TSTP Solution File: SET118-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET118-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.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 22:47:20 EDT 2022
% Result : Unsatisfiable 0.73s 1.14s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET118-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.32 % Computer : n024.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Jul 9 23:24:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.73/1.14 *** allocated 10000 integers for termspace/termends
% 0.73/1.14 *** allocated 10000 integers for clauses
% 0.73/1.14 *** allocated 10000 integers for justifications
% 0.73/1.14 Bliksem 1.12
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 Automatic Strategy Selection
% 0.73/1.14
% 0.73/1.14 Clauses:
% 0.73/1.14 [
% 0.73/1.14 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.73/1.14 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.73/1.14 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.73/1.14 ,
% 0.73/1.14 [ subclass( X, 'universal_class' ) ],
% 0.73/1.14 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.73/1.14 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.73/1.14 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.73/1.14 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.73/1.14 ,
% 0.73/1.14 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.73/1.14 ) ) ],
% 0.73/1.14 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.73/1.14 ) ) ],
% 0.73/1.14 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.73/1.14 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.73/1.14 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.73/1.14 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.73/1.14 X, Z ) ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.73/1.14 Y, T ) ],
% 0.73/1.14 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.73/1.14 ), 'cross_product'( Y, T ) ) ],
% 0.73/1.14 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.73/1.14 ), second( X ) ), X ) ],
% 0.73/1.14 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.73/1.14 'universal_class' ) ) ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.73/1.14 Y ) ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.73/1.14 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.73/1.14 , Y ), 'element_relation' ) ],
% 0.73/1.14 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.73/1.14 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.73/1.14 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.73/1.14 Z ) ) ],
% 0.73/1.14 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.73/1.14 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.73/1.14 member( X, Y ) ],
% 0.73/1.14 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.73/1.14 union( X, Y ) ) ],
% 0.73/1.14 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.73/1.14 intersection( complement( X ), complement( Y ) ) ) ),
% 0.73/1.14 'symmetric_difference'( X, Y ) ) ],
% 0.73/1.14 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.73/1.14 ,
% 0.73/1.14 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.73/1.14 ,
% 0.73/1.14 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.73/1.14 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.73/1.14 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.73/1.14 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.73/1.14 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.73/1.14 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.73/1.14 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.73/1.14 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.73/1.14 'cross_product'( 'universal_class', 'universal_class' ),
% 0.73/1.14 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.73/1.14 Y ), rotate( T ) ) ],
% 0.73/1.14 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.73/1.14 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.73/1.14 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.73/1.14 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.73/1.14 'cross_product'( 'universal_class', 'universal_class' ),
% 0.73/1.14 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.73/1.14 Z ), flip( T ) ) ],
% 0.73/1.14 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.73/1.14 inverse( X ) ) ],
% 0.73/1.14 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.73/1.14 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.73/1.14 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.73/1.14 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.73/1.14 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.73/1.14 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.73/1.14 ],
% 0.73/1.14 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.73/1.14 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.73/1.14 'universal_class' ) ) ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.73/1.14 successor( X ), Y ) ],
% 0.73/1.14 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.73/1.14 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.73/1.14 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.73/1.14 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.73/1.14 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.73/1.14 ,
% 0.73/1.14 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.73/1.14 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.73/1.14 [ inductive( omega ) ],
% 0.73/1.14 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.73/1.14 [ member( omega, 'universal_class' ) ],
% 0.73/1.14 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.73/1.14 , 'sum_class'( X ) ) ],
% 0.73/1.14 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.73/1.14 'universal_class' ) ],
% 0.73/1.14 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.73/1.14 'power_class'( X ) ) ],
% 0.73/1.14 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.73/1.14 'universal_class' ) ],
% 0.73/1.14 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.73/1.14 'universal_class' ) ) ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.73/1.14 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.73/1.14 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.73/1.14 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.73/1.14 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.73/1.14 ) ],
