TSTP Solution File: TOP007-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : TOP007-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n025.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  : 600s
% DateTime : Thu Jul 21 21:33:50 EDT 2022

% Result   : Timeout 300.02s 300.33s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : TOP007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.33  % Computer : n025.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun May 29 08:19:11 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.44/1.02  ============================== Prover9 ===============================
% 0.44/1.02  Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.02  Process 16465 was started by sandbox on n025.cluster.edu,
% 0.44/1.02  Sun May 29 08:19:12 2022
% 0.44/1.02  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16310_n025.cluster.edu".
% 0.44/1.02  ============================== end of head ===========================
% 0.44/1.02  
% 0.44/1.02  ============================== INPUT =================================
% 0.44/1.02  
% 0.44/1.02  % Reading from file /tmp/Prover9_16310_n025.cluster.edu
% 0.44/1.02  
% 0.44/1.02  set(prolog_style_variables).
% 0.44/1.02  set(auto2).
% 0.44/1.02      % set(auto2) -> set(auto).
% 0.44/1.02      % set(auto) -> set(auto_inference).
% 0.44/1.02      % set(auto) -> set(auto_setup).
% 0.44/1.02      % set(auto_setup) -> set(predicate_elim).
% 0.44/1.02      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.02      % set(auto) -> set(auto_limits).
% 0.44/1.02      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.02      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.02      % set(auto) -> set(auto_denials).
% 0.44/1.02      % set(auto) -> set(auto_process).
% 0.44/1.02      % set(auto2) -> assign(new_constants, 1).
% 0.44/1.02      % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.02      % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.02      % set(auto2) -> assign(max_hours, 1).
% 0.44/1.02      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.02      % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.02      % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.02      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.02      % set(auto2) -> set(sort_initial_sos).
% 0.44/1.02      % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.02      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.02      % set(auto2) -> assign(max_megs, 400).
% 0.44/1.02      % set(auto2) -> assign(stats, some).
% 0.44/1.02      % set(auto2) -> clear(echo_input).
% 0.44/1.02      % set(auto2) -> set(quiet).
% 0.44/1.02      % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.02      % set(auto2) -> clear(print_given).
% 0.44/1.02  assign(lrs_ticks,-1).
% 0.44/1.02  assign(sos_limit,10000).
% 0.44/1.02  assign(order,kbo).
% 0.44/1.02  set(lex_order_vars).
% 0.44/1.02  clear(print_given).
% 0.44/1.02  
% 0.44/1.02  % formulas(sos).  % not echoed (114 formulas)
% 0.44/1.02  
% 0.44/1.02  ============================== end of input ==========================
% 0.44/1.02  
% 0.44/1.02  % From the command line: assign(max_seconds, 300).
% 0.44/1.02  
% 0.44/1.02  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.02  
% 0.44/1.02  % Formulas that are not ordinary clauses:
% 0.44/1.02  
% 0.44/1.02  ============================== end of process non-clausal formulas ===
% 0.44/1.02  
% 0.44/1.02  ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.02  
% 0.44/1.02  ============================== PREDICATE ELIMINATION =================
% 0.44/1.02  1 topological_space(A,B) | -equal_sets(union_of_members(B),A) | -element_of_collection(empty_set,B) | -element_of_collection(A,B) | element_of_collection(f3(A,B),B) | subset_collections(f5(A,B),B) # label(topological_space_12) # label(axiom).  [assumption].
% 0.44/1.02  2 -topological_space(A,B) | -subset_collections(C,B) | element_of_collection(union_of_members(C),B) # label(topological_space_11) # label(axiom).  [assumption].
% 0.44/1.02  Derived: topological_space(A,B) | -equal_sets(union_of_members(B),A) | -element_of_collection(empty_set,B) | -element_of_collection(A,B) | element_of_collection(f3(A,B),B) | -topological_space(C,B) | element_of_collection(union_of_members(f5(A,B)),B).  [resolve(1,f,2,b)].
% 0.44/1.02  3 topological_space(A,B) | -equal_sets(union_of_members(B),A) | -element_of_collection(empty_set,B) | -element_of_collection(A,B) | element_of_collection(f4(A,B),B) | subset_collections(f5(A,B),B) # label(topological_space_14) # label(axiom).  [assumption].
% 0.44/1.02  Derived: topological_space(A,B) | -equal_sets(union_of_members(B),A) | -element_of_collection(empty_set,B) | -element_of_collection(A,B) | element_of_collection(f4(A,B),B) | -topological_space(C,B) | element_of_collection(union_of_members(f5(A,B)),B).  [resolve(3,f,2,b)].
% 0.44/1.02  4 topological_space(A,B) | -equal_sets(union_of_members(B),A) | -element_of_collection(empty_set,B) | -element_of_collection(A,B) | -element_of_collection(intersection_of_sets(f3(A,B),f4(A,B)),B) | subset_collections(f5(A,B),B) # label(topological_space_16) # label(axiom).  [assumption].
% 0.44/1.02  Derived: topological_space(A,B) | -equal_sets(union_of_members(B),A) | -element_of_collection(empty_set,B) | -element_of_collection(A,B) | -element_of_collection(intersection_of_sets(f3(A,B),f4(A,B)),B) | -topological_space(C,B) | element_of_collection(union_of_members(f5(A,B)),B).  [resolve(4,f,2,b)].
% 0.44/1.02  5 -finer(A,B,C) | subset_collections(B,A) # label(finer_topology_26) # label(axiom).  [assumption].
% 0.44/1.02  Derived: -finer(A,B,C) | -topological_space(D,A) | element_of_collection(union_of_members(B),A).  [resolve(5,b,2,b)].
% 0.44/1.02  6 finer(A,B,C) | -topological_space(C,A) | -topological_space(C,B) | -subset_collections(B,A) # label(finer_topology_27) # label(axiom).  [assumption].
% 0.44/1.02  Derived: finer(A,f5(B,A),C) | -topological_space(C,A) | -topological_space(C,f5(B,A)) | topological_space(B,A) | -equal_sets(union_of_members(A),B) | -element_of_collection(empty_set,A) | -element_of_collection(B,A) | element_of_collection(f3(B,A),A).  [resolve(6,d,1,f)].
% 0.44/1.02  Derived: finer(A,f5(B,A),C) | -topological_space(C,A) | -topological_space(C,f5(B,A)) | topological_space(B,A) | -equal_sets(union_of_members(A),B) | -element_of_collection(empty_set,A) | -element_of_collection(B,A) | element_of_collection(f4(B,A),A).  [resolve(6,d,3,f)].
% 0.44/1.02  Derived: finer(A,f5(B,A),C) | -topological_space(C,A) | -topological_space(C,f5(B,A)) | topological_space(B,A) | -equal_sets(union_of_members(A),B) | -element_of_collection(empty_set,A) | -element_of_collection(B,A) | -element_of_collection(intersection_of_sets(f3(B,A),f4(B,A)),A).  [resolve(6,d,4,f)].
% 0.44/1.02  Derived: finer(A,B,C) | -topological_space(C,A) | -topological_space(C,B) | -finer(A,B,D).  [resolve(6,d,5,b)].
% 0.44/1.02  7 -open_covering(A,B,C) | subset_collections(A,C) # label(open_covering_97) # label(axiom).  [assumption].
% 0.44/1.02  Derived: -open_covering(A,B,C) | -topological_space(D,C) | element_of_collection(union_of_members(A),C).  [resolve(7,b,2,b)].
