TSTP Solution File: NUM009-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM009-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n010.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 06:19:12 EDT 2022
% Result : Unsatisfiable 4.40s 4.78s
% Output : Refutation 4.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM009-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n010.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 : Thu Jul 7 11:59:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.71/1.11 *** allocated 10000 integers for termspace/termends
% 0.71/1.11 *** allocated 10000 integers for clauses
% 0.71/1.11 *** allocated 10000 integers for justifications
% 0.71/1.11 Bliksem 1.12
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Automatic Strategy Selection
% 0.71/1.11
% 0.71/1.11 Clauses:
% 0.71/1.11 [
% 0.71/1.11 [ ~( member( X, Y ) ), 'little_set'( X ) ],
% 0.71/1.11 [ 'little_set'( f1( X, Y ) ), =( X, Y ) ],
% 0.71/1.11 [ member( f1( X, Y ), X ), member( f1( X, Y ), Y ), =( X, Y ) ],
% 0.71/1.11 [ ~( member( f1( X, Y ), X ) ), ~( member( f1( X, Y ), Y ) ), =( X, Y )
% 0.71/1.11 ],
% 0.71/1.11 [ ~( member( X, 'non_ordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.11 =( X, Y ) ) ],
% 0.71/1.11 [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.11 =( X, Z ) ) ],
% 0.71/1.11 [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ],
% 0.71/1.11 [ =( 'singleton_set'( X ), 'non_ordered_pair'( X, X ) ) ],
% 0.71/1.11 [ =( 'ordered_pair'( X, Y ), 'non_ordered_pair'( 'singleton_set'( X ),
% 0.71/1.11 'non_ordered_pair'( X, Y ) ) ) ],
% 0.71/1.11 [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f2( X ) ) ],
% 0.71/1.11 [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f3( X ) ) ],
% 0.71/1.11 [ ~( 'ordered_pair_predicate'( X ) ), =( X, 'ordered_pair'( f2( X ), f3(
% 0.71/1.11 X ) ) ) ],
% 0.71/1.11 [ 'ordered_pair_predicate'( X ), ~( 'little_set'( Y ) ), ~( 'little_set'(
% 0.71/1.11 Z ) ), ~( =( X, 'ordered_pair'( Y, Z ) ) ) ],
% 0.71/1.11 [ ~( member( X, first( Y ) ) ), 'little_set'( f4( X, Y ) ) ],
% 0.71/1.11 [ ~( member( X, first( Y ) ) ), 'little_set'( f5( X, Y ) ) ],
% 0.71/1.11 [ ~( member( X, first( Y ) ) ), =( Y, 'ordered_pair'( f4( X, Y ), f5( X
% 0.71/1.11 , Y ) ) ) ],
% 0.71/1.11 [ ~( member( X, first( Y ) ) ), member( X, f4( X, Y ) ) ],
% 0.71/1.11 [ member( X, first( Y ) ), ~( 'little_set'( Z ) ), ~( 'little_set'( T )
% 0.71/1.11 ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, Z ) ) ],
% 0.71/1.11 [ ~( member( X, second( Y ) ) ), 'little_set'( f6( X, Y ) ) ],
% 0.71/1.11 [ ~( member( X, second( Y ) ) ), 'little_set'( f7( X, Y ) ) ],
% 0.71/1.11 [ ~( member( X, second( Y ) ) ), =( Y, 'ordered_pair'( f6( X, Y ), f7( X
% 0.71/1.11 , Y ) ) ) ],
% 0.71/1.11 [ ~( member( X, second( Y ) ) ), member( X, f7( X, Y ) ) ],
% 0.71/1.11 [ member( X, second( Y ) ), ~( 'little_set'( Z ) ), ~( 'little_set'( T )
% 0.71/1.11 ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, T ) ) ],
% 0.71/1.11 [ ~( member( X, estin ) ), 'ordered_pair_predicate'( X ) ],
% 0.71/1.11 [ ~( member( X, estin ) ), member( first( X ), second( X ) ) ],
% 0.71/1.11 [ member( X, estin ), ~( 'little_set'( X ) ), ~(
% 0.71/1.11 'ordered_pair_predicate'( X ) ), ~( member( first( X ), second( X ) ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.71/1.11 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.71/1.11 [ member( X, intersection( Y, Z ) ), ~( member( X, Y ) ), ~( member( X,
% 0.71/1.11 Z ) ) ],
% 0.71/1.11 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.71/1.11 [ member( X, complement( Y ) ), ~( 'little_set'( X ) ), member( X, Y ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ =( union( X, Y ), complement( intersection( complement( X ),
% 0.71/1.11 complement( Y ) ) ) ) ],
% 0.71/1.11 [ ~( member( X, 'domain_of'( Y ) ) ), 'ordered_pair_predicate'( f8( X, Y
% 0.71/1.11 ) ) ],
% 0.71/1.11 [ ~( member( X, 'domain_of'( Y ) ) ), member( f8( X, Y ), Y ) ],
% 0.71/1.11 [ ~( member( X, 'domain_of'( Y ) ) ), =( X, first( f8( X, Y ) ) ) ],
% 0.71/1.11 [ member( X, 'domain_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.11 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, first( Z )
% 0.71/1.11 ) ) ],
% 0.71/1.11 [ ~( member( X, 'cross_product'( Y, Z ) ) ), 'ordered_pair_predicate'( X
% 0.71/1.11 ) ],
% 0.71/1.11 [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( first( X ), Y ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( second( X ), Z ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ member( X, 'cross_product'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.11 'ordered_pair_predicate'( X ) ), ~( member( first( X ), Y ) ), ~( member(
% 0.71/1.11 second( X ), Z ) ) ],
% 0.71/1.11 [ ~( member( X, converse( Y ) ) ), 'ordered_pair_predicate'( X ) ],
% 0.71/1.11 [ ~( member( X, converse( Y ) ) ), member( 'ordered_pair'( second( X ),
% 0.71/1.11 first( X ) ), Y ) ],
% 0.71/1.11 [ member( X, converse( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.11 'ordered_pair_predicate'( X ) ), ~( member( 'ordered_pair'( second( X ),
% 0.71/1.11 first( X ) ), Y ) ) ],
% 0.71/1.11 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f9( X, Y ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f10( X, Y ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f11( X, Y ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, 'rotate_right'( Y ) ) ), =( X, 'ordered_pair'( f9( X, Y
% 0.71/1.11 ), 'ordered_pair'( f10( X, Y ), f11( X, Y ) ) ) ) ],
% 0.71/1.11 [ ~( member( X, 'rotate_right'( Y ) ) ), member( 'ordered_pair'( f10( X
% 0.71/1.11 , Y ), 'ordered_pair'( f11( X, Y ), f9( X, Y ) ) ), Y ) ],
% 0.71/1.11 [ member( X, 'rotate_right'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.11 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) ), ~(
% 0.71/1.11 =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 0.71/1.11 'ordered_pair'( T, 'ordered_pair'( U, Z ) ), Y ) ) ],
% 0.71/1.11 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f12( X, Y ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f13( X, Y ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f14( X, Y ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, 'flip_range_of'( Y ) ) ), =( X, 'ordered_pair'( f12( X,
% 0.71/1.11 Y ), 'ordered_pair'( f13( X, Y ), f14( X, Y ) ) ) ) ],
% 0.71/1.11 [ ~( member( X, 'flip_range_of'( Y ) ) ), member( 'ordered_pair'( f12( X
% 0.71/1.11 , Y ), 'ordered_pair'( f14( X, Y ), f13( X, Y ) ) ), Y ) ],
% 0.71/1.11 [ member( X, 'flip_range_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.11 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) ), ~(
% 0.71/1.11 =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 0.71/1.11 'ordered_pair'( Z, 'ordered_pair'( U, T ) ), Y ) ) ],
% 0.71/1.11 [ =( successor( X ), union( X, 'singleton_set'( X ) ) ) ],
% 0.71/1.11 [ ~( member( X, 'empty_set' ) ) ],
% 0.71/1.11 [ member( X, 'universal_set' ), ~( 'little_set'( X ) ) ],
% 0.71/1.11 [ 'little_set'( infinity ) ],
% 0.71/1.11 [ member( 'empty_set', infinity ) ],
% 0.71/1.11 [ ~( member( X, infinity ) ), member( successor( X ), infinity ) ],
% 0.71/1.11 [ ~( member( X, sigma( Y ) ) ), member( f16( X, Y ), Y ) ],
% 0.71/1.11 [ ~( member( X, sigma( Y ) ) ), member( X, f16( X, Y ) ) ],
% 0.71/1.11 [ member( X, sigma( Y ) ), ~( member( Z, Y ) ), ~( member( X, Z ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( 'little_set'( X ) ), 'little_set'( sigma( X ) ) ],
% 0.71/1.11 [ ~( subset( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.71/1.11 [ subset( X, Y ), member( f17( X, Y ), X ) ],
% 0.71/1.11 [ subset( X, Y ), ~( member( f17( X, Y ), Y ) ) ],
% 0.71/1.11 [ ~( 'proper_subset'( X, Y ) ), subset( X, Y ) ],
% 0.71/1.11 [ ~( 'proper_subset'( X, Y ) ), ~( =( X, Y ) ) ],
% 0.71/1.11 [ 'proper_subset'( X, Y ), ~( subset( X, Y ) ), =( X, Y ) ],
% 0.71/1.11 [ ~( member( X, powerset( Y ) ) ), subset( X, Y ) ],
% 0.71/1.11 [ member( X, powerset( Y ) ), ~( 'little_set'( X ) ), ~( subset( X, Y )
% 0.71/1.11 ) ],
% 0.71/1.11 [ ~( 'little_set'( X ) ), 'little_set'( powerset( X ) ) ],
% 0.71/1.11 [ ~( relation( X ) ), ~( member( Y, X ) ), 'ordered_pair_predicate'( Y )
% 0.71/1.11 ],
% 0.71/1.11 [ relation( X ), member( f18( X ), X ) ],
% 0.71/1.11 [ relation( X ), ~( 'ordered_pair_predicate'( f18( X ) ) ) ],
% 0.71/1.11 [ ~( 'single_valued_set'( X ) ), ~( 'little_set'( Y ) ), ~( 'little_set'(
% 0.71/1.11 Z ) ), ~( 'little_set'( T ) ), ~( member( 'ordered_pair'( Y, Z ), X ) ),
% 0.71/1.11 ~( member( 'ordered_pair'( Y, T ), X ) ), =( Z, T ) ],
% 0.71/1.11 [ 'single_valued_set'( X ), 'little_set'( f19( X ) ) ],
% 0.71/1.11 [ 'single_valued_set'( X ), 'little_set'( f20( X ) ) ],
% 0.71/1.11 [ 'single_valued_set'( X ), 'little_set'( f21( X ) ) ],
% 0.71/1.11 [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X ), f20( X ) )
% 0.71/1.11 , X ) ],
% 0.71/1.11 [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X ), f21( X ) )
% 0.71/1.11 , X ) ],
% 0.71/1.11 [ 'single_valued_set'( X ), ~( =( f20( X ), f21( X ) ) ) ],
% 0.71/1.11 [ ~( function( X ) ), relation( X ) ],
% 0.71/1.11 [ ~( function( X ) ), 'single_valued_set'( X ) ],
% 0.71/1.11 [ function( X ), ~( relation( X ) ), ~( 'single_valued_set'( X ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, image( Y, Z ) ) ), 'ordered_pair_predicate'( f22( X, Y,
% 0.71/1.11 Z ) ) ],
% 0.71/1.11 [ ~( member( X, image( Y, Z ) ) ), member( f22( X, Y, Z ), Z ) ],
