TSTP Solution File: SET025-9 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET025-9 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n019.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 22:45:43 EDT 2022
% Result : Unsatisfiable 0.80s 1.16s
% Output : Refutation 0.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET025-9 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Sun Jul 10 17:12:23 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.76/1.13 *** allocated 10000 integers for termspace/termends
% 0.76/1.13 *** allocated 10000 integers for clauses
% 0.76/1.13 *** allocated 10000 integers for justifications
% 0.76/1.13 Bliksem 1.12
% 0.76/1.13
% 0.76/1.13
% 0.76/1.13 Automatic Strategy Selection
% 0.76/1.13
% 0.76/1.13 Clauses:
% 0.76/1.13 [
% 0.76/1.13 [ ~( member( X, Y ) ), 'little_set'( X ) ],
% 0.76/1.13 [ 'little_set'( f1( X, Y ) ), =( X, Y ) ],
% 0.76/1.13 [ member( f1( X, Y ), X ), member( f1( X, Y ), Y ), =( X, Y ) ],
% 0.76/1.13 [ ~( member( f1( X, Y ), X ) ), ~( member( f1( X, Y ), Y ) ), =( X, Y )
% 0.76/1.13 ],
% 0.76/1.13 [ ~( member( X, 'non_ordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.76/1.13 =( X, Y ) ) ],
% 0.76/1.13 [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.76/1.13 =( X, Z ) ) ],
% 0.76/1.13 [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ],
% 0.76/1.13 [ =( 'singleton_set'( X ), 'non_ordered_pair'( X, X ) ) ],
% 0.76/1.13 [ =( 'ordered_pair'( X, Y ), 'non_ordered_pair'( 'singleton_set'( X ),
% 0.76/1.13 'non_ordered_pair'( X, Y ) ) ) ],
% 0.76/1.13 [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f2( X ) ) ],
% 0.76/1.13 [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f3( X ) ) ],
% 0.76/1.13 [ ~( 'ordered_pair_predicate'( X ) ), =( X, 'ordered_pair'( f2( X ), f3(
% 0.76/1.13 X ) ) ) ],
% 0.76/1.13 [ 'ordered_pair_predicate'( X ), ~( 'little_set'( Y ) ), ~( 'little_set'(
% 0.76/1.13 Z ) ), ~( =( X, 'ordered_pair'( Y, Z ) ) ) ],
% 0.76/1.13 [ ~( member( X, first( Y ) ) ), 'little_set'( f4( X, Y ) ) ],
% 0.76/1.13 [ ~( member( X, first( Y ) ) ), 'little_set'( f5( X, Y ) ) ],
% 0.76/1.13 [ ~( member( X, first( Y ) ) ), =( Y, 'ordered_pair'( f4( X, Y ), f5( X
% 0.76/1.13 , Y ) ) ) ],
% 0.76/1.13 [ ~( member( X, first( Y ) ) ), member( X, f4( X, Y ) ) ],
% 0.76/1.13 [ member( X, first( Y ) ), ~( 'little_set'( Z ) ), ~( 'little_set'( T )
% 0.76/1.13 ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, Z ) ) ],
% 0.76/1.13 [ ~( member( X, second( Y ) ) ), 'little_set'( f6( X, Y ) ) ],
% 0.76/1.13 [ ~( member( X, second( Y ) ) ), 'little_set'( f7( X, Y ) ) ],
% 0.76/1.13 [ ~( member( X, second( Y ) ) ), =( Y, 'ordered_pair'( f6( X, Y ), f7( X
% 0.76/1.13 , Y ) ) ) ],
% 0.76/1.13 [ ~( member( X, second( Y ) ) ), member( X, f7( X, Y ) ) ],
% 0.76/1.13 [ member( X, second( Y ) ), ~( 'little_set'( Z ) ), ~( 'little_set'( T )
% 0.76/1.13 ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, T ) ) ],
% 0.76/1.13 [ ~( member( X, estin ) ), 'ordered_pair_predicate'( X ) ],
% 0.76/1.13 [ ~( member( X, estin ) ), member( first( X ), second( X ) ) ],
% 0.76/1.13 [ member( X, estin ), ~( 'little_set'( X ) ), ~(
% 0.76/1.13 'ordered_pair_predicate'( X ) ), ~( member( first( X ), second( X ) ) ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.76/1.13 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.76/1.13 [ member( X, intersection( Y, Z ) ), ~( member( X, Y ) ), ~( member( X,
% 0.76/1.13 Z ) ) ],
% 0.76/1.13 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.76/1.13 [ member( X, complement( Y ) ), ~( 'little_set'( X ) ), member( X, Y ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ =( union( X, Y ), complement( intersection( complement( X ),
% 0.76/1.13 complement( Y ) ) ) ) ],
% 0.76/1.13 [ ~( member( X, 'domain_of'( Y ) ) ), 'ordered_pair_predicate'( f8( X, Y
% 0.76/1.13 ) ) ],
% 0.76/1.13 [ ~( member( X, 'domain_of'( Y ) ) ), member( f8( X, Y ), Y ) ],
% 0.76/1.13 [ ~( member( X, 'domain_of'( Y ) ) ), =( X, first( f8( X, Y ) ) ) ],
% 0.76/1.13 [ member( X, 'domain_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.76/1.13 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, first( Z )
% 0.76/1.13 ) ) ],
% 0.76/1.13 [ ~( member( X, 'cross_product'( Y, Z ) ) ), 'ordered_pair_predicate'( X
% 0.76/1.13 ) ],
% 0.76/1.13 [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( first( X ), Y ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( second( X ), Z ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ member( X, 'cross_product'( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.76/1.13 'ordered_pair_predicate'( X ) ), ~( member( first( X ), Y ) ), ~( member(
% 0.76/1.13 second( X ), Z ) ) ],
% 0.76/1.13 [ ~( member( X, converse( Y ) ) ), 'ordered_pair_predicate'( X ) ],
% 0.76/1.13 [ ~( member( X, converse( Y ) ) ), member( 'ordered_pair'( second( X ),
% 0.76/1.13 first( X ) ), Y ) ],
% 0.76/1.13 [ member( X, converse( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.76/1.13 'ordered_pair_predicate'( X ) ), ~( member( 'ordered_pair'( second( X ),
% 0.76/1.13 first( X ) ), Y ) ) ],
% 0.76/1.13 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f9( X, Y ) ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f10( X, Y ) ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f11( X, Y ) ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ ~( member( X, 'rotate_right'( Y ) ) ), =( X, 'ordered_pair'( f9( X, Y
% 0.76/1.13 ), 'ordered_pair'( f10( X, Y ), f11( X, Y ) ) ) ) ],
% 0.76/1.13 [ ~( member( X, 'rotate_right'( Y ) ) ), member( 'ordered_pair'( f10( X
% 0.76/1.13 , Y ), 'ordered_pair'( f11( X, Y ), f9( X, Y ) ) ), Y ) ],
% 0.76/1.13 [ member( X, 'rotate_right'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.76/1.13 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) ), ~(
