TSTP Solution File: SET085-7 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET085-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n015.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 22:46:48 EDT 2022
% Result : Unsatisfiable 2.75s 3.19s
% Output : Refutation 2.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET085-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sun Jul 10 06:41:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.72/1.11 *** allocated 10000 integers for termspace/termends
% 0.72/1.11 *** allocated 10000 integers for clauses
% 0.72/1.11 *** allocated 10000 integers for justifications
% 0.72/1.11 Bliksem 1.12
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Automatic Strategy Selection
% 0.72/1.11
% 0.72/1.11 Clauses:
% 0.72/1.11 [
% 0.72/1.11 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.72/1.11 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.72/1.11 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.72/1.11 ,
% 0.72/1.11 [ subclass( X, 'universal_class' ) ],
% 0.72/1.11 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.72/1.11 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.72/1.11 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.72/1.11 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.72/1.11 ,
% 0.72/1.11 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.72/1.11 ) ) ],
% 0.72/1.11 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.72/1.11 ) ) ],
% 0.72/1.11 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.72/1.11 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.72/1.11 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.72/1.11 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.72/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.72/1.11 X, Z ) ],
% 0.72/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.72/1.11 Y, T ) ],
% 0.72/1.11 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.72/1.11 ), 'cross_product'( Y, T ) ) ],
% 0.72/1.11 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.72/1.11 ), second( X ) ), X ) ],
% 0.72/1.11 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.72/1.11 'universal_class' ) ) ],
% 0.72/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.72/1.11 Y ) ],
% 0.72/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.72/1.11 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.72/1.11 , Y ), 'element_relation' ) ],
% 0.72/1.11 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.72/1.11 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.72/1.11 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.72/1.11 Z ) ) ],
% 0.72/1.11 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.72/1.11 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.72/1.11 member( X, Y ) ],
% 0.72/1.11 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.72/1.11 union( X, Y ) ) ],
% 0.72/1.11 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.72/1.11 intersection( complement( X ), complement( Y ) ) ) ),
% 0.72/1.11 'symmetric_difference'( X, Y ) ) ],
% 0.72/1.11 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.72/1.11 ,
% 0.72/1.11 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.72/1.11 ,
% 0.72/1.11 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.72/1.11 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.72/1.11 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.72/1.11 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.72/1.11 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.72/1.11 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.72/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.72/1.11 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.72/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.72/1.11 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.72/1.11 'cross_product'( 'universal_class', 'universal_class' ),
% 0.72/1.11 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.72/1.11 Y ), rotate( T ) ) ],
% 0.72/1.11 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.72/1.11 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.72/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.72/1.11 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.72/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.72/1.11 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.72/1.11 'cross_product'( 'universal_class', 'universal_class' ),
% 0.72/1.11 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.72/1.11 Z ), flip( T ) ) ],
% 0.72/1.11 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.72/1.11 inverse( X ) ) ],
% 0.72/1.11 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.72/1.11 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.72/1.11 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.72/1.11 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.72/1.11 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.72/1.11 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.72/1.11 ],
% 0.72/1.11 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.72/1.11 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.72/1.11 'universal_class' ) ) ],
% 0.72/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.72/1.11 successor( X ), Y ) ],
% 0.72/1.11 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.72/1.11 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.72/1.11 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.72/1.11 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.72/1.11 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.72/1.11 ,
% 0.72/1.11 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.72/1.11 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.72/1.11 [ inductive( omega ) ],
% 0.72/1.11 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.72/1.11 [ member( omega, 'universal_class' ) ],
% 0.72/1.11 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.72/1.11 , 'sum_class'( X ) ) ],
% 0.72/1.11 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.72/1.11 'universal_class' ) ],
% 0.72/1.11 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.72/1.11 'power_class'( X ) ) ],
% 0.72/1.11 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.72/1.11 'universal_class' ) ],
% 0.72/1.11 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.72/1.11 'universal_class' ) ) ],
% 0.72/1.11 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.72/1.11 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.72/1.11 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.72/1.11 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.72/1.11 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.72/1.11 ) ],
% 0.72/1.11 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.72/1.11 , 'identity_relation' ) ],
% 0.72/1.11 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.72/1.11 'single_valued_class'( X ) ],
% 0.72/1.11 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.72/1.11 'universal_class' ) ) ],
% 0.72/1.11 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.72/1.11 'identity_relation' ) ],
