TSTP Solution File: SET025-4 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET025-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n009.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 22:45:41 EDT 2022
% Result : Unsatisfiable 0.69s 1.12s
% Output : Refutation 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET025-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Mon Jul 11 00:16:07 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.69/1.10 *** allocated 10000 integers for termspace/termends
% 0.69/1.10 *** allocated 10000 integers for clauses
% 0.69/1.10 *** allocated 10000 integers for justifications
% 0.69/1.10 Bliksem 1.12
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 Automatic Strategy Selection
% 0.69/1.10
% 0.69/1.10 Clauses:
% 0.69/1.10 [
% 0.69/1.10 [ ~( member( X, Y ) ), 'little_set'( X ) ],
% 0.69/1.10 [ 'little_set'( f1( X, Y ) ), =( X, Y ) ],
% 0.69/1.10 [ member( f1( X, Y ), X ), member( f1( X, Y ), Y ), =( X, Y ) ],
% 0.69/1.10 [ ~( member( f1( X, Y ), X ) ), ~( member( f1( X, Y ), Y ) ), =( X, Y )
% 0.69/1.10 ],
% 0.69/1.10 [ ~( member( X, 'non_ordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.69/1.10 =( X, Y ) ) ],
% 0.69/1.10 [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.69/1.10 =( X, Z ) ) ],
% 0.69/1.10 [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ],
% 0.69/1.10 [ =( 'singleton_set'( X ), 'non_ordered_pair'( X, X ) ) ],
% 0.69/1.10 [ =( 'ordered_pair'( X, Y ), 'non_ordered_pair'( 'singleton_set'( X ),
% 0.69/1.10 'non_ordered_pair'( X, Y ) ) ) ],
% 0.69/1.10 [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f2( X ) ) ],
% 0.69/1.10 [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f3( X ) ) ],
% 0.69/1.10 [ ~( 'ordered_pair_predicate'( X ) ), =( X, 'ordered_pair'( f2( X ), f3(
% 0.69/1.10 X ) ) ) ],
% 0.69/1.10 [ 'ordered_pair_predicate'( X ), ~( 'little_set'( Y ) ), ~( 'little_set'(
% 0.69/1.10 Z ) ), ~( =( X, 'ordered_pair'( Y, Z ) ) ) ],
% 0.69/1.10 [ ~( member( X, first( Y ) ) ), 'little_set'( f4( X, Y ) ) ],
% 0.69/1.10 [ ~( member( X, first( Y ) ) ), 'little_set'( f5( X, Y ) ) ],
% 0.69/1.10 [ ~( member( X, first( Y ) ) ), =( Y, 'ordered_pair'( f4( X, Y ), f5( X
% 0.69/1.10 , Y ) ) ) ],
% 0.69/1.10 [ ~( member( X, first( Y ) ) ), member( X, f4( X, Y ) ) ],
% 0.69/1.10 [ member( X, first( Y ) ), ~( 'little_set'( Z ) ), ~( 'little_set'( T )
% 0.69/1.10 ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, Z ) ) ],
% 0.69/1.10 [ ~( member( X, second( Y ) ) ), 'little_set'( f6( X, Y ) ) ],
% 0.69/1.10 [ ~( member( X, second( Y ) ) ), 'little_set'( f7( X, Y ) ) ],
% 0.69/1.10 [ ~( member( X, second( Y ) ) ), =( Y, 'ordered_pair'( f6( X, Y ), f7( X
% 0.69/1.10 , Y ) ) ) ],
% 0.69/1.10 [ ~( member( X, second( Y ) ) ), member( X, f7( X, Y ) ) ],
% 0.69/1.10 [ member( X, second( Y ) ), ~( 'little_set'( Z ) ), ~( 'little_set'( T )
% 0.69/1.10 ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, T ) ) ],
% 0.69/1.10 [ ~( member( X, estin ) ), 'ordered_pair_predicate'( X ) ],
% 0.69/1.10 [ ~( member( X, estin ) ), member( first( X ), second( X ) ) ],
% 0.69/1.10 [ member( X, estin ), ~( 'little_set'( X ) ), ~(
% 0.69/1.10 'ordered_pair_predicate'( X ) ), ~( member( first( X ), second( X ) ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.69/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.69/1.10 [ member( X, intersection( Y, Z ) ), ~( member( X, Y ) ), ~( member( X,
% 0.69/1.10 Z ) ) ],
% 0.69/1.10 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.69/1.10 [ member( X, complement( Y ) ), ~( 'little_set'( X ) ), member( X, Y ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ =( union( X, Y ), complement( intersection( complement( X ),
% 0.69/1.10 complement( Y ) ) ) ) ],
% 0.69/1.10 [ ~( member( X, 'domain_of'( Y ) ) ), 'ordered_pair_predicate'( f8( X, Y
% 0.69/1.10 ) ) ],
% 0.69/1.10 [ ~( member( X, 'domain_of'( Y ) ) ), member( f8( X, Y ), Y ) ],
% 0.69/1.10 [ ~( member( X, 'domain_of'( Y ) ) ), =( X, first( f8( X, Y ) ) ) ],
% 0.69/1.10 [ member( X, 'domain_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.69/1.10 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, first( Z )
% 0.69/1.10 ) ) ],
% 0.69/1.10 [ ~( member( X, 'cross_product'( Y, Z ) ) ), 'ordered_pair_predicate'( X
% 0.69/1.10 ) ],
% 0.69/1.10 [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( first( X ), Y ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( second( X ), Z ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ member( X, 'cross_product'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.69/1.10 'ordered_pair_predicate'( X ) ), ~( member( first( X ), Y ) ), ~( member(
% 0.69/1.10 second( X ), Z ) ) ],
% 0.69/1.10 [ ~( member( X, converse( Y ) ) ), 'ordered_pair_predicate'( X ) ],
% 0.69/1.10 [ ~( member( X, converse( Y ) ) ), member( 'ordered_pair'( second( X ),
% 0.69/1.10 first( X ) ), Y ) ],
% 0.69/1.10 [ member( X, converse( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.69/1.10 'ordered_pair_predicate'( X ) ), ~( member( 'ordered_pair'( second( X ),
