TSTP Solution File: TOP003-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : TOP003-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %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 : 300s
% DateTime : Wed Jul 27 13:26:48 EDT 2022
% Result : Timeout 299.85s 300.01s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : TOP003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.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 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 01:57:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.74/1.95 ----- Otter 3.3f, August 2004 -----
% 1.74/1.95 The process was started by sandbox2 on n019.cluster.edu,
% 1.74/1.95 Wed Jul 27 01:57:37 2022
% 1.74/1.95 The command was "./otter". The process ID is 30597.
% 1.74/1.95
% 1.74/1.95 set(prolog_style_variables).
% 1.74/1.95 set(auto).
% 1.74/1.95 dependent: set(auto1).
% 1.74/1.95 dependent: set(process_input).
% 1.74/1.95 dependent: clear(print_kept).
% 1.74/1.95 dependent: clear(print_new_demod).
% 1.74/1.95 dependent: clear(print_back_demod).
% 1.74/1.95 dependent: clear(print_back_sub).
% 1.74/1.95 dependent: set(control_memory).
% 1.74/1.95 dependent: assign(max_mem, 12000).
% 1.74/1.95 dependent: assign(pick_given_ratio, 4).
% 1.74/1.95 dependent: assign(stats_level, 1).
% 1.74/1.95 dependent: assign(max_seconds, 10800).
% 1.74/1.95 clear(print_given).
% 1.74/1.95
% 1.74/1.95 list(usable).
% 1.74/1.95 0 [] -element_of_set(U,union_of_members(Vf))|element_of_set(U,f1(Vf,U)).
% 1.74/1.95 0 [] -element_of_set(U,union_of_members(Vf))|element_of_collection(f1(Vf,U),Vf).
% 1.74/1.95 0 [] element_of_set(U,union_of_members(Vf))| -element_of_set(U,Uu1)| -element_of_collection(Uu1,Vf).
% 1.74/1.95 0 [] -element_of_set(U,intersection_of_members(Vf))| -element_of_collection(Va,Vf)|element_of_set(U,Va).
% 1.74/1.95 0 [] element_of_set(U,intersection_of_members(Vf))|element_of_collection(f2(Vf,U),Vf).
% 1.74/1.95 0 [] element_of_set(U,intersection_of_members(Vf))| -element_of_set(U,f2(Vf,U)).
% 1.74/1.95 0 [] -topological_space(X,Vt)|e_qual_sets(union_of_members(Vt),X).
% 1.74/1.95 0 [] -topological_space(X,Vt)|element_of_collection(empty_set,Vt).
% 1.74/1.95 0 [] -topological_space(X,Vt)|element_of_collection(X,Vt).
% 1.74/1.95 0 [] -topological_space(X,Vt)| -element_of_collection(Y,Vt)| -element_of_collection(Z,Vt)|element_of_collection(intersection_of_sets(Y,Z),Vt).
% 1.74/1.95 0 [] -topological_space(X,Vt)| -subset_collections(Vf,Vt)|element_of_collection(union_of_members(Vf),Vt).
% 1.74/1.95 0 [] topological_space(X,Vt)| -e_qual_sets(union_of_members(Vt),X)| -element_of_collection(empty_set,Vt)| -element_of_collection(X,Vt)|element_of_collection(f3(X,Vt),Vt)|subset_collections(f5(X,Vt),Vt).
% 1.74/1.95 0 [] topological_space(X,Vt)| -e_qual_sets(union_of_members(Vt),X)| -element_of_collection(empty_set,Vt)| -element_of_collection(X,Vt)|element_of_collection(f3(X,Vt),Vt)| -element_of_collection(union_of_members(f5(X,Vt)),Vt).
% 1.74/1.95 0 [] topological_space(X,Vt)| -e_qual_sets(union_of_members(Vt),X)| -element_of_collection(empty_set,Vt)| -element_of_collection(X,Vt)|element_of_collection(f4(X,Vt),Vt)|subset_collections(f5(X,Vt),Vt).
% 1.74/1.95 0 [] topological_space(X,Vt)| -e_qual_sets(union_of_members(Vt),X)| -element_of_collection(empty_set,Vt)| -element_of_collection(X,Vt)|element_of_collection(f4(X,Vt),Vt)| -element_of_collection(union_of_members(f5(X,Vt)),Vt).