% 0.72/1.11 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.72/1.11 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.72/1.11 , function( X ) ],
% 0.72/1.11 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.72/1.11 X, Y ), 'universal_class' ) ],
% 0.72/1.11 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.72/1.11 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.72/1.11 ) ],
% 0.72/1.11 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.72/1.11 [ function( choice ) ],
% 0.72/1.11 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.72/1.11 apply( choice, X ), X ) ],
% 0.72/1.11 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.72/1.11 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.72/1.11 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.72/1.11 ,
% 0.72/1.11 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.72/1.11 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.72/1.11 , complement( compose( complement( 'element_relation' ), inverse(
% 0.72/1.11 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.72/1.11 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.72/1.11 'identity_relation' ) ],
% 0.72/1.11 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.72/1.11 , diagonalise( X ) ) ],
% 0.72/1.11 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.72/1.11 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.72/1.11 [ ~( operation( X ) ), function( X ) ],
% 0.72/1.11 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.72/1.11 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.72/1.11 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.72/1.11 'domain_of'( X ) ) ) ],
% 0.72/1.11 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 0.72/1.11 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 0.72/1.11 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 0.72/1.11 X ) ],
% 0.72/1.11 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 0.72/1.11 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 0.72/1.11 'domain_of'( X ) ) ],
% 0.72/1.11 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 0.72/1.11 'domain_of'( Z ) ) ) ],
% 0.72/1.11 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 0.72/1.11 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 0.72/1.11 ), compatible( X, Y, Z ) ],
% 0.72/1.11 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 0.72/1.11 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 0.72/1.11 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 0.72/1.11 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 0.72/1.11 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 0.72/1.11 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 0.72/1.11 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.72/1.11 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 0.72/1.11 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 0.72/1.11 , Y ) ],
% 0.72/1.11 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 0.72/1.11 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 0.72/1.11 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 0.72/1.11 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 0.72/1.11 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 0.72/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.72/1.11 X, 'unordered_pair'( X, Y ) ) ],
% 0.72/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.72/1.11 Y, 'unordered_pair'( X, Y ) ) ],
% 0.72/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.72/1.11 X, 'universal_class' ) ],
% 0.72/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.72/1.11 Y, 'universal_class' ) ],
% 0.72/1.11 [ subclass( X, X ) ],
% 0.72/1.11 [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass( X, Z ) ],
% 0.72/1.11 [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ), member(
% 0.72/1.11 'not_subclass_element'( Y, X ), Y ) ],
% 0.72/1.11 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X, Y ), member(
% 0.72/1.11 'not_subclass_element'( Y, X ), Y ) ],
% 0.72/1.11 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y, X ), member(
% 0.72/1.11 'not_subclass_element'( Y, X ), Y ) ],
% 0.72/1.11 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~( member(
% 0.72/1.11 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ],
% 0.72/1.11 [ ~( member( X, intersection( complement( Y ), Y ) ) ) ],
% 0.72/1.11 [ ~( member( X, 'null_class' ) ) ],
% 0.72/1.11 [ subclass( 'null_class', X ) ],
% 0.72/1.11 [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ],
% 0.72/1.11 [ =( X, 'null_class' ), member( 'not_subclass_element'( X, 'null_class'
% 0.72/1.11 ), X ) ],
% 0.72/1.11 [ member( 'null_class', 'universal_class' ) ],
% 0.72/1.11 [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) ) ],
% 0.72/1.11 [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ],
% 0.72/1.11 [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ],
% 0.72/1.11 [ member( X, 'universal_class' ), =( 'unordered_pair'( Y, X ), singleton(
% 0.72/1.11 Y ) ) ],
% 0.72/1.11 [ member( X, 'universal_class' ), =( 'unordered_pair'( X, Y ), singleton(
% 0.72/1.11 Y ) ) ],
% 0.72/1.11 [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 0.72/1.11 'universal_class' ), member( Y, 'universal_class' ) ],
% 0.72/1.11 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z ) ) ), ~(
% 0.72/1.11 member( 'ordered_pair'( Y, Z ), 'cross_product'( 'universal_class',
% 0.72/1.11 'universal_class' ) ) ), =( Y, Z ) ],
% 0.72/1.11 [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y ) ) ), ~(
% 0.72/1.11 member( 'ordered_pair'( X, Z ), 'cross_product'( 'universal_class',
% 0.72/1.11 'universal_class' ) ) ), =( X, Z ) ],
% 0.72/1.11 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( X, Y ),
% 0.72/1.11 'null_class' ) ) ],
% 0.72/1.11 [ ~( member( X, 'universal_class' ) ), ~( =( 'unordered_pair'( Y, X ),
% 0.72/1.11 'null_class' ) ) ],
% 0.72/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), ~( =(
% 0.72/1.11 'unordered_pair'( X, Y ), 'null_class' ) ) ],
% 2.75/3.19 [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass( 'unordered_pair'(
% 2.75/3.19 X, Z ), Y ) ],
% 2.75/3.19 [ member( singleton( X ), 'universal_class' ) ],
% 2.75/3.19 [ member( singleton( X ), 'unordered_pair'( Y, singleton( X ) ) ) ],
% 2.75/3.19 [ ~( member( X, 'universal_class' ) ), member( X, singleton( X ) ) ]
% 2.75/3.19 ,
% 2.75/3.19 [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X ),
% 2.75/3.19 'null_class' ) ) ],
% 2.75/3.19 [ member( 'null_class', singleton( 'null_class' ) ) ],
% 2.75/3.19 [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ],
% 2.75/3.19 [ member( X, 'universal_class' ), =( singleton( X ), 'null_class' ) ]
% 2.75/3.19 ,
% 2.75/3.19 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 2.75/3.19 'universal_class' ) ), =( X, Y ) ],
% 2.75/3.19 [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 2.75/3.19 'universal_class' ) ), =( X, Y ) ],
% 2.75/3.19 [ =( 'unordered_pair'( y, z ), singleton( x ) ) ],
% 2.75/3.19 [ member( x, 'universal_class' ) ],
% 2.75/3.19 [ ~( =( x, y ) ) ],
% 2.75/3.19 [ ~( =( x, z ) ) ]
% 2.75/3.19 ] .
