TSTP Solution File: SET075-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET075-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n022.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 22:46:37 EDT 2022
% Result : Unsatisfiable 2.07s 2.44s
% Output : Refutation 2.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET075-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sun Jul 10 19:20:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.73/1.10 *** allocated 10000 integers for termspace/termends
% 0.73/1.10 *** allocated 10000 integers for clauses
% 0.73/1.10 *** allocated 10000 integers for justifications
% 0.73/1.10 Bliksem 1.12
% 0.73/1.10
% 0.73/1.10
% 0.73/1.10 Automatic Strategy Selection
% 0.73/1.10
% 0.73/1.10 Clauses:
% 0.73/1.10 [
% 0.73/1.10 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.73/1.10 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.73/1.10 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.73/1.10 ,
% 0.73/1.10 [ subclass( X, 'universal_class' ) ],
% 0.73/1.10 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.73/1.10 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.73/1.10 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.73/1.10 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.73/1.10 ,
% 0.73/1.10 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.73/1.10 ) ) ],
% 0.73/1.10 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.73/1.10 ) ) ],
% 0.73/1.10 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.73/1.10 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.73/1.10 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.73/1.10 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.73/1.10 X, Z ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.73/1.10 Y, T ) ],
% 0.73/1.10 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.73/1.10 ), 'cross_product'( Y, T ) ) ],
% 0.73/1.10 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.73/1.10 ), second( X ) ), X ) ],
% 0.73/1.10 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.73/1.10 'universal_class' ) ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.73/1.10 Y ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.73/1.10 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.73/1.10 , Y ), 'element_relation' ) ],
% 0.73/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.73/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.73/1.10 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.73/1.10 Z ) ) ],
% 0.73/1.10 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.73/1.10 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.73/1.10 member( X, Y ) ],
% 0.73/1.10 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.73/1.10 union( X, Y ) ) ],
% 0.73/1.10 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.73/1.10 intersection( complement( X ), complement( Y ) ) ) ),
% 0.73/1.10 'symmetric_difference'( X, Y ) ) ],
% 0.73/1.10 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.73/1.10 ,
% 0.73/1.10 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.73/1.10 ,
% 0.73/1.10 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.73/1.10 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.73/1.10 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.73/1.10 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.73/1.10 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.73/1.10 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.73/1.10 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.73/1.10 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.73/1.10 'cross_product'( 'universal_class', 'universal_class' ),
% 0.73/1.10 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.73/1.10 Y ), rotate( T ) ) ],
% 0.73/1.10 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.73/1.10 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.73/1.10 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.73/1.10 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.73/1.10 'cross_product'( 'universal_class', 'universal_class' ),
% 0.73/1.10 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.73/1.10 Z ), flip( T ) ) ],
% 0.73/1.10 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.73/1.10 inverse( X ) ) ],
% 0.73/1.10 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.73/1.10 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.73/1.10 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.73/1.10 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.73/1.10 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.73/1.10 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.73/1.10 ],
% 0.73/1.10 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.73/1.10 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.73/1.10 'universal_class' ) ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.73/1.10 successor( X ), Y ) ],
% 0.73/1.10 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.73/1.10 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.73/1.10 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.73/1.10 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.73/1.10 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.73/1.10 ,
% 0.73/1.10 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.73/1.10 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.73/1.10 [ inductive( omega ) ],
% 0.73/1.10 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.73/1.10 [ member( omega, 'universal_class' ) ],
% 0.73/1.10 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.73/1.10 , 'sum_class'( X ) ) ],
% 0.73/1.10 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.73/1.10 'universal_class' ) ],
% 0.73/1.10 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.73/1.10 'power_class'( X ) ) ],
% 0.73/1.10 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.73/1.10 'universal_class' ) ],
% 0.73/1.10 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.73/1.10 'universal_class' ) ) ],
% 0.73/1.10 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.73/1.10 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.73/1.10 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.73/1.10 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.73/1.10 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.73/1.10 ) ],
% 0.73/1.10 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.73/1.10 , 'identity_relation' ) ],
% 0.73/1.10 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.73/1.10 'single_valued_class'( X ) ],
% 0.73/1.10 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.73/1.10 'universal_class' ) ) ],
% 0.73/1.10 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.73/1.10 'identity_relation' ) ],
% 0.73/1.10 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.73/1.10 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.73/1.10 , function( X ) ],
% 0.73/1.10 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.73/1.10 X, Y ), 'universal_class' ) ],
% 0.73/1.10 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.73/1.10 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.73/1.10 ) ],
% 0.73/1.10 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.73/1.10 [ function( choice ) ],
% 0.73/1.10 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.73/1.10 apply( choice, X ), X ) ],
% 0.73/1.10 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.73/1.10 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.73/1.10 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.73/1.10 ,
% 0.73/1.10 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.73/1.10 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.73/1.10 , complement( compose( complement( 'element_relation' ), inverse(
% 0.73/1.10 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.73/1.10 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.73/1.10 'identity_relation' ) ],
% 0.73/1.10 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.73/1.10 , diagonalise( X ) ) ],
% 0.73/1.10 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.73/1.10 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.73/1.10 [ ~( operation( X ) ), function( X ) ],
% 0.73/1.10 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.73/1.10 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.73/1.10 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.73/1.15 'domain_of'( X ) ) ) ],
% 0.73/1.15 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.73/1.15 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.73/1.15 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.73/1.15 X ) ],
% 0.73/1.15 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.73/1.15 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.73/1.15 'domain_of'( X ) ) ],
% 0.73/1.15 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.73/1.15 'domain_of'( Z ) ) ) ],
% 0.73/1.15 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.73/1.15 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.73/1.15 ), compatible( X, Y, Z ) ],
% 0.73/1.15 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.73/1.15 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.73/1.15 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.73/1.15 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.73/1.15 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.73/1.15 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.73/1.15 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.73/1.15 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.73/1.15 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.73/1.15 , Y ) ],
% 0.73/1.15 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.73/1.15 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.73/1.15 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.73/1.15 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.73/1.15 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.73/1.15 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.73/1.15 X, 'unordered_pair'( X, Y ) ) ],
% 0.73/1.15 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.73/1.15 Y, 'unordered_pair'( X, Y ) ) ],
% 0.73/1.15 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.73/1.15 X, 'universal_class' ) ],
% 0.73/1.15 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.73/1.15 Y, 'universal_class' ) ],
% 0.73/1.15 [ subclass( X, X ) ],
% 0.73/1.15 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.73/1.15 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.73/1.15 'not_subclass_element'( Y, X ), Y ) ],
% 0.73/1.15 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.73/1.15 'not_subclass_element'( Y, X ), Y ) ],
% 0.73/1.15 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.73/1.15 'not_subclass_element'( Y, X ), Y ) ],
% 0.73/1.15 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.73/1.15 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.73/1.15 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.73/1.15 [ ~( member( X, 'null_class' ) ) ],
% 0.73/1.15 [ subclass( 'null_class', X ) ],
% 0.73/1.15 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.73/1.15 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.73/1.15 ), X ) ],
% 0.73/1.15 [ member( 'null_class', 'universal_class' ) ],
% 0.73/1.15 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.73/1.15 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.73/1.15 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.73/1.15 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.73/1.15 Y ) ) ],
% 0.73/1.15 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.73/1.15 Y ) ) ],
% 0.73/1.15 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.73/1.15 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.73/1.15 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.73/1.15 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.73/1.15 'universal_class' ) ) ), =( Y, Z ) ],
% 0.73/1.15 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.73/1.15 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.73/1.15 'universal_class' ) ) ), =( X, Z ) ],
% 0.73/1.15 [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v ) ) ],
% 0.73/1.15 [ =( 'unordered_pair'( x, y ), 'null_class' ) ]
% 0.73/1.15 ] .