% 0.73/1.14 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.73/1.14 , 'identity_relation' ) ],
% 0.73/1.14 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.73/1.14 'single_valued_class'( X ) ],
% 0.73/1.14 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.73/1.14 'universal_class' ) ) ],
% 0.73/1.14 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.73/1.14 'identity_relation' ) ],
% 0.73/1.14 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.73/1.14 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.73/1.14 , function( X ) ],
% 0.73/1.14 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.73/1.14 X, Y ), 'universal_class' ) ],
% 0.73/1.14 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.73/1.14 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.73/1.14 ) ],
% 0.73/1.14 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.73/1.14 [ function( choice ) ],
% 0.73/1.14 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.73/1.14 apply( choice, X ), X ) ],
% 0.73/1.14 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.73/1.14 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.73/1.14 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.73/1.14 ,
% 0.73/1.14 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.73/1.14 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.73/1.14 , complement( compose( complement( 'element_relation' ), inverse(
% 0.73/1.14 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.73/1.14 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.73/1.14 'identity_relation' ) ],
% 0.73/1.14 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.73/1.14 , diagonalise( X ) ) ],
% 0.73/1.14 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.73/1.14 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.73/1.14 [ ~( operation( X ) ), function( X ) ],
% 0.73/1.14 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.73/1.14 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.73/1.14 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.73/1.14 'domain_of'( X ) ) ) ],
% 0.73/1.14 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.73/1.14 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.73/1.14 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.73/1.14 X ) ],
% 0.73/1.14 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.73/1.14 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.73/1.14 'domain_of'( X ) ) ],
% 0.73/1.14 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.73/1.14 'domain_of'( Z ) ) ) ],
% 0.73/1.14 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.73/1.14 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.73/1.14 ), compatible( X, Y, Z ) ],
% 0.73/1.14 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.73/1.14 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.73/1.14 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.73/1.14 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.73/1.14 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.73/1.14 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.73/1.14 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.73/1.14 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.73/1.14 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.73/1.14 , Y ) ],
% 0.73/1.14 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.73/1.14 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.73/1.14 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.73/1.14 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.73/1.14 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.73/1.14 X, 'unordered_pair'( X, Y ) ) ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.73/1.14 Y, 'unordered_pair'( X, Y ) ) ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.73/1.14 X, 'universal_class' ) ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.73/1.14 Y, 'universal_class' ) ],
% 0.73/1.14 [ subclass( X, X ) ],
% 0.73/1.14 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.73/1.14 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.73/1.14 'not_subclass_element'( Y, X ), Y ) ],
% 0.73/1.14 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.73/1.14 'not_subclass_element'( Y, X ), Y ) ],
% 0.73/1.14 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.73/1.14 'not_subclass_element'( Y, X ), Y ) ],
% 0.73/1.14 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.73/1.14 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.73/1.14 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.73/1.14 [ ~( member( X, 'null_class' ) ) ],
% 0.73/1.14 [ subclass( 'null_class', X ) ],
% 0.73/1.14 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.73/1.14 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.73/1.14 ), X ) ],
% 0.73/1.14 [ member( 'null_class', 'universal_class' ) ],
% 0.73/1.14 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.73/1.14 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.73/1.14 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.73/1.14 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.73/1.14 Y ) ) ],
% 0.73/1.14 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.73/1.14 Y ) ) ],
% 0.73/1.14 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.73/1.14 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.73/1.14 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.73/1.14 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.73/1.14 'universal_class' ) ) ), =( Y, Z ) ],
% 0.73/1.14 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.73/1.14 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.73/1.14 'universal_class' ) ) ), =( X, Z ) ],
% 0.73/1.14 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.73/1.14 'null_class' ) ) ],
% 0.73/1.14 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.73/1.14 'null_class' ) ) ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.73/1.14 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 0.73/1.14 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 0.73/1.14 X, Z ), Y ) ],
% 0.73/1.14 [ member( singleton( X ), 'universal_class' ) ],