% 0.76/1.13 =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 0.76/1.13 'ordered_pair'( T, 'ordered_pair'( U, Z ) ), Y ) ) ],
% 0.76/1.13 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f12( X, Y ) ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f13( X, Y ) ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f14( X, Y ) ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ ~( member( X, 'flip_range_of'( Y ) ) ), =( X, 'ordered_pair'( f12( X,
% 0.76/1.13 Y ), 'ordered_pair'( f13( X, Y ), f14( X, Y ) ) ) ) ],
% 0.76/1.13 [ ~( member( X, 'flip_range_of'( Y ) ) ), member( 'ordered_pair'( f12( X
% 0.76/1.13 , Y ), 'ordered_pair'( f14( X, Y ), f13( X, Y ) ) ), Y ) ],
% 0.76/1.13 [ member( X, 'flip_range_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.76/1.13 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) ), ~(
% 0.76/1.13 =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 0.76/1.13 'ordered_pair'( Z, 'ordered_pair'( U, T ) ), Y ) ) ],
% 0.76/1.13 [ =( successor( X ), union( X, 'singleton_set'( X ) ) ) ],
% 0.76/1.13 [ ~( member( X, 'empty_set' ) ) ],
% 0.76/1.13 [ member( X, 'universal_set' ), ~( 'little_set'( X ) ) ],
% 0.76/1.13 [ 'little_set'( infinity ) ],
% 0.76/1.13 [ member( 'empty_set', infinity ) ],
% 0.76/1.13 [ ~( member( X, infinity ) ), member( successor( X ), infinity ) ],
% 0.76/1.13 [ ~( member( X, sigma( Y ) ) ), member( f16( X, Y ), Y ) ],
% 0.76/1.13 [ ~( member( X, sigma( Y ) ) ), member( X, f16( X, Y ) ) ],
% 0.76/1.13 [ member( X, sigma( Y ) ), ~( member( Z, Y ) ), ~( member( X, Z ) ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ ~( 'little_set'( X ) ), 'little_set'( sigma( X ) ) ],
% 0.76/1.13 [ ~( subset( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.76/1.13 [ subset( X, Y ), member( f17( X, Y ), X ) ],
% 0.76/1.13 [ subset( X, Y ), ~( member( f17( X, Y ), Y ) ) ],
% 0.76/1.13 [ ~( 'proper_subset'( X, Y ) ), subset( X, Y ) ],
% 0.76/1.13 [ ~( 'proper_subset'( X, Y ) ), ~( =( X, Y ) ) ],
% 0.76/1.13 [ 'proper_subset'( X, Y ), ~( subset( X, Y ) ), =( X, Y ) ],
% 0.76/1.13 [ ~( member( X, powerset( Y ) ) ), subset( X, Y ) ],
% 0.76/1.13 [ member( X, powerset( Y ) ), ~( 'little_set'( X ) ), ~( subset( X, Y )
% 0.76/1.13 ) ],
% 0.76/1.13 [ ~( 'little_set'( X ) ), 'little_set'( powerset( X ) ) ],
% 0.76/1.13 [ ~( relation( X ) ), ~( member( Y, X ) ), 'ordered_pair_predicate'( Y )
% 0.76/1.13 ],
% 0.76/1.13 [ relation( X ), member( f18( X ), X ) ],
% 0.76/1.13 [ relation( X ), ~( 'ordered_pair_predicate'( f18( X ) ) ) ],
% 0.76/1.13 [ ~( 'single_valued_set'( X ) ), ~( 'little_set'( Y ) ), ~( 'little_set'(
% 0.76/1.13 Z ) ), ~( 'little_set'( T ) ), ~( member( 'ordered_pair'( Y, Z ), X ) ),
% 0.76/1.13 ~( member( 'ordered_pair'( Y, T ), X ) ), =( Z, T ) ],
% 0.76/1.13 [ 'single_valued_set'( X ), 'little_set'( f19( X ) ) ],
% 0.76/1.13 [ 'single_valued_set'( X ), 'little_set'( f20( X ) ) ],
% 0.76/1.13 [ 'single_valued_set'( X ), 'little_set'( f21( X ) ) ],
% 0.76/1.13 [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X ), f20( X ) )
% 0.76/1.13 , X ) ],
% 0.76/1.13 [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X ), f21( X ) )
% 0.76/1.13 , X ) ],
% 0.76/1.13 [ 'single_valued_set'( X ), ~( =( f20( X ), f21( X ) ) ) ],
% 0.76/1.13 [ ~( function( X ) ), relation( X ) ],
% 0.76/1.13 [ ~( function( X ) ), 'single_valued_set'( X ) ],
% 0.76/1.13 [ function( X ), ~( relation( X ) ), ~( 'single_valued_set'( X ) ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ ~( member( X, image( Y, Z ) ) ), 'ordered_pair_predicate'( f22( X, Y,
% 0.76/1.13 Z ) ) ],
% 0.76/1.13 [ ~( member( X, image( Y, Z ) ) ), member( f22( X, Y, Z ), Z ) ],
% 0.76/1.13 [ ~( member( X, image( Y, Z ) ) ), member( first( f22( X, Y, Z ) ), Y )
% 0.76/1.13 ],
% 0.76/1.13 [ ~( member( X, image( Y, Z ) ) ), =( second( f22( X, Y, Z ) ), X ) ]
% 0.76/1.13 ,
% 0.76/1.13 [ member( X, image( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.76/1.13 'ordered_pair_predicate'( T ) ), ~( member( T, Z ) ), ~( member( first( T
% 0.76/1.13 ), Y ) ), ~( =( second( T ), X ) ) ],
% 0.76/1.13 [ ~( 'little_set'( X ) ), ~( function( Y ) ), 'little_set'( image( X, Y
% 0.76/1.13 ) ) ],
% 0.76/1.13 [ ~( disjoint( X, Y ) ), ~( member( Z, X ) ), ~( member( Z, Y ) ) ],
% 0.76/1.14 [ disjoint( X, Y ), member( f23( X, Y ), X ) ],
% 0.76/1.14 [ disjoint( X, Y ), member( f23( X, Y ), Y ) ],
% 0.76/1.14 [ =( X, 'empty_set' ), member( f24( X ), X ) ],
% 0.76/1.14 [ =( X, 'empty_set' ), disjoint( f24( X ), X ) ],
% 0.76/1.14 [ function( f25 ) ],
% 0.76/1.14 [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( f26( X ), X ) ]
% 0.76/1.14 ,
% 0.76/1.14 [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( 'ordered_pair'( X
% 0.76/1.14 , f26( X ) ), f25 ) ],
% 0.76/1.14 [ ~( member( X, 'range_of'( Y ) ) ), 'ordered_pair_predicate'( f27( X, Y
% 0.76/1.14 ) ) ],
% 0.76/1.14 [ ~( member( X, 'range_of'( Y ) ) ), member( f27( X, Y ), Y ) ],
% 0.76/1.14 [ ~( member( X, 'range_of'( Y ) ) ), =( X, second( f27( X, Y ) ) ) ]
% 0.76/1.14 ,
% 0.76/1.14 [ member( X, 'range_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.76/1.14 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, second( Z
% 0.76/1.14 ) ) ) ],
% 0.76/1.14 [ ~( member( X, 'identity_relation' ) ), 'ordered_pair_predicate'( X ) ]
% 0.76/1.14 ,
% 0.76/1.14 [ ~( member( X, 'identity_relation' ) ), =( first( X ), second( X ) ) ]
% 0.76/1.14 ,
% 0.76/1.14 [ member( X, 'identity_relation' ), ~( 'little_set'( X ) ), ~(
% 0.76/1.14 'ordered_pair_predicate'( X ) ), ~( =( first( X ), second( X ) ) ) ],
% 0.76/1.14 [ =( restrict( X, Y ), intersection( X, 'cross_product'( Y,
% 0.76/1.14 'universal_set' ) ) ) ],
