TSTP Solution File: SET024-3 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET024-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Mon Jul 18 22:45:39 EDT 2022
% Result : Unsatisfiable 0.71s 1.11s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET024-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sun Jul 10 20:21:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.71/1.10 *** allocated 10000 integers for termspace/termends
% 0.71/1.10 *** allocated 10000 integers for clauses
% 0.71/1.10 *** allocated 10000 integers for justifications
% 0.71/1.10 Bliksem 1.12
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 Automatic Strategy Selection
% 0.71/1.10
% 0.71/1.10 Clauses:
% 0.71/1.10 [
% 0.71/1.10 [ ~( member( X, Y ) ), 'little_set'( X ) ],
% 0.71/1.10 [ 'little_set'( f1( X, Y ) ), =( X, Y ) ],
% 0.71/1.10 [ member( f1( X, Y ), X ), member( f1( X, Y ), Y ), =( X, Y ) ],
% 0.71/1.10 [ ~( member( f1( X, Y ), X ) ), ~( member( f1( X, Y ), Y ) ), =( X, Y )
% 0.71/1.10 ],
% 0.71/1.10 [ ~( member( X, 'non_ordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.10 =( X, Y ) ) ],
% 0.71/1.10 [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.10 =( X, Z ) ) ],
% 0.71/1.10 [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ],
% 0.71/1.10 [ =( 'singleton_set'( X ), 'non_ordered_pair'( X, X ) ) ],
% 0.71/1.10 [ =( 'ordered_pair'( X, Y ), 'non_ordered_pair'( 'singleton_set'( X ),
% 0.71/1.10 'non_ordered_pair'( X, Y ) ) ) ],
% 0.71/1.10 [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f2( X ) ) ],
% 0.71/1.10 [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f3( X ) ) ],
% 0.71/1.10 [ ~( 'ordered_pair_predicate'( X ) ), =( X, 'ordered_pair'( f2( X ), f3(
% 0.71/1.10 X ) ) ) ],
% 0.71/1.10 [ 'ordered_pair_predicate'( X ), ~( 'little_set'( Y ) ), ~( 'little_set'(
% 0.71/1.10 Z ) ), ~( =( X, 'ordered_pair'( Y, Z ) ) ) ],
% 0.71/1.10 [ ~( member( X, first( Y ) ) ), 'little_set'( f4( X, Y ) ) ],
% 0.71/1.10 [ ~( member( X, first( Y ) ) ), 'little_set'( f5( X, Y ) ) ],
% 0.71/1.10 [ ~( member( X, first( Y ) ) ), =( Y, 'ordered_pair'( f4( X, Y ), f5( X
% 0.71/1.10 , Y ) ) ) ],
% 0.71/1.10 [ ~( member( X, first( Y ) ) ), member( X, f4( X, Y ) ) ],
% 0.71/1.10 [ member( X, first( Y ) ), ~( 'little_set'( Z ) ), ~( 'little_set'( T )
% 0.71/1.10 ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, Z ) ) ],
% 0.71/1.10 [ ~( member( X, second( Y ) ) ), 'little_set'( f6( X, Y ) ) ],
% 0.71/1.10 [ ~( member( X, second( Y ) ) ), 'little_set'( f7( X, Y ) ) ],
% 0.71/1.10 [ ~( member( X, second( Y ) ) ), =( Y, 'ordered_pair'( f6( X, Y ), f7( X
% 0.71/1.10 , Y ) ) ) ],
% 0.71/1.10 [ ~( member( X, second( Y ) ) ), member( X, f7( X, Y ) ) ],
% 0.71/1.10 [ member( X, second( Y ) ), ~( 'little_set'( Z ) ), ~( 'little_set'( T )
% 0.71/1.10 ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, T ) ) ],
% 0.71/1.10 [ ~( member( X, estin ) ), 'ordered_pair_predicate'( X ) ],
% 0.71/1.10 [ ~( member( X, estin ) ), member( first( X ), second( X ) ) ],
% 0.71/1.10 [ member( X, estin ), ~( 'little_set'( X ) ), ~(
% 0.71/1.10 'ordered_pair_predicate'( X ) ), ~( member( first( X ), second( X ) ) ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.71/1.10 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.71/1.10 [ member( X, intersection( Y, Z ) ), ~( member( X, Y ) ), ~( member( X,
% 0.71/1.10 Z ) ) ],
% 0.71/1.10 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.71/1.10 [ member( X, complement( Y ) ), ~( 'little_set'( X ) ), member( X, Y ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ =( union( X, Y ), complement( intersection( complement( X ),
% 0.71/1.10 complement( Y ) ) ) ) ],
% 0.71/1.10 [ ~( member( X, 'domain_of'( Y ) ) ), 'ordered_pair_predicate'( f8( X, Y
% 0.71/1.10 ) ) ],
% 0.71/1.10 [ ~( member( X, 'domain_of'( Y ) ) ), member( f8( X, Y ), Y ) ],
% 0.71/1.10 [ ~( member( X, 'domain_of'( Y ) ) ), =( X, first( f8( X, Y ) ) ) ],
% 0.71/1.10 [ member( X, 'domain_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.10 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, first( Z )
% 0.71/1.10 ) ) ],
% 0.71/1.10 [ ~( member( X, 'cross_product'( Y, Z ) ) ), 'ordered_pair_predicate'( X
% 0.71/1.10 ) ],
% 0.71/1.10 [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( first( X ), Y ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( second( X ), Z ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ member( X, 'cross_product'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.10 'ordered_pair_predicate'( X ) ), ~( member( first( X ), Y ) ), ~( member(
% 0.71/1.10 second( X ), Z ) ) ],
% 0.71/1.10 [ ~( member( X, converse( Y ) ) ), 'ordered_pair_predicate'( X ) ],
% 0.71/1.10 [ ~( member( X, converse( Y ) ) ), member( 'ordered_pair'( second( X ),
% 0.71/1.10 first( X ) ), Y ) ],
% 0.71/1.10 [ member( X, converse( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.10 'ordered_pair_predicate'( X ) ), ~( member( 'ordered_pair'( second( X ),
% 0.71/1.10 first( X ) ), Y ) ) ],
% 0.71/1.10 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f9( X, Y ) ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f10( X, Y ) ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f11( X, Y ) ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( member( X, 'rotate_right'( Y ) ) ), =( X, 'ordered_pair'( f9( X, Y