% 0.71/1.11 [ ~( member( X, image( Y, Z ) ) ), member( first( f22( X, Y, Z ) ), Y )
% 0.71/1.11 ],
% 0.71/1.11 [ ~( member( X, image( Y, Z ) ) ), =( second( f22( X, Y, Z ) ), X ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ member( X, image( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.11 'ordered_pair_predicate'( T ) ), ~( member( T, Z ) ), ~( member( first( T
% 0.71/1.11 ), Y ) ), ~( =( second( T ), X ) ) ],
% 0.71/1.11 [ ~( 'little_set'( X ) ), ~( function( Y ) ), 'little_set'( image( X, Y
% 0.71/1.11 ) ) ],
% 0.71/1.11 [ ~( disjoint( X, Y ) ), ~( member( Z, X ) ), ~( member( Z, Y ) ) ],
% 0.71/1.11 [ disjoint( X, Y ), member( f23( X, Y ), X ) ],
% 0.71/1.11 [ disjoint( X, Y ), member( f23( X, Y ), Y ) ],
% 0.71/1.11 [ =( X, 'empty_set' ), member( f24( X ), X ) ],
% 0.71/1.11 [ =( X, 'empty_set' ), disjoint( f24( X ), X ) ],
% 0.71/1.11 [ function( f25 ) ],
% 0.71/1.11 [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( f26( X ), X ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( 'ordered_pair'( X
% 0.71/1.11 , f26( X ) ), f25 ) ],
% 0.71/1.11 [ ~( member( X, 'range_of'( Y ) ) ), 'ordered_pair_predicate'( f27( X, Y
% 0.71/1.11 ) ) ],
% 0.71/1.11 [ ~( member( X, 'range_of'( Y ) ) ), member( f27( X, Y ), Y ) ],
% 0.71/1.11 [ ~( member( X, 'range_of'( Y ) ) ), =( X, second( f27( X, Y ) ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ member( X, 'range_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.11 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, second( Z
% 0.71/1.11 ) ) ) ],
% 0.71/1.11 [ ~( member( X, 'identity_relation' ) ), 'ordered_pair_predicate'( X ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, 'identity_relation' ) ), =( first( X ), second( X ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ member( X, 'identity_relation' ), ~( 'little_set'( X ) ), ~(
% 0.71/1.11 'ordered_pair_predicate'( X ) ), ~( =( first( X ), second( X ) ) ) ],
% 0.71/1.11 [ =( restrict( X, Y ), intersection( X, 'cross_product'( Y,
% 0.71/1.11 'universal_set' ) ) ) ],
% 0.71/1.11 [ ~( 'one_to_one_function'( X ) ), function( X ) ],
% 0.71/1.11 [ ~( 'one_to_one_function'( X ) ), function( converse( X ) ) ],
% 0.71/1.11 [ 'one_to_one_function'( X ), ~( function( X ) ), ~( function( converse(
% 0.71/1.11 X ) ) ) ],
% 0.71/1.11 [ ~( member( X, apply( Y, Z ) ) ), 'ordered_pair_predicate'( f28( X, Y,
% 0.71/1.11 Z ) ) ],
% 0.71/1.11 [ ~( member( X, apply( Y, Z ) ) ), member( f28( X, Y, Z ), Y ) ],
% 0.71/1.11 [ ~( member( X, apply( Y, Z ) ) ), =( first( f28( X, Y, Z ) ), Z ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, apply( Y, Z ) ) ), member( X, second( f28( X, Y, Z ) ) )
% 0.71/1.11 ],
% 0.71/1.11 [ member( X, apply( Y, Z ) ), ~( 'ordered_pair_predicate'( T ) ), ~(
% 0.71/1.11 member( T, Y ) ), ~( =( first( T ), Z ) ), ~( member( X, second( T ) ) )
% 0.71/1.11 ],
% 0.71/1.11 [ =( 'apply_to_two_arguments'( X, Y, Z ), apply( X, 'ordered_pair'( Y, Z
% 0.71/1.11 ) ) ) ],
% 0.71/1.11 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.71/1.11 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 0.71/1.11 [ ~( maps( X, Y, Z ) ), subset( 'range_of'( X ), Z ) ],
% 0.71/1.11 [ maps( X, Y, Z ), ~( function( X ) ), ~( =( 'domain_of'( X ), Y ) ),
% 0.71/1.11 ~( subset( 'range_of'( X ), Z ) ) ],
% 0.71/1.11 [ ~( closed( X, Y ) ), 'little_set'( X ) ],
% 0.71/1.11 [ ~( closed( X, Y ) ), 'little_set'( Y ) ],
% 0.71/1.11 [ ~( closed( X, Y ) ), maps( Y, 'cross_product'( X, X ), X ) ],
% 0.71/1.11 [ closed( X, Y ), ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~(
% 0.71/1.11 maps( Y, 'cross_product'( X, X ), X ) ) ],
% 0.71/1.11 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f29( X, Y, Z ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f30( X, Y, Z ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f31( X, Y, Z ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, compose( Y, Z ) ) ), =( X, 'ordered_pair'( f29( X, Y, Z
% 0.71/1.11 ), f30( X, Y, Z ) ) ) ],
% 0.71/1.11 [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'( f29( X, Y,
% 0.71/1.11 Z ), f31( X, Y, Z ) ), Y ) ],
% 0.71/1.11 [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'( f31( X, Y,
% 0.71/1.11 Z ), f30( X, Y, Z ) ), Z ) ],
% 0.71/1.11 [ member( X, compose( Y, Z ) ), ~( 'little_set'( X ) ), ~( 'little_set'(
% 0.71/1.11 T ) ), ~( 'little_set'( U ) ), ~( 'little_set'( W ) ), ~( =( X,
% 0.71/1.11 'ordered_pair'( T, U ) ) ), ~( member( 'ordered_pair'( T, W ), Y ) ), ~(
% 0.71/1.11 member( 'ordered_pair'( W, U ), Z ) ) ],
% 0.71/1.11 [ ~( homomorphism( X, Y, Z, T, U ) ), closed( Y, Z ) ],
% 0.71/1.11 [ ~( homomorphism( X, Y, Z, T, U ) ), closed( T, U ) ],
% 0.71/1.11 [ ~( homomorphism( X, Y, Z, T, U ) ), maps( X, Y, T ) ],
% 0.71/1.11 [ ~( homomorphism( X, Y, Z, T, U ) ), ~( member( W, Y ) ), ~( member( V0
% 0.71/1.11 , Y ) ), =( apply( X, 'apply_to_two_arguments'( Z, W, V0 ) ),
% 0.71/1.11 'apply_to_two_arguments'( U, apply( X, W ), apply( X, V0 ) ) ) ],
% 0.71/1.11 [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.71/1.11 ), ~( maps( X, Y, T ) ), member( f32( X, Y, Z, T, U ), Y ) ],
% 0.71/1.11 [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.71/1.11 ), ~( maps( X, Y, T ) ), member( f33( X, Y, Z, T, U ), Y ) ],
% 0.71/1.11 [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.71/1.11 ), ~( maps( X, Y, T ) ), ~( =( apply( X, 'apply_to_two_arguments'( Z,
% 0.71/1.11 f32( X, Y, Z, T, U ), f33( X, Y, Z, T, U ) ) ), 'apply_to_two_arguments'(
% 0.71/1.11 U, apply( X, f32( X, Y, Z, T, U ) ), apply( X, f33( X, Y, Z, T, U ) ) ) )
% 0.71/1.11 ) ],
% 0.71/1.11 [ ~( associative( X, Y ) ), ~( member( Z, X ) ), ~( member( T, X ) ),
% 0.71/1.11 ~( member( U, X ) ), =( 'apply_to_two_arguments'( Y,
% 0.71/1.11 'apply_to_two_arguments'( Y, Z, T ), U ), 'apply_to_two_arguments'( Y, Z
% 0.71/1.11 , 'apply_to_two_arguments'( Y, T, U ) ) ) ],
% 0.71/1.11 [ associative( X, Y ), member( f34( X, Y ), X ) ],
% 0.71/1.11 [ associative( X, Y ), member( f35( X, Y ), X ) ],
% 0.71/1.11 [ associative( X, Y ), member( f36( X, Y ), X ) ],
% 0.71/1.11 [ associative( X, Y ), ~( =( 'apply_to_two_arguments'( Y,
% 0.71/1.11 'apply_to_two_arguments'( Y, f34( X, Y ), f35( X, Y ) ), f36( X, Y ) ),
% 0.71/1.11 'apply_to_two_arguments'( Y, f34( X, Y ), 'apply_to_two_arguments'( Y,
% 0.71/1.11 f35( X, Y ), f36( X, Y ) ) ) ) ) ],
% 0.71/1.11 [ ~( identity( X, Y, Z ) ), member( Z, X ) ],
% 0.71/1.11 [ ~( identity( X, Y, Z ) ), ~( member( T, X ) ), =(
% 0.71/1.11 'apply_to_two_arguments'( Y, Z, T ), T ) ],
% 0.71/1.11 [ ~( identity( X, Y, Z ) ), ~( member( T, X ) ), =(
% 0.71/1.11 'apply_to_two_arguments'( Y, T, Z ), T ) ],
% 0.71/1.11 [ identity( X, Y, Z ), ~( member( Z, X ) ), member( f37( X, Y, Z ), X )
% 0.71/1.11 ],
% 0.71/1.11 [ identity( X, Y, Z ), ~( member( Z, X ) ), ~( =(
% 0.71/1.11 'apply_to_two_arguments'( Y, Z, f37( X, Y, Z ) ), f37( X, Y, Z ) ) ), ~(
% 0.71/1.11 =( 'apply_to_two_arguments'( Y, f37( X, Y, Z ), Z ), f37( X, Y, Z ) ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( inverse( X, Y, Z, T ) ), maps( T, X, X ) ],
% 0.71/1.11 [ ~( inverse( X, Y, Z, T ) ), ~( member( U, X ) ), =(
% 0.71/1.11 'apply_to_two_arguments'( Y, apply( T, U ), U ), Z ) ],
% 0.71/1.11 [ ~( inverse( X, Y, Z, T ) ), ~( member( U, X ) ), =(
% 0.71/1.11 'apply_to_two_arguments'( Y, U, apply( T, U ) ), Z ) ],
% 0.71/1.11 [ inverse( X, Y, Z, T ), ~( maps( T, X, X ) ), member( f38( X, Y, Z, T )
% 0.71/1.11 , X ) ],
% 0.71/1.11 [ inverse( X, Y, Z, T ), ~( maps( T, X, X ) ), ~( =(
% 0.71/1.11 'apply_to_two_arguments'( Y, apply( T, f38( X, Y, Z, T ) ), f38( X, Y, Z
% 0.71/1.11 , T ) ), Z ) ), ~( =( 'apply_to_two_arguments'( Y, f38( X, Y, Z, T ),
% 0.71/1.11 apply( T, f38( X, Y, Z, T ) ) ), Z ) ) ],
% 0.71/1.11 [ ~( group( X, Y ) ), closed( X, Y ) ],
% 0.71/1.11 [ ~( group( X, Y ) ), associative( X, Y ) ],
% 0.71/1.11 [ ~( group( X, Y ) ), identity( X, Y, f39( X, Y ) ) ],
% 0.71/1.11 [ ~( group( X, Y ) ), inverse( X, Y, f39( X, Y ), f40( X, Y ) ) ],
% 0.71/1.11 [ group( X, Y ), ~( closed( X, Y ) ), ~( associative( X, Y ) ), ~(
% 0.71/1.11 identity( X, Y, Z ) ), ~( inverse( X, Y, Z, T ) ) ],
% 0.71/1.11 [ ~( commutes( X, Y ) ), ~( member( Z, X ) ), ~( member( T, X ) ), =(
% 0.71/1.11 'apply_to_two_arguments'( Y, Z, T ), 'apply_to_two_arguments'( Y, T, Z )
% 0.71/1.11 ) ],
% 0.71/1.11 [ commutes( X, Y ), member( f41( X, Y ), X ) ],
% 0.71/1.11 [ commutes( X, Y ), member( f42( X, Y ), X ) ],
% 0.71/1.11 [ commutes( X, Y ), ~( =( 'apply_to_two_arguments'( Y, f41( X, Y ), f42(
% 0.71/1.11 X, Y ) ), 'apply_to_two_arguments'( Y, f42( X, Y ), f41( X, Y ) ) ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, 'natural_numbers' ) ), ~( 'little_set'( Y ) ), ~( member(
% 0.71/1.11 'empty_set', Y ) ), member( f43( X, Y ), Y ), member( X, Y ) ],
% 0.71/1.11 [ ~( member( X, 'natural_numbers' ) ), ~( 'little_set'( Y ) ), ~( member(
% 0.71/1.11 'empty_set', Y ) ), ~( member( successor( f43( X, Y ) ), Y ) ), member( X
% 0.71/1.11 , Y ) ],
% 0.71/1.11 [ member( X, 'natural_numbers' ), ~( 'little_set'( X ) ), 'little_set'(
% 0.71/1.11 f44( X ) ) ],
% 0.71/1.11 [ member( X, 'natural_numbers' ), ~( 'little_set'( X ) ), member(
% 0.71/1.11 'empty_set', f44( X ) ) ],
% 0.71/1.11 [ member( X, 'natural_numbers' ), ~( 'little_set'( X ) ), ~( member( Y,
% 0.71/1.11 f44( X ) ) ), member( successor( Y ), f44( X ) ) ],
% 0.71/1.11 [ member( X, 'natural_numbers' ), ~( member( X, f44( X ) ) ) ],
% 0.71/1.11 [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), member( f45( X, Y ),