% 0.76/1.14 [ ~( 'one_to_one_function'( X ) ), function( X ) ],
% 0.76/1.14 [ ~( 'one_to_one_function'( X ) ), function( converse( X ) ) ],
% 0.76/1.14 [ 'one_to_one_function'( X ), ~( function( X ) ), ~( function( converse(
% 0.76/1.14 X ) ) ) ],
% 0.76/1.14 [ ~( member( X, apply( Y, Z ) ) ), 'ordered_pair_predicate'( f28( X, Y,
% 0.76/1.14 Z ) ) ],
% 0.76/1.14 [ ~( member( X, apply( Y, Z ) ) ), member( f28( X, Y, Z ), Y ) ],
% 0.76/1.14 [ ~( member( X, apply( Y, Z ) ) ), =( first( f28( X, Y, Z ) ), Z ) ]
% 0.76/1.14 ,
% 0.76/1.14 [ ~( member( X, apply( Y, Z ) ) ), member( X, second( f28( X, Y, Z ) ) )
% 0.76/1.14 ],
% 0.76/1.14 [ member( X, apply( Y, Z ) ), ~( 'ordered_pair_predicate'( T ) ), ~(
% 0.76/1.14 member( T, Y ) ), ~( =( first( T ), Z ) ), ~( member( X, second( T ) ) )
% 0.76/1.14 ],
% 0.76/1.14 [ =( 'apply_to_two_arguments'( X, Y, Z ), apply( X, 'ordered_pair'( Y, Z
% 0.76/1.14 ) ) ) ],
% 0.76/1.14 [ ~( maps( X, Y, Z ) ), function( X ) ],
% 0.76/1.14 [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ],
% 0.76/1.14 [ ~( maps( X, Y, Z ) ), subset( 'range_of'( X ), Z ) ],
% 0.76/1.14 [ maps( X, Y, Z ), ~( function( X ) ), ~( =( 'domain_of'( X ), Y ) ),
% 0.76/1.14 ~( subset( 'range_of'( X ), Z ) ) ],
% 0.76/1.14 [ ~( closed( X, Y ) ), 'little_set'( X ) ],
% 0.76/1.14 [ ~( closed( X, Y ) ), 'little_set'( Y ) ],
% 0.76/1.14 [ ~( closed( X, Y ) ), maps( Y, 'cross_product'( X, X ), X ) ],
% 0.76/1.14 [ closed( X, Y ), ~( 'little_set'( X ) ), ~( 'little_set'( Y ) ), ~(
% 0.76/1.14 maps( Y, 'cross_product'( X, X ), X ) ) ],
% 0.76/1.14 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f29( X, Y, Z ) ) ]
% 0.76/1.14 ,
% 0.76/1.14 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f30( X, Y, Z ) ) ]
% 0.76/1.14 ,
% 0.76/1.14 [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f31( X, Y, Z ) ) ]
% 0.76/1.14 ,
% 0.76/1.14 [ ~( member( X, compose( Y, Z ) ) ), =( X, 'ordered_pair'( f29( X, Y, Z
% 0.76/1.14 ), f30( X, Y, Z ) ) ) ],
% 0.76/1.14 [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'( f29( X, Y,
% 0.76/1.14 Z ), f31( X, Y, Z ) ), Y ) ],
% 0.76/1.14 [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'( f31( X, Y,
% 0.76/1.14 Z ), f30( X, Y, Z ) ), Z ) ],
% 0.76/1.14 [ member( X, compose( Y, Z ) ), ~( 'little_set'( X ) ), ~( 'little_set'(
% 0.76/1.14 T ) ), ~( 'little_set'( U ) ), ~( 'little_set'( W ) ), ~( =( X,
% 0.76/1.14 'ordered_pair'( T, U ) ) ), ~( member( 'ordered_pair'( T, W ), Y ) ), ~(
% 0.76/1.14 member( 'ordered_pair'( W, U ), Z ) ) ],
% 0.76/1.14 [ ~( homomorphism( X, Y, Z, T, U ) ), closed( Y, Z ) ],
% 0.76/1.14 [ ~( homomorphism( X, Y, Z, T, U ) ), closed( T, U ) ],
% 0.76/1.14 [ ~( homomorphism( X, Y, Z, T, U ) ), maps( X, Y, T ) ],
% 0.76/1.14 [ ~( homomorphism( X, Y, Z, T, U ) ), ~( member( W, Y ) ), ~( member( V0
% 0.76/1.14 , Y ) ), =( apply( X, 'apply_to_two_arguments'( Z, W, V0 ) ),
% 0.76/1.14 'apply_to_two_arguments'( U, apply( X, W ), apply( X, V0 ) ) ) ],
% 0.76/1.14 [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.76/1.14 ), ~( maps( X, Y, T ) ), member( f32( X, Y, Z, T, U ), Y ) ],
% 0.76/1.14 [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.76/1.14 ), ~( maps( X, Y, T ) ), member( f33( X, Y, Z, T, U ), Y ) ],
% 0.76/1.14 [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~( closed( T, U )
% 0.80/1.16 ), ~( maps( X, Y, T ) ), ~( =( apply( X, 'apply_to_two_arguments'( Z,
% 0.80/1.16 f32( X, Y, Z, T, U ), f33( X, Y, Z, T, U ) ) ), 'apply_to_two_arguments'(
% 0.80/1.16 U, apply( X, f32( X, Y, Z, T, U ) ), apply( X, f33( X, Y, Z, T, U ) ) ) )
% 0.80/1.16 ) ],
% 0.80/1.16 [ 'ordered_pair_predicate'( a ) ],
% 0.80/1.16 [ ~( 'little_set'( a ) ) ]
% 0.80/1.16 ] .
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 percentage equality = 0.131653, percentage horn = 0.860140
% 0.80/1.16 This is a problem with some equality
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 Options Used:
% 0.80/1.16
% 0.80/1.16 useres = 1
% 0.80/1.16 useparamod = 1
% 0.80/1.16 useeqrefl = 1
% 0.80/1.16 useeqfact = 1
% 0.80/1.16 usefactor = 1
% 0.80/1.16 usesimpsplitting = 0
% 0.80/1.16 usesimpdemod = 5
% 0.80/1.16 usesimpres = 3
% 0.80/1.16
% 0.80/1.16 resimpinuse = 1000
% 0.80/1.16 resimpclauses = 20000
% 0.80/1.16 substype = eqrewr
% 0.80/1.16 backwardsubs = 1
% 0.80/1.16 selectoldest = 5
% 0.80/1.16
% 0.80/1.16 litorderings [0] = split
% 0.80/1.16 litorderings [1] = extend the termordering, first sorting on arguments
% 0.80/1.16
% 0.80/1.16 termordering = kbo
% 0.80/1.16
% 0.80/1.16 litapriori = 0
% 0.80/1.16 termapriori = 1
% 0.80/1.16 litaposteriori = 0
% 0.80/1.16 termaposteriori = 0
% 0.80/1.16 demodaposteriori = 0
% 0.80/1.16 ordereqreflfact = 0
% 0.80/1.16
% 0.80/1.16 litselect = negord
% 0.80/1.16
% 0.80/1.16 maxweight = 15
% 0.80/1.16 maxdepth = 30000
% 0.80/1.16 maxlength = 115
% 0.80/1.16 maxnrvars = 195
% 0.80/1.16 excuselevel = 1
% 0.80/1.16 increasemaxweight = 1
% 0.80/1.16
% 0.80/1.16 maxselected = 10000000
% 0.80/1.16 maxnrclauses = 10000000
% 0.80/1.16
% 0.80/1.16 showgenerated = 0
% 0.80/1.16 showkept = 0
% 0.80/1.16 showselected = 0
% 0.80/1.16 showdeleted = 0
% 0.80/1.16 showresimp = 1
% 0.80/1.16 showstatus = 2000
% 0.80/1.16
% 0.80/1.16 prologoutput = 1
% 0.80/1.16 nrgoals = 5000000
% 0.80/1.16 totalproof = 1
% 0.80/1.16
% 0.80/1.16 Symbols occurring in the translation:
% 0.80/1.16
% 0.80/1.16 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.80/1.16 . [1, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.80/1.16 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 0.80/1.16 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.80/1.16 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.80/1.16 member [41, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.80/1.16 'little_set' [42, 1] (w:1, o:36, a:1, s:1, b:0),
