TSTP Solution File: TOP004-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : TOP004-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.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 : Thu Jul 21 21:20:15 EDT 2022
% Result : Unsatisfiable 0.69s 1.10s
% Output : Refutation 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : TOP004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sun May 29 14:20:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.69/1.10 *** allocated 10000 integers for termspace/termends
% 0.69/1.10 *** allocated 10000 integers for clauses
% 0.69/1.10 *** allocated 10000 integers for justifications
% 0.69/1.10 Bliksem 1.12
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 Automatic Strategy Selection
% 0.69/1.10
% 0.69/1.10 Clauses:
% 0.69/1.10 [
% 0.69/1.10 [ ~( 'element_of_set'( X, 'union_of_members'( Y ) ) ), 'element_of_set'(
% 0.69/1.10 X, f1( Y, X ) ) ],
% 0.69/1.10 [ ~( 'element_of_set'( X, 'union_of_members'( Y ) ) ),
% 0.69/1.10 'element_of_collection'( f1( Y, X ), Y ) ],
% 0.69/1.10 [ 'element_of_set'( X, 'union_of_members'( Y ) ), ~( 'element_of_set'( X
% 0.69/1.10 , Z ) ), ~( 'element_of_collection'( Z, Y ) ) ],
% 0.69/1.10 [ ~( 'element_of_set'( X, 'intersection_of_members'( Y ) ) ), ~(
% 0.69/1.10 'element_of_collection'( Z, Y ) ), 'element_of_set'( X, Z ) ],
% 0.69/1.10 [ 'element_of_set'( X, 'intersection_of_members'( Y ) ),
% 0.69/1.10 'element_of_collection'( f2( Y, X ), Y ) ],
% 0.69/1.10 [ 'element_of_set'( X, 'intersection_of_members'( Y ) ), ~(
% 0.69/1.10 'element_of_set'( X, f2( Y, X ) ) ) ],
% 0.69/1.10 [ ~( 'topological_space'( X, Y ) ), 'equal_sets'( 'union_of_members'( Y
% 0.69/1.10 ), X ) ],
% 0.69/1.10 [ ~( 'topological_space'( X, Y ) ), 'element_of_collection'( 'empty_set'
% 0.69/1.10 , Y ) ],
% 0.69/1.10 [ ~( 'topological_space'( X, Y ) ), 'element_of_collection'( X, Y ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( 'topological_space'( X, Y ) ), ~( 'element_of_collection'( Z, Y ) )
% 0.69/1.10 , ~( 'element_of_collection'( T, Y ) ), 'element_of_collection'(
% 0.69/1.10 'intersection_of_sets'( Z, T ), Y ) ],
% 0.69/1.10 [ ~( 'topological_space'( X, Y ) ), ~( 'subset_collections'( Z, Y ) ),
% 0.69/1.10 'element_of_collection'( 'union_of_members'( Z ), Y ) ],
% 0.69/1.10 [ 'topological_space'( X, Y ), ~( 'equal_sets'( 'union_of_members'( Y )
% 0.69/1.10 , X ) ), ~( 'element_of_collection'( 'empty_set', Y ) ), ~(
% 0.69/1.10 'element_of_collection'( X, Y ) ), 'element_of_collection'( f3( X, Y ), Y
% 0.69/1.10 ), 'subset_collections'( f5( X, Y ), Y ) ],
% 0.69/1.10 [ 'topological_space'( X, Y ), ~( 'equal_sets'( 'union_of_members'( Y )
% 0.69/1.10 , X ) ), ~( 'element_of_collection'( 'empty_set', Y ) ), ~(
% 0.69/1.10 'element_of_collection'( X, Y ) ), 'element_of_collection'( f3( X, Y ), Y
% 0.69/1.10 ), ~( 'element_of_collection'( 'union_of_members'( f5( X, Y ) ), Y ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ 'topological_space'( X, Y ), ~( 'equal_sets'( 'union_of_members'( Y )
% 0.69/1.10 , X ) ), ~( 'element_of_collection'( 'empty_set', Y ) ), ~(
% 0.69/1.10 'element_of_collection'( X, Y ) ), 'element_of_collection'( f4( X, Y ), Y
% 0.69/1.10 ), 'subset_collections'( f5( X, Y ), Y ) ],
% 0.69/1.10 [ 'topological_space'( X, Y ), ~( 'equal_sets'( 'union_of_members'( Y )
% 0.69/1.10 , X ) ), ~( 'element_of_collection'( 'empty_set', Y ) ), ~(
% 0.69/1.10 'element_of_collection'( X, Y ) ), 'element_of_collection'( f4( X, Y ), Y
% 0.69/1.10 ), ~( 'element_of_collection'( 'union_of_members'( f5( X, Y ) ), Y ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ 'topological_space'( X, Y ), ~( 'equal_sets'( 'union_of_members'( Y )
% 0.69/1.10 , X ) ), ~( 'element_of_collection'( 'empty_set', Y ) ), ~(
% 0.69/1.10 'element_of_collection'( X, Y ) ), ~( 'element_of_collection'(
% 0.69/1.10 'intersection_of_sets'( f3( X, Y ), f4( X, Y ) ), Y ) ),
% 0.69/1.10 'subset_collections'( f5( X, Y ), Y ) ],
% 0.69/1.10 [ 'topological_space'( X, Y ), ~( 'equal_sets'( 'union_of_members'( Y )
% 0.69/1.10 , X ) ), ~( 'element_of_collection'( 'empty_set', Y ) ), ~(
% 0.69/1.10 'element_of_collection'( X, Y ) ), ~( 'element_of_collection'(
% 0.69/1.10 'intersection_of_sets'( f3( X, Y ), f4( X, Y ) ), Y ) ), ~(
% 0.69/1.10 'element_of_collection'( 'union_of_members'( f5( X, Y ) ), Y ) ) ],
% 0.69/1.10 [ ~( open( X, Y, Z ) ), 'topological_space'( Y, Z ) ],
% 0.69/1.10 [ ~( open( X, Y, Z ) ), 'element_of_collection'( X, Z ) ],
% 0.69/1.10 [ open( X, Y, Z ), ~( 'topological_space'( Y, Z ) ), ~(
% 0.69/1.10 'element_of_collection'( X, Z ) ) ],
% 0.69/1.10 [ ~( closed( X, Y, Z ) ), 'topological_space'( Y, Z ) ],
% 0.69/1.10 [ ~( closed( X, Y, Z ) ), open( 'relative_complement_sets'( X, Y ), Y, Z
% 0.69/1.10 ) ],
% 0.69/1.10 [ closed( X, Y, Z ), ~( 'topological_space'( Y, Z ) ), ~( open(
% 0.69/1.10 'relative_complement_sets'( X, Y ), Y, Z ) ) ],
% 0.69/1.10 [ ~( finer( X, Y, Z ) ), 'topological_space'( Z, X ) ],
% 0.69/1.10 [ ~( finer( X, Y, Z ) ), 'topological_space'( Z, Y ) ],
% 0.69/1.10 [ ~( finer( X, Y, Z ) ), 'subset_collections'( Y, X ) ],
% 0.69/1.10 [ finer( X, Y, Z ), ~( 'topological_space'( Z, X ) ), ~(
% 0.69/1.10 'topological_space'( Z, Y ) ), ~( 'subset_collections'( Y, X ) ) ],
% 0.69/1.10 [ ~( basis( X, Y ) ), 'equal_sets'( 'union_of_members'( Y ), X ) ],
% 0.69/1.10 [ ~( basis( X, Y ) ), ~( 'element_of_set'( Z, X ) ), ~(
% 0.69/1.10 'element_of_collection'( T, Y ) ), ~( 'element_of_collection'( U, Y ) ),
% 0.69/1.10 ~( 'element_of_set'( Z, 'intersection_of_sets'( T, U ) ) ),
% 0.69/1.10 'element_of_set'( Z, f6( X, Y, Z, T, U ) ) ],
% 0.69/1.10 [ ~( basis( X, Y ) ), ~( 'element_of_set'( Z, X ) ), ~(
