%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET019-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 22:45:32 EDT 2022
% Result : Unsatisfiable 3.49s 3.85s
% Output : Refutation 3.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET019-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Mon Jul 11 07:49:28 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.73/1.11 *** allocated 10000 integers for termspace/termends
% 0.73/1.11 *** allocated 10000 integers for clauses
% 0.73/1.11 *** allocated 10000 integers for justifications
% 0.73/1.11 Bliksem 1.12
% 0.73/1.11
% 0.73/1.11
% 0.73/1.11 Automatic Strategy Selection
% 0.73/1.11
% 0.73/1.11 Clauses:
% 0.73/1.11 [
% 0.73/1.11 [ ~( member( X, Y ) ), 'little_set'( X ) ],
% 0.73/1.11 [ 'little_set'( f1( X, Y ) ), =( X, Y ) ],
% 0.73/1.11 [ member( f1( X, Y ), X ), member( f1( X, Y ), Y ), =( X, Y ) ],
% 0.73/1.11 [ ~( member( f1( X, Y ), X ) ), ~( member( f1( X, Y ), Y ) ), =( X, Y )
% 0.73/1.11 ],
% 0.73/1.11 [ ~( member( X, 'non_ordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.11 =( X, Y ) ) ],
% 0.73/1.11 [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.11 =( X, Z ) ) ],
% 0.73/1.11 [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ],
% 0.73/1.11 [ =( 'singleton_set'( X ), 'non_ordered_pair'( X, X ) ) ],
% 0.73/1.11 [ =( 'ordered_pair'( X, Y ), 'non_ordered_pair'( 'singleton_set'( X ),
% 0.73/1.11 'non_ordered_pair'( X, Y ) ) ) ],
% 0.73/1.11 [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f2( X ) ) ],
% 0.73/1.11 [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f3( X ) ) ],
% 0.73/1.11 [ ~( 'ordered_pair_predicate'( X ) ), =( X, 'ordered_pair'( f2( X ), f3(
% 0.73/1.11 X ) ) ) ],
% 0.73/1.11 [ 'ordered_pair_predicate'( X ), ~( 'little_set'( Y ) ), ~( 'little_set'(
% 0.73/1.11 Z ) ), ~( =( X, 'ordered_pair'( Y, Z ) ) ) ],
% 0.73/1.11 [ ~( member( X, first( Y ) ) ), 'little_set'( f4( X, Y ) ) ],
% 0.73/1.11 [ ~( member( X, first( Y ) ) ), 'little_set'( f5( X, Y ) ) ],
% 0.73/1.11 [ ~( member( X, first( Y ) ) ), =( Y, 'ordered_pair'( f4( X, Y ), f5( X
% 0.73/1.11 , Y ) ) ) ],
% 0.73/1.11 [ ~( member( X, first( Y ) ) ), member( X, f4( X, Y ) ) ],
% 0.73/1.11 [ member( X, first( Y ) ), ~( 'little_set'( Z ) ), ~( 'little_set'( T )
% 0.73/1.11 ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, Z ) ) ],
% 0.73/1.11 [ ~( member( X, second( Y ) ) ), 'little_set'( f6( X, Y ) ) ],
% 0.73/1.11 [ ~( member( X, second( Y ) ) ), 'little_set'( f7( X, Y ) ) ],
% 0.73/1.11 [ ~( member( X, second( Y ) ) ), =( Y, 'ordered_pair'( f6( X, Y ), f7( X
% 0.73/1.11 , Y ) ) ) ],
% 0.73/1.11 [ ~( member( X, second( Y ) ) ), member( X, f7( X, Y ) ) ],
% 0.73/1.11 [ member( X, second( Y ) ), ~( 'little_set'( Z ) ), ~( 'little_set'( T )
% 0.73/1.11 ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, T ) ) ],
% 0.73/1.11 [ ~( member( X, estin ) ), 'ordered_pair_predicate'( X ) ],
% 0.73/1.11 [ ~( member( X, estin ) ), member( first( X ), second( X ) ) ],
% 0.73/1.11 [ member( X, estin ), ~( 'little_set'( X ) ), ~(
% 0.73/1.11 'ordered_pair_predicate'( X ) ), ~( member( first( X ), second( X ) ) ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.73/1.11 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.73/1.11 [ member( X, intersection( Y, Z ) ), ~( member( X, Y ) ), ~( member( X,
% 0.73/1.11 Z ) ) ],
% 0.73/1.11 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.73/1.11 [ member( X, complement( Y ) ), ~( 'little_set'( X ) ), member( X, Y ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ =( union( X, Y ), complement( intersection( complement( X ),
% 0.73/1.11 complement( Y ) ) ) ) ],
% 0.73/1.11 [ ~( member( X, 'domain_of'( Y ) ) ), 'ordered_pair_predicate'( f8( X, Y
% 0.73/1.11 ) ) ],
% 0.73/1.11 [ ~( member( X, 'domain_of'( Y ) ) ), member( f8( X, Y ), Y ) ],
% 0.73/1.11 [ ~( member( X, 'domain_of'( Y ) ) ), =( X, first( f8( X, Y ) ) ) ],
% 0.73/1.11 [ member( X, 'domain_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.11 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, first( Z )
% 0.73/1.11 ) ) ],
% 0.73/1.11 [ ~( member( X, 'cross_product'( Y, Z ) ) ), 'ordered_pair_predicate'( X
% 0.73/1.11 ) ],
% 0.73/1.11 [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( first( X ), Y ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( second( X ), Z ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ member( X, 'cross_product'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.11 'ordered_pair_predicate'( X ) ), ~( member( first( X ), Y ) ), ~( member(
% 0.73/1.11 second( X ), Z ) ) ],
% 0.73/1.11 [ ~( member( X, converse( Y ) ) ), 'ordered_pair_predicate'( X ) ],
% 0.73/1.11 [ ~( member( X, converse( Y ) ) ), member( 'ordered_pair'( second( X ),
% 0.73/1.11 first( X ) ), Y ) ],
% 0.73/1.11 [ member( X, converse( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.11 'ordered_pair_predicate'( X ) ), ~( member( 'ordered_pair'( second( X ),
% 0.73/1.11 first( X ) ), Y ) ) ],