% 0.44/1.02  Derived: -open_covering(A,B,C) | finer(C,A,D) | -topological_space(D,C) | -topological_space(D,A).  [resolve(7,b,6,d)].
% 0.44/1.02  8 open_covering(A,B,C) | -topological_space(B,C) | -subset_collections(A,C) | -equal_sets(union_of_members(A),B) # label(open_covering_99) # label(axiom).  [assumption].
% 0.44/1.02  Derived: open_covering(f5(A,B),C,B) | -topological_space(C,B) | -equal_sets(union_of_members(f5(A,B)),C) | topological_space(A,B) | -equal_sets(union_of_members(B),A) | -element_of_collection(empty_set,B) | -element_of_collection(A,B) | element_of_collection(f3(A,B),B).  [resolve(8,c,1,f)].
% 0.44/1.02  Derived: open_covering(f5(A,B),C,B) | -topological_space(C,B) | -equal_sets(union_of_members(f5(A,B)),C) | topological_space(A,B) | -equal_sets(union_of_members(B),A) | -element_of_collection(empty_set,B) | -element_of_collection(A,B) | element_of_collection(f4(A,B),B).  [resolve(8,c,3,f)].
% 0.44/1.02  Derived: open_covering(f5(A,B),C,B) | -topological_space(C,B) | -equal_sets(union_of_members(f5(A,B)),C) | topological_space(A,B) | -equal_sets(union_of_members(B),A) | -element_of_collection(empty_set,B) | -element_of_collection(A,B) | -element_of_collection(intersection_of_sets(f3(A,B),f4(A,B)),B).  [resolve(8,c,4,f)].
% 0.44/1.02  Derived: open_covering(A,B,C) | -topological_space(B,C) | -equal_sets(union_of_members(A),B) | -finer(C,A,D).  [resolve(8,c,5,b)].
% 0.44/1.02  Derived: open_covering(A,B,C) | -topological_space(B,C) | -equal_sets(union_of_members(A),B) | -open_covering(A,D,C).  [resolve(8,c,7,b)].
% 0.44/1.02  9 -compact_space(A,B) | -open_covering(C,A,B) | subset_collections(f23(A,B,C),C) # label(compact_space_102) # label(axiom).  [assumption].
% 0.44/1.02  Derived: -compact_space(A,B) | -open_covering(C,A,B) | -topological_space(D,C) | element_of_collection(union_of_members(f23(A,B,C)),C).  [resolve(9,c,2,b)].
% 0.44/1.02  Derived: -compact_space(A,B) | -open_covering(C,A,B) | finer(C,f23(A,B,C),D) | -topological_space(D,C) | -topological_space(D,f23(A,B,C)).  [resolve(9,c,6,d)].
% 0.44/1.02  Derived: -compact_space(A,B) | -open_covering(C,A,B) | open_covering(f23(A,B,C),D,C) | -topological_space(D,C) | -equal_sets(union_of_members(f23(A,B,C)),D).  [resolve(9,c,8,c)].
% 0.44/1.02  10 compact_space(A,B) | -topological_space(A,B) | -finite(C) | -subset_collections(C,f24(A,B)) | -open_covering(C,A,B) # label(compact_space_105) # label(axiom).  [assumption].
% 0.44/1.02  Derived: compact_space(A,B) | -topological_space(A,B) | -finite(f5(C,f24(A,B))) | -open_covering(f5(C,f24(A,B)),A,B) | topological_space(C,f24(A,B)) | -equal_sets(union_of_members(f24(A,B)),C) | -element_of_collection(empty_set,f24(A,B)) | -element_of_collection(C,f24(A,B)) | element_of_collection(f3(C,f24(A,B)),f24(A,B)).  [resolve(10,d,1,f)].
% 0.44/1.02  Derived: compact_space(A,B) | -topological_space(A,B) | -finite(f5(C,f24(A,B))) | -open_covering(f5(C,f24(A,B)),A,B) | topological_space(C,f24(A,B)) | -equal_sets(union_of_members(f24(A,B)),C) | -element_of_collection(empty_set,f24(A,B)) | -element_of_collection(C,f24(A,B)) | element_of_collection(f4(C,f24(A,B)),f24(A,B)).  [resolve(10,d,3,f)].
% 0.44/1.02  Derived: compact_space(A,B) | -topological_space(A,B) | -finite(f5(C,f24(A,B))) | -open_covering(f5(C,f24(A,B)),A,B) | topological_space(C,f24(A,B)) | -equal_sets(union_of_members(f24(A,B)),C) | -element_of_collection(empty_set,f24(A,B)) | -element_of_collection(C,f24(A,B)) | -element_of_collection(intersection_of_sets(f3(C,f24(A,B)),f4(C,f24(A,B))),f24(A,B)).  [resolve(10,d,4,f)].
% 0.44/1.02  Derived: compact_space(A,B) | -topological_space(A,B) | -finite(C) | -open_covering(C,A,B) | -finer(f24(A,B),C,D).  [resolve(10,d,5,b)].
% 0.44/1.02  Derived: compact_space(A,B) | -topological_space(A,B) | -finite(C) | -open_covering(C,A,B) | -open_covering(C,D,f24(A,B)).  [resolve(10,d,7,b)].
% 0.44/1.02  Derived: compact_space(A,B) | -topological_space(A,B) | -finite(f23(C,D,f24(A,B))) | -open_covering(f23(C,D,f24(A,B)),A,B) | -compact_space(C,D) | -open_covering(f24(A,B),C,D).  [resolve(10,d,9,c)].
% 0.44/1.02  11 open(A,B,C) | -topological_space(B,C) | -element_of_collection(A,C) # label(open_set_20) # label(axiom).  [assumption].
% 0.44/1.02  12 -open(A,B,C) | topological_space(B,C) # label(open_set_18) # label(axiom).  [assumption].
% 0.44/1.02  13 -open(A,B,C) | element_of_collection(A,C) # label(open_set_19) # label(axiom).  [assumption].
% 0.44/1.02  14 -closed(A,B,C) | open(relative_complement_sets(A,B),B,C) # label(closed_set_22) # label(axiom).  [assumption].
% 0.44/1.02  Derived: -closed(A,B,C) | topological_space(B,C).  [resolve(14,b,12,a)].
% 0.44/1.02  Derived: -closed(A,B,C) | element_of_collection(relative_complement_sets(A,B),C).  [resolve(14,b,13,a)].
% 0.44/1.02  15 closed(A,B,C) | -topological_space(B,C) | -open(relative_complement_sets(A,B),B,C) # label(closed_set_23) # label(axiom).  [assumption].
% 0.44/1.02  Derived: closed(A,B,C) | -topological_space(B,C) | -topological_space(B,C) | -element_of_collection(relative_complement_sets(A,B),C).  [resolve(15,c,11,a)].
% 0.44/1.02  16 -element_of_set(A,interior(B,C,D)) | open(f13(B,C,D,A),C,D) # label(interior_51) # label(axiom).  [assumption].
% 0.44/1.02  Derived: -element_of_set(A,interior(B,C,D)) | topological_space(C,D).  [resolve(16,b,12,a)].
% 0.44/1.02  Derived: -element_of_set(A,interior(B,C,D)) | element_of_collection(f13(B,C,D,A),D).  [resolve(16,b,13,a)].