% 0.69/1.10 'element_of_collection'( T, Y ) ), ~( 'element_of_collection'( U, Y ) ),
% 0.69/1.10 ~( 'element_of_set'( Z, 'intersection_of_sets'( T, U ) ) ),
% 0.69/1.10 'element_of_collection'( f6( X, Y, Z, T, U ), Y ) ],
% 0.69/1.10 [ ~( basis( X, Y ) ), ~( 'element_of_set'( Z, X ) ), ~(
% 0.69/1.10 'element_of_collection'( T, Y ) ), ~( 'element_of_collection'( U, Y ) ),
% 0.69/1.10 ~( 'element_of_set'( Z, 'intersection_of_sets'( T, U ) ) ), 'subset_sets'(
% 0.69/1.10 f6( X, Y, Z, T, U ), 'intersection_of_sets'( T, U ) ) ],
% 0.69/1.10 [ basis( X, Y ), ~( 'equal_sets'( 'union_of_members'( Y ), X ) ),
% 0.69/1.10 'element_of_set'( f7( X, Y ), X ) ],
% 0.69/1.10 [ basis( X, Y ), ~( 'equal_sets'( 'union_of_members'( Y ), X ) ),
% 0.69/1.10 'element_of_collection'( f8( X, Y ), Y ) ],
% 0.69/1.10 [ basis( X, Y ), ~( 'equal_sets'( 'union_of_members'( Y ), X ) ),
% 0.69/1.10 'element_of_collection'( f9( X, Y ), Y ) ],
% 0.69/1.10 [ basis( X, Y ), ~( 'equal_sets'( 'union_of_members'( Y ), X ) ),
% 0.69/1.10 'element_of_set'( f7( X, Y ), 'intersection_of_sets'( f8( X, Y ), f9( X,
% 0.69/1.10 Y ) ) ) ],
% 0.69/1.10 [ basis( X, Y ), ~( 'equal_sets'( 'union_of_members'( Y ), X ) ), ~(
% 0.69/1.10 'element_of_set'( f7( X, Y ), Z ) ), ~( 'element_of_collection'( Z, Y ) )
% 0.69/1.10 , ~( 'subset_sets'( Z, 'intersection_of_sets'( f8( X, Y ), f9( X, Y ) ) )
% 0.69/1.10 ) ],
% 0.69/1.10 [ ~( 'element_of_collection'( X, 'top_of_basis'( Y ) ) ), ~(
% 0.69/1.10 'element_of_set'( Z, X ) ), 'element_of_set'( Z, f10( Y, X, Z ) ) ],
% 0.69/1.10 [ ~( 'element_of_collection'( X, 'top_of_basis'( Y ) ) ), ~(
% 0.69/1.10 'element_of_set'( Z, X ) ), 'element_of_collection'( f10( Y, X, Z ), Y )
% 0.69/1.10 ],
% 0.69/1.10 [ ~( 'element_of_collection'( X, 'top_of_basis'( Y ) ) ), ~(
% 0.69/1.10 'element_of_set'( Z, X ) ), 'subset_sets'( f10( Y, X, Z ), X ) ],
% 0.69/1.10 [ 'element_of_collection'( X, 'top_of_basis'( Y ) ), 'element_of_set'(
% 0.69/1.10 f11( Y, X ), X ) ],
% 0.69/1.10 [ 'element_of_collection'( X, 'top_of_basis'( Y ) ), ~( 'element_of_set'(
% 0.69/1.10 f11( Y, X ), Z ) ), ~( 'element_of_collection'( Z, Y ) ), ~(
% 0.69/1.10 'subset_sets'( Z, X ) ) ],
% 0.69/1.10 [ ~( 'element_of_collection'( X, 'subspace_topology'( Y, Z, T ) ) ),
% 0.69/1.10 'topological_space'( Y, Z ) ],
% 0.69/1.10 [ ~( 'element_of_collection'( X, 'subspace_topology'( Y, Z, T ) ) ),
% 0.69/1.10 'subset_sets'( T, Y ) ],
% 0.69/1.10 [ ~( 'element_of_collection'( X, 'subspace_topology'( Y, Z, T ) ) ),
% 0.69/1.10 'element_of_collection'( f12( Y, Z, T, X ), Z ) ],
% 0.69/1.10 [ ~( 'element_of_collection'( X, 'subspace_topology'( Y, Z, T ) ) ),
% 0.69/1.10 'equal_sets'( X, 'intersection_of_sets'( T, f12( Y, Z, T, X ) ) ) ],
% 0.69/1.10 [ 'element_of_collection'( X, 'subspace_topology'( Y, Z, T ) ), ~(
% 0.69/1.10 'topological_space'( Y, Z ) ), ~( 'subset_sets'( T, Y ) ), ~(
% 0.69/1.10 'element_of_collection'( U, Z ) ), ~( 'equal_sets'( X,
% 0.69/1.10 'intersection_of_sets'( T, U ) ) ) ],
% 0.69/1.10 [ ~( 'element_of_set'( X, interior( Y, Z, T ) ) ), 'topological_space'(
% 0.69/1.10 Z, T ) ],
% 0.69/1.10 [ ~( 'element_of_set'( X, interior( Y, Z, T ) ) ), 'subset_sets'( Y, Z )
% 0.69/1.10 ],
% 0.69/1.10 [ ~( 'element_of_set'( X, interior( Y, Z, T ) ) ), 'element_of_set'( X,
% 0.69/1.10 f13( Y, Z, T, X ) ) ],
% 0.69/1.10 [ ~( 'element_of_set'( X, interior( Y, Z, T ) ) ), 'subset_sets'( f13( Y
% 0.69/1.10 , Z, T, X ), Y ) ],
% 0.69/1.10 [ ~( 'element_of_set'( X, interior( Y, Z, T ) ) ), open( f13( Y, Z, T, X
% 0.69/1.10 ), Z, T ) ],
% 0.69/1.10 [ 'element_of_set'( X, interior( Y, Z, T ) ), ~( 'topological_space'( Z
% 0.69/1.10 , T ) ), ~( 'subset_sets'( Y, Z ) ), ~( 'element_of_set'( X, U ) ), ~(
% 0.69/1.10 'subset_sets'( U, Y ) ), ~( open( U, Z, T ) ) ],
% 0.69/1.10 [ ~( 'element_of_set'( X, closure( Y, Z, T ) ) ), 'topological_space'( Z
% 0.69/1.10 , T ) ],
% 0.69/1.10 [ ~( 'element_of_set'( X, closure( Y, Z, T ) ) ), 'subset_sets'( Y, Z )
% 0.69/1.10 ],
% 0.69/1.10 [ ~( 'element_of_set'( X, closure( Y, Z, T ) ) ), ~( 'subset_sets'( Y, U
% 0.69/1.10 ) ), ~( closed( U, Z, T ) ), 'element_of_set'( X, U ) ],
% 0.69/1.10 [ 'element_of_set'( X, closure( Y, Z, T ) ), ~( 'topological_space'( Z,
% 0.69/1.10 T ) ), ~( 'subset_sets'( Y, Z ) ), 'subset_sets'( Y, f14( Y, Z, T, X ) )
% 0.69/1.10 ],
% 0.69/1.10 [ 'element_of_set'( X, closure( Y, Z, T ) ), ~( 'topological_space'( Z,
% 0.69/1.10 T ) ), ~( 'subset_sets'( Y, Z ) ), closed( f14( Y, Z, T, X ), Z, T ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ 'element_of_set'( X, closure( Y, Z, T ) ), ~( 'topological_space'( Z,
% 0.69/1.10 T ) ), ~( 'subset_sets'( Y, Z ) ), ~( 'element_of_set'( X, f14( Y, Z, T,
% 0.69/1.10 X ) ) ) ],
% 0.69/1.10 [ ~( neighborhood( X, Y, Z, T ) ), 'topological_space'( Z, T ) ],
% 0.69/1.10 [ ~( neighborhood( X, Y, Z, T ) ), open( X, Z, T ) ],
% 0.69/1.10 [ ~( neighborhood( X, Y, Z, T ) ), 'element_of_set'( Y, X ) ],
% 0.69/1.10 [ neighborhood( X, Y, Z, T ), ~( 'topological_space'( Z, T ) ), ~( open(
% 0.69/1.10 X, Z, T ) ), ~( 'element_of_set'( Y, X ) ) ],
% 0.69/1.10 [ ~( 'limit_point'( X, Y, Z, T ) ), 'topological_space'( Z, T ) ],
% 0.69/1.10 [ ~( 'limit_point'( X, Y, Z, T ) ), 'subset_sets'( Y, Z ) ],
% 0.69/1.10 [ ~( 'limit_point'( X, Y, Z, T ) ), ~( neighborhood( U, X, Z, T ) ),
% 0.69/1.10 'element_of_set'( f15( X, Y, Z, T, U ), 'intersection_of_sets'( U, Y ) )
% 0.69/1.10 ],
% 0.69/1.10 [ ~( 'limit_point'( X, Y, Z, T ) ), ~( neighborhood( U, X, Z, T ) ), ~(
% 0.69/1.10 'eq_p'( f15( X, Y, Z, T, U ), X ) ) ],
% 0.69/1.10 [ 'limit_point'( X, Y, Z, T ), ~( 'topological_space'( Z, T ) ), ~(
% 0.69/1.10 'subset_sets'( Y, Z ) ), neighborhood( f16( X, Y, Z, T ), X, Z, T ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ 'limit_point'( X, Y, Z, T ), ~( 'topological_space'( Z, T ) ), ~(