% 1.74/1.95 0 [] topological_space(X,Vt)| -e_qual_sets(union_of_members(Vt),X)| -element_of_collection(empty_set,Vt)| -element_of_collection(X,Vt)| -element_of_collection(intersection_of_sets(f3(X,Vt),f4(X,Vt)),Vt)|subset_collections(f5(X,Vt),Vt).
% 1.74/1.95 0 [] topological_space(X,Vt)| -e_qual_sets(union_of_members(Vt),X)| -element_of_collection(empty_set,Vt)| -element_of_collection(X,Vt)| -element_of_collection(intersection_of_sets(f3(X,Vt),f4(X,Vt)),Vt)| -element_of_collection(union_of_members(f5(X,Vt)),Vt).
% 1.74/1.95 0 [] -open(U,X,Vt)|topological_space(X,Vt).
% 1.74/1.95 0 [] -open(U,X,Vt)|element_of_collection(U,Vt).
% 1.74/1.95 0 [] open(U,X,Vt)| -topological_space(X,Vt)| -element_of_collection(U,Vt).
% 1.74/1.95 0 [] -closed(U,X,Vt)|topological_space(X,Vt).
% 1.74/1.95 0 [] -closed(U,X,Vt)|open(relative_complement_sets(U,X),X,Vt).
% 1.74/1.95 0 [] closed(U,X,Vt)| -topological_space(X,Vt)| -open(relative_complement_sets(U,X),X,Vt).
% 1.74/1.95 0 [] -finer(Vt,Vs,X)|topological_space(X,Vt).
% 1.74/1.95 0 [] -finer(Vt,Vs,X)|topological_space(X,Vs).
% 1.74/1.95 0 [] -finer(Vt,Vs,X)|subset_collections(Vs,Vt).
% 1.74/1.95 0 [] finer(Vt,Vs,X)| -topological_space(X,Vt)| -topological_space(X,Vs)| -subset_collections(Vs,Vt).
% 1.74/1.95 0 [] -basis(X,Vf)|e_qual_sets(union_of_members(Vf),X).
% 1.74/1.95 0 [] -basis(X,Vf)| -element_of_set(Y,X)| -element_of_collection(Vb1,Vf)| -element_of_collection(Vb2,Vf)| -element_of_set(Y,intersection_of_sets(Vb1,Vb2))|element_of_set(Y,f6(X,Vf,Y,Vb1,Vb2)).
% 1.74/1.95 0 [] -basis(X,Vf)| -element_of_set(Y,X)| -element_of_collection(Vb1,Vf)| -element_of_collection(Vb2,Vf)| -element_of_set(Y,intersection_of_sets(Vb1,Vb2))|element_of_collection(f6(X,Vf,Y,Vb1,Vb2),Vf).
% 1.74/1.95 0 [] -basis(X,Vf)| -element_of_set(Y,X)| -element_of_collection(Vb1,Vf)| -element_of_collection(Vb2,Vf)| -element_of_set(Y,intersection_of_sets(Vb1,Vb2))|subset_sets(f6(X,Vf,Y,Vb1,Vb2),intersection_of_sets(Vb1,Vb2)).
% 1.74/1.95 0 [] basis(X,Vf)| -e_qual_sets(union_of_members(Vf),X)|element_of_set(f7(X,Vf),X).
% 1.74/1.95 0 [] basis(X,Vf)| -e_qual_sets(union_of_members(Vf),X)|element_of_collection(f8(X,Vf),Vf).
% 1.74/1.95 0 [] basis(X,Vf)| -e_qual_sets(union_of_members(Vf),X)|element_of_collection(f9(X,Vf),Vf).
% 1.74/1.95 0 [] basis(X,Vf)| -e_qual_sets(union_of_members(Vf),X)|element_of_set(f7(X,Vf),intersection_of_sets(f8(X,Vf),f9(X,Vf))).
% 1.74/1.95 0 [] basis(X,Vf)| -e_qual_sets(union_of_members(Vf),X)| -element_of_set(f7(X,Vf),Uu9)| -element_of_collection(Uu9,Vf)| -subset_sets(Uu9,intersection_of_sets(f8(X,Vf),f9(X,Vf))).