% 0.71/1.10 ), 'ordered_pair'( f10( X, Y ), f11( X, Y ) ) ) ) ],
% 0.71/1.10 [ ~( member( X, 'rotate_right'( Y ) ) ), member( 'ordered_pair'( f10( X
% 0.71/1.10 , Y ), 'ordered_pair'( f11( X, Y ), f9( X, Y ) ) ), Y ) ],
% 0.71/1.10 [ member( X, 'rotate_right'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.10 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) ), ~(
% 0.71/1.10 =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 0.71/1.10 'ordered_pair'( T, 'ordered_pair'( U, Z ) ), Y ) ) ],
% 0.71/1.10 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f12( X, Y ) ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f13( X, Y ) ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f14( X, Y ) ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( member( X, 'flip_range_of'( Y ) ) ), =( X, 'ordered_pair'( f12( X,
% 0.71/1.10 Y ), 'ordered_pair'( f13( X, Y ), f14( X, Y ) ) ) ) ],
% 0.71/1.10 [ ~( member( X, 'flip_range_of'( Y ) ) ), member( 'ordered_pair'( f12( X
% 0.71/1.10 , Y ), 'ordered_pair'( f14( X, Y ), f13( X, Y ) ) ), Y ) ],
% 0.71/1.10 [ member( X, 'flip_range_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.10 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) ), ~(
% 0.71/1.10 =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 0.71/1.10 'ordered_pair'( Z, 'ordered_pair'( U, T ) ), Y ) ) ],
% 0.71/1.10 [ =( successor( X ), union( X, 'singleton_set'( X ) ) ) ],
% 0.71/1.10 [ ~( member( X, 'empty_set' ) ) ],
% 0.71/1.10 [ member( X, 'universal_set' ), ~( 'little_set'( X ) ) ],
% 0.71/1.10 [ 'little_set'( infinity ) ],
% 0.71/1.10 [ member( 'empty_set', infinity ) ],
% 0.71/1.10 [ ~( member( X, infinity ) ), member( successor( X ), infinity ) ],
% 0.71/1.10 [ ~( member( X, sigma( Y ) ) ), member( f16( X, Y ), Y ) ],
% 0.71/1.10 [ ~( member( X, sigma( Y ) ) ), member( X, f16( X, Y ) ) ],
% 0.71/1.10 [ member( X, sigma( Y ) ), ~( member( Z, Y ) ), ~( member( X, Z ) ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( 'little_set'( X ) ), 'little_set'( sigma( X ) ) ],
% 0.71/1.10 [ ~( subset( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.71/1.10 [ subset( X, Y ), member( f17( X, Y ), X ) ],
% 0.71/1.10 [ subset( X, Y ), ~( member( f17( X, Y ), Y ) ) ],
% 0.71/1.10 [ ~( 'proper_subset'( X, Y ) ), subset( X, Y ) ],
% 0.71/1.10 [ ~( 'proper_subset'( X, Y ) ), ~( =( X, Y ) ) ],
% 0.71/1.10 [ 'proper_subset'( X, Y ), ~( subset( X, Y ) ), =( X, Y ) ],
% 0.71/1.10 [ ~( member( X, powerset( Y ) ) ), subset( X, Y ) ],
% 0.71/1.10 [ member( X, powerset( Y ) ), ~( 'little_set'( X ) ), ~( subset( X, Y )
% 0.71/1.10 ) ],
% 0.71/1.10 [ ~( 'little_set'( X ) ), 'little_set'( powerset( X ) ) ],
% 0.71/1.10 [ ~( relation( X ) ), ~( member( Y, X ) ), 'ordered_pair_predicate'( Y )
% 0.71/1.10 ],
% 0.71/1.10 [ relation( X ), member( f18( X ), X ) ],
% 0.71/1.10 [ relation( X ), ~( 'ordered_pair_predicate'( f18( X ) ) ) ],
% 0.71/1.10 [ ~( 'single_valued_set'( X ) ), ~( 'little_set'( Y ) ), ~( 'little_set'(
% 0.71/1.10 Z ) ), ~( 'little_set'( T ) ), ~( member( 'ordered_pair'( Y, Z ), X ) ),
% 0.71/1.10 ~( member( 'ordered_pair'( Y, T ), X ) ), =( Z, T ) ],
% 0.71/1.10 [ 'single_valued_set'( X ), 'little_set'( f19( X ) ) ],
% 0.71/1.10 [ 'single_valued_set'( X ), 'little_set'( f20( X ) ) ],
% 0.71/1.10 [ 'single_valued_set'( X ), 'little_set'( f21( X ) ) ],
% 0.71/1.10 [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X ), f20( X ) )
% 0.71/1.10 , X ) ],
% 0.71/1.10 [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X ), f21( X ) )
% 0.71/1.10 , X ) ],
% 0.71/1.10 [ 'single_valued_set'( X ), ~( =( f20( X ), f21( X ) ) ) ],
% 0.71/1.10 [ ~( function( X ) ), relation( X ) ],
% 0.71/1.10 [ ~( function( X ) ), 'single_valued_set'( X ) ],
% 0.71/1.10 [ function( X ), ~( relation( X ) ), ~( 'single_valued_set'( X ) ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( member( X, image( Y, Z ) ) ), 'ordered_pair_predicate'( f22( X, Y,
% 0.71/1.10 Z ) ) ],
% 0.71/1.10 [ ~( member( X, image( Y, Z ) ) ), member( f22( X, Y, Z ), Z ) ],
% 0.71/1.10 [ ~( member( X, image( Y, Z ) ) ), member( first( f22( X, Y, Z ) ), Y )
% 0.71/1.10 ],
% 0.71/1.10 [ ~( member( X, image( Y, Z ) ) ), =( second( f22( X, Y, Z ) ), X ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ member( X, image( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.10 'ordered_pair_predicate'( T ) ), ~( member( T, Z ) ), ~( member( first( T
% 0.71/1.10 ), Y ) ), ~( =( second( T ), X ) ) ],
% 0.71/1.10 [ ~( 'little_set'( X ) ), ~( function( Y ) ), 'little_set'( image( X, Y
% 0.71/1.10 ) ) ],
% 0.71/1.10 [ ~( disjoint( X, Y ) ), ~( member( Z, X ) ), ~( member( Z, Y ) ) ],
% 0.71/1.10 [ disjoint( X, Y ), member( f23( X, Y ), X ) ],
% 0.71/1.10 [ disjoint( X, Y ), member( f23( X, Y ), Y ) ],
% 0.71/1.10 [ =( X, 'empty_set' ), member( f24( X ), X ) ],
% 0.71/1.10 [ =( X, 'empty_set' ), disjoint( f24( X ), X ) ],
% 0.71/1.10 [ function( f25 ) ],
% 0.71/1.10 [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( f26( X ), X ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( 'ordered_pair'( X
% 0.71/1.10 , f26( X ) ), f25 ) ],
% 0.71/1.10 [ ~( member( X, 'range_of'( Y ) ) ), 'ordered_pair_predicate'( f27( X, Y