% 0.69/1.10 first( X ) ), Y ) ) ],
% 0.69/1.10 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f9( X, Y ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f10( X, Y ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f11( X, Y ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( member( X, 'rotate_right'( Y ) ) ), =( X, 'ordered_pair'( f9( X, Y
% 0.69/1.10 ), 'ordered_pair'( f10( X, Y ), f11( X, Y ) ) ) ) ],
% 0.69/1.10 [ ~( member( X, 'rotate_right'( Y ) ) ), member( 'ordered_pair'( f10( X
% 0.69/1.10 , Y ), 'ordered_pair'( f11( X, Y ), f9( X, Y ) ) ), Y ) ],
% 0.69/1.10 [ member( X, 'rotate_right'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.69/1.10 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) ), ~(
% 0.69/1.10 =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 0.69/1.10 'ordered_pair'( T, 'ordered_pair'( U, Z ) ), Y ) ) ],
% 0.69/1.10 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f12( X, Y ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f13( X, Y ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f14( X, Y ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( member( X, 'flip_range_of'( Y ) ) ), =( X, 'ordered_pair'( f12( X,
% 0.69/1.10 Y ), 'ordered_pair'( f13( X, Y ), f14( X, Y ) ) ) ) ],
% 0.69/1.10 [ ~( member( X, 'flip_range_of'( Y ) ) ), member( 'ordered_pair'( f12( X
% 0.69/1.10 , Y ), 'ordered_pair'( f14( X, Y ), f13( X, Y ) ) ), Y ) ],
% 0.69/1.10 [ member( X, 'flip_range_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.69/1.10 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) ), ~(
% 0.69/1.10 =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 0.69/1.10 'ordered_pair'( Z, 'ordered_pair'( U, T ) ), Y ) ) ],
% 0.69/1.10 [ =( successor( X ), union( X, 'singleton_set'( X ) ) ) ],
% 0.69/1.10 [ ~( member( X, 'empty_set' ) ) ],
% 0.69/1.10 [ member( X, 'universal_set' ), ~( 'little_set'( X ) ) ],
% 0.69/1.10 [ 'little_set'( infinity ) ],
% 0.69/1.10 [ member( 'empty_set', infinity ) ],
% 0.69/1.10 [ ~( member( X, infinity ) ), member( successor( X ), infinity ) ],
% 0.69/1.10 [ ~( member( X, sigma( Y ) ) ), member( f16( X, Y ), Y ) ],
% 0.69/1.10 [ ~( member( X, sigma( Y ) ) ), member( X, f16( X, Y ) ) ],
% 0.69/1.10 [ member( X, sigma( Y ) ), ~( member( Z, Y ) ), ~( member( X, Z ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( 'little_set'( X ) ), 'little_set'( sigma( X ) ) ],
% 0.69/1.10 [ ~( subset( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.69/1.10 [ subset( X, Y ), member( f17( X, Y ), X ) ],
% 0.69/1.10 [ subset( X, Y ), ~( member( f17( X, Y ), Y ) ) ],
% 0.69/1.10 [ ~( 'proper_subset'( X, Y ) ), subset( X, Y ) ],
% 0.69/1.10 [ ~( 'proper_subset'( X, Y ) ), ~( =( X, Y ) ) ],
% 0.69/1.10 [ 'proper_subset'( X, Y ), ~( subset( X, Y ) ), =( X, Y ) ],
% 0.69/1.10 [ ~( member( X, powerset( Y ) ) ), subset( X, Y ) ],
% 0.69/1.10 [ member( X, powerset( Y ) ), ~( 'little_set'( X ) ), ~( subset( X, Y )
% 0.69/1.10 ) ],
% 0.69/1.10 [ ~( 'little_set'( X ) ), 'little_set'( powerset( X ) ) ],
% 0.69/1.10 [ ~( relation( X ) ), ~( member( Y, X ) ), 'ordered_pair_predicate'( Y )
% 0.69/1.10 ],
% 0.69/1.10 [ relation( X ), member( f18( X ), X ) ],
% 0.69/1.10 [ relation( X ), ~( 'ordered_pair_predicate'( f18( X ) ) ) ],
% 0.69/1.10 [ ~( 'single_valued_set'( X ) ), ~( 'little_set'( Y ) ), ~( 'little_set'(
% 0.69/1.10 Z ) ), ~( 'little_set'( T ) ), ~( member( 'ordered_pair'( Y, Z ), X ) ),
% 0.69/1.10 ~( member( 'ordered_pair'( Y, T ), X ) ), =( Z, T ) ],
% 0.69/1.10 [ 'single_valued_set'( X ), 'little_set'( f19( X ) ) ],
% 0.69/1.10 [ 'single_valued_set'( X ), 'little_set'( f20( X ) ) ],
% 0.69/1.10 [ 'single_valued_set'( X ), 'little_set'( f21( X ) ) ],
% 0.69/1.10 [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X ), f20( X ) )
% 0.69/1.10 , X ) ],
% 0.69/1.10 [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X ), f21( X ) )
% 0.69/1.10 , X ) ],
% 0.69/1.10 [ 'single_valued_set'( X ), ~( =( f20( X ), f21( X ) ) ) ],
% 0.69/1.10 [ ~( function( X ) ), relation( X ) ],
% 0.69/1.10 [ ~( function( X ) ), 'single_valued_set'( X ) ],
% 0.69/1.10 [ function( X ), ~( relation( X ) ), ~( 'single_valued_set'( X ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( member( X, image( Y, Z ) ) ), 'ordered_pair_predicate'( f22( X, Y,
% 0.69/1.10 Z ) ) ],
% 0.69/1.10 [ ~( member( X, image( Y, Z ) ) ), member( f22( X, Y, Z ), Z ) ],
% 0.69/1.10 [ ~( member( X, image( Y, Z ) ) ), member( first( f22( X, Y, Z ) ), Y )
% 0.69/1.10 ],
% 0.69/1.10 [ ~( member( X, image( Y, Z ) ) ), =( second( f22( X, Y, Z ) ), X ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ member( X, image( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.69/1.10 'ordered_pair_predicate'( T ) ), ~( member( T, Z ) ), ~( member( first( T
% 0.69/1.10 ), Y ) ), ~( =( second( T ), X ) ) ],
% 0.69/1.10 [ ~( 'little_set'( X ) ), ~( function( Y ) ), 'little_set'( image( X, Y
% 0.69/1.10 ) ) ],
% 0.69/1.10 [ ~( disjoint( X, Y ) ), ~( member( Z, X ) ), ~( member( Z, Y ) ) ],
