%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : TOP017-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 : Thu Sep 24 03:53:39 PM UTC 2026
% Result : Satisfiable 0.10s 0.72s
% Output : Saturation 0.36s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U,Vf] :
( element_of_set(U,f1(Vf,U))
| ~ element_of_set(U,union_of_members(Vf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [U,Vf] :
( element_of_collection(f1(Vf,U),Vf)
| ~ element_of_set(U,union_of_members(Vf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [U,Vf,Uu1] :
( ~ element_of_collection(Uu1,Vf)
| ~ element_of_set(U,Uu1)
| element_of_set(U,union_of_members(Vf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U,Vf,Va] :
( element_of_set(U,Va)
| ~ element_of_collection(Va,Vf)
| ~ element_of_set(U,intersection_of_members(Vf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U,Vf] :
( element_of_collection(f2(Vf,U),Vf)
| element_of_set(U,intersection_of_members(Vf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U,Vf] :
( ~ element_of_set(U,f2(Vf,U))
| element_of_set(U,intersection_of_members(Vf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Vt] :
( equal_sets(union_of_members(Vt),X)
| ~ topological_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Vt] :
( element_of_collection(empty_set,Vt)
| ~ topological_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Vt] :
( element_of_collection(X,Vt)
| ~ topological_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Vt,Y,Z] :
( element_of_collection(intersection_of_sets(Y,Z),Vt)
| ~ element_of_collection(Z,Vt)
| ~ element_of_collection(Y,Vt)
| ~ topological_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Vt,Vf] :
( element_of_collection(union_of_members(Vf),Vt)
| ~ subset_collections(Vf,Vt)
| ~ topological_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Vt] :
( subset_collections(f5(X,Vt),Vt)
| element_of_collection(f3(X,Vt),Vt)
| ~ element_of_collection(X,Vt)
| ~ element_of_collection(empty_set,Vt)
| ~ equal_sets(union_of_members(Vt),X)
| topological_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Vt] :
( ~ element_of_collection(union_of_members(f5(X,Vt)),Vt)
| element_of_collection(f3(X,Vt),Vt)
| ~ element_of_collection(X,Vt)
| ~ element_of_collection(empty_set,Vt)
| ~ equal_sets(union_of_members(Vt),X)
| topological_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Vt] :
( subset_collections(f5(X,Vt),Vt)
| element_of_collection(f4(X,Vt),Vt)
| ~ element_of_collection(X,Vt)
| ~ element_of_collection(empty_set,Vt)
| ~ equal_sets(union_of_members(Vt),X)
| topological_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Vt] :
( ~ element_of_collection(union_of_members(f5(X,Vt)),Vt)
| element_of_collection(f4(X,Vt),Vt)
| ~ element_of_collection(X,Vt)
| ~ element_of_collection(empty_set,Vt)
| ~ equal_sets(union_of_members(Vt),X)
| topological_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Vt] :
( subset_collections(f5(X,Vt),Vt)
| ~ element_of_collection(intersection_of_sets(f3(X,Vt),f4(X,Vt)),Vt)
| ~ element_of_collection(X,Vt)
| ~ element_of_collection(empty_set,Vt)
| ~ equal_sets(union_of_members(Vt),X)
| topological_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Vt] :
( ~ element_of_collection(union_of_members(f5(X,Vt)),Vt)
| ~ element_of_collection(intersection_of_sets(f3(X,Vt),f4(X,Vt)),Vt)
| ~ element_of_collection(X,Vt)
| ~ element_of_collection(empty_set,Vt)
| ~ equal_sets(union_of_members(Vt),X)
| topological_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U,X,Vt] :
( topological_space(X,Vt)
| ~ open(U,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [U,X,Vt] :
( element_of_collection(U,Vt)