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 percentage equality = 0.233766, percentage horn = 0.871795
% 0.73/1.15 This is a problem with some equality
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 Options Used:
% 0.73/1.15
% 0.73/1.15 useres = 1
% 0.73/1.15 useparamod = 1
% 2.07/2.44 useeqrefl = 1
% 2.07/2.44 useeqfact = 1
% 2.07/2.44 usefactor = 1
% 2.07/2.44 usesimpsplitting = 0
% 2.07/2.44 usesimpdemod = 5
% 2.07/2.44 usesimpres = 3
% 2.07/2.44
% 2.07/2.44 resimpinuse = 1000
% 2.07/2.44 resimpclauses = 20000
% 2.07/2.44 substype = eqrewr
% 2.07/2.44 backwardsubs = 1
% 2.07/2.44 selectoldest = 5
% 2.07/2.44
% 2.07/2.44 litorderings [0] = split
% 2.07/2.44 litorderings [1] = extend the termordering, first sorting on arguments
% 2.07/2.44
% 2.07/2.44 termordering = kbo
% 2.07/2.44
% 2.07/2.44 litapriori = 0
% 2.07/2.44 termapriori = 1
% 2.07/2.44 litaposteriori = 0
% 2.07/2.44 termaposteriori = 0
% 2.07/2.44 demodaposteriori = 0
% 2.07/2.44 ordereqreflfact = 0
% 2.07/2.44
% 2.07/2.44 litselect = negord
% 2.07/2.44
% 2.07/2.44 maxweight = 15
% 2.07/2.44 maxdepth = 30000
% 2.07/2.44 maxlength = 115
% 2.07/2.44 maxnrvars = 195
% 2.07/2.44 excuselevel = 1
% 2.07/2.44 increasemaxweight = 1
% 2.07/2.44
% 2.07/2.44 maxselected = 10000000
% 2.07/2.44 maxnrclauses = 10000000
% 2.07/2.44
% 2.07/2.44 showgenerated = 0
% 2.07/2.44 showkept = 0
% 2.07/2.44 showselected = 0
% 2.07/2.44 showdeleted = 0
% 2.07/2.44 showresimp = 1
% 2.07/2.44 showstatus = 2000
% 2.07/2.44
% 2.07/2.44 prologoutput = 1
% 2.07/2.44 nrgoals = 5000000
% 2.07/2.44 totalproof = 1
% 2.07/2.44
% 2.07/2.44 Symbols occurring in the translation:
% 2.07/2.44
% 2.07/2.44 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.07/2.44 . [1, 2] (w:1, o:58, a:1, s:1, b:0),
% 2.07/2.44 ! [4, 1] (w:0, o:33, a:1, s:1, b:0),
% 2.07/2.44 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.07/2.44 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.07/2.44 subclass [41, 2] (w:1, o:83, a:1, s:1, b:0),
% 2.07/2.44 member [43, 2] (w:1, o:84, a:1, s:1, b:0),
% 2.07/2.44 'not_subclass_element' [44, 2] (w:1, o:85, a:1, s:1, b:0),
% 2.07/2.44 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 2.07/2.44 'unordered_pair' [46, 2] (w:1, o:86, a:1, s:1, b:0),
% 2.07/2.44 singleton [47, 1] (w:1, o:41, a:1, s:1, b:0),
% 2.07/2.44 'ordered_pair' [48, 2] (w:1, o:87, a:1, s:1, b:0),
% 2.07/2.44 'cross_product' [50, 2] (w:1, o:88, a:1, s:1, b:0),
% 2.07/2.44 first [52, 1] (w:1, o:42, a:1, s:1, b:0),
% 2.07/2.44 second [53, 1] (w:1, o:43, a:1, s:1, b:0),
% 2.07/2.44 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 2.07/2.44 intersection [55, 2] (w:1, o:90, a:1, s:1, b:0),
% 2.07/2.44 complement [56, 1] (w:1, o:44, a:1, s:1, b:0),
% 2.07/2.44 union [57, 2] (w:1, o:91, a:1, s:1, b:0),
% 2.07/2.44 'symmetric_difference' [58, 2] (w:1, o:92, a:1, s:1, b:0),
% 2.07/2.44 restrict [60, 3] (w:1, o:95, a:1, s:1, b:0),
% 2.07/2.44 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 2.07/2.44 'domain_of' [62, 1] (w:1, o:46, a:1, s:1, b:0),
% 2.07/2.44 rotate [63, 1] (w:1, o:38, a:1, s:1, b:0),
% 2.07/2.44 flip [65, 1] (w:1, o:47, a:1, s:1, b:0),
% 2.07/2.44 inverse [66, 1] (w:1, o:48, a:1, s:1, b:0),
% 2.07/2.44 'range_of' [67, 1] (w:1, o:39, a:1, s:1, b:0),
% 2.07/2.44 domain [68, 3] (w:1, o:97, a:1, s:1, b:0),
% 2.07/2.44 range [69, 3] (w:1, o:98, a:1, s:1, b:0),
% 2.07/2.44 image [70, 2] (w:1, o:89, a:1, s:1, b:0),
% 2.07/2.44 successor [71, 1] (w:1, o:49, a:1, s:1, b:0),
% 2.07/2.44 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 2.07/2.44 inductive [73, 1] (w:1, o:50, a:1, s:1, b:0),