% 0.69/1.10 'subset_sets'( Y, Z ) ), ~( 'element_of_set'( U, 'intersection_of_sets'(
% 0.69/1.10 f16( X, Y, Z, T ), Y ) ) ), 'eq_p'( U, X ) ],
% 0.69/1.10 [ ~( 'element_of_set'( X, boundary( Y, Z, T ) ) ), 'topological_space'(
% 0.69/1.10 Z, T ) ],
% 0.69/1.10 [ ~( 'element_of_set'( X, boundary( Y, Z, T ) ) ), 'element_of_set'( X,
% 0.69/1.10 closure( Y, Z, T ) ) ],
% 0.69/1.10 [ ~( 'element_of_set'( X, boundary( Y, Z, T ) ) ), 'element_of_set'( X,
% 0.69/1.10 closure( 'relative_complement_sets'( Y, Z ), Z, T ) ) ],
% 0.69/1.10 [ 'element_of_set'( X, boundary( Y, Z, T ) ), ~( 'topological_space'( Z
% 0.69/1.10 , T ) ), ~( 'element_of_set'( X, closure( Y, Z, T ) ) ), ~(
% 0.69/1.10 'element_of_set'( X, closure( 'relative_complement_sets'( Y, Z ), Z, T )
% 0.69/1.10 ) ) ],
% 0.69/1.10 [ ~( hausdorff( X, Y ) ), 'topological_space'( X, Y ) ],
% 0.69/1.10 [ ~( hausdorff( X, Y ) ), ~( 'element_of_set'( Z, X ) ), ~(
% 0.69/1.10 'element_of_set'( T, X ) ), 'eq_p'( Z, T ), neighborhood( f17( X, Y, Z, T
% 0.69/1.10 ), Z, X, Y ) ],
% 0.69/1.10 [ ~( hausdorff( X, Y ) ), ~( 'element_of_set'( Z, X ) ), ~(
% 0.69/1.10 'element_of_set'( T, X ) ), 'eq_p'( Z, T ), neighborhood( f18( X, Y, Z, T
% 0.69/1.10 ), T, X, Y ) ],
% 0.69/1.10 [ ~( hausdorff( X, Y ) ), ~( 'element_of_set'( Z, X ) ), ~(
% 0.69/1.10 'element_of_set'( T, X ) ), 'eq_p'( Z, T ), 'disjoint_s'( f17( X, Y, Z, T
% 0.69/1.10 ), f18( X, Y, Z, T ) ) ],
% 0.69/1.10 [ hausdorff( X, Y ), ~( 'topological_space'( X, Y ) ), 'element_of_set'(
% 0.69/1.10 f19( X, Y ), X ) ],
% 0.69/1.10 [ hausdorff( X, Y ), ~( 'topological_space'( X, Y ) ), 'element_of_set'(
% 0.69/1.10 f20( X, Y ), X ) ],
% 0.69/1.10 [ hausdorff( X, Y ), ~( 'topological_space'( X, Y ) ), ~( 'eq_p'( f19( X
% 0.69/1.10 , Y ), f20( X, Y ) ) ) ],
% 0.69/1.10 [ hausdorff( X, Y ), ~( 'topological_space'( X, Y ) ), ~( neighborhood(
% 0.69/1.10 Z, f19( X, Y ), X, Y ) ), ~( neighborhood( T, f20( X, Y ), X, Y ) ), ~(
% 0.69/1.10 'disjoint_s'( Z, T ) ) ],
% 0.69/1.10 [ ~( separation( X, Y, Z, T ) ), 'topological_space'( Z, T ) ],
% 0.69/1.10 [ ~( separation( X, Y, Z, T ) ), ~( 'equal_sets'( X, 'empty_set' ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( separation( X, Y, Z, T ) ), ~( 'equal_sets'( Y, 'empty_set' ) ) ]
% 0.69/1.10 ,
% 0.69/1.10 [ ~( separation( X, Y, Z, T ) ), 'element_of_collection'( X, T ) ],
% 0.69/1.10 [ ~( separation( X, Y, Z, T ) ), 'element_of_collection'( Y, T ) ],
% 0.69/1.10 [ ~( separation( X, Y, Z, T ) ), 'equal_sets'( 'union_of_sets'( X, Y ),
% 0.69/1.10 Z ) ],
% 0.69/1.10 [ ~( separation( X, Y, Z, T ) ), 'disjoint_s'( X, Y ) ],
% 0.69/1.10 [ separation( X, Y, Z, T ), ~( 'topological_space'( Z, T ) ),
% 0.69/1.10 'equal_sets'( X, 'empty_set' ), 'equal_sets'( Y, 'empty_set' ), ~(
% 0.69/1.10 'element_of_collection'( X, T ) ), ~( 'element_of_collection'( Y, T ) ),
% 0.69/1.10 ~( 'equal_sets'( 'union_of_sets'( X, Y ), Z ) ), ~( 'disjoint_s'( X, Y )
% 0.69/1.10 ) ],
% 0.69/1.10 [ ~( 'connected_space'( X, Y ) ), 'topological_space'( X, Y ) ],
% 0.69/1.10 [ ~( 'connected_space'( X, Y ) ), ~( separation( Z, T, X, Y ) ) ],
% 0.69/1.10 [ 'connected_space'( X, Y ), ~( 'topological_space'( X, Y ) ),
% 0.69/1.10 separation( f21( X, Y ), f22( X, Y ), X, Y ) ],
% 0.69/1.10 [ ~( 'connected_set'( X, Y, Z ) ), 'topological_space'( Y, Z ) ],
% 0.69/1.10 [ ~( 'connected_set'( X, Y, Z ) ), 'subset_sets'( X, Y ) ],
% 0.69/1.10 [ ~( 'connected_set'( X, Y, Z ) ), 'connected_space'( X,
% 0.69/1.10 'subspace_topology'( Y, Z, X ) ) ],
% 0.69/1.10 [ 'connected_set'( X, Y, Z ), ~( 'topological_space'( Y, Z ) ), ~(
% 0.69/1.10 'subset_sets'( X, Y ) ), ~( 'connected_space'( X, 'subspace_topology'( Y
% 0.69/1.10 , Z, X ) ) ) ],
% 0.69/1.10 [ ~( 'open_covering'( X, Y, Z ) ), 'topological_space'( Y, Z ) ],
% 0.69/1.10 [ ~( 'open_covering'( X, Y, Z ) ), 'subset_collections'( X, Z ) ],
% 0.69/1.10 [ ~( 'open_covering'( X, Y, Z ) ), 'equal_sets'( 'union_of_members'( X )
% 0.69/1.10 , Y ) ],
% 0.69/1.10 [ 'open_covering'( X, Y, Z ), ~( 'topological_space'( Y, Z ) ), ~(
% 0.69/1.10 'subset_collections'( X, Z ) ), ~( 'equal_sets'( 'union_of_members'( X )
% 0.69/1.10 , Y ) ) ],
% 0.69/1.10 [ ~( 'compact_space'( X, Y ) ), 'topological_space'( X, Y ) ],
% 0.69/1.10 [ ~( 'compact_space'( X, Y ) ), ~( 'open_covering'( Z, X, Y ) ), finite(
% 0.69/1.10 f23( X, Y, Z ) ) ],
% 0.69/1.10 [ ~( 'compact_space'( X, Y ) ), ~( 'open_covering'( Z, X, Y ) ),
% 0.69/1.10 'subset_collections'( f23( X, Y, Z ), Z ) ],
% 0.69/1.10 [ ~( 'compact_space'( X, Y ) ), ~( 'open_covering'( Z, X, Y ) ),
% 0.69/1.10 'open_covering'( f23( X, Y, Z ), X, Y ) ],
% 0.69/1.10 [ 'compact_space'( X, Y ), ~( 'topological_space'( X, Y ) ),
% 0.69/1.10 'open_covering'( f24( X, Y ), X, Y ) ],
% 0.69/1.10 [ 'compact_space'( X, Y ), ~( 'topological_space'( X, Y ) ), ~( finite(
% 0.69/1.10 Z ) ), ~( 'subset_collections'( Z, f24( X, Y ) ) ), ~( 'open_covering'( Z
% 0.69/1.10 , X, Y ) ) ],
% 0.69/1.10 [ ~( 'compact_set'( X, Y, Z ) ), 'topological_space'( Y, Z ) ],
% 0.69/1.10 [ ~( 'compact_set'( X, Y, Z ) ), 'subset_sets'( X, Y ) ],
% 0.69/1.10 [ ~( 'compact_set'( X, Y, Z ) ), 'compact_space'( X, 'subspace_topology'(
% 0.69/1.10 Y, Z, X ) ) ],
% 0.69/1.10 [ 'compact_set'( X, Y, Z ), ~( 'topological_space'( Y, Z ) ), ~(
% 0.69/1.10 'subset_sets'( X, Y ) ), ~( 'compact_space'( X, 'subspace_topology'( Y, Z
% 0.69/1.10 , X ) ) ) ],
% 0.69/1.10 [ basis( cx, f ) ],
% 0.69/1.10 [ 'element_of_collection'( X, 'top_of_basis'( f ) ) ],
% 0.69/1.10 [ 'element_of_collection'( X, 'top_of_basis'( f ) ) ],
% 0.69/1.10 [ ~( 'element_of_collection'( 'intersection_of_sets'( X, Y ),
% 0.69/1.10 'top_of_basis'( f ) ) ) ]
% 0.69/1.10 ] .