% 0.73/1.14 [ member( singleton( X ), 'unordered_pair'( Y, singleton( X ) ) ) ],
% 0.73/1.14 [ ~( member( X, 'universal_class' ) ), member( X, singleton( X ) ) ]
% 0.73/1.14 ,
% 0.73/1.14 [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X ),
% 0.73/1.14 'null_class' ) ) ],
% 0.73/1.14 [ member( 'null_class', singleton( 'null_class' ) ) ],
% 0.73/1.14 [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ],
% 0.73/1.14 [ member( X, 'universal_class' ), =( singleton( X ), 'null_class' ) ]
% 0.73/1.14 ,
% 0.73/1.14 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 0.73/1.14 'universal_class' ) ), =( X, Y ) ],
% 0.73/1.14 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 0.73/1.14 'universal_class' ) ), =( X, Y ) ],
% 0.73/1.14 [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~( member( Z,
% 0.73/1.14 'universal_class' ) ), =( Z, X ), =( Z, Y ) ],
% 0.73/1.14 [ ~( member( X, 'universal_class' ) ), member( 'member_of'( singleton( X
% 0.73/1.14 ) ), 'universal_class' ) ],
% 0.73/1.14 [ ~( member( X, 'universal_class' ) ), =( singleton( 'member_of'(
% 0.73/1.14 singleton( X ) ) ), singleton( X ) ) ],
% 0.73/1.14 [ member( 'member_of'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 0.73/1.14 ) ],
% 0.73/1.14 [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X ), X ) ],
% 0.73/1.14 [ ~( member( X, 'universal_class' ) ), =( 'member_of'( singleton( X ) )
% 0.73/1.14 , X ) ],
% 0.73/1.14 [ member( 'member_of1'( X ), 'universal_class' ), =( 'member_of'( X ), X
% 0.73/1.14 ) ],
% 0.73/1.14 [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'( X ), X ) ]
% 0.73/1.14 ,
% 0.73/1.14 [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 0.73/1.14 'universal_class' ) ],
% 0.73/1.14 [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y, X ) ), =(
% 0.73/1.14 'member_of'( X ), Y ) ],
% 0.73/1.14 [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ],
% 0.73/1.14 [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' ), =( singleton(
% 0.73/1.14 Y ), X ) ],
% 0.73/1.14 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 0.73/1.14 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 0.73/1.14 intersection( complement( singleton( 'not_subclass_element'( X,
% 0.73/1.14 'null_class' ) ) ), X ) ), =( singleton( 'not_subclass_element'( X,
% 0.73/1.14 'null_class' ) ), X ), =( X, 'null_class' ) ],
% 0.73/1.14 [ member( 'not_subclass_element'( intersection( complement( singleton(
% 0.73/1.14 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ), X ),
% 0.73/1.14 =( singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 0.73/1.14 'null_class' ) ],
% 0.73/1.14 [ ~( =( 'not_subclass_element'( intersection( complement( singleton(
% 0.73/1.14 'not_subclass_element'( X, 'null_class' ) ) ), X ), 'null_class' ),
% 0.73/1.14 'not_subclass_element'( X, 'null_class' ) ) ), =( singleton(
% 0.73/1.14 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 0.73/1.14 ,
% 0.73/1.14 [ =( 'unordered_pair'( X, Y ), union( singleton( X ), singleton( Y ) ) )
% 0.73/1.14 ],
% 0.73/1.14 [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ],
% 0.73/1.14 [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ],
% 0.73/1.14 [ member( 'unordered_pair'( X, singleton( Y ) ), 'ordered_pair'( X, Y )
% 0.73/1.14 ) ],
% 0.73/1.14 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, 'null_class'
% 0.73/1.14 ) ), 'ordered_pair'( X, Y ) ), member( Y, 'universal_class' ) ],
% 0.73/1.14 [ ~( member( X, 'universal_class' ) ), =( 'unordered_pair'( 'null_class'
% 0.73/1.14 , singleton( singleton( X ) ) ), 'ordered_pair'( Y, X ) ), member( Y,
% 0.73/1.14 'universal_class' ) ],
% 0.73/1.14 [ =( 'unordered_pair'( 'null_class', singleton( 'null_class' ) ),
% 0.73/1.14 'ordered_pair'( X, Y ) ), member( X, 'universal_class' ), member( Y,
% 0.73/1.14 'universal_class' ) ],
% 0.73/1.14 [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) ), ~( member( X
% 0.73/1.14 , 'universal_class' ) ), =( X, Z ) ],
% 0.73/1.14 [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) ), ~( member( Y
% 0.73/1.14 , 'universal_class' ) ), =( Y, T ) ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.73/1.14 , 'universal_class' ) ) ), member( 'ordered_pair'( first( 'ordered_pair'(
% 0.73/1.14 X, Y ) ), second( 'ordered_pair'( X, Y ) ) ), 'cross_product'(
% 0.73/1.14 'universal_class', 'universal_class' ) ) ],
% 0.73/1.14 [ member( 'ordered_pair'( first( X ), second( X ) ), 'cross_product'(
% 0.73/1.14 'universal_class', 'universal_class' ) ), =( first( X ), X ) ],
% 0.73/1.14 [ member( 'ordered_pair'( first( X ), second( X ) ), 'cross_product'(
% 0.73/1.14 'universal_class', 'universal_class' ) ), =( second( X ), X ) ],
% 0.73/1.14 [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( first( X ), X )
% 0.73/1.14 ],
% 0.73/1.14 [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( second( X ), X )
% 0.73/1.14 ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.73/1.14 , 'universal_class' ) ) ), =( first( 'ordered_pair'( X, Y ) ), X ) ],
% 0.73/1.14 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.73/1.14 , 'universal_class' ) ) ), =( second( 'ordered_pair'( X, Y ) ), Y ) ]
% 0.73/1.14 ,
% 0.73/1.14 [ member( 'ordered_pair'( first( X ), second( X ) ), 'cross_product'(
% 0.73/1.14 'universal_class', 'universal_class' ) ), =( first( X ), X ) ],
% 0.73/1.14 [ member( 'ordered_pair'( first( X ), second( X ) ), 'cross_product'(
% 0.73/1.14 'universal_class', 'universal_class' ) ), =( second( X ), X ) ],
% 0.73/1.14 [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( first( X ), X )
% 0.73/1.14 ],
% 0.73/1.14 [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =( second( X ), X )
% 0.73/1.14 ],
% 0.73/1.14 [ member( x, 'cross_product'( 'universal_class', 'universal_class' ) ) ]
% 0.73/1.14 ,
% 0.73/1.14 [ ~( member( x, 'universal_class' ) ) ]
% 0.73/1.14 ] .
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 percentage equality = 0.312883, percentage horn = 0.801242
% 0.73/1.14 This is a problem with some equality
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 Options Used:
% 0.73/1.14
% 0.73/1.14 useres = 1
% 0.73/1.14 useparamod = 1
% 0.73/1.14 useeqrefl = 1
% 0.73/1.14 useeqfact = 1
% 0.73/1.14 usefactor = 1
% 0.73/1.14 usesimpsplitting = 0
% 0.73/1.14 usesimpdemod = 5