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 percentage equality = 0.254826, percentage horn = 0.878788
% 2.75/3.19 This is a problem with some equality
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 Options Used:
% 2.75/3.19
% 2.75/3.19 useres = 1
% 2.75/3.19 useparamod = 1
% 2.75/3.19 useeqrefl = 1
% 2.75/3.19 useeqfact = 1
% 2.75/3.19 usefactor = 1
% 2.75/3.19 usesimpsplitting = 0
% 2.75/3.19 usesimpdemod = 5
% 2.75/3.19 usesimpres = 3
% 2.75/3.19
% 2.75/3.19 resimpinuse = 1000
% 2.75/3.19 resimpclauses = 20000
% 2.75/3.19 substype = eqrewr
% 2.75/3.19 backwardsubs = 1
% 2.75/3.19 selectoldest = 5
% 2.75/3.19
% 2.75/3.19 litorderings [0] = split
% 2.75/3.19 litorderings [1] = extend the termordering, first sorting on arguments
% 2.75/3.19
% 2.75/3.19 termordering = kbo
% 2.75/3.19
% 2.75/3.19 litapriori = 0
% 2.75/3.19 termapriori = 1
% 2.75/3.19 litaposteriori = 0
% 2.75/3.19 termaposteriori = 0
% 2.75/3.19 demodaposteriori = 0
% 2.75/3.19 ordereqreflfact = 0
% 2.75/3.19
% 2.75/3.19 litselect = negord
% 2.75/3.19
% 2.75/3.19 maxweight = 15
% 2.75/3.19 maxdepth = 30000
% 2.75/3.19 maxlength = 115
% 2.75/3.19 maxnrvars = 195
% 2.75/3.19 excuselevel = 1
% 2.75/3.19 increasemaxweight = 1
% 2.75/3.19
% 2.75/3.19 maxselected = 10000000
% 2.75/3.19 maxnrclauses = 10000000
% 2.75/3.19
% 2.75/3.19 showgenerated = 0
% 2.75/3.19 showkept = 0
% 2.75/3.19 showselected = 0
% 2.75/3.19 showdeleted = 0
% 2.75/3.19 showresimp = 1
% 2.75/3.19 showstatus = 2000
% 2.75/3.19
% 2.75/3.19 prologoutput = 1
% 2.75/3.19 nrgoals = 5000000
% 2.75/3.19 totalproof = 1
% 2.75/3.19
% 2.75/3.19 Symbols occurring in the translation:
% 2.75/3.19
% 2.75/3.19 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.75/3.19 . [1, 2] (w:1, o:57, a:1, s:1, b:0),
% 2.75/3.19 ! [4, 1] (w:0, o:32, a:1, s:1, b:0),
% 2.75/3.19 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.75/3.19 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.75/3.19 subclass [41, 2] (w:1, o:82, a:1, s:1, b:0),
% 2.75/3.19 member [43, 2] (w:1, o:83, a:1, s:1, b:0),
% 2.75/3.19 'not_subclass_element' [44, 2] (w:1, o:84, a:1, s:1, b:0),
% 2.75/3.19 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 2.75/3.19 'unordered_pair' [46, 2] (w:1, o:85, a:1, s:1, b:0),
% 2.75/3.19 singleton [47, 1] (w:1, o:40, a:1, s:1, b:0),
% 2.75/3.19 'ordered_pair' [48, 2] (w:1, o:86, a:1, s:1, b:0),
% 2.75/3.19 'cross_product' [50, 2] (w:1, o:87, a:1, s:1, b:0),
% 2.75/3.19 first [52, 1] (w:1, o:41, a:1, s:1, b:0),
% 2.75/3.19 second [53, 1] (w:1, o:42, a:1, s:1, b:0),
% 2.75/3.19 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 2.75/3.19 intersection [55, 2] (w:1, o:89, a:1, s:1, b:0),
% 2.75/3.19 complement [56, 1] (w:1, o:43, a:1, s:1, b:0),
% 2.75/3.19 union [57, 2] (w:1, o:90, a:1, s:1, b:0),
% 2.75/3.19 'symmetric_difference' [58, 2] (w:1, o:91, a:1, s:1, b:0),
% 2.75/3.19 restrict [60, 3] (w:1, o:94, a:1, s:1, b:0),
% 2.75/3.19 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 2.75/3.19 'domain_of' [62, 1] (w:1, o:45, a:1, s:1, b:0),
% 2.75/3.19 rotate [63, 1] (w:1, o:37, a:1, s:1, b:0),
% 2.75/3.19 flip [65, 1] (w:1, o:46, a:1, s:1, b:0),
% 2.75/3.19 inverse [66, 1] (w:1, o:47, a:1, s:1, b:0),
% 2.75/3.19 'range_of' [67, 1] (w:1, o:38, a:1, s:1, b:0),
% 2.75/3.19 domain [68, 3] (w:1, o:96, a:1, s:1, b:0),
% 2.75/3.19 range [69, 3] (w:1, o:97, a:1, s:1, b:0),
% 2.75/3.19 image [70, 2] (w:1, o:88, a:1, s:1, b:0),
% 2.75/3.19 successor [71, 1] (w:1, o:48, a:1, s:1, b:0),
% 2.75/3.19 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 2.75/3.19 inductive [73, 1] (w:1, o:49, a:1, s:1, b:0),
% 2.75/3.19 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 2.75/3.19 'sum_class' [75, 1] (w:1, o:50, a:1, s:1, b:0),
% 2.75/3.19 'power_class' [76, 1] (w:1, o:53, a:1, s:1, b:0),
% 2.75/3.19 compose [78, 2] (w:1, o:92, a:1, s:1, b:0),
% 2.75/3.19 'single_valued_class' [79, 1] (w:1, o:54, a:1, s:1, b:0),
% 2.75/3.19 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 2.75/3.19 function [82, 1] (w:1, o:55, a:1, s:1, b:0),
% 2.75/3.19 regular [83, 1] (w:1, o:39, a:1, s:1, b:0),
% 2.75/3.19 apply [84, 2] (w:1, o:93, a:1, s:1, b:0),
% 2.75/3.19 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 2.75/3.19 'one_to_one' [86, 1] (w:1, o:51, a:1, s:1, b:0),
% 2.75/3.19 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 2.75/3.19 diagonalise [88, 1] (w:1, o:56, a:1, s:1, b:0),
% 2.75/3.19 cantor [89, 1] (w:1, o:44, a:1, s:1, b:0),
% 2.75/3.19 operation [90, 1] (w:1, o:52, a:1, s:1, b:0),
% 2.75/3.19 compatible [94, 3] (w:1, o:95, a:1, s:1, b:0),
% 2.75/3.19 homomorphism [95, 3] (w:1, o:98, a:1, s:1, b:0),
% 2.75/3.19 'not_homomorphism1' [96, 3] (w:1, o:99, a:1, s:1, b:0),
% 2.75/3.19 'not_homomorphism2' [97, 3] (w:1, o:100, a:1, s:1, b:0),