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 percentage equality = 0.000000, percentage horn = 0.794643
% 0.69/1.10 This a non-horn, non-equality problem
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 Options Used:
% 0.69/1.10
% 0.69/1.10 useres = 1
% 0.69/1.10 useparamod = 0
% 0.69/1.10 useeqrefl = 0
% 0.69/1.10 useeqfact = 0
% 0.69/1.10 usefactor = 1
% 0.69/1.10 usesimpsplitting = 0
% 0.69/1.10 usesimpdemod = 0
% 0.69/1.10 usesimpres = 3
% 0.69/1.10
% 0.69/1.10 resimpinuse = 1000
% 0.69/1.10 resimpclauses = 20000
% 0.69/1.10 substype = standard
% 0.69/1.10 backwardsubs = 1
% 0.69/1.10 selectoldest = 5
% 0.69/1.10
% 0.69/1.10 litorderings [0] = split
% 0.69/1.10 litorderings [1] = liftord
% 0.69/1.10
% 0.69/1.10 termordering = none
% 0.69/1.10
% 0.69/1.10 litapriori = 1
% 0.69/1.10 termapriori = 0
% 0.69/1.10 litaposteriori = 0
% 0.69/1.10 termaposteriori = 0
% 0.69/1.10 demodaposteriori = 0
% 0.69/1.10 ordereqreflfact = 0
% 0.69/1.10
% 0.69/1.10 litselect = none
% 0.69/1.10
% 0.69/1.10 maxweight = 15
% 0.69/1.10 maxdepth = 30000
% 0.69/1.10 maxlength = 115
% 0.69/1.10 maxnrvars = 195
% 0.69/1.10 excuselevel = 1
% 0.69/1.10 increasemaxweight = 1
% 0.69/1.10
% 0.69/1.10 maxselected = 10000000
% 0.69/1.10 maxnrclauses = 10000000
% 0.69/1.10
% 0.69/1.10 showgenerated = 0
% 0.69/1.10 showkept = 0
% 0.69/1.10 showselected = 0
% 0.69/1.10 showdeleted = 0
% 0.69/1.10 showresimp = 1
% 0.69/1.10 showstatus = 2000
% 0.69/1.10
% 0.69/1.10 prologoutput = 1
% 0.69/1.10 nrgoals = 5000000
% 0.69/1.10 totalproof = 1
% 0.69/1.10
% 0.69/1.10 Symbols occurring in the translation:
% 0.69/1.10
% 0.69/1.10 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.69/1.10 . [1, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.69/1.10 ! [4, 1] (w:0, o:37, a:1, s:1, b:0),
% 0.69/1.10 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.10 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.10 'union_of_members' [41, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.69/1.10 'element_of_set' [42, 2] (w:1, o:74, a:1, s:1, b:0),
% 0.69/1.10 f1 [43, 2] (w:1, o:78, a:1, s:1, b:0),
% 0.69/1.10 'element_of_collection' [44, 2] (w:1, o:75, a:1, s:1, b:0),
% 0.69/1.10 'intersection_of_members' [46, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.69/1.10 f2 [48, 2] (w:1, o:81, a:1, s:1, b:0),
% 0.69/1.10 'topological_space' [51, 2] (w:1, o:85, a:1, s:1, b:0),
% 0.69/1.10 'equal_sets' [52, 2] (w:1, o:76, a:1, s:1, b:0),
% 0.69/1.10 'empty_set' [53, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.69/1.10 'intersection_of_sets' [56, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.69/1.10 'subset_collections' [57, 2] (w:1, o:83, a:1, s:1, b:0),
% 0.69/1.10 f3 [58, 2] (w:1, o:92, a:1, s:1, b:0),
% 0.69/1.10 f5 [59, 2] (w:1, o:94, a:1, s:1, b:0),
% 0.69/1.10 f4 [60, 2] (w:1, o:93, a:1, s:1, b:0),
% 0.69/1.10 open [61, 3] (w:1, o:100, a:1, s:1, b:0),
% 0.69/1.10 closed [62, 3] (w:1, o:102, a:1, s:1, b:0),
% 0.69/1.10 'relative_complement_sets' [63, 2] (w:1, o:82, a:1, s:1, b:0),
% 0.69/1.10 finer [65, 3] (w:1, o:103, a:1, s:1, b:0),
% 0.69/1.10 basis [66, 2] (w:1, o:95, a:1, s:1, b:0),
% 0.69/1.10 f6 [69, 5] (w:1, o:121, a:1, s:1, b:0),
% 0.69/1.10 'subset_sets' [70, 2] (w:1, o:84, a:1, s:1, b:0),
% 0.69/1.10 f7 [71, 2] (w:1, o:96, a:1, s:1, b:0),
% 0.69/1.10 f8 [72, 2] (w:1, o:97, a:1, s:1, b:0),
% 0.69/1.10 f9 [73, 2] (w:1, o:98, a:1, s:1, b:0),
% 0.69/1.10 'top_of_basis' [75, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.69/1.10 f10 [76, 3] (w:1, o:104, a:1, s:1, b:0),
% 0.69/1.10 f11 [77, 2] (w:1, o:79, a:1, s:1, b:0),
% 0.69/1.10 'subspace_topology' [79, 3] (w:1, o:105, a:1, s:1, b:0),
% 0.69/1.10 f12 [80, 4] (w:1, o:112, a:1, s:1, b:0),
% 0.69/1.10 interior [82, 3] (w:1, o:106, a:1, s:1, b:0),
% 0.69/1.10 f13 [83, 4] (w:1, o:113, a:1, s:1, b:0),
% 0.69/1.10 closure [85, 3] (w:1, o:107, a:1, s:1, b:0),
% 0.69/1.10 f14 [87, 4] (w:1, o:114, a:1, s:1, b:0),
% 0.69/1.10 neighborhood [88, 4] (w:1, o:115, a:1, s:1, b:0),
% 0.69/1.10 'limit_point' [89, 4] (w:1, o:116, a:1, s:1, b:0),
% 0.69/1.10 f15 [90, 5] (w:1, o:122, a:1, s:1, b:0),
% 0.69/1.10 'eq_p' [91, 2] (w:1, o:77, a:1, s:1, b:0),
% 0.69/1.10 f16 [92, 4] (w:1, o:117, a:1, s:1, b:0),
% 0.69/1.10 boundary [94, 3] (w:1, o:101, a:1, s:1, b:0),
% 0.69/1.10 hausdorff [95, 2] (w:1, o:86, a:1, s:1, b:0),
% 0.69/1.10 f17 [98, 4] (w:1, o:118, a:1, s:1, b:0),
% 0.69/1.10 f18 [99, 4] (w:1, o:119, a:1, s:1, b:0),
% 0.69/1.10 'disjoint_s' [100, 2] (w:1, o:73, a:1, s:1, b:0),
% 0.69/1.10 f19 [101, 2] (w:1, o:80, a:1, s:1, b:0),
% 0.69/1.10 f20 [102, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.69/1.10 separation [107, 4] (w:1, o:120, a:1, s:1, b:0),
% 0.69/1.10 'union_of_sets' [108, 2] (w:1, o:99, a:1, s:1, b:0),
% 0.69/1.10 'connected_space' [109, 2] (w:1, o:72, a:1, s:1, b:0),
% 0.69/1.10 f21 [110, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.69/1.10 f22 [111, 2] (w:1, o:90, a:1, s:1, b:0),
% 0.69/1.10 'connected_set' [112, 3] (w:1, o:109, a:1, s:1, b:0),
% 0.69/1.10 'open_covering' [113, 3] (w:1, o:110, a:1, s:1, b:0),
% 0.69/1.10 'compact_space' [114, 2] (w:1, o:71, a:1, s:1, b:0),
% 0.69/1.10 f23 [116, 3] (w:1, o:111, a:1, s:1, b:0),
% 0.69/1.10 finite [117, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.69/1.10 f24 [118, 2] (w:1, o:91, a:1, s:1, b:0),
% 0.69/1.10 'compact_set' [120, 3] (w:1, o:108, a:1, s:1, b:0),
% 0.69/1.10 cx [121, 0] (w:1, o:35, a:1, s:1, b:0),
% 0.69/1.10 f [122, 0] (w:1, o:36, a:1, s:1, b:0).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 Starting Search:
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 Bliksems!, er is een bewijs:
% 0.69/1.10 % SZS status Unsatisfiable
% 0.69/1.10 % SZS output start Refutation
% 0.69/1.10
% 0.69/1.10 clause( 110, [ 'element_of_collection'( X, 'top_of_basis'( f ) ) ] )
% 0.69/1.10 .
