TSTP Solution File: SET041-3 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET041-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Mon Jul 18 22:46:00 EDT 2022
% Result : Unsatisfiable 10.83s 11.23s
% Output : Refutation 10.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET041-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : bliksem %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sun Jul 10 13:00:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.73/1.12 *** allocated 10000 integers for termspace/termends
% 0.73/1.12 *** allocated 10000 integers for clauses
% 0.73/1.12 *** allocated 10000 integers for justifications
% 0.73/1.12 Bliksem 1.12
% 0.73/1.12
% 0.73/1.12
% 0.73/1.12 Automatic Strategy Selection
% 0.73/1.12
% 0.73/1.12 Clauses:
% 0.73/1.12 [
% 0.73/1.12 [ ~( member( X, Y ) ), 'little_set'( X ) ],
% 0.73/1.12 [ 'little_set'( f1( X, Y ) ), =( X, Y ) ],
% 0.73/1.12 [ member( f1( X, Y ), X ), member( f1( X, Y ), Y ), =( X, Y ) ],
% 0.73/1.12 [ ~( member( f1( X, Y ), X ) ), ~( member( f1( X, Y ), Y ) ), =( X, Y )
% 0.73/1.12 ],
% 0.73/1.12 [ ~( member( X, 'non_ordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.12 =( X, Y ) ) ],
% 0.73/1.12 [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.12 =( X, Z ) ) ],
% 0.73/1.12 [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ],
% 0.73/1.12 [ =( 'singleton_set'( X ), 'non_ordered_pair'( X, X ) ) ],
% 0.73/1.12 [ =( 'ordered_pair'( X, Y ), 'non_ordered_pair'( 'singleton_set'( X ),
% 0.73/1.12 'non_ordered_pair'( X, Y ) ) ) ],
% 0.73/1.12 [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f2( X ) ) ],
% 0.73/1.12 [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f3( X ) ) ],
% 0.73/1.12 [ ~( 'ordered_pair_predicate'( X ) ), =( X, 'ordered_pair'( f2( X ), f3(
% 0.73/1.12 X ) ) ) ],
% 0.73/1.12 [ 'ordered_pair_predicate'( X ), ~( 'little_set'( Y ) ), ~( 'little_set'(
% 0.73/1.12 Z ) ), ~( =( X, 'ordered_pair'( Y, Z ) ) ) ],
% 0.73/1.12 [ ~( member( X, first( Y ) ) ), 'little_set'( f4( X, Y ) ) ],
% 0.73/1.12 [ ~( member( X, first( Y ) ) ), 'little_set'( f5( X, Y ) ) ],
% 0.73/1.12 [ ~( member( X, first( Y ) ) ), =( Y, 'ordered_pair'( f4( X, Y ), f5( X
% 0.73/1.12 , Y ) ) ) ],
% 0.73/1.12 [ ~( member( X, first( Y ) ) ), member( X, f4( X, Y ) ) ],
% 0.73/1.12 [ member( X, first( Y ) ), ~( 'little_set'( Z ) ), ~( 'little_set'( T )
% 0.73/1.12 ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, Z ) ) ],
% 0.73/1.12 [ ~( member( X, second( Y ) ) ), 'little_set'( f6( X, Y ) ) ],
% 0.73/1.12 [ ~( member( X, second( Y ) ) ), 'little_set'( f7( X, Y ) ) ],
% 0.73/1.12 [ ~( member( X, second( Y ) ) ), =( Y, 'ordered_pair'( f6( X, Y ), f7( X
% 0.73/1.12 , Y ) ) ) ],
% 0.73/1.12 [ ~( member( X, second( Y ) ) ), member( X, f7( X, Y ) ) ],
% 0.73/1.12 [ member( X, second( Y ) ), ~( 'little_set'( Z ) ), ~( 'little_set'( T )
% 0.73/1.12 ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, T ) ) ],
% 0.73/1.12 [ ~( member( X, estin ) ), 'ordered_pair_predicate'( X ) ],
% 0.73/1.12 [ ~( member( X, estin ) ), member( first( X ), second( X ) ) ],
% 0.73/1.12 [ member( X, estin ), ~( 'little_set'( X ) ), ~(
% 0.73/1.12 'ordered_pair_predicate'( X ) ), ~( member( first( X ), second( X ) ) ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.73/1.12 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.73/1.12 [ member( X, intersection( Y, Z ) ), ~( member( X, Y ) ), ~( member( X,
% 0.73/1.12 Z ) ) ],
% 0.73/1.12 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.73/1.12 [ member( X, complement( Y ) ), ~( 'little_set'( X ) ), member( X, Y ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ =( union( X, Y ), complement( intersection( complement( X ),
% 0.73/1.12 complement( Y ) ) ) ) ],
% 0.73/1.12 [ ~( member( X, 'domain_of'( Y ) ) ), 'ordered_pair_predicate'( f8( X, Y
% 0.73/1.12 ) ) ],
% 0.73/1.12 [ ~( member( X, 'domain_of'( Y ) ) ), member( f8( X, Y ), Y ) ],
% 0.73/1.12 [ ~( member( X, 'domain_of'( Y ) ) ), =( X, first( f8( X, Y ) ) ) ],
% 0.73/1.12 [ member( X, 'domain_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.12 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, first( Z )
% 0.73/1.12 ) ) ],
% 0.73/1.12 [ ~( member( X, 'cross_product'( Y, Z ) ) ), 'ordered_pair_predicate'( X
% 0.73/1.12 ) ],
% 0.73/1.12 [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( first( X ), Y ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( second( X ), Z ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ member( X, 'cross_product'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.12 'ordered_pair_predicate'( X ) ), ~( member( first( X ), Y ) ), ~( member(
% 0.73/1.12 second( X ), Z ) ) ],
% 0.73/1.12 [ ~( member( X, converse( Y ) ) ), 'ordered_pair_predicate'( X ) ],
% 0.73/1.12 [ ~( member( X, converse( Y ) ) ), member( 'ordered_pair'( second( X ),
% 0.73/1.12 first( X ) ), Y ) ],
% 0.73/1.12 [ member( X, converse( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.12 'ordered_pair_predicate'( X ) ), ~( member( 'ordered_pair'( second( X ),
% 0.73/1.12 first( X ) ), Y ) ) ],
% 0.73/1.12 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f9( X, Y ) ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f10( X, Y ) ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f11( X, Y ) ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ ~( member( X, 'rotate_right'( Y ) ) ), =( X, 'ordered_pair'( f9( X, Y
% 0.73/1.12 ), 'ordered_pair'( f10( X, Y ), f11( X, Y ) ) ) ) ],
% 0.73/1.12 [ ~( member( X, 'rotate_right'( Y ) ) ), member( 'ordered_pair'( f10( X
% 0.73/1.12 , Y ), 'ordered_pair'( f11( X, Y ), f9( X, Y ) ) ), Y ) ],
% 0.73/1.12 [ member( X, 'rotate_right'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.12 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) ), ~(
% 0.73/1.12 =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 0.73/1.12 'ordered_pair'( T, 'ordered_pair'( U, Z ) ), Y ) ) ],
% 0.73/1.12 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f12( X, Y ) ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f13( X, Y ) ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f14( X, Y ) ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ ~( member( X, 'flip_range_of'( Y ) ) ), =( X, 'ordered_pair'( f12( X,
% 0.73/1.12 Y ), 'ordered_pair'( f13( X, Y ), f14( X, Y ) ) ) ) ],
% 0.73/1.12 [ ~( member( X, 'flip_range_of'( Y ) ) ), member( 'ordered_pair'( f12( X
% 0.73/1.12 , Y ), 'ordered_pair'( f14( X, Y ), f13( X, Y ) ) ), Y ) ],
% 0.73/1.12 [ member( X, 'flip_range_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.12 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) ), ~(
% 0.73/1.12 =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 0.73/1.12 'ordered_pair'( Z, 'ordered_pair'( U, T ) ), Y ) ) ],
% 0.73/1.12 [ =( successor( X ), union( X, 'singleton_set'( X ) ) ) ],
% 0.73/1.12 [ ~( member( X, 'empty_set' ) ) ],
% 0.73/1.12 [ member( X, 'universal_set' ), ~( 'little_set'( X ) ) ],
% 0.73/1.12 [ 'little_set'( infinity ) ],