% 0.73/1.11 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f9( X, Y ) ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f10( X, Y ) ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f11( X, Y ) ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ ~( member( X, 'rotate_right'( Y ) ) ), =( X, 'ordered_pair'( f9( X, Y
% 0.73/1.11 ), 'ordered_pair'( f10( X, Y ), f11( X, Y ) ) ) ) ],
% 0.73/1.11 [ ~( member( X, 'rotate_right'( Y ) ) ), member( 'ordered_pair'( f10( X
% 0.73/1.11 , Y ), 'ordered_pair'( f11( X, Y ), f9( X, Y ) ) ), Y ) ],
% 0.73/1.11 [ member( X, 'rotate_right'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.11 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) ), ~(
% 0.73/1.11 =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 0.73/1.11 'ordered_pair'( T, 'ordered_pair'( U, Z ) ), Y ) ) ],
% 0.73/1.11 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f12( X, Y ) ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f13( X, Y ) ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f14( X, Y ) ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ ~( member( X, 'flip_range_of'( Y ) ) ), =( X, 'ordered_pair'( f12( X,
% 0.73/1.11 Y ), 'ordered_pair'( f13( X, Y ), f14( X, Y ) ) ) ) ],
% 0.73/1.11 [ ~( member( X, 'flip_range_of'( Y ) ) ), member( 'ordered_pair'( f12( X
% 0.73/1.11 , Y ), 'ordered_pair'( f14( X, Y ), f13( X, Y ) ) ), Y ) ],
% 0.73/1.11 [ member( X, 'flip_range_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.11 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) ), ~(
% 0.73/1.11 =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 0.73/1.11 'ordered_pair'( Z, 'ordered_pair'( U, T ) ), Y ) ) ],
% 0.73/1.11 [ =( successor( X ), union( X, 'singleton_set'( X ) ) ) ],
% 0.73/1.11 [ ~( member( X, 'empty_set' ) ) ],
% 0.73/1.11 [ member( X, 'universal_set' ), ~( 'little_set'( X ) ) ],
% 0.73/1.11 [ 'little_set'( infinity ) ],
% 0.73/1.11 [ member( 'empty_set', infinity ) ],
% 0.73/1.11 [ ~( member( X, infinity ) ), member( successor( X ), infinity ) ],
% 0.73/1.11 [ ~( member( X, sigma( Y ) ) ), member( f16( X, Y ), Y ) ],
% 0.73/1.11 [ ~( member( X, sigma( Y ) ) ), member( X, f16( X, Y ) ) ],
% 0.73/1.11 [ member( X, sigma( Y ) ), ~( member( Z, Y ) ), ~( member( X, Z ) ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ ~( 'little_set'( X ) ), 'little_set'( sigma( X ) ) ],
% 0.73/1.11 [ ~( subset( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.73/1.11 [ subset( X, Y ), member( f17( X, Y ), X ) ],
% 0.73/1.11 [ subset( X, Y ), ~( member( f17( X, Y ), Y ) ) ],
% 0.73/1.11 [ ~( 'proper_subset'( X, Y ) ), subset( X, Y ) ],
% 0.73/1.11 [ ~( 'proper_subset'( X, Y ) ), ~( =( X, Y ) ) ],
% 0.73/1.11 [ 'proper_subset'( X, Y ), ~( subset( X, Y ) ), =( X, Y ) ],
% 0.73/1.11 [ ~( member( X, powerset( Y ) ) ), subset( X, Y ) ],
% 0.73/1.11 [ member( X, powerset( Y ) ), ~( 'little_set'( X ) ), ~( subset( X, Y )
% 0.73/1.11 ) ],
% 0.73/1.11 [ ~( 'little_set'( X ) ), 'little_set'( powerset( X ) ) ],
% 0.73/1.11 [ ~( relation( X ) ), ~( member( Y, X ) ), 'ordered_pair_predicate'( Y )
% 0.73/1.11 ],
% 0.73/1.11 [ relation( X ), member( f18( X ), X ) ],
% 0.73/1.11 [ relation( X ), ~( 'ordered_pair_predicate'( f18( X ) ) ) ],
% 0.73/1.11 [ ~( 'single_valued_set'( X ) ), ~( 'little_set'( Y ) ), ~( 'little_set'(
% 0.73/1.11 Z ) ), ~( 'little_set'( T ) ), ~( member( 'ordered_pair'( Y, Z ), X ) ),
% 0.73/1.11 ~( member( 'ordered_pair'( Y, T ), X ) ), =( Z, T ) ],
% 0.73/1.11 [ 'single_valued_set'( X ), 'little_set'( f19( X ) ) ],
% 0.73/1.11 [ 'single_valued_set'( X ), 'little_set'( f20( X ) ) ],
% 0.73/1.11 [ 'single_valued_set'( X ), 'little_set'( f21( X ) ) ],
% 0.73/1.11 [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X ), f20( X ) )
% 0.73/1.11 , X ) ],
% 0.73/1.11 [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X ), f21( X ) )
% 0.73/1.11 , X ) ],
% 0.73/1.11 [ 'single_valued_set'( X ), ~( =( f20( X ), f21( X ) ) ) ],
% 0.73/1.11 [ ~( function( X ) ), relation( X ) ],
% 0.73/1.11 [ ~( function( X ) ), 'single_valued_set'( X ) ],
% 0.73/1.11 [ function( X ), ~( relation( X ) ), ~( 'single_valued_set'( X ) ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ ~( member( X, image( Y, Z ) ) ), 'ordered_pair_predicate'( f22( X, Y,
% 0.73/1.11 Z ) ) ],
% 0.73/1.11 [ ~( member( X, image( Y, Z ) ) ), member( f22( X, Y, Z ), Z ) ],
% 0.73/1.11 [ ~( member( X, image( Y, Z ) ) ), member( first( f22( X, Y, Z ) ), Y )
% 0.73/1.11 ],
% 0.73/1.11 [ ~( member( X, image( Y, Z ) ) ), =( second( f22( X, Y, Z ) ), X ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ member( X, image( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.11 'ordered_pair_predicate'( T ) ), ~( member( T, Z ) ), ~( member( first( T
% 0.73/1.11 ), Y ) ), ~( =( second( T ), X ) ) ],
% 0.73/1.11 [ ~( 'little_set'( X ) ), ~( function( Y ) ), 'little_set'( image( X, Y
% 0.73/1.11 ) ) ],
% 0.73/1.11 [ ~( disjoint( X, Y ) ), ~( member( Z, X ) ), ~( member( Z, Y ) ) ],
% 0.73/1.11 [ disjoint( X, Y ), member( f23( X, Y ), X ) ],