% 0.69/1.10 clause( 111, [] )
% 0.69/1.10 .
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 % SZS output end Refutation
% 0.69/1.10 found a proof!
% 0.69/1.10
% 0.69/1.10 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.69/1.10
% 0.69/1.10 initialclauses(
% 0.69/1.10 [ clause( 113, [ ~( 'element_of_set'( X, 'union_of_members'( Y ) ) ),
% 0.69/1.10 'element_of_set'( X, f1( Y, X ) ) ] )
% 0.69/1.10 , clause( 114, [ ~( 'element_of_set'( X, 'union_of_members'( Y ) ) ),
% 0.69/1.10 'element_of_collection'( f1( Y, X ), Y ) ] )
% 0.69/1.10 , clause( 115, [ 'element_of_set'( X, 'union_of_members'( Y ) ), ~(
% 0.69/1.10 'element_of_set'( X, Z ) ), ~( 'element_of_collection'( Z, Y ) ) ] )
% 0.69/1.10 , clause( 116, [ ~( 'element_of_set'( X, 'intersection_of_members'( Y ) ) )
% 0.69/1.10 , ~( 'element_of_collection'( Z, Y ) ), 'element_of_set'( X, Z ) ] )
% 0.69/1.10 , clause( 117, [ 'element_of_set'( X, 'intersection_of_members'( Y ) ),
% 0.69/1.10 'element_of_collection'( f2( Y, X ), Y ) ] )
% 0.69/1.10 , clause( 118, [ 'element_of_set'( X, 'intersection_of_members'( Y ) ), ~(
% 0.69/1.10 'element_of_set'( X, f2( Y, X ) ) ) ] )
% 0.69/1.10 , clause( 119, [ ~( 'topological_space'( X, Y ) ), 'equal_sets'(
% 0.69/1.10 'union_of_members'( Y ), X ) ] )
% 0.69/1.10 , clause( 120, [ ~( 'topological_space'( X, Y ) ), 'element_of_collection'(
% 0.69/1.10 'empty_set', Y ) ] )
% 0.69/1.10 , clause( 121, [ ~( 'topological_space'( X, Y ) ), 'element_of_collection'(
% 0.69/1.10 X, Y ) ] )
% 0.69/1.10 , clause( 122, [ ~( 'topological_space'( X, Y ) ), ~(
% 0.69/1.10 'element_of_collection'( Z, Y ) ), ~( 'element_of_collection'( T, Y ) ),
% 0.69/1.10 'element_of_collection'( 'intersection_of_sets'( Z, T ), Y ) ] )
% 0.69/1.10 , clause( 123, [ ~( 'topological_space'( X, Y ) ), ~( 'subset_collections'(
% 0.69/1.10 Z, Y ) ), 'element_of_collection'( 'union_of_members'( Z ), Y ) ] )
% 0.69/1.10 , clause( 124, [ 'topological_space'( X, Y ), ~( 'equal_sets'(
% 0.69/1.10 'union_of_members'( Y ), X ) ), ~( 'element_of_collection'( 'empty_set',
% 0.69/1.10 Y ) ), ~( 'element_of_collection'( X, Y ) ), 'element_of_collection'( f3(
% 0.69/1.10 X, Y ), Y ), 'subset_collections'( f5( X, Y ), Y ) ] )
% 0.69/1.10 , clause( 125, [ 'topological_space'( X, Y ), ~( 'equal_sets'(
% 0.69/1.10 'union_of_members'( Y ), X ) ), ~( 'element_of_collection'( 'empty_set',
% 0.69/1.10 Y ) ), ~( 'element_of_collection'( X, Y ) ), 'element_of_collection'( f3(
% 0.69/1.10 X, Y ), Y ), ~( 'element_of_collection'( 'union_of_members'( f5( X, Y ) )
% 0.69/1.10 , Y ) ) ] )
% 0.69/1.10 , clause( 126, [ 'topological_space'( X, Y ), ~( 'equal_sets'(
% 0.69/1.10 'union_of_members'( Y ), X ) ), ~( 'element_of_collection'( 'empty_set',
% 0.69/1.10 Y ) ), ~( 'element_of_collection'( X, Y ) ), 'element_of_collection'( f4(
% 0.69/1.10 X, Y ), Y ), 'subset_collections'( f5( X, Y ), Y ) ] )
% 0.69/1.10 , clause( 127, [ 'topological_space'( X, Y ), ~( 'equal_sets'(
% 0.69/1.10 'union_of_members'( Y ), X ) ), ~( 'element_of_collection'( 'empty_set',
% 0.69/1.10 Y ) ), ~( 'element_of_collection'( X, Y ) ), 'element_of_collection'( f4(
% 0.69/1.10 X, Y ), Y ), ~( 'element_of_collection'( 'union_of_members'( f5( X, Y ) )
% 0.69/1.10 , Y ) ) ] )
% 0.69/1.10 , clause( 128, [ 'topological_space'( X, Y ), ~( 'equal_sets'(
% 0.69/1.10 'union_of_members'( Y ), X ) ), ~( 'element_of_collection'( 'empty_set',
% 0.69/1.10 Y ) ), ~( 'element_of_collection'( X, Y ) ), ~( 'element_of_collection'(
% 0.69/1.10 'intersection_of_sets'( f3( X, Y ), f4( X, Y ) ), Y ) ),
% 0.69/1.10 'subset_collections'( f5( X, Y ), Y ) ] )
% 0.69/1.10 , clause( 129, [ 'topological_space'( X, Y ), ~( 'equal_sets'(
% 0.69/1.10 'union_of_members'( Y ), X ) ), ~( 'element_of_collection'( 'empty_set',
% 0.69/1.10 Y ) ), ~( 'element_of_collection'( X, Y ) ), ~( 'element_of_collection'(
% 0.69/1.10 'intersection_of_sets'( f3( X, Y ), f4( X, Y ) ), Y ) ), ~(
% 0.69/1.10 'element_of_collection'( 'union_of_members'( f5( X, Y ) ), Y ) ) ] )
% 0.69/1.10 , clause( 130, [ ~( open( X, Y, Z ) ), 'topological_space'( Y, Z ) ] )
% 0.69/1.10 , clause( 131, [ ~( open( X, Y, Z ) ), 'element_of_collection'( X, Z ) ] )
% 0.69/1.10 , clause( 132, [ open( X, Y, Z ), ~( 'topological_space'( Y, Z ) ), ~(
% 0.69/1.10 'element_of_collection'( X, Z ) ) ] )
% 0.69/1.10 , clause( 133, [ ~( closed( X, Y, Z ) ), 'topological_space'( Y, Z ) ] )
% 0.69/1.10 , clause( 134, [ ~( closed( X, Y, Z ) ), open( 'relative_complement_sets'(
% 0.69/1.10 X, Y ), Y, Z ) ] )
% 0.69/1.10 , clause( 135, [ closed( X, Y, Z ), ~( 'topological_space'( Y, Z ) ), ~(
% 0.69/1.10 open( 'relative_complement_sets'( X, Y ), Y, Z ) ) ] )
% 0.69/1.10 , clause( 136, [ ~( finer( X, Y, Z ) ), 'topological_space'( Z, X ) ] )
% 0.69/1.10 , clause( 137, [ ~( finer( X, Y, Z ) ), 'topological_space'( Z, Y ) ] )
% 0.69/1.10 , clause( 138, [ ~( finer( X, Y, Z ) ), 'subset_collections'( Y, X ) ] )
% 0.69/1.10 , clause( 139, [ finer( X, Y, Z ), ~( 'topological_space'( Z, X ) ), ~(