% 2.07/2.44 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 2.07/2.44 'sum_class' [75, 1] (w:1, o:51, a:1, s:1, b:0),
% 2.07/2.44 'power_class' [76, 1] (w:1, o:54, a:1, s:1, b:0),
% 2.07/2.44 compose [78, 2] (w:1, o:93, a:1, s:1, b:0),
% 2.07/2.44 'single_valued_class' [79, 1] (w:1, o:55, a:1, s:1, b:0),
% 2.07/2.44 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 2.07/2.44 function [82, 1] (w:1, o:56, a:1, s:1, b:0),
% 2.07/2.44 regular [83, 1] (w:1, o:40, a:1, s:1, b:0),
% 2.07/2.44 apply [84, 2] (w:1, o:94, a:1, s:1, b:0),
% 2.07/2.44 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 2.07/2.44 'one_to_one' [86, 1] (w:1, o:52, a:1, s:1, b:0),
% 2.07/2.44 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 2.07/2.44 diagonalise [88, 1] (w:1, o:57, a:1, s:1, b:0),
% 2.07/2.44 cantor [89, 1] (w:1, o:45, a:1, s:1, b:0),
% 2.07/2.44 operation [90, 1] (w:1, o:53, a:1, s:1, b:0),
% 2.07/2.44 compatible [94, 3] (w:1, o:96, a:1, s:1, b:0),
% 2.07/2.44 homomorphism [95, 3] (w:1, o:99, a:1, s:1, b:0),
% 2.07/2.44 'not_homomorphism1' [96, 3] (w:1, o:100, a:1, s:1, b:0),
% 2.07/2.44 'not_homomorphism2' [97, 3] (w:1, o:101, a:1, s:1, b:0),
% 2.07/2.44 x [98, 0] (w:1, o:29, a:1, s:1, b:0),
% 2.07/2.44 y [99, 0] (w:1, o:30, a:1, s:1, b:0),
% 2.07/2.44 u [100, 0] (w:1, o:31, a:1, s:1, b:0),
% 2.07/2.44 v [101, 0] (w:1, o:32, a:1, s:1, b:0).
% 2.07/2.44
% 2.07/2.44
% 2.07/2.44 Starting Search:
% 2.07/2.44
% 2.07/2.44 Resimplifying inuse:
% 2.07/2.44 Done
% 2.07/2.44
% 2.07/2.44
% 2.07/2.44 Intermediate Status:
% 2.07/2.44 Generated: 4109
% 2.07/2.44 Kept: 2000
% 2.07/2.44 Inuse: 128
% 2.07/2.44 Deleted: 4
% 2.07/2.44 Deletedinuse: 4
% 2.07/2.44
% 2.07/2.44 Resimplifying inuse:
% 2.07/2.44 Done
% 2.07/2.44
% 2.07/2.44 Resimplifying inuse:
% 2.07/2.44 Done
% 2.07/2.44
% 2.07/2.44
% 2.07/2.44 Intermediate Status:
% 2.07/2.44 Generated: 9065
% 2.07/2.44 Kept: 4012
% 2.07/2.44 Inuse: 212
% 2.07/2.44 Deleted: 9
% 2.07/2.44 Deletedinuse: 9
% 2.07/2.44
% 2.07/2.44 Resimplifying inuse:
% 2.07/2.44 Done
% 2.07/2.44
% 2.07/2.44 Resimplifying inuse:
% 2.07/2.44 Done
% 2.07/2.44
% 2.07/2.44
% 2.07/2.44 Intermediate Status:
% 2.07/2.44 Generated: 14461
% 2.07/2.44 Kept: 6226
% 2.07/2.44 Inuse: 291
% 2.07/2.44 Deleted: 11
% 2.07/2.44 Deletedinuse: 11
% 2.07/2.44
% 2.07/2.44 Resimplifying inuse:
% 2.07/2.44 Done
% 2.07/2.44
% 2.07/2.44 Resimplifying inuse:
% 2.07/2.44 Done
% 2.07/2.44
% 2.07/2.44
% 2.07/2.44 Intermediate Status:
% 2.07/2.44 Generated: 20071
% 2.07/2.44 Kept: 8262
% 2.07/2.44 Inuse: 356
% 2.07/2.44 Deleted: 53
% 2.07/2.44 Deletedinuse: 53
% 2.07/2.44
% 2.07/2.44 Resimplifying inuse:
% 2.07/2.44 Done
% 2.07/2.44
% 2.07/2.44 Resimplifying inuse:
% 2.07/2.44 Done
% 2.07/2.44
% 2.07/2.44
% 2.07/2.44 Intermediate Status:
% 2.07/2.44 Generated: 27434
% 2.07/2.44 Kept: 10265
% 2.07/2.44 Inuse: 410
% 2.07/2.44 Deleted: 57
% 2.07/2.44 Deletedinuse: 57
% 2.07/2.44
% 2.07/2.44 Resimplifying inuse:
% 2.07/2.44 Done
% 2.07/2.44
% 2.07/2.44 Resimplifying inuse:
% 2.07/2.44 Done
% 2.07/2.44
% 2.07/2.44
% 2.07/2.44 Intermediate Status:
% 2.07/2.44 Generated: 35478
% 2.07/2.44 Kept: 12275
% 2.07/2.44 Inuse: 435
% 2.07/2.44 Deleted: 66
% 2.07/2.44 Deletedinuse: 58
% 2.07/2.44
% 2.07/2.44 Resimplifying inuse:
% 2.07/2.44 Done
% 2.07/2.44
% 2.07/2.44
% 2.07/2.44 Bliksems!, er is een bewijs:
% 2.07/2.44 % SZS status Unsatisfiable
% 2.07/2.44 % SZS output start Refutation
% 2.07/2.44
% 2.07/2.44 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 2.07/2.44 )
% 2.07/2.44 .