% 0.73/1.12 [ member( 'empty_set', infinity ) ],
% 0.73/1.12 [ ~( member( X, infinity ) ), member( successor( X ), infinity ) ],
% 0.73/1.12 [ ~( member( X, sigma( Y ) ) ), member( f16( X, Y ), Y ) ],
% 0.73/1.12 [ ~( member( X, sigma( Y ) ) ), member( X, f16( X, Y ) ) ],
% 0.73/1.12 [ member( X, sigma( Y ) ), ~( member( Z, Y ) ), ~( member( X, Z ) ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ ~( 'little_set'( X ) ), 'little_set'( sigma( X ) ) ],
% 0.73/1.12 [ ~( subset( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.73/1.12 [ subset( X, Y ), member( f17( X, Y ), X ) ],
% 0.73/1.12 [ subset( X, Y ), ~( member( f17( X, Y ), Y ) ) ],
% 0.73/1.12 [ ~( 'proper_subset'( X, Y ) ), subset( X, Y ) ],
% 0.73/1.12 [ ~( 'proper_subset'( X, Y ) ), ~( =( X, Y ) ) ],
% 0.73/1.12 [ 'proper_subset'( X, Y ), ~( subset( X, Y ) ), =( X, Y ) ],
% 0.73/1.12 [ ~( member( X, powerset( Y ) ) ), subset( X, Y ) ],
% 0.73/1.12 [ member( X, powerset( Y ) ), ~( 'little_set'( X ) ), ~( subset( X, Y )
% 0.73/1.12 ) ],
% 0.73/1.12 [ ~( 'little_set'( X ) ), 'little_set'( powerset( X ) ) ],
% 0.73/1.12 [ ~( relation( X ) ), ~( member( Y, X ) ), 'ordered_pair_predicate'( Y )
% 0.73/1.12 ],
% 0.73/1.12 [ relation( X ), member( f18( X ), X ) ],
% 0.73/1.12 [ relation( X ), ~( 'ordered_pair_predicate'( f18( X ) ) ) ],
% 0.73/1.12 [ ~( 'single_valued_set'( X ) ), ~( 'little_set'( Y ) ), ~( 'little_set'(
% 0.73/1.12 Z ) ), ~( 'little_set'( T ) ), ~( member( 'ordered_pair'( Y, Z ), X ) ),
% 0.73/1.12 ~( member( 'ordered_pair'( Y, T ), X ) ), =( Z, T ) ],
% 0.73/1.12 [ 'single_valued_set'( X ), 'little_set'( f19( X ) ) ],
% 0.73/1.12 [ 'single_valued_set'( X ), 'little_set'( f20( X ) ) ],
% 0.73/1.12 [ 'single_valued_set'( X ), 'little_set'( f21( X ) ) ],
% 0.73/1.12 [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X ), f20( X ) )
% 0.73/1.12 , X ) ],
% 0.73/1.12 [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X ), f21( X ) )
% 0.73/1.12 , X ) ],
% 0.73/1.12 [ 'single_valued_set'( X ), ~( =( f20( X ), f21( X ) ) ) ],
% 0.73/1.12 [ ~( function( X ) ), relation( X ) ],
% 0.73/1.12 [ ~( function( X ) ), 'single_valued_set'( X ) ],
% 0.73/1.12 [ function( X ), ~( relation( X ) ), ~( 'single_valued_set'( X ) ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ ~( member( X, image( Y, Z ) ) ), 'ordered_pair_predicate'( f22( X, Y,
% 0.73/1.12 Z ) ) ],
% 0.73/1.12 [ ~( member( X, image( Y, Z ) ) ), member( f22( X, Y, Z ), Z ) ],
% 0.73/1.12 [ ~( member( X, image( Y, Z ) ) ), member( first( f22( X, Y, Z ) ), Y )
% 0.73/1.12 ],
% 0.73/1.12 [ ~( member( X, image( Y, Z ) ) ), =( second( f22( X, Y, Z ) ), X ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ member( X, image( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.12 'ordered_pair_predicate'( T ) ), ~( member( T, Z ) ), ~( member( first( T
% 0.73/1.12 ), Y ) ), ~( =( second( T ), X ) ) ],
% 0.73/1.12 [ ~( 'little_set'( X ) ), ~( function( Y ) ), 'little_set'( image( X, Y
% 0.73/1.12 ) ) ],
% 0.73/1.12 [ ~( disjoint( X, Y ) ), ~( member( Z, X ) ), ~( member( Z, Y ) ) ],
% 0.73/1.12 [ disjoint( X, Y ), member( f23( X, Y ), X ) ],
% 0.73/1.12 [ disjoint( X, Y ), member( f23( X, Y ), Y ) ],
% 0.73/1.12 [ =( X, 'empty_set' ), member( f24( X ), X ) ],
% 0.73/1.12 [ =( X, 'empty_set' ), disjoint( f24( X ), X ) ],
% 0.73/1.12 [ function( f25 ) ],
% 0.73/1.12 [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( f26( X ), X ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( 'ordered_pair'( X
% 0.73/1.12 , f26( X ) ), f25 ) ],
% 0.73/1.12 [ ~( member( X, 'range_of'( Y ) ) ), 'ordered_pair_predicate'( f27( X, Y
% 0.73/1.12 ) ) ],
% 0.73/1.12 [ ~( member( X, 'range_of'( Y ) ) ), member( f27( X, Y ), Y ) ],
% 0.73/1.12 [ ~( member( X, 'range_of'( Y ) ) ), =( X, second( f27( X, Y ) ) ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ member( X, 'range_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.73/1.12 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, second( Z
% 0.73/1.12 ) ) ) ],
% 0.73/1.12 [ ~( member( X, 'identity_relation' ) ), 'ordered_pair_predicate'( X ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ ~( member( X, 'identity_relation' ) ), =( first( X ), second( X ) ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ member( X, 'identity_relation' ), ~( 'little_set'( X ) ), ~(
% 0.73/1.12 'ordered_pair_predicate'( X ) ), ~( =( first( X ), second( X ) ) ) ],
% 0.73/1.12 [ =( restrict( X, Y ), intersection( X, 'cross_product'( Y,
% 0.73/1.12 'universal_set' ) ) ) ],
% 0.73/1.12 [ ~( 'one_to_one_function'( X ) ), function( X ) ],
% 0.73/1.12 [ ~( 'one_to_one_function'( X ) ), function( converse( X ) ) ],
% 0.73/1.12 [ 'one_to_one_function'( X ), ~( function( X ) ), ~( function( converse(
% 0.73/1.12 X ) ) ) ],
% 0.73/1.12 [ ~( member( X, apply( Y, Z ) ) ), 'ordered_pair_predicate'( f28( X, Y,
% 0.73/1.12 Z ) ) ],
% 0.73/1.12 [ ~( member( X, apply( Y, Z ) ) ), member( f28( X, Y, Z ), Y ) ],
% 0.73/1.12 [ ~( member( X, apply( Y, Z ) ) ), =( first( f28( X, Y, Z ) ), Z ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ ~( member( X, apply( Y, Z ) ) ), member( X, second( f28( X, Y, Z ) ) )
% 0.73/1.12 ],
% 0.73/1.12 [ member( X, apply( Y, Z ) ), ~( 'ordered_pair_predicate'( T ) ), ~(
% 0.73/1.12 member( T, Y ) ), ~( =( first( T ), Z ) ), ~( member( X, second( T ) ) )
% 0.73/1.12 ],
% 0.73/1.12 [ =( 'apply_to_two_arguments'( X, Y, Z ), apply( X, 'ordered_pair'( Y, Z
% 0.73/1.12 ) ) ) ],
% 0.73/1.12 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.73/1.12 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 0.73/1.12 [ ~( maps( X, Y, Z ) ), subset( 'range_of'( X ), Z ) ],
% 0.73/1.12 [ maps( X, Y, Z ), ~( function( X ) ), ~( =( 'domain_of'( X ), Y ) ),
% 0.73/1.12 ~( subset( 'range_of'( X ), Z ) ) ],
% 0.73/1.12 [ ~( closed( X, Y ) ), 'little_set'( X ) ],
% 0.73/1.12 [ ~( closed( X, Y ) ), 'little_set'( Y ) ],
% 0.73/1.12 [ ~( closed( X, Y ) ), maps( Y, 'cross_product'( X, X ), X ) ],
% 0.73/1.12 [ closed( X, Y ), ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~(
% 0.73/1.12 maps( Y, 'cross_product'( X, X ), X ) ) ],
% 0.73/1.12 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f29( X, Y, Z ) ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f30( X, Y, Z ) ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f31( X, Y, Z ) ) ]
% 0.73/1.12 ,
% 0.73/1.12 [ ~( member( X, compose( Y, Z ) ) ), =( X, 'ordered_pair'( f29( X, Y, Z
% 0.73/1.12 ), f30( X, Y, Z ) ) ) ],
% 0.73/1.12 [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'( f29( X, Y,
% 0.73/1.12 Z ), f31( X, Y, Z ) ), Y ) ],
% 0.73/1.12 [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'( f31( X, Y,
% 0.73/1.12 Z ), f30( X, Y, Z ) ), Z ) ],
% 0.73/1.12 [ member( X, compose( Y, Z ) ), ~( 'little_set'( X ) ), ~( 'little_set'(
% 0.73/1.12 T ) ), ~( 'little_set'( U ) ), ~( 'little_set'( W ) ), ~( =( X,
% 0.73/1.12 'ordered_pair'( T, U ) ) ), ~( member( 'ordered_pair'( T, W ), Y ) ), ~(
% 0.73/1.12 member( 'ordered_pair'( W, U ), Z ) ) ],