% 0.73/1.11 [ disjoint( X, Y ), member( f23( X, Y ), Y ) ],
% 0.73/1.11 [ =( X, 'empty_set' ), member( f24( X ), X ) ],
% 0.73/1.11 [ =( X, 'empty_set' ), disjoint( f24( X ), X ) ],
% 0.73/1.11 [ function( f25 ) ],
% 0.73/1.11 [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( f26( X ), X ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( 'ordered_pair'( X
% 0.73/1.11 , f26( X ) ), f25 ) ],
% 0.73/1.11 [ ~( member( X, 'range_of'( Y ) ) ), 'ordered_pair_predicate'( f27( X, Y
% 0.73/1.11 ) ) ],
% 0.73/1.11 [ ~( member( X, 'range_of'( Y ) ) ), member( f27( X, Y ), Y ) ],
% 0.73/1.11 [ ~( member( X, 'range_of'( Y ) ) ), =( X, second( f27( X, Y ) ) ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ member( X, 'range_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.11 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, second( Z
% 0.73/1.11 ) ) ) ],
% 0.73/1.11 [ ~( member( X, 'identity_relation' ) ), 'ordered_pair_predicate'( X ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ ~( member( X, 'identity_relation' ) ), =( first( X ), second( X ) ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ member( X, 'identity_relation' ), ~( 'little_set'( X ) ), ~(
% 0.73/1.11 'ordered_pair_predicate'( X ) ), ~( =( first( X ), second( X ) ) ) ],
% 0.73/1.11 [ =( restrict( X, Y ), intersection( X, 'cross_product'( Y,
% 0.73/1.11 'universal_set' ) ) ) ],
% 0.73/1.11 [ ~( 'one_to_one_function'( X ) ), function( X ) ],
% 0.73/1.11 [ ~( 'one_to_one_function'( X ) ), function( converse( X ) ) ],
% 0.73/1.11 [ 'one_to_one_function'( X ), ~( function( X ) ), ~( function( converse(
% 0.73/1.11 X ) ) ) ],
% 0.73/1.11 [ ~( member( X, apply( Y, Z ) ) ), 'ordered_pair_predicate'( f28( X, Y,
% 0.73/1.11 Z ) ) ],
% 0.73/1.11 [ ~( member( X, apply( Y, Z ) ) ), member( f28( X, Y, Z ), Y ) ],
% 0.73/1.11 [ ~( member( X, apply( Y, Z ) ) ), =( first( f28( X, Y, Z ) ), Z ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ ~( member( X, apply( Y, Z ) ) ), member( X, second( f28( X, Y, Z ) ) )
% 0.73/1.11 ],
% 0.73/1.11 [ member( X, apply( Y, Z ) ), ~( 'ordered_pair_predicate'( T ) ), ~(
% 0.73/1.11 member( T, Y ) ), ~( =( first( T ), Z ) ), ~( member( X, second( T ) ) )
% 0.73/1.11 ],
% 0.73/1.11 [ =( 'apply_to_two_arguments'( X, Y, Z ), apply( X, 'ordered_pair'( Y, Z
% 0.73/1.11 ) ) ) ],
% 0.73/1.11 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.73/1.11 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 0.73/1.11 [ ~( maps( X, Y, Z ) ), subset( 'range_of'( X ), Z ) ],
% 0.73/1.11 [ maps( X, Y, Z ), ~( function( X ) ), ~( =( 'domain_of'( X ), Y ) ),
% 0.73/1.11 ~( subset( 'range_of'( X ), Z ) ) ],
% 0.73/1.11 [ ~( closed( X, Y ) ), 'little_set'( X ) ],
% 0.73/1.11 [ ~( closed( X, Y ) ), 'little_set'( Y ) ],
% 0.73/1.11 [ ~( closed( X, Y ) ), maps( Y, 'cross_product'( X, X ), X ) ],
% 0.73/1.11 [ closed( X, Y ), ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~(
% 0.73/1.11 maps( Y, 'cross_product'( X, X ), X ) ) ],
% 0.73/1.11 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f29( X, Y, Z ) ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f30( X, Y, Z ) ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f31( X, Y, Z ) ) ]
% 0.73/1.11 ,
% 0.73/1.11 [ ~( member( X, compose( Y, Z ) ) ), =( X, 'ordered_pair'( f29( X, Y, Z
% 0.73/1.11 ), f30( X, Y, Z ) ) ) ],
% 0.73/1.11 [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'( f29( X, Y,
% 0.73/1.11 Z ), f31( X, Y, Z ) ), Y ) ],
% 0.73/1.11 [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'( f31( X, Y,
% 0.73/1.11 Z ), f30( X, Y, Z ) ), Z ) ],
% 0.73/1.11 [ member( X, compose( Y, Z ) ), ~( 'little_set'( X ) ), ~( 'little_set'(
% 0.73/1.11 T ) ), ~( 'little_set'( U ) ), ~( 'little_set'( W ) ), ~( =( X,
% 0.73/1.11 'ordered_pair'( T, U ) ) ), ~( member( 'ordered_pair'( T, W ), Y ) ), ~(
% 0.73/1.11 member( 'ordered_pair'( W, U ), Z ) ) ],
% 0.73/1.11 [ ~( homomorphism( X, Y, Z, T, U ) ), closed( Y, Z ) ],
% 0.73/1.11 [ ~( homomorphism( X, Y, Z, T, U ) ), closed( T, U ) ],
% 0.73/1.11 [ ~( homomorphism( X, Y, Z, T, U ) ), maps( X, Y, T ) ],
% 0.73/1.11 [ ~( homomorphism( X, Y, Z, T, U ) ), ~( member( W, Y ) ), ~( member( V0
% 0.73/1.11 , Y ) ), =( apply( X, 'apply_to_two_arguments'( Z, W, V0 ) ),
% 0.73/1.11 'apply_to_two_arguments'( U, apply( X, W ), apply( X, V0 ) ) ) ],
% 0.73/1.11 [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.73/1.11 ), ~( maps( X, Y, T ) ), member( f32( X, Y, Z, T, U ), Y ) ],
% 0.73/1.11 [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.73/1.11 ), ~( maps( X, Y, T ) ), member( f33( X, Y, Z, T, U ), Y ) ],
% 0.73/1.11 [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 3.47/3.85 ), ~( maps( X, Y, T ) ), ~( =( apply( X, 'apply_to_two_arguments'( Z,
% 3.47/3.85 f32( X, Y, Z, T, U ), f33( X, Y, Z, T, U ) ) ), 'apply_to_two_arguments'(
% 3.47/3.85 U, apply( X, f32( X, Y, Z, T, U ) ), apply( X, f33( X, Y, Z, T, U ) ) ) )
% 3.47/3.85 ) ],
% 3.47/3.85 [ subset( b, a ) ],
% 3.47/3.85 [ subset( a, b ) ],
% 3.47/3.85 [ ~( =( a, b ) ) ]
% 3.47/3.85 ] .