% 0.71/1.10 ) ) ],
% 0.71/1.10 [ ~( member( X, 'range_of'( Y ) ) ), member( f27( X, Y ), Y ) ],
% 0.71/1.10 [ ~( member( X, 'range_of'( Y ) ) ), =( X, second( f27( X, Y ) ) ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ member( X, 'range_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.10 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, second( Z
% 0.71/1.10 ) ) ) ],
% 0.71/1.10 [ ~( member( X, 'identity_relation' ) ), 'ordered_pair_predicate'( X ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( member( X, 'identity_relation' ) ), =( first( X ), second( X ) ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ member( X, 'identity_relation' ), ~( 'little_set'( X ) ), ~(
% 0.71/1.10 'ordered_pair_predicate'( X ) ), ~( =( first( X ), second( X ) ) ) ],
% 0.71/1.10 [ =( restrict( X, Y ), intersection( X, 'cross_product'( Y,
% 0.71/1.10 'universal_set' ) ) ) ],
% 0.71/1.10 [ ~( 'one_to_one_function'( X ) ), function( X ) ],
% 0.71/1.10 [ ~( 'one_to_one_function'( X ) ), function( converse( X ) ) ],
% 0.71/1.10 [ 'one_to_one_function'( X ), ~( function( X ) ), ~( function( converse(
% 0.71/1.10 X ) ) ) ],
% 0.71/1.10 [ ~( member( X, apply( Y, Z ) ) ), 'ordered_pair_predicate'( f28( X, Y,
% 0.71/1.10 Z ) ) ],
% 0.71/1.10 [ ~( member( X, apply( Y, Z ) ) ), member( f28( X, Y, Z ), Y ) ],
% 0.71/1.10 [ ~( member( X, apply( Y, Z ) ) ), =( first( f28( X, Y, Z ) ), Z ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( member( X, apply( Y, Z ) ) ), member( X, second( f28( X, Y, Z ) ) )
% 0.71/1.10 ],
% 0.71/1.10 [ member( X, apply( Y, Z ) ), ~( 'ordered_pair_predicate'( T ) ), ~(
% 0.71/1.10 member( T, Y ) ), ~( =( first( T ), Z ) ), ~( member( X, second( T ) ) )
% 0.71/1.10 ],
% 0.71/1.10 [ =( 'apply_to_two_arguments'( X, Y, Z ), apply( X, 'ordered_pair'( Y, Z
% 0.71/1.10 ) ) ) ],
% 0.71/1.10 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.71/1.10 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 0.71/1.10 [ ~( maps( X, Y, Z ) ), subset( 'range_of'( X ), Z ) ],
% 0.71/1.10 [ maps( X, Y, Z ), ~( function( X ) ), ~( =( 'domain_of'( X ), Y ) ),
% 0.71/1.10 ~( subset( 'range_of'( X ), Z ) ) ],
% 0.71/1.10 [ ~( closed( X, Y ) ), 'little_set'( X ) ],
% 0.71/1.10 [ ~( closed( X, Y ) ), 'little_set'( Y ) ],
% 0.71/1.10 [ ~( closed( X, Y ) ), maps( Y, 'cross_product'( X, X ), X ) ],
% 0.71/1.10 [ closed( X, Y ), ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~(
% 0.71/1.10 maps( Y, 'cross_product'( X, X ), X ) ) ],
% 0.71/1.10 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f29( X, Y, Z ) ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f30( X, Y, Z ) ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f31( X, Y, Z ) ) ]
% 0.71/1.10 ,
% 0.71/1.10 [ ~( member( X, compose( Y, Z ) ) ), =( X, 'ordered_pair'( f29( X, Y, Z
% 0.71/1.10 ), f30( X, Y, Z ) ) ) ],
% 0.71/1.10 [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'( f29( X, Y,
% 0.71/1.10 Z ), f31( X, Y, Z ) ), Y ) ],
% 0.71/1.10 [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'( f31( X, Y,
% 0.71/1.10 Z ), f30( X, Y, Z ) ), Z ) ],
% 0.71/1.10 [ member( X, compose( Y, Z ) ), ~( 'little_set'( X ) ), ~( 'little_set'(
% 0.71/1.10 T ) ), ~( 'little_set'( U ) ), ~( 'little_set'( W ) ), ~( =( X,
% 0.71/1.10 'ordered_pair'( T, U ) ) ), ~( member( 'ordered_pair'( T, W ), Y ) ), ~(
% 0.71/1.10 member( 'ordered_pair'( W, U ), Z ) ) ],
% 0.71/1.10 [ ~( homomorphism( X, Y, Z, T, U ) ), closed( Y, Z ) ],
% 0.71/1.10 [ ~( homomorphism( X, Y, Z, T, U ) ), closed( T, U ) ],
% 0.71/1.10 [ ~( homomorphism( X, Y, Z, T, U ) ), maps( X, Y, T ) ],
% 0.71/1.10 [ ~( homomorphism( X, Y, Z, T, U ) ), ~( member( W, Y ) ), ~( member( V0
% 0.71/1.10 , Y ) ), =( apply( X, 'apply_to_two_arguments'( Z, W, V0 ) ),
% 0.71/1.10 'apply_to_two_arguments'( U, apply( X, W ), apply( X, V0 ) ) ) ],
% 0.71/1.10 [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.71/1.10 ), ~( maps( X, Y, T ) ), member( f32( X, Y, Z, T, U ), Y ) ],
% 0.71/1.10 [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.71/1.10 ), ~( maps( X, Y, T ) ), member( f33( X, Y, Z, T, U ), Y ) ],
% 0.71/1.10 [ 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 [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( =( 'ordered_pair'(
% 0.71/1.11 X, Z ), 'ordered_pair'( Y, T ) ) ), =( X, Y ) ],
% 0.71/1.11 [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( =(
% 0.71/1.11 'non_ordered_pair'( Z, X ), 'non_ordered_pair'( Z, Y ) ) ), =( X, Y ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( 'little_set'( Z ) )
% 0.71/1.11 , ~( 'little_set'( T ) ), ~( =( 'ordered_pair'( X, Y ), 'ordered_pair'( Z
% 0.71/1.11 , T ) ) ), =( Y, T ) ],
% 0.71/1.11 [ ~( subset( X, Y ) ), ~( subset( Y, X ) ), =( X, Y ) ],
% 0.71/1.11 [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), =( first(
% 0.71/1.11 'ordered_pair'( X, Y ) ), X ) ],
% 0.71/1.11 [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), =( second(
% 0.71/1.11 'ordered_pair'( X, Y ) ), Y ) ],
% 0.71/1.11 [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( first( X ) ) ],
% 0.71/1.11 [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( second( X ) ) ],
% 0.71/1.11 [ 'little_set'( a ) ],
% 0.71/1.11 [ ~( member( a, 'singleton_set'( a ) ) ) ]
% 0.71/1.11 ] .