% 0.73/1.12 [ ~( homomorphism( X, Y, Z, T, U ) ), closed( Y, Z ) ],
% 0.73/1.12 [ ~( homomorphism( X, Y, Z, T, U ) ), closed( T, U ) ],
% 0.73/1.12 [ ~( homomorphism( X, Y, Z, T, U ) ), maps( X, Y, T ) ],
% 0.73/1.12 [ ~( homomorphism( X, Y, Z, T, U ) ), ~( member( W, Y ) ), ~( member( V0
% 0.73/1.12 , Y ) ), =( apply( X, 'apply_to_two_arguments'( Z, W, V0 ) ),
% 0.73/1.12 'apply_to_two_arguments'( U, apply( X, W ), apply( X, V0 ) ) ) ],
% 0.73/1.12 [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.73/1.12 ), ~( maps( X, Y, T ) ), member( f32( X, Y, Z, T, U ), Y ) ],
% 0.73/1.12 [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.73/1.12 ), ~( maps( X, Y, T ) ), member( f33( X, Y, Z, T, U ), Y ) ],
% 0.73/1.12 [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.76/1.23 ), ~( maps( X, Y, T ) ), ~( =( apply( X, 'apply_to_two_arguments'( Z,
% 0.76/1.23 f32( X, Y, Z, T, U ), f33( X, Y, Z, T, U ) ) ), 'apply_to_two_arguments'(
% 0.76/1.23 U, apply( X, f32( X, Y, Z, T, U ) ), apply( X, f33( X, Y, Z, T, U ) ) ) )
% 0.76/1.23 ) ],
% 0.76/1.23 [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( =( 'ordered_pair'(
% 0.76/1.23 X, Z ), 'ordered_pair'( Y, T ) ) ), =( X, Y ) ],
% 0.76/1.23 [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( =(
% 0.76/1.23 'non_ordered_pair'( Z, X ), 'non_ordered_pair'( Z, Y ) ) ), =( X, Y ) ]
% 0.76/1.23 ,
% 0.76/1.23 [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( 'little_set'( Z ) )
% 0.76/1.23 , ~( 'little_set'( T ) ), ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z
% 0.76/1.23 , T ) ) ), =( Y, T ) ],
% 0.76/1.23 [ ~( subset( X, Y ) ), ~( subset( Y, X ) ), =( X, Y ) ],
% 0.76/1.23 [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), =( first(
% 0.76/1.23 'ordered_pair'( X, Y ) ), X ) ],
% 0.76/1.23 [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), =( second(
% 0.76/1.23 'ordered_pair'( X, Y ) ), Y ) ],
% 0.76/1.23 [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( first( X ) ) ],
% 0.76/1.23 [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( second( X ) ) ],
% 0.76/1.23 [ ~( 'little_set'( X ) ), member( X, 'singleton_set'( X ) ) ],
% 0.76/1.23 [ 'little_set'( 'ordered_pair'( X, Y ) ) ],
% 0.76/1.23 [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( X ) ],
% 0.76/1.23 [ ~( subset( X, Y ) ), ~( subset( Y, Z ) ), subset( X, Z ) ],
% 0.76/1.23 [ subset( apply( X, Y ), sigma( image( 'singleton_set'( Y ), X ) ) ) ]
% 0.76/1.23 ,
% 0.76/1.23 [ subset( image( 'singleton_set'( X ), Y ), apply( Y, X ) ) ],
% 0.76/1.23 [ ~( function( X ) ), 'little_set'( apply( X, Y ) ) ],
% 0.76/1.23 [ relation( compose( X, Y ) ) ],
% 0.76/1.23 [ subset( 'range_of'( compose( X, Y ) ), 'range_of'( X ) ) ],
% 0.76/1.23 [ ~( subset( 'range_of'( X ), 'domain_of'( Y ) ) ), =( 'domain_of'( X )
% 0.76/1.23 , 'domain_of'( compose( Y, X ) ) ) ],
% 0.76/1.23 [ ~( function( X ) ), ~( function( Y ) ), function( compose( Y, X ) ) ]
% 0.76/1.23 ,
% 0.76/1.23 [ ~( maps( X, Y, Z ) ), ~( maps( T, Z, U ) ), maps( compose( T, X ), Y,
% 0.76/1.23 U ) ],
% 0.76/1.23 [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( function( Z ) ),
% 0.76/1.23 ~( member( 'ordered_pair'( X, Y ), Z ) ), =( apply( Z, X ), Y ) ],
% 0.76/1.23 [ ~( function( X ) ), ~( member( Y, 'domain_of'( X ) ) ), ~( =( apply( X
% 0.76/1.23 , Y ), Z ) ), member( 'ordered_pair'( Y, Z ), X ) ],
% 0.76/1.23 [ ~( maps( X, Y, Z ) ), ~( member( T, Y ) ), member( apply( X, T ), Z )
% 0.76/1.23 ],
% 0.76/1.23 [ ~( function( X ) ), ~( member( Y, 'domain_of'( X ) ) ), subset( apply(
% 0.76/1.23 Z, apply( X, Y ) ), apply( compose( Z, X ), Y ) ) ],
% 0.76/1.23 [ ~( function( X ) ), subset( apply( compose( Y, X ), Z ), apply( Y,
% 0.76/1.23 apply( X, Z ) ) ) ],
% 0.76/1.23 [ function( 'a_function' ) ],
% 0.76/1.23 [ member( a, 'domain_of'( 'a_function' ) ) ],
% 0.76/1.23 [ ~( =( apply( 'another_function', apply( 'a_function', a ) ), apply(
% 0.76/1.23 compose( 'another_function', 'a_function' ), a ) ) ) ]
% 0.76/1.23 ] .
% 0.76/1.23
% 0.76/1.23
% 0.76/1.23 percentage equality = 0.141509, percentage horn = 0.881657
% 0.76/1.23 This is a problem with some equality
% 0.76/1.23
% 0.76/1.23
% 0.76/1.23
% 0.76/1.23 Options Used:
% 0.76/1.23
% 0.76/1.23 useres = 1
% 0.76/1.23 useparamod = 1
% 0.76/1.23 useeqrefl = 1
% 0.76/1.23 useeqfact = 1
% 0.76/1.23 usefactor = 1
% 0.76/1.23 usesimpsplitting = 0
% 0.76/1.23 usesimpdemod = 5
% 0.76/1.23 usesimpres = 3
% 0.76/1.23
% 0.76/1.23 resimpinuse = 1000
% 0.76/1.23 resimpclauses = 20000
% 0.76/1.23 substype = eqrewr
% 0.76/1.23 backwardsubs = 1
% 0.76/1.23 selectoldest = 5
% 0.76/1.23
% 0.76/1.23 litorderings [0] = split
% 0.76/1.23 litorderings [1] = extend the termordering, first sorting on arguments
% 0.76/1.23
% 0.76/1.23 termordering = kbo
% 0.76/1.23
% 0.76/1.23 litapriori = 0
% 0.76/1.23 termapriori = 1
% 0.76/1.23 litaposteriori = 0
% 0.76/1.23 termaposteriori = 0
% 0.76/1.23 demodaposteriori = 0
% 0.76/1.23 ordereqreflfact = 0
% 0.76/1.23
% 0.76/1.23 litselect = negord
% 0.76/1.23
% 0.76/1.23 maxweight = 15
% 0.76/1.23 maxdepth = 30000
% 0.76/1.23 maxlength = 115
% 0.76/1.23 maxnrvars = 195
% 0.76/1.23 excuselevel = 1
% 0.76/1.23 increasemaxweight = 1
% 0.76/1.23
% 0.76/1.23 maxselected = 10000000
% 0.76/1.23 maxnrclauses = 10000000
% 0.76/1.23
% 0.76/1.23 showgenerated = 0
% 0.76/1.23 showkept = 0
% 0.76/1.23 showselected = 0
% 0.76/1.23 showdeleted = 0
% 0.76/1.23 showresimp = 1
% 0.76/1.23 showstatus = 2000
% 0.76/1.23
% 0.76/1.23 prologoutput = 1
% 0.76/1.23 nrgoals = 5000000
% 0.76/1.23 totalproof = 1
% 0.76/1.23
% 0.76/1.23 Symbols occurring in the translation:
% 0.76/1.23
% 0.76/1.23 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.76/1.23 . [1, 2] (w:1, o:66, a:1, s:1, b:0),
% 0.76/1.23 ! [4, 1] (w:0, o:35, a:1, s:1, b:0),
% 0.76/1.23 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.76/1.23 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.76/1.23 member [41, 2] (w:1, o:91, a:1, s:1, b:0),
% 10.83/11.23 'little_set' [42, 1] (w:1, o:40, a:1, s:1, b:0),
% 10.83/11.23 f1 [43, 2] (w:1, o:92, a:1, s:1, b:0),
% 10.83/11.23 'non_ordered_pair' [45, 2] (w:1, o:93, a:1, s:1, b:0),
% 10.83/11.23 'singleton_set' [46, 1] (w:1, o:44, a:1, s:1, b:0),
% 10.83/11.23 'ordered_pair' [47, 2] (w:1, o:94, a:1, s:1, b:0),
% 10.83/11.23 'ordered_pair_predicate' [48, 1] (w:1, o:45, a:1, s:1, b:0),
% 10.83/11.23 f2 [49, 1] (w:1, o:48, a:1, s:1, b:0),
% 10.83/11.23 f3 [50, 1] (w:1, o:53, a:1, s:1, b:0),
% 10.83/11.23 first [52, 1] (w:1, o:54, a:1, s:1, b:0),
% 10.83/11.23 f4 [53, 2] (w:1, o:95, a:1, s:1, b:0),
% 10.83/11.23 f5 [54, 2] (w:1, o:96, a:1, s:1, b:0),
% 10.83/11.23 second [56, 1] (w:1, o:55, a:1, s:1, b:0),
% 10.83/11.23 f6 [57, 2] (w:1, o:97, a:1, s:1, b:0),
% 10.83/11.23 f7 [58, 2] (w:1, o:98, a:1, s:1, b:0),
% 10.83/11.23 estin [59, 0] (w:1, o:26, a:1, s:1, b:0),
% 10.83/11.23 intersection [60, 2] (w:1, o:100, a:1, s:1, b:0),
% 10.83/11.23 complement [61, 1] (w:1, o:56, a:1, s:1, b:0),
