%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : TOP016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 02:33:51 PM UTC 2026
% Result : Satisfiable 104.11s 15.96s
% Output : Saturation 108.58s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(u174,axiom,
subset_sets(relative_complement_sets(a,cx),cx) ).
cnf(u201,axiom,
( closed(f14(relative_complement_sets(a,cx),cx,ct,X0),cx,ct)
| ~ element_of_set(X0,sF3) ) ).
cnf(u356,axiom,
~ disjoint_s(sF0,sF1) ).
cnf(u691,axiom,
subset_sets(sF3,sF1) ).
cnf(u695,axiom,
( element_of_collection(sF1,top_of_basis(X0))
| ~ element_of_collection(sF3,X0) ) ).
cnf(u997,negated_conjecture,
subset_sets(a,sF0) ).
cnf(u1001,negated_conjecture,
closed(sF0,cx,ct) ).
cnf(u1005,negated_conjecture,
( ~ element_of_set(X0,f13(a,cx,ct,f20(sF3,X1)))
| element_of_set(X0,sF0)
| hausdorff(sF3,X1)
| ~ topological_space(sF3,X1) ) ).
cnf(u1028,axiom,
( ~ topological_space(sF3,X3)
| hausdorff(sF3,X3) ) ).
cnf(u1031,axiom,
( ~ closed(boundary(X0,X1,X2),cx,ct)
| subset_sets(X0,X1)
| ~ subset_sets(a,boundary(X0,X1,X2)) ) ).
cnf(u1035,axiom,
( ~ closed(boundary(X0,X1,X2),cx,ct)
| topological_space(X1,X2)
| ~ subset_sets(a,boundary(X0,X1,X2)) ) ).
cnf(u1408,axiom,
topological_space(X4,X5) ).
cnf(u1411,axiom,
( ~ element_of_set(X0,boundary(X1,X2,X3))
| subset_sets(X1,X2) ) ).
cnf(u5466,negated_conjecture,
~ disjoint_s(union_of_members(ct),sF0) ).
cnf(u5484,negated_conjecture,
~ disjoint_s(sF0,sF0) ).
cnf(u5530,negated_conjecture,
~ disjoint_s(union_of_members(X1),sF0) ).
cnf(u5541,axiom,
( topological_space(X1,X2)
| element_of_set(f11(subspace_topology(X1,X2,X3),sF1),sF3) ) ).
cnf(u5553,axiom,
( subset_sets(X1,X2)
| element_of_set(f11(subspace_topology(X2,X3,X1),sF1),sF3) ) ).
cnf(u5566,axiom,
element_of_collection(sF3,top_of_basis(X3)) ).
cnf(u5569,axiom,
( element_of_set(f11(subspace_topology(X4,X5,X6),closure(X0,X1,X2)),sF3)
| ~ subset_sets(X0,sF1)
| ~ closed(boundary(X0,X1,X2),cx,ct)
| ~ closed(sF1,X1,X2)
| topological_space(X4,X5)
| ~ subset_sets(a,boundary(X0,X1,X2)) ) ).
cnf(u5576,axiom,
( ~ topological_space(closure(X3,X4,X5),X6)
| hausdorff(closure(X3,X4,X5),X6)
| ~ subset_sets(X3,sF1)
| ~ closed(sF1,X4,X5) ) ).
cnf(u5579,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),sF3),sF3)
| topological_space(X0,X1) ) ).
cnf(u5583,axiom,
( ~ topological_space(sF1,X3)
| hausdorff(sF1,X3) ) ).
cnf(u5590,negated_conjecture,
( element_of_set(f11(subspace_topology(X0,X1,X2),union_of_members(ct)),union_of_members(ct))
| topological_space(X0,X1) ) ).
cnf(u5594,negated_conjecture,
( element_of_set(f11(subspace_topology(X0,X1,X2),f14(a,cx,ct,X3)),f14(a,cx,ct,X3))
| element_of_set(X3,sF3)
| topological_space(X0,X1) ) ).
cnf(u5598,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),closure(X3,X4,X5))
| ~ subset_sets(a,boundary(X3,X4,X5))
| ~ closed(boundary(X3,X4,X5),cx,ct)
| topological_space(X0,X1) ) ).
cnf(u5602,axiom,
( ~ topological_space(sF1,X3)
| basis(sF1,X3) ) ).
cnf(u5613,negated_conjecture,
( element_of_set(f11(subspace_topology(X0,X1,X2),f14(a,cx,ct,f11(X3,X4))),f14(a,cx,ct,f11(X3,X4)))
| ~ element_of_collection(sF3,X3)
| ~ subset_sets(sF3,X4)
| element_of_collection(X4,top_of_basis(X3))
| topological_space(X0,X1) ) ).
cnf(u5636,axiom,
( subset_sets(X1,f14(X1,X2,X3,X4))
| element_of_set(X4,union_of_members(top_of_basis(X0)))
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| ~ subset_sets(X1,X2) ) ).
cnf(u5658,axiom,
( element_of_set(f11(subspace_topology(X1,X2,X3),sF3),X4)
| ~ subset_sets(a,X4)
| ~ closed(X4,cx,ct)
| topological_space(X1,X2) ) ).
cnf(u5662,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),X6)
| ~ subset_sets(a,boundary(X3,X4,X5))
| ~ closed(boundary(X3,X4,X5),cx,ct)
| ~ subset_sets(X3,X6)
| ~ closed(X6,X4,X5)
| topological_space(X0,X1) ) ).
cnf(u5699,negated_conjecture,
subset_sets(union_of_members(ct),cx) ).
cnf(u5703,negated_conjecture,
( ~ element_of_collection(union_of_members(ct),X0)
| element_of_collection(cx,top_of_basis(X0)) ) ).
cnf(u5742,negated_conjecture,
( element_of_set(f11(X1,union_of_members(ct)),union_of_members(ct))
| element_of_set(f11(subspace_topology(X2,X3,X4),union_of_members(top_of_basis(X1))),union_of_members(top_of_basis(X1)))
| topological_space(X2,X3) ) ).
cnf(u5752,axiom,
( closed(f14(X1,X2,X3,X4),X2,X3)
| element_of_set(X4,union_of_members(top_of_basis(X0)))
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| ~ subset_sets(X1,X2) ) ).
cnf(u5757,axiom,
closed(sF1,cx,ct) ).
cnf(u5761,axiom,
( element_of_set(f11(X2,closure(X0,cx,ct)),sF3)
| element_of_set(X3,f14(X0,cx,ct,X1))
| ~ element_of_set(X3,sF3)
| ~ subset_sets(a,f14(X0,cx,ct,X1))
| ~ subset_sets(X0,cx)
| ~ subset_sets(X0,sF1)
| element_of_set(X1,union_of_members(top_of_basis(X2))) ) ).
cnf(u5765,axiom,
( element_of_set(f11(X2,closure(X0,cx,ct)),sF3)
| element_of_collection(sF3,top_of_basis(X3))
| ~ element_of_collection(f14(X0,cx,ct,X1),X3)
| ~ subset_sets(a,f14(X0,cx,ct,X1))
| ~ subset_sets(f14(X0,cx,ct,X1),sF3)
| ~ subset_sets(X0,cx)
| ~ subset_sets(X0,sF1)
| element_of_set(X1,union_of_members(top_of_basis(X2))) ) ).
cnf(u5769,axiom,
( element_of_set(f11(X2,closure(X0,cx,ct)),sF3)
| ~ subset_sets(a,f14(X0,cx,ct,X1))
| element_of_collection(sF3,top_of_basis(X3))
| element_of_set(f11(X3,sF3),f14(X0,cx,ct,X1))
| ~ subset_sets(X0,cx)
| ~ subset_sets(X0,sF1)
| element_of_set(X1,union_of_members(top_of_basis(X2))) ) ).
cnf(u5773,negated_conjecture,
( element_of_set(f11(X1,f14(a,cx,ct,X2)),f14(a,cx,ct,X2))
| element_of_set(f11(subspace_topology(X3,X4,X5),union_of_members(top_of_basis(X1))),union_of_members(top_of_basis(X1)))
| topological_space(X3,X4)
| element_of_set(X2,sF3) ) ).
cnf(u5777,negated_conjecture,
( element_of_set(X2,union_of_members(top_of_basis(X0)))
| ~ element_of_set(X2,sF3) ) ).
cnf(u5787,negated_conjecture,
subset_sets(a,sF1) ).
cnf(u5791,negated_conjecture,
( element_of_set(f11(X0,sF3),sF3)
| subset_sets(a,f14(a,cx,ct,X1))
| element_of_set(X1,union_of_members(top_of_basis(X0))) ) ).
cnf(u5825,negated_conjecture,
( element_of_set(f11(X0,sF3),sF3)
| closed(f14(a,cx,ct,X1),cx,ct)
| element_of_set(X1,union_of_members(top_of_basis(X0))) ) ).
cnf(u5834,axiom,
( element_of_set(f11(X0,closure(relative_complement_sets(a,cx),cx,ct)),sF1)
| element_of_collection(closure(relative_complement_sets(a,cx),cx,ct),top_of_basis(X0)) ) ).
cnf(u5837,axiom,
closed(sF3,cx,ct) ).
cnf(u5841,axiom,
subset_sets(relative_complement_sets(a,cx),sF3) ).
cnf(u5851,axiom,
( element_of_set(f19(closure(relative_complement_sets(a,cx),cx,ct),X0),sF1)
| hausdorff(closure(relative_complement_sets(a,cx),cx,ct),X0)
| ~ topological_space(closure(relative_complement_sets(a,cx),cx,ct),X0) ) ).
cnf(u5862,axiom,
( element_of_set(f20(closure(relative_complement_sets(a,cx),cx,ct),X0),sF1)
| hausdorff(closure(relative_complement_sets(a,cx),cx,ct),X0)
| ~ topological_space(closure(relative_complement_sets(a,cx),cx,ct),X0) ) ).
cnf(u6048,axiom,
( ~ element_of_set(X0,relative_complement_sets(a,cx))
| element_of_set(X0,interior(cx,cx,X1))
| ~ closed(a,cx,X1) ) ).
cnf(u6051,axiom,
subset_sets(cx,cx) ).
cnf(u6071,negated_conjecture,
( element_of_collection(union_of_members(f5(X0,ct)),ct)
| topological_space(X0,ct)
| ~ basis(X0,ct)
| ~ element_of_collection(X0,ct) ) ).
cnf(u6212,negated_conjecture,
topological_space(sF0,ct) ).
cnf(u6216,negated_conjecture,
( ~ element_of_set(X0,f13(a,cx,ct,X1))
| ~ element_of_set(X1,sF0)
| element_of_set(X0,interior(a,sF0,ct)) ) ).
cnf(u6227,negated_conjecture,
( ~ element_of_set(X0,f13(a,cx,ct,f20(sF0,X1)))
| hausdorff(sF0,X1)
| ~ topological_space(sF0,X1)
| element_of_set(X0,interior(a,sF0,ct)) ) ).
cnf(u6231,negated_conjecture,
( ~ element_of_set(X0,f13(a,cx,ct,f19(sF0,X1)))
| hausdorff(sF0,X1)
| ~ topological_space(sF0,X1)
| element_of_set(X0,interior(a,sF0,ct)) ) ).
cnf(u6243,negated_conjecture,
( ~ subset_sets(X1,sF0)
| hausdorff(closure(X1,X2,X3),X4)
| ~ topological_space(closure(X1,X2,X3),X4)
| element_of_set(X0,interior(a,sF0,ct))
| ~ element_of_set(X0,f13(a,cx,ct,f20(closure(X1,X2,X3),X4)))
| ~ closed(sF0,X2,X3) ) ).
cnf(u6248,negated_conjecture,
( ~ subset_sets(X1,sF0)
| hausdorff(closure(X1,X2,X3),X4)
| ~ topological_space(closure(X1,X2,X3),X4)
| element_of_set(X0,interior(a,sF0,ct))
| ~ element_of_set(X0,f13(a,cx,ct,f19(closure(X1,X2,X3),X4)))
| ~ closed(sF0,X2,X3) ) ).
cnf(u6355,negated_conjecture,
( element_of_collection(union_of_members(f5(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(ct))),ct)),ct)
| topological_space(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(ct))),ct)
| ~ element_of_collection(union_of_members(ct),subspace_topology(X1,X2,X0))
| ~ element_of_collection(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(ct))),ct) ) ).
cnf(u6484,negated_conjecture,
subset_sets(X0,X1) ).
cnf(u6606,negated_conjecture,
( ~ element_of_collection(sF0,X0)
| element_of_collection(sF3,top_of_basis(X0)) ) ).
cnf(u6609,negated_conjecture,
subset_sets(sF0,sF3) ).
cnf(u6960,negated_conjecture,
( element_of_set(X2,f14(a,cx,ct,X0))
| element_of_set(X0,interior(X3,X4,X5))
| ~ element_of_set(X2,sF3) ) ).
cnf(u9277,negated_conjecture,
~ disjoint_s(X2,X3) ).
cnf(u566,axiom,
( element_of_set(X4,interior(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,X3),cx,ct))
| ~ subset_sets(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,X3),cx)
| ~ element_of_set(X4,f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| ~ topological_space(sF0,X0)
| element_of_set(X3,closure(f13(a,cx,ct,f20(sF0,X0)),X1,X2))
| ~ subset_sets(f13(a,cx,ct,f20(sF0,X0)),X1)
| ~ topological_space(X1,X2) ) ).
cnf(u889,negated_conjecture,
( ~ element_of_set(f11(X1,f14(f14(a,cx,ct,X0),X2,X3,X4)),sF3)
| element_of_collection(f14(f14(a,cx,ct,X0),X2,X3,X4),top_of_basis(X1))
| ~ element_of_collection(f14(a,cx,ct,X0),X1)
| element_of_set(X0,sF3)
| element_of_set(X4,closure(f14(a,cx,ct,X0),X2,X3))
| ~ subset_sets(f14(a,cx,ct,X0),X2)
| ~ topological_space(X2,X3) ) ).
cnf(u770,axiom,
( ~ element_of_set(X5,intersection_of_sets(f16(X0,X1,X2,X3),X1))
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3)
| ~ topological_space(X2,X3)
| eq_p(f11(X4,intersection_of_sets(f16(X0,X1,X2,X3),X1)),X0)
| element_of_set(X5,union_of_members(top_of_basis(X4))) ) ).
cnf(u1176,negated_conjecture,
( ~ element_of_set(X1,f13(a,cx,ct,f7(sF0,X0)))
| element_of_set(X1,sF0)
| basis(sF0,X0)
| ~ topological_space(sF0,X0) ) ).
cnf(u2680,axiom,
( ~ closed(f13(closure(X0,X1,X2),X3,X4,f11(X8,closure(X7,X5,X6))),X1,X2)
| ~ subset_sets(X7,interior(closure(X0,X1,X2),X3,X4))
| element_of_collection(closure(X7,X5,X6),top_of_basis(X8))
| ~ closed(interior(closure(X0,X1,X2),X3,X4),X5,X6)
| ~ subset_sets(X0,f13(closure(X0,X1,X2),X3,X4,f11(X8,closure(X7,X5,X6))))
| ~ element_of_collection(f13(closure(X0,X1,X2),X3,X4,f11(X8,closure(X7,X5,X6))),X9)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X9)) ) ).
cnf(u4842,axiom,
( element_of_set(f7(intersection_of_sets(X0,X1),f24(intersection_of_sets(X0,X1),X2)),f6(X3,X4,f7(intersection_of_sets(X0,X1),f24(intersection_of_sets(X0,X1),X2)),X0,X1))
| basis(intersection_of_sets(X0,X1),f24(intersection_of_sets(X0,X1),X2))
| compact_space(intersection_of_sets(X0,X1),X2)
| ~ element_of_set(f7(intersection_of_sets(X0,X1),f24(intersection_of_sets(X0,X1),X2)),X3)
| ~ element_of_collection(X0,X4)
| ~ element_of_collection(X1,X4)
| ~ basis(X3,X4)
| ~ topological_space(intersection_of_sets(X0,X1),X2) ) ).
cnf(basis_for_topology_36,axiom,
( ~ subset_sets(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)))
| ~ equal_sets(union_of_members(X1),X0)
| ~ element_of_set(f7(X0,X1),X2)
| ~ element_of_collection(X2,X1)
| basis(X0,X1) ) ).
cnf(u631,axiom,
( element_of_set(f11(X0,intersection_of_members(X1)),X2)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ element_of_collection(X2,X1) ) ).
cnf(u5343,negated_conjecture,
( ~ open(union_of_members(ct),intersection_of_sets(X1,X2),X3)
| ~ disjoint_s(X0,union_of_members(ct))
| hausdorff(intersection_of_sets(X1,X2),X3)
| ~ open(X0,intersection_of_sets(X1,X2),X3)
| ~ element_of_set(f19(intersection_of_sets(X1,X2),X3),X0)
| ~ element_of_collection(X2,ct)
| ~ element_of_collection(X1,ct) ) ).
cnf(u877,negated_conjecture,
( ~ subset_sets(a,f14(X1,cx,ct,X2))
| element_of_collection(sF3,top_of_basis(X0))
| element_of_set(f11(X0,sF3),f14(X1,cx,ct,X2))
| element_of_set(X2,closure(X1,cx,ct))
| ~ subset_sets(X1,cx) ) ).
cnf(u1074,negated_conjecture,
( ~ closed(f13(a,cx,ct,f11(X4,sF0)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f11(X4,sF0)))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| element_of_set(f19(closure(X0,X1,X2),X3),sF0)
| element_of_collection(sF0,top_of_basis(X4)) ) ).
cnf(u9566,negated_conjecture,
( ~ element_of_set(X1,closure(relative_complement_sets(X2,X3),X3,X4))
| eq_p(X0,X1)
| ~ element_of_set(X0,boundary(X2,X3,X4)) ) ).
cnf(u1076,negated_conjecture,
( ~ closed(f13(a,cx,ct,f20(sF0,X4)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f20(sF0,X4)))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| element_of_set(f19(closure(X0,X1,X2),X3),sF0)
| ~ topological_space(sF0,X4)
| hausdorff(sF0,X4) ) ).
cnf(u322,axiom,
( open_covering(X2,X0,X1)
| ~ subset_collections(X2,X1)
| ~ topological_space(X0,X1)
| ~ topological_space(X0,X2) ) ).
cnf(u2850,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),closure(X3,X4,X5))
| subset_sets(X3,f14(X3,X4,X5,X6))
| topological_space(X0,X1)
| ~ subset_sets(X3,X4)
| ~ topological_space(X4,X5) ) ).
cnf(u4632,axiom,
( ~ element_of_collection(f10(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ element_of_collection(X3,top_of_basis(X2))
| ~ element_of_set(X4,X3)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X2)) ) ).
cnf(u4881,axiom,
( element_of_set(f7(closure(X0,X1,X2),f24(closure(X0,X1,X2),X3)),union_of_members(top_of_basis(X4)))
| basis(closure(X0,X1,X2),f24(closure(X0,X1,X2),X3))
| compact_space(closure(X0,X1,X2),X3)
| element_of_set(f11(X4,closure(X0,X1,X2)),sF3)
| ~ subset_sets(X0,sF1)
| ~ closed(sF1,X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u1289,axiom,
( element_of_set(f19(boundary(X1,X2,X3),X4),union_of_members(top_of_basis(X0)))
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| hausdorff(boundary(X1,X2,X3),X4)
| ~ topological_space(boundary(X1,X2,X3),X4) ) ).
cnf(u8099,negated_conjecture,
( element_of_set(f20(X0,X1),sF0)
| hausdorff(X0,X1) ) ).
cnf(u3591,axiom,
( element_of_set(f11(subspace_topology(X7,X8,X9),f13(X0,X1,X2,f11(X6,closure(X5,X3,X4)))),f13(X0,X1,X2,f11(X6,closure(X5,X3,X4))))
| ~ subset_sets(X5,interior(X0,X1,X2))
| element_of_collection(closure(X5,X3,X4),top_of_basis(X6))
| topological_space(X7,X8)
| ~ closed(interior(X0,X1,X2),X3,X4) ) ).
cnf(u153,negated_conjecture,
( ~ subset_sets(a,f14(X0,cx,ct,X1))
| ~ subset_sets(X0,cx)
| element_of_set(X1,closure(X0,cx,ct))
| ~ element_of_set(X2,sF3)
| element_of_set(X2,f14(X0,cx,ct,X1)) ) ).
cnf(u929,negated_conjecture,
( ~ closed(f1(ct,X4),X1,X2)
| ~ subset_sets(X0,f1(ct,X4))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ element_of_set(X4,cx)
| element_of_set(f20(closure(X0,X1,X2),X3),union_of_members(ct)) ) ).
cnf(u27674,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),interior(X3,X4,X5))
| element_of_set(f11(X1,union_of_members(ct)),union_of_members(ct))
| element_of_set(X2,f1(top_of_basis(X0),X2))
| ~ element_of_set(X2,cx) ) ).
cnf(u36067,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f10(X1,f1(top_of_basis(X1),f11(X0,union_of_members(ct))),f11(X0,union_of_members(ct))))
| limit_point(f11(X0,union_of_members(ct)),X2,X3,top_of_basis(X1))
| element_of_set(f11(X1,union_of_members(top_of_basis(X0))),sF0)
| ~ element_of_set(f11(X0,union_of_members(ct)),cx) ) ).
cnf(u3410,axiom,
( ~ closed(f13(a,cx,ct,f19(sF0,X0)),X3,X4)
| ~ topological_space(sF0,X0)
| element_of_set(f11(X1,boundary(X2,X3,X4)),union_of_members(ct))
| element_of_collection(boundary(X2,X3,X4),top_of_basis(X1))
| hausdorff(sF0,X0)
| ~ subset_sets(X2,f13(a,cx,ct,f19(sF0,X0))) ) ).
cnf(u5941,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,X2),X0)
| ~ element_of_set(X1,f13(a,cx,ct,X2))
| ~ topological_space(sF0,X0)
| element_of_set(X1,interior(a,sF0,X0))
| ~ element_of_set(X2,sF0) ) ).
cnf(u3680,axiom,
( ~ closed(f2(X4,f19(boundary(X0,X1,X2),X3)),X1,X2)
| ~ topological_space(boundary(X0,X1,X2),X3)
| ~ subset_sets(X0,f2(X4,f19(boundary(X0,X1,X2),X3)))
| element_of_set(f19(boundary(X0,X1,X2),X3),intersection_of_members(X4))
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u3810,axiom,
( element_of_set(f11(X2,sF3),f14(X1,cx,ct,f11(X0,closure(relative_complement_sets(X1,cx),cx,ct))))
| element_of_collection(closure(relative_complement_sets(X1,cx),cx,ct),top_of_basis(X0))
| ~ subset_sets(X1,cx)
| element_of_set(f11(X0,closure(relative_complement_sets(X1,cx),cx,ct)),boundary(X1,cx,ct))
| element_of_collection(sF3,top_of_basis(X2))
| ~ subset_sets(a,f14(X1,cx,ct,f11(X0,closure(relative_complement_sets(X1,cx),cx,ct)))) ) ).
cnf(u58797,negated_conjecture,
( open(f13(a,cx,subspace_topology(X0,X1,f13(a,X2,X3,f19(interior(a,X2,X3),X4))),X5),cx,subspace_topology(X0,X1,f13(a,X2,X3,f19(interior(a,X2,X3),X4))))
| hausdorff(interior(a,X2,X3),X4)
| ~ element_of_set(X5,f13(a,X2,X3,f19(interior(a,X2,X3),X4))) ) ).
cnf(u4636,axiom,
( ~ element_of_collection(interior(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| topological_space(X3,X4) ) ).
cnf(u947,axiom,
( closed(f14(relative_complement_sets(X4,X5),X5,X6,f20(closure(X0,X1,X2),X3)),X5,X6)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ closed(closure(X4,X5,X6),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(relative_complement_sets(X4,X5),X5)
| hausdorff(closure(X0,X1,X2),X3)
| element_of_set(f20(closure(X0,X1,X2),X3),boundary(X4,X5,X6)) ) ).
cnf(u2583,axiom,
( ~ element_of_collection(f10(X2,f13(a,cx,ct,X1),X0),X3)
| ~ element_of_collection(f13(a,cx,ct,X1),top_of_basis(X2))
| ~ element_of_set(X0,f13(a,cx,ct,X1))
| ~ topological_space(a,X3)
| ~ element_of_set(X4,f10(X2,f13(a,cx,ct,X1),X0))
| ~ element_of_set(X1,sF0)
| element_of_set(X4,interior(f13(a,cx,ct,X1),a,X3)) ) ).
cnf(u3241,axiom,
( ~ closed(X1,cx,ct)
| ~ topological_space(sF1,X0)
| ~ subset_sets(a,X1)
| element_of_set(f20(sF1,X0),X1)
| hausdorff(sF1,X0) ) ).
cnf(u3816,axiom,
( element_of_collection(f12(X3,X4,X5,relative_complement_sets(f14(X1,X2,subspace_topology(X3,X4,X5),f11(X0,closure(relative_complement_sets(X1,X2),X2,subspace_topology(X3,X4,X5)))),X2)),X4)
| element_of_collection(closure(relative_complement_sets(X1,X2),X2,subspace_topology(X3,X4,X5)),top_of_basis(X0))
| ~ subset_sets(X1,X2)
| element_of_set(f11(X0,closure(relative_complement_sets(X1,X2),X2,subspace_topology(X3,X4,X5))),boundary(X1,X2,subspace_topology(X3,X4,X5))) ) ).
cnf(u5337,axiom,
( ~ open(f13(X1,X2,X3,f20(closure(X4,X5,X6),X7)),closure(X4,X5,X6),X7)
| ~ disjoint_s(X0,f13(X1,X2,X3,f20(closure(X4,X5,X6),X7)))
| hausdorff(closure(X4,X5,X6),X7)
| ~ open(X0,closure(X4,X5,X6),X7)
| ~ element_of_set(f19(closure(X4,X5,X6),X7),X0)
| ~ subset_sets(X4,interior(X1,X2,X3))
| ~ closed(interior(X1,X2,X3),X5,X6) ) ).
cnf(u3169,negated_conjecture,
( closed(f14(relative_complement_sets(f13(a,cx,ct,X0),X1),X1,X2,X3),X1,X2)
| element_of_set(X4,interior(f14(f13(a,cx,ct,X0),X1,X2,X3),cx,ct))
| ~ subset_sets(relative_complement_sets(f13(a,cx,ct,X0),X1),X1)
| ~ subset_sets(f13(a,cx,ct,X0),X1)
| ~ topological_space(X1,X2)
| ~ subset_sets(f14(f13(a,cx,ct,X0),X1,X2,X3),cx)
| ~ element_of_set(X4,f13(a,cx,ct,X0))
| ~ element_of_set(X0,sF0)
| element_of_set(X3,boundary(f13(a,cx,ct,X0),X1,X2)) ) ).
cnf(u2948,axiom,
( open(f13(X4,X5,X6,f11(X0,boundary(X1,X2,X3))),X5,X6)
| ~ closed(interior(X4,X5,X6),X2,X3)
| ~ subset_sets(X1,interior(X4,X5,X6))
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(interior_51,axiom,
( ~ element_of_set(X0,interior(X1,X2,X3))
| open(f13(X1,X2,X3,X0),X2,X3) ) ).
cnf(u3369,axiom,
( ~ closed(closure(relative_complement_sets(X0,X1),X1,X2),X3,X4)
| ~ subset_sets(X5,closure(relative_complement_sets(X0,X1),X1,X2))
| element_of_collection(closure(X5,X3,X4),top_of_basis(X6))
| element_of_set(f11(X6,closure(X5,X3,X4)),boundary(X0,X1,X2))
| ~ closed(closure(X0,X1,X2),X3,X4)
| ~ subset_sets(X5,closure(X0,X1,X2)) ) ).
cnf(u58798,negated_conjecture,
( element_of_set(X5,f13(a,cx,subspace_topology(X0,X1,f13(a,X2,X3,f19(interior(a,X2,X3),X4))),X5))
| hausdorff(interior(a,X2,X3),X4)
| ~ element_of_set(X5,f13(a,X2,X3,f19(interior(a,X2,X3),X4))) ) ).
cnf(u2678,axiom,
( ~ element_of_set(f7(X0,X1),f13(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2,X3,f11(X7,closure(X6,X4,X5))))
| ~ subset_sets(X6,interior(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2,X3))
| element_of_collection(closure(X6,X4,X5),top_of_basis(X7))
| ~ equal_sets(union_of_members(X1),X0)
| ~ closed(interior(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2,X3),X4,X5)
| ~ element_of_collection(f13(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2,X3,f11(X7,closure(X6,X4,X5))),X1)
| basis(X0,X1) ) ).
cnf(limit_point_63,axiom,
( ~ limit_point(X0,X1,X2,X3)
| topological_space(X2,X3) ) ).
cnf(u6127,negated_conjecture,
( ~ closed(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X5,X6)
| ~ closed(sF0,X1,X2)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X3))
| element_of_set(f20(closure(X4,X5,X6),X7),sF0)
| hausdorff(closure(X4,X5,X6),X7)
| ~ subset_sets(X4,f13(a,cx,ct,f11(X3,closure(X0,X1,X2))))
| ~ subset_sets(X0,sF0)
| ~ topological_space(closure(X4,X5,X6),X7) ) ).
cnf(u1182,negated_conjecture,
( ~ closed(f13(a,cx,ct,f7(sF0,X4)),X1,X2)
| basis(sF0,X4)
| ~ topological_space(sF0,X4)
| hausdorff(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,f13(a,cx,ct,f7(sF0,X4)))
| element_of_set(f19(closure(X0,X1,X2),X3),sF0)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u56889,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f1(top_of_basis(X0),f11(X0,union_of_members(top_of_basis(X1)))))
| element_of_set(f11(X1,union_of_members(ct)),f1(X2,f11(X1,union_of_members(ct))))
| ~ element_of_set(f11(X0,union_of_members(top_of_basis(X1))),cx) ) ).
cnf(u3983,axiom,
( element_of_set(X7,f10(X1,f6(X3,top_of_basis(X1),f15(X4,X2,X5,X6,X0),X0,X2),X7))
| ~ element_of_collection(X2,top_of_basis(X1))
| ~ basis(X3,top_of_basis(X1))
| ~ element_of_set(f15(X4,X2,X5,X6,X0),X3)
| ~ neighborhood(X0,X4,X5,X6)
| ~ limit_point(X4,X2,X5,X6)
| ~ element_of_set(X7,f6(X3,top_of_basis(X1),f15(X4,X2,X5,X6,X0),X0,X2))
| ~ element_of_collection(X0,top_of_basis(X1)) ) ).
cnf(u36089,negated_conjecture,
( element_of_set(f11(X4,union_of_members(ct)),f13(X5,X6,X7,f11(X4,union_of_members(ct))))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| element_of_set(f11(X1,union_of_members(top_of_basis(X4))),sF0)
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u2361,axiom,
( element_of_set(f11(X4,f13(X0,X1,X2,f11(X3,interior(X0,X1,X2)))),f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))))
| element_of_collection(interior(X0,X1,X2),top_of_basis(X3))
| element_of_set(f11(X3,interior(X0,X1,X2)),union_of_members(top_of_basis(X4))) ) ).
cnf(u2899,axiom,
( ~ topological_space(X3,X4)
| element_of_set(f11(subspace_topology(X0,X1,X2),X3),X3)
| topological_space(X0,X1)
| hausdorff(X3,X4) ) ).
cnf(basis_for_topology_32,axiom,
( ~ equal_sets(union_of_members(X1),X0)
| basis(X0,X1)
| element_of_set(f7(X0,X1),X0) ) ).
cnf(u180,axiom,
( element_of_collection(f13(a,cx,ct,X0),ct)
| ~ element_of_set(X0,sF0) ) ).
cnf(u27439,axiom,
( element_of_set(f11(X1,f1(ct,X0)),f1(ct,X0))
| ~ element_of_set(X0,sF0)
| element_of_set(X0,f1(top_of_basis(X1),X0)) ) ).
cnf(u12961,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),union_of_members(X2))
| element_of_set(X1,f1(top_of_basis(X0),X1))
| ~ element_of_set(X1,cx) ) ).
cnf(u2975,axiom,
( ~ closed(f16(X4,X5,X6,X7),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f16(X4,X5,X6,X7))
| ~ topological_space(X6,X7)
| ~ subset_sets(X5,X6)
| limit_point(X4,X5,X6,X7)
| element_of_set(f11(X0,boundary(X1,X2,X3)),union_of_members(X7)) ) ).
cnf(u383,negated_conjecture,
( ~ element_of_set(X0,empty_set)
| element_of_set(X0,f1(ct,X0)) ) ).
cnf(u6024,negated_conjecture,
( element_of_set(X2,interior(f14(f13(a,cx,ct,f20(sF0,X1)),cx,ct,X0),cx,ct))
| ~ subset_sets(f13(a,cx,ct,f20(sF0,X1)),sF0)
| ~ subset_sets(f13(a,cx,ct,f20(sF0,X1)),cx)
| ~ topological_space(sF0,X1)
| ~ subset_sets(f14(f13(a,cx,ct,f20(sF0,X1)),cx,ct,X0),cx)
| ~ element_of_set(X2,f13(a,cx,ct,f20(sF0,X1)))
| hausdorff(sF0,X1)
| element_of_set(X0,sF0) ) ).
cnf(u387,axiom,
( element_of_collection(f8(X0,X1),X1)
| basis(X0,X1)
| ~ topological_space(X0,X1) ) ).
cnf(u5628,axiom,
( ~ element_of_set(f11(X0,boundary(X1,X2,X3)),closure(X4,X5,X6))
| ~ closed(closure(relative_complement_sets(X4,X5),X5,X6),X2,X3)
| ~ subset_sets(X1,closure(relative_complement_sets(X4,X5),X5,X6))
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| element_of_set(f11(X0,boundary(X1,X2,X3)),boundary(X4,X5,X6)) ) ).
cnf(u5949,negated_conjecture,
( ~ element_of_collection(f13(a,X2,X3,f19(interior(a,X2,X3),X4)),X0)
| ~ element_of_set(X1,f13(a,X2,X3,f19(interior(a,X2,X3),X4)))
| ~ topological_space(sF0,X0)
| element_of_set(X1,interior(a,sF0,X0))
| hausdorff(interior(a,X2,X3),X4)
| ~ topological_space(interior(a,X2,X3),X4) ) ).
cnf(u3202,axiom,
( open(f13(X4,X5,X6,f20(boundary(X0,X1,X2),X3)),X5,X6)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ closed(interior(X4,X5,X6),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u992,negated_conjecture,
( element_of_set(f20(f13(a,cx,ct,f20(closure(X2,X0,X1),X3)),X4),sF0)
| ~ subset_sets(X2,sF0)
| ~ topological_space(closure(X2,X0,X1),X3)
| hausdorff(closure(X2,X0,X1),X3)
| ~ closed(sF0,X0,X1)
| ~ topological_space(f13(a,cx,ct,f20(closure(X2,X0,X1),X3)),X4)
| hausdorff(f13(a,cx,ct,f20(closure(X2,X0,X1),X3)),X4) ) ).
cnf(u734,axiom,
( element_of_set(X5,closure(X2,X3,subspace_topology(X1,X4,X0)))
| subset_sets(X0,X1)
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,subspace_topology(X1,X4,X0)) ) ).
cnf(u1165,axiom,
( ~ element_of_set(f7(X0,X1),f13(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2,X3,f7(interior(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2,X3),X4)))
| basis(interior(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2,X3),X4)
| ~ equal_sets(union_of_members(X1),X0)
| ~ topological_space(interior(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2,X3),X4)
| ~ element_of_collection(f13(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2,X3,f7(interior(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2,X3),X4)),X1)
| basis(X0,X1) ) ).
cnf(u1967,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X4),closure(X5,X2,X3)),sF3)
| element_of_collection(boundary(X5,X2,X3),top_of_basis(X6))
| ~ closed(sF1,X2,X3)
| ~ subset_sets(X5,sF1)
| topological_space(X0,X1) ) ).
cnf(u2497,axiom,
( element_of_set(X0,f10(X2,f22(X1,top_of_basis(X2)),X0))
| ~ element_of_set(X0,f22(X1,top_of_basis(X2)))
| connected_space(X1,top_of_basis(X2))
| ~ topological_space(X1,top_of_basis(X2)) ) ).
cnf(u165,axiom,
( ~ element_of_set(X0,boundary(X1,X2,X3))
| subset_sets(relative_complement_sets(X1,X2),X2) ) ).
cnf(u3200,axiom,
( ~ closed(f9(X4,X5),X1,X2)
| ~ subset_sets(X0,f9(X4,X5))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(X4,X5)
| basis(X4,X5)
| element_of_set(f20(boundary(X0,X1,X2),X3),union_of_members(X5)) ) ).
cnf(u2697,axiom,
( ~ element_of_set(X9,f13(X0,X1,top_of_basis(subspace_topology(X2,X3,X4)),f19(closure(X7,X5,X6),X8)))
| ~ topological_space(closure(X7,X5,X6),X8)
| hausdorff(closure(X7,X5,X6),X8)
| ~ subset_sets(X7,interior(X0,X1,top_of_basis(subspace_topology(X2,X3,X4))))
| ~ closed(interior(X0,X1,top_of_basis(subspace_topology(X2,X3,X4))),X5,X6)
| topological_space(X2,X3) ) ).
cnf(u1374,axiom,
( element_of_set(f7(intersection_of_sets(X0,X1),X2),f6(X3,X4,f7(intersection_of_sets(X0,X1),X2),X0,X1))
| ~ element_of_collection(X0,X4)
| ~ element_of_collection(X1,X4)
| ~ basis(X3,X4)
| ~ element_of_set(f7(intersection_of_sets(X0,X1),X2),X3)
| basis(intersection_of_sets(X0,X1),X2)
| ~ topological_space(intersection_of_sets(X0,X1),X2) ) ).
cnf(u3902,axiom,
( subset_sets(f13(f14(X1,X2,X3,X4),X5,X6,f20(closure(X7,X8,X9),X10)),f14(f13(f14(X1,X2,X3,X4),X5,X6,f20(closure(X7,X8,X9),X10)),X2,X3,X0))
| element_of_set(X0,f14(X1,X2,X3,X4))
| ~ subset_sets(f13(f14(X1,X2,X3,X4),X5,X6,f20(closure(X7,X8,X9),X10)),X2)
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| ~ subset_sets(X7,interior(f14(X1,X2,X3,X4),X5,X6))
| ~ closed(interior(f14(X1,X2,X3,X4),X5,X6),X8,X9)
| ~ topological_space(closure(X7,X8,X9),X10)
| hausdorff(closure(X7,X8,X9),X10) ) ).
cnf(u1099,axiom,
( ~ element_of_set(f7(X1,X2),f13(intersection_of_sets(f8(X1,X2),f9(X1,X2)),X3,X4,f19(closure(X0,X5,X6),X7)))
| ~ closed(interior(intersection_of_sets(f8(X1,X2),f9(X1,X2)),X3,X4),X5,X6)
| ~ topological_space(closure(X0,X5,X6),X7)
| hausdorff(closure(X0,X5,X6),X7)
| ~ equal_sets(union_of_members(X2),X1)
| ~ subset_sets(X0,interior(intersection_of_sets(f8(X1,X2),f9(X1,X2)),X3,X4))
| ~ element_of_collection(f13(intersection_of_sets(f8(X1,X2),f9(X1,X2)),X3,X4,f19(closure(X0,X5,X6),X7)),X2)
| basis(X1,X2) ) ).
cnf(u744,axiom,
( element_of_set(f20(f1(ct,X0),X1),union_of_members(ct))
| ~ element_of_set(X0,sF0)
| ~ topological_space(f1(ct,X0),X1)
| hausdorff(f1(ct,X0),X1) ) ).
cnf(u42848,negated_conjecture,
( element_of_set(X3,f13(a,cx,subspace_topology(X0,X1,f13(a,cx,ct,f19(sF0,X2))),X3))
| hausdorff(sF0,X2)
| ~ element_of_set(X3,f13(a,cx,ct,f19(sF0,X2))) ) ).
cnf(u414,axiom,
( ~ subset_sets(X4,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)))
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ element_of_collection(X4,X5)
| ~ topological_space(X0,X5)
| ~ element_of_set(X6,X4)
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X6,interior(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X0,X5)) ) ).
cnf(u959,axiom,
( element_of_set(f20(closure(X0,X1,X2),X3),sF3)
| ~ subset_sets(X0,sF1)
| ~ closed(sF1,X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3) ) ).
cnf(u3605,axiom,
( element_of_set(X10,interior(f14(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8,f11(X9,closure(relative_complement_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7),X7,X8))),X1,X2))
| element_of_collection(closure(relative_complement_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7),X7,X8),top_of_basis(X9))
| ~ subset_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7)
| ~ closed(interior(X0,X1,X2),X4,X5)
| ~ topological_space(closure(X3,X4,X5),X6)
| hausdorff(closure(X3,X4,X5),X6)
| ~ subset_sets(f14(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8,f11(X9,closure(relative_complement_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7),X7,X8))),X1)
| ~ element_of_set(X10,f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)))
| ~ subset_sets(X3,interior(X0,X1,X2))
| element_of_set(f11(X9,closure(relative_complement_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7),X7,X8)),boundary(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8)) ) ).
cnf(u2467,axiom,
( open(f13(a,cx,ct,f7(sF0,X0)),cx,ct)
| ~ topological_space(sF0,X0)
| basis(sF0,X0) ) ).
cnf(u3484,negated_conjecture,
( ~ closed(f13(a,cx,ct,f11(X4,sF0)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f11(X4,sF0)))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| element_of_set(f7(closure(X0,X1,X2),X3),sF0)
| element_of_collection(sF0,top_of_basis(X4)) ) ).
cnf(u138,axiom,
( subset_sets(relative_complement_sets(X1,X2),f14(relative_complement_sets(X1,X2),X2,X3,X0))
| ~ subset_sets(relative_complement_sets(X1,X2),X2)
| ~ element_of_set(X0,closure(X1,X2,X3))
| element_of_set(X0,boundary(X1,X2,X3)) ) ).
cnf(u3172,axiom,
( closed(f14(relative_complement_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),X4,X5,X6),X4,X5)
| element_of_set(X7,interior(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,X6),X1,X2))
| ~ subset_sets(relative_complement_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),X4)
| ~ subset_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(X4,X5)
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ subset_sets(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,X6),X1)
| ~ element_of_set(X7,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X6,boundary(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5)) ) ).
cnf(u816,negated_conjecture,
( ~ element_of_collection(X3,subspace_topology(X1,X2,f14(a,cx,ct,X0)))
| ~ connected_set(f14(a,cx,ct,X0),X1,X2)
| ~ element_of_set(X4,X3)
| ~ subset_sets(X3,a)
| element_of_set(X4,interior(a,f14(a,cx,ct,X0),subspace_topology(X1,X2,f14(a,cx,ct,X0))))
| element_of_set(X0,sF3) ) ).
cnf(u3219,axiom,
( ~ closed(f13(X4,X5,X6,f20(interior(X4,X5,X6),X7)),X1,X2)
| ~ subset_sets(X0,f13(X4,X5,X6,f20(interior(X4,X5,X6),X7)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(interior(X4,X5,X6),X7)
| hausdorff(interior(X4,X5,X6),X7)
| element_of_set(f20(boundary(X0,X1,X2),X3),interior(X4,X5,X6)) ) ).
cnf(u3307,negated_conjecture,
( element_of_set(f20(f13(a,cx,ct,f7(sF0,X0)),X1),union_of_members(top_of_basis(X2)))
| ~ topological_space(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f7(sF0,X0)),X1)
| hausdorff(f13(a,cx,ct,f7(sF0,X0)),X1)
| element_of_set(f11(X2,sF0),sF0)
| basis(sF0,X0) ) ).
cnf(u481,axiom,
( element_of_set(f7(X0,f24(X0,X1)),X0)
| ~ topological_space(X0,X1)
| basis(X0,f24(X0,X1))
| compact_space(X0,X1) ) ).
cnf(u4645,axiom,
( ~ element_of_collection(f13(a,cx,ct,f19(sF0,X2)),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| hausdorff(sF0,X2)
| ~ topological_space(sF0,X2)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(ct)) ) ).
cnf(u12960,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),interior(X2,X3,X4))
| element_of_set(X1,f1(top_of_basis(X0),X1))
| ~ element_of_set(X1,cx) ) ).
cnf(u4777,axiom,
( element_of_collection(f21(X0,subspace_topology(X1,X2,X3)),subspace_topology(X4,X2,X3))
| ~ topological_space(X0,subspace_topology(X1,X2,X3))
| ~ topological_space(X4,X2)
| ~ subset_sets(X3,X4)
| connected_space(X0,subspace_topology(X1,X2,X3)) ) ).
cnf(u17803,negated_conjecture,
( ~ element_of_set(X2,intersection_of_members(X1))
| eq_p(X2,X0)
| ~ element_of_set(X0,intersection_of_members(X1)) ) ).
cnf(u6032,negated_conjecture,
( ~ element_of_set(f11(X2,f14(f14(a,cx,ct,X1),cx,ct,X0)),sF3)
| ~ subset_sets(f14(a,cx,ct,X1),sF0)
| ~ subset_sets(f14(a,cx,ct,X1),cx)
| ~ element_of_collection(f14(a,cx,ct,X1),X2)
| element_of_collection(f14(f14(a,cx,ct,X1),cx,ct,X0),top_of_basis(X2))
| element_of_set(X0,sF0)
| element_of_set(X1,sF3) ) ).
cnf(u1307,axiom,
( ~ topological_space(f1(X1,X3),X4)
| ~ subset_sets(X2,X0)
| limit_point(X3,X2,X0,X1)
| element_of_set(f19(f1(X1,X3),X4),union_of_members(X1))
| ~ topological_space(X0,X1)
| hausdorff(f1(X1,X3),X4) ) ).
cnf(u54509,negated_conjecture,
( ~ element_of_set(X7,f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)))
| hausdorff(interior(X1,X2,X3),X4)
| element_of_set(X7,f13(f14(f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)),X5,X6,X0),X2,X3,X7))
| element_of_set(X0,interior(X8,X9,X10)) ) ).
cnf(u7380,negated_conjecture,
( limit_point(X0,X4,X5,X6)
| element_of_set(f11(X7,interior(X1,X2,X3)),interior(X1,X2,X3))
| element_of_set(X0,union_of_members(top_of_basis(X7))) ) ).
cnf(subspace_topology_44,axiom,
( ~ element_of_collection(X0,subspace_topology(X1,X2,X3))
| element_of_collection(f12(X1,X2,X3,X0),X2) ) ).
cnf(u3654,axiom,
( ~ closed(relative_complement_sets(X0,closure(X1,X2,X3)),X2,X3)
| element_of_collection(boundary(X0,closure(X1,X2,X3),X4),top_of_basis(X5))
| ~ subset_sets(X1,relative_complement_sets(X0,closure(X1,X2,X3)))
| ~ element_of_collection(relative_complement_sets(X0,closure(X1,X2,X3)),X6)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X6)) ) ).
cnf(u4637,axiom,
( ~ element_of_collection(interior(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| subset_sets(X2,X3) ) ).
cnf(u5559,axiom,
( closed(f14(X0,X1,X2,f7(closure(relative_complement_sets(X0,X1),X1,X2),X3)),X1,X2)
| basis(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f7(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1) ) ).
cnf(u5331,axiom,
( ~ open(boundary(X1,X2,X3),closure(relative_complement_sets(X1,X2),X2,X3),X4)
| ~ disjoint_s(X0,boundary(X1,X2,X3))
| hausdorff(closure(relative_complement_sets(X1,X2),X2,X3),X4)
| ~ open(X0,closure(relative_complement_sets(X1,X2),X2,X3),X4)
| ~ element_of_set(f19(closure(relative_complement_sets(X1,X2),X2,X3),X4),X0)
| ~ subset_sets(relative_complement_sets(X1,X2),closure(X1,X2,X3))
| ~ closed(closure(X1,X2,X3),X2,X3) ) ).
cnf(u4781,axiom,
( ~ element_of_set(X6,f12(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5,f22(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))))
| ~ topological_space(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| connected_space(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| topological_space(X2,X3) ) ).
cnf(u2971,axiom,
( ~ closed(closure(X4,X5,X6),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,closure(X4,X5,X6))
| ~ closed(X7,X5,X6)
| ~ subset_sets(X4,X7)
| element_of_set(f11(X8,closure(X4,X5,X6)),X7)
| element_of_set(f11(X0,boundary(X1,X2,X3)),union_of_members(top_of_basis(X8))) ) ).
cnf(u1169,axiom,
( subset_sets(f13(a,cx,ct,f7(sF0,X0)),a)
| ~ topological_space(sF0,X0)
| basis(sF0,X0) ) ).
cnf(u36096,negated_conjecture,
( open(f13(X4,X5,X6,f11(X7,union_of_members(ct))),X5,X6)
| element_of_set(f11(X1,union_of_members(top_of_basis(X7))),interior(X8,X9,X10))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u4662,axiom,
( closed(f14(relative_complement_sets(X2,X3),X3,X4,f11(X0,intersection_of_members(X1))),X3,X4)
| ~ element_of_collection(closure(X2,X3,X4),X1)
| ~ subset_sets(relative_complement_sets(X2,X3),X3)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),boundary(X2,X3,X4)) ) ).
cnf(u856,axiom,
( ~ closed(closure(X4,X5,X6),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,closure(X4,X5,X6))
| subset_sets(X4,X5) ) ).
cnf(u27675,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),union_of_members(X3))
| element_of_set(f11(X1,union_of_members(ct)),union_of_members(ct))
| element_of_set(X2,f1(top_of_basis(X0),X2))
| ~ element_of_set(X2,cx) ) ).
cnf(u6364,axiom,
( element_of_set(f19(sF0,X0),f1(ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| ~ topological_space(sF0,X0) ) ).
cnf(u6105,axiom,
( element_of_set(X10,interior(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5,f11(X6,f14(closure(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5),X7,X8,X9))),X1,X2))
| ~ element_of_set(X10,f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))))
| element_of_collection(interior(X0,X1,X2),top_of_basis(X3))
| ~ subset_sets(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5,f11(X6,f14(closure(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5),X7,X8,X9))),X1)
| element_of_collection(f14(closure(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5),X7,X8,X9),top_of_basis(X6))
| ~ element_of_collection(closure(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5),X6)
| ~ subset_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4)
| ~ topological_space(X4,X5)
| element_of_set(X9,closure(closure(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5),X7,X8))
| ~ subset_sets(closure(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5),X7)
| ~ topological_space(X7,X8) ) ).
cnf(basis_for_topology_29,axiom,
( ~ element_of_set(X2,intersection_of_sets(X3,X4))
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X3,X1)
| ~ element_of_collection(X4,X1)
| ~ basis(X0,X1)
| element_of_set(X2,f6(X0,X1,X2,X3,X4)) ) ).
cnf(u4011,axiom,
( ~ closed(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X8,X9)
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| element_of_set(f19(closure(X7,X8,X9),X10),interior(X4,X5,X6))
| hausdorff(closure(X7,X8,X9),X10)
| ~ subset_sets(X7,f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)))
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X7,X8,X9),X10) ) ).
cnf(u1291,axiom,
( element_of_set(f19(closure(X1,X2,X3),X4),union_of_members(top_of_basis(X0)))
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| ~ topological_space(closure(X1,X2,X3),X4)
| hausdorff(closure(X1,X2,X3),X4) ) ).
cnf(u308,axiom,
( element_of_set(f19(boundary(X0,X1,X2),X3),X4)
| ~ topological_space(boundary(X0,X1,X2),X3)
| ~ subset_sets(X0,X4)
| ~ closed(X4,X1,X2)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u30097,negated_conjecture,
( open(f13(X2,X3,X4,f11(X0,f1(ct,X1))),X3,X4)
| element_of_set(X1,f1(top_of_basis(X0),X1))
| ~ element_of_set(X1,sF0) ) ).
cnf(u6713,negated_conjecture,
( ~ element_of_set(X3,sF0)
| ~ element_of_set(X2,X0)
| element_of_set(X2,interior(f13(a,cx,ct,X3),a,X1)) ) ).
cnf(u2622,axiom,
( element_of_set(f11(X7,f13(X1,X2,X3,f19(closure(X0,X4,X5),X6))),f13(X1,X2,X3,f19(closure(X0,X4,X5),X6)))
| ~ closed(interior(X1,X2,X3),X4,X5)
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| ~ subset_sets(X0,interior(X1,X2,X3))
| element_of_set(f19(closure(X0,X4,X5),X6),union_of_members(top_of_basis(X7))) ) ).
cnf(u1069,axiom,
( subset_sets(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X4)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3) ) ).
cnf(u955,axiom,
( element_of_set(f20(closure(X0,X1,X2),X3),closure(X4,X5,X6))
| ~ subset_sets(X0,boundary(X4,X5,X6))
| ~ closed(boundary(X4,X5,X6),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3) ) ).
cnf(u4272,axiom,
( element_of_set(X7,interior(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,f20(closure(relative_complement_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),X4,X5),X6)),X1,X2))
| ~ topological_space(closure(relative_complement_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),X4,X5),X6)
| hausdorff(closure(relative_complement_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),X4,X5),X6)
| ~ subset_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ subset_sets(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,f20(closure(relative_complement_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),X4,X5),X6)),X1)
| ~ element_of_set(X7,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(f20(closure(relative_complement_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),X4,X5),X6),boundary(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5)) ) ).
cnf(u1309,axiom,
( ~ topological_space(f1(X1,X3),X4)
| ~ subset_sets(X2,X0)
| limit_point(X3,X2,X0,X1)
| element_of_set(f20(f1(X1,X3),X4),union_of_members(X1))
| ~ topological_space(X0,X1)
| hausdorff(f1(X1,X3),X4) ) ).
cnf(u1432,axiom,
hausdorff(sF3,X0) ).
cnf(u2936,axiom,
( ~ closed(f1(X4,X5),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f1(X4,X5))
| ~ topological_space(X6,X4)
| ~ subset_sets(X7,X6)
| limit_point(X5,X7,X6,X4)
| element_of_set(f11(X0,boundary(X1,X2,X3)),union_of_members(X4)) ) ).
cnf(u3695,axiom,
( element_of_set(X13,interior(f14(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8,f11(X12,f14(closure(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8),X9,X10,X11))),X1,X2))
| ~ element_of_collection(closure(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8),X12)
| ~ subset_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7)
| ~ topological_space(X7,X8)
| element_of_set(X11,closure(closure(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8),X9,X10))
| ~ subset_sets(closure(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8),X9)
| ~ topological_space(X9,X10)
| ~ closed(interior(X0,X1,X2),X4,X5)
| ~ topological_space(closure(X3,X4,X5),X6)
| hausdorff(closure(X3,X4,X5),X6)
| ~ subset_sets(f14(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8,f11(X12,f14(closure(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8),X9,X10,X11))),X1)
| ~ element_of_set(X13,f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)))
| ~ subset_sets(X3,interior(X0,X1,X2))
| element_of_collection(f14(closure(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8),X9,X10,X11),top_of_basis(X12)) ) ).
cnf(u6774,axiom,
( element_of_set(X0,f10(X2,X1,X0))
| ~ element_of_set(X0,X1) ) ).
cnf(u30267,negated_conjecture,
( element_of_set(f11(X4,union_of_members(top_of_basis(X0))),f1(X5,f11(X4,union_of_members(top_of_basis(X0)))))
| open(f13(X1,X2,X3,f11(X0,union_of_members(ct))),X2,X3)
| element_of_set(X6,f1(top_of_basis(X4),X6))
| ~ element_of_set(X6,cx) ) ).
cnf(u29156,negated_conjecture,
( element_of_set(f11(X1,union_of_members(ct)),f1(top_of_basis(X0),f11(X1,union_of_members(ct))))
| element_of_set(f11(X0,union_of_members(top_of_basis(X1))),union_of_members(X5))
| ~ element_of_set(f11(X1,union_of_members(ct)),cx) ) ).
cnf(u3677,axiom,
( ~ closed(f2(X4,f11(X0,boundary(X1,X2,X3))),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| element_of_set(f11(X0,boundary(X1,X2,X3)),intersection_of_members(X4))
| ~ subset_sets(X1,f2(X4,f11(X0,boundary(X1,X2,X3)))) ) ).
cnf(u4641,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,X2),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),sF0)
| ~ element_of_set(X2,sF0) ) ).
cnf(u9540,negated_conjecture,
( eq_p(f20(boundary(X0,X1,X2),X3),X4)
| ~ element_of_set(X4,sF3)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u790,negated_conjecture,
( ~ element_of_set(X1,f13(a,cx,ct,f11(X0,sF0)))
| element_of_set(X1,sF0)
| element_of_collection(sF0,top_of_basis(X0)) ) ).
cnf(u5632,negated_conjecture,
( ~ subset_sets(a,f14(relative_complement_sets(X0,cx),cx,ct,X1))
| element_of_set(X1,boundary(X0,cx,ct))
| ~ subset_sets(relative_complement_sets(X0,cx),cx)
| ~ subset_sets(X0,cx)
| element_of_set(f11(X2,sF3),f14(relative_complement_sets(X0,cx),cx,ct,X1))
| element_of_collection(sF3,top_of_basis(X2))
| subset_sets(X0,f14(X0,cx,ct,X1)) ) ).
cnf(u1399,axiom,
( ~ element_of_set(X0,f12(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5,f16(X6,X7,X8,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))))
| topological_space(X2,X3)
| limit_point(X6,X7,X8,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| ~ topological_space(X8,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| ~ subset_sets(X7,X8) ) ).
cnf(u2650,axiom,
( ~ element_of_set(X4,f1(top_of_basis(subspace_topology(X0,X1,X2)),f11(X3,union_of_members(top_of_basis(subspace_topology(X0,X1,X2))))))
| element_of_collection(union_of_members(top_of_basis(subspace_topology(X0,X1,X2))),top_of_basis(X3))
| subset_sets(X2,X0) ) ).
cnf(u621,axiom,
( ~ element_of_set(f20(closure(relative_complement_sets(a,cx),cx,ct),X0),sF3)
| element_of_set(f20(closure(relative_complement_sets(a,cx),cx,ct),X0),sF1)
| hausdorff(closure(relative_complement_sets(a,cx),cx,ct),X0)
| ~ topological_space(closure(relative_complement_sets(a,cx),cx,ct),X0) ) ).
cnf(finer_topology_25,axiom,
( ~ finer(X0,X1,X2)
| topological_space(X2,X1) ) ).
cnf(u1330,axiom,
( element_of_set(f11(X0,f16(X1,X2,X3,X4)),f16(X1,X2,X3,X4))
| element_of_set(X1,union_of_members(top_of_basis(X0)))
| ~ subset_sets(X2,X3)
| limit_point(X1,X2,X3,X4)
| ~ topological_space(X3,X4) ) ).
cnf(topology_generated_40,axiom,
( element_of_collection(X0,top_of_basis(X1))
| element_of_set(f11(X1,X0),X0) ) ).
cnf(u2418,axiom,
( element_of_set(f11(X5,closure(X3,X1,X2)),union_of_members(top_of_basis(X4)))
| element_of_set(f11(X4,closure(X3,X1,X2)),X0)
| ~ subset_sets(X3,X0)
| ~ closed(X0,X1,X2)
| element_of_collection(closure(X3,X1,X2),top_of_basis(X5)) ) ).
cnf(u3512,axiom,
( ~ closed(f22(X4,X5),X1,X2)
| ~ subset_sets(X0,f22(X4,X5))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(X4,X5)
| connected_space(X4,X5)
| element_of_set(f7(closure(X0,X1,X2),X3),union_of_members(X5)) ) ).
cnf(u4888,axiom,
( basis(boundary(X0,X1,X2),f24(boundary(X0,X1,X2),X3))
| ~ topological_space(boundary(X0,X1,X2),X3)
| compact_space(boundary(X0,X1,X2),X3)
| subset_sets(relative_complement_sets(X0,X1),X1) ) ).
cnf(u5349,axiom,
( ~ element_of_set(f19(X1,X2),X0)
| ~ open(X1,X1,X2)
| hausdorff(X1,X2)
| ~ open(X0,X1,X2)
| ~ disjoint_s(X0,X1) ) ).
cnf(u4630,axiom,
( ~ element_of_collection(f8(X2,X3),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ topological_space(X2,X3)
| basis(X2,X3)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X3)) ) ).
cnf(u263,axiom,
( closed(f14(relative_complement_sets(X0,X1),X1,X2,f19(closure(X0,X1,X2),X3)),X1,X2)
| hausdorff(closure(X0,X1,X2),X3)
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| ~ topological_space(closure(X0,X1,X2),X3)
| element_of_set(f19(closure(X0,X1,X2),X3),boundary(X0,X1,X2)) ) ).
cnf(u3440,axiom,
( ~ closed(f13(a,cx,ct,f20(sF0,X0)),X3,X4)
| ~ topological_space(sF0,X0)
| element_of_set(f11(X1,closure(X2,X3,X4)),union_of_members(ct))
| element_of_collection(closure(X2,X3,X4),top_of_basis(X1))
| hausdorff(sF0,X0)
| ~ subset_sets(X2,f13(a,cx,ct,f20(sF0,X0))) ) ).
cnf(u3223,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ subset_sets(X4,X7)
| ~ closed(X7,X5,X6)
| element_of_set(f20(boundary(X0,X1,X2),X3),X7) ) ).
cnf(u33836,negated_conjecture,
( open(f13(a,cx,subspace_topology(X0,X1,f13(a,cx,ct,X2)),X3),cx,subspace_topology(X0,X1,f13(a,cx,ct,X2)))
| ~ element_of_set(X2,sF0)
| ~ element_of_set(X3,f13(a,cx,ct,X2)) ) ).
cnf(topological_space_14,axiom,
( ~ equal_sets(union_of_members(X1),X0)
| topological_space(X0,X1)
| ~ element_of_collection(empty_set,X1)
| ~ element_of_collection(X0,X1)
| element_of_collection(f4(X0,X1),X1)
| subset_collections(f5(X0,X1),X1) ) ).
cnf(u5253,axiom,
( ~ open(union_of_members(top_of_basis(X1)),X2,X3)
| ~ disjoint_s(X0,union_of_members(top_of_basis(X1)))
| hausdorff(X2,X3)
| ~ open(X0,X2,X3)
| ~ element_of_set(f19(X2,X3),X0)
| element_of_set(f11(X1,closure(X4,X5,X6)),sF3)
| subset_sets(X4,f14(X4,X5,X6,f20(X2,X3)))
| ~ closed(sF1,X5,X6)
| ~ subset_sets(X4,sF1)
| ~ subset_sets(X4,X5) ) ).
cnf(u4446,axiom,
( ~ element_of_set(X6,f12(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5,f2(subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5),X0)))
| element_of_set(X0,intersection_of_members(subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5)))
| subset_sets(X4,X2) ) ).
cnf(u5848,negated_conjecture,
( element_of_set(f11(X1,sF3),f14(a,cx,ct,f19(closure(relative_complement_sets(a,cx),cx,ct),X0)))
| ~ topological_space(closure(relative_complement_sets(a,cx),cx,ct),X0)
| hausdorff(closure(relative_complement_sets(a,cx),cx,ct),X0)
| element_of_collection(sF3,top_of_basis(X1))
| element_of_set(f19(closure(relative_complement_sets(a,cx),cx,ct),X0),sF1) ) ).
cnf(u3351,negated_conjecture,
( element_of_collection(f1(ct,f11(X0,boundary(X1,X2,X3))),ct)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ closed(empty_set,X2,X3)
| ~ subset_sets(X1,empty_set) ) ).
cnf(u937,axiom,
( ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| topological_space(X5,X6) ) ).
cnf(u711,axiom,
( subset_sets(X0,f14(X0,X1,X2,f11(X3,boundary(relative_complement_sets(X0,X1),X1,X2))))
| element_of_set(f11(X3,boundary(relative_complement_sets(X0,X1),X1,X2)),boundary(X0,X1,X2))
| element_of_collection(boundary(relative_complement_sets(X0,X1),X1,X2),top_of_basis(X3))
| ~ subset_sets(X0,X1) ) ).
cnf(u5031,axiom,
( ~ subset_sets(f1(X0,f11(X1,union_of_members(X0))),union_of_members(X0))
| ~ element_of_collection(f1(X0,f11(X1,union_of_members(X0))),X1)
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ) ).
cnf(u7581,negated_conjecture,
( element_of_set(f15(X1,X4,X2,X3,X0),f13(X5,X6,X7,f15(X1,X4,X2,X3,X0)))
| ~ limit_point(X1,X4,X2,X3)
| ~ neighborhood(X0,X1,X2,X3) ) ).
cnf(u1154,negated_conjecture,
( element_of_set(X3,interior(a,cx,subspace_topology(X1,X2,f13(a,cx,ct,f20(sF0,X0)))))
| ~ topological_space(cx,subspace_topology(X1,X2,f13(a,cx,ct,f20(sF0,X0))))
| ~ element_of_set(X3,f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| ~ topological_space(sF0,X0)
| ~ connected_set(f13(a,cx,ct,f20(sF0,X0)),X1,X2) ) ).
cnf(u3682,axiom,
( ~ closed(f2(X4,f20(closure(X0,X1,X2),X3)),X1,X2)
| hausdorff(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,f2(X4,f20(closure(X0,X1,X2),X3)))
| element_of_set(f20(closure(X0,X1,X2),X3),intersection_of_members(X4))
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u819,axiom,
( hausdorff(boundary(X0,X1,X2),subspace_topology(X3,X4,boundary(X0,X1,X2)))
| ~ connected_set(boundary(X0,X1,X2),X3,X4)
| topological_space(X1,X2) ) ).
cnf(u3782,axiom,
( element_of_collection(f14(closure(X0,X1,subspace_topology(X2,X3,X4)),X5,X6,X7),top_of_basis(X8))
| element_of_set(X7,closure(closure(X0,X1,subspace_topology(X2,X3,X4)),X5,X6))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,subspace_topology(X2,X3,X4))
| ~ element_of_collection(closure(X0,X1,subspace_topology(X2,X3,X4)),X8)
| ~ subset_sets(closure(X0,X1,subspace_topology(X2,X3,X4)),X5)
| ~ topological_space(X5,X6)
| topological_space(X2,X3) ) ).
cnf(u4640,axiom,
( ~ element_of_collection(f13(a,cx,ct,X2),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ element_of_set(X2,sF0)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(ct)) ) ).
cnf(u4016,axiom,
( ~ closed(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X8,X9)
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| element_of_set(f20(closure(X7,X8,X9),X10),interior(X4,X5,X6))
| hausdorff(closure(X7,X8,X9),X10)
| ~ subset_sets(X7,f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)))
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X7,X8,X9),X10) ) ).
cnf(u1296,axiom,
( element_of_set(f20(closure(X1,X2,X3),X4),union_of_members(top_of_basis(X0)))
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| ~ topological_space(closure(X1,X2,X3),X4)
| hausdorff(closure(X1,X2,X3),X4) ) ).
cnf(u13004,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),sF0)
| element_of_set(X1,f1(top_of_basis(X0),X1))
| ~ element_of_set(X1,cx) ) ).
cnf(u2820,axiom,
( element_of_set(f11(X2,f8(X0,X1)),union_of_members(X1))
| basis(X0,X1)
| ~ topological_space(X0,X1)
| element_of_collection(f8(X0,X1),top_of_basis(X2)) ) ).
cnf(u1086,axiom,
( ~ closed(boundary(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,boundary(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(relative_complement_sets(X4,X5),X7)
| ~ closed(X7,X5,X6)
| element_of_set(f19(closure(X0,X1,X2),X3),X7) ) ).
cnf(u33343,negated_conjecture,
( open(f13(a,sF0,subspace_topology(X0,X1,f13(a,cx,ct,X2)),X3),sF0,subspace_topology(X0,X1,f13(a,cx,ct,X2)))
| ~ element_of_set(X2,sF0)
| ~ element_of_set(X3,f13(a,cx,ct,X2)) ) ).
cnf(u26421,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f1(top_of_basis(X0),f11(X0,union_of_members(ct))))
| ~ element_of_set(f11(X0,union_of_members(ct)),cx) ) ).
cnf(u3632,axiom,
( element_of_collection(f18(X1,X3,X2,X0),X3)
| eq_p(X2,X0)
| ~ hausdorff(X1,X3)
| ~ element_of_set(X2,X1)
| ~ element_of_set(X0,X1) ) ).
cnf(u2643,negated_conjecture,
( element_of_set(f19(empty_set,X0),f1(ct,f19(empty_set,X0)))
| ~ topological_space(empty_set,X0)
| hausdorff(empty_set,X0) ) ).
cnf(u489,axiom,
( element_of_set(f20(f13(a,cx,ct,X0),X1),union_of_members(ct))
| ~ element_of_set(X0,sF0)
| ~ topological_space(f13(a,cx,ct,X0),X1)
| hausdorff(f13(a,cx,ct,X0),X1) ) ).
cnf(u288,negated_conjecture,
( element_of_set(f15(X0,X1,X2,X3,X4),union_of_members(ct))
| ~ element_of_collection(X1,ct)
| ~ element_of_collection(X4,ct)
| ~ neighborhood(X4,X0,X2,X3)
| ~ limit_point(X0,X1,X2,X3) ) ).
cnf(u436,axiom,
( element_of_set(f7(X0,X1),X0)
| basis(X0,X1)
| ~ topological_space(X0,X1) ) ).
cnf(u45112,negated_conjecture,
( ~ element_of_set(X5,relative_complement_sets(X1,X2))
| element_of_set(X5,f13(f14(relative_complement_sets(X1,X2),X3,X4,X0),X2,X6,X5))
| element_of_set(X0,X7) ) ).
cnf(u2938,negated_conjecture,
( element_of_set(f11(X0,boundary(X1,X2,X3)),f1(ct,f11(X0,boundary(X1,X2,X3))))
| ~ closed(empty_set,X2,X3)
| ~ subset_sets(X1,empty_set)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(u1306,axiom,
( ~ closed(f1(X1,X3),X6,X7)
| ~ subset_sets(X2,X0)
| limit_point(X3,X2,X0,X1)
| element_of_set(f11(X4,closure(X5,X6,X7)),union_of_members(X1))
| element_of_collection(closure(X5,X6,X7),top_of_basis(X4))
| ~ topological_space(X0,X1)
| ~ subset_sets(X5,f1(X1,X3)) ) ).
cnf(u573,axiom,
( element_of_set(f7(f22(X0,X1),X2),union_of_members(X1))
| connected_space(X0,X1)
| ~ topological_space(X0,X1)
| basis(f22(X0,X1),X2)
| ~ topological_space(f22(X0,X1),X2) ) ).
cnf(u6104,axiom,
( element_of_set(X7,interior(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5,f11(X6,closure(relative_complement_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4),X4,X5))),X1,X2))
| ~ element_of_set(X7,f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))))
| element_of_collection(interior(X0,X1,X2),top_of_basis(X3))
| ~ subset_sets(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5,f11(X6,closure(relative_complement_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4),X4,X5))),X1)
| element_of_set(f11(X6,closure(relative_complement_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4),X4,X5)),boundary(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5))
| element_of_collection(closure(relative_complement_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4),X4,X5),top_of_basis(X6))
| ~ subset_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4) ) ).
cnf(u131,axiom,
( open(f13(a,cx,ct,X0),cx,ct)
| ~ element_of_set(X0,sF0) ) ).
cnf(u3162,axiom,
( ~ subset_sets(X4,f14(relative_complement_sets(X0,X1),X1,X2,X3))
| element_of_set(X3,boundary(X0,X1,X2))
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| subset_sets(X0,f14(X0,X1,X2,X3))
| element_of_set(X5,f14(relative_complement_sets(X0,X1),X1,X2,X3))
| subset_sets(X4,f14(X4,X1,X2,X5))
| ~ subset_sets(X4,X1) ) ).
cnf(u9463,negated_conjecture,
connected_set(X2,X0,X1) ).
cnf(u2538,axiom,
( ~ element_of_set(X0,f10(top_of_basis(subspace_topology(X1,X2,X3)),X4,X5))
| subset_sets(X3,X1)
| ~ element_of_set(X5,X4)
| ~ element_of_collection(X4,top_of_basis(top_of_basis(subspace_topology(X1,X2,X3)))) ) ).
cnf(u1348,axiom,
( element_of_set(f11(X0,closure(X1,X2,X3)),closure(X1,X2,X3))
| element_of_set(f19(boundary(X1,X2,X3),X4),union_of_members(top_of_basis(X0)))
| hausdorff(boundary(X1,X2,X3),X4)
| ~ topological_space(boundary(X1,X2,X3),X4) ) ).
cnf(u990,negated_conjecture,
( ~ closed(f13(a,cx,ct,f20(closure(X2,X0,X1),X3)),X6,X7)
| ~ subset_sets(X2,sF0)
| ~ topological_space(closure(X2,X0,X1),X3)
| hausdorff(closure(X2,X0,X1),X3)
| element_of_set(f11(X4,closure(X5,X6,X7)),sF0)
| element_of_collection(closure(X5,X6,X7),top_of_basis(X4))
| ~ closed(sF0,X0,X1)
| ~ subset_sets(X5,f13(a,cx,ct,f20(closure(X2,X0,X1),X3))) ) ).
cnf(u3505,axiom,
( ~ closed(f16(X4,X5,X6,X7),X1,X2)
| ~ subset_sets(X0,f16(X4,X5,X6,X7))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(X6,X7)
| ~ subset_sets(X5,X6)
| limit_point(X4,X5,X6,X7)
| element_of_set(f7(closure(X0,X1,X2),X3),union_of_members(X7)) ) ).
cnf(u8098,negated_conjecture,
( element_of_set(f20(X0,X1),union_of_members(X2))
| hausdorff(X0,X1) ) ).
cnf(u16509,negated_conjecture,
( eq_p(f19(intersection_of_members(X2),X3),f19(intersection_of_members(X0),X1))
| hausdorff(intersection_of_members(X0),X1)
| hausdorff(intersection_of_members(X2),X3) ) ).
cnf(u4723,axiom,
( closed(f14(X0,X1,X2,X3),X1,X2)
| element_of_set(X3,f14(X0,X1,X2,X4))
| element_of_set(X4,closure(X0,X1,X2))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u864,axiom,
( ~ element_of_set(X5,closure(X0,X1,X2))
| ~ closed(X4,X1,X2)
| ~ subset_sets(X0,X4)
| element_of_set(f11(X3,closure(X0,X1,X2)),X4)
| element_of_set(X5,union_of_members(top_of_basis(X3))) ) ).
cnf(u240,axiom,
( ~ topological_space(interior(X0,X1,X2),X3)
| hausdorff(interior(X0,X1,X2),X3)
| topological_space(X1,X2) ) ).
cnf(u41907,negated_conjecture,
( element_of_set(X2,f13(f14(f13(a,cx,ct,f19(sF0,X0)),cx,ct,X1),cx,ct,X2))
| hausdorff(sF0,X0)
| element_of_set(X1,sF0)
| ~ element_of_set(X2,f13(a,cx,ct,f19(sF0,X0))) ) ).
cnf(u5940,negated_conjecture,
( ~ element_of_collection(f10(X2,a,X3),X0)
| ~ element_of_set(X1,f10(X2,a,X3))
| ~ topological_space(sF0,X0)
| element_of_set(X1,interior(a,sF0,X0))
| ~ element_of_set(X3,a)
| ~ element_of_collection(a,top_of_basis(X2)) ) ).
cnf(u584,axiom,
( closed(f14(X0,X1,X2,f19(closure(relative_complement_sets(X0,X1),X1,X2),X3)),X1,X2)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f19(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1) ) ).
cnf(topology_generated_37,axiom,
( ~ element_of_collection(X0,top_of_basis(X1))
| ~ element_of_set(X2,X0)
| element_of_set(X2,f10(X1,X0,X2)) ) ).
cnf(u4705,axiom,
( closed(f14(relative_complement_sets(X0,f14(X1,X2,X3,X4)),X2,X3,X5),X2,X3)
| element_of_collection(boundary(X0,f14(X1,X2,X3,X4),X6),top_of_basis(X7))
| element_of_set(X5,f14(X1,X2,X3,X4))
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| ~ subset_sets(relative_complement_sets(X0,f14(X1,X2,X3,X4)),X2) ) ).
cnf(u1299,axiom,
( element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| subset_sets(X1,f14(X1,X2,X3,X4))
| element_of_set(X4,union_of_members(top_of_basis(X0)))
| ~ closed(sF1,X2,X3)
| ~ subset_sets(X1,sF1)
| ~ subset_sets(X1,X2) ) ).
cnf(u949,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| topological_space(X5,X6) ) ).
cnf(u2976,axiom,
( ~ closed(boundary(X4,X5,X6),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,boundary(X4,X5,X6))
| subset_sets(X4,X5)
| element_of_set(f11(X0,boundary(X1,X2,X3)),union_of_members(top_of_basis(X7))) ) ).
cnf(u394,axiom,
( ~ subset_sets(X4,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)))
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ element_of_collection(X4,X5)
| ~ topological_space(X0,X5)
| ~ element_of_set(X6,X4)
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X6,interior(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X0,X5)) ) ).
cnf(u4859,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,f7(sF0,X0)),f24(f13(a,cx,ct,f7(sF0,X0)),X1)),sF0)
| basis(f13(a,cx,ct,f7(sF0,X0)),f24(f13(a,cx,ct,f7(sF0,X0)),X1))
| compact_space(f13(a,cx,ct,f7(sF0,X0)),X1)
| ~ topological_space(f13(a,cx,ct,f7(sF0,X0)),X1)
| basis(sF0,X0)
| ~ topological_space(sF0,X0) ) ).
cnf(u3070,negated_conjecture,
( ~ closed(f13(a,cx,ct,f19(closure(X4,X5,X6),X7)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f19(closure(X4,X5,X6),X7)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ closed(sF0,X5,X6)
| ~ subset_sets(X4,sF0)
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7)
| element_of_set(f19(boundary(X0,X1,X2),X3),sF0) ) ).
cnf(u1361,axiom,
( element_of_set(f20(closure(X1,X2,X3),X4),union_of_members(top_of_basis(X0)))
| element_of_set(f11(X0,sF3),sF3)
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| ~ topological_space(closure(X1,X2,X3),X4)
| hausdorff(closure(X1,X2,X3),X4) ) ).
cnf(u1077,negated_conjecture,
( ~ closed(f13(a,cx,ct,f20(closure(X4,X5,X6),X7)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f20(closure(X4,X5,X6),X7)))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ closed(sF0,X5,X6)
| ~ subset_sets(X4,sF0)
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7)
| element_of_set(f19(closure(X0,X1,X2),X3),sF0) ) ).
cnf(u814,axiom,
( hausdorff(closure(X0,X1,X2),subspace_topology(X3,X4,closure(X0,X1,X2)))
| ~ connected_set(closure(X0,X1,X2),X3,X4)
| topological_space(X1,X2) ) ).
cnf(u6076,negated_conjecture,
( element_of_set(f7(union_of_members(f24(X0,ct)),X1),union_of_members(ct))
| compact_space(X0,ct)
| ~ topological_space(X0,ct)
| basis(union_of_members(f24(X0,ct)),X1)
| ~ topological_space(union_of_members(f24(X0,ct)),X1) ) ).
cnf(u6360,axiom,
( element_of_set(f11(subspace_topology(X1,X2,X3),f13(a,cx,ct,f7(sF0,X0))),f13(a,cx,ct,f7(sF0,X0)))
| basis(sF0,X0)
| topological_space(X1,X2)
| ~ topological_space(sF0,X0) ) ).
cnf(topological_space_10,axiom,
( ~ topological_space(X0,X1)
| ~ element_of_collection(X2,X1)
| ~ element_of_collection(X3,X1)
| element_of_collection(intersection_of_sets(X2,X3),X1) ) ).
cnf(u6921,negated_conjecture,
( element_of_set(f19(X0,X1),interior(X2,X3,X4))
| hausdorff(X0,X1) ) ).
cnf(u34561,axiom,
( ~ subset_collections(f23(X1,f24(X2,X3),X0),X3)
| compact_space(X2,X3)
| ~ compact_space(X1,f24(X2,X3))
| ~ open_covering(X0,X1,f24(X2,X3)) ) ).
cnf(u6288,axiom,
( ~ subset_sets(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,X6),X1)
| element_of_set(X7,closure(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5))
| ~ subset_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(X4,X5)
| ~ topological_space(interior(X0,X1,X2),X3)
| element_of_set(X6,f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,X7))
| ~ element_of_set(X8,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X8,interior(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,X6),X1,X2)) ) ).
cnf(u4468,negated_conjecture,
( ~ subset_sets(union_of_members(ct),boundary(X1,X2,X3))
| ~ element_of_collection(union_of_members(ct),X0)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ closed(cx,X2,X3)
| ~ subset_sets(X1,cx) ) ).
cnf(u3982,axiom,
( ~ element_of_set(X9,f6(X5,top_of_basis(subspace_topology(X1,X2,X3)),f15(X6,X4,X7,X8,X0),X0,X4))
| ~ element_of_collection(X4,top_of_basis(subspace_topology(X1,X2,X3)))
| ~ basis(X5,top_of_basis(subspace_topology(X1,X2,X3)))
| ~ element_of_set(f15(X6,X4,X7,X8,X0),X5)
| ~ neighborhood(X0,X6,X7,X8)
| ~ limit_point(X6,X4,X7,X8)
| ~ element_of_collection(X0,top_of_basis(subspace_topology(X1,X2,X3)))
| topological_space(X1,X2) ) ).
cnf(u433,axiom,
( ~ element_of_set(f7(X1,X0),f13(intersection_of_sets(f8(X1,X0),f9(X1,X0)),X2,X3,f19(interior(intersection_of_sets(f8(X1,X0),f9(X1,X0)),X2,X3),X4)))
| ~ equal_sets(union_of_members(X0),X1)
| ~ element_of_collection(f13(intersection_of_sets(f8(X1,X0),f9(X1,X0)),X2,X3,f19(interior(intersection_of_sets(f8(X1,X0),f9(X1,X0)),X2,X3),X4)),X0)
| basis(X1,X0)
| hausdorff(interior(intersection_of_sets(f8(X1,X0),f9(X1,X0)),X2,X3),X4)
| ~ topological_space(interior(intersection_of_sets(f8(X1,X0),f9(X1,X0)),X2,X3),X4) ) ).
cnf(u4840,negated_conjecture,
( element_of_set(f7(empty_set,f24(empty_set,X0)),f1(ct,f7(empty_set,f24(empty_set,X0))))
| basis(empty_set,f24(empty_set,X0))
| compact_space(empty_set,X0)
| ~ topological_space(empty_set,X0) ) ).
cnf(u2901,axiom,
( ~ topological_space(closure(X4,X5,X6),X7)
| element_of_set(f11(subspace_topology(X0,X1,X2),X3),X3)
| hausdorff(closure(X4,X5,X6),X7)
| ~ subset_sets(X4,X3)
| ~ closed(X3,X5,X6)
| topological_space(X0,X1) ) ).
cnf(u3813,axiom,
( ~ subset_sets(X4,f14(X1,X2,X3,f11(X0,closure(relative_complement_sets(X1,X2),X2,X3))))
| element_of_collection(closure(relative_complement_sets(X1,X2),X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,X2)
| ~ subset_sets(X4,X2)
| element_of_set(f11(X0,closure(relative_complement_sets(X1,X2),X2,X3)),boundary(X1,X2,X3))
| closed(f14(X4,X2,X3,X5),X2,X3)
| element_of_set(X5,f14(X1,X2,X3,f11(X0,closure(relative_complement_sets(X1,X2),X2,X3)))) ) ).
cnf(u3083,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| topological_space(X7,X8)
| ~ closed(sF1,X5,X6)
| element_of_set(f11(subspace_topology(X7,X8,X9),closure(X4,X5,X6)),sF3)
| ~ subset_sets(X4,sF1) ) ).
cnf(u6345,axiom,
( element_of_set(X4,f14(X1,X2,X3,f11(X0,closure(relative_complement_sets(X1,X2),X2,X3))))
| element_of_set(f11(X0,closure(relative_complement_sets(X1,X2),X2,X3)),boundary(X1,X2,X3))
| ~ subset_sets(X1,X2)
| element_of_collection(closure(relative_complement_sets(X1,X2),X2,X3),top_of_basis(X0))
| subset_sets(X1,f14(X1,X2,X3,X4)) ) ).
cnf(u2715,axiom,
( ~ topological_space(union_of_members(subspace_topology(X0,X1,X2)),X3)
| hausdorff(union_of_members(subspace_topology(X0,X1,X2)),X3)
| topological_space(X0,X1) ) ).
cnf(u123,axiom,
( ~ element_of_set(X0,sF1)
| element_of_set(X0,sF3) ) ).
cnf(u2864,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),intersection_of_sets(f8(X3,X4),f9(X3,X4))),intersection_of_sets(f8(X3,X4),f9(X3,X4)))
| topological_space(X0,X1)
| ~ equal_sets(union_of_members(X4),X3)
| basis(X3,X4) ) ).
cnf(u143,axiom,
( ~ closed(X1,cx,ct)
| ~ subset_sets(a,X1)
| ~ element_of_set(X0,sF3)
| element_of_set(X0,X1) ) ).
cnf(u1340,axiom,
( ~ closed(boundary(X1,X2,X3),X6,X7)
| element_of_set(f11(X4,closure(X5,X6,X7)),union_of_members(top_of_basis(X0)))
| element_of_set(f11(X0,closure(X1,X2,X3)),closure(X1,X2,X3))
| ~ subset_sets(X5,boundary(X1,X2,X3))
| element_of_collection(closure(X5,X6,X7),top_of_basis(X4)) ) ).
cnf(u4653,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,f20(closure(X2,X3,X4),X5)),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ closed(sF0,X3,X4)
| ~ subset_sets(X2,sF0)
| ~ topological_space(closure(X2,X3,X4),X5)
| hausdorff(closure(X2,X3,X4),X5)
| element_of_set(f11(X0,intersection_of_members(X1)),sF0) ) ).
cnf(u986,negated_conjecture,
( ~ element_of_set(X4,f13(a,cx,ct,f20(closure(X0,X1,X2),X3)))
| ~ closed(sF0,X1,X2)
| ~ subset_sets(X0,sF0)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3)
| element_of_set(X4,sF0) ) ).
cnf(u5562,axiom,
( ~ closed(closure(relative_complement_sets(a,cx),cx,ct),X1,X2)
| ~ element_of_set(f19(closure(X0,X1,X2),X3),sF3)
| ~ subset_sets(X0,closure(relative_complement_sets(a,cx),cx,ct))
| element_of_set(f19(closure(X0,X1,X2),X3),sF1)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3) ) ).
cnf(u3755,axiom,
( ~ closed(boundary(X3,X4,X5),X7,X8)
| element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),X6)
| ~ closed(X6,X4,X5)
| ~ subset_sets(X3,X6)
| topological_space(X0,X1)
| ~ subset_sets(X9,boundary(X3,X4,X5))
| element_of_collection(closure(X9,X7,X8),top_of_basis(X10)) ) ).
cnf(u6401,axiom,
( ~ subset_sets(closure(X2,X3,X4),X1)
| element_of_set(X5,f14(X2,X3,X4,f11(X0,X1)))
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4)
| element_of_collection(X1,top_of_basis(X0))
| ~ element_of_collection(closure(X2,X3,X4),X0)
| closed(f14(X2,X3,X4,X5),X3,X4) ) ).
cnf(u2453,axiom,
( open(f13(a,cx,ct,f11(X0,sF0)),cx,ct)
| element_of_collection(sF0,top_of_basis(X0)) ) ).
cnf(u28259,negated_conjecture,
( open(f13(X1,X2,X3,f11(X4,union_of_members(top_of_basis(X0)))),X2,X3)
| element_of_set(f11(X0,union_of_members(ct)),f1(ct,f11(X0,union_of_members(ct))))
| element_of_set(X5,f1(top_of_basis(X4),X5))
| ~ element_of_set(X5,cx) ) ).
cnf(u3462,axiom,
( ~ closed(f1(X4,X5),X1,X2)
| ~ subset_sets(X0,f1(X4,X5))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(X6,X4)
| ~ subset_sets(X7,X6)
| limit_point(X5,X7,X6,X4)
| element_of_set(f7(closure(X0,X1,X2),X3),union_of_members(X4)) ) ).
cnf(u36083,negated_conjecture,
( element_of_set(f11(X1,union_of_members(top_of_basis(X4))),f13(X5,X6,X7,f11(X1,union_of_members(top_of_basis(X4)))))
| open(f13(X8,X9,X10,f11(X4,union_of_members(ct))),X9,X10)
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u252,axiom,
( element_of_set(f20(sF1,X0),sF3)
| hausdorff(sF1,X0)
| ~ topological_space(sF1,X0) ) ).
cnf(closed_set_22,axiom,
( open(relative_complement_sets(X0,X1),X1,X2)
| ~ closed(X0,X1,X2) ) ).
cnf(u4626,axiom,
( ~ element_of_set(f11(X0,intersection_of_members(X1)),X4)
| ~ element_of_collection(intersection_of_sets(X2,X3),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ element_of_collection(X2,X5)
| ~ element_of_collection(X3,X5)
| ~ basis(X4,X5)
| element_of_collection(f6(X4,X5,f11(X0,intersection_of_members(X1)),X2,X3),X5) ) ).
cnf(u945,axiom,
( ~ closed(f13(X4,X5,X6,f20(interior(X4,X5,X6),X7)),X1,X2)
| ~ subset_sets(X0,f13(X4,X5,X6,f20(interior(X4,X5,X6),X7)))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(interior(X4,X5,X6),X7)
| hausdorff(interior(X4,X5,X6),X7)
| element_of_set(f20(closure(X0,X1,X2),X3),interior(X4,X5,X6)) ) ).
cnf(u5332,negated_conjecture,
( ~ open(f14(a,cx,ct,f11(X1,X2)),sF3,X3)
| ~ disjoint_s(X0,f14(a,cx,ct,f11(X1,X2)))
| hausdorff(sF3,X3)
| ~ open(X0,sF3,X3)
| ~ element_of_set(f19(sF3,X3),X0)
| ~ element_of_collection(sF3,X1)
| element_of_collection(X2,top_of_basis(X1))
| ~ subset_sets(sF3,X2) ) ).
cnf(u3078,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| subset_sets(X4,X5) ) ).
cnf(u3493,axiom,
( ~ closed(f13(X4,X5,X6,f19(interior(X4,X5,X6),X7)),X1,X2)
| ~ subset_sets(X0,f13(X4,X5,X6,f19(interior(X4,X5,X6),X7)))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(interior(X4,X5,X6),X7)
| hausdorff(interior(X4,X5,X6),X7)
| element_of_set(f7(closure(X0,X1,X2),X3),interior(X4,X5,X6)) ) ).
cnf(u3688,axiom,
( element_of_set(X8,interior(f14(relative_complement_sets(X0,X1),X2,X3,f11(X7,f14(closure(relative_complement_sets(X0,X1),X2,X3),X4,X5,X6))),X1,X9))
| ~ element_of_collection(closure(relative_complement_sets(X0,X1),X2,X3),X7)
| ~ subset_sets(relative_complement_sets(X0,X1),X2)
| ~ topological_space(X2,X3)
| element_of_set(X6,closure(closure(relative_complement_sets(X0,X1),X2,X3),X4,X5))
| ~ subset_sets(closure(relative_complement_sets(X0,X1),X2,X3),X4)
| ~ topological_space(X4,X5)
| ~ subset_sets(f14(relative_complement_sets(X0,X1),X2,X3,f11(X7,f14(closure(relative_complement_sets(X0,X1),X2,X3),X4,X5,X6))),X1)
| ~ element_of_set(X8,relative_complement_sets(X0,X1))
| ~ closed(X0,X1,X9)
| element_of_collection(f14(closure(relative_complement_sets(X0,X1),X2,X3),X4,X5,X6),top_of_basis(X7)) ) ).
cnf(u5779,negated_conjecture,
( ~ element_of_set(f19(f13(a,cx,ct,f20(sF0,X1)),X2),X0)
| ~ open(sF0,f13(a,cx,ct,f20(sF0,X1)),X2)
| hausdorff(f13(a,cx,ct,f20(sF0,X1)),X2)
| ~ open(X0,f13(a,cx,ct,f20(sF0,X1)),X2)
| ~ disjoint_s(X0,sF0)
| ~ topological_space(sF0,X1)
| hausdorff(sF0,X1) ) ).
cnf(u928,axiom,
( ~ closed(f1(ct,X4),X1,X2)
| ~ subset_sets(X0,f1(ct,X4))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ element_of_set(X4,sF0)
| element_of_set(f20(closure(X0,X1,X2),X3),union_of_members(ct)) ) ).
cnf(u1164,axiom,
( ~ subset_sets(X4,f13(X0,X1,X2,f7(interior(X0,X1,X2),X3)))
| basis(interior(X0,X1,X2),X3)
| ~ element_of_collection(X4,X5)
| ~ topological_space(X0,X5)
| ~ element_of_set(X6,X4)
| ~ topological_space(interior(X0,X1,X2),X3)
| element_of_set(X6,interior(f13(X0,X1,X2,f7(interior(X0,X1,X2),X3)),X0,X5)) ) ).
cnf(u55325,negated_conjecture,
( ~ element_of_set(X9,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)))
| ~ element_of_set(X4,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)))
| eq_p(X5,X6)
| element_of_set(X4,f13(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X7,X8,X5),X1,X2,X4))
| element_of_set(X9,f13(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X7,X8,X6),X1,X2,X9))
| hausdorff(interior(X0,X1,X2),X3) ) ).
cnf(u827,axiom,
( closed(X0,X1,subspace_topology(X2,X3,relative_complement_sets(X0,X1)))
| ~ connected_set(relative_complement_sets(X0,X1),X2,X3)
| ~ topological_space(X1,subspace_topology(X2,X3,relative_complement_sets(X0,X1))) ) ).
cnf(u6718,negated_conjecture,
( closed(f14(X0,X1,X2,X3),X1,X2)
| element_of_set(X3,f14(X4,X1,X2,X5))
| element_of_set(X5,closure(X4,X1,X2)) ) ).
cnf(u237,axiom,
( element_of_set(f20(interior(X0,X1,X2),X3),f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3) ) ).
cnf(u1304,axiom,
( ~ topological_space(f1(X1,X3),X4)
| ~ subset_sets(X2,X0)
| limit_point(X3,X2,X0,X1)
| element_of_set(f7(f1(X1,X3),X4),union_of_members(X1))
| basis(f1(X1,X3),X4)
| ~ topological_space(X0,X1) ) ).
cnf(u4887,axiom,
( element_of_set(f7(boundary(X0,X1,X2),f24(boundary(X0,X1,X2),X3)),X4)
| basis(boundary(X0,X1,X2),f24(boundary(X0,X1,X2),X3))
| compact_space(boundary(X0,X1,X2),X3)
| ~ subset_sets(relative_complement_sets(X0,X1),X4)
| ~ closed(X4,X1,X2)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u6029,negated_conjecture,
( closed(f14(X1,X2,X3,f11(X4,f14(closure(X1,X2,X3),cx,ct,X0))),X2,X3)
| ~ subset_sets(closure(X1,X2,X3),sF0)
| ~ subset_sets(closure(X1,X2,X3),cx)
| ~ element_of_collection(closure(X1,X2,X3),X4)
| element_of_collection(f14(closure(X1,X2,X3),cx,ct,X0),top_of_basis(X4))
| element_of_set(X0,sF0)
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ) ).
cnf(u6134,axiom,
( ~ subset_sets(f10(X5,closure(X2,X3,X4),f11(X0,X1)),X1)
| ~ closed(sF1,X3,X4)
| element_of_set(f11(X5,closure(X2,X3,X4)),sF3)
| ~ subset_sets(X2,sF1)
| element_of_collection(X1,top_of_basis(X0))
| ~ element_of_collection(f10(X5,closure(X2,X3,X4),f11(X0,X1)),X0)
| ~ element_of_set(f11(X0,X1),closure(X2,X3,X4)) ) ).
cnf(u45076,negated_conjecture,
( element_of_set(X5,f13(f14(relative_complement_sets(X1,X2),X3,X4,X0),X2,X6,X5))
| element_of_set(X0,interior(X7,X8,X9))
| ~ element_of_set(X5,relative_complement_sets(X1,X2)) ) ).
cnf(u1277,axiom,
( element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ closed(sF1,X2,X3)
| element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| ~ subset_sets(X1,sF1) ) ).
cnf(u296,axiom,
( ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| subset_sets(X0,X1) ) ).
cnf(u1062,negated_conjecture,
( ~ closed(f1(ct,X4),X1,X2)
| ~ subset_sets(X0,f1(ct,X4))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ element_of_set(X4,cx)
| element_of_set(f19(closure(X0,X1,X2),X3),union_of_members(ct)) ) ).
cnf(u7973,negated_conjecture,
( open(f13(X1,X2,X3,f20(sF0,X0)),X2,X3)
| hausdorff(sF0,X0) ) ).
cnf(u2757,axiom,
( ~ topological_space(X7,subspace_topology(X2,X3,X4))
| ~ topological_space(X2,X3)
| ~ subset_sets(X4,X2)
| limit_point(X5,X0,X1,subspace_topology(X6,X3,X4))
| ~ topological_space(X1,subspace_topology(X6,X3,X4))
| element_of_collection(f1(subspace_topology(X2,X3,X4),X5),subspace_topology(X2,X3,X4))
| ~ subset_sets(X0,X1)
| ~ subset_sets(X0,X7) ) ).
cnf(u1018,axiom,
( ~ element_of_set(f20(closure(X0,X4,X5),X6),closure(X1,X2,X3))
| ~ closed(boundary(relative_complement_sets(X1,X2),X2,X3),X4,X5)
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| ~ subset_sets(X0,boundary(relative_complement_sets(X1,X2),X2,X3))
| element_of_set(f20(closure(X0,X4,X5),X6),boundary(X1,X2,X3)) ) ).
cnf(u2944,axiom,
( ~ closed(relative_complement_sets(X4,X5),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,relative_complement_sets(X4,X5))
| ~ closed(X4,X5,X6)
| element_of_set(f11(X0,boundary(X1,X2,X3)),union_of_members(X6)) ) ).
cnf(topological_space_7,axiom,
( equal_sets(union_of_members(X1),X0)
| ~ topological_space(X0,X1) ) ).
cnf(u2973,axiom,
( ~ closed(closure(X4,X5,X6),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,closure(X4,X5,X6))
| topological_space(X7,X8)
| ~ closed(sF1,X5,X6)
| element_of_set(f11(subspace_topology(X7,X8,X9),closure(X4,X5,X6)),sF3)
| ~ subset_sets(X4,sF1) ) ).
cnf(u1405,axiom,
( ~ element_of_set(X0,f16(X1,X2,X3,top_of_basis(subspace_topology(X4,X5,X6))))
| topological_space(X4,X5)
| limit_point(X1,X2,X3,top_of_basis(subspace_topology(X4,X5,X6)))
| ~ topological_space(X3,top_of_basis(subspace_topology(X4,X5,X6)))
| ~ subset_sets(X2,X3) ) ).
cnf(u5251,axiom,
( ~ open(union_of_members(top_of_basis(X1)),X2,X3)
| ~ disjoint_s(X0,union_of_members(top_of_basis(X1)))
| hausdorff(X2,X3)
| ~ open(X0,X2,X3)
| ~ element_of_set(f19(X2,X3),X0)
| closed(f14(X4,X5,X6,f20(X2,X3)),X5,X6)
| element_of_set(f11(X1,closure(X4,X5,X6)),sF3)
| ~ closed(sF1,X5,X6)
| ~ subset_sets(X4,sF1)
| ~ subset_sets(X4,X5) ) ).
cnf(u36058,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f10(X2,f1(top_of_basis(X2),f11(X0,union_of_members(top_of_basis(X1)))),f11(X0,union_of_members(top_of_basis(X1)))))
| limit_point(f11(X0,union_of_members(top_of_basis(X1))),X3,X4,top_of_basis(X2))
| element_of_set(f11(X1,union_of_members(ct)),interior(X5,X6,X7))
| element_of_set(X8,f1(top_of_basis(X0),X8))
| ~ element_of_set(X8,cx) ) ).
cnf(u3384,axiom,
( ~ element_of_set(X9,f12(X2,top_of_basis(subspace_topology(X3,X4,X5)),X6,f16(X7,X0,X1,subspace_topology(X8,top_of_basis(subspace_topology(X3,X4,X5)),X6))))
| ~ topological_space(X2,top_of_basis(subspace_topology(X3,X4,X5)))
| ~ subset_sets(X6,X2)
| limit_point(X7,X0,X1,subspace_topology(X8,top_of_basis(subspace_topology(X3,X4,X5)),X6))
| ~ topological_space(X1,subspace_topology(X8,top_of_basis(subspace_topology(X3,X4,X5)),X6))
| ~ subset_sets(X0,X1)
| topological_space(X3,X4) ) ).
cnf(u850,axiom,
( ~ closed(f13(X4,X5,X6,f19(interior(X4,X5,X6),X7)),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f13(X4,X5,X6,f19(interior(X4,X5,X6),X7)))
| ~ topological_space(interior(X4,X5,X6),X7)
| hausdorff(interior(X4,X5,X6),X7)
| element_of_set(f11(X0,closure(X1,X2,X3)),interior(X4,X5,X6)) ) ).
cnf(u1256,axiom,
( element_of_collection(f6(X3,X4,f11(X0,intersection_of_sets(X1,X2)),X1,X2),X4)
| ~ element_of_collection(X1,X4)
| ~ element_of_collection(X2,X4)
| ~ basis(X3,X4)
| ~ element_of_set(f11(X0,intersection_of_sets(X1,X2)),X3)
| element_of_collection(intersection_of_sets(X1,X2),top_of_basis(X0)) ) ).
cnf(u4908,axiom,
( ~ closed(sF1,X1,subspace_topology(X2,X3,X4))
| element_of_set(X5,union_of_members(top_of_basis(X6)))
| element_of_set(f11(X6,closure(X0,X1,subspace_topology(X2,X3,X4))),sF3)
| ~ subset_sets(X0,sF1)
| ~ subset_sets(X0,X1)
| element_of_collection(f12(X2,X3,X4,relative_complement_sets(f14(X0,X1,subspace_topology(X2,X3,X4),X5),X1)),X3) ) ).
cnf(u4634,axiom,
( open(f13(X2,X3,X4,f11(X0,intersection_of_members(X1))),X3,X4)
| ~ element_of_collection(interior(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0)) ) ).
cnf(u6570,negated_conjecture,
( ~ subset_sets(a,f14(X1,cx,ct,X2))
| ~ topological_space(sF3,X0)
| element_of_set(f7(sF3,X0),f14(X1,cx,ct,X2))
| basis(sF3,X0)
| element_of_set(X2,closure(X1,cx,ct))
| ~ subset_sets(X1,cx) ) ).
cnf(u3095,axiom,
( element_of_set(f19(boundary(X0,X1,X2),X3),sF3)
| ~ subset_sets(X0,sF1)
| ~ closed(sF1,X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u6342,axiom,
( element_of_set(X4,f14(X0,X1,X2,f19(boundary(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f19(boundary(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ subset_sets(X0,X1)
| ~ topological_space(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| hausdorff(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| subset_sets(X0,f14(X0,X1,X2,X4)) ) ).
cnf(u2983,axiom,
( ~ element_of_set(X7,boundary(X0,X1,X2))
| ~ closed(X6,X1,X2)
| ~ subset_sets(X0,X6)
| element_of_set(f11(subspace_topology(X3,X4,X5),boundary(X0,X1,X2)),X6)
| subset_sets(X5,X3) ) ).
cnf(u6258,negated_conjecture,
( ~ element_of_set(X1,union_of_members(f5(X0,ct)))
| ~ basis(X0,ct)
| ~ element_of_collection(X0,ct)
| topological_space(X0,ct)
| element_of_set(X1,union_of_members(ct)) ) ).
cnf(u116,axiom,
boundary(a,cx,ct) = sF1 ).
cnf(u4491,axiom,
( element_of_collection(f1(subspace_topology(X0,X1,X2),X3),subspace_topology(X6,X1,X2))
| limit_point(X3,X4,X5,subspace_topology(X0,X1,X2))
| ~ topological_space(X5,subspace_topology(X0,X1,X2))
| ~ topological_space(X6,X1)
| ~ subset_sets(X2,X6)
| ~ subset_sets(X4,X5) ) ).
cnf(u248,axiom,
( ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| subset_sets(relative_complement_sets(X0,X1),X1) ) ).
cnf(u7842,axiom,
( ~ connected_set(X0,X2,X3)
| connected_space(X0,X1) ) ).
cnf(u4853,axiom,
( basis(interior(X0,X1,X2),f24(interior(X0,X1,X2),X3))
| ~ topological_space(interior(X0,X1,X2),X3)
| compact_space(interior(X0,X1,X2),X3)
| topological_space(X1,X2) ) ).
cnf(u2965,axiom,
( ~ closed(f13(X4,X5,X6,f20(interior(X4,X5,X6),X7)),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f13(X4,X5,X6,f20(interior(X4,X5,X6),X7)))
| ~ topological_space(interior(X4,X5,X6),X7)
| hausdorff(interior(X4,X5,X6),X7)
| element_of_set(f11(X0,boundary(X1,X2,X3)),interior(X4,X5,X6)) ) ).
cnf(u809,axiom,
( basis(interior(X0,X1,X2),subspace_topology(X3,X4,interior(X0,X1,X2)))
| ~ connected_set(interior(X0,X1,X2),X3,X4)
| subset_sets(X0,X1) ) ).
cnf(u583,axiom,
( subset_sets(X0,f14(X0,X1,X2,f19(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f19(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1) ) ).
cnf(u6135,axiom,
( ~ open(f10(X5,closure(X2,X3,X4),f20(X0,X1)),X0,X1)
| ~ closed(sF1,X3,X4)
| element_of_set(f11(X5,closure(X2,X3,X4)),sF3)
| ~ subset_sets(X2,sF1)
| ~ disjoint_s(X6,f10(X5,closure(X2,X3,X4),f20(X0,X1)))
| ~ element_of_set(f20(X0,X1),closure(X2,X3,X4))
| hausdorff(X0,X1)
| ~ open(X6,X0,X1)
| ~ element_of_set(f19(X0,X1),X6) ) ).
cnf(u957,axiom,
( ~ closed(f22(X4,X5),X1,X2)
| ~ subset_sets(X0,f22(X4,X5))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(X4,X5)
| connected_space(X4,X5)
| element_of_set(f20(closure(X0,X1,X2),X3),union_of_members(X5)) ) ).
cnf(u6062,axiom,
( hausdorff(sF1,subspace_topology(X0,X1,sF1))
| ~ connected_set(sF1,X0,X1) ) ).
cnf(u5643,axiom,
( ~ connected_space(intersection_of_sets(X3,f12(X4,X5,X3,union_of_sets(X0,X1))),X2)
| equal_sets(X1,empty_set)
| ~ element_of_collection(X0,X2)
| ~ element_of_collection(X1,X2)
| ~ disjoint_s(X0,X1)
| ~ element_of_collection(union_of_sets(X0,X1),subspace_topology(X4,X5,X3))
| equal_sets(X0,empty_set) ) ).
cnf(u6293,axiom,
( closed(f14(X0,X1,X2,f11(X7,f14(closure(X0,X1,X2),X3,X4,X5))),X1,X2)
| element_of_set(X5,f14(closure(X0,X1,X2),X3,X4,X6))
| element_of_set(X6,closure(closure(X0,X1,X2),X3,X4))
| ~ topological_space(X3,X4)
| ~ element_of_collection(closure(X0,X1,X2),X7)
| element_of_collection(f14(closure(X0,X1,X2),X3,X4,X5),top_of_basis(X7))
| ~ subset_sets(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u3208,axiom,
( ~ closed(f13(a,cx,ct,X4),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,X4))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ element_of_set(X4,sF0)
| element_of_set(f20(boundary(X0,X1,X2),X3),union_of_members(ct)) ) ).
cnf(u1369,axiom,
( ~ element_of_set(f20(boundary(relative_complement_sets(a,cx),cx,ct),X0),sF3)
| element_of_set(f20(boundary(relative_complement_sets(a,cx),cx,ct),X0),sF1)
| ~ topological_space(boundary(relative_complement_sets(a,cx),cx,ct),X0)
| hausdorff(boundary(relative_complement_sets(a,cx),cx,ct),X0) ) ).
cnf(u3897,axiom,
( subset_sets(f13(f14(X1,X2,X3,X4),X5,X6,f11(X7,interior(f14(X1,X2,X3,X4),X5,X6))),f14(f13(f14(X1,X2,X3,X4),X5,X6,f11(X7,interior(f14(X1,X2,X3,X4),X5,X6))),X2,X3,X0))
| element_of_set(X0,f14(X1,X2,X3,X4))
| ~ subset_sets(f13(f14(X1,X2,X3,X4),X5,X6,f11(X7,interior(f14(X1,X2,X3,X4),X5,X6))),X2)
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| element_of_collection(interior(f14(X1,X2,X3,X4),X5,X6),top_of_basis(X7)) ) ).
cnf(u53913,negated_conjecture,
( ~ element_of_set(X8,closure(f13(X1,X2,X3,f19(interior(X1,X2,X3),X4)),X5,X6))
| hausdorff(interior(X1,X2,X3),X4)
| ~ element_of_set(X7,f13(X1,X2,X3,f19(interior(X1,X2,X3),X4)))
| eq_p(X0,X8)
| element_of_set(X7,f13(f14(f13(X1,X2,X3,f19(interior(X1,X2,X3),X4)),X5,X6,X0),X2,X3,X7)) ) ).
cnf(u233,axiom,
( ~ topological_space(f14(relative_complement_sets(X0,X1),X1,X3,X2),X5)
| ~ element_of_set(X2,closure(X0,X1,X3))
| element_of_set(X2,boundary(X0,X1,X3))
| ~ element_of_collection(X4,X5)
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| ~ element_of_set(X6,X4)
| ~ subset_sets(X4,relative_complement_sets(X0,X1))
| element_of_set(X6,interior(relative_complement_sets(X0,X1),f14(relative_complement_sets(X0,X1),X1,X3,X2),X5)) ) ).
cnf(open_set_18,axiom,
( ~ open(X0,X1,X2)
| topological_space(X1,X2) ) ).
cnf(u3599,axiom,
( element_of_set(X5,interior(f14(relative_complement_sets(X0,X1),X2,X3,f11(X4,closure(relative_complement_sets(relative_complement_sets(X0,X1),X2),X2,X3))),X1,X6))
| element_of_collection(closure(relative_complement_sets(relative_complement_sets(X0,X1),X2),X2,X3),top_of_basis(X4))
| ~ subset_sets(relative_complement_sets(X0,X1),X2)
| ~ subset_sets(f14(relative_complement_sets(X0,X1),X2,X3,f11(X4,closure(relative_complement_sets(relative_complement_sets(X0,X1),X2),X2,X3))),X1)
| ~ element_of_set(X5,relative_complement_sets(X0,X1))
| ~ closed(X0,X1,X6)
| element_of_set(f11(X4,closure(relative_complement_sets(relative_complement_sets(X0,X1),X2),X2,X3)),boundary(relative_complement_sets(X0,X1),X2,X3)) ) ).
cnf(u5890,negated_conjecture,
( ~ subset_sets(X0,a)
| ~ topological_space(sF0,X1)
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,X1)
| element_of_set(X2,interior(a,sF0,X1)) ) ).
cnf(u3487,negated_conjecture,
( ~ closed(f13(a,cx,ct,f19(sF0,X4)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f19(sF0,X4)))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| element_of_set(f7(closure(X0,X1,X2),X3),sF0)
| ~ topological_space(sF0,X4)
| hausdorff(sF0,X4) ) ).
cnf(u20932,negated_conjecture,
( element_of_set(X0,f1(subspace_topology(X2,X3,X1),X0))
| ~ element_of_set(X0,empty_set) ) ).
cnf(u899,axiom,
( ~ element_of_set(f7(boundary(relative_complement_sets(X0,X1),X1,X2),X3),closure(X0,X1,X2))
| basis(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ topological_space(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f7(boundary(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2)) ) ).
cnf(u3418,axiom,
( ~ closed(f13(a,cx,ct,f19(sF0,X0)),X2,X3)
| ~ topological_space(sF0,X0)
| element_of_set(f20(closure(X1,X2,X3),X4),union_of_members(ct))
| hausdorff(closure(X1,X2,X3),X4)
| ~ subset_sets(X1,f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| ~ topological_space(closure(X1,X2,X3),X4) ) ).
cnf(u3321,axiom,
( ~ subset_sets(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,X6),X1)
| element_of_set(X6,union_of_members(top_of_basis(X7)))
| ~ closed(sF1,X4,X5)
| ~ subset_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),sF1)
| ~ subset_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(interior(X0,X1,X2),X3)
| element_of_set(f11(X7,closure(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5)),sF3)
| ~ element_of_set(X8,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X8,interior(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,X6),X1,X2)) ) ).
cnf(u2551,axiom,
( topological_space(X0,subspace_topology(X1,X2,X0))
| ~ compact_set(X0,X1,X2) ) ).
cnf(u36126,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| element_of_set(f11(X1,union_of_members(ct)),union_of_members(X4))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u3106,axiom,
( ~ element_of_set(f19(boundary(X0,X1,X2),X3),closure(X4,X5,X6))
| ~ subset_sets(X0,closure(relative_complement_sets(X4,X5),X5,X6))
| ~ closed(closure(relative_complement_sets(X4,X5),X5,X6),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3)
| element_of_set(f19(boundary(X0,X1,X2),X3),boundary(X4,X5,X6)) ) ).
cnf(u2482,axiom,
( element_of_set(X0,f10(X4,closure(X1,X2,X3),X0))
| ~ element_of_set(X0,closure(X1,X2,X3))
| ~ closed(sF1,X2,X3)
| element_of_set(f11(X4,closure(X1,X2,X3)),sF3)
| ~ subset_sets(X1,sF1) ) ).
cnf(union_of_members_3,axiom,
( ~ element_of_collection(X2,X1)
| ~ element_of_set(X0,X2)
| element_of_set(X0,union_of_members(X1)) ) ).
cnf(u3449,axiom,
( ~ closed(f13(a,cx,ct,f20(sF0,X0)),X2,X3)
| ~ topological_space(sF0,X0)
| element_of_set(f20(closure(X1,X2,X3),X4),union_of_members(ct))
| hausdorff(closure(X1,X2,X3),X4)
| ~ subset_sets(X1,f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| ~ topological_space(closure(X1,X2,X3),X4) ) ).
cnf(u6026,negated_conjecture,
( element_of_set(X5,interior(f14(f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)),cx,ct,X0),X2,X3))
| ~ subset_sets(f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)),sF0)
| ~ subset_sets(f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)),cx)
| ~ topological_space(interior(X1,X2,X3),X4)
| ~ subset_sets(f14(f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)),cx,ct,X0),X2)
| ~ element_of_set(X5,f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)))
| hausdorff(interior(X1,X2,X3),X4)
| element_of_set(X0,sF0) ) ).
cnf(u2410,axiom,
( ~ element_of_set(X5,boundary(X3,X1,X2))
| ~ subset_sets(relative_complement_sets(X3,X1),X0)
| element_of_set(f11(X4,closure(relative_complement_sets(X3,X1),X1,X2)),X0)
| element_of_set(X5,union_of_members(top_of_basis(X4)))
| ~ closed(X0,X1,X2) ) ).
cnf(u13741,negated_conjecture,
( open(f13(f14(f13(a,cx,ct,X1),X2,X3,X4),cx,ct,X0),cx,ct)
| ~ element_of_set(X1,sF0)
| element_of_set(X4,closure(f13(a,cx,ct,X1),X2,X3))
| ~ element_of_set(X0,f13(a,cx,ct,X1)) ) ).
cnf(u862,axiom,
( ~ closed(f21(X4,X5),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f21(X4,X5))
| ~ topological_space(X4,X5)
| connected_space(X4,X5)
| element_of_set(f11(X0,closure(X1,X2,X3)),union_of_members(X5)) ) ).
cnf(u1262,axiom,
( element_of_collection(f6(X4,X6,f20(closure(X0,X1,X2),X3),X5,X7),X6)
| ~ element_of_collection(X5,X6)
| ~ element_of_collection(X7,X6)
| ~ basis(X4,X6)
| ~ element_of_set(f20(closure(X0,X1,X2),X3),X4)
| hausdorff(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,intersection_of_sets(X5,X7))
| ~ closed(intersection_of_sets(X5,X7),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u2799,axiom,
( ~ closed(f9(X0,X1),X4,X5)
| basis(X0,X1)
| element_of_set(f11(X2,closure(X3,X4,X5)),union_of_members(X1))
| element_of_collection(closure(X3,X4,X5),top_of_basis(X2))
| ~ topological_space(X0,X1)
| ~ subset_sets(X3,f9(X0,X1)) ) ).
cnf(u4063,axiom,
( ~ subset_sets(relative_complement_sets(X0,X1),closure(X0,X1,X2))
| ~ closed(closure(X0,X1,X2),X1,X2)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| topological_space(X4,X5)
| element_of_set(f11(subspace_topology(X4,X5,X6),boundary(X0,X1,X2)),boundary(X0,X1,X2)) ) ).