% 0.80/1.16 f1 [43, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.80/1.16 'non_ordered_pair' [45, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.80/1.16 'singleton_set' [46, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.80/1.16 'ordered_pair' [47, 2] (w:1, o:90, a:1, s:1, b:0),
% 0.80/1.16 'ordered_pair_predicate' [48, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.80/1.16 f2 [49, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.80/1.16 f3 [50, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.80/1.16 first [52, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.80/1.16 f4 [53, 2] (w:1, o:91, a:1, s:1, b:0),
% 0.80/1.16 f5 [54, 2] (w:1, o:92, a:1, s:1, b:0),
% 0.80/1.16 second [56, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.80/1.16 f6 [57, 2] (w:1, o:93, a:1, s:1, b:0),
% 0.80/1.16 f7 [58, 2] (w:1, o:94, a:1, s:1, b:0),
% 0.80/1.16 estin [59, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.80/1.16 intersection [60, 2] (w:1, o:96, a:1, s:1, b:0),
% 0.80/1.16 complement [61, 1] (w:1, o:52, a:1, s:1, b:0),
% 0.80/1.16 union [62, 2] (w:1, o:97, a:1, s:1, b:0),
% 0.80/1.16 'domain_of' [63, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.80/1.16 f8 [64, 2] (w:1, o:98, a:1, s:1, b:0),
% 0.80/1.16 'cross_product' [66, 2] (w:1, o:99, a:1, s:1, b:0),
% 0.80/1.16 converse [67, 1] (w:1, o:53, a:1, s:1, b:0),
% 0.80/1.16 'rotate_right' [68, 1] (w:1, o:37, a:1, s:1, b:0),
% 0.80/1.16 f9 [69, 2] (w:1, o:100, a:1, s:1, b:0),
% 0.80/1.16 f10 [70, 2] (w:1, o:101, a:1, s:1, b:0),
% 0.80/1.16 f11 [71, 2] (w:1, o:102, a:1, s:1, b:0),
% 0.80/1.16 'flip_range_of' [73, 1] (w:1, o:55, a:1, s:1, b:0),
% 0.80/1.16 f12 [74, 2] (w:1, o:103, a:1, s:1, b:0),
% 0.80/1.16 f13 [75, 2] (w:1, o:104, a:1, s:1, b:0),
% 0.80/1.16 f14 [76, 2] (w:1, o:105, a:1, s:1, b:0),
% 0.80/1.16 successor [77, 1] (w:1, o:56, a:1, s:1, b:0),
% 0.80/1.16 'empty_set' [78, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.80/1.16 'universal_set' [79, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.80/1.16 infinity [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.80/1.16 sigma [81, 1] (w:1, o:57, a:1, s:1, b:0),
% 0.80/1.16 f16 [82, 2] (w:1, o:106, a:1, s:1, b:0),
% 0.80/1.16 subset [83, 2] (w:1, o:108, a:1, s:1, b:0),
% 0.80/1.16 f17 [84, 2] (w:1, o:109, a:1, s:1, b:0),
% 0.80/1.16 'proper_subset' [85, 2] (w:1, o:110, a:1, s:1, b:0),
% 0.80/1.16 powerset [86, 1] (w:1, o:59, a:1, s:1, b:0),
% 0.80/1.16 relation [87, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.80/1.16 f18 [88, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.80/1.16 'single_valued_set' [89, 1] (w:1, o:60, a:1, s:1, b:0),
% 0.80/1.16 f19 [90, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.80/1.16 f20 [91, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.80/1.16 f21 [92, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.80/1.16 function [94, 1] (w:1, o:61, a:1, s:1, b:0),
% 0.80/1.16 image [95, 2] (w:1, o:95, a:1, s:1, b:0),
% 0.80/1.16 f22 [96, 3] (w:1, o:117, a:1, s:1, b:0),
% 0.80/1.16 disjoint [97, 2] (w:1, o:113, a:1, s:1, b:0),
% 0.80/1.16 f23 [98, 2] (w:1, o:114, a:1, s:1, b:0),
% 0.80/1.16 f24 [99, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.80/1.16 f25 [100, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.80/1.16 f26 [101, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.80/1.16 'range_of' [102, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.80/1.16 f27 [103, 2] (w:1, o:115, a:1, s:1, b:0),
% 0.80/1.16 'identity_relation' [104, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.80/1.16 restrict [105, 2] (w:1, o:107, a:1, s:1, b:0),
% 0.80/1.16 'one_to_one_function' [106, 1] (w:1, o:58, a:1, s:1, b:0),
% 0.80/1.16 apply [107, 2] (w:1, o:116, a:1, s:1, b:0),
% 0.80/1.16 f28 [108, 3] (w:1, o:118, a:1, s:1, b:0),
% 0.80/1.16 'apply_to_two_arguments' [109, 3] (w:1, o:119, a:1, s:1, b:0),
% 0.80/1.16 maps [110, 3] (w:1, o:120, a:1, s:1, b:0),
% 0.80/1.16 closed [112, 2] (w:1, o:111, a:1, s:1, b:0),
% 0.80/1.16 compose [114, 2] (w:1, o:112, a:1, s:1, b:0),
% 0.80/1.16 f29 [115, 3] (w:1, o:121, a:1, s:1, b:0),
% 0.80/1.16 f30 [116, 3] (w:1, o:122, a:1, s:1, b:0),
% 0.80/1.16 f31 [117, 3] (w:1, o:123, a:1, s:1, b:0),
% 0.80/1.16 homomorphism [123, 5] (w:1, o:124, a:1, s:1, b:0),
% 0.80/1.16 f32 [124, 5] (w:1, o:125, a:1, s:1, b:0),
% 0.80/1.16 f33 [125, 5] (w:1, o:126, a:1, s:1, b:0),
% 0.80/1.16 a [126, 0] (w:1, o:30, a:1, s:1, b:0).
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 Starting Search:
% 0.80/1.16
% 0.80/1.16 Resimplifying inuse:
% 0.80/1.16 Done
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 Bliksems!, er is een bewijs:
% 0.80/1.16 % SZS status Unsatisfiable
% 0.80/1.16 % SZS output start Refutation
% 0.80/1.16
% 0.80/1.16 clause( 7, [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ] )
% 0.80/1.16 .
% 0.80/1.16 clause( 9, [ =( 'non_ordered_pair'( 'singleton_set'( X ),
% 0.80/1.16 'non_ordered_pair'( X, Y ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.80/1.16 .
% 0.80/1.16 clause( 12, [ ~( 'ordered_pair_predicate'( X ) ), =( 'ordered_pair'( f2( X
% 0.80/1.16 ), f3( X ) ), X ) ] )
% 0.80/1.16 .
% 0.80/1.16 clause( 141, [ 'ordered_pair_predicate'( a ) ] )
% 0.80/1.16 .
% 0.80/1.16 clause( 142, [ ~( 'little_set'( a ) ) ] )
% 0.80/1.16 .
% 0.80/1.16 clause( 709, [ 'little_set'( 'ordered_pair'( X, Y ) ) ] )
% 0.80/1.16 .
% 0.80/1.16 clause( 944, [ 'little_set'( X ), ~( 'ordered_pair_predicate'( X ) ) ] )
% 0.80/1.16 .
% 0.80/1.16 clause( 1010, [] )
% 0.80/1.16 .
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 % SZS output end Refutation
% 0.80/1.16 found a proof!