% 0.69/1.10 [ disjoint( X, Y ), member( f23( X, Y ), X ) ],
% 0.69/1.10 [ disjoint( X, Y ), member( f23( X, Y ), Y ) ],
% 0.69/1.10 [ =( X, 'empty_set' ), member( f24( X ), X ) ],
% 0.69/1.10 [ =( X, 'empty_set' ), disjoint( f24( X ), X ) ],
% 0.69/1.10 [ function( f25 ) ],
% 0.69/1.10 [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( f26( X ), X ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( 'ordered_pair'( X
% 0.69/1.10 , f26( X ) ), f25 ) ],
% 0.69/1.10 [ ~( member( X, 'range_of'( Y ) ) ), 'ordered_pair_predicate'( f27( X, Y
% 0.69/1.10 ) ) ],
% 0.69/1.10 [ ~( member( X, 'range_of'( Y ) ) ), member( f27( X, Y ), Y ) ],
% 0.69/1.10 [ ~( member( X, 'range_of'( Y ) ) ), =( X, second( f27( X, Y ) ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ member( X, 'range_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.69/1.10 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, second( Z
% 0.69/1.10 ) ) ) ],
% 0.69/1.10 [ ~( member( X, 'identity_relation' ) ), 'ordered_pair_predicate'( X ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( member( X, 'identity_relation' ) ), =( first( X ), second( X ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ member( X, 'identity_relation' ), ~( 'little_set'( X ) ), ~(
% 0.69/1.10 'ordered_pair_predicate'( X ) ), ~( =( first( X ), second( X ) ) ) ],
% 0.69/1.10 [ =( restrict( X, Y ), intersection( X, 'cross_product'( Y,
% 0.69/1.10 'universal_set' ) ) ) ],
% 0.69/1.10 [ ~( 'one_to_one_function'( X ) ), function( X ) ],
% 0.69/1.10 [ ~( 'one_to_one_function'( X ) ), function( converse( X ) ) ],
% 0.69/1.10 [ 'one_to_one_function'( X ), ~( function( X ) ), ~( function( converse(
% 0.69/1.10 X ) ) ) ],
% 0.69/1.10 [ ~( member( X, apply( Y, Z ) ) ), 'ordered_pair_predicate'( f28( X, Y,
% 0.69/1.10 Z ) ) ],
% 0.69/1.10 [ ~( member( X, apply( Y, Z ) ) ), member( f28( X, Y, Z ), Y ) ],
% 0.69/1.10 [ ~( member( X, apply( Y, Z ) ) ), =( first( f28( X, Y, Z ) ), Z ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( member( X, apply( Y, Z ) ) ), member( X, second( f28( X, Y, Z ) ) )
% 0.69/1.10 ],
% 0.69/1.10 [ member( X, apply( Y, Z ) ), ~( 'ordered_pair_predicate'( T ) ), ~(
% 0.69/1.10 member( T, Y ) ), ~( =( first( T ), Z ) ), ~( member( X, second( T ) ) )
% 0.69/1.10 ],
% 0.69/1.10 [ =( 'apply_to_two_arguments'( X, Y, Z ), apply( X, 'ordered_pair'( Y, Z
% 0.69/1.10 ) ) ) ],
% 0.69/1.10 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.69/1.10 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 0.69/1.10 [ ~( maps( X, Y, Z ) ), subset( 'range_of'( X ), Z ) ],
% 0.69/1.10 [ maps( X, Y, Z ), ~( function( X ) ), ~( =( 'domain_of'( X ), Y ) ),
% 0.69/1.10 ~( subset( 'range_of'( X ), Z ) ) ],
% 0.69/1.10 [ ~( closed( X, Y ) ), 'little_set'( X ) ],
% 0.69/1.10 [ ~( closed( X, Y ) ), 'little_set'( Y ) ],
% 0.69/1.10 [ ~( closed( X, Y ) ), maps( Y, 'cross_product'( X, X ), X ) ],
% 0.69/1.10 [ closed( X, Y ), ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~(
% 0.69/1.10 maps( Y, 'cross_product'( X, X ), X ) ) ],
% 0.69/1.10 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f29( X, Y, Z ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f30( X, Y, Z ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f31( X, Y, Z ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( member( X, compose( Y, Z ) ) ), =( X, 'ordered_pair'( f29( X, Y, Z
% 0.69/1.10 ), f30( X, Y, Z ) ) ) ],
% 0.69/1.10 [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'( f29( X, Y,
% 0.69/1.10 Z ), f31( X, Y, Z ) ), Y ) ],
% 0.69/1.10 [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'( f31( X, Y,
% 0.69/1.10 Z ), f30( X, Y, Z ) ), Z ) ],
% 0.69/1.10 [ member( X, compose( Y, Z ) ), ~( 'little_set'( X ) ), ~( 'little_set'(
% 0.69/1.10 T ) ), ~( 'little_set'( U ) ), ~( 'little_set'( W ) ), ~( =( X,
% 0.69/1.10 'ordered_pair'( T, U ) ) ), ~( member( 'ordered_pair'( T, W ), Y ) ), ~(
% 0.69/1.10 member( 'ordered_pair'( W, U ), Z ) ) ],
% 0.69/1.10 [ ~( homomorphism( X, Y, Z, T, U ) ), closed( Y, Z ) ],
% 0.69/1.10 [ ~( homomorphism( X, Y, Z, T, U ) ), closed( T, U ) ],
% 0.69/1.10 [ ~( homomorphism( X, Y, Z, T, U ) ), maps( X, Y, T ) ],
% 0.69/1.10 [ ~( homomorphism( X, Y, Z, T, U ) ), ~( member( W, Y ) ), ~( member( V0
% 0.69/1.10 , Y ) ), =( apply( X, 'apply_to_two_arguments'( Z, W, V0 ) ),
% 0.69/1.10 'apply_to_two_arguments'( U, apply( X, W ), apply( X, V0 ) ) ) ],
% 0.69/1.10 [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.69/1.10 ), ~( maps( X, Y, T ) ), member( f32( X, Y, Z, T, U ), Y ) ],
% 0.69/1.10 [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.69/1.10 ), ~( maps( X, Y, T ) ), member( f33( X, Y, Z, T, U ), Y ) ],
% 0.69/1.10 [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.69/1.12 ), ~( maps( X, Y, T ) ), ~( =( apply( X, 'apply_to_two_arguments'( Z,
% 0.69/1.12 f32( X, Y, Z, T, U ), f33( X, Y, Z, T, U ) ) ), 'apply_to_two_arguments'(
% 0.69/1.12 U, apply( X, f32( X, Y, Z, T, U ) ), apply( X, f33( X, Y, Z, T, U ) ) ) )
% 0.69/1.12 ) ],
% 0.69/1.12 [ ~( 'little_set'( 'ordered_pair'( a, b ) ) ) ]
% 0.69/1.12 ] .