cnf(u5546,axiom,
( closed(f14(X3,X1,X2,X5),X1,X2)
| element_of_set(f11(X4,closure(X3,X1,X2)),X0)
| element_of_set(X5,union_of_members(top_of_basis(X4)))
| ~ subset_sets(X3,X0)
| ~ closed(X0,X1,X2)
| ~ subset_sets(X3,X1) ) ).
cnf(u53928,negated_conjecture,
( ~ element_of_set(X7,f13(X1,X2,X3,f19(interior(X1,X2,X3),X4)))
| hausdorff(interior(X1,X2,X3),X4)
| element_of_set(X7,f13(f14(f13(X1,X2,X3,f19(interior(X1,X2,X3),X4)),X5,X6,X0),X2,X3,X7))
| element_of_set(X0,interior(X8,X9,X10)) ) ).
cnf(u2979,axiom,
( ~ closed(boundary(X4,X5,X6),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,boundary(X4,X5,X6))
| topological_space(X5,X6) ) ).
cnf(u1402,axiom,
( ~ closed(X1,X2,top_of_basis(subspace_topology(X3,X4,X5)))
| topological_space(X3,X4)
| ~ element_of_set(X0,relative_complement_sets(X1,X2)) ) ).
cnf(u27802,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f13(X2,X3,X4,f11(X0,union_of_members(top_of_basis(X1)))))
| element_of_set(X5,f1(top_of_basis(X0),X5))
| ~ element_of_set(X5,cx)
| element_of_set(f11(X1,union_of_members(ct)),sF0) ) ).
cnf(u6285,negated_conjecture,
( ~ subset_sets(f14(f13(a,cx,ct,X0),X1,X2,X3),cx)
| element_of_set(X4,closure(f13(a,cx,ct,X0),X1,X2))
| ~ subset_sets(f13(a,cx,ct,X0),X1)
| ~ topological_space(X1,X2)
| element_of_set(X3,f14(f13(a,cx,ct,X0),X1,X2,X4))
| ~ element_of_set(X5,f13(a,cx,ct,X0))
| ~ element_of_set(X0,sF0)
| element_of_set(X5,interior(f14(f13(a,cx,ct,X0),X1,X2,X3),cx,ct)) ) ).
cnf(u18807,negated_conjecture,
( open(f13(X2,X3,X4,f11(X0,f1(ct,X1))),X3,X4)
| element_of_set(X1,f1(top_of_basis(X0),X1))
| ~ element_of_set(X1,cx) ) ).
cnf(u575,axiom,
( element_of_set(f20(f22(X0,X1),X2),union_of_members(X1))
| connected_space(X0,X1)
| ~ topological_space(X0,X1)
| ~ topological_space(f22(X0,X1),X2)
| hausdorff(f22(X0,X1),X2) ) ).
cnf(u3608,axiom,
( subset_sets(X0,f14(X0,X1,X2,f11(X6,f14(closure(X0,X1,X2),X3,X4,f11(X5,closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4))))))
| element_of_collection(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),top_of_basis(X5))
| ~ subset_sets(closure(X0,X1,X2),X3)
| ~ element_of_collection(closure(X0,X1,X2),X6)
| element_of_collection(f14(closure(X0,X1,X2),X3,X4,f11(X5,closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4))),top_of_basis(X6))
| element_of_set(f11(X5,closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4)),boundary(closure(X0,X1,X2),X3,X4))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u3055,axiom,
( ~ closed(f8(X4,X5),X1,X2)
| ~ subset_sets(X0,f8(X4,X5))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(X4,X5)
| basis(X4,X5)
| element_of_set(f19(boundary(X0,X1,X2),X3),union_of_members(X5)) ) ).
cnf(u4834,negated_conjecture,
( element_of_set(f7(f1(ct,X0),f24(f1(ct,X0),X1)),union_of_members(ct))
| basis(f1(ct,X0),f24(f1(ct,X0),X1))
| compact_space(f1(ct,X0),X1)
| ~ element_of_set(X0,cx)
| ~ topological_space(f1(ct,X0),X1) ) ).
cnf(u6616,negated_conjecture,
( ~ element_of_set(X0,f13(a,cx,ct,f11(X1,sF3)))
| element_of_collection(sF3,top_of_basis(X1))
| element_of_set(X0,sF0) ) ).
cnf(u6413,axiom,
( element_of_set(X4,f14(X0,X1,X2,f20(boundary(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f20(boundary(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ subset_sets(X0,X1)
| ~ topological_space(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| hausdorff(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| closed(f14(X0,X1,X2,X4),X1,X2) ) ).
cnf(u4265,axiom,
( element_of_set(f19(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5),boundary(X0,X1,subspace_topology(X2,X3,X4)))
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5)
| hausdorff(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5)
| ~ subset_sets(X0,X1)
| subset_sets(X4,X2) ) ).
cnf(u6087,negated_conjecture,
( ~ closed(union_of_members(f24(X0,ct)),X2,X3)
| compact_space(X0,ct)
| element_of_set(f20(closure(X1,X2,X3),X4),union_of_members(ct))
| hausdorff(closure(X1,X2,X3),X4)
| ~ subset_sets(X1,union_of_members(f24(X0,ct)))
| ~ topological_space(X0,ct)
| ~ topological_space(closure(X1,X2,X3),X4) ) ).
cnf(u7591,negated_conjecture,
( element_of_set(f11(X5,interior(X6,X7,X8)),interior(X6,X7,X8))
| element_of_set(f15(X1,X4,X2,X3,X0),union_of_members(top_of_basis(X5)))
| ~ limit_point(X1,X4,X2,X3)
| ~ neighborhood(X0,X1,X2,X3) ) ).
cnf(u2942,negated_conjecture,
( ~ closed(intersection_of_sets(X4,X5),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,intersection_of_sets(X4,X5))
| element_of_set(f11(X0,boundary(X1,X2,X3)),union_of_members(ct))
| ~ element_of_collection(X5,ct)
| ~ element_of_collection(X4,ct) ) ).
cnf(u3214,negated_conjecture,
( ~ closed(f13(a,cx,ct,f19(closure(X4,X5,X6),X7)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f19(closure(X4,X5,X6),X7)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ closed(sF0,X5,X6)
| ~ subset_sets(X4,sF0)
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7)
| element_of_set(f20(boundary(X0,X1,X2),X3),sF0) ) ).
cnf(u5948,negated_conjecture,
( ~ element_of_collection(f13(a,X2,X3,f11(X4,closure(X5,X6,X7))),X0)
| ~ element_of_set(X1,f13(a,X2,X3,f11(X4,closure(X5,X6,X7))))
| ~ topological_space(sF0,X0)
| element_of_set(X1,interior(a,sF0,X0))
| ~ closed(interior(a,X2,X3),X6,X7)
| ~ subset_sets(X5,interior(a,X2,X3))
| element_of_collection(closure(X5,X6,X7),top_of_basis(X4)) ) ).
cnf(u245,axiom,
( element_of_set(f20(closure(X0,X1,X2),X3),X4)
| hausdorff(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,X4)
| ~ closed(X4,X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u1283,axiom,
( element_of_set(f7(boundary(X1,X2,X3),X4),union_of_members(top_of_basis(X0)))
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| ~ topological_space(boundary(X1,X2,X3),X4)
| basis(boundary(X1,X2,X3),X4) ) ).
cnf(u4838,axiom,
( element_of_set(f7(f2(X0,X1),f24(f2(X0,X1),X2)),union_of_members(X0))
| basis(f2(X0,X1),f24(f2(X0,X1),X2))
| compact_space(f2(X0,X1),X2)
| element_of_set(X1,intersection_of_members(X0))
| ~ topological_space(f2(X0,X1),X2) ) ).
cnf(u6695,negated_conjecture,
( ~ element_of_set(X2,relative_complement_sets(X3,X1))
| ~ closed(X3,X1,X4)
| element_of_set(X2,interior(X0,X1,X4)) ) ).
cnf(u426,negated_conjecture,
( element_of_set(f20(f13(a,cx,ct,f20(sF0,X0)),X1),sF0)
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f20(sF0,X0)),X1)
| hausdorff(f13(a,cx,ct,f20(sF0,X0)),X1) ) ).
cnf(u1226,axiom,
( element_of_set(f7(f16(X3,X2,X0,X1),X4),union_of_members(X1))
| ~ subset_sets(X2,X0)
| limit_point(X3,X2,X0,X1)
| ~ topological_space(X0,X1)
| basis(f16(X3,X2,X0,X1),X4)
| ~ topological_space(f16(X3,X2,X0,X1),X4) ) ).
cnf(u4269,negated_conjecture,
( element_of_set(X4,interior(f14(f13(a,cx,ct,X0),X1,X2,f20(closure(relative_complement_sets(f13(a,cx,ct,X0),X1),X1,X2),X3)),cx,ct))
| ~ topological_space(closure(relative_complement_sets(f13(a,cx,ct,X0),X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(f13(a,cx,ct,X0),X1),X1,X2),X3)
| ~ subset_sets(f13(a,cx,ct,X0),X1)
| ~ subset_sets(f14(f13(a,cx,ct,X0),X1,X2,f20(closure(relative_complement_sets(f13(a,cx,ct,X0),X1),X1,X2),X3)),cx)
| ~ element_of_set(X4,f13(a,cx,ct,X0))
| ~ element_of_set(X0,sF0)
| element_of_set(f20(closure(relative_complement_sets(f13(a,cx,ct,X0),X1),X1,X2),X3),boundary(f13(a,cx,ct,X0),X1,X2)) ) ).
cnf(u5339,axiom,
( ~ open(f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)),interior(X1,X2,X3),X4)
| ~ disjoint_s(X0,f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)))
| hausdorff(interior(X1,X2,X3),X4)
| ~ open(X0,interior(X1,X2,X3),X4)
| ~ element_of_set(f19(interior(X1,X2,X3),X4),X0) ) ).
cnf(u373,axiom,
( element_of_collection(f12(X1,X2,X3,f9(X0,subspace_topology(X1,X2,X3))),X2)
| ~ topological_space(X0,subspace_topology(X1,X2,X3))
| basis(X0,subspace_topology(X1,X2,X3)) ) ).
cnf(u911,axiom,
( element_of_set(f19(relative_complement_sets(X0,X1),X3),union_of_members(X2))
| ~ closed(X0,X1,X2)
| ~ topological_space(relative_complement_sets(X0,X1),X3)
| hausdorff(relative_complement_sets(X0,X1),X3) ) ).
cnf(u6270,axiom,
( element_of_set(X4,f10(X3,closure(X0,X1,X2),X4))
| ~ subset_sets(sF3,closure(X0,X1,X2))
| ~ closed(sF1,X1,X2)
| ~ element_of_collection(sF3,X3)
| ~ element_of_set(X4,closure(X0,X1,X2))
| ~ subset_sets(X0,sF1) ) ).
cnf(u2547,axiom,
( ~ element_of_set(X0,f13(X1,X2,top_of_basis(subspace_topology(X3,X4,X5)),f19(interior(X1,X2,top_of_basis(subspace_topology(X3,X4,X5))),X6)))
| subset_sets(X5,X3)
| ~ topological_space(interior(X1,X2,top_of_basis(subspace_topology(X3,X4,X5))),X6)
| hausdorff(interior(X1,X2,top_of_basis(subspace_topology(X3,X4,X5))),X6) ) ).
cnf(u5971,axiom,
( ~ closed(boundary(X0,X1,X6),X3,X4)
| ~ topological_space(boundary(X2,X3,X4),X5)
| ~ subset_sets(X2,boundary(X0,X1,X6))
| subset_sets(X0,X1)
| hausdorff(boundary(X2,X3,X4),X5) ) ).
cnf(u4397,axiom,
( ~ closed(f10(X1,X0,X2),X4,X5)
| ~ element_of_set(X2,X0)
| element_of_set(f7(closure(X3,X4,X5),X6),union_of_members(X1))
| ~ topological_space(closure(X3,X4,X5),X6)
| ~ subset_sets(X3,f10(X1,X0,X2))
| ~ element_of_collection(X0,top_of_basis(X1))
| basis(closure(X3,X4,X5),X6) ) ).
cnf(u218,negated_conjecture,
( element_of_set(X0,union_of_members(ct))
| ~ element_of_set(X0,cx) ) ).
cnf(u2494,axiom,
( element_of_set(X0,f10(X2,f9(X1,top_of_basis(X2)),X0))
| ~ element_of_set(X0,f9(X1,top_of_basis(X2)))
| basis(X1,top_of_basis(X2))
| ~ topological_space(X1,top_of_basis(X2)) ) ).
cnf(u4894,axiom,
( element_of_set(f7(sF1,f24(sF1,X0)),sF3)
| basis(sF1,f24(sF1,X0))
| compact_space(sF1,X0)
| ~ topological_space(sF1,X0) ) ).
cnf(topological_space_15,axiom,
( ~ element_of_collection(union_of_members(f5(X0,X1)),X1)
| ~ equal_sets(union_of_members(X1),X0)
| ~ element_of_collection(empty_set,X1)
| ~ element_of_collection(X0,X1)
| element_of_collection(f4(X0,X1),X1)
| topological_space(X0,X1) ) ).
cnf(u1285,axiom,
( element_of_set(f11(X4,boundary(X1,X2,X3)),union_of_members(top_of_basis(X0)))
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X4)) ) ).
cnf(u6900,negated_conjecture,
( element_of_set(f20(boundary(X0,X1,X2),X3),interior(X4,X5,X6))
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u27994,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f13(X2,X3,X4,f11(X0,union_of_members(top_of_basis(X1)))))
| open(f13(X5,X6,X7,f11(X1,union_of_members(ct))),X6,X7)
| element_of_set(X8,f1(top_of_basis(X0),X8))
| ~ element_of_set(X8,cx) ) ).
cnf(u3459,axiom,
( ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,union_of_members(X4))
| ~ closed(union_of_members(X4),X1,X2)
| basis(closure(X0,X1,X2),X3)
| element_of_collection(f1(X4,f7(closure(X0,X1,X2),X3)),X4) ) ).
cnf(u5721,axiom,
( ~ element_of_set(X5,closure(X2,X3,subspace_topology(X0,X1,X4)))
| ~ subset_sets(relative_complement_sets(X2,X3),X3)
| topological_space(X0,X1)
| element_of_set(X5,boundary(X2,X3,subspace_topology(X0,X1,X4))) ) ).
cnf(u3604,axiom,
( element_of_set(X7,interior(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,f11(X6,closure(relative_complement_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),X4,X5))),X1,X2))
| element_of_collection(closure(relative_complement_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),X4,X5),top_of_basis(X6))
| ~ subset_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ subset_sets(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,f11(X6,closure(relative_complement_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),X4,X5))),X1)
| ~ element_of_set(X7,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(f11(X6,closure(relative_complement_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),X4,X5)),boundary(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5)) ) ).
cnf(u9696,negated_conjecture,
( eq_p(f20(boundary(X0,X1,X2),X3),X4)
| ~ element_of_set(X4,sF1)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u6107,axiom,
( element_of_set(X7,interior(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5,f20(closure(relative_complement_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4),X4,X5),X6)),X1,X2))
| ~ element_of_set(X7,f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))))
| element_of_collection(interior(X0,X1,X2),top_of_basis(X3))
| ~ subset_sets(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5,f20(closure(relative_complement_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4),X4,X5),X6)),X1)
| element_of_set(f20(closure(relative_complement_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4),X4,X5),X6),boundary(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5))
| ~ topological_space(closure(relative_complement_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4),X4,X5),X6)
| hausdorff(closure(relative_complement_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4),X4,X5),X6)
| ~ subset_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4) ) ).
cnf(u3806,axiom,
( basis(boundary(X0,X1,X2),subspace_topology(X3,X4,boundary(X0,X1,X2)))
| subset_sets(relative_complement_sets(X0,X1),X1)
| ~ connected_set(boundary(X0,X1,X2),X3,X4) ) ).
cnf(u917,axiom,
( ~ topological_space(interior(X0,X1,subspace_topology(X2,X3,X4)),X5)
| hausdorff(interior(X0,X1,subspace_topology(X2,X3,X4)),X5)
| topological_space(X2,X3) ) ).
cnf(u3334,axiom,
( element_of_set(f11(X5,union_of_members(top_of_basis(X1))),union_of_members(top_of_basis(X1)))
| element_of_set(f11(X1,closure(X2,X3,X4)),sF3)
| subset_sets(X2,f14(X2,X3,X4,X0))
| element_of_set(X0,union_of_members(top_of_basis(X5)))
| ~ subset_sets(X2,X3)
| ~ subset_sets(X2,sF1)
| ~ closed(sF1,X3,X4) ) ).
cnf(u3237,axiom,
( ~ closed(f22(X4,X5),X1,X2)
| ~ subset_sets(X0,f22(X4,X5))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(X4,X5)
| connected_space(X4,X5)
| element_of_set(f20(boundary(X0,X1,X2),X3),union_of_members(X5)) ) ).
cnf(u124,negated_conjecture,
element_of_collection(cx,ct) ).
cnf(u18803,negated_conjecture,
( element_of_set(f11(X1,f1(ct,X0)),union_of_members(X2))
| element_of_set(X0,f1(top_of_basis(X1),X0))
| ~ element_of_set(X0,cx) ) ).
cnf(u3165,axiom,
( ~ topological_space(X1,subspace_topology(X2,X3,X4))
| element_of_set(X5,boundary(X0,X1,subspace_topology(X2,X3,X4)))
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| ~ subset_sets(X0,X1)
| subset_sets(X0,f14(X0,X1,subspace_topology(X2,X3,X4),X5))
| topological_space(X2,X3) ) ).
cnf(u817,axiom,
( basis(boundary(X0,X1,X2),subspace_topology(X3,X4,boundary(X0,X1,X2)))
| ~ connected_set(boundary(X0,X1,X2),X3,X4)
| topological_space(X1,X2) ) ).
cnf(u331,axiom,
( ~ topological_space(X2,subspace_topology(X1,X3,X0))
| connected_space(X2,subspace_topology(X1,X3,X0))
| subset_sets(X0,X1) ) ).
cnf(u1249,axiom,
( ~ element_of_set(X4,f1(X0,X1))
| ~ topological_space(X3,X0)
| ~ subset_sets(X2,X3)
| limit_point(X1,X2,X3,X0)
| element_of_set(X4,union_of_members(X0)) ) ).
cnf(u6711,negated_conjecture,
( ~ element_of_set(X1,X2)
| element_of_set(X1,interior(a,sF0,X0)) ) ).
cnf(u6079,negated_conjecture,
( element_of_set(f11(X1,union_of_members(f24(X0,ct))),union_of_members(ct))
| compact_space(X0,ct)
| ~ topological_space(X0,ct)
| element_of_collection(union_of_members(f24(X0,ct)),top_of_basis(X1)) ) ).
cnf(u278,negated_conjecture,
( element_of_set(X0,f1(ct,X0))
| ~ element_of_set(X0,cx) ) ).
cnf(u29391,axiom,
( ~ subset_collections(f24(X0,f24(X0,X1)),X1)
| ~ finite(f24(X0,f24(X0,X1)))
| compact_space(X0,f24(X0,X1))
| compact_space(X0,X1) ) ).
cnf(u5273,axiom,
( ~ open(closure(X1,X2,X3),X4,X5)
| ~ disjoint_s(X0,closure(X1,X2,X3))
| hausdorff(X4,X5)
| ~ open(X0,X4,X5)
| ~ element_of_set(f19(X4,X5),X0)
| subset_sets(X1,f14(X1,X2,X3,f20(X4,X5)))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ) ).
cnf(u50874,negated_conjecture,
( open(f13(f14(f16(X2,X3,X0,X1),X4,X5,X6),X0,X1,X7),X0,X1)
| limit_point(X2,X3,X0,X1)
| element_of_set(X6,closure(f16(X2,X3,X0,X1),X4,X5))
| ~ element_of_set(X7,f16(X2,X3,X0,X1)) ) ).
cnf(compact_set_109,axiom,
( ~ compact_space(X0,subspace_topology(X1,X2,X0))
| ~ topological_space(X1,X2)
| ~ subset_sets(X0,X1)
| compact_set(X0,X1,X2) ) ).
cnf(u1371,axiom,
( closed(f14(X0,X1,X2,f20(boundary(relative_complement_sets(X0,X1),X1,X2),X3)),X1,X2)
| hausdorff(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f20(boundary(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ topological_space(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1) ) ).
cnf(u241,axiom,
( ~ topological_space(interior(X0,X1,X2),X3)
| hausdorff(interior(X0,X1,X2),X3)
| subset_sets(X0,X1) ) ).
cnf(u552,axiom,
( element_of_set(f7(intersection_of_members(X1),X2),X0)
| ~ element_of_collection(X0,X1)
| basis(intersection_of_members(X1),X2)
| ~ topological_space(intersection_of_members(X1),X2) ) ).
cnf(u768,axiom,
( ~ element_of_set(X2,boundary(X0,X1,X3))
| subset_sets(X0,X1)
| element_of_set(X2,union_of_members(top_of_basis(X4))) ) ).
cnf(u1318,axiom,
( element_of_set(f11(X0,union_of_members(X1)),union_of_members(X1))
| limit_point(X2,X3,X4,X1)
| element_of_set(X2,union_of_members(top_of_basis(X0)))
| ~ subset_sets(X3,X4)
| ~ topological_space(X4,X1) ) ).
cnf(u3833,axiom,
( element_of_set(f11(X2,f2(X1,X0)),union_of_members(X1))
| element_of_set(X0,intersection_of_members(X1))
| element_of_collection(f2(X1,X0),top_of_basis(X2)) ) ).
cnf(u36143,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| element_of_set(f11(X1,union_of_members(ct)),f13(X4,X5,X6,f11(X1,union_of_members(ct)))) ) ).
cnf(u29132,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f1(top_of_basis(X1),f11(X0,union_of_members(ct))))
| element_of_set(f11(X1,union_of_members(top_of_basis(X0))),sF0)
| ~ element_of_set(f11(X0,union_of_members(ct)),cx) ) ).
cnf(u41783,negated_conjecture,
( element_of_set(X4,f13(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,X3),cx,ct,X4))
| hausdorff(sF0,X0)
| element_of_set(X3,closure(f13(a,cx,ct,f20(sF0,X0)),X1,X2))
| ~ element_of_set(X4,f13(a,cx,ct,f20(sF0,X0))) ) ).
cnf(u6092,axiom,
( ~ element_of_collection(f13(sF3,X2,X3,f11(X4,closure(X5,X6,X7))),X0)
| ~ element_of_set(X1,f13(sF3,X2,X3,f11(X4,closure(X5,X6,X7))))
| ~ topological_space(sF1,X0)
| element_of_set(X1,interior(sF3,sF1,X0))
| ~ closed(interior(sF3,X2,X3),X6,X7)
| ~ subset_sets(X5,interior(sF3,X2,X3))
| element_of_collection(closure(X5,X6,X7),top_of_basis(X4)) ) ).
cnf(u907,axiom,
( ~ limit_point(X6,X4,X7,subspace_topology(X5,X2,X3))
| ~ subset_sets(X4,X0)
| ~ topological_space(X5,X2)
| ~ subset_sets(X3,X5)
| limit_point(X6,X4,X0,subspace_topology(X1,X2,X3))
| ~ topological_space(X0,subspace_topology(X1,X2,X3)) ) ).
cnf(u6020,negated_conjecture,
( ~ topological_space(f14(X1,cx,ct,X0),X3)
| ~ subset_sets(X1,sF0)
| ~ subset_sets(X1,cx)
| ~ element_of_collection(X2,X3)
| element_of_set(X0,sF0)
| ~ element_of_set(X4,X2)
| ~ subset_sets(X2,X1)
| element_of_set(X4,interior(X1,f14(X1,cx,ct,X0),X3)) ) ).
cnf(u4886,axiom,
( element_of_set(f7(boundary(X0,X1,X2),f24(boundary(X0,X1,X2),X3)),union_of_members(top_of_basis(X4)))
| basis(boundary(X0,X1,X2),f24(boundary(X0,X1,X2),X3))
| compact_space(boundary(X0,X1,X2),X3)
| subset_sets(X0,X1)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u3195,axiom,
( element_of_collection(f6(X6,X7,f20(boundary(X0,X1,X2),X3),X4,X5),X7)
| ~ subset_sets(X0,intersection_of_sets(X4,X5))
| ~ closed(intersection_of_sets(X4,X5),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ element_of_set(f20(boundary(X0,X1,X2),X3),X6)
| ~ element_of_collection(X4,X7)
| ~ element_of_collection(X5,X7)
| ~ basis(X6,X7)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u3827,axiom,
( ~ connected_set(X1,X2,X3)
| ~ element_of_set(X0,X1)
| element_of_set(f11(X4,union_of_members(subspace_topology(X2,X3,X1))),union_of_members(subspace_topology(X2,X3,X1)))
| element_of_set(X0,union_of_members(top_of_basis(X4))) ) ).
cnf(u6339,axiom,
( ~ closed(closure(relative_complement_sets(X4,X5),X5,X6),X1,X2)
| element_of_set(X7,f14(X4,X5,X6,f20(closure(X0,X1,X2),X3)))
| ~ subset_sets(X4,X5)
| ~ subset_sets(X0,closure(relative_complement_sets(X4,X5),X5,X6))
| subset_sets(X4,f14(X4,X5,X6,X7))
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3)
| element_of_set(f20(closure(X0,X1,X2),X3),boundary(X4,X5,X6)) ) ).
cnf(u976,axiom,
( ~ subset_sets(X7,f13(X1,X2,X3,f20(closure(X0,X4,X5),X6)))
| ~ closed(interior(X1,X2,X3),X4,X5)
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| ~ element_of_collection(X7,X8)
| ~ topological_space(X1,X8)
| ~ element_of_set(X9,X7)
| ~ subset_sets(X0,interior(X1,X2,X3))
| element_of_set(X9,interior(f13(X1,X2,X3,f20(closure(X0,X4,X5),X6)),X1,X8)) ) ).
cnf(u4890,axiom,
( element_of_set(f7(boundary(X0,X1,X2),f24(boundary(X0,X1,X2),X3)),closure(X0,X1,X2))
| basis(boundary(X0,X1,X2),f24(boundary(X0,X1,X2),X3))
| compact_space(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u4680,axiom,
( ~ element_of_set(X3,intersection_of_members(X0))
| ~ element_of_collection(X2,X0)
| element_of_set(f11(X1,intersection_of_members(X0)),X2)
| element_of_set(X3,union_of_members(top_of_basis(X1))) ) ).
cnf(u3757,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),X6)
| element_of_collection(closure(X3,X4,X5),top_of_basis(X7))
| ~ closed(X6,X4,X5)
| ~ subset_sets(X3,X6)
| topological_space(X0,X1) ) ).
cnf(u5252,negated_conjecture,
( ~ open(union_of_members(top_of_basis(X1)),X2,X3)
| ~ disjoint_s(X0,union_of_members(top_of_basis(X1)))
| hausdorff(X2,X3)
| ~ open(X0,X2,X3)
| ~ element_of_set(f19(X2,X3),X0)
| element_of_set(f11(X1,union_of_members(ct)),union_of_members(ct))
| ~ element_of_set(f20(X2,X3),cx) ) ).
cnf(u870,axiom,
( ~ closed(f13(closure(X0,X1,X2),X3,X4,f19(interior(closure(X0,X1,X2),X3,X4),X5)),X1,X2)
| ~ subset_sets(X0,f13(closure(X0,X1,X2),X3,X4,f19(interior(closure(X0,X1,X2),X3,X4),X5)))
| ~ element_of_collection(f13(closure(X0,X1,X2),X3,X4,f19(interior(closure(X0,X1,X2),X3,X4),X5)),X6)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X6))
| hausdorff(interior(closure(X0,X1,X2),X3,X4),X5)
| ~ topological_space(interior(closure(X0,X1,X2),X3,X4),X5) ) ).
cnf(u504,axiom,
( ~ subset_sets(f13(a,cx,ct,f19(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| ~ subset_sets(X1,cx)
| ~ element_of_set(X2,f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(X2,interior(X1,cx,ct)) ) ).
cnf(u1270,axiom,
( element_of_set(f11(X0,sF3),closure(X1,X2,X3))
| ~ closed(boundary(X1,X2,X3),cx,ct)
| ~ subset_sets(a,boundary(X1,X2,X3))
| element_of_collection(sF3,top_of_basis(X0)) ) ).
cnf(u553,axiom,
( element_of_set(f19(intersection_of_members(X1),X2),X0)
| ~ element_of_collection(X0,X1)
| ~ topological_space(intersection_of_members(X1),X2)
| hausdorff(intersection_of_members(X1),X2) ) ).
cnf(u1351,axiom,
( element_of_set(f20(X1,X2),union_of_members(top_of_basis(X0)))
| element_of_set(f11(X0,X1),X1)
| ~ topological_space(X1,X2)
| hausdorff(X1,X2) ) ).
cnf(u5140,axiom,
( ~ element_of_set(f11(X3,f14(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5,f11(X6,closure(relative_complement_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4),X4,X5)))),boundary(X0,X1,X2))
| element_of_collection(f14(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5,f11(X6,closure(relative_complement_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4),X4,X5))),top_of_basis(X3))
| ~ element_of_collection(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f11(X6,closure(relative_complement_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4),X4,X5)),boundary(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5))
| element_of_collection(closure(relative_complement_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4),X4,X5),top_of_basis(X6))
| ~ subset_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4) ) ).
cnf(u215,axiom,
( element_of_collection(f21(X0,X1),X1)
| connected_space(X0,X1)
| ~ topological_space(X0,X1) ) ).
cnf(u1282,axiom,
( ~ element_of_set(X4,boundary(X1,X2,X3))
| ~ subset_sets(relative_complement_sets(X1,X2),sF1)
| ~ closed(sF1,X2,X3)
| element_of_set(X4,union_of_members(top_of_basis(X0)))
| element_of_set(f11(X0,closure(relative_complement_sets(X1,X2),X2,X3)),sF3) ) ).
cnf(u5281,axiom,
( ~ open(f16(f20(X1,X2),X3,X4,X5),X1,X2)
| ~ disjoint_s(X0,f16(f20(X1,X2),X3,X4,X5))
| hausdorff(X1,X2)
| ~ open(X0,X1,X2)
| ~ element_of_set(f19(X1,X2),X0)
| ~ subset_sets(X3,X4)
| limit_point(f20(X1,X2),X3,X4,X5)
| ~ topological_space(X4,X5) ) ).
cnf(u120,axiom,
closure(a,cx,ct) = sF3 ).
cnf(u2426,axiom,
( ~ closed(boundary(X3,X1,X2),X6,X7)
| ~ subset_sets(X3,X0)
| element_of_set(f11(X4,closure(X3,X1,X2)),X0)
| element_of_set(f20(closure(X5,X6,X7),X8),union_of_members(top_of_basis(X4)))
| ~ subset_sets(X5,boundary(X3,X1,X2))
| ~ closed(X0,X1,X2)
| ~ topological_space(closure(X5,X6,X7),X8)
| hausdorff(closure(X5,X6,X7),X8) ) ).
cnf(u6021,negated_conjecture,
( element_of_set(X3,interior(f14(relative_complement_sets(X1,X2),cx,ct,X0),X2,X4))
| ~ subset_sets(relative_complement_sets(X1,X2),sF0)
| ~ subset_sets(relative_complement_sets(X1,X2),cx)
| ~ subset_sets(f14(relative_complement_sets(X1,X2),cx,ct,X0),X2)
| ~ element_of_set(X3,relative_complement_sets(X1,X2))
| ~ closed(X1,X2,X4)
| element_of_set(X0,sF0) ) ).
cnf(u3464,negated_conjecture,
( element_of_collection(f1(ct,f7(closure(X0,X1,X2),X3)),ct)
| ~ subset_sets(X0,empty_set)
| ~ closed(empty_set,X1,X2)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u4857,axiom,
( element_of_set(f7(f13(a,cx,ct,X0),f24(f13(a,cx,ct,X0),X1)),union_of_members(ct))
| basis(f13(a,cx,ct,X0),f24(f13(a,cx,ct,X0),X1))
| compact_space(f13(a,cx,ct,X0),X1)
| ~ element_of_set(X0,sF0)
| ~ topological_space(f13(a,cx,ct,X0),X1) ) ).
cnf(u1113,negated_conjecture,
( element_of_set(f19(f13(a,cx,ct,f19(closure(X2,X0,X1),X3)),X4),sF0)
| ~ subset_sets(X2,sF0)
| ~ topological_space(closure(X2,X0,X1),X3)
| hausdorff(closure(X2,X0,X1),X3)
| ~ closed(sF0,X0,X1)
| ~ topological_space(f13(a,cx,ct,f19(closure(X2,X0,X1),X3)),X4)
| hausdorff(f13(a,cx,ct,f19(closure(X2,X0,X1),X3)),X4) ) ).
cnf(u28032,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f1(ct,f11(X0,union_of_members(ct))))
| element_of_set(f11(X1,union_of_members(top_of_basis(X0))),sF0)
| element_of_set(X2,f1(top_of_basis(X1),X2))
| ~ element_of_set(X2,cx) ) ).
cnf(u343,axiom,
( element_of_collection(f12(X0,X1,X2,f22(X3,subspace_topology(X0,X1,X2))),X1)
| connected_space(X3,subspace_topology(X0,X1,X2))
| ~ topological_space(X3,subspace_topology(X0,X1,X2)) ) ).
cnf(u6112,axiom,
( ~ element_of_set(X2,f13(X0,X1,X3,f11(X4,interior(X0,X1,X3))))
| element_of_collection(interior(X0,X1,X3),top_of_basis(X4))
| element_of_set(X2,interior(X0,X1,X3)) ) ).
cnf(u5206,axiom,
( element_of_set(X4,f10(X2,f12(X1,top_of_basis(X2),X3,f9(X0,subspace_topology(X1,top_of_basis(X2),X3))),X4))
| basis(X0,subspace_topology(X1,top_of_basis(X2),X3))
| ~ element_of_set(X4,f12(X1,top_of_basis(X2),X3,f9(X0,subspace_topology(X1,top_of_basis(X2),X3))))
| ~ topological_space(X0,subspace_topology(X1,top_of_basis(X2),X3)) ) ).
cnf(u274,axiom,
( element_of_set(f19(boundary(X0,X1,X3),X4),X2)
| ~ closed(X2,X1,X3)
| ~ subset_sets(relative_complement_sets(X0,X1),X2)
| ~ topological_space(boundary(X0,X1,X3),X4)
| hausdorff(boundary(X0,X1,X3),X4) ) ).
cnf(u948,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X4,X7)
| ~ closed(X7,X5,X6)
| element_of_set(f20(closure(X0,X1,X2),X3),X7) ) ).
cnf(u3080,axiom,
( closed(f14(relative_complement_sets(X4,X5),X5,X6,f19(boundary(X0,X1,X2),X3)),X5,X6)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ closed(closure(X4,X5,X6),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ subset_sets(relative_complement_sets(X4,X5),X5)
| ~ topological_space(boundary(X0,X1,X2),X3)
| element_of_set(f19(boundary(X0,X1,X2),X3),boundary(X4,X5,X6)) ) ).
cnf(u3754,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),X6)
| element_of_collection(boundary(X3,X4,X5),top_of_basis(X7))
| ~ closed(X6,X4,X5)
| ~ subset_sets(X3,X6)
| topological_space(X0,X1) ) ).
cnf(u5807,axiom,
( element_of_set(X4,f14(X0,X1,X2,f19(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f19(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| subset_sets(X0,f14(X0,X1,X2,X4)) ) ).
cnf(compact_space_105,axiom,
( ~ subset_collections(X2,f24(X0,X1))
| ~ topological_space(X0,X1)
| ~ finite(X2)
| compact_space(X0,X1)
| ~ open_covering(X2,X0,X1) ) ).
cnf(u643,axiom,
( element_of_set(f11(X0,f13(X1,X2,X3,f19(interior(X1,X2,X3),X4))),interior(X1,X2,X3))
| ~ topological_space(interior(X1,X2,X3),X4)
| hausdorff(interior(X1,X2,X3),X4)
| element_of_collection(f13(X1,X2,X3,f19(interior(X1,X2,X3),X4)),top_of_basis(X0)) ) ).
cnf(u5012,axiom,
( ~ open_covering(f23(X0,f24(X1,X2),X3),X1,X2)
| ~ open_covering(X3,X0,f24(X1,X2))
| compact_space(X1,X2)
| ~ compact_space(X0,f24(X1,X2)) ) ).
cnf(u36124,negated_conjecture,
( open(f13(X4,X5,X6,f11(X1,union_of_members(ct))),X5,X6)
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u4846,axiom,
( element_of_set(f7(relative_complement_sets(X0,X1),f24(relative_complement_sets(X0,X1),X2)),union_of_members(X3))
| basis(relative_complement_sets(X0,X1),f24(relative_complement_sets(X0,X1),X2))
| compact_space(relative_complement_sets(X0,X1),X2)
| ~ closed(X0,X1,X3)
| ~ topological_space(relative_complement_sets(X0,X1),X2) ) ).
cnf(u3359,negated_conjecture,
( element_of_collection(f1(ct,f20(boundary(X0,X1,X2),X3)),ct)
| ~ topological_space(boundary(X0,X1,X2),X3)
| ~ subset_sets(X0,empty_set)
| ~ closed(empty_set,X1,X2)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u4277,axiom,
( subset_sets(X0,f14(X0,X1,X2,f11(X6,f14(closure(X0,X1,X2),X3,X4,f20(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5)))))
| ~ topological_space(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5)
| hausdorff(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5)
| ~ subset_sets(closure(X0,X1,X2),X3)
| ~ element_of_collection(closure(X0,X1,X2),X6)
| element_of_collection(f14(closure(X0,X1,X2),X3,X4,f20(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5)),top_of_basis(X6))
| element_of_set(f20(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5),boundary(closure(X0,X1,X2),X3,X4))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u4815,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),union_of_members(top_of_basis(X2)))
| element_of_set(X1,union_of_members(top_of_basis(X0)))
| element_of_set(f11(X2,union_of_members(ct)),union_of_members(ct))
| ~ element_of_set(X1,cx) ) ).
cnf(u3010,negated_conjecture,
( ~ element_of_set(X4,f13(a,cx,ct,f7(sF0,X0)))
| ~ topological_space(sF0,X0)
| element_of_set(f11(subspace_topology(X1,X2,X3),f13(a,cx,ct,f7(sF0,X0))),sF0)
| basis(sF0,X0)
| subset_sets(X3,X1) ) ).
cnf(u3193,axiom,
( ~ closed(intersection_of_sets(f16(X4,X5,X6,X7),X5),X1,X2)
| ~ subset_sets(X0,intersection_of_sets(f16(X4,X5,X6,X7),X5))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(X6,X7)
| ~ subset_sets(X5,X6)
| limit_point(X4,X5,X6,X7)
| eq_p(f20(boundary(X0,X1,X2),X3),X4) ) ).
cnf(u5258,negated_conjecture,
( ~ open(union_of_members(ct),X1,X2)
| ~ disjoint_s(X0,union_of_members(ct))
| hausdorff(X1,X2)
| ~ open(X0,X1,X2)
| ~ element_of_set(f19(X1,X2),X0)
| ~ element_of_set(f20(X1,X2),cx) ) ).
cnf(u36100,negated_conjecture,
( element_of_set(f11(X1,union_of_members(top_of_basis(X4))),f13(X5,X6,X7,f11(X1,union_of_members(top_of_basis(X4)))))
| element_of_set(f11(X4,union_of_members(ct)),interior(X8,X9,X10))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u36122,negated_conjecture,
( element_of_set(f11(X1,f1(ct,X0)),interior(X4,X5,X6))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(connected_set_94,axiom,
( connected_space(X0,subspace_topology(X1,X2,X0))
| ~ connected_set(X0,X1,X2) ) ).
cnf(u3683,axiom,
( ~ closed(f2(X4,f20(boundary(X0,X1,X2),X3)),X1,X2)
| ~ topological_space(boundary(X0,X1,X2),X3)
| ~ subset_sets(X0,f2(X4,f20(boundary(X0,X1,X2),X3)))
| element_of_set(f20(boundary(X0,X1,X2),X3),intersection_of_members(X4))
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u226,axiom,
( ~ topological_space(intersection_of_sets(X2,X3),X4)
| ~ subset_sets(X2,X0)
| ~ element_of_collection(X3,X1)
| element_of_collection(union_of_members(X4),subspace_topology(X0,X1,X2))
| ~ topological_space(X0,X1) ) ).
cnf(u6101,axiom,
( ~ subset_sets(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5,X6),X1)
| ~ element_of_set(X7,f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))))
| element_of_collection(interior(X0,X1,X2),top_of_basis(X3))
| element_of_set(X7,interior(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5,X6),X1,X2))
| element_of_set(f11(X8,closure(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5)),sF3)
| element_of_set(X6,union_of_members(top_of_basis(X8)))
| ~ closed(sF1,X4,X5)
| ~ subset_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),sF1)
| ~ subset_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4) ) ).
cnf(u2969,axiom,
( ~ closed(closure(X4,X5,X6),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,closure(X4,X5,X6))
| ~ subset_sets(X4,X7)
| ~ closed(X7,X5,X6)
| element_of_set(f11(X0,boundary(X1,X2,X3)),X7) ) ).
cnf(u43084,negated_conjecture,
( open(f13(a,cx,subspace_topology(X0,X1,f13(a,cx,ct,f20(sF0,X2))),X3),cx,subspace_topology(X0,X1,f13(a,cx,ct,f20(sF0,X2))))
| hausdorff(sF0,X2)
| ~ element_of_set(X3,f13(a,cx,ct,f20(sF0,X2))) ) ).
cnf(u41906,negated_conjecture,
( open(f13(f14(f13(a,cx,ct,f19(sF0,X0)),cx,ct,X1),cx,ct,X2),cx,ct)
| hausdorff(sF0,X0)
| element_of_set(X1,sF0)
| ~ element_of_set(X2,f13(a,cx,ct,f19(sF0,X0))) ) ).
cnf(u1134,axiom,
( ~ element_of_set(f19(closure(X0,X4,X5),X6),closure(X1,X2,X3))
| ~ closed(boundary(relative_complement_sets(X1,X2),X2,X3),X4,X5)
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| ~ subset_sets(X0,boundary(relative_complement_sets(X1,X2),X2,X3))
| element_of_set(f19(closure(X0,X4,X5),X6),boundary(X1,X2,X3)) ) ).
cnf(u388,axiom,
( element_of_collection(f8(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3),X3)
| basis(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3)
| ~ element_of_collection(union_of_members(X3),subspace_topology(X1,X2,X0)) ) ).
cnf(u3935,axiom,
( subset_sets(X0,f14(X0,X1,X2,f19(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f19(closure(relative_complement_sets(X0,X1),X1,X2),X3),closure(X0,X1,X2))
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3) ) ).
cnf(u1343,negated_conjecture,
( element_of_set(f15(X1,X2,X3,X4,X5),union_of_members(top_of_basis(X0)))
| element_of_set(f11(X0,union_of_members(ct)),union_of_members(ct))
| ~ element_of_collection(X2,ct)
| ~ element_of_collection(X5,ct)
| ~ neighborhood(X5,X1,X3,X4)
| ~ limit_point(X1,X2,X3,X4) ) ).
cnf(u5942,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,f7(sF0,X2)),X0)
| ~ element_of_set(X1,f13(a,cx,ct,f7(sF0,X2)))
| ~ topological_space(sF0,X0)
| element_of_set(X1,interior(a,sF0,X0))
| ~ topological_space(sF0,X2)
| basis(sF0,X2) ) ).
cnf(u6417,axiom,
( element_of_set(X4,f14(X0,X1,X2,f19(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f19(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ subset_sets(X0,X1)
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| closed(f14(X0,X1,X2,X4),X1,X2) ) ).
cnf(u2851,axiom,
( ~ element_of_set(X6,boundary(X3,X4,X5))
| element_of_set(f11(subspace_topology(X0,X1,X2),closure(relative_complement_sets(X3,X4),X4,X5)),closure(relative_complement_sets(X3,X4),X4,X5))
| topological_space(X0,X1) ) ).
cnf(u36137,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| open(f13(X4,X5,X6,f11(X1,f1(ct,X0))),X5,X6) ) ).
cnf(u3242,axiom,
( element_of_set(f20(boundary(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ subset_sets(relative_complement_sets(X0,X1),closure(X0,X1,X2))
| ~ closed(closure(X0,X1,X2),X1,X2)
| hausdorff(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ topological_space(boundary(relative_complement_sets(X0,X1),X1,X2),X3) ) ).
cnf(u595,axiom,
( ~ subset_sets(intersection_of_members(subspace_topology(X0,X1,X4)),X2)
| element_of_collection(X2,top_of_basis(X3))
| ~ element_of_collection(intersection_of_members(subspace_topology(X0,X1,X4)),X3)
| topological_space(X0,X1) ) ).
cnf(u4126,axiom,
( ~ element_of_collection(X0,top_of_basis(subspace_topology(X1,subspace_topology(X2,X3,X4),X5)))
| ~ element_of_set(X6,X0)
| subset_sets(X4,X2) ) ).
cnf(u4721,axiom,
( element_of_set(X3,f14(X0,X1,X2,f11(X4,f14(closure(X0,X1,X2),X5,X6,X7))))
| element_of_set(f11(X4,f14(closure(X0,X1,X2),X5,X6,X7)),closure(X0,X1,X2))
| closed(f14(X0,X1,X2,X3),X1,X2)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| element_of_collection(f14(closure(X0,X1,X2),X5,X6,X7),top_of_basis(X4))
| ~ element_of_collection(closure(X0,X1,X2),X4)
| element_of_set(X7,closure(closure(X0,X1,X2),X5,X6))
| ~ subset_sets(closure(X0,X1,X2),X5)
| ~ topological_space(X5,X6) ) ).
cnf(u2927,axiom,
( ~ closed(X4,X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,X4)
| topological_space(X5,X6)
| element_of_set(f11(subspace_topology(X5,X6,X7),X4),X4) ) ).
cnf(u3457,axiom,
( ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,X4)
| ~ closed(X4,X1,X2)
| basis(closure(X0,X1,X2),X3)
| element_of_set(f11(X5,X4),X4)
| element_of_set(f7(closure(X0,X1,X2),X3),union_of_members(top_of_basis(X5))) ) ).
cnf(u4706,axiom,
( closed(f14(f10(X0,f14(X1,X2,X3,X4),X5),X2,X3,X6),X2,X3)
| ~ subset_sets(f10(X0,f14(X1,X2,X3,X4),X5),X2)
| element_of_set(X6,f14(X1,X2,X3,X4))
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| ~ element_of_set(X5,f14(X1,X2,X3,X4))
| ~ element_of_collection(f14(X1,X2,X3,X4),top_of_basis(X0)) ) ).
cnf(u2800,axiom,
( element_of_set(f19(f9(X0,X1),X2),union_of_members(X1))
| basis(X0,X1)
| ~ topological_space(X0,X1)
| ~ topological_space(f9(X0,X1),X2)
| hausdorff(f9(X0,X1),X2) ) ).
cnf(u339,axiom,
( ~ equal_sets(f22(X0,X1),empty_set)
| ~ topological_space(X0,X1)
| connected_space(X0,X1) ) ).
cnf(u3882,negated_conjecture,
( element_of_set(X2,f10(X0,f13(a,cx,ct,f20(sF0,X1)),X2))
| ~ topological_space(sF0,X1)
| hausdorff(sF0,X1)
| ~ element_of_set(X2,f13(a,cx,ct,f20(sF0,X1)))
| element_of_set(f11(X0,f13(a,cx,ct,f20(sF0,X1))),sF0) ) ).
cnf(u286,axiom,
( ~ neighborhood(X2,f19(X0,X1),X0,X1)
| hausdorff(X0,X1)
| ~ disjoint_s(X2,X3)
| ~ open(X3,X0,X1)
| ~ element_of_set(f20(X0,X1),X3) ) ).
cnf(u944,axiom,
( ~ closed(f13(X4,X5,X6,f19(interior(X4,X5,X6),X7)),X1,X2)
| ~ subset_sets(X0,f13(X4,X5,X6,f19(interior(X4,X5,X6),X7)))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(interior(X4,X5,X6),X7)
| hausdorff(interior(X4,X5,X6),X7)
| element_of_set(f20(closure(X0,X1,X2),X3),interior(X4,X5,X6)) ) ).
cnf(u6416,axiom,
( element_of_set(X4,f14(X0,X1,X2,f19(boundary(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f19(boundary(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ subset_sets(X0,X1)
| ~ topological_space(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| hausdorff(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| closed(f14(X0,X1,X2,X4),X1,X2) ) ).
cnf(u192,axiom,
( element_of_set(X3,f16(X3,X2,X0,X1))
| ~ subset_sets(X2,X0)
| limit_point(X3,X2,X0,X1)
| ~ topological_space(X0,X1) ) ).
cnf(u36077,negated_conjecture,
( open(f13(X4,X5,X6,f11(X1,union_of_members(top_of_basis(X7)))),X5,X6)
| element_of_set(f11(X7,union_of_members(ct)),f1(X8,f11(X7,union_of_members(ct))))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u4885,axiom,
( element_of_set(f7(f16(X0,X1,X2,X3),f24(f16(X0,X1,X2,X3),X4)),union_of_members(X3))
| basis(f16(X0,X1,X2,X3),f24(f16(X0,X1,X2,X3),X4))
| compact_space(f16(X0,X1,X2,X3),X4)
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3)
| ~ topological_space(f16(X0,X1,X2,X3),X4) ) ).
cnf(u655,axiom,
( element_of_set(f11(X0,f22(X1,X2)),union_of_members(X2))
| ~ topological_space(X1,X2)
| connected_space(X1,X2)
| element_of_collection(f22(X1,X2),top_of_basis(X0)) ) ).
cnf(u1379,axiom,
( element_of_set(f19(closure(X0,X1,X2),X3),f6(X4,X6,f19(closure(X0,X1,X2),X3),X5,X7))
| ~ element_of_collection(X5,X6)
| ~ element_of_collection(X7,X6)
| ~ basis(X4,X6)
| ~ element_of_set(f19(closure(X0,X1,X2),X3),X4)
| hausdorff(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,intersection_of_sets(X5,X7))
| ~ closed(intersection_of_sets(X5,X7),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u2874,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),closure(X3,X4,X5))
| element_of_collection(boundary(X3,X4,X5),top_of_basis(X6))
| topological_space(X0,X1) ) ).
cnf(u2649,axiom,
( ~ element_of_set(X2,f1(X0,f11(X1,union_of_members(X0))))
| element_of_collection(union_of_members(X0),top_of_basis(X1))
| element_of_set(X2,union_of_members(X0)) ) ).
cnf(u5943,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,f11(X2,sF0)),X0)
| ~ element_of_set(X1,f13(a,cx,ct,f11(X2,sF0)))
| ~ topological_space(sF0,X0)
| element_of_set(X1,interior(a,sF0,X0))
| element_of_collection(sF0,top_of_basis(X2)) ) ).
cnf(u1098,axiom,
( ~ subset_sets(X7,f13(X1,X2,X3,f19(closure(X0,X4,X5),X6)))
| ~ closed(interior(X1,X2,X3),X4,X5)
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| ~ element_of_collection(X7,X8)
| ~ topological_space(X1,X8)
| ~ element_of_set(X9,X7)
| ~ subset_sets(X0,interior(X1,X2,X3))
| element_of_set(X9,interior(f13(X1,X2,X3,f19(closure(X0,X4,X5),X6)),X1,X8)) ) ).
cnf(u1326,axiom,
( element_of_set(f11(X0,closure(X1,X2,X3)),closure(X1,X2,X3))
| subset_sets(X1,f14(X1,X2,X3,X4))
| element_of_set(X4,union_of_members(top_of_basis(X0)))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ) ).
cnf(u4273,axiom,
( element_of_set(X7,interior(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,f20(closure(relative_complement_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),X4,X5),X6)),X1,X2))
| ~ topological_space(closure(relative_complement_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),X4,X5),X6)
| hausdorff(closure(relative_complement_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),X4,X5),X6)
| ~ subset_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ subset_sets(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,f20(closure(relative_complement_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),X4,X5),X6)),X1)
| ~ element_of_set(X7,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(f20(closure(relative_complement_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),X4,X5),X6),boundary(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5)) ) ).
cnf(u6109,axiom,
( ~ subset_sets(f13(a,cx,ct,f11(X0,sF0)),X1)
| ~ subset_sets(X1,cx)
| ~ element_of_set(X2,f13(a,cx,ct,f11(X0,sF0)))
| element_of_collection(sF0,top_of_basis(X0))
| element_of_set(X2,interior(X1,cx,ct)) ) ).
cnf(u3508,axiom,
( ~ closed(boundary(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,boundary(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| subset_sets(relative_complement_sets(X4,X5),X5) ) ).
cnf(u783,negated_conjecture,
( ~ element_of_collection(f13(a,X0,X1,f11(X2,interior(a,X0,X1))),X3)
| ~ topological_space(cx,X3)
| ~ element_of_set(X4,f13(a,X0,X1,f11(X2,interior(a,X0,X1))))
| element_of_collection(interior(a,X0,X1),top_of_basis(X2))
| element_of_set(X4,interior(a,cx,X3)) ) ).
cnf(u4258,axiom,
( ~ subset_sets(a,f14(X0,cx,ct,f19(closure(relative_complement_sets(X0,cx),cx,ct),X1)))
| element_of_set(f19(closure(relative_complement_sets(X0,cx),cx,ct),X1),boundary(X0,cx,ct))
| hausdorff(closure(relative_complement_sets(X0,cx),cx,ct),X1)
| ~ subset_sets(X0,cx)
| ~ subset_sets(f14(X0,cx,ct,f19(closure(relative_complement_sets(X0,cx),cx,ct),X1)),sF3)
| ~ topological_space(closure(relative_complement_sets(X0,cx),cx,ct),X1)
| ~ element_of_collection(f14(X0,cx,ct,f19(closure(relative_complement_sets(X0,cx),cx,ct),X1)),X2)
| element_of_collection(sF3,top_of_basis(X2)) ) ).
cnf(u2419,axiom,
( ~ closed(closure(X3,X1,X2),X7,X8)
| ~ subset_sets(X3,X0)
| element_of_set(f11(X4,closure(X3,X1,X2)),X0)
| element_of_set(f11(X5,closure(X6,X7,X8)),union_of_members(top_of_basis(X4)))
| element_of_collection(closure(X6,X7,X8),top_of_basis(X5))
| ~ closed(X0,X1,X2)
| ~ subset_sets(X6,closure(X3,X1,X2)) ) ).
cnf(u5737,axiom,
( ~ element_of_set(X5,closure(X2,X3,subspace_topology(X1,X4,X0)))
| ~ subset_sets(relative_complement_sets(X2,X3),X3)
| subset_sets(X0,X1)
| element_of_set(X5,boundary(X2,X3,subspace_topology(X1,X4,X0))) ) ).
cnf(u3203,axiom,
( subset_sets(f13(X4,X5,X6,f20(boundary(X0,X1,X2),X3)),X4)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ closed(interior(X4,X5,X6),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(connected_space_90,axiom,
( ~ separation(X2,X3,X0,X1)
| ~ connected_space(X0,X1) ) ).
cnf(u2366,axiom,
( element_of_set(X0,f17(X1,X3,X0,X2))
| ~ element_of_set(X2,X1)
| eq_p(X0,X2)
| ~ hausdorff(X1,X3)
| ~ element_of_set(X0,X1) ) ).
cnf(u4400,axiom,
( ~ closed(f10(X1,X0,X2),X5,X6)
| ~ element_of_set(X2,X0)
| element_of_set(f11(X3,boundary(X4,X5,X6)),union_of_members(X1))
| element_of_collection(boundary(X4,X5,X6),top_of_basis(X3))
| ~ element_of_collection(X0,top_of_basis(X1))
| ~ subset_sets(X4,f10(X1,X0,X2)) ) ).
cnf(u2638,negated_conjecture,
( element_of_set(f7(empty_set,X0),f1(ct,f7(empty_set,X0)))
| basis(empty_set,X0)
| ~ topological_space(empty_set,X0) ) ).
cnf(u2689,axiom,
( element_of_collection(f12(X2,X3,X4,f13(X0,X1,subspace_topology(X2,X3,X4),f20(closure(X7,X5,X6),X8))),X3)
| ~ topological_space(closure(X7,X5,X6),X8)
| hausdorff(closure(X7,X5,X6),X8)
| ~ subset_sets(X7,interior(X0,X1,subspace_topology(X2,X3,X4)))
| ~ closed(interior(X0,X1,subspace_topology(X2,X3,X4)),X5,X6) ) ).
cnf(u5544,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X4),closure(X5,X2,X3)),sF3)
| closed(f14(X5,X2,X3,X6),X2,X3)
| ~ closed(sF1,X2,X3)
| ~ subset_sets(X5,sF1)
| topological_space(X0,X1)
| ~ subset_sets(X5,X2) ) ).
cnf(u1231,axiom,
( element_of_set(f20(f16(X3,X2,X0,X1),X4),union_of_members(X1))
| ~ subset_sets(X2,X0)
| limit_point(X3,X2,X0,X1)
| ~ topological_space(X0,X1)
| ~ topological_space(f16(X3,X2,X0,X1),X4)
| hausdorff(f16(X3,X2,X0,X1),X4) ) ).
cnf(u453,axiom,
( element_of_set(f7(closure(X0,X1,X2),X3),X4)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,X4)
| ~ closed(X4,X1,X2)
| basis(closure(X0,X1,X2),X3) ) ).
cnf(u2981,axiom,
( ~ closed(f21(X4,X5),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f21(X4,X5))
| ~ topological_space(X4,X5)
| connected_space(X4,X5)
| element_of_set(f11(X0,boundary(X1,X2,X3)),union_of_members(X5)) ) ).
cnf(u2582,axiom,
( ~ element_of_set(f7(X1,X2),f10(X3,intersection_of_sets(f8(X1,X2),f9(X1,X2)),X0))
| ~ element_of_collection(intersection_of_sets(f8(X1,X2),f9(X1,X2)),top_of_basis(X3))
| ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_set(X0,intersection_of_sets(f8(X1,X2),f9(X1,X2)))
| ~ element_of_collection(f10(X3,intersection_of_sets(f8(X1,X2),f9(X1,X2)),X0),X2)
| basis(X1,X2) ) ).
cnf(u2698,axiom,
( element_of_set(X7,f10(X2,f13(X0,X1,top_of_basis(X2),f19(closure(X5,X3,X4),X6)),X7))
| ~ topological_space(closure(X5,X3,X4),X6)
| hausdorff(closure(X5,X3,X4),X6)
| ~ subset_sets(X5,interior(X0,X1,top_of_basis(X2)))
| ~ element_of_set(X7,f13(X0,X1,top_of_basis(X2),f19(closure(X5,X3,X4),X6)))
| ~ closed(interior(X0,X1,top_of_basis(X2)),X3,X4) ) ).
cnf(u384,negated_conjecture,
( ~ element_of_set(X0,empty_set)
| element_of_collection(f1(ct,X0),ct) ) ).
cnf(u5979,negated_conjecture,
( ~ topological_space(f14(a,cx,ct,X0),X3)
| element_of_set(X1,sF3)
| ~ element_of_collection(X2,X3)
| element_of_set(X0,f14(a,cx,ct,X1))
| ~ element_of_set(X4,X2)
| ~ subset_sets(X2,a)
| element_of_set(X4,interior(a,f14(a,cx,ct,X0),X3)) ) ).
cnf(u2795,axiom,
( element_of_set(f7(f9(X0,X1),X2),union_of_members(X1))
| basis(X0,X1)
| ~ topological_space(X0,X1)
| basis(f9(X0,X1),X2)
| ~ topological_space(f9(X0,X1),X2) ) ).
cnf(hausdorff_75,axiom,
( neighborhood(f18(X0,X1,X2,X3),X3,X0,X1)
| ~ element_of_set(X2,X0)
| ~ element_of_set(X3,X0)
| eq_p(X2,X3)
| ~ hausdorff(X0,X1) ) ).
cnf(u3041,axiom,
( ~ topological_space(boundary(X0,X1,X2),X3)
| ~ subset_sets(X0,X4)
| ~ closed(X4,X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f11(X5,X4),X4)
| element_of_set(f19(boundary(X0,X1,X2),X3),union_of_members(top_of_basis(X5))) ) ).
cnf(u223,negated_conjecture,
( element_of_collection(f1(ct,X0),ct)
| ~ element_of_set(X0,cx) ) ).
cnf(u27723,negated_conjecture,
( element_of_set(f11(X1,union_of_members(top_of_basis(X0))),interior(X2,X3,X4))
| element_of_set(f11(X0,union_of_members(ct)),union_of_members(X6))
| element_of_set(X5,f1(top_of_basis(X1),X5))
| ~ element_of_set(X5,cx) ) ).
cnf(u4873,axiom,
( element_of_set(f7(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),f24(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4)),interior(X0,X1,X2))
| basis(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),f24(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4))
| compact_space(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(interior(X0,X1,X2),X3)
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4) ) ).
cnf(u4012,axiom,
( ~ closed(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X8,X9)
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| element_of_set(f19(boundary(X7,X8,X9),X10),interior(X4,X5,X6))
| ~ topological_space(boundary(X7,X8,X9),X10)
| ~ subset_sets(X7,f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)))
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(boundary(X7,X8,X9),X10) ) ).
cnf(u1292,axiom,
( ~ closed(closure(X1,X2,X3),X5,X6)
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| element_of_set(f19(closure(X4,X5,X6),X7),union_of_members(top_of_basis(X0)))
| hausdorff(closure(X4,X5,X6),X7)
| ~ subset_sets(X4,closure(X1,X2,X3))
| element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| ~ topological_space(closure(X4,X5,X6),X7) ) ).
cnf(u4805,axiom,
( element_of_collection(f1(X1,f19(closure(X0,X2,X3),subspace_topology(X4,X5,closure(X0,X2,X3)))),X1)
| ~ closed(union_of_members(X1),X2,X3)
| hausdorff(closure(X0,X2,X3),subspace_topology(X4,X5,closure(X0,X2,X3)))
| ~ subset_sets(X0,union_of_members(X1))
| ~ connected_set(closure(X0,X2,X3),X4,X5) ) ).
cnf(u6304,axiom,
( element_of_set(f11(X5,f14(X1,X2,X3,X4)),f14(X1,X2,X3,X4))
| subset_sets(X1,f14(X1,X2,X3,X0))
| element_of_set(X0,union_of_members(top_of_basis(X5)))
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| element_of_set(X4,closure(X1,X2,X3)) ) ).
cnf(u2923,axiom,
( subset_collections(f5(X0,f24(X0,X1)),f24(X0,X1))
| ~ element_of_collection(empty_set,f24(X0,X1))
| ~ element_of_collection(X0,f24(X0,X1))
| element_of_collection(f4(X0,f24(X0,X1)),f24(X0,X1))
| topological_space(X0,f24(X0,X1))
| compact_space(X0,X1)
| ~ topological_space(X0,X1) ) ).
cnf(u3835,axiom,
( ~ closed(f2(X1,X0),X4,X5)
| element_of_set(f11(X2,boundary(X3,X4,X5)),union_of_members(X1))
| element_of_collection(boundary(X3,X4,X5),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1))
| ~ subset_sets(X3,f2(X1,X0)) ) ).
cnf(u1115,negated_conjecture,
( element_of_set(f20(f13(a,cx,ct,f19(closure(X2,X0,X1),X3)),X4),sF0)
| ~ subset_sets(X2,sF0)
| ~ topological_space(closure(X2,X0,X1),X3)
| hausdorff(closure(X2,X0,X1),X3)
| ~ closed(sF0,X0,X1)
| ~ topological_space(f13(a,cx,ct,f19(closure(X2,X0,X1),X3)),X4)
| hausdorff(f13(a,cx,ct,f19(closure(X2,X0,X1),X3)),X4) ) ).
cnf(u5951,negated_conjecture,
( ~ element_of_collection(f13(a,X2,X3,f20(interior(a,X2,X3),X4)),X0)
| ~ element_of_set(X1,f13(a,X2,X3,f20(interior(a,X2,X3),X4)))
| ~ topological_space(sF0,X0)
| element_of_set(X1,interior(a,sF0,X0))
| hausdorff(interior(a,X2,X3),X4)
| ~ topological_space(interior(a,X2,X3),X4) ) ).
cnf(u808,axiom,
( basis(interior(X0,X1,X2),subspace_topology(X3,X4,interior(X0,X1,X2)))
| ~ connected_set(interior(X0,X1,X2),X3,X4)
| topological_space(X1,X2) ) ).
cnf(u27803,negated_conjecture,
( open(f13(X2,X3,X4,f11(X0,union_of_members(top_of_basis(X1)))),X3,X4)
| element_of_set(X5,f1(top_of_basis(X0),X5))
| ~ element_of_set(X5,cx)
| element_of_set(f11(X1,union_of_members(ct)),sF0) ) ).
cnf(u550,axiom,
( element_of_set(f19(f21(X0,X1),X2),union_of_members(X1))
| connected_space(X0,X1)
| ~ topological_space(X0,X1)
| ~ topological_space(f21(X0,X1),X2)
| hausdorff(f21(X0,X1),X2) ) ).
cnf(u956,axiom,
( ~ closed(f21(X4,X5),X1,X2)
| ~ subset_sets(X0,f21(X4,X5))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(X4,X5)
| connected_space(X4,X5)
| element_of_set(f20(closure(X0,X1,X2),X3),union_of_members(X5)) ) ).
cnf(u204,axiom,
( element_of_collection(f16(X2,X0,X1,X3),X3)
| limit_point(X2,X0,X1,X3)
| ~ topological_space(X1,X3)
| ~ subset_sets(X0,X1) ) ).
cnf(u3963,negated_conjecture,
( ~ closed(f1(ct,f15(X1,X4,X2,X3,X0)),X6,X7)
| ~ limit_point(X1,X4,X2,X3)
| ~ element_of_collection(X4,ct)
| ~ element_of_collection(X0,ct)
| element_of_set(f20(closure(X5,X6,X7),X8),union_of_members(ct))
| hausdorff(closure(X5,X6,X7),X8)
| ~ subset_sets(X5,f1(ct,f15(X1,X4,X2,X3,X0)))
| ~ neighborhood(X0,X1,X2,X3)
| ~ topological_space(closure(X5,X6,X7),X8) ) ).
cnf(u651,axiom,
( element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| subset_sets(relative_complement_sets(X1,X2),X2) ) ).
cnf(u634,axiom,
( element_of_set(f11(X0,interior(X1,X2,X3)),f13(X1,X2,X3,f11(X0,interior(X1,X2,X3))))
| element_of_collection(interior(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(u6452,axiom,
( ~ closed(boundary(X5,X2,X3),X7,X8)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X1,X4,X0),closure(X5,X2,X3)),sF3)
| ~ subset_sets(X5,sF1)
| ~ subset_sets(X6,boundary(X5,X2,X3))
| subset_sets(X0,X1)
| ~ topological_space(closure(X6,X7,X8),X9)
| hausdorff(closure(X6,X7,X8),X9) ) ).
cnf(u2687,axiom,
( ~ element_of_set(X9,f13(X0,X1,top_of_basis(subspace_topology(X2,X3,X4)),f20(closure(X7,X5,X6),X8)))
| ~ topological_space(closure(X7,X5,X6),X8)
| hausdorff(closure(X7,X5,X6),X8)
| ~ subset_sets(X7,interior(X0,X1,top_of_basis(subspace_topology(X2,X3,X4))))
| ~ closed(interior(X0,X1,top_of_basis(subspace_topology(X2,X3,X4))),X5,X6)
| topological_space(X2,X3) ) ).
cnf(u6686,negated_conjecture,
( element_of_set(X2,f14(X0,cx,ct,X1))
| element_of_set(X1,closure(X0,cx,ct))
| ~ element_of_set(X2,sF3) ) ).
cnf(u4675,axiom,
( ~ element_of_collection(f21(X2,X3),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ topological_space(X2,X3)
| connected_space(X2,X3)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X3)) ) ).
cnf(u4122,axiom,
( ~ element_of_set(X7,f12(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5,f10(subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5),X0,X6)))
| ~ element_of_set(X6,X0)
| ~ element_of_collection(X0,top_of_basis(subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5)))
| subset_sets(X4,X2) ) ).
cnf(u3501,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| element_of_set(f11(X7,closure(X4,X5,X6)),sF3)
| ~ subset_sets(X4,sF1)
| ~ closed(sF1,X5,X6)
| element_of_set(f7(closure(X0,X1,X2),X3),union_of_members(top_of_basis(X7))) ) ).
cnf(u4905,axiom,
( ~ subset_sets(X5,f14(X0,X1,X2,X3))
| element_of_set(X3,union_of_members(top_of_basis(X4)))
| ~ closed(sF1,X1,X2)
| ~ subset_sets(X0,sF1)
| ~ subset_sets(X0,X1)
| ~ subset_sets(X5,X1)
| element_of_set(f11(X4,closure(X0,X1,X2)),sF3)
| closed(f14(X5,X1,X2,X6),X1,X2)
| element_of_set(X6,f14(X0,X1,X2,X3)) ) ).
cnf(u6289,axiom,
( ~ subset_sets(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,X6),X1)
| element_of_set(X7,closure(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5))
| ~ subset_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(X4,X5)
| ~ topological_space(interior(X0,X1,X2),X3)
| element_of_set(X6,f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,X7))
| ~ element_of_set(X8,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X8,interior(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,X6),X1,X2)) ) ).
cnf(compact_space_102,axiom,
( subset_collections(f23(X0,X1,X2),X2)
| ~ open_covering(X2,X0,X1)
| ~ compact_space(X0,X1) ) ).
cnf(u760,negated_conjecture,
( ~ element_of_set(X2,f13(a,cx,ct,X1))
| ~ element_of_set(X1,sF0)
| ~ topological_space(cx,top_of_basis(X0))
| element_of_set(f11(X0,f13(a,cx,ct,X1)),sF0)
| element_of_set(X2,interior(a,cx,top_of_basis(X0))) ) ).
cnf(u6455,axiom,
( ~ closed(closure(X5,X2,X3),X7,X8)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X1,X4,X0),closure(X5,X2,X3)),sF3)
| ~ subset_sets(X5,sF1)
| hausdorff(closure(X6,X7,X8),X9)
| ~ subset_sets(X6,closure(X5,X2,X3))
| subset_sets(X0,X1)
| ~ topological_space(closure(X6,X7,X8),X9) ) ).
cnf(u1095,axiom,
( element_of_set(f19(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ subset_sets(relative_complement_sets(X0,X1),closure(X0,X1,X2))
| ~ closed(closure(X0,X1,X2),X1,X2)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3) ) ).
cnf(u6106,axiom,
( element_of_set(X7,interior(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5,f19(closure(relative_complement_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4),X4,X5),X6)),X1,X2))
| ~ element_of_set(X7,f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))))
| element_of_collection(interior(X0,X1,X2),top_of_basis(X3))
| ~ subset_sets(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5,f19(closure(relative_complement_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4),X4,X5),X6)),X1)
| element_of_set(f19(closure(relative_complement_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4),X4,X5),X6),boundary(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5))
| ~ topological_space(closure(relative_complement_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4),X4,X5),X6)
| hausdorff(closure(relative_complement_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4),X4,X5),X6)
| ~ subset_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4) ) ).
cnf(u445,axiom,
( subset_sets(f13(X0,X1,X2,f7(interior(X0,X1,X2),X3)),X0)
| ~ topological_space(interior(X0,X1,X2),X3)
| basis(interior(X0,X1,X2),X3) ) ).
cnf(u30737,axiom,
( ~ compact_space(intersection_of_sets(X2,f12(X3,X4,X2,union_of_members(f24(X0,X1)))),X1)
| compact_space(X0,X1)
| ~ subset_collections(f24(X0,X1),X1) ) ).
cnf(u3598,axiom,
( ~ topological_space(f14(X0,X1,X2,f11(X3,closure(relative_complement_sets(X0,X1),X1,X2))),X5)
| element_of_collection(closure(relative_complement_sets(X0,X1),X1,X2),top_of_basis(X3))
| ~ subset_sets(X0,X1)
| ~ element_of_collection(X4,X5)
| element_of_set(f11(X3,closure(relative_complement_sets(X0,X1),X1,X2)),boundary(X0,X1,X2))
| ~ element_of_set(X6,X4)
| ~ subset_sets(X4,X0)
| element_of_set(X6,interior(X0,f14(X0,X1,X2,f11(X3,closure(relative_complement_sets(X0,X1),X1,X2))),X5)) ) ).
cnf(u1229,axiom,
( element_of_set(f19(f16(X3,X2,X0,X1),X4),union_of_members(X1))
| ~ subset_sets(X2,X0)
| limit_point(X3,X2,X0,X1)
| ~ topological_space(X0,X1)
| ~ topological_space(f16(X3,X2,X0,X1),X4)
| hausdorff(f16(X3,X2,X0,X1),X4) ) ).
cnf(u36057,negated_conjecture,
( element_of_set(f11(X0,f1(ct,X1)),f10(X2,f1(top_of_basis(X2),f11(X0,f1(ct,X1))),f11(X0,f1(ct,X1))))
| limit_point(f11(X0,f1(ct,X1)),X3,X4,top_of_basis(X2))
| ~ element_of_set(X1,cx)
| element_of_set(X1,f1(top_of_basis(X0),X1)) ) ).
cnf(u4255,negated_conjecture,
( ~ element_of_set(X3,f13(a,X0,X1,f19(interior(a,X0,X1),X2)))
| ~ topological_space(cx,X1)
| ~ topological_space(interior(a,X0,X1),X2)
| hausdorff(interior(a,X0,X1),X2)
| element_of_set(X3,interior(a,cx,X1)) ) ).
cnf(u4469,negated_conjecture,
( ~ subset_sets(union_of_members(ct),closure(X1,X2,X3))
| ~ element_of_collection(union_of_members(ct),X0)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ closed(cx,X2,X3)
| ~ subset_sets(X1,cx) ) ).
cnf(u5722,axiom,
( ~ element_of_set(f11(X0,intersection_of_members(X1)),closure(X2,X3,X4))
| ~ element_of_collection(closure(relative_complement_sets(X2,X3),X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),boundary(X2,X3,X4)) ) ).
cnf(u6903,negated_conjecture,
( element_of_set(f20(interior(X0,X1,X2),X3),interior(X4,X5,X6))
| hausdorff(interior(X0,X1,X2),X3) ) ).
cnf(separation_87,axiom,
( ~ separation(X0,X1,X2,X3)
| disjoint_s(X0,X1) ) ).
cnf(u729,axiom,
( ~ element_of_set(X3,relative_complement_sets(X0,X1))
| ~ closed(X0,X1,X2)
| element_of_set(X3,union_of_members(X2)) ) ).
cnf(u219,negated_conjecture,
( element_of_set(X0,union_of_members(ct))
| ~ element_of_set(X0,empty_set) ) ).
cnf(u6365,axiom,
( element_of_collection(f1(ct,f19(sF0,X0)),ct)
| hausdorff(sF0,X0)
| ~ topological_space(sF0,X0) ) ).
cnf(u36179,negated_conjecture,
( element_of_set(X0,f10(X3,f1(top_of_basis(X3),X0),X0))
| limit_point(X0,X1,X2,top_of_basis(X3)) ) ).
cnf(u930,axiom,
( ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,intersection_of_members(X4))
| ~ closed(intersection_of_members(X4),X1,X2)
| hausdorff(closure(X0,X1,X2),X3)
| ~ element_of_collection(X5,X4)
| element_of_set(f20(closure(X0,X1,X2),X3),X5) ) ).
cnf(u3940,axiom,
( subset_sets(X0,f14(X0,X1,X2,f19(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f19(closure(relative_complement_sets(X0,X1),X1,X2),X3),union_of_members(top_of_basis(X4)))
| element_of_set(f11(X4,boundary(X0,X1,X2)),boundary(X0,X1,X2))
| ~ subset_sets(X0,X1)
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3) ) ).
cnf(u6565,axiom,
( ~ element_of_set(X0,closure(X1,X2,X3))
| ~ closed(sF1,X2,X3)
| element_of_set(f11(X4,closure(X1,X2,X3)),sF3)
| ~ subset_sets(X1,sF1)
| element_of_set(X0,union_of_members(X4)) ) ).
cnf(u2631,axiom,
( ~ subset_sets(f18(X2,X4,X3,f11(X0,X1)),X1)
| eq_p(X3,f11(X0,X1))
| ~ hausdorff(X2,X4)
| ~ element_of_set(X3,X2)
| element_of_collection(X1,top_of_basis(X0))
| ~ element_of_collection(f18(X2,X4,X3,f11(X0,X1)),X0)
| ~ element_of_set(f11(X0,X1),X2) ) ).
cnf(u5984,negated_conjecture,
( ~ open(f14(a,cx,ct,X2),X0,X1)
| element_of_set(X2,sF3)
| ~ disjoint_s(X3,f14(a,cx,ct,X2))
| subset_sets(a,f14(a,cx,ct,f20(X0,X1)))
| hausdorff(X0,X1)
| ~ open(X3,X0,X1)
| ~ element_of_set(f19(X0,X1),X3) ) ).
cnf(u3175,axiom,
( closed(f14(relative_complement_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7),X7,X8,X9),X7,X8)
| element_of_set(X10,interior(f14(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8,X9),X1,X2))
| ~ subset_sets(relative_complement_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7),X7)
| ~ subset_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7)
| ~ topological_space(X7,X8)
| ~ closed(interior(X0,X1,X2),X4,X5)
| ~ topological_space(closure(X3,X4,X5),X6)
| hausdorff(closure(X3,X4,X5),X6)
| ~ subset_sets(f14(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8,X9),X1)
| ~ element_of_set(X10,f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)))
| ~ subset_sets(X3,interior(X0,X1,X2))
| element_of_set(X9,boundary(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8)) ) ).
cnf(u3812,axiom,
( ~ subset_sets(a,f14(X1,cx,ct,f11(X0,closure(relative_complement_sets(X1,cx),cx,ct))))
| element_of_collection(closure(relative_complement_sets(X1,cx),cx,ct),top_of_basis(X0))
| ~ subset_sets(X1,cx)
| element_of_set(f11(X0,closure(relative_complement_sets(X1,cx),cx,ct)),boundary(X1,cx,ct))
| ~ element_of_set(X2,sF3)
| element_of_set(X2,f14(X1,cx,ct,f11(X0,closure(relative_complement_sets(X1,cx),cx,ct)))) ) ).
cnf(u1259,axiom,
( element_of_collection(f6(X3,X4,f19(intersection_of_sets(X0,X1),X2),X0,X1),X4)
| ~ element_of_collection(X0,X4)
| ~ element_of_collection(X1,X4)
| ~ basis(X3,X4)
| ~ element_of_set(f19(intersection_of_sets(X0,X1),X2),X3)
| ~ topological_space(intersection_of_sets(X0,X1),X2)
| hausdorff(intersection_of_sets(X0,X1),X2) ) ).
cnf(u546,axiom,
( ~ subset_sets(closure(relative_complement_sets(X2,X3),X3,X4),X0)
| ~ element_of_collection(closure(relative_complement_sets(X2,X3),X3,X4),X1)
| element_of_collection(X0,top_of_basis(X1))
| ~ element_of_set(f11(X1,X0),boundary(X2,X3,X4)) ) ).
cnf(u5283,axiom,
( ~ open(f18(X1,X2,X3,f20(X4,X5)),X4,X5)
| ~ disjoint_s(X0,f18(X1,X2,X3,f20(X4,X5)))
| hausdorff(X4,X5)
| ~ open(X0,X4,X5)
| ~ element_of_set(f19(X4,X5),X0)
| ~ element_of_set(f20(X4,X5),X1)
| eq_p(X3,f20(X4,X5))
| ~ hausdorff(X1,X2)
| ~ element_of_set(X3,X1) ) ).
cnf(u20511,negated_conjecture,
( open(f13(X1,X2,X3,f11(X0,union_of_members(ct))),X2,X3)
| element_of_set(X4,f1(top_of_basis(X0),X4))
| ~ element_of_set(X4,sF0) ) ).
cnf(u2816,axiom,
( subset_collections(f5(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3),X3)
| ~ element_of_collection(empty_set,X3)
| ~ element_of_collection(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3)
| element_of_collection(f3(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3),X3)
| topological_space(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3)
| ~ element_of_collection(union_of_members(X3),subspace_topology(X1,X2,X0)) ) ).
cnf(u663,axiom,
( element_of_collection(boundary(X0,X1,X2),top_of_basis(X3))
| subset_sets(X0,X1) ) ).
cnf(u27747,negated_conjecture,
( element_of_set(f11(X1,union_of_members(ct)),union_of_members(ct))
| element_of_set(f11(X0,union_of_members(top_of_basis(X1))),sF0)
| element_of_set(X2,f1(top_of_basis(X0),X2))
| ~ element_of_set(X2,cx) ) ).
cnf(u933,axiom,
( ~ closed(relative_complement_sets(X4,X5),X1,X2)
| ~ subset_sets(X0,relative_complement_sets(X4,X5))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ closed(X4,X5,X6)
| element_of_set(f20(closure(X0,X1,X2),X3),union_of_members(X6)) ) ).
cnf(u4687,axiom,
( element_of_set(f11(X2,sF3),f14(X0,cx,ct,f20(closure(relative_complement_sets(X0,cx),cx,ct),X1)))
| element_of_set(f20(closure(relative_complement_sets(X0,cx),cx,ct),X1),boundary(X0,cx,ct))
| hausdorff(closure(relative_complement_sets(X0,cx),cx,ct),X1)
| ~ subset_sets(X0,cx)
| ~ topological_space(closure(relative_complement_sets(X0,cx),cx,ct),X1)
| element_of_collection(sF3,top_of_basis(X2))
| ~ subset_sets(a,f14(X0,cx,ct,f20(closure(relative_complement_sets(X0,cx),cx,ct),X1))) ) ).
cnf(u482,axiom,
( element_of_collection(f8(X0,f24(X0,X1)),f24(X0,X1))
| ~ topological_space(X0,X1)
| basis(X0,f24(X0,X1))
| compact_space(X0,X1) ) ).
cnf(u5130,axiom,
( ~ element_of_set(X6,f12(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5,f8(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))))
| basis(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| ~ topological_space(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| subset_sets(X4,X2) ) ).
cnf(u5558,axiom,
( subset_sets(X0,f14(X0,X1,X2,f7(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f7(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| basis(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1) ) ).
cnf(u3840,axiom,
( element_of_set(f20(f2(X1,X0),X2),union_of_members(X1))
| element_of_set(X0,intersection_of_members(X1))
| ~ topological_space(f2(X1,X0),X2)
| hausdorff(f2(X1,X0),X2) ) ).
cnf(connected_set_95,axiom,
( ~ connected_space(X0,subspace_topology(X1,X2,X0))
| ~ topological_space(X1,X2)
| ~ subset_sets(X0,X1)
| connected_set(X0,X1,X2) ) ).
cnf(u3216,negated_conjecture,
( ~ closed(f13(a,cx,ct,f20(sF0,X4)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f20(sF0,X4)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f20(boundary(X0,X1,X2),X3),sF0)
| ~ topological_space(sF0,X4)
| hausdorff(sF0,X4) ) ).
cnf(u2821,axiom,
( ~ closed(f8(X0,X1),X4,X5)
| basis(X0,X1)
| element_of_set(f11(X2,closure(X3,X4,X5)),union_of_members(X1))
| element_of_collection(closure(X3,X4,X5),top_of_basis(X2))
| ~ topological_space(X0,X1)
| ~ subset_sets(X3,f8(X0,X1)) ) ).
cnf(open_covering_98,axiom,
( ~ open_covering(X0,X1,X2)
| equal_sets(union_of_members(X0),X1) ) ).
cnf(u644,axiom,
( element_of_set(f11(X0,f13(X1,X2,X3,f20(interior(X1,X2,X3),X4))),interior(X1,X2,X3))
| ~ topological_space(interior(X1,X2,X3),X4)
| hausdorff(interior(X1,X2,X3),X4)
| element_of_collection(f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)),top_of_basis(X0)) ) ).
cnf(u3679,axiom,
( ~ closed(f2(X4,f19(closure(X0,X1,X2),X3)),X1,X2)
| hausdorff(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,f2(X4,f19(closure(X0,X1,X2),X3)))
| element_of_set(f19(closure(X0,X1,X2),X3),intersection_of_members(X4))
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u441,axiom,
( eq_p(f7(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4),X0)
| ~ topological_space(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4)
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3)
| basis(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4) ) ).
cnf(u979,axiom,
( ~ closed(f13(closure(X1,X2,X3),X4,X5,f20(closure(X0,X6,X7),X8)),X2,X3)
| ~ closed(interior(closure(X1,X2,X3),X4,X5),X6,X7)
| ~ topological_space(closure(X0,X6,X7),X8)
| hausdorff(closure(X0,X6,X7),X8)
| ~ subset_sets(X0,interior(closure(X1,X2,X3),X4,X5))
| ~ subset_sets(X1,f13(closure(X1,X2,X3),X4,X5,f20(closure(X0,X6,X7),X8)))
| ~ element_of_collection(f13(closure(X1,X2,X3),X4,X5,f20(closure(X0,X6,X7),X8)),X9)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X9)) ) ).
cnf(u3498,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ subset_sets(X4,X7)
| ~ closed(X7,X5,X6)
| element_of_set(f7(closure(X0,X1,X2),X3),X7) ) ).
cnf(u34575,axiom,
( ~ subset_collections(f24(X0,X2),f24(X1,f24(X0,X2)))
| compact_space(X1,f24(X0,X2))
| ~ compact_space(X0,f24(X1,f24(X0,X2)))
| compact_space(X0,X2) ) ).
cnf(u9883,negated_conjecture,
( eq_p(f19(boundary(X0,X1,X2),X3),f19(boundary(X4,X5,X6),X7))
| hausdorff(boundary(X4,X5,X6),X7)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u26872,axiom,
( element_of_set(f11(X0,union_of_members(ct)),f1(X1,f11(X0,union_of_members(ct))))
| element_of_set(X2,f1(top_of_basis(X0),X2))
| ~ element_of_set(X2,sF0) ) ).
cnf(u3186,axiom,
( element_of_set(f20(boundary(X0,X1,X2),X3),f1(X4,f20(boundary(X0,X1,X2),X3)))
| ~ subset_sets(X0,union_of_members(X4))
| ~ closed(union_of_members(X4),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u5263,axiom,
( ~ open(f1(X1,f20(X2,X3)),X2,X3)
| ~ disjoint_s(X0,f1(X1,f20(X2,X3)))
| hausdorff(X2,X3)
| ~ open(X0,X2,X3)
| ~ element_of_set(f19(X2,X3),X0)
| limit_point(f20(X2,X3),X4,X5,X1)
| ~ topological_space(X5,X1)
| ~ subset_sets(X4,X5) ) ).
cnf(u2671,axiom,
( ~ element_of_set(X5,f12(X1,top_of_basis(subspace_topology(X2,X3,X4)),X0,X0))
| ~ connected_set(X0,X1,top_of_basis(subspace_topology(X2,X3,X4)))
| topological_space(X2,X3) ) ).
cnf(u16453,negated_conjecture,
( eq_p(f19(intersection_of_members(X0),X1),X2)
| hausdorff(intersection_of_members(X0),X1)
| ~ element_of_set(X2,sF3) ) ).
cnf(separation_83,axiom,
( ~ separation(X0,X1,X2,X3)
| ~ equal_sets(X1,empty_set) ) ).
cnf(u20510,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f13(X1,X2,X3,f11(X0,union_of_members(ct))))
| element_of_set(X4,f1(top_of_basis(X0),X4))
| ~ element_of_set(X4,sF0) ) ).
cnf(u2490,axiom,
( element_of_set(X0,f10(X1,f10(top_of_basis(X1),X2,X3),X0))
| ~ element_of_set(X0,f10(top_of_basis(X1),X2,X3))
| ~ element_of_set(X3,X2)
| ~ element_of_collection(X2,top_of_basis(top_of_basis(X1))) ) ).
cnf(u1200,axiom,
( closed(f14(X0,X1,X2,f11(X3,f14(closure(X0,X1,X2),X4,X5,X6))),X1,X2)
| element_of_collection(f14(closure(X0,X1,X2),X4,X5,X6),top_of_basis(X3))
| ~ element_of_collection(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| element_of_set(X6,closure(closure(X0,X1,X2),X4,X5))
| ~ subset_sets(closure(X0,X1,X2),X4)
| ~ topological_space(X4,X5) ) ).
cnf(u1300,axiom,
( closed(f14(X1,X2,X3,X4),X2,X3)
| element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| element_of_set(X4,union_of_members(top_of_basis(X0)))
| ~ closed(sF1,X2,X3)
| ~ subset_sets(X1,sF1)
| ~ subset_sets(X1,X2) ) ).
cnf(u942,negated_conjecture,
( ~ closed(f13(a,cx,ct,f19(sF0,X4)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f19(sF0,X4)))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| element_of_set(f20(closure(X0,X1,X2),X3),sF0)
| ~ topological_space(sF0,X4)
| hausdorff(sF0,X4) ) ).
cnf(u3329,axiom,
( element_of_set(f11(X1,closure(X2,X3,X4)),sF3)
| subset_sets(X2,f14(X2,X3,X4,X0))
| element_of_collection(f1(top_of_basis(X1),X0),top_of_basis(X1))
| ~ subset_sets(X2,sF1)
| ~ subset_sets(X2,X3)
| ~ closed(sF1,X3,X4) ) ).
cnf(u3050,axiom,
( element_of_set(f19(boundary(X0,X1,X2),X3),f6(X6,X7,f19(boundary(X0,X1,X2),X3),X4,X5))
| ~ subset_sets(X0,intersection_of_sets(X4,X5))
| ~ closed(intersection_of_sets(X4,X5),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ element_of_set(f19(boundary(X0,X1,X2),X3),X6)
| ~ element_of_collection(X4,X7)
| ~ element_of_collection(X5,X7)
| ~ basis(X6,X7)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u2652,axiom,
( element_of_set(X2,f10(X0,f1(top_of_basis(X0),f11(X1,union_of_members(top_of_basis(X0)))),X2))
| ~ element_of_set(X2,f1(top_of_basis(X0),f11(X1,union_of_members(top_of_basis(X0)))))
| element_of_collection(union_of_members(top_of_basis(X0)),top_of_basis(X1)) ) ).
cnf(u3059,axiom,
( subset_sets(f13(X4,X5,X6,f19(boundary(X0,X1,X2),X3)),X4)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ closed(interior(X4,X5,X6),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u1354,axiom,
( element_of_set(f11(X0,f13(a,cx,ct,f20(sF0,X1))),f13(a,cx,ct,f20(sF0,X1)))
| element_of_set(f20(sF0,X1),union_of_members(top_of_basis(X0)))
| hausdorff(sF0,X1)
| ~ topological_space(sF0,X1) ) ).
cnf(limit_point_64,axiom,
( ~ limit_point(X0,X1,X2,X3)
| subset_sets(X1,X2) ) ).
cnf(u212,axiom,
( disjoint_s(f21(X0,X1),f22(X0,X1))
| connected_space(X0,X1)
| ~ topological_space(X0,X1) ) ).
cnf(u20432,negated_conjecture,
( ~ element_of_set(X0,empty_set)
| element_of_set(f11(X1,union_of_members(ct)),union_of_members(ct))
| element_of_set(X0,f1(top_of_basis(X1),X0)) ) ).
cnf(u415,negated_conjecture,
( ~ element_of_collection(f13(a,X0,X1,f20(interior(a,X0,X1),X2)),X3)
| ~ topological_space(interior(a,X0,X1),X2)
| ~ topological_space(cx,X3)
| ~ element_of_set(X4,f13(a,X0,X1,f20(interior(a,X0,X1),X2)))
| hausdorff(interior(a,X0,X1),X2)
| element_of_set(X4,interior(a,cx,X3)) ) ).
cnf(u3692,axiom,
( element_of_set(X10,interior(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,f11(X9,f14(closure(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5),X6,X7,X8))),X1,X2))
| ~ element_of_collection(closure(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5),X9)
| ~ subset_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(X4,X5)
| element_of_set(X8,closure(closure(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5),X6,X7))
| ~ subset_sets(closure(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5),X6)
| ~ topological_space(X6,X7)
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ subset_sets(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,f11(X9,f14(closure(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5),X6,X7,X8))),X1)
| ~ element_of_set(X10,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_collection(f14(closure(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5),X6,X7,X8),top_of_basis(X9)) ) ).
cnf(u3926,negated_conjecture,
( ~ element_of_set(f11(X4,f14(f14(a,cx,ct,X0),X1,X2,f19(closure(relative_complement_sets(f14(a,cx,ct,X0),X1),X1,X2),X3))),sF3)
| ~ topological_space(closure(relative_complement_sets(f14(a,cx,ct,X0),X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(f14(a,cx,ct,X0),X1),X1,X2),X3)
| ~ subset_sets(f14(a,cx,ct,X0),X1)
| ~ element_of_collection(f14(a,cx,ct,X0),X4)
| element_of_collection(f14(f14(a,cx,ct,X0),X1,X2,f19(closure(relative_complement_sets(f14(a,cx,ct,X0),X1),X1,X2),X3)),top_of_basis(X4))
| element_of_set(f19(closure(relative_complement_sets(f14(a,cx,ct,X0),X1),X1,X2),X3),boundary(f14(a,cx,ct,X0),X1,X2))
| element_of_set(X0,sF3) ) ).
cnf(u494,axiom,
( ~ element_of_set(X1,f1(ct,X0))
| ~ element_of_set(X0,sF0)
| element_of_set(X1,union_of_members(ct)) ) ).
cnf(u1313,negated_conjecture,
( ~ element_of_collection(f9(X0,X1),ct)
| ~ equal_sets(union_of_members(X1),X0)
| basis(X0,X1)
| ~ element_of_collection(f8(X0,X1),ct)
| element_of_set(f7(X0,X1),f1(ct,f7(X0,X1))) ) ).
cnf(u6078,negated_conjecture,
( ~ closed(union_of_members(f24(X0,ct)),X2,X3)
| compact_space(X0,ct)
| element_of_set(f7(closure(X1,X2,X3),X4),union_of_members(ct))
| ~ topological_space(closure(X1,X2,X3),X4)
| ~ subset_sets(X1,union_of_members(f24(X0,ct)))
| ~ topological_space(X0,ct)
| basis(closure(X1,X2,X3),X4) ) ).
cnf(u5800,axiom,
( element_of_collection(f6(X2,X1,f7(X0,X1),f8(X0,X1),f9(X0,X1)),X1)
| ~ basis(X2,X1)
| ~ element_of_set(f7(X0,X1),X2)
| basis(X0,X1)
| ~ topological_space(X0,X1) ) ).
cnf(u6414,axiom,
( element_of_set(X4,f14(X0,X1,X2,f20(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f20(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ subset_sets(X0,X1)
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| closed(f14(X0,X1,X2,X4),X1,X2) ) ).
cnf(u3075,axiom,
( ~ closed(f13(X4,X5,X6,f20(interior(X4,X5,X6),X7)),X1,X2)
| ~ subset_sets(X0,f13(X4,X5,X6,f20(interior(X4,X5,X6),X7)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(interior(X4,X5,X6),X7)
| hausdorff(interior(X4,X5,X6),X7)
| element_of_set(f19(boundary(X0,X1,X2),X3),interior(X4,X5,X6)) ) ).
cnf(u2725,axiom,
( ~ closed(closure(relative_complement_sets(X1,X2),X2,X3),X4,X5)
| ~ subset_sets(X0,closure(relative_complement_sets(X1,X2),X2,X3))
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| element_of_set(f19(closure(X0,X4,X5),X6),boundary(X1,X2,X3))
| ~ subset_sets(X0,closure(X1,X2,X3))
| ~ closed(closure(X1,X2,X3),X4,X5) ) ).
cnf(u636,axiom,
( subset_sets(f13(X1,X2,X3,f11(X0,interior(X1,X2,X3))),X1)
| element_of_collection(interior(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(u2954,axiom,
( ~ closed(f13(a,cx,ct,X4),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f13(a,cx,ct,X4))
| ~ element_of_set(X4,sF0)
| element_of_set(f11(X0,boundary(X1,X2,X3)),union_of_members(ct)) ) ).
cnf(u640,negated_conjecture,
( element_of_collection(f13(a,cx,ct,X1),top_of_basis(X0))
| element_of_set(f11(X0,f13(a,cx,ct,X1)),sF0)
| ~ element_of_set(X1,sF0) ) ).
cnf(u3921,axiom,
( element_of_set(X7,interior(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,f19(closure(relative_complement_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),X4,X5),X6)),X1,X2))
| ~ topological_space(closure(relative_complement_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),X4,X5),X6)
| hausdorff(closure(relative_complement_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),X4,X5),X6)
| ~ subset_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ subset_sets(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,f19(closure(relative_complement_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),X4,X5),X6)),X1)
| ~ element_of_set(X7,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(f19(closure(relative_complement_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),X4,X5),X6),boundary(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5)) ) ).
cnf(u305,axiom,
( ~ element_of_collection(relative_complement_sets(X2,X0),X1)
| closed(X2,X0,X1)
| ~ topological_space(X0,X1) ) ).
cnf(u2785,axiom,
( ~ closed(boundary(X0,X1,X2),cx,ct)
| ~ subset_sets(a,boundary(X0,X1,X2))
| element_of_collection(sF3,top_of_basis(X3))
| ~ closed(X4,X1,X2)
| ~ subset_sets(X0,X4)
| element_of_set(f11(X5,closure(X0,X1,X2)),X4)
| element_of_set(f11(X3,sF3),union_of_members(top_of_basis(X5))) ) ).
cnf(u991,negated_conjecture,
( element_of_set(f19(f13(a,cx,ct,f20(closure(X2,X0,X1),X3)),X4),sF0)
| ~ subset_sets(X2,sF0)
| ~ topological_space(closure(X2,X0,X1),X3)
| hausdorff(closure(X2,X0,X1),X3)
| ~ closed(sF0,X0,X1)
| ~ topological_space(f13(a,cx,ct,f20(closure(X2,X0,X1),X3)),X4)
| hausdorff(f13(a,cx,ct,f20(closure(X2,X0,X1),X3)),X4) ) ).
cnf(u6591,negated_conjecture,
( ~ subset_sets(f14(a,cx,ct,X0),sF3)
| element_of_set(X1,sF3)
| element_of_set(X0,f14(a,cx,ct,X1))
| ~ element_of_collection(f14(a,cx,ct,X0),X2)
| element_of_collection(sF3,top_of_basis(X2)) ) ).
cnf(u1237,axiom,
( limit_point(X0,X2,X3,X1)
| element_of_set(X0,f1(X1,X0))
| ~ topological_space(X3,X1)
| ~ subset_sets(X2,X3) ) ).
cnf(u2499,axiom,
( element_of_set(X0,f10(X3,f13(X1,X2,top_of_basis(X3),f19(interior(X1,X2,top_of_basis(X3)),X4)),X0))
| ~ element_of_set(X0,f13(X1,X2,top_of_basis(X3),f19(interior(X1,X2,top_of_basis(X3)),X4)))
| ~ topological_space(interior(X1,X2,top_of_basis(X3)),X4)
| hausdorff(interior(X1,X2,top_of_basis(X3)),X4) ) ).
cnf(u5015,axiom,
( element_of_set(f7(X0,f23(X0,X1,X2)),X0)
| ~ open_covering(X2,X0,X1)
| basis(X0,f23(X0,X1,X2))
| ~ compact_space(X0,X1) ) ).
cnf(u28541,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f1(X2,f11(X0,union_of_members(top_of_basis(X1)))))
| element_of_set(X3,f1(top_of_basis(X0),X3))
| element_of_set(f11(X1,union_of_members(ct)),sF0)
| ~ element_of_set(X3,cx) ) ).
cnf(u9623,negated_conjecture,
( ~ element_of_set(X4,closure(X5,X6,X7))
| eq_p(f19(boundary(X0,X1,X2),X3),X4)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u16750,negated_conjecture,
( ~ element_of_set(f15(f19(intersection_of_members(X0),X1),X2,X3,X4,X5),sF1)
| hausdorff(intersection_of_members(X0),X1)
| ~ neighborhood(X5,f19(intersection_of_members(X0),X1),X3,X4)
| ~ limit_point(f19(intersection_of_members(X0),X1),X2,X3,X4) ) ).
cnf(u4677,axiom,
( ~ element_of_set(X5,intersection_of_members(X0))
| ~ element_of_collection(X4,X0)
| element_of_set(f11(subspace_topology(X1,X2,X3),intersection_of_members(X0)),X4)
| subset_sets(X3,X1) ) ).
cnf(u36087,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| element_of_set(f11(X4,union_of_members(ct)),union_of_members(X5))
| element_of_set(f11(X1,union_of_members(top_of_basis(X4))),sF0)
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u938,axiom,
( ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| subset_sets(X4,X5) ) ).
cnf(u4809,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f1(ct,f11(X0,union_of_members(ct))))
| element_of_set(X1,union_of_members(top_of_basis(X0)))
| ~ element_of_set(X1,cx) ) ).
cnf(u4847,axiom,
( element_of_set(f7(f8(X0,X1),f24(f8(X0,X1),X2)),union_of_members(X1))
| basis(f8(X0,X1),f24(f8(X0,X1),X2))
| compact_space(f8(X0,X1),X2)
| ~ topological_space(X0,X1)
| basis(X0,X1)
| ~ topological_space(f8(X0,X1),X2) ) ).
cnf(u45670,negated_conjecture,
( ~ element_of_set(X2,relative_complement_sets(a,cx))
| eq_p(X1,X0)
| element_of_set(X2,f13(f14(relative_complement_sets(a,cx),cx,ct,X1),cx,X3,X2))
| ~ element_of_set(X0,sF1) ) ).
cnf(u6290,axiom,
( ~ subset_sets(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5,X6),X1)
| element_of_set(X7,closure(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5))
| ~ subset_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4)
| ~ topological_space(X4,X5)
| element_of_set(X6,f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5,X7))
| ~ element_of_set(X8,f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))))
| element_of_collection(interior(X0,X1,X2),top_of_basis(X3))
| element_of_set(X8,interior(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5,X6),X1,X2)) ) ).
cnf(u3467,axiom,
( element_of_set(f7(closure(X0,X1,X2),X3),f6(X6,X7,f7(closure(X0,X1,X2),X3),X4,X5))
| ~ subset_sets(X0,intersection_of_sets(X4,X5))
| ~ closed(intersection_of_sets(X4,X5),X1,X2)
| basis(closure(X0,X1,X2),X3)
| ~ element_of_set(f7(closure(X0,X1,X2),X3),X6)
| ~ element_of_collection(X4,X7)
| ~ element_of_collection(X5,X7)
| ~ basis(X6,X7)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u641,negated_conjecture,
( element_of_collection(f13(a,cx,ct,f19(sF0,X1)),top_of_basis(X0))
| element_of_set(f11(X0,f13(a,cx,ct,f19(sF0,X1))),sF0)
| ~ topological_space(sF0,X1)
| hausdorff(sF0,X1) ) ).
cnf(u828,axiom,
( ~ element_of_collection(f21(X0,X1),subspace_topology(X2,X3,f22(X0,X1)))
| ~ connected_set(f22(X0,X1),X2,X3)
| ~ topological_space(X0,X1)
| connected_space(X0,X1)
| ~ connected_space(X0,subspace_topology(X2,X3,f22(X0,X1))) ) ).
cnf(u1337,axiom,
( element_of_set(f11(X2,X1),union_of_members(top_of_basis(X0)))
| element_of_set(f11(X0,X1),X1)
| element_of_collection(X1,top_of_basis(X2)) ) ).
cnf(u554,axiom,
( element_of_set(f20(intersection_of_members(X1),X2),X0)
| ~ element_of_collection(X0,X1)
| ~ topological_space(intersection_of_members(X1),X2)
| hausdorff(intersection_of_members(X1),X2) ) ).
cnf(hausdorff_76,axiom,
( disjoint_s(f17(X0,X1,X2,X3),f18(X0,X1,X2,X3))
| ~ element_of_set(X2,X0)
| ~ element_of_set(X3,X0)
| eq_p(X2,X3)
| ~ hausdorff(X0,X1) ) ).
cnf(u3814,axiom,
( ~ subset_sets(X4,f14(X1,X2,X3,f11(X0,closure(relative_complement_sets(X1,X2),X2,X3))))
| element_of_collection(closure(relative_complement_sets(X1,X2),X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,X2)
| element_of_set(f11(X0,closure(relative_complement_sets(X1,X2),X2,X3)),boundary(X1,X2,X3))
| element_of_set(X5,f14(X1,X2,X3,f11(X0,closure(relative_complement_sets(X1,X2),X2,X3))))
| subset_sets(X4,f14(X4,X2,X3,X5))
| ~ subset_sets(X4,X2) ) ).
cnf(u20476,axiom,
( element_of_set(f11(X0,union_of_members(ct)),f1(ct,f11(X0,union_of_members(ct))))
| element_of_set(X1,f1(top_of_basis(X0),X1))
| ~ element_of_set(X1,sF0) ) ).
cnf(u523,axiom,
( element_of_set(X7,interior(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,X6),X1,X2))
| ~ subset_sets(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,X6),X1)
| ~ element_of_set(X7,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3)
| element_of_set(X6,closure(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5))
| ~ subset_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(X4,X5) ) ).
cnf(u3834,axiom,
( ~ closed(f2(X1,X0),X4,X5)
| element_of_set(f11(X2,closure(X3,X4,X5)),union_of_members(X1))
| element_of_collection(closure(X3,X4,X5),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1))
| ~ subset_sets(X3,f2(X1,X0)) ) ).
cnf(u6271,axiom,
( ~ subset_sets(sF3,closure(X0,X1,X2))
| ~ subset_sets(X0,sF1)
| ~ closed(sF1,X1,X2)
| ~ element_of_collection(sF3,X3)
| ~ element_of_set(X4,closure(X0,X1,X2))
| element_of_set(X4,union_of_members(top_of_basis(X3))) ) ).
cnf(u1335,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,X1),X2),union_of_members(top_of_basis(X0)))
| element_of_set(f11(X0,sF0),sF0)
| ~ topological_space(f13(a,cx,ct,X1),X2)
| basis(f13(a,cx,ct,X1),X2)
| ~ element_of_set(X1,sF0) ) ).
cnf(u6438,axiom,
( ~ closed(closure(X5,X2,X3),X7,X8)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X1,X4,X0),closure(X5,X2,X3)),sF3)
| ~ subset_sets(X5,sF1)
| ~ topological_space(closure(X6,X7,X8),X9)
| ~ subset_sets(X6,closure(X5,X2,X3))
| subset_sets(X0,X1)
| basis(closure(X6,X7,X8),X9) ) ).
cnf(u6022,negated_conjecture,
( element_of_set(X2,interior(f14(f13(a,cx,ct,X1),cx,ct,X0),cx,ct))
| ~ subset_sets(f13(a,cx,ct,X1),sF0)
| ~ subset_sets(f13(a,cx,ct,X1),cx)
| ~ subset_sets(f14(f13(a,cx,ct,X1),cx,ct,X0),cx)
| ~ element_of_set(X2,f13(a,cx,ct,X1))
| ~ element_of_set(X1,sF0)
| element_of_set(X0,sF0) ) ).
cnf(u16471,negated_conjecture,
( eq_p(f19(intersection_of_members(X4),X5),X0)
| limit_point(X0,X1,X2,X3)
| hausdorff(intersection_of_members(X4),X5) ) ).
cnf(u3836,axiom,
( element_of_set(f19(f2(X1,X0),X2),union_of_members(X1))
| element_of_set(X0,intersection_of_members(X1))
| ~ topological_space(f2(X1,X0),X2)
| hausdorff(f2(X1,X0),X2) ) ).
cnf(u1116,negated_conjecture,
( ~ closed(f13(a,cx,ct,f19(closure(X2,X0,X1),X3)),X5,X6)
| ~ subset_sets(X2,sF0)
| ~ topological_space(closure(X2,X0,X1),X3)
| hausdorff(closure(X2,X0,X1),X3)
| element_of_set(f20(closure(X4,X5,X6),X7),sF0)
| hausdorff(closure(X4,X5,X6),X7)
| ~ subset_sets(X4,f13(a,cx,ct,f19(closure(X2,X0,X1),X3)))
| ~ closed(sF0,X0,X1)
| ~ topological_space(closure(X4,X5,X6),X7) ) ).
cnf(u4824,negated_conjecture,
( ~ subset_sets(union_of_members(top_of_basis(X2)),X1)
| ~ element_of_set(f11(X0,X1),cx)
| element_of_collection(X1,top_of_basis(X0))
| ~ element_of_collection(union_of_members(top_of_basis(X2)),X0)
| element_of_set(f11(X2,union_of_members(ct)),union_of_members(ct)) ) ).
cnf(u3373,axiom,
( closed(f14(X0,X1,X2,f11(X6,closure(X5,X3,X4))),X1,X2)
| ~ subset_sets(X5,closure(relative_complement_sets(X0,X1),X1,X2))
| element_of_collection(closure(X5,X3,X4),top_of_basis(X6))
| element_of_set(f11(X6,closure(X5,X3,X4)),boundary(X0,X1,X2))
| ~ closed(closure(relative_complement_sets(X0,X1),X1,X2),X3,X4)
| ~ subset_sets(X0,X1) ) ).
cnf(u5338,axiom,
( ~ open(f13(a,cx,ct,f20(sF0,X1)),sF0,X1)
| ~ disjoint_s(X0,f13(a,cx,ct,f20(sF0,X1)))
| hausdorff(sF0,X1)
| ~ open(X0,sF0,X1)
| ~ element_of_set(f19(sF0,X1),X0) ) ).
cnf(u9377,negated_conjecture,
( ~ element_of_set(f20(boundary(X0,X4,X5),X6),closure(X1,X2,X3))
| hausdorff(boundary(X0,X4,X5),X6)
| element_of_set(f20(boundary(X0,X4,X5),X6),boundary(X1,X2,X3)) ) ).
cnf(u193,axiom,
( closed(f14(relative_complement_sets(X0,X1),X1,X2,X3),X1,X2)
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| element_of_set(X3,boundary(X0,X1,X2))
| closed(f14(X0,X1,X2,X3),X1,X2)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u6123,negated_conjecture,
( element_of_set(f19(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X4),sF0)
| ~ closed(sF0,X1,X2)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X3))
| ~ subset_sets(X0,sF0)
| ~ topological_space(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X4)
| hausdorff(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X4) ) ).
cnf(u632,axiom,
( eq_p(f11(X0,intersection_of_sets(f16(X1,X2,X3,X4),X2)),X1)
| element_of_collection(intersection_of_sets(f16(X1,X2,X3,X4),X2),top_of_basis(X0))
| ~ subset_sets(X2,X3)
| limit_point(X1,X2,X3,X4)
| ~ topological_space(X3,X4) ) ).
cnf(u1398,axiom,
( ~ element_of_set(X0,f9(X1,top_of_basis(subspace_topology(X2,X3,X4))))
| topological_space(X2,X3)
| basis(X1,top_of_basis(subspace_topology(X2,X3,X4)))
| ~ topological_space(X1,top_of_basis(subspace_topology(X2,X3,X4))) ) ).
cnf(u652,axiom,
( element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| topological_space(X2,X3) ) ).
cnf(u9790,negated_conjecture,
( ~ element_of_set(X0,boundary(X5,X6,X7))
| eq_p(X0,f20(boundary(X1,X2,X3),X4))
| hausdorff(boundary(X1,X2,X3),X4) ) ).
cnf(u855,axiom,
( ~ closed(closure(X4,X5,X6),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,closure(X4,X5,X6))
| topological_space(X5,X6) ) ).
cnf(u9505,negated_conjecture,
( ~ element_of_set(X1,sF1)
| eq_p(X1,X0)
| ~ element_of_set(X0,sF1) ) ).
cnf(u4676,axiom,
( ~ element_of_collection(f22(X2,X3),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ topological_space(X2,X3)
| connected_space(X2,X3)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X3)) ) ).
cnf(u54435,negated_conjecture,
( open(f13(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,X6),X1,X2,X7),X1,X2)
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X6,closure(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5))
| ~ element_of_set(X7,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3))) ) ).
cnf(u4127,axiom,
( ~ element_of_collection(X0,top_of_basis(subspace_topology(X1,subspace_topology(X2,X3,X4),X5)))
| ~ element_of_set(X6,X0)
| topological_space(X2,X3) ) ).
cnf(u45046,negated_conjecture,
( ~ element_of_set(X6,boundary(X1,X2,X3))
| ~ element_of_set(X4,relative_complement_sets(X1,X2))
| eq_p(X6,X0)
| element_of_set(X4,f13(f14(relative_complement_sets(X1,X2),X2,X3,X0),X2,X5,X4)) ) ).
cnf(u4006,axiom,
( element_of_set(f11(X7,f13(X4,X5,X6,f20(closure(X0,X1,X2),X3))),interior(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| element_of_collection(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),top_of_basis(X7)) ) ).
cnf(u1230,axiom,
( ~ closed(f16(X3,X2,X0,X1),X5,X6)
| ~ subset_sets(X2,X0)
| limit_point(X3,X2,X0,X1)
| element_of_set(f19(closure(X4,X5,X6),X7),union_of_members(X1))
| hausdorff(closure(X4,X5,X6),X7)
| ~ subset_sets(X4,f16(X3,X2,X0,X1))
| ~ topological_space(X0,X1)
| ~ topological_space(closure(X4,X5,X6),X7) ) ).
cnf(u19969,negated_conjecture,
( open(f13(f14(f13(a,cx,ct,X0),cx,ct,X1),cx,ct,X2),cx,ct)
| ~ element_of_set(X0,sF0)
| element_of_set(X1,sF0)
| ~ element_of_set(X2,f13(a,cx,ct,X0)) ) ).
cnf(u2672,axiom,
( element_of_set(X3,f10(X2,f12(X1,top_of_basis(X2),X0,X0),X3))
| ~ element_of_set(X3,f12(X1,top_of_basis(X2),X0,X0))
| ~ connected_set(X0,X1,top_of_basis(X2)) ) ).
cnf(u3356,negated_conjecture,
( element_of_collection(f1(ct,f20(empty_set,X0)),ct)
| ~ topological_space(empty_set,X0)
| hausdorff(empty_set,X0) ) ).
cnf(u4673,axiom,
( ~ element_of_collection(boundary(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| topological_space(X3,X4) ) ).
cnf(u8770,negated_conjecture,
hausdorff(closure(X0,X1,X2),X3) ).
cnf(u950,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| subset_sets(X4,X5) ) ).
cnf(u456,axiom,
( element_of_set(f7(boundary(X0,X1,X2),X3),X4)
| ~ topological_space(boundary(X0,X1,X2),X3)
| ~ subset_sets(relative_complement_sets(X0,X1),X4)
| ~ closed(X4,X1,X2)
| basis(boundary(X0,X1,X2),X3) ) ).
cnf(u5265,axiom,
( ~ open(intersection_of_members(subspace_topology(X1,X2,X3)),X4,X5)
| ~ disjoint_s(X0,intersection_of_members(subspace_topology(X1,X2,X3)))
| hausdorff(X4,X5)
| ~ open(X0,X4,X5)
| ~ element_of_set(f19(X4,X5),X0)
| topological_space(X1,X2) ) ).
cnf(u1222,axiom,
( element_of_collection(f12(X2,X3,X4,f10(subspace_topology(X2,X3,X4),X1,X0)),X3)
| ~ element_of_collection(X1,top_of_basis(subspace_topology(X2,X3,X4)))
| ~ element_of_set(X0,X1) ) ).
cnf(u6297,axiom,
( ~ subset_sets(f14(f16(X0,X1,X2,X3),X4,X5,X6),X2)
| element_of_set(X7,closure(f16(X0,X1,X2,X3),X4,X5))
| ~ subset_sets(f16(X0,X1,X2,X3),X4)
| ~ topological_space(X4,X5)
| limit_point(X0,X1,X2,X3)
| ~ topological_space(X2,X3)
| element_of_set(X6,f14(f16(X0,X1,X2,X3),X4,X5,X7))
| ~ element_of_set(X8,f16(X0,X1,X2,X3))
| ~ subset_sets(X1,X2)
| element_of_set(X8,interior(f14(f16(X0,X1,X2,X3),X4,X5,X6),X2,X3)) ) ).
cnf(u3044,axiom,
( ~ closed(f1(ct,X4),X1,X2)
| ~ subset_sets(X0,f1(ct,X4))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ element_of_set(X4,sF0)
| element_of_set(f19(boundary(X0,X1,X2),X3),union_of_members(ct)) ) ).
cnf(u291,axiom,
( ~ basis(intersection_of_sets(X0,X1),X2)
| ~ topological_space(X3,X4)
| ~ subset_sets(X0,X3)
| ~ element_of_collection(X1,X4)
| element_of_collection(union_of_members(X2),subspace_topology(X3,X4,X0)) ) ).