% 2.75/3.19 y [98, 0] (w:1, o:30, a:1, s:1, b:0),
% 2.75/3.19 z [99, 0] (w:1, o:31, a:1, s:1, b:0),
% 2.75/3.19 x [100, 0] (w:1, o:29, a:1, s:1, b:0).
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 Starting Search:
% 2.75/3.19
% 2.75/3.19 Resimplifying inuse:
% 2.75/3.19 Done
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 Intermediate Status:
% 2.75/3.19 Generated: 3817
% 2.75/3.19 Kept: 2011
% 2.75/3.19 Inuse: 118
% 2.75/3.19 Deleted: 2
% 2.75/3.19 Deletedinuse: 2
% 2.75/3.19
% 2.75/3.19 Resimplifying inuse:
% 2.75/3.19 Done
% 2.75/3.19
% 2.75/3.19 Resimplifying inuse:
% 2.75/3.19 Done
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 Intermediate Status:
% 2.75/3.19 Generated: 9524
% 2.75/3.19 Kept: 4220
% 2.75/3.19 Inuse: 201
% 2.75/3.19 Deleted: 8
% 2.75/3.19 Deletedinuse: 8
% 2.75/3.19
% 2.75/3.19 Resimplifying inuse:
% 2.75/3.19 Done
% 2.75/3.19
% 2.75/3.19 Resimplifying inuse:
% 2.75/3.19 Done
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 Intermediate Status:
% 2.75/3.19 Generated: 14596
% 2.75/3.19 Kept: 6237
% 2.75/3.19 Inuse: 279
% 2.75/3.19 Deleted: 47
% 2.75/3.19 Deletedinuse: 45
% 2.75/3.19
% 2.75/3.19 Resimplifying inuse:
% 2.75/3.19 Done
% 2.75/3.19
% 2.75/3.19 Resimplifying inuse:
% 2.75/3.19 Done
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 Intermediate Status:
% 2.75/3.19 Generated: 20591
% 2.75/3.19 Kept: 8254
% 2.75/3.19 Inuse: 329
% 2.75/3.19 Deleted: 55
% 2.75/3.19 Deletedinuse: 50
% 2.75/3.19
% 2.75/3.19 Resimplifying inuse:
% 2.75/3.19 Done
% 2.75/3.19
% 2.75/3.19 Resimplifying inuse:
% 2.75/3.19 Done
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 Intermediate Status:
% 2.75/3.19 Generated: 27139
% 2.75/3.19 Kept: 10293
% 2.75/3.19 Inuse: 391
% 2.75/3.19 Deleted: 68
% 2.75/3.19 Deletedinuse: 53
% 2.75/3.19
% 2.75/3.19 Resimplifying inuse:
% 2.75/3.19 Done
% 2.75/3.19
% 2.75/3.19 Resimplifying inuse:
% 2.75/3.19 Done
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 Intermediate Status:
% 2.75/3.19 Generated: 35262
% 2.75/3.19 Kept: 12298
% 2.75/3.19 Inuse: 432
% 2.75/3.19 Deleted: 71
% 2.75/3.19 Deletedinuse: 56
% 2.75/3.19
% 2.75/3.19 Resimplifying inuse:
% 2.75/3.19 Done
% 2.75/3.19
% 2.75/3.19 Resimplifying inuse:
% 2.75/3.19 Done
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 Intermediate Status:
% 2.75/3.19 Generated: 44030
% 2.75/3.19 Kept: 14304
% 2.75/3.19 Inuse: 468
% 2.75/3.19 Deleted: 86
% 2.75/3.19 Deletedinuse: 69
% 2.75/3.19
% 2.75/3.19 Resimplifying inuse:
% 2.75/3.19 Done
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 Intermediate Status:
% 2.75/3.19 Generated: 49208
% 2.75/3.19 Kept: 17068
% 2.75/3.19 Inuse: 489
% 2.75/3.19 Deleted: 88
% 2.75/3.19 Deletedinuse: 71
% 2.75/3.19
% 2.75/3.19 Resimplifying inuse:
% 2.75/3.19 Done
% 2.75/3.19
% 2.75/3.19 Resimplifying inuse:
% 2.75/3.19 Done
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 Intermediate Status:
% 2.75/3.19 Generated: 54876
% 2.75/3.19 Kept: 19090
% 2.75/3.19 Inuse: 502
% 2.75/3.19 Deleted: 89
% 2.75/3.19 Deletedinuse: 72
% 2.75/3.19
% 2.75/3.19 Resimplifying inuse:
% 2.75/3.19
% 2.75/3.19 Bliksems!, er is een bewijs:
% 2.75/3.19 % SZS status Unsatisfiable
% 2.75/3.19 % SZS output start Refutation
% 2.75/3.19
% 2.75/3.19 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z
% 2.75/3.19 ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.75/3.19 'unordered_pair'( Y, X ) ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 122, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 125, [ =( 'unordered_pair'( y, z ), singleton( x ) ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 126, [ member( x, 'universal_class' ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 127, [ ~( =( y, x ) ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 128, [ ~( =( z, x ) ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 129, [ ~( =( X, Y ) ), ~( member( Z, 'unordered_pair'( X, Y ) ) ),
% 2.75/3.19 =( Z, Y ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 161, [ =( X, Y ), ~( =( Y, X ) ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 450, [ member( x, 'unordered_pair'( X, x ) ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 482, [ member( x, singleton( x ) ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 588, [ ~( =( X, x ) ), ~( =( X, y ) ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 589, [ ~( =( X, x ) ), ~( =( X, z ) ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 15188, [ ~( member( X, singleton( x ) ) ), ~( =( X, y ) ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 19166, [ ~( member( X, singleton( x ) ) ), =( X, z ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 19340, [ ~( =( X, x ) ), ~( member( Y, 'unordered_pair'( X, x ) ) )
% 2.75/3.19 , ~( =( Y, z ) ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 20977, [ ~( member( X, singleton( x ) ) ) ] )