% 0.73/1.14 usesimpres = 3
% 0.73/1.14
% 0.73/1.14 resimpinuse = 1000
% 0.73/1.14 resimpclauses = 20000
% 0.73/1.14 substype = eqrewr
% 0.73/1.14 backwardsubs = 1
% 0.73/1.14 selectoldest = 5
% 0.73/1.14
% 0.73/1.14 litorderings [0] = split
% 0.73/1.14 litorderings [1] = extend the termordering, first sorting on arguments
% 0.73/1.14
% 0.73/1.14 termordering = kbo
% 0.73/1.14
% 0.73/1.14 litapriori = 0
% 0.73/1.14 termapriori = 1
% 0.73/1.14 litaposteriori = 0
% 0.73/1.14 termaposteriori = 0
% 0.73/1.14 demodaposteriori = 0
% 0.73/1.14 ordereqreflfact = 0
% 0.73/1.14
% 0.73/1.14 litselect = negord
% 0.73/1.14
% 0.73/1.14 maxweight = 15
% 0.73/1.14 maxdepth = 30000
% 0.73/1.14 maxlength = 115
% 0.73/1.14 maxnrvars = 195
% 0.73/1.14 excuselevel = 1
% 0.73/1.14 increasemaxweight = 1
% 0.73/1.14
% 0.73/1.14 maxselected = 10000000
% 0.73/1.14 maxnrclauses = 10000000
% 0.73/1.14
% 0.73/1.14 showgenerated = 0
% 0.73/1.14 showkept = 0
% 0.73/1.14 showselected = 0
% 0.73/1.14 showdeleted = 0
% 0.73/1.14 showresimp = 1
% 0.73/1.14 showstatus = 2000
% 0.73/1.14
% 0.73/1.14 prologoutput = 1
% 0.73/1.14 nrgoals = 5000000
% 0.73/1.14 totalproof = 1
% 0.73/1.14
% 0.73/1.14 Symbols occurring in the translation:
% 0.73/1.14
% 0.73/1.14 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.73/1.14 . [1, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.73/1.14 ! [4, 1] (w:0, o:30, a:1, s:1, b:0),
% 0.73/1.14 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.14 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.14 subclass [41, 2] (w:1, o:82, a:1, s:1, b:0),
% 0.73/1.14 member [43, 2] (w:1, o:83, a:1, s:1, b:0),
% 0.73/1.14 'not_subclass_element' [44, 2] (w:1, o:84, a:1, s:1, b:0),
% 0.73/1.14 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.73/1.14 'unordered_pair' [46, 2] (w:1, o:85, a:1, s:1, b:0),
% 0.73/1.14 singleton [47, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.73/1.14 'ordered_pair' [48, 2] (w:1, o:86, a:1, s:1, b:0),
% 0.73/1.14 'cross_product' [50, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.73/1.14 first [52, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.73/1.14 second [53, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.73/1.14 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.73/1.14 intersection [55, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.73/1.14 complement [56, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.73/1.14 union [57, 2] (w:1, o:90, a:1, s:1, b:0),
% 0.73/1.14 'symmetric_difference' [58, 2] (w:1, o:91, a:1, s:1, b:0),
% 0.73/1.14 restrict [60, 3] (w:1, o:94, a:1, s:1, b:0),
% 0.73/1.14 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.73/1.14 'domain_of' [62, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.73/1.14 rotate [63, 1] (w:1, o:35, a:1, s:1, b:0),
% 0.73/1.14 flip [65, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.73/1.14 inverse [66, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.73/1.14 'range_of' [67, 1] (w:1, o:36, a:1, s:1, b:0),
% 0.73/1.14 domain [68, 3] (w:1, o:96, a:1, s:1, b:0),
% 0.73/1.14 range [69, 3] (w:1, o:97, a:1, s:1, b:0),
% 0.73/1.14 image [70, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.73/1.14 successor [71, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.73/1.14 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.73/1.14 inductive [73, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.73/1.14 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.73/1.14 'sum_class' [75, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.73/1.14 'power_class' [76, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.73/1.14 compose [78, 2] (w:1, o:92, a:1, s:1, b:0),
% 0.73/1.14 'single_valued_class' [79, 1] (w:1, o:52, a:1, s:1, b:0),
% 0.73/1.14 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.73/1.14 function [82, 1] (w:1, o:53, a:1, s:1, b:0),
% 0.73/1.14 regular [83, 1] (w:1, o:37, a:1, s:1, b:0),
% 0.73/1.14 apply [84, 2] (w:1, o:93, a:1, s:1, b:0),
% 0.73/1.14 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.73/1.14 'one_to_one' [86, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.73/1.14 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 0.73/1.14 diagonalise [88, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.73/1.14 cantor [89, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.73/1.14 operation [90, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.73/1.14 compatible [94, 3] (w:1, o:95, a:1, s:1, b:0),
% 0.73/1.14 homomorphism [95, 3] (w:1, o:98, a:1, s:1, b:0),
% 0.73/1.14 'not_homomorphism1' [96, 3] (w:1, o:99, a:1, s:1, b:0),
% 0.73/1.14 'not_homomorphism2' [97, 3] (w:1, o:100, a:1, s:1, b:0),
% 0.73/1.14 'member_of' [98, 1] (w:1, o:55, a:1, s:1, b:0),
% 0.73/1.14 'member_of1' [99, 1] (w:1, o:56, a:1, s:1, b:0),
% 0.73/1.14 x [100, 0] (w:1, o:29, a:1, s:1, b:0).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 Starting Search:
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 Bliksems!, er is een bewijs:
% 0.73/1.14 % SZS status Unsatisfiable
% 0.73/1.14 % SZS output start Refutation
% 0.73/1.14
% 0.73/1.14 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.73/1.14 )
% 0.73/1.14 .
% 0.73/1.14 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 158, [ member( x, 'cross_product'( 'universal_class',
% 0.73/1.14 'universal_class' ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 159, [ ~( member( x, 'universal_class' ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 178, [ ~( member( x, X ) ) ] )
% 0.73/1.14 .
% 0.73/1.14 clause( 195, [] )
% 0.73/1.14 .
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 % SZS output end Refutation
% 0.73/1.14 found a proof!
% 0.73/1.14
% 0.73/1.14 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.73/1.14
% 0.73/1.14 initialclauses(
% 0.73/1.14 [ clause( 197, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y )
% 0.73/1.14 ] )
% 0.73/1.14 , clause( 198, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X,
% 0.73/1.14 Y ) ] )
% 0.73/1.14 , clause( 199, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass(
% 0.73/1.14 X, Y ) ] )
% 0.73/1.14 , clause( 200, [ subclass( X, 'universal_class' ) ] )