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 percentage equality = 0.145833, percentage horn = 0.867550
% 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
% 0.71/1.11
% 0.71/1.11 maxweight = 15
% 0.71/1.11 maxdepth = 30000
% 0.71/1.11 maxlength = 115
% 0.71/1.11 maxnrvars = 195
% 0.71/1.11 excuselevel = 1
% 0.71/1.11 increasemaxweight = 1
% 0.71/1.11
% 0.71/1.11 maxselected = 10000000
% 0.71/1.11 maxnrclauses = 10000000
% 0.71/1.11
% 0.71/1.11 showgenerated = 0
% 0.71/1.11 showkept = 0
% 0.71/1.11 showselected = 0
% 0.71/1.11 showdeleted = 0
% 0.71/1.11 showresimp = 1
% 0.71/1.11 showstatus = 2000
% 0.71/1.11
% 0.71/1.11 prologoutput = 1
% 0.71/1.11 nrgoals = 5000000
% 0.71/1.11 totalproof = 1
% 0.71/1.11
% 0.71/1.11 Symbols occurring in the translation:
% 0.71/1.11
% 0.71/1.11 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.71/1.11 . [1, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.71/1.11 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 0.71/1.11 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.11 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.11 member [41, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.71/1.11 'little_set' [42, 1] (w:1, o:36, a:1, s:1, b:0),
% 0.71/1.11 f1 [43, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.71/1.11 'non_ordered_pair' [45, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.71/1.11 'singleton_set' [46, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.71/1.11 'ordered_pair' [47, 2] (w:1, o:90, a:1, s:1, b:0),
% 0.71/1.11 'ordered_pair_predicate' [48, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.71/1.11 f2 [49, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.71/1.11 f3 [50, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.71/1.11 first [52, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.71/1.11 f4 [53, 2] (w:1, o:91, a:1, s:1, b:0),
% 0.71/1.11 f5 [54, 2] (w:1, o:92, a:1, s:1, b:0),
% 0.71/1.11 second [56, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.71/1.11 f6 [57, 2] (w:1, o:93, a:1, s:1, b:0),
% 0.71/1.11 f7 [58, 2] (w:1, o:94, a:1, s:1, b:0),
% 0.71/1.11 estin [59, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.71/1.11 intersection [60, 2] (w:1, o:96, a:1, s:1, b:0),
% 0.71/1.11 complement [61, 1] (w:1, o:52, a:1, s:1, b:0),
% 0.71/1.11 union [62, 2] (w:1, o:97, a:1, s:1, b:0),
% 0.71/1.11 'domain_of' [63, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.71/1.11 f8 [64, 2] (w:1, o:98, a:1, s:1, b:0),
% 0.71/1.11 'cross_product' [66, 2] (w:1, o:99, a:1, s:1, b:0),
% 0.71/1.11 converse [67, 1] (w:1, o:53, a:1, s:1, b:0),
% 0.71/1.11 'rotate_right' [68, 1] (w:1, o:37, a:1, s:1, b:0),
% 0.71/1.11 f9 [69, 2] (w:1, o:100, a:1, s:1, b:0),
% 0.71/1.11 f10 [70, 2] (w:1, o:101, a:1, s:1, b:0),
% 0.71/1.11 f11 [71, 2] (w:1, o:102, a:1, s:1, b:0),
% 0.71/1.11 'flip_range_of' [73, 1] (w:1, o:55, a:1, s:1, b:0),
% 0.71/1.11 f12 [74, 2] (w:1, o:103, a:1, s:1, b:0),
% 0.71/1.11 f13 [75, 2] (w:1, o:104, a:1, s:1, b:0),
% 0.71/1.11 f14 [76, 2] (w:1, o:105, a:1, s:1, b:0),
% 0.71/1.11 successor [77, 1] (w:1, o:56, a:1, s:1, b:0),
% 0.71/1.11 'empty_set' [78, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.71/1.11 'universal_set' [79, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.71/1.11 infinity [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.71/1.11 sigma [81, 1] (w:1, o:57, a:1, s:1, b:0),
% 0.71/1.11 f16 [82, 2] (w:1, o:106, a:1, s:1, b:0),
% 0.71/1.11 subset [83, 2] (w:1, o:108, a:1, s:1, b:0),
% 0.71/1.11 f17 [84, 2] (w:1, o:109, a:1, s:1, b:0),
% 0.71/1.11 'proper_subset' [85, 2] (w:1, o:110, a:1, s:1, b:0),
% 0.71/1.11 powerset [86, 1] (w:1, o:59, a:1, s:1, b:0),
% 0.71/1.11 relation [87, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.71/1.11 f18 [88, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.71/1.11 'single_valued_set' [89, 1] (w:1, o:60, a:1, s:1, b:0),
% 0.71/1.11 f19 [90, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.71/1.11 f20 [91, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.71/1.11 f21 [92, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.71/1.11 function [94, 1] (w:1, o:61, a:1, s:1, b:0),
% 0.71/1.11 image [95, 2] (w:1, o:95, a:1, s:1, b:0),
% 0.71/1.11 f22 [96, 3] (w:1, o:117, a:1, s:1, b:0),
% 0.71/1.11 disjoint [97, 2] (w:1, o:113, a:1, s:1, b:0),
% 0.71/1.11 f23 [98, 2] (w:1, o:114, a:1, s:1, b:0),
% 0.71/1.11 f24 [99, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.71/1.11 f25 [100, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.71/1.11 f26 [101, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.71/1.11 'range_of' [102, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.71/1.11 f27 [103, 2] (w:1, o:115, a:1, s:1, b:0),
% 0.71/1.11 'identity_relation' [104, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.71/1.11 restrict [105, 2] (w:1, o:107, a:1, s:1, b:0),
% 0.71/1.11 'one_to_one_function' [106, 1] (w:1, o:58, a:1, s:1, b:0),
% 0.71/1.11 apply [107, 2] (w:1, o:116, a:1, s:1, b:0),
% 0.71/1.11 f28 [108, 3] (w:1, o:118, a:1, s:1, b:0),
% 0.71/1.11 'apply_to_two_arguments' [109, 3] (w:1, o:119, a:1, s:1, b:0),
% 0.71/1.11 maps [110, 3] (w:1, o:120, a:1, s:1, b:0),
% 0.71/1.11 closed [112, 2] (w:1, o:111, a:1, s:1, b:0),
% 0.71/1.11 compose [114, 2] (w:1, o:112, a:1, s:1, b:0),
% 0.71/1.11 f29 [115, 3] (w:1, o:121, a:1, s:1, b:0),
% 0.71/1.11 f30 [116, 3] (w:1, o:122, a:1, s:1, b:0),
% 0.71/1.11 f31 [117, 3] (w:1, o:123, a:1, s:1, b:0),
% 0.71/1.11 homomorphism [123, 5] (w:1, o:124, a:1, s:1, b:0),
% 0.71/1.11 f32 [124, 5] (w:1, o:125, a:1, s:1, b:0),
% 0.71/1.11 f33 [125, 5] (w:1, o:126, a:1, s:1, b:0),
% 0.71/1.11 a [126, 0] (w:1, o:30, a:1, s:1, b:0).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Starting Search:
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Bliksems!, er is een bewijs:
% 0.71/1.11 % SZS status Unsatisfiable
% 0.71/1.11 % SZS output start Refutation
% 0.71/1.11
% 0.71/1.11 clause( 6, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( X )
% 0.71/1.11 ), ~( =( X, Z ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 8, [ =( 'non_ordered_pair'( X, X ), 'singleton_set'( X ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 149, [ 'little_set'( a ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 150, [ ~( member( a, 'singleton_set'( a ) ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 606, [ member( a, 'non_ordered_pair'( X, Y ) ), ~( =( a, Y ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 621, [ member( a, 'non_ordered_pair'( X, a ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 684, [] )
% 0.71/1.11 .
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 % SZS output end Refutation
% 0.71/1.11 found a proof!