% 3.47/3.85
% 3.47/3.85
% 3.47/3.85 percentage equality = 0.134078, percentage horn = 0.861111
% 3.47/3.85 This is a problem with some equality
% 3.47/3.85
% 3.47/3.85
% 3.47/3.85
% 3.47/3.85 Options Used:
% 3.47/3.85
% 3.47/3.85 useres = 1
% 3.47/3.85 useparamod = 1
% 3.47/3.85 useeqrefl = 1
% 3.47/3.85 useeqfact = 1
% 3.47/3.85 usefactor = 1
% 3.47/3.85 usesimpsplitting = 0
% 3.47/3.85 usesimpdemod = 5
% 3.47/3.85 usesimpres = 3
% 3.47/3.85
% 3.47/3.85 resimpinuse = 1000
% 3.47/3.85 resimpclauses = 20000
% 3.47/3.85 substype = eqrewr
% 3.47/3.85 backwardsubs = 1
% 3.47/3.85 selectoldest = 5
% 3.47/3.85
% 3.47/3.85 litorderings [0] = split
% 3.47/3.85 litorderings [1] = extend the termordering, first sorting on arguments
% 3.47/3.85
% 3.47/3.85 termordering = kbo
% 3.47/3.85
% 3.47/3.85 litapriori = 0
% 3.47/3.85 termapriori = 1
% 3.47/3.85 litaposteriori = 0
% 3.47/3.85 termaposteriori = 0
% 3.47/3.85 demodaposteriori = 0
% 3.47/3.85 ordereqreflfact = 0
% 3.47/3.85
% 3.47/3.85 litselect = negord
% 3.47/3.85
% 3.47/3.85 maxweight = 15
% 3.47/3.85 maxdepth = 30000
% 3.47/3.85 maxlength = 115
% 3.47/3.85 maxnrvars = 195
% 3.47/3.85 excuselevel = 1
% 3.47/3.85 increasemaxweight = 1
% 3.47/3.85
% 3.47/3.85 maxselected = 10000000
% 3.47/3.85 maxnrclauses = 10000000
% 3.47/3.85
% 3.47/3.85 showgenerated = 0
% 3.47/3.85 showkept = 0
% 3.47/3.85 showselected = 0
% 3.47/3.85 showdeleted = 0
% 3.47/3.85 showresimp = 1
% 3.47/3.85 showstatus = 2000
% 3.47/3.85
% 3.47/3.85 prologoutput = 1
% 3.47/3.85 nrgoals = 5000000
% 3.47/3.85 totalproof = 1
% 3.47/3.85
% 3.47/3.85 Symbols occurring in the translation:
% 3.47/3.85
% 3.47/3.85 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 3.47/3.85 . [1, 2] (w:1, o:63, a:1, s:1, b:0),
% 3.47/3.85 ! [4, 1] (w:0, o:32, a:1, s:1, b:0),
% 3.47/3.85 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.47/3.85 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.47/3.85 member [41, 2] (w:1, o:88, a:1, s:1, b:0),
% 3.47/3.85 'little_set' [42, 1] (w:1, o:37, a:1, s:1, b:0),
% 3.47/3.85 f1 [43, 2] (w:1, o:89, a:1, s:1, b:0),
% 3.47/3.85 'non_ordered_pair' [45, 2] (w:1, o:90, a:1, s:1, b:0),
% 3.47/3.85 'singleton_set' [46, 1] (w:1, o:41, a:1, s:1, b:0),
% 3.47/3.85 'ordered_pair' [47, 2] (w:1, o:91, a:1, s:1, b:0),
% 3.47/3.85 'ordered_pair_predicate' [48, 1] (w:1, o:42, a:1, s:1, b:0),
% 3.47/3.85 f2 [49, 1] (w:1, o:45, a:1, s:1, b:0),
% 3.47/3.85 f3 [50, 1] (w:1, o:50, a:1, s:1, b:0),
% 3.47/3.85 first [52, 1] (w:1, o:51, a:1, s:1, b:0),
% 3.47/3.85 f4 [53, 2] (w:1, o:92, a:1, s:1, b:0),
% 3.47/3.85 f5 [54, 2] (w:1, o:93, a:1, s:1, b:0),
% 3.47/3.85 second [56, 1] (w:1, o:52, a:1, s:1, b:0),
% 3.47/3.85 f6 [57, 2] (w:1, o:94, a:1, s:1, b:0),
% 3.47/3.85 f7 [58, 2] (w:1, o:95, a:1, s:1, b:0),
% 3.47/3.85 estin [59, 0] (w:1, o:24, a:1, s:1, b:0),
% 3.47/3.85 intersection [60, 2] (w:1, o:97, a:1, s:1, b:0),
% 3.47/3.85 complement [61, 1] (w:1, o:53, a:1, s:1, b:0),
% 3.47/3.85 union [62, 2] (w:1, o:98, a:1, s:1, b:0),
% 3.47/3.85 'domain_of' [63, 1] (w:1, o:55, a:1, s:1, b:0),
% 3.47/3.85 f8 [64, 2] (w:1, o:99, a:1, s:1, b:0),
% 3.47/3.85 'cross_product' [66, 2] (w:1, o:100, a:1, s:1, b:0),
% 3.47/3.85 converse [67, 1] (w:1, o:54, a:1, s:1, b:0),
% 3.47/3.85 'rotate_right' [68, 1] (w:1, o:38, a:1, s:1, b:0),
% 3.47/3.85 f9 [69, 2] (w:1, o:101, a:1, s:1, b:0),
% 3.47/3.85 f10 [70, 2] (w:1, o:102, a:1, s:1, b:0),
% 3.47/3.85 f11 [71, 2] (w:1, o:103, a:1, s:1, b:0),
% 3.47/3.85 'flip_range_of' [73, 1] (w:1, o:56, a:1, s:1, b:0),
% 3.47/3.85 f12 [74, 2] (w:1, o:104, a:1, s:1, b:0),
% 3.47/3.85 f13 [75, 2] (w:1, o:105, a:1, s:1, b:0),
% 3.47/3.85 f14 [76, 2] (w:1, o:106, a:1, s:1, b:0),
% 3.47/3.85 successor [77, 1] (w:1, o:57, a:1, s:1, b:0),
% 3.47/3.85 'empty_set' [78, 0] (w:1, o:25, a:1, s:1, b:0),
% 3.47/3.85 'universal_set' [79, 0] (w:1, o:26, a:1, s:1, b:0),
% 3.47/3.85 infinity [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 3.47/3.85 sigma [81, 1] (w:1, o:58, a:1, s:1, b:0),
% 3.47/3.85 f16 [82, 2] (w:1, o:107, a:1, s:1, b:0),
% 3.47/3.85 subset [83, 2] (w:1, o:109, a:1, s:1, b:0),
% 3.47/3.85 f17 [84, 2] (w:1, o:110, a:1, s:1, b:0),
% 3.47/3.85 'proper_subset' [85, 2] (w:1, o:111, a:1, s:1, b:0),
% 3.47/3.85 powerset [86, 1] (w:1, o:60, a:1, s:1, b:0),
% 3.47/3.85 relation [87, 1] (w:1, o:39, a:1, s:1, b:0),
% 3.47/3.85 f18 [88, 1] (w:1, o:43, a:1, s:1, b:0),
% 3.47/3.85 'single_valued_set' [89, 1] (w:1, o:61, a:1, s:1, b:0),
% 3.47/3.85 f19 [90, 1] (w:1, o:44, a:1, s:1, b:0),
% 3.47/3.85 f20 [91, 1] (w:1, o:46, a:1, s:1, b:0),
% 3.47/3.85 f21 [92, 1] (w:1, o:47, a:1, s:1, b:0),
% 3.47/3.85 function [94, 1] (w:1, o:62, a:1, s:1, b:0),
% 3.47/3.85 image [95, 2] (w:1, o:96, a:1, s:1, b:0),
% 3.47/3.85 f22 [96, 3] (w:1, o:118, a:1, s:1, b:0),
% 3.47/3.85 disjoint [97, 2] (w:1, o:114, a:1, s:1, b:0),
% 3.47/3.85 f23 [98, 2] (w:1, o:115, a:1, s:1, b:0),
% 3.47/3.85 f24 [99, 1] (w:1, o:48, a:1, s:1, b:0),
% 3.47/3.85 f25 [100, 0] (w:1, o:28, a:1, s:1, b:0),
% 3.47/3.85 f26 [101, 1] (w:1, o:49, a:1, s:1, b:0),
% 3.47/3.85 'range_of' [102, 1] (w:1, o:40, a:1, s:1, b:0),
% 3.47/3.85 f27 [103, 2] (w:1, o:116, a:1, s:1, b:0),
% 3.47/3.85 'identity_relation' [104, 0] (w:1, o:29, a:1, s:1, b:0),
% 3.47/3.85 restrict [105, 2] (w:1, o:108, a:1, s:1, b:0),
% 3.47/3.85 'one_to_one_function' [106, 1] (w:1, o:59, a:1, s:1, b:0),
% 3.47/3.85 apply [107, 2] (w:1, o:117, a:1, s:1, b:0),
% 3.47/3.85 f28 [108, 3] (w:1, o:119, a:1, s:1, b:0),
% 3.47/3.85 'apply_to_two_arguments' [109, 3] (w:1, o:120, a:1, s:1, b:0),
% 3.47/3.85 maps [110, 3] (w:1, o:121, a:1, s:1, b:0),
% 3.47/3.85 closed [112, 2] (w:1, o:112, a:1, s:1, b:0),
% 3.47/3.85 compose [114, 2] (w:1, o:113, a:1, s:1, b:0),
% 3.47/3.85 f29 [115, 3] (w:1, o:122, a:1, s:1, b:0),
% 3.49/3.85 f30 [116, 3] (w:1, o:123, a:1, s:1, b:0),
% 3.49/3.85 f31 [117, 3] (w:1, o:124, a:1, s:1, b:0),
% 3.49/3.85 homomorphism [123, 5] (w:1, o:125, a:1, s:1, b:0),
% 3.49/3.85 f32 [124, 5] (w:1, o:126, a:1, s:1, b:0),
% 3.49/3.85 f33 [125, 5] (w:1, o:127, a:1, s:1, b:0),
% 3.49/3.85 b [126, 0] (w:1, o:31, a:1, s:1, b:0),
% 3.49/3.85 a [127, 0] (w:1, o:30, a:1, s:1, b:0).