% 1.74/1.95 0 [] -element_of_collection(U,top_of_basis(Vf))| -element_of_set(X,U)|element_of_set(X,f10(Vf,U,X)).
% 1.74/1.95 0 [] -element_of_collection(U,top_of_basis(Vf))| -element_of_set(X,U)|element_of_collection(f10(Vf,U,X),Vf).
% 1.74/1.95 0 [] -element_of_collection(U,top_of_basis(Vf))| -element_of_set(X,U)|subset_sets(f10(Vf,U,X),U).
% 1.74/1.95 0 [] element_of_collection(U,top_of_basis(Vf))|element_of_set(f11(Vf,U),U).
% 1.74/1.95 0 [] element_of_collection(U,top_of_basis(Vf))| -element_of_set(f11(Vf,U),Uu11)| -element_of_collection(Uu11,Vf)| -subset_sets(Uu11,U).
% 1.74/1.95 0 [] -element_of_collection(U,subspace_topology(X,Vt,Y))|topological_space(X,Vt).
% 1.74/1.95 0 [] -element_of_collection(U,subspace_topology(X,Vt,Y))|subset_sets(Y,X).
% 1.74/1.95 0 [] -element_of_collection(U,subspace_topology(X,Vt,Y))|element_of_collection(f12(X,Vt,Y,U),Vt).
% 1.74/1.95 0 [] -element_of_collection(U,subspace_topology(X,Vt,Y))|e_qual_sets(U,intersection_of_sets(Y,f12(X,Vt,Y,U))).
% 1.74/1.95 0 [] element_of_collection(U,subspace_topology(X,Vt,Y))| -topological_space(X,Vt)| -subset_sets(Y,X)| -element_of_collection(Uu12,Vt)| -e_qual_sets(U,intersection_of_sets(Y,Uu12)).
% 1.74/1.95 0 [] -element_of_set(U,interior(Y,X,Vt))|topological_space(X,Vt).
% 1.74/1.95 0 [] -element_of_set(U,interior(Y,X,Vt))|subset_sets(Y,X).
% 1.74/1.95 0 [] -element_of_set(U,interior(Y,X,Vt))|element_of_set(U,f13(Y,X,Vt,U)).
% 1.74/1.95 0 [] -element_of_set(U,interior(Y,X,Vt))|subset_sets(f13(Y,X,Vt,U),Y).
% 1.74/1.95 0 [] -element_of_set(U,interior(Y,X,Vt))|open(f13(Y,X,Vt,U),X,Vt).
% 1.74/1.95 0 [] element_of_set(U,interior(Y,X,Vt))| -topological_space(X,Vt)| -subset_sets(Y,X)| -element_of_set(U,Uu13)| -subset_sets(Uu13,Y)| -open(Uu13,X,Vt).
% 1.74/1.95 0 [] -element_of_set(U,closure(Y,X,Vt))|topological_space(X,Vt).
% 1.74/1.95 0 [] -element_of_set(U,closure(Y,X,Vt))|subset_sets(Y,X).
% 1.74/1.95 0 [] -element_of_set(U,closure(Y,X,Vt))| -subset_sets(Y,V)| -closed(V,X,Vt)|element_of_set(U,V).
% 1.74/1.95 0 [] element_of_set(U,closure(Y,X,Vt))| -topological_space(X,Vt)| -subset_sets(Y,X)|subset_sets(Y,f14(Y,X,Vt,U)).
% 1.74/1.95 0 [] element_of_set(U,closure(Y,X,Vt))| -topological_space(X,Vt)| -subset_sets(Y,X)|closed(f14(Y,X,Vt,U),X,Vt).
% 1.74/1.95 0 [] element_of_set(U,closure(Y,X,Vt))| -topological_space(X,Vt)| -subset_sets(Y,X)| -element_of_set(U,f14(Y,X,Vt,U)).
% 1.74/1.95 0 [] -neighborhood(U,Y,X,Vt)|topological_space(X,Vt).
% 1.74/1.95 0 [] -neighborhood(U,Y,X,Vt)|open(U,X,Vt).
% 1.74/1.95 0 [] -neighborhood(U,Y,X,Vt)|element_of_set(Y,U).
% 1.74/1.95 0 [] neighborhood(U,Y,X,Vt)| -topological_space(X,Vt)| -open(U,X,Vt)| -element_of_set(Y,U).