% 0.71/1.11
% 0.71/1.11 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.71/1.11
% 0.71/1.11 initialclauses(
% 0.71/1.11 [ clause( 686, [ ~( member( X, Y ) ), 'little_set'( X ) ] )
% 0.71/1.11 , clause( 687, [ 'little_set'( f1( X, Y ) ), =( X, Y ) ] )
% 0.71/1.11 , clause( 688, [ member( f1( X, Y ), X ), member( f1( X, Y ), Y ), =( X, Y
% 0.71/1.11 ) ] )
% 0.71/1.11 , clause( 689, [ ~( member( f1( X, Y ), X ) ), ~( member( f1( X, Y ), Y ) )
% 0.71/1.11 , =( X, Y ) ] )
% 0.71/1.11 , clause( 690, [ ~( member( X, 'non_ordered_pair'( Y, Z ) ) ), =( X, Y ),
% 0.71/1.11 =( X, Z ) ] )
% 0.71/1.11 , clause( 691, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'(
% 0.71/1.11 X ) ), ~( =( X, Y ) ) ] )
% 0.71/1.11 , clause( 692, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'(
% 0.71/1.11 X ) ), ~( =( X, Z ) ) ] )
% 0.71/1.11 , clause( 693, [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ] )
% 0.71/1.11 , clause( 694, [ =( 'singleton_set'( X ), 'non_ordered_pair'( X, X ) ) ] )
% 0.71/1.11 , clause( 695, [ =( 'ordered_pair'( X, Y ), 'non_ordered_pair'(
% 0.71/1.11 'singleton_set'( X ), 'non_ordered_pair'( X, Y ) ) ) ] )
% 0.71/1.11 , clause( 696, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f2( X )
% 0.71/1.11 ) ] )
% 0.71/1.11 , clause( 697, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f3( X )
% 0.71/1.11 ) ] )
% 0.71/1.11 , clause( 698, [ ~( 'ordered_pair_predicate'( X ) ), =( X, 'ordered_pair'(
% 0.71/1.11 f2( X ), f3( X ) ) ) ] )
% 0.71/1.11 , clause( 699, [ 'ordered_pair_predicate'( X ), ~( 'little_set'( Y ) ), ~(
% 0.71/1.11 'little_set'( Z ) ), ~( =( X, 'ordered_pair'( Y, Z ) ) ) ] )
% 0.71/1.11 , clause( 700, [ ~( member( X, first( Y ) ) ), 'little_set'( f4( X, Y ) ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 701, [ ~( member( X, first( Y ) ) ), 'little_set'( f5( X, Y ) ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 702, [ ~( member( X, first( Y ) ) ), =( Y, 'ordered_pair'( f4( X
% 0.71/1.11 , Y ), f5( X, Y ) ) ) ] )
% 0.71/1.11 , clause( 703, [ ~( member( X, first( Y ) ) ), member( X, f4( X, Y ) ) ] )
% 0.71/1.11 , clause( 704, [ member( X, first( Y ) ), ~( 'little_set'( Z ) ), ~(
% 0.71/1.11 'little_set'( T ) ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, Z
% 0.71/1.11 ) ) ] )
% 0.71/1.11 , clause( 705, [ ~( member( X, second( Y ) ) ), 'little_set'( f6( X, Y ) )
% 0.71/1.11 ] )
% 0.71/1.11 , clause( 706, [ ~( member( X, second( Y ) ) ), 'little_set'( f7( X, Y ) )
% 0.71/1.11 ] )
% 0.71/1.11 , clause( 707, [ ~( member( X, second( Y ) ) ), =( Y, 'ordered_pair'( f6( X
% 0.71/1.11 , Y ), f7( X, Y ) ) ) ] )
% 0.71/1.11 , clause( 708, [ ~( member( X, second( Y ) ) ), member( X, f7( X, Y ) ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 709, [ member( X, second( Y ) ), ~( 'little_set'( Z ) ), ~(
% 0.71/1.11 'little_set'( T ) ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, T
% 0.71/1.11 ) ) ] )
% 0.71/1.11 , clause( 710, [ ~( member( X, estin ) ), 'ordered_pair_predicate'( X ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 711, [ ~( member( X, estin ) ), member( first( X ), second( X ) )
% 0.71/1.11 ] )
% 0.71/1.11 , clause( 712, [ 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 , clause( 713, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 714, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 715, [ member( X, intersection( Y, Z ) ), ~( member( X, Y ) ),
% 0.71/1.11 ~( member( X, Z ) ) ] )
% 0.71/1.11 , clause( 716, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 717, [ member( X, complement( Y ) ), ~( 'little_set'( X ) ),
% 0.71/1.11 member( X, Y ) ] )
% 0.71/1.11 , clause( 718, [ =( union( X, Y ), complement( intersection( complement( X
% 0.71/1.11 ), complement( Y ) ) ) ) ] )
% 0.71/1.11 , clause( 719, [ ~( member( X, 'domain_of'( Y ) ) ),
% 0.71/1.11 'ordered_pair_predicate'( f8( X, Y ) ) ] )
% 0.71/1.11 , clause( 720, [ ~( member( X, 'domain_of'( Y ) ) ), member( f8( X, Y ), Y
% 0.71/1.11 ) ] )
% 0.71/1.11 , clause( 721, [ ~( member( X, 'domain_of'( Y ) ) ), =( X, first( f8( X, Y
% 0.71/1.11 ) ) ) ] )
% 0.71/1.11 , clause( 722, [ 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 , clause( 723, [ ~( member( X, 'cross_product'( Y, Z ) ) ),
% 0.71/1.11 'ordered_pair_predicate'( X ) ] )
% 0.71/1.11 , clause( 724, [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( first(
% 0.71/1.11 X ), Y ) ] )
% 0.71/1.11 , clause( 725, [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( second(
% 0.71/1.11 X ), Z ) ] )
% 0.71/1.11 , clause( 726, [ member( X, 'cross_product'( Y, Z ) ), ~( 'little_set'( X )
% 0.71/1.11 ), ~( 'ordered_pair_predicate'( X ) ), ~( member( first( X ), Y ) ), ~(
% 0.71/1.11 member( second( X ), Z ) ) ] )
% 0.71/1.11 , clause( 727, [ ~( member( X, converse( Y ) ) ), 'ordered_pair_predicate'(
% 0.71/1.11 X ) ] )
% 0.71/1.11 , clause( 728, [ ~( member( X, converse( Y ) ) ), member( 'ordered_pair'(
% 0.71/1.11 second( X ), first( X ) ), Y ) ] )
% 0.71/1.11 , clause( 729, [ 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 , clause( 730, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f9( X
% 0.71/1.11 , Y ) ) ] )
% 0.71/1.11 , clause( 731, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f10(
% 0.71/1.11 X, Y ) ) ] )
% 0.71/1.11 , clause( 732, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f11(
% 0.71/1.11 X, Y ) ) ] )
% 0.71/1.11 , clause( 733, [ ~( member( X, 'rotate_right'( Y ) ) ), =( X,
% 0.71/1.11 'ordered_pair'( f9( X, Y ), 'ordered_pair'( f10( X, Y ), f11( X, Y ) ) )
% 0.71/1.11 ) ] )
% 0.71/1.11 , clause( 734, [ ~( member( X, 'rotate_right'( Y ) ) ), member(
% 0.71/1.11 'ordered_pair'( f10( X, Y ), 'ordered_pair'( f11( X, Y ), f9( X, Y ) ) )
% 0.71/1.11 , Y ) ] )
% 0.71/1.11 , clause( 735, [ 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 , clause( 736, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f12(