% 0.71/1.11 'natural_numbers' ), member( f46( X, Y ), 'natural_numbers' ), member( X
% 0.71/1.11 , Y ) ],
% 0.71/1.11 [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), member( f45( X, Y ),
% 0.71/1.11 'natural_numbers' ), member( f47( X, Y ), 'natural_numbers' ), member( X
% 0.71/1.11 , Y ) ],
% 0.71/1.11 [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), member( f45( X, Y ),
% 0.71/1.11 'natural_numbers' ), member( f48( X, Y ), 'natural_numbers' ), member( X
% 0.71/1.11 , Y ) ],
% 0.71/1.11 [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), member( f45( X, Y ),
% 0.71/1.11 'natural_numbers' ), member( 'ordered_pair'( 'ordered_pair'( f46( X, Y )
% 0.71/1.11 , f47( X, Y ) ), f48( X, Y ) ), Y ), member( X, Y ) ],
% 0.71/1.11 [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), member( f45( X, Y ),
% 0.71/1.11 'natural_numbers' ), ~( member( 'ordered_pair'( 'ordered_pair'( successor(
% 0.71/1.11 f46( X, Y ) ), f47( X, Y ) ), successor( f48( X, Y ) ) ), Y ) ), member(
% 0.71/1.11 X, Y ) ],
% 0.71/1.11 [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), ~( member(
% 0.71/1.11 'ordered_pair'( 'ordered_pair'( 'empty_set', f45( X, Y ) ), f45( X, Y ) )
% 0.71/1.11 , Y ) ), member( f46( X, Y ), 'natural_numbers' ), member( X, Y ) ],
% 0.71/1.11 [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), ~( member(
% 0.71/1.11 'ordered_pair'( 'ordered_pair'( 'empty_set', f45( X, Y ) ), f45( X, Y ) )
% 0.71/1.11 , Y ) ), member( f47( X, Y ), 'natural_numbers' ), member( X, Y ) ],
% 0.71/1.11 [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), ~( member(
% 0.71/1.11 'ordered_pair'( 'ordered_pair'( 'empty_set', f45( X, Y ) ), f45( X, Y ) )
% 0.71/1.11 , Y ) ), member( f48( X, Y ), 'natural_numbers' ), member( X, Y ) ],
% 0.71/1.11 [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), ~( member(
% 0.71/1.11 'ordered_pair'( 'ordered_pair'( 'empty_set', f45( X, Y ) ), f45( X, Y ) )
% 0.71/1.11 , Y ) ), member( 'ordered_pair'( 'ordered_pair'( f46( X, Y ), f47( X, Y )
% 0.71/1.11 ), f48( X, Y ) ), Y ), member( X, Y ) ],
% 0.71/1.11 [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), ~( member(
% 0.71/1.11 'ordered_pair'( 'ordered_pair'( 'empty_set', f45( X, Y ) ), f45( X, Y ) )
% 0.71/1.11 , Y ) ), ~( member( 'ordered_pair'( 'ordered_pair'( successor( f46( X, Y
% 0.71/1.11 ) ), f47( X, Y ) ), successor( f48( X, Y ) ) ), Y ) ), member( X, Y ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ member( X, plus ), ~( 'little_set'( X ) ), 'little_set'( f49( X ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ member( X, plus ), ~( 'little_set'( X ) ), ~( member( Y,
% 0.71/1.11 'natural_numbers' ) ), member( 'ordered_pair'( 'ordered_pair'(
% 0.71/1.11 'empty_set', Y ), Y ), f49( X ) ) ],
% 0.71/1.11 [ member( X, plus ), ~( 'little_set'( X ) ), ~( member( Y,
% 0.71/1.11 'natural_numbers' ) ), ~( member( Z, 'natural_numbers' ) ), ~( member( T
% 0.71/1.11 , 'natural_numbers' ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, Z
% 0.71/1.11 ), T ), f49( X ) ) ), member( 'ordered_pair'( 'ordered_pair'( successor(
% 0.71/1.11 Y ), Z ), successor( T ) ), f49( X ) ) ],
% 0.71/1.11 [ member( X, plus ), ~( member( X, f49( X ) ) ) ],
% 0.71/1.11 [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), member( f50( X, Y ),
% 0.71/1.11 'natural_numbers' ), member( f51( X, Y ), 'natural_numbers' ), member( X
% 0.71/1.11 , Y ) ],
% 0.71/1.11 [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), member( f50( X, Y ),
% 0.71/1.11 'natural_numbers' ), member( f52( X, Y ), 'natural_numbers' ), member( X
% 0.71/1.11 , Y ) ],
% 0.71/1.11 [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), member( f50( X, Y ),
% 0.71/1.11 'natural_numbers' ), member( f53( X, Y ), 'natural_numbers' ), member( X
% 0.71/1.11 , Y ) ],
% 0.71/1.11 [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), member( f50( X, Y ),
% 0.71/1.11 'natural_numbers' ), member( 'ordered_pair'( 'ordered_pair'( f51( X, Y )
% 0.71/1.11 , f52( X, Y ) ), f53( X, Y ) ), Y ), member( X, Y ) ],
% 0.71/1.11 [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), member( f50( X, Y ),
% 0.71/1.11 'natural_numbers' ), ~( member( 'ordered_pair'( 'ordered_pair'( successor(
% 0.71/1.11 f51( X, Y ) ), f52( X, Y ) ), 'apply_to_two_arguments'( plus, f53( X, Y )
% 0.71/1.11 , f52( X, Y ) ) ), Y ) ), member( X, Y ) ],
% 0.71/1.11 [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), ~( member(
% 0.71/1.11 'ordered_pair'( 'ordered_pair'( 'empty_set', f50( X, Y ) ), 'empty_set' )
% 0.71/1.11 , Y ) ), member( f51( X, Y ), 'natural_numbers' ), member( X, Y ) ],
% 0.71/1.11 [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), ~( member(
% 0.71/1.11 'ordered_pair'( 'ordered_pair'( 'empty_set', f50( X, Y ) ), 'empty_set' )
% 0.71/1.11 , Y ) ), member( f52( X, Y ), 'natural_numbers' ), member( X, Y ) ],
% 0.71/1.11 [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), ~( member(
% 0.71/1.11 'ordered_pair'( 'ordered_pair'( 'empty_set', f50( X, Y ) ), 'empty_set' )
% 0.71/1.11 , Y ) ), member( f53( X, Y ), 'natural_numbers' ), member( X, Y ) ],
% 0.71/1.11 [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), ~( member(
% 0.71/1.11 'ordered_pair'( 'ordered_pair'( 'empty_set', f50( X, Y ) ), 'empty_set' )
% 0.71/1.11 , Y ) ), member( 'ordered_pair'( 'ordered_pair'( f51( X, Y ), f52( X, Y )
% 0.71/1.11 ), f53( X, Y ) ), Y ), member( X, Y ) ],
% 0.71/1.11 [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), ~( member(
% 0.71/1.11 'ordered_pair'( 'ordered_pair'( 'empty_set', f50( X, Y ) ), 'empty_set' )
% 0.71/1.11 , Y ) ), ~( member( 'ordered_pair'( 'ordered_pair'( successor( f51( X, Y
% 0.71/1.11 ) ), f52( X, Y ) ), 'apply_to_two_arguments'( plus, f53( X, Y ), f52( X
% 0.71/1.11 , Y ) ) ), Y ) ), member( X, Y ) ],
% 0.71/1.11 [ member( X, times ), ~( 'little_set'( X ) ), 'little_set'( f54( X ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ member( X, times ), ~( 'little_set'( X ) ), ~( member( Y,
% 0.71/1.11 'natural_numbers' ) ), member( 'ordered_pair'( 'ordered_pair'(
% 0.71/1.11 'empty_set', Y ), 'empty_set' ), f54( X ) ) ],
% 0.71/1.11 [ member( X, times ), ~( 'little_set'( X ) ), ~( member( Y,
% 0.71/1.11 'natural_numbers' ) ), ~( member( Z, 'natural_numbers' ) ), ~( member( T
% 0.71/1.11 , 'natural_numbers' ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, Z
% 0.71/1.11 ), T ), f54( X ) ) ), member( 'ordered_pair'( 'ordered_pair'( successor(
% 0.71/1.11 Y ), Z ), 'apply_to_two_arguments'( plus, T, Z ) ), f54( X ) ) ],
% 0.71/1.11 [ member( X, times ), ~( member( X, f54( X ) ) ) ],
% 0.71/1.11 [ ~( member( X, 'prime_numbers' ) ), member( X, 'natural_numbers' ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, 'prime_numbers' ) ), ~( =( X, 'empty_set' ) ) ],
% 0.71/1.11 [ ~( member( X, 'prime_numbers' ) ), ~( =( X, successor( 'empty_set' ) )
% 0.71/1.11 ) ],
% 0.71/1.11 [ ~( member( X, 'prime_numbers' ) ), ~( member( Y, 'natural_numbers' ) )
% 0.71/1.11 , ~( member( Z, 'natural_numbers' ) ), ~( =( 'apply_to_two_arguments'(
% 0.71/1.11 times, Y, Z ), X ) ), member( Y, 'non_ordered_pair'( successor(
% 0.71/1.11 'empty_set' ), X ) ) ],
% 0.71/1.11 [ member( X, 'prime_numbers' ), ~( member( X, 'natural_numbers' ) ), =(
% 0.71/1.11 X, 'empty_set' ), =( X, successor( 'empty_set' ) ), member( f55( X ),
% 0.71/1.11 'natural_numbers' ) ],
% 0.71/1.11 [ member( X, 'prime_numbers' ), ~( member( X, 'natural_numbers' ) ), =(
% 0.71/1.11 X, 'empty_set' ), =( X, successor( 'empty_set' ) ), member( f56( X ),
% 0.71/1.11 'natural_numbers' ) ],
% 0.71/1.11 [ member( X, 'prime_numbers' ), ~( member( X, 'natural_numbers' ) ), =(
% 0.71/1.11 X, 'empty_set' ), =( X, successor( 'empty_set' ) ), =(
% 0.71/1.11 'apply_to_two_arguments'( times, f55( X ), f56( X ) ), X ) ],
% 0.71/1.11 [ member( X, 'prime_numbers' ), ~( member( X, 'natural_numbers' ) ), =(
% 0.71/1.11 X, 'empty_set' ), =( X, successor( 'empty_set' ) ), ~( member( f55( X ),
% 0.71/1.11 'non_ordered_pair'( successor( 'empty_set' ), X ) ) ) ],
% 0.71/1.11 [ ~( finite( X ) ), member( f57( X ), 'natural_numbers' ) ],
% 0.71/1.11 [ ~( finite( X ) ), maps( f58( X ), f57( X ), X ) ],
% 0.71/1.11 [ ~( finite( X ) ), =( 'range_of'( f58( X ) ), X ) ],
% 0.71/1.11 [ ~( finite( X ) ), 'one_to_one_function'( f58( X ) ) ],
% 0.71/1.11 [ finite( X ), ~( member( Y, 'natural_numbers' ) ), ~( maps( Z, Y, X ) )
% 0.71/1.11 , ~( =( 'range_of'( Z ), X ) ), ~( 'one_to_one_function'( Z ) ) ],
% 0.71/1.11 [ ~( member( X, 'twin_prime_numbers' ) ), member( X, 'prime_numbers' ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, 'twin_prime_numbers' ) ), member( successor( successor(
% 0.71/1.11 X ) ), 'prime_numbers' ) ],
% 0.71/1.11 [ member( X, 'twin_prime_numbers' ), ~( member( X, 'prime_numbers' ) ),
% 0.71/1.11 ~( member( successor( successor( X ) ), 'prime_numbers' ) ) ],
% 0.71/1.11 [ ~( member( X, 'even_numbers' ) ), member( X, 'natural_numbers' ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, 'even_numbers' ) ), member( f59( X ), 'natural_numbers'
% 0.71/1.11 ) ],
% 0.71/1.11 [ ~( member( X, 'even_numbers' ) ), =( 'apply_to_two_arguments'( plus,
% 0.71/1.11 f59( X ), f59( X ) ), X ) ],
% 0.71/1.11 [ member( X, 'even_numbers' ), ~( member( X, 'natural_numbers' ) ), ~(
% 0.71/1.11 member( Y, 'natural_numbers' ) ), ~( =( 'apply_to_two_arguments'( plus, Y
% 0.71/1.11 , Y ), X ) ) ],
% 0.71/1.11 [ ~( member( 'empty_set', 'natural_numbers' ) ) ]
% 0.71/1.11 ] .