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12 percentage equality = 0.132022, percentage horn = 0.859155
% 0.69/1.12 This is a problem with some equality
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12 Options Used:
% 0.69/1.12
% 0.69/1.12 useres = 1
% 0.69/1.12 useparamod = 1
% 0.69/1.12 useeqrefl = 1
% 0.69/1.12 useeqfact = 1
% 0.69/1.12 usefactor = 1
% 0.69/1.12 usesimpsplitting = 0
% 0.69/1.12 usesimpdemod = 5
% 0.69/1.12 usesimpres = 3
% 0.69/1.12
% 0.69/1.12 resimpinuse = 1000
% 0.69/1.12 resimpclauses = 20000
% 0.69/1.12 substype = eqrewr
% 0.69/1.12 backwardsubs = 1
% 0.69/1.12 selectoldest = 5
% 0.69/1.12
% 0.69/1.12 litorderings [0] = split
% 0.69/1.12 litorderings [1] = extend the termordering, first sorting on arguments
% 0.69/1.12
% 0.69/1.12 termordering = kbo
% 0.69/1.12
% 0.69/1.12 litapriori = 0
% 0.69/1.12 termapriori = 1
% 0.69/1.12 litaposteriori = 0
% 0.69/1.12 termaposteriori = 0
% 0.69/1.12 demodaposteriori = 0
% 0.69/1.12 ordereqreflfact = 0
% 0.69/1.12
% 0.69/1.12 litselect = negord
% 0.69/1.12
% 0.69/1.12 maxweight = 15
% 0.69/1.12 maxdepth = 30000
% 0.69/1.12 maxlength = 115
% 0.69/1.12 maxnrvars = 195
% 0.69/1.12 excuselevel = 1
% 0.69/1.12 increasemaxweight = 1
% 0.69/1.12
% 0.69/1.12 maxselected = 10000000
% 0.69/1.12 maxnrclauses = 10000000
% 0.69/1.12
% 0.69/1.12 showgenerated = 0
% 0.69/1.12 showkept = 0
% 0.69/1.12 showselected = 0
% 0.69/1.12 showdeleted = 0
% 0.69/1.12 showresimp = 1
% 0.69/1.12 showstatus = 2000
% 0.69/1.12
% 0.69/1.12 prologoutput = 1
% 0.69/1.12 nrgoals = 5000000
% 0.69/1.12 totalproof = 1
% 0.69/1.12
% 0.69/1.12 Symbols occurring in the translation:
% 0.69/1.12
% 0.69/1.12 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.69/1.12 . [1, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.69/1.12 ! [4, 1] (w:0, o:32, a:1, s:1, b:0),
% 0.69/1.12 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.12 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.12 member [41, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.69/1.12 'little_set' [42, 1] (w:1, o:37, a:1, s:1, b:0),
% 0.69/1.12 f1 [43, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.69/1.12 'non_ordered_pair' [45, 2] (w:1, o:90, a:1, s:1, b:0),
% 0.69/1.12 'singleton_set' [46, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.69/1.12 'ordered_pair' [47, 2] (w:1, o:91, a:1, s:1, b:0),
% 0.69/1.12 'ordered_pair_predicate' [48, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.69/1.12 f2 [49, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.69/1.12 f3 [50, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.69/1.12 first [52, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.69/1.12 f4 [53, 2] (w:1, o:92, a:1, s:1, b:0),
% 0.69/1.12 f5 [54, 2] (w:1, o:93, a:1, s:1, b:0),
% 0.69/1.12 second [56, 1] (w:1, o:52, a:1, s:1, b:0),
% 0.69/1.12 f6 [57, 2] (w:1, o:94, a:1, s:1, b:0),
% 0.69/1.12 f7 [58, 2] (w:1, o:95, a:1, s:1, b:0),
% 0.69/1.12 estin [59, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.69/1.12 intersection [60, 2] (w:1, o:97, a:1, s:1, b:0),
% 0.69/1.12 complement [61, 1] (w:1, o:53, a:1, s:1, b:0),
% 0.69/1.12 union [62, 2] (w:1, o:98, a:1, s:1, b:0),
% 0.69/1.12 'domain_of' [63, 1] (w:1, o:55, a:1, s:1, b:0),
% 0.69/1.12 f8 [64, 2] (w:1, o:99, a:1, s:1, b:0),
% 0.69/1.12 'cross_product' [66, 2] (w:1, o:100, a:1, s:1, b:0),
% 0.69/1.12 converse [67, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.69/1.12 'rotate_right' [68, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.69/1.12 f9 [69, 2] (w:1, o:101, a:1, s:1, b:0),
% 0.69/1.12 f10 [70, 2] (w:1, o:102, a:1, s:1, b:0),
% 0.69/1.12 f11 [71, 2] (w:1, o:103, a:1, s:1, b:0),
% 0.69/1.12 'flip_range_of' [73, 1] (w:1, o:56, a:1, s:1, b:0),
% 0.69/1.12 f12 [74, 2] (w:1, o:104, a:1, s:1, b:0),
% 0.69/1.12 f13 [75, 2] (w:1, o:105, a:1, s:1, b:0),
% 0.69/1.12 f14 [76, 2] (w:1, o:106, a:1, s:1, b:0),
% 0.69/1.12 successor [77, 1] (w:1, o:57, a:1, s:1, b:0),
% 0.69/1.12 'empty_set' [78, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.69/1.12 'universal_set' [79, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.69/1.12 infinity [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.69/1.12 sigma [81, 1] (w:1, o:58, a:1, s:1, b:0),
% 0.69/1.12 f16 [82, 2] (w:1, o:107, a:1, s:1, b:0),
% 0.69/1.12 subset [83, 2] (w:1, o:109, a:1, s:1, b:0),
% 0.69/1.12 f17 [84, 2] (w:1, o:110, a:1, s:1, b:0),
% 0.69/1.12 'proper_subset' [85, 2] (w:1, o:111, a:1, s:1, b:0),
% 0.69/1.12 powerset [86, 1] (w:1, o:60, a:1, s:1, b:0),
% 0.69/1.12 relation [87, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.69/1.12 f18 [88, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.69/1.12 'single_valued_set' [89, 1] (w:1, o:61, a:1, s:1, b:0),
% 0.69/1.12 f19 [90, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.69/1.12 f20 [91, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.69/1.12 f21 [92, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.69/1.12 function [94, 1] (w:1, o:62, a:1, s:1, b:0),
% 0.69/1.12 image [95, 2] (w:1, o:96, a:1, s:1, b:0),
% 0.69/1.12 f22 [96, 3] (w:1, o:118, a:1, s:1, b:0),
% 0.69/1.12 disjoint [97, 2] (w:1, o:114, a:1, s:1, b:0),
% 0.69/1.12 f23 [98, 2] (w:1, o:115, a:1, s:1, b:0),
% 0.69/1.12 f24 [99, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.69/1.12 f25 [100, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.69/1.12 f26 [101, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.69/1.12 'range_of' [102, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.69/1.12 f27 [103, 2] (w:1, o:116, a:1, s:1, b:0),
% 0.69/1.12 'identity_relation' [104, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.69/1.12 restrict [105, 2] (w:1, o:108, a:1, s:1, b:0),
% 0.69/1.12 'one_to_one_function' [106, 1] (w:1, o:59, a:1, s:1, b:0),
% 0.69/1.12 apply [107, 2] (w:1, o:117, a:1, s:1, b:0),
% 0.69/1.12 f28 [108, 3] (w:1, o:119, a:1, s:1, b:0),
% 0.69/1.12 'apply_to_two_arguments' [109, 3] (w:1, o:120, a:1, s:1, b:0),
% 0.69/1.12 maps [110, 3] (w:1, o:121, a:1, s:1, b:0),
% 0.69/1.12 closed [112, 2] (w:1, o:112, a:1, s:1, b:0),
% 0.69/1.12 compose [114, 2] (w:1, o:113, a:1, s:1, b:0),
% 0.69/1.12 f29 [115, 3] (w:1, o:122, a:1, s:1, b:0),
% 0.69/1.12 f30 [116, 3] (w:1, o:123, a:1, s:1, b:0),
% 0.69/1.12 f31 [117, 3] (w:1, o:124, a:1, s:1, b:0),
% 0.69/1.12 homomorphism [123, 5] (w:1, o:125, a:1, s:1, b:0),
% 0.69/1.12 f32 [124, 5] (w:1, o:126, a:1, s:1, b:0),
% 0.69/1.12 f33 [125, 5] (w:1, o:127, a:1, s:1, b:0),
% 0.69/1.12 a [126, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.69/1.12 b [127, 0] (w:1, o:31, a:1, s:1, b:0).
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12 Starting Search:
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12 Bliksems!, er is een bewijs:
% 0.69/1.12 % SZS status Unsatisfiable
% 0.69/1.12 % SZS output start Refutation
% 0.69/1.12
% 0.69/1.12 clause( 7, [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ] )
% 0.69/1.12 .
% 0.69/1.12 clause( 9, [ =( 'non_ordered_pair'( 'singleton_set'( X ),
% 0.69/1.12 'non_ordered_pair'( X, Y ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.69/1.12 .