% 0.71/1.11 X, Y ) ) ] )
% 0.71/1.11 , clause( 737, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f13(
% 0.71/1.11 X, Y ) ) ] )
% 0.71/1.11 , clause( 738, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f14(
% 0.71/1.11 X, Y ) ) ] )
% 0.71/1.11 , clause( 739, [ ~( member( X, 'flip_range_of'( Y ) ) ), =( X,
% 0.71/1.11 'ordered_pair'( f12( X, Y ), 'ordered_pair'( f13( X, Y ), f14( X, Y ) ) )
% 0.71/1.11 ) ] )
% 0.71/1.11 , clause( 740, [ ~( member( X, 'flip_range_of'( Y ) ) ), member(
% 0.71/1.11 'ordered_pair'( f12( X, Y ), 'ordered_pair'( f14( X, Y ), f13( X, Y ) ) )
% 0.71/1.11 , Y ) ] )
% 0.71/1.11 , clause( 741, [ 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 , clause( 742, [ =( successor( X ), union( X, 'singleton_set'( X ) ) ) ] )
% 0.71/1.11 , clause( 743, [ ~( member( X, 'empty_set' ) ) ] )
% 0.71/1.11 , clause( 744, [ member( X, 'universal_set' ), ~( 'little_set'( X ) ) ] )
% 0.71/1.11 , clause( 745, [ 'little_set'( infinity ) ] )
% 0.71/1.11 , clause( 746, [ member( 'empty_set', infinity ) ] )
% 0.71/1.11 , clause( 747, [ ~( member( X, infinity ) ), member( successor( X ),
% 0.71/1.11 infinity ) ] )
% 0.71/1.11 , clause( 748, [ ~( member( X, sigma( Y ) ) ), member( f16( X, Y ), Y ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 749, [ ~( member( X, sigma( Y ) ) ), member( X, f16( X, Y ) ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 750, [ member( X, sigma( Y ) ), ~( member( Z, Y ) ), ~( member( X
% 0.71/1.11 , Z ) ) ] )
% 0.71/1.11 , clause( 751, [ ~( 'little_set'( X ) ), 'little_set'( sigma( X ) ) ] )
% 0.71/1.11 , clause( 752, [ ~( subset( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 753, [ subset( X, Y ), member( f17( X, Y ), X ) ] )
% 0.71/1.11 , clause( 754, [ subset( X, Y ), ~( member( f17( X, Y ), Y ) ) ] )
% 0.71/1.11 , clause( 755, [ ~( 'proper_subset'( X, Y ) ), subset( X, Y ) ] )
% 0.71/1.11 , clause( 756, [ ~( 'proper_subset'( X, Y ) ), ~( =( X, Y ) ) ] )
% 0.71/1.11 , clause( 757, [ 'proper_subset'( X, Y ), ~( subset( X, Y ) ), =( X, Y ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 758, [ ~( member( X, powerset( Y ) ) ), subset( X, Y ) ] )
% 0.71/1.11 , clause( 759, [ member( X, powerset( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.11 subset( X, Y ) ) ] )
% 0.71/1.11 , clause( 760, [ ~( 'little_set'( X ) ), 'little_set'( powerset( X ) ) ] )
% 0.71/1.11 , clause( 761, [ ~( relation( X ) ), ~( member( Y, X ) ),
% 0.71/1.11 'ordered_pair_predicate'( Y ) ] )
% 0.71/1.11 , clause( 762, [ relation( X ), member( f18( X ), X ) ] )
% 0.71/1.11 , clause( 763, [ relation( X ), ~( 'ordered_pair_predicate'( f18( X ) ) ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 764, [ ~( 'single_valued_set'( X ) ), ~( 'little_set'( Y ) ), ~(
% 0.71/1.11 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( member( 'ordered_pair'( Y
% 0.71/1.11 , Z ), X ) ), ~( member( 'ordered_pair'( Y, T ), X ) ), =( Z, T ) ] )
% 0.71/1.11 , clause( 765, [ 'single_valued_set'( X ), 'little_set'( f19( X ) ) ] )
% 0.71/1.11 , clause( 766, [ 'single_valued_set'( X ), 'little_set'( f20( X ) ) ] )
% 0.71/1.11 , clause( 767, [ 'single_valued_set'( X ), 'little_set'( f21( X ) ) ] )
% 0.71/1.11 , clause( 768, [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X )
% 0.71/1.11 , f20( X ) ), X ) ] )
% 0.71/1.11 , clause( 769, [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X )
% 0.71/1.11 , f21( X ) ), X ) ] )
% 0.71/1.11 , clause( 770, [ 'single_valued_set'( X ), ~( =( f20( X ), f21( X ) ) ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 771, [ ~( function( X ) ), relation( X ) ] )
% 0.71/1.11 , clause( 772, [ ~( function( X ) ), 'single_valued_set'( X ) ] )
% 0.71/1.11 , clause( 773, [ function( X ), ~( relation( X ) ), ~( 'single_valued_set'(
% 0.71/1.11 X ) ) ] )
% 0.71/1.11 , clause( 774, [ ~( member( X, image( Y, Z ) ) ), 'ordered_pair_predicate'(
% 0.71/1.11 f22( X, Y, Z ) ) ] )
% 0.71/1.11 , clause( 775, [ ~( member( X, image( Y, Z ) ) ), member( f22( X, Y, Z ), Z
% 0.71/1.11 ) ] )
% 0.71/1.11 , clause( 776, [ ~( member( X, image( Y, Z ) ) ), member( first( f22( X, Y
% 0.71/1.11 , Z ) ), Y ) ] )
% 0.71/1.11 , clause( 777, [ ~( member( X, image( Y, Z ) ) ), =( second( f22( X, Y, Z )
% 0.71/1.11 ), X ) ] )
% 0.71/1.11 , clause( 778, [ 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 , clause( 779, [ ~( 'little_set'( X ) ), ~( function( Y ) ), 'little_set'(
% 0.71/1.11 image( X, Y ) ) ] )
% 0.71/1.11 , clause( 780, [ ~( disjoint( X, Y ) ), ~( member( Z, X ) ), ~( member( Z,
% 0.71/1.11 Y ) ) ] )
% 0.71/1.11 , clause( 781, [ disjoint( X, Y ), member( f23( X, Y ), X ) ] )
% 0.71/1.11 , clause( 782, [ disjoint( X, Y ), member( f23( X, Y ), Y ) ] )
% 0.71/1.11 , clause( 783, [ =( X, 'empty_set' ), member( f24( X ), X ) ] )
% 0.71/1.11 , clause( 784, [ =( X, 'empty_set' ), disjoint( f24( X ), X ) ] )
% 0.71/1.11 , clause( 785, [ function( f25 ) ] )
% 0.71/1.11 , clause( 786, [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( f26(
% 0.71/1.11 X ), X ) ] )
% 0.71/1.11 , clause( 787, [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member(
% 0.71/1.11 'ordered_pair'( X, f26( X ) ), f25 ) ] )
% 0.71/1.11 , clause( 788, [ ~( member( X, 'range_of'( Y ) ) ),
% 0.71/1.11 'ordered_pair_predicate'( f27( X, Y ) ) ] )
% 0.71/1.11 , clause( 789, [ ~( member( X, 'range_of'( Y ) ) ), member( f27( X, Y ), Y
% 0.71/1.11 ) ] )
% 0.71/1.11 , clause( 790, [ ~( member( X, 'range_of'( Y ) ) ), =( X, second( f27( X, Y
% 0.71/1.11 ) ) ) ] )
% 0.71/1.11 , clause( 791, [ 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 , clause( 792, [ ~( member( X, 'identity_relation' ) ),
% 0.71/1.11 'ordered_pair_predicate'( X ) ] )
% 0.71/1.11 , clause( 793, [ ~( member( X, 'identity_relation' ) ), =( first( X ),
% 0.71/1.11 second( X ) ) ] )