% 10.83/11.23 union [62, 2] (w:1, o:101, a:1, s:1, b:0),
% 10.83/11.23 'domain_of' [63, 1] (w:1, o:58, a:1, s:1, b:0),
% 10.83/11.23 f8 [64, 2] (w:1, o:102, a:1, s:1, b:0),
% 10.83/11.23 'cross_product' [66, 2] (w:1, o:103, a:1, s:1, b:0),
% 10.83/11.23 converse [67, 1] (w:1, o:57, a:1, s:1, b:0),
% 10.83/11.23 'rotate_right' [68, 1] (w:1, o:41, a:1, s:1, b:0),
% 10.83/11.23 f9 [69, 2] (w:1, o:104, a:1, s:1, b:0),
% 10.83/11.23 f10 [70, 2] (w:1, o:105, a:1, s:1, b:0),
% 10.83/11.23 f11 [71, 2] (w:1, o:106, a:1, s:1, b:0),
% 10.83/11.23 'flip_range_of' [73, 1] (w:1, o:59, a:1, s:1, b:0),
% 10.83/11.23 f12 [74, 2] (w:1, o:107, a:1, s:1, b:0),
% 10.83/11.23 f13 [75, 2] (w:1, o:108, a:1, s:1, b:0),
% 10.83/11.23 f14 [76, 2] (w:1, o:109, a:1, s:1, b:0),
% 10.83/11.23 successor [77, 1] (w:1, o:60, a:1, s:1, b:0),
% 10.83/11.23 'empty_set' [78, 0] (w:1, o:27, a:1, s:1, b:0),
% 10.83/11.23 'universal_set' [79, 0] (w:1, o:28, a:1, s:1, b:0),
% 10.83/11.23 infinity [80, 0] (w:1, o:29, a:1, s:1, b:0),
% 10.83/11.23 sigma [81, 1] (w:1, o:61, a:1, s:1, b:0),
% 10.83/11.23 f16 [82, 2] (w:1, o:110, a:1, s:1, b:0),
% 10.83/11.23 subset [83, 2] (w:1, o:112, a:1, s:1, b:0),
% 10.83/11.23 f17 [84, 2] (w:1, o:113, a:1, s:1, b:0),
% 10.83/11.23 'proper_subset' [85, 2] (w:1, o:114, a:1, s:1, b:0),
% 10.83/11.23 powerset [86, 1] (w:1, o:63, a:1, s:1, b:0),
% 10.83/11.23 relation [87, 1] (w:1, o:42, a:1, s:1, b:0),
% 10.83/11.23 f18 [88, 1] (w:1, o:46, a:1, s:1, b:0),
% 10.83/11.23 'single_valued_set' [89, 1] (w:1, o:64, a:1, s:1, b:0),
% 10.83/11.23 f19 [90, 1] (w:1, o:47, a:1, s:1, b:0),
% 10.83/11.23 f20 [91, 1] (w:1, o:49, a:1, s:1, b:0),
% 10.83/11.23 f21 [92, 1] (w:1, o:50, a:1, s:1, b:0),
% 10.83/11.23 function [94, 1] (w:1, o:65, a:1, s:1, b:0),
% 10.83/11.23 image [95, 2] (w:1, o:99, a:1, s:1, b:0),
% 10.83/11.23 f22 [96, 3] (w:1, o:121, a:1, s:1, b:0),
% 10.83/11.23 disjoint [97, 2] (w:1, o:117, a:1, s:1, b:0),
% 10.83/11.23 f23 [98, 2] (w:1, o:118, a:1, s:1, b:0),
% 10.83/11.23 f24 [99, 1] (w:1, o:51, a:1, s:1, b:0),
% 10.83/11.23 f25 [100, 0] (w:1, o:30, a:1, s:1, b:0),
% 10.83/11.23 f26 [101, 1] (w:1, o:52, a:1, s:1, b:0),
% 10.83/11.23 'range_of' [102, 1] (w:1, o:43, a:1, s:1, b:0),
% 10.83/11.23 f27 [103, 2] (w:1, o:119, a:1, s:1, b:0),
% 10.83/11.23 'identity_relation' [104, 0] (w:1, o:31, a:1, s:1, b:0),
% 10.83/11.23 restrict [105, 2] (w:1, o:111, a:1, s:1, b:0),
% 10.83/11.23 'one_to_one_function' [106, 1] (w:1, o:62, a:1, s:1, b:0),
% 10.83/11.23 apply [107, 2] (w:1, o:120, a:1, s:1, b:0),
% 10.83/11.23 f28 [108, 3] (w:1, o:122, a:1, s:1, b:0),
% 10.83/11.23 'apply_to_two_arguments' [109, 3] (w:1, o:123, a:1, s:1, b:0),
% 10.83/11.23 maps [110, 3] (w:1, o:124, a:1, s:1, b:0),
% 10.83/11.23 closed [112, 2] (w:1, o:115, a:1, s:1, b:0),
% 10.83/11.23 compose [114, 2] (w:1, o:116, a:1, s:1, b:0),
% 10.83/11.23 f29 [115, 3] (w:1, o:125, a:1, s:1, b:0),
% 10.83/11.23 f30 [116, 3] (w:1, o:126, a:1, s:1, b:0),
% 10.83/11.23 f31 [117, 3] (w:1, o:127, a:1, s:1, b:0),
% 10.83/11.23 homomorphism [123, 5] (w:1, o:128, a:1, s:1, b:0),
% 10.83/11.23 f32 [124, 5] (w:1, o:129, a:1, s:1, b:0),
% 10.83/11.23 f33 [125, 5] (w:1, o:130, a:1, s:1, b:0),
% 10.83/11.23 'a_function' [128, 0] (w:1, o:32, a:1, s:1, b:0),
% 10.83/11.23 a [129, 0] (w:1, o:33, a:1, s:1, b:0),
% 10.83/11.23 'another_function' [130, 0] (w:1, o:34, a:1, s:1, b:0).
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Starting Search:
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 3582
% 10.83/11.23 Kept: 2012
% 10.83/11.23 Inuse: 91
% 10.83/11.23 Deleted: 0
% 10.83/11.23 Deletedinuse: 0
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 6999
% 10.83/11.23 Kept: 4030
% 10.83/11.23 Inuse: 148
% 10.83/11.23 Deleted: 1
% 10.83/11.23 Deletedinuse: 0
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 10296
% 10.83/11.23 Kept: 6042
% 10.83/11.23 Inuse: 200
% 10.83/11.23 Deleted: 3
% 10.83/11.23 Deletedinuse: 0
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 14971
% 10.83/11.23 Kept: 8064
% 10.83/11.23 Inuse: 257
% 10.83/11.23 Deleted: 19
% 10.83/11.23 Deletedinuse: 10
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 19170
% 10.83/11.23 Kept: 10071
% 10.83/11.23 Inuse: 297
% 10.83/11.23 Deleted: 20
% 10.83/11.23 Deletedinuse: 10
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 21910
% 10.83/11.23 Kept: 12089
% 10.83/11.23 Inuse: 323
% 10.83/11.23 Deleted: 20
% 10.83/11.23 Deletedinuse: 10
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 28301
% 10.83/11.23 Kept: 14202
% 10.83/11.23 Inuse: 374
% 10.83/11.23 Deleted: 23
% 10.83/11.23 Deletedinuse: 11
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 34764
% 10.83/11.23 Kept: 16243
% 10.83/11.23 Inuse: 403
% 10.83/11.23 Deleted: 130
% 10.83/11.23 Deletedinuse: 107
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 39134
% 10.83/11.23 Kept: 18259
% 10.83/11.23 Inuse: 439
% 10.83/11.23 Deleted: 155
% 10.83/11.23 Deletedinuse: 108
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23 Resimplifying clauses:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 45708
% 10.83/11.23 Kept: 20263
% 10.83/11.23 Inuse: 468
% 10.83/11.23 Deleted: 3866
% 10.83/11.23 Deletedinuse: 108
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 56061
% 10.83/11.23 Kept: 22788
% 10.83/11.23 Inuse: 512
% 10.83/11.23 Deleted: 3879
% 10.83/11.23 Deletedinuse: 116
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 68022
% 10.83/11.23 Kept: 24905
% 10.83/11.23 Inuse: 527
% 10.83/11.23 Deleted: 3879
% 10.83/11.23 Deletedinuse: 116
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 72593
% 10.83/11.23 Kept: 26934
% 10.83/11.23 Inuse: 565
% 10.83/11.23 Deleted: 3879
% 10.83/11.23 Deletedinuse: 116
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 79123
% 10.83/11.23 Kept: 29063
% 10.83/11.23 Inuse: 597
% 10.83/11.23 Deleted: 3879
% 10.83/11.23 Deletedinuse: 116
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 84154
% 10.83/11.23 Kept: 31701
% 10.83/11.23 Inuse: 617
% 10.83/11.23 Deleted: 3880
% 10.83/11.23 Deletedinuse: 117
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 93181
% 10.83/11.23 Kept: 34914
% 10.83/11.23 Inuse: 627
% 10.83/11.23 Deleted: 3880
% 10.83/11.23 Deletedinuse: 117
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 99074
% 10.83/11.23 Kept: 36942
% 10.83/11.23 Inuse: 660
% 10.83/11.23 Deleted: 3880
% 10.83/11.23 Deletedinuse: 117
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 Intermediate Status:
% 10.83/11.23 Generated: 107418
% 10.83/11.23 Kept: 38957
% 10.83/11.23 Inuse: 690
% 10.83/11.23 Deleted: 3885
% 10.83/11.23 Deletedinuse: 118
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23 Resimplifying inuse:
% 10.83/11.23 Done
% 10.83/11.23
% 10.83/11.23 Resimplifying clauses:
% 10.83/11.23
% 10.83/11.23 Bliksems!, er is een bewijs:
% 10.83/11.23 % SZS status Unsatisfiable
% 10.83/11.23 % SZS output start Refutation
% 10.83/11.23
% 10.83/11.23 clause( 144, [ ~( subset( X, Y ) ), ~( subset( Y, X ) ), =( X, Y ) ] )
% 10.83/11.23 .