% 1.74/1.95 0 [] -limit_point(Z,Y,X,Vt)|topological_space(X,Vt).
% 1.74/1.95 0 [] -limit_point(Z,Y,X,Vt)|subset_sets(Y,X).
% 1.74/1.95 0 [] -limit_point(Z,Y,X,Vt)| -neighborhood(U,Z,X,Vt)|element_of_set(f15(Z,Y,X,Vt,U),intersection_of_sets(U,Y)).
% 1.74/1.95 0 [] -limit_point(Z,Y,X,Vt)| -neighborhood(U,Z,X,Vt)| -e_q_p(f15(Z,Y,X,Vt,U),Z).
% 1.74/1.95 0 [] limit_point(Z,Y,X,Vt)| -topological_space(X,Vt)| -subset_sets(Y,X)|neighborhood(f16(Z,Y,X,Vt),Z,X,Vt).
% 1.74/1.95 0 [] limit_point(Z,Y,X,Vt)| -topological_space(X,Vt)| -subset_sets(Y,X)| -element_of_set(Uu16,intersection_of_sets(f16(Z,Y,X,Vt),Y))|e_q_p(Uu16,Z).
% 1.74/1.95 0 [] -element_of_set(U,boundary(Y,X,Vt))|topological_space(X,Vt).
% 1.74/1.95 0 [] -element_of_set(U,boundary(Y,X,Vt))|element_of_set(U,closure(Y,X,Vt)).
% 1.74/1.95 0 [] -element_of_set(U,boundary(Y,X,Vt))|element_of_set(U,closure(relative_complement_sets(Y,X),X,Vt)).
% 1.74/1.95 0 [] element_of_set(U,boundary(Y,X,Vt))| -topological_space(X,Vt)| -element_of_set(U,closure(Y,X,Vt))| -element_of_set(U,closure(relative_complement_sets(Y,X),X,Vt)).
% 1.74/1.95 0 [] -hausdorff(X,Vt)|topological_space(X,Vt).
% 1.74/1.95 0 [] -hausdorff(X,Vt)| -element_of_set(X_1,X)| -element_of_set(X_2,X)|e_q_p(X_1,X_2)|neighborhood(f17(X,Vt,X_1,X_2),X_1,X,Vt).
% 1.74/1.95 0 [] -hausdorff(X,Vt)| -element_of_set(X_1,X)| -element_of_set(X_2,X)|e_q_p(X_1,X_2)|neighborhood(f18(X,Vt,X_1,X_2),X_2,X,Vt).
% 1.74/1.95 0 [] -hausdorff(X,Vt)| -element_of_set(X_1,X)| -element_of_set(X_2,X)|e_q_p(X_1,X_2)|disjoint_s(f17(X,Vt,X_1,X_2),f18(X,Vt,X_1,X_2)).
% 1.74/1.95 0 [] hausdorff(X,Vt)| -topological_space(X,Vt)|element_of_set(f19(X,Vt),X).
% 1.74/1.95 0 [] hausdorff(X,Vt)| -topological_space(X,Vt)|element_of_set(f20(X,Vt),X).
% 1.74/1.95 0 [] hausdorff(X,Vt)| -topological_space(X,Vt)| -e_q_p(f19(X,Vt),f20(X,Vt)).
% 1.74/1.95 0 [] hausdorff(X,Vt)| -topological_space(X,Vt)| -neighborhood(Uu19,f19(X,Vt),X,Vt)| -neighborhood(Uu20,f20(X,Vt),X,Vt)| -disjoint_s(Uu19,Uu20).
% 1.74/1.95 0 [] -separation(Va1,Va2,X,Vt)|topological_space(X,Vt).
% 1.74/1.95 0 [] -separation(Va1,Va2,X,Vt)| -e_qual_sets(Va1,empty_set).
% 1.74/1.95 0 [] -separation(Va1,Va2,X,Vt)| -e_qual_sets(Va2,empty_set).
% 1.74/1.95 0 [] -separation(Va1,Va2,X,Vt)|element_of_collection(Va1,Vt).
% 1.74/1.95 0 [] -separation(Va1,Va2,X,Vt)|element_of_collection(Va2,Vt).
% 1.74/1.95 0 [] -separation(Va1,Va2,X,Vt)|e_qual_sets(union_of_sets(Va1,Va2),X).