% 0.80/1.16
% 0.80/1.16 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.80/1.16
% 0.80/1.16 initialclauses(
% 0.80/1.16 [ clause( 1012, [ ~( member( X, Y ) ), 'little_set'( X ) ] )
% 0.80/1.16 , clause( 1013, [ 'little_set'( f1( X, Y ) ), =( X, Y ) ] )
% 0.80/1.16 , clause( 1014, [ member( f1( X, Y ), X ), member( f1( X, Y ), Y ), =( X, Y
% 0.80/1.16 ) ] )
% 0.80/1.16 , clause( 1015, [ ~( member( f1( X, Y ), X ) ), ~( member( f1( X, Y ), Y )
% 0.80/1.16 ), =( X, Y ) ] )
% 0.80/1.16 , clause( 1016, [ ~( member( X, 'non_ordered_pair'( Y, Z ) ) ), =( X, Y ),
% 0.80/1.16 =( X, Z ) ] )
% 0.80/1.16 , clause( 1017, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'(
% 0.80/1.16 X ) ), ~( =( X, Y ) ) ] )
% 0.80/1.16 , clause( 1018, [ member( X, 'non_ordered_pair'( Y, Z ) ), ~( 'little_set'(
% 0.80/1.16 X ) ), ~( =( X, Z ) ) ] )
% 0.80/1.16 , clause( 1019, [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ] )
% 0.80/1.16 , clause( 1020, [ =( 'singleton_set'( X ), 'non_ordered_pair'( X, X ) ) ]
% 0.80/1.16 )
% 0.80/1.16 , clause( 1021, [ =( 'ordered_pair'( X, Y ), 'non_ordered_pair'(
% 0.80/1.16 'singleton_set'( X ), 'non_ordered_pair'( X, Y ) ) ) ] )
% 0.80/1.16 , clause( 1022, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f2( X )
% 0.80/1.16 ) ] )
% 0.80/1.16 , clause( 1023, [ ~( 'ordered_pair_predicate'( X ) ), 'little_set'( f3( X )
% 0.80/1.16 ) ] )
% 0.80/1.16 , clause( 1024, [ ~( 'ordered_pair_predicate'( X ) ), =( X, 'ordered_pair'(
% 0.80/1.16 f2( X ), f3( X ) ) ) ] )
% 0.80/1.16 , clause( 1025, [ 'ordered_pair_predicate'( X ), ~( 'little_set'( Y ) ),
% 0.80/1.16 ~( 'little_set'( Z ) ), ~( =( X, 'ordered_pair'( Y, Z ) ) ) ] )
% 0.80/1.16 , clause( 1026, [ ~( member( X, first( Y ) ) ), 'little_set'( f4( X, Y ) )
% 0.80/1.16 ] )
% 0.80/1.16 , clause( 1027, [ ~( member( X, first( Y ) ) ), 'little_set'( f5( X, Y ) )
% 0.80/1.16 ] )
% 0.80/1.16 , clause( 1028, [ ~( member( X, first( Y ) ) ), =( Y, 'ordered_pair'( f4( X
% 0.80/1.16 , Y ), f5( X, Y ) ) ) ] )
% 0.80/1.16 , clause( 1029, [ ~( member( X, first( Y ) ) ), member( X, f4( X, Y ) ) ]
% 0.80/1.16 )
% 0.80/1.16 , clause( 1030, [ member( X, first( Y ) ), ~( 'little_set'( Z ) ), ~(
% 0.80/1.16 'little_set'( T ) ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, Z
% 0.80/1.16 ) ) ] )
% 0.80/1.16 , clause( 1031, [ ~( member( X, second( Y ) ) ), 'little_set'( f6( X, Y ) )
% 0.80/1.16 ] )
% 0.80/1.16 , clause( 1032, [ ~( member( X, second( Y ) ) ), 'little_set'( f7( X, Y ) )
% 0.80/1.16 ] )
% 0.80/1.16 , clause( 1033, [ ~( member( X, second( Y ) ) ), =( Y, 'ordered_pair'( f6(
% 0.80/1.16 X, Y ), f7( X, Y ) ) ) ] )
% 0.80/1.16 , clause( 1034, [ ~( member( X, second( Y ) ) ), member( X, f7( X, Y ) ) ]
% 0.80/1.16 )
% 0.80/1.16 , clause( 1035, [ member( X, second( Y ) ), ~( 'little_set'( Z ) ), ~(
% 0.80/1.16 'little_set'( T ) ), ~( =( Y, 'ordered_pair'( Z, T ) ) ), ~( member( X, T
% 0.80/1.16 ) ) ] )
% 0.80/1.16 , clause( 1036, [ ~( member( X, estin ) ), 'ordered_pair_predicate'( X ) ]
% 0.80/1.16 )
% 0.80/1.16 , clause( 1037, [ ~( member( X, estin ) ), member( first( X ), second( X )
% 0.80/1.16 ) ] )
% 0.80/1.16 , clause( 1038, [ member( X, estin ), ~( 'little_set'( X ) ), ~(
% 0.80/1.16 'ordered_pair_predicate'( X ) ), ~( member( first( X ), second( X ) ) ) ]
% 0.80/1.16 )
% 0.80/1.16 , clause( 1039, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 0.80/1.16 )
% 0.80/1.16 , clause( 1040, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 0.80/1.16 )
% 0.80/1.16 , clause( 1041, [ member( X, intersection( Y, Z ) ), ~( member( X, Y ) ),
% 0.80/1.16 ~( member( X, Z ) ) ] )
% 0.80/1.16 , clause( 1042, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 0.80/1.16 )
% 0.80/1.16 , clause( 1043, [ member( X, complement( Y ) ), ~( 'little_set'( X ) ),
% 0.80/1.16 member( X, Y ) ] )
% 0.80/1.16 , clause( 1044, [ =( union( X, Y ), complement( intersection( complement( X
% 0.80/1.16 ), complement( Y ) ) ) ) ] )
% 0.80/1.16 , clause( 1045, [ ~( member( X, 'domain_of'( Y ) ) ),
% 0.80/1.16 'ordered_pair_predicate'( f8( X, Y ) ) ] )
% 0.80/1.16 , clause( 1046, [ ~( member( X, 'domain_of'( Y ) ) ), member( f8( X, Y ), Y
% 0.80/1.16 ) ] )
% 0.80/1.16 , clause( 1047, [ ~( member( X, 'domain_of'( Y ) ) ), =( X, first( f8( X, Y
% 0.80/1.16 ) ) ) ] )
% 0.80/1.16 , clause( 1048, [ member( X, 'domain_of'( Y ) ), ~( 'little_set'( X ) ),
% 0.80/1.16 ~( 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, first(
% 0.80/1.16 Z ) ) ) ] )
% 0.80/1.16 , clause( 1049, [ ~( member( X, 'cross_product'( Y, Z ) ) ),
% 0.80/1.16 'ordered_pair_predicate'( X ) ] )
% 0.80/1.16 , clause( 1050, [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( first(
% 0.80/1.16 X ), Y ) ] )
% 0.80/1.16 , clause( 1051, [ ~( member( X, 'cross_product'( Y, Z ) ) ), member( second(
% 0.80/1.16 X ), Z ) ] )
% 0.80/1.16 , clause( 1052, [ member( X, 'cross_product'( Y, Z ) ), ~( 'little_set'( X
% 0.80/1.16 ) ), ~( 'ordered_pair_predicate'( X ) ), ~( member( first( X ), Y ) ),
% 0.80/1.16 ~( member( second( X ), Z ) ) ] )
% 0.80/1.16 , clause( 1053, [ ~( member( X, converse( Y ) ) ), 'ordered_pair_predicate'(
% 0.80/1.16 X ) ] )
% 0.80/1.16 , clause( 1054, [ ~( member( X, converse( Y ) ) ), member( 'ordered_pair'(
% 0.80/1.16 second( X ), first( X ) ), Y ) ] )
% 0.80/1.16 , clause( 1055, [ member( X, converse( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.80/1.16 'ordered_pair_predicate'( X ) ), ~( member( 'ordered_pair'( second( X ),
% 0.80/1.16 first( X ) ), Y ) ) ] )
% 0.80/1.16 , clause( 1056, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f9(
% 0.80/1.16 X, Y ) ) ] )
% 0.80/1.16 , clause( 1057, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f10(
% 0.80/1.16 X, Y ) ) ] )
% 0.80/1.16 , clause( 1058, [ ~( member( X, 'rotate_right'( Y ) ) ), 'little_set'( f11(
% 0.80/1.16 X, Y ) ) ] )
