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 9.43/9.79 , clause( 40266, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 9.43/9.79 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 9.43/9.79 , clause( 40267, [ member( x, z ) ] )
% 9.43/9.79 , clause( 40268, [ member( y, z ) ] )
% 9.43/9.79 , clause( 40269, [ ~( subclass( 'unordered_pair'( x, y ), z ) ) ] )
% 9.43/9.79 ] ).
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 subsumption(
% 9.43/9.79 clause( 1, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y )
% 9.43/9.79 ] )
% 9.43/9.79 , clause( 40150, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 9.43/9.79 , Y ) ] )
% 9.43/9.79 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 9.43/9.79 ), ==>( 1, 1 )] ) ).
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 subsumption(
% 9.43/9.79 clause( 2, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X
% 9.43/9.79 , Y ) ] )
% 9.43/9.79 , clause( 40151, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 9.43/9.79 subclass( X, Y ) ] )
% 9.43/9.79 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 9.43/9.79 ), ==>( 1, 1 )] ) ).
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 subsumption(
% 9.43/9.79 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 9.43/9.79 , clause( 40153, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 9.43/9.79 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 9.43/9.79 ), ==>( 1, 1 )] ) ).
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 subsumption(
% 9.43/9.79 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 9.43/9.79 , clause( 40155, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 9.43/9.79 ] )
% 9.43/9.79 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 9.43/9.79 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 subsumption(
% 9.43/9.79 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z
% 9.43/9.79 ) ] )
% 9.43/9.79 , clause( 40156, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 9.43/9.79 =( X, Z ) ] )
% 9.43/9.79 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 9.43/9.79 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 subsumption(
% 9.43/9.79 clause( 116, [ member( x, z ) ] )
% 9.43/9.79 , clause( 40267, [ member( x, z ) ] )
% 9.43/9.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 subsumption(
% 9.43/9.79 clause( 117, [ member( y, z ) ] )
% 9.43/9.79 , clause( 40268, [ member( y, z ) ] )
% 9.43/9.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 9.43/9.79
% 9.43/9.79
% 9.43/9.79 subsumption(
% 9.43/9.79 clause( 118, [ ~( subclass( 'unordered_pair'( x, y ), z ) ) ] )
% 9.43/9.79 , clause( 40269, [ ~( subclass( 'unordered_paCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------