cnf(u653,axiom,
( element_of_set(f11(X0,boundary(X1,X2,X3)),closure(X1,X2,X3))
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(u1362,axiom,
( ~ element_of_set(f7(X2,X3),f6(X1,X4,X0,f8(X2,X3),f9(X2,X3)))
| ~ element_of_collection(f8(X2,X3),X4)
| ~ element_of_collection(f9(X2,X3),X4)
| ~ element_of_set(X0,intersection_of_sets(f8(X2,X3),f9(X2,X3)))
| ~ basis(X1,X4)
| ~ equal_sets(union_of_members(X3),X2)
| ~ element_of_set(X0,X1)
| ~ element_of_collection(f6(X1,X4,X0,f8(X2,X3),f9(X2,X3)),X3)
| basis(X2,X3) ) ).
cnf(boundary_72,axiom,
( ~ element_of_set(X0,closure(relative_complement_sets(X1,X2),X2,X3))
| ~ topological_space(X2,X3)
| ~ element_of_set(X0,closure(X1,X2,X3))
| element_of_set(X0,boundary(X1,X2,X3)) ) ).
cnf(u3087,axiom,
( ~ closed(boundary(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,boundary(X4,X5,X6))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| subset_sets(X4,X5)
| element_of_set(f19(boundary(X0,X1,X2),X3),union_of_members(top_of_basis(X7))) ) ).
cnf(u6425,axiom,
( ~ closed(X5,X2,X3)
| element_of_set(X4,f14(X1,X2,X3,X0))
| ~ subset_sets(X1,X2)
| ~ subset_sets(X1,X5)
| closed(f14(X1,X2,X3,X4),X2,X3)
| element_of_set(X0,X5) ) ).
cnf(u27714,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f1(ct,f11(X0,union_of_members(ct))))
| element_of_set(f11(X1,union_of_members(top_of_basis(X0))),interior(X2,X3,X4))
| element_of_set(X5,f1(top_of_basis(X1),X5))
| ~ element_of_set(X5,cx) ) ).
cnf(u781,axiom,
( ~ element_of_set(f7(X0,X1),f13(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2,X3,f11(X4,interior(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2,X3))))
| ~ equal_sets(union_of_members(X1),X0)
| element_of_collection(interior(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2,X3),top_of_basis(X4))
| ~ element_of_collection(f13(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2,X3,f11(X4,interior(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2,X3))),X1)
| basis(X0,X1) ) ).
cnf(u423,negated_conjecture,
( ~ element_of_set(X1,f13(a,cx,ct,f20(sF0,X0)))
| element_of_set(X1,sF0)
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0) ) ).
cnf(u3472,axiom,
( ~ closed(f8(X4,X5),X1,X2)
| ~ subset_sets(X0,f8(X4,X5))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(X4,X5)
| basis(X4,X5)
| element_of_set(f7(closure(X0,X1,X2),X3),union_of_members(X5)) ) ).
cnf(u6286,axiom,
( ~ subset_sets(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,X3),cx)
| element_of_set(X4,closure(f13(a,cx,ct,f19(sF0,X0)),X1,X2))
| ~ subset_sets(f13(a,cx,ct,f19(sF0,X0)),X1)
| ~ topological_space(X1,X2)
| ~ topological_space(sF0,X0)
| element_of_set(X3,f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,X4))
| ~ element_of_set(X5,f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(X5,interior(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,X3),cx,ct)) ) ).
cnf(u434,axiom,
( ~ element_of_set(f7(X1,X0),f13(intersection_of_sets(f8(X1,X0),f9(X1,X0)),X2,X3,f20(interior(intersection_of_sets(f8(X1,X0),f9(X1,X0)),X2,X3),X4)))
| ~ equal_sets(union_of_members(X0),X1)
| ~ element_of_collection(f13(intersection_of_sets(f8(X1,X0),f9(X1,X0)),X2,X3,f20(interior(intersection_of_sets(f8(X1,X0),f9(X1,X0)),X2,X3),X4)),X0)
| basis(X1,X0)
| hausdorff(interior(intersection_of_sets(f8(X1,X0),f9(X1,X0)),X2,X3),X4)
| ~ topological_space(interior(intersection_of_sets(f8(X1,X0),f9(X1,X0)),X2,X3),X4) ) ).
cnf(u4616,negated_conjecture,
( ~ element_of_collection(f1(ct,X2),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ element_of_set(X2,cx)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(ct)) ) ).
cnf(u4664,axiom,
( ~ element_of_collection(closure(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X5,closure(X2,X3,X4)),sF3)
| ~ subset_sets(X2,sF1)
| ~ closed(sF1,X3,X4)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(top_of_basis(X5))) ) ).
cnf(u1321,axiom,
( element_of_set(f11(X0,f1(X1,X2)),f1(X1,X2))
| limit_point(X2,X3,X4,X1)
| element_of_set(X2,union_of_members(top_of_basis(X0)))
| ~ topological_space(X4,X1)
| ~ subset_sets(X3,X4) ) ).
cnf(u3779,axiom,
( ~ subset_sets(X7,f14(X0,X1,X2,f11(X6,f14(closure(X0,X1,X2),X3,X4,X5))))
| ~ element_of_collection(closure(X0,X1,X2),X6)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| element_of_set(X5,closure(closure(X0,X1,X2),X3,X4))
| ~ subset_sets(closure(X0,X1,X2),X3)
| ~ topological_space(X3,X4)
| element_of_collection(f14(closure(X0,X1,X2),X3,X4,X5),top_of_basis(X6))
| element_of_set(X8,f14(X0,X1,X2,f11(X6,f14(closure(X0,X1,X2),X3,X4,X5))))
| subset_sets(X7,f14(X7,X1,X2,X8))
| ~ subset_sets(X7,X1) ) ).
cnf(u30278,negated_conjecture,
( element_of_set(f11(X4,union_of_members(top_of_basis(X0))),f1(X5,f11(X4,union_of_members(top_of_basis(X0)))))
| element_of_set(f11(X0,union_of_members(ct)),union_of_members(X7))
| element_of_set(X6,f1(top_of_basis(X4),X6))
| ~ element_of_set(X6,cx) ) ).
cnf(u3088,axiom,
( ~ closed(boundary(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,boundary(X4,X5,X6))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ subset_sets(relative_complement_sets(X4,X5),X7)
| ~ closed(X7,X5,X6)
| element_of_set(f19(boundary(X0,X1,X2),X3),X7) ) ).
cnf(u3511,axiom,
( ~ closed(f21(X4,X5),X1,X2)
| ~ subset_sets(X0,f21(X4,X5))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(X4,X5)
| connected_space(X4,X5)
| element_of_set(f7(closure(X0,X1,X2),X3),union_of_members(X5)) ) ).
cnf(u36134,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f10(X0,f1(top_of_basis(X0),f11(X0,union_of_members(ct))),f11(X0,union_of_members(ct))))
| limit_point(f11(X0,union_of_members(ct)),X1,X2,top_of_basis(X0)) ) ).
cnf(u3442,axiom,
( element_of_set(f19(f13(a,cx,ct,f20(sF0,X0)),X1),union_of_members(ct))
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f20(sF0,X0)),X1)
| hausdorff(f13(a,cx,ct,f20(sF0,X0)),X1) ) ).
cnf(u6031,negated_conjecture,
( ~ element_of_set(f11(X4,f14(closure(relative_complement_sets(X1,X2),X2,X3),cx,ct,X0)),boundary(X1,X2,X3))
| ~ subset_sets(closure(relative_complement_sets(X1,X2),X2,X3),sF0)
| ~ subset_sets(closure(relative_complement_sets(X1,X2),X2,X3),cx)
| ~ element_of_collection(closure(relative_complement_sets(X1,X2),X2,X3),X4)
| element_of_collection(f14(closure(relative_complement_sets(X1,X2),X2,X3),cx,ct,X0),top_of_basis(X4))
| element_of_set(X0,sF0) ) ).
cnf(u3439,axiom,
( element_of_set(f11(X1,f13(a,cx,ct,f20(sF0,X0))),union_of_members(ct))
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0)
| element_of_collection(f13(a,cx,ct,f20(sF0,X0)),top_of_basis(X1)) ) ).
cnf(u45265,negated_conjecture,
( ~ element_of_set(X1,relative_complement_sets(a,cx))
| ~ element_of_set(X0,sF1)
| eq_p(X0,X2)
| element_of_set(X1,f13(f14(relative_complement_sets(a,cx),cx,ct,X2),cx,X3,X1)) ) ).
cnf(u851,axiom,
( ~ closed(f13(X4,X5,X6,f20(interior(X4,X5,X6),X7)),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f13(X4,X5,X6,f20(interior(X4,X5,X6),X7)))
| ~ topological_space(interior(X4,X5,X6),X7)
| hausdorff(interior(X4,X5,X6),X7)
| element_of_set(f11(X0,closure(X1,X2,X3)),interior(X4,X5,X6)) ) ).
cnf(u3370,axiom,
( ~ closed(closure(relative_complement_sets(X0,X1),X1,X2),X1,X2)
| ~ subset_sets(X0,closure(relative_complement_sets(X0,X1),X1,X2))
| element_of_collection(closure(X0,X1,X2),top_of_basis(X3))
| element_of_set(f11(X3,closure(X0,X1,X2)),boundary(X0,X1,X2)) ) ).
cnf(u4672,axiom,
( ~ element_of_collection(boundary(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| subset_sets(relative_complement_sets(X2,X3),X3) ) ).
cnf(u15155,negated_conjecture,
( open(f13(f14(relative_complement_sets(X1,X2),X2,X4,X5),X2,X3,X0),X2,X3)
| ~ element_of_set(X5,closure(X1,X2,X4))
| element_of_set(X5,boundary(X1,X2,X4))
| ~ element_of_set(X0,relative_complement_sets(X1,X2)) ) ).
cnf(u3047,axiom,
( ~ topological_space(boundary(X0,X1,X2),X3)
| ~ subset_sets(X0,intersection_of_members(X4))
| ~ closed(intersection_of_members(X4),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ element_of_collection(X5,X4)
| element_of_set(f19(boundary(X0,X1,X2),X3),X5) ) ).
cnf(u4057,negated_conjecture,
( element_of_set(f20(intersection_of_sets(X1,X0),X2),union_of_members(top_of_basis(X3)))
| element_of_set(f11(X3,union_of_members(ct)),union_of_members(ct))
| ~ topological_space(intersection_of_sets(X1,X0),X2)
| hausdorff(intersection_of_sets(X1,X0),X2)
| ~ element_of_collection(X1,ct)
| ~ element_of_collection(X0,ct) ) ).
cnf(u5135,axiom,
( ~ topological_space(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5))
| basis(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5))
| topological_space(X2,X3) ) ).
cnf(u3073,negated_conjecture,
( ~ closed(f13(a,cx,ct,f20(closure(X4,X5,X6),X7)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f20(closure(X4,X5,X6),X7)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ closed(sF0,X5,X6)
| ~ subset_sets(X4,sF0)
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7)
| element_of_set(f19(boundary(X0,X1,X2),X3),sF0) ) ).
cnf(u2980,axiom,
( element_of_set(f11(X0,boundary(X1,X2,X3)),closure(X4,X5,X6))
| ~ closed(boundary(X4,X5,X6),X2,X3)
| ~ subset_sets(X1,boundary(X4,X5,X6))
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(u2431,axiom,
( ~ closed(X1,cx,ct)
| ~ element_of_set(X0,sF3)
| ~ subset_sets(a,X1)
| element_of_set(f11(X2,sF3),X1)
| element_of_set(X0,union_of_members(top_of_basis(X2))) ) ).
cnf(u5269,axiom,
( ~ open(f13(a,cx,ct,f20(X1,X2)),X1,X2)
| ~ disjoint_s(X0,f13(a,cx,ct,f20(X1,X2)))
| hausdorff(X1,X2)
| ~ open(X0,X1,X2)
| ~ element_of_set(f19(X1,X2),X0)
| ~ element_of_set(f20(X1,X2),sF0) ) ).
cnf(u738,axiom,
( ~ element_of_collection(f13(f13(a,cx,ct,X0),X1,X2,f20(interior(f13(a,cx,ct,X0),X1,X2),X3)),X4)
| ~ topological_space(a,X4)
| ~ element_of_set(X5,f13(f13(a,cx,ct,X0),X1,X2,f20(interior(f13(a,cx,ct,X0),X1,X2),X3)))
| ~ element_of_set(X0,sF0)
| element_of_set(X5,interior(f13(a,cx,ct,X0),a,X4))
| hausdorff(interior(f13(a,cx,ct,X0),X1,X2),X3)
| ~ topological_space(interior(f13(a,cx,ct,X0),X1,X2),X3) ) ).
cnf(u2362,axiom,
( element_of_set(f11(X0,sF0),f13(a,cx,ct,f11(X0,sF0)))
| element_of_collection(sF0,top_of_basis(X0)) ) ).
cnf(u1072,axiom,
( ~ closed(f13(a,cx,ct,X4),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,X4))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ element_of_set(X4,sF0)
| element_of_set(f19(closure(X0,X1,X2),X3),union_of_members(ct)) ) ).
cnf(u3049,axiom,
( ~ closed(intersection_of_sets(f16(X4,X5,X6,X7),X5),X1,X2)
| ~ subset_sets(X0,intersection_of_sets(f16(X4,X5,X6,X7),X5))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(X6,X7)
| ~ subset_sets(X5,X6)
| limit_point(X4,X5,X6,X7)
| eq_p(f19(boundary(X0,X1,X2),X3),X4) ) ).
cnf(u320,axiom,
( ~ topological_space(X2,subspace_topology(X0,X1,X3))
| connected_space(X2,subspace_topology(X0,X1,X3))
| topological_space(X0,X1) ) ).
cnf(u4624,axiom,
( ~ element_of_collection(intersection_of_sets(f16(X2,X3,X4,X5),X3),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ topological_space(X4,X5)
| ~ subset_sets(X3,X4)
| limit_point(X2,X3,X4,X5)
| eq_p(f11(X0,intersection_of_members(X1)),X2) ) ).
cnf(u6128,negated_conjecture,
( ~ closed(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X5,X6)
| ~ closed(sF0,X1,X2)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X3))
| element_of_set(f20(boundary(X4,X5,X6),X7),sF0)
| ~ topological_space(boundary(X4,X5,X6),X7)
| ~ subset_sets(X4,f13(a,cx,ct,f11(X3,closure(X0,X1,X2))))
| ~ subset_sets(X0,sF0)
| hausdorff(boundary(X4,X5,X6),X7) ) ).
cnf(u4620,axiom,
( ~ element_of_collection(f2(X2,f11(X0,intersection_of_members(X1))),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),intersection_of_members(X2)) ) ).
cnf(u517,axiom,
( element_of_collection(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X2)
| ~ topological_space(interior(X0,X1,X2),X3)
| hausdorff(interior(X0,X1,X2),X3) ) ).
cnf(u2931,axiom,
( ~ closed(X4,X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,X4)
| element_of_set(f11(X5,X4),X4)
| element_of_set(f11(X0,boundary(X1,X2,X3)),union_of_members(top_of_basis(X5))) ) ).
cnf(u649,axiom,
( element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| subset_sets(X1,X2) ) ).
cnf(u1339,axiom,
( element_of_set(f11(X0,closure(X1,X2,X3)),closure(X1,X2,X3))
| element_of_set(f11(X4,boundary(X1,X2,X3)),union_of_members(top_of_basis(X0)))
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X4)) ) ).
cnf(u2951,axiom,
( ~ closed(interior(X4,X5,X6),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,interior(X4,X5,X6))
| subset_sets(X4,X5) ) ).
cnf(u4455,axiom,
( ~ element_of_set(X6,f9(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(top_of_basis(subspace_topology(X3,X4,X5))))),top_of_basis(subspace_topology(X3,X4,X5))))
| ~ element_of_collection(union_of_members(top_of_basis(subspace_topology(X3,X4,X5))),subspace_topology(X1,X2,X0))
| basis(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(top_of_basis(subspace_topology(X3,X4,X5))))),top_of_basis(subspace_topology(X3,X4,X5)))
| subset_sets(X5,X3) ) ).
cnf(u3324,axiom,
( ~ subset_sets(closure(X0,X1,X2),sF1)
| element_of_set(X5,union_of_members(top_of_basis(X6)))
| ~ closed(sF1,X3,X4)
| element_of_set(f11(X6,closure(closure(X0,X1,X2),X3,X4)),sF3)
| ~ subset_sets(closure(X0,X1,X2),X3)
| ~ element_of_collection(closure(X0,X1,X2),X7)
| element_of_collection(f14(closure(X0,X1,X2),X3,X4,X5),top_of_basis(X7))
| closed(f14(X0,X1,X2,f11(X7,f14(closure(X0,X1,X2),X3,X4,X5))),X1,X2)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u2642,negated_conjecture,
( element_of_set(f11(X0,closure(X1,X2,X3)),f1(ct,f11(X0,closure(X1,X2,X3))))
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ closed(empty_set,X2,X3)
| ~ subset_sets(X1,empty_set) ) ).
cnf(u287,axiom,
( element_of_set(X7,interior(f14(f16(X0,X1,X2,X3),X4,X5,X6),X2,X3))
| ~ topological_space(X2,X3)
| ~ subset_sets(f14(f16(X0,X1,X2,X3),X4,X5,X6),X2)
| ~ element_of_set(X7,f16(X0,X1,X2,X3))
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3)
| element_of_set(X6,closure(f16(X0,X1,X2,X3),X4,X5))
| ~ subset_sets(f16(X0,X1,X2,X3),X4)
| ~ topological_space(X4,X5) ) ).
cnf(u6056,negated_conjecture,
( subset_collections(f5(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(ct))),ct),ct)
| topological_space(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(ct))),ct)
| ~ element_of_collection(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(ct))),ct)
| ~ element_of_collection(union_of_members(ct),subspace_topology(X1,X2,X0)) ) ).
cnf(u3843,axiom,
( ~ closed(f2(X1,X0),X3,X4)
| element_of_set(f20(boundary(X2,X3,X4),X5),union_of_members(X1))
| ~ topological_space(boundary(X2,X3,X4),X5)
| ~ subset_sets(X2,f2(X1,X0))
| element_of_set(X0,intersection_of_members(X1))
| hausdorff(boundary(X2,X3,X4),X5) ) ).
cnf(u2972,axiom,
( ~ closed(closure(X4,X5,X6),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,closure(X4,X5,X6))
| element_of_set(f11(X7,closure(X4,X5,X6)),sF3)
| ~ subset_sets(X4,sF1)
| ~ closed(sF1,X5,X6)
| element_of_set(f11(X0,boundary(X1,X2,X3)),union_of_members(top_of_basis(X7))) ) ).
cnf(u29084,negated_conjecture,
( element_of_set(f11(X1,union_of_members(ct)),f1(X2,f11(X1,union_of_members(ct))))
| element_of_set(f11(X0,union_of_members(top_of_basis(X1))),sF0)
| element_of_set(X3,f1(top_of_basis(X0),X3))
| ~ element_of_set(X3,cx) ) ).
cnf(u4443,axiom,
( basis(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(subspace_topology(X3,X4,X5)))),subspace_topology(X3,X4,X5))
| ~ element_of_collection(union_of_members(subspace_topology(X3,X4,X5)),subspace_topology(X1,X2,X0))
| topological_space(X3,X4) ) ).
cnf(u766,axiom,
( limit_point(X0,X1,X2,subspace_topology(X3,subspace_topology(X4,X5,X6),X7))
| ~ topological_space(X2,subspace_topology(X3,subspace_topology(X4,X5,X6),X7))
| ~ subset_sets(X1,X2)
| topological_space(X4,X5) ) ).
cnf(u3166,axiom,
( ~ topological_space(X1,subspace_topology(X2,X3,X4))
| element_of_set(X5,boundary(X0,X1,subspace_topology(X2,X3,X4)))
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| ~ subset_sets(X0,X1)
| subset_sets(X0,f14(X0,X1,subspace_topology(X2,X3,X4),X5))
| subset_sets(X4,X2) ) ).
cnf(interior_49,axiom,
( ~ element_of_set(X0,interior(X1,X2,X3))
| element_of_set(X0,f13(X1,X2,X3,X0)) ) ).
cnf(u5346,axiom,
( ~ element_of_set(f19(closure(X2,X3,X4),X5),X0)
| ~ open(X1,closure(X2,X3,X4),X5)
| hausdorff(closure(X2,X3,X4),X5)
| ~ open(X0,closure(X2,X3,X4),X5)
| ~ disjoint_s(X0,X1)
| ~ subset_sets(X2,X1)
| ~ closed(X1,X3,X4) ) ).
cnf(boundary_69,axiom,
( ~ element_of_set(X0,boundary(X1,X2,X3))
| topological_space(X2,X3) ) ).
cnf(u735,axiom,
( element_of_set(X5,closure(X2,X3,subspace_topology(X0,X1,X4)))
| topological_space(X0,X1)
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,subspace_topology(X0,X1,X4)) ) ).
cnf(u981,axiom,
( ~ closed(interior(X0,X1,X2),cx,ct)
| ~ subset_sets(a,interior(X0,X1,X2))
| subset_sets(f13(X0,X1,X2,f20(sF3,X3)),X0)
| ~ topological_space(sF3,X3)
| hausdorff(sF3,X3) ) ).
cnf(u2729,axiom,
( closed(f14(X1,X2,X3,f19(closure(X0,X4,X5),X6)),X2,X3)
| ~ closed(closure(relative_complement_sets(X1,X2),X2,X3),X4,X5)
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| element_of_set(f19(closure(X0,X4,X5),X6),boundary(X1,X2,X3))
| ~ subset_sets(X0,closure(relative_complement_sets(X1,X2),X2,X3))
| ~ subset_sets(X1,X2) ) ).
cnf(u512,axiom,
( element_of_set(f7(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),interior(X0,X1,X2))
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3)
| basis(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4) ) ).
cnf(u1178,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,f7(sF0,X0)),X1),sF0)
| basis(sF0,X0)
| ~ topological_space(sF0,X0)
| basis(f13(a,cx,ct,f7(sF0,X0)),X1)
| ~ topological_space(f13(a,cx,ct,f7(sF0,X0)),X1) ) ).
cnf(u12977,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f13(X1,X2,X3,f11(X0,union_of_members(ct))))
| element_of_set(X4,f1(top_of_basis(X0),X4))
| ~ element_of_set(X4,cx) ) ).
cnf(u6348,axiom,
( element_of_set(f11(X6,closure(X1,X2,X3)),X5)
| subset_sets(X1,f14(X1,X2,X3,X4))
| element_of_set(X4,f14(X1,X2,X3,X0))
| element_of_set(X0,union_of_members(top_of_basis(X6)))
| ~ subset_sets(X1,X5)
| ~ closed(X5,X2,X3)
| ~ subset_sets(X1,X2) ) ).
cnf(u5732,axiom,
( element_of_set(f19(boundary(relative_complement_sets(X2,X3),X3,subspace_topology(X1,X4,X0)),X5),boundary(X2,X3,subspace_topology(X1,X4,X0)))
| ~ subset_sets(X2,X3)
| ~ topological_space(boundary(relative_complement_sets(X2,X3),X3,subspace_topology(X1,X4,X0)),X5)
| hausdorff(boundary(relative_complement_sets(X2,X3),X3,subspace_topology(X1,X4,X0)),X5)
| subset_sets(X0,X1) ) ).
cnf(u3460,axiom,
( ~ closed(f1(ct,X4),X1,X2)
| ~ subset_sets(X0,f1(ct,X4))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ element_of_set(X4,sF0)
| element_of_set(f7(closure(X0,X1,X2),X3),union_of_members(ct)) ) ).
cnf(u863,axiom,
( ~ closed(f22(X4,X5),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f22(X4,X5))
| ~ topological_space(X4,X5)
| connected_space(X4,X5)
| element_of_set(f11(X0,closure(X1,X2,X3)),union_of_members(X5)) ) ).
cnf(u601,axiom,
( element_of_set(f19(sF0,X0),f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| ~ topological_space(sF0,X0) ) ).
cnf(u6108,negated_conjecture,
( element_of_set(X5,interior(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),cx,ct,X4),X1,X2))
| ~ element_of_set(X5,f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))))
| element_of_collection(interior(X0,X1,X2),top_of_basis(X3))
| ~ subset_sets(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),cx,ct,X4),X1)
| element_of_set(X4,sF0)
| ~ subset_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),sF0)
| ~ subset_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),cx) ) ).
cnf(u3516,axiom,
( ~ closed(X1,cx,ct)
| ~ topological_space(sF3,X0)
| ~ subset_sets(a,X1)
| element_of_set(f7(sF3,X0),X1)
| basis(sF3,X0) ) ).
cnf(u20484,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),interior(X2,X3,X4))
| element_of_set(X1,f1(top_of_basis(X0),X1))
| ~ element_of_set(X1,sF0) ) ).
cnf(u5133,axiom,
( element_of_collection(f12(X2,X3,X4,f12(X1,subspace_topology(X2,X3,X4),X5,f8(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5)))),X3)
| basis(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5))
| ~ topological_space(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5)) ) ).
cnf(u6855,negated_conjecture,
( element_of_set(f15(X0,X1,X2,X3,X4),interior(X5,X6,X7))
| ~ neighborhood(X4,X0,X2,X3)
| ~ limit_point(X0,X1,X2,X3) ) ).
cnf(u3217,negated_conjecture,
( ~ closed(f13(a,cx,ct,f20(closure(X4,X5,X6),X7)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f20(closure(X4,X5,X6),X7)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ closed(sF0,X5,X6)
| ~ subset_sets(X4,sF0)
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7)
| element_of_set(f20(boundary(X0,X1,X2),X3),sF0) ) ).
cnf(u27749,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f13(X2,X3,X4,f11(X0,union_of_members(top_of_basis(X1)))))
| element_of_set(f11(X1,union_of_members(ct)),interior(X5,X6,X7))
| element_of_set(X8,f1(top_of_basis(X0),X8))
| ~ element_of_set(X8,cx) ) ).
cnf(u3211,negated_conjecture,
( ~ closed(f13(a,cx,ct,f11(X4,sF0)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f11(X4,sF0)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f20(boundary(X0,X1,X2),X3),sF0)
| element_of_collection(sF0,top_of_basis(X4)) ) ).
cnf(u2646,negated_conjecture,
( element_of_set(f20(empty_set,X0),f1(ct,f20(empty_set,X0)))
| ~ topological_space(empty_set,X0)
| hausdorff(empty_set,X0) ) ).
cnf(u3061,axiom,
( ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| subset_sets(X4,X5) ) ).
cnf(u4681,negated_conjecture,
( ~ subset_sets(union_of_members(ct),intersection_of_members(X1))
| ~ element_of_collection(cx,X1)
| ~ element_of_collection(union_of_members(ct),X0)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0)) ) ).
cnf(u3896,axiom,
( subset_sets(f13(f14(X1,X2,X3,X4),X5,X6,f7(interior(f14(X1,X2,X3,X4),X5,X6),X7)),f14(f13(f14(X1,X2,X3,X4),X5,X6,f7(interior(f14(X1,X2,X3,X4),X5,X6),X7)),X2,X3,X0))
| element_of_set(X0,f14(X1,X2,X3,X4))
| ~ subset_sets(f13(f14(X1,X2,X3,X4),X5,X6,f7(interior(f14(X1,X2,X3,X4),X5,X6),X7)),X2)
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| ~ topological_space(interior(f14(X1,X2,X3,X4),X5,X6),X7)
| basis(interior(f14(X1,X2,X3,X4),X5,X6),X7) ) ).
cnf(u5335,axiom,
( ~ open(closure(X1,X2,X3),closure(X4,X5,X6),X7)
| ~ disjoint_s(X0,closure(X1,X2,X3))
| hausdorff(closure(X4,X5,X6),X7)
| ~ open(X0,closure(X4,X5,X6),X7)
| ~ element_of_set(f19(closure(X4,X5,X6),X7),X0)
| ~ subset_sets(X4,boundary(X1,X2,X3))
| ~ closed(boundary(X1,X2,X3),X5,X6) ) ).
cnf(u4048,axiom,
( element_of_collection(f12(X3,X4,X5,relative_complement_sets(f14(relative_complement_sets(X0,X1),X1,subspace_topology(X3,X4,X5),X2),X1)),X4)
| element_of_set(X2,boundary(X0,X1,subspace_topology(X3,X4,X5)))
| closed(f14(X0,X1,subspace_topology(X3,X4,X5),X2),X1,subspace_topology(X3,X4,X5))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,subspace_topology(X3,X4,X5))
| ~ subset_sets(relative_complement_sets(X0,X1),X1) ) ).
cnf(u3758,axiom,
( ~ closed(closure(X3,X4,X5),X9,X10)
| element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),X6)
| ~ closed(X6,X4,X5)
| ~ subset_sets(X3,X6)
| element_of_collection(closure(X8,X9,X10),top_of_basis(X7))
| topological_space(X0,X1)
| ~ subset_sets(X8,closure(X3,X4,X5)) ) ).
cnf(u513,axiom,
( element_of_set(f19(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),interior(X0,X1,X2))
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ topological_space(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4)
| hausdorff(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4) ) ).
cnf(u36121,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| element_of_set(f11(X1,f1(ct,X0)),union_of_members(X4))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u2824,axiom,
( ~ closed(f8(X0,X1),X3,X4)
| basis(X0,X1)
| element_of_set(f19(closure(X2,X3,X4),X5),union_of_members(X1))
| hausdorff(closure(X2,X3,X4),X5)
| ~ subset_sets(X2,f8(X0,X1))
| ~ topological_space(X0,X1)
| ~ topological_space(closure(X2,X3,X4),X5) ) ).
cnf(u3189,negated_conjecture,
( ~ closed(f1(ct,X4),X1,X2)
| ~ subset_sets(X0,f1(ct,X4))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ element_of_set(X4,cx)
| element_of_set(f20(boundary(X0,X1,X2),X3),union_of_members(ct)) ) ).
cnf(u5254,axiom,
( ~ open(union_of_members(subspace_topology(X1,X2,X3)),X4,X5)
| ~ disjoint_s(X0,union_of_members(subspace_topology(X1,X2,X3)))
| hausdorff(X4,X5)
| ~ open(X0,X4,X5)
| ~ element_of_set(f19(X4,X5),X0)
| ~ element_of_set(f20(X4,X5),X3)
| ~ connected_set(X3,X1,X2) ) ).
cnf(u4665,axiom,
( ~ element_of_collection(closure(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| topological_space(X5,X6)
| ~ closed(sF1,X3,X4)
| element_of_set(f11(subspace_topology(X5,X6,X7),closure(X2,X3,X4)),sF3)
| ~ subset_sets(X2,sF1) ) ).
cnf(u6412,axiom,
( ~ closed(closure(relative_complement_sets(X4,X5),X5,X6),X1,X2)
| element_of_set(X7,f14(X4,X5,X6,f20(closure(X0,X1,X2),X3)))
| ~ subset_sets(X4,X5)
| ~ subset_sets(X0,closure(relative_complement_sets(X4,X5),X5,X6))
| closed(f14(X4,X5,X6,X7),X5,X6)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3)
| element_of_set(f20(closure(X0,X1,X2),X3),boundary(X4,X5,X6)) ) ).
cnf(u5680,axiom,
( ~ topological_space(X1,subspace_topology(X3,X4,X5))
| element_of_set(X2,boundary(X0,X1,subspace_topology(X3,X4,X5)))
| ~ subset_sets(X0,X1)
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| topological_space(X3,X4) ) ).
cnf(u10132,negated_conjecture,
( limit_point(f20(boundary(X0,X1,X2),X3),X4,X5,X6)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u1341,negated_conjecture,
( element_of_set(f11(X0,f14(a,cx,ct,X1)),f14(a,cx,ct,X1))
| element_of_set(f11(X2,sF3),union_of_members(top_of_basis(X0)))
| element_of_collection(sF3,top_of_basis(X2))
| element_of_set(X1,sF3) ) ).
cnf(u7387,negated_conjecture,
( limit_point(X0,X1,X2,X3)
| element_of_set(X0,sF0) ) ).
cnf(u888,negated_conjecture,
( ~ subset_sets(f14(a,cx,ct,X1),sF3)
| element_of_set(X1,sF3)
| ~ element_of_collection(f14(a,cx,ct,X1),X0)
| element_of_collection(sF3,top_of_basis(X0)) ) ).
cnf(u9621,negated_conjecture,
( ~ element_of_set(X4,closure(X5,X6,X7))
| eq_p(f20(boundary(X0,X1,X2),X3),X4)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u630,negated_conjecture,
( element_of_set(f11(X0,f1(ct,X1)),union_of_members(ct))
| ~ element_of_set(X1,cx)
| element_of_collection(f1(ct,X1),top_of_basis(X0)) ) ).
cnf(u908,axiom,
( element_of_set(f7(relative_complement_sets(X0,X1),X3),union_of_members(X2))
| ~ closed(X0,X1,X2)
| basis(relative_complement_sets(X0,X1),X3)
| ~ topological_space(relative_complement_sets(X0,X1),X3) ) ).
cnf(u762,axiom,
( ~ element_of_set(X6,f12(X3,X4,X5,f16(X0,X1,X2,subspace_topology(X3,X4,X5))))
| ~ topological_space(X2,subspace_topology(X3,X4,X5))
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,subspace_topology(X3,X4,X5))
| element_of_set(X6,union_of_members(X4)) ) ).
cnf(u5210,axiom,
( element_of_collection(f9(X0,subspace_topology(X1,X2,X3)),subspace_topology(X4,X2,X3))
| basis(X0,subspace_topology(X1,X2,X3))
| ~ topological_space(X4,X2)
| ~ subset_sets(X3,X4)
| ~ topological_space(X0,subspace_topology(X1,X2,X3)) ) ).
cnf(neighborhood_61,axiom,
( ~ neighborhood(X0,X1,X2,X3)
| element_of_set(X1,X0) ) ).
cnf(u36102,negated_conjecture,
( element_of_set(f11(X1,union_of_members(top_of_basis(X4))),interior(X5,X6,X7))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| element_of_set(f11(X4,union_of_members(ct)),union_of_members(X8))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u2541,axiom,
( ~ element_of_set(X0,f8(X1,top_of_basis(subspace_topology(X2,X3,X4))))
| subset_sets(X4,X2)
| basis(X1,top_of_basis(subspace_topology(X2,X3,X4)))
| ~ topological_space(X1,top_of_basis(subspace_topology(X2,X3,X4))) ) ).
cnf(limit_point_65,axiom,
( element_of_set(f15(X0,X1,X2,X3,X4),intersection_of_sets(X4,X1))
| ~ neighborhood(X4,X0,X2,X3)
| ~ limit_point(X0,X1,X2,X3) ) ).
cnf(u731,axiom,
( ~ closed(X0,X1,subspace_topology(X2,X3,X4))
| element_of_collection(f12(X2,X3,X4,relative_complement_sets(X0,X1)),X3) ) ).
cnf(u4786,axiom,
( element_of_collection(f22(X0,subspace_topology(X1,X2,X3)),subspace_topology(X4,X2,X3))
| ~ topological_space(X0,subspace_topology(X1,X2,X3))
| ~ topological_space(X4,X2)
| ~ subset_sets(X3,X4)
| connected_space(X0,subspace_topology(X1,X2,X3)) ) ).
cnf(u2838,negated_conjecture,
( element_of_set(f11(subspace_topology(X0,X1,X2),f1(ct,X3)),f1(ct,X3))
| topological_space(X0,X1)
| ~ element_of_set(X3,cx) ) ).
cnf(u6568,negated_conjecture,
( ~ subset_sets(a,f14(relative_complement_sets(X1,cx),cx,ct,X2))
| ~ topological_space(sF3,X0)
| element_of_set(f7(sF3,X0),f14(relative_complement_sets(X1,cx),cx,ct,X2))
| basis(sF3,X0)
| subset_sets(X1,f14(X1,cx,ct,X2))
| element_of_set(X2,boundary(X1,cx,ct))
| ~ subset_sets(relative_complement_sets(X1,cx),cx)
| ~ subset_sets(X1,cx) ) ).
cnf(u5664,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),X6)
| subset_sets(X3,f14(X3,X4,X5,X7))
| ~ closed(X6,X4,X5)
| ~ subset_sets(X3,X6)
| topological_space(X0,X1)
| ~ subset_sets(X3,X4) ) ).
cnf(u6340,axiom,
( element_of_set(X4,f14(X0,X1,X2,f20(boundary(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f20(boundary(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ subset_sets(X0,X1)
| ~ topological_space(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| hausdorff(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| subset_sets(X0,f14(X0,X1,X2,X4)) ) ).
cnf(u36140,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| element_of_set(f11(X1,union_of_members(ct)),f1(X4,f11(X1,union_of_members(ct)))) ) ).
cnf(u859,axiom,
( ~ closed(boundary(X4,X5,X6),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,boundary(X4,X5,X6))
| subset_sets(relative_complement_sets(X4,X5),X5) ) ).
cnf(u6750,axiom,
hausdorff(sF1,X0) ).
cnf(u34570,axiom,
( ~ subset_collections(f23(X0,X2,X3),f24(X1,f23(X0,X2,X3)))
| compact_space(X1,f23(X0,X2,X3))
| ~ open_covering(X3,X0,X2)
| ~ compact_space(X0,f24(X1,f23(X0,X2,X3)))
| ~ compact_space(X0,X2) ) ).
cnf(u2840,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),f1(X3,X4)),f1(X3,X4))
| limit_point(X4,X5,X6,X3)
| topological_space(X0,X1)
| ~ topological_space(X6,X3)
| ~ subset_sets(X5,X6) ) ).
cnf(u182,negated_conjecture,
( ~ subset_sets(f13(a,cx,ct,X0),X1)
| ~ subset_sets(X1,cx)
| ~ element_of_set(X2,f13(a,cx,ct,X0))
| ~ element_of_set(X0,sF0)
| element_of_set(X2,interior(X1,cx,ct)) ) ).
cnf(u712,axiom,
( closed(f14(X0,X1,X2,f11(X3,boundary(relative_complement_sets(X0,X1),X1,X2))),X1,X2)
| element_of_set(f11(X3,boundary(relative_complement_sets(X0,X1),X1,X2)),boundary(X0,X1,X2))
| element_of_collection(boundary(relative_complement_sets(X0,X1),X1,X2),top_of_basis(X3))
| ~ subset_sets(X0,X1) ) ).
cnf(u5795,negated_conjecture,
( element_of_set(f11(X1,sF3),f14(a,cx,ct,f11(X0,closure(relative_complement_sets(a,cx),cx,ct))))
| element_of_collection(closure(relative_complement_sets(a,cx),cx,ct),top_of_basis(X0))
| element_of_collection(sF3,top_of_basis(X1))
| element_of_set(f11(X0,closure(relative_complement_sets(a,cx),cx,ct)),sF1) ) ).
cnf(u2496,axiom,
( element_of_set(X0,f10(X2,f21(X1,top_of_basis(X2)),X0))
| ~ element_of_set(X0,f21(X1,top_of_basis(X2)))
| connected_space(X1,top_of_basis(X2))
| ~ topological_space(X1,top_of_basis(X2)) ) ).
cnf(u4879,axiom,
( closed(f14(relative_complement_sets(X0,X1),X1,X2,f7(closure(X0,X1,X2),f24(closure(X0,X1,X2),X3))),X1,X2)
| basis(closure(X0,X1,X2),f24(closure(X0,X1,X2),X3))
| compact_space(closure(X0,X1,X2),X3)
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| ~ topological_space(closure(X0,X1,X2),X3)
| element_of_set(f7(closure(X0,X1,X2),f24(closure(X0,X1,X2),X3)),boundary(X0,X1,X2)) ) ).
cnf(u21048,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f1(X1,f11(X0,union_of_members(ct))))
| element_of_set(X2,f1(top_of_basis(X0),X2))
| ~ element_of_set(X2,cx) ) ).
cnf(u3606,axiom,
( element_of_set(X10,interior(f14(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8,f11(X9,closure(relative_complement_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7),X7,X8))),X1,X2))
| element_of_collection(closure(relative_complement_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7),X7,X8),top_of_basis(X9))
| ~ subset_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7)
| ~ closed(interior(X0,X1,X2),X4,X5)
| ~ topological_space(closure(X3,X4,X5),X6)
| hausdorff(closure(X3,X4,X5),X6)
| ~ subset_sets(f14(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8,f11(X9,closure(relative_complement_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7),X7,X8))),X1)
| ~ element_of_set(X10,f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)))
| ~ subset_sets(X3,interior(X0,X1,X2))
| element_of_set(f11(X9,closure(relative_complement_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7),X7,X8)),boundary(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8)) ) ).
cnf(u927,axiom,
( ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,union_of_members(X4))
| ~ closed(union_of_members(X4),X1,X2)
| hausdorff(closure(X0,X1,X2),X3)
| element_of_collection(f1(X4,f20(closure(X0,X1,X2),X3)),X4) ) ).
cnf(u822,axiom,
( element_of_collection(f12(X1,X2,X0,X0),X2)
| ~ connected_set(X0,X1,X2) ) ).
cnf(u36097,negated_conjecture,
( element_of_set(f11(X4,union_of_members(ct)),f13(X5,X6,X7,f11(X4,union_of_members(ct))))
| element_of_set(f11(X1,union_of_members(top_of_basis(X4))),interior(X8,X9,X10))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u7972,negated_conjecture,
( element_of_set(f20(sF0,X0),f13(X1,X2,X3,f20(sF0,X0)))
| hausdorff(sF0,X0) ) ).
cnf(u3058,axiom,
( open(f13(X4,X5,X6,f19(boundary(X0,X1,X2),X3)),X5,X6)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ closed(interior(X4,X5,X6),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u7372,negated_conjecture,
( limit_point(X0,X4,X5,X6)
| open(f13(X1,X2,X3,X0),X2,X3) ) ).
cnf(u167,axiom,
( ~ subset_sets(X1,f13(a,cx,ct,X0))
| ~ element_of_collection(X1,X2)
| ~ topological_space(a,X2)
| ~ element_of_set(X3,X1)
| ~ element_of_set(X0,sF0)
| element_of_set(X3,interior(f13(a,cx,ct,X0),a,X2)) ) ).
cnf(u4585,axiom,
( ~ subset_sets(closure(X2,X3,subspace_topology(X0,X1,X4)),X5)
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,subspace_topology(X0,X1,X4))
| element_of_collection(X5,top_of_basis(X6))
| ~ element_of_collection(closure(X2,X3,subspace_topology(X0,X1,X4)),X6)
| topological_space(X0,X1) ) ).
cnf(u36061,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f10(X1,f1(top_of_basis(X1),f11(X0,union_of_members(ct))),f11(X0,union_of_members(ct))))
| limit_point(f11(X0,union_of_members(ct)),X2,X3,top_of_basis(X1))
| element_of_set(f11(X4,union_of_members(top_of_basis(X0))),sF0)
| element_of_set(X5,f1(top_of_basis(X4),X5))
| ~ element_of_set(X5,cx) ) ).
cnf(u24142,negated_conjecture,
( element_of_set(f11(X0,f1(ct,X1)),f1(X2,f11(X0,f1(ct,X1))))
| ~ element_of_set(X1,cx)
| element_of_set(X1,f1(top_of_basis(X0),X1)) ) ).
cnf(u3416,axiom,
( element_of_set(f20(f13(a,cx,ct,f19(sF0,X0)),X1),union_of_members(ct))
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f19(sF0,X0)),X1)
| hausdorff(f13(a,cx,ct,f19(sF0,X0)),X1) ) ).
cnf(u1010,axiom,
( ~ closed(boundary(X1,X2,X3),X4,X5)
| ~ subset_sets(X0,boundary(X1,X2,X3))
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| ~ subset_sets(X1,X7)
| ~ closed(X7,X2,X3)
| element_of_set(f20(closure(X0,X4,X5),X6),X7) ) ).
cnf(u1065,negated_conjecture,
( ~ closed(intersection_of_sets(X4,X5),X1,X2)
| ~ subset_sets(X0,intersection_of_sets(X4,X5))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| element_of_set(f19(closure(X0,X1,X2),X3),union_of_members(ct))
| ~ element_of_collection(X5,ct)
| ~ element_of_collection(X4,ct) ) ).
cnf(u3350,negated_conjecture,
( element_of_collection(f1(ct,f11(X0,closure(X1,X2,X3))),ct)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ closed(empty_set,X2,X3)
| ~ subset_sets(X1,empty_set) ) ).
cnf(u2489,axiom,
( element_of_set(X0,f10(X1,f2(top_of_basis(X1),X2),X0))
| ~ element_of_set(X0,f2(top_of_basis(X1),X2))
| element_of_set(X2,intersection_of_members(top_of_basis(X1))) ) ).
cnf(u5873,negated_conjecture,
( element_of_set(X0,f14(a,cx,ct,f11(X1,X2)))
| closed(f14(a,cx,ct,X0),cx,ct)
| ~ element_of_collection(sF3,X1)
| element_of_collection(X2,top_of_basis(X1))
| ~ subset_sets(sF3,X2) ) ).
cnf(u4275,axiom,
( element_of_set(X10,interior(f14(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8,f20(closure(relative_complement_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7),X7,X8),X9)),X1,X2))
| ~ topological_space(closure(relative_complement_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7),X7,X8),X9)
| hausdorff(closure(relative_complement_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7),X7,X8),X9)
| ~ subset_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7)
| ~ closed(interior(X0,X1,X2),X4,X5)
| ~ topological_space(closure(X3,X4,X5),X6)
| hausdorff(closure(X3,X4,X5),X6)
| ~ subset_sets(f14(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8,f20(closure(relative_complement_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7),X7,X8),X9)),X1)
| ~ element_of_set(X10,f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)))
| ~ subset_sets(X3,interior(X0,X1,X2))
| element_of_set(f20(closure(relative_complement_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7),X7,X8),X9),boundary(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8)) ) ).
cnf(u254,axiom,
( element_of_collection(f1(X0,f19(union_of_members(X0),X1)),X0)
| hausdorff(union_of_members(X0),X1)
| ~ topological_space(union_of_members(X0),X1) ) ).
cnf(u626,axiom,
( ~ element_of_collection(f21(X0,X1),top_of_basis(X2))
| element_of_set(f11(X2,f22(X0,X1)),f22(X0,X1))
| ~ topological_space(X0,X1)
| connected_space(X0,X1)
| ~ connected_space(X0,top_of_basis(X2)) ) ).
cnf(u4451,axiom,
( element_of_set(X0,intersection_of_members(subspace_topology(X1,subspace_topology(X2,X3,X4),X5)))
| topological_space(X2,X3) ) ).
cnf(closure_57,axiom,
( closed(f14(X1,X2,X3,X0),X2,X3)
| element_of_set(X0,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ) ).
cnf(u6218,negated_conjecture,
( ~ element_of_set(X0,f13(a,cx,ct,f20(sF0,X1)))
| ~ topological_space(sF0,top_of_basis(X2))
| element_of_set(X0,interior(a,sF0,top_of_basis(X2)))
| element_of_set(f11(X2,f13(a,cx,ct,f20(sF0,X1))),sF0)
| ~ topological_space(sF0,X1)
| hausdorff(sF0,X1) ) ).
cnf(u4650,axiom,
( ~ element_of_collection(f13(a,cx,ct,f20(sF0,X2)),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| hausdorff(sF0,X2)
| ~ topological_space(sF0,X2)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(ct)) ) ).
cnf(u841,axiom,
( open(f13(X4,X5,X6,f11(X0,closure(X1,X2,X3))),X5,X6)
| ~ closed(interior(X4,X5,X6),X2,X3)
| ~ subset_sets(X1,interior(X4,X5,X6))
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(u743,axiom,
( element_of_set(f19(f1(ct,X0),X1),union_of_members(ct))
| ~ element_of_set(X0,sF0)
| ~ topological_space(f1(ct,X0),X1)
| hausdorff(f1(ct,X0),X1) ) ).
cnf(u989,negated_conjecture,
( element_of_collection(f13(a,cx,ct,f20(closure(X2,X0,X1),X3)),top_of_basis(X4))
| ~ subset_sets(X2,sF0)
| ~ topological_space(closure(X2,X0,X1),X3)
| hausdorff(closure(X2,X0,X1),X3)
| element_of_set(f11(X4,f13(a,cx,ct,f20(closure(X2,X0,X1),X3))),sF0)
| ~ closed(sF0,X0,X1) ) ).
cnf(u3365,axiom,
( ~ closed(closure(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3,X4)
| ~ subset_sets(X5,closure(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2))
| element_of_collection(closure(X5,X3,X4),top_of_basis(X6))
| element_of_set(f11(X6,closure(X5,X3,X4)),boundary(relative_complement_sets(X0,X1),X1,X2))
| ~ element_of_set(f11(X6,closure(X5,X3,X4)),boundary(X0,X1,X2)) ) ).
cnf(u6347,axiom,
( element_of_set(f11(X5,closure(X1,X2,X3)),sF3)
| subset_sets(X1,f14(X1,X2,X3,X4))
| element_of_set(X4,f14(X1,X2,X3,X0))
| element_of_set(X0,union_of_members(top_of_basis(X5)))
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| ~ subset_sets(X1,X2) ) ).
cnf(u1186,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,f7(sF0,X0)),X1)
| basis(sF0,X0)
| ~ topological_space(cx,X1)
| ~ element_of_set(X2,f13(a,cx,ct,f7(sF0,X0)))
| ~ topological_space(sF0,X0)
| element_of_set(X2,interior(a,cx,X1)) ) ).
cnf(u6291,axiom,
( ~ subset_sets(f14(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8,X9),X1)
| element_of_set(X10,closure(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8))
| ~ subset_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7)
| ~ topological_space(X7,X8)
| ~ closed(interior(X0,X1,X2),X4,X5)
| ~ topological_space(closure(X3,X4,X5),X6)
| hausdorff(closure(X3,X4,X5),X6)
| element_of_set(X9,f14(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8,X10))
| ~ element_of_set(X11,f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)))
| ~ subset_sets(X3,interior(X0,X1,X2))
| element_of_set(X11,interior(f14(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8,X9),X1,X2)) ) ).
cnf(u2962,negated_conjecture,
( ~ closed(f13(a,cx,ct,f20(sF0,X4)),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f13(a,cx,ct,f20(sF0,X4)))
| element_of_set(f11(X0,boundary(X1,X2,X3)),sF0)
| ~ topological_space(sF0,X4)
| hausdorff(sF0,X4) ) ).
cnf(u6275,axiom,
( element_of_set(f11(X5,f10(X3,closure(X0,X1,X2),X4)),f10(X3,closure(X0,X1,X2),X4))
| ~ closed(sF1,X1,X2)
| ~ element_of_collection(sF3,X3)
| ~ element_of_set(X4,closure(X0,X1,X2))
| ~ subset_sets(X0,sF1)
| ~ subset_sets(sF3,closure(X0,X1,X2))
| element_of_set(X4,union_of_members(top_of_basis(X5))) ) ).
cnf(u4841,axiom,
( eq_p(f7(intersection_of_sets(f16(X0,X1,X2,X3),X1),f24(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4)),X0)
| basis(intersection_of_sets(f16(X0,X1,X2,X3),X1),f24(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4))
| compact_space(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4)
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3)
| ~ topological_space(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4) ) ).
cnf(u3920,axiom,
( element_of_set(X7,interior(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,f19(closure(relative_complement_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),X4,X5),X6)),X1,X2))
| ~ topological_space(closure(relative_complement_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),X4,X5),X6)
| hausdorff(closure(relative_complement_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),X4,X5),X6)
| ~ subset_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ subset_sets(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,f19(closure(relative_complement_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),X4,X5),X6)),X1)
| ~ element_of_set(X7,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(f19(closure(relative_complement_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),X4,X5),X6),boundary(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5)) ) ).
cnf(u1328,negated_conjecture,
( element_of_set(f11(X0,f14(a,cx,ct,X1)),f14(a,cx,ct,X1))
| element_of_set(X2,union_of_members(top_of_basis(X0)))
| ~ element_of_set(X2,sF3)
| element_of_set(X1,sF3) ) ).
cnf(u2934,axiom,
( ~ closed(f1(ct,X4),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f1(ct,X4))
| ~ element_of_set(X4,sF0)
| element_of_set(f11(X0,boundary(X1,X2,X3)),union_of_members(ct)) ) ).
cnf(subspace_topology_46,axiom,
( ~ equal_sets(X0,intersection_of_sets(X3,X4))
| ~ topological_space(X1,X2)
| ~ subset_sets(X3,X1)
| ~ element_of_collection(X4,X2)
| element_of_collection(X0,subspace_topology(X1,X2,X3)) ) ).
cnf(u724,axiom,
( element_of_collection(relative_complement_sets(X0,X1),X2)
| ~ closed(X0,X1,X2) ) ).
cnf(u2984,axiom,
( ~ element_of_set(X7,boundary(X0,X1,X2))
| ~ closed(X6,X1,X2)
| ~ subset_sets(X0,X6)
| element_of_set(f11(subspace_topology(X3,X4,X5),boundary(X0,X1,X2)),X6)
| topological_space(X3,X4) ) ).
cnf(u909,axiom,
( element_of_set(f11(X3,relative_complement_sets(X0,X1)),union_of_members(X2))
| ~ closed(X0,X1,X2)
| element_of_collection(relative_complement_sets(X0,X1),top_of_basis(X3)) ) ).
cnf(u2675,axiom,
( ~ connected_set(X0,X1,subspace_topology(X2,X3,X4))
| topological_space(X2,X3) ) ).
cnf(u2921,axiom,
( ~ basis(X0,X1)
| ~ element_of_collection(empty_set,X1)
| ~ element_of_collection(X0,X1)
| element_of_collection(f4(X0,X1),X1)
| subset_collections(f5(X0,X1),X1)
| topological_space(X0,X1) ) ).
cnf(u2695,axiom,
( ~ element_of_set(X7,f13(X0,X1,X2,f19(closure(X5,X3,X4),X6)))
| ~ topological_space(closure(X5,X3,X4),X6)
| hausdorff(closure(X5,X3,X4),X6)
| ~ subset_sets(X5,interior(X0,X1,X2))
| ~ closed(interior(X0,X1,X2),X3,X4)
| element_of_set(X7,union_of_members(X2)) ) ).
cnf(u5681,negated_conjecture,
( ~ subset_sets(a,f14(relative_complement_sets(X0,cx),cx,ct,X1))
| element_of_set(X1,boundary(X0,cx,ct))
| closed(f14(X0,cx,ct,X1),cx,ct)
| ~ subset_sets(X0,cx)
| ~ subset_sets(relative_complement_sets(X0,cx),cx)
| ~ element_of_set(X2,sF3)
| element_of_set(X2,f14(relative_complement_sets(X0,cx),cx,ct,X1)) ) ).
cnf(u4045,axiom,
( ~ subset_sets(X4,f14(relative_complement_sets(X0,X1),X1,X3,X2))
| element_of_set(X2,boundary(X0,X1,X3))
| closed(f14(X0,X1,X3,X2),X1,X3)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X3)
| ~ subset_sets(X4,X1)
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| closed(f14(X4,X1,X3,X5),X1,X3)
| element_of_set(X5,f14(relative_complement_sets(X0,X1),X1,X3,X2)) ) ).
cnf(u813,axiom,
( basis(closure(X0,X1,X2),subspace_topology(X3,X4,closure(X0,X1,X2)))
| ~ connected_set(closure(X0,X1,X2),X3,X4)
| subset_sets(X0,X1) ) ).
cnf(u163,axiom,
( ~ element_of_set(X0,boundary(X1,X2,X3))
| ~ subset_sets(relative_complement_sets(X1,X2),X4)
| ~ closed(X4,X2,X3)
| element_of_set(X0,X4) ) ).
cnf(u3194,axiom,
( element_of_set(f20(boundary(X0,X1,X2),X3),f6(X6,X7,f20(boundary(X0,X1,X2),X3),X4,X5))
| ~ subset_sets(X0,intersection_of_sets(X4,X5))
| ~ closed(intersection_of_sets(X4,X5),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ element_of_set(f20(boundary(X0,X1,X2),X3),X6)
| ~ element_of_collection(X4,X7)
| ~ element_of_collection(X5,X7)
| ~ basis(X6,X7)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u3481,axiom,
( ~ closed(f13(a,cx,ct,X4),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,X4))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ element_of_set(X4,sF0)
| element_of_set(f7(closure(X0,X1,X2),X3),union_of_members(ct)) ) ).
cnf(u4830,axiom,
( element_of_set(f7(X0,f24(X0,X1)),union_of_members(top_of_basis(X2)))
| basis(X0,f24(X0,X1))
| compact_space(X0,X1)
| element_of_set(f11(X2,X0),X0)
| ~ topological_space(X0,X1) ) ).
cnf(u36168,negated_conjecture,
( element_of_set(X0,f10(X3,f1(top_of_basis(X3),X0),X0))
| limit_point(X0,X4,X5,X6)
| limit_point(X0,X1,X7,X8) ) ).
cnf(u6907,negated_conjecture,
( element_of_set(f20(X0,X1),interior(X2,X3,X4))
| hausdorff(X0,X1) ) ).
cnf(u1380,axiom,
( element_of_set(f20(intersection_of_sets(X0,X1),X2),f6(X3,X4,f20(intersection_of_sets(X0,X1),X2),X0,X1))
| ~ element_of_collection(X0,X4)
| ~ element_of_collection(X1,X4)
| ~ basis(X3,X4)
| ~ element_of_set(f20(intersection_of_sets(X0,X1),X2),X3)
| ~ topological_space(intersection_of_sets(X0,X1),X2)
| hausdorff(intersection_of_sets(X0,X1),X2) ) ).
cnf(u1022,axiom,
( ~ closed(boundary(X0,X1,X2),cx,ct)
| ~ subset_sets(a,boundary(X0,X1,X2))
| ~ topological_space(sF3,X3)
| hausdorff(sF3,X3)
| ~ subset_sets(X0,X4)
| ~ closed(X4,X1,X2)
| element_of_set(f20(sF3,X3),X4) ) ).
cnf(u3409,axiom,
( ~ closed(f13(a,cx,ct,f19(sF0,X0)),X3,X4)
| ~ topological_space(sF0,X0)
| element_of_set(f11(X1,closure(X2,X3,X4)),union_of_members(ct))
| element_of_collection(closure(X2,X3,X4),top_of_basis(X1))
| hausdorff(sF0,X0)
| ~ subset_sets(X2,f13(a,cx,ct,f19(sF0,X0))) ) ).
cnf(u3609,negated_conjecture,
( ~ element_of_set(f11(X4,f14(f14(a,cx,ct,X0),X1,X2,f11(X3,closure(relative_complement_sets(f14(a,cx,ct,X0),X1),X1,X2)))),sF3)
| element_of_collection(closure(relative_complement_sets(f14(a,cx,ct,X0),X1),X1,X2),top_of_basis(X3))
| ~ subset_sets(f14(a,cx,ct,X0),X1)
| ~ element_of_collection(f14(a,cx,ct,X0),X4)
| element_of_collection(f14(f14(a,cx,ct,X0),X1,X2,f11(X3,closure(relative_complement_sets(f14(a,cx,ct,X0),X1),X1,X2))),top_of_basis(X4))
| element_of_set(f11(X3,closure(relative_complement_sets(f14(a,cx,ct,X0),X1),X1,X2)),boundary(f14(a,cx,ct,X0),X1,X2))
| element_of_set(X0,sF3) ) ).
cnf(u5802,axiom,
( element_of_collection(closure(X0,X1,X2),top_of_basis(X3))
| ~ subset_sets(X0,sF1)
| ~ subset_sets(sF3,closure(X0,X1,X2))
| ~ closed(sF1,X1,X2)
| ~ element_of_collection(sF3,X3) ) ).
cnf(u4627,negated_conjecture,
( ~ element_of_collection(intersection_of_sets(X2,X3),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(ct))
| ~ element_of_collection(X3,ct)
| ~ element_of_collection(X2,ct) ) ).
cnf(u2732,axiom,
( ~ element_of_set(X2,f1(X0,f20(union_of_members(X0),X1)))
| ~ topological_space(union_of_members(X0),X1)
| hausdorff(union_of_members(X0),X1)
| element_of_set(X2,union_of_members(X0)) ) ).
cnf(u3011,negated_conjecture,
( ~ element_of_set(X4,f13(a,cx,ct,f7(sF0,X0)))
| ~ topological_space(sF0,X0)
| element_of_set(f11(subspace_topology(X1,X2,X3),f13(a,cx,ct,f7(sF0,X0))),sF0)
| basis(sF0,X0)
| topological_space(X1,X2) ) ).
cnf(u4775,axiom,
( ~ topological_space(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5))
| connected_space(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5))
| subset_sets(X4,X2) ) ).
cnf(u638,axiom,
( element_of_collection(interior(X1,X2,X3),top_of_basis(X0))
| subset_sets(X1,X2) ) ).
cnf(u144,axiom,
( ~ closed(X1,X2,X3)
| ~ subset_sets(X0,X1)
| element_of_set(X4,X1)
| subset_sets(X0,f14(X0,X2,X3,X4))
| ~ subset_sets(X0,X2) ) ).
cnf(u2420,axiom,
( element_of_set(f19(boundary(X3,X1,X2),X5),union_of_members(top_of_basis(X4)))
| element_of_set(f11(X4,closure(X3,X1,X2)),X0)
| ~ subset_sets(X3,X0)
| ~ closed(X0,X1,X2)
| hausdorff(boundary(X3,X1,X2),X5)
| ~ topological_space(boundary(X3,X1,X2),X5) ) ).
cnf(u30726,axiom,
( ~ open_covering(f24(X0,X1),X2,X1)
| compact_space(X0,X1)
| ~ compact_space(X2,X1) ) ).
cnf(u1331,axiom,
( element_of_set(f7(X1,X2),union_of_members(top_of_basis(X0)))
| element_of_set(f11(X0,X1),X1)
| basis(X1,X2)
| ~ topological_space(X1,X2) ) ).
cnf(u853,axiom,
( closed(f14(relative_complement_sets(X4,X5),X5,X6,f11(X0,closure(X1,X2,X3))),X5,X6)
| ~ closed(closure(X4,X5,X6),X2,X3)
| ~ subset_sets(X1,closure(X4,X5,X6))
| ~ subset_sets(relative_complement_sets(X4,X5),X5)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| element_of_set(f11(X0,closure(X1,X2,X3)),boundary(X4,X5,X6)) ) ).
cnf(u3772,axiom,
( ~ closed(closure(X3,X4,X5),X8,X9)
| element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),X6)
| ~ closed(X6,X4,X5)
| ~ subset_sets(X3,X6)
| ~ topological_space(boundary(X7,X8,X9),X10)
| ~ subset_sets(X7,closure(X3,X4,X5))
| topological_space(X0,X1)
| hausdorff(boundary(X7,X8,X9),X10) ) ).
cnf(u4051,negated_conjecture,
( element_of_set(f20(intersection_of_sets(X1,X0),X2),f1(ct,f20(intersection_of_sets(X1,X0),X2)))
| ~ element_of_collection(X1,ct)
| ~ topological_space(intersection_of_sets(X1,X0),X2)
| hausdorff(intersection_of_sets(X1,X0),X2)
| ~ element_of_collection(X0,ct) ) ).
cnf(u6573,axiom,
( ~ subset_sets(sF3,closure(X0,X1,X2))
| ~ closed(sF1,X1,X2)
| ~ element_of_collection(sF3,X3)
| ~ element_of_set(X4,closure(X0,X1,X2))
| ~ subset_sets(X0,sF1)
| element_of_set(X4,union_of_members(X3)) ) ).
cnf(u4877,axiom,
( basis(closure(X0,X1,X2),f24(closure(X0,X1,X2),X3))
| ~ topological_space(closure(X0,X1,X2),X3)
| compact_space(closure(X0,X1,X2),X3)
| subset_sets(X0,X1) ) ).
cnf(u5009,axiom,
( ~ open_covering(X2,X0,X1)
| ~ compact_space(X0,X1)
| ~ topological_space(X3,X1)
| element_of_collection(union_of_members(f23(X0,X1,X2)),X1) ) ).
cnf(finer_topology_27,axiom,
( finer(X0,X1,X2)
| ~ topological_space(X2,X0)
| ~ topological_space(X2,X1)
| ~ subset_collections(X1,X0) ) ).
cnf(u4880,axiom,
( element_of_set(f7(closure(X0,X1,X2),f24(closure(X0,X1,X2),X3)),union_of_members(top_of_basis(X5)))
| element_of_set(f11(X5,closure(X0,X1,X2)),X4)
| compact_space(closure(X0,X1,X2),X3)
| ~ closed(X4,X1,X2)
| ~ subset_sets(X0,X4)
| basis(closure(X0,X1,X2),f24(closure(X0,X1,X2),X3))
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u36103,negated_conjecture,
( element_of_set(f11(X1,union_of_members(top_of_basis(X4))),interior(X5,X6,X7))
| element_of_set(f11(X4,union_of_members(ct)),interior(X8,X9,X10))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u6154,axiom,
( element_of_set(f7(sF3,X0),f14(X1,cx,ct,f11(X2,closure(relative_complement_sets(X1,cx),cx,ct))))
| ~ subset_sets(a,f14(X1,cx,ct,f11(X2,closure(relative_complement_sets(X1,cx),cx,ct))))
| ~ topological_space(sF3,X0)
| basis(sF3,X0)
| element_of_set(f11(X2,closure(relative_complement_sets(X1,cx),cx,ct)),boundary(X1,cx,ct))
| element_of_collection(closure(relative_complement_sets(X1,cx),cx,ct),top_of_basis(X2))
| ~ subset_sets(X1,cx) ) ).
cnf(subspace_topology_42,axiom,
( ~ element_of_collection(X0,subspace_topology(X1,X2,X3))
| topological_space(X1,X2) ) ).
cnf(u6953,negated_conjecture,
( ~ open(f14(a,cx,ct,X2),X0,X1)
| ~ element_of_set(X3,sF3)
| element_of_set(X2,sF3)
| ~ disjoint_s(X4,f14(a,cx,ct,X2))
| element_of_set(X3,f14(a,cx,ct,f20(X0,X1)))
| hausdorff(X0,X1)
| ~ open(X4,X0,X1)
| ~ element_of_set(f19(X0,X1),X4) ) ).
cnf(u30092,negated_conjecture,
( element_of_set(f11(X1,f1(ct,X0)),interior(X2,X3,X4))
| element_of_set(X0,f1(top_of_basis(X1),X0))
| ~ element_of_set(X0,sF0) ) ).
cnf(u6103,axiom,
( element_of_set(X7,interior(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5,X6),X1,X2))
| ~ element_of_set(X7,f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))))
| element_of_collection(interior(X0,X1,X2),top_of_basis(X3))
| ~ subset_sets(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5,X6),X1)
| element_of_set(X6,closure(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5))
| ~ subset_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4)
| ~ topological_space(X4,X5) ) ).
cnf(u2530,axiom,
( ~ element_of_set(X0,closure(X1,X2,X3))
| subset_sets(X4,X5)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X5,X6,X4),closure(X1,X2,X3)),sF3)
| ~ subset_sets(X1,sF1) ) ).
cnf(u20485,axiom,
( element_of_set(f11(X0,union_of_members(ct)),union_of_members(X2))
| element_of_set(X1,f1(top_of_basis(X0),X1))
| ~ element_of_set(X1,sF0) ) ).
cnf(u9380,negated_conjecture,
( ~ element_of_set(f19(boundary(X0,X4,X5),X6),closure(X1,X2,X3))
| hausdorff(boundary(X0,X4,X5),X6)
| element_of_set(f19(boundary(X0,X4,X5),X6),boundary(X1,X2,X3)) ) ).
cnf(u257,axiom,
( open(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X1,X2)
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3) ) ).
cnf(u1183,negated_conjecture,
( element_of_set(f20(f13(a,cx,ct,f7(sF0,X0)),X1),sF0)
| basis(sF0,X0)
| ~ topological_space(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f7(sF0,X0)),X1)
| hausdorff(f13(a,cx,ct,f7(sF0,X0)),X1) ) ).
cnf(u6783,negated_conjecture,
( ~ limit_point(X0,X1,X4,X5)
| limit_point(X0,X1,X2,X3) ) ).
cnf(u405,negated_conjecture,
( element_of_set(f19(f13(a,cx,ct,f19(sF0,X0)),X1),sF0)
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f19(sF0,X0)),X1)
| hausdorff(f13(a,cx,ct,f19(sF0,X0)),X1) ) ).
cnf(u2933,axiom,
( ~ closed(union_of_members(X4),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,union_of_members(X4))
| element_of_collection(f1(X4,f11(X0,boundary(X1,X2,X3))),X4) ) ).
cnf(u2691,axiom,
( ~ closed(interior(X0,X1,subspace_topology(X2,X3,X4)),X5,X6)
| ~ topological_space(closure(X7,X5,X6),X8)
| hausdorff(closure(X7,X5,X6),X8)
| ~ subset_sets(X7,interior(X0,X1,subspace_topology(X2,X3,X4)))
| topological_space(X2,X3) ) ).
cnf(u6784,axiom,
( ~ connected_space(X0,X2)
| connected_space(X0,X1) ) ).
cnf(u35352,axiom,
( element_of_set(f11(X0,union_of_members(ct)),f1(top_of_basis(X0),f11(X0,union_of_members(ct))))
| ~ element_of_set(f11(X0,union_of_members(ct)),sF0) ) ).
cnf(u5207,axiom,
( element_of_collection(f12(X2,X3,X4,f12(X1,subspace_topology(X2,X3,X4),X5,f9(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5)))),X3)
| basis(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5))
| ~ topological_space(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5)) ) ).
cnf(u3915,axiom,
( ~ topological_space(f14(X0,X1,X2,f19(closure(relative_complement_sets(X0,X1),X1,X2),X3)),X5)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1)
| ~ element_of_collection(X4,X5)
| element_of_set(f19(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ element_of_set(X6,X4)
| ~ subset_sets(X4,X0)
| element_of_set(X6,interior(X0,f14(X0,X1,X2,f19(closure(relative_complement_sets(X0,X1),X1,X2),X3)),X5)) ) ).
cnf(u28160,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f13(X2,X3,X4,f11(X0,union_of_members(top_of_basis(X1)))))
| element_of_set(f11(X1,union_of_members(ct)),f13(X5,X6,X7,f11(X1,union_of_members(ct))))
| element_of_set(X8,f1(top_of_basis(X0),X8))
| ~ element_of_set(X8,cx) ) ).
cnf(u2526,axiom,
( ~ element_of_set(X0,intersection_of_sets(f16(X1,X2,X3,X4),X2))
| subset_sets(X5,X6)
| eq_p(f11(subspace_topology(X6,X7,X5),intersection_of_sets(f16(X1,X2,X3,X4),X2)),X1)
| ~ subset_sets(X2,X3)
| limit_point(X1,X2,X3,X4)
| ~ topological_space(X3,X4) ) ).
cnf(u28229,negated_conjecture,
( element_of_set(f11(X4,union_of_members(top_of_basis(X0))),f13(X5,X6,X7,f11(X4,union_of_members(top_of_basis(X0)))))
| element_of_set(f11(X0,union_of_members(ct)),union_of_members(X9))
| element_of_set(X8,f1(top_of_basis(X4),X8))
| ~ element_of_set(X8,cx) ) ).
cnf(u2798,axiom,
( element_of_set(f11(X2,f9(X0,X1)),union_of_members(X1))
| basis(X0,X1)
| ~ topological_space(X0,X1)
| element_of_collection(f9(X0,X1),top_of_basis(X2)) ) ).
cnf(u50942,negated_conjecture,
( ~ element_of_set(X7,f16(X1,X2,X3,X4))
| limit_point(X1,X2,X3,X4)
| element_of_set(X7,f13(f14(f16(X1,X2,X3,X4),X5,X6,X0),X3,X4,X7))
| element_of_set(X0,union_of_members(X8)) ) ).
cnf(u3964,negated_conjecture,
( ~ closed(f1(ct,f15(X1,X4,X2,X3,X0)),X6,X7)
| ~ limit_point(X1,X4,X2,X3)
| ~ element_of_collection(X4,ct)
| ~ element_of_collection(X0,ct)
| element_of_set(f20(boundary(X5,X6,X7),X8),union_of_members(ct))
| ~ topological_space(boundary(X5,X6,X7),X8)
| ~ subset_sets(X5,f1(ct,f15(X1,X4,X2,X3,X0)))
| ~ neighborhood(X0,X1,X2,X3)
| hausdorff(boundary(X5,X6,X7),X8) ) ).
cnf(u2454,axiom,
( basis(boundary(X0,X1,X2),subspace_topology(X3,X4,boundary(X0,X1,X2)))
| subset_sets(X0,X1)
| ~ connected_set(boundary(X0,X1,X2),X3,X4) ) ).
cnf(u2875,axiom,
( ~ closed(boundary(X3,X4,X5),X6,X7)
| element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),closure(X3,X4,X5))
| topological_space(X0,X1)
| ~ subset_sets(X8,boundary(X3,X4,X5))
| element_of_collection(closure(X8,X6,X7),top_of_basis(X9)) ) ).
cnf(u4670,axiom,
( ~ element_of_collection(boundary(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| subset_sets(X2,X3)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(top_of_basis(X5))) ) ).
cnf(u1100,axiom,
( ~ element_of_collection(f13(f13(a,cx,ct,X1),X2,X3,f19(closure(X0,X4,X5),X6)),X7)
| ~ closed(interior(f13(a,cx,ct,X1),X2,X3),X4,X5)
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| ~ subset_sets(X0,interior(f13(a,cx,ct,X1),X2,X3))
| ~ topological_space(a,X7)
| ~ element_of_set(X8,f13(f13(a,cx,ct,X1),X2,X3,f19(closure(X0,X4,X5),X6)))
| ~ element_of_set(X1,sF0)
| element_of_set(X8,interior(f13(a,cx,ct,X1),a,X7)) ) ).
cnf(u1067,axiom,
( element_of_set(f19(closure(X0,X1,X2),X3),f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)))
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3) ) ).
cnf(u3167,axiom,
( ~ topological_space(f14(X0,X1,X2,X3),X5)
| element_of_set(X3,boundary(X0,X1,X2))
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| ~ element_of_collection(X4,X5)
| closed(f14(relative_complement_sets(X0,X1),X1,X2,X3),X1,X2)
| ~ element_of_set(X6,X4)
| ~ subset_sets(X4,X0)
| element_of_set(X6,interior(X0,f14(X0,X1,X2,X3),X5)) ) ).
cnf(u5630,negated_conjecture,
( ~ subset_sets(a,f14(relative_complement_sets(X0,cx),cx,ct,X1))
| element_of_set(X1,boundary(X0,cx,ct))
| ~ subset_sets(relative_complement_sets(X0,cx),cx)
| ~ subset_sets(X0,cx)
| subset_sets(X0,f14(X0,cx,ct,X1))
| ~ element_of_set(X2,sF3)
| element_of_set(X2,f14(relative_complement_sets(X0,cx),cx,ct,X1)) ) ).
cnf(u4874,axiom,
( element_of_set(f7(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),f24(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7)),interior(X0,X1,X2))
| basis(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),f24(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7))
| compact_space(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7)
| ~ topological_space(closure(X3,X4,X5),X6)
| hausdorff(closure(X3,X4,X5),X6)
| ~ closed(interior(X0,X1,X2),X4,X5)
| ~ subset_sets(X3,interior(X0,X1,X2))
| ~ topological_space(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7) ) ).
cnf(u780,axiom,
( ~ subset_sets(X4,f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))))
| ~ element_of_collection(X4,X5)
| ~ topological_space(X0,X5)
| ~ element_of_set(X6,X4)
| element_of_collection(interior(X0,X1,X2),top_of_basis(X3))
| element_of_set(X6,interior(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X0,X5)) ) ).
cnf(u3074,axiom,
( ~ closed(f13(X4,X5,X6,f19(interior(X4,X5,X6),X7)),X1,X2)
| ~ subset_sets(X0,f13(X4,X5,X6,f19(interior(X4,X5,X6),X7)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(interior(X4,X5,X6),X7)
| hausdorff(interior(X4,X5,X6),X7)
| element_of_set(f19(boundary(X0,X1,X2),X3),interior(X4,X5,X6)) ) ).
cnf(u6009,negated_conjecture,
( ~ open(f14(a,cx,ct,X2),X0,X1)
| element_of_set(X2,sF3)
| ~ disjoint_s(X3,f14(a,cx,ct,X2))
| closed(f14(a,cx,ct,f20(X0,X1)),cx,ct)
| hausdorff(X0,X1)
| ~ open(X3,X0,X1)
| ~ element_of_set(f19(X0,X1),X3) ) ).
cnf(u6102,axiom,
( closed(f14(relative_complement_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4),X4,X5,X6),X4,X5)
| element_of_set(X7,interior(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5,X6),X1,X2))
| element_of_collection(interior(X0,X1,X2),top_of_basis(X3))
| ~ element_of_set(X7,f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))))
| ~ subset_sets(f14(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5,X6),X1)
| element_of_set(X6,boundary(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4,X5))
| ~ subset_sets(relative_complement_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4),X4)
| ~ subset_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4)
| ~ topological_space(X4,X5) ) ).
cnf(u27666,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f1(top_of_basis(X1),f11(X0,union_of_members(top_of_basis(X1)))))
| element_of_set(X2,f1(top_of_basis(X0),X2))
| ~ element_of_set(X2,cx)
| element_of_set(f11(X1,union_of_members(ct)),union_of_members(ct)) ) ).
cnf(u2413,axiom,
( element_of_set(f7(closure(X3,X1,X2),X5),union_of_members(top_of_basis(X4)))
| element_of_set(f11(X4,closure(X3,X1,X2)),X0)
| ~ subset_sets(X3,X0)
| ~ closed(X0,X1,X2)
| basis(closure(X3,X1,X2),X5)
| ~ topological_space(closure(X3,X1,X2),X5) ) ).
cnf(u3325,axiom,
( ~ subset_sets(closure(X0,X1,X2),sF1)
| element_of_set(X5,union_of_members(top_of_basis(X6)))
| ~ closed(sF1,X3,X4)
| element_of_set(f11(X6,closure(closure(X0,X1,X2),X3,X4)),sF3)
| ~ subset_sets(closure(X0,X1,X2),X3)
| ~ element_of_collection(closure(X0,X1,X2),X7)
| element_of_collection(f14(closure(X0,X1,X2),X3,X4,X5),top_of_basis(X7))
| subset_sets(X0,f14(X0,X1,X2,f11(X7,f14(closure(X0,X1,X2),X3,X4,X5))))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u849,negated_conjecture,
( ~ closed(f13(a,cx,ct,f20(sF0,X4)),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f13(a,cx,ct,f20(sF0,X4)))
| element_of_set(f11(X0,closure(X1,X2,X3)),sF0)
| ~ topological_space(sF0,X4)
| hausdorff(sF0,X4) ) ).
cnf(u491,axiom,
( element_of_set(X0,f1(ct,X0))
| ~ element_of_set(X0,sF0) ) ).
cnf(u4709,axiom,
( closed(f14(f13(f14(X0,X1,X2,X3),X4,X5,f11(X6,closure(X7,X8,X9))),X1,X2,X10),X1,X2)
| ~ subset_sets(f13(f14(X0,X1,X2,X3),X4,X5,f11(X6,closure(X7,X8,X9))),X1)
| element_of_set(X10,f14(X0,X1,X2,X3))
| element_of_set(X3,closure(X0,X1,X2))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| ~ closed(interior(f14(X0,X1,X2,X3),X4,X5),X8,X9)
| ~ subset_sets(X7,interior(f14(X0,X1,X2,X3),X4,X5))
| element_of_collection(closure(X7,X8,X9),top_of_basis(X6)) ) ).
cnf(u438,axiom,
( element_of_set(f7(union_of_members(X0),X1),f1(X0,f7(union_of_members(X0),X1)))
| ~ topological_space(union_of_members(X0),X1)
| basis(union_of_members(X0),X1) ) ).
cnf(u1196,axiom,
( ~ element_of_set(f19(boundary(relative_complement_sets(a,cx),cx,ct),X0),sF3)
| element_of_set(f19(boundary(relative_complement_sets(a,cx),cx,ct),X0),sF1)
| ~ topological_space(boundary(relative_complement_sets(a,cx),cx,ct),X0)
| hausdorff(boundary(relative_complement_sets(a,cx),cx,ct),X0) ) ).
cnf(u710,axiom,
( ~ element_of_set(f11(X0,boundary(relative_complement_sets(a,cx),cx,ct)),sF3)
| element_of_set(f11(X0,boundary(relative_complement_sets(a,cx),cx,ct)),sF1)
| element_of_collection(boundary(relative_complement_sets(a,cx),cx,ct),top_of_basis(X0)) ) ).
cnf(u3453,axiom,
( ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,X4)
| ~ closed(X4,X1,X2)
| basis(closure(X0,X1,X2),X3)
| topological_space(X5,X6)
| element_of_set(f11(subspace_topology(X5,X6,X7),X4),X4) ) ).
cnf(u18842,negated_conjecture,
( element_of_set(f11(X0,f1(ct,X1)),sF0)
| element_of_set(X1,f1(top_of_basis(X0),X1))
| ~ element_of_set(X1,cx) ) ).
cnf(u141,negated_conjecture,
element_of_collection(empty_set,ct) ).
cnf(u41149,negated_conjecture,
( element_of_set(X4,f13(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,X3),cx,ct,X4))
| hausdorff(sF0,X0)
| element_of_set(X3,closure(f13(a,cx,ct,f19(sF0,X0)),X1,X2))
| ~ element_of_set(X4,f13(a,cx,ct,f19(sF0,X0))) ) ).
cnf(u1336,axiom,
( element_of_set(f7(sF1,X1),union_of_members(top_of_basis(X0)))
| element_of_set(f11(X0,sF3),sF3)
| ~ topological_space(sF1,X1)
| basis(sF1,X1) ) ).
cnf(closure_54,axiom,
( ~ element_of_set(X0,closure(X1,X2,X3))
| subset_sets(X1,X2) ) ).
cnf(u247,axiom,
( ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3)
| subset_sets(X0,X1) ) ).
cnf(u5667,negated_conjecture,
( ~ subset_sets(a,f14(X0,cx,ct,f11(X4,f14(closure(X0,cx,ct),X1,X2,X3))))
| ~ element_of_collection(closure(X0,cx,ct),X4)
| ~ subset_sets(X0,cx)
| element_of_set(X3,closure(closure(X0,cx,ct),X1,X2))
| ~ subset_sets(closure(X0,cx,ct),X1)
| ~ topological_space(X1,X2)
| element_of_collection(f14(closure(X0,cx,ct),X1,X2,X3),top_of_basis(X4))
| ~ element_of_set(X5,sF3)
| element_of_set(X5,f14(X0,cx,ct,f11(X4,f14(closure(X0,cx,ct),X1,X2,X3)))) ) ).
cnf(u1350,negated_conjecture,
( element_of_set(f19(f13(a,cx,ct,X1),X2),union_of_members(top_of_basis(X0)))
| element_of_set(f11(X0,sF0),sF0)
| hausdorff(f13(a,cx,ct,X1),X2)
| ~ topological_space(f13(a,cx,ct,X1),X2)
| ~ element_of_set(X1,sF0) ) ).
cnf(u732,axiom,
( ~ closed(X0,X1,subspace_topology(X2,X3,X4))
| subset_sets(X4,X2) ) ).
cnf(u29144,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f13(X2,X3,X4,f11(X0,union_of_members(top_of_basis(X1)))))
| ~ element_of_set(f11(X1,union_of_members(ct)),cx)
| element_of_set(f11(X1,union_of_members(ct)),f1(top_of_basis(X0),f11(X1,union_of_members(ct)))) ) ).
cnf(u4865,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,f19(closure(X0,X1,X2),X3)),f24(f13(a,cx,ct,f19(closure(X0,X1,X2),X3)),X4)),sF0)
| basis(f13(a,cx,ct,f19(closure(X0,X1,X2),X3)),f24(f13(a,cx,ct,f19(closure(X0,X1,X2),X3)),X4))
| compact_space(f13(a,cx,ct,f19(closure(X0,X1,X2),X3)),X4)
| ~ closed(sF0,X1,X2)
| ~ subset_sets(X0,sF0)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(f13(a,cx,ct,f19(closure(X0,X1,X2),X3)),X4) ) ).
cnf(u269,axiom,
( element_of_set(f19(boundary(X0,X1,X2),X3),closure(X0,X1,X2))
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u935,axiom,
( open(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X5,X6)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3) ) ).
cnf(u30743,axiom,
( compact_space(X0,subspace_topology(X1,X2,X3))
| ~ compact_set(X3,X1,X2) ) ).
cnf(u1181,negated_conjecture,
( element_of_set(f19(f13(a,cx,ct,f7(sF0,X0)),X1),sF0)
| basis(sF0,X0)
| ~ topological_space(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f7(sF0,X0)),X1)
| hausdorff(f13(a,cx,ct,f7(sF0,X0)),X1) ) ).
cnf(u2735,axiom,
( element_of_set(X2,f10(X0,f1(top_of_basis(X0),f20(union_of_members(top_of_basis(X0)),X1)),X2))
| ~ topological_space(union_of_members(top_of_basis(X0)),X1)
| ~ element_of_set(X2,f1(top_of_basis(X0),f20(union_of_members(top_of_basis(X0)),X1)))
| hausdorff(union_of_members(top_of_basis(X0)),X1) ) ).
cnf(u3595,axiom,
( element_of_set(f11(X7,f13(X0,X1,X2,f11(X6,closure(X5,X3,X4)))),f13(X0,X1,X2,f11(X6,closure(X5,X3,X4))))
| ~ subset_sets(X5,interior(X0,X1,X2))
| element_of_collection(closure(X5,X3,X4),top_of_basis(X6))
| ~ closed(interior(X0,X1,X2),X3,X4)
| element_of_set(f11(X6,closure(X5,X3,X4)),union_of_members(top_of_basis(X7))) ) ).
cnf(u4014,axiom,
( element_of_set(f20(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X7),interior(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X7)
| hausdorff(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X7) ) ).
cnf(u5867,negated_conjecture,
( ~ element_of_set(X4,f13(a,cx,ct,f11(X3,closure(X2,X0,X1))))
| ~ subset_sets(X2,sF0)
| ~ closed(sF0,X0,X1)
| element_of_collection(closure(X2,X0,X1),top_of_basis(X3))
| element_of_set(X4,sF0) ) ).
cnf(topology_generated_39,axiom,
( subset_sets(f10(X1,X0,X2),X0)
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ) ).
cnf(u19970,negated_conjecture,
( element_of_set(X2,f13(f14(f13(a,cx,ct,X0),cx,ct,X1),cx,ct,X2))
| ~ element_of_set(X0,sF0)
| element_of_set(X1,sF0)
| ~ element_of_set(X2,f13(a,cx,ct,X0)) ) ).
cnf(u4023,axiom,
( element_of_set(f7(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X7),interior(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X7)
| ~ topological_space(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X7) ) ).
cnf(u5796,negated_conjecture,
( subset_sets(a,f14(a,cx,ct,f11(X0,f14(sF3,X1,X2,X3))))
| element_of_collection(f14(sF3,X1,X2,X3),top_of_basis(X0))
| ~ element_of_collection(sF3,X0)
| element_of_set(X3,closure(sF3,X1,X2))
| ~ subset_sets(sF3,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u2815,axiom,
( subset_collections(f5(X0,f24(X0,X1)),f24(X0,X1))
| ~ element_of_collection(empty_set,f24(X0,X1))
| ~ element_of_collection(X0,f24(X0,X1))
| element_of_collection(f3(X0,f24(X0,X1)),f24(X0,X1))
| topological_space(X0,f24(X0,X1))
| compact_space(X0,X1)
| ~ topological_space(X0,X1) ) ).
cnf(u36092,negated_conjecture,
( open(f13(X4,X5,X6,f11(X1,union_of_members(top_of_basis(X7)))),X5,X6)
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx)
| element_of_set(f11(X7,union_of_members(ct)),sF0) ) ).
cnf(u4618,axiom,
( ~ element_of_collection(f1(X2,X3),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ topological_space(X4,X2)
| ~ subset_sets(X5,X4)
| limit_point(X3,X5,X4,X2)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X2)) ) ).
cnf(u17787,negated_conjecture,
( ~ element_of_set(X5,boundary(X0,X1,X2))
| hausdorff(intersection_of_members(X3),X4)
| eq_p(X5,f20(intersection_of_members(X3),X4)) ) ).
cnf(u902,axiom,
( element_of_collection(f12(X5,X2,X3,f16(X6,X4,X0,subspace_topology(X1,X2,X3))),X2)
| ~ subset_sets(X4,X0)
| ~ topological_space(X5,X2)
| ~ subset_sets(X3,X5)
| limit_point(X6,X4,X0,subspace_topology(X1,X2,X3))
| ~ topological_space(X0,subspace_topology(X1,X2,X3)) ) ).
cnf(u4666,axiom,
( ~ element_of_collection(closure(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| topological_space(X5,X6)
| element_of_set(f11(subspace_topology(X5,X6,X7),closure(X2,X3,X4)),X8)
| ~ closed(X8,X3,X4)
| ~ subset_sets(X2,X8) ) ).
cnf(u3917,negated_conjecture,
( element_of_set(X4,interior(f14(f13(a,cx,ct,X0),X1,X2,f19(closure(relative_complement_sets(f13(a,cx,ct,X0),X1),X1,X2),X3)),cx,ct))
| ~ topological_space(closure(relative_complement_sets(f13(a,cx,ct,X0),X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(f13(a,cx,ct,X0),X1),X1,X2),X3)
| ~ subset_sets(f13(a,cx,ct,X0),X1)
| ~ subset_sets(f14(f13(a,cx,ct,X0),X1,X2,f19(closure(relative_complement_sets(f13(a,cx,ct,X0),X1),X1,X2),X3)),cx)
| ~ element_of_set(X4,f13(a,cx,ct,X0))
| ~ element_of_set(X0,sF0)
| element_of_set(f19(closure(relative_complement_sets(f13(a,cx,ct,X0),X1),X1,X2),X3),boundary(f13(a,cx,ct,X0),X1,X2)) ) ).
cnf(u9792,negated_conjecture,
( ~ element_of_set(X0,boundary(X5,X6,X7))
| eq_p(X0,f19(boundary(X1,X2,X3),X4))
| hausdorff(boundary(X1,X2,X3),X4) ) ).
cnf(u733,axiom,
( ~ closed(X0,X1,subspace_topology(X2,X3,X4))
| topological_space(X2,X3) ) ).
cnf(u27800,negated_conjecture,
( element_of_set(f11(X1,union_of_members(top_of_basis(X0))),interior(X2,X3,X4))
| element_of_set(X5,f1(top_of_basis(X1),X5))
| element_of_set(f11(X0,union_of_members(ct)),sF0)
| ~ element_of_set(X5,cx) ) ).
cnf(open_set_20,axiom,
( open(X0,X1,X2)
| ~ topological_space(X1,X2)
| ~ element_of_collection(X0,X2) ) ).
cnf(u3842,axiom,
( ~ closed(f2(X1,X0),X3,X4)
| element_of_set(f20(closure(X2,X3,X4),X5),union_of_members(X1))
| hausdorff(closure(X2,X3,X4),X5)
| ~ subset_sets(X2,f2(X1,X0))
| element_of_set(X0,intersection_of_members(X1))
| ~ topological_space(closure(X2,X3,X4),X5) ) ).
cnf(u152,axiom,
( ~ element_of_set(X0,closure(X1,X2,X3))
| ~ subset_sets(relative_complement_sets(X1,X2),X2)
| closed(f14(relative_complement_sets(X1,X2),X2,X3,X0),X2,X3)
| element_of_set(X0,boundary(X1,X2,X3)) ) ).
cnf(u54548,negated_conjecture,
( ~ element_of_set(X7,f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)))
| hausdorff(interior(X1,X2,X3),X4)
| element_of_set(X7,f13(f14(f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)),X5,X6,X0),X2,X3,X7))
| element_of_set(X0,X8) ) ).
cnf(u6341,axiom,
( ~ closed(closure(relative_complement_sets(X4,X5),X5,X6),X1,X2)
| element_of_set(X7,f14(X4,X5,X6,f19(closure(X0,X1,X2),X3)))
| ~ subset_sets(X4,X5)
| ~ subset_sets(X0,closure(relative_complement_sets(X4,X5),X5,X6))
| subset_sets(X4,f14(X4,X5,X6,X7))
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3)
| element_of_set(f19(closure(X0,X1,X2),X3),boundary(X4,X5,X6)) ) ).
cnf(u17800,negated_conjecture,
hausdorff(intersection_of_members(X0),X1) ).
cnf(u861,axiom,
( element_of_set(f11(X0,closure(X1,X2,X3)),closure(X4,X5,X6))
| ~ closed(boundary(X4,X5,X6),X2,X3)
| ~ subset_sets(X1,boundary(X4,X5,X6))
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(u503,axiom,
( element_of_set(X7,interior(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,X6),X1,X2))
| ~ subset_sets(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,X6),X1)
| ~ element_of_set(X7,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3)
| element_of_set(X6,closure(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5))
| ~ subset_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(X4,X5) ) ).
cnf(u1060,axiom,
( ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,union_of_members(X4))
| ~ closed(union_of_members(X4),X1,X2)
| hausdorff(closure(X0,X1,X2),X3)
| element_of_collection(f1(X4,f19(closure(X0,X1,X2),X3)),X4) ) ).
cnf(u27722,negated_conjecture,
( element_of_set(f11(X1,union_of_members(top_of_basis(X0))),interior(X2,X3,X4))
| element_of_set(f11(X0,union_of_members(ct)),interior(X6,X7,X8))
| element_of_set(X5,f1(top_of_basis(X1),X5))
| ~ element_of_set(X5,cx) ) ).
cnf(u980,negated_conjecture,
( ~ element_of_collection(f13(a,X1,X2,f20(closure(X0,X3,X4),X5)),X6)
| ~ closed(interior(a,X1,X2),X3,X4)
| ~ topological_space(closure(X0,X3,X4),X5)
| hausdorff(closure(X0,X3,X4),X5)
| ~ topological_space(cx,X6)
| ~ element_of_set(X7,f13(a,X1,X2,f20(closure(X0,X3,X4),X5)))
| ~ subset_sets(X0,interior(a,X1,X2))
| element_of_set(X7,interior(a,cx,X6)) ) ).
cnf(u5330,axiom,
( ~ open(boundary(X1,X2,X3),closure(relative_complement_sets(X1,X2),X2,X3),X4)
| ~ disjoint_s(X0,boundary(X1,X2,X3))
| hausdorff(closure(relative_complement_sets(X1,X2),X2,X3),X4)
| ~ open(X0,closure(relative_complement_sets(X1,X2),X2,X3),X4)
| ~ element_of_set(f19(closure(relative_complement_sets(X1,X2),X2,X3),X4),X0)
| subset_sets(X1,f14(X1,X2,X3,f20(closure(relative_complement_sets(X1,X2),X2,X3),X4)))
| ~ subset_sets(X1,X2) ) ).
cnf(u1401,axiom,
( ~ element_of_set(X0,f22(X1,top_of_basis(subspace_topology(X2,X3,X4))))
| topological_space(X2,X3)
| connected_space(X1,top_of_basis(subspace_topology(X2,X3,X4)))
| ~ topological_space(X1,top_of_basis(subspace_topology(X2,X3,X4))) ) ).
cnf(u4458,axiom,
( element_of_collection(f12(X3,X4,X5,f9(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(subspace_topology(X3,X4,X5)))),subspace_topology(X3,X4,X5))),X4)
| ~ element_of_collection(union_of_members(subspace_topology(X3,X4,X5)),subspace_topology(X1,X2,X0))
| basis(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(subspace_topology(X3,X4,X5)))),subspace_topology(X3,X4,X5)) ) ).
cnf(u3168,axiom,
( closed(f14(relative_complement_sets(relative_complement_sets(X0,X1),X2),X2,X3,X4),X2,X3)
| element_of_set(X5,interior(f14(relative_complement_sets(X0,X1),X2,X3,X4),X1,X6))
| ~ subset_sets(relative_complement_sets(relative_complement_sets(X0,X1),X2),X2)
| ~ subset_sets(relative_complement_sets(X0,X1),X2)
| ~ topological_space(X2,X3)
| ~ subset_sets(f14(relative_complement_sets(X0,X1),X2,X3,X4),X1)
| ~ element_of_set(X5,relative_complement_sets(X0,X1))
| ~ closed(X0,X1,X6)
| element_of_set(X4,boundary(relative_complement_sets(X0,X1),X2,X3)) ) ).
cnf(u2892,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),f13(X3,X4,X5,f19(closure(X6,X7,X8),X9))),f13(X3,X4,X5,f19(closure(X6,X7,X8),X9)))
| topological_space(X0,X1)
| ~ subset_sets(X6,interior(X3,X4,X5))
| ~ closed(interior(X3,X4,X5),X7,X8)
| ~ topological_space(closure(X6,X7,X8),X9)
| hausdorff(closure(X6,X7,X8),X9) ) ).
cnf(u5866,negated_conjecture,
( closed(f14(a,cx,ct,X0),cx,ct)
| element_of_set(X0,f14(a,cx,ct,X1))
| element_of_set(X1,sF3) ) ).
cnf(interior_50,axiom,
( ~ element_of_set(X0,interior(X1,X2,X3))
| subset_sets(f13(X1,X2,X3,X0),X1) ) ).
cnf(u931,axiom,
( ~ closed(intersection_of_sets(f16(X4,X5,X6,X7),X5),X1,X2)
| ~ subset_sets(X0,intersection_of_sets(f16(X4,X5,X6,X7),X5))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(X6,X7)
| ~ subset_sets(X5,X6)
| limit_point(X4,X5,X6,X7)
| eq_p(f20(closure(X0,X1,X2),X3),X4) ) ).
cnf(u3450,axiom,
( ~ closed(f13(a,cx,ct,f20(sF0,X0)),X2,X3)
| ~ topological_space(sF0,X0)
| element_of_set(f20(boundary(X1,X2,X3),X4),union_of_members(ct))
| ~ topological_space(boundary(X1,X2,X3),X4)
| ~ subset_sets(X1,f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| hausdorff(boundary(X1,X2,X3),X4) ) ).
cnf(u3225,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ closed(X7,X5,X6)
| ~ subset_sets(X4,X7)
| element_of_set(f11(X8,closure(X4,X5,X6)),X7)
| element_of_set(f20(boundary(X0,X1,X2),X3),union_of_members(top_of_basis(X8))) ) ).
cnf(u36052,negated_conjecture,
( element_of_set(f20(X0,X1),f10(X2,f1(top_of_basis(X2),f20(X0,X1)),f20(X0,X1)))
| limit_point(f20(X0,X1),X3,X4,top_of_basis(X2))
| hausdorff(X0,X1) ) ).
cnf(u9315,axiom,
( ~ element_of_set(X0,sF1)
| element_of_set(X0,cx) ) ).
cnf(u6276,axiom,
( ~ subset_sets(f10(X3,closure(X0,X1,X2),f11(X4,X5)),X5)
| ~ closed(sF1,X1,X2)
| ~ element_of_collection(sF3,X3)
| ~ element_of_set(f11(X4,X5),closure(X0,X1,X2))
| ~ subset_sets(X0,sF1)
| element_of_collection(X5,top_of_basis(X4))
| ~ element_of_collection(f10(X3,closure(X0,X1,X2),f11(X4,X5)),X4)
| ~ subset_sets(sF3,closure(X0,X1,X2)) ) ).
cnf(u5132,axiom,
( element_of_set(X4,f10(X2,f12(X1,top_of_basis(X2),X3,f8(X0,subspace_topology(X1,top_of_basis(X2),X3))),X4))
| basis(X0,subspace_topology(X1,top_of_basis(X2),X3))
| ~ element_of_set(X4,f12(X1,top_of_basis(X2),X3,f8(X0,subspace_topology(X1,top_of_basis(X2),X3))))
| ~ topological_space(X0,subspace_topology(X1,top_of_basis(X2),X3)) ) ).
cnf(u6897,negated_conjecture,
( element_of_set(f20(f13(a,cx,ct,X0),X1),interior(X2,X3,X4))
| hausdorff(f13(a,cx,ct,X0),X1)
| ~ element_of_set(X0,sF0) ) ).
cnf(u3153,axiom,
( ~ open_covering(X0,X1,X2)
| ~ compact_space(X1,X2)
| ~ topological_space(X3,X0)
| element_of_collection(union_of_members(f23(X1,X2,X0)),X0) ) ).
cnf(u3060,axiom,
( ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| topological_space(X5,X6) ) ).
cnf(u9542,negated_conjecture,
( eq_p(f19(boundary(X0,X1,X2),X3),X4)
| ~ element_of_set(X4,sF3)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(basis_for_topology_35,axiom,
( element_of_set(f7(X0,X1),intersection_of_sets(f8(X0,X1),f9(X0,X1)))
| ~ equal_sets(union_of_members(X1),X0)
| basis(X0,X1) ) ).
cnf(u4447,axiom,
( ~ element_of_set(X6,f12(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5,f2(subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5),X0)))
| element_of_set(X0,intersection_of_members(subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5)))
| topological_space(X2,X3) ) ).
cnf(u5334,axiom,
( ~ closed(boundary(X1,X2,X3),cx,ct)
| ~ open(closure(X1,X2,X3),sF3,X4)
| hausdorff(sF3,X4)
| ~ open(X0,sF3,X4)
| ~ element_of_set(f19(sF3,X4),X0)
| ~ subset_sets(a,boundary(X1,X2,X3))
| ~ disjoint_s(X0,closure(X1,X2,X3)) ) ).
cnf(u5543,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X4),closure(X5,X2,X3)),sF3)
| subset_sets(X5,f14(X5,X2,X3,X6))
| ~ closed(sF1,X2,X3)
| ~ subset_sets(X5,sF1)
| topological_space(X0,X1)
| ~ subset_sets(X5,X2) ) ).
cnf(u894,axiom,
( ~ topological_space(boundary(X0,X1,X2),X3)
| basis(boundary(X0,X1,X2),X3)
| subset_sets(X0,X1) ) ).
cnf(u2791,axiom,
( ~ closed(boundary(X0,X1,X2),cx,ct)
| ~ subset_sets(a,boundary(X0,X1,X2))
| element_of_collection(sF3,top_of_basis(X3))
| element_of_set(f11(X4,closure(X0,X1,X2)),closure(X0,X1,X2))
| element_of_set(f11(X3,sF3),union_of_members(top_of_basis(X4))) ) ).
cnf(u38349,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f1(top_of_basis(X0),f11(X0,union_of_members(top_of_basis(X1)))))
| element_of_set(f11(X1,union_of_members(ct)),sF0)
| ~ element_of_set(f11(X0,union_of_members(top_of_basis(X1))),cx) ) ).
cnf(u33344,negated_conjecture,
( element_of_set(X3,f13(a,sF0,subspace_topology(X0,X1,f13(a,cx,ct,X2)),X3))
| ~ element_of_set(X2,sF0)
| ~ element_of_set(X3,f13(a,cx,ct,X2)) ) ).
cnf(u1375,axiom,
( element_of_set(f11(X0,intersection_of_sets(X1,X2)),f6(X3,X4,f11(X0,intersection_of_sets(X1,X2)),X1,X2))
| ~ element_of_collection(X1,X4)
| ~ element_of_collection(X2,X4)
| ~ basis(X3,X4)
| ~ element_of_set(f11(X0,intersection_of_sets(X1,X2)),X3)
| element_of_collection(intersection_of_sets(X1,X2),top_of_basis(X0)) ) ).
cnf(u1075,negated_conjecture,
( ~ closed(f13(a,cx,ct,f19(sF0,X4)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f19(sF0,X4)))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| element_of_set(f19(closure(X0,X1,X2),X3),sF0)
| ~ topological_space(sF0,X4)
| hausdorff(sF0,X4) ) ).
cnf(u597,axiom,
( ~ subset_sets(intersection_of_members(subspace_topology(X1,X4,X0)),X2)
| element_of_collection(X2,top_of_basis(X3))
| ~ element_of_collection(intersection_of_members(subspace_topology(X1,X4,X0)),X3)
| subset_sets(X0,X1) ) ).
cnf(u9913,negated_conjecture,
( element_of_set(f20(X0,X1),f1(X2,f20(X0,X1)))
| hausdorff(X0,X1) ) ).
cnf(u4647,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,f19(sF0,X2)),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),sF0)
| ~ topological_space(sF0,X2)
| hausdorff(sF0,X2) ) ).
cnf(u2736,axiom,
( element_of_collection(f12(X0,X1,X2,f1(subspace_topology(X0,X1,X2),f20(union_of_members(subspace_topology(X0,X1,X2)),X3))),X1)
| ~ topological_space(union_of_members(subspace_topology(X0,X1,X2)),X3)
| hausdorff(union_of_members(subspace_topology(X0,X1,X2)),X3) ) ).
cnf(topological_space_16,axiom,
( ~ element_of_collection(intersection_of_sets(f3(X0,X1),f4(X0,X1)),X1)
| ~ equal_sets(union_of_members(X1),X0)
| ~ element_of_collection(empty_set,X1)
| ~ element_of_collection(X0,X1)
| topological_space(X0,X1)
| subset_collections(f5(X0,X1),X1) ) ).
cnf(u6317,axiom,
( element_of_set(f11(X5,closure(X1,X2,X3)),closure(X1,X2,X3))
| subset_sets(X1,f14(X1,X2,X3,X4))
| element_of_set(X4,f14(X1,X2,X3,X0))
| element_of_set(X0,union_of_members(top_of_basis(X5)))
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2) ) ).
cnf(u6089,axiom,
( ~ element_of_collection(f10(X2,sF3,X3),X0)
| ~ element_of_set(X1,f10(X2,sF3,X3))
| ~ topological_space(sF1,X0)
| element_of_set(X1,interior(sF3,sF1,X0))
| ~ element_of_set(X3,sF3)
| ~ element_of_collection(sF3,top_of_basis(X2)) ) ).
cnf(u3199,axiom,
( ~ closed(f8(X4,X5),X1,X2)
| ~ subset_sets(X0,f8(X4,X5))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(X4,X5)
| basis(X4,X5)
| element_of_set(f20(boundary(X0,X1,X2),X3),union_of_members(X5)) ) ).
cnf(u2959,negated_conjecture,
( ~ closed(f13(a,cx,ct,f19(sF0,X4)),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f13(a,cx,ct,f19(sF0,X4)))
| element_of_set(f11(X0,boundary(X1,X2,X3)),sF0)
| ~ topological_space(sF0,X4)
| hausdorff(sF0,X4) ) ).
cnf(u499,axiom,
( open(f13(a,cx,ct,f19(sF0,X0)),cx,ct)
| hausdorff(sF0,X0)
| ~ topological_space(sF0,X0) ) ).
cnf(u3923,axiom,
( element_of_set(X10,interior(f14(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8,f19(closure(relative_complement_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7),X7,X8),X9)),X1,X2))
| ~ topological_space(closure(relative_complement_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7),X7,X8),X9)
| hausdorff(closure(relative_complement_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7),X7,X8),X9)
| ~ subset_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7)
| ~ closed(interior(X0,X1,X2),X4,X5)
| ~ topological_space(closure(X3,X4,X5),X6)
| hausdorff(closure(X3,X4,X5),X6)
| ~ subset_sets(f14(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8,f19(closure(relative_complement_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7),X7,X8),X9)),X1)
| ~ element_of_set(X10,f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)))
| ~ subset_sets(X3,interior(X0,X1,X2))
| element_of_set(f19(closure(relative_complement_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7),X7,X8),X9),boundary(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8)) ) ).
cnf(u6445,axiom,
( ~ closed(closure(X5,X2,X3),X8,X9)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X1,X4,X0),closure(X5,X2,X3)),sF3)
| ~ subset_sets(X5,sF1)
| element_of_collection(boundary(X7,X8,X9),top_of_basis(X6))
| subset_sets(X0,X1)
| ~ subset_sets(X7,closure(X5,X2,X3)) ) ).
cnf(u4635,axiom,
( subset_sets(f13(X2,X3,X4,f11(X0,intersection_of_members(X1))),X2)
| ~ element_of_collection(interior(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0)) ) ).
cnf(u446,axiom,
( ~ topological_space(interior(X0,X1,X2),X3)
| basis(interior(X0,X1,X2),X3)
| topological_space(X1,X2) ) ).
cnf(u2846,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),f13(a,cx,ct,X3)),f13(a,cx,ct,X3))
| topological_space(X0,X1)
| ~ element_of_set(X3,sF0) ) ).
cnf(u2500,axiom,
( element_of_set(X0,f10(X3,f13(X1,X2,top_of_basis(X3),f20(interior(X1,X2,top_of_basis(X3)),X4)),X0))
| ~ element_of_set(X0,f13(X1,X2,top_of_basis(X3),f20(interior(X1,X2,top_of_basis(X3)),X4)))
| ~ topological_space(interior(X1,X2,top_of_basis(X3)),X4)
| hausdorff(interior(X1,X2,top_of_basis(X3)),X4) ) ).
cnf(u784,axiom,
( subset_sets(f13(a,cx,ct,f11(X0,sF0)),a)
| element_of_collection(sF0,top_of_basis(X0)) ) ).
cnf(u6264,negated_conjecture,
( ~ basis(X0,ct)
| topological_space(X0,ct)
| ~ element_of_collection(X0,ct) ) ).
cnf(u2677,axiom,
( ~ subset_sets(X7,f13(X0,X1,X2,f11(X6,closure(X5,X3,X4))))
| ~ subset_sets(X5,interior(X0,X1,X2))
| element_of_collection(closure(X5,X3,X4),top_of_basis(X6))
| ~ element_of_collection(X7,X8)
| ~ topological_space(X0,X8)
| ~ element_of_set(X9,X7)
| ~ closed(interior(X0,X1,X2),X3,X4)
| element_of_set(X9,interior(f13(X0,X1,X2,f11(X6,closure(X5,X3,X4))),X0,X8)) ) ).
cnf(u2809,axiom,
( ~ closed(interior(X0,X1,X2),cx,ct)
| open(f13(X0,X1,X2,f11(X3,sF3)),X1,X2)
| ~ subset_sets(a,interior(X0,X1,X2))
| element_of_collection(sF3,top_of_basis(X3)) ) ).
cnf(u592,axiom,
( element_of_set(X0,intersection_of_members(subspace_topology(X1,X2,X3)))
| subset_sets(X3,X1) ) ).
cnf(u1258,axiom,
( element_of_collection(f6(X5,X6,f15(X0,X1,X2,X3,X4),X4,X1),X6)
| ~ element_of_collection(X4,X6)
| ~ element_of_collection(X1,X6)
| ~ basis(X5,X6)
| ~ element_of_set(f15(X0,X1,X2,X3,X4),X5)
| ~ neighborhood(X4,X0,X2,X3)
| ~ limit_point(X0,X1,X2,X3) ) ).
cnf(u3873,negated_conjecture,
( ~ element_of_set(X2,f13(a,cx,ct,f19(sF0,X1)))
| ~ topological_space(sF0,X1)
| hausdorff(sF0,X1)
| ~ topological_space(cx,top_of_basis(X0))
| element_of_set(f11(X0,f13(a,cx,ct,f19(sF0,X1))),sF0)
| element_of_set(X2,interior(a,cx,top_of_basis(X0))) ) ).
cnf(u5563,axiom,
( ~ closed(closure(relative_complement_sets(a,cx),cx,ct),X1,X2)
| ~ element_of_set(f20(closure(X0,X1,X2),X3),sF3)
| ~ subset_sets(X0,closure(relative_complement_sets(a,cx),cx,ct))
| element_of_set(f20(closure(X0,X1,X2),X3),sF1)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3) ) ).
cnf(u4305,negated_conjecture,
( ~ element_of_set(X3,f13(a,X0,X1,f20(interior(a,X0,X1),X2)))
| ~ topological_space(cx,X1)
| ~ topological_space(interior(a,X0,X1),X2)
| hausdorff(interior(a,X0,X1),X2)
| element_of_set(X3,interior(a,cx,X1)) ) ).
cnf(u277,negated_conjecture,
( ~ element_of_set(X1,f1(ct,X0))
| ~ element_of_set(X0,cx)
| element_of_set(X1,union_of_members(ct)) ) ).
cnf(u943,negated_conjecture,
( ~ closed(f13(a,cx,ct,f20(sF0,X4)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f20(sF0,X4)))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| element_of_set(f20(closure(X0,X1,X2),X3),sF0)
| ~ topological_space(sF0,X4)
| hausdorff(sF0,X4) ) ).
cnf(u759,negated_conjecture,
( ~ element_of_set(X2,f13(a,cx,ct,X1))
| ~ element_of_set(X1,sF0)
| element_of_set(f11(X0,f13(a,cx,ct,X1)),sF0)
| element_of_set(X2,union_of_members(top_of_basis(X0))) ) ).
cnf(u5137,axiom,
( ~ element_of_set(f11(X3,f14(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5,X6)),boundary(X0,X1,X2))
| element_of_collection(f14(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5,X6),top_of_basis(X3))
| ~ element_of_collection(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f11(X7,closure(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5)),sF3)
| element_of_set(X6,union_of_members(top_of_basis(X7)))
| ~ closed(sF1,X4,X5)
| ~ subset_sets(closure(relative_complement_sets(X0,X1),X1,X2),sF1)
| ~ subset_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4) ) ).
cnf(u2451,axiom,
( element_of_collection(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X2)
| element_of_collection(interior(X0,X1,X2),top_of_basis(X3)) ) ).
cnf(u6003,negated_conjecture,
( ~ subset_sets(X2,f14(a,cx,ct,X0))
| element_of_set(X1,sF3)
| element_of_set(X0,f14(a,cx,ct,X1))
| element_of_set(X3,f14(a,cx,ct,X0))
| subset_sets(X2,f14(X2,cx,ct,X3))
| ~ subset_sets(X2,cx) ) ).
cnf(u3468,axiom,
( element_of_collection(f6(X6,X7,f7(closure(X0,X1,X2),X3),X4,X5),X7)
| ~ subset_sets(X0,intersection_of_sets(X4,X5))
| ~ closed(intersection_of_sets(X4,X5),X1,X2)
| basis(closure(X0,X1,X2),X3)
| ~ element_of_set(f7(closure(X0,X1,X2),X3),X6)
| ~ element_of_collection(X4,X7)
| ~ element_of_collection(X5,X7)
| ~ basis(X6,X7)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u3051,axiom,
( element_of_collection(f6(X6,X7,f19(boundary(X0,X1,X2),X3),X4,X5),X7)
| ~ subset_sets(X0,intersection_of_sets(X4,X5))
| ~ closed(intersection_of_sets(X4,X5),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ element_of_set(f19(boundary(X0,X1,X2),X3),X6)
| ~ element_of_collection(X4,X7)
| ~ element_of_collection(X5,X7)
| ~ basis(X6,X7)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u250,axiom,
( element_of_set(f20(boundary(X0,X1,X2),X3),closure(X0,X1,X2))
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u7152,negated_conjecture,
( eq_p(f19(closure(X0,X5,X6),X7),X1)
| limit_point(X1,X2,X3,X4)
| hausdorff(closure(X0,X5,X6),X7) ) ).
cnf(u3156,axiom,
( ~ open_covering(f23(X2,X3,f24(X0,X1)),X0,X1)
| ~ compact_space(X2,X3)
| compact_space(X0,X1)
| ~ open_covering(f24(X0,X1),X2,X3) ) ).
cnf(interior_47,axiom,
( ~ element_of_set(X0,interior(X1,X2,X3))
| topological_space(X2,X3) ) ).
cnf(u1317,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),union_of_members(ct))
| element_of_set(X1,union_of_members(top_of_basis(X0)))
| ~ element_of_set(X1,cx) ) ).
cnf(u5847,negated_conjecture,
( element_of_set(X1,f14(a,cx,ct,f19(closure(relative_complement_sets(a,cx),cx,ct),X0)))
| ~ topological_space(closure(relative_complement_sets(a,cx),cx,ct),X0)
| hausdorff(closure(relative_complement_sets(a,cx),cx,ct),X0)
| ~ element_of_set(X1,sF3)
| element_of_set(f19(closure(relative_complement_sets(a,cx),cx,ct),X0),sF1) ) ).
cnf(u6295,axiom,
( ~ element_of_set(f11(X7,f14(closure(relative_complement_sets(X0,X1),X1,X2),X3,X4,X5)),boundary(X0,X1,X2))
| element_of_set(X6,closure(closure(relative_complement_sets(X0,X1),X1,X2),X3,X4))
| ~ subset_sets(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ topological_space(X3,X4)
| ~ element_of_collection(closure(relative_complement_sets(X0,X1),X1,X2),X7)
| element_of_collection(f14(closure(relative_complement_sets(X0,X1),X1,X2),X3,X4,X5),top_of_basis(X7))
| element_of_set(X5,f14(closure(relative_complement_sets(X0,X1),X1,X2),X3,X4,X6)) ) ).
cnf(u3084,axiom,
( ~ closed(f14(X4,X5,X6,f19(boundary(X0,X1,X2),X3)),X1,X2)
| ~ subset_sets(X0,f14(X4,X5,X6,f19(boundary(X0,X1,X2),X3)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(X5,X6)
| ~ subset_sets(X4,X5)
| element_of_set(f19(boundary(X0,X1,X2),X3),closure(X4,X5,X6)) ) ).
cnf(u2726,axiom,
( ~ closed(closure(relative_complement_sets(X0,X1),X1,X2),X1,X2)
| ~ subset_sets(X0,closure(relative_complement_sets(X0,X1),X1,X2))
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3)
| element_of_set(f19(closure(X0,X1,X2),X3),boundary(X0,X1,X2)) ) ).