% 0.69/1.12 clause( 141, [ ~( 'little_set'( 'ordered_pair'( a, b ) ) ) ] )
% 0.69/1.12 .
% 0.69/1.12 clause( 774, [ 'little_set'( 'ordered_pair'( X, Y ) ) ] )
% 0.69/1.12 .
% 0.69/1.12 clause( 788, [] )
% 0.69/1.12 .
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12 % SZS output end Refutation
% 0.69/1.12 found a proof!
% 0.69/1.12
% 0.69/1.12 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.69/1.12
% 0.69/1.12 initialclauses(
% 0.69/1.12 [ clause( 790, [ ~( member( X, Y ) ), 'little_set'( X ) ] )
% 0.69/1.12 , clause( 791, [ 'little_set'( f1( X, Y ) ), =( X, Y ) ] )
% 0.69/1.12 , clause( 792, [ member( f1( X, Y ), X ), member( f1( X, Y ), Y ), =( X, Y
% 0.69/1.12 ) ] )
% 0.69/1.12 , clause( 793, [ ~( member( f1( X, Y ), X ) ), ~( member( f1( X, Y ), Y ) )
% 0.69/1.12 , =( X, Y ) ] )
% 0.69/1.12 , clause( 794, [ ~( member( X, 'non_ordered_pair'( Y, Z ) ) ), =( X, Y ),
% 0.69/1.12 =( X, Z ) ] )
% 0.69/1.12 , clause( 795, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'(
% 0.69/1.12 X ) ), ~( =( X, Y ) ) ] )
% 0.69/1.12 , clause( 796, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'(
% 0.69/1.12 X ) ), ~( =( X, Z ) ) ] )
% 0.69/1.12 , clause( 797, [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ] )
% 0.69/1.12 , clause( 798, [ =( 'singleton_set'( X ), 'non_ordered_pair'( X, X ) ) ] )
% 0.69/1.12 , clause( 799, [ =( 'ordered_pair'( X, Y ), 'non_ordered_pair'(
% 0.69/1.12 'singleton_set'( X ), 'non_ordered_pair'( X, Y ) ) ) ] )
% 0.69/1.12 , clause( 800, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f2( X )
% 0.69/1.12 ) ] )
% 0.69/1.12 , clause( 801, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f3( X )
% 0.69/1.12 ) ] )
% 0.69/1.12 , clause( 802, [ ~( 'ordered_pair_predicate'( X ) ), =( X, 'ordered_pair'(
% 0.69/1.12 f2( X ), f3( X ) ) ) ] )
% 0.69/1.12 , clause( 803, [ 'ordered_pair_predicate'( X ), ~( 'little_set'( Y ) ), ~(
% 0.69/1.12 'little_set'( Z ) ), ~( =( X, 'ordered_pair'( Y, Z ) ) ) ] )
% 0.69/1.12 , clause( 804, [ ~( member( X, first( Y ) ) ), 'little_set'( f4( X, Y ) ) ]
% 0.69/1.12 )
% 0.69/1.12 , clause( 805, [ ~( member( X, first( Y ) ) ), 'little_set'( f5( X, Y ) ) ]
% 0.69/1.12 )
% 0.69/1.12 , clause( 806, [ ~( member( X, first( Y ) ) ), =( Y, 'ordered_pair'( f4( X
% 0.69/1.12 , Y ), f5( X, Y ) ) ) ] )
% 0.69/1.12 , clause( 807, [ ~( member( X, first( Y ) ) ), member( X, f4( X, Y ) ) ] )
% 0.69/1.12 , clause( 808, [ member( X, first( Y ) ), ~( 'little_set'( Z ) ), ~(
% 0.69/1.12 'little_set'( T ) ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, Z
% 0.69/1.12 ) ) ] )
% 0.69/1.12 , clause( 809, [ ~( member( X, second( Y ) ) ), 'little_set'( f6( X, Y ) )
% 0.69/1.12 ] )
% 0.69/1.12 , clause( 810, [ ~( member( X, second( Y ) ) ), 'little_set'( f7( X, Y ) )
% 0.69/1.12 ] )
% 0.69/1.12 , clause( 811, [ ~( member( X, second( Y ) ) ), =( Y, 'ordered_pair'( f6( X
% 0.69/1.12 , Y ), f7( X, Y ) ) ) ] )
% 0.69/1.12 , clause( 812, [ ~( member( X, second( Y ) ) ), member( X, f7( X, Y ) ) ]
% 0.69/1.12 )
% 0.69/1.12 , clause( 813, [ member( X, second( Y ) ), ~( 'little_set'( Z ) ), ~(
% 0.69/1.12 'little_set'( T ) ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, T
% 0.69/1.12 ) ) ] )
% 0.69/1.12 , clause( 814, [ ~( member( X, estin ) ), 'ordered_pair_predicate'( X ) ]
% 0.69/1.12 )
% 0.69/1.12 , clause( 815, [ ~( member( X, estin ) ), member( first( X ), second( X ) )
% 0.69/1.12 ] )
% 0.69/1.12 , clause( 816, [ member( X, estin ), ~( 'little_set'( X ) ), ~(
% 0.69/1.12 'ordered_pair_predicate'( X ) ), ~( member( first( X ), second( X ) ) ) ]
% 0.69/1.12 )
% 0.69/1.12 , clause( 817, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.69/1.12 )
% 0.69/1.12 , clause( 818, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 0.69/1.12 )
% 0.69/1.12 , clause( 819, [ member( X, intersection( Y, Z ) ), ~( member( X, Y ) ),
% 0.69/1.12 ~( member( X, Z ) ) ] )
% 0.69/1.12 , clause( 820, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 0.69/1.12 )
% 0.69/1.12 , clause( 821, [ member( X, complement( Y ) ), ~( 'little_set'( X ) ),
% 0.69/1.12 member( X, Y ) ] )
% 0.69/1.12 , clause( 822, [ =( union( X, Y ), complement( intersection( complement( X
% 0.69/1.12 ), complement( Y ) ) ) ) ] )
% 0.69/1.12 , clause( 823, [ ~( member( X, 'domain_of'( Y ) ) ),
% 0.69/1.12 'ordered_pair_predicate'( f8( X, Y ) ) ] )
% 0.69/1.12 , clause( 824, [ ~( member( X, 'domain_of'( Y ) ) ), member( f8( X, Y ), Y
% 0.69/1.12 ) ] )
% 0.69/1.12 , clause( 825, [ ~( member( X, 'domain_of'( Y ) ) ), =( X, first( f8( X, Y
% 0.69/1.12 ) ) ) ] )
% 0.69/1.12 , clause( 826, [ member( X, 'domain_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.69/1.12 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, first( Z )
% 0.69/1.12 ) ) ] )
% 0.69/1.12 , clause( 827, [ ~( member( X, 'cross_product'( Y, Z ) ) ),
% 0.69/1.12 'ordered_pair_predicate'( X ) ] )
% 0.69/1.12 , clause( 828, [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( first(
% 0.69/1.12 X ), Y ) ] )
% 0.69/1.12 , clause( 829, [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( second(
% 0.69/1.12 X ), Z ) ] )
% 0.69/1.12 , clause( 830, [ member( X, 'cross_product'( Y, Z ) ), ~( 'little_set'( X )
% 0.69/1.12 ), ~( 'ordered_pair_predicate'( X ) ), ~( member( first( X ), Y ) ), ~(
% 0.69/1.12 member( second( X ), Z ) ) ] )