% 2.75/3.19 .
% 2.75/3.19 clause( 20978, [] )
% 2.75/3.19 .
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 % SZS output end Refutation
% 2.75/3.19 found a proof!
% 2.75/3.19
% 2.75/3.19 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.75/3.19
% 2.75/3.19 initialclauses(
% 2.75/3.19 [ clause( 20980, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 2.75/3.19 ) ] )
% 2.75/3.19 , clause( 20981, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 2.75/3.19 , Y ) ] )
% 2.75/3.19 , clause( 20982, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 2.75/3.19 subclass( X, Y ) ] )
% 2.75/3.19 , clause( 20983, [ subclass( X, 'universal_class' ) ] )
% 2.75/3.19 , clause( 20984, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.75/3.19 , clause( 20985, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 2.75/3.19 , clause( 20986, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 2.75/3.19 ] )
% 2.75/3.19 , clause( 20987, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 2.75/3.19 =( X, Z ) ] )
% 2.75/3.19 , clause( 20988, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.75/3.19 'unordered_pair'( X, Y ) ) ] )
% 2.75/3.19 , clause( 20989, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.75/3.19 'unordered_pair'( Y, X ) ) ] )
% 2.75/3.19 , clause( 20990, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 2.75/3.19 )
% 2.75/3.19 , clause( 20991, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.75/3.19 , clause( 20992, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 2.75/3.19 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 2.75/3.19 , clause( 20993, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.75/3.19 ) ) ), member( X, Z ) ] )
% 2.75/3.19 , clause( 20994, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.75/3.19 ) ) ), member( Y, T ) ] )
% 2.75/3.19 , clause( 20995, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 2.75/3.19 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 2.75/3.19 , clause( 20996, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 2.75/3.19 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 2.75/3.19 , clause( 20997, [ subclass( 'element_relation', 'cross_product'(
% 2.75/3.19 'universal_class', 'universal_class' ) ) ] )
% 2.75/3.19 , clause( 20998, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 2.75/3.19 ), member( X, Y ) ] )
% 2.75/3.19 , clause( 20999, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 2.75/3.19 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 2.75/3.19 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 2.75/3.19 , clause( 21000, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 2.75/3.19 )
% 2.75/3.19 , clause( 21001, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 2.75/3.19 )
% 2.75/3.19 , clause( 21002, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 2.75/3.19 intersection( Y, Z ) ) ] )
% 2.75/3.19 , clause( 21003, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 2.75/3.19 )
% 2.75/3.19 , clause( 21004, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.75/3.19 complement( Y ) ), member( X, Y ) ] )
% 2.75/3.19 , clause( 21005, [ =( complement( intersection( complement( X ), complement(
% 2.75/3.19 Y ) ) ), union( X, Y ) ) ] )
% 2.75/3.19 , clause( 21006, [ =( intersection( complement( intersection( X, Y ) ),
% 2.75/3.19 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 2.75/3.19 'symmetric_difference'( X, Y ) ) ] )
% 2.75/3.19 , clause( 21007, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 2.75/3.19 X, Y, Z ) ) ] )
% 2.75/3.19 , clause( 21008, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 2.75/3.19 Z, X, Y ) ) ] )
% 2.75/3.19 , clause( 21009, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 2.75/3.19 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 2.75/3.19 , clause( 21010, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 2.75/3.19 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 2.75/3.19 'domain_of'( Y ) ) ] )
% 2.75/3.19 , clause( 21011, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 2.75/3.19 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.75/3.19 , clause( 21012, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.75/3.19 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 2.75/3.19 ] )
% 2.75/3.19 , clause( 21013, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.75/3.19 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 2.75/3.19 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.75/3.19 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 2.75/3.19 , Y ), rotate( T ) ) ] )
% 2.75/3.19 , clause( 21014, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 2.75/3.19 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 2.75/3.19 , clause( 21015, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.75/3.19 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 2.75/3.19 )