% 1.74/1.95 0 [] -separation(Va1,Va2,X,Vt)|disjoint_s(Va1,Va2).
% 1.74/1.95 0 [] separation(Va1,Va2,X,Vt)| -topological_space(X,Vt)|e_qual_sets(Va1,empty_set)|e_qual_sets(Va2,empty_set)| -element_of_collection(Va1,Vt)| -element_of_collection(Va2,Vt)| -e_qual_sets(union_of_sets(Va1,Va2),X)| -disjoint_s(Va1,Va2).
% 1.74/1.95 0 [] -connected_space(X,Vt)|topological_space(X,Vt).
% 1.74/1.95 0 [] -connected_space(X,Vt)| -separation(Va1,Va2,X,Vt).
% 1.74/1.95 0 [] connected_space(X,Vt)| -topological_space(X,Vt)|separation(f21(X,Vt),f22(X,Vt),X,Vt).
% 1.74/1.95 0 [] -connected_set(Va,X,Vt)|topological_space(X,Vt).
% 1.74/1.95 0 [] -connected_set(Va,X,Vt)|subset_sets(Va,X).
% 1.74/1.95 0 [] -connected_set(Va,X,Vt)|connected_space(Va,subspace_topology(X,Vt,Va)).
% 1.74/1.95 0 [] connected_set(Va,X,Vt)| -topological_space(X,Vt)| -subset_sets(Va,X)| -connected_space(Va,subspace_topology(X,Vt,Va)).
% 1.74/1.95 0 [] -open_covering(Vf,X,Vt)|topological_space(X,Vt).
% 1.74/1.95 0 [] -open_covering(Vf,X,Vt)|subset_collections(Vf,Vt).
% 1.74/1.95 0 [] -open_covering(Vf,X,Vt)|e_qual_sets(union_of_members(Vf),X).
% 1.74/1.95 0 [] open_covering(Vf,X,Vt)| -topological_space(X,Vt)| -subset_collections(Vf,Vt)| -e_qual_sets(union_of_members(Vf),X).
% 1.74/1.95 0 [] -compact_space(X,Vt)|topological_space(X,Vt).
% 1.74/1.95 0 [] -compact_space(X,Vt)| -open_covering(Vf1,X,Vt)|finite(f23(X,Vt,Vf1)).
% 1.74/1.95 0 [] -compact_space(X,Vt)| -open_covering(Vf1,X,Vt)|subset_collections(f23(X,Vt,Vf1),Vf1).
% 1.74/1.95 0 [] -compact_space(X,Vt)| -open_covering(Vf1,X,Vt)|open_covering(f23(X,Vt,Vf1),X,Vt).
% 1.74/1.95 0 [] compact_space(X,Vt)| -topological_space(X,Vt)|open_covering(f24(X,Vt),X,Vt).
% 1.74/1.95 0 [] compact_space(X,Vt)| -topological_space(X,Vt)| -finite(Uu24)| -subset_collections(Uu24,f24(X,Vt))| -open_covering(Uu24,X,Vt).
% 1.74/1.95 0 [] -compact_set(Va,X,Vt)|topological_space(X,Vt).
% 1.74/1.95 0 [] -compact_set(Va,X,Vt)|subset_sets(Va,X).
% 1.74/1.95 0 [] -compact_set(Va,X,Vt)|compact_space(Va,subspace_topology(X,Vt,Va)).
% 1.74/1.95 0 [] compact_set(Va,X,Vt)| -topological_space(X,Vt)| -subset_sets(Va,X)| -compact_space(Va,subspace_topology(X,Vt,Va)).
% 1.74/1.95 0 [] basis(cx,f).
% 1.74/1.95 0 [] -element_of_collection(cx,top_of_basis(f)).
% 1.74/1.95 end_of_list.
% 1.74/1.95
% 1.74/1.95 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=8.
% 1.74/1.95
% 1.74/1.95 This is a non-Horn set without equality. The strategy will
% 1.74/1.95 be ordered hyper_res, unit deletion, and factoring, with
% 1.74/1.95 satellites in sos and with nuclei in usable.
% 1.74/1.95
% 1.74/1.95 dependent: set(hyper_res).
% 1.74/1.95 dependent: set(factor).