% 10.83/11.23 clause( 164, [ ~( function( X ) ), ~( member( Y, 'domain_of'( X ) ) ),
% 10.83/11.23 subset( apply( Z, apply( X, Y ) ), apply( compose( Z, X ), Y ) ) ] )
% 10.83/11.23 .
% 10.83/11.23 clause( 165, [ ~( function( X ) ), subset( apply( compose( Y, X ), Z ),
% 10.83/11.23 apply( Y, apply( X, Z ) ) ) ] )
% 10.83/11.23 .
% 10.83/11.23 clause( 166, [ function( 'a_function' ) ] )
% 10.83/11.23 .
% 10.83/11.23 clause( 167, [ member( a, 'domain_of'( 'a_function' ) ) ] )
% 10.83/11.23 .
% 10.83/11.23 clause( 168, [ ~( =( apply( 'another_function', apply( 'a_function', a ) )
% 10.83/11.23 , apply( compose( 'another_function', 'a_function' ), a ) ) ) ] )
% 10.83/11.23 .
% 10.83/11.23 clause( 29263, [ subset( apply( X, apply( 'a_function', a ) ), apply(
% 10.83/11.23 compose( X, 'a_function' ), a ) ) ] )
% 10.83/11.23 .
% 10.83/11.23 clause( 29483, [ subset( apply( compose( X, 'a_function' ), Y ), apply( X,
% 10.83/11.23 apply( 'a_function', Y ) ) ) ] )
% 10.83/11.23 .
% 10.83/11.23 clause( 29754, [ ~( =( X, apply( compose( 'another_function', 'a_function'
% 10.83/11.23 ), a ) ) ), ~( subset( apply( 'another_function', apply( 'a_function', a
% 10.83/11.23 ) ), X ) ), ~( subset( X, apply( 'another_function', apply( 'a_function'
% 10.83/11.23 , a ) ) ) ) ] )
% 10.83/11.23 .
% 10.83/11.23 clause( 29849, [ ~( subset( apply( compose( 'another_function',
% 10.83/11.23 'a_function' ), a ), apply( 'another_function', apply( 'a_function', a )
% 10.83/11.23 ) ) ) ] )
% 10.83/11.23 .
% 10.83/11.23 clause( 40340, [] )
% 10.83/11.23 .
% 10.83/11.23
% 10.83/11.23
% 10.83/11.23 % SZS output end Refutation
% 10.83/11.23 found a proof!
% 10.83/11.23
% 10.83/11.23 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 10.83/11.23
% 10.83/11.23 initialclauses(
% 10.83/11.23 [ clause( 40342, [ ~( member( X, Y ) ), 'little_set'( X ) ] )
% 10.83/11.23 , clause( 40343, [ 'little_set'( f1( X, Y ) ), =( X, Y ) ] )
% 10.83/11.23 , clause( 40344, [ member( f1( X, Y ), X ), member( f1( X, Y ), Y ), =( X,
% 10.83/11.23 Y ) ] )
% 10.83/11.23 , clause( 40345, [ ~( member( f1( X, Y ), X ) ), ~( member( f1( X, Y ), Y )
% 10.83/11.23 ), =( X, Y ) ] )
% 10.83/11.23 , clause( 40346, [ ~( member( X, 'non_ordered_pair'( Y, Z ) ) ), =( X, Y )
% 10.83/11.23 , =( X, Z ) ] )
% 10.83/11.23 , clause( 40347, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'(
% 10.83/11.23 X ) ), ~( =( X, Y ) ) ] )
% 10.83/11.23 , clause( 40348, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'(
% 10.83/11.23 X ) ), ~( =( X, Z ) ) ] )
% 10.83/11.23 , clause( 40349, [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ] )
% 10.83/11.23 , clause( 40350, [ =( 'singleton_set'( X ), 'non_ordered_pair'( X, X ) ) ]
% 10.83/11.23 )
% 10.83/11.23 , clause( 40351, [ =( 'ordered_pair'( X, Y ), 'non_ordered_pair'(
% 10.83/11.23 'singleton_set'( X ), 'non_ordered_pair'( X, Y ) ) ) ] )
% 10.83/11.23 , clause( 40352, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f2( X
% 10.83/11.23 ) ) ] )
% 10.83/11.23 , clause( 40353, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f3( X
% 10.83/11.23 ) ) ] )
% 10.83/11.23 , clause( 40354, [ ~( 'ordered_pair_predicate'( X ) ), =( X, 'ordered_pair'(
% 10.83/11.23 f2( X ), f3( X ) ) ) ] )
% 10.83/11.23 , clause( 40355, [ 'ordered_pair_predicate'( X ), ~( 'little_set'( Y ) ),
% 10.83/11.23 ~( 'little_set'( Z ) ), ~( =( X, 'ordered_pair'( Y, Z ) ) ) ] )
% 10.83/11.23 , clause( 40356, [ ~( member( X, first( Y ) ) ), 'little_set'( f4( X, Y ) )
% 10.83/11.23 ] )
% 10.83/11.23 , clause( 40357, [ ~( member( X, first( Y ) ) ), 'little_set'( f5( X, Y ) )
% 10.83/11.23 ] )
% 10.83/11.23 , clause( 40358, [ ~( member( X, first( Y ) ) ), =( Y, 'ordered_pair'( f4(
% 10.83/11.23 X, Y ), f5( X, Y ) ) ) ] )
% 10.83/11.23 , clause( 40359, [ ~( member( X, first( Y ) ) ), member( X, f4( X, Y ) ) ]
% 10.83/11.23 )
% 10.83/11.23 , clause( 40360, [ member( X, first( Y ) ), ~( 'little_set'( Z ) ), ~(
% 10.83/11.23 'little_set'( T ) ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, Z
% 10.83/11.23 ) ) ] )
% 10.83/11.23 , clause( 40361, [ ~( member( X, second( Y ) ) ), 'little_set'( f6( X, Y )
% 10.83/11.23 ) ] )
% 10.83/11.23 , clause( 40362, [ ~( member( X, second( Y ) ) ), 'little_set'( f7( X, Y )
% 10.83/11.23 ) ] )
% 10.83/11.23 , clause( 40363, [ ~( member( X, second( Y ) ) ), =( Y, 'ordered_pair'( f6(
% 10.83/11.23 X, Y ), f7( X, Y ) ) ) ] )
% 10.83/11.23 , clause( 40364, [ ~( member( X, second( Y ) ) ), member( X, f7( X, Y ) ) ]
% 10.83/11.23 )
% 10.83/11.23 , clause( 40365, [ member( X, second( Y ) ), ~( 'little_set'( Z ) ), ~(
% 10.83/11.23 'little_set'( T ) ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, T
% 10.83/11.23 ) ) ] )
% 10.83/11.23 , clause( 40366, [ ~( member( X, estin ) ), 'ordered_pair_predicate'( X ) ]
% 10.83/11.23 )
% 10.83/11.23 , clause( 40367, [ ~( member( X, estin ) ), member( first( X ), second( X )
% 10.83/11.23 ) ] )
% 10.83/11.23 , clause( 40368, [ member( X, estin ), ~( 'little_set'( X ) ), ~(
% 10.83/11.23 'ordered_pair_predicate'( X ) ), ~( member( first( X ), second( X ) ) ) ]
% 10.83/11.23 )
% 10.83/11.23 , clause( 40369, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 10.83/11.23 )
% 10.83/11.23 , clause( 40370, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 10.83/11.23 )
% 10.83/11.23 , clause( 40371, [ member( X, intersection( Y, Z ) ), ~( member( X, Y ) ),
% 10.83/11.23 ~( member( X, Z ) ) ] )
% 10.83/11.23 , clause( 40372, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 10.83/11.23 )
% 10.83/11.23 , clause( 40373, [ member( X, complement( Y ) ), ~( 'little_set'( X ) ),
% 10.83/11.23 member( X, Y ) ] )
% 10.83/11.23 , clause( 40374, [ =( union( X, Y ), complement( intersection( complement(
% 10.83/11.23 X ), complement( Y ) ) ) ) ] )
% 10.83/11.23 , clause( 40375, [ ~( member( X, 'domain_of'( Y ) ) ),
% 10.83/11.23 'ordered_pair_predicate'( f8( X, Y ) ) ] )
% 10.83/11.23 , clause( 40376, [ ~( member( X, 'domain_of'( Y ) ) ), member( f8( X, Y ),
% 10.83/11.23 Y ) ] )
% 10.83/11.23 , clause( 40377, [ ~( member( X, 'domain_of'( Y ) ) ), =( X, first( f8( X,
% 10.83/11.23 Y ) ) ) ] )
% 10.83/11.23 , clause( 40378, [ member( X, 'domain_of'( Y ) ), ~( 'little_set'( X ) ),
% 10.83/11.23 ~( 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, first(
% 10.83/11.23 Z ) ) ) ] )
% 10.83/11.23 , clause( 40379, [ ~( member( X, 'cross_product'( Y, Z ) ) ),
% 10.83/11.23 'ordered_pair_predicate'( X ) ] )
% 10.83/11.23 , clause( 40380, [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( first(
% 10.83/11.23 X ), Y ) ] )
% 10.83/11.23 , clause( 40381, [ ~( member( X, 'cross_product'( Y, Z ) ) ), member(
% 10.83/11.23 second( X ), Z ) ] )
% 10.83/11.23 , clause( 40382, [ member( X, 'cross_product'( Y, Z ) ), ~( 'little_set'( X