% 2.07/2.44 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 7, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.07/2.44 'unordered_pair'( X, Y ) ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 11, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 2.07/2.44 singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 13, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) )
% 2.07/2.44 ), member( Y, T ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 100, [ ~( member( X, 'null_class' ) ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 102, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 105, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 106, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 113, [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v ) ) ]
% 2.07/2.44 )
% 2.07/2.44 .
% 2.07/2.44 clause( 114, [ =( 'unordered_pair'( x, y ), 'null_class' ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 387, [ ~( member( x, 'universal_class' ) ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 388, [ ~( member( x, X ) ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 640, [ ~( member( 'ordered_pair'( X, x ), 'cross_product'( Y, Z ) )
% 2.07/2.44 ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 12039, [ =( 'unordered_pair'( y, x ), 'null_class' ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 12169, [ subclass( singleton( y ), 'null_class' ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 12194, [ subclass( singleton( x ), 'null_class' ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 12197, [ =( singleton( y ), 'null_class' ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 12218, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 2.07/2.44 'null_class' ) ), 'ordered_pair'( X, y ) ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 12223, [ =( singleton( x ), 'null_class' ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 12272, [ =( 'ordered_pair'( X, y ), 'ordered_pair'( X, x ) ) ] )
% 2.07/2.44 .
% 2.07/2.44 clause( 13669, [] )
% 2.07/2.44 .
% 2.07/2.44
% 2.07/2.44
% 2.07/2.44 % SZS output end Refutation
% 2.07/2.44 found a proof!
% 2.07/2.44
% 2.07/2.44 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.07/2.44
% 2.07/2.44 initialclauses(
% 2.07/2.44 [ clause( 13671, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 2.07/2.44 ) ] )
% 2.07/2.44 , clause( 13672, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 2.07/2.44 , Y ) ] )
% 2.07/2.44 , clause( 13673, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 2.07/2.44 subclass( X, Y ) ] )
% 2.07/2.44 , clause( 13674, [ subclass( X, 'universal_class' ) ] )
% 2.07/2.44 , clause( 13675, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.07/2.44 , clause( 13676, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 2.07/2.45 , clause( 13677, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 2.07/2.45 ] )
% 2.07/2.45 , clause( 13678, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 2.07/2.45 =( X, Z ) ] )
% 2.07/2.45 , clause( 13679, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.07/2.45 'unordered_pair'( X, Y ) ) ] )
% 2.07/2.45 , clause( 13680, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.07/2.45 'unordered_pair'( Y, X ) ) ] )
% 2.07/2.45 , clause( 13681, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 2.07/2.45 )
% 2.07/2.45 , clause( 13682, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.07/2.45 , clause( 13683, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 2.07/2.45 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 2.07/2.45 , clause( 13684, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.07/2.45 ) ) ), member( X, Z ) ] )
% 2.07/2.45 , clause( 13685, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.07/2.45 ) ) ), member( Y, T ) ] )
% 2.07/2.45 , clause( 13686, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 2.07/2.45 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 2.07/2.45 , clause( 13687, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 2.07/2.45 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 2.07/2.45 , clause( 13688, [ subclass( 'element_relation', 'cross_product'(
% 2.07/2.45 'universal_class', 'universal_class' ) ) ] )
% 2.07/2.45 , clause( 13689, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 2.07/2.45 ), member( X, Y ) ] )
% 2.07/2.45 , clause( 13690, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 2.07/2.45 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 2.07/2.45 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 2.07/2.45 , clause( 13691, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 2.07/2.45 )
% 2.07/2.45 , clause( 13692, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 2.07/2.45 )
% 2.07/2.45 , clause( 13693, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 2.07/2.45 intersection( Y, Z ) ) ] )
% 2.07/2.45 , clause( 13694, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 2.07/2.45 )
% 2.07/2.45 , clause( 13695, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.07/2.45 complement( Y ) ), member( X, Y ) ] )
% 2.07/2.45 , clause( 13696, [ =( complement( intersection( complement( X ), complement(
% 2.07/2.45 Y ) ) ), union( X, Y ) ) ] )
% 2.07/2.45 , clause( 13697, [ =( intersection( complement( intersection( X, Y ) ),
% 2.07/2.45 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 2.07/2.45 'symmetric_difference'( X, Y ) ) ] )
% 2.07/2.45 , clause( 13698, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 2.07/2.45 X, Y, Z ) ) ] )
% 2.07/2.45 , clause( 13699, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 2.07/2.45 Z, X, Y ) ) ] )
% 2.07/2.45 , clause( 13700, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 2.07/2.45 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 2.07/2.45 , clause( 13701, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 2.07/2.45 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 2.07/2.45 'domain_of'( Y ) ) ] )
% 2.07/2.45 , clause( 13702, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 2.07/2.45 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.07/2.45 , clause( 13703, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.07/2.45 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 2.07/2.45 ] )
% 2.07/2.45 , clause( 13704, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.07/2.45 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 2.07/2.45 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.07/2.45 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 2.07/2.45 , Y ), rotate( T ) ) ] )