% 0.71/1.11 , clause( 794, [ member( X, 'identity_relation' ), ~( 'little_set'( X ) ),
% 0.71/1.11 ~( 'ordered_pair_predicate'( X ) ), ~( =( first( X ), second( X ) ) ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 795, [ =( restrict( X, Y ), intersection( X, 'cross_product'( Y,
% 0.71/1.11 'universal_set' ) ) ) ] )
% 0.71/1.11 , clause( 796, [ ~( 'one_to_one_function'( X ) ), function( X ) ] )
% 0.71/1.11 , clause( 797, [ ~( 'one_to_one_function'( X ) ), function( converse( X ) )
% 0.71/1.11 ] )
% 0.71/1.11 , clause( 798, [ 'one_to_one_function'( X ), ~( function( X ) ), ~(
% 0.71/1.11 function( converse( X ) ) ) ] )
% 0.71/1.11 , clause( 799, [ ~( member( X, apply( Y, Z ) ) ), 'ordered_pair_predicate'(
% 0.71/1.11 f28( X, Y, Z ) ) ] )
% 0.71/1.11 , clause( 800, [ ~( member( X, apply( Y, Z ) ) ), member( f28( X, Y, Z ), Y
% 0.71/1.11 ) ] )
% 0.71/1.11 , clause( 801, [ ~( member( X, apply( Y, Z ) ) ), =( first( f28( X, Y, Z )
% 0.71/1.11 ), Z ) ] )
% 0.71/1.11 , clause( 802, [ ~( member( X, apply( Y, Z ) ) ), member( X, second( f28( X
% 0.71/1.11 , Y, Z ) ) ) ] )
% 0.71/1.11 , clause( 803, [ member( X, apply( Y, Z ) ), ~( 'ordered_pair_predicate'( T
% 0.71/1.11 ) ), ~( member( T, Y ) ), ~( =( first( T ), Z ) ), ~( member( X, second(
% 0.71/1.11 T ) ) ) ] )
% 0.71/1.11 , clause( 804, [ =( 'apply_to_two_arguments'( X, Y, Z ), apply( X,
% 0.71/1.11 'ordered_pair'( Y, Z ) ) ) ] )
% 0.71/1.11 , clause( 805, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 0.71/1.11 , clause( 806, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 0.71/1.11 , clause( 807, [ ~( maps( X, Y, Z ) ), subset( 'range_of'( X ), Z ) ] )
% 0.71/1.11 , clause( 808, [ maps( X, Y, Z ), ~( function( X ) ), ~( =( 'domain_of'( X
% 0.71/1.11 ), Y ) ), ~( subset( 'range_of'( X ), Z ) ) ] )
% 0.71/1.11 , clause( 809, [ ~( closed( X, Y ) ), 'little_set'( X ) ] )
% 0.71/1.11 , clause( 810, [ ~( closed( X, Y ) ), 'little_set'( Y ) ] )
% 0.71/1.11 , clause( 811, [ ~( closed( X, Y ) ), maps( Y, 'cross_product'( X, X ), X )
% 0.71/1.11 ] )
% 0.71/1.11 , clause( 812, [ closed( X, Y ), ~( 'little_set'( X ) ), ~( 'little_set'( Y
% 0.71/1.11 ) ), ~( maps( Y, 'cross_product'( X, X ), X ) ) ] )
% 0.71/1.11 , clause( 813, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f29( X, Y
% 0.71/1.11 , Z ) ) ] )
% 0.71/1.11 , clause( 814, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f30( X, Y
% 0.71/1.11 , Z ) ) ] )
% 0.71/1.11 , clause( 815, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f31( X, Y
% 0.71/1.11 , Z ) ) ] )
% 0.71/1.11 , clause( 816, [ ~( member( X, compose( Y, Z ) ) ), =( X, 'ordered_pair'(
% 0.71/1.11 f29( X, Y, Z ), f30( X, Y, Z ) ) ) ] )
% 0.71/1.11 , clause( 817, [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'(
% 0.71/1.11 f29( X, Y, Z ), f31( X, Y, Z ) ), Y ) ] )
% 0.71/1.11 , clause( 818, [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'(
% 0.71/1.11 f31( X, Y, Z ), f30( X, Y, Z ) ), Z ) ] )
% 0.71/1.11 , clause( 819, [ member( X, compose( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.71/1.11 'little_set'( T ) ), ~( 'little_set'( U ) ), ~( 'little_set'( W ) ), ~(
% 0.71/1.11 =( X, 'ordered_pair'( T, U ) ) ), ~( member( 'ordered_pair'( T, W ), Y )
% 0.71/1.11 ), ~( member( 'ordered_pair'( W, U ), Z ) ) ] )
% 0.71/1.11 , clause( 820, [ ~( homomorphism( X, Y, Z, T, U ) ), closed( Y, Z ) ] )
% 0.71/1.11 , clause( 821, [ ~( homomorphism( X, Y, Z, T, U ) ), closed( T, U ) ] )
% 0.71/1.11 , clause( 822, [ ~( homomorphism( X, Y, Z, T, U ) ), maps( X, Y, T ) ] )
% 0.71/1.11 , clause( 823, [ ~( homomorphism( X, Y, Z, T, U ) ), ~( member( W, Y ) ),
% 0.71/1.11 ~( member( V0, Y ) ), =( apply( X, 'apply_to_two_arguments'( Z, W, V0 ) )
% 0.71/1.12 , 'apply_to_two_arguments'( U, apply( X, W ), apply( X, V0 ) ) ) ] )
% 0.71/1.12 , clause( 824, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~(
% 0.71/1.12 closed( T, U ) ), ~( maps( X, Y, T ) ), member( f32( X, Y, Z, T, U ), Y )
% 0.71/1.12 ] )
% 0.71/1.12 , clause( 825, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~(
% 0.71/1.12 closed( T, U ) ), ~( maps( X, Y, T ) ), member( f33( X, Y, Z, T, U ), Y )
% 0.71/1.12 ] )
% 0.71/1.12 , clause( 826, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~(
% 0.71/1.12 closed( T, U ) ), ~( maps( X, Y, T ) ), ~( =( apply( X,
% 0.71/1.12 'apply_to_two_arguments'( Z, f32( X, Y, Z, T, U ), f33( X, Y, Z, T, U ) )
% 0.71/1.12 ), 'apply_to_two_arguments'( U, apply( X, f32( X, Y, Z, T, U ) ), apply(
% 0.71/1.12 X, f33( X, Y, Z, T, U ) ) ) ) ) ] )
% 0.71/1.12 , clause( 827, [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( =(
% 0.71/1.12 'ordered_pair'( X, Z ), 'ordered_pair'( Y, T ) ) ), =( X, Y ) ] )
% 0.71/1.12 , clause( 828, [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~( =(
% 0.71/1.12 'non_ordered_pair'( Z, X ), 'non_ordered_pair'( Z, Y ) ) ), =( X, Y ) ]
% 0.71/1.12 )
% 0.71/1.12 , clause( 829, [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~(
% 0.71/1.12 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( =( 'ordered_pair'( X, Y )
% 0.71/1.12 , 'ordered_pair'( Z, T ) ) ), =( Y, T ) ] )
% 0.71/1.12 , clause( 830, [ ~( subset( X, Y ) ), ~( subset( Y, X ) ), =( X, Y ) ] )
% 0.71/1.12 , clause( 831, [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), =( first(
% 0.71/1.12 'ordered_pair'( X, Y ) ), X ) ] )
% 0.71/1.12 , clause( 832, [ ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), =( second(
% 0.71/1.12 'ordered_pair'( X, Y ) ), Y ) ] )
% 0.71/1.12 , clause( 833, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( first( X
% 0.71/1.12 ) ) ] )
% 0.71/1.12 , clause( 834, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( second(
% 0.71/1.12 X ) ) ] )
% 0.71/1.12 , clause( 835, [ 'little_set'( a ) ] )
% 0.71/1.12 , clause( 836, [ ~( member( a, 'singleton_set'( a ) ) ) ] )
% 0.71/1.12 ] ).