% 0.80/1.16 , clause( 1059, [ ~( member( X, 'rotate_right'( Y ) ) ), =( X,
% 0.80/1.16 'ordered_pair'( f9( X, Y ), 'ordered_pair'( f10( X, Y ), f11( X, Y ) ) )
% 0.80/1.16 ) ] )
% 0.80/1.16 , clause( 1060, [ ~( member( X, 'rotate_right'( Y ) ) ), member(
% 0.80/1.16 'ordered_pair'( f10( X, Y ), 'ordered_pair'( f11( X, Y ), f9( X, Y ) ) )
% 0.80/1.16 , Y ) ] )
% 0.80/1.16 , clause( 1061, [ member( X, 'rotate_right'( Y ) ), ~( 'little_set'( X ) )
% 0.80/1.16 , ~( 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) )
% 0.80/1.16 , ~( =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 0.80/1.16 'ordered_pair'( T, 'ordered_pair'( U, Z ) ), Y ) ) ] )
% 0.80/1.16 , clause( 1062, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f12(
% 0.80/1.16 X, Y ) ) ] )
% 0.80/1.16 , clause( 1063, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f13(
% 0.80/1.16 X, Y ) ) ] )
% 0.80/1.16 , clause( 1064, [ ~( member( X, 'flip_range_of'( Y ) ) ), 'little_set'( f14(
% 0.80/1.16 X, Y ) ) ] )
% 0.80/1.16 , clause( 1065, [ ~( member( X, 'flip_range_of'( Y ) ) ), =( X,
% 0.80/1.16 'ordered_pair'( f12( X, Y ), 'ordered_pair'( f13( X, Y ), f14( X, Y ) ) )
% 0.80/1.16 ) ] )
% 0.80/1.16 , clause( 1066, [ ~( member( X, 'flip_range_of'( Y ) ) ), member(
% 0.80/1.16 'ordered_pair'( f12( X, Y ), 'ordered_pair'( f14( X, Y ), f13( X, Y ) ) )
% 0.80/1.16 , Y ) ] )
% 0.80/1.16 , clause( 1067, [ member( X, 'flip_range_of'( Y ) ), ~( 'little_set'( X ) )
% 0.80/1.16 , ~( 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( 'little_set'( U ) )
% 0.80/1.16 , ~( =( X, 'ordered_pair'( Z, 'ordered_pair'( T, U ) ) ) ), ~( member(
% 0.80/1.16 'ordered_pair'( Z, 'ordered_pair'( U, T ) ), Y ) ) ] )
% 0.80/1.16 , clause( 1068, [ =( successor( X ), union( X, 'singleton_set'( X ) ) ) ]
% 0.80/1.16 )
% 0.80/1.16 , clause( 1069, [ ~( member( X, 'empty_set' ) ) ] )
% 0.80/1.16 , clause( 1070, [ member( X, 'universal_set' ), ~( 'little_set'( X ) ) ] )
% 0.80/1.16 , clause( 1071, [ 'little_set'( infinity ) ] )
% 0.80/1.16 , clause( 1072, [ member( 'empty_set', infinity ) ] )
% 0.80/1.16 , clause( 1073, [ ~( member( X, infinity ) ), member( successor( X ),
% 0.80/1.16 infinity ) ] )
% 0.80/1.16 , clause( 1074, [ ~( member( X, sigma( Y ) ) ), member( f16( X, Y ), Y ) ]
% 0.80/1.16 )
% 0.80/1.16 , clause( 1075, [ ~( member( X, sigma( Y ) ) ), member( X, f16( X, Y ) ) ]
% 0.80/1.16 )
% 0.80/1.16 , clause( 1076, [ member( X, sigma( Y ) ), ~( member( Z, Y ) ), ~( member(
% 0.80/1.16 X, Z ) ) ] )
% 0.80/1.16 , clause( 1077, [ ~( 'little_set'( X ) ), 'little_set'( sigma( X ) ) ] )
% 0.80/1.16 , clause( 1078, [ ~( subset( X, Y ) ), ~( member( Z, X ) ), member( Z, Y )
% 0.80/1.16 ] )
% 0.80/1.16 , clause( 1079, [ subset( X, Y ), member( f17( X, Y ), X ) ] )
% 0.80/1.16 , clause( 1080, [ subset( X, Y ), ~( member( f17( X, Y ), Y ) ) ] )
% 0.80/1.16 , clause( 1081, [ ~( 'proper_subset'( X, Y ) ), subset( X, Y ) ] )
% 0.80/1.16 , clause( 1082, [ ~( 'proper_subset'( X, Y ) ), ~( =( X, Y ) ) ] )
% 0.80/1.16 , clause( 1083, [ 'proper_subset'( X, Y ), ~( subset( X, Y ) ), =( X, Y ) ]
% 0.80/1.16 )
% 0.80/1.16 , clause( 1084, [ ~( member( X, powerset( Y ) ) ), subset( X, Y ) ] )
% 0.80/1.16 , clause( 1085, [ member( X, powerset( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.80/1.16 subset( X, Y ) ) ] )
% 0.80/1.16 , clause( 1086, [ ~( 'little_set'( X ) ), 'little_set'( powerset( X ) ) ]
% 0.80/1.16 )
% 0.80/1.16 , clause( 1087, [ ~( relation( X ) ), ~( member( Y, X ) ),
% 0.80/1.16 'ordered_pair_predicate'( Y ) ] )
% 0.80/1.16 , clause( 1088, [ relation( X ), member( f18( X ), X ) ] )
% 0.80/1.16 , clause( 1089, [ relation( X ), ~( 'ordered_pair_predicate'( f18( X ) ) )
% 0.80/1.16 ] )
% 0.80/1.16 , clause( 1090, [ ~( 'single_valued_set'( X ) ), ~( 'little_set'( Y ) ),
% 0.80/1.16 ~( 'little_set'( Z ) ), ~( 'little_set'( T ) ), ~( member( 'ordered_pair'(
% 0.80/1.16 Y, Z ), X ) ), ~( member( 'ordered_pair'( Y, T ), X ) ), =( Z, T ) ] )
% 0.80/1.16 , clause( 1091, [ 'single_valued_set'( X ), 'little_set'( f19( X ) ) ] )
% 0.80/1.16 , clause( 1092, [ 'single_valued_set'( X ), 'little_set'( f20( X ) ) ] )
% 0.80/1.16 , clause( 1093, [ 'single_valued_set'( X ), 'little_set'( f21( X ) ) ] )
% 0.80/1.16 , clause( 1094, [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X
% 0.80/1.16 ), f20( X ) ), X ) ] )
% 0.80/1.16 , clause( 1095, [ 'single_valued_set'( X ), member( 'ordered_pair'( f19( X
% 0.80/1.16 ), f21( X ) ), X ) ] )
% 0.80/1.16 , clause( 1096, [ 'single_valued_set'( X ), ~( =( f20( X ), f21( X ) ) ) ]
% 0.80/1.16 )
% 0.80/1.16 , clause( 1097, [ ~( function( X ) ), relation( X ) ] )
% 0.80/1.16 , clause( 1098, [ ~( function( X ) ), 'single_valued_set'( X ) ] )
% 0.80/1.16 , clause( 1099, [ function( X ), ~( relation( X ) ), ~( 'single_valued_set'(
% 0.80/1.16 X ) ) ] )
% 0.80/1.16 , clause( 1100, [ ~( member( X, image( Y, Z ) ) ), 'ordered_pair_predicate'(
% 0.80/1.16 f22( X, Y, Z ) ) ] )
% 0.80/1.16 , clause( 1101, [ ~( member( X, image( Y, Z ) ) ), member( f22( X, Y, Z ),
% 0.80/1.16 Z ) ] )
% 0.80/1.16 , clause( 1102, [ ~( member( X, image( Y, Z ) ) ), member( first( f22( X, Y
% 0.80/1.16 , Z ) ), Y ) ] )
% 0.80/1.16 , clause( 1103, [ ~( member( X, image( Y, Z ) ) ), =( second( f22( X, Y, Z
% 0.80/1.16 ) ), X ) ] )
% 0.80/1.16 , clause( 1104, [ member( X, image( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.80/1.16 'ordered_pair_predicate'( T ) ), ~( member( T, Z ) ), ~( member( first( T
% 0.80/1.16 ), Y ) ), ~( =( second( T ), X ) ) ] )
% 0.80/1.16 , clause( 1105, [ ~( 'little_set'( X ) ), ~( function( Y ) ), 'little_set'(
% 0.80/1.16 image( X, Y ) ) ] )
% 0.80/1.16 , clause( 1106, [ ~( disjoint( X, Y ) ), ~( member( Z, X ) ), ~( member( Z
% 0.80/1.16 , Y ) ) ] )
% 0.80/1.16 , clause( 1107, [ disjoint( X, Y ), member( f23( X, Y ), X ) ] )
% 0.80/1.16 , clause( 1108, [ disjoint( X, Y ), member( f23( X, Y ), Y ) ] )