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 percentage equality = 0.117739, percentage horn = 0.731818
% 0.71/1.11 This is a problem with some equality
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Options Used:
% 0.71/1.11
% 0.71/1.11 useres = 1
% 0.71/1.11 useparamod = 1
% 0.71/1.11 useeqrefl = 1
% 0.71/1.11 useeqfact = 1
% 0.71/1.11 usefactor = 1
% 0.71/1.11 usesimpsplitting = 0
% 0.71/1.11 usesimpdemod = 5
% 0.71/1.11 usesimpres = 3
% 0.71/1.11
% 0.71/1.11 resimpinuse = 1000
% 0.71/1.11 resimpclauses = 20000
% 0.71/1.11 substype = eqrewr
% 0.71/1.11 backwardsubs = 1
% 0.71/1.11 selectoldest = 5
% 0.71/1.11
% 0.71/1.11 litorderings [0] = split
% 0.71/1.11 litorderings [1] = extend the termordering, first sorting on arguments
% 0.71/1.11
% 0.71/1.11 termordering = kbo
% 0.71/1.11
% 0.71/1.11 litapriori = 0
% 0.71/1.11 termapriori = 1
% 0.71/1.11 litaposteriori = 0
% 0.71/1.11 termaposteriori = 0
% 0.71/1.11 demodaposteriori = 0
% 0.71/1.11 ordereqreflfact = 0
% 0.71/1.11
% 0.71/1.11 litselect = negord
% 3.71/4.13
% 3.71/4.13 maxweight = 15
% 3.71/4.13 maxdepth = 30000
% 3.71/4.13 maxlength = 115
% 3.71/4.13 maxnrvars = 195
% 3.71/4.13 excuselevel = 1
% 3.71/4.13 increasemaxweight = 1
% 3.71/4.13
% 3.71/4.13 maxselected = 10000000
% 3.71/4.13 maxnrclauses = 10000000
% 3.71/4.13
% 3.71/4.13 showgenerated = 0
% 3.71/4.13 showkept = 0
% 3.71/4.13 showselected = 0
% 3.71/4.13 showdeleted = 0
% 3.71/4.13 showresimp = 1
% 3.71/4.13 showstatus = 2000
% 3.71/4.13
% 3.71/4.13 prologoutput = 1
% 3.71/4.13 nrgoals = 5000000
% 3.71/4.13 totalproof = 1
% 3.71/4.13
% 3.71/4.13 Symbols occurring in the translation:
% 3.71/4.13
% 3.71/4.13 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 3.71/4.13 . [1, 2] (w:1, o:83, a:1, s:1, b:0),
% 3.71/4.13 ! [4, 1] (w:0, o:43, a:1, s:1, b:0),
% 3.71/4.13 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.71/4.13 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.71/4.13 member [41, 2] (w:1, o:108, a:1, s:1, b:0),
% 3.71/4.13 'little_set' [42, 1] (w:1, o:48, a:1, s:1, b:0),
% 3.71/4.13 f1 [43, 2] (w:1, o:109, a:1, s:1, b:0),
% 3.71/4.13 'non_ordered_pair' [45, 2] (w:1, o:110, a:1, s:1, b:0),
% 3.71/4.13 'singleton_set' [46, 1] (w:1, o:52, a:1, s:1, b:0),
% 3.71/4.13 'ordered_pair' [47, 2] (w:1, o:111, a:1, s:1, b:0),
% 3.71/4.13 'ordered_pair_predicate' [48, 1] (w:1, o:53, a:1, s:1, b:0),
% 3.71/4.13 f2 [49, 1] (w:1, o:56, a:1, s:1, b:0),
% 3.71/4.13 f3 [50, 1] (w:1, o:61, a:1, s:1, b:0),
% 3.71/4.13 first [52, 1] (w:1, o:62, a:1, s:1, b:0),
% 3.71/4.13 f4 [53, 2] (w:1, o:116, a:1, s:1, b:0),
% 3.71/4.13 f5 [54, 2] (w:1, o:125, a:1, s:1, b:0),
% 3.71/4.13 second [56, 1] (w:1, o:63, a:1, s:1, b:0),
% 3.71/4.13 f6 [57, 2] (w:1, o:130, a:1, s:1, b:0),
% 3.71/4.13 f7 [58, 2] (w:1, o:131, a:1, s:1, b:0),
% 3.71/4.13 estin [59, 0] (w:1, o:31, a:1, s:1, b:0),
% 3.71/4.13 intersection [60, 2] (w:1, o:133, a:1, s:1, b:0),
% 3.71/4.13 complement [61, 1] (w:1, o:64, a:1, s:1, b:0),
% 3.71/4.13 union [62, 2] (w:1, o:134, a:1, s:1, b:0),
% 3.71/4.13 'domain_of' [63, 1] (w:1, o:66, a:1, s:1, b:0),
% 3.71/4.13 f8 [64, 2] (w:1, o:135, a:1, s:1, b:0),
% 3.71/4.13 'cross_product' [66, 2] (w:1, o:136, a:1, s:1, b:0),
% 3.71/4.13 converse [67, 1] (w:1, o:65, a:1, s:1, b:0),
% 3.71/4.13 'rotate_right' [68, 1] (w:1, o:49, a:1, s:1, b:0),
% 3.71/4.13 f9 [69, 2] (w:1, o:137, a:1, s:1, b:0),
% 3.71/4.13 f10 [70, 2] (w:1, o:138, a:1, s:1, b:0),
% 3.71/4.13 f11 [71, 2] (w:1, o:139, a:1, s:1, b:0),
% 3.71/4.13 'flip_range_of' [73, 1] (w:1, o:67, a:1, s:1, b:0),
% 3.71/4.13 f12 [74, 2] (w:1, o:140, a:1, s:1, b:0),
% 3.71/4.13 f13 [75, 2] (w:1, o:141, a:1, s:1, b:0),
% 3.71/4.13 f14 [76, 2] (w:1, o:142, a:1, s:1, b:0),
% 3.71/4.13 successor [77, 1] (w:1, o:68, a:1, s:1, b:0),
% 3.71/4.13 'empty_set' [78, 0] (w:1, o:32, a:1, s:1, b:0),
% 3.71/4.13 'universal_set' [79, 0] (w:1, o:35, a:1, s:1, b:0),
% 3.71/4.13 infinity [80, 0] (w:1, o:36, a:1, s:1, b:0),
% 3.71/4.13 sigma [81, 1] (w:1, o:69, a:1, s:1, b:0),
% 3.71/4.13 f16 [82, 2] (w:1, o:143, a:1, s:1, b:0),
% 3.71/4.13 subset [83, 2] (w:1, o:145, a:1, s:1, b:0),
% 3.71/4.13 f17 [84, 2] (w:1, o:146, a:1, s:1, b:0),
% 3.71/4.13 'proper_subset' [85, 2] (w:1, o:147, a:1, s:1, b:0),
% 3.71/4.13 powerset [86, 1] (w:1, o:71, a:1, s:1, b:0),
% 3.71/4.13 relation [87, 1] (w:1, o:50, a:1, s:1, b:0),
% 3.71/4.13 f18 [88, 1] (w:1, o:54, a:1, s:1, b:0),
% 3.71/4.13 'single_valued_set' [89, 1] (w:1, o:72, a:1, s:1, b:0),
% 3.71/4.13 f19 [90, 1] (w:1, o:55, a:1, s:1, b:0),
% 3.71/4.13 f20 [91, 1] (w:1, o:57, a:1, s:1, b:0),
% 3.71/4.13 f21 [92, 1] (w:1, o:58, a:1, s:1, b:0),
% 3.71/4.13 function [94, 1] (w:1, o:73, a:1, s:1, b:0),
% 3.71/4.13 image [95, 2] (w:1, o:132, a:1, s:1, b:0),
% 3.71/4.13 f22 [96, 3] (w:1, o:157, a:1, s:1, b:0),
% 3.71/4.13 disjoint [97, 2] (w:1, o:151, a:1, s:1, b:0),
% 3.71/4.13 f23 [98, 2] (w:1, o:152, a:1, s:1, b:0),
% 3.71/4.13 f24 [99, 1] (w:1, o:59, a:1, s:1, b:0),
% 3.71/4.13 f25 [100, 0] (w:1, o:38, a:1, s:1, b:0),
% 3.71/4.13 f26 [101, 1] (w:1, o:60, a:1, s:1, b:0),
% 3.71/4.13 'range_of' [102, 1] (w:1, o:51, a:1, s:1, b:0),
% 3.71/4.13 f27 [103, 2] (w:1, o:153, a:1, s:1, b:0),
% 3.71/4.13 'identity_relation' [104, 0] (w:1, o:39, a:1, s:1, b:0),
% 3.71/4.13 restrict [105, 2] (w:1, o:144, a:1, s:1, b:0),
% 3.71/4.13 'one_to_one_function' [106, 1] (w:1, o:70, a:1, s:1, b:0),
% 3.71/4.13 apply [107, 2] (w:1, o:154, a:1, s:1, b:0),
% 3.71/4.13 f28 [108, 3] (w:1, o:158, a:1, s:1, b:0),
% 3.71/4.13 'apply_to_two_arguments' [109, 3] (w:1, o:159, a:1, s:1, b:0),
% 3.71/4.13 maps [110, 3] (w:1, o:160, a:1, s:1, b:0),
% 3.71/4.13 closed [112, 2] (w:1, o:148, a:1, s:1, b:0),
% 3.71/4.13 compose [114, 2] (w:1, o:149, a:1, s:1, b:0),
% 4.40/4.78 f29 [115, 3] (w:1, o:161, a:1, s:1, b:0),
% 4.40/4.78 f30 [116, 3] (w:1, o:162, a:1, s:1, b:0),
% 4.40/4.78 f31 [117, 3] (w:1, o:163, a:1, s:1, b:0),
% 4.40/4.78 homomorphism [123, 5] (w:1, o:168, a:1, s:1, b:0),
% 4.40/4.78 f32 [124, 5] (w:1, o:169, a:1, s:1, b:0),
% 4.40/4.78 f33 [125, 5] (w:1, o:170, a:1, s:1, b:0),
% 4.40/4.78 associative [126, 2] (w:1, o:155, a:1, s:1, b:0),
% 4.40/4.78 f34 [127, 2] (w:1, o:112, a:1, s:1, b:0),
% 4.40/4.78 f35 [128, 2] (w:1, o:113, a:1, s:1, b:0),
% 4.40/4.78 f36 [129, 2] (w:1, o:114, a:1, s:1, b:0),
% 4.40/4.78 identity [131, 3] (w:1, o:164, a:1, s:1, b:0),
% 4.40/4.78 f37 [132, 3] (w:1, o:165, a:1, s:1, b:0),
% 4.40/4.78 inverse [133, 4] (w:1, o:166, a:1, s:1, b:0),
% 4.40/4.78 f38 [134, 4] (w:1, o:167, a:1, s:1, b:0),
% 4.40/4.78 group [135, 2] (w:1, o:156, a:1, s:1, b:0),
% 4.40/4.78 f39 [136, 2] (w:1, o:115, a:1, s:1, b:0),
% 4.40/4.78 f40 [137, 2] (w:1, o:117, a:1, s:1, b:0),
% 4.40/4.78 commutes [138, 2] (w:1, o:150, a:1, s:1, b:0),
% 4.40/4.78 f41 [139, 2] (w:1, o:118, a:1, s:1, b:0),
% 4.40/4.78 f42 [140, 2] (w:1, o:119, a:1, s:1, b:0),
% 4.40/4.78 'natural_numbers' [141, 0] (w:1, o:40, a:1, s:1, b:0),
% 4.40/4.78 f43 [142, 2] (w:1, o:120, a:1, s:1, b:0),
% 4.40/4.78 f44 [143, 1] (w:1, o:74, a:1, s:1, b:0),
% 4.40/4.78 plus [145, 0] (w:1, o:41, a:1, s:1, b:0),
% 4.40/4.78 f45 [146, 2] (w:1, o:121, a:1, s:1, b:0),
% 4.40/4.78 f46 [147, 2] (w:1, o:122, a:1, s:1, b:0),
% 4.40/4.78 f47 [148, 2] (w:1, o:123, a:1, s:1, b:0),
% 4.40/4.78 f48 [149, 2] (w:1, o:124, a:1, s:1, b:0),
% 4.40/4.78 f49 [150, 1] (w:1, o:75, a:1, s:1, b:0),
% 4.40/4.78 times [154, 0] (w:1, o:33, a:1, s:1, b:0),
% 4.40/4.78 f50 [155, 2] (w:1, o:126, a:1, s:1, b:0),
% 4.40/4.78 f51 [156, 2] (w:1, o:127, a:1, s:1, b:0),
% 4.40/4.78 f52 [157, 2] (w:1, o:128, a:1, s:1, b:0),
% 4.40/4.78 f53 [158, 2] (w:1, o:129, a:1, s:1, b:0),
% 4.40/4.78 f54 [159, 1] (w:1, o:76, a:1, s:1, b:0),
% 4.40/4.78 'prime_numbers' [161, 0] (w:1, o:42, a:1, s:1, b:0),
% 4.40/4.78 f55 [162, 1] (w:1, o:77, a:1, s:1, b:0),
% 4.40/4.78 f56 [163, 1] (w:1, o:78, a:1, s:1, b:0),
% 4.40/4.78 finite [164, 1] (w:1, o:79, a:1, s:1, b:0),
% 4.40/4.78 f57 [165, 1] (w:1, o:80, a:1, s:1, b:0),
% 4.40/4.78 f58 [166, 1] (w:1, o:81, a:1, s:1, b:0),
% 4.40/4.78 'twin_prime_numbers' [168, 0] (w:1, o:34, a:1, s:1, b:0),
% 4.40/4.78 'even_numbers' [169, 0] (w:1, o:37, a:1, s:1, b:0),
% 4.40/4.78 f59 [170, 1] (w:1, o:82, a:1, s:1, b:0).
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 Starting Search:
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 Intermediate Status:
% 4.40/4.78 Generated: 3638
% 4.40/4.78 Kept: 2063
% 4.40/4.78 Inuse: 91
% 4.40/4.78 Deleted: 0
% 4.40/4.78 Deletedinuse: 0
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 Intermediate Status:
% 4.40/4.78 Generated: 7020
% 4.40/4.78 Kept: 4089
% 4.40/4.78 Inuse: 149
% 4.40/4.78 Deleted: 3
% 4.40/4.78 Deletedinuse: 0
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 Intermediate Status:
% 4.40/4.78 Generated: 10367
% 4.40/4.78 Kept: 6111
% 4.40/4.78 Inuse: 215
% 4.40/4.78 Deleted: 13
% 4.40/4.78 Deletedinuse: 0
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 Intermediate Status:
% 4.40/4.78 Generated: 15952
% 4.40/4.78 Kept: 8133
% 4.40/4.78 Inuse: 265
% 4.40/4.78 Deleted: 15
% 4.40/4.78 Deletedinuse: 0
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 Intermediate Status:
% 4.40/4.78 Generated: 19769
% 4.40/4.78 Kept: 10800
% 4.40/4.78 Inuse: 301
% 4.40/4.78 Deleted: 15
% 4.40/4.78 Deletedinuse: 0
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 Intermediate Status:
% 4.40/4.78 Generated: 25071
% 4.40/4.78 Kept: 12807
% 4.40/4.78 Inuse: 353
% 4.40/4.78 Deleted: 19
% 4.40/4.78 Deletedinuse: 1
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 Intermediate Status:
% 4.40/4.78 Generated: 31388
% 4.40/4.78 Kept: 15135
% 4.40/4.78 Inuse: 389
% 4.40/4.78 Deleted: 28
% 4.40/4.78 Deletedinuse: 1
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 Intermediate Status:
% 4.40/4.78 Generated: 37181
% 4.40/4.78 Kept: 17658
% 4.40/4.78 Inuse: 422
% 4.40/4.78 Deleted: 175
% 4.40/4.78 Deletedinuse: 101
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 Intermediate Status:
% 4.40/4.78 Generated: 43699
% 4.40/4.78 Kept: 19822
% 4.40/4.78 Inuse: 475
% 4.40/4.78 Deleted: 197
% 4.40/4.78 Deletedinuse: 101
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78 Resimplifying clauses:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 Intermediate Status:
% 4.40/4.78 Generated: 51364
% 4.40/4.78 Kept: 21857
% 4.40/4.78 Inuse: 513
% 4.40/4.78 Deleted: 3659
% 4.40/4.78 Deletedinuse: 108
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 Intermediate Status:
% 4.40/4.78 Generated: 56435
% 4.40/4.78 Kept: 24055
% 4.40/4.78 Inuse: 548
% 4.40/4.78 Deleted: 3659
% 4.40/4.78 Deletedinuse: 108
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 Intermediate Status:
% 4.40/4.78 Generated: 62138
% 4.40/4.78 Kept: 26072
% 4.40/4.78 Inuse: 587
% 4.40/4.78 Deleted: 3659
% 4.40/4.78 Deletedinuse: 108
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 Intermediate Status:
% 4.40/4.78 Generated: 66749
% 4.40/4.78 Kept: 28101
% 4.40/4.78 Inuse: 613
% 4.40/4.78 Deleted: 3659
% 4.40/4.78 Deletedinuse: 108
% 4.40/4.78
% 4.40/4.78 Resimplifying inuse:
% 4.40/4.78 Done
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 Bliksems!, er is een bewijs:
% 4.40/4.78 % SZS status Unsatisfiable
% 4.40/4.78 % SZS output start Refutation
% 4.40/4.78
% 4.40/4.78 clause( 0, [ ~( member( X, Y ) ), 'little_set'( X ) ] )
% 4.40/4.78 .