% 0.69/1.12 , clause( 831, [ ~( member( X, converse( Y ) ) ), 'ordered_pair_predicate'(
% 0.69/1.12 X ) ] )
% 0.69/1.12 , clause( 832, [ ~( member( X, converse( Y ) ) ), member( 'ordered_pair'(
% 0.69/1.12 second( X ), first( X ) ), Y ) ] )
% 0.69/1.12 , clause( 833, [ member( X, converse( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.69/1.12 'ordered_pair_predicate'( X ) ), ~( member( 'ordered_pair'( second( X ),
% 0.69/1.12 first( X ) ), Y ) ) ] )
% 0.69/1.12 , clause( 834, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f9( X
% 0.69/1.12 , Y ) ) ] )
% 0.69/1.12 , clause( 835, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f10(
% 0.69/1.12 X, Y ) ) ] )
% 0.69/1.12 , clause( 836, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f11(
% 0.69/1.12 X, Y ) ) ] )
% 0.69/1.12 , clause( 837, [ ~( member( X, 'rotate_right'( Y ) ) ), =( X,
% 0.69/1.12 'ordered_pair'( f9( X, Y ), 'ordered_pair'( f10( X, Y ), f11( X, Y ) ) )
% 0.69/1.12 ) ] )
% 0.69/1.12 , clause( 838, [ ~( member( X, 'rotate_right'( Y ) ) ), member(
% 0.69/1.12 'ordered_pair'( f10( X, Y ), 'ordered_pair'( f11( X, Y ), f9( X, Y ) ) )
% 0.69/1.12 , Y ) ] )
% 0.69/1.12 , clause( 839, [ member( X, 'rotate_right'( Y ) ), ~( 'little_set'( X ) ),
% 0.69/1.12 ~( 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) ),
% 0.69/1.12 ~( =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 0.69/1.12 'ordered_pair'( T, 'ordered_pair'( U, Z ) ), Y ) ) ] )
% 0.69/1.12 , clause( 840, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f12(
% 0.69/1.12 X, Y ) ) ] )
% 0.69/1.12 , clause( 841, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f13(
% 0.69/1.12 X, Y ) ) ] )
% 0.69/1.12 , clause( 842, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f14(
% 0.69/1.12 X, Y ) ) ] )
% 0.69/1.12 , clause( 843, [ ~( member( X, 'flip_range_of'( Y ) ) ), =( X,
% 0.69/1.12 'ordered_pair'( f12( X, Y ), 'ordered_pair'( f13( X, Y ), f14( X, Y ) ) )
% 0.69/1.12 ) ] )
% 0.69/1.12 , clause( 844, [ ~( member( X, 'flip_range_of'( Y ) ) ), member(
% 0.69/1.12 'ordered_pair'( f12( X, Y ), 'ordered_pair'( f14( X, Y ), f13( X, Y ) ) )
% 0.69/1.12 , Y ) ] )
% 0.69/1.12 , clause( 845, [ member( X, 'flip_range_of'( Y ) ), ~( 'little_set'( X ) )
% 0.69/1.12 , ~( 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) )
% 0.69/1.12 , ~( =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 0.69/1.12 'ordered_pair'( Z, 'ordered_pair'( U, T ) ), Y ) ) ] )
% 0.69/1.12 , clause( 846, [ =( successor( X ), union( X, 'singleton_set'( X ) ) ) ] )
% 0.69/1.12 , clause( 847, [ ~( member( X, 'empty_set' ) ) ] )
% 0.69/1.12 , clause( 848, [ member( X, 'universal_set' ), ~( 'little_set'( X ) ) ] )
% 0.69/1.12 , clause( 849, [ 'little_set'( infinity ) ] )
% 0.69/1.12 , clause( 850, [ member( 'empty_set', infinity ) ] )
% 0.69/1.12 , clause( 851, [ ~( member( X, infinity ) ), member( successor( X ),
% 0.69/1.12 infinity ) ] )
% 0.69/1.12 , clause( 852, [ ~( member( X, sigma( Y ) ) ), member( f16( X, Y ), Y ) ]
% 0.69/1.12 )
% 0.69/1.12 , clause( 853, [ ~( member( X, sigma( Y ) ) ), member( X, f16( X, Y ) ) ]
% 0.69/1.12 )
% 0.69/1.12 , clause( 854, [ member( X, sigma( Y ) ), ~( member( Z, Y ) ), ~( member( X
% 0.69/1.12 , Z ) ) ] )
% 0.69/1.12 , clause( 855, [ ~( 'little_set'( X ) ), 'little_set'( sigma( X ) ) ] )
% 0.69/1.12 , clause( 856, [ ~( subset( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.69/1.12 )
% 0.69/1.12 , clause( 857, [ subset( X, Y ), member( f17( X, Y ), X ) ] )
% 0.69/1.12 , clause( 858, [ subset( X, Y ), ~( member( f17( X, Y ), Y ) ) ] )
% 0.69/1.12 , clause( 859, [ ~( 'proper_subset'( X, Y ) ), subset( X, Y ) ] )
% 0.69/1.12 , clause( 860, [ ~( 'proper_subset'( X, Y ) ), ~( =( X, Y ) ) ] )
% 0.69/1.12 , clause( 861, [ 'proper_subset'( X, Y ), ~( subset( X, Y ) ), =( X, Y ) ]
% 0.69/1.12 )
% 0.69/1.12 , clause( 862, [ ~( member( X, powerset( Y ) ) ), subset( X, Y ) ] )
% 0.69/1.12 , clause( 863, [ member( X, powerset( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.69/1.12 subset( X, Y ) ) ] )
% 0.69/1.12 , clause( 864, [ ~( 'little_set'( X ) ), 'little_set'( powerset( X ) ) ] )
% 0.69/1.12 , clause( 865, [ ~( relation( X ) ), ~( member( Y, X ) ),
% 0.69/1.12 'ordered_pair_predicate'( Y ) ] )
% 0.69/1.12 , clause( 866, [ relation( X ), member( f18( X ), X ) ] )
% 0.69/1.12 , clause( 867, [ relation( X ), ~( 'ordered_pair_predicate'( f18( X ) ) ) ]
% 0.69/1.12 )
% 0.69/1.12 , clause( 868, [ ~( 'single_valued_set'( X ) ), ~( 'little_set'( Y ) ), ~(
% 0.69/1.12 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( member( 'ordered_pair'( Y
% 0.69/1.12 , Z ), X ) ), ~( member( 'ordered_pair'( Y, T ), X ) ), =( Z, T ) ] )
% 0.69/1.12 , clause( 869, [ 'single_valued_set'( X ), 'little_set'( f19( X ) ) ] )
% 0.69/1.12 , clause( 870, [ 'single_valued_set'( X ), 'little_set'( f20( X ) ) ] )
% 0.69/1.12 , clause( 871, [ 'single_valued_set'( X ), 'little_set'( f21( X ) ) ] )
% 0.69/1.12 , clause( 872, [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X )
% 0.69/1.12 , f20( X ) ), X ) ] )
% 0.69/1.12 , clause( 873, [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X )
% 0.69/1.12 , f21( X ) ), X ) ] )
% 0.69/1.12 , clause( 874, [ 'single_valued_set'( X ), ~( =( f20( X ), f21( X ) ) ) ]
% 0.69/1.12 )
% 0.69/1.12 , clause( 875, [ ~( function( X ) ), relation( X ) ] )