% 3.49/3.85
% 3.49/3.85
% 3.49/3.85 Starting Search:
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85
% 3.49/3.85 Intermediate Status:
% 3.49/3.85 Generated: 3668
% 3.49/3.85 Kept: 2071
% 3.49/3.85 Inuse: 91
% 3.49/3.85 Deleted: 0
% 3.49/3.85 Deletedinuse: 0
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85
% 3.49/3.85 Intermediate Status:
% 3.49/3.85 Generated: 7171
% 3.49/3.85 Kept: 4127
% 3.49/3.85 Inuse: 149
% 3.49/3.85 Deleted: 2
% 3.49/3.85 Deletedinuse: 0
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85
% 3.49/3.85 Intermediate Status:
% 3.49/3.85 Generated: 10823
% 3.49/3.85 Kept: 6214
% 3.49/3.85 Inuse: 213
% 3.49/3.85 Deleted: 18
% 3.49/3.85 Deletedinuse: 0
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85
% 3.49/3.85 Intermediate Status:
% 3.49/3.85 Generated: 16410
% 3.49/3.85 Kept: 8241
% 3.49/3.85 Inuse: 259
% 3.49/3.85 Deleted: 18
% 3.49/3.85 Deletedinuse: 0
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85
% 3.49/3.85 Intermediate Status:
% 3.49/3.85 Generated: 20086
% 3.49/3.85 Kept: 10913
% 3.49/3.85 Inuse: 293
% 3.49/3.85 Deleted: 18
% 3.49/3.85 Deletedinuse: 0
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85
% 3.49/3.85 Intermediate Status:
% 3.49/3.85 Generated: 25428
% 3.49/3.85 Kept: 12917
% 3.49/3.85 Inuse: 346
% 3.49/3.85 Deleted: 23
% 3.49/3.85 Deletedinuse: 1
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85
% 3.49/3.85 Intermediate Status:
% 3.49/3.85 Generated: 31702
% 3.49/3.85 Kept: 15203
% 3.49/3.85 Inuse: 380
% 3.49/3.85 Deleted: 32
% 3.49/3.85 Deletedinuse: 1
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85
% 3.49/3.85 Intermediate Status:
% 3.49/3.85 Generated: 37544
% 3.49/3.85 Kept: 17732
% 3.49/3.85 Inuse: 413
% 3.49/3.85 Deleted: 179
% 3.49/3.85 Deletedinuse: 101
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85
% 3.49/3.85 Intermediate Status:
% 3.49/3.85 Generated: 43900
% 3.49/3.85 Kept: 19779
% 3.49/3.85 Inuse: 460
% 3.49/3.85 Deleted: 207
% 3.49/3.85 Deletedinuse: 101
% 3.49/3.85
% 3.49/3.85 Resimplifying inuse:
% 3.49/3.85 Done
% 3.49/3.85
% 3.49/3.85 Resimplifying clauses:
% 3.49/3.85
% 3.49/3.85 Bliksems!, er is een bewijs:
% 3.49/3.85 % SZS status Unsatisfiable
% 3.49/3.85 % SZS output start Refutation
% 3.49/3.85
% 3.49/3.85 clause( 2, [ member( f1( X, Y ), X ), member( f1( X, Y ), Y ), =( X, Y ) ]
% 3.49/3.85 )
% 3.49/3.85 .
% 3.49/3.85 clause( 3, [ ~( member( f1( X, Y ), X ) ), ~( member( f1( X, Y ), Y ) ),
% 3.49/3.85 =( X, Y ) ] )
% 3.49/3.85 .
% 3.49/3.85 clause( 66, [ ~( subset( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ] )
% 3.49/3.85 .
% 3.49/3.85 clause( 141, [ subset( b, a ) ] )
% 3.49/3.85 .
% 3.49/3.85 clause( 142, [ subset( a, b ) ] )
% 3.49/3.85 .
% 3.49/3.85 clause( 143, [ ~( =( b, a ) ) ] )
% 3.49/3.85 .
% 3.49/3.85 clause( 252, [ ~( =( X, a ) ), member( f1( b, X ), b ), member( f1( b, X )
% 3.49/3.85 , X ) ] )
% 3.49/3.85 .
% 3.49/3.85 clause( 261, [ member( f1( b, a ), b ), member( f1( b, a ), a ) ] )
% 3.49/3.85 .
% 3.49/3.85 clause( 298, [ ~( =( X, a ) ), ~( member( f1( b, X ), b ) ), ~( member( f1(
% 3.49/3.85 b, X ), X ) ) ] )
% 3.49/3.85 .
% 3.49/3.85 clause( 305, [ ~( member( f1( b, a ), b ) ), ~( member( f1( b, a ), a ) ) ]
% 3.49/3.85 )
% 3.49/3.85 .
% 3.49/3.85 clause( 9309, [ ~( member( X, b ) ), member( X, a ) ] )
% 3.49/3.85 .
% 3.49/3.85 clause( 9310, [ ~( member( X, a ) ), member( X, b ) ] )
% 3.49/3.85 .
% 3.49/3.85 clause( 20107, [ ~( member( f1( b, a ), a ) ) ] )
% 3.49/3.85 .
% 3.49/3.85 clause( 20109, [] )
% 3.49/3.85 .
% 3.49/3.85
% 3.49/3.85
% 3.49/3.85 % SZS output end Refutation
% 3.49/3.85 found a proof!