% 2.07/2.45 , clause( 13705, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 2.07/2.45 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.07/2.45 , clause( 13706, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.07/2.45 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 2.07/2.45 )
% 2.07/2.45 , clause( 13707, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.07/2.45 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 2.07/2.45 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.07/2.45 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 2.07/2.45 , Z ), flip( T ) ) ] )
% 2.07/2.45 , clause( 13708, [ =( 'domain_of'( flip( 'cross_product'( X,
% 2.07/2.45 'universal_class' ) ) ), inverse( X ) ) ] )
% 2.07/2.45 , clause( 13709, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 2.07/2.45 , clause( 13710, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 2.07/2.45 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 2.07/2.45 , clause( 13711, [ =( second( 'not_subclass_element'( restrict( X,
% 2.07/2.45 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 2.07/2.45 , clause( 13712, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 2.07/2.45 image( X, Y ) ) ] )
% 2.07/2.45 , clause( 13713, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 2.07/2.45 , clause( 13714, [ subclass( 'successor_relation', 'cross_product'(
% 2.07/2.45 'universal_class', 'universal_class' ) ) ] )
% 2.07/2.45 , clause( 13715, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 2.07/2.45 ) ), =( successor( X ), Y ) ] )
% 2.07/2.45 , clause( 13716, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 2.07/2.45 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 2.07/2.45 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 2.07/2.45 , clause( 13717, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 2.07/2.45 , clause( 13718, [ ~( inductive( X ) ), subclass( image(
% 2.07/2.45 'successor_relation', X ), X ) ] )
% 2.07/2.45 , clause( 13719, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 2.07/2.45 'successor_relation', X ), X ) ), inductive( X ) ] )
% 2.07/2.45 , clause( 13720, [ inductive( omega ) ] )
% 2.07/2.45 , clause( 13721, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 2.07/2.45 , clause( 13722, [ member( omega, 'universal_class' ) ] )
% 2.07/2.45 , clause( 13723, [ =( 'domain_of'( restrict( 'element_relation',
% 2.07/2.45 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 2.07/2.45 , clause( 13724, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 2.07/2.45 X ), 'universal_class' ) ] )
% 2.07/2.45 , clause( 13725, [ =( complement( image( 'element_relation', complement( X
% 2.07/2.45 ) ) ), 'power_class'( X ) ) ] )
% 2.07/2.45 , clause( 13726, [ ~( member( X, 'universal_class' ) ), member(
% 2.07/2.45 'power_class'( X ), 'universal_class' ) ] )
% 2.07/2.45 , clause( 13727, [ subclass( compose( X, Y ), 'cross_product'(
% 2.07/2.45 'universal_class', 'universal_class' ) ) ] )
% 2.07/2.45 , clause( 13728, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 2.07/2.45 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 2.07/2.45 , clause( 13729, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 2.07/2.45 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 2.07/2.45 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 2.07/2.45 ) ] )
% 2.07/2.45 , clause( 13730, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 2.07/2.45 inverse( X ) ), 'identity_relation' ) ] )
% 2.07/2.45 , clause( 13731, [ ~( subclass( compose( X, inverse( X ) ),
% 2.07/2.45 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 2.07/2.45 , clause( 13732, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 2.07/2.45 'universal_class', 'universal_class' ) ) ] )
% 2.07/2.45 , clause( 13733, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 2.07/2.45 , 'identity_relation' ) ] )
% 2.07/2.45 , clause( 13734, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 2.07/2.45 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 2.07/2.45 'identity_relation' ) ), function( X ) ] )
% 2.07/2.45 , clause( 13735, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 2.07/2.45 , member( image( X, Y ), 'universal_class' ) ] )
% 2.07/2.45 , clause( 13736, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 2.07/2.45 , clause( 13737, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 2.07/2.45 , 'null_class' ) ] )
% 2.07/2.45 , clause( 13738, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 2.07/2.45 Y ) ) ] )
% 2.07/2.45 , clause( 13739, [ function( choice ) ] )
% 2.07/2.45 , clause( 13740, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 2.07/2.45 ), member( apply( choice, X ), X ) ] )
% 2.07/2.45 , clause( 13741, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 2.07/2.45 , clause( 13742, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 2.07/2.45 , clause( 13743, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 2.07/2.45 'one_to_one'( X ) ] )
% 2.07/2.45 , clause( 13744, [ =( intersection( 'cross_product'( 'universal_class',
% 2.07/2.45 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 2.07/2.45 'universal_class' ), complement( compose( complement( 'element_relation'
% 2.07/2.45 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 2.07/2.45 , clause( 13745, [ =( intersection( inverse( 'subset_relation' ),
% 2.07/2.45 'subset_relation' ), 'identity_relation' ) ] )
% 2.07/2.45 , clause( 13746, [ =( complement( 'domain_of'( intersection( X,
% 2.07/2.45 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 2.07/2.45 , clause( 13747, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 2.07/2.45 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 2.07/2.45 , clause( 13748, [ ~( operation( X ) ), function( X ) ] )
% 2.07/2.45 , clause( 13749, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 2.07/2.45 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.07/2.45 ] )
% 2.07/2.45 , clause( 13750, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 2.07/2.45 'domain_of'( 'domain_of'( X ) ) ) ] )
% 2.07/2.45 , clause( 13751, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 2.07/2.45 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.07/2.45 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 2.07/2.45 operation( X ) ] )
% 2.07/2.45 , clause( 13752, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 2.07/2.45 , clause( 13753, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 2.07/2.45 Y ) ), 'domain_of'( X ) ) ] )