% 0.80/1.16 , clause( 1109, [ =( X, 'empty_set' ), member( f24( X ), X ) ] )
% 0.80/1.16 , clause( 1110, [ =( X, 'empty_set' ), disjoint( f24( X ), X ) ] )
% 0.80/1.16 , clause( 1111, [ function( f25 ) ] )
% 0.80/1.16 , clause( 1112, [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member( f26(
% 0.80/1.16 X ), X ) ] )
% 0.80/1.16 , clause( 1113, [ ~( 'little_set'( X ) ), =( X, 'empty_set' ), member(
% 0.80/1.16 'ordered_pair'( X, f26( X ) ), f25 ) ] )
% 0.80/1.16 , clause( 1114, [ ~( member( X, 'range_of'( Y ) ) ),
% 0.80/1.16 'ordered_pair_predicate'( f27( X, Y ) ) ] )
% 0.80/1.16 , clause( 1115, [ ~( member( X, 'range_of'( Y ) ) ), member( f27( X, Y ), Y
% 0.80/1.16 ) ] )
% 0.80/1.16 , clause( 1116, [ ~( member( X, 'range_of'( Y ) ) ), =( X, second( f27( X,
% 0.80/1.16 Y ) ) ) ] )
% 0.80/1.16 , clause( 1117, [ member( X, 'range_of'( Y ) ), ~( 'little_set'( X ) ), ~(
% 0.80/1.16 'ordered_pair_predicate'( Z ) ), ~( member( Z, Y ) ), ~( =( X, second( Z
% 0.80/1.16 ) ) ) ] )
% 0.80/1.16 , clause( 1118, [ ~( member( X, 'identity_relation' ) ),
% 0.80/1.16 'ordered_pair_predicate'( X ) ] )
% 0.80/1.16 , clause( 1119, [ ~( member( X, 'identity_relation' ) ), =( first( X ),
% 0.80/1.16 second( X ) ) ] )
% 0.80/1.16 , clause( 1120, [ member( X, 'identity_relation' ), ~( 'little_set'( X ) )
% 0.80/1.16 , ~( 'ordered_pair_predicate'( X ) ), ~( =( first( X ), second( X ) ) ) ]
% 0.80/1.16 )
% 0.80/1.16 , clause( 1121, [ =( restrict( X, Y ), intersection( X, 'cross_product'( Y
% 0.80/1.16 , 'universal_set' ) ) ) ] )
% 0.80/1.16 , clause( 1122, [ ~( 'one_to_one_function'( X ) ), function( X ) ] )
% 0.80/1.16 , clause( 1123, [ ~( 'one_to_one_function'( X ) ), function( converse( X )
% 0.80/1.16 ) ] )
% 0.80/1.16 , clause( 1124, [ 'one_to_one_function'( X ), ~( function( X ) ), ~(
% 0.80/1.16 function( converse( X ) ) ) ] )
% 0.80/1.16 , clause( 1125, [ ~( member( X, apply( Y, Z ) ) ), 'ordered_pair_predicate'(
% 0.80/1.16 f28( X, Y, Z ) ) ] )
% 0.80/1.16 , clause( 1126, [ ~( member( X, apply( Y, Z ) ) ), member( f28( X, Y, Z ),
% 0.80/1.16 Y ) ] )
% 0.80/1.16 , clause( 1127, [ ~( member( X, apply( Y, Z ) ) ), =( first( f28( X, Y, Z )
% 0.80/1.16 ), Z ) ] )
% 0.80/1.16 , clause( 1128, [ ~( member( X, apply( Y, Z ) ) ), member( X, second( f28(
% 0.80/1.16 X, Y, Z ) ) ) ] )
% 0.80/1.16 , clause( 1129, [ member( X, apply( Y, Z ) ), ~( 'ordered_pair_predicate'(
% 0.80/1.16 T ) ), ~( member( T, Y ) ), ~( =( first( T ), Z ) ), ~( member( X, second(
% 0.80/1.16 T ) ) ) ] )
% 0.80/1.16 , clause( 1130, [ =( 'apply_to_two_arguments'( X, Y, Z ), apply( X,
% 0.80/1.16 'ordered_pair'( Y, Z ) ) ) ] )
% 0.80/1.16 , clause( 1131, [ ~( maps( X, Y, Z ) ), function( X ) ] )
% 0.80/1.16 , clause( 1132, [ ~( maps( X, Y, Z ) ), =( 'domain_of'( X ), Y ) ] )
% 0.80/1.16 , clause( 1133, [ ~( maps( X, Y, Z ) ), subset( 'range_of'( X ), Z ) ] )
% 0.80/1.16 , clause( 1134, [ maps( X, Y, Z ), ~( function( X ) ), ~( =( 'domain_of'( X
% 0.80/1.16 ), Y ) ), ~( subset( 'range_of'( X ), Z ) ) ] )
% 0.80/1.16 , clause( 1135, [ ~( closed( X, Y ) ), 'little_set'( X ) ] )
% 0.80/1.16 , clause( 1136, [ ~( closed( X, Y ) ), 'little_set'( Y ) ] )
% 0.80/1.16 , clause( 1137, [ ~( closed( X, Y ) ), maps( Y, 'cross_product'( X, X ), X
% 0.80/1.16 ) ] )
% 0.80/1.16 , clause( 1138, [ closed( X, Y ), ~( 'little_set'( X ) ), ~( 'little_set'(
% 0.80/1.16 Y ) ), ~( maps( Y, 'cross_product'( X, X ), X ) ) ] )
% 0.80/1.16 , clause( 1139, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f29( X,
% 0.80/1.16 Y, Z ) ) ] )
% 0.80/1.16 , clause( 1140, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f30( X,
% 0.80/1.16 Y, Z ) ) ] )
% 0.80/1.16 , clause( 1141, [ ~( member( X, compose( Y, Z ) ) ), 'little_set'( f31( X,
% 0.80/1.16 Y, Z ) ) ] )
% 0.80/1.16 , clause( 1142, [ ~( member( X, compose( Y, Z ) ) ), =( X, 'ordered_pair'(
% 0.80/1.16 f29( X, Y, Z ), f30( X, Y, Z ) ) ) ] )
% 0.80/1.16 , clause( 1143, [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'(
% 0.80/1.16 f29( X, Y, Z ), f31( X, Y, Z ) ), Y ) ] )
% 0.80/1.16 , clause( 1144, [ ~( member( X, compose( Y, Z ) ) ), member( 'ordered_pair'(
% 0.80/1.16 f31( X, Y, Z ), f30( X, Y, Z ) ), Z ) ] )
% 0.80/1.16 , clause( 1145, [ member( X, compose( Y, Z ) ), ~( 'little_set'( X ) ), ~(
% 0.80/1.16 'little_set'( T ) ), ~( 'little_set'( U ) ), ~( 'little_set'( W ) ), ~(
% 0.80/1.16 =( X, 'ordered_pair'( T, U ) ) ), ~( member( 'ordered_pair'( T, W ), Y )
% 0.80/1.16 ), ~( member( 'ordered_pair'( W, U ), Z ) ) ] )
% 0.80/1.16 , clause( 1146, [ ~( homomorphism( X, Y, Z, T, U ) ), closed( Y, Z ) ] )
% 0.80/1.16 , clause( 1147, [ ~( homomorphism( X, Y, Z, T, U ) ), closed( T, U ) ] )
% 0.80/1.16 , clause( 1148, [ ~( homomorphism( X, Y, Z, T, U ) ), maps( X, Y, T ) ] )
% 0.80/1.16 , clause( 1149, [ ~( homomorphism( X, Y, Z, T, U ) ), ~( member( W, Y ) ),
% 0.80/1.16 ~( member( V0, Y ) ), =( apply( X, 'apply_to_two_arguments'( Z, W, V0 ) )
% 0.80/1.16 , 'apply_to_two_arguments'( U, apply( X, W ), apply( X, V0 ) ) ) ] )
% 0.80/1.16 , clause( 1150, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~(
% 0.80/1.16 closed( T, U ) ), ~( maps( X, Y, T ) ), member( f32( X, Y, Z, T, U ), Y )
% 0.80/1.16 ] )
% 0.80/1.16 , clause( 1151, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~(
% 0.80/1.16 closed( T, U ) ), ~( maps( X, Y, T ) ), member( f33( X, Y, Z, T, U ), Y )
% 0.80/1.16 ] )
% 0.80/1.16 , clause( 1152, [ homomorphism( X, Y, Z, T, U ), ~( closed( Y, Z ) ), ~(
% 0.80/1.16 closed( T, U ) ), ~( maps( X, Y, T ) ), ~( =( apply( X,
% 0.80/1.16 'apply_to_two_arguments'( Z, f32( X, Y, Z, T, U ), f33( X, Y, Z, T, U ) )
% 0.80/1.16 ), 'apply_to_two_arguments'( U, apply( X, f32( X, Y, Z, T, U ) ), apply(
% 0.80/1.16 X, f33( X, Y, Z, T, U ) ) ) ) ) ] )
% 0.80/1.16 , clause( 1153, [ 'ordered_pair_predicate'( a ) ] )
% 0.80/1.16 , clause( 1154, [ ~( 'little_set'( a ) ) ] )
% 0.80/1.16 ] ).