% 3.49/3.85
% 3.49/3.85 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 3.49/3.85
% 3.49/3.85 initialclauses(
% 3.49/3.85 [ clause( 20111, [ ~( member( X, Y ) ), 'little_set'( X ) ] )
% 3.49/3.85 , clause( 20112, [ 'little_set'( f1( X, Y ) ), =( X, Y ) ] )
% 3.49/3.85 , clause( 20113, [ member( f1( X, Y ), X ), member( f1( X, Y ), Y ), =( X,
% 3.49/3.85 Y ) ] )
% 3.49/3.85 , clause( 20114, [ ~( member( f1( X, Y ), X ) ), ~( member( f1( X, Y ), Y )
% 3.49/3.85 ), =( X, Y ) ] )
% 3.49/3.85 , clause( 20115, [ ~( member( X, 'non_ordered_pair'( Y, Z ) ) ), =( X, Y )
% 3.49/3.85 , =( X, Z ) ] )
% 3.49/3.85 , clause( 20116, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'(
% 3.49/3.85 X ) ), ~( =( X, Y ) ) ] )
% 3.49/3.85 , clause( 20117, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'(
% 3.49/3.85 X ) ), ~( =( X, Z ) ) ] )
% 3.49/3.85 , clause( 20118, [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ] )
% 3.49/3.85 , clause( 20119, [ =( 'singleton_set'( X ), 'non_ordered_pair'( X, X ) ) ]
% 3.49/3.85 )
% 3.49/3.85 , clause( 20120, [ =( 'ordered_pair'( X, Y ), 'non_ordered_pair'(
% 3.49/3.85 'singleton_set'( X ), 'non_ordered_pair'( X, Y ) ) ) ] )
% 3.49/3.85 , clause( 20121, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f2( X
% 3.49/3.85 ) ) ] )
% 3.49/3.85 , clause( 20122, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f3( X
% 3.49/3.85 ) ) ] )
% 3.49/3.85 , clause( 20123, [ ~( 'ordered_pair_predicate'( X ) ), =( X, 'ordered_pair'(
% 3.49/3.85 f2( X ), f3( X ) ) ) ] )
% 3.49/3.85 , clause( 20124, [ 'ordered_pair_predicate'( X ), ~( 'little_set'( Y ) ),
% 3.49/3.85 ~( 'little_set'( Z ) ), ~( =( X, 'ordered_pair'( Y, Z ) ) ) ] )
% 3.49/3.85 , clause( 20125, [ ~( member( X, first( Y ) ) ), 'little_set'( f4( X, Y ) )
% 3.49/3.85 ] )
% 3.49/3.85 , clause( 20126, [ ~( member( X, first( Y ) ) ), 'little_set'( f5( X, Y ) )
% 3.49/3.85 ] )
% 3.49/3.85 , clause( 20127, [ ~( member( X, first( Y ) ) ), =( Y, 'ordered_pair'( f4(
% 3.49/3.85 X, Y ), f5( X, Y ) ) ) ] )
% 3.49/3.85 , clause( 20128, [ ~( member( X, first( Y ) ) ), member( X, f4( X, Y ) ) ]
% 3.49/3.85 )
% 3.49/3.85 , clause( 20129, [ member( X, first( Y ) ), ~( 'little_set'( Z ) ), ~(
% 3.49/3.85 'little_set'( T ) ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, Z
% 3.49/3.85 ) ) ] )
% 3.49/3.85 , clause( 20130, [ ~( member( X, second( Y ) ) ), 'little_set'( f6( X, Y )
% 3.49/3.85 ) ] )
% 3.49/3.85 , clause( 20131, [ ~( member( X, second( Y ) ) ), 'little_set'( f7( X, Y )
% 3.49/3.85 ) ] )
% 3.49/3.85 , clause( 20132, [ ~( member( X, second( Y ) ) ), =( Y, 'ordered_pair'( f6(
% 3.49/3.85 X, Y ), f7( X, Y ) ) ) ] )
% 3.49/3.85 , clause( 20133, [ ~( member( X, second( Y ) ) ), member( X, f7( X, Y ) ) ]
% 3.49/3.85 )
% 3.49/3.85 , clause( 20134, [ member( X, second( Y ) ), ~( 'little_set'( Z ) ), ~(
% 3.49/3.85 'little_set'( T ) ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, T
% 3.49/3.85 ) ) ] )
% 3.49/3.85 , clause( 20135, [ ~( member( X, estin ) ), 'ordered_pair_predicate'( X ) ]
% 3.49/3.85 )
% 3.49/3.85 , clause( 20136, [ ~( member( X, estin ) ), member( first( X ), second( X )
% 3.49/3.85 ) ] )
% 3.49/3.85 , clause( 20137, [ member( X, estin ), ~( 'little_set'( X ) ), ~(
% 3.49/3.85 'ordered_pair_predicate'( X ) ), ~( member( first( X ), second( X ) ) ) ]
% 3.49/3.85 )
% 3.49/3.85 , clause( 20138, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 3.49/3.85 )
% 3.49/3.85 , clause( 20139, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 3.49/3.85 )
% 3.49/3.85 , clause( 20140, [ member( X, intersection( Y, Z ) ), ~( member( X, Y ) ),
% 3.49/3.85 ~( member( X, Z ) ) ] )
% 3.49/3.85 , clause( 20141, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 3.49/3.85 )
% 3.49/3.85 , clause( 20142, [ member( X, complement( Y ) ), ~( 'little_set'( X ) ),
% 3.49/3.85 member( X, Y ) ] )
% 3.49/3.85 , clause( 20143, [ =( union( X, Y ), complement( intersection( complement(
% 3.49/3.85 X ), complement( Y ) ) ) ) ] )
% 3.49/3.85 , clause( 20144, [ ~( member( X, 'domain_of'( Y ) ) ),
% 3.49/3.85 'ordered_pair_predicate'( f8( X, Y ) ) ] )
% 3.49/3.85 , clause( 20145, [ ~( member( X, 'domain_of'( Y ) ) ), member( f8( X, Y ),
% 3.49/3.85 Y ) ] )
% 3.49/3.85 , clause( 20146, [ ~( member( X, 'domain_of'( Y ) ) ), =( X, first( f8( X,
% 3.49/3.85 Y ) ) ) ] )
% 3.49/3.85 , clause( 20147, [ member( X, 'domain_of'( Y ) ), ~( 'little_set'( X ) ),
% 3.49/3.85 ~( 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, first(
% 3.49/3.85 Z ) ) ) ] )
% 3.49/3.85 , clause( 20148, [ ~( member( X, 'cross_product'( Y, Z ) ) ),
% 3.49/3.85 'ordered_pair_predicate'( X ) ] )
% 3.49/3.85 , clause( 20149, [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( first(
% 3.49/3.85 X ), Y ) ] )
% 3.49/3.85 , clause( 20150, [ ~( member( X, 'cross_product'( Y, Z ) ) ), member(
% 3.49/3.85 second( X ), Z ) ] )
% 3.49/3.85 , clause( 20151, [ member( X, 'cross_product'( Y, Z ) ), ~( 'little_set'( X
% 3.49/3.85 ) ), ~( 'ordered_pair_predicate'( X ) ), ~( member( first( X ), Y ) ),