% 1.74/1.95 dependent: set(unit_deletion).
% 1.74/1.95
% 1.74/1.95 ------------> process usable:
% 1.74/1.95 ** KEPT (pick-wt=9): 1 [] -element_of_set(A,union_of_members(B))|element_of_set(A,f1(B,A)).
% 1.74/1.95 ** KEPT (pick-wt=9): 2 [] -element_of_set(A,union_of_members(B))|element_of_collection(f1(B,A),B).
% 1.74/1.95 ** KEPT (pick-wt=10): 3 [] element_of_set(A,union_of_members(B))| -element_of_set(A,C)| -element_of_collection(C,B).
% 1.74/1.95 ** KEPT (pick-wt=10): 4 [] -element_of_set(A,intersection_of_members(B))| -element_of_collection(C,B)|element_of_set(A,C).
% 1.74/1.95 ** KEPT (pick-wt=9): 5 [] element_of_set(A,intersection_of_members(B))| -element_of_set(A,f2(B,A)).
% 1.74/1.95 ** KEPT (pick-wt=7): 6 [] -topological_space(A,B)|e_qual_sets(union_of_members(B),A).
% 1.74/1.95 ** KEPT (pick-wt=6): 7 [] -topological_space(A,B)|element_of_collection(empty_set,B).
% 1.74/1.95 ** KEPT (pick-wt=6): 8 [] -topological_space(A,B)|element_of_collection(A,B).
% 1.74/1.95 ** KEPT (pick-wt=14): 9 [] -topological_space(A,B)| -element_of_collection(C,B)| -element_of_collection(D,B)|element_of_collection(intersection_of_sets(C,D),B).
% 1.74/1.95 ** KEPT (pick-wt=10): 10 [] -topological_space(A,B)| -subset_collections(C,B)|element_of_collection(union_of_members(C),B).
% 1.74/1.95 ** KEPT (pick-wt=23): 11 [] topological_space(A,B)| -e_qual_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).
% 1.74/1.95 ** KEPT (pick-wt=24): 12 [] topological_space(A,B)| -e_qual_sets(union_of_members(B),A)| -element_of_collection(empty_set,B)| -element_of_collection(A,B)|element_of_collection(f3(A,B),B)| -element_of_collection(union_of_members(f5(A,B)),B).
% 1.74/1.95 ** KEPT (pick-wt=23): 13 [] topological_space(A,B)| -e_qual_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).
% 1.74/1.95 ** KEPT (pick-wt=24): 14 [] topological_space(A,B)| -e_qual_sets(union_of_members(B),A)| -element_of_collection(empty_set,B)| -element_of_collection(A,B)|element_of_collection(f4(A,B),B)| -element_of_collection(union_of_members(f5(A,B)),B).
% 1.74/1.95 ** KEPT (pick-wt=27): 15 [] topological_space(A,B)| -e_qual_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).
% 1.74/1.95 ** KEPT (pick-wt=28): 16 [] topological_space(A,B)| -e_qual_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)| -element_of_collection(union_of_members(f5(A,B)),B).
% 1.74/1.95 ** KEPT (pick-wt=7): 17 [] -open(A,B,C)|topological_space(B,C).
% 1.74/1.95 ** KEPT (pick-wt=7): 18 [] -open(A,B,C)|element_of_collection(A,C).
% 1.74/1.95 ** KEPT (pick-wt=10): 19 [] open(A,B,C)| -topological_space(B,C)| -element_of_collection(A,C).
% 1.74/1.95 ** KEPT (pick-wt=7): 20 [] -closed(A,B,C)|topological_space(B,C).
% 1.74/1.95 ** KEPT (pick-wt=10): 21 [] -closed(A,B,C)|open(relative_complement_sets(A,B),B,C).
% 1.74/1.95 ** KEPT (pick-wt=13): 22 [] closed(A,B,C)| -topological_space(B,C)| -open(relative_complement_sets(A,B),B,C).
% 1.74/1.95 ** KEPT (pick-wt=7): 23 [] -finer(A,B,C)|topological_space(C,A).
% 1.74/1.95 ** KEPT (pick-wt=7): 24 [] -finer(A,B,C)|topological_space(C,B).
% 1.74/1.95 ** KEPT (pick-wt=7): 25 [] -finer(A,B,C)|subset_collections(B,A).