% 0.73/1.14 , clause( 201, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 0.73/1.14 , clause( 202, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 0.73/1.14 , clause( 203, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ]
% 0.73/1.14 )
% 0.73/1.14 , clause( 204, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =(
% 0.73/1.14 X, Z ) ] )
% 0.73/1.14 , clause( 205, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.73/1.14 'unordered_pair'( X, Y ) ) ] )
% 0.73/1.14 , clause( 206, [ ~( member( X, 'universal_class' ) ), member( X,
% 0.73/1.14 'unordered_pair'( Y, X ) ) ] )
% 0.73/1.14 , clause( 207, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ] )
% 0.73/1.14 , clause( 208, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 0.73/1.14 , clause( 209, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 0.73/1.14 singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.73/1.14 , clause( 210, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T )
% 0.73/1.14 ) ), member( X, Z ) ] )
% 0.73/1.14 , clause( 211, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T )
% 0.73/1.14 ) ), member( Y, T ) ] )
% 0.73/1.14 , clause( 212, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 0.73/1.14 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 0.73/1.14 , clause( 213, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 0.73/1.14 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 0.73/1.14 , clause( 214, [ subclass( 'element_relation', 'cross_product'(
% 0.73/1.14 'universal_class', 'universal_class' ) ) ] )
% 0.73/1.14 , clause( 215, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) )
% 0.73/1.14 , member( X, Y ) ] )
% 0.73/1.14 , clause( 216, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.73/1.14 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 0.73/1.14 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 0.73/1.14 , clause( 217, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.73/1.14 )
% 0.73/1.14 , clause( 218, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 0.73/1.14 )
% 0.73/1.14 , clause( 219, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 0.73/1.14 intersection( Y, Z ) ) ] )
% 0.73/1.14 , clause( 220, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 0.73/1.14 )
% 0.73/1.14 , clause( 221, [ ~( member( X, 'universal_class' ) ), member( X, complement(
% 0.73/1.14 Y ) ), member( X, Y ) ] )
% 0.73/1.14 , clause( 222, [ =( complement( intersection( complement( X ), complement(
% 0.73/1.14 Y ) ) ), union( X, Y ) ) ] )
% 0.73/1.14 , clause( 223, [ =( intersection( complement( intersection( X, Y ) ),
% 0.73/1.14 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 0.73/1.14 'symmetric_difference'( X, Y ) ) ] )
% 0.73/1.14 , clause( 224, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X
% 0.73/1.14 , Y, Z ) ) ] )
% 0.73/1.14 , clause( 225, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z
% 0.73/1.14 , X, Y ) ) ] )
% 0.73/1.14 , clause( 226, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 0.73/1.14 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 0.73/1.14 , clause( 227, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 0.73/1.14 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 0.73/1.14 'domain_of'( Y ) ) ] )
% 0.73/1.14 , clause( 228, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.73/1.14 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.73/1.14 , clause( 229, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.73/1.14 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 0.73/1.14 ] )
% 0.73/1.14 , clause( 230, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.73/1.14 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 0.73/1.14 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.73/1.14 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 0.73/1.14 , Y ), rotate( T ) ) ] )
% 0.73/1.14 , clause( 231, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.73/1.14 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 0.73/1.14 , clause( 232, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 0.73/1.14 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 0.73/1.14 )
% 0.73/1.14 , clause( 233, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T
% 0.73/1.14 ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 0.73/1.14 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 0.73/1.14 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 0.73/1.14 , Z ), flip( T ) ) ] )
% 0.73/1.14 , clause( 234, [ =( 'domain_of'( flip( 'cross_product'( X,
% 0.73/1.14 'universal_class' ) ) ), inverse( X ) ) ] )
% 0.73/1.14 , clause( 235, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 0.73/1.14 , clause( 236, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 0.73/1.14 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 0.73/1.14 , clause( 237, [ =( second( 'not_subclass_element'( restrict( X, singleton(
% 0.73/1.14 Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 0.73/1.14 , clause( 238, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 0.73/1.14 image( X, Y ) ) ] )
% 0.73/1.14 , clause( 239, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 0.73/1.14 , clause( 240, [ subclass( 'successor_relation', 'cross_product'(
% 0.73/1.14 'universal_class', 'universal_class' ) ) ] )
% 0.73/1.14 , clause( 241, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' )
% 0.73/1.14 ), =( successor( X ), Y ) ] )
% 0.73/1.14 , clause( 242, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X
% 0.73/1.14 , Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 0.73/1.14 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 0.73/1.14 , clause( 243, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 0.73/1.14 , clause( 244, [ ~( inductive( X ) ), subclass( image( 'successor_relation'
% 0.73/1.14 , X ), X ) ] )
% 0.73/1.14 , clause( 245, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.73/1.14 'successor_relation', X ), X ) ), inductive( X ) ] )
% 0.73/1.14 , clause( 246, [ inductive( omega ) ] )
% 0.73/1.14 , clause( 247, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 0.73/1.14 , clause( 248, [ member( omega, 'universal_class' ) ] )
% 0.73/1.14 , clause( 249, [ =( 'domain_of'( restrict( 'element_relation',