% 4.40/4.78 clause( 60, [ member( 'empty_set', infinity ) ] )
% 4.40/4.78 .
% 4.40/4.78 clause( 168, [ member( X, 'natural_numbers' ), ~( 'little_set'( X ) ),
% 4.40/4.78 member( 'empty_set', f44( X ) ) ] )
% 4.40/4.78 .
% 4.40/4.78 clause( 170, [ member( X, 'natural_numbers' ), ~( member( X, f44( X ) ) ) ]
% 4.40/4.78 )
% 4.40/4.78 .
% 4.40/4.78 clause( 219, [ ~( member( 'empty_set', 'natural_numbers' ) ) ] )
% 4.40/4.78 .
% 4.40/4.78 clause( 297, [ 'little_set'( 'empty_set' ) ] )
% 4.40/4.78 .
% 4.40/4.78 clause( 28475, [ member( 'empty_set', f44( 'empty_set' ) ) ] )
% 4.40/4.78 .
% 4.40/4.78 clause( 29047, [] )
% 4.40/4.78 .
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 % SZS output end Refutation
% 4.40/4.78 found a proof!
% 4.40/4.78
% 4.40/4.78 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 4.40/4.78
% 4.40/4.78 initialclauses(
% 4.40/4.78 [ clause( 29049, [ ~( member( X, Y ) ), 'little_set'( X ) ] )
% 4.40/4.78 , clause( 29050, [ 'little_set'( f1( X, Y ) ), =( X, Y ) ] )
% 4.40/4.78 , clause( 29051, [ member( f1( X, Y ), X ), member( f1( X, Y ), Y ), =( X,
% 4.40/4.78 Y ) ] )
% 4.40/4.78 , clause( 29052, [ ~( member( f1( X, Y ), X ) ), ~( member( f1( X, Y ), Y )
% 4.40/4.78 ), =( X, Y ) ] )
% 4.40/4.78 , clause( 29053, [ ~( member( X, 'non_ordered_pair'( Y, Z ) ) ), =( X, Y )
% 4.40/4.78 , =( X, Z ) ] )
% 4.40/4.78 , clause( 29054, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'(
% 4.40/4.78 X ) ), ~( =( X, Y ) ) ] )
% 4.40/4.78 , clause( 29055, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'(
% 4.40/4.78 X ) ), ~( =( X, Z ) ) ] )
% 4.40/4.78 , clause( 29056, [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ] )
% 4.40/4.78 , clause( 29057, [ =( 'singleton_set'( X ), 'non_ordered_pair'( X, X ) ) ]
% 4.40/4.78 )
% 4.40/4.78 , clause( 29058, [ =( 'ordered_pair'( X, Y ), 'non_ordered_pair'(
% 4.40/4.78 'singleton_set'( X ), 'non_ordered_pair'( X, Y ) ) ) ] )
% 4.40/4.78 , clause( 29059, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f2( X
% 4.40/4.78 ) ) ] )
% 4.40/4.78 , clause( 29060, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f3( X
% 4.40/4.78 ) ) ] )
% 4.40/4.78 , clause( 29061, [ ~( 'ordered_pair_predicate'( X ) ), =( X, 'ordered_pair'(
% 4.40/4.78 f2( X ), f3( X ) ) ) ] )
% 4.40/4.78 , clause( 29062, [ 'ordered_pair_predicate'( X ), ~( 'little_set'( Y ) ),
% 4.40/4.78 ~( 'little_set'( Z ) ), ~( =( X, 'ordered_pair'( Y, Z ) ) ) ] )
% 4.40/4.78 , clause( 29063, [ ~( member( X, first( Y ) ) ), 'little_set'( f4( X, Y ) )
% 4.40/4.78 ] )
% 4.40/4.78 , clause( 29064, [ ~( member( X, first( Y ) ) ), 'little_set'( f5( X, Y ) )
% 4.40/4.78 ] )
% 4.40/4.78 , clause( 29065, [ ~( member( X, first( Y ) ) ), =( Y, 'ordered_pair'( f4(
% 4.40/4.78 X, Y ), f5( X, Y ) ) ) ] )
% 4.40/4.78 , clause( 29066, [ ~( member( X, first( Y ) ) ), member( X, f4( X, Y ) ) ]
% 4.40/4.78 )
% 4.40/4.78 , clause( 29067, [ member( X, first( Y ) ), ~( 'little_set'( Z ) ), ~(
% 4.40/4.78 'little_set'( T ) ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, Z
% 4.40/4.78 ) ) ] )
% 4.40/4.78 , clause( 29068, [ ~( member( X, second( Y ) ) ), 'little_set'( f6( X, Y )
% 4.40/4.78 ) ] )
% 4.40/4.78 , clause( 29069, [ ~( member( X, second( Y ) ) ), 'little_set'( f7( X, Y )
% 4.40/4.78 ) ] )
% 4.40/4.78 , clause( 29070, [ ~( member( X, second( Y ) ) ), =( Y, 'ordered_pair'( f6(
% 4.40/4.78 X, Y ), f7( X, Y ) ) ) ] )
% 4.40/4.78 , clause( 29071, [ ~( member( X, second( Y ) ) ), member( X, f7( X, Y ) ) ]
% 4.40/4.78 )
% 4.40/4.78 , clause( 29072, [ member( X, second( Y ) ), ~( 'little_set'( Z ) ), ~(
% 4.40/4.78 'little_set'( T ) ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, T
% 4.40/4.78 ) ) ] )
% 4.40/4.78 , clause( 29073, [ ~( member( X, estin ) ), 'ordered_pair_predicate'( X ) ]
% 4.40/4.78 )
% 4.40/4.78 , clause( 29074, [ ~( member( X, estin ) ), member( first( X ), second( X )
% 4.40/4.78 ) ] )
% 4.40/4.78 , clause( 29075, [ member( X, estin ), ~( 'little_set'( X ) ), ~(
% 4.40/4.78 'ordered_pair_predicate'( X ) ), ~( member( first( X ), second( X ) ) ) ]
% 4.40/4.78 )
% 4.40/4.78 , clause( 29076, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 4.40/4.78 )
% 4.40/4.78 , clause( 29077, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 4.40/4.78 )
% 4.40/4.78 , clause( 29078, [ member( X, intersection( Y, Z ) ), ~( member( X, Y ) ),
% 4.40/4.78 ~( member( X, Z ) ) ] )
% 4.40/4.78 , clause( 29079, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 4.40/4.78 )
% 4.40/4.78 , clause( 29080, [ member( X, complement( Y ) ), ~( 'little_set'( X ) ),
% 4.40/4.78 member( X, Y ) ] )
% 4.40/4.78 , clause( 29081, [ =( union( X, Y ), complement( intersection( complement(
% 4.40/4.78 X ), complement( Y ) ) ) ) ] )
% 4.40/4.78 , clause( 29082, [ ~( member( X, 'domain_of'( Y ) ) ),
% 4.40/4.78 'ordered_pair_predicate'( f8( X, Y ) ) ] )
% 4.40/4.78 , clause( 29083, [ ~( member( X, 'domain_of'( Y ) ) ), member( f8( X, Y ),
% 4.40/4.78 Y ) ] )
% 4.40/4.78 , clause( 29084, [ ~( member( X, 'domain_of'( Y ) ) ), =( X, first( f8( X,
% 4.40/4.78 Y ) ) ) ] )
% 4.40/4.78 , clause( 29085, [ member( X, 'domain_of'( Y ) ), ~( 'little_set'( X ) ),
% 4.40/4.78 ~( 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, first(
% 4.40/4.78 Z ) ) ) ] )
% 4.40/4.78 , clause( 29086, [ ~( member( X, 'cross_product'( Y, Z ) ) ),
% 4.40/4.78 'ordered_pair_predicate'( X ) ] )
% 4.40/4.78 , clause( 29087, [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( first(
% 4.40/4.78 X ), Y ) ] )
% 4.40/4.78 , clause( 29088, [ ~( member( X, 'cross_product'( Y, Z ) ) ), member(
% 4.40/4.78 second( X ), Z ) ] )
% 4.40/4.78 , clause( 29089, [ member( X, 'cross_product'( Y, Z ) ), ~( 'little_set'( X
% 4.40/4.78 ) ), ~( 'ordered_pair_predicate'( X ) ), ~( member( first( X ), Y ) ),
% 4.40/4.78 ~( member( second( X ), Z ) ) ] )
% 4.40/4.78 , clause( 29090, [ ~( member( X, converse( Y ) ) ),
% 4.40/4.78 'ordered_pair_predicate'( X ) ] )
% 4.40/4.78 , clause( 29091, [ ~( member( X, converse( Y ) ) ), member( 'ordered_pair'(
% 4.40/4.78 second( X ), first( X ) ), Y ) ] )
% 4.40/4.78 , clause( 29092, [ member( X, converse( Y ) ), ~( 'little_set'( X ) ), ~(
% 4.40/4.78 'ordered_pair_predicate'( X ) ), ~( member( 'ordered_pair'( second( X ),
% 4.40/4.78 first( X ) ), Y ) ) ] )
% 4.40/4.78 , clause( 29093, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f9(
% 4.40/4.78 X, Y ) ) ] )
% 4.40/4.78 , clause( 29094, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f10(
% 4.40/4.78 X, Y ) ) ] )
% 4.40/4.78 , clause( 29095, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f11(
% 4.40/4.78 X, Y ) ) ] )
% 4.40/4.78 , clause( 29096, [ ~( member( X, 'rotate_right'( Y ) ) ), =( X,
% 4.40/4.78 'ordered_pair'( f9( X, Y ), 'ordered_pair'( f10( X, Y ), f11( X, Y ) ) )
% 4.40/4.78 ) ] )
% 4.40/4.78 , clause( 29097, [ ~( member( X, 'rotate_right'( Y ) ) ), member(
% 4.40/4.78 'ordered_pair'( f10( X, Y ), 'ordered_pair'( f11( X, Y ), f9( X, Y ) ) )
% 4.40/4.78 , Y ) ] )
% 4.40/4.78 , clause( 29098, [ member( X, 'rotate_right'( Y ) ), ~( 'little_set'( X ) )
% 4.40/4.78 , ~( 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) )
% 4.40/4.78 , ~( =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 4.40/4.78 'ordered_pair'( T, 'ordered_pair'( U, Z ) ), Y ) ) ] )
% 4.40/4.78 , clause( 29099, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'(
% 4.40/4.78 f12( X, Y ) ) ] )
% 4.40/4.78 , clause( 29100, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'(
% 4.40/4.78 f13( X, Y ) ) ] )
% 4.40/4.78 , clause( 29101, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'(
% 4.40/4.78 f14( X, Y ) ) ] )
% 4.40/4.78 , clause( 29102, [ ~( member( X, 'flip_range_of'( Y ) ) ), =( X,
% 4.40/4.78 'ordered_pair'( f12( X, Y ), 'ordered_pair'( f13( X, Y ), f14( X, Y ) ) )
% 4.40/4.78 ) ] )
% 4.40/4.78 , clause( 29103, [ ~( member( X, 'flip_range_of'( Y ) ) ), member(
% 4.40/4.78 'ordered_pair'( f12( X, Y ), 'ordered_pair'( f14( X, Y ), f13( X, Y ) ) )
% 4.40/4.78 , Y ) ] )
% 4.40/4.78 , clause( 29104, [ member( X, 'flip_range_of'( Y ) ), ~( 'little_set'( X )
% 4.40/4.78 ), ~( 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U )
% 4.40/4.78 ), ~( =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 4.40/4.78 'ordered_pair'( Z, 'ordered_pair'( U, T ) ), Y ) ) ] )
% 4.40/4.78 , clause( 29105, [ =( successor( X ), union( X, 'singleton_set'( X ) ) ) ]
% 4.40/4.78 )
% 4.40/4.78 , clause( 29106, [ ~( member( X, 'empty_set' ) ) ] )
% 4.40/4.78 , clause( 29107, [ member( X, 'universal_set' ), ~( 'little_set'( X ) ) ]
% 4.40/4.78 )
% 4.40/4.78 , clause( 29108, [ 'little_set'( infinity ) ] )
% 4.40/4.78 , clause( 29109, [ member( 'empty_set', infinity ) ] )
% 4.40/4.78 , clause( 29110, [ ~( member( X, infinity ) ), member( successor( X ),
% 4.40/4.78 infinity ) ] )
% 4.40/4.78 , clause( 29111, [ ~( member( X, sigma( Y ) ) ), member( f16( X, Y ), Y ) ]
% 4.40/4.78 )
% 4.40/4.78 , clause( 29112, [ ~( member( X, sigma( Y ) ) ), member( X, f16( X, Y ) ) ]
% 4.40/4.78 )
% 4.40/4.78 , clause( 29113, [ member( X, sigma( Y ) ), ~( member( Z, Y ) ), ~( member(
% 4.40/4.78 X, Z ) ) ] )
% 4.40/4.78 , clause( 29114, [ ~( 'little_set'( X ) ), 'little_set'( sigma( X ) ) ] )
% 4.40/4.78 , clause( 29115, [ ~( subset( X, Y ) ), ~( member( Z, X ) ), member( Z, Y )
% 4.40/4.78 ] )
% 4.40/4.78 , clause( 29116, [ subset( X, Y ), member( f17( X, Y ), X ) ] )
% 4.40/4.78 , clause( 29117, [ subset( X, Y ), ~( member( f17( X, Y ), Y ) ) ] )
% 4.40/4.78 , clause( 29118, [ ~( 'proper_subset'( X, Y ) ), subset( X, Y ) ] )