cnf(u4612,axiom,
( ~ element_of_collection(X2,X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X3,X2),X2)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(top_of_basis(X3))) ) ).
cnf(u1110,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,f19(closure(X2,X0,X1),X3)),X4),sF0)
| ~ subset_sets(X2,sF0)
| ~ topological_space(closure(X2,X0,X1),X3)
| hausdorff(closure(X2,X0,X1),X3)
| ~ closed(sF0,X0,X1)
| basis(f13(a,cx,ct,f19(closure(X2,X0,X1),X3)),X4)
| ~ topological_space(f13(a,cx,ct,f19(closure(X2,X0,X1),X3)),X4) ) ).
cnf(u3419,axiom,
( ~ closed(f13(a,cx,ct,f19(sF0,X0)),X2,X3)
| ~ topological_space(sF0,X0)
| element_of_set(f20(boundary(X1,X2,X3),X4),union_of_members(ct))
| ~ topological_space(boundary(X1,X2,X3),X4)
| ~ subset_sets(X1,f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| hausdorff(boundary(X1,X2,X3),X4) ) ).
cnf(u3838,axiom,
( ~ closed(f2(X1,X0),X3,X4)
| element_of_set(f19(closure(X2,X3,X4),X5),union_of_members(X1))
| hausdorff(closure(X2,X3,X4),X5)
| ~ subset_sets(X2,f2(X1,X0))
| element_of_set(X0,intersection_of_members(X1))
| ~ topological_space(closure(X2,X3,X4),X5) ) ).
cnf(u593,axiom,
( element_of_set(X0,intersection_of_members(subspace_topology(X1,X2,X3)))
| topological_space(X1,X2) ) ).
cnf(u235,axiom,
( element_of_collection(f1(X0,f20(union_of_members(X0),X1)),X0)
| hausdorff(union_of_members(X0),X1)
| ~ topological_space(union_of_members(X0),X1) ) ).
cnf(u443,axiom,
( element_of_set(f7(interior(X0,X1,X2),X3),f13(X0,X1,X2,f7(interior(X0,X1,X2),X3)))
| ~ topological_space(interior(X0,X1,X2),X3)
| basis(interior(X0,X1,X2),X3) ) ).
cnf(basis_for_topology_28,axiom,
( equal_sets(union_of_members(X1),X0)
| ~ basis(X0,X1) ) ).
cnf(u20546,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),sF0)
| element_of_set(X1,f1(top_of_basis(X0),X1))
| ~ element_of_set(X1,sF0) ) ).
cnf(u4478,axiom,
( ~ element_of_set(X6,f12(X0,X1,X2,f1(subspace_topology(X0,X1,X2),X3)))
| ~ subset_sets(X4,X5)
| ~ topological_space(X5,subspace_topology(X0,X1,X2))
| limit_point(X3,X4,X5,subspace_topology(X0,X1,X2))
| element_of_set(X6,union_of_members(X1)) ) ).
cnf(u2955,negated_conjecture,
( ~ closed(f13(a,cx,ct,X4),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f13(a,cx,ct,X4))
| element_of_set(f11(X0,boundary(X1,X2,X3)),sF0)
| ~ element_of_set(X4,sF0) ) ).
cnf(u5983,negated_conjecture,
( ~ subset_sets(f14(a,cx,ct,X2),X1)
| element_of_set(X2,sF3)
| element_of_collection(X1,top_of_basis(X0))
| ~ element_of_collection(f14(a,cx,ct,X2),X0)
| subset_sets(a,f14(a,cx,ct,f11(X0,X1))) ) ).
cnf(u840,axiom,
( element_of_set(f11(X0,closure(X1,X2,X3)),f13(X4,X5,X6,f11(X0,closure(X1,X2,X3))))
| ~ closed(interior(X4,X5,X6),X2,X3)
| ~ subset_sets(X1,interior(X4,X5,X6))
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(u1068,axiom,
( open(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X5,X6)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3) ) ).
cnf(u582,axiom,
( ~ element_of_set(f19(closure(relative_complement_sets(a,cx),cx,ct),X0),sF3)
| element_of_set(f19(closure(relative_complement_sets(a,cx),cx,ct),X0),sF1)
| hausdorff(closure(relative_complement_sets(a,cx),cx,ct),X0)
| ~ topological_space(closure(relative_complement_sets(a,cx),cx,ct),X0) ) ).
cnf(u549,axiom,
( element_of_set(f7(f21(X0,X1),X2),union_of_members(X1))
| connected_space(X0,X1)
| ~ topological_space(X0,X1)
| basis(f21(X0,X1),X2)
| ~ topological_space(f21(X0,X1),X2) ) ).
cnf(u3380,axiom,
( element_of_set(f20(closure(X2,X0,X1),X3),X4)
| ~ subset_sets(X2,sF3)
| hausdorff(closure(X2,X0,X1),X3)
| ~ topological_space(closure(X2,X0,X1),X3)
| ~ subset_sets(a,X4)
| ~ closed(X4,cx,ct)
| ~ closed(sF3,X0,X1) ) ).
cnf(topological_space_13,axiom,
( ~ element_of_collection(union_of_members(f5(X0,X1)),X1)
| ~ equal_sets(union_of_members(X1),X0)
| ~ element_of_collection(empty_set,X1)
| ~ element_of_collection(X0,X1)
| element_of_collection(f3(X0,X1),X1)
| topological_space(X0,X1) ) ).
cnf(u28359,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f1(X1,f11(X0,union_of_members(ct))))
| element_of_set(f11(X2,union_of_members(top_of_basis(X0))),interior(X3,X4,X5))
| element_of_set(X6,f1(top_of_basis(X2),X6))
| ~ element_of_set(X6,cx) ) ).
cnf(u3086,axiom,
( ~ closed(f16(X4,X5,X6,X7),X1,X2)
| ~ subset_sets(X0,f16(X4,X5,X6,X7))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(X6,X7)
| ~ subset_sets(X5,X6)
| limit_point(X4,X5,X6,X7)
| element_of_set(f19(boundary(X0,X1,X2),X3),union_of_members(X7)) ) ).
cnf(u2674,axiom,
( ~ connected_set(X0,X1,subspace_topology(X2,X3,X4))
| subset_sets(X4,X2) ) ).
cnf(u3290,negated_conjecture,
( element_of_set(f20(f13(a,cx,ct,f20(sF0,X0)),X1),union_of_members(top_of_basis(X2)))
| hausdorff(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f20(sF0,X0)),X1)
| hausdorff(f13(a,cx,ct,f20(sF0,X0)),X1)
| element_of_set(f11(X2,sF0),sF0)
| ~ topological_space(sF0,X0) ) ).
cnf(u53460,negated_conjecture,
( element_of_set(X5,f13(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),cx,ct,X4),X1,X2,X5))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X4,sF0)
| ~ element_of_set(X5,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3))) ) ).
cnf(u3318,axiom,
( ~ subset_sets(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,X3),cx)
| element_of_set(X3,union_of_members(top_of_basis(X4)))
| ~ closed(sF1,X1,X2)
| ~ subset_sets(f13(a,cx,ct,f19(sF0,X0)),sF1)
| ~ subset_sets(f13(a,cx,ct,f19(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| element_of_set(f11(X4,closure(f13(a,cx,ct,f19(sF0,X0)),X1,X2)),sF3)
| ~ element_of_set(X5,f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(X5,interior(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,X3),cx,ct)) ) ).
cnf(u4835,negated_conjecture,
( element_of_set(f7(f1(ct,f15(X0,X1,X2,X3,X4)),f24(f1(ct,f15(X0,X1,X2,X3,X4)),X5)),union_of_members(ct))
| basis(f1(ct,f15(X0,X1,X2,X3,X4)),f24(f1(ct,f15(X0,X1,X2,X3,X4)),X5))
| compact_space(f1(ct,f15(X0,X1,X2,X3,X4)),X5)
| ~ neighborhood(X4,X0,X2,X3)
| ~ limit_point(X0,X1,X2,X3)
| ~ element_of_collection(X1,ct)
| ~ element_of_collection(X4,ct)
| ~ topological_space(f1(ct,f15(X0,X1,X2,X3,X4)),X5) ) ).
cnf(u807,axiom,
( element_of_collection(union_of_members(subspace_topology(X2,X3,intersection_of_sets(X0,X1))),subspace_topology(X4,X5,X0))
| ~ subset_sets(X0,X4)
| ~ element_of_collection(X1,X5)
| ~ connected_set(intersection_of_sets(X0,X1),X2,X3)
| ~ topological_space(X4,X5) ) ).
cnf(u2749,axiom,
( ~ closed(closure(relative_complement_sets(X0,X1),X1,X2),X1,X2)
| ~ subset_sets(X0,closure(relative_complement_sets(X0,X1),X1,X2))
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3)
| element_of_set(f20(closure(X0,X1,X2),X3),boundary(X0,X1,X2)) ) ).
cnf(u3414,axiom,
( ~ closed(f13(a,cx,ct,f19(sF0,X0)),X2,X3)
| ~ topological_space(sF0,X0)
| element_of_set(f19(closure(X1,X2,X3),X4),union_of_members(ct))
| hausdorff(closure(X1,X2,X3),X4)
| ~ subset_sets(X1,f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| ~ topological_space(closure(X1,X2,X3),X4) ) ).
cnf(u939,axiom,
( ~ closed(f13(a,cx,ct,X4),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,X4))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ element_of_set(X4,sF0)
| element_of_set(f20(closure(X0,X1,X2),X3),union_of_members(ct)) ) ).
cnf(u6559,negated_conjecture,
( element_of_set(X2,f14(a,cx,ct,X0))
| element_of_set(X0,f14(a,cx,ct,X1))
| ~ element_of_set(X2,sF3)
| element_of_set(X1,sF3) ) ).
cnf(u3056,axiom,
( ~ closed(f9(X4,X5),X1,X2)
| ~ subset_sets(X0,f9(X4,X5))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(X4,X5)
| basis(X4,X5)
| element_of_set(f19(boundary(X0,X1,X2),X3),union_of_members(X5)) ) ).
cnf(u3895,axiom,
( subset_sets(f10(X5,f14(X1,X2,X3,X4),X6),f14(f10(X5,f14(X1,X2,X3,X4),X6),X2,X3,X0))
| element_of_set(X0,f14(X1,X2,X3,X4))
| ~ subset_sets(f10(X5,f14(X1,X2,X3,X4),X6),X2)
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| ~ element_of_set(X6,f14(X1,X2,X3,X4))
| ~ element_of_collection(f14(X1,X2,X3,X4),top_of_basis(X5)) ) ).
cnf(u1255,axiom,
( element_of_collection(f6(X3,X4,f7(intersection_of_sets(X0,X1),X2),X0,X1),X4)
| ~ element_of_collection(X0,X4)
| ~ element_of_collection(X1,X4)
| ~ basis(X3,X4)
| ~ element_of_set(f7(intersection_of_sets(X0,X1),X2),X3)
| basis(intersection_of_sets(X0,X1),X2)
| ~ topological_space(intersection_of_sets(X0,X1),X2) ) ).
cnf(u1979,axiom,
( ~ closed(closure(X5,X2,X3),X7,X8)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X0,X1,X4),closure(X5,X2,X3)),sF3)
| ~ subset_sets(X5,sF1)
| hausdorff(closure(X6,X7,X8),X9)
| ~ subset_sets(X6,closure(X5,X2,X3))
| topological_space(X0,X1)
| ~ topological_space(closure(X6,X7,X8),X9) ) ).
cnf(u6418,axiom,
( ~ closed(closure(relative_complement_sets(X4,X5),X5,X6),X2,X3)
| element_of_set(X7,f14(X4,X5,X6,f11(X0,closure(X1,X2,X3))))
| ~ subset_sets(X4,X5)
| closed(f14(X4,X5,X6,X7),X5,X6)
| ~ subset_sets(X1,closure(relative_complement_sets(X4,X5),X5,X6))
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| element_of_set(f11(X0,closure(X1,X2,X3)),boundary(X4,X5,X6)) ) ).
cnf(u6415,axiom,
( ~ closed(closure(relative_complement_sets(X4,X5),X5,X6),X1,X2)
| element_of_set(X7,f14(X4,X5,X6,f19(closure(X0,X1,X2),X3)))
| ~ subset_sets(X4,X5)
| ~ subset_sets(X0,closure(relative_complement_sets(X4,X5),X5,X6))
| closed(f14(X4,X5,X6,X7),X5,X6)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3)
| element_of_set(f19(closure(X0,X1,X2),X3),boundary(X4,X5,X6)) ) ).
cnf(u774,axiom,
( ~ element_of_collection(f16(X2,X0,X1,X3),X5)
| limit_point(X2,X0,X1,X3)
| ~ limit_point(X2,X0,X4,X5)
| ~ topological_space(X1,X3)
| ~ subset_sets(X0,X1) ) ).
cnf(u408,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,f19(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| ~ topological_space(cx,X1)
| ~ element_of_set(X2,f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(X2,interior(a,cx,X1)) ) ).
cnf(u6008,negated_conjecture,
( ~ subset_sets(f14(a,cx,ct,X2),X1)
| element_of_set(X2,sF3)
| element_of_collection(X1,top_of_basis(X0))
| ~ element_of_collection(f14(a,cx,ct,X2),X0)
| closed(f14(a,cx,ct,f11(X0,X1)),cx,ct) ) ).
cnf(u4276,axiom,
( closed(f14(X0,X1,X2,f11(X6,f14(closure(X0,X1,X2),X3,X4,f20(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5)))),X1,X2)
| ~ topological_space(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5)
| hausdorff(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5)
| ~ subset_sets(closure(X0,X1,X2),X3)
| ~ element_of_collection(closure(X0,X1,X2),X6)
| element_of_collection(f14(closure(X0,X1,X2),X3,X4,f20(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5)),top_of_basis(X6))
| element_of_set(f20(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5),boundary(closure(X0,X1,X2),X3,X4))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u45473,negated_conjecture,
( ~ element_of_set(X4,boundary(X1,X2,X5))
| eq_p(X3,X4)
| element_of_set(X0,f13(f14(relative_complement_sets(X1,X2),X2,X5,X3),X2,X6,X0))
| ~ element_of_set(X0,relative_complement_sets(X1,X2)) ) ).
cnf(u1383,axiom,
( ~ element_of_set(X0,intersection_of_sets(f16(X1,X2,X3,X4),X2))
| topological_space(X5,X6)
| eq_p(f11(subspace_topology(X5,X6,X7),intersection_of_sets(f16(X1,X2,X3,X4),X2)),X1)
| ~ subset_sets(X2,X3)
| limit_point(X1,X2,X3,X4)
| ~ topological_space(X3,X4) ) ).
cnf(u1064,axiom,
( ~ closed(intersection_of_sets(f16(X4,X5,X6,X7),X5),X1,X2)
| ~ subset_sets(X0,intersection_of_sets(f16(X4,X5,X6,X7),X5))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(X6,X7)
| ~ subset_sets(X5,X6)
| limit_point(X4,X5,X6,X7)
| eq_p(f19(closure(X0,X1,X2),X3),X4) ) ).
cnf(u4260,axiom,
( ~ subset_sets(X4,f14(X0,X1,X2,f19(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f19(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1)
| ~ subset_sets(X4,X1)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| closed(f14(X4,X1,X2,X5),X1,X2)
| element_of_set(X5,f14(X0,X1,X2,f19(closure(relative_complement_sets(X0,X1),X1,X2),X3))) ) ).
cnf(u1314,negated_conjecture,
( ~ element_of_collection(f9(X0,X1),ct)
| ~ equal_sets(union_of_members(X1),X0)
| basis(X0,X1)
| ~ element_of_collection(f8(X0,X1),ct)
| element_of_collection(f1(ct,f7(X0,X1)),ct) ) ).
cnf(finer_topology_24,axiom,
( ~ finer(X0,X1,X2)
| topological_space(X2,X0) ) ).
cnf(u4629,axiom,
( ~ element_of_collection(relative_complement_sets(X2,X3),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ closed(X2,X3,X4)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X4)) ) ).
cnf(u3496,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| topological_space(X5,X6) ) ).
cnf(u962,axiom,
( ~ element_of_set(f20(closure(X0,X1,X2),X3),closure(X4,X5,X6))
| ~ subset_sets(X0,closure(relative_complement_sets(X4,X5),X5,X6))
| ~ closed(closure(relative_complement_sets(X4,X5),X5,X6),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3)
| element_of_set(f20(closure(X0,X1,X2),X3),boundary(X4,X5,X6)) ) ).
cnf(u5128,axiom,
( ~ element_of_set(X4,f12(X1,X2,X3,f8(X0,subspace_topology(X1,X2,X3))))
| basis(X0,subspace_topology(X1,X2,X3))
| ~ topological_space(X0,subspace_topology(X1,X2,X3))
| element_of_set(X4,union_of_members(X2)) ) ).
cnf(u375,axiom,
( ~ topological_space(X0,subspace_topology(X1,X2,X3))
| basis(X0,subspace_topology(X1,X2,X3))
| topological_space(X1,X2) ) ).
cnf(u741,axiom,
( element_of_set(f7(f1(ct,X0),X1),union_of_members(ct))
| ~ element_of_set(X0,sF0)
| basis(f1(ct,X0),X1)
| ~ topological_space(f1(ct,X0),X1) ) ).
cnf(u36065,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f10(X0,f1(top_of_basis(X0),f11(X0,union_of_members(top_of_basis(X1)))),f11(X0,union_of_members(top_of_basis(X1)))))
| limit_point(f11(X0,union_of_members(top_of_basis(X1))),X2,X3,top_of_basis(X0))
| element_of_set(f11(X1,union_of_members(ct)),interior(X4,X5,X6))
| ~ element_of_set(f11(X0,union_of_members(top_of_basis(X1))),cx) ) ).
cnf(u2686,axiom,
( ~ element_of_set(X9,f13(X0,X1,top_of_basis(subspace_topology(X2,X3,X4)),f20(closure(X7,X5,X6),X8)))
| ~ topological_space(closure(X7,X5,X6),X8)
| hausdorff(closure(X7,X5,X6),X8)
| ~ subset_sets(X7,interior(X0,X1,top_of_basis(subspace_topology(X2,X3,X4))))
| ~ closed(interior(X0,X1,top_of_basis(subspace_topology(X2,X3,X4))),X5,X6)
| subset_sets(X4,X2) ) ).
cnf(u4399,axiom,
( ~ closed(f10(X1,X0,X2),X5,X6)
| ~ element_of_set(X2,X0)
| element_of_set(f11(X3,closure(X4,X5,X6)),union_of_members(X1))
| element_of_collection(closure(X4,X5,X6),top_of_basis(X3))
| ~ element_of_collection(X0,top_of_basis(X1))
| ~ subset_sets(X4,f10(X1,X0,X2)) ) ).
cnf(u2488,axiom,
( element_of_set(X0,f10(X1,sF1,X0))
| ~ element_of_set(X0,sF1)
| element_of_set(f11(X1,sF1),sF3) ) ).
cnf(u7946,negated_conjecture,
( open(f13(X2,X3,X4,f19(X0,X1)),X3,X4)
| hausdorff(X0,X1) ) ).
cnf(topological_space_9,axiom,
( ~ topological_space(X0,X1)
| element_of_collection(X0,X1) ) ).
cnf(u675,axiom,
( element_of_set(f11(X3,closure(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2)),boundary(relative_complement_sets(X0,X1),X1,X2))
| element_of_collection(closure(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),top_of_basis(X3))
| ~ element_of_set(f11(X3,closure(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2)),boundary(X0,X1,X2)) ) ).
cnf(u3335,axiom,
( ~ subset_sets(union_of_members(top_of_basis(X2)),X1)
| subset_sets(X3,f14(X3,X4,X5,f11(X0,X1)))
| ~ closed(sF1,X4,X5)
| ~ subset_sets(X3,sF1)
| ~ subset_sets(X3,X4)
| element_of_collection(X1,top_of_basis(X0))
| ~ element_of_collection(union_of_members(top_of_basis(X2)),X0)
| element_of_set(f11(X2,closure(X3,X4,X5)),sF3) ) ).
cnf(u921,axiom,
( element_of_collection(f12(X2,X3,X4,f13(X0,X1,subspace_topology(X2,X3,X4),f20(interior(X0,X1,subspace_topology(X2,X3,X4)),X5))),X3)
| hausdorff(interior(X0,X1,subspace_topology(X2,X3,X4)),X5)
| ~ topological_space(interior(X0,X1,subspace_topology(X2,X3,X4)),X5) ) ).
cnf(u2416,axiom,
( element_of_set(f11(X5,boundary(X3,X1,X2)),union_of_members(top_of_basis(X4)))
| element_of_set(f11(X4,closure(X3,X1,X2)),X0)
| ~ subset_sets(X3,X0)
| ~ closed(X0,X1,X2)
| element_of_collection(boundary(X3,X1,X2),top_of_basis(X5)) ) ).
cnf(u17792,negated_conjecture,
( ~ element_of_set(X5,closure(X0,X1,X2))
| eq_p(f20(intersection_of_members(X3),X4),X5)
| hausdorff(intersection_of_members(X3),X4) ) ).
cnf(u1167,axiom,
( ~ closed(f13(closure(X0,X1,X2),X3,X4,f7(interior(closure(X0,X1,X2),X3,X4),X5)),X1,X2)
| basis(interior(closure(X0,X1,X2),X3,X4),X5)
| ~ topological_space(interior(closure(X0,X1,X2),X3,X4),X5)
| ~ subset_sets(X0,f13(closure(X0,X1,X2),X3,X4,f7(interior(closure(X0,X1,X2),X3,X4),X5)))
| ~ element_of_collection(f13(closure(X0,X1,X2),X3,X4,f7(interior(closure(X0,X1,X2),X3,X4),X5)),X6)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X6)) ) ).
cnf(u27799,negated_conjecture,
( element_of_set(f11(X1,union_of_members(ct)),interior(X2,X3,X4))
| element_of_set(f11(X0,union_of_members(top_of_basis(X1))),sF0)
| element_of_set(X5,f1(top_of_basis(X0),X5))
| ~ element_of_set(X5,cx) ) ).
cnf(u6709,negated_conjecture,
( ~ element_of_set(X1,X2)
| element_of_set(X1,interior(sF3,sF1,X0)) ) ).
cnf(u3042,axiom,
( element_of_set(f19(boundary(X0,X1,X2),X3),f1(X4,f19(boundary(X0,X1,X2),X3)))
| ~ subset_sets(X0,union_of_members(X4))
| ~ closed(union_of_members(X4),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u6588,negated_conjecture,
( element_of_collection(sF3,top_of_basis(X0))
| element_of_set(f11(X0,sF3),sF0) ) ).
cnf(u3097,axiom,
( ~ closed(X1,cx,ct)
| ~ topological_space(sF1,X0)
| ~ subset_sets(a,X1)
| element_of_set(f19(sF1,X0),X1)
| hausdorff(sF1,X0) ) ).
cnf(u4009,axiom,
( element_of_set(f19(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X7),interior(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X7)
| hausdorff(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X7) ) ).
cnf(u3783,axiom,
( element_of_collection(f14(closure(X0,X1,subspace_topology(X2,X3,X4)),X5,X6,X7),top_of_basis(X8))
| element_of_set(X7,closure(closure(X0,X1,subspace_topology(X2,X3,X4)),X5,X6))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,subspace_topology(X2,X3,X4))
| ~ element_of_collection(closure(X0,X1,subspace_topology(X2,X3,X4)),X8)
| ~ subset_sets(closure(X0,X1,subspace_topology(X2,X3,X4)),X5)
| ~ topological_space(X5,X6)
| subset_sets(X4,X2) ) ).
cnf(u2932,axiom,
( ~ closed(union_of_members(X4),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,union_of_members(X4))
| element_of_set(f11(X0,boundary(X1,X2,X3)),f1(X4,f11(X0,boundary(X1,X2,X3)))) ) ).
cnf(u3064,axiom,
( ~ closed(f13(a,cx,ct,X4),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,X4))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ element_of_set(X4,sF0)
| element_of_set(f19(boundary(X0,X1,X2),X3),union_of_members(ct)) ) ).
cnf(u4440,axiom,
( element_of_set(X4,f10(X3,f8(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(top_of_basis(X3)))),top_of_basis(X3)),X4))
| ~ element_of_collection(union_of_members(top_of_basis(X3)),subspace_topology(X1,X2,X0))
| ~ element_of_set(X4,f8(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(top_of_basis(X3)))),top_of_basis(X3)))
| basis(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(top_of_basis(X3)))),top_of_basis(X3)) ) ).
cnf(u6133,axiom,
( element_of_set(f11(X5,f10(X4,closure(X1,X2,X3),X0)),f10(X4,closure(X1,X2,X3),X0))
| ~ closed(sF1,X2,X3)
| element_of_set(f11(X4,closure(X1,X2,X3)),sF3)
| ~ subset_sets(X1,sF1)
| ~ element_of_set(X0,closure(X1,X2,X3))
| element_of_set(X0,union_of_members(top_of_basis(X5))) ) ).
cnf(u36071,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| limit_point(X0,X4,X5,X6) ) ).
cnf(u36095,negated_conjecture,
( element_of_set(f11(X4,union_of_members(ct)),interior(X5,X6,X7))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| element_of_set(f11(X1,union_of_members(top_of_basis(X4))),sF0)
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u272,axiom,
( ~ element_of_set(f19(closure(relative_complement_sets(X0,X1),X1,X2),X3),closure(X0,X1,X2))
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f19(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2)) ) ).
cnf(u1038,axiom,
( hausdorff(sF3,subspace_topology(X0,X1,sF3))
| ~ connected_set(sF3,X0,X1) ) ).
cnf(u4917,axiom,
( element_of_set(f11(X0,closure(X1,X2,X3)),union_of_members(top_of_basis(X5)))
| closed(f14(X1,X2,X3,X4),X2,X3)
| element_of_set(X4,union_of_members(top_of_basis(X0)))
| ~ subset_sets(X1,sF1)
| ~ subset_sets(X1,X2)
| element_of_set(f11(X5,sF3),sF3)
| ~ closed(sF1,X2,X3) ) ).
cnf(u3218,axiom,
( ~ closed(f13(X4,X5,X6,f19(interior(X4,X5,X6),X7)),X1,X2)
| ~ subset_sets(X0,f13(X4,X5,X6,f19(interior(X4,X5,X6),X7)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(interior(X4,X5,X6),X7)
| hausdorff(interior(X4,X5,X6),X7)
| element_of_set(f20(boundary(X0,X1,X2),X3),interior(X4,X5,X6)) ) ).
cnf(u206,axiom,
( ~ subset_sets(f16(X2,X0,X1,X3),X4)
| limit_point(X2,X0,X1,X3)
| ~ topological_space(X1,X3)
| ~ subset_sets(X4,X1)
| ~ element_of_set(X5,f16(X2,X0,X1,X3))
| ~ subset_sets(X0,X1)
| element_of_set(X5,interior(X4,X1,X3)) ) ).
cnf(u3317,negated_conjecture,
( ~ subset_sets(f14(f13(a,cx,ct,X0),X1,X2,X3),cx)
| element_of_set(X3,union_of_members(top_of_basis(X4)))
| ~ closed(sF1,X1,X2)
| ~ subset_sets(f13(a,cx,ct,X0),sF1)
| ~ subset_sets(f13(a,cx,ct,X0),X1)
| element_of_set(f11(X4,closure(f13(a,cx,ct,X0),X1,X2)),sF3)
| ~ element_of_set(X5,f13(a,cx,ct,X0))
| ~ element_of_set(X0,sF0)
| element_of_set(X5,interior(f14(f13(a,cx,ct,X0),X1,X2,X3),cx,ct)) ) ).
cnf(u4444,axiom,
( ~ element_of_set(X4,f12(X1,X2,X3,f2(subspace_topology(X1,X2,X3),X0)))
| element_of_set(X0,intersection_of_members(subspace_topology(X1,X2,X3)))
| element_of_set(X4,union_of_members(X2)) ) ).
cnf(u3146,axiom,
( element_of_set(f11(subspace_topology(X4,X5,X6),f13(X0,X1,X2,f7(interior(X0,X1,X2),X3))),f13(X0,X1,X2,f7(interior(X0,X1,X2),X3)))
| basis(interior(X0,X1,X2),X3)
| topological_space(X4,X5)
| ~ topological_space(interior(X0,X1,X2),X3) ) ).
cnf(u3731,axiom,
( element_of_collection(f6(X4,subspace_topology(X2,X3,f9(X0,X1)),f7(X0,X1),f8(X0,X1),f9(X0,X1)),subspace_topology(X2,X3,f9(X0,X1)))
| ~ element_of_set(f7(X0,X1),X4)
| ~ basis(X4,subspace_topology(X2,X3,f9(X0,X1)))
| ~ element_of_collection(f8(X0,X1),subspace_topology(X2,X3,f9(X0,X1)))
| ~ equal_sets(union_of_members(X1),X0)
| basis(X0,X1)
| ~ connected_set(f9(X0,X1),X2,X3) ) ).
cnf(u5961,axiom,
( ~ closed(boundary(X0,X1,X6),X4,X5)
| element_of_collection(boundary(X3,X4,X5),top_of_basis(X2))
| subset_sets(X0,X1)
| ~ subset_sets(X3,boundary(X0,X1,X6)) ) ).
cnf(u1976,axiom,
( ~ closed(boundary(X5,X2,X3),X7,X8)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X0,X1,X4),closure(X5,X2,X3)),sF3)
| ~ subset_sets(X5,sF1)
| ~ subset_sets(X6,boundary(X5,X2,X3))
| topological_space(X0,X1)
| ~ topological_space(closure(X6,X7,X8),X9)
| hausdorff(closure(X6,X7,X8),X9) ) ).
cnf(u742,axiom,
( element_of_set(f11(X1,f1(ct,X0)),union_of_members(ct))
| ~ element_of_set(X0,sF0)
| element_of_collection(f1(ct,X0),top_of_basis(X1)) ) ).
cnf(u27838,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),sF0)
| element_of_set(X2,f1(top_of_basis(X0),X2))
| element_of_set(f11(X1,union_of_members(ct)),sF0)
| ~ element_of_set(X2,cx) ) ).
cnf(u3489,axiom,
( ~ closed(f13(a,cx,ct,f20(sF0,X4)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f20(sF0,X4)))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| hausdorff(sF0,X4)
| ~ topological_space(sF0,X4)
| element_of_set(f7(closure(X0,X1,X2),X3),union_of_members(ct)) ) ).
cnf(u2756,axiom,
( ~ topological_space(X7,subspace_topology(X2,X3,X4))
| ~ topological_space(X2,X3)
| ~ subset_sets(X4,X2)
| limit_point(X5,X0,X1,subspace_topology(X6,X3,X4))
| ~ topological_space(X1,subspace_topology(X6,X3,X4))
| element_of_set(X5,f1(subspace_topology(X2,X3,X4),X5))
| ~ subset_sets(X0,X1)
| ~ subset_sets(X0,X7) ) ).
cnf(u5016,axiom,
( element_of_collection(f8(X0,f23(X0,X1,X2)),f23(X0,X1,X2))
| ~ open_covering(X2,X0,X1)
| basis(X0,f23(X0,X1,X2))
| ~ compact_space(X0,X1) ) ).
cnf(u371,axiom,
( element_of_collection(f9(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3),X3)
| basis(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3)
| ~ element_of_collection(union_of_members(X3),subspace_topology(X1,X2,X0)) ) ).
cnf(u3689,negated_conjecture,
( element_of_set(X7,interior(f14(f13(a,cx,ct,X0),X1,X2,f11(X6,f14(closure(f13(a,cx,ct,X0),X1,X2),X3,X4,X5))),cx,ct))
| ~ element_of_collection(closure(f13(a,cx,ct,X0),X1,X2),X6)
| ~ subset_sets(f13(a,cx,ct,X0),X1)
| ~ topological_space(X1,X2)
| element_of_set(X5,closure(closure(f13(a,cx,ct,X0),X1,X2),X3,X4))
| ~ subset_sets(closure(f13(a,cx,ct,X0),X1,X2),X3)
| ~ topological_space(X3,X4)
| ~ subset_sets(f14(f13(a,cx,ct,X0),X1,X2,f11(X6,f14(closure(f13(a,cx,ct,X0),X1,X2),X3,X4,X5))),cx)
| ~ element_of_set(X7,f13(a,cx,ct,X0))
| ~ element_of_set(X0,sF0)
| element_of_collection(f14(closure(f13(a,cx,ct,X0),X1,X2),X3,X4,X5),top_of_basis(X6)) ) ).
cnf(u4776,axiom,
( ~ topological_space(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5))
| connected_space(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5))
| topological_space(X2,X3) ) ).
cnf(u318,axiom,
( limit_point(X2,X3,X4,subspace_topology(X0,X1,X5))
| topological_space(X0,X1)
| ~ topological_space(X4,subspace_topology(X0,X1,X5))
| ~ subset_sets(X3,X4) ) ).
cnf(u848,negated_conjecture,
( ~ closed(f13(a,cx,ct,f19(sF0,X4)),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f13(a,cx,ct,f19(sF0,X4)))
| element_of_set(f11(X0,closure(X1,X2,X3)),sF0)
| ~ topological_space(sF0,X4)
| hausdorff(sF0,X4) ) ).
cnf(u590,axiom,
( ~ element_of_set(X2,f2(X1,X0))
| element_of_set(X0,intersection_of_members(X1))
| element_of_set(X2,union_of_members(X1)) ) ).
cnf(u2481,negated_conjecture,
( element_of_set(X0,f10(X2,f13(a,cx,ct,X1),X0))
| ~ element_of_set(X0,f13(a,cx,ct,X1))
| element_of_set(f11(X2,f13(a,cx,ct,X1)),sF0)
| ~ element_of_set(X1,sF0) ) ).
cnf(closed_set_21,axiom,
( ~ closed(X0,X1,X2)
| topological_space(X1,X2) ) ).
cnf(u4614,axiom,
( ~ element_of_collection(union_of_members(X2),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_collection(f1(X2,f11(X0,intersection_of_members(X1))),X2) ) ).
cnf(u5020,axiom,
( element_of_collection(union_of_members(f23(intersection_of_sets(X0,X1),X2,X3)),subspace_topology(X4,X5,X0))
| ~ open_covering(X3,intersection_of_sets(X0,X1),X2)
| ~ topological_space(X4,X5)
| ~ subset_sets(X0,X4)
| ~ element_of_collection(X1,X5)
| ~ compact_space(intersection_of_sets(X0,X1),X2) ) ).
cnf(u2681,negated_conjecture,
( ~ element_of_collection(f13(a,X0,X1,f11(X5,closure(X4,X2,X3))),X6)
| ~ subset_sets(X4,interior(a,X0,X1))
| element_of_collection(closure(X4,X2,X3),top_of_basis(X5))
| ~ topological_space(cx,X6)
| ~ element_of_set(X7,f13(a,X0,X1,f11(X5,closure(X4,X2,X3))))
| ~ closed(interior(a,X0,X1),X2,X3)
| element_of_set(X7,interior(a,cx,X6)) ) ).
cnf(u3901,axiom,
( subset_sets(f13(f14(X1,X2,X3,X4),X5,X6,f20(interior(f14(X1,X2,X3,X4),X5,X6),X7)),f14(f13(f14(X1,X2,X3,X4),X5,X6,f20(interior(f14(X1,X2,X3,X4),X5,X6),X7)),X2,X3,X0))
| element_of_set(X0,f14(X1,X2,X3,X4))
| ~ subset_sets(f13(f14(X1,X2,X3,X4),X5,X6,f20(interior(f14(X1,X2,X3,X4),X5,X6),X7)),X2)
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| hausdorff(interior(f14(X1,X2,X3,X4),X5,X6),X7)
| ~ topological_space(interior(f14(X1,X2,X3,X4),X5,X6),X7) ) ).
cnf(u36254,negated_conjecture,
( element_of_set(X0,f10(X4,f1(top_of_basis(X4),X0),X0))
| limit_point(X0,X1,X2,X3) ) ).
cnf(u3886,negated_conjecture,
( ~ element_of_set(X2,f13(a,cx,ct,f20(sF0,X1)))
| ~ topological_space(sF0,X1)
| hausdorff(sF0,X1)
| ~ topological_space(cx,top_of_basis(X0))
| element_of_set(f11(X0,f13(a,cx,ct,f20(sF0,X1))),sF0)
| element_of_set(X2,interior(a,cx,top_of_basis(X0))) ) ).
cnf(u506,axiom,
( ~ element_of_set(X4,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)))
| ~ topological_space(interior(X0,X1,X2),X3)
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X4,interior(X0,X1,X2)) ) ).
cnf(u4839,negated_conjecture,
( element_of_collection(f1(ct,f7(empty_set,f24(empty_set,X0))),ct)
| basis(empty_set,f24(empty_set,X0))
| compact_space(empty_set,X0)
| ~ topological_space(empty_set,X0) ) ).
cnf(u3412,axiom,
( element_of_set(f19(f13(a,cx,ct,f19(sF0,X0)),X1),union_of_members(ct))
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f19(sF0,X0)),X1)
| hausdorff(f13(a,cx,ct,f19(sF0,X0)),X1) ) ).
cnf(u815,axiom,
( hausdorff(closure(X0,X1,X2),subspace_topology(X3,X4,closure(X0,X1,X2)))
| ~ connected_set(closure(X0,X1,X2),X3,X4)
| subset_sets(X0,X1) ) ).
cnf(u1345,axiom,
( ~ topological_space(closure(X2,X3,X4),X5)
| element_of_set(f19(closure(X2,X3,X4),X5),union_of_members(top_of_basis(X0)))
| hausdorff(closure(X2,X3,X4),X5)
| ~ subset_sets(X2,X1)
| ~ closed(X1,X3,X4)
| element_of_set(f11(X0,X1),X1) ) ).
cnf(u1061,axiom,
( ~ closed(f1(ct,X4),X1,X2)
| ~ subset_sets(X0,f1(ct,X4))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ element_of_set(X4,sF0)
| element_of_set(f19(closure(X0,X1,X2),X3),union_of_members(ct)) ) ).
cnf(u5641,axiom,
( ~ element_of_set(f7(closure(X0,X1,X2),X3),closure(X4,X5,X6))
| ~ subset_sets(X0,closure(relative_complement_sets(X4,X5),X5,X6))
| ~ closed(closure(relative_complement_sets(X4,X5),X5,X6),X1,X2)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| element_of_set(f7(closure(X0,X1,X2),X3),boundary(X4,X5,X6)) ) ).
cnf(u3235,axiom,
( element_of_set(f20(boundary(X0,X1,X2),X3),closure(X4,X5,X6))
| ~ subset_sets(X0,boundary(X4,X5,X6))
| ~ closed(boundary(X4,X5,X6),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u2960,negated_conjecture,
( ~ closed(f13(a,cx,ct,f19(closure(X4,X5,X6),X7)),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f13(a,cx,ct,f19(closure(X4,X5,X6),X7)))
| ~ closed(sF0,X5,X6)
| ~ subset_sets(X4,sF0)
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7)
| element_of_set(f11(X0,boundary(X1,X2,X3)),sF0) ) ).
cnf(u5711,axiom,
( ~ closed(closure(relative_complement_sets(X2,X3),X3,subspace_topology(X0,X1,X4)),X5,X6)
| ~ subset_sets(X2,X3)
| topological_space(X0,X1)
| ~ subset_sets(X7,closure(relative_complement_sets(X2,X3),X3,subspace_topology(X0,X1,X4)))
| element_of_collection(closure(X7,X5,X6),top_of_basis(X8))
| element_of_set(f11(X8,closure(X7,X5,X6)),boundary(X2,X3,subspace_topology(X0,X1,X4))) ) ).
cnf(u2670,axiom,
( ~ element_of_set(X5,f12(X1,top_of_basis(subspace_topology(X2,X3,X4)),X0,X0))
| ~ connected_set(X0,X1,top_of_basis(subspace_topology(X2,X3,X4)))
| subset_sets(X4,X2) ) ).
cnf(u485,axiom,
( element_of_collection(union_of_members(f24(intersection_of_sets(X0,X1),X2)),subspace_topology(X3,X4,X0))
| ~ topological_space(intersection_of_sets(X0,X1),X2)
| ~ topological_space(X3,X4)
| ~ subset_sets(X0,X3)
| ~ element_of_collection(X1,X4)
| compact_space(intersection_of_sets(X0,X1),X2) ) ).
cnf(u2730,axiom,
( element_of_collection(f12(X0,X1,X2,relative_complement_sets(f14(X3,X4,subspace_topology(X0,X1,X2),X5),X4)),X1)
| element_of_set(X5,closure(X3,X4,subspace_topology(X0,X1,X2)))
| ~ subset_sets(X3,X4)
| ~ topological_space(X4,subspace_topology(X0,X1,X2)) ) ).
cnf(u416,axiom,
( subset_sets(f13(a,cx,ct,f20(sF0,X0)),a)
| hausdorff(sF0,X0)
| ~ topological_space(sF0,X0) ) ).
cnf(u36106,negated_conjecture,
( element_of_set(f11(X1,union_of_members(top_of_basis(X4))),f13(X5,X6,X7,f11(X1,union_of_members(top_of_basis(X4)))))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx)
| element_of_set(f11(X4,union_of_members(ct)),union_of_members(ct)) ) ).
cnf(u6292,axiom,
( ~ subset_sets(f14(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8,X9),X1)
| element_of_set(X10,closure(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8))
| ~ subset_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7)
| ~ topological_space(X7,X8)
| ~ closed(interior(X0,X1,X2),X4,X5)
| ~ topological_space(closure(X3,X4,X5),X6)
| hausdorff(closure(X3,X4,X5),X6)
| element_of_set(X9,f14(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8,X10))
| ~ element_of_set(X11,f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)))
| ~ subset_sets(X3,interior(X0,X1,X2))
| element_of_set(X11,interior(f14(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8,X9),X1,X2)) ) ).
cnf(u2699,axiom,
( element_of_collection(f12(X2,X3,X4,f13(X0,X1,subspace_topology(X2,X3,X4),f19(closure(X7,X5,X6),X8))),X3)
| ~ topological_space(closure(X7,X5,X6),X8)
| hausdorff(closure(X7,X5,X6),X8)
| ~ subset_sets(X7,interior(X0,X1,subspace_topology(X2,X3,X4)))
| ~ closed(interior(X0,X1,subspace_topology(X2,X3,X4)),X5,X6) ) ).
cnf(compact_set_107,axiom,
( ~ compact_set(X0,X1,X2)
| subset_sets(X0,X1) ) ).
cnf(u2945,axiom,
( ~ closed(f8(X4,X5),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f8(X4,X5))
| ~ topological_space(X4,X5)
| basis(X4,X5)
| element_of_set(f11(X0,boundary(X1,X2,X3)),union_of_members(X5)) ) ).
cnf(u36123,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| element_of_set(f11(X1,union_of_members(ct)),sF0)
| ~ element_of_set(X0,cx) ) ).
cnf(u255,axiom,
( eq_p(f19(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4),X0)
| hausdorff(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4)
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3)
| ~ topological_space(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4) ) ).
cnf(u36055,negated_conjecture,
( element_of_set(f19(X0,X1),f10(X2,f1(top_of_basis(X2),f19(X0,X1)),f19(X0,X1)))
| limit_point(f19(X0,X1),X3,X4,top_of_basis(X2))
| hausdorff(X0,X1) ) ).
cnf(u1324,axiom,
( element_of_set(f11(X0,f13(a,cx,ct,X1)),f13(a,cx,ct,X1))
| element_of_set(X1,union_of_members(top_of_basis(X0)))
| ~ element_of_set(X1,sF0) ) ).
cnf(u4655,axiom,
( ~ element_of_collection(f13(X2,X3,X4,f19(closure(X5,X6,X7),X8)),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ topological_space(closure(X5,X6,X7),X8)
| hausdorff(closure(X5,X6,X7),X8)
| ~ closed(interior(X2,X3,X4),X6,X7)
| ~ subset_sets(X5,interior(X2,X3,X4))
| element_of_set(f11(X0,intersection_of_members(X1)),interior(X2,X3,X4)) ) ).
cnf(u4837,axiom,
( element_of_set(f7(intersection_of_members(X0),f24(intersection_of_members(X0),X1)),X2)
| basis(intersection_of_members(X0),f24(intersection_of_members(X0),X1))
| compact_space(intersection_of_members(X0),X1)
| ~ element_of_collection(X2,X0)
| ~ topological_space(intersection_of_members(X0),X1) ) ).
cnf(u4279,axiom,
( element_of_set(X7,interior(f14(f16(X0,X1,X2,X3),X4,X5,f20(closure(relative_complement_sets(f16(X0,X1,X2,X3),X4),X4,X5),X6)),X2,X3))
| ~ topological_space(closure(relative_complement_sets(f16(X0,X1,X2,X3),X4),X4,X5),X6)
| hausdorff(closure(relative_complement_sets(f16(X0,X1,X2,X3),X4),X4,X5),X6)
| ~ subset_sets(f16(X0,X1,X2,X3),X4)
| limit_point(X0,X1,X2,X3)
| ~ topological_space(X2,X3)
| ~ subset_sets(f14(f16(X0,X1,X2,X3),X4,X5,f20(closure(relative_complement_sets(f16(X0,X1,X2,X3),X4),X4,X5),X6)),X2)
| ~ element_of_set(X7,f16(X0,X1,X2,X3))
| ~ subset_sets(X1,X2)
| element_of_set(f20(closure(relative_complement_sets(f16(X0,X1,X2,X3),X4),X4,X5),X6),boundary(f16(X0,X1,X2,X3),X4,X5)) ) ).
cnf(topological_space_17,axiom,
( ~ element_of_collection(intersection_of_sets(f3(X0,X1),f4(X0,X1)),X1)
| ~ equal_sets(union_of_members(X1),X0)
| ~ element_of_collection(empty_set,X1)
| ~ element_of_collection(X0,X1)
| topological_space(X0,X1)
| ~ element_of_collection(union_of_members(f5(X0,X1)),X1) ) ).
cnf(u5549,axiom,
( ~ subset_sets(f13(X0,X1,X2,f7(interior(X0,X1,X2),X3)),X4)
| basis(interior(X0,X1,X2),X3)
| ~ subset_sets(X4,X1)
| ~ element_of_set(X5,f13(X0,X1,X2,f7(interior(X0,X1,X2),X3)))
| ~ topological_space(interior(X0,X1,X2),X3)
| element_of_set(X5,interior(X4,X1,X2)) ) ).
cnf(u36066,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f10(X1,f1(top_of_basis(X1),f11(X0,union_of_members(ct))),f11(X0,union_of_members(ct))))
| element_of_set(f11(X1,union_of_members(top_of_basis(X0))),interior(X4,X5,X6))
| limit_point(f11(X0,union_of_members(ct)),X2,X3,top_of_basis(X1))
| ~ element_of_set(f11(X0,union_of_members(ct)),cx) ) ).
cnf(u19370,axiom,
( element_of_set(f11(X1,union_of_members(ct)),union_of_members(ct))
| element_of_set(X0,f1(top_of_basis(X1),X0))
| ~ element_of_set(X0,sF0) ) ).
cnf(u16518,negated_conjecture,
( limit_point(f20(intersection_of_members(X0),X1),X2,X3,X4)
| hausdorff(intersection_of_members(X0),X1) ) ).
cnf(u860,axiom,
( ~ closed(boundary(X4,X5,X6),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,boundary(X4,X5,X6))
| topological_space(X5,X6) ) ).
cnf(u4851,axiom,
( open(f13(X0,X1,X2,f7(interior(X0,X1,X2),f24(interior(X0,X1,X2),X3))),X1,X2)
| basis(interior(X0,X1,X2),f24(interior(X0,X1,X2),X3))
| compact_space(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3) ) ).
cnf(u236,axiom,
( eq_p(f20(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4),X0)
| hausdorff(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4)
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3)
| ~ topological_space(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4) ) ).
cnf(u3867,negated_conjecture,
( ~ element_of_set(X4,f13(a,cx,ct,f19(sF0,X3)))
| ~ topological_space(sF0,X3)
| hausdorff(sF0,X3)
| element_of_set(f11(subspace_topology(X0,X1,X2),f13(a,cx,ct,f19(sF0,X3))),sF0)
| subset_sets(X2,X0) ) ).
cnf(u2493,axiom,
( element_of_set(X0,f10(X2,f8(X1,top_of_basis(X2)),X0))
| ~ element_of_set(X0,f8(X1,top_of_basis(X2)))
| basis(X1,top_of_basis(X2))
| ~ topological_space(X1,top_of_basis(X2)) ) ).
cnf(u6155,axiom,
( element_of_set(f7(sF3,X0),f14(X1,cx,ct,f19(closure(relative_complement_sets(X1,cx),cx,ct),X2)))
| ~ subset_sets(a,f14(X1,cx,ct,f19(closure(relative_complement_sets(X1,cx),cx,ct),X2)))
| ~ topological_space(sF3,X0)
| basis(sF3,X0)
| ~ topological_space(closure(relative_complement_sets(X1,cx),cx,ct),X2)
| element_of_set(f19(closure(relative_complement_sets(X1,cx),cx,ct),X2),boundary(X1,cx,ct))
| hausdorff(closure(relative_complement_sets(X1,cx),cx,ct),X2)
| ~ subset_sets(X1,cx) ) ).
cnf(u6706,negated_conjecture,
( ~ element_of_set(X5,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X5,interior(X4,X1,X2)) ) ).
cnf(u3507,axiom,
( ~ closed(boundary(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,boundary(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ subset_sets(relative_complement_sets(X4,X5),X7)
| ~ closed(X7,X5,X6)
| element_of_set(f7(closure(X0,X1,X2),X3),X7) ) ).
cnf(u6303,axiom,
( element_of_set(f11(subspace_topology(X5,X6,X7),f14(X1,X2,X3,X4)),f14(X1,X2,X3,X4))
| subset_sets(X1,f14(X1,X2,X3,X0))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| topological_space(X5,X6)
| element_of_set(X4,closure(X1,X2,X3)) ) ).
cnf(u3190,axiom,
( ~ closed(f1(X4,X5),X1,X2)
| ~ subset_sets(X0,f1(X4,X5))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(X6,X4)
| ~ subset_sets(X7,X6)
| limit_point(X5,X7,X6,X4)
| element_of_set(f20(boundary(X0,X1,X2),X3),union_of_members(X4)) ) ).
cnf(u9347,axiom,
( element_of_set(f20(sF0,X0),f1(ct,f20(sF0,X0)))
| hausdorff(sF0,X0) ) ).
cnf(u4707,axiom,
( closed(f14(f13(f14(X0,X1,X2,X3),X4,X5,f7(interior(f14(X0,X1,X2,X3),X4,X5),X6)),X1,X2,X7),X1,X2)
| ~ subset_sets(f13(f14(X0,X1,X2,X3),X4,X5,f7(interior(f14(X0,X1,X2,X3),X4,X5),X6)),X1)
| element_of_set(X7,f14(X0,X1,X2,X3))
| element_of_set(X3,closure(X0,X1,X2))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| ~ topological_space(interior(f14(X0,X1,X2,X3),X4,X5),X6)
| basis(interior(f14(X0,X1,X2,X3),X4,X5),X6) ) ).
cnf(u390,axiom,
( element_of_collection(f12(X1,X2,X3,f8(X0,subspace_topology(X1,X2,X3))),X2)
| ~ topological_space(X0,subspace_topology(X1,X2,X3))
| basis(X0,subspace_topology(X1,X2,X3)) ) ).
cnf(u1276,axiom,
( ~ element_of_set(f11(X6,closure(X5,X3,X4)),closure(X0,X1,X2))
| ~ subset_sets(X5,boundary(relative_complement_sets(X0,X1),X1,X2))
| element_of_collection(closure(X5,X3,X4),top_of_basis(X6))
| ~ closed(boundary(relative_complement_sets(X0,X1),X1,X2),X3,X4)
| element_of_set(f11(X6,closure(X5,X3,X4)),boundary(X0,X1,X2)) ) ).
cnf(u811,axiom,
( hausdorff(interior(X0,X1,X2),subspace_topology(X3,X4,interior(X0,X1,X2)))
| ~ connected_set(interior(X0,X1,X2),X3,X4)
| topological_space(X1,X2) ) ).
cnf(u3405,axiom,
( element_of_set(f7(f13(a,cx,ct,f19(sF0,X0)),X1),union_of_members(ct))
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0)
| basis(f13(a,cx,ct,f19(sF0,X0)),X1)
| ~ topological_space(f13(a,cx,ct,f19(sF0,X0)),X1) ) ).
cnf(u6311,axiom,
( closed(f14(relative_complement_sets(X1,X2),X2,X3,X0),X2,X3)
| subset_sets(X1,f14(X1,X2,X3,X4))
| element_of_set(X4,f14(X1,X2,X3,X0))
| ~ topological_space(X2,X3)
| ~ subset_sets(relative_complement_sets(X1,X2),X2)
| ~ subset_sets(X1,X2)
| element_of_set(X0,boundary(X1,X2,X3)) ) ).
cnf(u221,axiom,
( ~ element_of_set(X1,f13(a,cx,ct,X0))
| ~ element_of_set(X0,sF0)
| element_of_set(X1,union_of_members(ct)) ) ).
cnf(u1288,axiom,
( ~ closed(closure(X1,X2,X3),X6,X7)
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(X4,closure(X5,X6,X7)),union_of_members(top_of_basis(X0)))
| element_of_collection(closure(X5,X6,X7),top_of_basis(X4))
| element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| ~ subset_sets(X5,closure(X1,X2,X3)) ) ).
cnf(u6375,axiom,
( ~ subset_sets(X5,f14(X0,X1,X2,X3))
| element_of_set(X4,closure(X0,X1,X2))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| ~ subset_sets(X5,X1)
| element_of_set(X3,f14(X0,X1,X2,X4))
| closed(f14(X5,X1,X2,X6),X1,X2)
| element_of_set(X6,f14(X0,X1,X2,X3)) ) ).
cnf(intersection_of_members_6,axiom,
( ~ element_of_set(X0,f2(X1,X0))
| element_of_set(X0,intersection_of_members(X1)) ) ).
cnf(u3672,axiom,
( ~ element_of_set(X5,union_of_members(f24(intersection_of_sets(X0,X1),X2)))
| ~ topological_space(X3,X4)
| ~ subset_sets(X0,X3)
| ~ element_of_collection(X1,X4)
| compact_space(intersection_of_sets(X0,X1),X2)
| ~ topological_space(intersection_of_sets(X0,X1),X2)
| element_of_set(X5,union_of_members(subspace_topology(X3,X4,X0))) ) ).
cnf(u3465,negated_conjecture,
( element_of_set(f7(closure(X0,X1,X2),X3),f1(ct,f7(closure(X0,X1,X2),X3)))
| ~ subset_sets(X0,empty_set)
| ~ closed(empty_set,X1,X2)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u15156,negated_conjecture,
( element_of_set(X0,f13(f14(relative_complement_sets(X1,X2),X2,X4,X5),X2,X3,X0))
| ~ element_of_set(X5,closure(X1,X2,X4))
| element_of_set(X5,boundary(X1,X2,X4))
| ~ element_of_set(X0,relative_complement_sets(X1,X2)) ) ).
cnf(u30302,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f1(top_of_basis(X0),f11(X0,union_of_members(top_of_basis(X1)))))
| element_of_set(f11(X1,union_of_members(ct)),interior(X2,X3,X4))
| ~ element_of_set(f11(X0,union_of_members(top_of_basis(X1))),cx) ) ).
cnf(u1261,axiom,
( element_of_collection(f6(X3,X4,f20(intersection_of_sets(X0,X1),X2),X0,X1),X4)
| ~ element_of_collection(X0,X4)
| ~ element_of_collection(X1,X4)
| ~ basis(X3,X4)
| ~ element_of_set(f20(intersection_of_sets(X0,X1),X2),X3)
| ~ topological_space(intersection_of_sets(X0,X1),X2)
| hausdorff(intersection_of_sets(X0,X1),X2) ) ).
cnf(u1078,axiom,
( ~ closed(f13(X4,X5,X6,f19(interior(X4,X5,X6),X7)),X1,X2)
| ~ subset_sets(X0,f13(X4,X5,X6,f19(interior(X4,X5,X6),X7)))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(interior(X4,X5,X6),X7)
| hausdorff(interior(X4,X5,X6),X7)
| element_of_set(f19(closure(X0,X1,X2),X3),interior(X4,X5,X6)) ) ).
cnf(u280,axiom,
( element_of_set(f20(union_of_members(X0),X1),f1(X0,f20(union_of_members(X0),X1)))
| ~ topological_space(union_of_members(X0),X1)
| hausdorff(union_of_members(X0),X1) ) ).
cnf(u1970,axiom,
( ~ closed(closure(X5,X2,X3),X8,X9)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X0,X1,X4),closure(X5,X2,X3)),sF3)
| ~ subset_sets(X5,sF1)
| element_of_collection(closure(X7,X8,X9),top_of_basis(X6))
| topological_space(X0,X1)
| ~ subset_sets(X7,closure(X5,X2,X3)) ) ).
cnf(u6344,axiom,
( element_of_set(X4,f14(X1,X2,X3,f11(X0,boundary(relative_complement_sets(X1,X2),X2,X3))))
| element_of_set(f11(X0,boundary(relative_complement_sets(X1,X2),X2,X3)),boundary(X1,X2,X3))
| ~ subset_sets(X1,X2)
| element_of_collection(boundary(relative_complement_sets(X1,X2),X2,X3),top_of_basis(X0))
| subset_sets(X1,f14(X1,X2,X3,X4)) ) ).
cnf(u3021,negated_conjecture,
( element_of_set(f19(f13(a,cx,ct,f19(sF0,X0)),X1),union_of_members(top_of_basis(X2)))
| hausdorff(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f19(sF0,X0)),X1)
| hausdorff(f13(a,cx,ct,f19(sF0,X0)),X1)
| element_of_set(f11(X2,sF0),sF0)
| ~ topological_space(sF0,X0) ) ).
cnf(u4038,axiom,
( ~ closed(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X8,X9)
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| element_of_set(f20(boundary(X7,X8,X9),X10),interior(X4,X5,X6))
| ~ topological_space(boundary(X7,X8,X9),X10)
| ~ subset_sets(X7,f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)))
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(boundary(X7,X8,X9),X10) ) ).
cnf(u43085,negated_conjecture,
( element_of_set(X3,f13(a,cx,subspace_topology(X0,X1,f13(a,cx,ct,f20(sF0,X2))),X3))
| hausdorff(sF0,X2)
| ~ element_of_set(X3,f13(a,cx,ct,f20(sF0,X2))) ) ).
cnf(u5754,axiom,
( ~ subset_sets(sF3,closure(X1,X2,X3))
| element_of_set(X4,union_of_members(top_of_basis(X0)))
| ~ closed(sF1,X2,X3)
| ~ subset_sets(X1,sF1)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ element_of_collection(sF3,X0)
| closed(f14(X1,X2,X3,X4),X2,X3) ) ).
cnf(u2957,negated_conjecture,
( ~ closed(f13(a,cx,ct,f11(X4,sF0)),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f13(a,cx,ct,f11(X4,sF0)))
| element_of_set(f11(X0,boundary(X1,X2,X3)),sF0)
| element_of_collection(sF0,top_of_basis(X4)) ) ).
cnf(u4452,axiom,
( element_of_collection(f2(subspace_topology(X1,X2,X3),X0),subspace_topology(X4,X2,X3))
| ~ topological_space(X4,X2)
| ~ subset_sets(X3,X4)
| element_of_set(X0,intersection_of_members(subspace_topology(X1,X2,X3))) ) ).
cnf(u2964,axiom,
( ~ closed(f13(X4,X5,X6,f19(interior(X4,X5,X6),X7)),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f13(X4,X5,X6,f19(interior(X4,X5,X6),X7)))
| ~ topological_space(interior(X4,X5,X6),X7)
| hausdorff(interior(X4,X5,X6),X7)
| element_of_set(f11(X0,boundary(X1,X2,X3)),interior(X4,X5,X6)) ) ).
cnf(u834,axiom,
( ~ closed(union_of_members(X4),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,union_of_members(X4))
| element_of_collection(f1(X4,f11(X0,closure(X1,X2,X3))),X4) ) ).
cnf(u4833,axiom,
( element_of_set(f7(f1(ct,X0),f24(f1(ct,X0),X1)),union_of_members(ct))
| basis(f1(ct,X0),f24(f1(ct,X0),X1))
| compact_space(f1(ct,X0),X1)
| ~ element_of_set(X0,sF0)
| ~ topological_space(f1(ct,X0),X1) ) ).
cnf(u2744,axiom,
( ~ closed(closure(relative_complement_sets(relative_complement_sets(X1,X2),X2),X2,X3),X4,X5)
| ~ subset_sets(X0,closure(relative_complement_sets(relative_complement_sets(X1,X2),X2),X2,X3))
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| element_of_set(f20(closure(X0,X4,X5),X6),boundary(relative_complement_sets(X1,X2),X2,X3))
| ~ element_of_set(f20(closure(X0,X4,X5),X6),boundary(X1,X2,X3)) ) ).
cnf(u36145,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| element_of_set(f11(X1,union_of_members(ct)),interior(X4,X5,X6)) ) ).
cnf(u4671,axiom,
( ~ element_of_collection(boundary(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ subset_sets(relative_complement_sets(X2,X3),X5)
| ~ closed(X5,X3,X4)
| element_of_set(f11(X0,intersection_of_members(X1)),X5) ) ).
cnf(u6083,negated_conjecture,
( element_of_set(f19(union_of_members(f24(X0,ct)),X1),union_of_members(ct))
| compact_space(X0,ct)
| ~ topological_space(X0,ct)
| ~ topological_space(union_of_members(f24(X0,ct)),X1)
| hausdorff(union_of_members(f24(X0,ct)),X1) ) ).
cnf(u4268,axiom,
( element_of_set(X5,interior(f14(relative_complement_sets(X0,X1),X2,X3,f20(closure(relative_complement_sets(relative_complement_sets(X0,X1),X2),X2,X3),X4)),X1,X6))
| ~ topological_space(closure(relative_complement_sets(relative_complement_sets(X0,X1),X2),X2,X3),X4)
| hausdorff(closure(relative_complement_sets(relative_complement_sets(X0,X1),X2),X2,X3),X4)
| ~ subset_sets(relative_complement_sets(X0,X1),X2)
| ~ subset_sets(f14(relative_complement_sets(X0,X1),X2,X3,f20(closure(relative_complement_sets(relative_complement_sets(X0,X1),X2),X2,X3),X4)),X1)
| ~ element_of_set(X5,relative_complement_sets(X0,X1))
| ~ closed(X0,X1,X6)
| element_of_set(f20(closure(relative_complement_sets(relative_complement_sets(X0,X1),X2),X2,X3),X4),boundary(relative_complement_sets(X0,X1),X2,X3)) ) ).
cnf(u3079,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ subset_sets(X4,X7)
| ~ closed(X7,X5,X6)
| element_of_set(f19(boundary(X0,X1,X2),X3),X7) ) ).
cnf(u3997,negated_conjecture,
( element_of_set(f11(X5,f1(ct,f15(X1,X4,X2,X3,X0))),f1(ct,f15(X1,X4,X2,X3,X0)))
| element_of_set(f15(X1,X4,X2,X3,X0),union_of_members(top_of_basis(X5)))
| ~ limit_point(X1,X4,X2,X3)
| ~ element_of_collection(X4,ct)
| ~ neighborhood(X0,X1,X2,X3)
| ~ element_of_collection(X0,ct) ) ).
cnf(u5006,axiom,
( subset_collections(f23(X1,X2,X0),X2)
| ~ compact_space(X1,X2)
| ~ open_covering(X0,X1,X2) ) ).
cnf(u3358,negated_conjecture,
( element_of_collection(f1(ct,f20(closure(X0,X1,X2),X3)),ct)
| hausdorff(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,empty_set)
| ~ closed(empty_set,X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(compact_space_100,axiom,
( ~ compact_space(X0,X1)
| topological_space(X0,X1) ) ).
cnf(u3922,axiom,
( element_of_set(X10,interior(f14(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8,f19(closure(relative_complement_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7),X7,X8),X9)),X1,X2))
| ~ topological_space(closure(relative_complement_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7),X7,X8),X9)
| hausdorff(closure(relative_complement_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7),X7,X8),X9)
| ~ subset_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7)
| ~ closed(interior(X0,X1,X2),X4,X5)
| ~ topological_space(closure(X3,X4,X5),X6)
| hausdorff(closure(X3,X4,X5),X6)
| ~ subset_sets(f14(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8,f19(closure(relative_complement_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7),X7,X8),X9)),X1)
| ~ element_of_set(X10,f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)))
| ~ subset_sets(X3,interior(X0,X1,X2))
| element_of_set(f19(closure(relative_complement_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7),X7,X8),X9),boundary(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8)) ) ).
cnf(u232,axiom,
( ~ element_of_set(X2,f21(X0,X1))
| ~ topological_space(X0,X1)
| connected_space(X0,X1)
| element_of_set(X2,union_of_members(X1)) ) ).
cnf(u547,negated_conjecture,
( ~ subset_sets(f14(a,cx,ct,X2),X0)
| ~ element_of_collection(f14(a,cx,ct,X2),X1)
| element_of_collection(X0,top_of_basis(X1))
| ~ element_of_set(f11(X1,X0),sF3)
| element_of_set(X2,sF3) ) ).
cnf(u793,negated_conjecture,
( element_of_collection(f13(a,cx,ct,f11(X1,sF0)),top_of_basis(X0))
| element_of_collection(sF0,top_of_basis(X1))
| element_of_set(f11(X0,f13(a,cx,ct,f11(X1,sF0))),sF0) ) ).
cnf(u4622,negated_conjecture,
( element_of_collection(f1(ct,f11(X0,intersection_of_members(X1))),ct)
| ~ element_of_collection(empty_set,X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0)) ) ).
cnf(u941,negated_conjecture,
( ~ closed(f13(a,cx,ct,f11(X4,sF0)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f11(X4,sF0)))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| element_of_set(f20(closure(X0,X1,X2),X3),sF0)
| element_of_collection(sF0,top_of_basis(X4)) ) ).
cnf(u455,axiom,
( ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| subset_sets(X0,X1) ) ).
cnf(u1138,axiom,
( element_of_set(X10,interior(f14(f13(X0,X1,X2,f19(closure(X5,X3,X4),X6)),X7,X8,X9),X1,X2))
| ~ topological_space(closure(X5,X3,X4),X6)
| hausdorff(closure(X5,X3,X4),X6)
| ~ subset_sets(f14(f13(X0,X1,X2,f19(closure(X5,X3,X4),X6)),X7,X8,X9),X1)
| ~ element_of_set(X10,f13(X0,X1,X2,f19(closure(X5,X3,X4),X6)))
| ~ subset_sets(X5,interior(X0,X1,X2))
| ~ closed(interior(X0,X1,X2),X3,X4)
| element_of_set(X9,closure(f13(X0,X1,X2,f19(closure(X5,X3,X4),X6)),X7,X8))
| ~ subset_sets(f13(X0,X1,X2,f19(closure(X5,X3,X4),X6)),X7)
| ~ topological_space(X7,X8) ) ).
cnf(u16507,negated_conjecture,
( eq_p(X0,f19(intersection_of_members(X1),X2))
| hausdorff(intersection_of_members(X1),X2)
| ~ element_of_set(X0,sF1) ) ).
cnf(u3320,axiom,
( ~ subset_sets(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,X6),X1)
| element_of_set(X6,union_of_members(top_of_basis(X7)))
| ~ closed(sF1,X4,X5)
| ~ subset_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),sF1)
| ~ subset_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(interior(X0,X1,X2),X3)
| element_of_set(f11(X7,closure(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5)),sF3)
| ~ element_of_set(X8,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X8,interior(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,X6),X1,X2)) ) ).
cnf(u4434,axiom,
( ~ subset_sets(relative_complement_sets(X0,X1),closure(X0,X1,X2))
| ~ closed(closure(X0,X1,X2),X1,X2)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f11(X4,boundary(X0,X1,X2)),boundary(X0,X1,X2))
| element_of_set(f20(closure(relative_complement_sets(X0,X1),X1,X2),X3),union_of_members(top_of_basis(X4))) ) ).
cnf(u1353,axiom,
( element_of_set(f11(X0,f13(X1,X2,X3,f20(interior(X1,X2,X3),X4))),f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)))
| element_of_set(f20(interior(X1,X2,X3),X4),union_of_members(top_of_basis(X0)))
| hausdorff(interior(X1,X2,X3),X4)
| ~ topological_space(interior(X1,X2,X3),X4) ) ).
cnf(u4844,negated_conjecture,
( element_of_set(f7(intersection_of_sets(X0,X1),f24(intersection_of_sets(X0,X1),X2)),union_of_members(ct))
| basis(intersection_of_sets(X0,X1),f24(intersection_of_sets(X0,X1),X2))
| compact_space(intersection_of_sets(X0,X1),X2)
| ~ topological_space(intersection_of_sets(X0,X1),X2)
| ~ element_of_collection(X1,ct)
| ~ element_of_collection(X0,ct) ) ).
cnf(u217,negated_conjecture,
( element_of_collection(intersection_of_sets(X0,X1),ct)
| ~ element_of_collection(X1,ct)
| ~ element_of_collection(X0,ct) ) ).
cnf(union_of_members_2,axiom,
( ~ element_of_set(X0,union_of_members(X1))
| element_of_collection(f1(X1,X0),X1) ) ).
cnf(u4623,negated_conjecture,
( element_of_set(f11(X0,intersection_of_members(X1)),f1(ct,f11(X0,intersection_of_members(X1))))
| ~ element_of_collection(empty_set,X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0)) ) ).
cnf(u3474,axiom,
( element_of_set(f7(closure(X0,X1,X2),X3),f13(X4,X5,X6,f7(closure(X0,X1,X2),X3)))
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ closed(interior(X4,X5,X6),X1,X2)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u9886,negated_conjecture,
( element_of_set(f19(X0,X1),f1(X2,f19(X0,X1)))
| hausdorff(X0,X1) ) ).
cnf(u3766,axiom,
( ~ topological_space(boundary(X3,X4,X5),X7)
| element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),X6)
| ~ closed(X6,X4,X5)
| ~ subset_sets(X3,X6)
| hausdorff(boundary(X3,X4,X5),X7)
| topological_space(X0,X1) ) ).
cnf(u345,axiom,
( equal_sets(union_of_members(f24(X0,X1)),X0)
| compact_space(X0,X1)
| ~ topological_space(X0,X1) ) ).
cnf(u2873,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),f13(X3,X4,X5,f11(X6,interior(X3,X4,X5)))),f13(X3,X4,X5,f11(X6,interior(X3,X4,X5))))
| topological_space(X0,X1)
| element_of_collection(interior(X3,X4,X5),top_of_basis(X6)) ) ).
cnf(u4832,axiom,
( element_of_collection(f1(X0,f7(union_of_members(X0),f24(union_of_members(X0),X1))),X0)
| basis(union_of_members(X0),f24(union_of_members(X0),X1))
| compact_space(union_of_members(X0),X1)
| ~ topological_space(union_of_members(X0),X1) ) ).
cnf(u1342,axiom,
( element_of_set(f15(X3,X2,X4,X5,X1),union_of_members(top_of_basis(X0)))
| element_of_set(f11(X0,intersection_of_sets(X1,X2)),intersection_of_sets(X1,X2))
| ~ neighborhood(X1,X3,X4,X5)
| ~ limit_point(X3,X2,X4,X5) ) ).
cnf(u30738,axiom,
( ~ subset_collections(f24(X0,X1),X1)
| ~ compact_space(X2,X1)
| compact_space(X0,X1) ) ).
cnf(u3090,axiom,
( ~ closed(boundary(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,boundary(X4,X5,X6))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| topological_space(X5,X6) ) ).
cnf(u6091,axiom,
( ~ element_of_collection(f13(sF3,X2,X3,f11(X4,interior(sF3,X2,X3))),X0)
| ~ element_of_set(X1,f13(sF3,X2,X3,f11(X4,interior(sF3,X2,X3))))
| ~ topological_space(sF1,X0)
| element_of_set(X1,interior(sF3,sF1,X0))
| element_of_collection(interior(sF3,X2,X3),top_of_basis(X4)) ) ).
cnf(u3012,negated_conjecture,
( element_of_set(X2,f10(X1,f13(a,cx,ct,f7(sF0,X0)),X2))
| ~ topological_space(sF0,X0)
| element_of_set(f11(X1,f13(a,cx,ct,f7(sF0,X0))),sF0)
| ~ element_of_set(X2,f13(a,cx,ct,f7(sF0,X0)))
| basis(sF0,X0) ) ).
cnf(u5272,axiom,
( ~ open(closure(X1,X2,X3),X4,X5)
| ~ disjoint_s(X0,closure(X1,X2,X3))
| hausdorff(X4,X5)
| ~ open(X0,X4,X5)
| ~ element_of_set(f19(X4,X5),X0)
| closed(f14(X1,X2,X3,f20(X4,X5)),X2,X3)
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ) ).
cnf(u5014,axiom,
( subset_collections(f5(X0,f23(X0,X1,X2)),f23(X0,X1,X2))
| ~ open_covering(X2,X0,X1)
| topological_space(X0,f23(X0,X1,X2))
| ~ element_of_collection(empty_set,f23(X0,X1,X2))
| ~ element_of_collection(X0,f23(X0,X1,X2))
| element_of_collection(f4(X0,f23(X0,X1,X2)),f23(X0,X1,X2))
| ~ compact_space(X0,X1) ) ).
cnf(u4867,axiom,
( element_of_set(f7(f13(a,cx,ct,f20(sF0,X0)),f24(f13(a,cx,ct,f20(sF0,X0)),X1)),union_of_members(ct))
| basis(f13(a,cx,ct,f20(sF0,X0)),f24(f13(a,cx,ct,f20(sF0,X0)),X1))
| compact_space(f13(a,cx,ct,f20(sF0,X0)),X1)
| hausdorff(sF0,X0)
| ~ topological_space(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f20(sF0,X0)),X1) ) ).
cnf(u5735,axiom,
( element_of_set(f7(closure(relative_complement_sets(X2,X3),X3,subspace_topology(X1,X4,X0)),X5),boundary(X2,X3,subspace_topology(X1,X4,X0)))
| ~ subset_sets(X2,X3)
| ~ topological_space(closure(relative_complement_sets(X2,X3),X3,subspace_topology(X1,X4,X0)),X5)
| basis(closure(relative_complement_sets(X2,X3),X3,subspace_topology(X1,X4,X0)),X5)
| subset_sets(X0,X1) ) ).
cnf(u36120,negated_conjecture,
( open(f13(X4,X5,X6,f11(X1,f1(ct,X0))),X5,X6)
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u1332,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),union_of_members(ct))
| element_of_set(f7(X1,X2),union_of_members(top_of_basis(X0)))
| basis(X1,X2)
| ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(f9(X1,X2),ct)
| ~ element_of_collection(f8(X1,X2),ct) ) ).
cnf(u846,negated_conjecture,
( ~ closed(f13(a,cx,ct,X4),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f13(a,cx,ct,X4))
| element_of_set(f11(X0,closure(X1,X2,X3)),sF0)
| ~ element_of_set(X4,sF0) ) ).
cnf(u4257,axiom,
( element_of_set(f11(X2,sF3),f14(X0,cx,ct,f19(closure(relative_complement_sets(X0,cx),cx,ct),X1)))
| element_of_set(f19(closure(relative_complement_sets(X0,cx),cx,ct),X1),boundary(X0,cx,ct))
| hausdorff(closure(relative_complement_sets(X0,cx),cx,ct),X1)
| ~ subset_sets(X0,cx)
| ~ topological_space(closure(relative_complement_sets(X0,cx),cx,ct),X1)
| element_of_collection(sF3,top_of_basis(X2))
| ~ subset_sets(a,f14(X0,cx,ct,f19(closure(relative_complement_sets(X0,cx),cx,ct),X1))) ) ).
cnf(u5557,axiom,
( ~ element_of_set(f7(closure(relative_complement_sets(a,cx),cx,ct),X0),sF3)
| element_of_set(f7(closure(relative_complement_sets(a,cx),cx,ct),X0),sF1)
| ~ topological_space(closure(relative_complement_sets(a,cx),cx,ct),X0)
| basis(closure(relative_complement_sets(a,cx),cx,ct),X0) ) ).
cnf(u7957,negated_conjecture,
( element_of_set(f19(X0,X1),sF0)
| hausdorff(X0,X1) ) ).
cnf(u6566,negated_conjecture,
( element_of_set(f7(sF3,X0),sF0)
| ~ topological_space(sF3,X0)
| basis(sF3,X0) ) ).
cnf(u677,axiom,
( ~ element_of_set(f11(X0,closure(relative_complement_sets(a,cx),cx,ct)),sF3)
| element_of_set(f11(X0,closure(relative_complement_sets(a,cx),cx,ct)),sF1)
| element_of_collection(closure(relative_complement_sets(a,cx),cx,ct),top_of_basis(X0)) ) ).
cnf(u2425,axiom,
( element_of_set(f20(boundary(X3,X1,X2),X5),union_of_members(top_of_basis(X4)))
| element_of_set(f11(X4,closure(X3,X1,X2)),X0)
| ~ subset_sets(X3,X0)
| ~ closed(X0,X1,X2)
| hausdorff(boundary(X3,X1,X2),X5)
| ~ topological_space(boundary(X3,X1,X2),X5) ) ).
cnf(u2963,negated_conjecture,
( ~ closed(f13(a,cx,ct,f20(closure(X4,X5,X6),X7)),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f13(a,cx,ct,f20(closure(X4,X5,X6),X7)))
| ~ closed(sF0,X5,X6)
| ~ subset_sets(X4,sF0)
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7)
| element_of_set(f11(X0,boundary(X1,X2,X3)),sF0) ) ).
cnf(u1386,negated_conjecture,
( ~ element_of_set(X0,f13(a,cx,ct,X1))
| topological_space(X2,X3)
| element_of_set(f11(subspace_topology(X2,X3,X4),f13(a,cx,ct,X1)),sF0)
| ~ element_of_set(X1,sF0) ) ).
cnf(u5257,negated_conjecture,
( ~ open(union_of_members(ct),X1,X2)
| ~ disjoint_s(X0,union_of_members(ct))
| hausdorff(X1,X2)
| ~ open(X0,X1,X2)
| ~ element_of_set(f19(X1,X2),X0)
| ~ element_of_set(f20(X1,X2),empty_set) ) ).
cnf(open_covering_96,axiom,
( ~ open_covering(X0,X1,X2)
| topological_space(X1,X2) ) ).
cnf(u244,axiom,
( closed(f14(relative_complement_sets(X0,X1),X1,X2,f20(closure(X0,X1,X2),X3)),X1,X2)
| hausdorff(closure(X0,X1,X2),X3)
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| ~ topological_space(closure(X0,X1,X2),X3)
| element_of_set(f20(closure(X0,X1,X2),X3),boundary(X0,X1,X2)) ) ).
cnf(u3151,axiom,
( element_of_set(f7(sF0,X0),f13(a,cx,ct,f7(sF0,X0)))
| ~ topological_space(sF0,X0)
| basis(sF0,X0) ) ).
cnf(u3383,axiom,
( ~ element_of_set(X9,f12(X2,top_of_basis(subspace_topology(X3,X4,X5)),X6,f16(X7,X0,X1,subspace_topology(X8,top_of_basis(subspace_topology(X3,X4,X5)),X6))))
| ~ topological_space(X2,top_of_basis(subspace_topology(X3,X4,X5)))
| ~ subset_sets(X6,X2)
| limit_point(X7,X0,X1,subspace_topology(X8,top_of_basis(subspace_topology(X3,X4,X5)),X6))
| ~ topological_space(X1,subspace_topology(X8,top_of_basis(subspace_topology(X3,X4,X5)),X6))
| ~ subset_sets(X0,X1)
| subset_sets(X5,X3) ) ).
cnf(u36125,negated_conjecture,
( element_of_set(f11(X1,union_of_members(ct)),f13(X4,X5,X6,f11(X1,union_of_members(ct))))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u805,axiom,
( element_of_collection(empty_set,subspace_topology(X1,X2,X0))
| ~ connected_set(X0,X1,X2) ) ).
cnf(u447,axiom,
( ~ topological_space(interior(X0,X1,X2),X3)
| basis(interior(X0,X1,X2),X3)
| subset_sets(X0,X1) ) ).
cnf(u6088,negated_conjecture,
( ~ closed(union_of_members(f24(X0,ct)),X2,X3)
| compact_space(X0,ct)
| element_of_set(f20(boundary(X1,X2,X3),X4),union_of_members(ct))
| ~ topological_space(boundary(X1,X2,X3),X4)
| ~ subset_sets(X1,union_of_members(f24(X0,ct)))
| ~ topological_space(X0,ct)
| hausdorff(boundary(X1,X2,X3),X4) ) ).
cnf(u1059,axiom,
( element_of_set(f19(closure(X0,X1,X2),X3),f1(X4,f19(closure(X0,X1,X2),X3)))
| ~ subset_sets(X0,union_of_members(X4))
| ~ closed(union_of_members(X4),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3) ) ).
cnf(u3596,axiom,
( ~ closed(interior(X1,X2,X3),cx,ct)
| element_of_set(f11(X0,sF3),f13(X1,X2,X3,f11(X0,sF3)))
| ~ subset_sets(a,interior(X1,X2,X3))
| element_of_collection(sF3,top_of_basis(X0)) ) ).
cnf(u3925,axiom,
( subset_sets(X0,f14(X0,X1,X2,f11(X6,f14(closure(X0,X1,X2),X3,X4,f19(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5)))))
| ~ topological_space(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5)
| hausdorff(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5)
| ~ subset_sets(closure(X0,X1,X2),X3)
| ~ element_of_collection(closure(X0,X1,X2),X6)
| element_of_collection(f14(closure(X0,X1,X2),X3,X4,f19(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5)),top_of_basis(X6))
| element_of_set(f19(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5),boundary(closure(X0,X1,X2),X3,X4))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u58037,negated_conjecture,
( ~ element_of_set(X2,f13(a,cx,ct,f20(sF0,X1)))
| ~ element_of_set(X0,f13(a,cx,ct,f20(sF0,X1)))
| eq_p(X3,X4)
| element_of_set(X2,f13(f14(f13(a,cx,ct,f20(sF0,X1)),X5,X6,X3),cx,ct,X2))
| element_of_set(X0,f13(f14(f13(a,cx,ct,f20(sF0,X1)),X5,X6,X4),cx,ct,X0))
| hausdorff(sF0,X1) ) ).
cnf(u3326,negated_conjecture,
( ~ element_of_set(f11(X5,f14(f14(a,cx,ct,X0),X1,X2,X3)),sF3)
| element_of_set(X3,union_of_members(top_of_basis(X4)))
| ~ closed(sF1,X1,X2)
| ~ subset_sets(f14(a,cx,ct,X0),sF1)
| ~ subset_sets(f14(a,cx,ct,X0),X1)
| ~ element_of_collection(f14(a,cx,ct,X0),X5)
| element_of_collection(f14(f14(a,cx,ct,X0),X1,X2,X3),top_of_basis(X5))
| element_of_set(f11(X4,closure(f14(a,cx,ct,X0),X1,X2)),sF3)
| element_of_set(X0,sF3) ) ).
cnf(u6132,axiom,
( element_of_set(f11(subspace_topology(X5,X6,X7),f10(X4,closure(X1,X2,X3),X0)),f10(X4,closure(X1,X2,X3),X0))
| ~ closed(sF1,X2,X3)
| element_of_set(f11(X4,closure(X1,X2,X3)),sF3)
| ~ subset_sets(X1,sF1)
| topological_space(X5,X6)
| ~ element_of_set(X0,closure(X1,X2,X3)) ) ).
cnf(u3610,axiom,
( element_of_set(X7,interior(f14(f16(X0,X1,X2,X3),X4,X5,f11(X6,closure(relative_complement_sets(f16(X0,X1,X2,X3),X4),X4,X5))),X2,X3))
| element_of_collection(closure(relative_complement_sets(f16(X0,X1,X2,X3),X4),X4,X5),top_of_basis(X6))
| ~ subset_sets(f16(X0,X1,X2,X3),X4)
| limit_point(X0,X1,X2,X3)
| ~ topological_space(X2,X3)
| ~ subset_sets(f14(f16(X0,X1,X2,X3),X4,X5,f11(X6,closure(relative_complement_sets(f16(X0,X1,X2,X3),X4),X4,X5))),X2)
| ~ element_of_set(X7,f16(X0,X1,X2,X3))
| ~ subset_sets(X1,X2)
| element_of_set(f11(X6,closure(relative_complement_sets(f16(X0,X1,X2,X3),X4),X4,X5)),boundary(f16(X0,X1,X2,X3),X4,X5)) ) ).
cnf(u41148,negated_conjecture,
( open(f13(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,X3),cx,ct,X4),cx,ct)
| hausdorff(sF0,X0)
| element_of_set(X3,closure(f13(a,cx,ct,f19(sF0,X0)),X1,X2))
| ~ element_of_set(X4,f13(a,cx,ct,f19(sF0,X0))) ) ).
cnf(u540,negated_conjecture,
( ~ element_of_set(f11(X1,X0),cx)
| ~ element_of_collection(union_of_members(ct),X1)
| ~ subset_sets(union_of_members(ct),X0)
| element_of_collection(X0,top_of_basis(X1)) ) ).
cnf(u2986,axiom,
( ~ element_of_set(X5,boundary(X0,X1,X2))
| ~ closed(X4,X1,X2)
| ~ subset_sets(X0,X4)
| element_of_set(f11(X3,boundary(X0,X1,X2)),X4)
| element_of_set(X5,union_of_members(top_of_basis(X3))) ) ).
cnf(u672,axiom,
( element_of_set(X1,union_of_members(top_of_basis(X0)))
| ~ element_of_set(X1,sF1)
| element_of_set(f11(X0,sF1),sF3) ) ).
cnf(u6567,negated_conjecture,
( element_of_set(f7(sF3,X0),f14(X1,cx,ct,f11(X2,f14(closure(X1,cx,ct),X3,X4,X5))))
| ~ subset_sets(a,f14(X1,cx,ct,f11(X2,f14(closure(X1,cx,ct),X3,X4,X5))))
| ~ topological_space(sF3,X0)
| basis(sF3,X0)
| element_of_collection(f14(closure(X1,cx,ct),X3,X4,X5),top_of_basis(X2))
| ~ element_of_collection(closure(X1,cx,ct),X2)
| ~ subset_sets(X1,cx)
| element_of_set(X5,closure(closure(X1,cx,ct),X3,X4))
| ~ subset_sets(closure(X1,cx,ct),X3)
| ~ topological_space(X3,X4) ) ).
cnf(u3953,negated_conjecture,
( ~ closed(f1(ct,f15(X1,X4,X2,X3,X0)),X6,X7)
| ~ limit_point(X1,X4,X2,X3)
| ~ element_of_collection(X4,ct)
| ~ element_of_collection(X0,ct)
| element_of_set(f7(closure(X5,X6,X7),X8),union_of_members(ct))
| ~ topological_space(closure(X5,X6,X7),X8)
| ~ subset_sets(X5,f1(ct,f15(X1,X4,X2,X3,X0)))
| ~ neighborhood(X0,X1,X2,X3)
| basis(closure(X5,X6,X7),X8) ) ).
cnf(u437,axiom,
( element_of_set(f7(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3),intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))))
| basis(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3)
| ~ element_of_collection(union_of_members(X3),subspace_topology(X1,X2,X0)) ) ).
cnf(u5748,axiom,
( ~ element_of_set(f7(closure(relative_complement_sets(X0,X1),X1,X2),f24(closure(relative_complement_sets(X0,X1),X1,X2),X3)),closure(X0,X1,X2))
| basis(closure(relative_complement_sets(X0,X1),X1,X2),f24(closure(relative_complement_sets(X0,X1),X1,X2),X3))
| compact_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f7(closure(relative_complement_sets(X0,X1),X1,X2),f24(closure(relative_complement_sets(X0,X1),X1,X2),X3)),boundary(X0,X1,X2)) ) ).
cnf(u10123,negated_conjecture,
( eq_p(f19(boundary(X0,X1,X2),X3),X7)
| limit_point(X7,X6,X4,X5)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u1269,axiom,
( ~ closed(boundary(X0,X1,X2),X3,X4)
| ~ subset_sets(X5,boundary(X0,X1,X2))
| element_of_collection(closure(X5,X3,X4),top_of_basis(X6))
| subset_sets(X0,X1) ) ).
cnf(u3669,axiom,
( element_of_collection(f12(X3,X4,X0,union_of_members(f24(intersection_of_sets(X0,X1),X2))),X4)
| ~ topological_space(X3,X4)
| ~ subset_sets(X0,X3)
| ~ element_of_collection(X1,X4)
| compact_space(intersection_of_sets(X0,X1),X2)
| ~ topological_space(intersection_of_sets(X0,X1),X2) ) ).
cnf(u2531,axiom,
( ~ element_of_set(X0,closure(X1,X2,X3))
| subset_sets(X4,X5)
| element_of_set(f11(subspace_topology(X5,X6,X4),closure(X1,X2,X3)),X7)
| ~ closed(X7,X2,X3)
| ~ subset_sets(X1,X7) ) ).
cnf(u1978,axiom,
( ~ topological_space(closure(X5,X2,X3),X6)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X0,X1,X4),closure(X5,X2,X3)),sF3)
| ~ subset_sets(X5,sF1)
| topological_space(X0,X1)
| hausdorff(closure(X5,X2,X3),X6) ) ).
cnf(u830,axiom,
( ~ limit_point(X0,X1,X6,subspace_topology(X4,X5,f16(X0,X1,X2,X3)))
| limit_point(X0,X1,X2,X3)
| ~ connected_set(f16(X0,X1,X2,X3),X4,X5)
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2) ) ).
cnf(u5136,axiom,
( element_of_collection(f8(X0,subspace_topology(X1,X2,X3)),subspace_topology(X4,X2,X3))
| basis(X0,subspace_topology(X1,X2,X3))
| ~ topological_space(X4,X2)
| ~ subset_sets(X3,X4)
| ~ topological_space(X0,subspace_topology(X1,X2,X3)) ) ).
cnf(u2478,axiom,
( element_of_set(X0,f10(X5,intersection_of_sets(f16(X1,X2,X3,X4),X2),X0))
| eq_p(f11(X5,intersection_of_sets(f16(X1,X2,X3,X4),X2)),X1)
| ~ element_of_set(X0,intersection_of_sets(f16(X1,X2,X3,X4),X2))
| ~ subset_sets(X2,X3)
| limit_point(X1,X2,X3,X4)
| ~ topological_space(X3,X4) ) ).
cnf(u2817,axiom,
( element_of_set(f7(f8(X0,X1),X2),union_of_members(X1))
| basis(X0,X1)
| ~ topological_space(X0,X1)
| basis(f8(X0,X1),X2)
| ~ topological_space(f8(X0,X1),X2) ) ).
cnf(u2459,axiom,
( element_of_set(X2,f18(X1,X3,X0,X2))
| ~ element_of_set(X2,X1)
| eq_p(X0,X2)
| ~ hausdorff(X1,X3)
| ~ element_of_set(X0,X1) ) ).
cnf(u6002,negated_conjecture,
( ~ subset_sets(X2,f14(a,cx,ct,X0))
| element_of_set(X1,sF3)
| ~ subset_sets(X2,cx)
| element_of_set(X0,f14(a,cx,ct,X1))
| closed(f14(X2,cx,ct,X3),cx,ct)
| element_of_set(X3,f14(a,cx,ct,X0)) ) ).
cnf(u5278,negated_conjecture,
( ~ open(f14(a,cx,ct,X1),X2,X3)
| ~ disjoint_s(X0,f14(a,cx,ct,X1))
| hausdorff(X2,X3)
| ~ open(X0,X2,X3)
| ~ element_of_set(f19(X2,X3),X0)
| ~ element_of_set(f20(X2,X3),sF3)
| element_of_set(X1,sF3) ) ).
cnf(u1397,axiom,
( ~ element_of_set(X0,f8(X1,top_of_basis(subspace_topology(X2,X3,X4))))
| topological_space(X2,X3)
| basis(X1,top_of_basis(subspace_topology(X2,X3,X4)))
| ~ topological_space(X1,top_of_basis(subspace_topology(X2,X3,X4))) ) ).
cnf(u3436,axiom,
( element_of_set(f7(f13(a,cx,ct,f20(sF0,X0)),X1),union_of_members(ct))
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0)
| basis(f13(a,cx,ct,f20(sF0,X0)),X1)
| ~ topological_space(f13(a,cx,ct,f20(sF0,X0)),X1) ) ).
cnf(u842,axiom,
( subset_sets(f13(X4,X5,X6,f11(X0,closure(X1,X2,X3))),X4)
| ~ closed(interior(X4,X5,X6),X2,X3)
| ~ subset_sets(X1,interior(X4,X5,X6))
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(u492,axiom,
( element_of_collection(f1(ct,X0),ct)
| ~ element_of_set(X0,sF0) ) ).
cnf(u6096,axiom,
( ~ element_of_collection(f13(sF3,X2,X3,f20(closure(X4,X5,X6),X7)),X0)
| ~ element_of_set(X1,f13(sF3,X2,X3,f20(closure(X4,X5,X6),X7)))
| ~ topological_space(sF1,X0)
| element_of_set(X1,interior(sF3,sF1,X0))
| ~ subset_sets(X4,interior(sF3,X2,X3))
| ~ closed(interior(sF3,X2,X3),X5,X6)
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7) ) ).
cnf(u3499,axiom,
( closed(f14(relative_complement_sets(X4,X5),X5,X6,f7(closure(X0,X1,X2),X3)),X5,X6)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ closed(closure(X4,X5,X6),X1,X2)
| basis(closure(X0,X1,X2),X3)
| ~ subset_sets(relative_complement_sets(X4,X5),X5)
| ~ topological_space(closure(X0,X1,X2),X3)
| element_of_set(f7(closure(X0,X1,X2),X3),boundary(X4,X5,X6)) ) ).
cnf(u55123,negated_conjecture,
( ~ element_of_set(X0,closure(f13(a,cx,ct,f19(sF0,X1)),X2,X3))
| hausdorff(sF0,X1)
| ~ element_of_set(X4,f13(a,cx,ct,f19(sF0,X1)))
| eq_p(X5,X0)
| element_of_set(X4,f13(f14(f13(a,cx,ct,f19(sF0,X1)),X2,X3,X5),cx,ct,X4)) ) ).
cnf(u4860,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,f11(X0,sF0)),f24(f13(a,cx,ct,f11(X0,sF0)),X1)),sF0)
| basis(f13(a,cx,ct,f11(X0,sF0)),f24(f13(a,cx,ct,f11(X0,sF0)),X1))
| compact_space(f13(a,cx,ct,f11(X0,sF0)),X1)
| ~ topological_space(f13(a,cx,ct,f11(X0,sF0)),X1)
| element_of_collection(sF0,top_of_basis(X0)) ) ).
cnf(u34576,axiom,
( ~ compact_space(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),f24(X4,X3))
| compact_space(X4,X3)
| ~ subset_collections(X3,f24(X4,X3)) ) ).
cnf(u36086,negated_conjecture,
( element_of_set(f11(X4,union_of_members(ct)),f13(X5,X6,X7,f11(X4,union_of_members(ct))))
| open(f13(X8,X9,X10,f11(X1,union_of_members(top_of_basis(X4)))),X9,X10)
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(compact_set_108,axiom,
( compact_space(X0,subspace_topology(X1,X2,X0))
| ~ compact_set(X0,X1,X2) ) ).
cnf(u29059,negated_conjecture,
( element_of_set(f11(X1,union_of_members(ct)),f1(X5,f11(X1,union_of_members(ct))))
| element_of_set(f11(X0,union_of_members(top_of_basis(X1))),union_of_members(X7))
| element_of_set(X6,f1(top_of_basis(X0),X6))
| ~ element_of_set(X6,cx) ) ).
cnf(u30093,axiom,
( element_of_set(f11(X1,f1(ct,X0)),union_of_members(X2))
| element_of_set(X0,f1(top_of_basis(X1),X0))
| ~ element_of_set(X0,sF0) ) ).
cnf(u4410,axiom,
( ~ closed(f10(X1,X0,X2),X4,X5)
| ~ element_of_set(X2,X0)
| element_of_set(f20(boundary(X3,X4,X5),X6),union_of_members(X1))
| ~ topological_space(boundary(X3,X4,X5),X6)
| ~ subset_sets(X3,f10(X1,X0,X2))
| ~ element_of_collection(X0,top_of_basis(X1))
| hausdorff(boundary(X3,X4,X5),X6) ) ).
cnf(u4052,negated_conjecture,
( element_of_collection(f1(ct,f20(intersection_of_sets(X1,X0),X2)),ct)
| ~ element_of_collection(X1,ct)
| ~ topological_space(intersection_of_sets(X1,X0),X2)
| hausdorff(intersection_of_sets(X1,X0),X2)
| ~ element_of_collection(X0,ct) ) ).
cnf(u801,negated_conjecture,
( ~ topological_space(f14(a,cx,ct,f11(X0,X1)),X3)
| element_of_collection(X1,top_of_basis(X0))
| ~ subset_sets(sF3,X1)
| ~ element_of_collection(X2,X3)
| ~ element_of_collection(sF3,X0)
| ~ element_of_set(X4,X2)
| ~ subset_sets(X2,a)
| element_of_set(X4,interior(a,f14(a,cx,ct,f11(X0,X1)),X3)) ) ).
cnf(u16458,negated_conjecture,
( ~ element_of_set(X5,boundary(X0,X1,X2))
| hausdorff(intersection_of_members(X3),X4)
| eq_p(X5,f19(intersection_of_members(X3),X4)) ) ).
cnf(u1233,axiom,
( limit_point(X3,X2,X0,X1)
| element_of_set(X3,union_of_members(X1))
| ~ subset_sets(X2,X0)
| ~ topological_space(X0,X1) ) ).
cnf(u4264,axiom,
( element_of_set(f19(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5),boundary(X0,X1,subspace_topology(X2,X3,X4)))
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5)
| hausdorff(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5)
| ~ subset_sets(X0,X1)
| topological_space(X2,X3) ) ).
cnf(u3349,negated_conjecture,
( element_of_collection(f1(ct,f11(X0,empty_set)),ct)
| element_of_collection(empty_set,top_of_basis(X0)) ) ).
cnf(u6054,negated_conjecture,
( subset_collections(f5(X0,ct),ct)
| topological_space(X0,ct)
| ~ element_of_collection(X0,ct)
| ~ basis(X0,ct) ) ).
cnf(u4261,axiom,
( ~ subset_sets(X4,f14(X0,X1,X2,f19(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f19(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(X5,f14(X0,X1,X2,f19(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| subset_sets(X4,f14(X4,X1,X2,X5))
| ~ subset_sets(X4,X1) ) ).
cnf(connected_set_93,axiom,
( ~ connected_set(X0,X1,X2)
| subset_sets(X0,X1) ) ).
cnf(u1355,axiom,
( element_of_set(f11(X0,closure(X1,X2,X3)),closure(X1,X2,X3))
| element_of_set(f20(boundary(X1,X2,X3),X4),union_of_members(top_of_basis(X0)))
| hausdorff(boundary(X1,X2,X3),X4)
| ~ topological_space(boundary(X1,X2,X3),X4) ) ).
cnf(u225,axiom,
( ~ element_of_set(X4,f16(X0,X1,X2,X3))
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3)
| element_of_set(X4,union_of_members(X3)) ) ).
cnf(u6156,axiom,
( element_of_set(f7(sF3,X0),f14(X1,cx,ct,f20(closure(relative_complement_sets(X1,cx),cx,ct),X2)))
| ~ subset_sets(a,f14(X1,cx,ct,f20(closure(relative_complement_sets(X1,cx),cx,ct),X2)))
| ~ topological_space(sF3,X0)
| basis(sF3,X0)
| ~ topological_space(closure(relative_complement_sets(X1,cx),cx,ct),X2)
| element_of_set(f20(closure(relative_complement_sets(X1,cx),cx,ct),X2),boundary(X1,cx,ct))
| hausdorff(closure(relative_complement_sets(X1,cx),cx,ct),X2)
| ~ subset_sets(X1,cx) ) ).
cnf(u4691,axiom,
( ~ subset_sets(X4,f14(X0,X1,X2,f20(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f20(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(X5,f14(X0,X1,X2,f20(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| subset_sets(X4,f14(X4,X1,X2,X5))
| ~ subset_sets(X4,X1) ) ).
cnf(u6085,negated_conjecture,
( ~ closed(union_of_members(f24(X0,ct)),X2,X3)
| compact_space(X0,ct)
| element_of_set(f19(boundary(X1,X2,X3),X4),union_of_members(ct))
| ~ topological_space(boundary(X1,X2,X3),X4)
| ~ subset_sets(X1,union_of_members(f24(X0,ct)))
| ~ topological_space(X0,ct)
| hausdorff(boundary(X1,X2,X3),X4) ) ).
cnf(u9881,negated_conjecture,
( eq_p(f20(boundary(X0,X1,X2),X3),f19(boundary(X4,X5,X6),X7))
| hausdorff(boundary(X4,X5,X6),X7)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u17786,negated_conjecture,
( eq_p(f20(intersection_of_members(X3),X4),f19(intersection_of_members(X5),X6))
| hausdorff(intersection_of_members(X5),X6)
| hausdorff(intersection_of_members(X3),X4) ) ).
cnf(u4892,axiom,
( element_of_set(f7(f22(X0,X1),f24(f22(X0,X1),X2)),union_of_members(X1))
| basis(f22(X0,X1),f24(f22(X0,X1),X2))
| compact_space(f22(X0,X1),X2)
| ~ topological_space(X0,X1)
| connected_space(X0,X1)
| ~ topological_space(f22(X0,X1),X2) ) ).
cnf(u4708,axiom,
( closed(f14(f13(f14(X0,X1,X2,X3),X4,X5,f11(X6,interior(f14(X0,X1,X2,X3),X4,X5))),X1,X2,X7),X1,X2)
| ~ subset_sets(f13(f14(X0,X1,X2,X3),X4,X5,f11(X6,interior(f14(X0,X1,X2,X3),X4,X5))),X1)
| element_of_set(X7,f14(X0,X1,X2,X3))
| element_of_set(X3,closure(X0,X1,X2))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| element_of_collection(interior(f14(X0,X1,X2,X3),X4,X5),top_of_basis(X6)) ) ).
cnf(u6910,negated_conjecture,
( element_of_set(f19(f13(a,cx,ct,X0),X1),interior(X2,X3,X4))
| hausdorff(f13(a,cx,ct,X0),X1)
| ~ element_of_set(X0,sF0) ) ).
cnf(u6420,axiom,
( element_of_set(X4,f14(X1,X2,X3,f11(X0,closure(relative_complement_sets(X1,X2),X2,X3))))
| element_of_set(f11(X0,closure(relative_complement_sets(X1,X2),X2,X3)),boundary(X1,X2,X3))
| ~ subset_sets(X1,X2)
| element_of_collection(closure(relative_complement_sets(X1,X2),X2,X3),top_of_basis(X0))
| closed(f14(X1,X2,X3,X4),X2,X3) ) ).
cnf(u3910,axiom,
( subset_sets(X1,f14(X1,X2,X3,X0))
| element_of_set(X0,f14(X1,X2,X3,X4))
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ) ).
cnf(u214,axiom,
( element_of_collection(f22(X0,X1),X1)
| connected_space(X0,X1)
| ~ topological_space(X0,X1) ) ).
cnf(u5282,axiom,
( ~ open(f17(X1,X2,f20(X3,X4),X5),X3,X4)
| ~ disjoint_s(X0,f17(X1,X2,f20(X3,X4),X5))
| hausdorff(X3,X4)
| ~ open(X0,X3,X4)
| ~ element_of_set(f19(X3,X4),X0)
| ~ element_of_set(X5,X1)
| eq_p(f20(X3,X4),X5)
| ~ hausdorff(X1,X2)
| ~ element_of_set(f20(X3,X4),X1) ) ).
cnf(u4782,axiom,
( element_of_set(X4,f10(X2,f12(X1,top_of_basis(X2),X3,f22(X0,subspace_topology(X1,top_of_basis(X2),X3))),X4))
| ~ topological_space(X0,subspace_topology(X1,top_of_basis(X2),X3))
| ~ element_of_set(X4,f12(X1,top_of_basis(X2),X3,f22(X0,subspace_topology(X1,top_of_basis(X2),X3))))
| connected_space(X0,subspace_topology(X1,top_of_basis(X2),X3)) ) ).
cnf(u30096,negated_conjecture,
( element_of_set(f11(X0,f1(ct,X1)),f13(X2,X3,X4,f11(X0,f1(ct,X1))))
| ~ element_of_set(X1,sF0)
| element_of_set(X1,f1(top_of_basis(X0),X1)) ) ).
cnf(u2688,axiom,
( element_of_set(X7,f10(X2,f13(X0,X1,top_of_basis(X2),f20(closure(X5,X3,X4),X6)),X7))
| ~ topological_space(closure(X5,X3,X4),X6)
| hausdorff(closure(X5,X3,X4),X6)
| ~ subset_sets(X5,interior(X0,X1,top_of_basis(X2)))
| ~ element_of_set(X7,f13(X0,X1,top_of_basis(X2),f20(closure(X5,X3,X4),X6)))
| ~ closed(interior(X0,X1,top_of_basis(X2)),X3,X4) ) ).
cnf(u1112,negated_conjecture,
( ~ closed(f13(a,cx,ct,f19(closure(X2,X0,X1),X3)),X6,X7)
| ~ subset_sets(X2,sF0)
| ~ topological_space(closure(X2,X0,X1),X3)
| hausdorff(closure(X2,X0,X1),X3)
| element_of_set(f11(X4,closure(X5,X6,X7)),sF0)
| element_of_collection(closure(X5,X6,X7),top_of_basis(X4))
| ~ closed(sF0,X0,X1)
| ~ subset_sets(X5,f13(a,cx,ct,f19(closure(X2,X0,X1),X3))) ) ).
cnf(u9604,negated_conjecture,
( ~ element_of_set(X4,closure(X0,X1,X2))
| eq_p(f19(boundary(X0,X1,X2),X3),X4)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u854,axiom,
( ~ closed(closure(X4,X5,X6),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,closure(X4,X5,X6))
| ~ subset_sets(X4,X7)
| ~ closed(X7,X5,X6)
| element_of_set(f11(X0,closure(X1,X2,X3)),X7) ) ).
cnf(u488,axiom,
( element_of_set(f19(f13(a,cx,ct,X0),X1),union_of_members(ct))
| ~ element_of_set(X0,sF0)
| ~ topological_space(f13(a,cx,ct,X0),X1)
| hausdorff(f13(a,cx,ct,X0),X1) ) ).
cnf(u5955,axiom,
( ~ closed(boundary(X0,X1,X6),X3,X4)
| ~ topological_space(closure(X2,X3,X4),X5)
| ~ subset_sets(X2,boundary(X0,X1,X6))
| subset_sets(X0,X1)
| basis(closure(X2,X3,X4),X5) ) ).
cnf(u1254,axiom,
( ~ element_of_collection(f9(X0,X1),X3)
| ~ element_of_collection(f8(X0,X1),X3)
| ~ element_of_set(f7(X0,X1),X2)
| ~ basis(X2,X3)
| element_of_collection(f6(X2,X3,f7(X0,X1),f8(X0,X1),f9(X0,X1)),X3)
| ~ equal_sets(union_of_members(X1),X0)
| basis(X0,X1) ) ).
cnf(u3817,axiom,
( element_of_set(f11(X0,closure(relative_complement_sets(X1,X2),X2,subspace_topology(X3,X4,X5))),boundary(X1,X2,subspace_topology(X3,X4,X5)))
| element_of_collection(closure(relative_complement_sets(X1,X2),X2,subspace_topology(X3,X4,X5)),top_of_basis(X0))
| ~ subset_sets(X1,X2)
| topological_space(X3,X4) ) ).
cnf(u3869,negated_conjecture,
( element_of_set(X2,f10(X0,f13(a,cx,ct,f19(sF0,X1)),X2))
| ~ topological_space(sF0,X1)
| hausdorff(sF0,X1)
| ~ element_of_set(X2,f13(a,cx,ct,f19(sF0,X1)))
| element_of_set(f11(X0,f13(a,cx,ct,f19(sF0,X1))),sF0) ) ).
cnf(u4878,axiom,
( element_of_set(f7(closure(X0,X1,X2),f24(closure(X0,X1,X2),X3)),X4)
| basis(closure(X0,X1,X2),f24(closure(X0,X1,X2),X3))
| compact_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,X4)
| ~ closed(X4,X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u1394,axiom,
( ~ element_of_set(X0,f2(top_of_basis(subspace_topology(X1,X2,X3)),X4))
| topological_space(X1,X2)
| element_of_set(X4,intersection_of_members(top_of_basis(subspace_topology(X1,X2,X3)))) ) ).
cnf(compact_space_104,axiom,
( open_covering(f24(X0,X1),X0,X1)
| ~ topological_space(X0,X1)
| compact_space(X0,X1) ) ).
cnf(u6716,negated_conjecture,
( ~ element_of_set(X8,f13(X0,X1,X2,f19(closure(X5,X3,X4),X6)))
| hausdorff(closure(X5,X3,X4),X6)
| ~ closed(interior(X0,X1,X2),X3,X4)
| element_of_set(X8,interior(X7,X1,X2)) ) ).
cnf(u6390,axiom,
( closed(f14(relative_complement_sets(X1,X2),X2,X3,X0),X2,X3)
| closed(f14(X1,X2,X3,X4),X2,X3)
| element_of_set(X4,f14(X1,X2,X3,X0))
| ~ topological_space(X2,X3)
| ~ subset_sets(relative_complement_sets(X1,X2),X2)
| ~ subset_sets(X1,X2)
| element_of_set(X0,boundary(X1,X2,X3)) ) ).
cnf(u4694,axiom,
( element_of_set(f20(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5),boundary(X0,X1,subspace_topology(X2,X3,X4)))
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5)
| hausdorff(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5)
| ~ subset_sets(X0,X1)
| topological_space(X2,X3) ) ).
cnf(u4128,axiom,
( element_of_collection(f10(subspace_topology(X1,X2,X3),X0,X4),subspace_topology(X5,X2,X3))
| ~ element_of_set(X4,X0)
| ~ topological_space(X5,X2)
| ~ subset_sets(X3,X5)
| ~ element_of_collection(X0,top_of_basis(subspace_topology(X1,X2,X3))) ) ).
cnf(u327,negated_conjecture,
( element_of_set(f20(f1(ct,X0),X1),union_of_members(ct))
| ~ element_of_set(X0,cx)
| ~ topological_space(f1(ct,X0),X1)
| hausdorff(f1(ct,X0),X1) ) ).
cnf(u4826,axiom,
( element_of_set(f11(subspace_topology(X2,X3,X4),X0),X0)
| basis(X0,f24(X0,X1))
| compact_space(X0,X1)
| topological_space(X2,X3)
| ~ topological_space(X0,X1) ) ).
cnf(u4125,axiom,
( element_of_collection(f12(X2,X3,X4,f12(X1,subspace_topology(X2,X3,X4),X5,f10(subspace_topology(X1,subspace_topology(X2,X3,X4),X5),X0,X6))),X3)
| ~ element_of_set(X6,X0)
| ~ element_of_collection(X0,top_of_basis(subspace_topology(X1,subspace_topology(X2,X3,X4),X5))) ) ).
cnf(u3463,axiom,
( ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,intersection_of_members(X4))
| ~ closed(intersection_of_members(X4),X1,X2)
| basis(closure(X0,X1,X2),X3)
| ~ element_of_collection(X5,X4)
| element_of_set(f7(closure(X0,X1,X2),X3),X5) ) ).
cnf(u258,axiom,
( subset_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X0)
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3) ) ).
cnf(u932,negated_conjecture,
( ~ closed(intersection_of_sets(X4,X5),X1,X2)
| ~ subset_sets(X0,intersection_of_sets(X4,X5))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| element_of_set(f20(closure(X0,X1,X2),X3),union_of_members(ct))
| ~ element_of_collection(X5,ct)
| ~ element_of_collection(X4,ct) ) ).
cnf(u3192,negated_conjecture,
( element_of_set(f20(boundary(X0,X1,X2),X3),f1(ct,f20(boundary(X0,X1,X2),X3)))
| ~ subset_sets(X0,empty_set)
| ~ closed(empty_set,X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u27814,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),union_of_members(X6))
| element_of_set(X5,f1(top_of_basis(X0),X5))
| ~ element_of_set(X5,cx)
| element_of_set(f11(X1,union_of_members(ct)),sF0) ) ).
cnf(u4483,axiom,
( element_of_collection(f12(X1,X2,X3,f12(X0,subspace_topology(X1,X2,X3),X4,f1(subspace_topology(X0,subspace_topology(X1,X2,X3),X4),X5))),X2)
| limit_point(X5,X6,X7,subspace_topology(X0,subspace_topology(X1,X2,X3),X4))
| ~ topological_space(X7,subspace_topology(X0,subspace_topology(X1,X2,X3),X4))
| ~ subset_sets(X6,X7) ) ).
cnf(u4869,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,f20(sF0,X0)),f24(f13(a,cx,ct,f20(sF0,X0)),X1)),sF0)
| basis(f13(a,cx,ct,f20(sF0,X0)),f24(f13(a,cx,ct,f20(sF0,X0)),X1))
| compact_space(f13(a,cx,ct,f20(sF0,X0)),X1)
| ~ topological_space(f13(a,cx,ct,f20(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0) ) ).
cnf(connected_space_89,axiom,
( ~ connected_space(X0,X1)
| topological_space(X0,X1) ) ).
cnf(u6378,axiom,
( element_of_collection(f12(X2,X3,X4,relative_complement_sets(f14(X0,X1,subspace_topology(X2,X3,X4),X5),X1)),X3)
| element_of_set(X5,f14(X0,X1,subspace_topology(X2,X3,X4),X6))
| element_of_set(X6,closure(X0,X1,subspace_topology(X2,X3,X4)))
| ~ topological_space(X1,subspace_topology(X2,X3,X4))
| ~ subset_sets(X0,X1) ) ).
cnf(u3415,axiom,
( ~ closed(f13(a,cx,ct,f19(sF0,X0)),X2,X3)
| ~ topological_space(sF0,X0)
| element_of_set(f19(boundary(X1,X2,X3),X4),union_of_members(ct))
| ~ topological_space(boundary(X1,X2,X3),X4)
| ~ subset_sets(X1,f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| hausdorff(boundary(X1,X2,X3),X4) ) ).
cnf(u3881,negated_conjecture,
( ~ element_of_set(X4,f13(a,cx,ct,f20(sF0,X3)))
| ~ topological_space(sF0,X3)
| hausdorff(sF0,X3)
| element_of_set(f11(subspace_topology(X0,X1,X2),f13(a,cx,ct,f20(sF0,X3))),sF0)
| topological_space(X0,X1) ) ).
cnf(u548,axiom,
( ~ subset_sets(f16(f11(X1,X0),X2,X3,X4),X0)
| ~ element_of_collection(f16(f11(X1,X0),X2,X3,X4),X1)
| element_of_collection(X0,top_of_basis(X1))
| ~ subset_sets(X2,X3)
| limit_point(f11(X1,X0),X2,X3,X4)
| ~ topological_space(X3,X4) ) ).
cnf(u3346,negated_conjecture,
( element_of_collection(f1(ct,f7(empty_set,X0)),ct)
| basis(empty_set,X0)
| ~ topological_space(empty_set,X0) ) ).
cnf(u6063,negated_conjecture,
( ~ element_of_set(X1,union_of_members(f24(X0,ct)))
| ~ topological_space(X0,ct)
| compact_space(X0,ct)
| element_of_set(X1,union_of_members(ct)) ) ).
cnf(u33595,negated_conjecture,
( element_of_set(f11(X4,union_of_members(top_of_basis(X0))),f1(top_of_basis(X4),f11(X4,union_of_members(top_of_basis(X0)))))
| open(f13(X1,X2,X3,f11(X0,union_of_members(ct))),X2,X3)
| ~ element_of_set(f11(X4,union_of_members(top_of_basis(X0))),cx) ) ).
cnf(u3872,negated_conjecture,
( ~ element_of_set(X2,f13(a,cx,ct,f19(sF0,X1)))
| ~ topological_space(sF0,X1)
| hausdorff(sF0,X1)
| element_of_set(f11(X0,f13(a,cx,ct,f19(sF0,X1))),sF0)
| element_of_set(X2,union_of_members(top_of_basis(X0))) ) ).
cnf(u3177,axiom,
( subset_sets(X0,f14(X0,X1,X2,f11(X6,f14(closure(X0,X1,X2),X3,X4,X5))))
| closed(f14(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4,X5),X3,X4)
| ~ subset_sets(relative_complement_sets(closure(X0,X1,X2),X3),X3)
| ~ subset_sets(closure(X0,X1,X2),X3)
| ~ topological_space(X3,X4)
| ~ element_of_collection(closure(X0,X1,X2),X6)
| element_of_collection(f14(closure(X0,X1,X2),X3,X4,X5),top_of_basis(X6))
| element_of_set(X5,boundary(closure(X0,X1,X2),X3,X4))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u1360,axiom,
( element_of_set(f20(sF1,X1),union_of_members(top_of_basis(X0)))
| element_of_set(f11(X0,sF3),sF3)
| hausdorff(sF1,X1)
| ~ topological_space(sF1,X1) ) ).