% 0.73/1.14 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 0.73/1.14 , clause( 250, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 0.73/1.14 X ), 'universal_class' ) ] )
% 0.73/1.14 , clause( 251, [ =( complement( image( 'element_relation', complement( X )
% 0.73/1.14 ) ), 'power_class'( X ) ) ] )
% 0.73/1.14 , clause( 252, [ ~( member( X, 'universal_class' ) ), member( 'power_class'(
% 0.73/1.14 X ), 'universal_class' ) ] )
% 0.73/1.14 , clause( 253, [ subclass( compose( X, Y ), 'cross_product'(
% 0.73/1.14 'universal_class', 'universal_class' ) ) ] )
% 0.73/1.14 , clause( 254, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 0.73/1.14 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 0.73/1.14 , clause( 255, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ),
% 0.73/1.14 ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.73/1.14 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.73/1.14 ) ] )
% 0.73/1.14 , clause( 256, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 0.73/1.14 inverse( X ) ), 'identity_relation' ) ] )
% 0.73/1.14 , clause( 257, [ ~( subclass( compose( X, inverse( X ) ),
% 0.73/1.14 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 0.73/1.14 , clause( 258, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 0.73/1.14 'universal_class', 'universal_class' ) ) ] )
% 0.73/1.14 , clause( 259, [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.73/1.14 'identity_relation' ) ] )
% 0.73/1.14 , clause( 260, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 0.73/1.14 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 0.73/1.14 'identity_relation' ) ), function( X ) ] )
% 0.73/1.14 , clause( 261, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ),
% 0.73/1.14 member( image( X, Y ), 'universal_class' ) ] )
% 0.73/1.14 , clause( 262, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 0.73/1.14 , clause( 263, [ =( X, 'null_class' ), =( intersection( X, regular( X ) ),
% 0.73/1.14 'null_class' ) ] )
% 0.73/1.14 , clause( 264, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y
% 0.73/1.14 ) ) ] )
% 0.73/1.14 , clause( 265, [ function( choice ) ] )
% 0.73/1.14 , clause( 266, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' )
% 0.73/1.14 , member( apply( choice, X ), X ) ] )
% 0.73/1.14 , clause( 267, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 0.73/1.14 , clause( 268, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 0.73/1.14 , clause( 269, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 0.73/1.14 'one_to_one'( X ) ] )
% 0.73/1.14 , clause( 270, [ =( intersection( 'cross_product'( 'universal_class',
% 0.73/1.14 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 0.73/1.14 'universal_class' ), complement( compose( complement( 'element_relation'
% 0.73/1.14 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 0.73/1.14 , clause( 271, [ =( intersection( inverse( 'subset_relation' ),
% 0.73/1.14 'subset_relation' ), 'identity_relation' ) ] )
% 0.73/1.14 , clause( 272, [ =( complement( 'domain_of'( intersection( X,
% 0.73/1.14 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 0.73/1.14 , clause( 273, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 0.73/1.14 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 0.73/1.14 , clause( 274, [ ~( operation( X ) ), function( X ) ] )
% 0.73/1.14 , clause( 275, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 0.73/1.14 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.73/1.14 ] )
% 0.73/1.14 , clause( 276, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 0.73/1.14 'domain_of'( 'domain_of'( X ) ) ) ] )
% 0.73/1.14 , clause( 277, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 0.73/1.14 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 0.73/1.14 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 0.73/1.14 operation( X ) ] )
% 0.73/1.14 , clause( 278, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 0.73/1.14 , clause( 279, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y
% 0.73/1.14 ) ), 'domain_of'( X ) ) ] )
% 0.73/1.14 , clause( 280, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 0.73/1.14 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 0.73/1.14 , clause( 281, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) )
% 0.73/1.14 , 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 0.73/1.14 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 0.73/1.14 , clause( 282, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 0.73/1.14 , clause( 283, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 0.73/1.14 , clause( 284, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 0.73/1.14 , clause( 285, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T
% 0.73/1.14 , U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ),
% 0.73/1.14 apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ] )
% 0.73/1.14 , clause( 286, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z
% 0.73/1.14 , X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.73/1.14 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.73/1.14 , Y ) ] )
% 0.73/1.14 , clause( 287, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z
% 0.73/1.14 , X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'(
% 0.73/1.14 Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z,
% 0.73/1.14 apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.73/1.14 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ] )
% 0.73/1.14 , clause( 288, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T )
% 0.73/1.14 ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 0.73/1.14 , clause( 289, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T )
% 0.73/1.14 ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 0.73/1.14 , clause( 290, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T )
% 0.73/1.14 ) ), member( X, 'universal_class' ) ] )
% 0.73/1.14 , clause( 291, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T )
% 0.73/1.14 ) ), member( Y, 'universal_class' ) ] )
% 0.73/1.14 , clause( 292, [ subclass( X, X ) ] )
% 0.73/1.14 , clause( 293, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X
% 0.73/1.14 , Z ) ] )
% 0.73/1.14 , clause( 294, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 0.73/1.14 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 0.73/1.14 , clause( 295, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y