% 0.44/1.02  17 element_of_set(A,interior(B,C,D)) | -topological_space(C,D) | -subset_sets(B,C) | -element_of_set(A,E) | -subset_sets(E,B) | -open(E,C,D) # label(interior_52) # label(axiom).  [assumption].
% 0.44/1.02  Derived: element_of_set(A,interior(B,C,D)) | -topological_space(C,D) | -subset_sets(B,C) | -element_of_set(A,E) | -subset_sets(E,B) | -topological_space(C,D) | -element_of_collection(E,D).  [resolve(17,f,11,a)].
% 0.44/1.02  Derived: element_of_set(A,interior(B,C,D)) | -topological_space(C,D) | -subset_sets(B,C) | -element_of_set(A,relative_complement_sets(E,C)) | -subset_sets(relative_complement_sets(E,C),B) | -closed(E,C,D).  [resolve(17,f,14,b)].
% 0.44/1.02  Derived: element_of_set(A,interior(B,C,D)) | -topological_space(C,D) | -subset_sets(B,C) | -element_of_set(A,f13(E,C,D,F)) | -subset_sets(f13(E,C,D,F),B) | -element_of_set(F,interior(E,C,D)).  [resolve(17,f,16,b)].
% 0.44/1.02  18 -neighborhood(A,B,C,D) | open(A,C,D) # label(neighborhood_60) # label(axiom).  [assumption].
% 0.44/1.02  Derived: -neighborhood(A,B,C,D) | topological_space(C,D).  [resolve(18,b,12,a)].
% 0.44/1.02  Derived: -neighborhood(A,B,C,D) | element_of_collection(A,D).  [resolve(18,b,13,a)].
% 0.44/1.02  Derived: -neighborhood(relative_complement_sets(A,B),C,B,D) | closed(A,B,D) | -topological_space(B,D).  [resolve(18,b,15,c)].
% 0.44/1.02  Derived: -neighborhood(A,B,C,D) | element_of_set(E,interior(F,C,D)) | -topological_space(C,D) | -subset_sets(F,C) | -element_of_set(E,A) | -subset_sets(A,F).  [resolve(18,b,17,f)].
% 0.44/1.02  19 neighborhood(A,B,C,D) | -topological_space(C,D) | -open(A,C,D) | -element_of_set(B,A) # label(neighborhood_62) # label(axiom).  [assumption].
% 0.44/1.02  Derived: neighborhood(A,B,C,D) | -topological_space(C,D) | -element_of_set(B,A) | -topological_space(C,D) | -element_of_collection(A,D).  [resolve(19,c,11,a)].
% 0.44/1.02  Derived: neighborhood(relative_complement_sets(A,B),C,B,D) | -topological_space(B,D) | -element_of_set(C,relative_complement_sets(A,B)) | -closed(A,B,D).  [resolve(19,c,14,b)].
% 0.44/1.02  Derived: neighborhood(f13(A,B,C,D),E,B,C) | -topological_space(B,C) | -element_of_set(E,f13(A,B,C,D)) | -element_of_set(D,interior(A,B,C)).  [resolve(19,c,16,b)].
% 0.44/1.02  Derived: neighborhood(A,B,C,D) | -topological_space(C,D) | -element_of_set(B,A) | -neighborhood(A,E,C,D).  [resolve(19,c,18,b)].
% 0.44/1.02  20 -open(a,cx,ct) # label(problem_2_116) # label(negated_conjecture).  [assumption].
% 0.44/1.02  Derived: -topological_space(cx,ct) | -element_of_collection(a,ct).  [resolve(20,a,11,a)].
% 0.44/1.02  Derived: -neighborhood(a,A,cx,ct).  [resolve(20,a,18,b)].
% 0.44/1.02  21 element_of_set(A,closure(B,C,D)) | -topological_space(C,D) | -subset_sets(B,C) | closed(f14(B,C,D,A),C,D) # label(closure_57) # label(axiom).  [assumption].
% 0.44/1.02  22 -closed(A,B,C) | topological_space(B,C) # label(closed_set_21) # label(axiom).  [assumption].
% 0.44/1.02  23 -element_of_set(A,closure(B,C,D)) | -subset_sets(B,E) | -closed(E,C,D) | element_of_set(A,E) # label(closure_55) # label(axiom).  [assumption].
% 0.44/1.02  Derived: element_of_set(A,closure(B,C,D)) | -topological_space(C,D) | -subset_sets(B,C) | -element_of_set(E,closure(F,C,D)) | -subset_sets(F,f14(B,C,D,A)) | element_of_set(E,f14(B,C,D,A)).  [resolve(21,d,23,c)].
% 0.44/1.02  24 -closed(A,B,C) | topological_space(B,C).  [resolve(14,b,12,a)].
% 0.44/1.02  25 -closed(A,B,C) | element_of_collection(relative_complement_sets(A,B),C).  [resolve(14,b,13,a)].
% 0.44/1.02  Derived: element_of_collection(relative_complement_sets(f14(A,B,C,D),B),C) | element_of_set(D,closure(A,B,C)) | -topological_space(B,C) | -subset_sets(A,B).  [resolve(25,a,21,d)].
% 0.44/1.02  26 closed(A,B,C) | -topological_space(B,C) | -topological_space(B,C) | -element_of_collection(relative_complement_sets(A,B),C).  [resolve(15,c,11,a)].
% 0.44/1.02  Derived: -topological_space(A,B) | -topological_space(A,B) | -element_of_collection(relative_complement_sets(C,A),B) | -element_of_set(D,closure(E,A,B)) | -subset_sets(E,C) | element_of_set(D,C).  [resolve(26,a,23,c)].
% 0.44/1.02  27 element_of_set(A,interior(B,C,D)) | -topological_space(C,D) | -subset_sets(B,C) | -element_of_set(A,relative_complement_sets(E,C)) | -subset_sets(relative_complement_sets(E,C),B) | -closed(E,C,D).  [resolve(17,f,14,b)].
% 0.44/1.02  Derived: element_of_set(A,interior(B,C,D)) | -topological_space(C,D) | -subset_sets(B,C) | -element_of_set(A,relative_complement_sets(f14(E,C,D,F),C)) | -subset_sets(relative_complement_sets(f14(E,C,D,F),C),B) | element_of_set(F,closure(E,C,D)) | -topological_space(C,D) | -subset_sets(E,C).  [resolve(27,f,21,d)].
% 0.44/1.02  Derived: element_of_set(A,interior(B,C,D)) | -topological_space(C,D) | -subset_sets(B,C) | -element_of_set(A,relative_complement_sets(E,C)) | -subset_sets(relative_complement_sets(E,C),B) | -topological_space(C,D) | -topological_space(C,D) | -element_of_collection(relative_complement_sets(E,C),D).  [resolve(27,f,26,a)].
% 0.44/1.02  28 -neighborhood(relative_complement_sets(A,B),C,B,D) | closed(A,B,D) | -topological_space(B,D).  [resolve(18,b,15,c)].
% 0.44/1.02  Derived: -neighborhood(relative_complement_sets(A,B),C,B,D) | -topological_space(B,D) | -element_of_set(E,closure(F,B,D)) | -subset_sets(F,A) | element_of_set(E,A).  [resolve(28,b,23,c)].
% 0.44/1.02  Derived: -neighborhood(relative_complement_sets(A,B),C,B,D) | -topological_space(B,D) | element_of_collection(relative_complement_sets(A,B),D).  [resolve(28,b,25,a)].