% 10.83/11.23 ) ), ~( 'ordered_pair_predicate'( X ) ), ~( member( first( X ), Y ) ),
% 10.83/11.23 ~( member( second( X ), Z ) ) ] )
% 10.83/11.23 , clause( 40383, [ ~( member( X, converse( Y ) ) ),
% 10.83/11.23 'ordered_pair_predicate'( X ) ] )
% 10.83/11.23 , clause( 40384, [ ~( member( X, converse( Y ) ) ), member( 'ordered_pair'(
% 10.83/11.23 second( X ), first( X ) ), Y ) ] )
% 10.83/11.23 , clause( 40385, [ member( X, converse( Y ) ), ~( 'little_set'( X ) ), ~(
% 10.83/11.23 'ordered_pair_predicate'( X ) ), ~( member( 'ordered_pair'( second( X ),
% 10.83/11.23 first( X ) ), Y ) ) ] )
% 10.83/11.23 , clause( 40386, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f9(
% 10.83/11.23 X, Y ) ) ] )
% 10.83/11.23 , clause( 40387, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f10(
% 10.83/11.23 X, Y ) ) ] )
% 10.83/11.23 , clause( 40388, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f11(
% 10.83/11.23 X, Y ) ) ] )
% 10.83/11.23 , clause( 40389, [ ~( member( X, 'rotate_right'( Y ) ) ), =( X,
% 10.83/11.23 'ordered_pair'( f9( X, Y ), 'ordered_pair'( f10( X, Y ), f11( X, Y ) ) )
% 10.83/11.23 ) ] )
% 10.83/11.23 , clause( 40390, [ ~( member( X, 'rotate_right'( Y ) ) ), member(
% 10.83/11.23 'ordered_pair'( f10( X, Y ), 'ordered_pair'( f11( X, Y ), f9( X, Y ) ) )
% 10.83/11.23 , Y ) ] )
% 10.83/11.23 , clause( 40391, [ member( X, 'rotate_right'( Y ) ), ~( 'little_set'( X ) )
% 10.83/11.23 , ~( 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) )
% 10.83/11.23 , ~( =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 10.83/11.23 'ordered_pair'( T, 'ordered_pair'( U, Z ) ), Y ) ) ] )
% 10.83/11.23 , clause( 40392, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'(
% 10.83/11.23 f12( X, Y ) ) ] )
% 10.83/11.23 , clause( 40393, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'(
% 10.83/11.23 f13( X, Y ) ) ] )
% 10.83/11.23 , clause( 40394, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'(
% 10.83/11.23 f14( X, Y ) ) ] )
% 10.83/11.23 , clause( 40395, [ ~( member( X, 'flip_range_of'( Y ) ) ), =( X,
% 10.83/11.23 'ordered_pair'( f12( X, Y ), 'ordered_pair'( f13( X, Y ), f14( X, Y ) ) )
% 10.83/11.23 ) ] )
% 10.83/11.23 , clause( 40396, [ ~( member( X, 'flip_range_of'( Y ) ) ), member(
% 10.83/11.23 'ordered_pair'( f12( X, Y ), 'ordered_pair'( f14( X, Y ), f13( X, Y ) ) )
% 10.83/11.23 , Y ) ] )
% 10.83/11.23 , clause( 40397, [ member( X, 'flip_range_of'( Y ) ), ~( 'little_set'( X )
% 10.83/11.23 ), ~( 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U )
% 10.83/11.23 ), ~( =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 10.83/11.23 'ordered_pair'( Z, 'ordered_pair'( U, T ) ), Y ) ) ] )
% 10.83/11.23 , clause( 40398, [ =( successor( X ), union( X, 'singleton_set'( X ) ) ) ]
% 10.83/11.23 )
% 10.83/11.23 , clause( 40399, [ ~( member( X, 'empty_set' ) ) ] )
% 10.83/11.23 , clause( 40400, [ member( X, 'universal_set' ), ~( 'little_set'( X ) ) ]
% 10.83/11.23 )
% 10.83/11.23 , clause( 40401, [ 'little_set'( infinity ) ] )
% 10.83/11.23 , clause( 40402, [ member( 'empty_set', infinity ) ] )
% 10.83/11.23 , clause( 40403, [ ~( member( X, infinity ) ), member( successor( X ),
% 10.83/11.23 infinity ) ] )
% 10.83/11.23 , clause( 40404, [ ~( member( X, sigma( Y ) ) ), member( f16( X, Y ), Y ) ]
% 10.83/11.23 )
% 10.83/11.23 , clause( 40405, [ ~( member( X, sigma( Y ) ) ), member( X, f16( X, Y ) ) ]
% 10.83/11.23 )
% 10.83/11.23 , clause( 40406, [ member( X, sigma( Y ) ), ~( member( Z, Y ) ), ~( member(
% 10.83/11.23 X, Z ) ) ] )
% 10.83/11.23 , clause( 40407, [ ~( 'little_set'( X ) ), 'little_set'( sigma( X ) ) ] )
% 10.83/11.23 , clause( 40408, [ ~( subset( X, Y ) ), ~( member( Z, X ) ), member( Z, Y )
% 10.83/11.23 ] )
% 10.83/11.23 , clause( 40409, [ subset( X, Y ), member( f17( X, Y ), X ) ] )
% 10.83/11.23 , clause( 40410, [ subset( X, Y ), ~( member( f17( X, Y ), Y ) ) ] )
% 10.83/11.23 , clause( 40411, [ ~( 'proper_subset'( X, Y ) ), subset( X, Y ) ] )
% 10.83/11.23 , clause( 40412, [ ~( 'proper_subset'( X, Y ) ), ~( =( X, Y ) ) ] )
% 10.83/11.23 , clause( 40413, [ 'proper_subset'( X, Y ), ~( subset( X, Y ) ), =( X, Y )
% 10.83/11.23 ] )
% 10.83/11.23 , clause( 40414, [ ~( member( X, powerset( Y ) ) ), subset( X, Y ) ] )
% 10.83/11.23 , clause( 40415, [ member( X, powerset( Y ) ), ~( 'little_set'( X ) ), ~(
% 10.83/11.23 subset( X, Y ) ) ] )
% 10.83/11.23 , clause( 40416, [ ~( 'little_set'( X ) ), 'little_set'( powerset( X ) ) ]
% 10.83/11.23 )
% 10.83/11.23 , clause( 40417, [ ~( relation( X ) ), ~( member( Y, X ) ),
% 10.83/11.23 'ordered_pair_predicate'( Y ) ] )
% 10.83/11.23 , clause( 40418, [ relation( X ), member( f18( X ), X ) ] )
% 10.83/11.23 , clause( 40419, [ relation( X ), ~( 'ordered_pair_predicate'( f18( X ) ) )
% 10.83/11.23 ] )
% 10.83/11.23 , clause( 40420, [ ~( 'single_valued_set'( X ) ), ~( 'little_set'( Y ) ),
% 10.83/11.23 ~( 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( member( 'ordered_pair'(
% 10.83/11.23 Y, Z ), X ) ), ~( member( 'ordered_pair'( Y, T ), X ) ), =( Z, T ) ] )
% 10.83/11.23 , clause( 40421, [ 'single_valued_set'( X ), 'little_set'( f19( X ) ) ] )
% 10.83/11.23 , clause( 40422, [ 'single_valued_set'( X ), 'little_set'( f20( X ) ) ] )
% 10.83/11.23 , clause( 40423, [ 'single_valued_set'( X ), 'little_set'( f21( X ) ) ] )
% 10.83/11.23 , clause( 40424, [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X
% 10.83/11.23 ), f20( X ) ), X ) ] )
% 10.83/11.23 , clause( 40425, [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X
% 10.83/11.23 ), f21( X ) ), X ) ] )
% 10.83/11.23 , clause( 40426, [ 'single_valued_set'( X ), ~( =( f20( X ), f21( X ) ) ) ]
% 10.83/11.23 )
% 10.83/11.23 , clause( 40427, [ ~( function( X ) ), relation( X ) ] )
% 10.83/11.23 , clause( 40428, [ ~( function( X ) ), 'single_valued_set'( X ) ] )
% 10.83/11.23 , clause( 40429, [ function( X ), ~( relation( X ) ), ~(
% 10.83/11.23 'single_valued_set'( X ) ) ] )
% 10.83/11.23 , clause( 40430, [ ~( member( X, image( Y, Z ) ) ),
% 10.83/11.23 'ordered_pair_predicate'( f22( X, Y, Z ) ) ] )
% 10.83/11.23 , clause( 40431, [ ~( member( X, image( Y, Z ) ) ), member( f22( X, Y, Z )
% 10.83/11.23 , Z ) ] )
% 10.83/11.23 , clause( 40432, [ ~( member( X, image( Y, Z ) ) ), member( first( f22( X,
% 10.83/11.23 Y, Z ) ), Y ) ] )
% 10.83/11.23 , clause( 40433, [ ~( member( X, image( Y, Z ) ) ), =( second( f22( X, Y, Z
% 10.83/11.23 ) ), X ) ] )
% 10.83/11.23 , clause( 40434, [ member( X, image( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 10.83/11.23 'ordered_pair_predicate'( T ) ), ~( member( T, Z ) ), ~( member( first( T
% 10.83/11.23 ), Y ) ), ~( =( second( T ), X ) ) ] )
% 10.83/11.23 , clause( 40435, [ ~( 'little_set'( X ) ), ~( function( Y ) ), 'little_set'(
% 10.83/11.23 image( X, Y ) ) ] )