% 0.73/1.14 ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 0.73/1.14 , clause( 296, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X
% 0.73/1.14 ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 0.73/1.14 , clause( 297, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 0.73/1.14 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 0.73/1.14 , clause( 298, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ] )
% 0.73/1.14 , clause( 299, [ ~( member( X, 'null_class' ) ) ] )
% 0.73/1.14 , clause( 300, [ subclass( 'null_class', X ) ] )
% 0.73/1.14 , clause( 301, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 0.73/1.14 )
% 0.73/1.14 , clause( 302, [ =( X, 'null_class' ), member( 'not_subclass_element'( X,
% 0.73/1.14 'null_class' ), X ) ] )
% 0.73/1.14 , clause( 303, [ member( 'null_class', 'universal_class' ) ] )
% 0.73/1.14 , clause( 304, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ]
% 0.73/1.14 )
% 0.73/1.14 , clause( 305, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ] )
% 0.73/1.14 , clause( 306, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ] )
% 0.73/1.14 , clause( 307, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X
% 0.73/1.14 ), singleton( Y ) ) ] )
% 0.73/1.14 , clause( 308, [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y
% 0.73/1.14 ), singleton( Y ) ) ] )
% 0.73/1.14 , clause( 309, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.73/1.14 'universal_class' ), member( Y, 'universal_class' ) ] )
% 0.73/1.14 , clause( 310, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) )
% 0.73/1.14 ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class'
% 0.73/1.14 , 'universal_class' ) ) ), =( Y, Z ) ] )
% 0.73/1.14 , clause( 311, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) )
% 0.73/1.14 ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class'
% 0.73/1.14 , 'universal_class' ) ) ), =( X, Z ) ] )
% 0.73/1.14 , clause( 312, [ ~( member( X, 'universal_class' ) ), ~( =(
% 0.73/1.14 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 0.73/1.14 , clause( 313, [ ~( member( X, 'universal_class' ) ), ~( =(
% 0.73/1.14 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 0.73/1.14 , clause( 314, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T )
% 0.73/1.14 ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 0.73/1.14 , clause( 315, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 0.73/1.14 'unordered_pair'( X, Z ), Y ) ] )
% 0.73/1.14 , clause( 316, [ member( singleton( X ), 'universal_class' ) ] )
% 0.73/1.14 , clause( 317, [ member( singleton( X ), 'unordered_pair'( Y, singleton( X
% 0.73/1.14 ) ) ) ] )
% 0.73/1.14 , clause( 318, [ ~( member( X, 'universal_class' ) ), member( X, singleton(
% 0.73/1.14 X ) ) ] )
% 0.73/1.14 , clause( 319, [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X )
% 0.73/1.14 , 'null_class' ) ) ] )
% 0.73/1.14 , clause( 320, [ member( 'null_class', singleton( 'null_class' ) ) ] )
% 0.73/1.14 , clause( 321, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 0.73/1.14 , clause( 322, [ member( X, 'universal_class' ), =( singleton( X ),
% 0.73/1.14 'null_class' ) ] )
% 0.73/1.14 , clause( 323, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 0.73/1.14 'universal_class' ) ), =( X, Y ) ] )
% 0.73/1.14 , clause( 324, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 0.73/1.14 'universal_class' ) ), =( X, Y ) ] )
% 0.73/1.14 , clause( 325, [ ~( =( 'unordered_pair'( X, Y ), singleton( Z ) ) ), ~(
% 0.73/1.14 member( Z, 'universal_class' ) ), =( Z, X ), =( Z, Y ) ] )
% 0.73/1.14 , clause( 326, [ ~( member( X, 'universal_class' ) ), member( 'member_of'(
% 0.73/1.14 singleton( X ) ), 'universal_class' ) ] )
% 0.73/1.14 , clause( 327, [ ~( member( X, 'universal_class' ) ), =( singleton(
% 0.73/1.14 'member_of'( singleton( X ) ) ), singleton( X ) ) ] )
% 0.73/1.14 , clause( 328, [ member( 'member_of'( X ), 'universal_class' ), =(
% 0.73/1.14 'member_of'( X ), X ) ] )
% 0.73/1.14 , clause( 329, [ =( singleton( 'member_of'( X ) ), X ), =( 'member_of'( X )
% 0.73/1.14 , X ) ] )
% 0.73/1.14 , clause( 330, [ ~( member( X, 'universal_class' ) ), =( 'member_of'(
% 0.73/1.14 singleton( X ) ), X ) ] )
% 0.73/1.14 , clause( 331, [ member( 'member_of1'( X ), 'universal_class' ), =(
% 0.73/1.14 'member_of'( X ), X ) ] )
% 0.73/1.14 , clause( 332, [ =( singleton( 'member_of1'( X ) ), X ), =( 'member_of'( X
% 0.73/1.14 ), X ) ] )
% 0.73/1.14 , clause( 333, [ ~( =( singleton( 'member_of'( X ) ), X ) ), member( X,
% 0.73/1.14 'universal_class' ) ] )
% 0.73/1.14 , clause( 334, [ ~( =( singleton( 'member_of'( X ) ), X ) ), ~( member( Y,
% 0.73/1.14 X ) ), =( 'member_of'( X ), Y ) ] )
% 0.73/1.14 , clause( 335, [ ~( member( X, Y ) ), subclass( singleton( X ), Y ) ] )
% 0.73/1.14 , clause( 336, [ ~( subclass( X, singleton( Y ) ) ), =( X, 'null_class' ),
% 0.73/1.14 =( singleton( Y ), X ) ] )
% 0.73/1.14 , clause( 337, [ member( 'not_subclass_element'( intersection( complement(
% 0.73/1.14 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 0.73/1.14 'null_class' ), intersection( complement( singleton(
% 0.73/1.14 'not_subclass_element'( X, 'null_class' ) ) ), X ) ), =( singleton(
% 0.73/1.14 'not_subclass_element'( X, 'null_class' ) ), X ), =( X, 'null_class' ) ]
% 0.73/1.14 )
% 0.73/1.14 , clause( 338, [ member( 'not_subclass_element'( intersection( complement(
% 0.73/1.14 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 0.73/1.14 'null_class' ), X ), =( singleton( 'not_subclass_element'( X,
% 0.73/1.14 'null_class' ) ), X ), =( X, 'null_class' ) ] )
% 0.73/1.14 , clause( 339, [ ~( =( 'not_subclass_element'( intersection( complement(
% 0.73/1.14 singleton( 'not_subclass_element'( X, 'null_class' ) ) ), X ),
% 0.73/1.14 'null_class' ), 'not_subclass_element'( X, 'null_class' ) ) ), =(
% 0.73/1.14 singleton( 'not_subclass_element'( X, 'null_class' ) ), X ), =( X,
% 0.73/1.14 'null_class' ) ] )
% 0.73/1.14 , clause( 340, [ =( 'unordered_pair'( X, Y ), union( singleton( X ),
% 0.73/1.14 singleton( Y ) ) ) ] )
% 0.73/1.14 , clause( 341, [ member( 'ordered_pair'( X, Y ), 'universal_class' ) ] )
% 0.73/1.14 , clause( 342, [ member( singleton( X ), 'ordered_pair'( X, Y ) ) ] )