% 4.40/4.78 , clause( 29119, [ ~( 'proper_subset'( X, Y ) ), ~( =( X, Y ) ) ] )
% 4.40/4.78 , clause( 29120, [ 'proper_subset'( X, Y ), ~( subset( X, Y ) ), =( X, Y )
% 4.40/4.78 ] )
% 4.40/4.78 , clause( 29121, [ ~( member( X, powerset( Y ) ) ), subset( X, Y ) ] )
% 4.40/4.78 , clause( 29122, [ member( X, powerset( Y ) ), ~( 'little_set'( X ) ), ~(
% 4.40/4.78 subset( X, Y ) ) ] )
% 4.40/4.78 , clause( 29123, [ ~( 'little_set'( X ) ), 'little_set'( powerset( X ) ) ]
% 4.40/4.78 )
% 4.40/4.78 , clause( 29124, [ ~( relation( X ) ), ~( member( Y, X ) ),
% 4.40/4.78 'ordered_pair_predicate'( Y ) ] )
% 4.40/4.78 , clause( 29125, [ relation( X ), member( f18( X ), X ) ] )
% 4.40/4.78 , clause( 29126, [ relation( X ), ~( 'ordered_pair_predicate'( f18( X ) ) )
% 4.40/4.78 ] )
% 4.40/4.78 , clause( 29127, [ ~( 'single_valued_set'( X ) ), ~( 'little_set'( Y ) ),
% 4.40/4.78 ~( 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( member( 'ordered_pair'(
% 4.40/4.78 Y, Z ), X ) ), ~( member( 'ordered_pair'( Y, T ), X ) ), =( Z, T ) ] )
% 4.40/4.78 , clause( 29128, [ 'single_valued_set'( X ), 'little_set'( f19( X ) ) ] )
% 4.40/4.78 , clause( 29129, [ 'single_valued_set'( X ), 'little_set'( f20( X ) ) ] )
% 4.40/4.78 , clause( 29130, [ 'single_valued_set'( X ), 'little_set'( f21( X ) ) ] )
% 4.40/4.78 , clause( 29131, [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X
% 4.40/4.78 ), f20( X ) ), X ) ] )
% 4.40/4.78 , clause( 29132, [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X
% 4.40/4.78 ), f21( X ) ), X ) ] )
% 4.40/4.78 , clause( 29133, [ 'single_valued_set'( X ), ~( =( f20( X ), f21( X ) ) ) ]
% 4.40/4.78 )
% 4.40/4.78 , clause( 29134, [ ~( function( X ) ), relation( X ) ] )
% 4.40/4.78 , clause( 29135, [ ~( function( X ) ), 'single_valued_set'( X ) ] )
% 4.40/4.78 , clause( 29136, [ function( X ), ~( relation( X ) ), ~(
% 4.40/4.78 'single_valued_set'( X ) ) ] )
% 4.40/4.78 , clause( 29137, [ ~( member( X, image( Y, Z ) ) ),
% 4.40/4.78 'ordered_pair_predicate'( f22( X, Y, Z ) ) ] )
% 4.40/4.78 , clause( 29138, [ ~( member( X, image( Y, Z ) ) ), member( f22( X, Y, Z )
% 4.40/4.78 , Z ) ] )
% 4.40/4.78 , clause( 29139, [ ~( member( X, image( Y, Z ) ) ), member( first( f22( X,
% 4.40/4.78 Y, Z ) ), Y ) ] )
% 4.40/4.78 , clause( 29140, [ ~( member( X, image( Y, Z ) ) ), =( second( f22( X, Y, Z
% 4.40/4.78 ) ), X ) ] )
% 4.40/4.78 , clause( 29141, [ member( X, image( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 4.40/4.78 'ordered_pair_predicate'( T ) ), ~( member( T, Z ) ), ~( member( first( T
% 4.40/4.78 ), Y ) ), ~( =( second( T ), X ) ) ] )
% 4.40/4.78 , clause( 29142, [ ~( 'little_set'( X ) ), ~( function( Y ) ), 'little_set'(
% 4.40/4.78 image( X, Y ) ) ] )
% 4.40/4.78 , clause( 29143, [ ~( disjoint( X, Y ) ), ~( member( Z, X ) ), ~( member( Z
% 4.40/4.78 , Y ) ) ] )
% 4.40/4.78 , clause( 29144, [ disjoint( X, Y ), member( f23( X, Y ), X ) ] )
% 4.40/4.78 , clause( 29145, [ disjoint( X, Y ), member( f23( X, Y ), Y ) ] )
% 4.40/4.78 , clause( 29146, [ =( X, 'empty_set' ), member( f24( X ), X ) ] )
% 4.40/4.78 , clause( 29147, [ =( X, 'empty_set' ), disjoint( f24( X ), X ) ] )
% 4.40/4.78 , clause( 29148, [ function( f25 ) ] )
% 4.40/4.78 , clause( 29149, [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( f26(
% 4.40/4.78 X ), X ) ] )
% 4.40/4.78 , clause( 29150, [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member(
% 4.40/4.78 'ordered_pair'( X, f26( X ) ), f25 ) ] )
% 4.40/4.78 , clause( 29151, [ ~( member( X, 'range_of'( Y ) ) ),
% 4.40/4.78 'ordered_pair_predicate'( f27( X, Y ) ) ] )
% 4.40/4.78 , clause( 29152, [ ~( member( X, 'range_of'( Y ) ) ), member( f27( X, Y ),
% 4.40/4.78 Y ) ] )
% 4.40/4.78 , clause( 29153, [ ~( member( X, 'range_of'( Y ) ) ), =( X, second( f27( X
% 4.40/4.78 , Y ) ) ) ] )
% 4.40/4.78 , clause( 29154, [ member( X, 'range_of'( Y ) ), ~( 'little_set'( X ) ),
% 4.40/4.78 ~( 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, second(
% 4.40/4.78 Z ) ) ) ] )
% 4.40/4.78 , clause( 29155, [ ~( member( X, 'identity_relation' ) ),
% 4.40/4.78 'ordered_pair_predicate'( X ) ] )
% 4.40/4.78 , clause( 29156, [ ~( member( X, 'identity_relation' ) ), =( first( X ),
% 4.40/4.78 second( X ) ) ] )
% 4.40/4.78 , clause( 29157, [ member( X, 'identity_relation' ), ~( 'little_set'( X ) )
% 4.40/4.78 , ~( 'ordered_pair_predicate'( X ) ), ~( =( first( X ), second( X ) ) ) ]
% 4.40/4.78 )
% 4.40/4.78 , clause( 29158, [ =( restrict( X, Y ), intersection( X, 'cross_product'( Y
% 4.40/4.78 , 'universal_set' ) ) ) ] )
% 4.40/4.78 , clause( 29159, [ ~( 'one_to_one_function'( X ) ), function( X ) ] )
% 4.40/4.78 , clause( 29160, [ ~( 'one_to_one_function'( X ) ), function( converse( X )
% 4.40/4.78 ) ] )
% 4.40/4.78 , clause( 29161, [ 'one_to_one_function'( X ), ~( function( X ) ), ~(
% 4.40/4.78 function( converse( X ) ) ) ] )
% 4.40/4.78 , clause( 29162, [ ~( member( X, apply( Y, Z ) ) ),
% 4.40/4.78 'ordered_pair_predicate'( f28( X, Y, Z ) ) ] )
% 4.40/4.78 , clause( 29163, [ ~( member( X, apply( Y, Z ) ) ), member( f28( X, Y, Z )
% 4.40/4.78 , Y ) ] )
% 4.40/4.78 , clause( 29164, [ ~( member( X, apply( Y, Z ) ) ), =( first( f28( X, Y, Z
% 4.40/4.78 ) ), Z ) ] )
% 4.40/4.78 , clause( 29165, [ ~( member( X, apply( Y, Z ) ) ), member( X, second( f28(
% 4.40/4.78 X, Y, Z ) ) ) ] )
% 4.40/4.78 , clause( 29166, [ member( X, apply( Y, Z ) ), ~( 'ordered_pair_predicate'(
% 4.40/4.78 T ) ), ~( member( T, Y ) ), ~( =( first( T ), Z ) ), ~( member( X, second(
% 4.40/4.78 T ) ) ) ] )
% 4.40/4.78 , clause( 29167, [ =( 'apply_to_two_arguments'( X, Y, Z ), apply( X,
% 4.40/4.78 'ordered_pair'( Y, Z ) ) ) ] )
% 4.40/4.78 , clause( 29168, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 4.40/4.78 , clause( 29169, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 4.40/4.78 , clause( 29170, [ ~( maps( X, Y, Z ) ), subset( 'range_of'( X ), Z ) ] )
% 4.40/4.78 , clause( 29171, [ maps( X, Y, Z ), ~( function( X ) ), ~( =( 'domain_of'(
% 4.40/4.78 X ), Y ) ), ~( subset( 'range_of'( X ), Z ) ) ] )
% 4.40/4.78 , clause( 29172, [ ~( closed( X, Y ) ), 'little_set'( X ) ] )
% 4.40/4.78 , clause( 29173, [ ~( closed( X, Y ) ), 'little_set'( Y ) ] )
% 4.40/4.78 , clause( 29174, [ ~( closed( X, Y ) ), maps( Y, 'cross_product'( X, X ), X
% 4.40/4.78 ) ] )
% 4.40/4.78 , clause( 29175, [ closed( X, Y ), ~( 'little_set'( X ) ), ~( 'little_set'(
% 4.40/4.78 Y ) ), ~( maps( Y, 'cross_product'( X, X ), X ) ) ] )
% 4.40/4.78 , clause( 29176, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f29( X
% 4.40/4.78 , Y, Z ) ) ] )
% 4.40/4.78 , clause( 29177, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f30( X
% 4.40/4.78 , Y, Z ) ) ] )
% 4.40/4.78 , clause( 29178, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f31( X
% 4.40/4.78 , Y, Z ) ) ] )
% 4.40/4.78 , clause( 29179, [ ~( member( X, compose( Y, Z ) ) ), =( X, 'ordered_pair'(
% 4.40/4.78 f29( X, Y, Z ), f30( X, Y, Z ) ) ) ] )
% 4.40/4.78 , clause( 29180, [ ~( member( X, compose( Y, Z ) ) ), member(
% 4.40/4.78 'ordered_pair'( f29( X, Y, Z ), f31( X, Y, Z ) ), Y ) ] )
% 4.40/4.78 , clause( 29181, [ ~( member( X, compose( Y, Z ) ) ), member(
% 4.40/4.78 'ordered_pair'( f31( X, Y, Z ), f30( X, Y, Z ) ), Z ) ] )
% 4.40/4.78 , clause( 29182, [ member( X, compose( Y, Z ) ), ~( 'little_set'( X ) ),
% 4.40/4.78 ~( 'little_set'( T ) ), ~( 'little_set'( U ) ), ~( 'little_set'( W ) ),
% 4.40/4.78 ~( =( X, 'ordered_pair'( T, U ) ) ), ~( member( 'ordered_pair'( T, W ), Y
% 4.40/4.78 ) ), ~( member( 'ordered_pair'( W, U ), Z ) ) ] )
% 4.40/4.78 , clause( 29183, [ ~( homomorphism( X, Y, Z, T, U ) ), closed( Y, Z ) ] )
% 4.40/4.78 , clause( 29184, [ ~( homomorphism( X, Y, Z, T, U ) ), closed( T, U ) ] )
% 4.40/4.78 , clause( 29185, [ ~( homomorphism( X, Y, Z, T, U ) ), maps( X, Y, T ) ] )
% 4.40/4.78 , clause( 29186, [ ~( homomorphism( X, Y, Z, T, U ) ), ~( member( W, Y ) )
% 4.40/4.78 , ~( member( V0, Y ) ), =( apply( X, 'apply_to_two_arguments'( Z, W, V0 )
% 4.40/4.78 ), 'apply_to_two_arguments'( U, apply( X, W ), apply( X, V0 ) ) ) ] )
% 4.40/4.78 , clause( 29187, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~(
% 4.40/4.78 closed( T, U ) ), ~( maps( X, Y, T ) ), member( f32( X, Y, Z, T, U ), Y )
% 4.40/4.78 ] )
% 4.40/4.78 , clause( 29188, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~(
% 4.40/4.78 closed( T, U ) ), ~( maps( X, Y, T ) ), member( f33( X, Y, Z, T, U ), Y )
% 4.40/4.78 ] )
% 4.40/4.78 , clause( 29189, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~(
% 4.40/4.78 closed( T, U ) ), ~( maps( X, Y, T ) ), ~( =( apply( X,
% 4.40/4.78 'apply_to_two_arguments'( Z, f32( X, Y, Z, T, U ), f33( X, Y, Z, T, U ) )
% 4.40/4.78 ), 'apply_to_two_arguments'( U, apply( X, f32( X, Y, Z, T, U ) ), apply(
% 4.40/4.78 X, f33( X, Y, Z, T, U ) ) ) ) ) ] )
% 4.40/4.78 , clause( 29190, [ ~( associative( X, Y ) ), ~( member( Z, X ) ), ~( member(
% 4.40/4.78 T, X ) ), ~( member( U, X ) ), =( 'apply_to_two_arguments'( Y,
% 4.40/4.78 'apply_to_two_arguments'( Y, Z, T ), U ), 'apply_to_two_arguments'( Y, Z
% 4.40/4.78 , 'apply_to_two_arguments'( Y, T, U ) ) ) ] )
% 4.40/4.78 , clause( 29191, [ associative( X, Y ), member( f34( X, Y ), X ) ] )
% 4.40/4.78 , clause( 29192, [ associative( X, Y ), member( f35( X, Y ), X ) ] )
% 4.40/4.78 , clause( 29193, [ associative( X, Y ), member( f36( X, Y ), X ) ] )
% 4.40/4.78 , clause( 29194, [ associative( X, Y ), ~( =( 'apply_to_two_arguments'( Y,
% 4.40/4.78 'apply_to_two_arguments'( Y, f34( X, Y ), f35( X, Y ) ), f36( X, Y ) ),