% 0.69/1.10 'topological_space'( Z, Y ) ), ~( 'subset_collections'( Y, X ) ) ] )
% 0.69/1.10 , clause( 140, [ ~( basis( X, Y ) ), 'equal_sets'( 'union_of_members'( Y )
% 0.69/1.10 , X ) ] )
% 0.69/1.10 , clause( 141, [ ~( basis( X, Y ) ), ~( 'element_of_set'( Z, X ) ), ~(
% 0.69/1.10 'element_of_collection'( T, Y ) ), ~( 'element_of_collection'( U, Y ) ),
% 0.69/1.10 ~( 'element_of_set'( Z, 'intersection_of_sets'( T, U ) ) ),
% 0.69/1.10 'element_of_set'( Z, f6( X, Y, Z, T, U ) ) ] )
% 0.69/1.10 , clause( 142, [ ~( basis( X, Y ) ), ~( 'element_of_set'( Z, X ) ), ~(
% 0.69/1.10 'element_of_collection'( T, Y ) ), ~( 'element_of_collection'( U, Y ) ),
% 0.69/1.10 ~( 'element_of_set'( Z, 'intersection_of_sets'( T, U ) ) ),
% 0.69/1.10 'element_of_collection'( f6( X, Y, Z, T, U ), Y ) ] )
% 0.69/1.10 , clause( 143, [ ~( basis( X, Y ) ), ~( 'element_of_set'( Z, X ) ), ~(
% 0.69/1.10 'element_of_collection'( T, Y ) ), ~( 'element_of_collection'( U, Y ) ),
% 0.69/1.10 ~( 'element_of_set'( Z, 'intersection_of_sets'( T, U ) ) ), 'subset_sets'(
% 0.69/1.10 f6( X, Y, Z, T, U ), 'intersection_of_sets'( T, U ) ) ] )
% 0.69/1.10 , clause( 144, [ basis( X, Y ), ~( 'equal_sets'( 'union_of_members'( Y ), X
% 0.69/1.10 ) ), 'element_of_set'( f7( X, Y ), X ) ] )
% 0.69/1.10 , clause( 145, [ basis( X, Y ), ~( 'equal_sets'( 'union_of_members'( Y ), X
% 0.69/1.10 ) ), 'element_of_collection'( f8( X, Y ), Y ) ] )
% 0.69/1.10 , clause( 146, [ basis( X, Y ), ~( 'equal_sets'( 'union_of_members'( Y ), X
% 0.69/1.10 ) ), 'element_of_collection'( f9( X, Y ), Y ) ] )
% 0.69/1.10 , clause( 147, [ basis( X, Y ), ~( 'equal_sets'( 'union_of_members'( Y ), X
% 0.69/1.10 ) ), 'element_of_set'( f7( X, Y ), 'intersection_of_sets'( f8( X, Y ),
% 0.69/1.10 f9( X, Y ) ) ) ] )
% 0.69/1.10 , clause( 148, [ basis( X, Y ), ~( 'equal_sets'( 'union_of_members'( Y ), X
% 0.69/1.10 ) ), ~( 'element_of_set'( f7( X, Y ), Z ) ), ~( 'element_of_collection'(
% 0.69/1.10 Z, Y ) ), ~( 'subset_sets'( Z, 'intersection_of_sets'( f8( X, Y ), f9( X
% 0.69/1.10 , Y ) ) ) ) ] )
% 0.69/1.10 , clause( 149, [ ~( 'element_of_collection'( X, 'top_of_basis'( Y ) ) ),
% 0.69/1.10 ~( 'element_of_set'( Z, X ) ), 'element_of_set'( Z, f10( Y, X, Z ) ) ] )
% 0.69/1.10 , clause( 150, [ ~( 'element_of_collection'( X, 'top_of_basis'( Y ) ) ),
% 0.69/1.10 ~( 'element_of_set'( Z, X ) ), 'element_of_collection'( f10( Y, X, Z ), Y
% 0.69/1.10 ) ] )
% 0.69/1.10 , clause( 151, [ ~( 'element_of_collection'( X, 'top_of_basis'( Y ) ) ),
% 0.69/1.10 ~( 'element_of_set'( Z, X ) ), 'subset_sets'( f10( Y, X, Z ), X ) ] )
% 0.69/1.10 , clause( 152, [ 'element_of_collection'( X, 'top_of_basis'( Y ) ),
% 0.69/1.10 'element_of_set'( f11( Y, X ), X ) ] )
% 0.69/1.10 , clause( 153, [ 'element_of_collection'( X, 'top_of_basis'( Y ) ), ~(
% 0.69/1.10 'element_of_set'( f11( Y, X ), Z ) ), ~( 'element_of_collection'( Z, Y )
% 0.69/1.10 ), ~( 'subset_sets'( Z, X ) ) ] )
% 0.69/1.10 , clause( 154, [ ~( 'element_of_collection'( X, 'subspace_topology'( Y, Z,
% 0.69/1.10 T ) ) ), 'topological_space'( Y, Z ) ] )
% 0.69/1.10 , clause( 155, [ ~( 'element_of_collection'( X, 'subspace_topology'( Y, Z,
% 0.69/1.10 T ) ) ), 'subset_sets'( T, Y ) ] )
% 0.69/1.10 , clause( 156, [ ~( 'element_of_collection'( X, 'subspace_topology'( Y, Z,
% 0.69/1.10 T ) ) ), 'element_of_collection'( f12( Y, Z, T, X ), Z ) ] )
% 0.69/1.10 , clause( 157, [ ~( 'element_of_collection'( X, 'subspace_topology'( Y, Z,
% 0.69/1.10 T ) ) ), 'equal_sets'( X, 'intersection_of_sets'( T, f12( Y, Z, T, X ) )
% 0.69/1.10 ) ] )
% 0.69/1.10 , clause( 158, [ 'element_of_collection'( X, 'subspace_topology'( Y, Z, T )
% 0.69/1.10 ), ~( 'topological_space'( Y, Z ) ), ~( 'subset_sets'( T, Y ) ), ~(
% 0.69/1.10 'element_of_collection'( U, Z ) ), ~( 'equal_sets'( X,
% 0.69/1.10 'intersection_of_sets'( T, U ) ) ) ] )
% 0.69/1.10 , clause( 159, [ ~( 'element_of_set'( X, interior( Y, Z, T ) ) ),
% 0.69/1.10 'topological_space'( Z, T ) ] )
% 0.69/1.10 , clause( 160, [ ~( 'element_of_set'( X, interior( Y, Z, T ) ) ),
% 0.69/1.10 'subset_sets'( Y, Z ) ] )
% 0.69/1.10 , clause( 161, [ ~( 'element_of_set'( X, interior( Y, Z, T ) ) ),
% 0.69/1.10 'element_of_set'( X, f13( Y, Z, T, X ) ) ] )
% 0.69/1.10 , clause( 162, [ ~( 'element_of_set'( X, interior( Y, Z, T ) ) ),
% 0.69/1.10 'subset_sets'( f13( Y, Z, T, X ), Y ) ] )
% 0.69/1.10 , clause( 163, [ ~( 'element_of_set'( X, interior( Y, Z, T ) ) ), open( f13(
% 0.69/1.10 Y, Z, T, X ), Z, T ) ] )
% 0.69/1.10 , clause( 164, [ 'element_of_set'( X, interior( Y, Z, T ) ), ~(
% 0.69/1.10 'topological_space'( Z, T ) ), ~( 'subset_sets'( Y, Z ) ), ~(
% 0.69/1.10 'element_of_set'( X, U ) ), ~( 'subset_sets'( U, Y ) ), ~( open( U, Z, T
% 0.69/1.10 ) ) ] )
% 0.69/1.10 , clause( 165, [ ~( 'element_of_set'( X, closure( Y, Z, T ) ) ),
% 0.69/1.10 'topological_space'( Z, T ) ] )
% 0.69/1.10 , clause( 166, [ ~( 'element_of_set'( X, closure( Y, Z, T ) ) ),
% 0.69/1.10 'subset_sets'( Y, Z ) ] )
% 0.69/1.10 , clause( 167, [ ~( 'element_of_set'( X, closure( Y, Z, T ) ) ), ~(