% 1.74/1.95 ** KEPT (pick-wt=13): 26 [] finer(A,B,C)| -topological_space(C,A)| -topological_space(C,B)| -subset_collections(B,A).
% 1.74/1.95 ** KEPT (pick-wt=7): 27 [] -basis(A,B)|e_qual_sets(union_of_members(B),A).
% 1.74/1.95 ** KEPT (pick-wt=25): 28 [] -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)).
% 1.74/1.95 ** KEPT (pick-wt=25): 29 [] -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).
% 1.74/1.95 ** KEPT (pick-wt=27): 30 [] -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)).
% 1.74/1.95 ** KEPT (pick-wt=12): 31 [] basis(A,B)| -e_qual_sets(union_of_members(B),A)|element_of_set(f7(A,B),A).
% 1.74/1.95 ** KEPT (pick-wt=12): 32 [] basis(A,B)| -e_qual_sets(union_of_members(B),A)|element_of_collection(f8(A,B),B).
% 1.74/1.95 ** KEPT (pick-wt=12): 33 [] basis(A,B)| -e_qual_sets(union_of_members(B),A)|element_of_collection(f9(A,B),B).
% 1.74/1.95 ** KEPT (pick-wt=18): 34 [] basis(A,B)| -e_qual_sets(union_of_members(B),A)|element_of_set(f7(A,B),intersection_of_sets(f8(A,B),f9(A,B))).
% 1.74/1.95 ** KEPT (pick-wt=24): 35 [] basis(A,B)| -e_qual_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))).
% 1.74/1.95 ** KEPT (pick-wt=13): 36 [] -element_of_collection(A,top_of_basis(B))| -element_of_set(C,A)|element_of_set(C,f10(B,A,C)).
% 1.74/1.95 ** KEPT (pick-wt=13): 37 [] -element_of_collection(A,top_of_basis(B))| -element_of_set(C,A)|element_of_collection(f10(B,A,C),B).
% 1.74/1.95 ** KEPT (pick-wt=13): 38 [] -element_of_collection(A,top_of_basis(B))| -element_of_set(C,A)|subset_sets(f10(B,A,C),A).
% 1.74/1.95 ** KEPT (pick-wt=15): 39 [] element_of_collection(A,top_of_basis(B))| -element_of_set(f11(B,A),C)| -element_of_collection(C,B)| -subset_sets(C,A).
% 1.74/1.95 ** KEPT (pick-wt=9): 40 [] -element_of_collection(A,subspace_topology(B,C,D))|topological_space(B,C).
% 1.74/1.95 ** KEPT (pick-wt=9): 41 [] -element_of_collection(A,subspace_topology(B,C,D))|subset_sets(D,B).
% 1.74/1.95 ** KEPT (pick-wt=13): 42 [] -element_of_collection(A,subspace_topology(B,C,D))|element_of_collection(f12(B,C,D,A),C).
% 1.74/1.95 ** KEPT (pick-wt=15): 43 [] -element_of_collection(A,subspace_topology(B,C,D))|e_qual_sets(A,intersection_of_sets(D,f12(B,C,D,A))).
% 1.74/1.95 ** KEPT (pick-wt=20): 44 [] element_of_collection(A,subspace_topology(B,C,D))| -topological_space(B,C)| -subset_sets(D,B)| -element_of_collection(E,C)| -e_qual_sets(A,intersection_of_sets(D,E)).
% 1.74/1.95 ** KEPT (pick-wt=9): 45 [] -element_of_set(A,interior(B,C,D))|topological_space(C,D).
% 1.74/1.95 ** KEPT (pick-wt=9): 46 [] -element_of_set(A,interior(B,C,D))|subset_sets(B,C).
% 1.74/1.95 ** KEPT (pick-wt=13): 47 [] -element_of_set(A,interior(B,C,D))|element_of_set(A,f13(B,C,D,A)).
% 1.74/1.95 ** KEPT (pick-wt=13): 48 [] -element_of_set(A,interior(B,C,D))|subset_sets(f13(B,C,D,A),B).
% 1.74/1.95 ** KEPT (pick-wt=14): 49 [] -element_of_set(A,interior(B,C,D))|open(f13(B,C,D,A),C,D).