% 2.75/3.19 , clause( 21016, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 2.75/3.19 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 2.75/3.19 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 2.75/3.19 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 2.75/3.19 , Z ), flip( T ) ) ] )
% 2.75/3.19 , clause( 21017, [ =( 'domain_of'( flip( 'cross_product'( X,
% 2.75/3.19 'universal_class' ) ) ), inverse( X ) ) ] )
% 2.75/3.19 , clause( 21018, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 2.75/3.19 , clause( 21019, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 2.75/3.19 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 2.75/3.19 , clause( 21020, [ =( second( 'not_subclass_element'( restrict( X,
% 2.75/3.19 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 2.75/3.19 , clause( 21021, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 2.75/3.19 image( X, Y ) ) ] )
% 2.75/3.19 , clause( 21022, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 2.75/3.19 , clause( 21023, [ subclass( 'successor_relation', 'cross_product'(
% 2.75/3.19 'universal_class', 'universal_class' ) ) ] )
% 2.75/3.19 , clause( 21024, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 2.75/3.19 ) ), =( successor( X ), Y ) ] )
% 2.75/3.19 , clause( 21025, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 2.75/3.19 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 2.75/3.19 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 2.75/3.19 , clause( 21026, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 2.75/3.19 , clause( 21027, [ ~( inductive( X ) ), subclass( image(
% 2.75/3.19 'successor_relation', X ), X ) ] )
% 2.75/3.19 , clause( 21028, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 2.75/3.19 'successor_relation', X ), X ) ), inductive( X ) ] )
% 2.75/3.19 , clause( 21029, [ inductive( omega ) ] )
% 2.75/3.19 , clause( 21030, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 2.75/3.19 , clause( 21031, [ member( omega, 'universal_class' ) ] )
% 2.75/3.19 , clause( 21032, [ =( 'domain_of'( restrict( 'element_relation',
% 2.75/3.19 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 2.75/3.19 , clause( 21033, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 2.75/3.19 X ), 'universal_class' ) ] )
% 2.75/3.19 , clause( 21034, [ =( complement( image( 'element_relation', complement( X
% 2.75/3.19 ) ) ), 'power_class'( X ) ) ] )
% 2.75/3.19 , clause( 21035, [ ~( member( X, 'universal_class' ) ), member(
% 2.75/3.19 'power_class'( X ), 'universal_class' ) ] )
% 2.75/3.19 , clause( 21036, [ subclass( compose( X, Y ), 'cross_product'(
% 2.75/3.19 'universal_class', 'universal_class' ) ) ] )
% 2.75/3.19 , clause( 21037, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 2.75/3.19 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 2.75/3.19 , clause( 21038, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 2.75/3.19 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 2.75/3.19 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 2.75/3.19 ) ] )
% 2.75/3.19 , clause( 21039, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 2.75/3.19 inverse( X ) ), 'identity_relation' ) ] )
% 2.75/3.19 , clause( 21040, [ ~( subclass( compose( X, inverse( X ) ),
% 2.75/3.19 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 2.75/3.19 , clause( 21041, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 2.75/3.19 'universal_class', 'universal_class' ) ) ] )
% 2.75/3.19 , clause( 21042, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 2.75/3.19 , 'identity_relation' ) ] )
% 2.75/3.19 , clause( 21043, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 2.75/3.19 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 2.75/3.19 'identity_relation' ) ), function( X ) ] )
% 2.75/3.19 , clause( 21044, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 2.75/3.19 , member( image( X, Y ), 'universal_class' ) ] )
% 2.75/3.19 , clause( 21045, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 2.75/3.19 , clause( 21046, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 2.75/3.19 , 'null_class' ) ] )
% 2.75/3.19 , clause( 21047, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 2.75/3.19 Y ) ) ] )
% 2.75/3.19 , clause( 21048, [ function( choice ) ] )
% 2.75/3.19 , clause( 21049, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 2.75/3.19 ), member( apply( choice, X ), X ) ] )
% 2.75/3.19 , clause( 21050, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 2.75/3.19 , clause( 21051, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 2.75/3.19 , clause( 21052, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 2.75/3.19 'one_to_one'( X ) ] )