% 0.69/1.10 'subset_sets'( Y, U ) ), ~( closed( U, Z, T ) ), 'element_of_set'( X, U )
% 0.69/1.10 ] )
% 0.69/1.10 , clause( 168, [ 'element_of_set'( X, closure( Y, Z, T ) ), ~(
% 0.69/1.10 'topological_space'( Z, T ) ), ~( 'subset_sets'( Y, Z ) ), 'subset_sets'(
% 0.69/1.10 Y, f14( Y, Z, T, X ) ) ] )
% 0.69/1.10 , clause( 169, [ 'element_of_set'( X, closure( Y, Z, T ) ), ~(
% 0.69/1.10 'topological_space'( Z, T ) ), ~( 'subset_sets'( Y, Z ) ), closed( f14( Y
% 0.69/1.10 , Z, T, X ), Z, T ) ] )
% 0.69/1.10 , clause( 170, [ 'element_of_set'( X, closure( Y, Z, T ) ), ~(
% 0.69/1.10 'topological_space'( Z, T ) ), ~( 'subset_sets'( Y, Z ) ), ~(
% 0.69/1.10 'element_of_set'( X, f14( Y, Z, T, X ) ) ) ] )
% 0.69/1.10 , clause( 171, [ ~( neighborhood( X, Y, Z, T ) ), 'topological_space'( Z, T
% 0.69/1.10 ) ] )
% 0.69/1.10 , clause( 172, [ ~( neighborhood( X, Y, Z, T ) ), open( X, Z, T ) ] )
% 0.69/1.10 , clause( 173, [ ~( neighborhood( X, Y, Z, T ) ), 'element_of_set'( Y, X )
% 0.69/1.10 ] )
% 0.69/1.10 , clause( 174, [ neighborhood( X, Y, Z, T ), ~( 'topological_space'( Z, T )
% 0.69/1.10 ), ~( open( X, Z, T ) ), ~( 'element_of_set'( Y, X ) ) ] )
% 0.69/1.10 , clause( 175, [ ~( 'limit_point'( X, Y, Z, T ) ), 'topological_space'( Z,
% 0.69/1.10 T ) ] )
% 0.69/1.10 , clause( 176, [ ~( 'limit_point'( X, Y, Z, T ) ), 'subset_sets'( Y, Z ) ]
% 0.69/1.10 )
% 0.69/1.10 , clause( 177, [ ~( 'limit_point'( X, Y, Z, T ) ), ~( neighborhood( U, X, Z
% 0.69/1.10 , T ) ), 'element_of_set'( f15( X, Y, Z, T, U ), 'intersection_of_sets'(
% 0.69/1.10 U, Y ) ) ] )
% 0.69/1.10 , clause( 178, [ ~( 'limit_point'( X, Y, Z, T ) ), ~( neighborhood( U, X, Z
% 0.69/1.10 , T ) ), ~( 'eq_p'( f15( X, Y, Z, T, U ), X ) ) ] )
% 0.69/1.10 , clause( 179, [ 'limit_point'( X, Y, Z, T ), ~( 'topological_space'( Z, T
% 0.69/1.10 ) ), ~( 'subset_sets'( Y, Z ) ), neighborhood( f16( X, Y, Z, T ), X, Z,
% 0.69/1.10 T ) ] )
% 0.69/1.10 , clause( 180, [ 'limit_point'( X, Y, Z, T ), ~( 'topological_space'( Z, T
% 0.69/1.10 ) ), ~( 'subset_sets'( Y, Z ) ), ~( 'element_of_set'( U,
% 0.69/1.10 'intersection_of_sets'( f16( X, Y, Z, T ), Y ) ) ), 'eq_p'( U, X ) ] )
% 0.69/1.10 , clause( 181, [ ~( 'element_of_set'( X, boundary( Y, Z, T ) ) ),
% 0.69/1.10 'topological_space'( Z, T ) ] )
% 0.69/1.10 , clause( 182, [ ~( 'element_of_set'( X, boundary( Y, Z, T ) ) ),
% 0.69/1.10 'element_of_set'( X, closure( Y, Z, T ) ) ] )
% 0.69/1.10 , clause( 183, [ ~( 'element_of_set'( X, boundary( Y, Z, T ) ) ),
% 0.69/1.10 'element_of_set'( X, closure( 'relative_complement_sets'( Y, Z ), Z, T )
% 0.69/1.10 ) ] )
% 0.69/1.10 , clause( 184, [ 'element_of_set'( X, boundary( Y, Z, T ) ), ~(
% 0.69/1.10 'topological_space'( Z, T ) ), ~( 'element_of_set'( X, closure( Y, Z, T )
% 0.69/1.10 ) ), ~( 'element_of_set'( X, closure( 'relative_complement_sets'( Y, Z )
% 0.69/1.10 , Z, T ) ) ) ] )
% 0.69/1.10 , clause( 185, [ ~( hausdorff( X, Y ) ), 'topological_space'( X, Y ) ] )
% 0.69/1.10 , clause( 186, [ ~( hausdorff( X, Y ) ), ~( 'element_of_set'( Z, X ) ), ~(
% 0.69/1.10 'element_of_set'( T, X ) ), 'eq_p'( Z, T ), neighborhood( f17( X, Y, Z, T
% 0.69/1.10 ), Z, X, Y ) ] )
% 0.69/1.10 , clause( 187, [ ~( hausdorff( X, Y ) ), ~( 'element_of_set'( Z, X ) ), ~(
% 0.69/1.10 'element_of_set'( T, X ) ), 'eq_p'( Z, T ), neighborhood( f18( X, Y, Z, T
% 0.69/1.10 ), T, X, Y ) ] )
% 0.69/1.10 , clause( 188, [ ~( hausdorff( X, Y ) ), ~( 'element_of_set'( Z, X ) ), ~(
% 0.69/1.10 'element_of_set'( T, X ) ), 'eq_p'( Z, T ), 'disjoint_s'( f17( X, Y, Z, T
% 0.69/1.10 ), f18( X, Y, Z, T ) ) ] )
% 0.69/1.10 , clause( 189, [ hausdorff( X, Y ), ~( 'topological_space'( X, Y ) ),
% 0.69/1.10 'element_of_set'( f19( X, Y ), X ) ] )
% 0.69/1.10 , clause( 190, [ hausdorff( X, Y ), ~( 'topological_space'( X, Y ) ),
% 0.69/1.10 'element_of_set'( f20( X, Y ), X ) ] )
% 0.69/1.10 , clause( 191, [ hausdorff( X, Y ), ~( 'topological_space'( X, Y ) ), ~(
% 0.69/1.10 'eq_p'( f19( X, Y ), f20( X, Y ) ) ) ] )
% 0.69/1.10 , clause( 192, [ hausdorff( X, Y ), ~( 'topological_space'( X, Y ) ), ~(
% 0.69/1.10 neighborhood( Z, f19( X, Y ), X, Y ) ), ~( neighborhood( T, f20( X, Y ),
% 0.69/1.10 X, Y ) ), ~( 'disjoint_s'( Z, T ) ) ] )
% 0.69/1.10 , clause( 193, [ ~( separation( X, Y, Z, T ) ), 'topological_space'( Z, T )
% 0.69/1.10 ] )
% 0.69/1.10 , clause( 194, [ ~( separation( X, Y, Z, T ) ), ~( 'equal_sets'( X,
% 0.69/1.10 'empty_set' ) ) ] )
% 0.69/1.10 , clause( 195, [ ~( separation( X, Y, Z, T ) ), ~( 'equal_sets'( Y,
% 0.69/1.10 'empty_set' ) ) ] )
% 0.69/1.10 , clause( 196, [ ~( separation( X, Y, Z, T ) ), 'element_of_collection'( X
% 0.69/1.10 , T ) ] )
% 0.69/1.10 , clause( 197, [ ~( separation( X, Y, Z, T ) ), 'element_of_collection'( Y
% 0.69/1.10 , T ) ] )
% 0.69/1.10 , clause( 198, [ ~( separation( X, Y, Z, T ) ), 'equal_sets'(
% 0.69/1.10 'union_of_sets'( X, Y ), Z ) ] )
% 0.69/1.10 , clause( 199, [ ~( separation( X, Y, Z, T ) ), 'disjoint_s'( X, Y ) ] )
% 0.69/1.10 , clause( 200, [ separation( X, Y, Z, T ), ~( 'topological_space'( Z, T ) )
% 0.69/1.10 , 'equal_sets'( X, 'empty_set' ), 'equal_sets'( Y, 'empty_set' ), ~(