% 0.69/1.12 , clause( 876, [ ~( function( X ) ), 'single_valued_set'( X ) ] )
% 0.69/1.12 , clause( 877, [ function( X ), ~( relation( X ) ), ~( 'single_valued_set'(
% 0.69/1.12 X ) ) ] )
% 0.69/1.12 , clause( 878, [ ~( member( X, image( Y, Z ) ) ), 'ordered_pair_predicate'(
% 0.69/1.12 f22( X, Y, Z ) ) ] )
% 0.69/1.12 , clause( 879, [ ~( member( X, image( Y, Z ) ) ), member( f22( X, Y, Z ), Z
% 0.69/1.12 ) ] )
% 0.69/1.12 , clause( 880, [ ~( member( X, image( Y, Z ) ) ), member( first( f22( X, Y
% 0.69/1.12 , Z ) ), Y ) ] )
% 0.69/1.12 , clause( 881, [ ~( member( X, image( Y, Z ) ) ), =( second( f22( X, Y, Z )
% 0.69/1.12 ), X ) ] )
% 0.69/1.12 , clause( 882, [ member( X, image( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.69/1.12 'ordered_pair_predicate'( T ) ), ~( member( T, Z ) ), ~( member( first( T
% 0.69/1.12 ), Y ) ), ~( =( second( T ), X ) ) ] )
% 0.69/1.12 , clause( 883, [ ~( 'little_set'( X ) ), ~( function( Y ) ), 'little_set'(
% 0.69/1.12 image( X, Y ) ) ] )
% 0.69/1.12 , clause( 884, [ ~( disjoint( X, Y ) ), ~( member( Z, X ) ), ~( member( Z,
% 0.69/1.12 Y ) ) ] )
% 0.69/1.12 , clause( 885, [ disjoint( X, Y ), member( f23( X, Y ), X ) ] )
% 0.69/1.12 , clause( 886, [ disjoint( X, Y ), member( f23( X, Y ), Y ) ] )
% 0.69/1.12 , clause( 887, [ =( X, 'empty_set' ), member( f24( X ), X ) ] )
% 0.69/1.12 , clause( 888, [ =( X, 'empty_set' ), disjoint( f24( X ), X ) ] )
% 0.69/1.12 , clause( 889, [ function( f25 ) ] )
% 0.69/1.12 , clause( 890, [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( f26(
% 0.69/1.12 X ), X ) ] )
% 0.69/1.12 , clause( 891, [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member(
% 0.69/1.12 'ordered_pair'( X, f26( X ) ), f25 ) ] )
% 0.69/1.12 , clause( 892, [ ~( member( X, 'range_of'( Y ) ) ),
% 0.69/1.12 'ordered_pair_predicate'( f27( X, Y ) ) ] )
% 0.69/1.12 , clause( 893, [ ~( member( X, 'range_of'( Y ) ) ), member( f27( X, Y ), Y
% 0.69/1.12 ) ] )
% 0.69/1.12 , clause( 894, [ ~( member( X, 'range_of'( Y ) ) ), =( X, second( f27( X, Y
% 0.69/1.12 ) ) ) ] )
% 0.69/1.12 , clause( 895, [ member( X, 'range_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.69/1.12 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, second( Z
% 0.69/1.12 ) ) ) ] )
% 0.69/1.12 , clause( 896, [ ~( member( X, 'identity_relation' ) ),
% 0.69/1.12 'ordered_pair_predicate'( X ) ] )
% 0.69/1.12 , clause( 897, [ ~( member( X, 'identity_relation' ) ), =( first( X ),
% 0.69/1.12 second( X ) ) ] )
% 0.69/1.12 , clause( 898, [ member( X, 'identity_relation' ), ~( 'little_set'( X ) ),
% 0.69/1.12 ~( 'ordered_pair_predicate'( X ) ), ~( =( first( X ), second( X ) ) ) ]
% 0.69/1.12 )
% 0.69/1.12 , clause( 899, [ =( restrict( X, Y ), intersection( X, 'cross_product'( Y,
% 0.69/1.12 'universal_set' ) ) ) ] )
% 0.69/1.12 , clause( 900, [ ~( 'one_to_one_function'( X ) ), function( X ) ] )
% 0.69/1.12 , clause( 901, [ ~( 'one_to_one_function'( X ) ), function( converse( X ) )
% 0.69/1.12 ] )
% 0.69/1.12 , clause( 902, [ 'one_to_one_function'( X ), ~( function( X ) ), ~(
% 0.69/1.12 function( converse( X ) ) ) ] )
% 0.69/1.12 , clause( 903, [ ~( member( X, apply( Y, Z ) ) ), 'ordered_pair_predicate'(
% 0.69/1.12 f28( X, Y, Z ) ) ] )
% 0.69/1.12 , clause( 904, [ ~( member( X, apply( Y, Z ) ) ), member( f28( X, Y, Z ), Y
% 0.69/1.12 ) ] )
% 0.69/1.12 , clause( 905, [ ~( member( X, apply( Y, Z ) ) ), =( first( f28( X, Y, Z )
% 0.69/1.12 ), Z ) ] )
% 0.69/1.12 , clause( 906, [ ~( member( X, apply( Y, Z ) ) ), member( X, second( f28( X
% 0.69/1.12 , Y, Z ) ) ) ] )
% 0.69/1.12 , clause( 907, [ member( X, apply( Y, Z ) ), ~( 'ordered_pair_predicate'( T
% 0.69/1.12 ) ), ~( member( T, Y ) ), ~( =( first( T ), Z ) ), ~( member( X, second(
% 0.69/1.12 T ) ) ) ] )
% 0.69/1.12 , clause( 908, [ =( 'apply_to_two_arguments'( X, Y, Z ), apply( X,
% 0.69/1.12 'ordered_pair'( Y, Z ) ) ) ] )
% 0.69/1.12 , clause( 909, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 0.69/1.12 , clause( 910, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 0.69/1.12 , clause( 911, [ ~( maps( X, Y, Z ) ), subset( 'range_of'( X ), Z ) ] )
% 0.69/1.12 , clause( 912, [ maps( X, Y, Z ), ~( function( X ) ), ~( =( 'domain_of'( X
% 0.69/1.12 ), Y ) ), ~( subset( 'range_of'( X ), Z ) ) ] )
% 0.69/1.12 , clause( 913, [ ~( closed( X, Y ) ), 'little_set'( X ) ] )
% 0.69/1.12 , clause( 914, [ ~( closed( X, Y ) ), 'little_set'( Y ) ] )
% 0.69/1.12 , clause( 915, [ ~( closed( X, Y ) ), maps( Y, 'cross_product'( X, X ), X )
% 0.69/1.12 ] )
% 0.69/1.12 , clause( 916, [ closed( X, Y ), ~( 'little_set'( X ) ), ~( 'little_set'( Y
% 0.69/1.12 ) ), ~( maps( Y, 'cross_product'( X, X ), X ) ) ] )
% 0.69/1.12 , clause( 917, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f29( X, Y
% 0.69/1.12 , Z ) ) ] )
% 0.69/1.12 , clause( 918, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f30( X, Y
% 0.69/1.12 , Z ) ) ] )
% 0.69/1.12 , clause( 919, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f31( X, Y
% 0.69/1.12 , Z ) ) ] )
% 0.69/1.12 , clause( 920, [ ~( member( X, compose( Y, Z ) ) ), =( X, 'ordered_pair'(
% 0.69/1.12 f29( X, Y, Z ), f30( X, Y, Z ) ) ) ] )
% 0.69/1.12 , clause( 921, [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'(
% 0.69/1.12 f29( X, Y, Z ), f31( X, Y, Z ) ), Y ) ] )