cnf(u5870,negated_conjecture,
( element_of_set(X0,f14(a,cx,ct,f11(X1,X2)))
| subset_sets(a,f14(a,cx,ct,X0))
| ~ element_of_collection(sF3,X1)
| element_of_collection(X2,top_of_basis(X1))
| ~ subset_sets(sF3,X2) ) ).
cnf(hausdorff_78,axiom,
( element_of_set(f20(X0,X1),X0)
| ~ topological_space(X0,X1)
| hausdorff(X0,X1) ) ).
cnf(u6363,axiom,
( element_of_set(f7(sF0,X0),union_of_members(ct))
| basis(sF0,X0)
| ~ topological_space(sF0,X0) ) ).
cnf(u210,negated_conjecture,
( element_of_set(X1,f14(a,cx,ct,X0))
| ~ element_of_set(X1,sF3)
| element_of_set(X0,sF3) ) ).
cnf(u3016,negated_conjecture,
( ~ element_of_set(X2,f13(a,cx,ct,f7(sF0,X0)))
| ~ topological_space(sF0,X0)
| element_of_set(f11(X1,f13(a,cx,ct,f7(sF0,X0))),sF0)
| ~ topological_space(cx,top_of_basis(X1))
| basis(sF0,X0)
| element_of_set(X2,interior(a,cx,top_of_basis(X1))) ) ).
cnf(u6027,negated_conjecture,
( element_of_set(X8,interior(f14(f13(X1,X2,X3,f20(closure(X4,X5,X6),X7)),cx,ct,X0),X2,X3))
| ~ subset_sets(f13(X1,X2,X3,f20(closure(X4,X5,X6),X7)),sF0)
| ~ subset_sets(f13(X1,X2,X3,f20(closure(X4,X5,X6),X7)),cx)
| ~ closed(interior(X1,X2,X3),X5,X6)
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7)
| ~ subset_sets(f14(f13(X1,X2,X3,f20(closure(X4,X5,X6),X7)),cx,ct,X0),X2)
| ~ element_of_set(X8,f13(X1,X2,X3,f20(closure(X4,X5,X6),X7)))
| ~ subset_sets(X4,interior(X1,X2,X3))
| element_of_set(X0,sF0) ) ).
cnf(u3081,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ closed(X7,X5,X6)
| ~ subset_sets(X4,X7)
| element_of_set(f11(X8,closure(X4,X5,X6)),X7)
| element_of_set(f19(boundary(X0,X1,X2),X3),union_of_members(top_of_basis(X8))) ) ).
cnf(u27763,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f13(X1,X2,X3,f11(X0,union_of_members(ct))))
| element_of_set(f11(X4,union_of_members(top_of_basis(X0))),interior(X5,X6,X7))
| element_of_set(X8,f1(top_of_basis(X4),X8))
| ~ element_of_set(X8,cx) ) ).
cnf(u500,axiom,
( ~ subset_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ subset_sets(X4,X1)
| ~ element_of_set(X5,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X5,interior(X4,X1,X2)) ) ).
cnf(u3924,axiom,
( closed(f14(X0,X1,X2,f11(X6,f14(closure(X0,X1,X2),X3,X4,f19(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5)))),X1,X2)
| ~ topological_space(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5)
| hausdorff(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5)
| ~ subset_sets(closure(X0,X1,X2),X3)
| ~ element_of_collection(closure(X0,X1,X2),X6)
| element_of_collection(f14(closure(X0,X1,X2),X3,X4,f19(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5)),top_of_basis(X6))
| element_of_set(f19(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),X5),boundary(closure(X0,X1,X2),X3,X4))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u1327,axiom,
( ~ element_of_set(X4,boundary(X1,X2,X3))
| element_of_set(X4,union_of_members(top_of_basis(X0)))
| element_of_set(f11(X0,closure(relative_complement_sets(X1,X2),X2,X3)),closure(relative_complement_sets(X1,X2),X2,X3)) ) ).
cnf(u2783,axiom,
( ~ closed(boundary(X0,X1,X2),cx,ct)
| ~ subset_sets(a,boundary(X0,X1,X2))
| element_of_collection(sF3,top_of_basis(X3))
| ~ subset_sets(X0,X4)
| ~ closed(X4,X1,X2)
| element_of_set(f11(X3,sF3),X4) ) ).
cnf(u2835,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),union_of_members(X3)),union_of_members(X3))
| limit_point(X4,X5,X6,X3)
| topological_space(X0,X1)
| ~ subset_sets(X5,X6)
| ~ topological_space(X6,X3) ) ).
cnf(u195,axiom,
( closed(f14(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2,X3),X1,X2)
| ~ subset_sets(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1)
| element_of_set(X3,boundary(relative_complement_sets(X0,X1),X1,X2))
| ~ element_of_set(X3,boundary(X0,X1,X2)) ) ).
cnf(u3747,axiom,
( ~ element_of_set(X7,boundary(X3,X4,X5))
| element_of_set(f11(subspace_topology(X0,X1,X2),closure(relative_complement_sets(X3,X4),X4,X5)),X6)
| ~ closed(X6,X4,X5)
| ~ subset_sets(relative_complement_sets(X3,X4),X6)
| topological_space(X0,X1) ) ).
cnf(u28637,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f13(X2,X3,X4,f11(X0,union_of_members(top_of_basis(X1)))))
| element_of_set(X5,f1(top_of_basis(X0),X5))
| ~ element_of_set(X5,cx)
| element_of_set(f11(X1,union_of_members(ct)),f1(ct,f11(X1,union_of_members(ct)))) ) ).
cnf(u2911,axiom,
( ~ closed(boundary(X3,X4,X5),X7,X8)
| element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),closure(X3,X4,X5))
| ~ subset_sets(X6,boundary(X3,X4,X5))
| topological_space(X0,X1)
| ~ topological_space(closure(X6,X7,X8),X9)
| hausdorff(closure(X6,X7,X8),X9) ) ).
cnf(u2422,axiom,
( element_of_set(f19(closure(X3,X1,X2),X5),union_of_members(top_of_basis(X4)))
| element_of_set(f11(X4,closure(X3,X1,X2)),X0)
| ~ subset_sets(X3,X0)
| ~ closed(X0,X1,X2)
| ~ topological_space(closure(X3,X1,X2),X5)
| hausdorff(closure(X3,X1,X2),X5) ) ).
cnf(u2935,negated_conjecture,
( ~ closed(f1(ct,X4),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f1(ct,X4))
| ~ element_of_set(X4,cx)
| element_of_set(f11(X0,boundary(X1,X2,X3)),union_of_members(ct)) ) ).
cnf(u323,axiom,
( open_covering(X3,intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X4)
| ~ subset_collections(X3,X4)
| ~ topological_space(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X4)
| ~ element_of_collection(union_of_members(X3),subspace_topology(X1,X2,X0)) ) ).
cnf(u3769,axiom,
( ~ topological_space(closure(X3,X4,X5),X7)
| element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),X6)
| ~ closed(X6,X4,X5)
| ~ subset_sets(X3,X6)
| topological_space(X0,X1)
| hausdorff(closure(X3,X4,X5),X7) ) ).
cnf(u4608,axiom,
( ~ element_of_collection(X2,X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| topological_space(X3,X4)
| element_of_set(f11(subspace_topology(X3,X4,X5),X2),X2) ) ).
cnf(u3491,negated_conjecture,
( ~ closed(f13(a,cx,ct,f20(sF0,X4)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f20(sF0,X4)))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| element_of_set(f7(closure(X0,X1,X2),X3),sF0)
| ~ topological_space(sF0,X4)
| hausdorff(sF0,X4) ) ).
cnf(u2712,axiom,
( element_of_set(X2,f10(X0,f1(top_of_basis(X0),f19(union_of_members(top_of_basis(X0)),X1)),X2))
| ~ topological_space(union_of_members(top_of_basis(X0)),X1)
| ~ element_of_set(X2,f1(top_of_basis(X0),f19(union_of_members(top_of_basis(X0)),X1)))
| hausdorff(union_of_members(top_of_basis(X0)),X1) ) ).
cnf(u670,axiom,
( ~ element_of_set(f11(X3,boundary(relative_complement_sets(X0,X1),X1,X2)),closure(X0,X1,X2))
| element_of_collection(boundary(relative_complement_sets(X0,X1),X1,X2),top_of_basis(X3))
| element_of_set(f11(X3,boundary(relative_complement_sets(X0,X1),X1,X2)),boundary(X0,X1,X2)) ) ).
cnf(u3198,axiom,
( ~ closed(relative_complement_sets(X4,X5),X1,X2)
| ~ subset_sets(X0,relative_complement_sets(X4,X5))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ closed(X4,X5,X6)
| element_of_set(f20(boundary(X0,X1,X2),X3),union_of_members(X6)) ) ).
cnf(u3052,negated_conjecture,
( ~ closed(intersection_of_sets(X4,X5),X1,X2)
| ~ subset_sets(X0,intersection_of_sets(X4,X5))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f19(boundary(X0,X1,X2),X3),union_of_members(ct))
| ~ element_of_collection(X5,ct)
| ~ element_of_collection(X4,ct) ) ).
cnf(compact_space_101,axiom,
( finite(f23(X0,X1,X2))
| ~ open_covering(X2,X0,X1)
| ~ compact_space(X0,X1) ) ).
cnf(u767,axiom,
( element_of_collection(f16(X0,X1,X2,subspace_topology(X3,X4,X5)),subspace_topology(X6,X4,X5))
| ~ topological_space(X2,subspace_topology(X3,X4,X5))
| ~ subset_sets(X1,X2)
| ~ topological_space(X6,X4)
| ~ subset_sets(X5,X6)
| limit_point(X0,X1,X2,subspace_topology(X3,X4,X5)) ) ).
cnf(u1363,axiom,
( ~ subset_sets(X5,f6(X1,X3,X0,X2,X4))
| ~ element_of_collection(X2,X3)
| ~ element_of_collection(X4,X3)
| ~ element_of_set(X0,intersection_of_sets(X2,X4))
| ~ basis(X1,X3)
| ~ element_of_collection(X5,X6)
| ~ topological_space(intersection_of_sets(X2,X4),X6)
| ~ element_of_set(X7,X5)
| ~ element_of_set(X0,X1)
| element_of_set(X7,interior(f6(X1,X3,X0,X2,X4),intersection_of_sets(X2,X4),X6)) ) ).
cnf(u1013,axiom,
( element_of_set(f20(sF3,X0),closure(X1,X2,X3))
| ~ subset_sets(a,boundary(X1,X2,X3))
| ~ closed(boundary(X1,X2,X3),cx,ct)
| ~ topological_space(sF3,X0)
| hausdorff(sF3,X0) ) ).
cnf(u53858,negated_conjecture,
( element_of_set(X7,f13(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,X6),X1,X2,X7))
| element_of_set(X6,closure(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5))
| hausdorff(interior(X0,X1,X2),X3)
| ~ element_of_set(X7,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3))) ) ).
cnf(u544,axiom,
( ~ subset_sets(closure(X2,X3,X4),X0)
| ~ element_of_collection(closure(X2,X3,X4),X1)
| element_of_collection(X0,top_of_basis(X1))
| closed(f14(X2,X3,X4,f11(X1,X0)),X3,X4)
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4) ) ).
cnf(u6439,axiom,
( element_of_set(f11(subspace_topology(X1,X4,X0),closure(X5,X2,X3)),sF3)
| element_of_collection(boundary(X5,X2,X3),top_of_basis(X6))
| ~ closed(sF1,X2,X3)
| ~ subset_sets(X5,sF1)
| subset_sets(X0,X1) ) ).
cnf(u458,axiom,
( ~ topological_space(boundary(X0,X1,X2),X3)
| basis(boundary(X0,X1,X2),X3)
| topological_space(X1,X2) ) ).
cnf(u3492,negated_conjecture,
( ~ closed(f13(a,cx,ct,f20(closure(X4,X5,X6),X7)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f20(closure(X4,X5,X6),X7)))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ closed(sF0,X5,X6)
| ~ subset_sets(X4,sF0)
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7)
| element_of_set(f7(closure(X0,X1,X2),X3),sF0) ) ).
cnf(u1141,axiom,
( ~ element_of_set(X7,f13(X0,X1,X2,f19(closure(X5,X3,X4),X6)))
| ~ topological_space(closure(X5,X3,X4),X6)
| hausdorff(closure(X5,X3,X4),X6)
| ~ closed(interior(X0,X1,X2),X3,X4)
| ~ subset_sets(X5,interior(X0,X1,X2))
| element_of_set(X7,interior(X0,X1,X2)) ) ).
cnf(u5734,axiom,
( element_of_set(f11(X5,boundary(relative_complement_sets(X2,X3),X3,subspace_topology(X1,X4,X0))),boundary(X2,X3,subspace_topology(X1,X4,X0)))
| ~ subset_sets(X2,X3)
| element_of_collection(boundary(relative_complement_sets(X2,X3),X3,subspace_topology(X1,X4,X0)),top_of_basis(X5))
| subset_sets(X0,X1) ) ).
cnf(u3314,axiom,
( element_of_set(f11(X0,closure(X1,X2,X3)),union_of_members(top_of_basis(X5)))
| subset_sets(X1,f14(X1,X2,X3,X4))
| element_of_set(X4,union_of_members(top_of_basis(X0)))
| ~ subset_sets(X1,sF1)
| ~ subset_sets(X1,X2)
| element_of_set(f11(X5,sF3),sF3)
| ~ closed(sF1,X2,X3) ) ).
cnf(u3420,axiom,
( element_of_set(f19(sF0,X0),union_of_members(ct))
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0) ) ).
cnf(u4919,axiom,
( closed(f14(X2,X3,X4,X0),X3,X4)
| element_of_set(f11(X1,closure(X2,X3,X4)),sF3)
| element_of_collection(f1(top_of_basis(X1),X0),top_of_basis(X1))
| ~ subset_sets(X2,sF1)
| ~ subset_sets(X2,X3)
| ~ closed(sF1,X3,X4) ) ).
cnf(hausdorff_74,axiom,
( neighborhood(f17(X0,X1,X2,X3),X2,X0,X1)
| ~ element_of_set(X2,X0)
| ~ element_of_set(X3,X0)
| eq_p(X2,X3)
| ~ hausdorff(X0,X1) ) ).
cnf(u2350,negated_conjecture,
( element_of_collection(union_of_members(f24(X0,ct)),ct)
| compact_space(X0,ct)
| ~ topological_space(X0,ct) ) ).
cnf(u30132,negated_conjecture,
( element_of_set(f11(X0,f1(ct,X1)),sF0)
| element_of_set(X1,f1(top_of_basis(X0),X1))
| ~ element_of_set(X1,sF0) ) ).
cnf(u7956,negated_conjecture,
( element_of_set(f19(X0,X1),union_of_members(X2))
| hausdorff(X0,X1) ) ).
cnf(u4669,axiom,
( ~ element_of_collection(f16(X2,X3,X4,X5),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ topological_space(X4,X5)
| ~ subset_sets(X3,X4)
| limit_point(X2,X3,X4,X5)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X5)) ) ).
cnf(u3839,axiom,
( ~ closed(f2(X1,X0),X3,X4)
| element_of_set(f19(boundary(X2,X3,X4),X5),union_of_members(X1))
| ~ topological_space(boundary(X2,X3,X4),X5)
| ~ subset_sets(X2,f2(X1,X0))
| element_of_set(X0,intersection_of_members(X1))
| hausdorff(boundary(X2,X3,X4),X5) ) ).
cnf(u58891,negated_conjecture,
( open(f13(a,cx,subspace_topology(X0,X1,f13(a,X2,X3,f20(interior(a,X2,X3),X4))),X5),cx,subspace_topology(X0,X1,f13(a,X2,X3,f20(interior(a,X2,X3),X4))))
| hausdorff(interior(a,X2,X3),X4)
| ~ element_of_set(X5,f13(a,X2,X3,f20(interior(a,X2,X3),X4))) ) ).
cnf(u2956,negated_conjecture,
( ~ closed(f13(a,cx,ct,f7(sF0,X4)),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f13(a,cx,ct,f7(sF0,X4)))
| element_of_set(f11(X0,boundary(X1,X2,X3)),sF0)
| basis(sF0,X4)
| ~ topological_space(sF0,X4) ) ).
cnf(u4713,axiom,
( closed(f14(f13(f14(X0,X1,X2,X3),X4,X5,f20(closure(X6,X7,X8),X9)),X1,X2,X10),X1,X2)
| ~ subset_sets(f13(f14(X0,X1,X2,X3),X4,X5,f20(closure(X6,X7,X8),X9)),X1)
| element_of_set(X10,f14(X0,X1,X2,X3))
| element_of_set(X3,closure(X0,X1,X2))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| ~ subset_sets(X6,interior(f14(X0,X1,X2,X3),X4,X5))
| ~ closed(interior(f14(X0,X1,X2,X3),X4,X5),X7,X8)
| ~ topological_space(closure(X6,X7,X8),X9)
| hausdorff(closure(X6,X7,X8),X9) ) ).
cnf(u2810,axiom,
( ~ subset_sets(f13(X0,X1,X2,f11(X6,closure(X5,X3,X4))),X7)
| ~ subset_sets(X5,interior(X0,X1,X2))
| element_of_collection(closure(X5,X3,X4),top_of_basis(X6))
| ~ subset_sets(X7,X1)
| ~ element_of_set(X8,f13(X0,X1,X2,f11(X6,closure(X5,X3,X4))))
| ~ closed(interior(X0,X1,X2),X3,X4)
| element_of_set(X8,interior(X7,X1,X2)) ) ).
cnf(u5141,axiom,
( ~ element_of_set(f11(X3,f14(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5,f11(X6,f14(closure(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5),X7,X8,X9)))),boundary(X0,X1,X2))
| element_of_collection(f14(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5,f11(X6,f14(closure(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5),X7,X8,X9))),top_of_basis(X3))
| ~ element_of_collection(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_collection(f14(closure(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5),X7,X8,X9),top_of_basis(X6))
| ~ element_of_collection(closure(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5),X6)
| ~ subset_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4)
| ~ topological_space(X4,X5)
| element_of_set(X9,closure(closure(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5),X7,X8))
| ~ subset_sets(closure(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5),X7)
| ~ topological_space(X7,X8) ) ).
cnf(u36136,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| element_of_set(f11(X1,f1(ct,X0)),sF0) ) ).
cnf(u4711,axiom,
( closed(f14(f13(f14(X0,X1,X2,X3),X4,X5,f19(closure(X6,X7,X8),X9)),X1,X2,X10),X1,X2)
| ~ subset_sets(f13(f14(X0,X1,X2,X3),X4,X5,f19(closure(X6,X7,X8),X9)),X1)
| element_of_set(X10,f14(X0,X1,X2,X3))
| element_of_set(X3,closure(X0,X1,X2))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| ~ subset_sets(X6,interior(f14(X0,X1,X2,X3),X4,X5))
| ~ closed(interior(f14(X0,X1,X2,X3),X4,X5),X7,X8)
| ~ topological_space(closure(X6,X7,X8),X9)
| hausdorff(closure(X6,X7,X8),X9) ) ).
cnf(u545,axiom,
( ~ subset_sets(closure(X2,X3,X4),X0)
| ~ element_of_collection(closure(X2,X3,X4),X1)
| element_of_collection(X0,top_of_basis(X1))
| subset_sets(X2,f14(X2,X3,X4,f11(X1,X0)))
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4) ) ).
cnf(u187,negated_conjecture,
( ~ element_of_set(X0,f13(a,cx,ct,X1))
| element_of_set(X0,sF0)
| ~ element_of_set(X1,sF0) ) ).
cnf(u5138,axiom,
( ~ element_of_set(f11(X3,f14(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5,X6)),boundary(X0,X1,X2))
| element_of_collection(f14(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5,X6),top_of_basis(X3))
| ~ element_of_collection(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| closed(f14(relative_complement_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4),X4,X5,X6),X4,X5)
| element_of_set(X6,boundary(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5))
| ~ subset_sets(relative_complement_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4),X4)
| ~ subset_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4)
| ~ topological_space(X4,X5) ) ).
cnf(u45012,negated_conjecture,
( open(f13(f14(relative_complement_sets(X1,X2),X4,X5,X6),X2,X3,X0),X2,X3)
| element_of_set(X6,closure(relative_complement_sets(X1,X2),X4,X5))
| ~ element_of_set(X0,relative_complement_sets(X1,X2)) ) ).
cnf(u3093,axiom,
( ~ closed(f22(X4,X5),X1,X2)
| ~ subset_sets(X0,f22(X4,X5))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(X4,X5)
| connected_space(X4,X5)
| element_of_set(f19(boundary(X0,X1,X2),X3),union_of_members(X5)) ) ).
cnf(u4005,axiom,
( ~ closed(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X8,X9)
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| element_of_set(f7(closure(X7,X8,X9),X10),interior(X4,X5,X6))
| ~ topological_space(closure(X7,X8,X9),X10)
| ~ subset_sets(X7,f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X7,X8,X9),X10) ) ).
cnf(u27939,negated_conjecture,
( open(f13(X4,X5,X6,f11(X7,union_of_members(top_of_basis(X0)))),X5,X6)
| element_of_set(f11(X0,union_of_members(ct)),union_of_members(X9))
| element_of_set(X8,f1(top_of_basis(X7),X8))
| ~ element_of_set(X8,cx) ) ).
cnf(u2907,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),f13(X3,X4,X5,f20(interior(X3,X4,X5),X6))),f13(X3,X4,X5,f20(interior(X3,X4,X5),X6)))
| topological_space(X0,X1)
| hausdorff(interior(X3,X4,X5),X6)
| ~ topological_space(interior(X3,X4,X5),X6) ) ).
cnf(u315,axiom,
( ~ element_of_set(f19(boundary(relative_complement_sets(X0,X1),X1,X2),X3),closure(X0,X1,X2))
| ~ topological_space(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| hausdorff(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f19(boundary(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2)) ) ).
cnf(u53265,negated_conjecture,
( open(f13(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),cx,ct,X4),X1,X2,X5),X1,X2)
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X4,sF0)
| ~ element_of_set(X5,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3))) ) ).
cnf(u6424,axiom,
( closed(f14(X1,X2,X3,X4),X2,X3)
| element_of_set(f11(X6,closure(X1,X2,X3)),X5)
| element_of_set(X4,f14(X1,X2,X3,X0))
| element_of_set(X0,union_of_members(top_of_basis(X6)))
| ~ subset_sets(X1,X5)
| ~ closed(X5,X2,X3)
| ~ subset_sets(X1,X2) ) ).
cnf(u792,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,f11(X0,sF0)),X1),sF0)
| element_of_collection(sF0,top_of_basis(X0))
| basis(f13(a,cx,ct,f11(X0,sF0)),X1)
| ~ topological_space(f13(a,cx,ct,f11(X0,sF0)),X1) ) ).
cnf(u534,axiom,
( element_of_collection(f13(a,cx,ct,f20(sF0,X0)),ct)
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0) ) ).
cnf(u940,negated_conjecture,
( ~ closed(f13(a,cx,ct,X4),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,X4))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| element_of_set(f20(closure(X0,X1,X2),X3),sF0)
| ~ element_of_set(X4,sF0) ) ).
cnf(u9850,negated_conjecture,
( eq_p(X0,f20(boundary(X1,X2,X3),X4))
| ~ element_of_set(X0,sF1)
| hausdorff(boundary(X1,X2,X3),X4) ) ).
cnf(u666,axiom,
( ~ subset_sets(closure(X0,X1,X2),boundary(X0,X1,X2))
| ~ element_of_collection(closure(X0,X1,X2),X3)
| element_of_collection(boundary(X0,X1,X2),top_of_basis(X3)) ) ).
cnf(u5829,negated_conjecture,
( element_of_set(X1,f14(a,cx,ct,f11(X0,closure(relative_complement_sets(a,cx),cx,ct))))
| element_of_collection(closure(relative_complement_sets(a,cx),cx,ct),top_of_basis(X0))
| ~ element_of_set(X1,sF3)
| element_of_set(f11(X0,closure(relative_complement_sets(a,cx),cx,ct)),sF1) ) ).
cnf(open_covering_97,axiom,
( ~ open_covering(X0,X1,X2)
| subset_collections(X0,X2) ) ).
cnf(u3445,axiom,
( ~ closed(f13(a,cx,ct,f20(sF0,X0)),X2,X3)
| ~ topological_space(sF0,X0)
| element_of_set(f19(boundary(X1,X2,X3),X4),union_of_members(ct))
| ~ topological_space(boundary(X1,X2,X3),X4)
| ~ subset_sets(X1,f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| hausdorff(boundary(X1,X2,X3),X4) ) ).
cnf(u4690,axiom,
( ~ subset_sets(X4,f14(X0,X1,X2,f20(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f20(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1)
| ~ subset_sets(X4,X1)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| closed(f14(X4,X1,X2,X5),X1,X2)
| element_of_set(X5,f14(X0,X1,X2,f20(closure(relative_complement_sets(X0,X1),X1,X2),X3))) ) ).
cnf(u3048,negated_conjecture,
( element_of_set(f19(boundary(X0,X1,X2),X3),f1(ct,f19(boundary(X0,X1,X2),X3)))
| ~ subset_sets(X0,empty_set)
| ~ closed(empty_set,X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u3880,negated_conjecture,
( ~ element_of_set(X4,f13(a,cx,ct,f20(sF0,X3)))
| ~ topological_space(sF0,X3)
| hausdorff(sF0,X3)
| element_of_set(f11(subspace_topology(X0,X1,X2),f13(a,cx,ct,f20(sF0,X3))),sF0)
| subset_sets(X2,X0) ) ).
cnf(u53266,negated_conjecture,
( element_of_set(X5,f13(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),cx,ct,X4),X1,X2,X5))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X4,sF0)
| ~ element_of_set(X5,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3))) ) ).
cnf(u1228,axiom,
( ~ closed(f16(X3,X2,X0,X1),X6,X7)
| ~ subset_sets(X2,X0)
| limit_point(X3,X2,X0,X1)
| element_of_set(f11(X4,closure(X5,X6,X7)),union_of_members(X1))
| element_of_collection(closure(X5,X6,X7),top_of_basis(X4))
| ~ topological_space(X0,X1)
| ~ subset_sets(X5,f16(X3,X2,X0,X1)) ) ).
cnf(u54639,negated_conjecture,
( ~ element_of_set(X0,f13(a,cx,ct,f20(sF0,X1)))
| hausdorff(sF0,X1)
| element_of_set(X0,f13(f14(f13(a,cx,ct,f20(sF0,X1)),X2,X3,X4),cx,ct,X0))
| element_of_set(X4,interior(X5,X6,X7)) ) ).
cnf(u3485,axiom,
( ~ closed(f13(a,cx,ct,f19(sF0,X4)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f19(sF0,X4)))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| hausdorff(sF0,X4)
| ~ topological_space(sF0,X4)
| element_of_set(f7(closure(X0,X1,X2),X3),union_of_members(ct)) ) ).
cnf(u6782,axiom,
closed(X0,X1,X2) ).
cnf(u4033,axiom,
( ~ closed(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X8,X9)
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| element_of_set(f19(closure(X7,X8,X9),X10),interior(X4,X5,X6))
| hausdorff(closure(X7,X8,X9),X10)
| ~ subset_sets(X7,f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)))
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X7,X8,X9),X10) ) ).
cnf(u4449,axiom,
( element_of_collection(f12(X2,X3,X4,f12(X1,subspace_topology(X2,X3,X4),X5,f2(subspace_topology(X1,subspace_topology(X2,X3,X4),X5),X0))),X3)
| element_of_set(X0,intersection_of_members(subspace_topology(X1,subspace_topology(X2,X3,X4),X5))) ) ).
cnf(u1286,axiom,
( ~ closed(boundary(X1,X2,X3),X6,X7)
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(X4,closure(X5,X6,X7)),union_of_members(top_of_basis(X0)))
| element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| ~ subset_sets(X5,boundary(X1,X2,X3))
| element_of_collection(closure(X5,X6,X7),top_of_basis(X4)) ) ).
cnf(separation_86,axiom,
( ~ separation(X0,X1,X2,X3)
| equal_sets(union_of_sets(X0,X1),X2) ) ).
cnf(u6710,negated_conjecture,
( ~ element_of_set(X1,X2)
| element_of_set(X1,interior(a,cx,X0)) ) ).
cnf(u5118,negated_conjecture,
( element_of_set(f11(X3,f14(a,cx,ct,X1)),f14(a,cx,ct,X1))
| element_of_set(f11(X0,f14(a,cx,ct,X1)),union_of_members(top_of_basis(X3)))
| element_of_set(X2,union_of_members(top_of_basis(X0)))
| element_of_set(X1,sF3)
| ~ element_of_set(X2,sF3) ) ).
cnf(u29187,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f1(X2,f11(X0,union_of_members(top_of_basis(X1)))))
| element_of_set(X3,f1(top_of_basis(X0),X3))
| ~ element_of_set(X3,cx)
| element_of_set(f11(X1,union_of_members(ct)),union_of_members(ct)) ) ).
cnf(u6093,axiom,
( ~ element_of_collection(f13(sF3,X2,X3,f19(interior(sF3,X2,X3),X4)),X0)
| ~ element_of_set(X1,f13(sF3,X2,X3,f19(interior(sF3,X2,X3),X4)))
| ~ topological_space(sF1,X0)
| element_of_set(X1,interior(sF3,sF1,X0))
| hausdorff(interior(sF3,X2,X3),X4)
| ~ topological_space(interior(sF3,X2,X3),X4) ) ).
cnf(u429,axiom,
( ~ subset_sets(X1,f13(a,cx,ct,f20(sF0,X0)))
| ~ topological_space(sF0,X0)
| ~ element_of_collection(X1,X2)
| ~ topological_space(a,X2)
| ~ element_of_set(X3,X1)
| hausdorff(sF0,X0)
| element_of_set(X3,interior(f13(a,cx,ct,f20(sF0,X0)),a,X2)) ) ).
cnf(u6916,negated_conjecture,
( element_of_set(f19(interior(X0,X1,X2),X3),interior(X4,X5,X6))
| hausdorff(interior(X0,X1,X2),X3) ) ).
cnf(u36142,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| open(f13(X4,X5,X6,f11(X1,union_of_members(ct))),X5,X6) ) ).
cnf(u1126,axiom,
( ~ closed(boundary(X1,X2,X3),X4,X5)
| ~ subset_sets(X0,boundary(X1,X2,X3))
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| ~ subset_sets(X1,X7)
| ~ closed(X7,X2,X3)
| element_of_set(f19(closure(X0,X4,X5),X6),X7) ) ).
cnf(u978,axiom,
( ~ element_of_collection(f13(f13(a,cx,ct,X1),X2,X3,f20(closure(X0,X4,X5),X6)),X7)
| ~ closed(interior(f13(a,cx,ct,X1),X2,X3),X4,X5)
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| ~ subset_sets(X0,interior(f13(a,cx,ct,X1),X2,X3))
| ~ topological_space(a,X7)
| ~ element_of_set(X8,f13(f13(a,cx,ct,X1),X2,X3,f20(closure(X0,X4,X5),X6)))
| ~ element_of_set(X1,sF0)
| element_of_set(X8,interior(f13(a,cx,ct,X1),a,X7)) ) ).
cnf(u6646,negated_conjecture,
( element_of_set(f20(boundary(X0,X1,X2),X3),sF0)
| ~ closed(sF3,X1,X2)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u557,axiom,
( element_of_set(X4,interior(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,X3),cx,ct))
| ~ subset_sets(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,X3),cx)
| ~ element_of_set(X4,f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| ~ topological_space(sF0,X0)
| element_of_set(X3,closure(f13(a,cx,ct,f19(sF0,X0)),X1,X2))
| ~ subset_sets(f13(a,cx,ct,f19(sF0,X0)),X1)
| ~ topological_space(X1,X2) ) ).
cnf(boundary_71,axiom,
( element_of_set(X0,closure(relative_complement_sets(X1,X2),X2,X3))
| ~ element_of_set(X0,boundary(X1,X2,X3)) ) ).
cnf(u3037,axiom,
( ~ topological_space(boundary(X0,X1,X2),X3)
| ~ subset_sets(X0,X4)
| ~ closed(X4,X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| topological_space(X5,X6)
| element_of_set(f11(subspace_topology(X5,X6,X7),X4),X4) ) ).
cnf(u2611,axiom,
( element_of_set(f11(X7,f13(X1,X2,X3,f20(closure(X0,X4,X5),X6))),f13(X1,X2,X3,f20(closure(X0,X4,X5),X6)))
| ~ closed(interior(X1,X2,X3),X4,X5)
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| ~ subset_sets(X0,interior(X1,X2,X3))
| element_of_set(f20(closure(X0,X4,X5),X6),union_of_members(top_of_basis(X7))) ) ).
cnf(u17780,negated_conjecture,
( eq_p(f20(intersection_of_members(X0),X1),X2)
| hausdorff(intersection_of_members(X0),X1)
| ~ element_of_set(X2,sF3) ) ).
cnf(u5131,axiom,
( ~ element_of_set(X6,f12(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5,f8(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))))
| basis(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| ~ topological_space(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| topological_space(X2,X3) ) ).
cnf(u36088,negated_conjecture,
( open(f13(X4,X5,X6,f11(X7,union_of_members(ct))),X5,X6)
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| element_of_set(f11(X1,union_of_members(top_of_basis(X7))),sF0)
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u914,axiom,
( ~ element_of_set(X4,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3)
| element_of_set(X4,union_of_members(X2)) ) ).
cnf(u4046,axiom,
( ~ subset_sets(X4,f14(relative_complement_sets(X0,X1),X1,X3,X2))
| element_of_set(X2,boundary(X0,X1,X3))
| closed(f14(X0,X1,X3,X2),X1,X3)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X3)
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| element_of_set(X5,f14(relative_complement_sets(X0,X1),X1,X3,X2))
| subset_sets(X4,f14(X4,X1,X3,X5))
| ~ subset_sets(X4,X1) ) ).
cnf(u4405,axiom,
( ~ closed(f10(X1,X0,X2),X4,X5)
| ~ element_of_set(X2,X0)
| element_of_set(f19(boundary(X3,X4,X5),X6),union_of_members(X1))
| ~ topological_space(boundary(X3,X4,X5),X6)
| ~ subset_sets(X3,f10(X1,X0,X2))
| ~ element_of_collection(X0,top_of_basis(X1))
| hausdorff(boundary(X3,X4,X5),X6) ) ).
cnf(u7673,negated_conjecture,
( element_of_set(X0,union_of_members(X1))
| limit_point(X0,X5,X6,X7) ) ).
cnf(u16462,negated_conjecture,
( ~ element_of_set(X5,closure(X0,X1,X2))
| eq_p(f19(intersection_of_members(X3),X4),X5)
| hausdorff(intersection_of_members(X3),X4) ) ).
cnf(u3376,axiom,
( ~ subset_sets(X1,f13(a,cx,ct,f11(X0,sF0)))
| ~ element_of_collection(X1,X2)
| ~ topological_space(a,X2)
| ~ element_of_set(X3,X1)
| element_of_collection(sF0,top_of_basis(X0))
| element_of_set(X3,interior(f13(a,cx,ct,f11(X0,sF0)),a,X2)) ) ).
cnf(u5344,axiom,
( ~ element_of_set(f19(boundary(X2,X3,X4),X5),X0)
| ~ open(X1,boundary(X2,X3,X4),X5)
| hausdorff(boundary(X2,X3,X4),X5)
| ~ open(X0,boundary(X2,X3,X4),X5)
| ~ disjoint_s(X0,X1)
| ~ subset_sets(X2,X1)
| ~ closed(X1,X3,X4) ) ).
cnf(u804,axiom,
( element_of_collection(intersection_of_sets(X3,X4),subspace_topology(X1,X2,X0))
| ~ element_of_collection(X3,subspace_topology(X1,X2,X0))
| ~ element_of_collection(X4,subspace_topology(X1,X2,X0))
| ~ connected_set(X0,X1,X2) ) ).
cnf(u6322,axiom,
( ~ subset_sets(closure(X2,X3,X4),X1)
| element_of_set(X5,f14(X2,X3,X4,f11(X0,X1)))
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4)
| element_of_collection(X1,top_of_basis(X0))
| ~ element_of_collection(closure(X2,X3,X4),X0)
| subset_sets(X2,f14(X2,X3,X4,X5)) ) ).
cnf(u530,axiom,
( element_of_set(f19(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),interior(X0,X1,X2))
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ topological_space(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4)
| hausdorff(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4) ) ).
cnf(u936,axiom,
( subset_sets(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X4)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3) ) ).
cnf(u6442,axiom,
( element_of_set(f11(subspace_topology(X1,X4,X0),closure(X5,X2,X3)),sF3)
| element_of_collection(closure(X5,X2,X3),top_of_basis(X6))
| ~ closed(sF1,X2,X3)
| ~ subset_sets(X5,sF1)
| subset_sets(X0,X1) ) ).
cnf(u4002,axiom,
( element_of_set(f7(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X7),interior(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X7)
| ~ topological_space(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X7) ) ).
cnf(u36094,negated_conjecture,
( element_of_set(f11(X1,union_of_members(top_of_basis(X4))),interior(X5,X6,X7))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| element_of_set(f11(X4,union_of_members(ct)),sF0)
| ~ element_of_set(X0,cx) ) ).
cnf(u873,axiom,
( ~ closed(X0,cx,ct)
| ~ subset_sets(X0,sF3)
| ~ subset_sets(a,X0)
| ~ element_of_collection(X0,X1)
| element_of_collection(sF3,top_of_basis(X1)) ) ).
cnf(u647,axiom,
( element_of_set(f11(X0,closure(X1,X2,X3)),X4)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ closed(X4,X2,X3)
| ~ subset_sets(X1,X4) ) ).
cnf(u3919,axiom,
( element_of_set(X4,interior(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,f19(closure(relative_complement_sets(f13(a,cx,ct,f20(sF0,X0)),X1),X1,X2),X3)),cx,ct))
| ~ topological_space(closure(relative_complement_sets(f13(a,cx,ct,f20(sF0,X0)),X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(f13(a,cx,ct,f20(sF0,X0)),X1),X1,X2),X3)
| ~ subset_sets(f13(a,cx,ct,f20(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| ~ subset_sets(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,f19(closure(relative_complement_sets(f13(a,cx,ct,f20(sF0,X0)),X1),X1,X2),X3)),cx)
| ~ element_of_set(X4,f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(f19(closure(relative_complement_sets(f13(a,cx,ct,f20(sF0,X0)),X1),X1,X2),X3),boundary(f13(a,cx,ct,f20(sF0,X0)),X1,X2)) ) ).
cnf(u6126,negated_conjecture,
( element_of_set(f20(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X4),sF0)
| ~ closed(sF0,X1,X2)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X3))
| ~ subset_sets(X0,sF0)
| ~ topological_space(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X4)
| hausdorff(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X4) ) ).
cnf(u1090,axiom,
( ~ closed(f21(X4,X5),X1,X2)
| ~ subset_sets(X0,f21(X4,X5))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(X4,X5)
| connected_space(X4,X5)
| element_of_set(f19(closure(X0,X1,X2),X3),union_of_members(X5)) ) ).
cnf(u271,axiom,
( element_of_set(f19(sF1,X0),sF3)
| hausdorff(sF1,X0)
| ~ topological_space(sF1,X0) ) ).
cnf(u7153,negated_conjecture,
( eq_p(f20(closure(X0,X5,X6),X7),X1)
| limit_point(X1,X2,X3,X4)
| hausdorff(closure(X0,X5,X6),X7) ) ).
cnf(u466,axiom,
( element_of_collection(union_of_sets(f21(intersection_of_sets(X0,X1),X2),f22(intersection_of_sets(X0,X1),X2)),subspace_topology(X3,X4,X0))
| ~ topological_space(intersection_of_sets(X0,X1),X2)
| ~ topological_space(X3,X4)
| ~ subset_sets(X0,X3)
| ~ element_of_collection(X1,X4)
| connected_space(intersection_of_sets(X0,X1),X2) ) ).
cnf(u4862,axiom,
( element_of_set(f7(f13(a,cx,ct,f19(sF0,X0)),f24(f13(a,cx,ct,f19(sF0,X0)),X1)),union_of_members(ct))
| basis(f13(a,cx,ct,f19(sF0,X0)),f24(f13(a,cx,ct,f19(sF0,X0)),X1))
| compact_space(f13(a,cx,ct,f19(sF0,X0)),X1)
| hausdorff(sF0,X0)
| ~ topological_space(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f19(sF0,X0)),X1) ) ).
cnf(u3961,negated_conjecture,
( element_of_set(f20(f1(ct,f15(X1,X4,X2,X3,X0)),X5),union_of_members(ct))
| ~ limit_point(X1,X4,X2,X3)
| ~ element_of_collection(X4,ct)
| ~ element_of_collection(X0,ct)
| ~ neighborhood(X0,X1,X2,X3)
| ~ topological_space(f1(ct,f15(X1,X4,X2,X3,X0)),X5)
| hausdorff(f1(ct,f15(X1,X4,X2,X3,X0)),X5) ) ).
cnf(u29392,axiom,
( ~ subset_collections(f24(X2,f24(X0,X1)),X1)
| ~ finite(f24(X2,f24(X0,X1)))
| compact_space(X2,f24(X0,X1))
| compact_space(X0,X1) ) ).
cnf(u977,axiom,
( ~ element_of_set(f7(X1,X2),f13(intersection_of_sets(f8(X1,X2),f9(X1,X2)),X3,X4,f20(closure(X0,X5,X6),X7)))
| ~ closed(interior(intersection_of_sets(f8(X1,X2),f9(X1,X2)),X3,X4),X5,X6)
| ~ topological_space(closure(X0,X5,X6),X7)
| hausdorff(closure(X0,X5,X6),X7)
| ~ equal_sets(union_of_members(X2),X1)
| ~ subset_sets(X0,interior(intersection_of_sets(f8(X1,X2),f9(X1,X2)),X3,X4))
| ~ element_of_collection(f13(intersection_of_sets(f8(X1,X2),f9(X1,X2)),X3,X4,f20(closure(X0,X5,X6),X7)),X2)
| basis(X1,X2) ) ).
cnf(separation_82,axiom,
( ~ separation(X0,X1,X2,X3)
| ~ equal_sets(X0,empty_set) ) ).
cnf(u6383,axiom,
( element_of_set(f11(X5,f14(X1,X2,X3,X4)),f14(X1,X2,X3,X4))
| closed(f14(X1,X2,X3,X0),X2,X3)
| element_of_set(X0,union_of_members(top_of_basis(X5)))
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| element_of_set(X4,closure(X1,X2,X3)) ) ).
cnf(u6435,axiom,
( ~ topological_space(boundary(X5,X2,X3),X6)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X1,X4,X0),closure(X5,X2,X3)),sF3)
| ~ subset_sets(X5,sF1)
| subset_sets(X0,X1)
| basis(boundary(X5,X2,X3),X6) ) ).
cnf(u5954,axiom,
( basis(boundary(X0,X1,X2),f24(boundary(X0,X1,X2),X3))
| ~ topological_space(boundary(X0,X1,X2),X3)
| subset_sets(X0,X1)
| compact_space(boundary(X0,X1,X2),X3) ) ).
cnf(u2802,axiom,
( ~ closed(f9(X0,X1),X3,X4)
| basis(X0,X1)
| element_of_set(f19(closure(X2,X3,X4),X5),union_of_members(X1))
| hausdorff(closure(X2,X3,X4),X5)
| ~ subset_sets(X2,f9(X0,X1))
| ~ topological_space(X0,X1)
| ~ topological_space(closure(X2,X3,X4),X5) ) ).
cnf(u5946,negated_conjecture,
( ~ element_of_collection(f13(a,X2,X3,f7(interior(a,X2,X3),X4)),X0)
| ~ element_of_set(X1,f13(a,X2,X3,f7(interior(a,X2,X3),X4)))
| ~ topological_space(sF0,X0)
| element_of_set(X1,interior(a,sF0,X0))
| ~ topological_space(interior(a,X2,X3),X4)
| basis(interior(a,X2,X3),X4) ) ).
cnf(u425,negated_conjecture,
( element_of_set(f19(f13(a,cx,ct,f20(sF0,X0)),X1),sF0)
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f20(sF0,X0)),X1)
| hausdorff(f13(a,cx,ct,f20(sF0,X0)),X1) ) ).
cnf(u9738,negated_conjecture,
( ~ element_of_set(X1,boundary(X2,X3,X4))
| ~ element_of_set(X0,boundary(X2,X3,X4))
| eq_p(X0,X1) ) ).
cnf(u3482,negated_conjecture,
( ~ closed(f13(a,cx,ct,X4),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,X4))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| element_of_set(f7(closure(X0,X1,X2),X3),sF0)
| ~ element_of_set(X4,sF0) ) ).
cnf(u372,axiom,
( ~ element_of_set(X2,f9(X0,X1))
| ~ topological_space(X0,X1)
| basis(X0,X1)
| element_of_set(X2,union_of_members(X1)) ) ).
cnf(u3170,axiom,
( closed(f14(relative_complement_sets(f13(a,cx,ct,f19(sF0,X0)),X1),X1,X2,X3),X1,X2)
| element_of_set(X4,interior(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,X3),cx,ct))
| ~ subset_sets(relative_complement_sets(f13(a,cx,ct,f19(sF0,X0)),X1),X1)
| ~ subset_sets(f13(a,cx,ct,f19(sF0,X0)),X1)
| ~ topological_space(X1,X2)
| ~ topological_space(sF0,X0)
| ~ subset_sets(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,X3),cx)
| ~ element_of_set(X4,f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(X3,boundary(f13(a,cx,ct,f19(sF0,X0)),X1,X2)) ) ).
cnf(u2655,axiom,
( element_of_collection(union_of_members(subspace_topology(X0,X1,X2)),top_of_basis(X3))
| topological_space(X0,X1) ) ).
cnf(u2546,axiom,
( ~ closed(X1,X2,top_of_basis(subspace_topology(X4,X5,X3)))
| subset_sets(X3,X4)
| ~ element_of_set(X0,relative_complement_sets(X1,X2)) ) ).
cnf(u5256,axiom,
( ~ open(union_of_members(ct),X1,X2)
| ~ disjoint_s(X0,union_of_members(ct))
| hausdorff(X1,X2)
| ~ open(X0,X1,X2)
| ~ element_of_set(f19(X1,X2),X0)
| ~ element_of_set(f20(X1,X2),sF0) ) ).
cnf(u2543,axiom,
( ~ element_of_set(X0,f12(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5,f16(X6,X7,X8,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))))
| subset_sets(X4,X2)
| limit_point(X6,X7,X8,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| ~ topological_space(X8,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| ~ subset_sets(X7,X8) ) ).
cnf(limit_point_67,axiom,
( neighborhood(f16(X0,X1,X2,X3),X0,X2,X3)
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3) ) ).
cnf(u3098,axiom,
( element_of_set(f19(boundary(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ subset_sets(relative_complement_sets(X0,X1),closure(X0,X1,X2))
| ~ closed(closure(X0,X1,X2),X1,X2)
| hausdorff(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ topological_space(boundary(relative_complement_sets(X0,X1),X1,X2),X3) ) ).
cnf(u5682,negated_conjecture,
( ~ subset_sets(a,f14(relative_complement_sets(X0,cx),cx,ct,X1))
| element_of_set(X1,boundary(X0,cx,ct))
| closed(f14(X0,cx,ct,X1),cx,ct)
| ~ subset_sets(X0,cx)
| ~ subset_sets(f14(relative_complement_sets(X0,cx),cx,ct,X1),sF3)
| ~ subset_sets(relative_complement_sets(X0,cx),cx)
| ~ element_of_collection(f14(relative_complement_sets(X0,cx),cx,ct,X1),X2)
| element_of_collection(sF3,top_of_basis(X2)) ) ).
cnf(u6090,axiom,
( ~ element_of_collection(f13(sF3,X2,X3,f7(interior(sF3,X2,X3),X4)),X0)
| ~ element_of_set(X1,f13(sF3,X2,X3,f7(interior(sF3,X2,X3),X4)))
| ~ topological_space(sF1,X0)
| element_of_set(X1,interior(sF3,sF1,X0))
| ~ topological_space(interior(sF3,X2,X3),X4)
| basis(interior(sF3,X2,X3),X4) ) ).
cnf(u2351,axiom,
( element_of_collection(union_of_members(f24(X0,subspace_topology(X1,X2,X3))),subspace_topology(X1,X2,X3))
| compact_space(X0,subspace_topology(X1,X2,X3))
| ~ topological_space(X0,subspace_topology(X1,X2,X3))
| ~ connected_set(X3,X1,X2) ) ).
cnf(u1184,negated_conjecture,
( ~ closed(f13(a,cx,ct,f7(sF0,X4)),X1,X2)
| basis(sF0,X4)
| ~ topological_space(sF0,X4)
| hausdorff(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,f13(a,cx,ct,f7(sF0,X4)))
| element_of_set(f20(closure(X0,X1,X2),X3),sF0)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u1284,axiom,
( element_of_set(f7(closure(X1,X2,X3),X4),union_of_members(top_of_basis(X0)))
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| basis(closure(X1,X2,X3),X4)
| ~ topological_space(closure(X1,X2,X3),X4) ) ).
cnf(u926,axiom,
( element_of_set(f20(closure(X0,X1,X2),X3),f1(X4,f20(closure(X0,X1,X2),X3)))
| ~ subset_sets(X0,union_of_members(X4))
| ~ closed(union_of_members(X4),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3) ) ).
cnf(u3441,axiom,
( ~ closed(f13(a,cx,ct,f20(sF0,X0)),X3,X4)
| ~ topological_space(sF0,X0)
| element_of_set(f11(X1,boundary(X2,X3,X4)),union_of_members(ct))
| element_of_collection(boundary(X2,X3,X4),top_of_basis(X1))
| hausdorff(sF0,X0)
| ~ subset_sets(X2,f13(a,cx,ct,f20(sF0,X0))) ) ).
cnf(u5821,negated_conjecture,
( element_of_collection(f1(ct,f7(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(ct))),ct)),ct)
| basis(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(ct))),ct)
| ~ element_of_collection(union_of_members(ct),subspace_topology(X1,X2,X0)) ) ).
cnf(u5706,axiom,
( element_of_set(f20(boundary(relative_complement_sets(X2,X3),X3,subspace_topology(X0,X1,X4)),X5),boundary(X2,X3,subspace_topology(X0,X1,X4)))
| ~ subset_sets(X2,X3)
| ~ topological_space(boundary(relative_complement_sets(X2,X3),X3,subspace_topology(X0,X1,X4)),X5)
| hausdorff(boundary(relative_complement_sets(X2,X3),X3,subspace_topology(X0,X1,X4)),X5)
| topological_space(X0,X1) ) ).
cnf(u4659,axiom,
( ~ element_of_collection(closure(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| topological_space(X3,X4) ) ).
cnf(u3043,axiom,
( ~ topological_space(boundary(X0,X1,X2),X3)
| ~ subset_sets(X0,union_of_members(X4))
| ~ closed(union_of_members(X4),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_collection(f1(X4,f19(boundary(X0,X1,X2),X3)),X4) ) ).
cnf(u4679,axiom,
( element_of_set(X3,f10(X1,intersection_of_members(X0),X3))
| element_of_set(f11(X1,intersection_of_members(X0)),X2)
| ~ element_of_set(X3,intersection_of_members(X0))
| ~ element_of_collection(X2,X0) ) ).
cnf(u542,negated_conjecture,
( ~ subset_sets(f1(ct,f11(X1,X0)),X0)
| ~ element_of_collection(f1(ct,f11(X1,X0)),X1)
| element_of_collection(X0,top_of_basis(X1))
| ~ element_of_set(f11(X1,X0),cx) ) ).
cnf(u6349,axiom,
( ~ closed(X5,X2,X3)
| element_of_set(X4,f14(X1,X2,X3,X0))
| ~ subset_sets(X1,X2)
| ~ subset_sets(X1,X5)
| subset_sets(X1,f14(X1,X2,X3,X4))
| element_of_set(X0,X5) ) ).
cnf(u12978,negated_conjecture,
( open(f13(X1,X2,X3,f11(X0,union_of_members(ct))),X2,X3)
| element_of_set(X4,f1(top_of_basis(X0),X4))
| ~ element_of_set(X4,cx) ) ).
cnf(u639,axiom,
( element_of_set(f11(X0,f13(a,cx,ct,X1)),union_of_members(ct))
| ~ element_of_set(X1,sF0)
| element_of_collection(f13(a,cx,ct,X1),top_of_basis(X0)) ) ).
cnf(u885,negated_conjecture,
( element_of_set(f11(X0,sF3),f14(a,cx,ct,f11(X1,X2)))
| element_of_collection(sF3,top_of_basis(X0))
| ~ element_of_collection(sF3,X1)
| element_of_collection(X2,top_of_basis(X1))
| ~ subset_sets(sF3,X2) ) ).
cnf(u38060,negated_conjecture,
( element_of_set(f20(f1(top_of_basis(X3),X0),X4),f10(X3,f1(top_of_basis(X3),X0),f20(f1(top_of_basis(X3),X0),X4)))
| limit_point(X0,X1,X5,X6)
| hausdorff(f1(top_of_basis(X3),X0),X4) ) ).
cnf(u18802,negated_conjecture,
( element_of_set(f11(X1,f1(ct,X0)),interior(X2,X3,X4))
| element_of_set(X0,f1(top_of_basis(X1),X0))
| ~ element_of_set(X0,cx) ) ).
cnf(u1082,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X4,X7)
| ~ closed(X7,X5,X6)
| element_of_set(f19(closure(X0,X1,X2),X3),X7) ) ).
cnf(u3676,axiom,
( ~ closed(f2(X4,f11(X0,closure(X1,X2,X3))),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| element_of_set(f11(X0,closure(X1,X2,X3)),intersection_of_members(X4))
| ~ subset_sets(X1,f2(X4,f11(X0,closure(X1,X2,X3)))) ) ).
cnf(u7984,negated_conjecture,
( element_of_set(f20(sF0,X0),sF0)
| hausdorff(sF0,X0) ) ).
cnf(u478,axiom,
( ~ element_of_collection(f22(X0,X1),X2)
| ~ element_of_collection(f21(X0,X1),X2)
| ~ topological_space(X0,X1)
| connected_space(X0,X1)
| ~ connected_space(X0,X2) ) ).
cnf(u2696,axiom,
( ~ element_of_set(X9,f13(X0,X1,top_of_basis(subspace_topology(X2,X3,X4)),f19(closure(X7,X5,X6),X8)))
| ~ topological_space(closure(X7,X5,X6),X8)
| hausdorff(closure(X7,X5,X6),X8)
| ~ subset_sets(X7,interior(X0,X1,top_of_basis(subspace_topology(X2,X3,X4))))
| ~ closed(interior(X0,X1,top_of_basis(subspace_topology(X2,X3,X4))),X5,X6)
| subset_sets(X4,X2) ) ).
cnf(u1297,axiom,
( ~ closed(closure(X1,X2,X3),X5,X6)
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| element_of_set(f20(closure(X4,X5,X6),X7),union_of_members(top_of_basis(X0)))
| hausdorff(closure(X4,X5,X6),X7)
| ~ subset_sets(X4,closure(X1,X2,X3))
| element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| ~ topological_space(closure(X4,X5,X6),X7) ) ).
cnf(u36141,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| element_of_set(f11(X1,union_of_members(ct)),sF0) ) ).
cnf(u6296,negated_conjecture,
( ~ element_of_set(f11(X5,f14(f14(a,cx,ct,X0),X1,X2,X3)),sF3)
| element_of_set(X4,closure(f14(a,cx,ct,X0),X1,X2))
| ~ subset_sets(f14(a,cx,ct,X0),X1)
| ~ topological_space(X1,X2)
| ~ element_of_collection(f14(a,cx,ct,X0),X5)
| element_of_collection(f14(f14(a,cx,ct,X0),X1,X2,X3),top_of_basis(X5))
| element_of_set(X3,f14(f14(a,cx,ct,X0),X1,X2,X4))
| element_of_set(X0,sF3) ) ).
cnf(u3187,axiom,
( ~ topological_space(boundary(X0,X1,X2),X3)
| ~ subset_sets(X0,union_of_members(X4))
| ~ closed(union_of_members(X4),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_collection(f1(X4,f20(boundary(X0,X1,X2),X3)),X4) ) ).
cnf(u2709,axiom,
( ~ element_of_set(X2,f1(X0,f19(union_of_members(X0),X1)))
| ~ topological_space(union_of_members(X0),X1)
| hausdorff(union_of_members(X0),X1)
| element_of_set(X2,union_of_members(X0)) ) ).
cnf(u4457,axiom,
( element_of_set(X4,f10(X3,f9(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(top_of_basis(X3)))),top_of_basis(X3)),X4))
| ~ element_of_collection(union_of_members(top_of_basis(X3)),subspace_topology(X1,X2,X0))
| ~ element_of_set(X4,f9(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(top_of_basis(X3)))),top_of_basis(X3)))
| basis(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(top_of_basis(X3)))),top_of_basis(X3)) ) ).
cnf(u3066,negated_conjecture,
( ~ closed(f13(a,cx,ct,f7(sF0,X4)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f7(sF0,X4)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f19(boundary(X0,X1,X2),X3),sF0)
| basis(sF0,X4)
| ~ topological_space(sF0,X4) ) ).
cnf(u4771,axiom,
( ~ element_of_set(X6,f12(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5,f21(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))))
| ~ topological_space(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| connected_space(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| subset_sets(X4,X2) ) ).
cnf(u27876,negated_conjecture,
( open(f13(X1,X2,X3,f11(X0,union_of_members(ct))),X2,X3)
| element_of_set(f11(X4,union_of_members(top_of_basis(X0))),sF0)
| element_of_set(X5,f1(top_of_basis(X4),X5))
| ~ element_of_set(X5,cx) ) ).
cnf(u4404,axiom,
( ~ closed(f10(X1,X0,X2),X4,X5)
| ~ element_of_set(X2,X0)
| element_of_set(f19(closure(X3,X4,X5),X6),union_of_members(X1))
| hausdorff(closure(X3,X4,X5),X6)
| ~ subset_sets(X3,f10(X1,X0,X2))
| ~ element_of_collection(X0,top_of_basis(X1))
| ~ topological_space(closure(X3,X4,X5),X6) ) ).
cnf(u4906,axiom,
( ~ subset_sets(X5,f14(X0,X1,X2,X3))
| element_of_set(X3,union_of_members(top_of_basis(X4)))
| ~ closed(sF1,X1,X2)
| ~ subset_sets(X0,sF1)
| ~ subset_sets(X0,X1)
| element_of_set(f11(X4,closure(X0,X1,X2)),sF3)
| element_of_set(X6,f14(X0,X1,X2,X3))
| subset_sets(X5,f14(X5,X1,X2,X6))
| ~ subset_sets(X5,X1) ) ).
cnf(u289,negated_conjecture,
( element_of_set(f19(intersection_of_sets(X0,X1),X2),union_of_members(ct))
| ~ element_of_collection(X1,ct)
| ~ element_of_collection(X0,ct)
| ~ topological_space(intersection_of_sets(X0,X1),X2)
| hausdorff(intersection_of_sets(X0,X1),X2) ) ).
cnf(u16452,negated_conjecture,
( element_of_set(f19(intersection_of_members(X0),X1),X2)
| hausdorff(intersection_of_members(X0),X1) ) ).
cnf(u2837,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),f1(ct,X3)),f1(ct,X3))
| topological_space(X0,X1)
| ~ element_of_set(X3,sF0) ) ).
cnf(u9384,negated_conjecture,
( element_of_set(f19(boundary(X0,X4,X5),X6),X7)
| hausdorff(boundary(X0,X4,X5),X6) ) ).
cnf(u1221,axiom,
( ~ element_of_set(X3,f10(X2,X1,X0))
| ~ element_of_collection(X1,top_of_basis(X2))
| ~ element_of_set(X0,X1)
| element_of_set(X3,union_of_members(X2)) ) ).
cnf(u3749,axiom,
( ~ topological_space(boundary(X3,X4,X5),X7)
| element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),X6)
| ~ closed(X6,X4,X5)
| ~ subset_sets(X3,X6)
| topological_space(X0,X1)
| basis(boundary(X3,X4,X5),X7) ) ).
cnf(u2651,axiom,
( ~ element_of_set(X4,f1(top_of_basis(subspace_topology(X0,X1,X2)),f11(X3,union_of_members(top_of_basis(subspace_topology(X0,X1,X2))))))
| element_of_collection(union_of_members(top_of_basis(subspace_topology(X0,X1,X2))),top_of_basis(X3))
| topological_space(X0,X1) ) ).
cnf(neighborhood_59,axiom,
( ~ neighborhood(X0,X1,X2,X3)
| topological_space(X2,X3) ) ).
cnf(u5714,axiom,
( element_of_set(f7(closure(relative_complement_sets(X2,X3),X3,subspace_topology(X0,X1,X4)),X5),boundary(X2,X3,subspace_topology(X0,X1,X4)))
| ~ subset_sets(X2,X3)
| ~ topological_space(closure(relative_complement_sets(X2,X3),X3,subspace_topology(X0,X1,X4)),X5)
| basis(closure(relative_complement_sets(X2,X3),X3,subspace_topology(X0,X1,X4)),X5)
| topological_space(X0,X1) ) ).
cnf(u2539,axiom,
( ~ element_of_set(X0,f1(top_of_basis(subspace_topology(X1,X2,X3)),X4))
| subset_sets(X3,X1)
| limit_point(X4,X5,X6,top_of_basis(subspace_topology(X1,X2,X3)))
| ~ topological_space(X6,top_of_basis(subspace_topology(X1,X2,X3)))
| ~ subset_sets(X5,X6) ) ).
cnf(hausdorff_79,axiom,
( ~ eq_p(f19(X0,X1),f20(X0,X1))
| ~ topological_space(X0,X1)
| hausdorff(X0,X1) ) ).
cnf(u1349,axiom,
( ~ closed(boundary(X1,X2,X3),X5,X6)
| element_of_set(f19(closure(X4,X5,X6),X7),union_of_members(top_of_basis(X0)))
| ~ subset_sets(X4,boundary(X1,X2,X3))
| element_of_set(f11(X0,closure(X1,X2,X3)),closure(X1,X2,X3))
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7) ) ).
cnf(u3868,negated_conjecture,
( ~ element_of_set(X4,f13(a,cx,ct,f19(sF0,X3)))
| ~ topological_space(sF0,X3)
| hausdorff(sF0,X3)
| element_of_set(f11(subspace_topology(X0,X1,X2),f13(a,cx,ct,f19(sF0,X3))),sF0)
| topological_space(X0,X1) ) ).
cnf(u5139,axiom,
( ~ element_of_set(f11(X3,f14(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5,X6)),boundary(X0,X1,X2))
| element_of_collection(f14(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5,X6),top_of_basis(X3))
| ~ element_of_collection(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(X6,closure(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5))
| ~ subset_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4)
| ~ topological_space(X4,X5) ) ).
cnf(u4270,axiom,
( element_of_set(X4,interior(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,f20(closure(relative_complement_sets(f13(a,cx,ct,f19(sF0,X0)),X1),X1,X2),X3)),cx,ct))
| ~ topological_space(closure(relative_complement_sets(f13(a,cx,ct,f19(sF0,X0)),X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(f13(a,cx,ct,f19(sF0,X0)),X1),X1,X2),X3)
| ~ subset_sets(f13(a,cx,ct,f19(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| ~ subset_sets(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,f20(closure(relative_complement_sets(f13(a,cx,ct,f19(sF0,X0)),X1),X1,X2),X3)),cx)
| ~ element_of_set(X4,f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(f20(closure(relative_complement_sets(f13(a,cx,ct,f19(sF0,X0)),X1),X1,X2),X3),boundary(f13(a,cx,ct,f19(sF0,X0)),X1,X2)) ) ).
cnf(u3477,axiom,
( ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| topological_space(X5,X6) ) ).
cnf(u5249,axiom,
( ~ open(union_of_members(X1),X2,X3)
| ~ disjoint_s(X0,union_of_members(X1))
| hausdorff(X2,X3)
| ~ open(X0,X2,X3)
| ~ element_of_set(f19(X2,X3),X0)
| limit_point(f20(X2,X3),X4,X5,X1)
| ~ subset_sets(X4,X5)
| ~ topological_space(X5,X1) ) ).
cnf(u8087,negated_conjecture,
( element_of_set(f20(X0,X1),f13(X2,X3,X4,f20(X0,X1)))
| hausdorff(X0,X1) ) ).
cnf(u3691,axiom,
( element_of_set(X7,interior(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,f11(X6,f14(closure(f13(a,cx,ct,f20(sF0,X0)),X1,X2),X3,X4,X5))),cx,ct))
| ~ element_of_collection(closure(f13(a,cx,ct,f20(sF0,X0)),X1,X2),X6)
| ~ subset_sets(f13(a,cx,ct,f20(sF0,X0)),X1)
| ~ topological_space(X1,X2)
| element_of_set(X5,closure(closure(f13(a,cx,ct,f20(sF0,X0)),X1,X2),X3,X4))
| ~ subset_sets(closure(f13(a,cx,ct,f20(sF0,X0)),X1,X2),X3)
| ~ topological_space(X3,X4)
| ~ topological_space(sF0,X0)
| ~ subset_sets(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,f11(X6,f14(closure(f13(a,cx,ct,f20(sF0,X0)),X1,X2),X3,X4,X5))),cx)
| ~ element_of_set(X7,f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_collection(f14(closure(f13(a,cx,ct,f20(sF0,X0)),X1,X2),X3,X4,X5),top_of_basis(X6)) ) ).
cnf(u2974,axiom,
( ~ closed(f14(X4,X5,X6,f11(X0,boundary(X1,X2,X3))),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f14(X4,X5,X6,f11(X0,boundary(X1,X2,X3))))
| ~ topological_space(X5,X6)
| ~ subset_sets(X4,X5)
| element_of_set(f11(X0,boundary(X1,X2,X3)),closure(X4,X5,X6)) ) ).
cnf(u753,axiom,
( ~ element_of_set(X1,f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| ~ topological_space(sF0,X0)
| element_of_set(X1,union_of_members(ct)) ) ).
cnf(u5143,axiom,
( ~ element_of_set(f11(X3,f14(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5,f20(closure(relative_complement_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4),X4,X5),X6))),boundary(X0,X1,X2))
| element_of_collection(f14(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5,f20(closure(relative_complement_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4),X4,X5),X6)),top_of_basis(X3))
| ~ element_of_collection(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f20(closure(relative_complement_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4),X4,X5),X6),boundary(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5))
| ~ topological_space(closure(relative_complement_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4),X4,X5),X6)
| hausdorff(closure(relative_complement_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4),X4,X5),X6)
| ~ subset_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4) ) ).
cnf(u812,axiom,
( basis(closure(X0,X1,X2),subspace_topology(X3,X4,closure(X0,X1,X2)))
| ~ connected_set(closure(X0,X1,X2),X3,X4)
| topological_space(X1,X2) ) ).
cnf(u538,axiom,
( ~ element_of_set(f11(X1,X0),sF0)
| ~ element_of_collection(union_of_members(ct),X1)
| ~ subset_sets(union_of_members(ct),X0)
| element_of_collection(X0,top_of_basis(X1)) ) ).
cnf(u10441,negated_conjecture,
( eq_p(f20(boundary(X0,X1,X2),X3),X7)
| limit_point(X7,X6,X4,X5)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u635,axiom,
( open(f13(X1,X2,X3,f11(X0,interior(X1,X2,X3))),X2,X3)
| element_of_collection(interior(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(u279,axiom,
( element_of_set(f19(union_of_members(X0),X1),f1(X0,f19(union_of_members(X0),X1)))
| ~ topological_space(union_of_members(X0),X1)
| hausdorff(union_of_members(X0),X1) ) ).
cnf(u395,negated_conjecture,
( ~ element_of_collection(f13(a,X0,X1,f19(interior(a,X0,X1),X2)),X3)
| ~ topological_space(interior(a,X0,X1),X2)
| ~ topological_space(cx,X3)
| ~ element_of_set(X4,f13(a,X0,X1,f19(interior(a,X0,X1),X2)))
| hausdorff(interior(a,X0,X1),X2)
| element_of_set(X4,interior(a,cx,X3)) ) ).
cnf(u6346,axiom,
( element_of_set(X4,f14(X0,X1,X2,f7(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f7(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ subset_sets(X0,X1)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| basis(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| subset_sets(X0,f14(X0,X1,X2,X4)) ) ).
cnf(u342,axiom,
( element_of_collection(f12(X0,X1,X2,f21(X3,subspace_topology(X0,X1,X2))),X1)
| connected_space(X3,subspace_topology(X0,X1,X2))
| ~ topological_space(X3,subspace_topology(X0,X1,X2)) ) ).
cnf(interior_52,axiom,
( ~ open(X4,X2,X3)
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| ~ element_of_set(X0,X4)
| ~ subset_sets(X4,X1)
| element_of_set(X0,interior(X1,X2,X3)) ) ).
cnf(u4652,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,f20(sF0,X2)),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),sF0)
| ~ topological_space(sF0,X2)
| hausdorff(sF0,X2) ) ).
cnf(u1975,axiom,
( ~ topological_space(boundary(X5,X2,X3),X6)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X0,X1,X4),closure(X5,X2,X3)),sF3)
| ~ subset_sets(X5,sF1)
| hausdorff(boundary(X5,X2,X3),X6)
| topological_space(X0,X1) ) ).
cnf(u36079,negated_conjecture,
( element_of_set(f11(X1,union_of_members(top_of_basis(X4))),f1(X5,f11(X1,union_of_members(top_of_basis(X4)))))
| element_of_set(f11(X4,union_of_members(ct)),interior(X6,X7,X8))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u4663,axiom,
( ~ element_of_collection(closure(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ closed(X5,X3,X4)
| ~ subset_sets(X2,X5)
| element_of_set(f11(X6,closure(X2,X3,X4)),X5)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(top_of_basis(X6))) ) ).
cnf(u3818,axiom,
( element_of_set(f11(X0,closure(relative_complement_sets(X1,X2),X2,subspace_topology(X3,X4,X5))),boundary(X1,X2,subspace_topology(X3,X4,X5)))
| element_of_collection(closure(relative_complement_sets(X1,X2),X2,subspace_topology(X3,X4,X5)),top_of_basis(X0))
| ~ subset_sets(X1,X2)
| subset_sets(X5,X3) ) ).
cnf(u30266,negated_conjecture,
( element_of_set(f11(X4,union_of_members(top_of_basis(X0))),f1(X5,f11(X4,union_of_members(top_of_basis(X0)))))
| element_of_set(f11(X0,union_of_members(ct)),f13(X1,X2,X3,f11(X0,union_of_members(ct))))
| element_of_set(X6,f1(top_of_basis(X4),X6))
| ~ element_of_set(X6,cx) ) ).
cnf(u2950,axiom,
( ~ closed(interior(X4,X5,X6),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,interior(X4,X5,X6))
| topological_space(X5,X6) ) ).
cnf(u1382,axiom,
( ~ element_of_set(X0,X1)
| topological_space(X2,X3)
| element_of_set(f11(subspace_topology(X2,X3,X4),X1),X1) ) ).
cnf(u764,axiom,
( element_of_collection(f12(X4,X5,X6,f12(X3,subspace_topology(X4,X5,X6),X7,f16(X0,X1,X2,subspace_topology(X3,subspace_topology(X4,X5,X6),X7)))),X5)
| ~ topological_space(X2,subspace_topology(X3,subspace_topology(X4,X5,X6),X7))
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,subspace_topology(X3,subspace_topology(X4,X5,X6),X7)) ) ).
cnf(u1079,axiom,
( ~ closed(f13(X4,X5,X6,f20(interior(X4,X5,X6),X7)),X1,X2)
| ~ subset_sets(X0,f13(X4,X5,X6,f20(interior(X4,X5,X6),X7)))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(interior(X4,X5,X6),X7)
| hausdorff(interior(X4,X5,X6),X7)
| element_of_set(f19(closure(X0,X1,X2),X3),interior(X4,X5,X6)) ) ).
cnf(u301,axiom,
( ~ element_of_set(f20(boundary(relative_complement_sets(X0,X1),X1,X2),X3),closure(X0,X1,X2))
| ~ topological_space(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| hausdorff(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f20(boundary(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2)) ) ).
cnf(u839,negated_conjecture,
( ~ closed(intersection_of_sets(X4,X5),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,intersection_of_sets(X4,X5))
| element_of_set(f11(X0,closure(X1,X2,X3)),union_of_members(ct))
| ~ element_of_collection(X5,ct)
| ~ element_of_collection(X4,ct) ) ).
cnf(u36138,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| element_of_set(f11(X1,f1(ct,X0)),union_of_members(X4)) ) ).
cnf(u6571,negated_conjecture,
( element_of_set(f7(sF3,X0),f14(a,cx,ct,X1))
| element_of_set(X1,f14(a,cx,ct,X2))
| basis(sF3,X0)
| ~ topological_space(sF3,X0)
| element_of_set(X2,sF3) ) ).
cnf(u6084,negated_conjecture,
( ~ closed(union_of_members(f24(X0,ct)),X2,X3)
| compact_space(X0,ct)
| element_of_set(f19(closure(X1,X2,X3),X4),union_of_members(ct))
| hausdorff(closure(X1,X2,X3),X4)
| ~ subset_sets(X1,union_of_members(f24(X0,ct)))
| ~ topological_space(X0,ct)
| ~ topological_space(closure(X1,X2,X3),X4) ) ).
cnf(u5328,axiom,
( ~ element_of_set(f19(sF1,X1),X0)
| ~ open(sF3,sF1,X1)
| hausdorff(sF1,X1)
| ~ open(X0,sF1,X1)
| ~ disjoint_s(X0,sF3) ) ).
cnf(u50926,negated_conjecture,
( ~ element_of_set(X8,closure(f16(X1,X2,X3,X4),X5,X6))
| limit_point(X1,X2,X3,X4)
| ~ element_of_set(X7,f16(X1,X2,X3,X4))
| eq_p(X0,X8)
| element_of_set(X7,f13(f14(f16(X1,X2,X3,X4),X5,X6,X0),X3,X4,X7)) ) ).
cnf(u36068,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f10(X0,f1(top_of_basis(X0),f11(X0,union_of_members(ct))),f11(X0,union_of_members(ct))))
| limit_point(f11(X0,union_of_members(ct)),X1,X2,top_of_basis(X0))
| ~ element_of_set(f11(X0,union_of_members(ct)),cx) ) ).
cnf(u2909,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),f13(X3,X4,X5,f20(closure(X6,X7,X8),X9))),f13(X3,X4,X5,f20(closure(X6,X7,X8),X9)))
| topological_space(X0,X1)
| ~ subset_sets(X6,interior(X3,X4,X5))
| ~ closed(interior(X3,X4,X5),X7,X8)
| ~ topological_space(closure(X6,X7,X8),X9)
| hausdorff(closure(X6,X7,X8),X9) ) ).
cnf(u6647,negated_conjecture,
( element_of_set(f20(closure(X0,X1,X2),X3),sF0)
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(sF3,X1,X2) ) ).
cnf(u3916,axiom,
( element_of_set(X5,interior(f14(relative_complement_sets(X0,X1),X2,X3,f19(closure(relative_complement_sets(relative_complement_sets(X0,X1),X2),X2,X3),X4)),X1,X6))
| ~ topological_space(closure(relative_complement_sets(relative_complement_sets(X0,X1),X2),X2,X3),X4)
| hausdorff(closure(relative_complement_sets(relative_complement_sets(X0,X1),X2),X2,X3),X4)
| ~ subset_sets(relative_complement_sets(X0,X1),X2)
| ~ subset_sets(f14(relative_complement_sets(X0,X1),X2,X3,f19(closure(relative_complement_sets(relative_complement_sets(X0,X1),X2),X2,X3),X4)),X1)
| ~ element_of_set(X5,relative_complement_sets(X0,X1))
| ~ closed(X0,X1,X6)
| element_of_set(f19(closure(relative_complement_sets(relative_complement_sets(X0,X1),X2),X2,X3),X4),boundary(relative_complement_sets(X0,X1),X2,X3)) ) ).
cnf(u3821,axiom,
( element_of_set(X0,f1(subspace_topology(X2,X3,X1),X0))
| ~ connected_set(X1,X2,X3)
| ~ element_of_set(X0,X1) ) ).
cnf(u4409,axiom,
( ~ closed(f10(X1,X0,X2),X4,X5)
| ~ element_of_set(X2,X0)
| element_of_set(f20(closure(X3,X4,X5),X6),union_of_members(X1))
| hausdorff(closure(X3,X4,X5),X6)
| ~ subset_sets(X3,f10(X1,X0,X2))
| ~ element_of_collection(X0,top_of_basis(X1))
| ~ topological_space(closure(X3,X4,X5),X6) ) ).
cnf(u6578,axiom,
( element_of_set(f11(subspace_topology(X1,X4,X0),closure(X5,X2,X3)),sF3)
| closed(f14(X5,X2,X3,X6),X2,X3)
| ~ closed(sF1,X2,X3)
| ~ subset_sets(X5,sF1)
| subset_sets(X0,X1)
| ~ subset_sets(X5,X2) ) ).
cnf(u6575,negated_conjecture,
( ~ subset_sets(a,f14(X0,cx,ct,X1))
| element_of_set(X2,closure(X0,cx,ct))
| ~ subset_sets(X0,cx)
| ~ topological_space(sF3,X3)
| element_of_set(X1,f14(X0,cx,ct,X2))
| element_of_set(f7(sF3,X3),f14(X0,cx,ct,X1))
| basis(sF3,X3) ) ).
cnf(u2584,axiom,
( ~ closed(f10(X4,closure(X1,X2,X3),X0),X2,X3)
| ~ element_of_collection(closure(X1,X2,X3),top_of_basis(X4))
| ~ element_of_set(X0,closure(X1,X2,X3))
| ~ subset_sets(X1,f10(X4,closure(X1,X2,X3),X0))
| ~ element_of_collection(f10(X4,closure(X1,X2,X3),X0),X5)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X5)) ) ).
cnf(u934,axiom,
( element_of_set(f20(closure(X0,X1,X2),X3),f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)))
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3) ) ).
cnf(u9852,negated_conjecture,
( eq_p(f20(boundary(X0,X1,X2),X3),f20(boundary(X4,X5,X6),X7))
| hausdorff(boundary(X4,X5,X6),X7)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u1310,axiom,
( ~ closed(f1(X1,X3),X5,X6)
| ~ subset_sets(X2,X0)
| limit_point(X3,X2,X0,X1)
| element_of_set(f20(closure(X4,X5,X6),X7),union_of_members(X1))
| hausdorff(closure(X4,X5,X6),X7)
| ~ subset_sets(X4,f1(X1,X3))
| ~ topological_space(X0,X1)
| ~ topological_space(closure(X4,X5,X6),X7) ) ).
cnf(u2924,axiom,
( subset_collections(f5(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3),X3)
| ~ element_of_collection(empty_set,X3)
| ~ element_of_collection(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3)
| element_of_collection(f4(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3),X3)
| topological_space(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3)
| ~ element_of_collection(union_of_members(X3),subspace_topology(X1,X2,X0)) ) ).
cnf(u1415,axiom,
element_of_collection(X0,X1) ).
cnf(u29048,negated_conjecture,
( open(f13(X2,X3,X4,f11(X0,union_of_members(top_of_basis(X1)))),X3,X4)
| element_of_set(f11(X1,union_of_members(ct)),f1(X5,f11(X1,union_of_members(ct))))
| element_of_set(X6,f1(top_of_basis(X0),X6))
| ~ element_of_set(X6,cx) ) ).
cnf(u765,axiom,
( limit_point(X0,X1,X2,subspace_topology(X3,subspace_topology(X4,X5,X6),X7))
| ~ topological_space(X2,subspace_topology(X3,subspace_topology(X4,X5,X6),X7))
| ~ subset_sets(X1,X2)
| subset_sets(X6,X4) ) ).
cnf(u45061,negated_conjecture,
( ~ element_of_set(X7,closure(relative_complement_sets(X1,X2),X3,X4))
| ~ element_of_set(X5,relative_complement_sets(X1,X2))
| eq_p(X0,X7)
| element_of_set(X5,f13(f14(relative_complement_sets(X1,X2),X3,X4,X0),X2,X6,X5)) ) ).
cnf(u5679,axiom,
( ~ topological_space(X1,subspace_topology(X3,X4,X5))
| element_of_set(X2,boundary(X0,X1,subspace_topology(X3,X4,X5)))
| ~ subset_sets(X0,X1)
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| subset_sets(X5,X3) ) ).
cnf(u1346,axiom,
( element_of_set(f11(X0,f13(X1,X2,X3,f19(interior(X1,X2,X3),X4))),f13(X1,X2,X3,f19(interior(X1,X2,X3),X4)))
| element_of_set(f19(interior(X1,X2,X3),X4),union_of_members(top_of_basis(X0)))
| hausdorff(interior(X1,X2,X3),X4)
| ~ topological_space(interior(X1,X2,X3),X4) ) ).
cnf(u36090,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| element_of_set(f11(X1,union_of_members(top_of_basis(X4))),sF0)
| limit_point(X0,X2,X3,top_of_basis(X1))
| element_of_set(f11(X4,union_of_members(ct)),sF0)
| ~ element_of_set(X0,cx) ) ).
cnf(u184,negated_conjecture,
( element_of_set(X4,interior(f14(f13(a,cx,ct,X0),X1,X2,X3),cx,ct))
| ~ element_of_set(X4,f13(a,cx,ct,X0))
| ~ element_of_set(X0,sF0)
| ~ subset_sets(f14(f13(a,cx,ct,X0),X1,X2,X3),cx)
| element_of_set(X3,closure(f13(a,cx,ct,X0),X1,X2))
| ~ subset_sets(f13(a,cx,ct,X0),X1)
| ~ topological_space(X1,X2) ) ).
cnf(u33594,negated_conjecture,
( element_of_set(f11(X4,union_of_members(top_of_basis(X0))),f1(top_of_basis(X4),f11(X4,union_of_members(top_of_basis(X0)))))
| element_of_set(f11(X0,union_of_members(ct)),f13(X1,X2,X3,f11(X0,union_of_members(ct))))
| ~ element_of_set(f11(X4,union_of_members(top_of_basis(X0))),cx) ) ).
cnf(u5669,negated_conjecture,
( element_of_set(f11(X5,sF3),f14(X0,cx,ct,f11(X4,f14(closure(X0,cx,ct),X1,X2,X3))))
| ~ element_of_collection(closure(X0,cx,ct),X4)
| ~ subset_sets(X0,cx)
| element_of_set(X3,closure(closure(X0,cx,ct),X1,X2))
| ~ subset_sets(closure(X0,cx,ct),X1)
| ~ topological_space(X1,X2)
| element_of_collection(f14(closure(X0,cx,ct),X1,X2,X3),top_of_basis(X4))
| element_of_collection(sF3,top_of_basis(X5))
| ~ subset_sets(a,f14(X0,cx,ct,f11(X4,f14(closure(X0,cx,ct),X1,X2,X3)))) ) ).
cnf(u5731,axiom,
( ~ closed(closure(relative_complement_sets(X2,X3),X3,subspace_topology(X1,X4,X0)),X6,X7)
| ~ subset_sets(X2,X3)
| ~ subset_sets(X5,closure(relative_complement_sets(X2,X3),X3,subspace_topology(X1,X4,X0)))
| subset_sets(X0,X1)
| ~ topological_space(closure(X5,X6,X7),X8)
| hausdorff(closure(X5,X6,X7),X8)
| element_of_set(f19(closure(X5,X6,X7),X8),boundary(X2,X3,subspace_topology(X1,X4,X0))) ) ).
cnf(u519,axiom,
( open(f13(a,cx,ct,f20(sF0,X0)),cx,ct)
| hausdorff(sF0,X0)
| ~ topological_space(sF0,X0) ) ).
cnf(u3624,axiom,
( subset_sets(X1,f14(X1,X2,X3,f11(X0,closure(relative_complement_sets(X1,X2),X2,X3))))
| element_of_set(f11(X0,closure(relative_complement_sets(X1,X2),X2,X3)),union_of_members(top_of_basis(X4)))
| element_of_set(f11(X4,boundary(X1,X2,X3)),boundary(X1,X2,X3))
| ~ subset_sets(X1,X2)
| element_of_collection(closure(relative_complement_sets(X1,X2),X2,X3),top_of_basis(X0)) ) ).
cnf(u2711,axiom,
( ~ element_of_set(X4,f1(top_of_basis(subspace_topology(X0,X1,X2)),f19(union_of_members(top_of_basis(subspace_topology(X0,X1,X2))),X3)))
| ~ topological_space(union_of_members(top_of_basis(subspace_topology(X0,X1,X2))),X3)
| hausdorff(union_of_members(top_of_basis(subspace_topology(X0,X1,X2))),X3)
| topological_space(X0,X1) ) ).
cnf(u3471,axiom,
( ~ closed(relative_complement_sets(X4,X5),X1,X2)
| ~ subset_sets(X0,relative_complement_sets(X4,X5))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ closed(X4,X5,X6)
| element_of_set(f7(closure(X0,X1,X2),X3),union_of_members(X6)) ) ).
cnf(u338,axiom,
( ~ equal_sets(f21(X0,X1),empty_set)
| ~ topological_space(X0,X1)
| connected_space(X0,X1) ) ).
cnf(u1012,axiom,
( ~ closed(boundary(X1,X2,X3),X4,X5)
| ~ subset_sets(X0,boundary(X1,X2,X3))
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| subset_sets(X1,X2) ) ).
cnf(u36109,negated_conjecture,
( element_of_set(f11(X1,union_of_members(top_of_basis(X4))),f1(top_of_basis(X4),f11(X1,union_of_members(top_of_basis(X4)))))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx)
| element_of_set(f11(X4,union_of_members(ct)),union_of_members(ct)) ) ).
cnf(u1305,axiom,
( element_of_set(f11(X4,f1(X1,X3)),union_of_members(X1))
| limit_point(X3,X2,X0,X1)
| ~ subset_sets(X2,X0)
| ~ topological_space(X0,X1)
| element_of_collection(f1(X1,X3),top_of_basis(X4)) ) ).
cnf(u9285,negated_conjecture,
connected_space(X0,X1) ).
cnf(u3607,axiom,
( closed(f14(X0,X1,X2,f11(X6,f14(closure(X0,X1,X2),X3,X4,f11(X5,closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4))))),X1,X2)
| element_of_collection(closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4),top_of_basis(X5))
| ~ subset_sets(closure(X0,X1,X2),X3)
| ~ element_of_collection(closure(X0,X1,X2),X6)
| element_of_collection(f14(closure(X0,X1,X2),X3,X4,f11(X5,closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4))),top_of_basis(X6))
| element_of_set(f11(X5,closure(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4)),boundary(closure(X0,X1,X2),X3,X4))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u3072,negated_conjecture,
( ~ closed(f13(a,cx,ct,f20(sF0,X4)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f20(sF0,X4)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f19(boundary(X0,X1,X2),X3),sF0)
| ~ topological_space(sF0,X4)
| hausdorff(sF0,X4) ) ).
cnf(u4871,axiom,
( element_of_set(f7(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),f24(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4)),interior(X0,X1,X2))
| basis(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),f24(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4))
| compact_space(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(interior(X0,X1,X2),X3)
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4) ) ).
cnf(u3832,axiom,
( ~ closed(f2(X1,X0),X3,X4)
| element_of_set(f7(closure(X2,X3,X4),X5),union_of_members(X1))
| ~ topological_space(closure(X2,X3,X4),X5)
| ~ subset_sets(X2,f2(X1,X0))
| element_of_set(X0,intersection_of_members(X1))
| basis(closure(X2,X3,X4),X5) ) ).
cnf(u628,axiom,
( element_of_set(f11(X0,union_of_members(X1)),f1(X1,f11(X0,union_of_members(X1))))
| element_of_collection(union_of_members(X1),top_of_basis(X0)) ) ).
cnf(u27764,negated_conjecture,
( open(f13(X1,X2,X3,f11(X0,union_of_members(ct))),X2,X3)
| element_of_set(f11(X4,union_of_members(top_of_basis(X0))),interior(X5,X6,X7))
| element_of_set(X8,f1(top_of_basis(X4),X8))
| ~ element_of_set(X8,cx) ) ).
cnf(u54057,negated_conjecture,
( ~ element_of_set(X0,f13(a,cx,ct,f19(sF0,X1)))
| hausdorff(sF0,X1)
| element_of_set(X0,f13(f14(f13(a,cx,ct,f19(sF0,X1)),X2,X3,X4),cx,ct,X0))
| element_of_set(X4,interior(X5,X6,X7)) ) ).
cnf(u835,axiom,
( ~ closed(f1(ct,X4),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f1(ct,X4))
| ~ element_of_set(X4,sF0)
| element_of_set(f11(X0,closure(X1,X2,X3)),union_of_members(ct)) ) ).
cnf(u3354,negated_conjecture,
( element_of_collection(f1(ct,f19(closure(X0,X1,X2),X3)),ct)
| hausdorff(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,empty_set)
| ~ closed(empty_set,X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u4613,axiom,
( ~ element_of_collection(union_of_members(X2),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),f1(X2,f11(X0,intersection_of_members(X1)))) ) ).
cnf(u27887,negated_conjecture,
( element_of_set(f11(X4,union_of_members(top_of_basis(X0))),sF0)
| element_of_set(f11(X0,union_of_members(ct)),union_of_members(X6))
| element_of_set(X5,f1(top_of_basis(X4),X5))
| ~ element_of_set(X5,cx) ) ).
cnf(u5550,negated_conjecture,
( ~ element_of_collection(union_of_members(f5(X0,ct)),ct)
| ~ element_of_collection(X0,ct)
| topological_space(X0,ct)
| ~ equal_sets(union_of_members(ct),X0) ) ).
cnf(u4288,axiom,
( subset_sets(X0,f14(X0,X1,X2,f20(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f20(closure(relative_complement_sets(X0,X1),X1,X2),X3),closure(X0,X1,X2))
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3) ) ).
cnf(u51287,negated_conjecture,
( ~ element_of_set(X9,f16(X0,X1,X2,X3))
| ~ element_of_set(X4,f16(X0,X1,X2,X3))
| eq_p(X5,X6)
| element_of_set(X4,f13(f14(f16(X0,X1,X2,X3),X7,X8,X5),X2,X3,X4))
| element_of_set(X9,f13(f14(f16(X0,X1,X2,X3),X7,X8,X6),X2,X3,X9))
| limit_point(X0,X1,X2,X3) ) ).
cnf(u158,negated_conjecture,
( ~ subset_sets(X0,a)
| ~ topological_space(cx,X1)
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,X1)
| element_of_set(X2,interior(a,cx,X1)) ) ).
cnf(u3185,axiom,
( ~ topological_space(boundary(X0,X1,X2),X3)
| ~ subset_sets(X0,X4)
| ~ closed(X4,X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f11(X5,X4),X4)
| element_of_set(f20(boundary(X0,X1,X2),X3),union_of_members(top_of_basis(X5))) ) ).
cnf(u5007,axiom,
( equal_sets(union_of_members(f23(X1,X2,X0)),X1)
| ~ compact_space(X1,X2)
| ~ open_covering(X0,X1,X2) ) ).
cnf(u2690,axiom,
( ~ closed(interior(X0,X1,subspace_topology(X2,X3,X4)),X5,X6)
| ~ topological_space(closure(X7,X5,X6),X8)
| hausdorff(closure(X7,X5,X6),X8)
| ~ subset_sets(X7,interior(X0,X1,subspace_topology(X2,X3,X4)))
| subset_sets(X4,X2) ) ).
cnf(u4631,axiom,
( ~ element_of_collection(f9(X2,X3),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ topological_space(X2,X3)
| basis(X2,X3)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X3)) ) ).
cnf(u6421,axiom,
( element_of_set(X4,f14(X0,X1,X2,f7(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f7(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ subset_sets(X0,X1)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| basis(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| closed(f14(X0,X1,X2,X4),X1,X2) ) ).
cnf(u53459,negated_conjecture,
( open(f13(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),cx,ct,X4),X1,X2,X5),X1,X2)
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X4,sF0)
| ~ element_of_set(X5,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3))) ) ).
cnf(u3494,axiom,
( ~ closed(f13(X4,X5,X6,f20(interior(X4,X5,X6),X7)),X1,X2)
| ~ subset_sets(X0,f13(X4,X5,X6,f20(interior(X4,X5,X6),X7)))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(interior(X4,X5,X6),X7)
| hausdorff(interior(X4,X5,X6),X7)
| element_of_set(f7(closure(X0,X1,X2),X3),interior(X4,X5,X6)) ) ).
cnf(u151,axiom,
( ~ closed(X4,X2,X3)
| ~ subset_sets(X1,X2)
| ~ subset_sets(X1,X4)
| closed(f14(X1,X2,X3,X0),X2,X3)
| element_of_set(X0,X4) ) ).
cnf(u6951,negated_conjecture,
( element_of_set(f11(X3,f14(a,cx,ct,X1)),f14(a,cx,ct,X1))
| element_of_set(X2,f14(a,cx,ct,X0))
| element_of_set(X0,union_of_members(top_of_basis(X3)))
| element_of_set(X1,sF3)
| ~ element_of_set(X2,sF3) ) ).
cnf(u5668,negated_conjecture,
( ~ subset_sets(a,f14(X0,cx,ct,f11(X4,f14(closure(X0,cx,ct),X1,X2,X3))))
| ~ element_of_collection(closure(X0,cx,ct),X4)
| ~ subset_sets(X0,cx)
| element_of_set(X3,closure(closure(X0,cx,ct),X1,X2))
| ~ subset_sets(closure(X0,cx,ct),X1)
| ~ topological_space(X1,X2)
| ~ subset_sets(f14(X0,cx,ct,f11(X4,f14(closure(X0,cx,ct),X1,X2,X3))),sF3)
| element_of_collection(f14(closure(X0,cx,ct),X1,X2,X3),top_of_basis(X4))
| ~ element_of_collection(f14(X0,cx,ct,f11(X4,f14(closure(X0,cx,ct),X1,X2,X3))),X5)
| element_of_collection(sF3,top_of_basis(X5)) ) ).
cnf(u1198,axiom,
( closed(f14(X0,X1,X2,f19(boundary(relative_complement_sets(X0,X1),X1,X2),X3)),X1,X2)
| hausdorff(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f19(boundary(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ topological_space(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1) ) ).
cnf(u452,axiom,
( closed(f14(relative_complement_sets(X0,X1),X1,X2,f7(closure(X0,X1,X2),X3)),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| basis(closure(X0,X1,X2),X3)
| element_of_set(f7(closure(X0,X1,X2),X3),boundary(X0,X1,X2)) ) ).
cnf(u629,axiom,
( element_of_collection(f1(X1,f11(X0,union_of_members(X1))),X1)
| element_of_collection(union_of_members(X1),top_of_basis(X0)) ) ).
cnf(u761,negated_conjecture,
( element_of_set(f7(X1,X0),union_of_members(ct))
| basis(X1,X0)
| ~ equal_sets(union_of_members(X0),X1)
| ~ element_of_collection(f9(X1,X0),ct)
| ~ element_of_collection(f8(X1,X0),ct) ) ).
cnf(interior_48,axiom,
( ~ element_of_set(X0,interior(X1,X2,X3))
| subset_sets(X1,X2) ) ).
cnf(u6121,negated_conjecture,
( ~ closed(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X6,X7)
| ~ closed(sF0,X1,X2)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X3))
| element_of_set(f11(X4,closure(X5,X6,X7)),sF0)
| element_of_collection(closure(X5,X6,X7),top_of_basis(X4))
| ~ subset_sets(X0,sF0)
| ~ subset_sets(X5,f13(a,cx,ct,f11(X3,closure(X0,X1,X2)))) ) ).
cnf(limit_point_68,axiom,
( ~ element_of_set(X4,intersection_of_sets(f16(X0,X1,X2,X3),X1))
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3)
| eq_p(X4,X0) ) ).
cnf(u3620,axiom,
( subset_sets(X1,f14(X1,X2,X3,f11(X0,closure(relative_complement_sets(X1,X2),X2,X3))))
| element_of_set(f11(subspace_topology(X4,X5,X6),boundary(X1,X2,X3)),boundary(X1,X2,X3))
| ~ subset_sets(X1,X2)
| topological_space(X4,X5)
| element_of_collection(closure(relative_complement_sets(X1,X2),X2,X3),top_of_basis(X0)) ) ).
cnf(u4071,negated_conjecture,
( element_of_set(X5,interior(a,cx,subspace_topology(X0,X1,f13(a,X2,X3,f11(X4,interior(a,X2,X3))))))
| ~ element_of_set(X5,f13(a,X2,X3,f11(X4,interior(a,X2,X3))))
| element_of_collection(interior(a,X2,X3),top_of_basis(X4))
| ~ topological_space(cx,subspace_topology(X0,X1,f13(a,X2,X3,f11(X4,interior(a,X2,X3)))))
| ~ connected_set(f13(a,X2,X3,f11(X4,interior(a,X2,X3))),X0,X1) ) ).
cnf(u3521,axiom,
( element_of_collection(f17(X1,X3,X2,X0),X3)
| eq_p(X2,X0)
| ~ hausdorff(X1,X3)
| ~ element_of_set(X2,X1)
| ~ element_of_set(X0,X1) ) ).
cnf(u403,negated_conjecture,
( ~ element_of_set(X1,f13(a,cx,ct,f19(sF0,X0)))
| element_of_set(X1,sF0)
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0) ) ).
cnf(u3955,negated_conjecture,
( ~ closed(f1(ct,f15(X1,X4,X2,X3,X0)),X7,X8)
| ~ limit_point(X1,X4,X2,X3)
| ~ element_of_collection(X4,ct)
| ~ element_of_collection(X0,ct)
| element_of_set(f11(X5,closure(X6,X7,X8)),union_of_members(ct))
| element_of_collection(closure(X6,X7,X8),top_of_basis(X5))
| ~ neighborhood(X0,X1,X2,X3)
| ~ subset_sets(X6,f1(ct,f15(X1,X4,X2,X3,X0))) ) ).
cnf(u3721,axiom,
( ~ subset_sets(boundary(X0,X1,X2),closure(relative_complement_sets(X0,X1),X1,X2))
| ~ subset_sets(relative_complement_sets(X0,X1),closure(X0,X1,X2))
| element_of_collection(closure(relative_complement_sets(X0,X1),X1,X2),top_of_basis(X3))
| ~ element_of_collection(boundary(X0,X1,X2),X3)
| ~ closed(closure(X0,X1,X2),X1,X2) ) ).
cnf(u3759,axiom,
( ~ closed(closure(X3,X4,X5),X9,X10)
| element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),X6)
| ~ closed(X6,X4,X5)
| ~ subset_sets(X3,X6)
| element_of_collection(boundary(X8,X9,X10),top_of_basis(X7))
| topological_space(X0,X1)
| ~ subset_sets(X8,closure(X3,X4,X5)) ) ).
cnf(u4667,axiom,
( ~ element_of_collection(f14(X2,X3,X4,f11(X0,intersection_of_members(X1))),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ topological_space(X3,X4)
| ~ subset_sets(X2,X3)
| element_of_set(f11(X0,intersection_of_members(X1)),closure(X2,X3,X4)) ) ).
cnf(u350,axiom,
( ~ topological_space(X2,X1)
| ~ topological_space(X0,X1)
| compact_space(X0,X1)
| element_of_collection(union_of_members(f24(X0,X1)),X1) ) ).
cnf(u2878,axiom,
( ~ limit_point(X5,X4,X6,X7)
| element_of_set(f11(subspace_topology(X0,X1,X2),intersection_of_sets(X3,X4)),intersection_of_sets(X3,X4))
| ~ neighborhood(X3,X5,X6,X7)
| topological_space(X0,X1) ) ).
cnf(u1108,negated_conjecture,
( ~ element_of_set(X4,f13(a,cx,ct,f19(closure(X0,X1,X2),X3)))
| ~ closed(sF0,X1,X2)
| ~ subset_sets(X0,sF0)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3)
| element_of_set(X4,sF0) ) ).
cnf(u4660,axiom,
( ~ element_of_collection(closure(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| subset_sets(X2,X3) ) ).
cnf(u495,axiom,
( ~ subset_sets(X0,f14(X1,X2,X3,X4))
| element_of_set(X5,f14(X1,X2,X3,X4))
| subset_sets(X0,f14(X0,X2,X3,X5))
| ~ subset_sets(X0,X2)
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ) ).
cnf(basis_for_topology_33,axiom,
( ~ equal_sets(union_of_members(X1),X0)
| basis(X0,X1)
| element_of_collection(f8(X0,X1),X1) ) ).
cnf(u2581,axiom,
( ~ subset_sets(X3,f10(X2,X1,X0))
| ~ element_of_collection(X1,top_of_basis(X2))
| ~ element_of_collection(X3,X4)
| ~ topological_space(X1,X4)
| ~ element_of_set(X5,X3)
| ~ element_of_set(X0,X1)
| element_of_set(X5,interior(f10(X2,X1,X0),X1,X4)) ) ).
cnf(u4774,axiom,
( element_of_collection(f12(X2,X3,X4,f12(X1,subspace_topology(X2,X3,X4),X5,f21(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5)))),X3)
| ~ topological_space(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5))
| connected_space(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5)) ) ).
cnf(u965,negated_conjecture,
( ~ subset_sets(a,f14(X1,cx,ct,X2))
| hausdorff(sF3,X0)
| element_of_set(f20(sF3,X0),f14(X1,cx,ct,X2))
| ~ topological_space(sF3,X0)
| element_of_set(X2,closure(X1,cx,ct))
| ~ subset_sets(X1,cx) ) ).
cnf(u2713,axiom,
( element_of_collection(f12(X0,X1,X2,f1(subspace_topology(X0,X1,X2),f19(union_of_members(subspace_topology(X0,X1,X2)),X3))),X1)
| ~ topological_space(union_of_members(subspace_topology(X0,X1,X2)),X3)
| hausdorff(union_of_members(subspace_topology(X0,X1,X2)),X3) ) ).
cnf(u6007,negated_conjecture,
( element_of_set(f11(X2,f14(a,cx,ct,X1)),f14(a,cx,ct,X1))
| element_of_set(X0,union_of_members(top_of_basis(X2)))
| element_of_set(X1,sF3)
| closed(f14(a,cx,ct,X0),cx,ct) ) ).
cnf(u2805,axiom,
( ~ closed(f9(X0,X1),X3,X4)
| basis(X0,X1)
| element_of_set(f20(closure(X2,X3,X4),X5),union_of_members(X1))
| hausdorff(closure(X2,X3,X4),X5)
| ~ subset_sets(X2,f9(X0,X1))
| ~ topological_space(X0,X1)
| ~ topological_space(closure(X2,X3,X4),X5) ) ).
cnf(u3322,axiom,
( ~ subset_sets(f14(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8,X9),X1)
| element_of_set(X9,union_of_members(top_of_basis(X10)))
| ~ closed(sF1,X7,X8)
| ~ subset_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),sF1)
| ~ subset_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7)
| ~ closed(interior(X0,X1,X2),X4,X5)
| ~ topological_space(closure(X3,X4,X5),X6)
| hausdorff(closure(X3,X4,X5),X6)
| element_of_set(f11(X10,closure(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8)),sF3)
| ~ element_of_set(X11,f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)))
| ~ subset_sets(X3,interior(X0,X1,X2))
| element_of_set(X11,interior(f14(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8,X9),X1,X2)) ) ).
cnf(u2641,negated_conjecture,
( element_of_set(f11(X0,empty_set),f1(ct,f11(X0,empty_set)))
| element_of_collection(empty_set,top_of_basis(X0)) ) ).
cnf(u4648,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,f19(closure(X2,X3,X4),X5)),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ closed(sF0,X3,X4)
| ~ subset_sets(X2,sF0)
| ~ topological_space(closure(X2,X3,X4),X5)
| hausdorff(closure(X2,X3,X4),X5)
| element_of_set(f11(X0,intersection_of_members(X1)),sF0) ) ).
cnf(u847,negated_conjecture,
( ~ closed(f13(a,cx,ct,f11(X4,sF0)),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f13(a,cx,ct,f11(X4,sF0)))
| element_of_set(f11(X0,closure(X1,X2,X3)),sF0)
| element_of_collection(sF0,top_of_basis(X4)) ) ).
cnf(u4625,axiom,
( element_of_set(f11(X0,intersection_of_members(X1)),f6(X4,X5,f11(X0,intersection_of_members(X1)),X2,X3))
| ~ element_of_collection(intersection_of_sets(X2,X3),X1)
| ~ element_of_set(f11(X0,intersection_of_members(X1)),X4)
| ~ element_of_collection(X2,X5)
| ~ element_of_collection(X3,X5)
| ~ basis(X4,X5)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0)) ) ).
cnf(u1093,axiom,
( element_of_set(f19(closure(X0,X1,X2),X3),sF3)
| ~ subset_sets(X0,sF1)
| ~ closed(sF1,X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3) ) ).
cnf(u2483,axiom,
( element_of_set(X0,f10(X4,closure(X1,X2,X3),X0))
| element_of_set(f11(X4,closure(X1,X2,X3)),X5)
| ~ element_of_set(X0,closure(X1,X2,X3))
| ~ closed(X5,X2,X3)
| ~ subset_sets(X1,X5) ) ).
cnf(u5801,negated_conjecture,
( closed(f14(a,cx,ct,f11(X0,f14(sF3,X1,X2,X3))),cx,ct)
| element_of_collection(f14(sF3,X1,X2,X3),top_of_basis(X0))
| ~ element_of_collection(sF3,X0)
| element_of_set(X3,closure(sF3,X1,X2))
| ~ subset_sets(sF3,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u2430,axiom,
( ~ closed(closure(X3,X1,X2),X6,X7)
| ~ subset_sets(X3,X0)
| element_of_set(f11(X4,closure(X3,X1,X2)),X0)
| element_of_set(f20(closure(X5,X6,X7),X8),union_of_members(top_of_basis(X4)))
| hausdorff(closure(X5,X6,X7),X8)
| ~ subset_sets(X5,closure(X3,X1,X2))
| ~ closed(X0,X1,X2)
| ~ topological_space(closure(X5,X6,X7),X8) ) ).
cnf(u3188,axiom,
( ~ closed(f1(ct,X4),X1,X2)
| ~ subset_sets(X0,f1(ct,X4))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ element_of_set(X4,sF0)
| element_of_set(f20(boundary(X0,X1,X2),X3),union_of_members(ct)) ) ).
cnf(u3201,axiom,
( element_of_set(f20(boundary(X0,X1,X2),X3),f13(X4,X5,X6,f20(boundary(X0,X1,X2),X3)))
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ closed(interior(X4,X5,X6),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u4772,axiom,
( ~ element_of_set(X6,f12(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5,f21(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))))
| ~ topological_space(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| connected_space(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| topological_space(X2,X3) ) ).
cnf(u3323,axiom,
( ~ subset_sets(f14(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8,X9),X1)
| element_of_set(X9,union_of_members(top_of_basis(X10)))
| ~ closed(sF1,X7,X8)
| ~ subset_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),sF1)
| ~ subset_sets(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7)
| ~ closed(interior(X0,X1,X2),X4,X5)
| ~ topological_space(closure(X3,X4,X5),X6)
| hausdorff(closure(X3,X4,X5),X6)
| element_of_set(f11(X10,closure(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8)),sF3)
| ~ element_of_set(X11,f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)))
| ~ subset_sets(X3,interior(X0,X1,X2))
| element_of_set(X11,interior(f14(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7,X8,X9),X1,X2)) ) ).
cnf(u497,axiom,
( element_of_collection(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X2)
| ~ topological_space(interior(X0,X1,X2),X3)
| hausdorff(interior(X0,X1,X2),X3) ) ).
cnf(u2630,axiom,
( element_of_set(f11(X4,f18(X1,X3,X2,X0)),f18(X1,X3,X2,X0))
| element_of_set(X0,union_of_members(top_of_basis(X4)))
| ~ hausdorff(X1,X3)
| ~ element_of_set(X2,X1)
| eq_p(X2,X0)
| ~ element_of_set(X0,X1) ) ).
cnf(u794,negated_conjecture,
( element_of_set(f19(f13(a,cx,ct,f11(X0,sF0)),X1),sF0)
| element_of_collection(sF0,top_of_basis(X0))
| ~ topological_space(f13(a,cx,ct,f11(X0,sF0)),X1)
| hausdorff(f13(a,cx,ct,f11(X0,sF0)),X1) ) ).
cnf(u444,axiom,
( open(f13(X0,X1,X2,f7(interior(X0,X1,X2),X3)),X1,X2)
| ~ topological_space(interior(X0,X1,X2),X3)
| basis(interior(X0,X1,X2),X3) ) ).
cnf(u448,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,X0),X1),sF0)
| ~ topological_space(f13(a,cx,ct,X0),X1)
| basis(f13(a,cx,ct,X0),X1)
| ~ element_of_set(X0,sF0) ) ).
cnf(u3451,axiom,
( element_of_set(f20(sF0,X0),union_of_members(ct))
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0) ) ).
cnf(u36144,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| element_of_set(f11(X1,union_of_members(ct)),union_of_members(X4)) ) ).
cnf(u625,axiom,
( ~ element_of_set(X2,X0)
| element_of_set(f11(X1,X0),X0)
| element_of_set(X2,union_of_members(top_of_basis(X1))) ) ).
cnf(u139,negated_conjecture,
( subset_sets(a,f14(a,cx,ct,X0))
| element_of_set(X0,sF3) ) ).
cnf(u6274,axiom,
( element_of_set(f11(subspace_topology(X5,X6,X7),f10(X3,closure(X0,X1,X2),X4)),f10(X3,closure(X0,X1,X2),X4))
| ~ closed(sF1,X1,X2)
| ~ element_of_collection(sF3,X3)
| ~ element_of_set(X4,closure(X0,X1,X2))
| ~ subset_sets(X0,sF1)
| topological_space(X5,X6)
| ~ subset_sets(sF3,closure(X0,X1,X2)) ) ).
cnf(u3173,axiom,
( closed(f14(relative_complement_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),X4,X5,X6),X4,X5)
| element_of_set(X7,interior(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,X6),X1,X2))
| ~ subset_sets(relative_complement_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),X4)
| ~ subset_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(X4,X5)
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ subset_sets(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,X6),X1)
| ~ element_of_set(X7,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X6,boundary(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5)) ) ).
cnf(neighborhood_60,axiom,
( ~ neighborhood(X0,X1,X2,X3)
| open(X0,X2,X3) ) ).
cnf(u54809,negated_conjecture,
( ~ element_of_set(X0,f13(a,cx,ct,f20(sF0,X1)))
| hausdorff(sF0,X1)
| element_of_set(X0,f13(f14(f13(a,cx,ct,f20(sF0,X1)),X2,X3,X4),cx,ct,X0))
| element_of_set(X4,X5) ) ).
cnf(u1356,axiom,
( ~ closed(boundary(X1,X2,X3),X5,X6)
| element_of_set(f20(closure(X4,X5,X6),X7),union_of_members(top_of_basis(X0)))
| ~ subset_sets(X4,boundary(X1,X2,X3))
| element_of_set(f11(X0,closure(X1,X2,X3)),closure(X1,X2,X3))
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7) ) ).
cnf(u1338,axiom,
( ~ closed(X1,X4,X5)
| element_of_set(f11(X2,closure(X3,X4,X5)),union_of_members(top_of_basis(X0)))
| element_of_collection(closure(X3,X4,X5),top_of_basis(X2))
| element_of_set(f11(X0,X1),X1)
| ~ subset_sets(X3,X1) ) ).
cnf(u2529,negated_conjecture,
( ~ element_of_set(X0,f13(a,cx,ct,X1))
| subset_sets(X2,X3)
| element_of_set(f11(subspace_topology(X3,X4,X2),f13(a,cx,ct,X1)),sF0)
| ~ element_of_set(X1,sF0) ) ).
cnf(u1179,negated_conjecture,
( element_of_collection(f13(a,cx,ct,f7(sF0,X1)),top_of_basis(X0))
| basis(sF0,X1)
| ~ topological_space(sF0,X1)
| element_of_set(f11(X0,f13(a,cx,ct,f7(sF0,X1))),sF0) ) ).
cnf(u5857,negated_conjecture,
( element_of_set(X1,f14(a,cx,ct,f20(closure(relative_complement_sets(a,cx),cx,ct),X0)))
| ~ topological_space(closure(relative_complement_sets(a,cx),cx,ct),X0)
| hausdorff(closure(relative_complement_sets(a,cx),cx,ct),X0)
| ~ element_of_set(X1,sF3)
| element_of_set(f20(closure(relative_complement_sets(a,cx),cx,ct),X0),sF1) ) ).
cnf(u872,axiom,
( ~ closed(f13(closure(X0,X1,X2),X3,X4,f11(X5,interior(closure(X0,X1,X2),X3,X4))),X1,X2)
| ~ subset_sets(X0,f13(closure(X0,X1,X2),X3,X4,f11(X5,interior(closure(X0,X1,X2),X3,X4))))
| ~ element_of_collection(f13(closure(X0,X1,X2),X3,X4,f11(X5,interior(closure(X0,X1,X2),X3,X4))),X6)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X6))
| element_of_collection(interior(closure(X0,X1,X2),X3,X4),top_of_basis(X5)) ) ).
cnf(u5261,negated_conjecture,
( ~ open(f1(ct,f20(X1,X2)),X1,X2)
| ~ disjoint_s(X0,f1(ct,f20(X1,X2)))
| hausdorff(X1,X2)
| ~ open(X0,X1,X2)
| ~ element_of_set(f19(X1,X2),X0)
| ~ element_of_set(f20(X1,X2),cx) ) ).
cnf(u4439,axiom,
( ~ element_of_set(X6,f8(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(top_of_basis(subspace_topology(X3,X4,X5))))),top_of_basis(subspace_topology(X3,X4,X5))))
| ~ element_of_collection(union_of_members(top_of_basis(subspace_topology(X3,X4,X5))),subspace_topology(X1,X2,X0))
| basis(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(top_of_basis(subspace_topology(X3,X4,X5))))),top_of_basis(subspace_topology(X3,X4,X5)))
| topological_space(X3,X4) ) ).
cnf(u4656,axiom,
( ~ element_of_collection(f13(X2,X3,X4,f20(interior(X2,X3,X4),X5)),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ topological_space(interior(X2,X3,X4),X5)
| hausdorff(interior(X2,X3,X4),X5)
| element_of_set(f11(X0,intersection_of_members(X1)),interior(X2,X3,X4)) ) ).
cnf(u5709,axiom,
( element_of_set(f19(boundary(relative_complement_sets(X2,X3),X3,subspace_topology(X0,X1,X4)),X5),boundary(X2,X3,subspace_topology(X0,X1,X4)))
| ~ subset_sets(X2,X3)
| ~ topological_space(boundary(relative_complement_sets(X2,X3),X3,subspace_topology(X0,X1,X4)),X5)
| hausdorff(boundary(relative_complement_sets(X2,X3),X3,subspace_topology(X0,X1,X4)),X5)
| topological_space(X0,X1) ) ).
cnf(subspace_topology_45,axiom,
( equal_sets(X0,intersection_of_sets(X3,f12(X1,X2,X3,X0)))
| ~ element_of_collection(X0,subspace_topology(X1,X2,X3)) ) ).
cnf(u4027,axiom,
( element_of_set(f11(X7,f13(X4,X5,X6,f19(closure(X0,X1,X2),X3))),interior(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| element_of_collection(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),top_of_basis(X7)) ) ).
cnf(u2525,axiom,
( ~ element_of_set(X0,X1)
| subset_sets(X2,X3)
| element_of_set(f11(subspace_topology(X3,X4,X2),X1),X1) ) ).
cnf(u5822,negated_conjecture,
( element_of_collection(f1(ct,f7(X0,ct)),ct)
| basis(X0,ct)
| ~ topological_space(X0,ct) ) ).
cnf(u715,axiom,
( topological_space(X0,subspace_topology(X1,X2,X0))
| ~ connected_set(X0,X1,X2) ) ).
cnf(u961,axiom,
( element_of_set(f20(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ subset_sets(relative_complement_sets(X0,X1),closure(X0,X1,X2))
| ~ closed(closure(X0,X1,X2),X1,X2)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3) ) ).
cnf(u5125,negated_conjecture,
( element_of_set(f11(X1,f14(a,cx,ct,X2)),f14(a,cx,ct,X2))
| element_of_set(f11(X3,union_of_members(top_of_basis(X1))),union_of_members(top_of_basis(X1)))
| element_of_set(X0,union_of_members(top_of_basis(X3)))
| element_of_set(X2,sF3)
| ~ element_of_set(X0,sF3) ) ).
cnf(u53857,negated_conjecture,
( open(f13(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,X6),X1,X2,X7),X1,X2)
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X6,closure(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5))
| ~ element_of_set(X7,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3))) ) ).