% 0.44/1.02  29 neighborhood(relative_complement_sets(A,B),C,B,D) | -topological_space(B,D) | -element_of_set(C,relative_complement_sets(A,B)) | -closed(A,B,D).  [resolve(19,c,14,b)].
% 0.44/1.02  Derived: neighborhood(relative_complement_sets(f14(A,B,C,D),B),E,B,C) | -topological_space(B,C) | -element_of_set(E,relative_complement_sets(f14(A,B,C,D),B)) | element_of_set(D,closure(A,B,C)) | -topological_space(B,C) | -subset_sets(A,B).  [resolve(29,d,21,d)].
% 0.44/1.02  Derived: neighborhood(relative_complement_sets(A,B),C,B,D) | -topological_space(B,D) | -element_of_set(C,relative_complement_sets(A,B)) | -topological_space(B,D) | -topological_space(B,D) | -element_of_collection(relative_complement_sets(A,B),D).  [resolve(29,d,26,a)].
% 0.44/1.03  30 basis(A,B) | -equal_sets(union_of_members(B),A) | element_of_set(f7(A,B),A) # label(basis_for_topology_32) # label(axiom).  [assumption].
% 0.44/1.03  31 -basis(A,B) | equal_sets(union_of_members(B),A) # label(basis_for_topology_28) # label(axiom).  [assumption].
% 0.44/1.03  32 -basis(A,B) | -element_of_set(C,A) | -element_of_collection(D,B) | -element_of_collection(E,B) | -element_of_set(C,intersection_of_sets(D,E)) | element_of_set(C,f6(A,B,C,D,E)) # label(basis_for_topology_29) # label(axiom).  [assumption].
% 0.44/1.03  33 -basis(A,B) | -element_of_set(C,A) | -element_of_collection(D,B) | -element_of_collection(E,B) | -element_of_set(C,intersection_of_sets(D,E)) | element_of_collection(f6(A,B,C,D,E),B) # label(basis_for_topology_30) # label(axiom).  [assumption].
% 0.44/1.03  34 -basis(A,B) | -element_of_set(C,A) | -element_of_collection(D,B) | -element_of_collection(E,B) | -element_of_set(C,intersection_of_sets(D,E)) | subset_sets(f6(A,B,C,D,E),intersection_of_sets(D,E)) # label(basis_for_topology_31) # label(axiom).  [assumption].
% 0.44/1.03  Derived: -equal_sets(union_of_members(A),B) | element_of_set(f7(B,A),B) | -element_of_set(C,B) | -element_of_collection(D,A) | -element_of_collection(E,A) | -element_of_set(C,intersection_of_sets(D,E)) | element_of_set(C,f6(B,A,C,D,E)).  [resolve(30,a,32,a)].
% 0.44/1.03  Derived: -equal_sets(union_of_members(A),B) | element_of_set(f7(B,A),B) | -element_of_set(C,B) | -element_of_collection(D,A) | -element_of_collection(E,A) | -element_of_set(C,intersection_of_sets(D,E)) | element_of_collection(f6(B,A,C,D,E),A).  [resolve(30,a,33,a)].
% 0.44/1.03  Derived: -equal_sets(union_of_members(A),B) | element_of_set(f7(B,A),B) | -element_of_set(C,B) | -element_of_collection(D,A) | -element_of_collection(E,A) | -element_of_set(C,intersection_of_sets(D,E)) | subset_sets(f6(B,A,C,D,E),intersection_of_sets(D,E)).  [resolve(30,a,34,a)].
% 0.44/1.03  35 basis(A,B) | -equal_sets(union_of_members(B),A) | element_of_collection(f8(A,B),B) # label(basis_for_topology_33) # label(axiom).  [assumption].
% 0.44/1.03  Derived: -equal_sets(union_of_members(A),B) | element_of_collection(f8(B,A),A) | -element_of_set(C,B) | -element_of_collection(D,A) | -element_of_collection(E,A) | -element_of_set(C,intersection_of_sets(D,E)) | element_of_set(C,f6(B,A,C,D,E)).  [resolve(35,a,32,a)].
% 0.44/1.03  Derived: -equal_sets(union_of_members(A),B) | element_of_collection(f8(B,A),A) | -element_of_set(C,B) | -element_of_collection(D,A) | -element_of_collection(E,A) | -element_of_set(C,intersection_of_sets(D,E)) | element_of_collection(f6(B,A,C,D,E),A).  [resolve(35,a,33,a)].
% 0.44/1.03  Derived: -equal_sets(union_of_members(A),B) | element_of_collection(f8(B,A),A) | -element_of_set(C,B) | -element_of_collection(D,A) | -element_of_collection(E,A) | -element_of_set(C,intersection_of_sets(D,E)) | subset_sets(f6(B,A,C,D,E),intersection_of_sets(D,E)).  [resolve(35,a,34,a)].
% 0.44/1.03  36 basis(A,B) | -equal_sets(union_of_members(B),A) | element_of_collection(f9(A,B),B) # label(basis_for_topology_34) # label(axiom).  [assumption].
% 0.44/1.03  Derived: -equal_sets(union_of_members(A),B) | element_of_collection(f9(B,A),A) | -element_of_set(C,B) | -element_of_collection(D,A) | -element_of_collection(E,A) | -element_of_set(C,intersection_of_sets(D,E)) | element_of_set(C,f6(B,A,C,D,E)).  [resolve(36,a,32,a)].
% 0.44/1.03  Derived: -equal_sets(union_of_members(A),B) | element_of_collection(f9(B,A),A) | -element_of_set(C,B) | -element_of_collection(D,A) | -element_of_collection(E,A) | -element_of_set(C,intersection_of_sets(D,E)) | element_of_collection(f6(B,A,C,D,E),A).  [resolve(36,a,33,a)].
% 0.44/1.03  Derived: -equal_sets(union_of_members(A),B) | element_of_collection(f9(B,A),A) | -element_of_set(C,B) | -element_of_collection(D,A) | -element_of_collection(E,A) | -element_of_set(C,intersection_of_sets(D,E)) | subset_sets(f6(B,A,C,D,E),intersection_of_sets(D,E)).  [resolve(36,a,34,a)].
% 0.44/1.03  37 basis(A,B) | -equal_sets(union_of_members(B),A) | element_of_set(f7(A,B),intersection_of_sets(f8(A,B),f9(A,B))) # label(basis_for_topology_35) # label(axiom).  [assumption].
% 0.44/1.03  Derived: -equal_sets(union_of_members(A),B) | element_of_set(f7(B,A),intersection_of_sets(f8(B,A),f9(B,A))) | -element_of_set(C,B) | -element_of_collection(D,A) | -element_of_collection(E,A) | -element_of_set(C,intersection_of_sets(D,E)) | element_of_set(C,f6(B,A,C,D,E)).  [resolve(37,a,32,a)].
% 0.44/1.03  Derived: -equal_sets(union_of_members(A),B) | element_of_set(f7(B,A),intersection_of_sets(f8(B,A),f9(B,A))) | -element_of_set(C,B) | -element_of_collection(D,A) | -element_of_collection(E,A) | -element_of_set(C,intersection_of_sets(D,E)) | element_of_collection(f6(B,A,C,D,E),A).  [resolve(37,a,33,a)].