% 2.75/3.19 , clause( 21053, [ =( intersection( 'cross_product'( 'universal_class',
% 2.75/3.19 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 2.75/3.19 'universal_class' ), complement( compose( complement( 'element_relation'
% 2.75/3.19 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 2.75/3.19 , clause( 21054, [ =( intersection( inverse( 'subset_relation' ),
% 2.75/3.19 'subset_relation' ), 'identity_relation' ) ] )
% 2.75/3.19 , clause( 21055, [ =( complement( 'domain_of'( intersection( X,
% 2.75/3.19 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 2.75/3.19 , clause( 21056, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 2.75/3.19 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 2.75/3.19 , clause( 21057, [ ~( operation( X ) ), function( X ) ] )
% 2.75/3.19 , clause( 21058, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 2.75/3.19 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.75/3.19 ] )
% 2.75/3.19 , clause( 21059, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 2.75/3.19 'domain_of'( 'domain_of'( X ) ) ) ] )
% 2.75/3.19 , clause( 21060, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 2.75/3.19 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 2.75/3.19 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 2.75/3.19 operation( X ) ] )
% 2.75/3.19 , clause( 21061, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 2.75/3.19 , clause( 21062, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 2.75/3.19 Y ) ), 'domain_of'( X ) ) ] )
% 2.75/3.19 , clause( 21063, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 2.75/3.19 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 2.75/3.19 , clause( 21064, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 2.75/3.19 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 2.75/3.19 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 2.75/3.19 , clause( 21065, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 2.75/3.19 , clause( 21066, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 2.75/3.19 , clause( 21067, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 2.75/3.19 , clause( 21068, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 2.75/3.19 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 2.75/3.19 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 2.75/3.19 )
% 2.75/3.19 , clause( 21069, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.75/3.19 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 2.75/3.19 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 2.75/3.19 , Y ) ] )
% 2.75/3.19 , clause( 21070, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 2.75/3.19 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 2.75/3.19 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 2.75/3.19 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 2.75/3.19 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 2.75/3.19 )
% 2.75/3.19 , clause( 21071, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.75/3.19 ) ) ), member( X, 'unordered_pair'( X, Y ) ) ] )
% 2.75/3.19 , clause( 21072, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.75/3.19 ) ) ), member( Y, 'unordered_pair'( X, Y ) ) ] )
% 2.75/3.19 , clause( 21073, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.75/3.19 ) ) ), member( X, 'universal_class' ) ] )
% 2.75/3.19 , clause( 21074, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.75/3.19 ) ) ), member( Y, 'universal_class' ) ] )
% 2.75/3.19 , clause( 21075, [ subclass( X, X ) ] )
% 2.75/3.19 , clause( 21076, [ ~( subclass( X, Y ) ), ~( subclass( Y, Z ) ), subclass(
% 2.75/3.19 X, Z ) ] )
% 2.75/3.19 , clause( 21077, [ =( X, Y ), member( 'not_subclass_element'( X, Y ), X ),
% 2.75/3.19 member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.75/3.19 , clause( 21078, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( X,
% 2.75/3.19 Y ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.75/3.19 , clause( 21079, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), =( Y,
% 2.75/3.19 X ), member( 'not_subclass_element'( Y, X ), Y ) ] )
% 2.75/3.19 , clause( 21080, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), ~(
% 2.75/3.19 member( 'not_subclass_element'( Y, X ), X ) ), =( X, Y ) ] )
% 2.75/3.19 , clause( 21081, [ ~( member( X, intersection( complement( Y ), Y ) ) ) ]
% 2.75/3.19 )
% 2.75/3.19 , clause( 21082, [ ~( member( X, 'null_class' ) ) ] )
% 2.75/3.19 , clause( 21083, [ subclass( 'null_class', X ) ] )
% 2.75/3.19 , clause( 21084, [ ~( subclass( X, 'null_class' ) ), =( X, 'null_class' ) ]
% 2.75/3.19 )
% 2.75/3.19 , clause( 21085, [ =( X, 'null_class' ), member( 'not_subclass_element'( X
% 2.75/3.19 , 'null_class' ), X ) ] )
% 2.75/3.19 , clause( 21086, [ member( 'null_class', 'universal_class' ) ] )