cnf(u54510,negated_conjecture,
( ~ element_of_set(X7,f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)))
| hausdorff(interior(X1,X2,X3),X4)
| element_of_set(X7,f13(f14(f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)),X5,X6,X0),X2,X3,X7))
| element_of_set(X0,union_of_members(X8)) ) ).
cnf(u2653,axiom,
( element_of_collection(f12(X0,X1,X2,f1(subspace_topology(X0,X1,X2),f11(X3,union_of_members(subspace_topology(X0,X1,X2))))),X1)
| element_of_collection(union_of_members(subspace_topology(X0,X1,X2)),top_of_basis(X3)) ) ).
cnf(u1085,axiom,
( ~ closed(f14(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X1,X2)
| ~ subset_sets(X0,f14(X4,X5,X6,f19(closure(X0,X1,X2),X3)))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(X5,X6)
| ~ subset_sets(X4,X5)
| element_of_set(f19(closure(X0,X1,X2),X3),closure(X4,X5,X6)) ) ).
cnf(u843,axiom,
( ~ closed(interior(X4,X5,X6),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,interior(X4,X5,X6))
| topological_space(X5,X6) ) ).
cnf(u6443,axiom,
( ~ element_of_collection(closure(X5,X2,X3),X7)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X1,X4,X0),closure(X5,X2,X3)),sF3)
| ~ subset_sets(X5,sF1)
| element_of_collection(intersection_of_members(X7),top_of_basis(X6))
| subset_sets(X0,X1) ) ).
cnf(u5665,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),X6)
| closed(f14(X3,X4,X5,X7),X4,X5)
| ~ closed(X6,X4,X5)
| ~ subset_sets(X3,X6)
| topological_space(X0,X1)
| ~ subset_sets(X3,X4) ) ).
cnf(u5733,axiom,
( ~ closed(closure(relative_complement_sets(X2,X3),X3,subspace_topology(X1,X4,X0)),X5,X6)
| ~ subset_sets(X2,X3)
| subset_sets(X0,X1)
| ~ subset_sets(X7,closure(relative_complement_sets(X2,X3),X3,subspace_topology(X1,X4,X0)))
| element_of_collection(closure(X7,X5,X6),top_of_basis(X8))
| element_of_set(f11(X8,closure(X7,X5,X6)),boundary(X2,X3,subspace_topology(X1,X4,X0))) ) ).
cnf(u36130,negated_conjecture,
( element_of_set(f20(f1(top_of_basis(X0),X1),X2),f10(X0,f1(top_of_basis(X0),X1),f20(f1(top_of_basis(X0),X1),X2)))
| limit_point(X1,X3,X4,top_of_basis(X0))
| hausdorff(f1(top_of_basis(X0),X1),X2) ) ).
cnf(u11130,negated_conjecture,
( ~ element_of_set(f15(f20(boundary(X0,X1,X2),X3),X4,X5,X6,X7),sF1)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ neighborhood(X7,f20(boundary(X0,X1,X2),X3),X5,X6) ) ).
cnf(u166,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,X0),X1)
| ~ topological_space(cx,X1)
| ~ element_of_set(X2,f13(a,cx,ct,X0))
| ~ element_of_set(X0,sF0)
| element_of_set(X2,interior(a,cx,X1)) ) ).
cnf(u36080,negated_conjecture,
( element_of_set(f11(X1,union_of_members(top_of_basis(X4))),f13(X5,X6,X7,f11(X1,union_of_members(top_of_basis(X4)))))
| element_of_set(f11(X4,union_of_members(ct)),f13(X8,X9,X10,f11(X4,union_of_members(ct))))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u3693,axiom,
( element_of_set(X10,interior(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,f11(X9,f14(closure(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5),X6,X7,X8))),X1,X2))
| ~ element_of_collection(closure(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5),X9)
| ~ subset_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(X4,X5)
| element_of_set(X8,closure(closure(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5),X6,X7))
| ~ subset_sets(closure(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5),X6)
| ~ topological_space(X6,X7)
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ subset_sets(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,f11(X9,f14(closure(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5),X6,X7,X8))),X1)
| ~ element_of_set(X10,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_collection(f14(closure(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5),X6,X7,X8),top_of_basis(X9)) ) ).
cnf(u509,axiom,
( element_of_collection(f13(a,cx,ct,f19(sF0,X0)),ct)
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0) ) ).
cnf(u9697,negated_conjecture,
( eq_p(f19(boundary(X0,X1,X2),X3),X4)
| ~ element_of_set(X4,sF1)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u806,axiom,
( element_of_collection(X0,subspace_topology(X1,X2,X0))
| ~ connected_set(X0,X1,X2) ) ).
cnf(u440,negated_conjecture,
( element_of_set(f7(f1(ct,X0),X1),union_of_members(ct))
| ~ topological_space(f1(ct,X0),X1)
| ~ element_of_set(X0,cx)
| basis(f1(ct,X0),X1) ) ).
cnf(u3603,axiom,
( element_of_set(X7,interior(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,f11(X6,closure(relative_complement_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),X4,X5))),X1,X2))
| element_of_collection(closure(relative_complement_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),X4,X5),top_of_basis(X6))
| ~ subset_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ subset_sets(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5,f11(X6,closure(relative_complement_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),X4,X5))),X1)
| ~ element_of_set(X7,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(f11(X6,closure(relative_complement_sets(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),X4,X5)),boundary(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4,X5)) ) ).
cnf(u1287,axiom,
( element_of_set(f11(X4,closure(X1,X2,X3)),union_of_members(top_of_basis(X0)))
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X4)) ) ).
cnf(u637,axiom,
( element_of_collection(interior(X1,X2,X3),top_of_basis(X0))
| topological_space(X2,X3) ) ).
cnf(u2476,axiom,
( element_of_set(X3,union_of_members(subspace_topology(X1,X2,X0)))
| ~ element_of_set(X3,empty_set)
| ~ connected_set(X0,X1,X2) ) ).
cnf(u619,axiom,
( element_of_set(f20(closure(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3),boundary(relative_complement_sets(X0,X1),X1,X2))
| ~ topological_space(closure(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3)
| ~ element_of_set(f20(closure(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3),boundary(X0,X1,X2)) ) ).
cnf(closure_56,axiom,
( subset_sets(X1,f14(X1,X2,X3,X0))
| element_of_set(X0,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ) ).
cnf(u4661,axiom,
( ~ element_of_collection(closure(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ subset_sets(X2,X5)
| ~ closed(X5,X3,X4)
| element_of_set(f11(X0,intersection_of_members(X1)),X5) ) ).
cnf(u6947,negated_conjecture,
( ~ open(f14(a,cx,ct,X2),X0,X1)
| ~ element_of_set(f20(X0,X1),sF3)
| element_of_set(X3,sF3)
| ~ disjoint_s(X4,f14(a,cx,ct,X2))
| element_of_set(X2,f14(a,cx,ct,X3))
| hausdorff(X0,X1)
| ~ open(X4,X0,X1)
| ~ element_of_set(f19(X0,X1),X4) ) ).
cnf(u1049,axiom,
( element_of_set(X10,interior(f14(f13(X0,X1,X2,f20(closure(X5,X3,X4),X6)),X7,X8,X9),X1,X2))
| ~ topological_space(closure(X5,X3,X4),X6)
| hausdorff(closure(X5,X3,X4),X6)
| ~ subset_sets(f14(f13(X0,X1,X2,f20(closure(X5,X3,X4),X6)),X7,X8,X9),X1)
| ~ element_of_set(X10,f13(X0,X1,X2,f20(closure(X5,X3,X4),X6)))
| ~ subset_sets(X5,interior(X0,X1,X2))
| ~ closed(interior(X0,X1,X2),X3,X4)
| element_of_set(X9,closure(f13(X0,X1,X2,f20(closure(X5,X3,X4),X6)),X7,X8))
| ~ subset_sets(f13(X0,X1,X2,f20(closure(X5,X3,X4),X6)),X7)
| ~ topological_space(X7,X8) ) ).
cnf(u5642,axiom,
( ~ subset_sets(f17(X1,X3,X2,X0),X4)
| eq_p(X2,X0)
| ~ hausdorff(X1,X3)
| ~ element_of_set(X2,X1)
| ~ subset_sets(X4,X1)
| ~ element_of_set(X5,f17(X1,X3,X2,X0))
| ~ element_of_set(X0,X1)
| element_of_set(X5,interior(X4,X1,X3)) ) ).
cnf(u3328,axiom,
( element_of_set(f11(X1,closure(X2,X3,X4)),sF3)
| subset_sets(X2,f14(X2,X3,X4,X0))
| element_of_set(X0,f1(top_of_basis(X1),X0))
| ~ subset_sets(X2,sF1)
| ~ subset_sets(X2,X3)
| ~ closed(sF1,X3,X4) ) ).
cnf(u3239,axiom,
( element_of_set(f20(boundary(X0,X1,X2),X3),sF3)
| ~ subset_sets(X0,sF1)
| ~ closed(sF1,X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u6557,negated_conjecture,
( ~ element_of_set(X0,sF3)
| element_of_set(X0,sF0) ) ).
cnf(u884,negated_conjecture,
( element_of_set(f11(X0,sF3),f14(a,cx,ct,X1))
| element_of_collection(sF3,top_of_basis(X0))
| element_of_set(X1,sF3) ) ).
cnf(u610,axiom,
( element_of_set(f20(sF0,X0),f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| ~ topological_space(sF0,X0) ) ).
cnf(u6437,axiom,
( basis(closure(X5,X2,X3),f24(closure(X5,X2,X3),X6))
| element_of_set(f11(subspace_topology(X1,X4,X0),closure(X5,X2,X3)),sF3)
| ~ closed(sF1,X2,X3)
| ~ subset_sets(X5,sF1)
| ~ topological_space(closure(X5,X2,X3),X6)
| subset_sets(X0,X1)
| compact_space(closure(X5,X2,X3),X6) ) ).
cnf(u5573,axiom,
( ~ closed(boundary(relative_complement_sets(X0,X1),X1,X2),cx,ct)
| ~ subset_sets(a,boundary(relative_complement_sets(X0,X1),X1,X2))
| element_of_collection(sF3,top_of_basis(X3))
| ~ element_of_set(f11(X3,sF3),closure(X0,X1,X2))
| element_of_set(f11(X3,sF3),boundary(X0,X1,X2)) ) ).
cnf(topology_generated_41,axiom,
( ~ element_of_set(f11(X1,X0),X2)
| element_of_collection(X0,top_of_basis(X1))
| ~ element_of_collection(X2,X1)
| ~ subset_sets(X2,X0) ) ).
cnf(u3367,axiom,
( ~ closed(closure(relative_complement_sets(X1,X2),X2,X3),cx,ct)
| ~ element_of_set(f11(X0,sF3),closure(X1,X2,X3))
| ~ subset_sets(a,closure(relative_complement_sets(X1,X2),X2,X3))
| element_of_collection(sF3,top_of_basis(X0))
| element_of_set(f11(X0,sF3),boundary(X1,X2,X3)) ) ).
cnf(u953,axiom,
( ~ closed(boundary(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,boundary(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| subset_sets(relative_complement_sets(X4,X5),X5) ) ).
cnf(u727,axiom,
( element_of_set(X4,interior(f14(relative_complement_sets(X0,X1),X1,X2,X3),X1,X5))
| ~ element_of_set(X4,relative_complement_sets(X0,X1))
| ~ closed(X0,X1,X5)
| ~ subset_sets(f14(relative_complement_sets(X0,X1),X1,X2,X3),X1)
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| ~ element_of_set(X3,closure(X0,X1,X2))
| element_of_set(X3,boundary(X0,X1,X2)) ) ).
cnf(u36132,negated_conjecture,
( element_of_set(f19(f1(top_of_basis(X0),X1),X2),f10(X0,f1(top_of_basis(X0),X1),f19(f1(top_of_basis(X0),X1),X2)))
| limit_point(X1,X3,X4,top_of_basis(X0))
| hausdorff(f1(top_of_basis(X0),X1),X2) ) ).
cnf(u973,negated_conjecture,
( element_of_set(f20(sF3,X0),f14(a,cx,ct,f11(X1,X2)))
| hausdorff(sF3,X0)
| ~ topological_space(sF3,X0)
| ~ element_of_collection(sF3,X1)
| element_of_collection(X2,top_of_basis(X1))
| ~ subset_sets(sF3,X2) ) ).
cnf(u6028,negated_conjecture,
( element_of_set(X8,interior(f14(f13(X1,X2,X3,f19(closure(X4,X5,X6),X7)),cx,ct,X0),X2,X3))
| ~ subset_sets(f13(X1,X2,X3,f19(closure(X4,X5,X6),X7)),sF0)
| ~ subset_sets(f13(X1,X2,X3,f19(closure(X4,X5,X6),X7)),cx)
| ~ closed(interior(X1,X2,X3),X5,X6)
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7)
| ~ subset_sets(f14(f13(X1,X2,X3,f19(closure(X4,X5,X6),X7)),cx,ct,X0),X2)
| ~ element_of_set(X8,f13(X1,X2,X3,f19(closure(X4,X5,X6),X7)))
| ~ subset_sets(X4,interior(X1,X2,X3))
| element_of_set(X0,sF0) ) ).
cnf(u36127,negated_conjecture,
( element_of_set(f11(X1,union_of_members(ct)),interior(X4,X5,X6))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u48640,negated_conjecture,
( open(f13(f14(f16(X0,X1,X2,X3),cx,ct,X4),X2,X3,X5),X2,X3)
| ~ element_of_set(X5,f16(X0,X1,X2,X3))
| element_of_set(X4,sF0)
| limit_point(X0,X1,X2,X3) ) ).
cnf(u818,axiom,
( hausdorff(boundary(X0,X1,X2),subspace_topology(X3,X4,boundary(X0,X1,X2)))
| ~ connected_set(boundary(X0,X1,X2),X3,X4)
| subset_sets(X0,X1) ) ).
cnf(u4617,negated_conjecture,
( ~ element_of_collection(f1(ct,f15(X2,X3,X4,X5,X6)),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ neighborhood(X6,X2,X4,X5)
| ~ limit_point(X2,X3,X4,X5)
| ~ element_of_collection(X3,ct)
| ~ element_of_collection(X6,ct)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(ct)) ) ).
cnf(basis_for_topology_30,axiom,
( ~ element_of_set(X2,intersection_of_sets(X3,X4))
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X3,X1)
| ~ element_of_collection(X4,X1)
| ~ basis(X0,X1)
| element_of_collection(f6(X0,X1,X2,X3,X4),X1) ) ).
cnf(u38015,negated_conjecture,
( element_of_set(f19(f1(top_of_basis(X3),X0),X4),f10(X3,f1(top_of_basis(X3),X0),f19(f1(top_of_basis(X3),X0),X4)))
| limit_point(X0,X1,X5,X6)
| hausdorff(f1(top_of_basis(X3),X0),X4) ) ).
cnf(u7371,negated_conjecture,
( limit_point(X0,X4,X5,X6)
| element_of_set(X0,f13(X1,X2,X3,X0)) ) ).
cnf(u708,axiom,
( element_of_set(f11(X3,boundary(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2)),boundary(relative_complement_sets(X0,X1),X1,X2))
| element_of_collection(boundary(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),top_of_basis(X3))
| ~ element_of_set(f11(X3,boundary(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2)),boundary(X0,X1,X2)) ) ).
cnf(u2968,axiom,
( ~ closed(closure(X4,X5,X6),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,closure(X4,X5,X6))
| subset_sets(X4,X5) ) ).
cnf(u6057,axiom,
( basis(sF1,subspace_topology(X0,X1,sF1))
| ~ connected_set(sF1,X0,X1) ) ).
cnf(u55324,negated_conjecture,
( ~ element_of_set(X0,closure(f13(a,cx,ct,f20(sF0,X1)),X2,X3))
| hausdorff(sF0,X1)
| ~ element_of_set(X4,f13(a,cx,ct,f20(sF0,X1)))
| eq_p(X5,X0)
| element_of_set(X4,f13(f14(f13(a,cx,ct,f20(sF0,X1)),X2,X3,X5),cx,ct,X4)) ) ).
cnf(u2807,axiom,
( element_of_collection(f13(X0,X1,X2,f11(X6,closure(X5,X3,X4))),X2)
| ~ subset_sets(X5,interior(X0,X1,X2))
| element_of_collection(closure(X5,X3,X4),top_of_basis(X6))
| ~ closed(interior(X0,X1,X2),X3,X4) ) ).
cnf(u3250,axiom,
( ~ element_of_set(f20(boundary(X0,X1,X2),X3),closure(X4,X5,X6))
| ~ subset_sets(X0,closure(relative_complement_sets(X4,X5),X5,X6))
| ~ closed(closure(relative_complement_sets(X4,X5),X5,X6),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3)
| element_of_set(f20(boundary(X0,X1,X2),X3),boundary(X4,X5,X6)) ) ).
cnf(u5327,axiom,
( ~ element_of_set(f19(closure(X1,X2,X3),X4),X0)
| ~ open(sF3,closure(X1,X2,X3),X4)
| hausdorff(closure(X1,X2,X3),X4)
| ~ open(X0,closure(X1,X2,X3),X4)
| ~ disjoint_s(X0,sF3)
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3) ) ).
cnf(u36062,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f10(X1,f1(top_of_basis(X1),f11(X0,union_of_members(ct))),f11(X0,union_of_members(ct))))
| open(f13(X4,X5,X6,f11(X7,union_of_members(top_of_basis(X0)))),X5,X6)
| limit_point(f11(X0,union_of_members(ct)),X2,X3,top_of_basis(X1))
| element_of_set(X8,f1(top_of_basis(X7),X8))
| ~ element_of_set(X8,cx) ) ).
cnf(u2498,axiom,
( element_of_set(X0,f10(X3,relative_complement_sets(X1,X2),X0))
| ~ element_of_set(X0,relative_complement_sets(X1,X2))
| ~ closed(X1,X2,top_of_basis(X3)) ) ).
cnf(u5026,axiom,
( element_of_set(f11(subspace_topology(X2,X3,X4),f1(X0,f11(X1,union_of_members(X0)))),f1(X0,f11(X1,union_of_members(X0))))
| topological_space(X2,X3)
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ) ).
cnf(u633,negated_conjecture,
( element_of_set(f11(X0,intersection_of_sets(X1,X2)),union_of_members(ct))
| element_of_collection(intersection_of_sets(X1,X2),top_of_basis(X0))
| ~ element_of_collection(X2,ct)
| ~ element_of_collection(X1,ct) ) ).
cnf(u3178,negated_conjecture,
( ~ element_of_set(f11(X4,f14(f14(a,cx,ct,X0),X1,X2,X3)),sF3)
| element_of_set(X3,boundary(f14(a,cx,ct,X0),X1,X2))
| ~ subset_sets(relative_complement_sets(f14(a,cx,ct,X0),X1),X1)
| ~ subset_sets(f14(a,cx,ct,X0),X1)
| ~ topological_space(X1,X2)
| ~ element_of_collection(f14(a,cx,ct,X0),X4)
| element_of_collection(f14(f14(a,cx,ct,X0),X1,X2,X3),top_of_basis(X4))
| closed(f14(relative_complement_sets(f14(a,cx,ct,X0),X1),X1,X2,X3),X1,X2)
| element_of_set(X0,sF3) ) ).
cnf(u3054,axiom,
( ~ closed(relative_complement_sets(X4,X5),X1,X2)
| ~ subset_sets(X0,relative_complement_sets(X4,X5))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ closed(X4,X5,X6)
| element_of_set(f19(boundary(X0,X1,X2),X3),union_of_members(X6)) ) ).
cnf(u2554,negated_conjecture,
( element_of_set(X3,interior(a,cx,subspace_topology(X1,X2,f13(a,cx,ct,f7(sF0,X0)))))
| ~ topological_space(cx,subspace_topology(X1,X2,f13(a,cx,ct,f7(sF0,X0))))
| ~ element_of_set(X3,f13(a,cx,ct,f7(sF0,X0)))
| ~ topological_space(sF0,X0)
| basis(sF0,X0)
| ~ connected_set(f13(a,cx,ct,f7(sF0,X0)),X1,X2) ) ).
cnf(u2786,axiom,
( ~ closed(boundary(X0,X1,X2),cx,ct)
| ~ subset_sets(a,boundary(X0,X1,X2))
| element_of_collection(sF3,top_of_basis(X3))
| element_of_set(f11(X4,closure(X0,X1,X2)),sF3)
| ~ subset_sets(X0,sF1)
| ~ closed(sF1,X1,X2)
| element_of_set(f11(X3,sF3),union_of_members(top_of_basis(X4))) ) ).
cnf(u4657,axiom,
( ~ element_of_collection(f13(X2,X3,X4,f20(closure(X5,X6,X7),X8)),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ topological_space(closure(X5,X6,X7),X8)
| hausdorff(closure(X5,X6,X7),X8)
| ~ closed(interior(X2,X3,X4),X6,X7)
| ~ subset_sets(X5,interior(X2,X3,X4))
| element_of_set(f11(X0,intersection_of_members(X1)),interior(X2,X3,X4)) ) ).
cnf(u3668,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,f20(sF0,X0)),X1),union_of_members(top_of_basis(X2)))
| basis(f13(a,cx,ct,f20(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0)
| element_of_set(f11(X2,sF0),sF0)
| ~ topological_space(f13(a,cx,ct,f20(sF0,X0)),X1) ) ).
cnf(u36059,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f10(X1,f1(top_of_basis(X1),f11(X0,union_of_members(ct))),f11(X0,union_of_members(ct))))
| limit_point(f11(X0,union_of_members(ct)),X2,X3,top_of_basis(X1))
| element_of_set(X4,f1(top_of_basis(X0),X4))
| ~ element_of_set(X4,cx) ) ).
cnf(u4642,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,f7(sF0,X2)),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),sF0)
| basis(sF0,X2)
| ~ topological_space(sF0,X2) ) ).
cnf(u275,axiom,
( element_of_set(f20(boundary(X0,X1,X3),X4),X2)
| ~ closed(X2,X1,X3)
| ~ subset_sets(relative_complement_sets(X0,X1),X2)
| ~ topological_space(boundary(X0,X1,X3),X4)
| hausdorff(boundary(X0,X1,X3),X4) ) ).
cnf(u6598,negated_conjecture,
( ~ subset_sets(a,f14(X0,cx,ct,X1))
| element_of_set(X2,closure(X0,cx,ct))
| ~ subset_sets(X0,cx)
| ~ subset_sets(f14(X0,cx,ct,X1),sF3)
| element_of_set(X1,f14(X0,cx,ct,X2))
| ~ element_of_collection(f14(X0,cx,ct,X1),X3)
| element_of_collection(sF3,top_of_basis(X3)) ) ).
cnf(u1187,axiom,
( ~ subset_sets(X1,f13(a,cx,ct,f7(sF0,X0)))
| basis(sF0,X0)
| ~ element_of_collection(X1,X2)
| ~ topological_space(a,X2)
| ~ element_of_set(X3,X1)
| ~ topological_space(sF0,X0)
| element_of_set(X3,interior(f13(a,cx,ct,f7(sF0,X0)),a,X2)) ) ).
cnf(u6707,negated_conjecture,
( ~ element_of_set(X2,f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(X2,interior(X1,cx,ct)) ) ).
cnf(u2457,axiom,
( open(f18(X1,X3,X0,X2),X1,X3)
| ~ element_of_set(X2,X1)
| eq_p(X0,X2)
| ~ hausdorff(X1,X3)
| ~ element_of_set(X0,X1) ) ).
cnf(u4448,axiom,
( element_of_set(X4,f10(X2,f12(X1,top_of_basis(X2),X3,f2(subspace_topology(X1,top_of_basis(X2),X3),X0)),X4))
| ~ element_of_set(X4,f12(X1,top_of_basis(X2),X3,f2(subspace_topology(X1,top_of_basis(X2),X3),X0)))
| element_of_set(X0,intersection_of_members(subspace_topology(X1,top_of_basis(X2),X3))) ) ).
cnf(u622,axiom,
( subset_sets(X0,f14(X0,X1,X2,f20(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f20(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1) ) ).
cnf(u128,axiom,
( subset_sets(f13(a,cx,ct,X0),a)
| ~ element_of_set(X0,sF0) ) ).
cnf(closure_53,axiom,
( ~ element_of_set(X0,closure(X1,X2,X3))
| topological_space(X2,X3) ) ).
cnf(u591,axiom,
( element_of_collection(f12(X1,X2,X3,f2(subspace_topology(X1,X2,X3),X0)),X2)
| element_of_set(X0,intersection_of_members(subspace_topology(X1,X2,X3))) ) ).
cnf(u1315,axiom,
( element_of_set(f11(X0,union_of_members(ct)),union_of_members(ct))
| element_of_set(X1,union_of_members(top_of_basis(X0)))
| ~ element_of_set(X1,sF0) ) ).
cnf(u837,axiom,
( ~ closed(intersection_of_members(X4),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,intersection_of_members(X4))
| ~ element_of_collection(X5,X4)
| element_of_set(f11(X0,closure(X1,X2,X3)),X5) ) ).
cnf(u2585,negated_conjecture,
( ~ element_of_collection(f10(X1,a,X0),X2)
| ~ element_of_collection(a,top_of_basis(X1))
| ~ topological_space(cx,X2)
| ~ element_of_set(X3,f10(X1,a,X0))
| ~ element_of_set(X0,a)
| element_of_set(X3,interior(a,cx,X2)) ) ).
cnf(u4778,axiom,
( ~ element_of_set(X4,f12(X1,X2,X3,f22(X0,subspace_topology(X1,X2,X3))))
| ~ topological_space(X0,subspace_topology(X1,X2,X3))
| connected_space(X0,subspace_topology(X1,X2,X3))
| element_of_set(X4,union_of_members(X2)) ) ).
cnf(u5545,axiom,
( element_of_set(f11(X4,closure(X3,X1,X2)),X0)
| subset_sets(X3,f14(X3,X1,X2,X5))
| element_of_set(X5,union_of_members(top_of_basis(X4)))
| ~ subset_sets(X3,X0)
| ~ closed(X0,X1,X2)
| ~ subset_sets(X3,X1) ) ).
cnf(u4035,axiom,
( element_of_set(f20(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X7),interior(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X7)
| hausdorff(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X7) ) ).
cnf(u34577,axiom,
( ~ compact_space(X0,f24(X1,X2))
| compact_space(X1,X2)
| ~ subset_collections(X2,f24(X1,X2)) ) ).
cnf(u54494,negated_conjecture,
( ~ element_of_set(X8,closure(f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)),X5,X6))
| hausdorff(interior(X1,X2,X3),X4)
| ~ element_of_set(X7,f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)))
| eq_p(X0,X8)
| element_of_set(X7,f13(f14(f13(X1,X2,X3,f20(interior(X1,X2,X3),X4)),X5,X6,X0),X2,X3,X7)) ) ).
cnf(u6045,axiom,
( ~ subset_sets(X0,relative_complement_sets(a,cx))
| ~ topological_space(cx,X1)
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,X1)
| element_of_set(X2,interior(relative_complement_sets(a,cx),cx,X1)) ) ).
cnf(u3444,axiom,
( ~ closed(f13(a,cx,ct,f20(sF0,X0)),X2,X3)
| ~ topological_space(sF0,X0)
| element_of_set(f19(closure(X1,X2,X3),X4),union_of_members(ct))
| hausdorff(closure(X1,X2,X3),X4)
| ~ subset_sets(X1,f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| ~ topological_space(closure(X1,X2,X3),X4) ) ).
cnf(u3927,axiom,
( element_of_set(X7,interior(f14(f16(X0,X1,X2,X3),X4,X5,f19(closure(relative_complement_sets(f16(X0,X1,X2,X3),X4),X4,X5),X6)),X2,X3))
| ~ topological_space(closure(relative_complement_sets(f16(X0,X1,X2,X3),X4),X4,X5),X6)
| hausdorff(closure(relative_complement_sets(f16(X0,X1,X2,X3),X4),X4,X5),X6)
| ~ subset_sets(f16(X0,X1,X2,X3),X4)
| limit_point(X0,X1,X2,X3)
| ~ topological_space(X2,X3)
| ~ subset_sets(f14(f16(X0,X1,X2,X3),X4,X5,f19(closure(relative_complement_sets(f16(X0,X1,X2,X3),X4),X4,X5),X6)),X2)
| ~ element_of_set(X7,f16(X0,X1,X2,X3))
| ~ subset_sets(X1,X2)
| element_of_set(f19(closure(relative_complement_sets(f16(X0,X1,X2,X3),X4),X4,X5),X6),boundary(f16(X0,X1,X2,X3),X4,X5)) ) ).
cnf(u1377,axiom,
( element_of_set(f15(X0,X1,X2,X3,X4),f6(X5,X6,f15(X0,X1,X2,X3,X4),X4,X1))
| ~ element_of_collection(X4,X6)
| ~ element_of_collection(X1,X6)
| ~ basis(X5,X6)
| ~ element_of_set(f15(X0,X1,X2,X3,X4),X5)
| ~ neighborhood(X4,X0,X2,X3)
| ~ limit_point(X0,X1,X2,X3) ) ).
cnf(u1066,axiom,
( ~ closed(relative_complement_sets(X4,X5),X1,X2)
| ~ subset_sets(X0,relative_complement_sets(X4,X5))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ closed(X4,X5,X6)
| element_of_set(f19(closure(X0,X1,X2),X3),union_of_members(X6)) ) ).
cnf(u3619,axiom,
( subset_sets(X1,f14(X1,X2,X3,f11(X0,closure(relative_complement_sets(X1,X2),X2,X3))))
| element_of_set(f11(X0,closure(relative_complement_sets(X1,X2),X2,X3)),closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| element_of_collection(closure(relative_complement_sets(X1,X2),X2,X3),top_of_basis(X0)) ) ).
cnf(u6023,negated_conjecture,
( element_of_set(X2,interior(f14(f13(a,cx,ct,f19(sF0,X1)),cx,ct,X0),cx,ct))
| ~ subset_sets(f13(a,cx,ct,f19(sF0,X1)),sF0)
| ~ subset_sets(f13(a,cx,ct,f19(sF0,X1)),cx)
| ~ topological_space(sF0,X1)
| ~ subset_sets(f14(f13(a,cx,ct,f19(sF0,X1)),cx,ct,X0),cx)
| ~ element_of_set(X2,f13(a,cx,ct,f19(sF0,X1)))
| hausdorff(sF0,X1)
| element_of_set(X0,sF0) ) ).
cnf(u36215,negated_conjecture,
( element_of_set(f11(X3,union_of_members(ct)),interior(X4,X5,X6))
| element_of_set(X0,f10(X3,f1(top_of_basis(X3),X0),X0))
| limit_point(X0,X1,X7,X8)
| ~ element_of_set(X0,cx) ) ).
cnf(u3372,axiom,
( ~ closed(closure(relative_complement_sets(X0,X1),X1,X2),X3,X4)
| ~ subset_sets(X5,closure(relative_complement_sets(X0,X1),X1,X2))
| element_of_collection(closure(X5,X3,X4),top_of_basis(X6))
| element_of_set(f11(X6,closure(X5,X3,X4)),boundary(X0,X1,X2))
| subset_sets(X0,f14(X0,X1,X2,f11(X6,closure(X5,X3,X4))))
| ~ subset_sets(X0,X1) ) ).
cnf(finer_topology_26,axiom,
( ~ finer(X0,X1,X2)
| subset_collections(X1,X0) ) ).
cnf(u3327,axiom,
( ~ subset_sets(f14(f16(X0,X1,X2,X3),X4,X5,X6),X2)
| element_of_set(X6,union_of_members(top_of_basis(X7)))
| ~ closed(sF1,X4,X5)
| ~ subset_sets(f16(X0,X1,X2,X3),sF1)
| ~ subset_sets(f16(X0,X1,X2,X3),X4)
| limit_point(X0,X1,X2,X3)
| ~ topological_space(X2,X3)
| element_of_set(f11(X7,closure(f16(X0,X1,X2,X3),X4,X5)),sF3)
| ~ element_of_set(X8,f16(X0,X1,X2,X3))
| ~ subset_sets(X1,X2)
| element_of_set(X8,interior(f14(f16(X0,X1,X2,X3),X4,X5,X6),X2,X3)) ) ).
cnf(u5646,axiom,
( ~ subset_sets(f18(X1,X3,X2,X0),X4)
| eq_p(X2,X0)
| ~ hausdorff(X1,X3)
| ~ element_of_set(X2,X1)
| ~ subset_sets(X4,X1)
| ~ element_of_set(X5,f18(X1,X3,X2,X0))
| ~ element_of_set(X0,X1)
| element_of_set(X5,interior(X4,X1,X3)) ) ).
cnf(u6599,negated_conjecture,
( ~ subset_sets(a,f14(X0,cx,ct,X1))
| element_of_set(X2,closure(X0,cx,ct))
| ~ subset_sets(X0,cx)
| element_of_set(f11(X3,sF3),f14(X0,cx,ct,X1))
| element_of_collection(sF3,top_of_basis(X3))
| element_of_set(X1,f14(X0,cx,ct,X2)) ) ).
cnf(u5780,negated_conjecture,
( ~ element_of_set(f19(f13(a,cx,ct,f19(sF0,X1)),X2),X0)
| ~ open(sF0,f13(a,cx,ct,f19(sF0,X1)),X2)
| hausdorff(f13(a,cx,ct,f19(sF0,X1)),X2)
| ~ open(X0,f13(a,cx,ct,f19(sF0,X1)),X2)
| ~ disjoint_s(X0,sF0)
| ~ topological_space(sF0,X1)
| hausdorff(sF0,X1) ) ).
cnf(u389,axiom,
( ~ element_of_set(X2,f8(X0,X1))
| ~ topological_space(X0,X1)
| basis(X0,X1)
| element_of_set(X2,union_of_members(X1)) ) ).
cnf(u2908,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),f13(a,cx,ct,f20(sF0,X3))),f13(a,cx,ct,f20(sF0,X3)))
| topological_space(X0,X1)
| hausdorff(sF0,X3)
| ~ topological_space(sF0,X3) ) ).
cnf(u2803,axiom,
( element_of_set(f20(f9(X0,X1),X2),union_of_members(X1))
| basis(X0,X1)
| ~ topological_space(X0,X1)
| ~ topological_space(f9(X0,X1),X2)
| hausdorff(f9(X0,X1),X2) ) ).
cnf(u7731,negated_conjecture,
( element_of_set(f15(X0,X1,X2,X3,X4),union_of_members(X5))
| ~ neighborhood(X4,X0,X2,X3)
| ~ limit_point(X0,X1,X2,X3) ) ).
cnf(u5915,negated_conjecture,
( closed(f14(X0,cx,ct,X1),cx,ct)
| ~ subset_sets(X0,sF0)
| ~ subset_sets(X0,cx)
| element_of_set(X1,sF0) ) ).
cnf(u6586,negated_conjecture,
( element_of_set(X1,f14(a,cx,ct,X0))
| ~ element_of_set(X1,sF3)
| element_of_set(X0,sF0) ) ).
cnf(topological_space_11,axiom,
( ~ subset_collections(X2,X1)
| ~ topological_space(X0,X1)
| element_of_collection(union_of_members(X2),X1) ) ).
cnf(u2977,axiom,
( ~ closed(boundary(X4,X5,X6),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,boundary(X4,X5,X6))
| ~ subset_sets(relative_complement_sets(X4,X5),X7)
| ~ closed(X7,X5,X6)
| element_of_set(f11(X0,boundary(X1,X2,X3)),X7) ) ).
cnf(u159,negated_conjecture,
( ~ topological_space(f14(a,cx,ct,X2),X1)
| ~ element_of_collection(X0,X1)
| ~ element_of_set(X3,X0)
| ~ subset_sets(X0,a)
| element_of_set(X3,interior(a,f14(a,cx,ct,X2),X1))
| element_of_set(X2,sF3) ) ).
cnf(u3957,negated_conjecture,
( element_of_set(f19(f1(ct,f15(X1,X4,X2,X3,X0)),X5),union_of_members(ct))
| ~ limit_point(X1,X4,X2,X3)
| ~ element_of_collection(X4,ct)
| ~ element_of_collection(X0,ct)
| ~ neighborhood(X0,X1,X2,X3)
| ~ topological_space(f1(ct,f15(X1,X4,X2,X3,X0)),X5)
| hausdorff(f1(ct,f15(X1,X4,X2,X3,X0)),X5) ) ).
cnf(u3715,axiom,
( element_of_set(f11(subspace_topology(X4,X5,X6),boundary(X0,X1,X2)),boundary(X0,X1,X2))
| element_of_collection(closure(relative_complement_sets(X0,X1),X1,X2),top_of_basis(X3))
| ~ subset_sets(relative_complement_sets(X0,X1),closure(X0,X1,X2))
| topological_space(X4,X5)
| ~ closed(closure(X0,X1,X2),X1,X2) ) ).
cnf(u6202,negated_conjecture,
( element_of_set(X0,interior(a,sF0,subspace_topology(X2,X3,f13(a,cx,ct,X1))))
| ~ topological_space(sF0,subspace_topology(X2,X3,f13(a,cx,ct,X1)))
| ~ element_of_set(X0,f13(a,cx,ct,X1))
| ~ element_of_set(X1,sF0)
| ~ connected_set(f13(a,cx,ct,X1),X2,X3) ) ).
cnf(u2859,axiom,
( ~ topological_space(X3,X4)
| element_of_set(f11(subspace_topology(X0,X1,X2),X3),X3)
| basis(X3,X4)
| topological_space(X0,X1) ) ).
cnf(u3885,negated_conjecture,
( ~ element_of_set(X2,f13(a,cx,ct,f20(sF0,X1)))
| ~ topological_space(sF0,X1)
| hausdorff(sF0,X1)
| element_of_set(f11(X0,f13(a,cx,ct,f20(sF0,X1))),sF0)
| element_of_set(X2,union_of_members(top_of_basis(X0))) ) ).
cnf(u3771,axiom,
( ~ closed(closure(X3,X4,X5),X8,X9)
| element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),X6)
| ~ closed(X6,X4,X5)
| ~ subset_sets(X3,X6)
| hausdorff(closure(X7,X8,X9),X10)
| ~ subset_sets(X7,closure(X3,X4,X5))
| topological_space(X0,X1)
| ~ topological_space(closure(X7,X8,X9),X10) ) ).
cnf(u5712,axiom,
( element_of_set(f11(X5,boundary(relative_complement_sets(X2,X3),X3,subspace_topology(X0,X1,X4))),boundary(X2,X3,subspace_topology(X0,X1,X4)))
| ~ subset_sets(X2,X3)
| element_of_collection(boundary(relative_complement_sets(X2,X3),X3,subspace_topology(X0,X1,X4)),top_of_basis(X5))
| topological_space(X0,X1) ) ).
cnf(u1969,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X4),closure(X5,X2,X3)),sF3)
| element_of_collection(closure(X5,X2,X3),top_of_basis(X6))
| ~ closed(sF1,X2,X3)
| ~ subset_sets(X5,sF1)
| topological_space(X0,X1) ) ).
cnf(u30993,axiom,
( element_of_set(f11(X0,f1(ct,X1)),f1(X2,f11(X0,f1(ct,X1))))
| ~ element_of_set(X1,sF0)
| element_of_set(X1,f1(top_of_basis(X0),X1)) ) ).
cnf(u892,axiom,
( element_of_set(f7(boundary(X0,X1,X2),X3),X4)
| basis(boundary(X0,X1,X2),X3)
| ~ subset_sets(X0,X4)
| ~ closed(X4,X1,X2)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u3478,axiom,
( ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| subset_sets(X4,X5) ) ).
cnf(u49413,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f1(X2,f11(X0,union_of_members(top_of_basis(X1)))))
| element_of_set(f11(X1,union_of_members(ct)),f1(top_of_basis(X0),f11(X1,union_of_members(ct))))
| ~ element_of_set(f11(X1,union_of_members(ct)),cx) ) ).
cnf(u140,axiom,
( element_of_set(X0,f13(a,cx,ct,X0))
| ~ element_of_set(X0,sF0) ) ).
cnf(u36063,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f10(X1,f1(top_of_basis(X1),f11(X0,union_of_members(ct))),f11(X0,union_of_members(ct))))
| limit_point(f11(X0,union_of_members(ct)),X2,X3,top_of_basis(X1))
| element_of_set(X4,f1(top_of_basis(X0),X4))
| ~ element_of_set(X4,sF0) ) ).
cnf(u4442,axiom,
( basis(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(subspace_topology(X3,X4,X5)))),subspace_topology(X3,X4,X5))
| ~ element_of_collection(union_of_members(subspace_topology(X3,X4,X5)),subspace_topology(X1,X2,X0))
| subset_sets(X5,X3) ) ).
cnf(u829,axiom,
( element_of_collection(X3,subspace_topology(X6,subspace_topology(X4,X5,f12(X0,X1,X2,X3)),X2))
| ~ topological_space(X6,subspace_topology(X4,X5,f12(X0,X1,X2,X3)))
| ~ subset_sets(X2,X6)
| ~ element_of_collection(X3,subspace_topology(X0,X1,X2))
| ~ connected_set(f12(X0,X1,X2,X3),X4,X5) ) ).
cnf(u833,axiom,
( element_of_set(f11(X0,closure(X1,X2,X3)),f1(X4,f11(X0,closure(X1,X2,X3))))
| ~ closed(union_of_members(X4),X2,X3)
| ~ subset_sets(X1,union_of_members(X4))
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(u1403,axiom,
( ~ element_of_set(X0,f13(X1,X2,top_of_basis(subspace_topology(X3,X4,X5)),f19(interior(X1,X2,top_of_basis(subspace_topology(X3,X4,X5))),X6)))
| topological_space(X3,X4)
| ~ topological_space(interior(X1,X2,top_of_basis(subspace_topology(X3,X4,X5))),X6)
| hausdorff(interior(X1,X2,top_of_basis(subspace_topology(X3,X4,X5))),X6) ) ).
cnf(u826,negated_conjecture,
( element_of_set(X3,interior(a,cx,subspace_topology(X1,X2,f13(a,cx,ct,X0))))
| ~ topological_space(cx,subspace_topology(X1,X2,f13(a,cx,ct,X0)))
| ~ element_of_set(X3,f13(a,cx,ct,X0))
| ~ element_of_set(X0,sF0)
| ~ connected_set(f13(a,cx,ct,X0),X1,X2) ) ).
cnf(u3509,axiom,
( ~ closed(boundary(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,boundary(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| topological_space(X5,X6) ) ).
cnf(u6086,negated_conjecture,
( element_of_set(f20(union_of_members(f24(X0,ct)),X1),union_of_members(ct))
| compact_space(X0,ct)
| ~ topological_space(X0,ct)
| ~ topological_space(union_of_members(f24(X0,ct)),X1)
| hausdorff(union_of_members(f24(X0,ct)),X1) ) ).
cnf(u4293,axiom,
( subset_sets(X0,f14(X0,X1,X2,f20(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f20(closure(relative_complement_sets(X0,X1),X1,X2),X3),union_of_members(top_of_basis(X4)))
| element_of_set(f11(X4,boundary(X0,X1,X2)),boundary(X0,X1,X2))
| ~ subset_sets(X0,X1)
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3) ) ).
cnf(u1180,negated_conjecture,
( ~ closed(f13(a,cx,ct,f7(sF0,X4)),X2,X3)
| basis(sF0,X4)
| ~ topological_space(sF0,X4)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| element_of_set(f11(X0,closure(X1,X2,X3)),sF0)
| ~ subset_sets(X1,f13(a,cx,ct,f7(sF0,X4))) ) ).
cnf(u50158,negated_conjecture,
( element_of_set(f19(f12(X3,top_of_basis(X4),X5,f1(subspace_topology(X3,top_of_basis(X4),X5),X0)),X6),f10(X4,f12(X3,top_of_basis(X4),X5,f1(subspace_topology(X3,top_of_basis(X4),X5),X0)),f19(f12(X3,top_of_basis(X4),X5,f1(subspace_topology(X3,top_of_basis(X4),X5),X0)),X6)))
| limit_point(X0,X1,X7,X8)
| hausdorff(f12(X3,top_of_basis(X4),X5,f1(subspace_topology(X3,top_of_basis(X4),X5),X0)),X6) ) ).
cnf(u4848,axiom,
( element_of_set(f7(f9(X0,X1),f24(f9(X0,X1),X2)),union_of_members(X1))
| basis(f9(X0,X1),f24(f9(X0,X1),X2))
| compact_space(f9(X0,X1),X2)
| ~ topological_space(X0,X1)
| basis(X0,X1)
| ~ topological_space(f9(X0,X1),X2) ) ).
cnf(u5202,axiom,
( ~ element_of_set(X4,f12(X1,X2,X3,f9(X0,subspace_topology(X1,X2,X3))))
| basis(X0,subspace_topology(X1,X2,X3))
| ~ topological_space(X0,subspace_topology(X1,X2,X3))
| element_of_set(X4,union_of_members(X2)) ) ).
cnf(u253,axiom,
( ~ element_of_set(f20(closure(relative_complement_sets(X0,X1),X1,X2),X3),closure(X0,X1,X2))
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f20(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2)) ) ).
cnf(u1320,negated_conjecture,
( element_of_set(f11(X0,f1(ct,X1)),f1(ct,X1))
| element_of_set(X1,union_of_members(top_of_basis(X0)))
| ~ element_of_set(X1,cx) ) ).
cnf(u1333,axiom,
( element_of_set(f11(X0,intersection_of_sets(f8(X1,X2),f9(X1,X2))),intersection_of_sets(f8(X1,X2),f9(X1,X2)))
| element_of_set(f7(X1,X2),union_of_members(top_of_basis(X0)))
| ~ equal_sets(union_of_members(X2),X1)
| basis(X1,X2) ) ).
cnf(topology_generated_38,axiom,
( element_of_collection(f10(X1,X0,X2),X1)
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ) ).
cnf(u5260,axiom,
( ~ open(f1(ct,f20(X1,X2)),X1,X2)
| ~ disjoint_s(X0,f1(ct,f20(X1,X2)))
| hausdorff(X1,X2)
| ~ open(X0,X1,X2)
| ~ element_of_set(f19(X1,X2),X0)
| ~ element_of_set(f20(X1,X2),sF0) ) ).
cnf(u3030,axiom,
( ~ element_of_set(X5,union_of_sets(f21(intersection_of_sets(X0,X1),X2),f22(intersection_of_sets(X0,X1),X2)))
| ~ topological_space(X3,X4)
| ~ subset_sets(X0,X3)
| ~ element_of_collection(X1,X4)
| connected_space(intersection_of_sets(X0,X1),X2)
| ~ topological_space(intersection_of_sets(X0,X1),X2)
| element_of_set(X5,union_of_members(subspace_topology(X3,X4,X0))) ) ).
cnf(u53929,negated_conjecture,
( ~ element_of_set(X7,f13(X1,X2,X3,f19(interior(X1,X2,X3),X4)))
| hausdorff(interior(X1,X2,X3),X4)
| element_of_set(X7,f13(f14(f13(X1,X2,X3,f19(interior(X1,X2,X3),X4)),X5,X6,X0),X2,X3,X7))
| element_of_set(X0,union_of_members(X8)) ) ).
cnf(u716,axiom,
( ~ subset_sets(X0,f14(X2,X1,X3,X4))
| ~ subset_sets(X0,X1)
| closed(f14(X0,X1,X3,X5),X1,X3)
| element_of_set(X5,f14(X2,X1,X3,X4))
| element_of_set(X4,closure(X2,X1,X3))
| ~ subset_sets(X2,X1)
| ~ topological_space(X1,X3) ) ).
cnf(u543,axiom,
( ~ subset_sets(f13(a,cx,ct,f11(X1,X0)),X0)
| ~ element_of_collection(f13(a,cx,ct,f11(X1,X0)),X1)
| element_of_collection(X0,top_of_basis(X1))
| ~ element_of_set(f11(X1,X0),sF0) ) ).
cnf(u41782,negated_conjecture,
( open(f13(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,X3),cx,ct,X4),cx,ct)
| hausdorff(sF0,X0)
| element_of_set(X3,closure(f13(a,cx,ct,f20(sF0,X0)),X1,X2))
| ~ element_of_set(X4,f13(a,cx,ct,f20(sF0,X0))) ) ).
cnf(u9368,negated_conjecture,
( limit_point(X0,X1,X2,X3)
| element_of_set(X0,f1(X5,X0)) ) ).
cnf(u3811,axiom,
( ~ subset_sets(a,f14(X1,cx,ct,f11(X0,closure(relative_complement_sets(X1,cx),cx,ct))))
| element_of_collection(closure(relative_complement_sets(X1,cx),cx,ct),top_of_basis(X0))
| ~ subset_sets(X1,cx)
| ~ subset_sets(f14(X1,cx,ct,f11(X0,closure(relative_complement_sets(X1,cx),cx,ct))),sF3)
| element_of_set(f11(X0,closure(relative_complement_sets(X1,cx),cx,ct)),boundary(X1,cx,ct))
| ~ element_of_collection(f14(X1,cx,ct,f11(X0,closure(relative_complement_sets(X1,cx),cx,ct))),X2)
| element_of_collection(sF3,top_of_basis(X2)) ) ).
cnf(u2473,axiom,
( element_of_collection(f12(X1,X2,X0,empty_set),X2)
| ~ connected_set(X0,X1,X2) ) ).
cnf(u3092,axiom,
( ~ closed(f21(X4,X5),X1,X2)
| ~ subset_sets(X0,f21(X4,X5))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(X4,X5)
| connected_space(X4,X5)
| element_of_set(f19(boundary(X0,X1,X2),X3),union_of_members(X5)) ) ).
cnf(u6376,axiom,
( ~ subset_sets(X5,f14(X0,X1,X2,X3))
| element_of_set(X4,closure(X0,X1,X2))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| element_of_set(X3,f14(X0,X1,X2,X4))
| element_of_set(X6,f14(X0,X1,X2,X3))
| subset_sets(X5,f14(X5,X1,X2,X6))
| ~ subset_sets(X5,X1) ) ).
cnf(u6915,negated_conjecture,
( element_of_set(f19(sF0,X0),interior(X1,X2,X3))
| hausdorff(sF0,X0) ) ).
cnf(closed_set_23,axiom,
( ~ open(relative_complement_sets(X0,X1),X1,X2)
| ~ topological_space(X1,X2)
| closed(X0,X1,X2) ) ).
cnf(u2989,axiom,
( element_of_set(f11(X0,boundary(relative_complement_sets(X1,X2),X2,X3)),boundary(X1,X2,X3))
| ~ closed(closure(X1,X2,X3),X2,X3)
| ~ subset_sets(relative_complement_sets(X1,X2),closure(X1,X2,X3))
| element_of_collection(boundary(relative_complement_sets(X1,X2),X2,X3),top_of_basis(X0)) ) ).
cnf(u1293,axiom,
( element_of_set(f20(boundary(X1,X2,X3),X4),union_of_members(top_of_basis(X0)))
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| hausdorff(boundary(X1,X2,X3),X4)
| ~ topological_space(boundary(X1,X2,X3),X4) ) ).
cnf(u4007,axiom,
( ~ closed(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X9,X10)
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| element_of_set(f11(X7,closure(X8,X9,X10)),interior(X4,X5,X6))
| element_of_collection(closure(X8,X9,X10),top_of_basis(X7))
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X8,f13(X4,X5,X6,f20(closure(X0,X1,X2),X3))) ) ).
cnf(u7582,negated_conjecture,
( open(f13(X5,X6,X7,f15(X1,X4,X2,X3,X0)),X6,X7)
| ~ limit_point(X1,X4,X2,X3)
| ~ neighborhood(X0,X1,X2,X3) ) ).
cnf(u36076,negated_conjecture,
( element_of_set(f11(X4,union_of_members(ct)),f1(X5,f11(X4,union_of_members(ct))))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| element_of_set(f11(X1,union_of_members(top_of_basis(X4))),sF0)
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u866,axiom,
( ~ closed(X1,cx,ct)
| element_of_set(f11(X0,sF3),X1)
| element_of_collection(sF3,top_of_basis(X0))
| ~ subset_sets(a,X1) ) ).
cnf(u1272,axiom,
( ~ subset_sets(closure(X0,X1,X2),closure(X5,X3,X4))
| ~ subset_sets(X5,boundary(X0,X1,X2))
| element_of_collection(closure(X5,X3,X4),top_of_basis(X6))
| ~ element_of_collection(closure(X0,X1,X2),X6)
| ~ closed(boundary(X0,X1,X2),X3,X4) ) ).
cnf(u2648,negated_conjecture,
( element_of_set(f20(closure(X0,X1,X2),X3),f1(ct,f20(closure(X0,X1,X2),X3)))
| hausdorff(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,empty_set)
| ~ closed(empty_set,X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u6115,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X4),sF0)
| ~ closed(sF0,X1,X2)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X3))
| ~ subset_sets(X0,sF0)
| basis(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X4)
| ~ topological_space(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X4) ) ).
cnf(u2542,axiom,
( ~ element_of_set(X0,f9(X1,top_of_basis(subspace_topology(X2,X3,X4))))
| subset_sets(X4,X2)
| basis(X1,top_of_basis(subspace_topology(X2,X3,X4)))
| ~ topological_space(X1,top_of_basis(subspace_topology(X2,X3,X4))) ) ).
cnf(u6361,axiom,
( element_of_set(f11(X1,f13(a,cx,ct,f7(sF0,X0))),f13(a,cx,ct,f7(sF0,X0)))
| basis(sF0,X0)
| ~ topological_space(sF0,X0)
| element_of_set(f7(sF0,X0),union_of_members(top_of_basis(X1))) ) ).
cnf(u4029,axiom,
( ~ closed(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X9,X10)
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| element_of_set(f11(X7,boundary(X8,X9,X10)),interior(X4,X5,X6))
| element_of_collection(boundary(X8,X9,X10),top_of_basis(X7))
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X8,f13(X4,X5,X6,f19(closure(X0,X1,X2),X3))) ) ).
cnf(u4619,axiom,
( ~ element_of_collection(intersection_of_members(X2),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ element_of_collection(X3,X2)
| element_of_set(f11(X0,intersection_of_members(X1)),X3) ) ).
cnf(intersection_of_members_4,axiom,
( ~ element_of_set(X0,intersection_of_members(X1))
| ~ element_of_collection(X2,X1)
| element_of_set(X0,X2) ) ).
cnf(u4870,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,f20(closure(X0,X1,X2),X3)),f24(f13(a,cx,ct,f20(closure(X0,X1,X2),X3)),X4)),sF0)
| basis(f13(a,cx,ct,f20(closure(X0,X1,X2),X3)),f24(f13(a,cx,ct,f20(closure(X0,X1,X2),X3)),X4))
| compact_space(f13(a,cx,ct,f20(closure(X0,X1,X2),X3)),X4)
| ~ closed(sF0,X1,X2)
| ~ subset_sets(X0,sF0)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(f13(a,cx,ct,f20(closure(X0,X1,X2),X3)),X4) ) ).
cnf(u3954,negated_conjecture,
( element_of_set(f11(X5,f1(ct,f15(X1,X4,X2,X3,X0))),union_of_members(ct))
| ~ limit_point(X1,X4,X2,X3)
| ~ element_of_collection(X4,ct)
| ~ element_of_collection(X0,ct)
| ~ neighborhood(X0,X1,X2,X3)
| element_of_collection(f1(ct,f15(X1,X4,X2,X3,X0)),top_of_basis(X5)) ) ).
cnf(u28305,negated_conjecture,
( element_of_set(f11(X4,union_of_members(top_of_basis(X0))),union_of_members(X5))
| element_of_set(f11(X0,union_of_members(ct)),union_of_members(X7))
| element_of_set(X6,f1(top_of_basis(X4),X6))
| ~ element_of_set(X6,cx) ) ).
cnf(u825,axiom,
( element_of_set(X3,union_of_members(subspace_topology(X1,X2,X0)))
| ~ element_of_set(X3,X0)
| ~ connected_set(X0,X1,X2) ) ).
cnf(u33905,negated_conjecture,
( open(f13(f14(relative_complement_sets(X0,X1),cx,ct,X2),X1,X4,X3),X1,X4)
| element_of_set(X2,sF0)
| ~ element_of_set(X3,relative_complement_sets(X0,X1)) ) ).
cnf(u4654,axiom,
( ~ element_of_collection(f13(X2,X3,X4,f19(interior(X2,X3,X4),X5)),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ topological_space(interior(X2,X3,X4),X5)
| hausdorff(interior(X2,X3,X4),X5)
| element_of_set(f11(X0,intersection_of_members(X1)),interior(X2,X3,X4)) ) ).
cnf(u845,axiom,
( ~ closed(f13(a,cx,ct,X4),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f13(a,cx,ct,X4))
| ~ element_of_set(X4,sF0)
| element_of_set(f11(X0,closure(X1,X2,X3)),union_of_members(ct)) ) ).
cnf(u487,axiom,
( element_of_set(f7(f13(a,cx,ct,X0),X1),union_of_members(ct))
| ~ element_of_set(X0,sF0)
| basis(f13(a,cx,ct,X0),X1)
| ~ topological_space(f13(a,cx,ct,X0),X1) ) ).
cnf(u5959,axiom,
( ~ element_of_collection(boundary(X0,X1,X4),X3)
| element_of_collection(intersection_of_members(X3),top_of_basis(X2))
| subset_sets(X0,X1) ) ).
cnf(u1042,axiom,
( element_of_collection(f13(X1,X2,X3,f20(closure(X0,X4,X5),X6)),X3)
| ~ closed(interior(X1,X2,X3),X4,X5)
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| ~ subset_sets(X0,interior(X1,X2,X3)) ) ).
cnf(u3697,axiom,
( subset_sets(X0,f14(X0,X1,X2,f11(X9,f14(closure(X0,X1,X2),X3,X4,f11(X8,f14(closure(closure(X0,X1,X2),X3,X4),X5,X6,X7))))))
| ~ element_of_collection(closure(closure(X0,X1,X2),X3,X4),X8)
| ~ subset_sets(closure(X0,X1,X2),X3)
| ~ topological_space(X3,X4)
| element_of_set(X7,closure(closure(closure(X0,X1,X2),X3,X4),X5,X6))
| ~ subset_sets(closure(closure(X0,X1,X2),X3,X4),X5)
| ~ topological_space(X5,X6)
| ~ element_of_collection(closure(X0,X1,X2),X9)
| element_of_collection(f14(closure(X0,X1,X2),X3,X4,f11(X8,f14(closure(closure(X0,X1,X2),X3,X4),X5,X6,X7))),top_of_basis(X9))
| element_of_collection(f14(closure(closure(X0,X1,X2),X3,X4),X5,X6,X7),top_of_basis(X8))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u6350,axiom,
( ~ element_of_set(X0,closure(X1,X2,X3))
| element_of_set(X4,f14(relative_complement_sets(X1,X2),X2,X3,X0))
| ~ subset_sets(relative_complement_sets(X1,X2),X2)
| subset_sets(relative_complement_sets(X1,X2),f14(relative_complement_sets(X1,X2),X2,X3,X4))
| element_of_set(X0,boundary(X1,X2,X3)) ) ).
cnf(u5547,negated_conjecture,
( ~ equal_sets(union_of_members(ct),X0)
| ~ element_of_collection(X0,ct)
| topological_space(X0,ct)
| subset_collections(f5(X0,ct),ct) ) ).
cnf(u4289,axiom,
( subset_sets(X0,f14(X0,X1,X2,f20(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f11(subspace_topology(X4,X5,X6),boundary(X0,X1,X2)),boundary(X0,X1,X2))
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1)
| topological_space(X4,X5)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3) ) ).
cnf(u3224,axiom,
( closed(f14(relative_complement_sets(X4,X5),X5,X6,f20(boundary(X0,X1,X2),X3)),X5,X6)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ closed(closure(X4,X5,X6),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ subset_sets(relative_complement_sets(X4,X5),X5)
| ~ topological_space(boundary(X0,X1,X2),X3)
| element_of_set(f20(boundary(X0,X1,X2),X3),boundary(X4,X5,X6)) ) ).
cnf(u5781,negated_conjecture,
( ~ element_of_set(f19(f13(a,cx,ct,f7(sF0,X1)),X2),X0)
| ~ open(sF0,f13(a,cx,ct,f7(sF0,X1)),X2)
| hausdorff(f13(a,cx,ct,f7(sF0,X1)),X2)
| ~ open(X0,f13(a,cx,ct,f7(sF0,X1)),X2)
| ~ disjoint_s(X0,sF0)
| basis(sF0,X1)
| ~ topological_space(sF0,X1) ) ).
cnf(u4406,axiom,
( element_of_set(f20(f10(X1,X0,X2),X3),union_of_members(X1))
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1))
| ~ topological_space(f10(X1,X0,X2),X3)
| hausdorff(f10(X1,X0,X2),X3) ) ).
cnf(u3687,axiom,
( ~ topological_space(f14(X0,X1,X2,f11(X6,f14(closure(X0,X1,X2),X3,X4,X5))),X8)
| ~ element_of_collection(closure(X0,X1,X2),X6)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| element_of_set(X5,closure(closure(X0,X1,X2),X3,X4))
| ~ subset_sets(closure(X0,X1,X2),X3)
| ~ topological_space(X3,X4)
| ~ element_of_collection(X7,X8)
| element_of_collection(f14(closure(X0,X1,X2),X3,X4,X5),top_of_basis(X6))
| ~ element_of_set(X9,X7)
| ~ subset_sets(X7,X0)
| element_of_set(X9,interior(X0,f14(X0,X1,X2,f11(X6,f14(closure(X0,X1,X2),X3,X4,X5))),X8)) ) ).
cnf(u249,axiom,
( ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| topological_space(X1,X2) ) ).
cnf(u55124,negated_conjecture,
( ~ element_of_set(X9,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)))
| ~ element_of_set(X4,f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)))
| eq_p(X5,X6)
| element_of_set(X4,f13(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X7,X8,X5),X1,X2,X4))
| element_of_set(X9,f13(f14(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X7,X8,X6),X1,X2,X9))
| hausdorff(interior(X0,X1,X2),X3) ) ).
cnf(basis_for_topology_34,axiom,
( ~ equal_sets(union_of_members(X1),X0)
| basis(X0,X1)
| element_of_collection(f9(X0,X1),X1) ) ).
cnf(u580,axiom,
( element_of_set(f19(closure(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3),boundary(relative_complement_sets(X0,X1),X1,X2))
| ~ topological_space(closure(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3)
| ~ element_of_set(f19(closure(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3),boundary(X0,X1,X2)) ) ).
cnf(open_set_19,axiom,
( ~ open(X0,X1,X2)
| element_of_collection(X0,X2) ) ).
cnf(u3506,axiom,
( ~ closed(boundary(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,boundary(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| subset_sets(X4,X5)
| element_of_set(f7(closure(X0,X1,X2),X3),union_of_members(top_of_basis(X7))) ) ).
cnf(u6095,axiom,
( ~ element_of_collection(f13(sF3,X2,X3,f20(interior(sF3,X2,X3),X4)),X0)
| ~ element_of_set(X1,f13(sF3,X2,X3,f20(interior(sF3,X2,X3),X4)))
| ~ topological_space(sF1,X0)
| element_of_set(X1,interior(sF3,sF1,X0))
| hausdorff(interior(sF3,X2,X3),X4)
| ~ topological_space(interior(sF3,X2,X3),X4) ) ).
cnf(u3503,axiom,
( ~ closed(f14(X4,X5,X6,f7(closure(X0,X1,X2),X3)),X1,X2)
| ~ subset_sets(X0,f14(X4,X5,X6,f7(closure(X0,X1,X2),X3)))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(X5,X6)
| ~ subset_sets(X4,X5)
| element_of_set(f7(closure(X0,X1,X2),X3),closure(X4,X5,X6)) ) ).
cnf(u50941,negated_conjecture,
( ~ element_of_set(X7,f16(X1,X2,X3,X4))
| limit_point(X1,X2,X3,X4)
| element_of_set(X7,f13(f14(f16(X1,X2,X3,X4),X5,X6,X0),X3,X4,X7))
| element_of_set(X0,interior(X8,X9,X10)) ) ).
cnf(u1203,negated_conjecture,
( closed(f14(a,cx,ct,f11(X1,X0)),cx,ct)
| ~ element_of_collection(sF3,X1)
| element_of_collection(X0,top_of_basis(X1))
| ~ subset_sets(sF3,X0) ) ).
cnf(u377,axiom,
( ~ neighborhood(f16(X0,X1,X4,X5),X0,X2,X3)
| ~ topological_space(X4,X5)
| ~ subset_sets(X1,X4)
| limit_point(X0,X1,X4,X5)
| ~ limit_point(X0,X1,X2,X3) ) ).
cnf(u915,axiom,
( element_of_collection(f12(X2,X3,X4,f13(X0,X1,subspace_topology(X2,X3,X4),f19(interior(X0,X1,subspace_topology(X2,X3,X4)),X5))),X3)
| hausdorff(interior(X0,X1,subspace_topology(X2,X3,X4)),X5)
| ~ topological_space(interior(X0,X1,subspace_topology(X2,X3,X4)),X5) ) ).
cnf(u2679,axiom,
( ~ element_of_collection(f13(f13(a,cx,ct,X0),X1,X2,f11(X6,closure(X5,X3,X4))),X7)
| ~ subset_sets(X5,interior(f13(a,cx,ct,X0),X1,X2))
| element_of_collection(closure(X5,X3,X4),top_of_basis(X6))
| ~ closed(interior(f13(a,cx,ct,X0),X1,X2),X3,X4)
| ~ topological_space(a,X7)
| ~ element_of_set(X8,f13(f13(a,cx,ct,X0),X1,X2,f11(X6,closure(X5,X3,X4))))
| ~ element_of_set(X0,sF0)
| element_of_set(X8,interior(f13(a,cx,ct,X0),a,X7)) ) ).
cnf(u3209,negated_conjecture,
( ~ closed(f13(a,cx,ct,X4),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,X4))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f20(boundary(X0,X1,X2),X3),sF0)
| ~ element_of_set(X4,sF0) ) ).
cnf(u4274,axiom,
( element_of_set(X10,interior(f14(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8,f20(closure(relative_complement_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7),X7,X8),X9)),X1,X2))
| ~ topological_space(closure(relative_complement_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7),X7,X8),X9)
| hausdorff(closure(relative_complement_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7),X7,X8),X9)
| ~ subset_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7)
| ~ closed(interior(X0,X1,X2),X4,X5)
| ~ topological_space(closure(X3,X4,X5),X6)
| hausdorff(closure(X3,X4,X5),X6)
| ~ subset_sets(f14(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8,f20(closure(relative_complement_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7),X7,X8),X9)),X1)
| ~ element_of_set(X10,f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)))
| ~ subset_sets(X3,interior(X0,X1,X2))
| element_of_set(f20(closure(relative_complement_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7),X7,X8),X9),boundary(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8)) ) ).
cnf(u4401,axiom,
( element_of_set(f19(f10(X1,X0,X2),X3),union_of_members(X1))
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1))
| ~ topological_space(f10(X1,X0,X2),X3)
| hausdorff(f10(X1,X0,X2),X3) ) ).
cnf(u238,axiom,
( open(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X1,X2)
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3) ) ).
cnf(u4898,axiom,
( element_of_collection(f1(X1,f20(closure(X0,X2,X3),subspace_topology(X4,X5,closure(X0,X2,X3)))),X1)
| ~ closed(union_of_members(X1),X2,X3)
| hausdorff(closure(X0,X2,X3),subspace_topology(X4,X5,closure(X0,X2,X3)))
| ~ subset_sets(X0,union_of_members(X1))
| ~ connected_set(closure(X0,X2,X3),X4,X5) ) ).
cnf(u2967,axiom,
( ~ closed(closure(X4,X5,X6),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,closure(X4,X5,X6))
| topological_space(X5,X6) ) ).
cnf(u5333,negated_conjecture,
( ~ open(f14(a,cx,ct,X1),sF3,X2)
| ~ disjoint_s(X0,f14(a,cx,ct,X1))
| hausdorff(sF3,X2)
| ~ open(X0,sF3,X2)
| ~ element_of_set(f19(sF3,X2),X0)
| element_of_set(X1,sF3) ) ).
cnf(u3179,axiom,
( closed(f14(relative_complement_sets(f16(X0,X1,X2,X3),X4),X4,X5,X6),X4,X5)
| element_of_set(X7,interior(f14(f16(X0,X1,X2,X3),X4,X5,X6),X2,X3))
| ~ subset_sets(relative_complement_sets(f16(X0,X1,X2,X3),X4),X4)
| ~ subset_sets(f16(X0,X1,X2,X3),X4)
| ~ topological_space(X4,X5)
| limit_point(X0,X1,X2,X3)
| ~ topological_space(X2,X3)
| ~ subset_sets(f14(f16(X0,X1,X2,X3),X4,X5,X6),X2)
| ~ element_of_set(X7,f16(X0,X1,X2,X3))
| ~ subset_sets(X1,X2)
| element_of_set(X6,boundary(f16(X0,X1,X2,X3),X4,X5)) ) ).
cnf(u5639,axiom,
( ~ closed(closure(relative_complement_sets(a,cx),cx,ct),X2,X3)
| ~ element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| element_of_set(f11(X0,closure(X1,X2,X3)),sF1)
| ~ subset_sets(X1,closure(relative_complement_sets(a,cx),cx,ct))
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(u3728,negated_conjecture,
( element_of_set(f19(intersection_of_sets(X1,X0),X2),union_of_members(top_of_basis(X3)))
| element_of_set(f11(X3,union_of_members(ct)),union_of_members(ct))
| ~ topological_space(intersection_of_sets(X1,X0),X2)
| hausdorff(intersection_of_sets(X1,X0),X2)
| ~ element_of_collection(X1,ct)
| ~ element_of_collection(X0,ct) ) ).
cnf(u1194,axiom,
( element_of_set(f19(boundary(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3),boundary(relative_complement_sets(X0,X1),X1,X2))
| hausdorff(boundary(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3)
| ~ topological_space(boundary(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3)
| ~ element_of_set(f19(boundary(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3),boundary(X0,X1,X2)) ) ).
cnf(u5729,axiom,
( ~ closed(closure(relative_complement_sets(X2,X3),X3,subspace_topology(X1,X4,X0)),X6,X7)
| ~ subset_sets(X2,X3)
| ~ subset_sets(X5,closure(relative_complement_sets(X2,X3),X3,subspace_topology(X1,X4,X0)))
| subset_sets(X0,X1)
| ~ topological_space(closure(X5,X6,X7),X8)
| hausdorff(closure(X5,X6,X7),X8)
| element_of_set(f20(closure(X5,X6,X7),X8),boundary(X2,X3,subspace_topology(X1,X4,X0))) ) ).
cnf(u1278,axiom,
( ~ element_of_set(X4,closure(X3,X0,X1))
| element_of_set(f11(X2,closure(X3,X0,X1)),sF3)
| ~ subset_sets(X3,sF1)
| ~ closed(sF1,X0,X1)
| element_of_set(X4,union_of_members(top_of_basis(X2))) ) ).
cnf(u4394,axiom,
( element_of_set(f7(f10(X1,X0,X2),X3),union_of_members(X1))
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1))
| basis(f10(X1,X0,X2),X3)
| ~ topological_space(f10(X1,X0,X2),X3) ) ).
cnf(u1359,negated_conjecture,
( element_of_set(f20(f13(a,cx,ct,X1),X2),union_of_members(top_of_basis(X0)))
| element_of_set(f11(X0,sF0),sF0)
| hausdorff(f13(a,cx,ct,X1),X2)
| ~ topological_space(f13(a,cx,ct,X1),X2)
| ~ element_of_set(X1,sF0) ) ).
cnf(u5858,negated_conjecture,
( element_of_set(f11(X1,sF3),f14(a,cx,ct,f20(closure(relative_complement_sets(a,cx),cx,ct),X0)))
| ~ topological_space(closure(relative_complement_sets(a,cx),cx,ct),X0)
| hausdorff(closure(relative_complement_sets(a,cx),cx,ct),X0)
| element_of_collection(sF3,top_of_basis(X1))
| element_of_set(f20(closure(relative_complement_sets(a,cx),cx,ct),X0),sF1) ) ).
cnf(u1290,axiom,
( ~ closed(boundary(X1,X2,X3),X5,X6)
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| element_of_set(f19(closure(X4,X5,X6),X7),union_of_members(top_of_basis(X0)))
| ~ subset_sets(X4,boundary(X1,X2,X3))
| element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7) ) ).
cnf(u3226,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f11(X7,closure(X4,X5,X6)),sF3)
| ~ subset_sets(X4,sF1)
| ~ closed(sF1,X5,X6)
| element_of_set(f20(boundary(X0,X1,X2),X3),union_of_members(top_of_basis(X7))) ) ).
cnf(u3015,negated_conjecture,
( ~ element_of_set(X2,f13(a,cx,ct,f7(sF0,X0)))
| ~ topological_space(sF0,X0)
| element_of_set(f11(X1,f13(a,cx,ct,f7(sF0,X0))),sF0)
| basis(sF0,X0)
| element_of_set(X2,union_of_members(top_of_basis(X1))) ) ).
cnf(u4450,axiom,
( element_of_set(X0,intersection_of_members(subspace_topology(X1,subspace_topology(X2,X3,X4),X5)))
| subset_sets(X4,X2) ) ).
cnf(u4924,axiom,
( element_of_set(f11(X5,union_of_members(top_of_basis(X1))),union_of_members(top_of_basis(X1)))
| closed(f14(X2,X3,X4,X0),X3,X4)
| element_of_set(f11(X1,closure(X2,X3,X4)),sF3)
| element_of_set(X0,union_of_members(top_of_basis(X5)))
| ~ subset_sets(X2,X3)
| ~ subset_sets(X2,sF1)
| ~ closed(sF1,X3,X4) ) ).
cnf(u351,axiom,
( separation(X3,X4,intersection_of_sets(X0,f12(X1,X2,X0,union_of_sets(X3,X4))),X5)
| equal_sets(X3,empty_set)
| equal_sets(X4,empty_set)
| ~ element_of_collection(X3,X5)
| ~ element_of_collection(X4,X5)
| ~ topological_space(intersection_of_sets(X0,f12(X1,X2,X0,union_of_sets(X3,X4))),X5)
| ~ disjoint_s(X3,X4)
| ~ element_of_collection(union_of_sets(X3,X4),subspace_topology(X1,X2,X0)) ) ).
cnf(u6120,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X5)
| ~ closed(sF0,X1,X2)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X3))
| element_of_set(f11(X4,intersection_of_members(X5)),sF0)
| element_of_collection(intersection_of_members(X5),top_of_basis(X4))
| ~ subset_sets(X0,sF0) ) ).
cnf(u483,axiom,
( element_of_collection(f9(X0,f24(X0,X1)),f24(X0,X1))
| ~ topological_space(X0,X1)
| basis(X0,f24(X0,X1))
| compact_space(X0,X1) ) ).
cnf(u4026,axiom,
( ~ closed(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X8,X9)
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| element_of_set(f7(closure(X7,X8,X9),X10),interior(X4,X5,X6))
| ~ topological_space(closure(X7,X8,X9),X10)
| ~ subset_sets(X7,f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X7,X8,X9),X10) ) ).
cnf(u960,axiom,
( ~ closed(X1,cx,ct)
| hausdorff(sF3,X0)
| ~ subset_sets(a,X1)
| element_of_set(f20(sF3,X0),X1)
| ~ topological_space(sF3,X0) ) ).
cnf(u6708,negated_conjecture,
( ~ element_of_set(X2,f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(X2,interior(X1,cx,ct)) ) ).
cnf(u6343,axiom,
( ~ closed(closure(relative_complement_sets(X4,X5),X5,X6),X2,X3)
| element_of_set(X7,f14(X4,X5,X6,f11(X0,closure(X1,X2,X3))))
| ~ subset_sets(X4,X5)
| subset_sets(X4,f14(X4,X5,X6,X7))
| ~ subset_sets(X1,closure(relative_complement_sets(X4,X5),X5,X6))
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| element_of_set(f11(X0,closure(X1,X2,X3)),boundary(X4,X5,X6)) ) ).
cnf(u3230,axiom,
( ~ closed(f16(X4,X5,X6,X7),X1,X2)
| ~ subset_sets(X0,f16(X4,X5,X6,X7))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(X6,X7)
| ~ subset_sets(X5,X6)
| limit_point(X4,X5,X6,X7)
| element_of_set(f20(boundary(X0,X1,X2),X3),union_of_members(X7)) ) ).
cnf(u4259,axiom,
( ~ subset_sets(a,f14(X0,cx,ct,f19(closure(relative_complement_sets(X0,cx),cx,ct),X1)))
| element_of_set(f19(closure(relative_complement_sets(X0,cx),cx,ct),X1),boundary(X0,cx,ct))
| hausdorff(closure(relative_complement_sets(X0,cx),cx,ct),X1)
| ~ subset_sets(X0,cx)
| ~ topological_space(closure(relative_complement_sets(X0,cx),cx,ct),X1)
| ~ element_of_set(X2,sF3)
| element_of_set(X2,f14(X0,cx,ct,f19(closure(relative_complement_sets(X0,cx),cx,ct),X1))) ) ).
cnf(u50141,negated_conjecture,
( element_of_set(f20(f12(X2,top_of_basis(X3),X4,f1(subspace_topology(X2,top_of_basis(X3),X4),X5)),X6),f10(X3,f12(X2,top_of_basis(X3),X4,f1(subspace_topology(X2,top_of_basis(X3),X4),X5)),f20(f12(X2,top_of_basis(X3),X4,f1(subspace_topology(X2,top_of_basis(X3),X4),X5)),X6)))
| limit_point(X5,X0,X1,subspace_topology(X2,top_of_basis(X3),X4))
| hausdorff(f12(X2,top_of_basis(X3),X4,f1(subspace_topology(X2,top_of_basis(X3),X4),X5)),X6) ) ).
cnf(u2890,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),f13(X3,X4,X5,f19(interior(X3,X4,X5),X6))),f13(X3,X4,X5,f19(interior(X3,X4,X5),X6)))
| topological_space(X0,X1)
| hausdorff(interior(X3,X4,X5),X6)
| ~ topological_space(interior(X3,X4,X5),X6) ) ).
cnf(u2793,axiom,
( ~ closed(boundary(X0,X1,X2),cx,ct)
| ~ subset_sets(a,boundary(X0,X1,X2))
| element_of_collection(sF3,top_of_basis(X3))
| ~ element_of_collection(closure(X0,X1,X2),X3)
| ~ subset_sets(closure(X0,X1,X2),sF3) ) ).
cnf(u576,negated_conjecture,
( element_of_set(f15(X2,X0,X3,X4,X1),f1(ct,f15(X2,X0,X3,X4,X1)))
| ~ element_of_collection(X1,ct)
| ~ neighborhood(X1,X2,X3,X4)
| ~ limit_point(X2,X0,X3,X4)
| ~ element_of_collection(X0,ct) ) ).
cnf(u27394,axiom,
( ~ subset_collections(f23(X0,X1,f24(X2,X3)),X3)
| compact_space(X2,X3)
| ~ open_covering(f24(X2,X3),X0,X1)
| ~ compact_space(X0,X1) ) ).
cnf(u2721,axiom,
( ~ closed(closure(relative_complement_sets(relative_complement_sets(X1,X2),X2),X2,X3),X4,X5)
| ~ subset_sets(X0,closure(relative_complement_sets(relative_complement_sets(X1,X2),X2),X2,X3))
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| element_of_set(f19(closure(X0,X4,X5),X6),boundary(relative_complement_sets(X1,X2),X2,X3))
| ~ element_of_set(f19(closure(X0,X4,X5),X6),boundary(X1,X2,X3)) ) ).
cnf(u261,negated_conjecture,
( element_of_set(f19(f13(a,cx,ct,X0),X1),sF0)
| hausdorff(f13(a,cx,ct,X0),X1)
| ~ topological_space(f13(a,cx,ct,X0),X1)
| ~ element_of_set(X0,sF0) ) ).
cnf(u16524,negated_conjecture,
( ~ element_of_set(X2,boundary(X3,X4,X5))
| hausdorff(intersection_of_members(X0),X1)
| eq_p(f19(intersection_of_members(X0),X1),X2) ) ).
cnf(u6648,negated_conjecture,
( element_of_set(f19(boundary(X0,X1,X2),X3),sF0)
| ~ closed(sF3,X1,X2)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u2827,axiom,
( ~ closed(f8(X0,X1),X3,X4)
| basis(X0,X1)
| element_of_set(f20(closure(X2,X3,X4),X5),union_of_members(X1))
| hausdorff(closure(X2,X3,X4),X5)
| ~ subset_sets(X2,f8(X0,X1))
| ~ topological_space(X0,X1)
| ~ topological_space(closure(X2,X3,X4),X5) ) ).
cnf(u234,axiom,
( ~ element_of_set(X2,f22(X0,X1))
| ~ topological_space(X0,X1)
| connected_space(X0,X1)
| element_of_set(X2,union_of_members(X1)) ) ).
cnf(u7945,negated_conjecture,
( element_of_set(f19(X0,X1),f13(X2,X3,X4,f19(X0,X1)))
| hausdorff(X0,X1) ) ).
cnf(u2849,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),closure(X3,X4,X5))
| closed(f14(X3,X4,X5,X6),X4,X5)
| topological_space(X0,X1)
| ~ subset_sets(X3,X4)
| ~ topological_space(X4,X5) ) ).
cnf(u2491,axiom,
( ~ element_of_set(X0,f1(top_of_basis(X1),X2))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X2),X0))
| limit_point(X2,X3,X4,top_of_basis(X1))
| ~ topological_space(X4,top_of_basis(X1))
| ~ subset_sets(X3,X4) ) ).
cnf(basis_for_topology_31,axiom,
( subset_sets(f6(X0,X1,X2,X3,X4),intersection_of_sets(X3,X4))
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X3,X1)
| ~ element_of_collection(X4,X1)
| ~ element_of_set(X2,intersection_of_sets(X3,X4))
| ~ basis(X0,X1) ) ).
cnf(u449,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,f19(sF0,X0)),X1),sF0)
| ~ topological_space(f13(a,cx,ct,f19(sF0,X0)),X1)
| basis(f13(a,cx,ct,f19(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0) ) ).
cnf(u3196,negated_conjecture,
( ~ closed(intersection_of_sets(X4,X5),X1,X2)
| ~ subset_sets(X0,intersection_of_sets(X4,X5))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f20(boundary(X0,X1,X2),X3),union_of_members(ct))
| ~ element_of_collection(X5,ct)
| ~ element_of_collection(X4,ct) ) ).
cnf(u3475,axiom,
( open(f13(X4,X5,X6,f7(closure(X0,X1,X2),X3)),X5,X6)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ closed(interior(X4,X5,X6),X1,X2)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u4761,axiom,
( ~ subset_sets(closure(X2,X3,subspace_topology(X1,X4,X0)),X5)
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,subspace_topology(X1,X4,X0))
| element_of_collection(X5,top_of_basis(X6))
| ~ element_of_collection(closure(X2,X3,subspace_topology(X1,X4,X0)),X6)
| subset_sets(X0,X1) ) ).
cnf(u396,axiom,
( subset_sets(f13(a,cx,ct,f19(sF0,X0)),a)
| hausdorff(sF0,X0)
| ~ topological_space(sF0,X0) ) ).
cnf(u17779,negated_conjecture,
( element_of_set(f20(intersection_of_members(X0),X1),X2)
| hausdorff(intersection_of_members(X0),X1) ) ).
cnf(u3035,negated_conjecture,
( element_of_set(f19(f13(a,cx,ct,f7(sF0,X0)),X1),union_of_members(top_of_basis(X2)))
| ~ topological_space(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f7(sF0,X0)),X1)
| hausdorff(f13(a,cx,ct,f7(sF0,X0)),X1)
| element_of_set(f11(X2,sF0),sF0)
| basis(sF0,X0) ) ).
cnf(u5950,negated_conjecture,
( ~ element_of_collection(f13(a,X2,X3,f19(closure(X4,X5,X6),X7)),X0)
| ~ element_of_set(X1,f13(a,X2,X3,f19(closure(X4,X5,X6),X7)))
| ~ topological_space(sF0,X0)
| element_of_set(X1,interior(a,sF0,X0))
| ~ subset_sets(X4,interior(a,X2,X3))
| ~ closed(interior(a,X2,X3),X5,X6)
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7) ) ).
cnf(u3822,axiom,
( element_of_collection(f1(subspace_topology(X2,X3,X1),X0),subspace_topology(X2,X3,X1))
| ~ connected_set(X1,X2,X3)
| ~ element_of_set(X0,X1) ) ).
cnf(u577,negated_conjecture,
( element_of_collection(f1(ct,f15(X2,X0,X3,X4,X1)),ct)
| ~ element_of_collection(X1,ct)
| ~ neighborhood(X1,X2,X3,X4)
| ~ limit_point(X2,X0,X3,X4)
| ~ element_of_collection(X0,ct) ) ).
cnf(u5631,negated_conjecture,
( ~ subset_sets(a,f14(relative_complement_sets(X0,cx),cx,ct,X1))
| element_of_set(X1,boundary(X0,cx,ct))
| ~ subset_sets(relative_complement_sets(X0,cx),cx)
| ~ subset_sets(X0,cx)
| ~ subset_sets(f14(relative_complement_sets(X0,cx),cx,ct,X1),sF3)
| subset_sets(X0,f14(X0,cx,ct,X1))
| ~ element_of_collection(f14(relative_complement_sets(X0,cx),cx,ct,X1),X2)
| element_of_collection(sF3,top_of_basis(X2)) ) ).
cnf(topological_space_12,axiom,
( ~ equal_sets(union_of_members(X1),X0)
| topological_space(X0,X1)
| ~ element_of_collection(empty_set,X1)
| ~ element_of_collection(X0,X1)
| element_of_collection(f3(X0,X1),X1)
| subset_collections(f5(X0,X1),X1) ) ).
cnf(u3750,axiom,
( ~ topological_space(closure(X3,X4,X5),X7)
| element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),X6)
| ~ closed(X6,X4,X5)
| ~ subset_sets(X3,X6)
| basis(closure(X3,X4,X5),X7)
| topological_space(X0,X1) ) ).
cnf(u4037,axiom,
( ~ closed(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X8,X9)
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| element_of_set(f20(closure(X7,X8,X9),X10),interior(X4,X5,X6))
| hausdorff(closure(X7,X8,X9),X10)
| ~ subset_sets(X7,f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)))
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X7,X8,X9),X10) ) ).
cnf(u3067,negated_conjecture,
( ~ closed(f13(a,cx,ct,f11(X4,sF0)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f11(X4,sF0)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f19(boundary(X0,X1,X2),X3),sF0)
| element_of_collection(sF0,top_of_basis(X4)) ) ).
cnf(u6207,negated_conjecture,
( ~ element_of_set(X0,f13(a,cx,ct,X1))
| ~ topological_space(sF0,top_of_basis(X2))
| element_of_set(X0,interior(a,sF0,top_of_basis(X2)))
| ~ element_of_set(X1,sF0)
| element_of_set(f11(X2,f13(a,cx,ct,X1)),sF0) ) ).
cnf(u3381,axiom,
( ~ element_of_set(X7,f12(X2,X3,X4,f16(X5,X0,X1,subspace_topology(X6,X3,X4))))
| ~ topological_space(X2,X3)
| ~ subset_sets(X4,X2)
| limit_point(X5,X0,X1,subspace_topology(X6,X3,X4))
| ~ topological_space(X1,subspace_topology(X6,X3,X4))
| ~ subset_sets(X0,X1)
| element_of_set(X7,union_of_members(X3)) ) ).
cnf(u4678,axiom,
( ~ element_of_set(X5,intersection_of_members(X0))
| ~ element_of_collection(X4,X0)
| element_of_set(f11(subspace_topology(X1,X2,X3),intersection_of_members(X0)),X4)
| topological_space(X1,X2) ) ).
cnf(u294,axiom,
( element_of_set(f20(boundary(X0,X1,X2),X3),X4)
| ~ topological_space(boundary(X0,X1,X2),X3)
| ~ subset_sets(X0,X4)
| ~ closed(X4,X1,X2)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u952,axiom,
( ~ closed(boundary(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,boundary(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(relative_complement_sets(X4,X5),X7)
| ~ closed(X7,X5,X6)
| element_of_set(f20(closure(X0,X1,X2),X3),X7) ) ).
cnf(u1052,axiom,
( ~ element_of_set(X7,f13(X0,X1,X2,f20(closure(X5,X3,X4),X6)))
| ~ topological_space(closure(X5,X3,X4),X6)
| hausdorff(closure(X5,X3,X4),X6)
| ~ closed(interior(X0,X1,X2),X3,X4)
| ~ subset_sets(X5,interior(X0,X1,X2))
| element_of_set(X7,interior(X0,X1,X2)) ) ).
cnf(u972,negated_conjecture,
( element_of_set(f20(sF3,X0),f14(a,cx,ct,X1))
| hausdorff(sF3,X0)
| element_of_set(X1,sF3)
| ~ topological_space(sF3,X0) ) ).
cnf(u6572,negated_conjecture,
( element_of_set(f7(sF3,X0),f14(a,cx,ct,f11(X1,X2)))
| ~ topological_space(sF3,X0)
| basis(sF3,X0)
| ~ element_of_collection(sF3,X1)
| element_of_collection(X2,top_of_basis(X1))
| ~ subset_sets(sF3,X2) ) ).
cnf(u6283,axiom,
( ~ subset_sets(f14(relative_complement_sets(X0,X1),X2,X3,X4),X1)
| element_of_set(X5,closure(relative_complement_sets(X0,X1),X2,X3))
| ~ subset_sets(relative_complement_sets(X0,X1),X2)
| ~ topological_space(X2,X3)
| element_of_set(X4,f14(relative_complement_sets(X0,X1),X2,X3,X5))
| ~ element_of_set(X6,relative_complement_sets(X0,X1))
| ~ closed(X0,X1,X7)
| element_of_set(X6,interior(f14(relative_complement_sets(X0,X1),X2,X3,X4),X1,X7)) ) ).
cnf(u5274,axiom,
( ~ open(closure(relative_complement_sets(X1,X2),X2,X3),X4,X5)
| ~ disjoint_s(X0,closure(relative_complement_sets(X1,X2),X2,X3))
| hausdorff(X4,X5)
| ~ open(X0,X4,X5)
| ~ element_of_set(f19(X4,X5),X0)
| ~ element_of_set(f20(X4,X5),boundary(X1,X2,X3)) ) ).
cnf(u45013,negated_conjecture,
( element_of_set(X0,f13(f14(relative_complement_sets(X1,X2),X4,X5,X6),X2,X3,X0))
| element_of_set(X6,closure(relative_complement_sets(X1,X2),X4,X5))
| ~ element_of_set(X0,relative_complement_sets(X1,X2)) ) ).
cnf(u1387,axiom,
( ~ element_of_set(X0,closure(X1,X2,X3))
| topological_space(X4,X5)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X4,X5,X6),closure(X1,X2,X3)),sF3)
| ~ subset_sets(X1,sF1) ) ).
cnf(u4850,axiom,
( element_of_set(f7(interior(X0,X1,X2),f24(interior(X0,X1,X2),X3)),f13(X0,X1,X2,f7(interior(X0,X1,X2),f24(interior(X0,X1,X2),X3))))
| basis(interior(X0,X1,X2),f24(interior(X0,X1,X2),X3))
| compact_space(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3) ) ).
cnf(u3829,axiom,
( element_of_set(f7(f2(X1,X0),X2),union_of_members(X1))
| element_of_set(X0,intersection_of_members(X1))
| basis(f2(X1,X0),X2)
| ~ topological_space(f2(X1,X0),X2) ) ).
cnf(u1334,axiom,
( element_of_set(f11(X0,closure(X1,X2,X3)),closure(X1,X2,X3))
| element_of_set(f7(boundary(X1,X2,X3),X4),union_of_members(top_of_basis(X0)))
| ~ topological_space(boundary(X1,X2,X3),X4)
| basis(boundary(X1,X2,X3),X4) ) ).
cnf(u6117,negated_conjecture,
( ~ closed(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X5,X6)
| ~ closed(sF0,X1,X2)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X3))
| element_of_set(f7(closure(X4,X5,X6),X7),sF0)
| ~ topological_space(closure(X4,X5,X6),X7)
| ~ subset_sets(X4,f13(a,cx,ct,f11(X3,closure(X0,X1,X2))))
| ~ subset_sets(X0,sF0)
| basis(closure(X4,X5,X6),X7) ) ).
cnf(u2733,axiom,
( ~ element_of_set(X4,f1(top_of_basis(subspace_topology(X0,X1,X2)),f20(union_of_members(top_of_basis(subspace_topology(X0,X1,X2))),X3)))
| ~ topological_space(union_of_members(top_of_basis(subspace_topology(X0,X1,X2))),X3)
| hausdorff(union_of_members(top_of_basis(subspace_topology(X0,X1,X2))),X3)
| subset_sets(X2,X0) ) ).
cnf(u1037,axiom,
( ~ closed(boundary(relative_complement_sets(X0,X1),X1,X2),cx,ct)
| ~ subset_sets(a,boundary(relative_complement_sets(X0,X1),X1,X2))
| ~ topological_space(sF3,X3)
| hausdorff(sF3,X3)
| ~ element_of_set(f20(sF3,X3),closure(X0,X1,X2))
| element_of_set(f20(sF3,X3),boundary(X0,X1,X2)) ) ).
cnf(u6440,axiom,
( ~ closed(boundary(X5,X2,X3),X6,X7)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X1,X4,X0),closure(X5,X2,X3)),sF3)
| ~ subset_sets(X5,sF1)
| subset_sets(X0,X1)
| ~ subset_sets(X8,boundary(X5,X2,X3))
| element_of_collection(closure(X8,X6,X7),top_of_basis(X9)) ) ).
cnf(u2710,axiom,
( ~ element_of_set(X4,f1(top_of_basis(subspace_topology(X0,X1,X2)),f19(union_of_members(top_of_basis(subspace_topology(X0,X1,X2))),X3)))
| ~ topological_space(union_of_members(top_of_basis(subspace_topology(X0,X1,X2))),X3)
| hausdorff(union_of_members(top_of_basis(subspace_topology(X0,X1,X2))),X3)
| subset_sets(X2,X0) ) ).
cnf(u4481,axiom,
( ~ element_of_set(X8,f12(X0,top_of_basis(subspace_topology(X1,X2,X3)),X4,f1(subspace_topology(X0,top_of_basis(subspace_topology(X1,X2,X3)),X4),X5)))
| ~ subset_sets(X6,X7)
| ~ topological_space(X7,subspace_topology(X0,top_of_basis(subspace_topology(X1,X2,X3)),X4))
| limit_point(X5,X6,X7,subspace_topology(X0,top_of_basis(subspace_topology(X1,X2,X3)),X4))
| topological_space(X1,X2) ) ).
cnf(u246,axiom,
( ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3)
| topological_space(X1,X2) ) ).
cnf(u5859,negated_conjecture,
( ~ subset_sets(f14(a,cx,ct,f20(closure(relative_complement_sets(a,cx),cx,ct),X0)),sF3)
| ~ topological_space(closure(relative_complement_sets(a,cx),cx,ct),X0)
| hausdorff(closure(relative_complement_sets(a,cx),cx,ct),X0)
| element_of_set(f20(closure(relative_complement_sets(a,cx),cx,ct),X0),sF1)
| ~ element_of_collection(f14(a,cx,ct,f20(closure(relative_complement_sets(a,cx),cx,ct),X0)),X1)
| element_of_collection(sF3,top_of_basis(X1)) ) ).
cnf(u9375,negated_conjecture,
( element_of_set(f20(boundary(X0,X1,X2),X3),sF3)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u1239,axiom,
( ~ subset_sets(union_of_members(X2),X1)
| ~ subset_sets(X3,X4)
| ~ topological_space(X4,X2)
| element_of_collection(X1,top_of_basis(X0))
| ~ element_of_collection(union_of_members(X2),X0)
| limit_point(f11(X0,X1),X3,X4,X2) ) ).
cnf(u1963,axiom,
( ~ element_of_set(X6,boundary(X5,X2,X3))
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X0,X1,X4),closure(relative_complement_sets(X5,X2),X2,X3)),sF3)
| ~ subset_sets(relative_complement_sets(X5,X2),sF1)
| topological_space(X0,X1) ) ).
cnf(u461,axiom,
( element_of_set(f7(sF1,X0),sF3)
| ~ topological_space(sF1,X0)
| basis(sF1,X0) ) ).
cnf(u6305,axiom,
( ~ subset_sets(f14(X2,X3,X4,X5),X1)
| element_of_set(X5,closure(X2,X3,X4))
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4)
| element_of_collection(X1,top_of_basis(X0))
| ~ element_of_collection(f14(X2,X3,X4,X5),X0)
| subset_sets(X2,f14(X2,X3,X4,f11(X0,X1))) ) ).
cnf(u1144,negated_conjecture,
( element_of_set(X3,interior(a,cx,subspace_topology(X1,X2,f13(a,cx,ct,f19(sF0,X0)))))
| ~ topological_space(cx,subspace_topology(X1,X2,f13(a,cx,ct,f19(sF0,X0))))
| ~ element_of_set(X3,f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| ~ topological_space(sF0,X0)
| ~ connected_set(f13(a,cx,ct,f19(sF0,X0)),X1,X2) ) ).
cnf(u4926,axiom,
( ~ subset_sets(union_of_members(top_of_basis(X2)),X1)
| element_of_set(f11(X2,closure(X3,X4,X5)),sF3)
| ~ closed(sF1,X4,X5)
| ~ subset_sets(X3,sF1)
| ~ subset_sets(X3,X4)
| element_of_collection(X1,top_of_basis(X0))
| ~ element_of_collection(union_of_members(top_of_basis(X2)),X0)
| closed(f14(X3,X4,X5,f11(X0,X1)),X4,X5) ) ).
cnf(u1367,axiom,
( element_of_set(f20(boundary(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3),boundary(relative_complement_sets(X0,X1),X1,X2))
| hausdorff(boundary(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3)
| ~ topological_space(boundary(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3)
| ~ element_of_set(f20(boundary(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3),boundary(X0,X1,X2)) ) ).
cnf(u2871,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),X3),X3)
| element_of_collection(X3,top_of_basis(X4))
| topological_space(X0,X1) ) ).
cnf(u231,axiom,
( eq_p(f15(X4,X1,X5,X6,f16(X0,X1,X2,X3)),X0)
| ~ limit_point(X4,X1,X5,X6)
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3)
| ~ neighborhood(f16(X0,X1,X2,X3),X4,X5,X6) ) ).
cnf(topological_space_8,axiom,
( ~ topological_space(X0,X1)
| element_of_collection(empty_set,X1) ) ).
cnf(u6081,negated_conjecture,
( ~ closed(union_of_members(f24(X0,ct)),X3,X4)
| compact_space(X0,ct)
| element_of_set(f11(X1,closure(X2,X3,X4)),union_of_members(ct))
| element_of_collection(closure(X2,X3,X4),top_of_basis(X1))
| ~ topological_space(X0,ct)
| ~ subset_sets(X2,union_of_members(f24(X0,ct))) ) ).
cnf(u4480,axiom,
( ~ element_of_set(X8,f12(X0,top_of_basis(subspace_topology(X1,X2,X3)),X4,f1(subspace_topology(X0,top_of_basis(subspace_topology(X1,X2,X3)),X4),X5)))
| ~ subset_sets(X6,X7)
| ~ topological_space(X7,subspace_topology(X0,top_of_basis(subspace_topology(X1,X2,X3)),X4))
| limit_point(X5,X6,X7,subspace_topology(X0,top_of_basis(subspace_topology(X1,X2,X3)),X4))
| subset_sets(X3,X1) ) ).
cnf(u6294,axiom,
( subset_sets(X0,f14(X0,X1,X2,f11(X7,f14(closure(X0,X1,X2),X3,X4,X5))))
| element_of_set(X5,f14(closure(X0,X1,X2),X3,X4,X6))
| element_of_set(X6,closure(closure(X0,X1,X2),X3,X4))
| ~ topological_space(X3,X4)
| ~ element_of_collection(closure(X0,X1,X2),X7)
| element_of_collection(f14(closure(X0,X1,X2),X3,X4,X5),top_of_basis(X7))
| ~ subset_sets(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u17784,negated_conjecture,
( eq_p(f20(intersection_of_members(X0),X1),X2)
| hausdorff(intersection_of_members(X0),X1)
| ~ element_of_set(X2,sF1) ) ).
cnf(u4858,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,X0),f24(f13(a,cx,ct,X0),X1)),sF0)
| basis(f13(a,cx,ct,X0),f24(f13(a,cx,ct,X0),X1))
| compact_space(f13(a,cx,ct,X0),X1)
| ~ topological_space(f13(a,cx,ct,X0),X1)
| ~ element_of_set(X0,sF0) ) ).
cnf(u3408,axiom,
( element_of_set(f11(X1,f13(a,cx,ct,f19(sF0,X0))),union_of_members(ct))
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0)
| element_of_collection(f13(a,cx,ct,f19(sF0,X0)),top_of_basis(X1)) ) ).
cnf(u3319,axiom,
( ~ subset_sets(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,X3),cx)
| element_of_set(X3,union_of_members(top_of_basis(X4)))
| ~ closed(sF1,X1,X2)
| ~ subset_sets(f13(a,cx,ct,f20(sF0,X0)),sF1)
| ~ subset_sets(f13(a,cx,ct,f20(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| element_of_set(f11(X4,closure(f13(a,cx,ct,f20(sF0,X0)),X1,X2)),sF3)
| ~ element_of_set(X5,f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(X5,interior(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,X3),cx,ct)) ) ).
cnf(u290,negated_conjecture,
( element_of_set(f20(intersection_of_sets(X0,X1),X2),union_of_members(ct))
| ~ element_of_collection(X1,ct)
| ~ element_of_collection(X0,ct)
| ~ topological_space(intersection_of_sets(X0,X1),X2)
| hausdorff(intersection_of_sets(X0,X1),X2) ) ).
cnf(u836,negated_conjecture,
( ~ closed(f1(ct,X4),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f1(ct,X4))
| ~ element_of_set(X4,cx)
| element_of_set(f11(X0,closure(X1,X2,X3)),union_of_members(ct)) ) ).
cnf(u28172,negated_conjecture,
( element_of_set(f11(X1,union_of_members(ct)),f13(X5,X6,X7,f11(X1,union_of_members(ct))))
| element_of_set(f11(X0,union_of_members(top_of_basis(X1))),union_of_members(X9))
| element_of_set(X8,f1(top_of_basis(X0),X8))
| ~ element_of_set(X8,cx) ) ).
cnf(u4034,axiom,
( ~ closed(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X8,X9)
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| element_of_set(f19(boundary(X7,X8,X9),X10),interior(X4,X5,X6))
| ~ topological_space(boundary(X7,X8,X9),X10)
| ~ subset_sets(X7,f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)))
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(boundary(X7,X8,X9),X10) ) ).
cnf(u121,negated_conjecture,
~ equal_sets(sF2,sF3) ).
cnf(u6282,axiom,
( ~ topological_space(f14(X0,X1,X2,X3),X6)
| element_of_set(X4,closure(X0,X1,X2))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| ~ element_of_collection(X5,X6)
| element_of_set(X3,f14(X0,X1,X2,X4))
| ~ element_of_set(X7,X5)
| ~ subset_sets(X5,X0)
| element_of_set(X7,interior(X0,f14(X0,X1,X2,X3),X6)) ) ).
cnf(u3447,axiom,
( element_of_set(f20(f13(a,cx,ct,f20(sF0,X0)),X1),union_of_members(ct))
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f20(sF0,X0)),X1)
| hausdorff(f13(a,cx,ct,f20(sF0,X0)),X1) ) ).
cnf(u905,axiom,
( ~ element_of_set(X7,f16(X6,X4,X0,subspace_topology(X1,X2,X3)))
| ~ subset_sets(X4,X0)
| ~ topological_space(X5,X2)
| ~ subset_sets(X3,X5)
| limit_point(X6,X4,X0,subspace_topology(X1,X2,X3))
| ~ topological_space(X0,subspace_topology(X1,X2,X3))
| element_of_set(X7,union_of_members(subspace_topology(X5,X2,X3))) ) ).
cnf(u2548,axiom,
( ~ element_of_set(X0,f13(X1,X2,top_of_basis(subspace_topology(X3,X4,X5)),f20(interior(X1,X2,top_of_basis(subspace_topology(X3,X4,X5))),X6)))
| subset_sets(X5,X3)
| ~ topological_space(interior(X1,X2,top_of_basis(subspace_topology(X3,X4,X5))),X6)
| hausdorff(interior(X1,X2,top_of_basis(subspace_topology(X3,X4,X5))),X6) ) ).
cnf(u3699,axiom,
( element_of_set(X10,interior(f14(f16(X0,X1,X2,X3),X4,X5,f11(X9,f14(closure(f16(X0,X1,X2,X3),X4,X5),X6,X7,X8))),X2,X3))
| ~ element_of_collection(closure(f16(X0,X1,X2,X3),X4,X5),X9)
| ~ subset_sets(f16(X0,X1,X2,X3),X4)
| ~ topological_space(X4,X5)
| element_of_set(X8,closure(closure(f16(X0,X1,X2,X3),X4,X5),X6,X7))
| ~ subset_sets(closure(f16(X0,X1,X2,X3),X4,X5),X6)
| ~ topological_space(X6,X7)
| limit_point(X0,X1,X2,X3)
| ~ topological_space(X2,X3)
| ~ subset_sets(f14(f16(X0,X1,X2,X3),X4,X5,f11(X9,f14(closure(f16(X0,X1,X2,X3),X4,X5),X6,X7,X8))),X2)
| ~ element_of_set(X10,f16(X0,X1,X2,X3))
| ~ subset_sets(X1,X2)
| element_of_collection(f14(closure(f16(X0,X1,X2,X3),X4,X5),X6,X7,X8),top_of_basis(X9)) ) ).
cnf(u3378,axiom,
( element_of_set(f19(closure(X2,X0,X1),X3),X4)
| ~ subset_sets(X2,sF3)
| hausdorff(closure(X2,X0,X1),X3)
| ~ topological_space(closure(X2,X0,X1),X3)
| ~ subset_sets(a,X4)
| ~ closed(X4,cx,ct)
| ~ closed(sF3,X0,X1) ) ).
cnf(u1250,axiom,
( element_of_collection(f12(X0,X1,X2,f1(subspace_topology(X0,X1,X2),X3)),X1)
| limit_point(X3,X4,X5,subspace_topology(X0,X1,X2))
| ~ subset_sets(X4,X5)
| ~ topological_space(X5,subspace_topology(X0,X1,X2)) ) ).
cnf(u3650,axiom,
( ~ element_of_set(X4,relative_complement_sets(X0,X1))
| ~ subset_sets(X1,X1)
| element_of_collection(boundary(X0,X1,X2),top_of_basis(X3))
| ~ closed(X0,X1,X5)
| element_of_set(X4,interior(X1,X1,X5)) ) ).
cnf(u5560,axiom,
( ~ connected_set(X0,X1,X2)
| ~ topological_space(X3,X2)
| ~ subset_sets(X0,X3)
| element_of_collection(X0,subspace_topology(X3,X2,X0)) ) ).
cnf(u3026,negated_conjecture,
( element_of_set(f19(f13(a,cx,ct,f20(sF0,X0)),X1),union_of_members(top_of_basis(X2)))
| hausdorff(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f20(sF0,X0)),X1)
| hausdorff(f13(a,cx,ct,f20(sF0,X0)),X1)
| element_of_set(f11(X2,sF0),sF0)
| ~ topological_space(sF0,X0) ) ).
cnf(u4278,negated_conjecture,
( ~ element_of_set(f11(X4,f14(f14(a,cx,ct,X0),X1,X2,f20(closure(relative_complement_sets(f14(a,cx,ct,X0),X1),X1,X2),X3))),sF3)
| ~ topological_space(closure(relative_complement_sets(f14(a,cx,ct,X0),X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(f14(a,cx,ct,X0),X1),X1,X2),X3)
| ~ subset_sets(f14(a,cx,ct,X0),X1)
| ~ element_of_collection(f14(a,cx,ct,X0),X4)
| element_of_collection(f14(f14(a,cx,ct,X0),X1,X2,f20(closure(relative_complement_sets(f14(a,cx,ct,X0),X1),X1,X2),X3)),top_of_basis(X4))
| element_of_set(f20(closure(relative_complement_sets(f14(a,cx,ct,X0),X1),X1,X2),X3),boundary(f14(a,cx,ct,X0),X1,X2))
| element_of_set(X0,sF3) ) ).
cnf(u30742,axiom,
( ~ compact_space(X0,X1)
| compact_space(X2,X1) ) ).
cnf(u3984,axiom,
( element_of_collection(f12(X1,X2,X3,f6(X5,subspace_topology(X1,X2,X3),f15(X6,X4,X7,X8,X0),X0,X4)),X2)
| ~ element_of_collection(X4,subspace_topology(X1,X2,X3))
| ~ basis(X5,subspace_topology(X1,X2,X3))
| ~ element_of_set(f15(X6,X4,X7,X8,X0),X5)
| ~ neighborhood(X0,X6,X7,X8)
| ~ limit_point(X6,X4,X7,X8)
| ~ element_of_collection(X0,subspace_topology(X1,X2,X3)) ) ).
cnf(problem_11_151,negated_conjecture,
topological_space(cx,ct) ).
cnf(u3316,axiom,
( ~ subset_sets(f14(relative_complement_sets(X0,X1),X2,X3,X4),X1)
| element_of_set(X4,union_of_members(top_of_basis(X5)))
| ~ closed(sF1,X2,X3)
| ~ subset_sets(relative_complement_sets(X0,X1),sF1)
| ~ subset_sets(relative_complement_sets(X0,X1),X2)
| element_of_set(f11(X5,closure(relative_complement_sets(X0,X1),X2,X3)),sF3)
| ~ element_of_set(X6,relative_complement_sets(X0,X1))
| ~ closed(X0,X1,X7)
| element_of_set(X6,interior(f14(relative_complement_sets(X0,X1),X2,X3,X4),X1,X7)) ) ).
cnf(u242,negated_conjecture,
( element_of_set(f20(f13(a,cx,ct,X0),X1),sF0)
| hausdorff(f13(a,cx,ct,X0),X1)
| ~ topological_space(f13(a,cx,ct,X0),X1)
| ~ element_of_set(X0,sF0) ) ).
cnf(u5205,axiom,
( ~ element_of_set(X6,f12(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5,f9(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))))
| basis(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| ~ topological_space(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| topological_space(X2,X3) ) ).
cnf(u4918,axiom,
( closed(f14(X2,X3,X4,X0),X3,X4)
| element_of_set(f11(X1,closure(X2,X3,X4)),sF3)
| element_of_set(X0,f1(top_of_basis(X1),X0))
| ~ subset_sets(X2,sF1)
| ~ subset_sets(X2,X3)
| ~ closed(sF1,X3,X4) ) ).
cnf(u3690,axiom,
( element_of_set(X7,interior(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,f11(X6,f14(closure(f13(a,cx,ct,f19(sF0,X0)),X1,X2),X3,X4,X5))),cx,ct))
| ~ element_of_collection(closure(f13(a,cx,ct,f19(sF0,X0)),X1,X2),X6)
| ~ subset_sets(f13(a,cx,ct,f19(sF0,X0)),X1)
| ~ topological_space(X1,X2)
| element_of_set(X5,closure(closure(f13(a,cx,ct,f19(sF0,X0)),X1,X2),X3,X4))
| ~ subset_sets(closure(f13(a,cx,ct,f19(sF0,X0)),X1,X2),X3)
| ~ topological_space(X3,X4)
| ~ topological_space(sF0,X0)
| ~ subset_sets(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,f11(X6,f14(closure(f13(a,cx,ct,f19(sF0,X0)),X1,X2),X3,X4,X5))),cx)
| ~ element_of_set(X7,f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_collection(f14(closure(f13(a,cx,ct,f19(sF0,X0)),X1,X2),X3,X4,X5),top_of_basis(X6)) ) ).
cnf(u3600,negated_conjecture,
( element_of_set(X4,interior(f14(f13(a,cx,ct,X0),X1,X2,f11(X3,closure(relative_complement_sets(f13(a,cx,ct,X0),X1),X1,X2))),cx,ct))
| element_of_collection(closure(relative_complement_sets(f13(a,cx,ct,X0),X1),X1,X2),top_of_basis(X3))
| ~ subset_sets(f13(a,cx,ct,X0),X1)
| ~ subset_sets(f14(f13(a,cx,ct,X0),X1,X2,f11(X3,closure(relative_complement_sets(f13(a,cx,ct,X0),X1),X1,X2))),cx)
| ~ element_of_set(X4,f13(a,cx,ct,X0))
| ~ element_of_set(X0,sF0)
| element_of_set(f11(X3,closure(relative_complement_sets(f13(a,cx,ct,X0),X1),X1,X2)),boundary(f13(a,cx,ct,X0),X1,X2)) ) ).
cnf(u457,axiom,
( ~ topological_space(boundary(X0,X1,X2),X3)
| basis(boundary(X0,X1,X2),X3)
| subset_sets(relative_complement_sets(X0,X1),X1) ) ).
cnf(u2985,axiom,
( element_of_set(X5,f10(X3,boundary(X0,X1,X2),X5))
| element_of_set(f11(X3,boundary(X0,X1,X2)),X4)
| ~ subset_sets(X0,X4)
| ~ element_of_set(X5,boundary(X0,X1,X2))
| ~ closed(X4,X1,X2) ) ).
cnf(u256,axiom,
( element_of_set(f19(interior(X0,X1,X2),X3),f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3) ) ).
cnf(u4263,axiom,
( element_of_collection(f12(X2,X3,X4,relative_complement_sets(f14(X0,X1,subspace_topology(X2,X3,X4),f19(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5)),X1)),X3)
| element_of_set(f19(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5),boundary(X0,X1,subspace_topology(X2,X3,X4)))
| hausdorff(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5)
| ~ subset_sets(X0,X1)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5) ) ).
cnf(u11131,negated_conjecture,
hausdorff(boundary(X0,X1,X2),X3) ).
cnf(u3956,negated_conjecture,
( ~ closed(f1(ct,f15(X1,X4,X2,X3,X0)),X7,X8)
| ~ limit_point(X1,X4,X2,X3)
| ~ element_of_collection(X4,ct)
| ~ element_of_collection(X0,ct)
| element_of_set(f11(X5,boundary(X6,X7,X8)),union_of_members(ct))
| element_of_collection(boundary(X6,X7,X8),top_of_basis(X5))
| ~ neighborhood(X0,X1,X2,X3)
| ~ subset_sets(X6,f1(ct,f15(X1,X4,X2,X3,X0))) ) ).
cnf(u6789,negated_conjecture,
( ~ open(f14(a,cx,ct,X2),X0,X1)
| element_of_set(X2,sF0)
| ~ disjoint_s(X3,f14(a,cx,ct,X2))
| ~ element_of_set(f20(X0,X1),sF3)
| hausdorff(X0,X1)
| ~ open(X3,X0,X1)
| ~ element_of_set(f19(X0,X1),X3) ) ).
cnf(u5730,axiom,
( element_of_set(f20(boundary(relative_complement_sets(X2,X3),X3,subspace_topology(X1,X4,X0)),X5),boundary(X2,X3,subspace_topology(X1,X4,X0)))
| ~ subset_sets(X2,X3)
| ~ topological_space(boundary(relative_complement_sets(X2,X3),X3,subspace_topology(X1,X4,X0)),X5)
| hausdorff(boundary(relative_complement_sets(X2,X3),X3,subspace_topology(X1,X4,X0)),X5)
| subset_sets(X0,X1) ) ).
cnf(u3500,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ closed(X7,X5,X6)
| ~ subset_sets(X4,X7)
| element_of_set(f11(X8,closure(X4,X5,X6)),X7)
| element_of_set(f7(closure(X0,X1,X2),X3),union_of_members(top_of_basis(X8))) ) ).
cnf(u2867,axiom,
( ~ topological_space(boundary(X3,X4,X5),X6)
| element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),closure(X3,X4,X5))
| topological_space(X0,X1)
| basis(boundary(X3,X4,X5),X6) ) ).
cnf(u4854,axiom,
( basis(interior(X0,X1,X2),f24(interior(X0,X1,X2),X3))
| ~ topological_space(interior(X0,X1,X2),X3)
| compact_space(interior(X0,X1,X2),X3)
| subset_sets(X0,X1) ) ).
cnf(u3651,axiom,
( ~ subset_sets(X4,relative_complement_sets(X0,X1))
| ~ element_of_collection(X4,X5)
| ~ topological_space(X1,X5)
| ~ element_of_set(X6,X4)
| element_of_collection(boundary(X0,X1,X2),top_of_basis(X3))
| element_of_set(X6,interior(relative_complement_sets(X0,X1),X1,X5)) ) ).
cnf(u1968,axiom,
( ~ closed(boundary(X5,X2,X3),X6,X7)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X0,X1,X4),closure(X5,X2,X3)),sF3)
| ~ subset_sets(X5,sF1)
| topological_space(X0,X1)
| ~ subset_sets(X8,boundary(X5,X2,X3))
| element_of_collection(closure(X8,X6,X7),top_of_basis(X9)) ) ).