% 0.69/1.10 'element_of_collection'( X, T ) ), ~( 'element_of_collection'( Y, T ) ),
% 0.69/1.10 ~( 'equal_sets'( 'union_of_sets'( X, Y ), Z ) ), ~( 'disjoint_s'( X, Y )
% 0.69/1.10 ) ] )
% 0.69/1.10 , clause( 201, [ ~( 'connected_space'( X, Y ) ), 'topological_space'( X, Y
% 0.69/1.10 ) ] )
% 0.69/1.10 , clause( 202, [ ~( 'connected_space'( X, Y ) ), ~( separation( Z, T, X, Y
% 0.69/1.10 ) ) ] )
% 0.69/1.10 , clause( 203, [ 'connected_space'( X, Y ), ~( 'topological_space'( X, Y )
% 0.69/1.10 ), separation( f21( X, Y ), f22( X, Y ), X, Y ) ] )
% 0.69/1.10 , clause( 204, [ ~( 'connected_set'( X, Y, Z ) ), 'topological_space'( Y, Z
% 0.69/1.10 ) ] )
% 0.69/1.10 , clause( 205, [ ~( 'connected_set'( X, Y, Z ) ), 'subset_sets'( X, Y ) ]
% 0.69/1.10 )
% 0.69/1.10 , clause( 206, [ ~( 'connected_set'( X, Y, Z ) ), 'connected_space'( X,
% 0.69/1.10 'subspace_topology'( Y, Z, X ) ) ] )
% 0.69/1.10 , clause( 207, [ 'connected_set'( X, Y, Z ), ~( 'topological_space'( Y, Z )
% 0.69/1.10 ), ~( 'subset_sets'( X, Y ) ), ~( 'connected_space'( X,
% 0.69/1.10 'subspace_topology'( Y, Z, X ) ) ) ] )
% 0.69/1.10 , clause( 208, [ ~( 'open_covering'( X, Y, Z ) ), 'topological_space'( Y, Z
% 0.69/1.10 ) ] )
% 0.69/1.10 , clause( 209, [ ~( 'open_covering'( X, Y, Z ) ), 'subset_collections'( X,
% 0.69/1.10 Z ) ] )
% 0.69/1.10 , clause( 210, [ ~( 'open_covering'( X, Y, Z ) ), 'equal_sets'(
% 0.69/1.10 'union_of_members'( X ), Y ) ] )
% 0.69/1.10 , clause( 211, [ 'open_covering'( X, Y, Z ), ~( 'topological_space'( Y, Z )
% 0.69/1.10 ), ~( 'subset_collections'( X, Z ) ), ~( 'equal_sets'(
% 0.69/1.10 'union_of_members'( X ), Y ) ) ] )
% 0.69/1.10 , clause( 212, [ ~( 'compact_space'( X, Y ) ), 'topological_space'( X, Y )
% 0.69/1.10 ] )
% 0.69/1.10 , clause( 213, [ ~( 'compact_space'( X, Y ) ), ~( 'open_covering'( Z, X, Y
% 0.69/1.10 ) ), finite( f23( X, Y, Z ) ) ] )
% 0.69/1.10 , clause( 214, [ ~( 'compact_space'( X, Y ) ), ~( 'open_covering'( Z, X, Y
% 0.69/1.10 ) ), 'subset_collections'( f23( X, Y, Z ), Z ) ] )
% 0.69/1.10 , clause( 215, [ ~( 'compact_space'( X, Y ) ), ~( 'open_covering'( Z, X, Y
% 0.69/1.10 ) ), 'open_covering'( f23( X, Y, Z ), X, Y ) ] )
% 0.69/1.10 , clause( 216, [ 'compact_space'( X, Y ), ~( 'topological_space'( X, Y ) )
% 0.69/1.10 , 'open_covering'( f24( X, Y ), X, Y ) ] )
% 0.69/1.10 , clause( 217, [ 'compact_space'( X, Y ), ~( 'topological_space'( X, Y ) )
% 0.69/1.10 , ~( finite( Z ) ), ~( 'subset_collections'( Z, f24( X, Y ) ) ), ~(
% 0.69/1.10 'open_covering'( Z, X, Y ) ) ] )
% 0.69/1.10 , clause( 218, [ ~( 'compact_set'( X, Y, Z ) ), 'topological_space'( Y, Z )
% 0.69/1.10 ] )
% 0.69/1.10 , clause( 219, [ ~( 'compact_set'( X, Y, Z ) ), 'subset_sets'( X, Y ) ] )
% 0.69/1.10 , clause( 220, [ ~( 'compact_set'( X, Y, Z ) ), 'compact_space'( X,
% 0.69/1.10 'subspace_topology'( Y, Z, X ) ) ] )
% 0.69/1.10 , clause( 221, [ 'compact_set'( X, Y, Z ), ~( 'topological_space'( Y, Z ) )
% 0.69/1.10 , ~( 'subset_sets'( X, Y ) ), ~( 'compact_space'( X, 'subspace_topology'(
% 0.69/1.10 Y, Z, X ) ) ) ] )
% 0.69/1.10 , clause( 222, [ basis( cx, f ) ] )
% 0.69/1.10 , clause( 223, [ 'element_of_collection'( X, 'top_of_basis'( f ) ) ] )
% 0.69/1.10 , clause( 224, [ 'element_of_collection'( X, 'top_of_basis'( f ) ) ] )
% 0.69/1.10 , clause( 225, [ ~( 'element_of_collection'( 'intersection_of_sets'( X, Y )
% 0.69/1.10 , 'top_of_basis'( f ) ) ) ] )
% 0.69/1.10 ] ).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 subsumption(
% 0.69/1.10 clause( 110, [ 'element_of_collection'( X, 'top_of_basis'( f ) ) ] )
% 0.69/1.10 , clause( 223, [ 'element_of_collection'( X, 'top_of_basis'( f ) ) ] )
% 0.69/1.10 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 resolution(
% 0.69/1.10 clause( 272, [] )
% 0.69/1.10 , clause( 225, [ ~( 'element_of_collection'( 'intersection_of_sets'( X, Y )
% 0.69/1.10 , 'top_of_basis'( f ) ) ) ] )
% 0.69/1.10 , 0, clause( 110, [ 'element_of_collection'( X, 'top_of_basis'( f ) ) ] )
% 0.69/1.10 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 0.69/1.10 , 'intersection_of_sets'( X, Y ) )] )).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 subsumption(
% 0.69/1.10 clause( 111, [] )
% 0.69/1.10 , clause( 272, [] )
% 0.69/1.10 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 end.
% 0.69/1.10
% 0.69/1.10 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.69/1.10
% 0.69/1.10 Memory use:
% 0.69/1.10
% 0.69/1.10 space for terms: 5855
% 0.69/1.10 space for clauses: 7162
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 clauses generated: 113
% 0.69/1.10 clauses kept: 112
% 0.69/1.10 clauses selected: 0
% 0.69/1.10 clauses deleted: 0
% 0.69/1.10 clauses inuse deleted: 0
% 0.69/1.10
% 0.69/1.10 subsentry: 29
% 0.69/1.10 literals s-matched: 20
% 0.69/1.10 literals matched: 19
% 0.69/1.10 full subsumption: 0
% 0.69/1.10
% 0.69/1.10 checksum: 2098479643
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 Bliksem ended
%------------------------------------------------------------------------------