% 0.44/1.03  Derived: -equal_sets(union_of_members(A),B) | element_of_set(f7(B,A),intersection_of_sets(f8(B,A),f9(B,A))) | -element_of_set(C,B) | -element_of_collection(D,A) | -element_of_collection(E,A) | -element_of_set(C,intersection_of_sets(D,E)) | subset_sets(f6(B,A,C,D,E),intersection_of_sets(D,E)).  [resolve(37,a,34,a)].
% 0.44/1.03  38 basis(A,B) | -equal_sets(union_of_members(B),A) | -element_of_set(f7(A,B),C) | -element_of_collection(C,B) | -subset_sets(C,intersection_of_sets(f8(A,B),f9(A,B))) # label(basis_for_topology_36) # label(axiom).  [assumption].
% 0.44/1.03  Derived: -equal_sets(union_of_members(A),B) | -element_of_set(f7(B,A),C) | -element_of_collection(C,A) | -subset_sets(C,intersection_of_sets(f8(B,A),f9(B,A))) | -element_of_set(D,B) | -element_of_collection(E,A) | -element_of_collection(F,A) | -element_of_set(D,intersection_of_sets(E,F)) | element_of_set(D,f6(B,A,D,E,F)).  [resolve(38,a,32,a)].
% 0.44/1.03  Derived: -equal_sets(union_of_members(A),B) | -element_of_set(f7(B,A),C) | -element_of_collection(C,A) | -subset_sets(C,intersection_of_sets(f8(B,A),f9(B,A))) | -element_of_set(D,B) | -element_of_collection(E,A) | -element_of_collection(F,A) | -element_of_set(D,intersection_of_sets(E,F)) | element_of_collection(f6(B,A,D,E,F),A).  [resolve(38,a,33,a)].
% 0.44/1.03  Derived: -equal_sets(union_of_members(A),B) | -element_of_set(f7(B,A),C) | -element_of_collection(C,A) | -subset_sets(C,intersection_of_sets(f8(B,A),f9(B,A))) | -element_of_set(D,B) | -element_of_collection(E,A) | -element_of_collection(F,A) | -element_of_set(D,intersection_of_sets(E,F)) | subset_sets(f6(B,A,D,E,F),intersection_of_sets(E,F)).  [resolve(38,a,34,a)].
% 0.44/1.03  39 limit_point(A,B,C,D) | -topological_space(C,D) | -subset_sets(B,C) | neighborhood(f16(A,B,C,D),A,C,D) # label(limit_point_67) # label(axiom).  [assumption].
% 0.44/1.03  40 -limit_point(A,B,C,D) | topological_space(C,D) # label(limit_point_63) # label(axiom).  [assumption].
% 0.44/1.03  41 -limit_point(A,B,C,D) | subset_sets(B,C) # label(limit_point_64) # label(axiom).  [assumption].
% 0.44/1.03  42 -limit_point(A,B,C,D) | -neighborhood(E,A,C,D) | element_of_set(f15(A,B,C,D,E),intersection_of_sets(E,B)) # label(limit_point_65) # label(axiom).  [assumption].
% 0.44/1.03  43 -limit_point(A,B,C,D) | -neighborhood(E,A,C,D) | -eq_p(f15(A,B,C,D,E),A) # label(limit_point_66) # label(axiom).  [assumption].
% 0.44/1.03  Derived: -topological_space(A,B) | -subset_sets(C,A) | neighborhood(f16(D,C,A,B),D,A,B) | -neighborhood(E,D,A,B) | element_of_set(f15(D,C,A,B,E),intersection_of_sets(E,C)).  [resolve(39,a,42,a)].
% 0.44/1.03  Derived: -topological_space(A,B) | -subset_sets(C,A) | neighborhood(f16(D,C,A,B),D,A,B) | -neighborhood(E,D,A,B) | -eq_p(f15(D,C,A,B,E),D).  [resolve(39,a,43,a)].
% 0.44/1.03  44 limit_point(A,B,C,D) | -topological_space(C,D) | -subset_sets(B,C) | -element_of_set(E,intersection_of_sets(f16(A,B,C,D),B)) | eq_p(E,A) # label(limit_point_68) # label(axiom).  [assumption].
% 0.44/1.03  Derived: -topological_space(A,B) | -subset_sets(C,A) | -element_of_set(D,intersection_of_sets(f16(E,C,A,B),C)) | eq_p(D,E) | -neighborhood(F,E,A,B) | element_of_set(f15(E,C,A,B,F),intersection_of_sets(F,C)).  [resolve(44,a,42,a)].
% 0.44/1.03  Derived: -topological_space(A,B) | -subset_sets(C,A) | -element_of_set(D,intersection_of_sets(f16(E,C,A,B),C)) | eq_p(D,E) | -neighborhood(F,E,A,B) | -eq_p(f15(E,C,A,B,F),E).  [resolve(44,a,43,a)].
% 0.44/1.03  45 hausdorff(A,B) | -topological_space(A,B) | element_of_set(f19(A,B),A) # label(hausdorff_77) # label(axiom).  [assumption].
% 0.44/1.03  46 -hausdorff(A,B) | topological_space(A,B) # label(hausdorff_73) # label(axiom).  [assumption].
% 0.44/1.04  47 -hausdorff(A,B) | -element_of_set(C,A) | -element_of_set(D,A) | eq_p(C,D) | neighborhood(f17(A,B,C,D),C,A,B) # label(hausdorff_74) # label(axiom).  [assumption].
% 0.44/1.04  48 -hausdorff(A,B) | -element_of_set(C,A) | -element_of_set(D,A) | eq_p(C,D) | neighborhood(f18(A,B,C,D),D,A,B) # label(hausdorff_75) # label(axiom).  [assumption].
% 0.44/1.04  49 -hausdorff(A,B) | -element_of_set(C,A) | -element_of_set(D,A) | eq_p(C,D) | disjoint_s(f17(A,B,C,D),f18(A,B,C,D)) # label(hausdorff_76) # label(axiom).  [assumption].
% 0.44/1.04  Derived: -topological_space(A,B) | element_of_set(f19(A,B),A) | -element_of_set(C,A) | -element_of_set(D,A) | eq_p(C,D) | neighborhood(f17(A,B,C,D),C,A,B).  [resolve(45,a,47,a)].
% 0.44/1.04  Derived: -topological_space(A,B) | element_of_set(f19(A,B),A) | -element_of_set(C,A) | -element_of_set(D,A) | eq_p(C,D) | neighborhood(f18(A,B,C,D),D,A,B).  [resolve(45,a,48,a)].
% 0.44/1.04  Derived: -topological_space(A,B) | element_of_set(f19(A,B),A) | -element_of_set(C,A) | -element_of_set(D,A) | eq_p(C,D) | disjoint_s(f17(A,B,C,D),f18(A,B,C,D)).  [resolve(45,a,49,a)].
% 0.44/1.04  50 hausdorff(A,B) | -topological_space(A,B) | element_of_set(f20(A,B),A) # label(hausdorff_78) # label(axiom).  [assumption].
% 0.44/1.04  Derived: -topological_space(A,B) | element_of_set(f20(A,B),A) | -element_of_set(C,A) | -element_of_set(D,A) | eq_p(C,D) | neighborhood(f17(A,B,C,D),C,A,B).  [resolve(50,a,47,a)].
% 0.44/1.04  Derived: -topological_space(A,B) | element_of_set(f20(A,B),A) | -element_of_set(C,A) | -element_of_set(D,A) | eq_p(C,D) | neighborhood(f18(A,B,C,D),D,A,B).  [resolve(50,a,48,a)].