% 0.69/1.12 , clause( 922, [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'(
% 0.69/1.12 f31( X, Y, Z ), f30( X, Y, Z ) ), Z ) ] )
% 0.69/1.12 , clause( 923, [ member( X, compose( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.69/1.12 'little_set'( T ) ), ~( 'little_set'( U ) ), ~( 'little_set'( W ) ), ~(
% 0.69/1.12 =( X, 'ordered_pair'( T, U ) ) ), ~( member( 'ordered_pair'( T, W ), Y )
% 0.69/1.12 ), ~( member( 'ordered_pair'( W, U ), Z ) ) ] )
% 0.69/1.12 , clause( 924, [ ~( homomorphism( X, Y, Z, T, U ) ), closed( Y, Z ) ] )
% 0.69/1.12 , clause( 925, [ ~( homomorphism( X, Y, Z, T, U ) ), closed( T, U ) ] )
% 0.69/1.12 , clause( 926, [ ~( homomorphism( X, Y, Z, T, U ) ), maps( X, Y, T ) ] )
% 0.69/1.12 , clause( 927, [ ~( homomorphism( X, Y, Z, T, U ) ), ~( member( W, Y ) ),
% 0.69/1.12 ~( member( V0, Y ) ), =( apply( X, 'apply_to_two_arguments'( Z, W, V0 ) )
% 0.69/1.12 , 'apply_to_two_arguments'( U, apply( X, W ), apply( X, V0 ) ) ) ] )
% 0.69/1.12 , clause( 928, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~(
% 0.69/1.12 closed( T, U ) ), ~( maps( X, Y, T ) ), member( f32( X, Y, Z, T, U ), Y )
% 0.69/1.12 ] )
% 0.69/1.12 , clause( 929, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~(
% 0.69/1.12 closed( T, U ) ), ~( maps( X, Y, T ) ), member( f33( X, Y, Z, T, U ), Y )
% 0.69/1.12 ] )
% 0.69/1.12 , clause( 930, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~(
% 0.69/1.12 closed( T, U ) ), ~( maps( X, Y, T ) ), ~( =( apply( X,
% 0.69/1.12 'apply_to_two_arguments'( Z, f32( X, Y, Z, T, U ), f33( X, Y, Z, T, U ) )
% 0.69/1.12 ), 'apply_to_two_arguments'( U, apply( X, f32( X, Y, Z, T, U ) ), apply(
% 0.69/1.12 X, f33( X, Y, Z, T, U ) ) ) ) ) ] )
% 0.69/1.12 , clause( 931, [ ~( 'little_set'( 'ordered_pair'( a, b ) ) ) ] )
% 0.69/1.12 ] ).
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12 subsumption(
% 0.69/1.12 clause( 7, [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ] )
% 0.69/1.12 , clause( 797, [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ] )
% 0.69/1.12 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.69/1.12 )] ) ).
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12 eqswap(
% 0.69/1.12 clause( 957, [ =( 'non_ordered_pair'( 'singleton_set'( X ),
% 0.69/1.12 'non_ordered_pair'( X, Y ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.69/1.12 , clause( 799, [ =( 'ordered_pair'( X, Y ), 'non_ordered_pair'(
% 0.69/1.12 'singleton_set'( X ), 'non_ordered_pair'( X, Y ) ) ) ] )
% 0.69/1.12 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12 subsumption(
% 0.69/1.12 clause( 9, [ =( 'non_ordered_pair'( 'singleton_set'( X ),
% 0.69/1.12 'non_ordered_pair'( X, Y ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.69/1.12 , clause( 957, [ =( 'non_ordered_pair'( 'singleton_set'( X ),
% 0.69/1.12 'non_ordered_pair'( X, Y ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.69/1.12 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.69/1.12 )] ) ).
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12 subsumption(
% 0.69/1.12 clause( 141, [ ~( 'little_set'( 'ordered_pair'( a, b ) ) ) ] )
% 0.69/1.12 , clause( 931, [ ~( 'little_set'( 'ordered_pair'( a, b ) ) ) ] )
% 0.69/1.12 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12 paramod(
% 0.69/1.12 clause( 1131, [ 'little_set'( 'ordered_pair'( X, Y ) ) ] )
% 0.69/1.12 , clause( 9, [ =( 'non_ordered_pair'( 'singleton_set'( X ),
% 0.69/1.12 'non_ordered_pair'( X, Y ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.69/1.12 , 0, clause( 7, [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ] )
% 0.69/1.12 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.69/1.12 :=( X, 'singleton_set'( X ) ), :=( Y, 'non_ordered_pair'( X, Y ) )] )
% 0.69/1.12 ).
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12 subsumption(
% 0.69/1.12 clause( 774, [ 'little_set'( 'ordered_pair'( X, Y ) ) ] )
% 0.69/1.12 , clause( 1131, [ 'little_set'( 'ordered_pair'( X, Y ) ) ] )
% 0.69/1.12 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.69/1.12 )] ) ).
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12 resolution(
% 0.69/1.12 clause( 1132, [] )
% 0.69/1.12 , clause( 141, [ ~( 'little_set'( 'ordered_pair'( a, b ) ) ) ] )
% 0.69/1.12 , 0, clause( 774, [ 'little_set'( 'ordered_pair'( X, Y ) ) ] )
% 0.69/1.12 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, b )] )
% 0.69/1.12 ).
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12 subsumption(
% 0.69/1.12 clause( 788, [] )
% 0.69/1.12 , clause( 1132, [] )
% 0.69/1.12 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12 end.
% 0.69/1.12
% 0.69/1.12 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.69/1.12
% 0.69/1.12 Memory use:
% 0.69/1.12
% 0.69/1.12 space for terms: 15254
% 0.69/1.12 space for clauses: 40575
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12 clauses generated: 1615
% 0.69/1.12 clauses kept: 789
% 0.69/1.12 clauses selected: 47
% 0.69/1.12 clauses deleted: 0
% 0.69/1.12 clauses inuse deleted: 0
% 0.69/1.12
% 0.69/1.12 subsentry: 3068
% 0.69/1.12 literals s-matched: 2216
% 0.69/1.12 literals matched: 1727
% 0.69/1.12 full subsumption: 875
% 0.69/1.12
% 0.69/1.12 checksum: -1555913780
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12 Bliksem ended
%------------------------------------------------------------------------------