% 10.83/11.23 , clause( 40436, [ ~( disjoint( X, Y ) ), ~( member( Z, X ) ), ~( member( Z
% 10.83/11.23 , Y ) ) ] )
% 10.83/11.23 , clause( 40437, [ disjoint( X, Y ), member( f23( X, Y ), X ) ] )
% 10.83/11.23 , clause( 40438, [ disjoint( X, Y ), member( f23( X, Y ), Y ) ] )
% 10.83/11.23 , clause( 40439, [ =( X, 'empty_set' ), member( f24( X ), X ) ] )
% 10.83/11.23 , clause( 40440, [ =( X, 'empty_set' ), disjoint( f24( X ), X ) ] )
% 10.83/11.23 , clause( 40441, [ function( f25 ) ] )
% 10.83/11.23 , clause( 40442, [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( f26(
% 10.83/11.23 X ), X ) ] )
% 10.83/11.23 , clause( 40443, [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member(
% 10.83/11.23 'ordered_pair'( X, f26( X ) ), f25 ) ] )
% 10.83/11.23 , clause( 40444, [ ~( member( X, 'range_of'( Y ) ) ),
% 10.83/11.23 'ordered_pair_predicate'( f27( X, Y ) ) ] )
% 10.83/11.23 , clause( 40445, [ ~( member( X, 'range_of'( Y ) ) ), member( f27( X, Y ),
% 10.83/11.23 Y ) ] )
% 10.83/11.23 , clause( 40446, [ ~( member( X, 'range_of'( Y ) ) ), =( X, second( f27( X
% 10.83/11.23 , Y ) ) ) ] )
% 10.83/11.23 , clause( 40447, [ member( X, 'range_of'( Y ) ), ~( 'little_set'( X ) ),
% 10.83/11.23 ~( 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, second(
% 10.83/11.23 Z ) ) ) ] )
% 10.83/11.23 , clause( 40448, [ ~( member( X, 'identity_relation' ) ),
% 10.83/11.23 'ordered_pair_predicate'( X ) ] )
% 10.83/11.23 , clause( 40449, [ ~( member( X, 'identity_relation' ) ), =( first( X ),
% 10.83/11.23 second( X ) ) ] )
% 10.83/11.23 , clause( 40450, [ member( X, 'identity_relation' ), ~( 'little_set'( X ) )
% 10.83/11.23 , ~( 'ordered_pair_predicate'( X ) ), ~( =( first( X ), second( X ) ) ) ]
% 10.83/11.23 )
% 10.83/11.23 , clause( 40451, [ =( restrict( X, Y ), intersection( X, 'cross_product'( Y
% 10.83/11.23 , 'universal_set' ) ) ) ] )
% 10.83/11.23 , clause( 40452, [ ~( 'one_to_one_function'( X ) ), function( X ) ] )
% 10.83/11.23 , clause( 40453, [ ~( 'one_to_one_function'( X ) ), function( converse( X )
% 10.83/11.23 ) ] )
% 10.83/11.23 , clause( 40454, [ 'one_to_one_function'( X ), ~( function( X ) ), ~(
% 10.83/11.23 function( converse( X ) ) ) ] )
% 10.83/11.23 , clause( 40455, [ ~( member( X, apply( Y, Z ) ) ),
% 10.83/11.23 'ordered_pair_predicate'( f28( X, Y, Z ) ) ] )
% 10.83/11.23 , clause( 40456, [ ~( member( X, apply( Y, Z ) ) ), member( f28( X, Y, Z )
% 10.83/11.23 , Y ) ] )
% 10.83/11.23 , clause( 40457, [ ~( member( X, apply( Y, Z ) ) ), =( first( f28( X, Y, Z
% 10.83/11.23 ) ), Z ) ] )
% 10.83/11.23 , clause( 40458, [ ~( member( X, apply( Y, Z ) ) ), member( X, second( f28(
% 10.83/11.23 X, Y, Z ) ) ) ] )
% 10.83/11.23 , clause( 40459, [ member( X, apply( Y, Z ) ), ~( 'ordered_pair_predicate'(
% 10.83/11.23 T ) ), ~( member( T, Y ) ), ~( =( first( T ), Z ) ), ~( member( X, second(
% 10.83/11.23 T ) ) ) ] )
% 10.83/11.23 , clause( 40460, [ =( 'apply_to_two_arguments'( X, Y, Z ), apply( X,
% 10.83/11.23 'ordered_pair'( Y, Z ) ) ) ] )
% 10.83/11.23 , clause( 40461, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 10.83/11.23 , clause( 40462, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 10.83/11.23 , clause( 40463, [ ~( maps( X, Y, Z ) ), subset( 'range_of'( X ), Z ) ] )
% 10.83/11.23 , clause( 40464, [ maps( X, Y, Z ), ~( function( X ) ), ~( =( 'domain_of'(
% 10.83/11.23 X ), Y ) ), ~( subset( 'range_of'( X ), Z ) ) ] )
% 10.83/11.23 , clause( 40465, [ ~( closed( X, Y ) ), 'little_set'( X ) ] )
% 10.83/11.23 , clause( 40466, [ ~( closed( X, Y ) ), 'little_set'( Y ) ] )
% 10.83/11.23 , clause( 40467, [ ~( closed( X, Y ) ), maps( Y, 'cross_product'( X, X ), X
% 10.83/11.23 ) ] )
% 10.83/11.23 , clause( 40468, [ closed( X, Y ), ~( 'little_set'( X ) ), ~( 'little_set'(
% 10.83/11.23 Y ) ), ~( maps( Y, 'cross_product'( X, X ), X ) ) ] )
% 10.83/11.23 , clause( 40469, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f29( X
% 10.83/11.23 , Y, Z ) ) ] )
% 10.83/11.23 , clause( 40470, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f30( X
% 10.83/11.23 , Y, Z ) ) ] )
% 10.83/11.23 , clause( 40471, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f31( X
% 10.83/11.23 , Y, Z ) ) ] )
% 10.83/11.23 , clause( 40472, [ ~( member( X, compose( Y, Z ) ) ), =( X, 'ordered_pair'(
% 10.83/11.23 f29( X, Y, Z ), f30( X, Y, Z ) ) ) ] )
% 10.83/11.23 , clause( 40473, [ ~( member( X, compose( Y, Z ) ) ), member(
% 10.83/11.23 'ordered_pair'( f29( X, Y, Z ), f31( X, Y, Z ) ), Y ) ] )
% 10.83/11.23 , clause( 40474, [ ~( member( X, compose( Y, Z ) ) ), member(
% 10.83/11.23 'ordered_pair'( f31( X, Y, Z ), f30( X, Y, Z ) ), Z ) ] )
% 10.83/11.23 , clause( 40475, [ member( X, compose( Y, Z ) ), ~( 'little_set'( X ) ),
% 10.83/11.23 ~( 'little_set'( T ) ), ~( 'little_set'( U ) ), ~( 'little_set'( W ) ),
% 10.83/11.23 ~( =( X, 'ordered_pair'( T, U ) ) ), ~( member( 'ordered_pair'( T, W ), Y
% 10.83/11.23 ) ), ~( member( 'ordered_pair'( W, U ), Z ) ) ] )
% 10.83/11.23 , clause( 40476, [ ~( homomorphism( X, Y, Z, T, U ) ), closed( Y, Z ) ] )
% 10.83/11.23 , clause( 40477, [ ~( homomorphism( X, Y, Z, T, U ) ), closed( T, U ) ] )
% 10.83/11.23 , clause( 40478, [ ~( homomorphism( X, Y, Z, T, U ) ), maps( X, Y, T ) ] )
% 10.83/11.23 , clause( 40479, [ ~( homomorphism( X, Y, Z, T, U ) ), ~( member( W, Y ) )
% 10.83/11.23 , ~( member( V0, Y ) ), =( apply( X, 'apply_to_two_arguments'( Z, W, V0 )
% 10.83/11.23 ), 'apply_to_two_arguments'( U, apply( X, W ), apply( X, V0 ) ) ) ] )
% 10.83/11.23 , clause( 40480, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~(
% 10.83/11.23 closed( T, U ) ), ~( maps( X, Y, T ) ), member( f32( X, Y, Z, T, U ), Y )
% 10.83/11.23 ] )
% 10.83/11.23 , clause( 40481, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~(
% 10.83/11.23 closed( T, U ) ), ~( maps( X, Y, T ) ), member( f33( X, Y, Z, T, U ), Y )
% 10.83/11.23 ] )
% 10.83/11.23 , clause( 40482, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~(
% 10.83/11.23 closed( T, U ) ), ~( maps( X, Y, T ) ), ~( =( apply( X,
% 10.83/11.23 'apply_to_two_arguments'( Z, f32( X, Y, Z, T, U ), f33( X, Y, Z, T, U ) )
% 10.83/11.23 ), 'apply_to_two_arguments'( U, apply( X, f32( X, Y, Z, T, U ) ), apply(
% 10.83/11.23 X, f33( X, Y, Z, T, U ) ) ) ) ) ] )
% 10.83/11.23 , clause( 40483, [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( =(
% 10.83/11.23 'ordered_pair'( X, Z ), 'ordered_pair'( Y, T ) ) ), =( X, Y ) ] )
% 10.83/11.23 , clause( 40484, [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( =(
% 10.83/11.23 'non_ordered_pair'( Z, X ), 'non_ordered_pair'( Z, Y ) ) ), =( X, Y ) ]
% 10.83/11.23 )
% 10.83/11.23 , clause( 40485, [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~(
% 10.83/11.23 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( =( 'ordered_pair'( X, Y )
% 10.83/11.23 , 'ordered_pair'( Z, T ) ) ), =( Y, T ) ] )