% 2.75/3.19 , clause( 21087, [ =( 'unordered_pair'( X, Y ), 'unordered_pair'( Y, X ) )
% 2.75/3.19 ] )
% 2.75/3.19 , clause( 21088, [ subclass( singleton( X ), 'unordered_pair'( X, Y ) ) ]
% 2.75/3.19 )
% 2.75/3.19 , clause( 21089, [ subclass( singleton( X ), 'unordered_pair'( Y, X ) ) ]
% 2.75/3.19 )
% 2.75/3.19 , clause( 21090, [ member( X, 'universal_class' ), =( 'unordered_pair'( Y,
% 2.75/3.19 X ), singleton( Y ) ) ] )
% 2.75/3.19 , clause( 21091, [ member( X, 'universal_class' ), =( 'unordered_pair'( X,
% 2.75/3.19 Y ), singleton( Y ) ) ] )
% 2.75/3.19 , clause( 21092, [ =( 'unordered_pair'( X, Y ), 'null_class' ), member( X,
% 2.75/3.19 'universal_class' ), member( Y, 'universal_class' ) ] )
% 2.75/3.19 , clause( 21093, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( X, Z )
% 2.75/3.19 ) ), ~( member( 'ordered_pair'( Y, Z ), 'cross_product'(
% 2.75/3.19 'universal_class', 'universal_class' ) ) ), =( Y, Z ) ] )
% 2.75/3.19 , clause( 21094, [ ~( =( 'unordered_pair'( X, Y ), 'unordered_pair'( Z, Y )
% 2.75/3.19 ) ), ~( member( 'ordered_pair'( X, Z ), 'cross_product'(
% 2.75/3.19 'universal_class', 'universal_class' ) ) ), =( X, Z ) ] )
% 2.75/3.19 , clause( 21095, [ ~( member( X, 'universal_class' ) ), ~( =(
% 2.75/3.19 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 2.75/3.19 , clause( 21096, [ ~( member( X, 'universal_class' ) ), ~( =(
% 2.75/3.19 'unordered_pair'( Y, X ), 'null_class' ) ) ] )
% 2.75/3.19 , clause( 21097, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 2.75/3.19 ) ) ), ~( =( 'unordered_pair'( X, Y ), 'null_class' ) ) ] )
% 2.75/3.19 , clause( 21098, [ ~( member( X, Y ) ), ~( member( Z, Y ) ), subclass(
% 2.75/3.19 'unordered_pair'( X, Z ), Y ) ] )
% 2.75/3.19 , clause( 21099, [ member( singleton( X ), 'universal_class' ) ] )
% 2.75/3.19 , clause( 21100, [ member( singleton( X ), 'unordered_pair'( Y, singleton(
% 2.75/3.19 X ) ) ) ] )
% 2.75/3.19 , clause( 21101, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.75/3.19 singleton( X ) ) ] )
% 2.75/3.19 , clause( 21102, [ ~( member( X, 'universal_class' ) ), ~( =( singleton( X
% 2.75/3.19 ), 'null_class' ) ) ] )
% 2.75/3.19 , clause( 21103, [ member( 'null_class', singleton( 'null_class' ) ) ] )
% 2.75/3.19 , clause( 21104, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 2.75/3.19 , clause( 21105, [ member( X, 'universal_class' ), =( singleton( X ),
% 2.75/3.19 'null_class' ) ] )
% 2.75/3.19 , clause( 21106, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( X,
% 2.75/3.19 'universal_class' ) ), =( X, Y ) ] )
% 2.75/3.19 , clause( 21107, [ ~( =( singleton( X ), singleton( Y ) ) ), ~( member( Y,
% 2.75/3.19 'universal_class' ) ), =( X, Y ) ] )
% 2.75/3.19 , clause( 21108, [ =( 'unordered_pair'( y, z ), singleton( x ) ) ] )
% 2.75/3.19 , clause( 21109, [ member( x, 'universal_class' ) ] )
% 2.75/3.19 , clause( 21110, [ ~( =( x, y ) ) ] )
% 2.75/3.19 , clause( 21111, [ ~( =( x, z ) ) ] )
% 2.75/3.19 ] ).
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 subsumption(
% 2.75/3.19 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.75/3.19 , clause( 20984, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 2.75/3.19 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.75/3.19 ), ==>( 1, 1 )] ) ).
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 subsumption(
% 2.75/3.19 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 2.75/3.19 , clause( 20986, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 2.75/3.19 ] )
% 2.75/3.19 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.75/3.19 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 subsumption(
% 2.75/3.19 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z
% 2.75/3.19 ) ] )
% 2.75/3.19 , clause( 20987, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 2.75/3.19 =( X, Z ) ] )
% 2.75/3.19 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.75/3.19 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 subsumption(
% 2.75/3.19 clause( 8, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.75/3.19 'unordered_pair'( Y, X ) ) ] )
% 2.75/3.19 , clause( 20989, [ ~( member( X, 'universal_class' ) ), member( X,
% 2.75/3.19 'unordered_pair'( Y, X ) ) ] )
% 2.75/3.19 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.75/3.19 ), ==>( 1, 1 )] ) ).
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 subsumption(
% 2.75/3.19 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.75/3.19 , clause( 20991, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 2.75/3.19 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.75/3.19
% 2.75/3.19
% 2.75/3.19 subsumption(
% 2.75/3.19 clause( 122, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 2.75/3.19 , clause( 21104, [ ~( member( X, singletonCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------