% 4.40/4.78 'apply_to_two_arguments'( Y, f34( X, Y ), 'apply_to_two_arguments'( Y,
% 4.40/4.78 f35( X, Y ), f36( X, Y ) ) ) ) ) ] )
% 4.40/4.78 , clause( 29195, [ ~( identity( X, Y, Z ) ), member( Z, X ) ] )
% 4.40/4.78 , clause( 29196, [ ~( identity( X, Y, Z ) ), ~( member( T, X ) ), =(
% 4.40/4.78 'apply_to_two_arguments'( Y, Z, T ), T ) ] )
% 4.40/4.78 , clause( 29197, [ ~( identity( X, Y, Z ) ), ~( member( T, X ) ), =(
% 4.40/4.78 'apply_to_two_arguments'( Y, T, Z ), T ) ] )
% 4.40/4.78 , clause( 29198, [ identity( X, Y, Z ), ~( member( Z, X ) ), member( f37( X
% 4.40/4.78 , Y, Z ), X ) ] )
% 4.40/4.78 , clause( 29199, [ identity( X, Y, Z ), ~( member( Z, X ) ), ~( =(
% 4.40/4.78 'apply_to_two_arguments'( Y, Z, f37( X, Y, Z ) ), f37( X, Y, Z ) ) ), ~(
% 4.40/4.78 =( 'apply_to_two_arguments'( Y, f37( X, Y, Z ), Z ), f37( X, Y, Z ) ) ) ]
% 4.40/4.78 )
% 4.40/4.78 , clause( 29200, [ ~( inverse( X, Y, Z, T ) ), maps( T, X, X ) ] )
% 4.40/4.78 , clause( 29201, [ ~( inverse( X, Y, Z, T ) ), ~( member( U, X ) ), =(
% 4.40/4.78 'apply_to_two_arguments'( Y, apply( T, U ), U ), Z ) ] )
% 4.40/4.78 , clause( 29202, [ ~( inverse( X, Y, Z, T ) ), ~( member( U, X ) ), =(
% 4.40/4.78 'apply_to_two_arguments'( Y, U, apply( T, U ) ), Z ) ] )
% 4.40/4.78 , clause( 29203, [ inverse( X, Y, Z, T ), ~( maps( T, X, X ) ), member( f38(
% 4.40/4.78 X, Y, Z, T ), X ) ] )
% 4.40/4.78 , clause( 29204, [ inverse( X, Y, Z, T ), ~( maps( T, X, X ) ), ~( =(
% 4.40/4.78 'apply_to_two_arguments'( Y, apply( T, f38( X, Y, Z, T ) ), f38( X, Y, Z
% 4.40/4.78 , T ) ), Z ) ), ~( =( 'apply_to_two_arguments'( Y, f38( X, Y, Z, T ),
% 4.40/4.78 apply( T, f38( X, Y, Z, T ) ) ), Z ) ) ] )
% 4.40/4.78 , clause( 29205, [ ~( group( X, Y ) ), closed( X, Y ) ] )
% 4.40/4.78 , clause( 29206, [ ~( group( X, Y ) ), associative( X, Y ) ] )
% 4.40/4.78 , clause( 29207, [ ~( group( X, Y ) ), identity( X, Y, f39( X, Y ) ) ] )
% 4.40/4.78 , clause( 29208, [ ~( group( X, Y ) ), inverse( X, Y, f39( X, Y ), f40( X,
% 4.40/4.78 Y ) ) ] )
% 4.40/4.78 , clause( 29209, [ group( X, Y ), ~( closed( X, Y ) ), ~( associative( X, Y
% 4.40/4.78 ) ), ~( identity( X, Y, Z ) ), ~( inverse( X, Y, Z, T ) ) ] )
% 4.40/4.78 , clause( 29210, [ ~( commutes( X, Y ) ), ~( member( Z, X ) ), ~( member( T
% 4.40/4.78 , X ) ), =( 'apply_to_two_arguments'( Y, Z, T ), 'apply_to_two_arguments'(
% 4.40/4.78 Y, T, Z ) ) ] )
% 4.40/4.78 , clause( 29211, [ commutes( X, Y ), member( f41( X, Y ), X ) ] )
% 4.40/4.78 , clause( 29212, [ commutes( X, Y ), member( f42( X, Y ), X ) ] )
% 4.40/4.78 , clause( 29213, [ commutes( X, Y ), ~( =( 'apply_to_two_arguments'( Y, f41(
% 4.40/4.78 X, Y ), f42( X, Y ) ), 'apply_to_two_arguments'( Y, f42( X, Y ), f41( X,
% 4.40/4.78 Y ) ) ) ) ] )
% 4.40/4.78 , clause( 29214, [ ~( member( X, 'natural_numbers' ) ), ~( 'little_set'( Y
% 4.40/4.78 ) ), ~( member( 'empty_set', Y ) ), member( f43( X, Y ), Y ), member( X
% 4.40/4.78 , Y ) ] )
% 4.40/4.78 , clause( 29215, [ ~( member( X, 'natural_numbers' ) ), ~( 'little_set'( Y
% 4.40/4.78 ) ), ~( member( 'empty_set', Y ) ), ~( member( successor( f43( X, Y ) )
% 4.40/4.78 , Y ) ), member( X, Y ) ] )
% 4.40/4.78 , clause( 29216, [ member( X, 'natural_numbers' ), ~( 'little_set'( X ) ),
% 4.40/4.78 'little_set'( f44( X ) ) ] )
% 4.40/4.78 , clause( 29217, [ member( X, 'natural_numbers' ), ~( 'little_set'( X ) ),
% 4.40/4.78 member( 'empty_set', f44( X ) ) ] )
% 4.40/4.78 , clause( 29218, [ member( X, 'natural_numbers' ), ~( 'little_set'( X ) ),
% 4.40/4.78 ~( member( Y, f44( X ) ) ), member( successor( Y ), f44( X ) ) ] )
% 4.40/4.78 , clause( 29219, [ member( X, 'natural_numbers' ), ~( member( X, f44( X ) )
% 4.40/4.78 ) ] )
% 4.40/4.78 , clause( 29220, [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), member(
% 4.40/4.78 f45( X, Y ), 'natural_numbers' ), member( f46( X, Y ), 'natural_numbers'
% 4.40/4.78 ), member( X, Y ) ] )
% 4.40/4.78 , clause( 29221, [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), member(
% 4.40/4.78 f45( X, Y ), 'natural_numbers' ), member( f47( X, Y ), 'natural_numbers'
% 4.40/4.78 ), member( X, Y ) ] )
% 4.40/4.78 , clause( 29222, [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), member(
% 4.40/4.78 f45( X, Y ), 'natural_numbers' ), member( f48( X, Y ), 'natural_numbers'
% 4.40/4.78 ), member( X, Y ) ] )
% 4.40/4.78 , clause( 29223, [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), member(
% 4.40/4.78 f45( X, Y ), 'natural_numbers' ), member( 'ordered_pair'( 'ordered_pair'(
% 4.40/4.78 f46( X, Y ), f47( X, Y ) ), f48( X, Y ) ), Y ), member( X, Y ) ] )
% 4.40/4.78 , clause( 29224, [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), member(
% 4.40/4.78 f45( X, Y ), 'natural_numbers' ), ~( member( 'ordered_pair'(
% 4.40/4.78 'ordered_pair'( successor( f46( X, Y ) ), f47( X, Y ) ), successor( f48(
% 4.40/4.78 X, Y ) ) ), Y ) ), member( X, Y ) ] )
% 4.40/4.78 , clause( 29225, [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), ~(
% 4.40/4.78 member( 'ordered_pair'( 'ordered_pair'( 'empty_set', f45( X, Y ) ), f45(
% 4.40/4.78 X, Y ) ), Y ) ), member( f46( X, Y ), 'natural_numbers' ), member( X, Y )
% 4.40/4.78 ] )
% 4.40/4.78 , clause( 29226, [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), ~(
% 4.40/4.78 member( 'ordered_pair'( 'ordered_pair'( 'empty_set', f45( X, Y ) ), f45(
% 4.40/4.78 X, Y ) ), Y ) ), member( f47( X, Y ), 'natural_numbers' ), member( X, Y )
% 4.40/4.78 ] )
% 4.40/4.78 , clause( 29227, [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), ~(
% 4.40/4.78 member( 'ordered_pair'( 'ordered_pair'( 'empty_set', f45( X, Y ) ), f45(
% 4.40/4.78 X, Y ) ), Y ) ), member( f48( X, Y ), 'natural_numbers' ), member( X, Y )
% 4.40/4.78 ] )
% 4.40/4.78 , clause( 29228, [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), ~(
% 4.40/4.78 member( 'ordered_pair'( 'ordered_pair'( 'empty_set', f45( X, Y ) ), f45(
% 4.40/4.78 X, Y ) ), Y ) ), member( 'ordered_pair'( 'ordered_pair'( f46( X, Y ), f47(
% 4.40/4.78 X, Y ) ), f48( X, Y ) ), Y ), member( X, Y ) ] )
% 4.40/4.78 , clause( 29229, [ ~( member( X, plus ) ), ~( 'little_set'( Y ) ), ~(
% 4.40/4.78 member( 'ordered_pair'( 'ordered_pair'( 'empty_set', f45( X, Y ) ), f45(
% 4.40/4.78 X, Y ) ), Y ) ), ~( member( 'ordered_pair'( 'ordered_pair'( successor(
% 4.40/4.78 f46( X, Y ) ), f47( X, Y ) ), successor( f48( X, Y ) ) ), Y ) ), member(
% 4.40/4.78 X, Y ) ] )
% 4.40/4.78 , clause( 29230, [ member( X, plus ), ~( 'little_set'( X ) ), 'little_set'(
% 4.40/4.78 f49( X ) ) ] )
% 4.40/4.78 , clause( 29231, [ member( X, plus ), ~( 'little_set'( X ) ), ~( member( Y
% 4.40/4.78 , 'natural_numbers' ) ), member( 'ordered_pair'( 'ordered_pair'(
% 4.40/4.78 'empty_set', Y ), Y ), f49( X ) ) ] )
% 4.40/4.78 , clause( 29232, [ member( X, plus ), ~( 'little_set'( X ) ), ~( member( Y
% 4.40/4.78 , 'natural_numbers' ) ), ~( member( Z, 'natural_numbers' ) ), ~( member(
% 4.40/4.78 T, 'natural_numbers' ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, Z
% 4.40/4.78 ), T ), f49( X ) ) ), member( 'ordered_pair'( 'ordered_pair'( successor(
% 4.40/4.78 Y ), Z ), successor( T ) ), f49( X ) ) ] )
% 4.40/4.78 , clause( 29233, [ member( X, plus ), ~( member( X, f49( X ) ) ) ] )
% 4.40/4.78 , clause( 29234, [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), member(
% 4.40/4.78 f50( X, Y ), 'natural_numbers' ), member( f51( X, Y ), 'natural_numbers'
% 4.40/4.78 ), member( X, Y ) ] )
% 4.40/4.78 , clause( 29235, [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), member(
% 4.40/4.78 f50( X, Y ), 'natural_numbers' ), member( f52( X, Y ), 'natural_numbers'
% 4.40/4.78 ), member( X, Y ) ] )
% 4.40/4.78 , clause( 29236, [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), member(
% 4.40/4.78 f50( X, Y ), 'natural_numbers' ), member( f53( X, Y ), 'natural_numbers'
% 4.40/4.78 ), member( X, Y ) ] )
% 4.40/4.78 , clause( 29237, [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), member(
% 4.40/4.78 f50( X, Y ), 'natural_numbers' ), member( 'ordered_pair'( 'ordered_pair'(
% 4.40/4.78 f51( X, Y ), f52( X, Y ) ), f53( X, Y ) ), Y ), member( X, Y ) ] )
% 4.40/4.78 , clause( 29238, [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), member(
% 4.40/4.78 f50( X, Y ), 'natural_numbers' ), ~( member( 'ordered_pair'(
% 4.40/4.78 'ordered_pair'( successor( f51( X, Y ) ), f52( X, Y ) ),
% 4.40/4.78 'apply_to_two_arguments'( plus, f53( X, Y ), f52( X, Y ) ) ), Y ) ),
% 4.40/4.78 member( X, Y ) ] )
% 4.40/4.78 , clause( 29239, [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), ~(
% 4.40/4.78 member( 'ordered_pair'( 'ordered_pair'( 'empty_set', f50( X, Y ) ),
% 4.40/4.78 'empty_set' ), Y ) ), member( f51( X, Y ), 'natural_numbers' ), member( X
% 4.40/4.78 , Y ) ] )
% 4.40/4.78 , clause( 29240, [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), ~(
% 4.40/4.78 member( 'ordered_pair'( 'ordered_pair'( 'empty_set', f50( X, Y ) ),
% 4.40/4.78 'empty_set' ), Y ) ), member( f52( X, Y ), 'natural_numbers' ), member( X
% 4.40/4.78 , Y ) ] )
% 4.40/4.78 , clause( 29241, [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), ~(
% 4.40/4.78 member( 'ordered_pair'( 'ordered_pair'( 'empty_set', f50( X, Y ) ),
% 4.40/4.78 'empty_set' ), Y ) ), member( f53( X, Y ), 'natural_numbers' ), member( X
% 4.40/4.78 , Y ) ] )
% 4.40/4.78 , clause( 29242, [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), ~(
% 4.40/4.78 member( 'ordered_pair'( 'ordered_pair'( 'empty_set', f50( X, Y ) ),