% 10.83/11.23 , clause( 40486, [ ~( subset( X, Y ) ), ~( subset( Y, X ) ), =( X, Y ) ] )
% 10.83/11.23 , clause( 40487, [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), =( first(
% 10.83/11.23 'ordered_pair'( X, Y ) ), X ) ] )
% 10.83/11.23 , clause( 40488, [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), =(
% 10.83/11.23 second( 'ordered_pair'( X, Y ) ), Y ) ] )
% 10.83/11.23 , clause( 40489, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( first(
% 10.83/11.23 X ) ) ] )
% 10.83/11.23 , clause( 40490, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( second(
% 10.83/11.23 X ) ) ] )
% 10.83/11.23 , clause( 40491, [ ~( 'little_set'( X ) ), member( X, 'singleton_set'( X )
% 10.83/11.23 ) ] )
% 10.83/11.23 , clause( 40492, [ 'little_set'( 'ordered_pair'( X, Y ) ) ] )
% 10.83/11.23 , clause( 40493, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( X ) ]
% 10.83/11.23 )
% 10.83/11.23 , clause( 40494, [ ~( subset( X, Y ) ), ~( subset( Y, Z ) ), subset( X, Z )
% 10.83/11.23 ] )
% 10.83/11.23 , clause( 40495, [ subset( apply( X, Y ), sigma( image( 'singleton_set'( Y
% 10.83/11.23 ), X ) ) ) ] )
% 10.83/11.23 , clause( 40496, [ subset( image( 'singleton_set'( X ), Y ), apply( Y, X )
% 10.83/11.23 ) ] )
% 10.83/11.23 , clause( 40497, [ ~( function( X ) ), 'little_set'( apply( X, Y ) ) ] )
% 10.83/11.23 , clause( 40498, [ relation( compose( X, Y ) ) ] )
% 10.83/11.23 , clause( 40499, [ subset( 'range_of'( compose( X, Y ) ), 'range_of'( X ) )
% 10.83/11.24 ] )
% 10.83/11.24 , clause( 40500, [ ~( subset( 'range_of'( X ), 'domain_of'( Y ) ) ), =(
% 10.83/11.24 'domain_of'( X ), 'domain_of'( compose( Y, X ) ) ) ] )
% 10.83/11.24 , clause( 40501, [ ~( function( X ) ), ~( function( Y ) ), function(
% 10.83/11.24 compose( Y, X ) ) ] )
% 10.83/11.24 , clause( 40502, [ ~( maps( X, Y, Z ) ), ~( maps( T, Z, U ) ), maps(
% 10.83/11.24 compose( T, X ), Y, U ) ] )
% 10.83/11.24 , clause( 40503, [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~(
% 10.83/11.24 function( Z ) ), ~( member( 'ordered_pair'( X, Y ), Z ) ), =( apply( Z, X
% 10.83/11.24 ), Y ) ] )
% 10.83/11.24 , clause( 40504, [ ~( function( X ) ), ~( member( Y, 'domain_of'( X ) ) ),
% 10.83/11.24 ~( =( apply( X, Y ), Z ) ), member( 'ordered_pair'( Y, Z ), X ) ] )
% 10.83/11.24 , clause( 40505, [ ~( maps( X, Y, Z ) ), ~( member( T, Y ) ), member( apply(
% 10.83/11.24 X, T ), Z ) ] )
% 10.83/11.24 , clause( 40506, [ ~( function( X ) ), ~( member( Y, 'domain_of'( X ) ) ),
% 10.83/11.24 subset( apply( Z, apply( X, Y ) ), apply( compose( Z, X ), Y ) ) ] )
% 10.83/11.24 , clause( 40507, [ ~( function( X ) ), subset( apply( compose( Y, X ), Z )
% 10.83/11.24 , apply( Y, apply( X, Z ) ) ) ] )
% 10.83/11.24 , clause( 40508, [ function( 'a_function' ) ] )
% 10.83/11.24 , clause( 40509, [ member( a, 'domain_of'( 'a_function' ) ) ] )
% 10.83/11.24 , clause( 40510, [ ~( =( apply( 'another_function', apply( 'a_function', a
% 10.83/11.24 ) ), apply( compose( 'another_function', 'a_function' ), a ) ) ) ] )
% 10.83/11.24 ] ).
% 10.83/11.24
% 10.83/11.24
% 10.83/11.24
% 10.83/11.24 subsumption(
% 10.83/11.24 clause( 144, [ ~( subset( X, Y ) ), ~( subset( Y, X ) ), =( X, Y ) ] )
% 10.83/11.24 , clause( 40486, [ ~( subset( X, Y ) ), ~( subset( Y, X ) ), =( X, Y ) ] )
% 10.83/11.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 10.83/11.24 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 10.83/11.24
% 10.83/11.24
% 10.83/11.24 subsumption(
% 10.83/11.24 clause( 164, [ ~( function( X ) ), ~( member( Y, 'domain_of'( X ) ) ),
% 10.83/11.24 subset( apply( Z, apply( X, Y ) ), apply( compose( Z, X ), Y ) ) ] )
% 10.83/11.24 , clause( 40506, [ ~( function( X ) ), ~( member( Y, 'domain_of'( X ) ) ),
% 10.83/11.24 subset( apply( Z, apply( X, Y ) ), apply( compose( Z, X ), Y ) ) ] )
% 10.83/11.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 10.83/11.24 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 10.83/11.24
% 10.83/11.24
% 10.83/11.24 subsumption(
% 10.83/11.24 clause( 165, [ ~( function( X ) ), subset( apply( compose( Y, X ), Z ),
% 10.83/11.24 apply( Y, apply( X, Z ) ) ) ] )
% 10.83/11.24 , clause( 40507, [ ~( function( X ) ), subset( apply( compose( Y, X ), Z )
% 10.83/11.24 , apply( Y, apply( X, Z ) ) ) ] )
% 10.83/11.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 10.83/11.24 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 10.83/11.24
% 10.83/11.24
% 10.83/11.24 subsumption(
% 10.83/11.24 clause( 166, [ function( 'a_function' ) ] )
% 10.83/11.24 , clause( 40508, [ function( 'a_function' ) ] )
% 10.83/11.24 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 10.83/11.24
% 10.83/11.24
% 10.83/11.24 subsumption(
% 10.83/11.24 clause( 167, [ member( a, 'domain_of'( 'a_function' ) ) ] )
% 10.83/11.24 , clause( 40509, [ member( a, 'domain_of'( 'a_function' ) ) ] )
% 10.83/11.24 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 10.83/11.24
% 10.83/11.24
% 10.83/11.24 subsumption(
% 10.83/11.24 clause( 168, [ ~( =( apply( 'another_function', apply( 'a_function', a ) )
% 10.83/11.24 , apply( compose( 'another_function', 'a_function' ), a ) ) ) ] )
% 10.83/11.24 , clause( 40510, [ ~( =( apply( 'another_function', apply( 'a_function', a
% 10.83/11.24 ) ), apply( compose( 'another_function', 'a_function' ), a ) ) ) ] )
% 10.83/11.24 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 10.83/11.24
% 10.83/11.24
% 10.83/11.24 resolution(
% 10.83/11.24 clause( 41788, [ ~( function( 'a_function' ) ), subset( apply( X, apply(
% 10.83/11.24 'a_function', a ) ), apply( compose( X, 'a_function' ), a ) ) ] )
% 10.83/11.24 , clause( 164, [ ~( function( X ) ), ~( member( Y, 'domain_of'( X ) ) ),
% 10.83/11.24 subset( apply( Z, apply( X, Y ) ), apply( compose( Z, X ), Y ) ) ] )
% 10.83/11.24 , 1, clause( 167, [ member( a, 'domain_of'( 'a_function' ) ) ] )
% 10.83/11.24 , 0, substitution( 0, [ :=( X, 'a_function' ), :=( Y, a ), :=( Z, X )] ),
% 10.83/11.24 substitution( 1, [] )).
% 10.83/11.24
% 10.83/11.24
% 10.83/11.24 resolution(
% 10.83/11.24 clause( 41789, [ subset( apply( X, apply( 'a_function', a ) ), apply(
% 10.83/11.24 compose( X, 'a_function' ), a ) ) ] )
% 10.83/11.24 , clause( 41788, [ ~( function( 'a_function' ) ), subset( apply( X, apply(
% 10.83/11.24 'a_function', a ) ), apply( compose( X, 'a_function' ), a ) ) ] )
% 10.83/11.24 , 0, clause( 166, [ function( 'a_function' ) ] )
% 10.83/11.24 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 10.83/11.24
% 10.83/11.24
% 10.83/11.24 subsumption(
% 10.83/11.24 clause( 29263, [ subset( apply( X, apply( 'a_function', a ) ), apply(
% 10.83/11.24 compose( X, 'a_function' ), a ) ) ] )
% 10.83/11.24 , clause( 41789, [ subset( apply( X, apply( 'a_fuCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------