cnf(u1216,negated_conjecture,
( ~ subset_sets(f14(a,cx,ct,f11(X1,X0)),X3)
| ~ subset_sets(sF3,X0)
| ~ element_of_set(f11(X2,X3),sF3)
| ~ element_of_collection(sF3,X1)
| element_of_collection(X3,top_of_basis(X2))
| ~ element_of_collection(f14(a,cx,ct,f11(X1,X0)),X2)
| element_of_collection(X0,top_of_basis(X1)) ) ).
cnf(u33606,negated_conjecture,
( ~ element_of_set(f11(X4,union_of_members(top_of_basis(X0))),cx)
| element_of_set(f11(X4,union_of_members(top_of_basis(X0))),f1(top_of_basis(X4),f11(X4,union_of_members(top_of_basis(X0)))))
| element_of_set(f11(X0,union_of_members(ct)),union_of_members(X5)) ) ).
cnf(u36060,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f10(X1,f1(top_of_basis(X1),f11(X0,union_of_members(ct))),f11(X0,union_of_members(ct))))
| element_of_set(f11(X4,union_of_members(top_of_basis(X0))),interior(X5,X6,X7))
| limit_point(f11(X0,union_of_members(ct)),X2,X3,top_of_basis(X1))
| element_of_set(X8,f1(top_of_basis(X4),X8))
| ~ element_of_set(X8,cx) ) ).
cnf(u3473,axiom,
( ~ closed(f9(X4,X5),X1,X2)
| ~ subset_sets(X0,f9(X4,X5))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(X4,X5)
| basis(X4,X5)
| element_of_set(f7(closure(X0,X1,X2),X3),union_of_members(X5)) ) ).
cnf(u50178,negated_conjecture,
( element_of_set(f20(f12(X3,top_of_basis(X4),X5,f1(subspace_topology(X3,top_of_basis(X4),X5),X0)),X6),f10(X4,f12(X3,top_of_basis(X4),X5,f1(subspace_topology(X3,top_of_basis(X4),X5),X0)),f20(f12(X3,top_of_basis(X4),X5,f1(subspace_topology(X3,top_of_basis(X4),X5),X0)),X6)))
| limit_point(X0,X1,X7,X8)
| hausdorff(f12(X3,top_of_basis(X4),X5,f1(subspace_topology(X3,top_of_basis(X4),X5),X0)),X6) ) ).
cnf(u370,axiom,
( element_of_collection(f9(X0,X1),X1)
| basis(X0,X1)
| ~ topological_space(X0,X1) ) ).
cnf(u3898,axiom,
( subset_sets(f13(f14(X1,X2,X3,X4),X5,X6,f11(X7,closure(X8,X9,X10))),f14(f13(f14(X1,X2,X3,X4),X5,X6,f11(X7,closure(X8,X9,X10))),X2,X3,X0))
| element_of_set(X0,f14(X1,X2,X3,X4))
| ~ subset_sets(f13(f14(X1,X2,X3,X4),X5,X6,f11(X7,closure(X8,X9,X10))),X2)
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| ~ closed(interior(f14(X1,X2,X3,X4),X5,X6),X9,X10)
| ~ subset_sets(X8,interior(f14(X1,X2,X3,X4),X5,X6))
| element_of_collection(closure(X8,X9,X10),top_of_basis(X7)) ) ).
cnf(u1267,axiom,
( ~ closed(boundary(X0,X1,X2),X3,X4)
| ~ subset_sets(X5,boundary(X0,X1,X2))
| element_of_collection(closure(X5,X3,X4),top_of_basis(X6))
| ~ subset_sets(X0,X7)
| ~ closed(X7,X1,X2)
| element_of_set(f11(X6,closure(X5,X3,X4)),X7) ) ).
cnf(u4695,axiom,
( element_of_set(f20(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5),boundary(X0,X1,subspace_topology(X2,X3,X4)))
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5)
| hausdorff(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5)
| ~ subset_sets(X0,X1)
| subset_sets(X4,X2) ) ).
cnf(u2537,axiom,
( ~ element_of_set(X0,f2(top_of_basis(subspace_topology(X1,X2,X3)),X4))
| subset_sets(X3,X1)
| element_of_set(X4,intersection_of_members(top_of_basis(subspace_topology(X1,X2,X3)))) ) ).
cnf(u3231,axiom,
( ~ closed(boundary(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,boundary(X4,X5,X6))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| subset_sets(X4,X5)
| element_of_set(f20(boundary(X0,X1,X2),X3),union_of_members(top_of_basis(X7))) ) ).
cnf(u3601,axiom,
( element_of_set(X4,interior(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,f11(X3,closure(relative_complement_sets(f13(a,cx,ct,f19(sF0,X0)),X1),X1,X2))),cx,ct))
| element_of_collection(closure(relative_complement_sets(f13(a,cx,ct,f19(sF0,X0)),X1),X1,X2),top_of_basis(X3))
| ~ subset_sets(f13(a,cx,ct,f19(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| ~ subset_sets(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,f11(X3,closure(relative_complement_sets(f13(a,cx,ct,f19(sF0,X0)),X1),X1,X2))),cx)
| ~ element_of_set(X4,f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(f11(X3,closure(relative_complement_sets(f13(a,cx,ct,f19(sF0,X0)),X1),X1,X2)),boundary(f13(a,cx,ct,f19(sF0,X0)),X1,X2)) ) ).
cnf(u2465,axiom,
( element_of_collection(f13(X0,X1,X2,f7(interior(X0,X1,X2),X3)),X2)
| basis(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3) ) ).
cnf(intersection_of_members_5,axiom,
( element_of_collection(f2(X1,X0),X1)
| element_of_set(X0,intersection_of_members(X1)) ) ).
cnf(u8088,negated_conjecture,
( open(f13(X2,X3,X4,f20(X0,X1)),X3,X4)
| hausdorff(X0,X1) ) ).
cnf(u1395,axiom,
( ~ element_of_set(X0,f10(top_of_basis(subspace_topology(X1,X2,X3)),X4,X5))
| topological_space(X1,X2)
| ~ element_of_set(X5,X4)
| ~ element_of_collection(X4,top_of_basis(top_of_basis(subspace_topology(X1,X2,X3)))) ) ).
cnf(u5782,negated_conjecture,
( ~ element_of_set(f19(f13(a,cx,ct,X1),X2),X0)
| ~ open(sF0,f13(a,cx,ct,X1),X2)
| hausdorff(f13(a,cx,ct,X1),X2)
| ~ open(X0,f13(a,cx,ct,X1),X2)
| ~ disjoint_s(X0,sF0)
| ~ element_of_set(X1,sF0) ) ).
cnf(u2412,axiom,
( element_of_set(f7(boundary(X3,X1,X2),X5),union_of_members(top_of_basis(X4)))
| element_of_set(f11(X4,closure(X3,X1,X2)),X0)
| ~ subset_sets(X3,X0)
| ~ closed(X0,X1,X2)
| ~ topological_space(boundary(X3,X1,X2),X5)
| basis(boundary(X3,X1,X2),X5) ) ).
cnf(u27700,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f13(X2,X3,X4,f11(X0,union_of_members(top_of_basis(X1)))))
| element_of_set(X5,f1(top_of_basis(X0),X5))
| ~ element_of_set(X5,cx)
| element_of_set(f11(X1,union_of_members(ct)),union_of_members(ct)) ) ).
cnf(u1114,negated_conjecture,
( ~ closed(f13(a,cx,ct,f19(closure(X2,X0,X1),X3)),X5,X6)
| ~ subset_sets(X2,sF0)
| ~ topological_space(closure(X2,X0,X1),X3)
| hausdorff(closure(X2,X0,X1),X3)
| element_of_set(f19(closure(X4,X5,X6),X7),sF0)
| hausdorff(closure(X4,X5,X6),X7)
| ~ subset_sets(X4,f13(a,cx,ct,f19(closure(X2,X0,X1),X3)))
| ~ closed(sF0,X0,X1)
| ~ topological_space(closure(X4,X5,X6),X7) ) ).
cnf(u2544,axiom,
( ~ element_of_set(X0,f21(X1,top_of_basis(subspace_topology(X2,X3,X4))))
| subset_sets(X4,X2)
| connected_space(X1,top_of_basis(subspace_topology(X2,X3,X4)))
| ~ topological_space(X1,top_of_basis(subspace_topology(X2,X3,X4))) ) ).
cnf(u490,axiom,
( element_of_set(X0,union_of_members(ct))
| ~ element_of_set(X0,sF0) ) ).
cnf(u28006,negated_conjecture,
( open(f13(X5,X6,X7,f11(X1,union_of_members(ct))),X6,X7)
| element_of_set(f11(X0,union_of_members(top_of_basis(X1))),union_of_members(X9))
| element_of_set(X8,f1(top_of_basis(X0),X8))
| ~ element_of_set(X8,cx) ) ).
cnf(u1166,axiom,
( ~ element_of_collection(f13(f13(a,cx,ct,X0),X1,X2,f7(interior(f13(a,cx,ct,X0),X1,X2),X3)),X4)
| basis(interior(f13(a,cx,ct,X0),X1,X2),X3)
| ~ topological_space(interior(f13(a,cx,ct,X0),X1,X2),X3)
| ~ topological_space(a,X4)
| ~ element_of_set(X5,f13(f13(a,cx,ct,X0),X1,X2,f7(interior(f13(a,cx,ct,X0),X1,X2),X3)))
| ~ element_of_set(X0,sF0)
| element_of_set(X5,interior(f13(a,cx,ct,X0),a,X4)) ) ).
cnf(u4773,axiom,
( element_of_set(X4,f10(X2,f12(X1,top_of_basis(X2),X3,f21(X0,subspace_topology(X1,top_of_basis(X2),X3))),X4))
| ~ topological_space(X0,subspace_topology(X1,top_of_basis(X2),X3))
| ~ element_of_set(X4,f12(X1,top_of_basis(X2),X3,f21(X0,subspace_topology(X1,top_of_basis(X2),X3))))
| connected_space(X0,subspace_topology(X1,top_of_basis(X2),X3)) ) ).
cnf(u799,negated_conjecture,
( subset_sets(a,f14(a,cx,ct,f11(X1,X0)))
| ~ element_of_collection(sF3,X1)
| element_of_collection(X0,top_of_basis(X1))
| ~ subset_sets(sF3,X0) ) ).
cnf(u1045,axiom,
( ~ subset_sets(f13(X1,X2,X3,f20(closure(X0,X4,X5),X6)),X7)
| ~ closed(interior(X1,X2,X3),X4,X5)
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| ~ subset_sets(X7,X2)
| ~ element_of_set(X8,f13(X1,X2,X3,f20(closure(X0,X4,X5),X6)))
| ~ subset_sets(X0,interior(X1,X2,X3))
| element_of_set(X8,interior(X7,X2,X3)) ) ).
cnf(u5638,axiom,
( ~ subset_sets(sF3,closure(X1,X2,X3))
| element_of_set(X4,union_of_members(top_of_basis(X0)))
| ~ closed(sF1,X2,X3)
| ~ subset_sets(X1,sF1)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ element_of_collection(sF3,X0)
| subset_sets(X1,f14(X1,X2,X3,X4)) ) ).
cnf(u3722,negated_conjecture,
( element_of_set(f19(intersection_of_sets(X1,X0),X2),f1(ct,f19(intersection_of_sets(X1,X0),X2)))
| ~ element_of_collection(X1,ct)
| ~ topological_space(intersection_of_sets(X1,X0),X2)
| hausdorff(intersection_of_sets(X1,X0),X2)
| ~ element_of_collection(X0,ct) ) ).
cnf(compact_set_106,axiom,
( ~ compact_set(X0,X1,X2)
| topological_space(X1,X2) ) ).
cnf(u36098,negated_conjecture,
( element_of_set(f11(X4,union_of_members(ct)),interior(X5,X6,X7))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| element_of_set(f11(X1,union_of_members(top_of_basis(X4))),union_of_members(X8))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u2363,axiom,
( ~ subset_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),interior(X0,X1,X2))
| ~ element_of_collection(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X3)
| element_of_collection(interior(X0,X1,X2),top_of_basis(X3)) ) ).
cnf(u2654,axiom,
( element_of_collection(union_of_members(subspace_topology(X0,X1,X2)),top_of_basis(X3))
| subset_sets(X2,X0) ) ).
cnf(u6384,axiom,
( ~ subset_sets(f14(X2,X3,X4,X5),X1)
| element_of_set(X5,closure(X2,X3,X4))
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4)
| element_of_collection(X1,top_of_basis(X0))
| ~ element_of_collection(f14(X2,X3,X4,X5),X0)
| closed(f14(X2,X3,X4,f11(X0,X1)),X3,X4) ) ).
cnf(u321,axiom,
( open_covering(X2,X0,X1)
| ~ subset_collections(X2,X1)
| ~ topological_space(X0,X1)
| ~ basis(X0,X2) ) ).
cnf(u1257,axiom,
( element_of_collection(f6(X4,X6,f11(X0,closure(X1,X2,X3)),X5,X7),X6)
| ~ element_of_collection(X5,X6)
| ~ element_of_collection(X7,X6)
| ~ basis(X4,X6)
| ~ element_of_set(f11(X0,closure(X1,X2,X3)),X4)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ closed(intersection_of_sets(X5,X7),X2,X3)
| ~ subset_sets(X1,intersection_of_sets(X5,X7)) ) ).
cnf(u469,axiom,
( separation(f21(X0,X1),f22(X0,X1),X0,X2)
| ~ topological_space(X0,X1)
| ~ topological_space(X0,X2)
| ~ element_of_collection(f21(X0,X1),X2)
| ~ element_of_collection(f22(X0,X1),X2)
| connected_space(X0,X1) ) ).
cnf(u2988,axiom,
( ~ closed(X1,cx,ct)
| element_of_set(f11(X0,sF1),X1)
| element_of_collection(sF1,top_of_basis(X0))
| ~ subset_sets(a,X1) ) ).
cnf(u2755,axiom,
( ~ topological_space(X7,subspace_topology(X2,X3,X4))
| ~ topological_space(X2,X3)
| ~ subset_sets(X4,X2)
| limit_point(X5,X0,X1,subspace_topology(X6,X3,X4))
| ~ topological_space(X1,subspace_topology(X6,X3,X4))
| element_of_set(X5,union_of_members(subspace_topology(X2,X3,X4)))
| ~ subset_sets(X0,X7)
| ~ subset_sets(X0,X1) ) ).
cnf(u2714,axiom,
( ~ topological_space(union_of_members(subspace_topology(X0,X1,X2)),X3)
| hausdorff(union_of_members(subspace_topology(X0,X1,X2)),X3)
| subset_sets(X2,X0) ) ).
cnf(u3781,axiom,
( element_of_collection(f12(X2,X3,X4,relative_complement_sets(f14(X0,X1,subspace_topology(X2,X3,X4),f11(X8,f14(closure(X0,X1,subspace_topology(X2,X3,X4)),X5,X6,X7))),X1)),X3)
| ~ element_of_collection(closure(X0,X1,subspace_topology(X2,X3,X4)),X8)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,subspace_topology(X2,X3,X4))
| element_of_set(X7,closure(closure(X0,X1,subspace_topology(X2,X3,X4)),X5,X6))
| ~ subset_sets(closure(X0,X1,subspace_topology(X2,X3,X4)),X5)
| ~ topological_space(X5,X6)
| element_of_collection(f14(closure(X0,X1,subspace_topology(X2,X3,X4)),X5,X6,X7),top_of_basis(X8)) ) ).
cnf(u36082,negated_conjecture,
( open(f13(X4,X5,X6,f11(X7,union_of_members(ct))),X5,X6)
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| element_of_set(f11(X1,union_of_members(top_of_basis(X7))),union_of_members(X8))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u9879,negated_conjecture,
( eq_p(X0,f19(boundary(X1,X2,X3),X4))
| ~ element_of_set(X0,sF1)
| hausdorff(boundary(X1,X2,X3),X4) ) ).
cnf(u3694,axiom,
( element_of_set(X13,interior(f14(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8,f11(X12,f14(closure(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8),X9,X10,X11))),X1,X2))
| ~ element_of_collection(closure(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8),X12)
| ~ subset_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7)
| ~ topological_space(X7,X8)
| element_of_set(X11,closure(closure(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8),X9,X10))
| ~ subset_sets(closure(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8),X9)
| ~ topological_space(X9,X10)
| ~ closed(interior(X0,X1,X2),X4,X5)
| ~ topological_space(closure(X3,X4,X5),X6)
| hausdorff(closure(X3,X4,X5),X6)
| ~ subset_sets(f14(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8,f11(X12,f14(closure(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8),X9,X10,X11))),X1)
| ~ element_of_set(X13,f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)))
| ~ subset_sets(X3,interior(X0,X1,X2))
| element_of_collection(f14(closure(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8),X9,X10,X11),top_of_basis(X12)) ) ).
cnf(connected_space_91,axiom,
( separation(f21(X0,X1),f22(X0,X1),X0,X1)
| ~ topological_space(X0,X1)
| connected_space(X0,X1) ) ).
cnf(u3057,axiom,
( element_of_set(f19(boundary(X0,X1,X2),X3),f13(X4,X5,X6,f19(boundary(X0,X1,X2),X3)))
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ closed(interior(X4,X5,X6),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u239,axiom,
( subset_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X0)
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3) ) ).
cnf(u29083,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f1(top_of_basis(X1),f11(X0,union_of_members(ct))))
| element_of_set(f11(X1,union_of_members(top_of_basis(X0))),interior(X2,X3,X4))
| ~ element_of_set(f11(X0,union_of_members(ct)),cx) ) ).
cnf(u782,axiom,
( ~ element_of_collection(f13(f13(a,cx,ct,X0),X1,X2,f11(X3,interior(f13(a,cx,ct,X0),X1,X2))),X4)
| element_of_collection(interior(f13(a,cx,ct,X0),X1,X2),top_of_basis(X3))
| ~ topological_space(a,X4)
| ~ element_of_set(X5,f13(f13(a,cx,ct,X0),X1,X2,f11(X3,interior(f13(a,cx,ct,X0),X1,X2))))
| ~ element_of_set(X0,sF0)
| element_of_set(X5,interior(f13(a,cx,ct,X0),a,X4)) ) ).
cnf(u4621,axiom,
( ~ element_of_collection(f2(X2,X3),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(X3,intersection_of_members(X2))
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X2)) ) ).
cnf(u6569,negated_conjecture,
( element_of_set(f7(sF3,X0),f14(relative_complement_sets(X1,cx),cx,ct,X2))
| ~ subset_sets(a,f14(relative_complement_sets(X1,cx),cx,ct,X2))
| ~ topological_space(sF3,X0)
| basis(sF3,X0)
| ~ subset_sets(relative_complement_sets(X1,cx),cx)
| element_of_set(X2,boundary(X1,cx,ct))
| closed(f14(X1,cx,ct,X2),cx,ct)
| ~ subset_sets(X1,cx) ) ).
cnf(u2939,axiom,
( ~ closed(intersection_of_sets(f16(X4,X5,X6,X7),X5),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,intersection_of_sets(f16(X4,X5,X6,X7),X5))
| ~ topological_space(X6,X7)
| ~ subset_sets(X5,X6)
| limit_point(X4,X5,X6,X7)
| eq_p(f11(X0,boundary(X1,X2,X3)),X4) ) ).
cnf(u36050,negated_conjecture,
( element_of_set(f20(sF0,X0),f10(X1,f1(top_of_basis(X1),f20(sF0,X0)),f20(sF0,X0)))
| limit_point(f20(sF0,X0),X2,X3,top_of_basis(X1))
| hausdorff(sF0,X0) ) ).
cnf(u3723,negated_conjecture,
( element_of_collection(f1(ct,f19(intersection_of_sets(X1,X0),X2)),ct)
| ~ element_of_collection(X1,ct)
| ~ topological_space(intersection_of_sets(X1,X0),X2)
| hausdorff(intersection_of_sets(X1,X0),X2)
| ~ element_of_collection(X0,ct) ) ).
cnf(u33906,negated_conjecture,
( element_of_set(X3,f13(f14(relative_complement_sets(X0,X1),cx,ct,X2),X1,X4,X3))
| element_of_set(X2,sF0)
| ~ element_of_set(X3,relative_complement_sets(X0,X1)) ) ).
cnf(u36107,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| element_of_set(f11(X1,union_of_members(top_of_basis(X4))),union_of_members(X5))
| element_of_set(f11(X4,union_of_members(ct)),union_of_members(ct))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u2549,axiom,
( ~ element_of_set(X0,f16(X1,X2,X3,top_of_basis(subspace_topology(X4,X5,X6))))
| subset_sets(X6,X4)
| limit_point(X1,X2,X3,top_of_basis(subspace_topology(X4,X5,X6)))
| ~ topological_space(X3,top_of_basis(subspace_topology(X4,X5,X6)))
| ~ subset_sets(X2,X3) ) ).
cnf(u844,axiom,
( ~ closed(interior(X4,X5,X6),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,interior(X4,X5,X6))
| subset_sets(X4,X5) ) ).
cnf(u6444,axiom,
( ~ closed(closure(X5,X2,X3),X8,X9)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X1,X4,X0),closure(X5,X2,X3)),sF3)
| ~ subset_sets(X5,sF1)
| element_of_collection(closure(X7,X8,X9),top_of_basis(X6))
| subset_sets(X0,X1)
| ~ subset_sets(X7,closure(X5,X2,X3)) ) ).
cnf(u220,negated_conjecture,
( ~ element_of_set(X0,intersection_of_sets(X1,X2))
| element_of_set(X0,union_of_members(ct))
| ~ element_of_collection(X2,ct)
| ~ element_of_collection(X1,ct) ) ).
cnf(u6576,negated_conjecture,
( ~ subset_sets(a,f14(X0,cx,ct,X1))
| element_of_set(X2,closure(X0,cx,ct))
| ~ subset_sets(X0,cx)
| element_of_set(X1,f14(X0,cx,ct,X2))
| ~ element_of_set(X3,sF3)
| element_of_set(X3,f14(X0,cx,ct,X1)) ) ).
cnf(u2477,axiom,
( element_of_set(X0,f10(X2,X1,X0))
| element_of_set(f11(X2,X1),X1)
| ~ element_of_set(X0,X1) ) ).
cnf(union_of_members_1,axiom,
( ~ element_of_set(X0,union_of_members(X1))
| element_of_set(X0,f1(X1,X0)) ) ).
cnf(u3696,axiom,
( closed(f14(X0,X1,X2,f11(X9,f14(closure(X0,X1,X2),X3,X4,f11(X8,f14(closure(closure(X0,X1,X2),X3,X4),X5,X6,X7))))),X1,X2)
| ~ element_of_collection(closure(closure(X0,X1,X2),X3,X4),X8)
| ~ subset_sets(closure(X0,X1,X2),X3)
| ~ topological_space(X3,X4)
| element_of_set(X7,closure(closure(closure(X0,X1,X2),X3,X4),X5,X6))
| ~ subset_sets(closure(closure(X0,X1,X2),X3,X4),X5)
| ~ topological_space(X5,X6)
| ~ element_of_collection(closure(X0,X1,X2),X9)
| element_of_collection(f14(closure(X0,X1,X2),X3,X4,f11(X8,f14(closure(closure(X0,X1,X2),X3,X4),X5,X6,X7))),top_of_basis(X9))
| element_of_collection(f14(closure(closure(X0,X1,X2),X3,X4),X5,X6,X7),top_of_basis(X8))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u9776,negated_conjecture,
( eq_p(X0,f20(boundary(relative_complement_sets(X1,X2),X2,X3),X4))
| ~ element_of_set(X0,boundary(X1,X2,X3))
| hausdorff(boundary(relative_complement_sets(X1,X2),X2,X3),X4) ) ).
cnf(u537,axiom,
( ~ open_covering(f24(X2,f24(X0,X1)),X0,X1)
| compact_space(X0,X1)
| ~ finite(f24(X2,f24(X0,X1)))
| compact_space(X2,f24(X0,X1))
| ~ topological_space(X2,f24(X0,X1)) ) ).
cnf(u6432,axiom,
( ~ element_of_set(X6,boundary(X5,X2,X3))
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X1,X4,X0),closure(relative_complement_sets(X5,X2),X2,X3)),sF3)
| ~ subset_sets(relative_complement_sets(X5,X2),sF1)
| subset_sets(X0,X1) ) ).
cnf(u1376,axiom,
( element_of_set(f11(X0,closure(X1,X2,X3)),f6(X4,X6,f11(X0,closure(X1,X2,X3)),X5,X7))
| ~ element_of_collection(X5,X6)
| ~ element_of_collection(X7,X6)
| ~ basis(X4,X6)
| ~ element_of_set(f11(X0,closure(X1,X2,X3)),X4)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ closed(intersection_of_sets(X5,X7),X2,X3)
| ~ subset_sets(X1,intersection_of_sets(X5,X7)) ) ).
cnf(u795,negated_conjecture,
( element_of_set(f20(f13(a,cx,ct,f11(X0,sF0)),X1),sF0)
| element_of_collection(sF0,top_of_basis(X0))
| ~ topological_space(f13(a,cx,ct,f11(X0,sF0)),X1)
| hausdorff(f13(a,cx,ct,f11(X0,sF0)),X1) ) ).
cnf(u3517,axiom,
( element_of_set(f7(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ subset_sets(relative_complement_sets(X0,X1),closure(X0,X1,X2))
| ~ closed(closure(X0,X1,X2),X1,X2)
| basis(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3) ) ).
cnf(u4816,negated_conjecture,
( element_of_set(f11(X1,union_of_members(ct)),union_of_members(ct))
| element_of_set(X0,f1(top_of_basis(X1),X0))
| ~ element_of_set(X0,cx) ) ).
cnf(u4769,axiom,
( ~ element_of_set(X4,f12(X1,X2,X3,f21(X0,subspace_topology(X1,X2,X3))))
| ~ topological_space(X0,subspace_topology(X1,X2,X3))
| connected_space(X0,subspace_topology(X1,X2,X3))
| element_of_set(X4,union_of_members(X2)) ) ).
cnf(u6094,axiom,
( ~ element_of_collection(f13(sF3,X2,X3,f19(closure(X4,X5,X6),X7)),X0)
| ~ element_of_set(X1,f13(sF3,X2,X3,f19(closure(X4,X5,X6),X7)))
| ~ topological_space(sF1,X0)
| element_of_set(X1,interior(sF3,sF1,X0))
| ~ subset_sets(X4,interior(sF3,X2,X3))
| ~ closed(interior(sF3,X2,X3),X5,X6)
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7) ) ).
cnf(u1400,axiom,
( ~ element_of_set(X0,f21(X1,top_of_basis(subspace_topology(X2,X3,X4))))
| topological_space(X2,X3)
| connected_space(X1,top_of_basis(subspace_topology(X2,X3,X4)))
| ~ topological_space(X1,top_of_basis(subspace_topology(X2,X3,X4))) ) ).
cnf(u5279,negated_conjecture,
( ~ open(f14(a,cx,ct,f11(X1,X2)),X3,X4)
| ~ disjoint_s(X0,f14(a,cx,ct,f11(X1,X2)))
| hausdorff(X3,X4)
| ~ open(X0,X3,X4)
| ~ element_of_set(f19(X3,X4),X0)
| element_of_collection(X2,top_of_basis(X1))
| ~ subset_sets(sF3,X2)
| ~ element_of_set(f20(X3,X4),sF3)
| ~ element_of_collection(sF3,X1) ) ).
cnf(u118,axiom,
union_of_sets(sF0,sF1) = sF2 ).
cnf(u648,axiom,
( element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| topological_space(X2,X3) ) ).
cnf(u15221,negated_conjecture,
( element_of_set(f11(X1,f1(ct,X0)),f1(ct,X0))
| ~ element_of_set(X0,cx)
| element_of_set(X0,f1(top_of_basis(X1),X0)) ) ).
cnf(u3828,axiom,
( ~ subset_sets(union_of_members(subspace_topology(X3,X4,X2)),X1)
| ~ connected_set(X2,X3,X4)
| element_of_collection(X1,top_of_basis(X0))
| ~ element_of_collection(union_of_members(subspace_topology(X3,X4,X2)),X0)
| ~ element_of_set(f11(X0,X1),X2) ) ).
cnf(u1111,negated_conjecture,
( element_of_collection(f13(a,cx,ct,f19(closure(X2,X0,X1),X3)),top_of_basis(X4))
| ~ subset_sets(X2,sF0)
| ~ topological_space(closure(X2,X0,X1),X3)
| hausdorff(closure(X2,X0,X1),X3)
| element_of_set(f11(X4,f13(a,cx,ct,f19(closure(X2,X0,X1),X3))),sF0)
| ~ closed(sF0,X0,X1) ) ).
cnf(u6125,negated_conjecture,
( ~ closed(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X5,X6)
| ~ closed(sF0,X1,X2)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X3))
| element_of_set(f19(boundary(X4,X5,X6),X7),sF0)
| ~ topological_space(boundary(X4,X5,X6),X7)
| ~ subset_sets(X4,f13(a,cx,ct,f11(X3,closure(X0,X1,X2))))
| ~ subset_sets(X0,sF0)
| hausdorff(boundary(X4,X5,X6),X7) ) ).
cnf(u3960,negated_conjecture,
( ~ closed(f1(ct,f15(X1,X4,X2,X3,X0)),X6,X7)
| ~ limit_point(X1,X4,X2,X3)
| ~ element_of_collection(X4,ct)
| ~ element_of_collection(X0,ct)
| element_of_set(f19(boundary(X5,X6,X7),X8),union_of_members(ct))
| ~ topological_space(boundary(X5,X6,X7),X8)
| ~ subset_sets(X5,f1(ct,f15(X1,X4,X2,X3,X0)))
| ~ neighborhood(X0,X1,X2,X3)
| hausdorff(boundary(X5,X6,X7),X8) ) ).
cnf(u36099,negated_conjecture,
( open(f13(X4,X5,X6,f11(X1,union_of_members(top_of_basis(X7)))),X5,X6)
| element_of_set(f11(X7,union_of_members(ct)),interior(X8,X9,X10))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u1232,axiom,
( ~ closed(f16(X3,X2,X0,X1),X5,X6)
| ~ subset_sets(X2,X0)
| limit_point(X3,X2,X0,X1)
| element_of_set(f20(closure(X4,X5,X6),X7),union_of_members(X1))
| hausdorff(closure(X4,X5,X6),X7)
| ~ subset_sets(X4,f16(X3,X2,X0,X1))
| ~ topological_space(X0,X1)
| ~ topological_space(closure(X4,X5,X6),X7) ) ).
cnf(u1245,axiom,
( ~ subset_sets(f1(X2,f11(X0,X1)),X1)
| ~ topological_space(X4,X2)
| ~ subset_sets(X3,X4)
| element_of_collection(X1,top_of_basis(X0))
| ~ element_of_collection(f1(X2,f11(X0,X1)),X0)
| limit_point(f11(X0,X1),X3,X4,X2) ) ).
cnf(u264,axiom,
( element_of_set(f19(closure(X0,X1,X2),X3),X4)
| hausdorff(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,X4)
| ~ closed(X4,X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u2645,negated_conjecture,
( element_of_set(f19(closure(X0,X1,X2),X3),f1(ct,f19(closure(X0,X1,X2),X3)))
| hausdorff(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,empty_set)
| ~ closed(empty_set,X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u53967,negated_conjecture,
( ~ element_of_set(X7,f13(X1,X2,X3,f19(interior(X1,X2,X3),X4)))
| hausdorff(interior(X1,X2,X3),X4)
| element_of_set(X7,f13(f14(f13(X1,X2,X3,f19(interior(X1,X2,X3),X4)),X5,X6,X0),X2,X3,X7))
| element_of_set(X0,X8) ) ).
cnf(u4780,axiom,
( ~ element_of_set(X6,f12(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5,f22(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))))
| ~ topological_space(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| connected_space(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| subset_sets(X4,X2) ) ).
cnf(u526,axiom,
( ~ element_of_set(X4,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)))
| ~ topological_space(interior(X0,X1,X2),X3)
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X4,interior(X0,X1,X2)) ) ).
cnf(compact_space_103,axiom,
( open_covering(f23(X0,X1,X2),X0,X1)
| ~ open_covering(X2,X0,X1)
| ~ compact_space(X0,X1) ) ).
cnf(u3069,negated_conjecture,
( ~ closed(f13(a,cx,ct,f19(sF0,X4)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f19(sF0,X4)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f19(boundary(X0,X1,X2),X3),sF0)
| ~ topological_space(sF0,X4)
| hausdorff(sF0,X4) ) ).
cnf(u1373,axiom,
( element_of_set(f7(X0,X1),f6(X2,X3,f7(X0,X1),f8(X0,X1),f9(X0,X1)))
| ~ element_of_collection(f8(X0,X1),X3)
| ~ element_of_collection(f9(X0,X1),X3)
| ~ basis(X2,X3)
| ~ element_of_set(f7(X0,X1),X2)
| ~ equal_sets(union_of_members(X1),X0)
| basis(X0,X1) ) ).
cnf(u7983,negated_conjecture,
( element_of_set(f20(sF0,X0),union_of_members(X1))
| hausdorff(sF0,X0) ) ).
cnf(u3352,negated_conjecture,
( element_of_collection(f1(ct,f19(empty_set,X0)),ct)
| ~ topological_space(empty_set,X0)
| hausdorff(empty_set,X0) ) ).
cnf(u1224,axiom,
( ~ element_of_collection(X1,top_of_basis(subspace_topology(X2,X3,X4)))
| ~ element_of_set(X0,X1)
| topological_space(X2,X3) ) ).
cnf(u2728,axiom,
( ~ closed(closure(relative_complement_sets(X1,X2),X2,X3),X4,X5)
| ~ subset_sets(X0,closure(relative_complement_sets(X1,X2),X2,X3))
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| element_of_set(f19(closure(X0,X4,X5),X6),boundary(X1,X2,X3))
| subset_sets(X1,f14(X1,X2,X3,f19(closure(X0,X4,X5),X6)))
| ~ subset_sets(X1,X2) ) ).
cnf(u4876,axiom,
( basis(closure(X0,X1,X2),f24(closure(X0,X1,X2),X3))
| ~ topological_space(closure(X0,X1,X2),X3)
| compact_space(closure(X0,X1,X2),X3)
| topological_space(X1,X2) ) ).
cnf(u3191,axiom,
( ~ topological_space(boundary(X0,X1,X2),X3)
| ~ subset_sets(X0,intersection_of_members(X4))
| ~ closed(intersection_of_members(X4),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ element_of_collection(X5,X4)
| element_of_set(f20(boundary(X0,X1,X2),X3),X5) ) ).
cnf(u50875,negated_conjecture,
( element_of_set(X7,f13(f14(f16(X2,X3,X0,X1),X4,X5,X6),X0,X1,X7))
| element_of_set(X6,closure(f16(X2,X3,X0,X1),X4,X5))
| limit_point(X2,X3,X0,X1)
| ~ element_of_set(X7,f16(X2,X3,X0,X1)) ) ).
cnf(u868,axiom,
( ~ subset_sets(X4,closure(X1,X2,X3))
| ~ closed(X4,X2,X3)
| ~ subset_sets(X1,X4)
| ~ element_of_collection(X4,X0)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(u27701,negated_conjecture,
( open(f13(X2,X3,X4,f11(X0,union_of_members(top_of_basis(X1)))),X3,X4)
| element_of_set(f11(X1,union_of_members(ct)),union_of_members(ct))
| element_of_set(X5,f1(top_of_basis(X0),X5))
| ~ element_of_set(X5,cx) ) ).
cnf(separation_84,axiom,
( ~ separation(X0,X1,X2,X3)
| element_of_collection(X0,X3) ) ).
cnf(u216,axiom,
( equal_sets(union_of_sets(f21(X0,X1),f22(X0,X1)),X0)
| connected_space(X0,X1)
| ~ topological_space(X0,X1) ) ).
cnf(u5816,axiom,
( element_of_set(X4,f14(X0,X1,X2,f20(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f20(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| subset_sets(X0,f14(X0,X1,X2,X4)) ) ).
cnf(u531,axiom,
( element_of_set(f20(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),interior(X0,X1,X2))
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ topological_space(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4)
| hausdorff(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4) ) ).
cnf(u4864,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,f19(sF0,X0)),f24(f13(a,cx,ct,f19(sF0,X0)),X1)),sF0)
| basis(f13(a,cx,ct,f19(sF0,X0)),f24(f13(a,cx,ct,f19(sF0,X0)),X1))
| compact_space(f13(a,cx,ct,f19(sF0,X0)),X1)
| ~ topological_space(f13(a,cx,ct,f19(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0) ) ).
cnf(u679,axiom,
( closed(f14(X0,X1,X2,f11(X3,closure(relative_complement_sets(X0,X1),X1,X2))),X1,X2)
| element_of_set(f11(X3,closure(relative_complement_sets(X0,X1),X1,X2)),boundary(X0,X1,X2))
| element_of_collection(closure(relative_complement_sets(X0,X1),X1,X2),top_of_basis(X3))
| ~ subset_sets(X0,X1) ) ).
cnf(u36112,negated_conjecture,
( element_of_set(f11(X1,union_of_members(ct)),f1(X4,f11(X1,union_of_members(ct))))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u6030,negated_conjecture,
( subset_sets(X1,f14(X1,X2,X3,f11(X4,f14(closure(X1,X2,X3),cx,ct,X0))))
| ~ subset_sets(closure(X1,X2,X3),sF0)
| ~ subset_sets(closure(X1,X2,X3),cx)
| ~ element_of_collection(closure(X1,X2,X3),X4)
| element_of_collection(f14(closure(X1,X2,X3),cx,ct,X0),top_of_basis(X4))
| element_of_set(X0,sF0)
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ) ).
cnf(u1122,axiom,
( ~ subset_sets(f13(X1,X2,X3,f19(closure(X0,X4,X5),X6)),X7)
| ~ closed(interior(X1,X2,X3),X4,X5)
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| ~ subset_sets(X7,X2)
| ~ element_of_set(X8,f13(X1,X2,X3,f19(closure(X0,X4,X5),X6)))
| ~ subset_sets(X0,interior(X1,X2,X3))
| element_of_set(X8,interior(X7,X2,X3)) ) ).
cnf(u3993,negated_conjecture,
( element_of_set(f11(subspace_topology(X5,X6,X7),f1(ct,f15(X1,X4,X2,X3,X0))),f1(ct,f15(X1,X4,X2,X3,X0)))
| ~ neighborhood(X0,X1,X2,X3)
| ~ limit_point(X1,X4,X2,X3)
| ~ element_of_collection(X4,ct)
| topological_space(X5,X6)
| ~ element_of_collection(X0,ct) ) ).
cnf(u16789,negated_conjecture,
( ~ element_of_set(f20(intersection_of_members(X0),X1),sF1)
| hausdorff(intersection_of_members(X0),X1) ) ).
cnf(u48641,negated_conjecture,
( element_of_set(X5,f13(f14(f16(X0,X1,X2,X3),cx,ct,X4),X2,X3,X5))
| ~ element_of_set(X5,f16(X0,X1,X2,X3))
| element_of_set(X4,sF0)
| limit_point(X0,X1,X2,X3) ) ).
cnf(u3767,axiom,
( ~ closed(boundary(X3,X4,X5),X8,X9)
| element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),X6)
| ~ closed(X6,X4,X5)
| ~ subset_sets(X3,X6)
| ~ subset_sets(X7,boundary(X3,X4,X5))
| topological_space(X0,X1)
| ~ topological_space(closure(X7,X8,X9),X10)
| hausdorff(closure(X7,X8,X9),X10) ) ).
cnf(u3232,axiom,
( ~ closed(boundary(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,boundary(X4,X5,X6))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ subset_sets(relative_complement_sets(X4,X5),X7)
| ~ closed(X7,X5,X6)
| element_of_set(f20(boundary(X0,X1,X2),X3),X7) ) ).
cnf(u4123,axiom,
( ~ element_of_set(X7,f12(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5,f10(subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5),X0,X6)))
| ~ element_of_set(X6,X0)
| ~ element_of_collection(X0,top_of_basis(subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5)))
| topological_space(X2,X3) ) ).
cnf(u2428,axiom,
( element_of_set(f20(closure(X3,X1,X2),X5),union_of_members(top_of_basis(X4)))
| element_of_set(f11(X4,closure(X3,X1,X2)),X0)
| ~ subset_sets(X3,X0)
| ~ closed(X0,X1,X2)
| ~ topological_space(closure(X3,X1,X2),X5)
| hausdorff(closure(X3,X1,X2),X5) ) ).
cnf(u114,axiom,
interior(a,cx,ct) = sF0 ).
cnf(u6287,axiom,
( ~ subset_sets(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,X3),cx)
| element_of_set(X4,closure(f13(a,cx,ct,f20(sF0,X0)),X1,X2))
| ~ subset_sets(f13(a,cx,ct,f20(sF0,X0)),X1)
| ~ topological_space(X1,X2)
| ~ topological_space(sF0,X0)
| element_of_set(X3,f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,X4))
| ~ element_of_set(X5,f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(X5,interior(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,X3),cx,ct)) ) ).
cnf(u2858,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),f18(X3,X4,X5,X6)),f18(X3,X4,X5,X6))
| topological_space(X0,X1)
| ~ element_of_set(X6,X3)
| eq_p(X5,X6)
| ~ hausdorff(X3,X4)
| ~ element_of_set(X5,X3) ) ).
cnf(u3458,axiom,
( element_of_set(f7(closure(X0,X1,X2),X3),f1(X4,f7(closure(X0,X1,X2),X3)))
| ~ subset_sets(X0,union_of_members(X4))
| ~ closed(union_of_members(X4),X1,X2)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u5708,axiom,
( ~ closed(closure(relative_complement_sets(X2,X3),X3,subspace_topology(X0,X1,X4)),X6,X7)
| ~ subset_sets(X2,X3)
| ~ subset_sets(X5,closure(relative_complement_sets(X2,X3),X3,subspace_topology(X0,X1,X4)))
| topological_space(X0,X1)
| ~ topological_space(closure(X5,X6,X7),X8)
| hausdorff(closure(X5,X6,X7),X8)
| element_of_set(f19(closure(X5,X6,X7),X8),boundary(X2,X3,subspace_topology(X0,X1,X4))) ) ).
cnf(u5250,negated_conjecture,
( ~ open(union_of_members(top_of_basis(X1)),X2,X3)
| ~ disjoint_s(X0,union_of_members(top_of_basis(X1)))
| hausdorff(X2,X3)
| ~ open(X0,X2,X3)
| ~ element_of_set(f19(X2,X3),X0)
| element_of_set(f11(X1,f14(a,cx,ct,X4)),f14(a,cx,ct,X4))
| ~ element_of_set(f20(X2,X3),sF3)
| element_of_set(X4,sF3) ) ).
cnf(u329,axiom,
( limit_point(X2,X3,X4,subspace_topology(X1,X5,X0))
| subset_sets(X0,X1)
| ~ topological_space(X4,subspace_topology(X1,X5,X0))
| ~ subset_sets(X3,X4) ) ).
cnf(u2857,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),f17(X3,X4,X5,X6)),f17(X3,X4,X5,X6))
| topological_space(X0,X1)
| ~ element_of_set(X6,X3)
| eq_p(X5,X6)
| ~ hausdorff(X3,X4)
| ~ element_of_set(X5,X3) ) ).
cnf(u3514,axiom,
( element_of_set(f7(closure(X0,X1,X2),X3),sF3)
| ~ subset_sets(X0,sF1)
| ~ closed(sF1,X1,X2)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u9899,negated_conjecture,
( element_of_set(f20(sF0,X0),f1(X1,f20(sF0,X0)))
| hausdorff(sF0,X0) ) ).
cnf(u276,axiom,
( ~ subset_sets(relative_complement_sets(a,cx),X1)
| ~ element_of_set(X0,sF1)
| ~ closed(X1,cx,ct)
| element_of_set(X0,X1) ) ).
cnf(u4267,axiom,
( ~ topological_space(f14(X0,X1,X2,f20(closure(relative_complement_sets(X0,X1),X1,X2),X3)),X5)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1)
| ~ element_of_collection(X4,X5)
| element_of_set(f20(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| ~ element_of_set(X6,X4)
| ~ subset_sets(X4,X0)
| element_of_set(X6,interior(X0,f14(X0,X1,X2,f20(closure(relative_complement_sets(X0,X1),X1,X2),X3)),X5)) ) ).
cnf(u1223,axiom,
( ~ element_of_collection(X1,top_of_basis(subspace_topology(X2,X3,X4)))
| ~ element_of_set(X0,X1)
| subset_sets(X4,X2) ) ).
cnf(u4028,axiom,
( ~ closed(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X9,X10)
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| element_of_set(f11(X7,closure(X8,X9,X10)),interior(X4,X5,X6))
| element_of_collection(closure(X8,X9,X10),top_of_basis(X7))
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X8,f13(X4,X5,X6,f19(closure(X0,X1,X2),X3))) ) ).
cnf(u4438,axiom,
( ~ element_of_set(X6,f8(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(top_of_basis(subspace_topology(X3,X4,X5))))),top_of_basis(subspace_topology(X3,X4,X5))))
| ~ element_of_collection(union_of_members(top_of_basis(subspace_topology(X3,X4,X5))),subspace_topology(X1,X2,X0))
| basis(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(top_of_basis(subspace_topology(X3,X4,X5))))),top_of_basis(subspace_topology(X3,X4,X5)))
| subset_sets(X5,X3) ) ).
cnf(open_covering_99,axiom,
( ~ equal_sets(union_of_members(X0),X1)
| ~ topological_space(X1,X2)
| ~ subset_collections(X0,X2)
| open_covering(X0,X1,X2) ) ).
cnf(u6396,axiom,
( element_of_set(f11(X5,closure(X1,X2,X3)),closure(X1,X2,X3))
| closed(f14(X1,X2,X3,X4),X2,X3)
| element_of_set(X4,f14(X1,X2,X3,X0))
| element_of_set(X0,union_of_members(top_of_basis(X5)))
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2) ) ).
cnf(u6122,negated_conjecture,
( ~ closed(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X6,X7)
| ~ closed(sF0,X1,X2)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X3))
| element_of_set(f11(X4,boundary(X5,X6,X7)),sF0)
| element_of_collection(boundary(X5,X6,X7),top_of_basis(X4))
| ~ subset_sets(X0,sF0)
| ~ subset_sets(X5,f13(a,cx,ct,f11(X3,closure(X0,X1,X2)))) ) ).
cnf(u1316,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),union_of_members(ct))
| element_of_set(X1,union_of_members(top_of_basis(X0)))
| ~ element_of_set(X1,empty_set) ) ).
cnf(u3345,axiom,
( element_of_set(f11(X3,closure(X2,X0,X1)),X4)
| element_of_collection(closure(X2,X0,X1),top_of_basis(X3))
| ~ subset_sets(X2,sF3)
| ~ subset_sets(a,X4)
| ~ closed(X4,cx,ct)
| ~ closed(sF3,X0,X1) ) ).
cnf(u4271,axiom,
( element_of_set(X4,interior(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,f20(closure(relative_complement_sets(f13(a,cx,ct,f20(sF0,X0)),X1),X1,X2),X3)),cx,ct))
| ~ topological_space(closure(relative_complement_sets(f13(a,cx,ct,f20(sF0,X0)),X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(f13(a,cx,ct,f20(sF0,X0)),X1),X1,X2),X3)
| ~ subset_sets(f13(a,cx,ct,f20(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| ~ subset_sets(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,f20(closure(relative_complement_sets(f13(a,cx,ct,f20(sF0,X0)),X1),X1,X2),X3)),cx)
| ~ element_of_set(X4,f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(f20(closure(relative_complement_sets(f13(a,cx,ct,f20(sF0,X0)),X1),X1,X2),X3),boundary(f13(a,cx,ct,f20(sF0,X0)),X1,X2)) ) ).
cnf(u5846,negated_conjecture,
( subset_sets(a,f14(a,cx,ct,X0))
| element_of_set(X0,f14(a,cx,ct,X1))
| element_of_set(X1,sF3) ) ).
cnf(u344,axiom,
( subset_collections(f24(X0,X1),X1)
| compact_space(X0,X1)
| ~ topological_space(X0,X1) ) ).
cnf(u46686,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f1(X2,f11(X0,union_of_members(top_of_basis(X1)))))
| element_of_set(f11(X1,union_of_members(ct)),f1(X3,f11(X1,union_of_members(ct))))
| element_of_set(X4,f1(top_of_basis(X0),X4))
| ~ element_of_set(X4,cx) ) ).
cnf(u4248,axiom,
( ~ element_of_set(X6,union_of_members(subspace_topology(X4,X5,intersection_of_sets(X0,X2))))
| ~ element_of_collection(X2,X3)
| ~ connected_set(intersection_of_sets(X0,X2),X4,X5)
| ~ topological_space(X1,X3)
| ~ subset_sets(X0,X1)
| element_of_set(X6,union_of_members(subspace_topology(X1,X3,X0))) ) ).
cnf(u661,axiom,
( element_of_set(f11(X3,boundary(X0,X1,X2)),X4)
| element_of_collection(boundary(X0,X1,X2),top_of_basis(X3))
| ~ closed(X4,X1,X2)
| ~ subset_sets(X0,X4) ) ).
cnf(u2668,axiom,
( ~ element_of_set(X3,f12(X1,X2,X0,X0))
| ~ connected_set(X0,X1,X2)
| element_of_set(X3,union_of_members(X2)) ) ).
cnf(u2947,axiom,
( element_of_set(f11(X0,boundary(X1,X2,X3)),f13(X4,X5,X6,f11(X0,boundary(X1,X2,X3))))
| ~ closed(interior(X4,X5,X6),X2,X3)
| ~ subset_sets(X1,interior(X4,X5,X6))
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(u1370,axiom,
( subset_sets(X0,f14(X0,X1,X2,f20(boundary(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f20(boundary(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| hausdorff(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ topological_space(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1) ) ).
cnf(u574,axiom,
( element_of_set(f19(f22(X0,X1),X2),union_of_members(X1))
| connected_space(X0,X1)
| ~ topological_space(X0,X1)
| ~ topological_space(f22(X0,X1),X2)
| hausdorff(f22(X0,X1),X2) ) ).
cnf(hausdorff_80,axiom,
( ~ neighborhood(X3,f20(X0,X1),X0,X1)
| ~ topological_space(X0,X1)
| ~ neighborhood(X2,f19(X0,X1),X0,X1)
| hausdorff(X0,X1)
| ~ disjoint_s(X2,X3) ) ).
cnf(u33837,negated_conjecture,
( element_of_set(X3,f13(a,cx,subspace_topology(X0,X1,f13(a,cx,ct,X2)),X3))
| ~ element_of_set(X2,sF0)
| ~ element_of_set(X3,f13(a,cx,ct,X2)) ) ).
cnf(u50142,negated_conjecture,
( element_of_set(f19(f12(X2,top_of_basis(X3),X4,f1(subspace_topology(X2,top_of_basis(X3),X4),X5)),X6),f10(X3,f12(X2,top_of_basis(X3),X4,f1(subspace_topology(X2,top_of_basis(X3),X4),X5)),f19(f12(X2,top_of_basis(X3),X4,f1(subspace_topology(X2,top_of_basis(X3),X4),X5)),X6)))
| limit_point(X5,X0,X1,subspace_topology(X2,top_of_basis(X3),X4))
| hausdorff(f12(X2,top_of_basis(X3),X4,f1(subspace_topology(X2,top_of_basis(X3),X4),X5)),X6) ) ).
cnf(u3652,axiom,
( ~ element_of_set(f7(X1,X2),relative_complement_sets(X0,intersection_of_sets(f8(X1,X2),f9(X1,X2))))
| ~ equal_sets(union_of_members(X2),X1)
| element_of_collection(boundary(X0,intersection_of_sets(f8(X1,X2),f9(X1,X2)),X3),top_of_basis(X4))
| ~ element_of_collection(relative_complement_sets(X0,intersection_of_sets(f8(X1,X2),f9(X1,X2))),X2)
| basis(X1,X2) ) ).
cnf(u4817,negated_conjecture,
( element_of_collection(f1(top_of_basis(X1),X0),top_of_basis(X1))
| element_of_set(f11(X1,union_of_members(ct)),union_of_members(ct))
| ~ element_of_set(X0,cx) ) ).
cnf(u41715,negated_conjecture,
( open(f13(f14(f13(a,cx,ct,f20(sF0,X0)),cx,ct,X1),cx,ct,X2),cx,ct)
| hausdorff(sF0,X0)
| element_of_set(X1,sF0)
| ~ element_of_set(X2,f13(a,cx,ct,f20(sF0,X0))) ) ).
cnf(u45077,negated_conjecture,
( ~ element_of_set(X5,relative_complement_sets(X1,X2))
| element_of_set(X5,f13(f14(relative_complement_sets(X1,X2),X3,X4,X0),X2,X6,X5))
| element_of_set(X0,union_of_members(X7)) ) ).
cnf(u4252,negated_conjecture,
( element_of_set(X5,interior(a,cx,subspace_topology(X3,X4,f13(a,X0,X1,f19(interior(a,X0,X1),X2)))))
| ~ topological_space(cx,subspace_topology(X3,X4,f13(a,X0,X1,f19(interior(a,X0,X1),X2))))
| ~ element_of_set(X5,f13(a,X0,X1,f19(interior(a,X0,X1),X2)))
| hausdorff(interior(a,X0,X1),X2)
| ~ topological_space(interior(a,X0,X1),X2)
| ~ connected_set(f13(a,X0,X1,f19(interior(a,X0,X1),X2)),X3,X4) ) ).
cnf(u3987,axiom,
( ~ element_of_collection(X0,subspace_topology(X1,X2,f14(X3,X4,X5,X6)))
| ~ element_of_set(X7,X0)
| ~ subset_sets(X0,X3)
| element_of_set(X7,interior(X3,f14(X3,X4,X5,X6),subspace_topology(X1,X2,f14(X3,X4,X5,X6))))
| element_of_set(X6,closure(X3,X4,X5))
| ~ subset_sets(X3,X4)
| ~ topological_space(X4,X5)
| ~ connected_set(f14(X3,X4,X5,X6),X1,X2) ) ).
cnf(u3899,axiom,
( subset_sets(f13(f14(X1,X2,X3,X4),X5,X6,f19(interior(f14(X1,X2,X3,X4),X5,X6),X7)),f14(f13(f14(X1,X2,X3,X4),X5,X6,f19(interior(f14(X1,X2,X3,X4),X5,X6),X7)),X2,X3,X0))
| element_of_set(X0,f14(X1,X2,X3,X4))
| ~ subset_sets(f13(f14(X1,X2,X3,X4),X5,X6,f19(interior(f14(X1,X2,X3,X4),X5,X6),X7)),X2)
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| hausdorff(interior(f14(X1,X2,X3,X4),X5,X6),X7)
| ~ topological_space(interior(f14(X1,X2,X3,X4),X5,X6),X7) ) ).
cnf(u1308,axiom,
( ~ closed(f1(X1,X3),X5,X6)
| ~ subset_sets(X2,X0)
| limit_point(X3,X2,X0,X1)
| element_of_set(f19(closure(X4,X5,X6),X7),union_of_members(X1))
| hausdorff(closure(X4,X5,X6),X7)
| ~ subset_sets(X4,f1(X1,X3))
| ~ topological_space(X0,X1)
| ~ topological_space(closure(X4,X5,X6),X7) ) ).
cnf(u36056,negated_conjecture,
( element_of_set(f15(X0,X1,X2,X3,X4),f10(X5,f1(top_of_basis(X5),f15(X0,X1,X2,X3,X4)),f15(X0,X1,X2,X3,X4)))
| limit_point(f15(X0,X1,X2,X3,X4),X6,X7,top_of_basis(X5))
| ~ limit_point(X0,X1,X2,X3)
| ~ neighborhood(X4,X0,X2,X3) ) ).
cnf(u2910,axiom,
( ~ topological_space(boundary(X3,X4,X5),X6)
| element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),closure(X3,X4,X5))
| hausdorff(boundary(X3,X4,X5),X6)
| topological_space(X0,X1) ) ).
cnf(u1329,negated_conjecture,
( element_of_set(f11(X0,f14(a,cx,ct,f11(X1,X2))),f14(a,cx,ct,f11(X1,X2)))
| element_of_set(X3,union_of_members(top_of_basis(X0)))
| element_of_collection(X2,top_of_basis(X1))
| ~ subset_sets(sF3,X2)
| ~ element_of_set(X3,sF3)
| ~ element_of_collection(sF3,X1) ) ).
cnf(u36064,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f10(X1,f1(top_of_basis(X1),f11(X0,union_of_members(top_of_basis(X1)))),f11(X0,union_of_members(top_of_basis(X1)))))
| limit_point(f11(X0,union_of_members(top_of_basis(X1))),X2,X3,top_of_basis(X1))
| element_of_set(X4,f1(top_of_basis(X0),X4))
| ~ element_of_set(X4,cx)
| element_of_set(f11(X1,union_of_members(ct)),union_of_members(ct)) ) ).
cnf(u5916,negated_conjecture,
( subset_sets(X0,f14(X0,cx,ct,X1))
| element_of_set(X1,sF0)
| ~ subset_sets(X0,sF0)
| ~ subset_sets(X0,cx) ) ).
cnf(u3823,axiom,
( ~ connected_set(X1,X2,X3)
| ~ element_of_set(X0,X1)
| topological_space(X4,X5)
| element_of_set(f11(subspace_topology(X4,X5,X6),union_of_members(subspace_topology(X2,X3,X1))),union_of_members(subspace_topology(X2,X3,X1))) ) ).
cnf(u3091,axiom,
( element_of_set(f19(boundary(X0,X1,X2),X3),closure(X4,X5,X6))
| ~ subset_sets(X0,boundary(X4,X5,X6))
| ~ closed(boundary(X4,X5,X6),X1,X2)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(boundary(X0,X1,X2),X3) ) ).
cnf(u524,axiom,
( ~ subset_sets(f13(a,cx,ct,f20(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| ~ subset_sets(X1,cx)
| ~ element_of_set(X2,f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(X2,interior(X1,cx,ct)) ) ).
cnf(u2970,axiom,
( closed(f14(relative_complement_sets(X4,X5),X5,X6,f11(X0,boundary(X1,X2,X3))),X5,X6)
| ~ closed(closure(X4,X5,X6),X2,X3)
| ~ subset_sets(X1,closure(X4,X5,X6))
| ~ subset_sets(relative_complement_sets(X4,X5),X5)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| element_of_set(f11(X0,boundary(X1,X2,X3)),boundary(X4,X5,X6)) ) ).
cnf(u656,axiom,
( ~ subset_sets(X1,X1)
| ~ element_of_collection(X1,X0)
| element_of_collection(X1,top_of_basis(X0)) ) ).
cnf(u13742,negated_conjecture,
( element_of_set(X0,f13(f14(f13(a,cx,ct,X1),X2,X3,X4),cx,ct,X0))
| ~ element_of_set(X1,sF0)
| element_of_set(X4,closure(f13(a,cx,ct,X1),X2,X3))
| ~ element_of_set(X0,f13(a,cx,ct,X1)) ) ).
cnf(u3950,negated_conjecture,
( element_of_set(f7(f1(ct,f15(X1,X4,X2,X3,X0)),X5),union_of_members(ct))
| ~ limit_point(X1,X4,X2,X3)
| ~ element_of_collection(X4,ct)
| ~ element_of_collection(X0,ct)
| ~ neighborhood(X0,X1,X2,X3)
| basis(f1(ct,f15(X1,X4,X2,X3,X0)),X5)
| ~ topological_space(f1(ct,f15(X1,X4,X2,X3,X0)),X5) ) ).
cnf(u2872,axiom,
( ~ closed(X3,X6,X7)
| element_of_set(f11(subspace_topology(X0,X1,X2),X3),X3)
| element_of_collection(closure(X5,X6,X7),top_of_basis(X4))
| topological_space(X0,X1)
| ~ subset_sets(X5,X3) ) ).
cnf(u1119,axiom,
( element_of_collection(f13(X1,X2,X3,f19(closure(X0,X4,X5),X6)),X3)
| ~ closed(interior(X1,X2,X3),X4,X5)
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| ~ subset_sets(X0,interior(X1,X2,X3)) ) ).
cnf(u6719,negated_conjecture,
( ~ element_of_set(X3,X0)
| element_of_set(X3,interior(X4,X2,X1)) ) ).
cnf(u341,axiom,
( element_of_collection(f12(X0,X1,X2,f16(X3,X4,X5,subspace_topology(X0,X1,X2))),X1)
| limit_point(X3,X4,X5,subspace_topology(X0,X1,X2))
| ~ topological_space(X5,subspace_topology(X0,X1,X2))
| ~ subset_sets(X4,X5) ) ).
cnf(u7142,negated_conjecture,
( ~ element_of_set(X1,sF3)
| element_of_set(X1,X0) ) ).
cnf(u1253,negated_conjecture,
( ~ element_of_set(X5,f1(ct,f15(X1,X4,X2,X3,X0)))
| ~ neighborhood(X0,X1,X2,X3)
| ~ limit_point(X1,X4,X2,X3)
| ~ element_of_collection(X4,ct)
| ~ element_of_collection(X0,ct)
| element_of_set(X5,union_of_members(ct)) ) ).
cnf(u3653,axiom,
( ~ element_of_collection(relative_complement_sets(X0,f13(a,cx,ct,X1)),X4)
| element_of_collection(boundary(X0,f13(a,cx,ct,X1),X2),top_of_basis(X3))
| ~ topological_space(a,X4)
| ~ element_of_set(X5,relative_complement_sets(X0,f13(a,cx,ct,X1)))
| ~ element_of_set(X1,sF0)
| element_of_set(X5,interior(f13(a,cx,ct,X1),a,X4)) ) ).
cnf(u3046,axiom,
( ~ closed(f1(X4,X5),X1,X2)
| ~ subset_sets(X0,f1(X4,X5))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(X6,X4)
| ~ subset_sets(X7,X6)
| limit_point(X5,X7,X6,X4)
| element_of_set(f19(boundary(X0,X1,X2),X3),union_of_members(X4)) ) ).
cnf(u5204,axiom,
( ~ element_of_set(X6,f12(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5,f9(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))))
| basis(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| ~ topological_space(X0,subspace_topology(X1,top_of_basis(subspace_topology(X2,X3,X4)),X5))
| subset_sets(X4,X2) ) ).
cnf(u4872,axiom,
( element_of_set(f7(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),f24(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7)),interior(X0,X1,X2))
| basis(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),f24(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7))
| compact_space(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7)
| ~ topological_space(closure(X3,X4,X5),X6)
| hausdorff(closure(X3,X4,X5),X6)
| ~ closed(interior(X0,X1,X2),X4,X5)
| ~ subset_sets(X3,interior(X0,X1,X2))
| ~ topological_space(f13(X0,X1,X2,f19(closure(X3,X4,X5),X6)),X7) ) ).
cnf(problem_11_152,negated_conjecture,
subset_sets(a,cx) ).
cnf(u5013,axiom,
( subset_collections(f5(X0,f23(X0,X1,X2)),f23(X0,X1,X2))
| ~ open_covering(X2,X0,X1)
| topological_space(X0,f23(X0,X1,X2))
| ~ element_of_collection(empty_set,f23(X0,X1,X2))
| ~ element_of_collection(X0,f23(X0,X1,X2))
| element_of_collection(f3(X0,f23(X0,X1,X2)),f23(X0,X1,X2))
| ~ compact_space(X0,X1) ) ).
cnf(u1381,axiom,
( element_of_set(f20(closure(X0,X1,X2),X3),f6(X4,X6,f20(closure(X0,X1,X2),X3),X5,X7))
| ~ element_of_collection(X5,X6)
| ~ element_of_collection(X7,X6)
| ~ basis(X4,X6)
| ~ element_of_set(f20(closure(X0,X1,X2),X3),X4)
| hausdorff(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,intersection_of_sets(X5,X7))
| ~ closed(intersection_of_sets(X5,X7),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u3900,axiom,
( subset_sets(f13(f14(X1,X2,X3,X4),X5,X6,f19(closure(X7,X8,X9),X10)),f14(f13(f14(X1,X2,X3,X4),X5,X6,f19(closure(X7,X8,X9),X10)),X2,X3,X0))
| element_of_set(X0,f14(X1,X2,X3,X4))
| ~ subset_sets(f13(f14(X1,X2,X3,X4),X5,X6,f19(closure(X7,X8,X9),X10)),X2)
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| ~ subset_sets(X7,interior(f14(X1,X2,X3,X4),X5,X6))
| ~ closed(interior(f14(X1,X2,X3,X4),X5,X6),X8,X9)
| ~ topological_space(closure(X7,X8,X9),X10)
| hausdorff(closure(X7,X8,X9),X10) ) ).
cnf(u4831,axiom,
( element_of_set(f7(union_of_members(X0),f24(union_of_members(X0),X1)),f1(X0,f7(union_of_members(X0),f24(union_of_members(X0),X1))))
| basis(union_of_members(X0),f24(union_of_members(X0),X1))
| compact_space(union_of_members(X0),X1)
| ~ topological_space(union_of_members(X0),X1) ) ).
cnf(u4843,axiom,
( element_of_collection(f6(X3,X4,f7(intersection_of_sets(X0,X1),f24(intersection_of_sets(X0,X1),X2)),X0,X1),X4)
| basis(intersection_of_sets(X0,X1),f24(intersection_of_sets(X0,X1),X2))
| compact_space(intersection_of_sets(X0,X1),X2)
| ~ element_of_set(f7(intersection_of_sets(X0,X1),f24(intersection_of_sets(X0,X1),X2)),X3)
| ~ element_of_collection(X0,X4)
| ~ element_of_collection(X1,X4)
| ~ basis(X3,X4)
| ~ topological_space(intersection_of_sets(X0,X1),X2) ) ).
cnf(u1404,axiom,
( ~ element_of_set(X0,f13(X1,X2,top_of_basis(subspace_topology(X3,X4,X5)),f20(interior(X1,X2,top_of_basis(subspace_topology(X3,X4,X5))),X6)))
| topological_space(X3,X4)
| ~ topological_space(interior(X1,X2,top_of_basis(subspace_topology(X3,X4,X5))),X6)
| hausdorff(interior(X1,X2,top_of_basis(subspace_topology(X3,X4,X5))),X6) ) ).
cnf(u954,axiom,
( ~ closed(boundary(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,boundary(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| topological_space(X5,X6) ) ).
cnf(u54436,negated_conjecture,
( element_of_set(X7,f13(f14(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5,X6),X1,X2,X7))
| element_of_set(X6,closure(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4,X5))
| hausdorff(interior(X0,X1,X2),X3)
| ~ element_of_set(X7,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3))) ) ).
cnf(u5018,axiom,
( open_covering(f23(X0,X1,X2),X0,X3)
| ~ open_covering(X2,X0,X1)
| ~ topological_space(X0,X3)
| ~ subset_collections(f23(X0,X1,X2),X3)
| ~ compact_space(X0,X1) ) ).
cnf(u3502,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| topological_space(X7,X8)
| ~ closed(sF1,X5,X6)
| element_of_set(f11(subspace_topology(X7,X8,X9),closure(X4,X5,X6)),sF3)
| ~ subset_sets(X4,sF1) ) ).
cnf(u3483,negated_conjecture,
( ~ closed(f13(a,cx,ct,f7(sF0,X4)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f7(sF0,X4)))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| element_of_set(f7(closure(X0,X1,X2),X3),sF0)
| basis(sF0,X4)
| ~ topological_space(sF0,X4) ) ).
cnf(u657,axiom,
( ~ element_of_set(f11(X0,closure(relative_complement_sets(X1,X2),X2,X3)),closure(X1,X2,X3))
| element_of_collection(closure(relative_complement_sets(X1,X2),X2,X3),top_of_basis(X0))
| element_of_set(f11(X0,closure(relative_complement_sets(X1,X2),X2,X3)),boundary(X1,X2,X3)) ) ).
cnf(u2421,axiom,
( ~ closed(boundary(X3,X1,X2),X6,X7)
| ~ subset_sets(X3,X0)
| element_of_set(f11(X4,closure(X3,X1,X2)),X0)
| element_of_set(f19(closure(X5,X6,X7),X8),union_of_members(top_of_basis(X4)))
| ~ subset_sets(X5,boundary(X3,X1,X2))
| ~ closed(X0,X1,X2)
| ~ topological_space(closure(X5,X6,X7),X8)
| hausdorff(closure(X5,X6,X7),X8) ) ).
cnf(u5108,axiom,
( element_of_set(f11(subspace_topology(X7,X8,X9),f6(X3,X1,f15(X4,X2,X5,X6,X0),X0,X2)),f6(X3,X1,f15(X4,X2,X5,X6,X0),X0,X2))
| ~ element_of_collection(X2,X1)
| ~ basis(X3,X1)
| ~ element_of_set(f15(X4,X2,X5,X6,X0),X3)
| ~ neighborhood(X0,X4,X5,X6)
| ~ limit_point(X4,X2,X5,X6)
| topological_space(X7,X8)
| ~ element_of_collection(X0,X1) ) ).
cnf(u34560,axiom,
( ~ subset_collections(f23(X1,f24(X1,X2),X0),X2)
| compact_space(X1,X2)
| ~ compact_space(X1,f24(X1,X2))
| ~ open_covering(X0,X1,f24(X1,X2)) ) ).
cnf(u5945,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,f20(sF0,X2)),X0)
| ~ element_of_set(X1,f13(a,cx,ct,f20(sF0,X2)))
| ~ topological_space(sF0,X0)
| element_of_set(X1,interior(a,sF0,X0))
| hausdorff(sF0,X2)
| ~ topological_space(sF0,X2) ) ).
cnf(connected_set_92,axiom,
( ~ connected_set(X0,X1,X2)
| topological_space(X1,X2) ) ).
cnf(u58892,negated_conjecture,
( element_of_set(X5,f13(a,cx,subspace_topology(X0,X1,f13(a,X2,X3,f20(interior(a,X2,X3),X4))),X5))
| hausdorff(interior(a,X2,X3),X4)
| ~ element_of_set(X5,f13(a,X2,X3,f20(interior(a,X2,X3),X4))) ) ).
cnf(u9508,negated_conjecture,
( ~ element_of_set(X1,sF3)
| eq_p(X1,X0)
| ~ element_of_set(X0,sF3) ) ).
cnf(u4710,axiom,
( closed(f14(f13(f14(X0,X1,X2,X3),X4,X5,f19(interior(f14(X0,X1,X2,X3),X4,X5),X6)),X1,X2,X7),X1,X2)
| ~ subset_sets(f13(f14(X0,X1,X2,X3),X4,X5,f19(interior(f14(X0,X1,X2,X3),X4,X5),X6)),X1)
| element_of_set(X7,f14(X0,X1,X2,X3))
| element_of_set(X3,closure(X0,X1,X2))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| hausdorff(interior(f14(X0,X1,X2,X3),X4,X5),X6)
| ~ topological_space(interior(f14(X0,X1,X2,X3),X4,X5),X6) ) ).
cnf(u539,negated_conjecture,
( ~ element_of_set(f11(X1,X0),empty_set)
| ~ element_of_collection(union_of_members(ct),X1)
| ~ subset_sets(union_of_members(ct),X0)
| element_of_collection(X0,top_of_basis(X1)) ) ).
cnf(u29145,negated_conjecture,
( open(f13(X2,X3,X4,f11(X0,union_of_members(top_of_basis(X1)))),X3,X4)
| element_of_set(f11(X1,union_of_members(ct)),f1(top_of_basis(X0),f11(X1,union_of_members(ct))))
| ~ element_of_set(f11(X1,union_of_members(ct)),cx) ) ).
cnf(u5264,axiom,
( ~ open(intersection_of_members(subspace_topology(X1,X2,X3)),X4,X5)
| ~ disjoint_s(X0,intersection_of_members(subspace_topology(X1,X2,X3)))
| hausdorff(X4,X5)
| ~ open(X0,X4,X5)
| ~ element_of_set(f19(X4,X5),X0)
| subset_sets(X3,X1) ) ).
cnf(u36119,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| element_of_set(f11(X1,f1(ct,X0)),sF0)
| ~ element_of_set(X0,cx) ) ).
cnf(u374,axiom,
( ~ topological_space(X0,subspace_topology(X1,X2,X3))
| basis(X0,subspace_topology(X1,X2,X3))
| subset_sets(X3,X1) ) ).
cnf(u27761,negated_conjecture,
( element_of_set(f11(X1,union_of_members(ct)),interior(X5,X6,X7))
| element_of_set(f11(X0,union_of_members(top_of_basis(X1))),union_of_members(X9))
| element_of_set(X8,f1(top_of_basis(X0),X8))
| ~ element_of_set(X8,cx) ) ).
cnf(u646,axiom,
( closed(f14(relative_complement_sets(X1,X2),X2,X3,f11(X0,closure(X1,X2,X3))),X2,X3)
| ~ subset_sets(relative_complement_sets(X1,X2),X2)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| element_of_set(f11(X0,closure(X1,X2,X3)),boundary(X1,X2,X3)) ) ).
cnf(u4688,axiom,
( ~ subset_sets(a,f14(X0,cx,ct,f20(closure(relative_complement_sets(X0,cx),cx,ct),X1)))
| element_of_set(f20(closure(relative_complement_sets(X0,cx),cx,ct),X1),boundary(X0,cx,ct))
| hausdorff(closure(relative_complement_sets(X0,cx),cx,ct),X1)
| ~ subset_sets(X0,cx)
| ~ subset_sets(f14(X0,cx,ct,f20(closure(relative_complement_sets(X0,cx),cx,ct),X1)),sF3)
| ~ topological_space(closure(relative_complement_sets(X0,cx),cx,ct),X1)
| ~ element_of_collection(f14(X0,cx,ct,f20(closure(relative_complement_sets(X0,cx),cx,ct),X1)),X2)
| element_of_collection(sF3,top_of_basis(X2)) ) ).
cnf(u4398,axiom,
( element_of_set(f11(X3,f10(X1,X0,X2)),union_of_members(X1))
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1))
| element_of_collection(f10(X1,X0,X2),top_of_basis(X3)) ) ).
cnf(hausdorff_77,axiom,
( element_of_set(f19(X0,X1),X0)
| ~ topological_space(X0,X1)
| hausdorff(X0,X1) ) ).
cnf(u3698,negated_conjecture,
( ~ element_of_set(f11(X7,f14(f14(a,cx,ct,X0),X1,X2,f11(X6,f14(closure(f14(a,cx,ct,X0),X1,X2),X3,X4,X5)))),sF3)
| ~ element_of_collection(closure(f14(a,cx,ct,X0),X1,X2),X6)
| ~ subset_sets(f14(a,cx,ct,X0),X1)
| ~ topological_space(X1,X2)
| element_of_set(X5,closure(closure(f14(a,cx,ct,X0),X1,X2),X3,X4))
| ~ subset_sets(closure(f14(a,cx,ct,X0),X1,X2),X3)
| ~ topological_space(X3,X4)
| ~ element_of_collection(f14(a,cx,ct,X0),X7)
| element_of_collection(f14(f14(a,cx,ct,X0),X1,X2,f11(X6,f14(closure(f14(a,cx,ct,X0),X1,X2),X3,X4,X5))),top_of_basis(X7))
| element_of_collection(f14(closure(f14(a,cx,ct,X0),X1,X2),X3,X4,X5),top_of_basis(X6))
| element_of_set(X0,sF3) ) ).
cnf(u3150,axiom,
( element_of_set(f11(X4,f13(X0,X1,X2,f7(interior(X0,X1,X2),X3))),f13(X0,X1,X2,f7(interior(X0,X1,X2),X3)))
| basis(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3)
| element_of_set(f7(interior(X0,X1,X2),X3),union_of_members(top_of_basis(X4))) ) ).
cnf(u520,axiom,
( ~ subset_sets(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ subset_sets(X4,X1)
| ~ element_of_set(X5,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X5,interior(X4,X1,X2)) ) ).
cnf(u2982,axiom,
( ~ closed(f22(X4,X5),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f22(X4,X5))
| ~ topological_space(X4,X5)
| connected_space(X4,X5)
| element_of_set(f11(X0,boundary(X1,X2,X3)),union_of_members(X5)) ) ).
cnf(u668,axiom,
( element_of_collection(sF1,top_of_basis(X0))
| element_of_set(f11(X0,sF1),sF3) ) ).
cnf(u6382,axiom,
( element_of_set(f11(subspace_topology(X5,X6,X7),f14(X1,X2,X3,X4)),f14(X1,X2,X3,X4))
| closed(f14(X1,X2,X3,X0),X2,X3)
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| topological_space(X5,X6)
| element_of_set(X4,closure(X1,X2,X3)) ) ).
cnf(u34564,axiom,
( ~ open_covering(X1,X2,f24(X0,X1))
| ~ compact_space(X2,f24(X0,X1))
| compact_space(X0,X1) ) ).
cnf(u871,axiom,
( ~ closed(f13(closure(X0,X1,X2),X3,X4,f20(interior(closure(X0,X1,X2),X3,X4),X5)),X1,X2)
| ~ subset_sets(X0,f13(closure(X0,X1,X2),X3,X4,f20(interior(closure(X0,X1,X2),X3,X4),X5)))
| ~ element_of_collection(f13(closure(X0,X1,X2),X3,X4,f20(interior(closure(X0,X1,X2),X3,X4),X5)),X6)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X6))
| hausdorff(interior(closure(X0,X1,X2),X3,X4),X5)
| ~ topological_space(interior(closure(X0,X1,X2),X3,X4),X5) ) ).
cnf(u2813,axiom,
( ~ basis(X0,X1)
| ~ element_of_collection(empty_set,X1)
| ~ element_of_collection(X0,X1)
| element_of_collection(f3(X0,X1),X1)
| subset_collections(f5(X0,X1),X1)
| topological_space(X0,X1) ) ).
cnf(u6116,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),f24(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X4)),sF0)
| ~ closed(sF0,X1,X2)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X3))
| ~ subset_sets(X0,sF0)
| ~ topological_space(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X4)
| basis(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),f24(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X4))
| compact_space(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X4) ) ).
cnf(u36093,negated_conjecture,
( element_of_set(f11(X1,union_of_members(top_of_basis(X4))),f13(X5,X6,X7,f11(X1,union_of_members(top_of_basis(X4)))))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx)
| element_of_set(f11(X4,union_of_members(ct)),sF0) ) ).
cnf(u2941,axiom,
( element_of_collection(f6(X6,X7,f11(X0,boundary(X1,X2,X3)),X4,X5),X7)
| ~ closed(intersection_of_sets(X4,X5),X2,X3)
| ~ subset_sets(X1,intersection_of_sets(X4,X5))
| ~ element_of_set(f11(X0,boundary(X1,X2,X3)),X6)
| ~ element_of_collection(X4,X7)
| ~ element_of_collection(X5,X7)
| ~ basis(X6,X7)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(u1965,axiom,
( ~ topological_space(closure(X5,X2,X3),X6)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X0,X1,X4),closure(X5,X2,X3)),sF3)
| ~ subset_sets(X5,sF1)
| basis(closure(X5,X2,X3),X6)
| topological_space(X0,X1) ) ).
cnf(u3959,negated_conjecture,
( ~ closed(f1(ct,f15(X1,X4,X2,X3,X0)),X6,X7)
| ~ limit_point(X1,X4,X2,X3)
| ~ element_of_collection(X4,ct)
| ~ element_of_collection(X0,ct)
| element_of_set(f19(closure(X5,X6,X7),X8),union_of_members(ct))
| hausdorff(closure(X5,X6,X7),X8)
| ~ subset_sets(X5,f1(ct,f15(X1,X4,X2,X3,X0)))
| ~ neighborhood(X0,X1,X2,X3)
| ~ topological_space(closure(X5,X6,X7),X8) ) ).
cnf(u5275,axiom,
( ~ open(closure(X1,X2,subspace_topology(X3,X4,X5)),X6,X7)
| ~ disjoint_s(X0,closure(X1,X2,subspace_topology(X3,X4,X5)))
| hausdorff(X6,X7)
| ~ open(X0,X6,X7)
| ~ element_of_set(f19(X6,X7),X0)
| subset_sets(X5,X3)
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,subspace_topology(X3,X4,X5)) ) ).
cnf(u7934,axiom,
( element_of_set(X0,f1(top_of_basis(X1),X0))
| element_of_set(f11(X1,sF1),sF3)
| ~ element_of_set(X0,sF1) ) ).
cnf(u1096,axiom,
( ~ element_of_set(f19(closure(X0,X1,X2),X3),closure(X4,X5,X6))
| ~ subset_sets(X0,closure(relative_complement_sets(X4,X5),X5,X6))
| ~ closed(closure(relative_complement_sets(X4,X5),X5,X6),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3)
| element_of_set(f19(closure(X0,X1,X2),X3),boundary(X4,X5,X6)) ) ).
cnf(u838,axiom,
( ~ closed(intersection_of_sets(f16(X4,X5,X6,X7),X5),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,intersection_of_sets(f16(X4,X5,X6,X7),X5))
| ~ topological_space(X6,X7)
| ~ subset_sets(X5,X6)
| limit_point(X4,X5,X6,X7)
| eq_p(f11(X0,closure(X1,X2,X3)),X4) ) ).
cnf(u4852,axiom,
( subset_sets(f13(X0,X1,X2,f7(interior(X0,X1,X2),f24(interior(X0,X1,X2),X3))),X0)
| basis(interior(X0,X1,X2),f24(interior(X0,X1,X2),X3))
| compact_space(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3) ) ).
cnf(u1238,axiom,
( limit_point(X0,X2,X3,X1)
| element_of_collection(f1(X1,X0),X1)
| ~ topological_space(X3,X1)
| ~ subset_sets(X2,X3) ) ).
cnf(u36084,negated_conjecture,
( open(f13(X4,X5,X6,f11(X1,union_of_members(top_of_basis(X7)))),X5,X6)
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| element_of_set(f11(X7,union_of_members(ct)),union_of_members(X8))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u5120,negated_conjecture,
( element_of_set(f11(X1,f14(a,cx,ct,X2)),f14(a,cx,ct,X2))
| element_of_collection(f1(top_of_basis(X1),X0),top_of_basis(X1))
| element_of_set(X2,sF3)
| ~ element_of_set(X0,sF3) ) ).
cnf(u5548,axiom,
( ~ subset_sets(f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))),X4)
| ~ subset_sets(X4,X1)
| ~ element_of_set(X5,f13(X0,X1,X2,f11(X3,interior(X0,X1,X2))))
| element_of_collection(interior(X0,X1,X2),top_of_basis(X3))
| element_of_set(X5,interior(X4,X1,X2)) ) ).
cnf(u36085,negated_conjecture,
( open(f13(X4,X5,X6,f11(X1,union_of_members(top_of_basis(X7)))),X5,X6)
| open(f13(X8,X9,X10,f11(X7,union_of_members(ct))),X9,X10)
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u1378,axiom,
( element_of_set(f19(intersection_of_sets(X0,X1),X2),f6(X3,X4,f19(intersection_of_sets(X0,X1),X2),X0,X1))
| ~ element_of_collection(X0,X4)
| ~ element_of_collection(X1,X4)
| ~ basis(X3,X4)
| ~ element_of_set(f19(intersection_of_sets(X0,X1),X2),X3)
| ~ topological_space(intersection_of_sets(X0,X1),X2)
| hausdorff(intersection_of_sets(X0,X1),X2) ) ).
cnf(u6119,negated_conjecture,
( element_of_collection(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),top_of_basis(X4))
| ~ closed(sF0,X1,X2)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X3))
| element_of_set(f11(X4,f13(a,cx,ct,f11(X3,closure(X0,X1,X2)))),sF0)
| ~ subset_sets(X0,sF0) ) ).
cnf(separation_88,axiom,
( ~ equal_sets(union_of_sets(X0,X1),X2)
| ~ topological_space(X2,X3)
| equal_sets(X0,empty_set)
| equal_sets(X1,empty_set)
| ~ element_of_collection(X0,X3)
| ~ element_of_collection(X1,X3)
| separation(X0,X1,X2,X3)
| ~ disjoint_s(X0,X1) ) ).
cnf(u4693,axiom,
( element_of_collection(f12(X2,X3,X4,relative_complement_sets(f14(X0,X1,subspace_topology(X2,X3,X4),f20(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5)),X1)),X3)
| element_of_set(f20(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5),boundary(X0,X1,subspace_topology(X2,X3,X4)))
| hausdorff(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5)
| ~ subset_sets(X0,X1)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4)),X5) ) ).
cnf(u9779,negated_conjecture,
( eq_p(X0,f19(boundary(relative_complement_sets(X1,X2),X2,X3),X4))
| ~ element_of_set(X0,boundary(X1,X2,X3))
| hausdorff(boundary(relative_complement_sets(X1,X2),X2,X3),X4) ) ).
cnf(u551,axiom,
( element_of_set(f20(f21(X0,X1),X2),union_of_members(X1))
| connected_space(X0,X1)
| ~ topological_space(X0,X1)
| ~ topological_space(f21(X0,X1),X2)
| hausdorff(f21(X0,X1),X2) ) ).
cnf(u1209,negated_conjecture,
( ~ subset_sets(X2,f14(a,cx,ct,f11(X0,X1)))
| element_of_collection(X1,top_of_basis(X0))
| ~ subset_sets(sF3,X1)
| ~ element_of_collection(sF3,X0)
| element_of_set(X3,f14(a,cx,ct,f11(X0,X1)))
| subset_sets(X2,f14(X2,cx,ct,X3))
| ~ subset_sets(X2,cx) ) ).
cnf(u439,axiom,
( element_of_collection(f1(X0,f7(union_of_members(X0),X1)),X0)
| ~ topological_space(union_of_members(X0),X1)
| basis(union_of_members(X0),X1) ) ).
cnf(u6080,negated_conjecture,
( ~ element_of_collection(union_of_members(f24(X0,ct)),X2)
| compact_space(X0,ct)
| element_of_set(f11(X1,intersection_of_members(X2)),union_of_members(ct))
| element_of_collection(intersection_of_members(X2),top_of_basis(X1))
| ~ topological_space(X0,ct) ) ).
cnf(u3488,negated_conjecture,
( ~ closed(f13(a,cx,ct,f19(closure(X4,X5,X6),X7)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f19(closure(X4,X5,X6),X7)))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ closed(sF0,X5,X6)
| ~ subset_sets(X4,sF0)
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7)
| element_of_set(f7(closure(X0,X1,X2),X3),sF0) ) ).
cnf(u810,axiom,
( hausdorff(interior(X0,X1,X2),subspace_topology(X3,X4,interior(X0,X1,X2)))
| ~ connected_set(interior(X0,X1,X2),X3,X4)
| subset_sets(X0,X1) ) ).
cnf(u916,axiom,
( ~ topological_space(interior(X0,X1,subspace_topology(X2,X3,X4)),X5)
| hausdorff(interior(X0,X1,subspace_topology(X2,X3,X4)),X5)
| subset_sets(X4,X2) ) ).
cnf(u3176,axiom,
( closed(f14(X0,X1,X2,f11(X6,f14(closure(X0,X1,X2),X3,X4,X5))),X1,X2)
| closed(f14(relative_complement_sets(closure(X0,X1,X2),X3),X3,X4,X5),X3,X4)
| ~ subset_sets(relative_complement_sets(closure(X0,X1,X2),X3),X3)
| ~ subset_sets(closure(X0,X1,X2),X3)
| ~ topological_space(X3,X4)
| ~ element_of_collection(closure(X0,X1,X2),X6)
| element_of_collection(f14(closure(X0,X1,X2),X3,X4,X5),top_of_basis(X6))
| element_of_set(X5,boundary(closure(X0,X1,X2),X3,X4))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u642,negated_conjecture,
( element_of_collection(f13(a,cx,ct,f20(sF0,X1)),top_of_basis(X0))
| element_of_set(f11(X0,f13(a,cx,ct,f20(sF0,X1))),sF0)
| ~ topological_space(sF0,X1)
| hausdorff(sF0,X1) ) ).
cnf(u9601,negated_conjecture,
( ~ element_of_set(X4,closure(X0,X1,X2))
| eq_p(f20(boundary(X0,X1,X2),X3),X4)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u2825,axiom,
( element_of_set(f20(f8(X0,X1),X2),union_of_members(X1))
| basis(X0,X1)
| ~ topological_space(X0,X1)
| ~ topological_space(f8(X0,X1),X2)
| hausdorff(f8(X0,X1),X2) ) ).
cnf(hausdorff_73,axiom,
( ~ hausdorff(X0,X1)
| topological_space(X0,X1) ) ).
cnf(u6124,negated_conjecture,
( ~ closed(f13(a,cx,ct,f11(X3,closure(X0,X1,X2))),X5,X6)
| ~ closed(sF0,X1,X2)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X3))
| element_of_set(f19(closure(X4,X5,X6),X7),sF0)
| hausdorff(closure(X4,X5,X6),X7)
| ~ subset_sets(X4,f13(a,cx,ct,f11(X3,closure(X0,X1,X2))))
| ~ subset_sets(X0,sF0)
| ~ topological_space(closure(X4,X5,X6),X7) ) ).
cnf(u4883,axiom,
( basis(closure(X0,X1,X2),f24(closure(X0,X1,X2),X3))
| element_of_set(f11(subspace_topology(X4,X5,X6),closure(X0,X1,X2)),X7)
| compact_space(closure(X0,X1,X2),X3)
| topological_space(X4,X5)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ closed(X7,X1,X2)
| ~ subset_sets(X0,X7) ) ).
cnf(u3330,axiom,
( element_of_set(f11(subspace_topology(X5,X6,X7),union_of_members(top_of_basis(X1))),union_of_members(top_of_basis(X1)))
| element_of_set(f11(X1,closure(X2,X3,X4)),sF3)
| subset_sets(X2,f14(X2,X3,X4,X0))
| ~ subset_sets(X2,sF1)
| ~ subset_sets(X2,X3)
| topological_space(X5,X6)
| ~ closed(sF1,X3,X4) ) ).
cnf(u6939,negated_conjecture,
( element_of_set(X0,interior(X1,X2,X3))
| limit_point(X0,X4,X5,X6) ) ).
cnf(u4245,axiom,
( element_of_collection(f12(X1,X3,X0,union_of_members(subspace_topology(X4,X5,intersection_of_sets(X0,X2)))),X3)
| ~ element_of_collection(X2,X3)
| ~ connected_set(intersection_of_sets(X0,X2),X4,X5)
| ~ topological_space(X1,X3)
| ~ subset_sets(X0,X1) ) ).
cnf(u4633,axiom,
( element_of_set(f11(X0,intersection_of_members(X1)),f13(X2,X3,X4,f11(X0,intersection_of_members(X1))))
| ~ element_of_collection(interior(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0)) ) ).
cnf(u867,axiom,
( element_of_set(f11(X0,closure(relative_complement_sets(X1,X2),X2,X3)),boundary(X1,X2,X3))
| ~ closed(closure(X1,X2,X3),X2,X3)
| ~ subset_sets(relative_complement_sets(X1,X2),closure(X1,X2,X3))
| element_of_collection(closure(relative_complement_sets(X1,X2),X2,X3),top_of_basis(X0)) ) ).
cnf(u3386,axiom,
( element_of_collection(f12(X3,X4,X5,f12(X2,subspace_topology(X3,X4,X5),X6,f16(X7,X0,X1,subspace_topology(X8,subspace_topology(X3,X4,X5),X6)))),X4)
| ~ topological_space(X2,subspace_topology(X3,X4,X5))
| ~ subset_sets(X6,X2)
| limit_point(X7,X0,X1,subspace_topology(X8,subspace_topology(X3,X4,X5),X6))
| ~ topological_space(X1,subspace_topology(X8,subspace_topology(X3,X4,X5),X6))
| ~ subset_sets(X0,X1) ) ).
cnf(u3161,axiom,
( ~ subset_sets(X4,f14(relative_complement_sets(X0,X1),X1,X2,X3))
| element_of_set(X3,boundary(X0,X1,X2))
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| ~ subset_sets(X4,X1)
| subset_sets(X0,f14(X0,X1,X2,X3))
| closed(f14(X4,X1,X2,X5),X1,X2)
| element_of_set(X5,f14(relative_complement_sets(X0,X1),X1,X2,X3)) ) ).
cnf(u27928,negated_conjecture,
( open(f13(X4,X5,X6,f11(X7,union_of_members(top_of_basis(X0)))),X5,X6)
| open(f13(X1,X2,X3,f11(X0,union_of_members(ct))),X2,X3)
| element_of_set(X8,f1(top_of_basis(X7),X8))
| ~ element_of_set(X8,cx) ) ).
cnf(u1344,axiom,
( element_of_set(f19(X1,X2),union_of_members(top_of_basis(X0)))
| element_of_set(f11(X0,X1),X1)
| ~ topological_space(X1,X2)
| hausdorff(X1,X2) ) ).
cnf(u190,axiom,
( open(f16(X3,X2,X0,X1),X0,X1)
| ~ subset_sets(X2,X0)
| limit_point(X3,X2,X0,X1)
| ~ topological_space(X0,X1) ) ).
cnf(u3089,axiom,
( ~ closed(boundary(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,boundary(X4,X5,X6))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| subset_sets(relative_complement_sets(X4,X5),X5) ) ).
cnf(u9378,negated_conjecture,
( element_of_set(f19(boundary(X0,X1,X2),X3),sF3)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u194,axiom,
( closed(f14(relative_complement_sets(X0,X1),X1,X2,X3),X1,X2)
| subset_sets(X0,f14(X0,X1,X2,X3))
| element_of_set(X3,boundary(X0,X1,X2))
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2) ) ).
cnf(u4124,axiom,
( element_of_set(X5,f10(X2,f12(X1,top_of_basis(X2),X3,f10(subspace_topology(X1,top_of_basis(X2),X3),X0,X4)),X5))
| ~ element_of_set(X4,X0)
| ~ element_of_set(X5,f12(X1,top_of_basis(X2),X3,f10(subspace_topology(X1,top_of_basis(X2),X3),X0,X4)))
| ~ element_of_collection(X0,top_of_basis(subspace_topology(X1,top_of_basis(X2),X3))) ) ).
cnf(u1260,axiom,
( element_of_collection(f6(X4,X6,f19(closure(X0,X1,X2),X3),X5,X7),X6)
| ~ element_of_collection(X5,X6)
| ~ element_of_collection(X7,X6)
| ~ basis(X4,X6)
| ~ element_of_set(f19(closure(X0,X1,X2),X3),X4)
| hausdorff(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,intersection_of_sets(X5,X7))
| ~ closed(intersection_of_sets(X5,X7),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u6715,negated_conjecture,
( ~ element_of_set(X5,f16(X0,X1,X2,X3))
| limit_point(X0,X1,X2,X3)
| element_of_set(X5,interior(X4,X2,X3)) ) ).
cnf(u57867,negated_conjecture,
( ~ element_of_set(X2,f13(a,cx,ct,f19(sF0,X1)))
| ~ element_of_set(X0,f13(a,cx,ct,f19(sF0,X1)))
| eq_p(X3,X4)
| element_of_set(X2,f13(f14(f13(a,cx,ct,f19(sF0,X1)),X5,X6,X3),cx,ct,X2))
| element_of_set(X0,f13(f14(f13(a,cx,ct,f19(sF0,X1)),X5,X6,X4),cx,ct,X0))
| hausdorff(sF0,X1) ) ).
cnf(u3065,negated_conjecture,
( ~ closed(f13(a,cx,ct,X4),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,X4))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f19(boundary(X0,X1,X2),X3),sF0)
| ~ element_of_set(X4,sF0) ) ).
cnf(u1102,negated_conjecture,
( ~ element_of_collection(f13(a,X1,X2,f19(closure(X0,X3,X4),X5)),X6)
| ~ closed(interior(a,X1,X2),X3,X4)
| ~ topological_space(closure(X0,X3,X4),X5)
| hausdorff(closure(X0,X3,X4),X5)
| ~ topological_space(cx,X6)
| ~ element_of_set(X7,f13(a,X1,X2,f19(closure(X0,X3,X4),X5)))
| ~ subset_sets(X0,interior(a,X1,X2))
| element_of_set(X7,interior(a,cx,X6)) ) ).
cnf(u484,axiom,
( open_covering(f24(X0,X1),X0,X2)
| ~ topological_space(X0,X1)
| ~ topological_space(X0,X2)
| ~ subset_collections(f24(X0,X1),X2)
| compact_space(X0,X1) ) ).
cnf(u4031,axiom,
( element_of_set(f19(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X7),interior(X4,X5,X6))
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X7)
| hausdorff(f13(X4,X5,X6,f19(closure(X0,X1,X2),X3)),X7) ) ).
cnf(u4120,axiom,
( ~ element_of_set(X5,f12(X1,X2,X3,f10(subspace_topology(X1,X2,X3),X0,X4)))
| ~ element_of_set(X4,X0)
| ~ element_of_collection(X0,top_of_basis(subspace_topology(X1,X2,X3)))
| element_of_set(X5,union_of_members(X2)) ) ).
cnf(u5910,axiom,
( ~ subset_sets(X0,sF3)
| ~ topological_space(sF1,X1)
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,X1)
| element_of_set(X2,interior(sF3,sF1,X1)) ) ).
cnf(u5030,axiom,
( element_of_set(f11(X2,f1(X0,f11(X1,union_of_members(X0)))),f1(X0,f11(X1,union_of_members(X0))))
| element_of_collection(union_of_members(X0),top_of_basis(X1))
| element_of_set(f11(X1,union_of_members(X0)),union_of_members(top_of_basis(X2))) ) ).
cnf(u4920,axiom,
( element_of_set(f11(subspace_topology(X5,X6,X7),union_of_members(top_of_basis(X1))),union_of_members(top_of_basis(X1)))
| closed(f14(X2,X3,X4,X0),X3,X4)
| element_of_set(f11(X1,closure(X2,X3,X4)),sF3)
| ~ subset_sets(X2,sF1)
| ~ subset_sets(X2,X3)
| topological_space(X5,X6)
| ~ closed(sF1,X3,X4) ) ).
cnf(u3210,negated_conjecture,
( ~ closed(f13(a,cx,ct,f7(sF0,X4)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f7(sF0,X4)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f20(boundary(X0,X1,X2),X3),sF0)
| basis(sF0,X4)
| ~ topological_space(sF0,X4) ) ).
cnf(u29047,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f13(X2,X3,X4,f11(X0,union_of_members(top_of_basis(X1)))))
| element_of_set(f11(X1,union_of_members(ct)),f1(X5,f11(X1,union_of_members(ct))))
| element_of_set(X6,f1(top_of_basis(X0),X6))
| ~ element_of_set(X6,cx) ) ).
cnf(u6025,negated_conjecture,
( element_of_set(X5,interior(f14(f13(X1,X2,X3,f19(interior(X1,X2,X3),X4)),cx,ct,X0),X2,X3))
| ~ subset_sets(f13(X1,X2,X3,f19(interior(X1,X2,X3),X4)),sF0)
| ~ subset_sets(f13(X1,X2,X3,f19(interior(X1,X2,X3),X4)),cx)
| ~ topological_space(interior(X1,X2,X3),X4)
| ~ subset_sets(f14(f13(X1,X2,X3,f19(interior(X1,X2,X3),X4)),cx,ct,X0),X2)
| ~ element_of_set(X5,f13(X1,X2,X3,f19(interior(X1,X2,X3),X4)))
| hausdorff(interior(X1,X2,X3),X4)
| element_of_set(X0,sF0) ) ).
cnf(u6385,axiom,
( ~ open(f14(X2,X3,X4,X5),X0,X1)
| element_of_set(X5,closure(X2,X3,X4))
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4)
| ~ disjoint_s(X6,f14(X2,X3,X4,X5))
| closed(f14(X2,X3,X4,f20(X0,X1)),X3,X4)
| hausdorff(X0,X1)
| ~ open(X6,X0,X1)
| ~ element_of_set(f19(X0,X1),X6) ) ).
cnf(u4689,axiom,
( ~ subset_sets(a,f14(X0,cx,ct,f20(closure(relative_complement_sets(X0,cx),cx,ct),X1)))
| element_of_set(f20(closure(relative_complement_sets(X0,cx),cx,ct),X1),boundary(X0,cx,ct))
| hausdorff(closure(relative_complement_sets(X0,cx),cx,ct),X1)
| ~ subset_sets(X0,cx)
| ~ topological_space(closure(relative_complement_sets(X0,cx),cx,ct),X1)
| ~ element_of_set(X2,sF3)
| element_of_set(X2,f14(X0,cx,ct,f20(closure(relative_complement_sets(X0,cx),cx,ct),X1))) ) ).
cnf(u1073,negated_conjecture,
( ~ closed(f13(a,cx,ct,X4),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,X4))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| element_of_set(f19(closure(X0,X1,X2),X3),sF0)
| ~ element_of_set(X4,sF0) ) ).
cnf(u4674,axiom,
( element_of_set(f11(X0,intersection_of_members(X1)),closure(X2,X3,X4))
| ~ element_of_collection(boundary(X2,X3,X4),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0)) ) ).
cnf(u9854,negated_conjecture,
( eq_p(f19(boundary(X0,X1,X2),X3),f20(boundary(X4,X5,X6),X7))
| hausdorff(boundary(X4,X5,X6),X7)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u4822,negated_conjecture,
( element_of_set(f11(X2,union_of_members(top_of_basis(X1))),union_of_members(top_of_basis(X1)))
| element_of_set(X0,union_of_members(top_of_basis(X2)))
| ~ element_of_set(X0,cx)
| element_of_set(f11(X1,union_of_members(ct)),union_of_members(ct)) ) ).
cnf(u3753,axiom,
( ~ closed(closure(X3,X4,X5),X8,X9)
| element_of_set(f11(subspace_topology(X0,X1,X2),closure(X3,X4,X5)),X6)
| ~ closed(X6,X4,X5)
| ~ subset_sets(X3,X6)
| ~ topological_space(closure(X7,X8,X9),X10)
| ~ subset_sets(X7,closure(X3,X4,X5))
| topological_space(X0,X1)
| basis(closure(X7,X8,X9),X10) ) ).
cnf(u1219,axiom,
( ~ disjoint_s(f16(f19(X0,X1),X2,X0,X1),X3)
| hausdorff(X0,X1)
| ~ open(X3,X0,X1)
| ~ element_of_set(f20(X0,X1),X3)
| ~ subset_sets(X2,X0)
| limit_point(f19(X0,X1),X2,X0,X1) ) ).
cnf(u382,axiom,
( ~ open(f16(X3,X2,X0,X1),X4,X5)
| ~ subset_sets(X2,X0)
| limit_point(X3,X2,X0,X1)
| ~ limit_point(X3,X2,X4,X5)
| ~ topological_space(X0,X1) ) ).
cnf(u912,axiom,
( element_of_set(f20(relative_complement_sets(X0,X1),X3),union_of_members(X2))
| ~ closed(X0,X1,X2)
| ~ topological_space(relative_complement_sets(X0,X1),X3)
| hausdorff(relative_complement_sets(X0,X1),X3) ) ).
cnf(u654,axiom,
( element_of_set(f11(X0,f21(X1,X2)),union_of_members(X2))
| ~ topological_space(X1,X2)
| connected_space(X1,X2)
| element_of_collection(f21(X1,X2),top_of_basis(X0)) ) ).
cnf(u42847,negated_conjecture,
( open(f13(a,cx,subspace_topology(X0,X1,f13(a,cx,ct,f19(sF0,X2))),X3),cx,subspace_topology(X0,X1,f13(a,cx,ct,f19(sF0,X2))))
| hausdorff(sF0,X2)
| ~ element_of_set(X3,f13(a,cx,ct,f19(sF0,X2))) ) ).
cnf(u2545,axiom,
( ~ element_of_set(X0,f22(X1,top_of_basis(subspace_topology(X2,X3,X4))))
| subset_sets(X4,X2)
| connected_space(X1,top_of_basis(subspace_topology(X2,X3,X4)))
| ~ topological_space(X1,top_of_basis(subspace_topology(X2,X3,X4))) ) ).
cnf(separation_85,axiom,
( ~ separation(X0,X1,X2,X3)
| element_of_collection(X1,X3) ) ).
cnf(u1347,axiom,
( element_of_set(f11(X0,f13(a,cx,ct,f19(sF0,X1))),f13(a,cx,ct,f19(sF0,X1)))
| element_of_set(f19(sF0,X1),union_of_members(top_of_basis(X0)))
| hausdorff(sF0,X1)
| ~ topological_space(sF0,X1) ) ).
cnf(u4810,negated_conjecture,
( element_of_collection(f1(ct,f11(X0,union_of_members(ct))),ct)
| element_of_set(X1,union_of_members(top_of_basis(X0)))
| ~ element_of_set(X1,cx) ) ).
cnf(u3045,negated_conjecture,
( ~ closed(f1(ct,X4),X1,X2)
| ~ subset_sets(X0,f1(ct,X4))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ element_of_set(X4,cx)
| element_of_set(f19(boundary(X0,X1,X2),X3),union_of_members(ct)) ) ).
cnf(u1294,axiom,
( ~ closed(boundary(X1,X2,X3),X5,X6)
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| element_of_set(f20(closure(X4,X5,X6),X7),union_of_members(top_of_basis(X0)))
| ~ subset_sets(X4,boundary(X1,X2,X3))
| element_of_set(f11(X0,closure(X1,X2,X3)),sF3)
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7) ) ).
cnf(u9383,negated_conjecture,
( element_of_set(f20(boundary(X0,X4,X5),X6),X7)
| hausdorff(boundary(X0,X4,X5),X6) ) ).
cnf(u2673,axiom,
( element_of_collection(f12(X2,X3,X4,f12(X1,subspace_topology(X2,X3,X4),X0,X0)),X3)
| ~ connected_set(X0,X1,subspace_topology(X2,X3,X4)) ) ).
cnf(u3476,axiom,
( subset_sets(f13(X4,X5,X6,f7(closure(X0,X1,X2),X3)),X4)
| ~ subset_sets(X0,interior(X4,X5,X6))
| ~ closed(interior(X4,X5,X6),X1,X2)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u2495,axiom,
( element_of_set(X0,f10(X2,f12(X1,top_of_basis(X2),X3,f16(X4,X5,X6,subspace_topology(X1,top_of_basis(X2),X3))),X0))
| ~ element_of_set(X0,f12(X1,top_of_basis(X2),X3,f16(X4,X5,X6,subspace_topology(X1,top_of_basis(X2),X3))))
| limit_point(X4,X5,X6,subspace_topology(X1,top_of_basis(X2),X3))
| ~ topological_space(X6,subspace_topology(X1,top_of_basis(X2),X3))
| ~ subset_sets(X5,X6) ) ).
cnf(u6754,axiom,
( ~ element_of_set(X0,X1)
| element_of_set(X0,union_of_members(X2)) ) ).
cnf(u5705,axiom,
( ~ closed(closure(relative_complement_sets(X2,X3),X3,subspace_topology(X0,X1,X4)),X6,X7)
| ~ subset_sets(X2,X3)
| ~ subset_sets(X5,closure(relative_complement_sets(X2,X3),X3,subspace_topology(X0,X1,X4)))
| topological_space(X0,X1)
| ~ topological_space(closure(X5,X6,X7),X8)
| hausdorff(closure(X5,X6,X7),X8)
| element_of_set(f20(closure(X5,X6,X7),X8),boundary(X2,X3,subspace_topology(X0,X1,X4))) ) ).
cnf(u3236,axiom,
( ~ closed(f21(X4,X5),X1,X2)
| ~ subset_sets(X0,f21(X4,X5))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(X4,X5)
| connected_space(X4,X5)
| element_of_set(f20(boundary(X0,X1,X2),X3),union_of_members(X5)) ) ).
cnf(u4836,axiom,
( ~ topological_space(f1(X0,X1),X2)
| basis(f1(X0,X1),f24(f1(X0,X1),X2))
| compact_space(f1(X0,X1),X2)
| ~ topological_space(X3,X0)
| ~ subset_sets(X4,X3)
| limit_point(X1,X4,X3,X0)
| element_of_set(f7(f1(X0,X1),f24(f1(X0,X1),X2)),union_of_members(X0)) ) ).
cnf(u2734,axiom,
( ~ element_of_set(X4,f1(top_of_basis(subspace_topology(X0,X1,X2)),f20(union_of_members(top_of_basis(subspace_topology(X0,X1,X2))),X3)))
| ~ topological_space(union_of_members(top_of_basis(subspace_topology(X0,X1,X2))),X3)
| hausdorff(union_of_members(top_of_basis(subspace_topology(X0,X1,X2))),X3)
| topological_space(X0,X1) ) ).
cnf(u988,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,f20(closure(X2,X0,X1),X3)),X4),sF0)
| ~ subset_sets(X2,sF0)
| ~ topological_space(closure(X2,X0,X1),X3)
| hausdorff(closure(X2,X0,X1),X3)
| ~ closed(sF0,X0,X1)
| basis(f13(a,cx,ct,f20(closure(X2,X0,X1),X3)),X4)
| ~ topological_space(f13(a,cx,ct,f20(closure(X2,X0,X1),X3)),X4) ) ).
cnf(u2949,axiom,
( subset_sets(f13(X4,X5,X6,f11(X0,boundary(X1,X2,X3))),X4)
| ~ closed(interior(X4,X5,X6),X2,X3)
| ~ subset_sets(X1,interior(X4,X5,X6))
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(neighborhood_62,axiom,
( neighborhood(X0,X1,X2,X3)
| ~ topological_space(X2,X3)
| ~ open(X0,X2,X3)
| ~ element_of_set(X1,X0) ) ).
cnf(u28649,negated_conjecture,
( element_of_set(f11(X1,union_of_members(ct)),f1(ct,f11(X1,union_of_members(ct))))
| element_of_set(f11(X0,union_of_members(top_of_basis(X1))),union_of_members(X6))
| element_of_set(X5,f1(top_of_basis(X0),X5))
| ~ element_of_set(X5,cx) ) ).
cnf(u6075,negated_conjecture,
( ~ topological_space(X3,f24(X0,ct))
| compact_space(X0,ct)
| element_of_set(X1,union_of_members(ct))
| limit_point(X1,X2,X3,f24(X0,ct))
| ~ subset_sets(X2,X3)
| ~ topological_space(X0,ct) ) ).
cnf(u3355,negated_conjecture,
( element_of_collection(f1(ct,f19(boundary(X0,X1,X2),X3)),ct)
| ~ topological_space(boundary(X0,X1,X2),X3)
| ~ subset_sets(X0,empty_set)
| ~ closed(empty_set,X1,X2)
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u428,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,f20(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| ~ topological_space(cx,X1)
| ~ element_of_set(X2,f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(X2,interior(a,cx,X1)) ) ).
cnf(u529,axiom,
( element_of_set(f7(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4),interior(X0,X1,X2))
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3)
| basis(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4)
| ~ topological_space(f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)),X4) ) ).
cnf(u5112,axiom,
( element_of_set(f11(X7,f6(X3,X1,f15(X4,X2,X5,X6,X0),X0,X2)),f6(X3,X1,f15(X4,X2,X5,X6,X0),X0,X2))
| element_of_set(f15(X4,X2,X5,X6,X0),union_of_members(top_of_basis(X7)))
| ~ basis(X3,X1)
| ~ element_of_set(f15(X4,X2,X5,X6,X0),X3)
| ~ neighborhood(X0,X4,X5,X6)
| ~ limit_point(X4,X2,X5,X6)
| ~ element_of_collection(X2,X1)
| ~ element_of_collection(X0,X1) ) ).
cnf(u858,axiom,
( ~ closed(boundary(X4,X5,X6),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,boundary(X4,X5,X6))
| ~ subset_sets(relative_complement_sets(X4,X5),X7)
| ~ closed(X7,X5,X6)
| element_of_set(f11(X0,closure(X1,X2,X3)),X7) ) ).
cnf(u6306,axiom,
( ~ open(f14(X2,X3,X4,X5),X0,X1)
| element_of_set(X5,closure(X2,X3,X4))
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4)
| ~ disjoint_s(X6,f14(X2,X3,X4,X5))
| subset_sets(X2,f14(X2,X3,X4,f20(X0,X1)))
| hausdorff(X0,X1)
| ~ open(X6,X0,X1)
| ~ element_of_set(f19(X0,X1),X6) ) ).
cnf(u3077,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| topological_space(X5,X6) ) ).
cnf(u36091,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| element_of_set(f11(X1,union_of_members(top_of_basis(X4))),union_of_members(X5))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx)
| element_of_set(f11(X4,union_of_members(ct)),sF0) ) ).
cnf(u3980,axiom,
( ~ element_of_set(X7,f6(X3,X1,f15(X4,X2,X5,X6,X0),X0,X2))
| ~ element_of_collection(X2,X1)
| ~ basis(X3,X1)
| ~ element_of_set(f15(X4,X2,X5,X6,X0),X3)
| ~ neighborhood(X0,X4,X5,X6)
| ~ limit_point(X4,X2,X5,X6)
| ~ element_of_collection(X0,X1)
| element_of_set(X7,union_of_members(X1)) ) ).
cnf(u1388,axiom,
( ~ element_of_set(X0,closure(X1,X2,X3))
| topological_space(X4,X5)
| element_of_set(f11(subspace_topology(X4,X5,X6),closure(X1,X2,X3)),X7)
| ~ closed(X7,X2,X3)
| ~ subset_sets(X1,X7) ) ).
cnf(u50978,negated_conjecture,
( ~ element_of_set(X7,f16(X1,X2,X3,X4))
| limit_point(X1,X2,X3,X4)
| element_of_set(X7,f13(f14(f16(X1,X2,X3,X4),X5,X6,X0),X3,X4,X7))
| element_of_set(X0,X8) ) ).
cnf(u2891,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),f13(a,cx,ct,f19(sF0,X3))),f13(a,cx,ct,f19(sF0,X3)))
| topological_space(X0,X1)
| hausdorff(sF0,X3)
| ~ topological_space(sF0,X3) ) ).
cnf(u1089,axiom,
( element_of_set(f19(closure(X0,X1,X2),X3),closure(X4,X5,X6))
| ~ subset_sets(X0,boundary(X4,X5,X6))
| ~ closed(boundary(X4,X5,X6),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(closure(X0,X1,X2),X3) ) ).
cnf(u9503,negated_conjecture,
( ~ element_of_set(X4,closure(X1,X2,X3))
| eq_p(X4,X0)
| ~ element_of_set(X0,closure(X1,X2,X3)) ) ).
cnf(u1211,negated_conjecture,
( element_of_set(X2,f14(a,cx,ct,f11(X0,X1)))
| element_of_collection(X1,top_of_basis(X0))
| ~ subset_sets(sF3,X1)
| ~ element_of_set(X2,sF3)
| ~ element_of_collection(sF3,X0) ) ).
cnf(u7592,negated_conjecture,
( element_of_set(f15(X0,X1,X2,X3,X4),sF0)
| ~ neighborhood(X4,X0,X2,X3)
| ~ limit_point(X0,X1,X2,X3) ) ).
cnf(u776,axiom,
( ~ limit_point(X0,X1,X4,X3)
| limit_point(X0,X1,X2,X3)
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2) ) ).
cnf(u2501,axiom,
( element_of_set(X0,f10(X4,f16(X1,X2,X3,top_of_basis(X4)),X0))
| ~ element_of_set(X0,f16(X1,X2,X3,top_of_basis(X4)))
| limit_point(X1,X2,X3,top_of_basis(X4))
| ~ topological_space(X3,top_of_basis(X4))
| ~ subset_sets(X2,X3) ) ).
cnf(u6426,axiom,
( ~ element_of_set(X0,closure(X1,X2,X3))
| element_of_set(X4,f14(relative_complement_sets(X1,X2),X2,X3,X0))
| ~ subset_sets(relative_complement_sets(X1,X2),X2)
| closed(f14(relative_complement_sets(X1,X2),X2,X3,X4),X2,X3)
| element_of_set(X0,boundary(X1,X2,X3)) ) ).
cnf(u650,axiom,
( element_of_set(f11(X0,boundary(X1,X2,X3)),X4)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ closed(X4,X2,X3)
| ~ subset_sets(relative_complement_sets(X1,X2),X4) ) ).
cnf(u3315,axiom,
( ~ topological_space(f14(X0,X1,X2,X3),X6)
| element_of_set(X3,union_of_members(top_of_basis(X4)))
| ~ closed(sF1,X1,X2)
| ~ subset_sets(X0,sF1)
| ~ subset_sets(X0,X1)
| ~ element_of_collection(X5,X6)
| element_of_set(f11(X4,closure(X0,X1,X2)),sF3)
| ~ element_of_set(X7,X5)
| ~ subset_sets(X5,X0)
| element_of_set(X7,interior(X0,f14(X0,X1,X2,X3),X6)) ) ).
cnf(u2557,axiom,
( hausdorff(boundary(X0,X1,X2),subspace_topology(X3,X4,boundary(X0,X1,X2)))
| subset_sets(relative_complement_sets(X0,X1),X1)
| ~ connected_set(boundary(X0,X1,X2),X3,X4) ) ).
cnf(separation_81,axiom,
( ~ separation(X0,X1,X2,X3)
| topological_space(X2,X3) ) ).
cnf(u6219,negated_conjecture,
( ~ element_of_set(X0,f13(a,cx,ct,f19(sF0,X1)))
| ~ topological_space(sF0,top_of_basis(X2))
| element_of_set(X0,interior(a,sF0,top_of_basis(X2)))
| element_of_set(f11(X2,f13(a,cx,ct,f19(sF0,X1))),sF0)
| ~ topological_space(sF0,X1)
| hausdorff(sF0,X1) ) ).