% 2.07/2.45 , clause( 13754, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 2.07/2.45 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 2.07/2.45 , clause( 13755, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 2.07/2.45 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 2.07/2.45 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 2.07/2.45 , clause( 13756, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 2.07/2.45 , clause( 13757, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 2.07/2.45 , clause( 13758, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 2.07/2.45 , clause( 13759, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 2.07/2.45 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 2.07/2.45 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 2.07/2.45 )
% 2.07/2.45 , clause( 13760, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.07/2.45 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 2.07/2.45 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 2.07/2.45 , Y ) ] )
% 2.07/2.45 , clause( 13761, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.07/2.45 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 2.07/2.45 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 2.07/2.45 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 2.07/2.45 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 2.07/2.45 )
% 2.07/2.45 , clause( 13762, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.07/2.45 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 2.07/2.45 , clause( 13763, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.07/2.45 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 2.07/2.45 , clause( 13764, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.07/2.45 ) ) ), member( X, 'universal_class' ) ] )
% 2.07/2.45 , clause( 13765, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.07/2.45 ) ) ), member( Y, 'universal_class' ) ] )
% 2.07/2.45 , clause( 13766, [ subclass( X, X ) ] )
% 2.07/2.45 , clause( 13767, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 2.07/2.45 X, Z ) ] )
% 2.07/2.45 , clause( 13768, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 2.07/2.45 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.07/2.45 , clause( 13769, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 2.07/2.45 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.07/2.45 , clause( 13770, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 2.07/2.45 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.07/2.45 , clause( 13771, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 2.07/2.45 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 2.07/2.45 , clause( 13772, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 2.07/2.45 )
% 2.07/2.45 , clause( 13773, [ ~( member( X, 'null_class' ) ) ] )
% 2.07/2.45 , clause( 13774, [ subclass( 'null_class', X ) ] )
% 2.07/2.45 , clause( 13775, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 2.07/2.45 )
% 2.07/2.45 , clause( 13776, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 2.07/2.45 , 'null_class' ), X ) ] )
% 2.07/2.45 , clause( 13777, [ member( 'null_class', 'universal_class' ) ] )
% 2.07/2.45 , clause( 13778, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 2.07/2.45 ] )
% 2.07/2.45 , clause( 13779, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 2.07/2.45 )
% 2.07/2.45 , clause( 13780, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 2.07/2.45 )
% 2.07/2.45 , clause( 13781, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 2.07/2.45 X ), singleton( Y ) ) ] )
% 2.07/2.45 , clause( 13782, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 2.07/2.45 Y ), singleton( Y ) ) ] )
% 2.07/2.45 , clause( 13783, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 2.07/2.45 'universal_class' ), member( Y, 'universal_class' ) ] )
% 2.07/2.45 , clause( 13784, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 2.07/2.45 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 2.07/2.45 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 2.07/2.45 , clause( 13785, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 2.07/2.45 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 2.07/2.45 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 2.07/2.45 , clause( 13786, [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v )
% 2.07/2.45 ) ] )
% 2.07/2.45 , clause( 13787, [ =( 'unordered_pair'( x, y ), 'null_class' ) ] )
% 2.07/2.45 ] ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 2.07/2.45 )
% 2.07/2.45 , clause( 13671, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 2.07/2.45 ) ] )
% 2.07/2.45 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.07/2.45 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 2.07/2.45 , clause( 13674, [ subclass( X, 'universal_class' ) ] )
% 2.07/2.45 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 7, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.07/2.45 'unordered_pair'( X, Y ) ) ] )
% 2.07/2.45 , clause( 13679, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.07/2.45 'unordered_pair'( X, Y ) ) ] )
% 2.07/2.45 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.07/2.45 ), ==>( 1, 1 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 11, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 2.07/2.45 singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 2.07/2.45 , clause( 13683, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 2.07/2.45 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 2.07/2.45 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.07/2.45 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 13, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) )
% 2.07/2.45 ), member( Y, T ) ] )
% 2.07/2.45 , clause( 13685, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.07/2.45 ) ) ), member( Y, T ) ] )
% 2.07/2.45 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 2.07/2.45 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 100, [ ~( member( X, 'null_class' ) ) ] )
% 2.07/2.45 , clause( 13773, [ ~( member( X, 'null_class' ) ) ] )
% 2.07/2.45 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 102, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ] )
% 2.07/2.45 , clause( 13775, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 2.07/2.45 )
% 2.07/2.45 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 2.07/2.45 1 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 105, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ] )
% 2.07/2.45 , clause( 13778, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 2.07/2.45 ] )
% 2.07/2.45 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.07/2.45 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 106, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ] )
% 2.07/2.45 , clause( 13779, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 2.07/2.45 )