% 1.74/1.95 ** KEPT (pick-wt=22): 50 [] 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).
% 1.74/1.95 ** KEPT (pick-wt=9): 51 [] -element_of_set(A,closure(B,C,D))|topological_space(C,D).
% 1.74/1.95 ** KEPT (pick-wt=9): 52 [] -element_of_set(A,closure(B,C,D))|subset_sets(B,C).
% 1.74/1.95 ** KEPT (pick-wt=16): 53 [] -element_of_set(A,closure(B,C,D))| -subset_sets(B,E)| -closed(E,C,D)|element_of_set(A,E).
% 1.74/1.95 ** KEPT (pick-wt=19): 54 [] element_of_set(A,closure(B,C,D))| -topological_space(C,D)| -subset_sets(B,C)|subset_sets(B,f14(B,C,D,A)).
% 1.74/1.95 ** KEPT (pick-wt=20): 55 [] element_of_set(A,closure(B,C,D))| -topological_space(C,D)| -subset_sets(B,C)|closed(f14(B,C,D,A),C,D).
% 1.74/1.95 ** KEPT (pick-wt=19): 56 [] element_of_set(A,closure(B,C,D))| -topological_space(C,D)| -subset_sets(B,C)| -element_of_set(A,f14(B,C,D,A)).
% 1.74/1.95 ** KEPT (pick-wt=8): 57 [] -neighborhood(A,B,C,D)|topological_space(C,D).
% 1.74/1.95 ** KEPT (pick-wt=9): 58 [] -neighborhood(A,B,C,D)|open(A,C,D).
% 1.74/1.95 ** KEPT (pick-wt=8): 59 [] -neighborhood(A,B,C,D)|element_of_set(B,A).
% 1.74/1.95 ** KEPT (pick-wt=15): 60 [] neighborhood(A,B,C,D)| -topological_space(C,D)| -open(A,C,D)| -element_of_set(B,A).
% 1.74/1.95 ** KEPT (pick-wt=8): 61 [] -limit_point(A,B,C,D)|topological_space(C,D).
% 1.74/1.95 ** KEPT (pick-wt=8): 62 [] -limit_point(A,B,C,D)|subset_sets(B,C).
% 1.74/1.95 ** KEPT (pick-wt=20): 63 [] -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)).
% 1.74/1.95 ** KEPT (pick-wt=18): 64 [] -limit_point(A,B,C,D)| -neighborhood(E,A,C,D)| -e_q_p(f15(A,B,C,D,E),A).
% 1.74/1.95 ** KEPT (pick-wt=20): 65 [] limit_point(A,B,C,D)| -topological_space(C,D)| -subset_sets(B,C)|neighborhood(f16(A,B,C,D),A,C,D).
% 1.74/1.95 ** KEPT (pick-wt=23): 66 [] 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))|e_q_p(E,A).
% 1.74/1.95 ** KEPT (pick-wt=9): 67 [] -element_of_set(A,boundary(B,C,D))|topological_space(C,D).
% 1.74/1.95 ** KEPT (pick-wt=12): 68 [] -element_of_set(A,boundary(B,C,D))|element_of_set(A,closure(B,C,D)).
% 1.74/1.95 ** KEPT (pick-wt=14): 69 [] -element_of_set(A,boundary(B,C,D))|element_of_set(A,closure(relative_complement_sets(B,C),C,D)).
% 1.74/1.95 ** KEPT (pick-wt=23): 70 [] element_of_set(A,boundary(B,C,D))| -topological_space(C,D)| -element_of_set(A,closure(B,C,D))| -element_of_set(A,closure(relative_complement_sets(B,C),C,D)).
% 1.74/1.95 ** KEPT (pick-wt=6): 71 [] -hausdorff(A,B)|topological_space(A,B).
% 1.74/1.95 ** KEPT (pick-wt=21): 72 [] -hausdorff(A,B)| -element_of_set(C,A)| -element_of_set(D,A)|e_q_p(C,D)|neighborhood(f17(A,B,C,D),C,A,B).
% 1.74/1.95 ** KEPT (pick-wt=21): 73 [] -hausdorff(A,B)| -element_of_set(Alarm clock
% 299.85/300.01 Otter interrupted
% 299.85/300.01 PROOF NOT FOUND
%------------------------------------------------------------------------------