% 3.49/3.85 ~( member( second( X ), Z ) ) ] )
% 3.49/3.85 , clause( 20152, [ ~( member( X, converse( Y ) ) ),
% 3.49/3.85 'ordered_pair_predicate'( X ) ] )
% 3.49/3.85 , clause( 20153, [ ~( member( X, converse( Y ) ) ), member( 'ordered_pair'(
% 3.49/3.85 second( X ), first( X ) ), Y ) ] )
% 3.49/3.85 , clause( 20154, [ member( X, converse( Y ) ), ~( 'little_set'( X ) ), ~(
% 3.49/3.85 'ordered_pair_predicate'( X ) ), ~( member( 'ordered_pair'( second( X ),
% 3.49/3.85 first( X ) ), Y ) ) ] )
% 3.49/3.85 , clause( 20155, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f9(
% 3.49/3.85 X, Y ) ) ] )
% 3.49/3.85 , clause( 20156, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f10(
% 3.49/3.85 X, Y ) ) ] )
% 3.49/3.85 , clause( 20157, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f11(
% 3.49/3.85 X, Y ) ) ] )
% 3.49/3.85 , clause( 20158, [ ~( member( X, 'rotate_right'( Y ) ) ), =( X,
% 3.49/3.85 'ordered_pair'( f9( X, Y ), 'ordered_pair'( f10( X, Y ), f11( X, Y ) ) )
% 3.49/3.85 ) ] )
% 3.49/3.85 , clause( 20159, [ ~( member( X, 'rotate_right'( Y ) ) ), member(
% 3.49/3.85 'ordered_pair'( f10( X, Y ), 'ordered_pair'( f11( X, Y ), f9( X, Y ) ) )
% 3.49/3.85 , Y ) ] )
% 3.49/3.85 , clause( 20160, [ member( X, 'rotate_right'( Y ) ), ~( 'little_set'( X ) )
% 3.49/3.85 , ~( 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) )
% 3.49/3.85 , ~( =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 3.49/3.85 'ordered_pair'( T, 'ordered_pair'( U, Z ) ), Y ) ) ] )
% 3.49/3.85 , clause( 20161, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'(
% 3.49/3.85 f12( X, Y ) ) ] )
% 3.49/3.85 , clause( 20162, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'(
% 3.49/3.85 f13( X, Y ) ) ] )
% 3.49/3.85 , clause( 20163, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'(
% 3.49/3.85 f14( X, Y ) ) ] )
% 3.49/3.85 , clause( 20164, [ ~( member( X, 'flip_range_of'( Y ) ) ), =( X,
% 3.49/3.85 'ordered_pair'( f12( X, Y ), 'ordered_pair'( f13( X, Y ), f14( X, Y ) ) )
% 3.49/3.85 ) ] )
% 3.49/3.85 , clause( 20165, [ ~( member( X, 'flip_range_of'( Y ) ) ), member(
% 3.49/3.85 'ordered_pair'( f12( X, Y ), 'ordered_pair'( f14( X, Y ), f13( X, Y ) ) )
% 3.49/3.85 , Y ) ] )
% 3.49/3.85 , clause( 20166, [ member( X, 'flip_range_of'( Y ) ), ~( 'little_set'( X )
% 3.49/3.85 ), ~( 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U )
% 3.49/3.85 ), ~( =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 3.49/3.85 'ordered_pair'( Z, 'ordered_pair'( U, T ) ), Y ) ) ] )
% 3.49/3.85 , clause( 20167, [ =( successor( X ), union( X, 'singleton_set'( X ) ) ) ]
% 3.49/3.85 )
% 3.49/3.85 , clause( 20168, [ ~( member( X, 'empty_set' ) ) ] )
% 3.49/3.85 , clause( 20169, [ member( X, 'universal_set' ), ~( 'little_set'( X ) ) ]
% 3.49/3.85 )
% 3.49/3.85 , clause( 20170, [ 'little_set'( infinity ) ] )
% 3.49/3.85 , clause( 20171, [ member( 'empty_set', infinity ) ] )
% 3.49/3.85 , clause( 20172, [ ~( member( X, infinity ) ), member( successor( X ),
% 3.49/3.85 infinity ) ] )
% 3.49/3.85 , clause( 20173, [ ~( member( X, sigma( Y ) ) ), member( f16( X, Y ), Y ) ]
% 3.49/3.85 )
% 3.49/3.85 , clause( 20174, [ ~( member( X, sigma( Y ) ) ), member( X, f16( X, Y ) ) ]
% 3.49/3.85 )
% 3.49/3.85 , clause( 20175, [ member( X, sigma( Y ) ), ~( member( Z, Y ) ), ~( member(
% 3.49/3.85 X, Z ) ) ] )
% 3.49/3.85 , clause( 20176, [ ~( 'little_set'( X ) ), 'little_set'( sigma( X ) ) ] )
% 3.49/3.85 , clause( 20177, [ ~( subset( X, Y ) ), ~( member( Z, X ) ), member( Z, Y )
% 3.49/3.85 ] )
% 3.49/3.85 , clause( 20178, [ subset( X, Y ), member( f17( X, Y ), X ) ] )
% 3.49/3.85 , clause( 20179, [ subset( X, Y ), ~( member( f17( X, Y ), Y ) ) ] )
% 3.49/3.85 , clause( 20180, [ ~( 'proper_subset'( X, Y ) ), subset( X, Y ) ] )
% 3.49/3.85 , clause( 20181, [ ~( 'proper_subset'( X, Y ) ), ~( =( X, Y ) ) ] )
% 3.49/3.85 , clause( 20182, [ 'proper_subset'( X, Y ), ~( subset( X, Y ) ), =( X, Y )
% 3.49/3.85 ] )
% 3.49/3.85 , clause( 20183, [ ~( member( X, powerset( Y ) ) ), subset( X, Y ) ] )
% 3.49/3.85 , clause( 20184, [ member( X, powerset( Y ) ), ~( 'little_set'( X ) ), ~(
% 3.49/3.85 subset( X, Y ) ) ] )
% 3.49/3.85 , clause( 20185, [ ~( 'little_set'( X ) ), 'little_set'( powerset( X ) ) ]
% 3.49/3.85 )
% 3.49/3.85 , clause( 20186, [ ~( relation( X ) ), ~( member( Y, X ) ),
% 3.49/3.85 'ordered_pair_predicate'( Y ) ] )
% 3.49/3.85 , clause( 20187, [ relation( X ), member( f18( X ), X ) ] )
% 3.49/3.85 , clause( 20188, [ relation( X ), ~( 'ordered_pair_predicate'( f18( X ) ) )
% 3.49/3.85 ] )
% 3.49/3.85 , clause( 20189, [ ~( 'single_valued_set'( X ) ), ~( 'little_set'( Y ) ),
% 3.49/3.85 ~( 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( member( 'ordered_pair'(
% 3.49/3.85 Y, Z ), X ) ), ~( member( 'ordered_pair'( Y, T ), X ) ), =( Z, T ) ] )
% 3.49/3.85 , clause( 20190, [ 'single_valued_set'( X ), 'little_set'( f19( X ) ) ] )
% 3.49/3.85 , clause( 20191, [ 'single_valued_set'( X ), 'little_set'( f20( X ) ) ] )