| ~ open(U,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [U,X,Vt] :
( ~ element_of_collection(U,Vt)
| ~ topological_space(X,Vt)
| open(U,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [U,X,Vt] :
( topological_space(X,Vt)
| ~ closed(U,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [U,X,Vt] :
( open(relative_complement_sets(U,X),X,Vt)
| ~ closed(U,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [U,X,Vt] :
( ~ open(relative_complement_sets(U,X),X,Vt)
| ~ topological_space(X,Vt)
| closed(U,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Vt,Vs,X] :
( topological_space(X,Vt)
| ~ finer(Vt,Vs,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [Vt,Vs,X] :
( topological_space(X,Vs)
| ~ finer(Vt,Vs,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [Vt,Vs,X] :
( subset_collections(Vs,Vt)
| ~ finer(Vt,Vs,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [Vt,Vs,X] :
( ~ subset_collections(Vs,Vt)
| ~ topological_space(X,Vs)
| ~ topological_space(X,Vt)
| finer(Vt,Vs,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X,Vf] :
( equal_sets(union_of_members(Vf),X)
| ~ basis(X,Vf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X,Vf,Y,Vb1,Vb2] :
( element_of_set(Y,f6(X,Vf,Y,Vb1,Vb2))
| ~ element_of_set(Y,intersection_of_sets(Vb1,Vb2))
| ~ element_of_collection(Vb2,Vf)
| ~ element_of_collection(Vb1,Vf)
| ~ element_of_set(Y,X)
| ~ basis(X,Vf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X,Vf,Y,Vb1,Vb2] :
( element_of_collection(f6(X,Vf,Y,Vb1,Vb2),Vf)
| ~ element_of_set(Y,intersection_of_sets(Vb1,Vb2))
| ~ element_of_collection(Vb2,Vf)
| ~ element_of_collection(Vb1,Vf)
| ~ element_of_set(Y,X)
| ~ basis(X,Vf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X,Vf,Y,Vb1,Vb2] :
( subset_sets(f6(X,Vf,Y,Vb1,Vb2),intersection_of_sets(Vb1,Vb2))
| ~ element_of_set(Y,intersection_of_sets(Vb1,Vb2))
| ~ element_of_collection(Vb2,Vf)
| ~ element_of_collection(Vb1,Vf)
| ~ element_of_set(Y,X)
| ~ basis(X,Vf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [X,Vf] :
( element_of_set(f7(X,Vf),X)
| ~ equal_sets(union_of_members(Vf),X)
| basis(X,Vf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X,Vf] :
( element_of_collection(f8(X,Vf),Vf)
| ~ equal_sets(union_of_members(Vf),X)
| basis(X,Vf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [X,Vf] :
( element_of_collection(f9(X,Vf),Vf)
| ~ equal_sets(union_of_members(Vf),X)
| basis(X,Vf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [X,Vf] :
( element_of_set(f7(X,Vf),intersection_of_sets(f8(X,Vf),f9(X,Vf)))
| ~ equal_sets(union_of_members(Vf),X)
| basis(X,Vf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [X,Vf,Uu9] :
( ~ subset_sets(Uu9,intersection_of_sets(f8(X,Vf),f9(X,Vf)))
| ~ element_of_collection(Uu9,Vf)
| ~ element_of_set(f7(X,Vf),Uu9)
| ~ equal_sets(union_of_members(Vf),X)
| basis(X,Vf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U,Vf,X] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U,Vf,X] :
( element_of_collection(f10(Vf,U,X),Vf)
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [U,Vf,X] :
( subset_sets(f10(Vf,U,X),U)
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [U,Vf] :
( element_of_set(f11(Vf,U),U)
| element_of_collection(U,top_of_basis(Vf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [U,Vf,Uu11] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [U,X,Vt,Y] :
( topological_space(X,Vt)
| ~ element_of_collection(U,subspace_topology(X,Vt,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [U,X,Vt,Y] :
( subset_sets(Y,X)
| ~ element_of_collection(U,subspace_topology(X,Vt,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [U,X,Vt,Y] :
( element_of_collection(f12(X,Vt,Y,U),Vt)