% 2.07/2.45 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.07/2.45 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 113, [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v ) ) ]
% 2.07/2.45 )
% 2.07/2.45 , clause( 13786, [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v )
% 2.07/2.45 ) ] )
% 2.07/2.45 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 114, [ =( 'unordered_pair'( x, y ), 'null_class' ) ] )
% 2.07/2.45 , clause( 13787, [ =( 'unordered_pair'( x, y ), 'null_class' ) ] )
% 2.07/2.45 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 paramod(
% 2.07/2.45 clause( 14179, [ member( x, 'null_class' ), ~( member( x, 'universal_class'
% 2.07/2.45 ) ) ] )
% 2.07/2.45 , clause( 114, [ =( 'unordered_pair'( x, y ), 'null_class' ) ] )
% 2.07/2.45 , 0, clause( 7, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.07/2.45 'unordered_pair'( X, Y ) ) ] )
% 2.07/2.45 , 1, 2, substitution( 0, [] ), substitution( 1, [ :=( X, x ), :=( Y, y )] )
% 2.07/2.45 ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 resolution(
% 2.07/2.45 clause( 14180, [ ~( member( x, 'universal_class' ) ) ] )
% 2.07/2.45 , clause( 100, [ ~( member( X, 'null_class' ) ) ] )
% 2.07/2.45 , 0, clause( 14179, [ member( x, 'null_class' ), ~( member( x,
% 2.07/2.45 'universal_class' ) ) ] )
% 2.07/2.45 , 0, substitution( 0, [ :=( X, x )] ), substitution( 1, [] )).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 387, [ ~( member( x, 'universal_class' ) ) ] )
% 2.07/2.45 , clause( 14180, [ ~( member( x, 'universal_class' ) ) ] )
% 2.07/2.45 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 resolution(
% 2.07/2.45 clause( 14181, [ ~( subclass( X, 'universal_class' ) ), ~( member( x, X ) )
% 2.07/2.45 ] )
% 2.07/2.45 , clause( 387, [ ~( member( x, 'universal_class' ) ) ] )
% 2.07/2.45 , 0, clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 2.07/2.45 ) ] )
% 2.07/2.45 , 2, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y,
% 2.07/2.45 'universal_class' ), :=( Z, x )] )).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 resolution(
% 2.07/2.45 clause( 14182, [ ~( member( x, X ) ) ] )
% 2.07/2.45 , clause( 14181, [ ~( subclass( X, 'universal_class' ) ), ~( member( x, X )
% 2.07/2.45 ) ] )
% 2.07/2.45 , 0, clause( 3, [ subclass( X, 'universal_class' ) ] )
% 2.07/2.45 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 2.07/2.45 ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 388, [ ~( member( x, X ) ) ] )
% 2.07/2.45 , clause( 14182, [ ~( member( x, X ) ) ] )
% 2.07/2.45 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 resolution(
% 2.07/2.45 clause( 14183, [ ~( member( 'ordered_pair'( Y, x ), 'cross_product'( Z, X )
% 2.07/2.45 ) ) ] )
% 2.07/2.45 , clause( 388, [ ~( member( x, X ) ) ] )
% 2.07/2.45 , 0, clause( 13, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.07/2.45 ) ) ), member( Y, T ) ] )
% 2.07/2.45 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, Y ), :=( Y
% 2.07/2.45 , x ), :=( Z, Z ), :=( T, X )] )).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 640, [ ~( member( 'ordered_pair'( X, x ), 'cross_product'( Y, Z ) )
% 2.07/2.45 ) ] )
% 2.07/2.45 , clause( 14183, [ ~( member( 'ordered_pair'( Y, x ), 'cross_product'( Z, X
% 2.07/2.45 ) ) ) ] )
% 2.07/2.45 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 2.07/2.45 permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 eqswap(
% 2.07/2.45 clause( 14184, [ =( 'null_class', 'unordered_pair'( x, y ) ) ] )
% 2.07/2.45 , clause( 114, [ =( 'unordered_pair'( x, y ), 'null_class' ) ] )
% 2.07/2.45 , 0, substitution( 0, [] )).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 paramod(
% 2.07/2.45 clause( 14185, [ =( 'null_class', 'unordered_pair'( y, x ) ) ] )
% 2.07/2.45 , clause( 105, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ]
% 2.07/2.45 )
% 2.07/2.45 , 0, clause( 14184, [ =( 'null_class', 'unordered_pair'( x, y ) ) ] )
% 2.07/2.45 , 0, 2, substitution( 0, [ :=( X, x ), :=( Y, y )] ), substitution( 1, [] )
% 2.07/2.45 ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 eqswap(
% 2.07/2.45 clause( 14188, [ =( 'unordered_pair'( y, x ), 'null_class' ) ] )
% 2.07/2.45 , clause( 14185, [ =( 'null_class', 'unordered_pair'( y, x ) ) ] )
% 2.07/2.45 , 0, substitution( 0, [] )).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 12039, [ =( 'unordered_pair'( y, x ), 'null_class' ) ] )
% 2.07/2.45 , clause( 14188, [ =( 'unordered_pair'( y, x ), 'null_class' ) ] )
% 2.07/2.45 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 paramod(
% 2.07/2.45 clause( 14190, [ subclass( singleton( y ), 'null_class' ) ] )
% 2.07/2.45 , clause( 12039, [ =( 'unordered_pair'( y, x ), 'null_class' ) ] )
% 2.07/2.45 , 0, clause( 106, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 2.07/2.45 )
% 2.07/2.45 , 0, 3, substitution( 0, [] ), substitution( 1, [ :=( X, y ), :=( Y, x )] )
% 2.07/2.45 ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 12169, [ subclass( singleton( y ), 'null_class' ) ] )
% 2.07/2.45 , clause( 14190, [ subclass( singleton( y ), 'null_class' ) ] )
% 2.07/2.45 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 paramod(
% 2.07/2.45 clause( 14192, [ subclass( singleton( x ), 'null_class' ) ] )
% 2.07/2.45 , clause( 114, [ =( 'unordered_pair'( x, y ), 'null_class' ) ] )
% 2.07/2.45 , 0, clause( 106, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 2.07/2.45 )
% 2.07/2.45 , 0, 3, substitution( 0, [] ), substitution( 1, [ :=( X, x ), :=( Y, y )] )
% 2.07/2.45 ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 12194, [ subclass( singleton( x ), 'null_class' ) ] )
% 2.07/2.45 , clause( 14192, [ subclass( singleton( x ), 'null_class' ) ] )
% 2.07/2.45 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 eqswap(
% 2.07/2.45 clause( 14193, [ =( 'null_class', X ), ~( subclass( X, 'null_class' ) ) ]
% 2.07/2.45 )
% 2.07/2.45 , clause( 102, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 2.07/2.45 )
% 2.07/2.45 , 1, substitution( 0, [ :=( X, X )] )).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 resolution(
% 2.07/2.45 clause( 14194, [ =( 'null_class', singleton( y ) ) ] )
% 2.07/2.45 , clause( 14193, [ =( 'null_class', X ), ~( subclass( X, 'null_class' ) ) ]
% 2.07/2.45 )
% 2.07/2.45 , 1, clause( 12169, [ subclass( singleton( y ), 'null_class' ) ] )
% 2.07/2.45 , 0, substitution( 0, [ :=( X, singleton( y ) )] ), substitution( 1, [] )
% 2.07/2.45 ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 eqswap(
% 2.07/2.45 clause( 14195, [ =( singleton( y ), 'null_class' ) ] )
% 2.07/2.45 , clause( 14194, [ =( 'null_class', singleton( y ) ) ] )
% 2.07/2.45 , 0, substitution( 0, [] )).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 12197, [ =( singleton( y ), 'null_class' ) ] )