% 0.44/1.04  Derived: -topological_space(A,B) | element_of_set(f20(A,B),A) | -element_of_set(C,A) | -element_of_set(D,A) | eq_p(C,D) | disjoint_s(f17(A,B,C,D),f18(A,B,C,D)).  [resolve(50,a,49,a)].
% 0.44/1.04  51 hausdorff(A,B) | -topological_space(A,B) | -eq_p(f19(A,B),f20(A,B)) # label(hausdorff_79) # label(axiom).  [assumption].
% 0.44/1.04  Derived: -topological_space(A,B) | -eq_p(f19(A,B),f20(A,B)) | -element_of_set(C,A) | -element_of_set(D,A) | eq_p(C,D) | neighborhood(f17(A,B,C,D),C,A,B).  [resolve(51,a,47,a)].
% 0.44/1.04  Derived: -topological_space(A,B) | -eq_p(f19(A,B),f20(A,B)) | -element_of_set(C,A) | -element_of_set(D,A) | eq_p(C,D) | neighborhood(f18(A,B,C,D),D,A,B).  [resolve(51,a,48,a)].
% 0.44/1.04  Derived: -topological_space(A,B) | -eq_p(f19(A,B),f20(A,B)) | -element_of_set(C,A) | -element_of_set(D,A) | eq_p(C,D) | disjoint_s(f17(A,B,C,D),f18(A,B,C,D)).  [resolve(51,a,49,a)].
% 0.44/1.04  52 hausdorff(A,B) | -topological_space(A,B) | -neighborhood(C,f19(A,B),A,B) | -neighborhood(D,f20(A,B),A,B) | -disjoint_s(C,D) # label(hausdorff_80) # label(axiom).  [assumption].
% 0.44/1.04  Derived: -topological_space(A,B) | -neighborhood(C,f19(A,B),A,B) | -neighborhood(D,f20(A,B),A,B) | -disjoint_s(C,D) | -element_of_set(E,A) | -element_of_set(F,A) | eq_p(E,F) | neighborhood(f17(A,B,E,F),E,A,B).  [resolve(52,a,47,a)].
% 0.44/1.04  Derived: -topological_space(A,B) | -neighborhood(C,f19(A,B),A,B) | -neighborhood(D,f20(A,B),A,B) | -disjoint_s(C,D) | -element_of_set(E,A) | -element_of_set(F,A) | eq_p(E,F) | neighborhood(f18(A,B,E,F),F,A,B).  [resolve(52,a,48,a)].
% 0.44/1.04  Derived: -topological_space(A,B) | -neighborhood(C,f19(A,B),A,B) | -neighborhood(D,f20(A,B),A,B) | -disjoint_s(C,D) | -element_of_set(E,A) | -element_of_set(F,A) | eq_p(E,F) | disjoint_s(f17(A,B,E,F),f18(A,B,E,F)).  [resolve(52,a,49,a)].
% 0.44/1.04  53 separation(A,B,C,D) | -topological_space(C,D) | equal_sets(A,empty_set) | equal_sets(B,empty_set) | -element_of_collection(A,D) | -element_of_collection(B,D) | -equal_sets(union_of_sets(A,B),C) | -disjoint_s(A,B) # label(separation_88) # label(axiom).  [assumption].
% 0.44/1.04  54 -separation(A,B,C,D) | topological_space(C,D) # label(separation_81) # label(axiom).  [assumption].
% 0.44/1.04  55 -separation(A,B,C,D) | -equal_sets(A,empty_set) # label(separation_82) # label(axiom).  [assumption].
% 0.44/1.04  56 -separation(A,B,C,D) | -equal_sets(B,empty_set) # label(separation_83) # label(axiom).  [assumption].
% 0.44/1.04  57 -separation(A,B,C,D) | element_of_collection(A,D) # label(separation_84) # label(axiom).  [assumption].
% 0.44/1.04  58 -separation(A,B,C,D) | element_of_collection(B,D) # label(separation_85) # label(axiom).  [assumption].
% 0.44/1.04  59 -separation(A,B,C,D) | equal_sets(union_of_sets(A,B),C) # label(separation_86) # label(axiom).  [assumption].
% 0.44/1.04  60 -separation(A,B,C,D) | disjoint_s(A,B) # label(separation_87) # label(axiom).  [assumption].
% 0.44/1.04  61 -connected_space(A,B) | -separation(C,D,A,B) # label(connected_space_90) # label(axiom).  [assumption].
% 0.44/1.04  Derived: -connected_space(A,B) | -topological_space(A,B) | equal_sets(C,empty_set) | equal_sets(D,empty_set) | -element_of_collection(C,B) | -element_of_collection(D,B) | -equal_sets(union_of_sets(C,D),A) | -disjoint_s(C,D).  [resolve(61,b,53,a)].
% 0.44/1.04  62 connected_space(A,B) | -topological_space(A,B) | separation(f21(A,B),f22(A,B),A,B) # label(connected_space_91) # label(axiom).  [assumption].
% 0.44/1.04  Derived: connected_space(A,B) | -topological_space(A,B) | -equal_sets(f21(A,B),empty_set).  [resolve(62,c,55,a)].
% 0.44/1.04  Derived: connected_space(A,B) | -topological_space(A,B) | -equal_sets(f22(A,B),empty_set).  [resolve(62,c,56,a)].
% 0.44/1.04  Derived: connected_space(A,B) | -topological_space(A,B) | element_of_collection(f21(A,B),B).  [resolve(62,c,57,a)].
% 0.44/1.04  Derived: connected_space(A,B) | -topological_space(A,B) | element_of_collection(f22(A,B),B).  [resolve(62,c,58,a)].
% 0.44/1.04  Derived: connected_space(A,B) | -topological_space(A,B) | equal_sets(union_of_sets(f21(A,B),f22(A,B)),A).  [resolve(62,c,59,a)].
% 0.44/1.04  Derived: connected_space(A,B) | -topological_space(A,B) | disjoint_s(f21(A,B),f22(A,B)).  [resolve(62,c,60,a)].
% 0.44/1.04  63 -connected_set(A,B,C) | connected_space(A,subspace_topology(B,C,A)) # label(connected_set_94) # label(axiom).  [assumption].
% 0.44/1.04  64 -connected_space(A,B) | topological_space(A,B) # label(connected_space_89) # label(axiom).  [assumption].
% 0.44/1.04  Derived: -connected_set(A,B,C) | topological_space(A,subspace_topology(B,C,A)).  [resolve(63,b,64,a)].
% 0.44/1.04  65 connected_set(A,B,C) | -topological_space(B,C) | -subset_sets(A,B) | -connected_space(A,subspace_topology(B,C,A)) # label(connected_set_95) # label(axiom).  [assumption].
% 0.44/1.04  66 -connected_space(A,B) | -topological_space(A,B) | equal_sets(C,empty_set) | equal_sets(D,empty_set) | -element_of_collection(C,B) | -element_of_collection(D,B) | -equal_sets(union_of_sets(C,D),A) | -disjoint_s(C,D).  [resolve(61,b,53,a)].
% 0.44/1.04  Derived: -topological_space(A,subspace_topology(B,C,A)) | equal_sets(D,empty_set) | equal_sets(E,empty_set) | -element_of_collection(D,subspace_topology(B,C,A)) | -element_of_collection(E,subspace_topology(B,C,A)) | -equal_sets(union_of_sets(D,E),A) | -disjoint_s(D,E) | -connected_set(A,B,C).  [resolve(66,a,63,b)].