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 subsumption(
% 0.71/1.12 clause( 6, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( X )
% 0.71/1.12 ), ~( =( X, Z ) ) ] )
% 0.71/1.12 , clause( 692, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'(
% 0.71/1.12 X ) ), ~( =( X, Z ) ) ] )
% 0.71/1.12 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.71/1.12 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 eqswap(
% 0.71/1.12 clause( 861, [ =( 'non_ordered_pair'( X, X ), 'singleton_set'( X ) ) ] )
% 0.71/1.12 , clause( 694, [ =( 'singleton_set'( X ), 'non_ordered_pair'( X, X ) ) ] )
% 0.71/1.12 , 0, substitution( 0, [ :=( X, X )] )).
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 subsumption(
% 0.71/1.12 clause( 8, [ =( 'non_ordered_pair'( X, X ), 'singleton_set'( X ) ) ] )
% 0.71/1.12 , clause( 861, [ =( 'non_ordered_pair'( X, X ), 'singleton_set'( X ) ) ] )
% 0.71/1.12 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 subsumption(
% 0.71/1.12 clause( 149, [ 'little_set'( a ) ] )
% 0.71/1.12 , clause( 835, [ 'little_set'( a ) ] )
% 0.71/1.12 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 subsumption(
% 0.71/1.12 clause( 150, [ ~( member( a, 'singleton_set'( a ) ) ) ] )
% 0.71/1.12 , clause( 836, [ ~( member( a, 'singleton_set'( a ) ) ) ] )
% 0.71/1.12 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 eqswap(
% 0.71/1.12 clause( 1276, [ ~( =( Y, X ) ), member( X, 'non_ordered_pair'( Z, Y ) ),
% 0.71/1.12 ~( 'little_set'( X ) ) ] )
% 0.71/1.12 , clause( 6, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( X
% 0.71/1.12 ) ), ~( =( X, Z ) ) ] )
% 0.71/1.12 , 2, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 resolution(
% 0.71/1.12 clause( 1277, [ ~( =( X, a ) ), member( a, 'non_ordered_pair'( Y, X ) ) ]
% 0.71/1.12 )
% 0.71/1.12 , clause( 1276, [ ~( =( Y, X ) ), member( X, 'non_ordered_pair'( Z, Y ) ),
% 0.71/1.12 ~( 'little_set'( X ) ) ] )
% 0.71/1.12 , 2, clause( 149, [ 'little_set'( a ) ] )
% 0.71/1.12 , 0, substitution( 0, [ :=( X, a ), :=( Y, X ), :=( Z, Y )] ),
% 0.71/1.12 substitution( 1, [] )).
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 eqswap(
% 0.71/1.12 clause( 1278, [ ~( =( a, X ) ), member( a, 'non_ordered_pair'( Y, X ) ) ]
% 0.71/1.12 )
% 0.71/1.12 , clause( 1277, [ ~( =( X, a ) ), member( a, 'non_ordered_pair'( Y, X ) ) ]
% 0.71/1.12 )
% 0.71/1.12 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 subsumption(
% 0.71/1.12 clause( 606, [ member( a, 'non_ordered_pair'( X, Y ) ), ~( =( a, Y ) ) ] )
% 0.71/1.12 , clause( 1278, [ ~( =( a, X ) ), member( a, 'non_ordered_pair'( Y, X ) ) ]
% 0.71/1.12 )
% 0.71/1.12 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 1
% 0.71/1.12 ), ==>( 1, 0 )] ) ).
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 eqswap(
% 0.71/1.12 clause( 1279, [ ~( =( X, a ) ), member( a, 'non_ordered_pair'( Y, X ) ) ]
% 0.71/1.12 )
% 0.71/1.12 , clause( 606, [ member( a, 'non_ordered_pair'( X, Y ) ), ~( =( a, Y ) ) ]
% 0.71/1.12 )
% 0.71/1.12 , 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 eqrefl(
% 0.71/1.12 clause( 1280, [ member( a, 'non_ordered_pair'( X, a ) ) ] )
% 0.71/1.12 , clause( 1279, [ ~( =( X, a ) ), member( a, 'non_ordered_pair'( Y, X ) ) ]
% 0.71/1.12 )
% 0.71/1.12 , 0, substitution( 0, [ :=( X, a ), :=( Y, X )] )).
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 subsumption(
% 0.71/1.12 clause( 621, [ member( a, 'non_ordered_pair'( X, a ) ) ] )
% 0.71/1.12 , clause( 1280, [ member( a, 'non_ordered_pair'( X, a ) ) ] )
% 0.71/1.12 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 paramod(
% 0.71/1.12 clause( 1282, [ member( a, 'singleton_set'( a ) ) ] )
% 0.71/1.12 , clause( 8, [ =( 'non_ordered_pair'( X, X ), 'singleton_set'( X ) ) ] )
% 0.71/1.12 , 0, clause( 621, [ member( a, 'non_ordered_pair'( X, a ) ) ] )
% 0.71/1.12 , 0, 2, substitution( 0, [ :=( X, a )] ), substitution( 1, [ :=( X, a )] )
% 0.71/1.12 ).
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 resolution(
% 0.71/1.12 clause( 1283, [] )
% 0.71/1.12 , clause( 150, [ ~( member( a, 'singleton_set'( a ) ) ) ] )
% 0.71/1.12 , 0, clause( 1282, [ member( a, 'singleton_set'( a ) ) ] )
% 0.71/1.12 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 subsumption(
% 0.71/1.12 clause( 684, [] )
% 0.71/1.12 , clause( 1283, [] )
% 0.71/1.12 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 end.
% 0.71/1.12
% 0.71/1.12 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.71/1.12
% 0.71/1.12 Memory use:
% 0.71/1.12
% 0.71/1.12 space for terms: 14002
% 0.71/1.12 space for clauses: 35867
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 clauses generated: 1433
% 0.71/1.12 clauses kept: 685
% 0.71/1.12 clauses selected: 41
% 0.71/1.12 clauses deleted: 0
% 0.71/1.12 clauses inuse deleted: 0
% 0.71/1.12
% 0.71/1.12 subsentry: 4881
% 0.71/1.12 literals s-matched: 3471
% 0.71/1.12 literals matched: 2156
% 0.71/1.12 full subsumption: 1156
% 0.71/1.12
% 0.71/1.12 checksum: -1193136908
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 Bliksem ended
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