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 subsumption(
% 0.80/1.16 clause( 7, [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ] )
% 0.80/1.16 , clause( 1019, [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ] )
% 0.80/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.80/1.16 )] ) ).
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 eqswap(
% 0.80/1.16 clause( 1180, [ =( 'non_ordered_pair'( 'singleton_set'( X ),
% 0.80/1.16 'non_ordered_pair'( X, Y ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.80/1.16 , clause( 1021, [ =( 'ordered_pair'( X, Y ), 'non_ordered_pair'(
% 0.80/1.16 'singleton_set'( X ), 'non_ordered_pair'( X, Y ) ) ) ] )
% 0.80/1.16 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 subsumption(
% 0.80/1.16 clause( 9, [ =( 'non_ordered_pair'( 'singleton_set'( X ),
% 0.80/1.16 'non_ordered_pair'( X, Y ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.80/1.16 , clause( 1180, [ =( 'non_ordered_pair'( 'singleton_set'( X ),
% 0.80/1.16 'non_ordered_pair'( X, Y ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.80/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.80/1.16 )] ) ).
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 eqswap(
% 0.80/1.16 clause( 1195, [ =( 'ordered_pair'( f2( X ), f3( X ) ), X ), ~(
% 0.80/1.16 'ordered_pair_predicate'( X ) ) ] )
% 0.80/1.16 , clause( 1024, [ ~( 'ordered_pair_predicate'( X ) ), =( X, 'ordered_pair'(
% 0.80/1.16 f2( X ), f3( X ) ) ) ] )
% 0.80/1.16 , 1, substitution( 0, [ :=( X, X )] )).
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 subsumption(
% 0.80/1.16 clause( 12, [ ~( 'ordered_pair_predicate'( X ) ), =( 'ordered_pair'( f2( X
% 0.80/1.16 ), f3( X ) ), X ) ] )
% 0.80/1.16 , clause( 1195, [ =( 'ordered_pair'( f2( X ), f3( X ) ), X ), ~(
% 0.80/1.16 'ordered_pair_predicate'( X ) ) ] )
% 0.80/1.16 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 0.80/1.16 0 )] ) ).
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 subsumption(
% 0.80/1.16 clause( 141, [ 'ordered_pair_predicate'( a ) ] )
% 0.80/1.16 , clause( 1153, [ 'ordered_pair_predicate'( a ) ] )
% 0.80/1.16 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 subsumption(
% 0.80/1.16 clause( 142, [ ~( 'little_set'( a ) ) ] )
% 0.80/1.16 , clause( 1154, [ ~( 'little_set'( a ) ) ] )
% 0.80/1.16 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 paramod(
% 0.80/1.16 clause( 1541, [ 'little_set'( 'ordered_pair'( X, Y ) ) ] )
% 0.80/1.16 , clause( 9, [ =( 'non_ordered_pair'( 'singleton_set'( X ),
% 0.80/1.16 'non_ordered_pair'( X, Y ) ), 'ordered_pair'( X, Y ) ) ] )
% 0.80/1.16 , 0, clause( 7, [ 'little_set'( 'non_ordered_pair'( X, Y ) ) ] )
% 0.80/1.16 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.80/1.16 :=( X, 'singleton_set'( X ) ), :=( Y, 'non_ordered_pair'( X, Y ) )] )
% 0.80/1.16 ).
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 subsumption(
% 0.80/1.16 clause( 709, [ 'little_set'( 'ordered_pair'( X, Y ) ) ] )
% 0.80/1.16 , clause( 1541, [ 'little_set'( 'ordered_pair'( X, Y ) ) ] )
% 0.80/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.80/1.16 )] ) ).
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 paramod(
% 0.80/1.16 clause( 1543, [ 'little_set'( X ), ~( 'ordered_pair_predicate'( X ) ) ] )
% 0.80/1.16 , clause( 12, [ ~( 'ordered_pair_predicate'( X ) ), =( 'ordered_pair'( f2(
% 0.80/1.16 X ), f3( X ) ), X ) ] )
% 0.80/1.16 , 1, clause( 709, [ 'little_set'( 'ordered_pair'( X, Y ) ) ] )
% 0.80/1.16 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, f2( X )
% 0.80/1.16 ), :=( Y, f3( X ) )] )).
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 subsumption(
% 0.80/1.16 clause( 944, [ 'little_set'( X ), ~( 'ordered_pair_predicate'( X ) ) ] )
% 0.80/1.16 , clause( 1543, [ 'little_set'( X ), ~( 'ordered_pair_predicate'( X ) ) ]
% 0.80/1.16 )
% 0.80/1.16 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.80/1.16 1 )] ) ).
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 resolution(
% 0.80/1.16 clause( 1544, [ 'little_set'( a ) ] )
% 0.80/1.16 , clause( 944, [ 'little_set'( X ), ~( 'ordered_pair_predicate'( X ) ) ] )
% 0.80/1.16 , 1, clause( 141, [ 'ordered_pair_predicate'( a ) ] )
% 0.80/1.16 , 0, substitution( 0, [ :=( X, a )] ), substitution( 1, [] )).
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 resolution(
% 0.80/1.16 clause( 1545, [] )
% 0.80/1.16 , clause( 142, [ ~( 'little_set'( a ) ) ] )
% 0.80/1.16 , 0, clause( 1544, [ 'little_set'( a ) ] )
% 0.80/1.16 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 subsumption(
% 0.80/1.16 clause( 1010, [] )
% 0.80/1.16 , clause( 1545, [] )
% 0.80/1.16 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 end.
% 0.80/1.16
% 0.80/1.16 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.80/1.16
% 0.80/1.16 Memory use:
% 0.80/1.16
% 0.80/1.16 space for terms: 17711
% 0.80/1.16 space for clauses: 52154
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 clauses generated: 1990
% 0.80/1.16 clauses kept: 1011
% 0.80/1.16 clauses selected: 64
% 0.80/1.16 clauses deleted: 0
% 0.80/1.16 clauses inuse deleted: 0
% 0.80/1.16
% 0.80/1.16 subsentry: 4908
% 0.80/1.16 literals s-matched: 3499
% 0.80/1.16 literals matched: 2574
% 0.80/1.16 full subsumption: 1237
% 0.80/1.16
% 0.80/1.16 checksum: -1002660694
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 Bliksem ended
%------------------------------------------------------------------------------