% 3.49/3.85 , clause( 20192, [ 'single_valued_set'( X ), 'little_set'( f21( X ) ) ] )
% 3.49/3.85 , clause( 20193, [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X
% 3.49/3.85 ), f20( X ) ), X ) ] )
% 3.49/3.85 , clause( 20194, [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X
% 3.49/3.85 ), f21( X ) ), X ) ] )
% 3.49/3.85 , clause( 20195, [ 'single_valued_set'( X ), ~( =( f20( X ), f21( X ) ) ) ]
% 3.49/3.85 )
% 3.49/3.85 , clause( 20196, [ ~( function( X ) ), relation( X ) ] )
% 3.49/3.85 , clause( 20197, [ ~( function( X ) ), 'single_valued_set'( X ) ] )
% 3.49/3.85 , clause( 20198, [ function( X ), ~( relation( X ) ), ~(
% 3.49/3.85 'single_valued_set'( X ) ) ] )
% 3.49/3.85 , clause( 20199, [ ~( member( X, image( Y, Z ) ) ),
% 3.49/3.85 'ordered_pair_predicate'( f22( X, Y, Z ) ) ] )
% 3.49/3.85 , clause( 20200, [ ~( member( X, image( Y, Z ) ) ), member( f22( X, Y, Z )
% 3.49/3.85 , Z ) ] )
% 3.49/3.85 , clause( 20201, [ ~( member( X, image( Y, Z ) ) ), member( first( f22( X,
% 3.49/3.85 Y, Z ) ), Y ) ] )
% 3.49/3.85 , clause( 20202, [ ~( member( X, image( Y, Z ) ) ), =( second( f22( X, Y, Z
% 3.49/3.85 ) ), X ) ] )
% 3.49/3.85 , clause( 20203, [ member( X, image( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 3.49/3.85 'ordered_pair_predicate'( T ) ), ~( member( T, Z ) ), ~( member( first( T
% 3.49/3.85 ), Y ) ), ~( =( second( T ), X ) ) ] )
% 3.49/3.85 , clause( 20204, [ ~( 'little_set'( X ) ), ~( function( Y ) ), 'little_set'(
% 3.49/3.85 image( X, Y ) ) ] )
% 3.49/3.85 , clause( 20205, [ ~( disjoint( X, Y ) ), ~( member( Z, X ) ), ~( member( Z
% 3.49/3.85 , Y ) ) ] )
% 3.49/3.85 , clause( 20206, [ disjoint( X, Y ), member( f23( X, Y ), X ) ] )
% 3.49/3.85 , clause( 20207, [ disjoint( X, Y ), member( f23( X, Y ), Y ) ] )
% 3.49/3.85 , clause( 20208, [ =( X, 'empty_set' ), member( f24( X ), X ) ] )
% 3.49/3.85 , clause( 20209, [ =( X, 'empty_set' ), disjoint( f24( X ), X ) ] )
% 3.49/3.85 , clause( 20210, [ function( f25 ) ] )
% 3.49/3.85 , clause( 20211, [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( f26(
% 3.49/3.85 X ), X ) ] )
% 3.49/3.85 , clause( 20212, [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member(
% 3.49/3.85 'ordered_pair'( X, f26( X ) ), f25 ) ] )
% 3.49/3.85 , clause( 20213, [ ~( member( X, 'range_of'( Y ) ) ),
% 3.49/3.85 'ordered_pair_predicate'( f27( X, Y ) ) ] )
% 3.49/3.85 , clause( 20214, [ ~( member( X, 'range_of'( Y ) ) ), member( f27( X, Y ),
% 3.49/3.85 Y ) ] )
% 3.49/3.85 , clause( 20215, [ ~( member( X, 'range_of'( Y ) ) ), =( X, second( f27( X
% 3.49/3.85 , Y ) ) ) ] )
% 3.49/3.85 , clause( 20216, [ member( X, 'range_of'( Y ) ), ~( 'little_set'( X ) ),
% 3.49/3.85 ~( 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, second(
% 3.49/3.85 Z ) ) ) ] )
% 3.49/3.85 , clause( 20217, [ ~( member( X, 'identity_relation' ) ),
% 3.49/3.85 'ordered_pair_predicate'( X ) ] )
% 3.49/3.85 , clause( 20218, [ ~( member( X, 'identity_relation' ) ), =( first( X ),
% 3.49/3.85 second( X ) ) ] )
% 3.49/3.85 , clause( 20219, [ member( X, 'identity_relation' ), ~( 'little_set'( X ) )
% 3.49/3.85 , ~( 'ordered_pair_predicate'( X ) ), ~( =( first( X ), second( X ) ) ) ]
% 3.49/3.85 )
% 3.49/3.85 , clause( 20220, [ =( restrict( X, Y ), intersection( X, 'cross_product'( Y
% 3.49/3.85 , 'universal_set' ) ) ) ] )
% 3.49/3.85 , clause( 20221, [ ~( 'one_to_one_function'( X ) ), function( X ) ] )
% 3.49/3.85 , clause( 20222, [ ~( 'one_to_one_function'( X ) ), function( converse( X )
% 3.49/3.85 ) ] )
% 3.49/3.85 , clause( 20223, [ 'one_to_one_function'( X ), ~( function( X ) ), ~(
% 3.49/3.85 function( converse( X ) ) ) ] )
% 3.49/3.85 , clause( 20224, [ ~( member( X, apply( Y, Z ) ) ),
% 3.49/3.85 'ordered_pair_predicate'( f28( X, Y, Z ) ) ] )
% 3.49/3.85 , clause( 20225, [ ~( member( X, apply( Y, Z ) ) ), member( f28( X, Y, Z )
% 3.49/3.85 , Y ) ] )
% 3.49/3.85 , clause( 20226, [ ~( member( X, apply( Y, Z ) ) ), =( first( f28( X, Y, Z
% 3.49/3.85 ) ), Z ) ] )
% 3.49/3.85 , clause( 20227, [ ~( member( X, apply( Y, Z ) ) ), member( X, second( f28(
% 3.49/3.85 X, Y, Z ) ) ) ] )
% 3.49/3.85 , clause( 20228, [ member( X, apply( Y, Z ) ), ~( 'ordered_pair_predicate'(
% 3.49/3.85 T ) ), ~( member( T, Y ) ), ~( =( first( T ), Z ) ), ~( member( X, second(
% 3.49/3.85 T ) ) ) ] )
% 3.49/3.85 , clause( 20229, [ =( 'apply_to_two_arguments'( X, Y, Z ), apply( X,
% 3.49/3.85 'ordered_pair'( Y, Z ) ) ) ] )
% 3.49/3.85 , clause( 20230, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 3.49/3.85 , clause( 20231, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 3.49/3.85 , clause( 20232, [ ~( maps( X, Y, Z ) ), subset( 'range_of'( X ), Z ) ] )
% 3.49/3.85 , clause( 20233, [ maps( X, Y, Z ), ~( function( X ) ), ~( =( 'domain_of'(
% 3.49/3.85 X ), Y ) ), ~( subset( 'range_of'( X ), Z ) ) ] )
% 3.49/3.85 , clause( 20234, [ ~( closed( X, Y ) ), 'little_set'( X ) ] )
% 3.49/3.85 , clause( 20235, [ ~( closed( X, Y ) ), 'little_set'( Y )Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------