% 4.40/4.78 'empty_set' ), Y ) ), member( 'ordered_pair'( 'ordered_pair'( f51( X, Y )
% 4.40/4.78 , f52( X, Y ) ), f53( X, Y ) ), Y ), member( X, Y ) ] )
% 4.40/4.78 , clause( 29243, [ ~( member( X, times ) ), ~( 'little_set'( Y ) ), ~(
% 4.40/4.78 member( 'ordered_pair'( 'ordered_pair'( 'empty_set', f50( X, Y ) ),
% 4.40/4.78 'empty_set' ), Y ) ), ~( member( 'ordered_pair'( 'ordered_pair'(
% 4.40/4.78 successor( f51( X, Y ) ), f52( X, Y ) ), 'apply_to_two_arguments'( plus,
% 4.40/4.78 f53( X, Y ), f52( X, Y ) ) ), Y ) ), member( X, Y ) ] )
% 4.40/4.78 , clause( 29244, [ member( X, times ), ~( 'little_set'( X ) ), 'little_set'(
% 4.40/4.78 f54( X ) ) ] )
% 4.40/4.78 , clause( 29245, [ member( X, times ), ~( 'little_set'( X ) ), ~( member( Y
% 4.40/4.78 , 'natural_numbers' ) ), member( 'ordered_pair'( 'ordered_pair'(
% 4.40/4.78 'empty_set', Y ), 'empty_set' ), f54( X ) ) ] )
% 4.40/4.78 , clause( 29246, [ member( X, times ), ~( 'little_set'( X ) ), ~( member( Y
% 4.40/4.78 , 'natural_numbers' ) ), ~( member( Z, 'natural_numbers' ) ), ~( member(
% 4.40/4.78 T, 'natural_numbers' ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, Z
% 4.40/4.78 ), T ), f54( X ) ) ), member( 'ordered_pair'( 'ordered_pair'( successor(
% 4.40/4.78 Y ), Z ), 'apply_to_two_arguments'( plus, T, Z ) ), f54( X ) ) ] )
% 4.40/4.78 , clause( 29247, [ member( X, times ), ~( member( X, f54( X ) ) ) ] )
% 4.40/4.78 , clause( 29248, [ ~( member( X, 'prime_numbers' ) ), member( X,
% 4.40/4.78 'natural_numbers' ) ] )
% 4.40/4.78 , clause( 29249, [ ~( member( X, 'prime_numbers' ) ), ~( =( X, 'empty_set'
% 4.40/4.78 ) ) ] )
% 4.40/4.78 , clause( 29250, [ ~( member( X, 'prime_numbers' ) ), ~( =( X, successor(
% 4.40/4.78 'empty_set' ) ) ) ] )
% 4.40/4.78 , clause( 29251, [ ~( member( X, 'prime_numbers' ) ), ~( member( Y,
% 4.40/4.78 'natural_numbers' ) ), ~( member( Z, 'natural_numbers' ) ), ~( =(
% 4.40/4.78 'apply_to_two_arguments'( times, Y, Z ), X ) ), member( Y,
% 4.40/4.78 'non_ordered_pair'( successor( 'empty_set' ), X ) ) ] )
% 4.40/4.78 , clause( 29252, [ member( X, 'prime_numbers' ), ~( member( X,
% 4.40/4.78 'natural_numbers' ) ), =( X, 'empty_set' ), =( X, successor( 'empty_set'
% 4.40/4.78 ) ), member( f55( X ), 'natural_numbers' ) ] )
% 4.40/4.78 , clause( 29253, [ member( X, 'prime_numbers' ), ~( member( X,
% 4.40/4.78 'natural_numbers' ) ), =( X, 'empty_set' ), =( X, successor( 'empty_set'
% 4.40/4.78 ) ), member( f56( X ), 'natural_numbers' ) ] )
% 4.40/4.78 , clause( 29254, [ member( X, 'prime_numbers' ), ~( member( X,
% 4.40/4.78 'natural_numbers' ) ), =( X, 'empty_set' ), =( X, successor( 'empty_set'
% 4.40/4.78 ) ), =( 'apply_to_two_arguments'( times, f55( X ), f56( X ) ), X ) ] )
% 4.40/4.78 , clause( 29255, [ member( X, 'prime_numbers' ), ~( member( X,
% 4.40/4.78 'natural_numbers' ) ), =( X, 'empty_set' ), =( X, successor( 'empty_set'
% 4.40/4.78 ) ), ~( member( f55( X ), 'non_ordered_pair'( successor( 'empty_set' ),
% 4.40/4.78 X ) ) ) ] )
% 4.40/4.78 , clause( 29256, [ ~( finite( X ) ), member( f57( X ), 'natural_numbers' )
% 4.40/4.78 ] )
% 4.40/4.78 , clause( 29257, [ ~( finite( X ) ), maps( f58( X ), f57( X ), X ) ] )
% 4.40/4.78 , clause( 29258, [ ~( finite( X ) ), =( 'range_of'( f58( X ) ), X ) ] )
% 4.40/4.78 , clause( 29259, [ ~( finite( X ) ), 'one_to_one_function'( f58( X ) ) ] )
% 4.40/4.78 , clause( 29260, [ finite( X ), ~( member( Y, 'natural_numbers' ) ), ~(
% 4.40/4.78 maps( Z, Y, X ) ), ~( =( 'range_of'( Z ), X ) ), ~( 'one_to_one_function'(
% 4.40/4.78 Z ) ) ] )
% 4.40/4.78 , clause( 29261, [ ~( member( X, 'twin_prime_numbers' ) ), member( X,
% 4.40/4.78 'prime_numbers' ) ] )
% 4.40/4.78 , clause( 29262, [ ~( member( X, 'twin_prime_numbers' ) ), member(
% 4.40/4.78 successor( successor( X ) ), 'prime_numbers' ) ] )
% 4.40/4.78 , clause( 29263, [ member( X, 'twin_prime_numbers' ), ~( member( X,
% 4.40/4.78 'prime_numbers' ) ), ~( member( successor( successor( X ) ),
% 4.40/4.78 'prime_numbers' ) ) ] )
% 4.40/4.78 , clause( 29264, [ ~( member( X, 'even_numbers' ) ), member( X,
% 4.40/4.78 'natural_numbers' ) ] )
% 4.40/4.78 , clause( 29265, [ ~( member( X, 'even_numbers' ) ), member( f59( X ),
% 4.40/4.78 'natural_numbers' ) ] )
% 4.40/4.78 , clause( 29266, [ ~( member( X, 'even_numbers' ) ), =(
% 4.40/4.78 'apply_to_two_arguments'( plus, f59( X ), f59( X ) ), X ) ] )
% 4.40/4.78 , clause( 29267, [ member( X, 'even_numbers' ), ~( member( X,
% 4.40/4.78 'natural_numbers' ) ), ~( member( Y, 'natural_numbers' ) ), ~( =(
% 4.40/4.78 'apply_to_two_arguments'( plus, Y, Y ), X ) ) ] )
% 4.40/4.78 , clause( 29268, [ ~( member( 'empty_set', 'natural_numbers' ) ) ] )
% 4.40/4.78 ] ).
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 subsumption(
% 4.40/4.78 clause( 0, [ ~( member( X, Y ) ), 'little_set'( X ) ] )
% 4.40/4.78 , clause( 29049, [ ~( member( X, Y ) ), 'little_set'( X ) ] )
% 4.40/4.78 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 4.40/4.78 ), ==>( 1, 1 )] ) ).
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 subsumption(
% 4.40/4.78 clause( 60, [ member( 'empty_set', infinity ) ] )
% 4.40/4.78 , clause( 29109, [ member( 'empty_set', infinity ) ] )
% 4.40/4.78 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 subsumption(
% 4.40/4.78 clause( 168, [ member( X, 'natural_numbers' ), ~( 'little_set'( X ) ),
% 4.40/4.78 member( 'empty_set', f44( X ) ) ] )
% 4.40/4.78 , clause( 29217, [ member( X, 'natural_numbers' ), ~( 'little_set'( X ) ),
% 4.40/4.78 member( 'empty_set', f44( X ) ) ] )
% 4.40/4.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 4.40/4.78 1 ), ==>( 2, 2 )] ) ).
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 subsumption(
% 4.40/4.78 clause( 170, [ member( X, 'natural_numbers' ), ~( member( X, f44( X ) ) ) ]
% 4.40/4.78 )
% 4.40/4.78 , clause( 29219, [ member( X, 'natural_numbers' ), ~( member( X, f44( X ) )
% 4.40/4.78 ) ] )
% 4.40/4.78 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 4.40/4.78 1 )] ) ).
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 subsumption(
% 4.40/4.78 clause( 219, [ ~( member( 'empty_set', 'natural_numbers' ) ) ] )
% 4.40/4.78 , clause( 29268, [ ~( member( 'empty_set', 'natural_numbers' ) ) ] )
% 4.40/4.78 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 resolution(
% 4.40/4.78 clause( 29983, [ 'little_set'( 'empty_set' ) ] )
% 4.40/4.78 , clause( 0, [ ~( member( X, Y ) ), 'little_set'( X ) ] )
% 4.40/4.78 , 0, clause( 60, [ member( 'empty_set', infinity ) ] )
% 4.40/4.78 , 0, substitution( 0, [ :=( X, 'empty_set' ), :=( Y, infinity )] ),
% 4.40/4.78 substitution( 1, [] )).
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 subsumption(
% 4.40/4.78 clause( 297, [ 'little_set'( 'empty_set' ) ] )
% 4.40/4.78 , clause( 29983, [ 'little_set'( 'empty_set' ) ] )
% 4.40/4.78 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 resolution(
% 4.40/4.78 clause( 29984, [ member( 'empty_set', 'natural_numbers' ), member(
% 4.40/4.78 'empty_set', f44( 'empty_set' ) ) ] )
% 4.40/4.78 , clause( 168, [ member( X, 'natural_numbers' ), ~( 'little_set'( X ) ),
% 4.40/4.78 member( 'empty_set', f44( X ) ) ] )
% 4.40/4.78 , 1, clause( 297, [ 'little_set'( 'empty_set' ) ] )
% 4.40/4.78 , 0, substitution( 0, [ :=( X, 'empty_set' )] ), substitution( 1, [] )).
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 resolution(
% 4.40/4.78 clause( 29985, [ member( 'empty_set', f44( 'empty_set' ) ) ] )
% 4.40/4.78 , clause( 219, [ ~( member( 'empty_set', 'natural_numbers' ) ) ] )
% 4.40/4.78 , 0, clause( 29984, [ member( 'empty_set', 'natural_numbers' ), member(
% 4.40/4.78 'empty_set', f44( 'empty_set' ) ) ] )
% 4.40/4.78 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 subsumption(
% 4.40/4.78 clause( 28475, [ member( 'empty_set', f44( 'empty_set' ) ) ] )
% 4.40/4.78 , clause( 29985, [ member( 'empty_set', f44( 'empty_set' ) ) ] )
% 4.40/4.78 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 resolution(
% 4.40/4.78 clause( 29986, [ member( 'empty_set', 'natural_numbers' ) ] )
% 4.40/4.78 , clause( 170, [ member( X, 'natural_numbers' ), ~( member( X, f44( X ) ) )
% 4.40/4.78 ] )
% 4.40/4.78 , 1, clause( 28475, [ member( 'empty_set', f44( 'empty_set' ) ) ] )
% 4.40/4.78 , 0, substitution( 0, [ :=( X, 'empty_set' )] ), substitution( 1, [] )).
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 resolution(
% 4.40/4.78 clause( 29987, [] )
% 4.40/4.78 , clause( 219, [ ~( member( 'empty_set', 'natural_numbers' ) ) ] )
% 4.40/4.78 , 0, clause( 29986, [ member( 'empty_set', 'natural_numbers' ) ] )
% 4.40/4.78 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 subsumption(
% 4.40/4.78 clause( 29047, [] )
% 4.40/4.78 , clause( 29987, [] )
% 4.40/4.78 , substitution( 0, [] ), permutation( 0, [] ) ).
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 end.
% 4.40/4.78
% 4.40/4.78 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 4.40/4.78
% 4.40/4.78 Memory use:
% 4.40/4.78
% 4.40/4.78 space for terms: 502821
% 4.40/4.78 space for clauses: 1545418
% 4.40/4.78
% 4.40/4.78
% 4.40/4.78 clauses generated: 68736
% 4.40/4.78 clauses kept: 29048
% 4.40/4.78 clauses selected: 628
% 4.40/4.78 clauses deleted: 3659
% 4.40/4.78 clauses inuse deleted: 108
% 4.40/4.78
% 4.40/4.78 subsentry: 129010
% 4.40/4.78 literals s-matched: 91401
% 4.40/4.78 literals matched: 87791
% 4.44/4.78 full subsumption: 34214
% 4.44/4.78
% 4.44/4.78 checksum: -151924097
% 4.44/4.78
% 4.44/4.78
% 4.44/4.78 Bliksem ended
%------------------------------------------------------------------------------