% 0.44/1.04  67 connected_space(A,B) | -topological_space(A,B) | -equal_sets(f21(A,B),empty_set).  [resolve(62,c,55,a)].
% 0.44/1.04  Derived: -topological_space(A,subspace_topology(B,C,A)) | -equal_sets(f21(A,subspace_topology(B,C,A)),empty_set) | connected_set(A,B,C) | -topological_space(B,C) | -subset_sets(A,B).  [resolve(67,a,65,d)].
% 0.44/1.04  Derived: -topological_space(A,B) | -equal_sets(f21(A,B),empty_set) | -topological_space(A,B) | equal_sets(C,empty_set) | equal_sets(D,empty_set) | -element_of_collection(C,B) | -element_of_collection(D,B) | -equal_sets(union_of_sets(C,D),A) | -disjoint_s(C,D).  [resolve(67,a,66,a)].
% 0.44/1.04  68 connected_space(A,B) | -topological_space(A,B) | -equal_sets(f22(A,B),empty_set).  [resolve(62,c,56,a)].
% 0.44/1.04  Derived: -topological_space(A,subspace_topology(B,C,A)) | -equal_sets(f22(A,subspace_topology(B,C,A)),empty_set) | connected_set(A,B,C) | -topological_space(B,C) | -subset_sets(A,B).  [resolve(68,a,65,d)].
% 0.44/1.04  Derived: -topological_space(A,B) | -equal_sets(f22(A,B),empty_set) | -topological_space(A,B) | equal_sets(C,empty_set) | equal_sets(D,empty_set) | -element_of_collection(C,B) | -element_of_collection(D,B) | -equal_sets(union_of_sets(C,D),A) | -disjoint_s(C,D).  [resolve(68,a,66,a)].
% 0.44/1.04  69 connected_space(A,B) | -topological_space(A,B) | element_of_collection(f21(A,B),B).  [resolve(62,c,57,a)].
% 0.44/1.04  Derived: -topological_space(A,subspace_topology(B,C,A)) | element_of_collection(f21(A,subspace_topology(B,C,A)),subspace_topology(B,C,A)) | connected_set(A,B,C) | -topological_space(B,C) | -subset_sets(A,B).  [resolve(69,a,65,d)].
% 0.44/1.04  Derived: -topological_space(A,B) | element_of_collection(f21(A,B),B) | -topological_space(A,B) | equal_sets(C,empty_set) | equal_sets(D,empty_set) | -element_of_collection(C,B) | -element_of_collection(D,B) | -equal_sets(union_of_sets(C,D),A) | -disjoint_s(C,D).  [resolve(69,a,66,a)].
% 0.44/1.05  70 connected_space(A,B) | -topological_space(A,B) | element_of_collection(f22(A,B),B).  [resolve(62,c,58,a)].
% 0.44/1.05  Derived: -topological_space(A,subspace_topology(B,C,A)) | element_of_collection(f22(A,subspace_topology(B,C,A)),subspace_topology(B,C,A)) | connected_set(A,B,C) | -topological_space(B,C) | -subset_sets(A,B).  [resolve(70,a,65,d)].
% 0.44/1.05  Derived: -topological_space(A,B) | element_of_collection(f22(A,B),B) | -topological_space(A,B) | equal_sets(C,empty_set) | equal_sets(D,empty_set) | -element_of_collection(C,B) | -element_of_collection(D,B) | -equal_sets(union_of_sets(C,D),A) | -disjoint_s(C,D).  [resolve(70,a,66,a)].
% 0.44/1.05  71 connected_space(A,B) | -topological_space(A,B) | equal_sets(union_of_sets(f21(A,B),f22(A,B)),A).  [resolve(62,c,59,a)].
% 0.44/1.05  Derived: -topological_space(A,subspace_topology(B,C,A)) | equal_sets(union_of_sets(f21(A,subspace_topology(B,C,A)),f22(A,subspace_topology(B,C,A))),A) | connected_set(A,B,C) | -topological_space(B,C) | -subset_sets(A,B).  [resolve(71,a,65,d)].
% 0.44/1.05  Derived: -topological_space(A,B) | equal_sets(union_of_sets(f21(A,B),f22(A,B)),A) | -topological_space(A,B) | equal_sets(C,empty_set) | equal_sets(D,empty_set) | -element_of_collection(C,B) | -element_of_collection(D,B) | -equal_sets(union_of_sets(C,D),A) | -disjoint_s(C,D).  [resolve(71,a,66,a)].
% 0.44/1.05  72 connected_space(A,B) | -topological_space(A,B) | disjoint_s(f21(A,B),f22(A,B)).  [resolve(62,c,60,a)].
% 0.44/1.05  Derived: -topological_space(A,subspace_topology(B,C,A)) | disjoint_s(f21(A,subspace_topology(B,C,A)),f22(A,subspace_topology(B,C,A))) | connected_set(A,B,C) | -topological_space(B,C) | -subset_sets(A,B).  [resolve(72,a,65,d)].
% 0.44/1.05  Derived: -topological_space(A,B) | disjoint_s(f21(A,B),f22(A,B)) | -topological_space(A,B) | equal_sets(C,empty_set) | equal_sets(D,empty_set) | -element_of_collection(C,B) | -element_of_collection(D,B) | -equal_sets(union_of_sets(C,D),A) | -disjoint_s(C,D).  [resolve(72,a,66,a)].
% 0.44/1.05  73 -topological_space(A,subspace_topology(B,C,A)) | -equal_sets(f21(A,subspace_topology(B,C,A)),empty_set) | connected_set(A,B,C) | -topological_space(B,C) | -subset_sets(A,B).  [resolve(67,a,65,d)].
% 0.44/1.05  74 -connected_set(A,B,C) | topological_space(B,C) # label(connected_set_92) # label(axiom).  [assumption].
% 0.44/1.05  75 -connected_set(A,B,C) | subset_sets(A,B) # label(connected_set_93) # label(axiom).  [assumption].
% 0.44/1.05  76 -connected_set(A,B,C) | topological_space(A,subspace_topology(B,C,A)).  [resolve(63,b,64,a)].
% 0.44/1.05  77 -topological_space(A,subspace_topology(B,C,A)) | equal_sets(D,empty_set) | equal_sets(E,empty_set) | -element_of_collection(D,subspace_topology(B,C,A)) | -element_of_collection(E,subspace_topology(B,C,A)) | -equal_sets(union_of_sets(D,E),A) | -disjoint_s(D,E) | -connected_set(A,B,C).  [resolve(66,a,63,b)].
% 0.44/1.05  78 -topological_space(A,subspace_topology(B,C,A)) | -equal_sets(f22(A,subspace_topology(B,C,A)),empty_set) | connected_set(A,B,C) | -topological_space(B,C) | -subset_sets(A,B).  [resolve(68,a,65,d)].
% 0.44/1.05  79 -topological_space(A,subspace_topology(B,C,A)) | element_of_collection(f21(A,subspace_topology(B,C,A)),subspace_topology(B,C,A)) | connected_set(A,B,C) | -topological_space(B,C) | -subset_sets(A,B).  [resolve(69,a,65,d)].
% 0.44/1.05  80 -topological_space(A,subspace_topology(B,C,A)) | element_of_collection(f22(A,subspace_topology(B,C,A)),subspace_topology(B,C,A)) | connected_set(A,B,C) | -topological_space(B,C) | -subset_sets(A,B).  [resolve(70,a,65,d)].