% 0.73/1.14 , clause( 343, [ member( 'unordered_pair'( X, singleton( Y ) ),
% 0.73/1.14 'ordered_pair'( X, Y ) ) ] )
% 0.73/1.14 , clause( 344, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X,
% 0.73/1.14 'null_class' ) ), 'ordered_pair'( X, Y ) ), member( Y, 'universal_class'
% 0.73/1.14 ) ] )
% 0.73/1.14 , clause( 345, [ ~( member( X, 'universal_class' ) ), =( 'unordered_pair'(
% 0.73/1.14 'null_class', singleton( singleton( X ) ) ), 'ordered_pair'( Y, X ) ),
% 0.73/1.14 member( Y, 'universal_class' ) ] )
% 0.73/1.14 , clause( 346, [ =( 'unordered_pair'( 'null_class', singleton( 'null_class'
% 0.73/1.14 ) ), 'ordered_pair'( X, Y ) ), member( X, 'universal_class' ), member( Y
% 0.73/1.14 , 'universal_class' ) ] )
% 0.73/1.14 , clause( 347, [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) ),
% 0.73/1.14 ~( member( X, 'universal_class' ) ), =( X, Z ) ] )
% 0.73/1.14 , clause( 348, [ ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z, T ) ) ),
% 0.73/1.14 ~( member( Y, 'universal_class' ) ), =( Y, T ) ] )
% 0.73/1.14 , clause( 349, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.73/1.14 'universal_class', 'universal_class' ) ) ), member( 'ordered_pair'( first(
% 0.73/1.14 'ordered_pair'( X, Y ) ), second( 'ordered_pair'( X, Y ) ) ),
% 0.73/1.14 'cross_product'( 'universal_class', 'universal_class' ) ) ] )
% 0.73/1.14 , clause( 350, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 0.73/1.14 'cross_product'( 'universal_class', 'universal_class' ) ), =( first( X )
% 0.73/1.14 , X ) ] )
% 0.73/1.14 , clause( 351, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 0.73/1.14 'cross_product'( 'universal_class', 'universal_class' ) ), =( second( X )
% 0.73/1.14 , X ) ] )
% 0.73/1.14 , clause( 352, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 0.73/1.14 first( X ), X ) ] )
% 0.73/1.14 , clause( 353, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 0.73/1.14 second( X ), X ) ] )
% 0.73/1.14 , clause( 354, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.73/1.14 'universal_class', 'universal_class' ) ) ), =( first( 'ordered_pair'( X,
% 0.73/1.14 Y ) ), X ) ] )
% 0.73/1.14 , clause( 355, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 0.73/1.14 'universal_class', 'universal_class' ) ) ), =( second( 'ordered_pair'( X
% 0.73/1.14 , Y ) ), Y ) ] )
% 0.73/1.14 , clause( 356, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 0.73/1.14 'cross_product'( 'universal_class', 'universal_class' ) ), =( first( X )
% 0.73/1.14 , X ) ] )
% 0.73/1.14 , clause( 357, [ member( 'ordered_pair'( first( X ), second( X ) ),
% 0.73/1.14 'cross_product'( 'universal_class', 'universal_class' ) ), =( second( X )
% 0.73/1.14 , X ) ] )
% 0.73/1.14 , clause( 358, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 0.73/1.14 first( X ), X ) ] )
% 0.73/1.14 , clause( 359, [ =( 'ordered_pair'( first( X ), second( X ) ), X ), =(
% 0.73/1.14 second( X ), X ) ] )
% 0.73/1.14 , clause( 360, [ member( x, 'cross_product'( 'universal_class',
% 0.73/1.14 'universal_class' ) ) ] )
% 0.73/1.14 , clause( 361, [ ~( member( x, 'universal_class' ) ) ] )
% 0.73/1.14 ] ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.73/1.14 )
% 0.73/1.14 , clause( 197, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y )
% 0.73/1.14 ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.73/1.14 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 3, [ subclass( X, 'universal_class' ) ] )
% 0.73/1.14 , clause( 200, [ subclass( X, 'universal_class' ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 158, [ member( x, 'cross_product'( 'universal_class',
% 0.73/1.14 'universal_class' ) ) ] )
% 0.73/1.14 , clause( 360, [ member( x, 'cross_product'( 'universal_class',
% 0.73/1.14 'universal_class' ) ) ] )
% 0.73/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 159, [ ~( member( x, 'universal_class' ) ) ] )
% 0.73/1.14 , clause( 361, [ ~( member( x, 'universal_class' ) ) ] )
% 0.73/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 resolution(
% 0.73/1.14 clause( 666, [ ~( subclass( X, 'universal_class' ) ), ~( member( x, X ) ) ]
% 0.73/1.14 )
% 0.73/1.14 , clause( 159, [ ~( member( x, 'universal_class' ) ) ] )
% 0.73/1.14 , 0, clause( 0, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 0.73/1.14 ) ] )
% 0.73/1.14 , 2, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y,
% 0.73/1.14 'universal_class' ), :=( Z, x )] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 resolution(
% 0.73/1.14 clause( 667, [ ~( member( x, X ) ) ] )
% 0.73/1.14 , clause( 666, [ ~( subclass( X, 'universal_class' ) ), ~( member( x, X ) )
% 0.73/1.14 ] )
% 0.73/1.14 , 0, clause( 3, [ subclass( X, 'universal_class' ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.73/1.14 ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 178, [ ~( member( x, X ) ) ] )
% 0.73/1.14 , clause( 667, [ ~( member( x, X ) ) ] )
% 0.73/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 resolution(
% 0.73/1.14 clause( 668, [] )
% 0.73/1.14 , clause( 178, [ ~( member( x, X ) ) ] )
% 0.73/1.14 , 0, clause( 158, [ member( x, 'cross_product'( 'universal_class',
% 0.73/1.14 'universal_class' ) ) ] )
% 0.73/1.14 , 0, substitution( 0, [ :=( X, 'cross_product'( 'universal_class',
% 0.73/1.14 'universal_class' ) )] ), substitution( 1, [] )).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 subsumption(
% 0.73/1.14 clause( 195, [] )
% 0.73/1.14 , clause( 668, [] )
% 0.73/1.14 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 end.
% 0.73/1.14
% 0.73/1.14 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.73/1.14
% 0.73/1.14 Memory use:
% 0.73/1.14
% 0.73/1.14 space for terms: 6806
% 0.73/1.14 space for clauses: 14112
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 clauses generated: 246
% 0.73/1.14 clauses kept: 196
% 0.73/1.14 clauses selected: 24
% 0.73/1.14 clauses deleted: 1
% 0.73/1.14 clauses inuse deleted: 0
% 0.73/1.14
% 0.73/1.14 subsentry: 3081
% 0.73/1.14 literals s-matched: 1648
% 0.73/1.14 literals matched: 1646
% 0.73/1.14 full subsumption: 367
% 0.73/1.14
% 0.73/1.14 checksum: 255752418
% 0.73/1.14
% 0.73/1.14
% 0.73/1.14 Bliksem ended
%------------------------------------------------------------------------------