cnf(u993,negated_conjecture,
( ~ closed(f13(a,cx,ct,f20(closure(X2,X0,X1),X3)),X5,X6)
| ~ subset_sets(X2,sF0)
| ~ topological_space(closure(X2,X0,X1),X3)
| hausdorff(closure(X2,X0,X1),X3)
| element_of_set(f20(closure(X4,X5,X6),X7),sF0)
| hausdorff(closure(X4,X5,X6),X7)
| ~ subset_sets(X4,f13(a,cx,ct,f20(closure(X2,X0,X1),X3)))
| ~ closed(sF0,X0,X1)
| ~ topological_space(closure(X4,X5,X6),X7) ) ).
cnf(u6367,axiom,
( element_of_set(f19(sF0,X0),union_of_members(top_of_basis(X1)))
| element_of_set(f11(X1,union_of_members(ct)),union_of_members(ct))
| hausdorff(sF0,X0)
| ~ topological_space(sF0,X0) ) ).
cnf(u6419,axiom,
( element_of_set(X4,f14(X1,X2,X3,f11(X0,boundary(relative_complement_sets(X1,X2),X2,X3))))
| element_of_set(f11(X0,boundary(relative_complement_sets(X1,X2),X2,X3)),boundary(X1,X2,X3))
| ~ subset_sets(X1,X2)
| element_of_collection(boundary(relative_complement_sets(X1,X2),X2,X3),top_of_basis(X0))
| closed(f14(X1,X2,X3,X4),X2,X3) ) ).
cnf(u1964,axiom,
( ~ topological_space(boundary(X5,X2,X3),X6)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X0,X1,X4),closure(X5,X2,X3)),sF3)
| ~ subset_sets(X5,sF1)
| topological_space(X0,X1)
| basis(boundary(X5,X2,X3),X6) ) ).
cnf(u454,axiom,
( ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| topological_space(X1,X2) ) ).
cnf(u5017,axiom,
( element_of_collection(f9(X0,f23(X0,X1,X2)),f23(X0,X1,X2))
| ~ open_covering(X2,X0,X1)
| basis(X0,f23(X0,X1,X2))
| ~ compact_space(X0,X1) ) ).
cnf(u2685,axiom,
( ~ element_of_set(X7,f13(X0,X1,X2,f20(closure(X5,X3,X4),X6)))
| ~ topological_space(closure(X5,X3,X4),X6)
| hausdorff(closure(X5,X3,X4),X6)
| ~ subset_sets(X5,interior(X0,X1,X2))
| ~ closed(interior(X0,X1,X2),X3,X4)
| element_of_set(X7,union_of_members(X2)) ) ).
cnf(u2667,axiom,
( ~ subset_sets(f17(X1,X4,f11(X2,X3),X0),X3)
| eq_p(f11(X2,X3),X0)
| ~ hausdorff(X1,X4)
| ~ element_of_set(f11(X2,X3),X1)
| element_of_collection(X3,top_of_basis(X2))
| ~ element_of_collection(f17(X1,X4,f11(X2,X3),X0),X2)
| ~ element_of_set(X0,X1) ) ).
cnf(u875,negated_conjecture,
( ~ subset_sets(a,f14(X0,cx,ct,X1))
| ~ subset_sets(f14(X0,cx,ct,X1),sF3)
| ~ element_of_collection(f14(X0,cx,ct,X1),X2)
| element_of_collection(sF3,top_of_basis(X2))
| element_of_set(X1,closure(X0,cx,ct))
| ~ subset_sets(X0,cx) ) ).
cnf(u3469,negated_conjecture,
( ~ closed(intersection_of_sets(X4,X5),X1,X2)
| ~ subset_sets(X0,intersection_of_sets(X4,X5))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| element_of_set(f7(closure(X0,X1,X2),X3),union_of_members(ct))
| ~ element_of_collection(X5,ct)
| ~ element_of_collection(X4,ct) ) ).
cnf(u2562,axiom,
( element_of_set(f7(closure(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3),boundary(relative_complement_sets(X0,X1),X1,X2))
| basis(closure(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3)
| ~ topological_space(closure(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3)
| ~ element_of_set(f7(closure(relative_complement_sets(relative_complement_sets(X0,X1),X1),X1,X2),X3),boundary(X0,X1,X2)) ) ).
cnf(u3894,axiom,
( subset_sets(relative_complement_sets(X5,f14(X1,X2,X3,X4)),f14(relative_complement_sets(X5,f14(X1,X2,X3,X4)),X2,X3,X0))
| element_of_collection(boundary(X5,f14(X1,X2,X3,X4),X6),top_of_basis(X7))
| ~ subset_sets(relative_complement_sets(X5,f14(X1,X2,X3,X4)),X2)
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| element_of_set(X0,f14(X1,X2,X3,X4)) ) ).
cnf(u1352,axiom,
( ~ topological_space(closure(X2,X3,X4),X5)
| element_of_set(f20(closure(X2,X3,X4),X5),union_of_members(top_of_basis(X0)))
| hausdorff(closure(X2,X3,X4),X5)
| ~ subset_sets(X2,X1)
| ~ closed(X1,X3,X4)
| element_of_set(f11(X0,X1),X1) ) ).
cnf(u2856,axiom,
( element_of_set(f11(subspace_topology(X0,X1,X2),f16(X3,X4,X5,X6)),f16(X3,X4,X5,X6))
| topological_space(X0,X1)
| ~ subset_sets(X4,X5)
| limit_point(X3,X4,X5,X6)
| ~ topological_space(X5,X6) ) ).
cnf(boundary_70,axiom,
( ~ element_of_set(X0,boundary(X1,X2,X3))
| element_of_set(X0,closure(X1,X2,X3)) ) ).
cnf(u728,axiom,
( element_of_set(X5,interior(f14(relative_complement_sets(X0,X1),X2,X3,X4),X1,X6))
| ~ element_of_set(X5,relative_complement_sets(X0,X1))
| ~ closed(X0,X1,X6)
| ~ subset_sets(f14(relative_complement_sets(X0,X1),X2,X3,X4),X1)
| element_of_set(X4,closure(relative_complement_sets(X0,X1),X2,X3))
| ~ subset_sets(relative_complement_sets(X0,X1),X2)
| ~ topological_space(X2,X3) ) ).
cnf(u4849,axiom,
( element_of_set(f7(f10(X0,X1,X2),f24(f10(X0,X1,X2),X3)),union_of_members(X0))
| basis(f10(X0,X1,X2),f24(f10(X0,X1,X2),X3))
| compact_space(f10(X0,X1,X2),X3)
| ~ element_of_collection(X1,top_of_basis(X0))
| ~ element_of_set(X2,X1)
| ~ topological_space(f10(X0,X1,X2),X3) ) ).
cnf(u6423,axiom,
( closed(f14(X1,X2,X3,X4),X2,X3)
| element_of_set(f11(X5,closure(X1,X2,X3)),sF3)
| element_of_set(X4,f14(X1,X2,X3,X0))
| element_of_set(X0,union_of_members(top_of_basis(X5)))
| ~ subset_sets(X1,sF1)
| ~ closed(sF1,X2,X3)
| ~ subset_sets(X1,X2) ) ).
cnf(u3597,axiom,
( ~ subset_sets(f13(X0,X1,X2,f11(X6,closure(X5,X3,X4))),closure(X5,X3,X4))
| ~ subset_sets(X5,interior(X0,X1,X2))
| element_of_collection(closure(X5,X3,X4),top_of_basis(X6))
| ~ element_of_collection(f13(X0,X1,X2,f11(X6,closure(X5,X3,X4))),X6)
| ~ closed(interior(X0,X1,X2),X3,X4) ) ).
cnf(u54224,negated_conjecture,
( ~ element_of_set(X0,f13(a,cx,ct,f19(sF0,X1)))
| hausdorff(sF0,X1)
| element_of_set(X0,f13(f14(f13(a,cx,ct,f19(sF0,X1)),X2,X3,X4),cx,ct,X0))
| element_of_set(X4,X5) ) ).
cnf(u9317,negated_conjecture,
( ~ element_of_set(X0,sF1)
| element_of_set(X0,X1) ) ).
cnf(u16457,negated_conjecture,
( eq_p(f19(intersection_of_members(X0),X1),X2)
| hausdorff(intersection_of_members(X0),X1)
| ~ element_of_set(X2,sF1) ) ).
cnf(u5944,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,f19(sF0,X2)),X0)
| ~ element_of_set(X1,f13(a,cx,ct,f19(sF0,X2)))
| ~ topological_space(sF0,X0)
| element_of_set(X1,interior(a,sF0,X0))
| hausdorff(sF0,X2)
| ~ topological_space(sF0,X2) ) ).
cnf(u4437,axiom,
( ~ element_of_set(X4,f8(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3))
| ~ element_of_collection(union_of_members(X3),subspace_topology(X1,X2,X0))
| basis(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3)
| element_of_set(X4,union_of_members(X3)) ) ).
cnf(u27875,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f13(X1,X2,X3,f11(X0,union_of_members(ct))))
| element_of_set(f11(X4,union_of_members(top_of_basis(X0))),sF0)
| element_of_set(X5,f1(top_of_basis(X4),X5))
| ~ element_of_set(X5,cx) ) ).
cnf(u1319,axiom,
( element_of_set(f11(X0,f1(ct,X1)),f1(ct,X1))
| element_of_set(X1,union_of_members(top_of_basis(X0)))
| ~ element_of_set(X1,sF0) ) ).
cnf(u5818,axiom,
( element_of_collection(f6(X4,X3,f7(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3),f8(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3),f9(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3)),X3)
| ~ element_of_collection(union_of_members(X3),subspace_topology(X1,X2,X0))
| ~ element_of_set(f7(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3),X4)
| ~ basis(X4,X3)
| basis(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3) ) ).
cnf(u541,axiom,
( ~ subset_sets(f1(ct,f11(X1,X0)),X0)
| ~ element_of_collection(f1(ct,f11(X1,X0)),X1)
| element_of_collection(X0,top_of_basis(X1))
| ~ element_of_set(f11(X1,X0),sF0) ) ).
cnf(u5134,axiom,
( ~ topological_space(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5))
| basis(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5))
| subset_sets(X4,X2) ) ).
cnf(u45146,negated_conjecture,
( element_of_set(X4,f13(f14(relative_complement_sets(X5,X6),X7,X8,X0),X6,X9,X4))
| open(f13(X1,X2,X3,X0),X2,X3)
| ~ element_of_set(X4,relative_complement_sets(X5,X6)) ) ).
cnf(u4302,negated_conjecture,
( element_of_set(X5,interior(a,cx,subspace_topology(X3,X4,f13(a,X0,X1,f20(interior(a,X0,X1),X2)))))
| ~ topological_space(cx,subspace_topology(X3,X4,f13(a,X0,X1,f20(interior(a,X0,X1),X2))))
| ~ element_of_set(X5,f13(a,X0,X1,f20(interior(a,X0,X1),X2)))
| hausdorff(interior(a,X0,X1),X2)
| ~ topological_space(interior(a,X0,X1),X2)
| ~ connected_set(f13(a,X0,X1,f20(interior(a,X0,X1),X2)),X3,X4) ) ).
cnf(u4882,axiom,
( basis(closure(X0,X1,X2),f24(closure(X0,X1,X2),X3))
| element_of_set(f11(subspace_topology(X4,X5,X6),closure(X0,X1,X2)),sF3)
| compact_space(closure(X0,X1,X2),X3)
| topological_space(X4,X5)
| ~ closed(sF1,X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,sF1) ) ).
cnf(u5276,axiom,
( ~ open(closure(X1,X2,subspace_topology(X3,X4,X5)),X6,X7)
| ~ disjoint_s(X0,closure(X1,X2,subspace_topology(X3,X4,X5)))
| hausdorff(X6,X7)
| ~ open(X0,X6,X7)
| ~ element_of_set(f19(X6,X7),X0)
| topological_space(X3,X4)
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,subspace_topology(X3,X4,X5)) ) ).
cnf(u1081,axiom,
( closed(f14(relative_complement_sets(X4,X5),X5,X6,f19(closure(X0,X1,X2),X3)),X5,X6)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ closed(closure(X4,X5,X6),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(relative_complement_sets(X4,X5),X5)
| hausdorff(closure(X0,X1,X2),X3)
| element_of_set(f19(closure(X0,X1,X2),X3),boundary(X4,X5,X6)) ) ).
cnf(u5952,negated_conjecture,
( ~ element_of_collection(f13(a,X2,X3,f20(closure(X4,X5,X6),X7)),X0)
| ~ element_of_set(X1,f13(a,X2,X3,f20(closure(X4,X5,X6),X7)))
| ~ topological_space(sF0,X0)
| element_of_set(X1,interior(a,sF0,X0))
| ~ subset_sets(X4,interior(a,X2,X3))
| ~ closed(interior(a,X2,X3),X5,X6)
| ~ topological_space(closure(X4,X5,X6),X7)
| hausdorff(closure(X4,X5,X6),X7) ) ).
cnf(u3918,axiom,
( element_of_set(X4,interior(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,f19(closure(relative_complement_sets(f13(a,cx,ct,f19(sF0,X0)),X1),X1,X2),X3)),cx,ct))
| ~ topological_space(closure(relative_complement_sets(f13(a,cx,ct,f19(sF0,X0)),X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(f13(a,cx,ct,f19(sF0,X0)),X1),X1,X2),X3)
| ~ subset_sets(f13(a,cx,ct,f19(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| ~ subset_sets(f14(f13(a,cx,ct,f19(sF0,X0)),X1,X2,f19(closure(relative_complement_sets(f13(a,cx,ct,f19(sF0,X0)),X1),X1,X2),X3)),cx)
| ~ element_of_set(X4,f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(f19(closure(relative_complement_sets(f13(a,cx,ct,f19(sF0,X0)),X1),X1,X2),X3),boundary(f13(a,cx,ct,f19(sF0,X0)),X1,X2)) ) ).
cnf(u41716,negated_conjecture,
( element_of_set(X2,f13(f14(f13(a,cx,ct,f20(sF0,X0)),cx,ct,X1),cx,ct,X2))
| hausdorff(sF0,X0)
| element_of_set(X1,sF0)
| ~ element_of_set(X2,f13(a,cx,ct,f20(sF0,X0))) ) ).
cnf(u1227,axiom,
( element_of_set(f11(X4,f16(X3,X2,X0,X1)),union_of_members(X1))
| ~ subset_sets(X2,X0)
| limit_point(X3,X2,X0,X1)
| ~ topological_space(X0,X1)
| element_of_collection(f16(X3,X2,X0,X1),top_of_basis(X4)) ) ).
cnf(u514,axiom,
( element_of_set(f20(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4),interior(X0,X1,X2))
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3)
| ~ topological_space(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4)
| hausdorff(f13(X0,X1,X2,f19(interior(X0,X1,X2),X3)),X4) ) ).
cnf(u920,axiom,
( ~ element_of_set(X4,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| ~ topological_space(interior(X0,X1,X2),X3)
| element_of_set(X4,union_of_members(X2)) ) ).
cnf(u2424,axiom,
( ~ closed(closure(X3,X1,X2),X6,X7)
| ~ subset_sets(X3,X0)
| element_of_set(f11(X4,closure(X3,X1,X2)),X0)
| element_of_set(f19(closure(X5,X6,X7),X8),union_of_members(top_of_basis(X4)))
| hausdorff(closure(X5,X6,X7),X8)
| ~ subset_sets(X5,closure(X3,X1,X2))
| ~ closed(X0,X1,X2)
| ~ topological_space(closure(X5,X6,X7),X8) ) ).
cnf(u36078,negated_conjecture,
( element_of_set(f11(X4,union_of_members(ct)),f1(X5,f11(X4,union_of_members(ct))))
| element_of_set(f11(X1,union_of_members(top_of_basis(X4))),interior(X6,X7,X8))
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| ~ element_of_set(X0,cx) ) ).
cnf(u6649,negated_conjecture,
( element_of_set(f19(closure(X0,X1,X2),X3),sF0)
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(sF3,X1,X2) ) ).
cnf(u857,axiom,
( ~ closed(f14(X4,X5,X6,f11(X0,closure(X1,X2,X3))),X2,X3)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f14(X4,X5,X6,f11(X0,closure(X1,X2,X3))))
| ~ topological_space(X5,X6)
| ~ subset_sets(X4,X5)
| element_of_set(f11(X0,closure(X1,X2,X3)),closure(X4,X5,X6)) ) ).
cnf(u6717,negated_conjecture,
( ~ element_of_set(X8,f13(X0,X1,X2,f20(closure(X5,X3,X4),X6)))
| hausdorff(closure(X5,X3,X4),X6)
| ~ closed(interior(X0,X1,X2),X3,X4)
| element_of_set(X8,interior(X7,X1,X2)) ) ).
cnf(u3981,axiom,
( ~ element_of_set(X9,f6(X5,top_of_basis(subspace_topology(X1,X2,X3)),f15(X6,X4,X7,X8,X0),X0,X4))
| ~ element_of_collection(X4,top_of_basis(subspace_topology(X1,X2,X3)))
| ~ basis(X5,top_of_basis(subspace_topology(X1,X2,X3)))
| ~ element_of_set(f15(X6,X4,X7,X8,X0),X5)
| ~ neighborhood(X0,X6,X7,X8)
| ~ limit_point(X6,X4,X7,X8)
| ~ element_of_collection(X0,top_of_basis(subspace_topology(X1,X2,X3)))
| subset_sets(X3,X1) ) ).
cnf(u4891,axiom,
( element_of_set(f7(f21(X0,X1),f24(f21(X0,X1),X2)),union_of_members(X1))
| basis(f21(X0,X1),f24(f21(X0,X1),X2))
| compact_space(f21(X0,X1),X2)
| ~ topological_space(X0,X1)
| connected_space(X0,X1)
| ~ topological_space(f21(X0,X1),X2) ) ).
cnf(u2682,axiom,
( ~ closed(interior(X0,X1,X2),cx,ct)
| subset_sets(f13(X0,X1,X2,f11(X3,sF3)),X0)
| ~ subset_sets(a,interior(X0,X1,X2))
| element_of_collection(sF3,top_of_basis(X3)) ) ).
cnf(u6577,axiom,
( element_of_set(f11(subspace_topology(X1,X4,X0),closure(X5,X2,X3)),sF3)
| subset_sets(X5,f14(X5,X2,X3,X6))
| ~ closed(sF1,X2,X3)
| ~ subset_sets(X5,sF1)
| subset_sets(X0,X1)
| ~ subset_sets(X5,X2) ) ).
cnf(u3602,axiom,
( element_of_set(X4,interior(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,f11(X3,closure(relative_complement_sets(f13(a,cx,ct,f20(sF0,X0)),X1),X1,X2))),cx,ct))
| element_of_collection(closure(relative_complement_sets(f13(a,cx,ct,f20(sF0,X0)),X1),X1,X2),top_of_basis(X3))
| ~ subset_sets(f13(a,cx,ct,f20(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| ~ subset_sets(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,f11(X3,closure(relative_complement_sets(f13(a,cx,ct,f20(sF0,X0)),X1),X1,X2))),cx)
| ~ element_of_set(X4,f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(f11(X3,closure(relative_complement_sets(f13(a,cx,ct,f20(sF0,X0)),X1),X1,X2)),boundary(f13(a,cx,ct,f20(sF0,X0)),X1,X2)) ) ).
cnf(u4783,axiom,
( element_of_collection(f12(X2,X3,X4,f12(X1,subspace_topology(X2,X3,X4),X5,f22(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5)))),X3)
| ~ topological_space(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5))
| connected_space(X0,subspace_topology(X1,subspace_topology(X2,X3,X4),X5)) ) ).
cnf(u450,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,f20(sF0,X0)),X1),sF0)
| ~ topological_space(f13(a,cx,ct,f20(sF0,X0)),X1)
| basis(f13(a,cx,ct,f20(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0) ) ).
cnf(u2978,axiom,
( ~ closed(boundary(X4,X5,X6),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,boundary(X4,X5,X6))
| subset_sets(relative_complement_sets(X4,X5),X5) ) ).
cnf(u3908,axiom,
( element_of_set(X0,f14(X1,X2,X3,f11(X4,f14(closure(X1,X2,X3),X5,X6,X7))))
| element_of_set(f11(X4,f14(closure(X1,X2,X3),X5,X6,X7)),closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| subset_sets(X1,f14(X1,X2,X3,X0))
| ~ topological_space(X2,X3)
| element_of_collection(f14(closure(X1,X2,X3),X5,X6,X7),top_of_basis(X4))
| ~ element_of_collection(closure(X1,X2,X3),X4)
| element_of_set(X7,closure(closure(X1,X2,X3),X5,X6))
| ~ subset_sets(closure(X1,X2,X3),X5)
| ~ topological_space(X5,X6) ) ).
cnf(u3936,axiom,
( subset_sets(X0,f14(X0,X1,X2,f19(closure(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f11(subspace_topology(X4,X5,X6),boundary(X0,X1,X2)),boundary(X0,X1,X2))
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1)
| topological_space(X4,X5)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3) ) ).
cnf(u3719,axiom,
( ~ subset_sets(relative_complement_sets(X0,X1),closure(X0,X1,X2))
| ~ closed(closure(X0,X1,X2),X1,X2)
| element_of_collection(closure(relative_complement_sets(X0,X1),X1,X2),top_of_basis(X3))
| element_of_set(f11(X4,boundary(X0,X1,X2)),boundary(X0,X1,X2))
| element_of_set(f11(X3,closure(relative_complement_sets(X0,X1),X1,X2)),union_of_members(top_of_basis(X4))) ) ).
cnf(u45482,negated_conjecture,
( ~ element_of_set(X8,relative_complement_sets(X1,X2))
| eq_p(X3,X4)
| element_of_set(X0,f13(f14(relative_complement_sets(X1,X2),X5,X6,X3),X2,X7,X0))
| element_of_set(X8,f13(f14(relative_complement_sets(X1,X2),X5,X6,X4),X2,X9,X8))
| ~ element_of_set(X0,relative_complement_sets(X1,X2)) ) ).
cnf(u6705,negated_conjecture,
( ~ element_of_set(X5,f13(X0,X1,X2,f20(interior(X0,X1,X2),X3)))
| hausdorff(interior(X0,X1,X2),X3)
| element_of_set(X5,interior(X4,X1,X2)) ) ).
cnf(u27643,negated_conjecture,
( element_of_set(f11(X1,union_of_members(top_of_basis(X2))),union_of_members(top_of_basis(X2)))
| element_of_set(X0,f1(top_of_basis(X1),X0))
| element_of_set(f11(X2,union_of_members(ct)),union_of_members(ct))
| ~ element_of_set(X0,cx) ) ).
cnf(u16749,negated_conjecture,
( ~ element_of_set(f20(intersection_of_members(X0),X1),sF3)
| hausdorff(intersection_of_members(X0),X1) ) ).
cnf(limit_point_66,axiom,
( ~ eq_p(f15(X0,X1,X2,X3,X4),X0)
| ~ neighborhood(X4,X0,X2,X3)
| ~ limit_point(X0,X1,X2,X3) ) ).
cnf(u5142,axiom,
( ~ element_of_set(f11(X3,f14(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5,f19(closure(relative_complement_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4),X4,X5),X6))),boundary(X0,X1,X2))
| element_of_collection(f14(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5,f19(closure(relative_complement_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4),X4,X5),X6)),top_of_basis(X3))
| ~ element_of_collection(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f19(closure(relative_complement_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4),X4,X5),X6),boundary(closure(relative_complement_sets(X0,X1),X1,X2),X4,X5))
| ~ topological_space(closure(relative_complement_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4),X4,X5),X6)
| hausdorff(closure(relative_complement_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4),X4,X5),X6)
| ~ subset_sets(closure(relative_complement_sets(X0,X1),X1,X2),X4) ) ).
cnf(u409,axiom,
( ~ subset_sets(X1,f13(a,cx,ct,f19(sF0,X0)))
| ~ topological_space(sF0,X0)
| ~ element_of_collection(X1,X2)
| ~ topological_space(a,X2)
| ~ element_of_set(X3,X1)
| hausdorff(sF0,X0)
| element_of_set(X3,interior(f13(a,cx,ct,f19(sF0,X0)),a,X2)) ) ).
cnf(u2937,axiom,
( ~ closed(intersection_of_members(X4),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,intersection_of_members(X4))
| ~ element_of_collection(X5,X4)
| element_of_set(f11(X0,boundary(X1,X2,X3)),X5) ) ).
cnf(u3466,axiom,
( ~ closed(intersection_of_sets(f16(X4,X5,X6,X7),X5),X1,X2)
| ~ subset_sets(X0,intersection_of_sets(f16(X4,X5,X6,X7),X5))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(X6,X7)
| ~ subset_sets(X5,X6)
| limit_point(X4,X5,X6,X7)
| eq_p(f7(closure(X0,X1,X2),X3),X4) ) ).
cnf(u3164,axiom,
( element_of_collection(f12(X2,X3,X4,relative_complement_sets(f14(relative_complement_sets(X0,X1),X1,subspace_topology(X2,X3,X4),X5),X1)),X3)
| subset_sets(X0,f14(X0,X1,subspace_topology(X2,X3,X4),X5))
| ~ subset_sets(relative_complement_sets(X0,X1),X1)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,subspace_topology(X2,X3,X4))
| element_of_set(X5,boundary(X0,X1,subspace_topology(X2,X3,X4))) ) ).
cnf(u6408,axiom,
( ~ open(closure(X2,X3,X4),X0,X1)
| element_of_set(X5,f14(X2,X3,X4,f20(X0,X1)))
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4)
| ~ disjoint_s(X6,closure(X2,X3,X4))
| closed(f14(X2,X3,X4,X5),X3,X4)
| hausdorff(X0,X1)
| ~ open(X6,X0,X1)
| ~ element_of_set(f19(X0,X1),X6) ) ).
cnf(u6694,negated_conjecture,
( ~ element_of_set(X1,f13(a,cx,ct,X2))
| ~ element_of_set(X2,sF0)
| element_of_set(X1,interior(X0,cx,ct)) ) ).
cnf(u5336,axiom,
( ~ open(closure(X1,X2,X3),boundary(X1,X2,X3),X4)
| ~ disjoint_s(X0,closure(X1,X2,X3))
| hausdorff(boundary(X1,X2,X3),X4)
| ~ open(X0,boundary(X1,X2,X3),X4)
| ~ element_of_set(f19(boundary(X1,X2,X3),X4),X0) ) ).
cnf(u3082,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f11(X7,closure(X4,X5,X6)),sF3)
| ~ subset_sets(X4,sF1)
| ~ closed(sF1,X5,X6)
| element_of_set(f19(boundary(X0,X1,X2),X3),union_of_members(top_of_basis(X7))) ) ).
cnf(u3497,axiom,
( ~ closed(closure(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,closure(X4,X5,X6))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| subset_sets(X4,X5) ) ).
cnf(u1987,negated_conjecture,
basis(X0,X1) ).
cnf(u1168,negated_conjecture,
( ~ element_of_collection(f13(a,X0,X1,f7(interior(a,X0,X1),X2)),X3)
| basis(interior(a,X0,X1),X2)
| ~ topological_space(cx,X3)
| ~ element_of_set(X4,f13(a,X0,X1,f7(interior(a,X0,X1),X2)))
| ~ topological_space(interior(a,X0,X1),X2)
| element_of_set(X4,interior(a,cx,X3)) ) ).
cnf(u1396,axiom,
( ~ element_of_set(X0,f1(top_of_basis(subspace_topology(X1,X2,X3)),X4))
| topological_space(X1,X2)
| limit_point(X4,X5,X6,top_of_basis(subspace_topology(X1,X2,X3)))
| ~ topological_space(X6,top_of_basis(subspace_topology(X1,X2,X3)))
| ~ subset_sets(X5,X6) ) ).
cnf(u910,axiom,
( ~ closed(relative_complement_sets(X0,X1),X5,X6)
| element_of_set(f11(X3,closure(X4,X5,X6)),union_of_members(X2))
| element_of_collection(closure(X4,X5,X6),top_of_basis(X3))
| ~ closed(X0,X1,X2)
| ~ subset_sets(X4,relative_complement_sets(X0,X1)) ) ).
cnf(u6456,axiom,
( ~ closed(closure(X5,X2,X3),X7,X8)
| ~ closed(sF1,X2,X3)
| element_of_set(f11(subspace_topology(X1,X4,X0),closure(X5,X2,X3)),sF3)
| ~ subset_sets(X5,sF1)
| ~ topological_space(boundary(X6,X7,X8),X9)
| ~ subset_sets(X6,closure(X5,X2,X3))
| subset_sets(X0,X1)
| hausdorff(boundary(X6,X7,X8),X9) ) ).
cnf(u1208,negated_conjecture,
( ~ subset_sets(X2,f14(a,cx,ct,f11(X0,X1)))
| element_of_collection(X1,top_of_basis(X0))
| ~ subset_sets(sF3,X1)
| ~ subset_sets(X2,cx)
| ~ element_of_collection(sF3,X0)
| closed(f14(X2,cx,ct,X3),cx,ct)
| element_of_set(X3,f14(a,cx,ct,f11(X0,X1))) ) ).
cnf(u3625,axiom,
( subset_sets(X1,f14(X1,X2,X3,f11(X0,closure(relative_complement_sets(X1,X2),X2,X3))))
| element_of_collection(closure(relative_complement_sets(X1,X2),X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,X2)
| ~ element_of_collection(boundary(X1,X2,X3),X0)
| ~ subset_sets(boundary(X1,X2,X3),closure(relative_complement_sets(X1,X2),X2,X3)) ) ).
cnf(u1091,axiom,
( ~ closed(f22(X4,X5),X1,X2)
| ~ subset_sets(X0,f22(X4,X5))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(X4,X5)
| connected_space(X4,X5)
| element_of_set(f19(closure(X0,X1,X2),X3),union_of_members(X5)) ) ).
cnf(u5127,negated_conjecture,
( ~ subset_sets(union_of_members(top_of_basis(X2)),X1)
| ~ element_of_set(f11(X0,X1),sF3)
| element_of_set(X3,sF3)
| element_of_collection(X1,top_of_basis(X0))
| ~ element_of_collection(union_of_members(top_of_basis(X2)),X0)
| element_of_set(f11(X2,f14(a,cx,ct,X3)),f14(a,cx,ct,X3)) ) ).
cnf(u2748,axiom,
( ~ closed(closure(relative_complement_sets(X1,X2),X2,X3),X4,X5)
| ~ subset_sets(X0,closure(relative_complement_sets(X1,X2),X2,X3))
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| element_of_set(f20(closure(X0,X4,X5),X6),boundary(X1,X2,X3))
| ~ subset_sets(X0,closure(X1,X2,X3))
| ~ closed(closure(X1,X2,X3),X4,X5) ) ).
cnf(u3027,axiom,
( element_of_collection(f12(X3,X4,X0,union_of_sets(f21(intersection_of_sets(X0,X1),X2),f22(intersection_of_sets(X0,X1),X2))),X4)
| ~ topological_space(X3,X4)
| ~ subset_sets(X0,X3)
| ~ element_of_collection(X1,X4)
| connected_space(intersection_of_sets(X0,X1),X2)
| ~ topological_space(intersection_of_sets(X0,X1),X2) ) ).
cnf(u2752,axiom,
( closed(f14(X1,X2,X3,f20(closure(X0,X4,X5),X6)),X2,X3)
| ~ closed(closure(relative_complement_sets(X1,X2),X2,X3),X4,X5)
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| element_of_set(f20(closure(X0,X4,X5),X6),boundary(X1,X2,X3))
| ~ subset_sets(X0,closure(relative_complement_sets(X1,X2),X2,X3))
| ~ subset_sets(X1,X2) ) ).
cnf(u160,axiom,
( ~ topological_space(f14(X2,X3,X4,X5),X1)
| ~ element_of_collection(X0,X1)
| ~ element_of_set(X6,X0)
| ~ subset_sets(X0,X2)
| element_of_set(X6,interior(X2,f14(X2,X3,X4,X5),X1))
| element_of_set(X5,closure(X2,X3,X4))
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4) ) ).
cnf(u6033,negated_conjecture,
( element_of_set(X5,interior(f14(f16(X1,X2,X3,X4),cx,ct,X0),X3,X4))
| ~ subset_sets(f16(X1,X2,X3,X4),sF0)
| ~ subset_sets(f16(X1,X2,X3,X4),cx)
| limit_point(X1,X2,X3,X4)
| ~ topological_space(X3,X4)
| ~ subset_sets(f14(f16(X1,X2,X3,X4),cx,ct,X0),X3)
| ~ element_of_set(X5,f16(X1,X2,X3,X4))
| ~ subset_sets(X2,X3)
| element_of_set(X0,sF0) ) ).
cnf(u2417,axiom,
( ~ closed(boundary(X3,X1,X2),X7,X8)
| ~ subset_sets(X3,X0)
| element_of_set(f11(X4,closure(X3,X1,X2)),X0)
| element_of_set(f11(X5,closure(X6,X7,X8)),union_of_members(top_of_basis(X4)))
| ~ closed(X0,X1,X2)
| ~ subset_sets(X6,boundary(X3,X1,X2))
| element_of_collection(closure(X6,X7,X8),top_of_basis(X5)) ) ).
cnf(u623,axiom,
( closed(f14(X0,X1,X2,f20(closure(relative_complement_sets(X0,X1),X1,X2),X3)),X1,X2)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f20(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1) ) ).
cnf(u4482,axiom,
( ~ element_of_set(X6,f12(X0,top_of_basis(X1),X2,f1(subspace_topology(X0,top_of_basis(X1),X2),X3)))
| ~ subset_sets(X4,X5)
| ~ topological_space(X5,subspace_topology(X0,top_of_basis(X1),X2))
| limit_point(X3,X4,X5,subspace_topology(X0,top_of_basis(X1),X2))
| element_of_set(X6,f10(X1,f12(X0,top_of_basis(X1),X2,f1(subspace_topology(X0,top_of_basis(X1),X2),X3)),X6)) ) ).
cnf(u869,axiom,
( ~ element_of_set(f11(X0,closure(X1,X2,X3)),closure(X4,X5,X6))
| ~ closed(closure(relative_complement_sets(X4,X5),X5,X6),X2,X3)
| ~ subset_sets(X1,closure(relative_complement_sets(X4,X5),X5,X6))
| element_of_collection(closure(X1,X2,X3),top_of_basis(X0))
| element_of_set(f11(X0,closure(X1,X2,X3)),boundary(X4,X5,X6)) ) ).
cnf(u2364,axiom,
( open(f17(X1,X3,X0,X2),X1,X3)
| ~ element_of_set(X2,X1)
| eq_p(X0,X2)
| ~ hausdorff(X1,X3)
| ~ element_of_set(X0,X1) ) ).
cnf(u4682,axiom,
( ~ subset_sets(X2,intersection_of_members(X1))
| ~ element_of_collection(X2,X1)
| ~ element_of_collection(X2,X0)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0)) ) ).
cnf(u5683,negated_conjecture,
( element_of_set(f11(X2,sF3),f14(relative_complement_sets(X0,cx),cx,ct,X1))
| element_of_set(X1,boundary(X0,cx,ct))
| closed(f14(X0,cx,ct,X1),cx,ct)
| ~ subset_sets(X0,cx)
| ~ subset_sets(relative_complement_sets(X0,cx),cx)
| element_of_collection(sF3,top_of_basis(X2))
| ~ subset_sets(a,f14(relative_complement_sets(X0,cx),cx,ct,X1)) ) ).
cnf(u3660,negated_conjecture,
( element_of_set(f7(f13(a,cx,ct,f19(sF0,X0)),X1),union_of_members(top_of_basis(X2)))
| basis(f13(a,cx,ct,f19(sF0,X0)),X1)
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0)
| element_of_set(f11(X2,sF0),sF0)
| ~ topological_space(f13(a,cx,ct,f19(sF0,X0)),X1) ) ).
cnf(u4067,axiom,
( ~ subset_sets(relative_complement_sets(X0,X1),closure(X0,X1,X2))
| ~ closed(closure(X0,X1,X2),X1,X2)
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| hausdorff(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f11(X4,boundary(X0,X1,X2)),boundary(X0,X1,X2))
| element_of_set(f19(closure(relative_complement_sets(X0,X1),X1,X2),X3),union_of_members(top_of_basis(X4))) ) ).
cnf(u442,negated_conjecture,
( element_of_set(f7(intersection_of_sets(X0,X1),X2),union_of_members(ct))
| ~ topological_space(intersection_of_sets(X0,X1),X2)
| basis(intersection_of_sets(X0,X1),X2)
| ~ element_of_collection(X1,ct)
| ~ element_of_collection(X0,ct) ) ).
cnf(u6077,negated_conjecture,
( element_of_set(f7(union_of_members(f24(X0,ct)),f24(union_of_members(f24(X0,ct)),X1)),union_of_members(ct))
| compact_space(X0,ct)
| ~ topological_space(X0,ct)
| ~ topological_space(union_of_members(f24(X0,ct)),X1)
| basis(union_of_members(f24(X0,ct)),f24(union_of_members(f24(X0,ct)),X1))
| compact_space(union_of_members(f24(X0,ct)),X1) ) ).
cnf(u462,axiom,
( ~ element_of_set(f7(closure(relative_complement_sets(X0,X1),X1,X2),X3),closure(X0,X1,X2))
| ~ topological_space(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| basis(closure(relative_complement_sets(X0,X1),X1,X2),X3)
| element_of_set(f7(closure(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2)) ) ).
cnf(u2990,axiom,
( ~ subset_sets(X4,boundary(X1,X2,X3))
| ~ closed(X4,X2,X3)
| ~ subset_sets(X1,X4)
| ~ element_of_collection(X4,X0)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(u1220,axiom,
( ~ element_of_set(f20(X0,X1),X3)
| ~ disjoint_s(X2,X3)
| ~ open(X3,X0,X1)
| hausdorff(X0,X1)
| ~ open(X2,X0,X1)
| ~ element_of_set(f19(X0,X1),X2) ) ).
cnf(u2946,axiom,
( ~ closed(f9(X4,X5),X2,X3)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0))
| ~ subset_sets(X1,f9(X4,X5))
| ~ topological_space(X4,X5)
| basis(X4,X5)
| element_of_set(f11(X0,boundary(X1,X2,X3)),union_of_members(X5)) ) ).
cnf(u3375,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,f11(X0,sF0)),X1)
| ~ topological_space(cx,X1)
| ~ element_of_set(X2,f13(a,cx,ct,f11(X0,sF0)))
| element_of_collection(sF0,top_of_basis(X0))
| element_of_set(X2,interior(a,cx,X1)) ) ).
cnf(u4486,axiom,
( ~ topological_space(X6,subspace_topology(X7,X4,X5))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,subspace_topology(X3,X4,X5))
| ~ subset_sets(X1,X6)
| ~ topological_space(X3,X4)
| ~ subset_sets(X5,X3)
| limit_point(X0,X1,X6,subspace_topology(X7,X4,X5))
| element_of_collection(f12(X3,X4,X5,f1(subspace_topology(X3,X4,X5),X0)),X4) ) ).
cnf(u3171,axiom,
( closed(f14(relative_complement_sets(f13(a,cx,ct,f20(sF0,X0)),X1),X1,X2,X3),X1,X2)
| element_of_set(X4,interior(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,X3),cx,ct))
| ~ subset_sets(relative_complement_sets(f13(a,cx,ct,f20(sF0,X0)),X1),X1)
| ~ subset_sets(f13(a,cx,ct,f20(sF0,X0)),X1)
| ~ topological_space(X1,X2)
| ~ topological_space(sF0,X0)
| ~ subset_sets(f14(f13(a,cx,ct,f20(sF0,X0)),X1,X2,X3),cx)
| ~ element_of_set(X4,f13(a,cx,ct,f20(sF0,X0)))
| hausdorff(sF0,X0)
| element_of_set(X3,boundary(f13(a,cx,ct,f20(sF0,X0)),X1,X2)) ) ).
cnf(closure_58,axiom,
( ~ element_of_set(X0,f14(X1,X2,X3,X0))
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| element_of_set(X0,closure(X1,X2,X3)) ) ).
cnf(u3174,axiom,
( closed(f14(relative_complement_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7),X7,X8,X9),X7,X8)
| element_of_set(X10,interior(f14(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8,X9),X1,X2))
| ~ subset_sets(relative_complement_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7),X7)
| ~ subset_sets(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7)
| ~ topological_space(X7,X8)
| ~ closed(interior(X0,X1,X2),X4,X5)
| ~ topological_space(closure(X3,X4,X5),X6)
| hausdorff(closure(X3,X4,X5),X6)
| ~ subset_sets(f14(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8,X9),X1)
| ~ element_of_set(X10,f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)))
| ~ subset_sets(X3,interior(X0,X1,X2))
| element_of_set(X9,boundary(f13(X0,X1,X2,f20(closure(X3,X4,X5),X6)),X7,X8)) ) ).
cnf(u4008,axiom,
( ~ closed(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X9,X10)
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| element_of_set(f11(X7,boundary(X8,X9,X10)),interior(X4,X5,X6))
| element_of_collection(boundary(X8,X9,X10),top_of_basis(X7))
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X8,f13(X4,X5,X6,f20(closure(X0,X1,X2),X3))) ) ).
cnf(u4017,axiom,
( ~ closed(f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X8,X9)
| hausdorff(closure(X0,X1,X2),X3)
| ~ closed(interior(X4,X5,X6),X1,X2)
| ~ subset_sets(X0,interior(X4,X5,X6))
| element_of_set(f20(boundary(X7,X8,X9),X10),interior(X4,X5,X6))
| ~ topological_space(boundary(X7,X8,X9),X10)
| ~ subset_sets(X7,f13(X4,X5,X6,f20(closure(X0,X1,X2),X3)))
| ~ topological_space(closure(X0,X1,X2),X3)
| hausdorff(boundary(X7,X8,X9),X10) ) ).
cnf(u273,axiom,
( ~ element_of_collection(f12(X1,X2,X3,X0),X5)
| ~ topological_space(X4,X5)
| ~ subset_sets(X3,X4)
| ~ element_of_collection(X0,subspace_topology(X1,X2,X3))
| element_of_collection(X0,subspace_topology(X4,X5,X3)) ) ).
cnf(u28307,negated_conjecture,
( element_of_set(f11(X0,union_of_members(top_of_basis(X1))),f1(X2,f11(X0,union_of_members(top_of_basis(X1)))))
| element_of_set(f11(X1,union_of_members(ct)),interior(X3,X4,X5))
| element_of_set(X6,f1(top_of_basis(X0),X6))
| ~ element_of_set(X6,cx) ) ).
cnf(u6082,negated_conjecture,
( ~ closed(union_of_members(f24(X0,ct)),X3,X4)
| compact_space(X0,ct)
| element_of_set(f11(X1,boundary(X2,X3,X4)),union_of_members(ct))
| element_of_collection(boundary(X2,X3,X4),top_of_basis(X1))
| ~ topological_space(X0,ct)
| ~ subset_sets(X2,union_of_members(f24(X0,ct))) ) ).
cnf(u12952,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f1(ct,f11(X0,union_of_members(ct))))
| element_of_set(X1,f1(top_of_basis(X0),X1))
| ~ element_of_set(X1,cx) ) ).
cnf(u2940,axiom,
( element_of_set(f11(X0,boundary(X1,X2,X3)),f6(X6,X7,f11(X0,boundary(X1,X2,X3)),X4,X5))
| ~ closed(intersection_of_sets(X4,X5),X2,X3)
| ~ subset_sets(X1,intersection_of_sets(X4,X5))
| ~ element_of_set(f11(X0,boundary(X1,X2,X3)),X6)
| ~ element_of_collection(X4,X7)
| ~ element_of_collection(X5,X7)
| ~ basis(X6,X7)
| element_of_collection(boundary(X1,X2,X3),top_of_basis(X0)) ) ).
cnf(u2666,axiom,
( element_of_set(f11(X4,f17(X1,X3,X2,X0)),f17(X1,X3,X2,X0))
| element_of_set(X2,union_of_members(top_of_basis(X4)))
| ~ hausdorff(X1,X3)
| ~ element_of_set(X2,X1)
| eq_p(X2,X0)
| ~ element_of_set(X0,X1) ) ).
cnf(u3778,axiom,
( ~ subset_sets(X7,f14(X0,X1,X2,f11(X6,f14(closure(X0,X1,X2),X3,X4,X5))))
| ~ element_of_collection(closure(X0,X1,X2),X6)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| element_of_set(X5,closure(closure(X0,X1,X2),X3,X4))
| ~ subset_sets(closure(X0,X1,X2),X3)
| ~ topological_space(X3,X4)
| ~ subset_sets(X7,X1)
| element_of_collection(f14(closure(X0,X1,X2),X3,X4,X5),top_of_basis(X6))
| closed(f14(X7,X1,X2,X8),X1,X2)
| element_of_set(X8,f14(X0,X1,X2,f11(X6,f14(closure(X0,X1,X2),X3,X4,X5)))) ) ).
cnf(u5947,negated_conjecture,
( ~ element_of_collection(f13(a,X2,X3,f11(X4,interior(a,X2,X3))),X0)
| ~ element_of_set(X1,f13(a,X2,X3,f11(X4,interior(a,X2,X3))))
| ~ topological_space(sF0,X0)
| element_of_set(X1,interior(a,sF0,X0))
| element_of_collection(interior(a,X2,X3),top_of_basis(X4)) ) ).
cnf(u6329,axiom,
( ~ open(closure(X2,X3,X4),X0,X1)
| element_of_set(X5,f14(X2,X3,X4,f20(X0,X1)))
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4)
| ~ disjoint_s(X6,closure(X2,X3,X4))
| subset_sets(X2,f14(X2,X3,X4,X5))
| hausdorff(X0,X1)
| ~ open(X6,X0,X1)
| ~ element_of_set(f19(X0,X1),X6) ) ).
cnf(subspace_topology_43,axiom,
( ~ element_of_collection(X0,subspace_topology(X1,X2,X3))
| subset_sets(X3,X1) ) ).
cnf(u678,axiom,
( subset_sets(X0,f14(X0,X1,X2,f11(X3,closure(relative_complement_sets(X0,X1),X1,X2))))
| element_of_set(f11(X3,closure(relative_complement_sets(X0,X1),X1,X2)),boundary(X0,X1,X2))
| element_of_collection(closure(relative_complement_sets(X0,X1),X1,X2),top_of_basis(X3))
| ~ subset_sets(X0,X1) ) ).
cnf(u17785,negated_conjecture,
( eq_p(f19(intersection_of_members(X5),X6),f20(intersection_of_members(X3),X4))
| hausdorff(intersection_of_members(X5),X6)
| hausdorff(intersection_of_members(X3),X4) ) ).
cnf(u459,axiom,
( element_of_set(f7(boundary(X0,X1,X2),X3),closure(X0,X1,X2))
| ~ topological_space(boundary(X0,X1,X2),X3)
| basis(boundary(X0,X1,X2),X3) ) ).
cnf(u3228,axiom,
( ~ closed(f14(X4,X5,X6,f20(boundary(X0,X1,X2),X3)),X1,X2)
| ~ subset_sets(X0,f14(X4,X5,X6,f20(boundary(X0,X1,X2),X3)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| ~ topological_space(X5,X6)
| ~ subset_sets(X4,X5)
| element_of_set(f20(boundary(X0,X1,X2),X3),closure(X4,X5,X6)) ) ).
cnf(u4712,axiom,
( closed(f14(f13(f14(X0,X1,X2,X3),X4,X5,f20(interior(f14(X0,X1,X2,X3),X4,X5),X6)),X1,X2,X7),X1,X2)
| ~ subset_sets(f13(f14(X0,X1,X2,X3),X4,X5,f20(interior(f14(X0,X1,X2,X3),X4,X5),X6)),X1)
| element_of_set(X7,f14(X0,X1,X2,X3))
| element_of_set(X3,closure(X0,X1,X2))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| hausdorff(interior(f14(X0,X1,X2,X3),X4,X5),X6)
| ~ topological_space(interior(f14(X0,X1,X2,X3),X4,X5),X6) ) ).
cnf(u16263,negated_conjecture,
( element_of_set(f15(X1,X4,X2,X3,X0),f1(X5,f15(X1,X4,X2,X3,X0)))
| ~ limit_point(X1,X4,X2,X3)
| ~ neighborhood(X0,X1,X2,X3) ) ).
cnf(u3675,axiom,
( ~ closed(f2(X4,f7(closure(X0,X1,X2),X3)),X1,X2)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,f2(X4,f7(closure(X0,X1,X2),X3)))
| element_of_set(f7(closure(X0,X1,X2),X3),intersection_of_members(X4))
| basis(closure(X0,X1,X2),X3) ) ).
cnf(closure_55,axiom,
( ~ element_of_set(X0,closure(X1,X2,X3))
| ~ subset_sets(X1,X4)
| ~ closed(X4,X2,X3)
| element_of_set(X0,X4) ) ).
cnf(u5982,negated_conjecture,
( element_of_set(f11(X2,f14(a,cx,ct,X1)),f14(a,cx,ct,X1))
| element_of_set(X0,union_of_members(top_of_basis(X2)))
| element_of_set(X1,sF3)
| subset_sets(a,f14(a,cx,ct,X0)) ) ).
cnf(u737,axiom,
( ~ element_of_collection(f13(f13(a,cx,ct,X0),X1,X2,f19(interior(f13(a,cx,ct,X0),X1,X2),X3)),X4)
| ~ topological_space(a,X4)
| ~ element_of_set(X5,f13(f13(a,cx,ct,X0),X1,X2,f19(interior(f13(a,cx,ct,X0),X1,X2),X3)))
| ~ element_of_set(X0,sF0)
| element_of_set(X5,interior(f13(a,cx,ct,X0),a,X4))
| hausdorff(interior(f13(a,cx,ct,X0),X1,X2),X3)
| ~ topological_space(interior(f13(a,cx,ct,X0),X1,X2),X3) ) ).
cnf(u2822,axiom,
( element_of_set(f19(f8(X0,X1),X2),union_of_members(X1))
| basis(X0,X1)
| ~ topological_space(X0,X1)
| ~ topological_space(f8(X0,X1),X2)
| hausdorff(f8(X0,X1),X2) ) ).
cnf(u796,axiom,
( subset_sets(X0,f14(X0,X1,X2,f11(X3,f14(closure(X0,X1,X2),X4,X5,X6))))
| element_of_collection(f14(closure(X0,X1,X2),X4,X5,X6),top_of_basis(X3))
| ~ element_of_collection(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| element_of_set(X6,closure(closure(X0,X1,X2),X4,X5))
| ~ subset_sets(closure(X0,X1,X2),X4)
| ~ topological_space(X4,X5) ) ).
cnf(u3510,axiom,
( element_of_set(f7(closure(X0,X1,X2),X3),closure(X4,X5,X6))
| ~ subset_sets(X0,boundary(X4,X5,X6))
| ~ closed(boundary(X4,X5,X6),X1,X2)
| basis(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3) ) ).
cnf(u3285,negated_conjecture,
( element_of_set(f20(f13(a,cx,ct,f19(sF0,X0)),X1),union_of_members(top_of_basis(X2)))
| hausdorff(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f19(sF0,X0)),X1)
| hausdorff(f13(a,cx,ct,f19(sF0,X0)),X1)
| element_of_set(f11(X2,sF0),sF0)
| ~ topological_space(sF0,X0) ) ).
cnf(u36139,negated_conjecture,
( element_of_set(X0,f10(X1,f1(top_of_basis(X1),X0),X0))
| limit_point(X0,X2,X3,top_of_basis(X1))
| element_of_set(f11(X1,f1(ct,X0)),interior(X4,X5,X6)) ) ).
cnf(u3461,negated_conjecture,
( ~ closed(f1(ct,X4),X1,X2)
| ~ subset_sets(X0,f1(ct,X4))
| ~ topological_space(closure(X0,X1,X2),X3)
| basis(closure(X0,X1,X2),X3)
| ~ element_of_set(X4,cx)
| element_of_set(f7(closure(X0,X1,X2),X3),union_of_members(ct)) ) ).
cnf(u2751,axiom,
( ~ closed(closure(relative_complement_sets(X1,X2),X2,X3),X4,X5)
| ~ subset_sets(X0,closure(relative_complement_sets(X1,X2),X2,X3))
| ~ topological_space(closure(X0,X4,X5),X6)
| hausdorff(closure(X0,X4,X5),X6)
| element_of_set(f20(closure(X0,X4,X5),X6),boundary(X1,X2,X3))
| subset_sets(X1,f14(X1,X2,X3,f20(closure(X0,X4,X5),X6)))
| ~ subset_sets(X1,X2) ) ).
cnf(u3213,negated_conjecture,
( ~ closed(f13(a,cx,ct,f19(sF0,X4)),X1,X2)
| ~ subset_sets(X0,f13(a,cx,ct,f19(sF0,X4)))
| ~ topological_space(boundary(X0,X1,X2),X3)
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f20(boundary(X0,X1,X2),X3),sF0)
| ~ topological_space(sF0,X4)
| hausdorff(sF0,X4) ) ).
cnf(u27750,negated_conjecture,
( open(f13(X2,X3,X4,f11(X0,union_of_members(top_of_basis(X1)))),X3,X4)
| element_of_set(f11(X1,union_of_members(ct)),interior(X5,X6,X7))
| element_of_set(X8,f1(top_of_basis(X0),X8))
| ~ element_of_set(X8,cx) ) ).
cnf(u1101,axiom,
( ~ closed(f13(closure(X1,X2,X3),X4,X5,f19(closure(X0,X6,X7),X8)),X2,X3)
| ~ closed(interior(closure(X1,X2,X3),X4,X5),X6,X7)
| ~ topological_space(closure(X0,X6,X7),X8)
| hausdorff(closure(X0,X6,X7),X8)
| ~ subset_sets(X0,interior(closure(X1,X2,X3),X4,X5))
| ~ subset_sets(X1,f13(closure(X1,X2,X3),X4,X5,f19(closure(X0,X6,X7),X8)))
| ~ element_of_collection(f13(closure(X1,X2,X3),X4,X5,f19(closure(X0,X6,X7),X8)),X9)
| element_of_collection(closure(X1,X2,X3),top_of_basis(X9)) ) ).
cnf(u9283,negated_conjecture,
( ~ hausdorff(X1,X3)
| ~ element_of_set(X2,X1)
| eq_p(X0,X2)
| ~ element_of_set(X0,X1) ) ).
cnf(u4643,negated_conjecture,
( ~ element_of_collection(f13(a,cx,ct,f11(X2,sF0)),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),sF0)
| element_of_collection(sF0,top_of_basis(X2)) ) ).
cnf(u326,negated_conjecture,
( element_of_set(f19(f1(ct,X0),X1),union_of_members(ct))
| ~ element_of_set(X0,cx)
| ~ topological_space(f1(ct,X0),X1)
| hausdorff(f1(ct,X0),X1) ) ).
cnf(u4889,axiom,
( basis(boundary(X0,X1,X2),f24(boundary(X0,X1,X2),X3))
| ~ topological_space(boundary(X0,X1,X2),X3)
| compact_space(boundary(X0,X1,X2),X3)
| topological_space(X1,X2) ) ).
cnf(u1212,negated_conjecture,
( ~ subset_sets(f14(a,cx,ct,f11(X0,X1)),sF3)
| element_of_collection(X1,top_of_basis(X0))
| ~ subset_sets(sF3,X1)
| ~ element_of_collection(sF3,X0)
| ~ element_of_collection(f14(a,cx,ct,f11(X0,X1)),X2)
| element_of_collection(sF3,top_of_basis(X2)) ) ).
cnf(u726,axiom,
( ~ subset_sets(relative_complement_sets(X0,X1),X3)
| ~ subset_sets(X3,X1)
| ~ element_of_set(X4,relative_complement_sets(X0,X1))
| ~ closed(X0,X1,X2)
| element_of_set(X4,interior(X3,X1,X2)) ) ).
cnf(u157,axiom,
( ~ subset_sets(X3,X0)
| ~ element_of_collection(X2,X1)
| ~ topological_space(X0,X1)
| ~ element_of_set(X4,X2)
| ~ subset_sets(X2,X3)
| element_of_set(X4,interior(X3,X0,X1)) ) ).
cnf(u18806,negated_conjecture,
( element_of_set(f11(X0,f1(ct,X1)),f13(X2,X3,X4,f11(X0,f1(ct,X1))))
| ~ element_of_set(X1,cx)
| element_of_set(X1,f1(top_of_basis(X0),X1)) ) ).
cnf(u3385,axiom,
( element_of_set(X7,f10(X3,f12(X2,top_of_basis(X3),X4,f16(X5,X0,X1,subspace_topology(X6,top_of_basis(X3),X4))),X7))
| ~ topological_space(X2,top_of_basis(X3))
| ~ subset_sets(X4,X2)
| limit_point(X5,X0,X1,subspace_topology(X6,top_of_basis(X3),X4))
| ~ topological_space(X1,subspace_topology(X6,top_of_basis(X3),X4))
| ~ element_of_set(X7,f12(X2,top_of_basis(X3),X4,f16(X5,X0,X1,subspace_topology(X6,top_of_basis(X3),X4))))
| ~ subset_sets(X0,X1) ) ).
cnf(u4453,axiom,
( ~ element_of_set(X4,f9(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3))
| ~ element_of_collection(union_of_members(X3),subspace_topology(X1,X2,X0))
| basis(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(X3))),X3)
| element_of_set(X4,union_of_members(X3)) ) ).
cnf(u5119,negated_conjecture,
( element_of_set(f11(X1,f14(a,cx,ct,X2)),f14(a,cx,ct,X2))
| element_of_set(X0,f1(top_of_basis(X1),X0))
| element_of_set(X2,sF3)
| ~ element_of_set(X0,sF3) ) ).
cnf(u748,axiom,
( ~ element_of_set(X1,f13(a,cx,ct,f19(sF0,X0)))
| hausdorff(sF0,X0)
| ~ topological_space(sF0,X0)
| element_of_set(X1,union_of_members(ct)) ) ).
cnf(u6220,negated_conjecture,
( ~ element_of_set(X0,f13(a,cx,ct,f7(sF0,X1)))
| ~ topological_space(sF0,top_of_basis(X2))
| element_of_set(X0,interior(a,sF0,top_of_basis(X2)))
| basis(sF0,X1)
| ~ topological_space(sF0,X1)
| element_of_set(f11(X2,f13(a,cx,ct,f7(sF0,X1))),sF0) ) ).
cnf(u1063,axiom,
( ~ topological_space(closure(X0,X1,X2),X3)
| ~ subset_sets(X0,intersection_of_members(X4))
| ~ closed(intersection_of_members(X4),X1,X2)
| hausdorff(closure(X0,X1,X2),X3)
| ~ element_of_collection(X5,X4)
| element_of_set(f19(closure(X0,X1,X2),X3),X5) ) ).
cnf(u285,axiom,
( ~ disjoint_s(X2,f16(f20(X0,X1),X3,X0,X1))
| hausdorff(X0,X1)
| ~ neighborhood(X2,f19(X0,X1),X0,X1)
| ~ subset_sets(X3,X0)
| limit_point(f20(X0,X1),X3,X0,X1) ) ).
cnf(u951,axiom,
( ~ closed(f14(X4,X5,X6,f20(closure(X0,X1,X2),X3)),X1,X2)
| ~ subset_sets(X0,f14(X4,X5,X6,f20(closure(X0,X1,X2),X3)))
| hausdorff(closure(X0,X1,X2),X3)
| ~ topological_space(closure(X0,X1,X2),X3)
| ~ topological_space(X5,X6)
| ~ subset_sets(X4,X5)
| element_of_set(f20(closure(X0,X1,X2),X3),closure(X4,X5,X6)) ) ).
cnf(u6592,negated_conjecture,
( element_of_set(f11(X2,sF3),f14(a,cx,ct,X0))
| element_of_set(X0,f14(a,cx,ct,X1))
| element_of_set(X1,sF3)
| element_of_collection(sF3,top_of_basis(X2)) ) ).
cnf(u1197,axiom,
( subset_sets(X0,f14(X0,X1,X2,f19(boundary(relative_complement_sets(X0,X1),X1,X2),X3)))
| element_of_set(f19(boundary(relative_complement_sets(X0,X1),X1,X2),X3),boundary(X0,X1,X2))
| hausdorff(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ topological_space(boundary(relative_complement_sets(X0,X1),X1,X2),X3)
| ~ subset_sets(X0,X1) ) ).
cnf(u6913,negated_conjecture,
( element_of_set(f19(boundary(X0,X1,X2),X3),interior(X4,X5,X6))
| hausdorff(boundary(X0,X1,X2),X3) ) ).
cnf(u27927,negated_conjecture,
( element_of_set(f11(X0,union_of_members(ct)),f13(X1,X2,X3,f11(X0,union_of_members(ct))))
| open(f13(X4,X5,X6,f11(X7,union_of_members(top_of_basis(X0)))),X5,X6)
| element_of_set(X8,f1(top_of_basis(X7),X8))
| ~ element_of_set(X8,cx) ) ).
cnf(u406,negated_conjecture,
( element_of_set(f20(f13(a,cx,ct,f19(sF0,X0)),X1),sF0)
| ~ topological_space(sF0,X0)
| hausdorff(sF0,X0)
| ~ topological_space(f13(a,cx,ct,f19(sF0,X0)),X1)
| hausdorff(f13(a,cx,ct,f19(sF0,X0)),X1) ) ).
cnf(u4441,axiom,
( element_of_collection(f12(X3,X4,X5,f8(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(subspace_topology(X3,X4,X5)))),subspace_topology(X3,X4,X5))),X4)
| ~ element_of_collection(union_of_members(subspace_topology(X3,X4,X5)),subspace_topology(X1,X2,X0))
| basis(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(subspace_topology(X3,X4,X5)))),subspace_topology(X3,X4,X5)) ) ).
cnf(u6277,axiom,
( ~ open(f10(X3,closure(X0,X1,X2),f20(X4,X5)),X4,X5)
| ~ closed(sF1,X1,X2)
| ~ element_of_collection(sF3,X3)
| ~ element_of_set(f20(X4,X5),closure(X0,X1,X2))
| ~ subset_sets(X0,sF1)
| ~ disjoint_s(X6,f10(X3,closure(X0,X1,X2),f20(X4,X5)))
| ~ subset_sets(sF3,closure(X0,X1,X2))
| hausdorff(X4,X5)
| ~ open(X6,X4,X5)
| ~ element_of_set(f19(X4,X5),X6) ) ).
cnf(u6902,negated_conjecture,
( element_of_set(f20(sF0,X0),interior(X1,X2,X3))
| hausdorff(sF0,X0) ) ).
cnf(u4615,axiom,
( ~ element_of_collection(f1(ct,X2),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| ~ element_of_set(X2,sF0)
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(ct)) ) ).
cnf(u1325,axiom,
( element_of_set(f11(X0,closure(X1,X2,X3)),closure(X1,X2,X3))
| closed(f14(X1,X2,X3,X4),X2,X3)
| element_of_set(X4,union_of_members(top_of_basis(X0)))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ) ).
cnf(u4456,axiom,
( ~ element_of_set(X6,f9(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(top_of_basis(subspace_topology(X3,X4,X5))))),top_of_basis(subspace_topology(X3,X4,X5))))
| ~ element_of_collection(union_of_members(top_of_basis(subspace_topology(X3,X4,X5))),subspace_topology(X1,X2,X0))
| basis(intersection_of_sets(X0,f12(X1,X2,X0,union_of_members(top_of_basis(subspace_topology(X3,X4,X5))))),top_of_basis(subspace_topology(X3,X4,X5)))
| topological_space(X3,X4) ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n006.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 18:48:55 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.98/2.39 % (51953)Input is clausal, will run a generic CNF schedule.
% 11.98/2.39 % (51961)lrs+10_1_sil=8000:sp=occurrence:random_seed=381498778:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 11.98/2.39 % (51961)Instruction limit reached!
% 11.98/2.39 % (51961)------------------------------
% 11.98/2.39 % (51961)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.98/2.39 % (51961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.98/2.39 % (51961)CaDiCaL version: 2.1.3
% 11.98/2.39 % (51961)Termination reason: Instruction limit
% 11.98/2.39 % (51961)Termination phase: Saturation
% 11.98/2.39 % (51961)Time elapsed: 0.036 s
% 11.98/2.39 % (51961)Peak memory usage: 88 MB
% 11.98/2.39 % (51961)Instructions burned: 107 (million)
% 11.98/2.39 % (51962)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1742872564:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 11.98/2.39 % (51958)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3467319746:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 11.98/2.39 % (51960)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1029738663:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 11.98/2.39 % (51964)dis-21_1_sil=8000:lcm=predicate:random_seed=575146196:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 11.98/2.39 % (51959)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1213106522:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 11.98/2.39 % (51963)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=570760068:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 11.98/2.39 % (51963)Refutation not found, incomplete strategy
% 11.98/2.39 % (51963)------------------------------
% 11.98/2.39 % (51963)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.98/2.39 % (51963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.98/2.39 % (51963)CaDiCaL version: 2.1.3
% 11.98/2.39 % (51963)Termination reason: Refutation not found, incomplete strategy
% 11.98/2.39 % (51963)Time elapsed: 0.005 s
% 11.98/2.39 % (51963)Peak memory usage: 87 MB
% 11.98/2.39 % (51963)Instructions burned: 8 (million)
% 11.98/2.39 % (51962)Instruction limit reached!
% 11.98/2.39 % (51962)------------------------------
% 11.98/2.39 % (51962)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.98/2.39 % (51962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.98/2.39 % (51962)CaDiCaL version: 2.1.3
% 11.98/2.39 % (51962)Termination reason: Instruction limit
% 11.98/2.39 % (51962)Termination phase: Saturation
% 11.98/2.39 % (51962)Time elapsed: 0.064 s
% 11.98/2.39 % (51962)Peak memory usage: 87 MB
% 11.98/2.39 % (51962)Instructions burned: 114 (million)
% 11.98/2.39 % (51964)Instruction limit reached!
% 11.98/2.39 % (51964)------------------------------
% 11.98/2.39 % (51964)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.98/2.39 % (51964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.98/2.39 % (51964)CaDiCaL version: 2.1.3
% 11.98/2.39 % (51964)Termination reason: Instruction limit
% 11.98/2.39 % (51964)Termination phase: Saturation
% 11.98/2.39 % (51964)Time elapsed: 0.067 s
% 11.98/2.39 % (51964)Peak memory usage: 88 MB
% 11.98/2.39 % (51964)Instructions burned: 118 (million)
% 11.98/2.39 % (51966)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2441801227:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 11.98/2.39 % (51966)Refutation not found, incomplete strategy
% 11.98/2.39 % (51966)------------------------------
% 11.98/2.39 % (51966)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.98/2.39 % (51966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.98/2.39 % (51966)CaDiCaL version: 2.1.3
% 11.98/2.39 % (51966)Termination reason: Refutation not found, incomplete strategy
% 11.98/2.39 % (51966)Time elapsed: 0.001 s
% 11.98/2.39 % (51966)Peak memory usage: 87 MB
% 11.98/2.39 % (51966)Instructions burned: 1 (million)
% 11.98/2.39 % (51973)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1569463132:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 17.89/3.14 % (51974)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=4009566928:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 17.89/3.14 % (51974)Refutation not found, incomplete strategy
% 17.89/3.14 % (51974)------------------------------
% 17.89/3.14 % (51974)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.89/3.14 % (51974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.89/3.14 % (51974)CaDiCaL version: 2.1.3
% 17.89/3.14 % (51974)Termination reason: Refutation not found, incomplete strategy
% 17.89/3.14 % (51974)Time elapsed: 0.003 s
% 17.89/3.14 % (51974)Peak memory usage: 87 MB
% 17.89/3.14 % (51974)Instructions burned: 3 (million)
% 17.89/3.14 % (51963)------------------------------
% 17.89/3.14 % (51963)------------------------------
% 17.89/3.14 % (51966)------------------------------
% 17.89/3.14 % (51966)------------------------------
% 17.89/3.14 % (51973)Instruction limit reached!
% 17.89/3.14 % (51973)------------------------------
% 17.89/3.14 % (51973)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.89/3.14 % (51973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.89/3.14 % (51973)CaDiCaL version: 2.1.3
% 17.89/3.14 % (51973)Termination reason: Instruction limit
% 17.89/3.14 % (51973)Termination phase: Saturation
% 17.89/3.14 % (51973)Time elapsed: 0.095 s
% 17.89/3.14 % (51973)Peak memory usage: 92 MB
% 17.89/3.14 % (51973)Instructions burned: 189 (million)
% 17.89/3.14 % (51979)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=376014477:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 17.89/3.14 % (51979)Refutation not found, incomplete strategy
% 17.89/3.14 % (51979)------------------------------
% 17.89/3.14 % (51979)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.89/3.14 % (51979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.89/3.14 % (51979)CaDiCaL version: 2.1.3
% 17.89/3.14 % (51979)Termination reason: Refutation not found, incomplete strategy
% 17.89/3.14 % (51979)Time elapsed: 0.002 s
% 17.89/3.14 % (51979)Peak memory usage: 87 MB
% 17.89/3.14 % (51979)Instructions burned: 5 (million)
% 17.89/3.14 % (51978)lrs+10_64_to=lpo:sil=8000:random_seed=3888492873:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 17.89/3.14 % (51978)Instruction limit reached!
% 17.89/3.14 % (51978)------------------------------
% 17.89/3.14 % (51978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.89/3.14 % (51978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.89/3.14 % (51978)CaDiCaL version: 2.1.3
% 17.89/3.14 % (51978)Termination reason: Instruction limit
% 17.89/3.14 % (51978)Termination phase: Saturation
% 17.89/3.14 % (51978)Time elapsed: 0.069 s
% 17.89/3.14 % (51978)Peak memory usage: 87 MB
% 17.89/3.14 % (51978)Instructions burned: 127 (million)
% 17.89/3.14 % (51974)------------------------------
% 17.89/3.14 % (51974)------------------------------
% 17.89/3.14 % (51980)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1199851198:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 17.89/3.14 % (51979)------------------------------
% 17.89/3.14 % (51979)------------------------------
% 17.89/3.14 % (51980)Instruction limit reached!
% 17.89/3.14 % (51980)------------------------------
% 17.89/3.14 % (51980)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.89/3.14 % (51980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.89/3.14 % (51980)CaDiCaL version: 2.1.3
% 17.89/3.14 % (51980)Termination reason: Instruction limit
% 17.89/3.14 % (51980)Termination phase: Saturation
% 17.89/3.14 % (51980)Time elapsed: 0.107 s
% 17.89/3.14 % (51980)Peak memory usage: 90 MB
% 17.89/3.14 % (51980)Instructions burned: 157 (million)
% 17.89/3.14 % (51983)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1352394942:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 17.89/3.14 % (51985)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=2008073628:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 17.89/3.14 % (51986)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=586270643:i=107_2992 on theBenchmark for (2992ds/107Mi)
% 17.89/3.14 % (51986)Instruction limit reached!
% 17.89/3.14 % (51986)------------------------------
% 24.27/4.07 % (51986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/4.07 % (51986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/4.07 % (51986)CaDiCaL version: 2.1.3
% 24.27/4.07 % (51986)Termination reason: Instruction limit
% 24.27/4.07 % (51986)Termination phase: Saturation
% 24.27/4.07 % (51986)Time elapsed: 0.032 s
% 24.27/4.07 % (51986)Peak memory usage: 88 MB
% 24.27/4.07 % (51986)Instructions burned: 108 (million)
% 24.27/4.07 % (51985)Instruction limit reached!
% 24.27/4.07 % (51985)------------------------------
% 24.27/4.07 % (51985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/4.07 % (51985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/4.07 % (51985)CaDiCaL version: 2.1.3
% 24.27/4.07 % (51985)Termination reason: Instruction limit
% 24.27/4.07 % (51985)Termination phase: Saturation
% 24.27/4.07 % (51985)Time elapsed: 0.053 s
% 24.27/4.07 % (51985)Peak memory usage: 89 MB
% 24.27/4.07 % (51985)Instructions burned: 107 (million)
% 24.27/4.07 % (51987)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=2236556204:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2992 on theBenchmark for (2992ds/242Mi)
% 24.27/4.07 % (51987)Refutation not found, incomplete strategy
% 24.27/4.07 % (51987)------------------------------
% 24.27/4.07 % (51987)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/4.07 % (51987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/4.07 % (51987)CaDiCaL version: 2.1.3
% 24.27/4.07 % (51987)Termination reason: Refutation not found, incomplete strategy
% 24.27/4.07 % (51987)Time elapsed: 0.007 s
% 24.27/4.07 % (51987)Peak memory usage: 88 MB
% 24.27/4.07 % (51987)Instructions burned: 11 (million)
% 24.27/4.07 % (51991)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=2713786101:cond=fast:i=5208:av=off_2991 on theBenchmark for (2991ds/5208Mi)
% 24.27/4.07 % (51992)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=500079836:i=134:sd=2:doe=on:ss=axioms:sgt=14_2991 on theBenchmark for (2991ds/134Mi)
% 24.27/4.07 % (51992)Refutation not found, incomplete strategy
% 24.27/4.07 % (51992)------------------------------
% 24.27/4.07 % (51992)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/4.07 % (51992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/4.07 % (51992)CaDiCaL version: 2.1.3
% 24.27/4.07 % (51992)Termination reason: Refutation not found, incomplete strategy
% 24.27/4.07 % (51992)Time elapsed: 0.004 s
% 24.27/4.07 % (51992)Peak memory usage: 88 MB
% 24.27/4.07 % (51992)Instructions burned: 5 (million)
% 24.27/4.07 % (51987)------------------------------
% 24.27/4.07 % (51987)------------------------------
% 24.27/4.07 % (51992)------------------------------
% 24.27/4.07 % (51992)------------------------------
% 24.27/4.07 % (51996)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=2756882221:i=499:bd=all_2988 on theBenchmark for (2988ds/499Mi)
% 24.27/4.07 % (51997)lrs+10_64_to=lpo:sil=8000:prc=on:sp=reverse_frequency:nwc=5:alpa=false:flr=on:random_seed=397912869:i=191:fgj=on:bd=all_2987 on theBenchmark for (2987ds/191Mi)
% 24.27/4.07 % (51997)Instruction limit reached!
% 24.27/4.07 % (51997)------------------------------
% 24.27/4.07 % (51997)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/4.07 % (51997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/4.07 % (51997)CaDiCaL version: 2.1.3
% 24.27/4.07 % (51997)Termination reason: Instruction limit
% 24.27/4.07 % (51997)Termination phase: Saturation
% 24.27/4.07 % (51997)Time elapsed: 0.111 s
% 24.27/4.07 % (51997)Peak memory usage: 90 MB
% 24.27/4.07 % (51997)Instructions burned: 191 (million)
% 24.27/4.07 % (51996)Instruction limit reached!
% 24.27/4.07 % (51996)------------------------------
% 24.27/4.07 % (51996)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/4.07 % (51996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/4.07 % (51996)CaDiCaL version: 2.1.3
% 24.27/4.07 % (51996)Termination reason: Instruction limit
% 24.27/4.07 % (51996)Termination phase: Saturation
% 24.27/4.07 % (51996)Time elapsed: 0.295 s
% 24.27/4.07 % (51996)Peak memory usage: 96 MB
% 24.27/4.07 % (51996)Instructions burned: 500 (million)
% 24.27/4.07 % (52000)lrs-11_32_anc=all:sil=8000:spb=goal_then_units:sac=on:random_seed=1562027145:i=264:kws=precedence:fsr=off_2984 on theBenchmark for (2984ds/264Mi)
% 32.50/5.36 % (52001)lrs-22_64_to=lpo:sil=8000:sp=const_frequency:urr=ec_only:nwc=4:flr=on:random_seed=635327761:cond=on:i=156:bs=on:gtg=exists_all:er=known_2983 on theBenchmark for (2983ds/156Mi)
% 32.50/5.36 % (52001)Refutation not found, incomplete strategy
% 32.50/5.36 % (52001)------------------------------
% 32.50/5.36 % (52001)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.50/5.36 % (52001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.50/5.36 % (52001)CaDiCaL version: 2.1.3
% 32.50/5.36 % (52001)Termination reason: Refutation not found, incomplete strategy
% 32.50/5.36 % (52001)Time elapsed: 0.006 s
% 32.50/5.36 % (52001)Peak memory usage: 88 MB
% 32.50/5.36 % (52001)Instructions burned: 9 (million)
% 32.50/5.36 % (52000)Instruction limit reached!
% 32.50/5.36 % (52000)------------------------------
% 32.50/5.36 % (52000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.50/5.36 % (52000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.50/5.36 % (52000)CaDiCaL version: 2.1.3
% 32.50/5.36 % (52000)Termination reason: Instruction limit
% 32.50/5.36 % (52000)Termination phase: Saturation
% 32.50/5.36 % (52000)Time elapsed: 0.147 s
% 32.50/5.36 % (52000)Peak memory usage: 90 MB
% 32.50/5.36 % (52000)Instructions burned: 264 (million)
% 32.50/5.36 % (52001)------------------------------
% 32.50/5.36 % (52001)------------------------------
% 32.50/5.36 % (52004)lrs-1010_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:sp=reverse_frequency:spb=units:lcm=predicate:urr=on:s2agt=8:updr=off:random_seed=604155160:i=3256:kws=precedence:bd=preordered:av=off_2981 on theBenchmark for (2981ds/3256Mi)
% 32.50/5.36 % (51960)Refutation not found, incomplete strategy
% 32.50/5.36 % (51960)------------------------------
% 32.50/5.36 % (51960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.50/5.36 % (51960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.50/5.36 % (51960)CaDiCaL version: 2.1.3
% 32.50/5.36 % (51960)Termination reason: Refutation not found, incomplete strategy
% 32.50/5.36 % (51960)Time elapsed: 1.901 s
% 32.50/5.36 % (51960)Peak memory usage: 143 MB
% 32.50/5.36 % (51960)Instructions burned: 2807 (million)
% 32.50/5.36 % (51983)Instruction limit reached!
% 32.50/5.36 % (51983)------------------------------
% 32.50/5.36 % (51983)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.50/5.36 % (51983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.50/5.36 % (51983)CaDiCaL version: 2.1.3
% 32.50/5.36 % (51983)Termination reason: Instruction limit
% 32.50/5.36 % (51983)Termination phase: Saturation
% 32.50/5.36 % (51983)Time elapsed: 1.389 s
% 32.50/5.36 % (51983)Peak memory usage: 149 MB
% 32.50/5.36 % (51983)Instructions burned: 3396 (million)
% 32.50/5.36 % (52005)dis+1003_128_sil=8000:tgt=full:fd=off:random_seed=3121024425:i=537:av=off:ss=included_2979 on theBenchmark for (2979ds/537Mi)
% 32.50/5.36 % (51960)------------------------------
% 32.50/5.36 % (51960)------------------------------
% 32.50/5.36 % (52007)ott+1010_32_to=lpo:sil=8000:urr=on:nwc=4:random_seed=3839913578:i=180:bd=preordered:av=off_2978 on theBenchmark for (2978ds/180Mi)
% 32.50/5.36 % (52007)Instruction limit reached!
% 32.50/5.36 % (52007)------------------------------
% 32.50/5.36 % (52007)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.50/5.36 % (52007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.50/5.36 % (52007)CaDiCaL version: 2.1.3
% 32.50/5.36 % (52007)Termination reason: Instruction limit
% 32.50/5.36 % (52007)Termination phase: Saturation
% 32.50/5.36 % (52007)Time elapsed: 0.047 s
% 32.50/5.36 % (52007)Peak memory usage: 91 MB
% 32.50/5.36 % (52007)Instructions burned: 180 (million)
% 32.50/5.36 % (52005)Instruction limit reached!
% 32.50/5.36 % (52005)------------------------------
% 32.50/5.36 % (52005)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.50/5.36 % (52005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.50/5.36 % (52005)CaDiCaL version: 2.1.3
% 32.50/5.36 % (52005)Termination reason: Instruction limit
% 32.50/5.36 % (52005)Termination phase: Saturation
% 32.50/5.36 % (52005)Time elapsed: 0.238 s
% 32.50/5.36 % (52005)Peak memory usage: 89 MB
% 32.50/5.36 % (52005)Instructions burned: 540 (million)
% 32.50/5.36 % (52011)lrs-1010_1024_to=lpo:sil=8000:tgt=ground:plsq=on:plsqc=1:sas=cadical:plsqr=1,32:sp=arity:lma=off:spb=goal:acc=on:bce=on:nwc=1.2:alpa=false:random_seed=2217749937:i=412:gtgl=4:gtg=exists_all_2976 on theBenchmark for (2976ds/412Mi)
% 49.52/7.76 % (52010)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:sas=cadical:sp=reverse_frequency:bsr=on:alpa=false:sac=on:random_seed=4204673553:i=10307:s2at=3:bs=on:bd=preordered:fsd=on_2976 on theBenchmark for (2976ds/10307Mi)
% 49.52/7.76 % (52011)Instruction limit reached!
% 49.52/7.76 % (52011)------------------------------
% 49.52/7.76 % (52011)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 49.52/7.76 % (52011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 49.52/7.76 % (52011)CaDiCaL version: 2.1.3
% 49.52/7.76 % (52011)Termination reason: Instruction limit
% 49.52/7.76 % (52011)Termination phase: Saturation
% 49.52/7.76 % (52011)Time elapsed: 0.092 s
% 49.52/7.76 % (52011)Peak memory usage: 90 MB
% 49.52/7.76 % (52011)Instructions burned: 416 (million)
% 49.52/7.76 % (52012)ott+1002_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:etr=on:spb=units:urr=on:bsr=unit_only:gs=on:s2agt=16:br=off:random_seed=2955181199:s2pl=no:i=8478:s2at=4:nm=6_2975 on theBenchmark for (2975ds/8478Mi)
% 49.52/7.76 % (52015)ott-1011_2_sil=32000:bsd=on:sp=reverse_frequency:erd=off:urr=on:rnwc=on:gs=on:s2agt=70:updr=off:lftc=20:random_seed=1984042813:s2a=on:i=303:s2at=2:sd=1:kws=inv_arity:bs=on:ins=10:fdi=1024:sup=off:ss=included_2974 on theBenchmark for (2974ds/303Mi)
% 49.52/7.76 % (52015)Refutation not found, incomplete strategy
% 49.52/7.76 % (52015)------------------------------
% 49.52/7.76 % (52015)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 49.52/7.76 % (52015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 49.52/7.76 % (52015)CaDiCaL version: 2.1.3
% 49.52/7.76 % (52015)Termination reason: Refutation not found, incomplete strategy
% 49.52/7.76 % (52015)Time elapsed: 0.001 s
% 49.52/7.76 % (52015)Peak memory usage: 88 MB
% 49.52/7.76 % (52015)Instructions burned: 1 (million)
% 49.52/7.76 % (52015)------------------------------
% 49.52/7.76 % (52015)------------------------------
% 49.52/7.76 % (52018)lrs+10_1_to=lpo:sil=16000:fde=none:sos=on:urr=on:bsr=on:random_seed=2061627807:st=4:i=720:sd=3:fsr=off:ss=axioms_2971 on theBenchmark for (2971ds/720Mi)
% 49.52/7.76 % (51958)Refutation not found, incomplete strategy
% 49.52/7.76 % (51958)------------------------------
% 49.52/7.76 % (51958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 49.52/7.76 % (51958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 49.52/7.76 % (51958)CaDiCaL version: 2.1.3
% 49.52/7.76 % (51958)Termination reason: Refutation not found, incomplete strategy
% 49.52/7.76 % (51958)Time elapsed: 2.817 s
% 49.52/7.76 % (51958)Peak memory usage: 154 MB
% 49.52/7.76 % (51958)Instructions burned: 4179 (million)
% 49.52/7.76 % (52018)Instruction limit reached!
% 49.52/7.76 % (52018)------------------------------
% 49.52/7.76 % (52018)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 49.52/7.76 % (52018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 49.52/7.76 % (52018)CaDiCaL version: 2.1.3
% 49.52/7.76 % (52018)Termination reason: Instruction limit
% 49.52/7.76 % (52018)Termination phase: Saturation
% 49.52/7.76 % (52018)Time elapsed: 0.200 s
% 49.52/7.76 % (52018)Peak memory usage: 103 MB
% 49.52/7.76 % (52018)Instructions burned: 722 (million)
% 49.52/7.76 % (51991)Instruction limit reached!
% 49.52/7.76 % (51991)------------------------------
% 49.52/7.76 % (51991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 49.52/7.76 % (51991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 49.52/7.76 % (51991)CaDiCaL version: 2.1.3
% 49.52/7.76 % (51991)Termination reason: Instruction limit
% 49.52/7.76 % (51991)Termination phase: Saturation
% 49.52/7.76 % (51991)Time elapsed: 2.235 s
% 49.52/7.76 % (51991)Peak memory usage: 140 MB
% 49.52/7.76 % (51991)Instructions burned: 5209 (million)
% 49.52/7.76 % (51958)------------------------------
% 49.52/7.76 % (51958)------------------------------
% 49.52/7.76 % (52020)lrs-20_1_to=lpo:sil=32000:tgt=ground:sp=reverse_frequency:spb=goal:urr=on:bsr=unit_only:nwc=1.5:random_seed=1513179331:i=598:bs=on:bd=preordered:av=off:ss=axioms_2968 on theBenchmark for (2968ds/598Mi)
% 49.52/7.76 % (52021)dis-1010_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:sp=occurrence:random_seed=3564986470:i=2989:sd=3:ss=axioms:sgt=60_2967 on theBenchmark for (2967ds/2989Mi)
% 49.52/7.76 % (52022)dis+1011_1_ncem=casc2026/models/loop5.pt:sil=8000:tgt=full:npcc=on:bsd=on:sp=const_min:spb=goal_then_units:lcm=predicate:urr=ec_only:s2agt=16:random_seed=50723471:i=1997:bd=preordered:av=off:gtg=all:gsp=on_2967 on theBenchmark for (2967ds/1997Mi)
% 67.57/10.29 % (52020)Instruction limit reached!
% 67.57/10.29 % (52020)------------------------------
% 67.57/10.29 % (52020)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 67.57/10.29 % (52020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 67.57/10.29 % (52020)CaDiCaL version: 2.1.3
% 67.57/10.29 % (52020)Termination reason: Instruction limit
% 67.57/10.29 % (52020)Termination phase: Saturation
% 67.57/10.29 % (52020)Time elapsed: 0.178 s
% 67.57/10.29 % (52020)Peak memory usage: 90 MB
% 67.57/10.29 % (52020)Instructions burned: 600 (million)
% 67.57/10.29 % (52026)lrs-1010_1_to=lpo:ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:drc=off:sp=unary_frequency:urr=ec_only:fd=preordered:random_seed=285263775:i=2088:bd=preordered:av=off_2965 on theBenchmark for (2965ds/2088Mi)
% 67.57/10.29 % (52004)Instruction limit reached!
% 67.57/10.29 % (52004)------------------------------
% 67.57/10.29 % (52004)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 67.57/10.29 % (52004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 67.57/10.29 % (52004)CaDiCaL version: 2.1.3
% 67.57/10.29 % (52004)Termination reason: Instruction limit
% 67.57/10.29 % (52004)Termination phase: Saturation
% 67.57/10.29 % (52004)Time elapsed: 1.791 s
% 67.57/10.29 % (52004)Peak memory usage: 158 MB
% 67.57/10.29 % (52004)Instructions burned: 3257 (million)
% 67.57/10.29 % (52028)lrs+1010_64:1_anc=all:to=lpo:sil=16000:fde=none:sp=const_frequency:urr=full:sac=on:random_seed=1588845037:i=1098:nicw=on_2961 on theBenchmark for (2961ds/1098Mi)
% 67.57/10.29 % (52022)Refutation not found, incomplete strategy
% 67.57/10.29 % (52022)------------------------------
% 67.57/10.29 % (52022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 67.57/10.29 % (52022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 67.57/10.29 % (52022)CaDiCaL version: 2.1.3
% 67.57/10.29 % (52022)Termination reason: Refutation not found, incomplete strategy
% 67.57/10.29 % (52022)Time elapsed: 0.653 s
% 67.57/10.29 % (52022)Peak memory usage: 129 MB
% 67.57/10.29 % (52022)Instructions burned: 984 (million)
% 67.57/10.29 % (52022)------------------------------
% 67.57/10.29 % (52022)------------------------------
% 67.57/10.29 % (52030)lrs-1011_32:1_to=lpo:sil=32000:tgt=ground:sos=on:spb=goal_then_units:acc=on:random_seed=680762454:i=433:bd=preordered_2956 on theBenchmark for (2956ds/433Mi)
% 67.57/10.29 % (52028)Instruction limit reached!
% 67.57/10.29 % (52028)------------------------------
% 67.57/10.29 % (52028)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 67.57/10.29 % (52028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 67.57/10.29 % (52028)CaDiCaL version: 2.1.3
% 67.57/10.29 % (52028)Termination reason: Instruction limit
% 67.57/10.29 % (52028)Termination phase: Saturation
% 67.57/10.29 % (52028)Time elapsed: 0.616 s
% 67.57/10.29 % (52028)Peak memory usage: 101 MB
% 67.57/10.29 % (52028)Instructions burned: 1099 (million)
% 67.57/10.29 % (52021)Instruction limit reached!
% 67.57/10.29 % (52021)------------------------------
% 67.57/10.29 % (52021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 67.57/10.29 % (52021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 67.57/10.29 % (52021)CaDiCaL version: 2.1.3
% 67.57/10.29 % (52021)Termination reason: Instruction limit
% 67.57/10.29 % (52021)Termination phase: Saturation
% 67.57/10.29 % (52021)Time elapsed: 1.281 s
% 67.57/10.29 % (52021)Peak memory usage: 144 MB
% 67.57/10.29 % (52021)Instructions burned: 2993 (million)
% 67.57/10.29 % (52026)Instruction limit reached!
% 67.57/10.29 % (52026)------------------------------
% 67.57/10.29 % (52026)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 67.57/10.29 % (52026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 67.57/10.29 % (52026)CaDiCaL version: 2.1.3
% 67.57/10.29 % (52026)Termination reason: Instruction limit
% 67.57/10.29 % (52026)Termination phase: Saturation
% 67.57/10.29 % (52026)Time elapsed: 1.106 s
% 67.57/10.29 % (52026)Peak memory usage: 138 MB
% 67.57/10.29 % (52026)Instructions burned: 2088 (million)
% 67.57/10.29 % (52030)Instruction limit reached!
% 67.57/10.29 % (52030)------------------------------
% 67.57/10.29 % (52030)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 67.57/10.29 % (52030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 67.57/10.29 % (52030)CaDiCaL version: 2.1.3
% 67.57/10.29 % (52030)Termination reason: Instruction limit
% 78.39/11.87 % (52030)Termination phase: Saturation
% 78.39/11.87 % (52030)Time elapsed: 0.235 s
% 78.39/11.87 % (52030)Peak memory usage: 91 MB
% 78.39/11.87 % (52030)Instructions burned: 434 (million)
% 78.39/11.87 % (52033)lrs+35_1_ncem=casc2026/models/loop8.pt:sil=64000:npcc=on:sp=reverse_arity:urr=full:rp=on:br=off:random_seed=2753819601:i=6922:s2at=5:sd=3:bd=all:ss=axioms:er=known:sgt=32_2953 on theBenchmark for (2953ds/6922Mi)
% 78.39/11.87 % (52032)lrs+1002_1_ncem=casc2026/models/loop3.pt:sil=32000:npcc=on:prc=on:etr=on:spb=goal:flr=on:random_seed=4247184348:st=5.37:cond=on:i=2942:s2at=20:aac=none:fgj=on:bs=on:gtg=exists_sym:ss=axioms:er=filter:sgt=16_2953 on theBenchmark for (2953ds/2942Mi)
% 78.39/11.87 % (52034)dis+10_5:1_sil=8000:tgt=full:plsq=on:plsqc=1:plsqr=32,1:urr=on:fd=off:nwc=0.5:br=off:slsqc=3:slsq=on:random_seed=1456186551:s2a=on:i=596:s2at=2.3:gtgl=5:gtg=all:sup=off_2952 on theBenchmark for (2952ds/596Mi)
% 78.39/11.87 % (52035)lrs+21_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=non_intro:urr=on:fd=preordered:random_seed=2214448481:i=4123:kws=inv_frequency:bd=preordered:av=off:er=known_2952 on theBenchmark for (2952ds/4123Mi)
% 78.39/11.87 % (52034)Instruction limit reached!
% 78.39/11.87 % (52034)------------------------------
% 78.39/11.87 % (52034)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 78.39/11.87 % (52034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 78.39/11.87 % (52034)CaDiCaL version: 2.1.3
% 78.39/11.87 % (52034)Termination reason: Instruction limit
% 78.39/11.87 % (52034)Termination phase: Saturation
% 78.39/11.87 % (52034)Time elapsed: 0.295 s
% 78.39/11.87 % (52034)Peak memory usage: 103 MB
% 78.39/11.87 % (52034)Instructions burned: 598 (million)
% 78.39/11.87 % (52040)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=49349019:i=16411:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2948 on theBenchmark for (2948ds/16411Mi)
% 78.39/11.87 % (52032)Instruction limit reached!
% 78.39/11.87 % (52032)------------------------------
% 78.39/11.87 % (52032)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 78.39/11.87 % (52032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 78.39/11.87 % (52032)CaDiCaL version: 2.1.3
% 78.39/11.87 % (52032)Termination reason: Instruction limit
% 78.39/11.87 % (52032)Termination phase: Saturation
% 78.39/11.87 % (52032)Time elapsed: 1.920 s
% 78.39/11.87 % (52032)Peak memory usage: 142 MB
% 78.39/11.87 % (52032)Instructions burned: 2943 (million)
% 78.39/11.87 % (52033)Instruction limit reached!
% 78.39/11.87 % (52033)------------------------------
% 78.39/11.87 % (52033)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 78.39/11.87 % (52033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 78.39/11.87 % (52033)CaDiCaL version: 2.1.3
% 78.39/11.87 % (52033)Termination reason: Instruction limit
% 78.39/11.87 % (52033)Termination phase: Saturation
% 78.39/11.87 % (52033)Time elapsed: 2.041 s
% 78.39/11.87 % (52033)Peak memory usage: 192 MB
% 78.39/11.87 % (52033)Instructions burned: 6924 (million)
% 78.39/11.87 % (52042)lrs+0_1_ncem=casc2026/models/loop1.pt:sil=8000:tgt=full:npcc=on:sp=reverse_frequency:gs=on:random_seed=3881838280:i=1670:kws=inv_precedence:bd=all:av=off:gtg=exists_all_2932 on theBenchmark for (2932ds/1670Mi)
% 78.39/11.87 % (52043)lrs+1011_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:prc=on:drc=off:fde=unused:sp=reverse_frequency:updr=off:random_seed=1896562060:st=3:cond=fast:i=1722:sd=2:ss=included:fsd=on_2931 on theBenchmark for (2931ds/1722Mi)
% 78.39/11.87 % (52012)Instruction limit reached!
% 78.39/11.87 % (52012)------------------------------
% 78.39/11.87 % (52012)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 78.39/11.87 % (52012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 78.39/11.87 % (52012)CaDiCaL version: 2.1.3
% 78.39/11.87 % (52012)Termination reason: Instruction limit
% 78.39/11.87 % (52012)Termination phase: Saturation
% 78.39/11.87 % (52012)Time elapsed: 4.325 s
% 78.39/11.87 % (52012)Peak memory usage: 204 MB
% 78.39/11.87 % (52012)Instructions burned: 8479 (million)
% 78.39/11.87 % (52035)Instruction limit reached!
% 78.39/11.87 % (52035)------------------------------
% 78.39/11.87 % (52035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 78.39/11.87 % (52035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 78.39/11.87 % (52035)CaDiCaL version: 2.1.3
% 78.39/11.87 % (52035)Termination reason: Instruction limit
% 91.79/13.69 % (52035)Termination phase: Saturation
% 91.79/13.69 % (52035)Time elapsed: 2.241 s
% 91.79/13.69 % (52035)Peak memory usage: 159 MB
% 91.79/13.69 % (52035)Instructions burned: 4125 (million)
% 91.79/13.69 % (52046)ott-1004_1_anc=all_dependent:to=lpo:ncem=casc2026/models/loop8.pt:sil=32000:tgt=full:npcc=on:sas=cadical:sp=const_frequency:acc=on:urr=ec_only:gs=on:s2agt=40:alpa=false:sac=on:random_seed=2340193406:cts=off:cond=on:i=9530:bs=on:fsd=on_2930 on theBenchmark for (2930ds/9530Mi)
% 91.79/13.69 % (52047)lrs+10_1_ncem=casc2026/models/loop4.pt:sil=64000:npcc=on:sp=occurrence:random_seed=1430820815:st=2:i=4495:sd=10:ss=included_2928 on theBenchmark for (2928ds/4495Mi)
% 91.79/13.69 % (52043)Refutation not found, incomplete strategy
% 91.79/13.69 % (52043)------------------------------
% 91.79/13.69 % (52043)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 91.79/13.69 % (52043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 91.79/13.69 % (52043)CaDiCaL version: 2.1.3
% 91.79/13.69 % (52043)Termination reason: Refutation not found, incomplete strategy
% 91.79/13.69 % (52043)Time elapsed: 0.380 s
% 91.79/13.69 % (52043)Peak memory usage: 129 MB
% 91.79/13.69 % (52043)Instructions burned: 926 (million)
% 91.79/13.69 % (52043)------------------------------
% 91.79/13.69 % (52043)------------------------------
% 91.79/13.69 % (52050)lrs+1002_1_sfv=off:ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=reverse_arity:spb=non_intro:s2agt=16:random_seed=2442800707:cond=fast:i=4920:s2at=1.9:kws=inv_frequency:av=off:er=filter_2925 on theBenchmark for (2925ds/4920Mi)
% 91.79/13.69 % (52042)Instruction limit reached!
% 91.79/13.69 % (52042)------------------------------
% 91.79/13.69 % (52042)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 91.79/13.69 % (52042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 91.79/13.69 % (52042)CaDiCaL version: 2.1.3
% 91.79/13.69 % (52042)Termination reason: Instruction limit
% 91.79/13.69 % (52042)Termination phase: Saturation
% 91.79/13.69 % (52042)Time elapsed: 1.054 s
% 91.79/13.69 % (52042)Peak memory usage: 136 MB
% 91.79/13.69 % (52042)Instructions burned: 1671 (million)
% 91.79/13.69 % (52052)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:tgt=ground:npcc=on:sp=const_frequency:lcm=reverse:bce=on:bsr=unit_only:random_seed=3058910226:cts=off:cond=on:i=2083:s2at=-1:fgj=on:av=off_2920 on theBenchmark for (2920ds/2083Mi)
% 91.79/13.69 % (52010)Instruction limit reached!
% 91.79/13.69 % (52010)------------------------------
% 91.79/13.69 % (52010)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 91.79/13.69 % (52010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 91.79/13.69 % (52010)CaDiCaL version: 2.1.3
% 91.79/13.69 % (52010)Termination reason: Instruction limit
% 91.79/13.69 % (52010)Termination phase: Saturation
% 91.79/13.69 % (52010)Time elapsed: 6.830 s
% 91.79/13.69 % (52010)Peak memory usage: 190 MB
% 91.79/13.69 % (52010)Instructions burned: 10307 (million)
% 91.79/13.69 % (52050)Instruction limit reached!
% 91.79/13.69 % (52050)------------------------------
% 91.79/13.69 % (52050)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 91.79/13.69 % (52050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 91.79/13.69 % (52050)CaDiCaL version: 2.1.3
% 91.79/13.69 % (52050)Termination reason: Instruction limit
% 91.79/13.69 % (52050)Termination phase: Saturation
% 91.79/13.69 % (52050)Time elapsed: 1.730 s
% 91.79/13.69 % (52050)Peak memory usage: 161 MB
% 91.79/13.69 % (52050)Instructions burned: 4922 (million)
% 91.79/13.69 % (52055)dis+10_64_sil=16000:tgt=full:plsq=on:prc=on:drc=off:plsqc=2:plsqr=32,1:spb=goal:random_seed=3487321778:i=1258:av=off_2906 on theBenchmark for (2906ds/1258Mi)
% 91.79/13.69 % (52054)lrs+31_1_to=lpo:ncem=casc2026/models/loop2.pt:sil=16000:npcc=on:sp=weighted_frequency:sos=all:spb=units:lcm=predicate:bsr=on:gs=on:random_seed=921629833:i=4629:av=off:gsp=on_2906 on theBenchmark for (2906ds/4629Mi)
% 91.79/13.69 % (52052)Instruction limit reached!
% 91.79/13.69 % (52052)------------------------------
% 91.79/13.69 % (52052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 91.79/13.69 % (52052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 91.79/13.69 % (52052)CaDiCaL version: 2.1.3
% 91.79/13.69 % (52052)Termination reason: Instruction limit
% 91.79/13.69 % (52052)Termination phase: Saturation
% 91.79/13.69 % (52052)Time elapsed: 1.347 s
% 91.79/13.69 % (52052)Peak memory usage: 136 MB
% 91.79/13.69 % (52052)Instructions burned: 2084 (million)
% 91.79/13.69 % (52058)ott+1_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:fdtod=off:random_seed=4112027467:i=7343:av=off:ss=included_2905 on theBenchmark for (2905ds/7343Mi)
% 104.11/15.96 % (52055)Instruction limit reached!
% 104.11/15.96 % (52055)------------------------------
% 104.11/15.96 % (52055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 104.11/15.96 % (52055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 104.11/15.96 % (52055)CaDiCaL version: 2.1.3
% 104.11/15.96 % (52055)Termination reason: Instruction limit
% 104.11/15.96 % (52055)Termination phase: Saturation
% 104.11/15.96 % (52055)Time elapsed: 0.374 s
% 104.11/15.96 % (52055)Peak memory usage: 94 MB
% 104.11/15.96 % (52055)Instructions burned: 1259 (million)
% 104.11/15.96 % (52060)lrs-1002_1_to=lpo:sil=16000:sp=reverse_arity:sos=on:random_seed=2335258205:i=1325:sd=2:ss=axioms:sgt=16_2901 on theBenchmark for (2901ds/1325Mi)
% 104.11/15.96 % (52060)Refutation not found, incomplete strategy
% 104.11/15.96 % (52060)------------------------------
% 104.11/15.96 % (52060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 104.11/15.96 % (52060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 104.11/15.96 % (52060)CaDiCaL version: 2.1.3
% 104.11/15.96 % (52060)Termination reason: Refutation not found, incomplete strategy
% 104.11/15.96 % (52060)Time elapsed: 0.001 s
% 104.11/15.96 % (52060)Peak memory usage: 87 MB
% 104.11/15.96 % (52060)Instructions burned: 1 (million)
% 104.11/15.96 % (52060)------------------------------
% 104.11/15.96 % (52060)------------------------------
% 104.11/15.96 % (52058)Refutation not found, incomplete strategy
% 104.11/15.96 % (52058)------------------------------
% 104.11/15.96 % (52058)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 104.11/15.96 % (52058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 104.11/15.96 % (52058)CaDiCaL version: 2.1.3
% 104.11/15.96 % (52058)Termination reason: Refutation not found, incomplete strategy
% 104.11/15.96 % (52058)Time elapsed: 0.605 s
% 104.11/15.96 % (52058)Peak memory usage: 128 MB
% 104.11/15.96 % (52058)Instructions burned: 913 (million)
% 104.11/15.96 % (52047)Instruction limit reached!
% 104.11/15.96 % (52047)------------------------------
% 104.11/15.96 % (52047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 104.11/15.96 % (52047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 104.11/15.96 % (52047)CaDiCaL version: 2.1.3
% 104.11/15.96 % (52047)Termination reason: Instruction limit
% 104.11/15.96 % (52047)Termination phase: Saturation
% 104.11/15.96 % (52047)Time elapsed: 3.0000 s
% 104.11/15.96 % (52047)Peak memory usage: 156 MB
% 104.11/15.96 % (52047)Instructions burned: 4495 (million)
% 104.11/15.96 % (52062)dis+1011_1_to=lpo:ncem=casc2026/models/loop8.pt:sil=32000:tgt=ground:npcc=on:prc=on:sp=arity:lma=off:spb=intro:urr=ec_only:sac=on:random_seed=1551886040:st=3.9:cond=fast:i=2646:s2at=1.8:sd=5:amm=off:gtg=position:ss=axioms:fsd=on_2898 on theBenchmark for (2898ds/2646Mi)
% 104.11/15.96 % (52058)------------------------------
% 104.11/15.96 % (52058)------------------------------
% 104.11/15.96 % (52063)dis-1003_1_ncem=casc2026/models/loop7.pt:sil=64000:npcc=on:sp=arity:sos=on:urr=on:random_seed=1095994676:i=1489:sd=2:ep=R:ss=axioms_2897 on theBenchmark for (2897ds/1489Mi)
% 104.11/15.96 % (52065)lrs+20_1_ncem=casc2026/models/loop3.pt:sil=32000:npcc=on:fde=unused:sp=occurrence:sos=on:lcm=predicate:urr=full:sac=on:random_seed=3540507884:i=1503_2896 on theBenchmark for (2896ds/1503Mi)
% 104.11/15.96 % (52063)Refutation not found, incomplete strategy
% 104.11/15.96 % (52063)------------------------------
% 104.11/15.96 % (52063)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 104.11/15.96 % (52063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 104.11/15.96 % (52063)CaDiCaL version: 2.1.3
% 104.11/15.96 % (52063)Termination reason: Refutation not found, incomplete strategy
% 104.11/15.96 % (52063)Time elapsed: 0.596 s
% 104.11/15.96 % (52063)Peak memory usage: 128 MB
% 104.11/15.96 % (52063)Instructions burned: 905 (million)
% 104.11/15.96 % (52065)Instruction limit reached!
% 104.11/15.96 % (52065)------------------------------
% 104.11/15.96 % (52065)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 104.11/15.96 % (52065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 104.11/15.96 % (52065)CaDiCaL version: 2.1.3
% 104.11/15.96 % (52065)Termination reason: Instruction limit
% 104.11/15.96 % (52065)Termination phase: Saturation
% 104.11/15.96 % (52065)Time elapsed: 0.694 s
% 104.11/15.96 % (52065)Peak memory usage: 134 MB
% 104.11/15.96 % (52065)Instructions burned: 1505 (million)
% 104.11/15.96 % (52063)------------------------------
% 104.11/15.96 % (52063)------------------------------
% 104.11/15.96 % (52068)lrs+10_1_ncem=casc2026/models/loop3.pt:sil=16000:tgt=ground:npcc=on:random_seed=3940238451:i=13942:kws=frequency_2887 on theBenchmark for (2887ds/13942Mi)
% 104.11/15.96 % (52069)lrs-1002_1_to=lpo:ncem=casc2026/models/loop4.pt:sil=16000:npcc=on:bsd=on:sp=unary_frequency:spb=goal:lcm=predicate:acc=on:urr=full:bce=on:bsr=unit_only:s2agt=64:sac=on:random_seed=1835601674:i=3604:fsr=off:er=filter_2887 on theBenchmark for (2887ds/3604Mi)
% 104.11/15.96 % (52062)Instruction limit reached!
% 104.11/15.96 % (52062)------------------------------
% 104.11/15.96 % (52062)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 104.11/15.96 % (52062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 104.11/15.96 % (52062)CaDiCaL version: 2.1.3
% 104.11/15.96 % (52062)Termination reason: Instruction limit
% 104.11/15.96 % (52062)Termination phase: Saturation
% 104.11/15.96 % (52062)Time elapsed: 1.225 s
% 104.11/15.96 % (52062)Peak memory usage: 139 MB
% 104.11/15.96 % (52062)Instructions burned: 2646 (million)
% 104.11/15.96 % (52072)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=32000:npcc=on:random_seed=1373638331:i=1876:sd=1:ss=included:sgt=32_2884 on theBenchmark for (2884ds/1876Mi)
% 104.11/15.96 % (52072)Refutation not found, incomplete strategy
% 104.11/15.96 % (52072)------------------------------
% 104.11/15.96 % (52072)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 104.11/15.96 % (52072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 104.11/15.96 % (52072)CaDiCaL version: 2.1.3
% 104.11/15.96 % (52072)Termination reason: Refutation not found, incomplete strategy
% 104.11/15.96 % (52072)Time elapsed: 0.372 s
% 104.11/15.96 % (52072)Peak memory usage: 128 MB
% 104.11/15.96 % (52072)Instructions burned: 1024 (million)
% 104.11/15.96 % (52072)------------------------------
% 104.11/15.96 % (52072)------------------------------
% 104.11/15.96 % (52054)Instruction limit reached!
% 104.11/15.96 % (52054)------------------------------
% 104.11/15.96 % (52054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 104.11/15.96 % (52054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 104.11/15.96 % (52054)CaDiCaL version: 2.1.3
% 104.11/15.96 % (52054)Termination reason: Instruction limit
% 104.11/15.96 % (52054)Termination phase: Saturation
% 104.11/15.96 % (52054)Time elapsed: 2.747 s
% 104.11/15.96 % (52054)Peak memory usage: 154 MB
% 104.11/15.96 % (52054)Instructions burned: 4630 (million)
% 104.11/15.96 % (52074)lrs+10_1_to=lpo:ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:fde=none:sp=arity:urr=on:br=off:random_seed=4239225504:i=1932:bd=preordered:ins=10:sup=off:ss=axioms_2878 on theBenchmark for (2878ds/1932Mi)
% 104.11/15.96 % (52075)dis-1010_1_ncem=casc2026/models/loop1.pt:sil=8000:npcc=on:fde=unused:etr=on:sp=weighted_frequency:spb=goal_then_units:urr=ec_only:fd=preordered:kmz=on:random_seed=3822531666:s2pl=on:cond=fast:i=1980:s2at=2:kws=inv_precedence:doe=on:ins=1:av=off:gsp=on_2877 on theBenchmark for (2877ds/1980Mi)
% 104.11/15.96 % (52074)Refutation not found, incomplete strategy
% 104.11/15.96 % (52074)------------------------------
% 104.11/15.96 % (52074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 104.11/15.96 % (52074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 104.11/15.96 % (52074)CaDiCaL version: 2.1.3
% 104.11/15.96 % (52074)Termination reason: Refutation not found, incomplete strategy
% 104.11/15.96 % (52074)Time elapsed: 0.350 s
% 104.11/15.96 % (52074)Peak memory usage: 127 MB
% 104.11/15.96 % (52074)Instructions burned: 906 (million)
% 104.11/15.96 % (52074)------------------------------
% 104.11/15.96 % (52074)------------------------------
% 104.11/15.96 % (52078)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:npcc=on:sp=unary_first:sos=all:spb=units:urr=on:br=off:random_seed=2633503288:i=3902:kws=inv_arity_squared:fgj=on:ss=axioms:sgt=11_2871 on theBenchmark for (2871ds/3902Mi)
% 104.11/15.96 % (52046)Instruction limit reached!
% 104.11/15.96 % (52046)------------------------------
% 104.11/15.96 % (52046)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 104.11/15.96 % (52046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 104.11/15.96 % (52046)CaDiCaL version: 2.1.3
% 104.11/15.96 % (52046)Termination reason: Instruction limit
% 104.11/15.96 % (52046)Termination phase: Saturation
% 104.11/15.96 % (52046)Time elapsed: 5.889 s
% 104.11/15.96 % (52046)Peak memory usage: 164 MB
% 104.11/15.96 % (52046)Instructions burned: 9530 (million)
% 104.11/15.96 % (52080)dis+10_32_sil=16000:tgt=ground:drc=off:sas=cadical:acc=on:alpa=false:avsqc=3:random_seed=3742492938:avsq=on:i=3916:aac=none:amm=off_2869 on theBenchmark for (2869ds/3916Mi)
% 104.11/15.96 % (52080)Refutation not found, incomplete strategy
% 104.11/15.96 % (52080)------------------------------
% 104.11/15.96 % (52080)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 104.11/15.96 % (52080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 104.11/15.96 % (52080)CaDiCaL version: 2.1.3
% 104.11/15.96 % (52080)Termination reason: Refutation not found, incomplete strategy
% 104.11/15.96 % (52080)Time elapsed: 0.055 s
% 104.11/15.96 % (52080)Peak memory usage: 90 MB
% 104.11/15.96 % (52080)Instructions burned: 81 (million)
% 104.11/15.96 % (52069)Instruction limit reached!
% 104.11/15.96 % (52069)------------------------------
% 104.11/15.96 % (52069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 104.11/15.96 % (52069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 104.11/15.96 % (52069)CaDiCaL version: 2.1.3
% 104.11/15.96 % (52069)Termination reason: Instruction limit
% 104.11/15.96 % (52069)Termination phase: Saturation
% 104.11/15.96 % (52069)Time elapsed: 2.015 s
% 104.11/15.96 % (52069)Peak memory usage: 156 MB
% 104.11/15.96 % (52069)Instructions burned: 3604 (million)
% 104.11/15.96 % (52080)------------------------------
% 104.11/15.96 % (52080)------------------------------
% 104.11/15.96 % (52082)dis+10_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=full:npcc=on:drc=ordering:lcm=predicate:random_seed=1074390152:cond=on:i=3940:av=off:er=known_2865 on theBenchmark for (2865ds/3940Mi)
% 104.11/15.96 % (52083)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:sp=reverse_frequency:bce=on:random_seed=1031846725:s2pl=on:i=3980:gtgl=3:kws=precedence:fgj=on:gtg=all_2865 on theBenchmark for (2865ds/3980Mi)
% 104.11/15.96 % (52075)Instruction limit reached!
% 104.11/15.96 % (52075)------------------------------
% 104.11/15.96 % (52075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 104.11/15.96 % (52075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 104.11/15.96 % (52075)CaDiCaL version: 2.1.3
% 104.11/15.96 % (52075)Termination reason: Instruction limit
% 104.11/15.96 % (52075)Termination phase: Saturation
% 104.11/15.96 % (52075)Time elapsed: 1.309 s
% 104.11/15.96 % (52075)Peak memory usage: 136 MB
% 104.11/15.96 % (52075)Instructions burned: 1980 (million)
% 104.11/15.96 % (52086)lrs+1011_1_ncem=casc2026/models/loop8.pt:sil=32000:tgt=ground:npcc=on:prc=on:sp=reverse_frequency:spb=units:lsd=20:urr=ec_only:bce=on:fd=off:kmz=on:random_seed=3203672741:i=2087:s2at=3:kws=frequency:av=off:fsr=off_2863 on theBenchmark for (2863ds/2087Mi)
% 104.11/15.96 % (52078)Instruction limit reached!
% 104.11/15.96 % (52078)------------------------------
% 104.11/15.96 % (52078)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 104.11/15.96 % (52078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 104.11/15.96 % (52078)CaDiCaL version: 2.1.3
% 104.11/15.96 % (52078)Termination reason: Instruction limit
% 104.11/15.96 % (52078)Termination phase: Saturation
% 104.11/15.96 % (52078)Time elapsed: 1.139 s
% 104.11/15.96 % (52078)Peak memory usage: 162 MB
% 104.11/15.96 % (52078)Instructions burned: 3905 (million)
% 104.11/15.96 % (52088)ott-1004_1_anc=all_dependent:to=lpo:ncem=casc2026/models/loop5.pt:sil=8000:tgt=full:npcc=on:sas=cadical:sp=const_frequency:acc=on:urr=ec_only:gs=on:s2agt=40:alpa=false:sac=on:random_seed=2478612755:cts=off:cond=on:i=4272:bs=on:fsd=on_2859 on theBenchmark for (2859ds/4272Mi)
% 104.11/15.96 % (52068)First to succeed.
% 104.11/15.96 % (52068)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-51953"
% 104.11/15.96 % (52086)Instruction limit reached!
% 104.11/15.96 % (52086)------------------------------
% 104.11/15.96 % (52086)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 104.11/15.96 % (52086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 104.11/15.96 % (52086)CaDiCaL version: 2.1.3
% 104.11/15.96 % (52086)Termination reason: Instruction limit
% 104.11/15.96 % (52086)Termination phase: Saturation
% 104.11/15.96 % (52086)Time elapsed: 1.378 s
% 104.11/15.96 % (52086)Peak memory usage: 138 MB
% 104.11/15.96 % (52086)Instructions burned: 2088 (million)
% 104.11/15.96 % SZS status Satisfiable for theBenchmark
% 104.11/15.96 % SZS output start Saturation.
% See solution above
% 108.58/16.18 % SZS output start Definitions and Model Updates.
% 108.58/16.18 % SZS output end Definitions and Model Updates.
% 108.58/16.18 % (52068)------------------------------
% 108.58/16.18 % (52068)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 108.58/16.18 % (52068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 108.58/16.18 % (52068)CaDiCaL version: 2.1.3
% 108.58/16.18 % (52068)Termination reason: Satisfiable
% 108.58/16.18 % (52068)Time elapsed: 3.614 s
% 108.58/16.18 % (52068)Peak memory usage: 164 MB
% 108.58/16.18 % (52068)Instructions burned: 5904 (million)
% 108.58/16.18 % (52068)------------------------------
% 108.58/16.18 % (52068)------------------------------
% 108.58/16.18 % (51953)Success in time 15.33 s
% 108.58/16.18 % Vampire exiting
%------------------------------------------------------------------------------