% 2.07/2.45 , clause( 14195, [ =( singleton( y ), 'null_class' ) ] )
% 2.07/2.45 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 eqswap(
% 2.07/2.45 clause( 14197, [ =( 'ordered_pair'( X, Y ), 'unordered_pair'( singleton( X
% 2.07/2.45 ), 'unordered_pair'( X, singleton( Y ) ) ) ) ] )
% 2.07/2.45 , clause( 11, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 2.07/2.45 singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 2.07/2.45 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 paramod(
% 2.07/2.45 clause( 14199, [ =( 'ordered_pair'( X, y ), 'unordered_pair'( singleton( X
% 2.07/2.45 ), 'unordered_pair'( X, 'null_class' ) ) ) ] )
% 2.07/2.45 , clause( 12197, [ =( singleton( y ), 'null_class' ) ] )
% 2.07/2.45 , 0, clause( 14197, [ =( 'ordered_pair'( X, Y ), 'unordered_pair'(
% 2.07/2.45 singleton( X ), 'unordered_pair'( X, singleton( Y ) ) ) ) ] )
% 2.07/2.45 , 0, 9, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, y )] )
% 2.07/2.45 ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 eqswap(
% 2.07/2.45 clause( 14201, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 2.07/2.45 'null_class' ) ), 'ordered_pair'( X, y ) ) ] )
% 2.07/2.45 , clause( 14199, [ =( 'ordered_pair'( X, y ), 'unordered_pair'( singleton(
% 2.07/2.45 X ), 'unordered_pair'( X, 'null_class' ) ) ) ] )
% 2.07/2.45 , 0, substitution( 0, [ :=( X, X )] )).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 12218, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 2.07/2.45 'null_class' ) ), 'ordered_pair'( X, y ) ) ] )
% 2.07/2.45 , clause( 14201, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 2.07/2.45 , 'null_class' ) ), 'ordered_pair'( X, y ) ) ] )
% 2.07/2.45 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 eqswap(
% 2.07/2.45 clause( 14202, [ =( 'null_class', X ), ~( subclass( X, 'null_class' ) ) ]
% 2.07/2.45 )
% 2.07/2.45 , clause( 102, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 2.07/2.45 )
% 2.07/2.45 , 1, substitution( 0, [ :=( X, X )] )).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 resolution(
% 2.07/2.45 clause( 14203, [ =( 'null_class', singleton( x ) ) ] )
% 2.07/2.45 , clause( 14202, [ =( 'null_class', X ), ~( subclass( X, 'null_class' ) ) ]
% 2.07/2.45 )
% 2.07/2.45 , 1, clause( 12194, [ subclass( singleton( x ), 'null_class' ) ] )
% 2.07/2.45 , 0, substitution( 0, [ :=( X, singleton( x ) )] ), substitution( 1, [] )
% 2.07/2.45 ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 eqswap(
% 2.07/2.45 clause( 14204, [ =( singleton( x ), 'null_class' ) ] )
% 2.07/2.45 , clause( 14203, [ =( 'null_class', singleton( x ) ) ] )
% 2.07/2.45 , 0, substitution( 0, [] )).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 12223, [ =( singleton( x ), 'null_class' ) ] )
% 2.07/2.45 , clause( 14204, [ =( singleton( x ), 'null_class' ) ] )
% 2.07/2.45 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 eqswap(
% 2.07/2.45 clause( 14206, [ =( 'ordered_pair'( X, Y ), 'unordered_pair'( singleton( X
% 2.07/2.45 ), 'unordered_pair'( X, singleton( Y ) ) ) ) ] )
% 2.07/2.45 , clause( 11, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 2.07/2.45 singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 2.07/2.45 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 paramod(
% 2.07/2.45 clause( 14209, [ =( 'ordered_pair'( X, x ), 'unordered_pair'( singleton( X
% 2.07/2.45 ), 'unordered_pair'( X, 'null_class' ) ) ) ] )
% 2.07/2.45 , clause( 12223, [ =( singleton( x ), 'null_class' ) ] )
% 2.07/2.45 , 0, clause( 14206, [ =( 'ordered_pair'( X, Y ), 'unordered_pair'(
% 2.07/2.45 singleton( X ), 'unordered_pair'( X, singleton( Y ) ) ) ) ] )
% 2.07/2.45 , 0, 9, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, x )] )
% 2.07/2.45 ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 paramod(
% 2.07/2.45 clause( 14210, [ =( 'ordered_pair'( X, x ), 'ordered_pair'( X, y ) ) ] )
% 2.07/2.45 , clause( 12218, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 2.07/2.45 , 'null_class' ) ), 'ordered_pair'( X, y ) ) ] )
% 2.07/2.45 , 0, clause( 14209, [ =( 'ordered_pair'( X, x ), 'unordered_pair'(
% 2.07/2.45 singleton( X ), 'unordered_pair'( X, 'null_class' ) ) ) ] )
% 2.07/2.45 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 2.07/2.45 ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 eqswap(
% 2.07/2.45 clause( 14211, [ =( 'ordered_pair'( X, y ), 'ordered_pair'( X, x ) ) ] )
% 2.07/2.45 , clause( 14210, [ =( 'ordered_pair'( X, x ), 'ordered_pair'( X, y ) ) ] )
% 2.07/2.45 , 0, substitution( 0, [ :=( X, X )] )).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 12272, [ =( 'ordered_pair'( X, y ), 'ordered_pair'( X, x ) ) ] )
% 2.07/2.45 , clause( 14211, [ =( 'ordered_pair'( X, y ), 'ordered_pair'( X, x ) ) ] )
% 2.07/2.45 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 paramod(
% 2.07/2.45 clause( 14213, [ member( 'ordered_pair'( x, x ), 'cross_product'( u, v ) )
% 2.07/2.45 ] )
% 2.07/2.45 , clause( 12272, [ =( 'ordered_pair'( X, y ), 'ordered_pair'( X, x ) ) ] )
% 2.07/2.45 , 0, clause( 113, [ member( 'ordered_pair'( x, y ), 'cross_product'( u, v )
% 2.07/2.45 ) ] )
% 2.07/2.45 , 0, 1, substitution( 0, [ :=( X, x )] ), substitution( 1, [] )).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 resolution(
% 2.07/2.45 clause( 14214, [] )
% 2.07/2.45 , clause( 640, [ ~( member( 'ordered_pair'( X, x ), 'cross_product'( Y, Z )
% 2.07/2.45 ) ) ] )
% 2.07/2.45 , 0, clause( 14213, [ member( 'ordered_pair'( x, x ), 'cross_product'( u, v
% 2.07/2.45 ) ) ] )
% 2.07/2.45 , 0, substitution( 0, [ :=( X, x ), :=( Y, u ), :=( Z, v )] ),
% 2.07/2.45 substitution( 1, [] )).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 subsumption(
% 2.07/2.45 clause( 13669, [] )
% 2.07/2.45 , clause( 14214, [] )
% 2.07/2.45 , substitution( 0, [] ), permutation( 0, [] ) ).
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 end.
% 2.07/2.45
% 2.07/2.45 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.07/2.45
% 2.07/2.45 Memory use:
% 2.07/2.45
% 2.07/2.45 space for terms: 245695
% 2.07/2.45 space for clauses: 648791
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 clauses generated: 43163
% 2.07/2.45 clauses kept: 13670
% 2.07/2.45 clauses selected: 449
% 2.07/2.45 clauses deleted: 85
% 2.07/2.45 clauses inuse deleted: 63
% 2.07/2.45
% 2.07/2.45 subsentry: 112745
% 2.07/2.45 literals s-matched: 81898
% 2.07/2.45 literals matched: 79356
% 2.07/2.45 full subsumption: 40485
% 2.07/2.45
% 2.07/2.45 checksum: 591664390
% 2.07/2.45
% 2.07/2.45
% 2.07/2.45 Bliksem ended
%------------------------------------------------------------------------------