% 0.44/1.05  81 -topological_space(A,subspace_topology(B,C,A)) | equal_sets(union_of_sets(f21(A,subspace_topology(B,C,A)),f22(A,subspace_topology(B,C,A))),A) | connected_set(A,B,C) | -topological_space(B,C) | -subset_sets(A,B).  [resolve(71,a,65,d)].
% 0.44/1.05  82 -topological_space(A,subspace_topology(B,C,A)) | disjoint_s(f21(A,subspace_topology(B,C,A)),f22(A,subspace_topology(B,C,A))) | connected_set(A,B,C) | -topological_space(B,C) | -subset_sets(A,B).  [resolve(72,a,65,d)].
% 0.44/1.05  83 compact_space(A,B) | -topological_space(A,B) | -finite(f5(C,f24(A,B))) | -open_covering(f5(C,f24(A,B)),A,B) | topological_space(C,f24(A,B)) | -equal_sets(union_of_members(f24(A,B)),C) | -element_of_collection(empty_set,f24(A,B)) | -element_of_collection(C,f24(A,B)) | element_of_collection(f3(C,f24(A,B)),f24(A,B)).  [resolve(10,d,1,f)].
% 1.61/1.91  84 -compact_space(A,B) | -open_covering(C,A,B) | finite(f23(A,B,C)) # label(compact_space_101) # label(axiom).  [assumption].
% 1.61/1.91  85 compact_space(A,B) | -topological_space(A,B) | -finite(f5(C,f24(A,B))) | -open_covering(f5(C,f24(A,B)),A,B) | topological_space(C,f24(A,B)) | -equal_sets(union_of_members(f24(A,B)),C) | -element_of_collection(empty_set,f24(A,B)) | -element_of_collection(C,f24(A,B)) | element_of_collection(f4(C,f24(A,B)),f24(A,B)).  [resolve(10,d,3,f)].
% 1.61/1.91  86 compact_space(A,B) | -topological_space(A,B) | -finite(f5(C,f24(A,B))) | -open_covering(f5(C,f24(A,B)),A,B) | topological_space(C,f24(A,B)) | -equal_sets(union_of_members(f24(A,B)),C) | -element_of_collection(empty_set,f24(A,B)) | -element_of_collection(C,f24(A,B)) | -element_of_collection(intersection_of_sets(f3(C,f24(A,B)),f4(C,f24(A,B))),f24(A,B)).  [resolve(10,d,4,f)].
% 1.61/1.91  87 compact_space(A,B) | -topological_space(A,B) | -finite(C) | -open_covering(C,A,B) | -finer(f24(A,B),C,D).  [resolve(10,d,5,b)].
% 1.61/1.91  Derived: compact_space(A,B) | -topological_space(A,B) | -open_covering(f23(C,D,E),A,B) | -finer(f24(A,B),f23(C,D,E),F) | -compact_space(C,D) | -open_covering(E,C,D).  [resolve(87,c,84,c)].
% 1.61/1.91  88 compact_space(A,B) | -topological_space(A,B) | -finite(C) | -open_covering(C,A,B) | -open_covering(C,D,f24(A,B)).  [resolve(10,d,7,b)].
% 1.61/1.91  Derived: compact_space(A,B) | -topological_space(A,B) | -open_covering(f23(C,D,E),A,B) | -open_covering(f23(C,D,E),F,f24(A,B)) | -compact_space(C,D) | -open_covering(E,C,D).  [resolve(88,c,84,c)].
% 1.61/1.91  89 compact_space(A,B) | -topological_space(A,B) | -finite(f23(C,D,f24(A,B))) | -open_covering(f23(C,D,f24(A,B)),A,B) | -compact_space(C,D) | -open_covering(f24(A,B),C,D).  [resolve(10,d,9,c)].
% 1.61/1.91  Derived: compact_space(A,B) | -topological_space(A,B) | -open_covering(f23(C,D,f24(A,B)),A,B) | -compact_space(C,D) | -open_covering(f24(A,B),C,D) | -compact_space(C,D) | -open_covering(f24(A,B),C,D).  [resolve(89,c,84,c)].
% 1.61/1.91  90 compact_set(A,B,C) | -topological_space(B,C) | -subset_sets(A,B) | -compact_space(A,subspace_topology(B,C,A)) # label(compact_set_109) # label(axiom).  [assumption].
% 1.61/1.91  91 -compact_set(A,B,C) | topological_space(B,C) # label(compact_set_106) # label(axiom).  [assumption].
% 1.61/1.91  92 -compact_set(A,B,C) | subset_sets(A,B) # label(compact_set_107) # label(axiom).  [assumption].
% 1.61/1.91  93 -compact_set(A,B,C) | compact_space(A,subspace_topology(B,C,A)) # label(compact_set_108) # label(axiom).  [assumption].
% 1.61/1.91  
% 1.61/1.91  ============================== end predicate elimination =============
% 1.61/1.91  
% 1.61/1.91  Auto_denials:  (non-Horn, no changes).
% 1.61/1.91  
% 1.61/1.91  Term ordering decisions:
% 1.61/1.91  Function symbol KB weights:  empty_set=1. a=1. cx=1. ct=1. intersection_of_sets=1. f5=1. relative_complement_sets=1. f19=1. f20=1. f7=1. f8=1. f9=1. f3=1. f4=1. union_of_sets=1. f24=1. f21=1. f22=1. f1=1. f11=1. f2=1. union_of_members=1. top_of_basis=1. intersection_of_members=1. f30=1. closure=1. interior=1. f23=1. subspace_topology=1. boundary=1. f10=1. f14=1. f17=1. f18=1. f13=1. f16=1. f12=1. f6=1. f15=1.
% 1.61/1.91  
% 1.61/1.91  ============================== end of process initial clauses ========
% 1.61/1.91  
% 1.61/1.91  ============================== CLAUSES FOR SEARCH ====================
% 1.61/1.91  
% 1.61/1.91  ============================== end of clauses for search =============
% 1.61/1.91  
% 1.61/1.91  ============================== SEARCH ================================
% 1.61/1.91  
% 1.61/1.91  % Starting search at 0.09 seconds.
% 1.61/1.91  
% 1.61/1.91  NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 261 (0.00 of 0.49 sec).
% 1.61/1.91  
% 1.61/1.91  Low Water (keep): wt=77.000, iters=3342
% 1.61/1.91  
% 1.61/1.91  Low Water (keep): wt=71.000, iters=3344
% 1.61/1.91  
% 1.61/1.91  Low Water (keep): wt=59.000, iters=3466
% 1.61/1.91  
% 1.61/1.91  Low Water (keep): wt=56.000, iters=3536
% 1.61/1.91  
% 1.61/1.91  Low Water (keep): wt=53.000, iters=3479
% 1.61/1.91  
% 1.61/1.91  Low Water (keep): wt=50.000, iters=3460
% 1.61/1.91  
% 1.61/1.91  Low Water (keep): wt=46.000, iters=3451
% 1.61/1.91  
% 1.61/1.91  Low Water (keep): wt=44.000, iters=3345
% 1.61/1.91  
% 1.61/1.91  Low Water (keep): wt=40.000, iters=3445
% 1.61/1.91  
% 1.61/1.91  Low Water (keep): wt=37.000, iters=3576
% 1.61/1.91  
% 1.61/1.91  Low Water (displace): id=2626, Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------