| ~ element_of_collection(U,subspace_topology(X,Vt,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [U,X,Vt,Y] :
( equal_sets(U,intersection_of_sets(Y,f12(X,Vt,Y,U)))
| ~ element_of_collection(U,subspace_topology(X,Vt,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [U,X,Vt,Y,Uu12] :
( ~ equal_sets(U,intersection_of_sets(Y,Uu12))
| ~ element_of_collection(Uu12,Vt)
| ~ subset_sets(Y,X)
| ~ topological_space(X,Vt)
| element_of_collection(U,subspace_topology(X,Vt,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [U,Y,X,Vt] :
( topological_space(X,Vt)
| ~ element_of_set(U,interior(Y,X,Vt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [U,Y,X,Vt] :
( subset_sets(Y,X)
| ~ element_of_set(U,interior(Y,X,Vt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [U,Y,X,Vt] :
( element_of_set(U,f13(Y,X,Vt,U))
| ~ element_of_set(U,interior(Y,X,Vt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [U,Y,X,Vt] :
( subset_sets(f13(Y,X,Vt,U),Y)
| ~ element_of_set(U,interior(Y,X,Vt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U,Y,X,Vt] :
( open(f13(Y,X,Vt,U),X,Vt)
| ~ element_of_set(U,interior(Y,X,Vt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [U,Y,X,Vt,Uu13] :
( ~ open(Uu13,X,Vt)
| ~ subset_sets(Uu13,Y)
| ~ element_of_set(U,Uu13)
| ~ subset_sets(Y,X)
| ~ topological_space(X,Vt)
| element_of_set(U,interior(Y,X,Vt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [U,Y,X,Vt] :
( topological_space(X,Vt)
| ~ element_of_set(U,closure(Y,X,Vt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [U,Y,X,Vt] :
( subset_sets(Y,X)
| ~ element_of_set(U,closure(Y,X,Vt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [U,Y,X,Vt,V] :
( element_of_set(U,V)
| ~ closed(V,X,Vt)
| ~ subset_sets(Y,V)
| ~ element_of_set(U,closure(Y,X,Vt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [U,Y,X,Vt] :
( subset_sets(Y,f14(Y,X,Vt,U))
| ~ subset_sets(Y,X)
| ~ topological_space(X,Vt)
| element_of_set(U,closure(Y,X,Vt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U,Y,X,Vt] :
( closed(f14(Y,X,Vt,U),X,Vt)
| ~ subset_sets(Y,X)
| ~ topological_space(X,Vt)
| element_of_set(U,closure(Y,X,Vt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U,Y,X,Vt] :
( ~ element_of_set(U,f14(Y,X,Vt,U))
| ~ subset_sets(Y,X)
| ~ topological_space(X,Vt)
| element_of_set(U,closure(Y,X,Vt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [U,Y,X,Vt] :
( topological_space(X,Vt)
| ~ neighborhood(U,Y,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [U,Y,X,Vt] :
( open(U,X,Vt)
| ~ neighborhood(U,Y,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [U,Y,X,Vt] :
( element_of_set(Y,U)
| ~ neighborhood(U,Y,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,axiom,
! [U,Y,X,Vt] :
( ~ element_of_set(Y,U)
| ~ open(U,X,Vt)
| ~ topological_space(X,Vt)
| neighborhood(U,Y,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,axiom,
! [Z,Y,X,Vt] :
( topological_space(X,Vt)
| ~ limit_point(Z,Y,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,axiom,
! [Z,Y,X,Vt] :
( subset_sets(Y,X)
| ~ limit_point(Z,Y,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [Z,Y,X,Vt,U] :
( element_of_set(f15(Z,Y,X,Vt,U),intersection_of_sets(U,Y))
| ~ neighborhood(U,Z,X,Vt)
| ~ limit_point(Z,Y,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [Z,Y,X,Vt,U] :
( ~ eq_p(f15(Z,Y,X,Vt,U),Z)
| ~ neighborhood(U,Z,X,Vt)
| ~ limit_point(Z,Y,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [Z,Y,X,Vt] :
( neighborhood(f16(Z,Y,X,Vt),Z,X,Vt)
| ~ subset_sets(Y,X)
| ~ topological_space(X,Vt)
| limit_point(Z,Y,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [Z,Y,X,Vt,Uu16] :
( eq_p(Uu16,Z)
| ~ element_of_set(Uu16,intersection_of_sets(f16(Z,Y,X,Vt),Y))
| ~ subset_sets(Y,X)
| ~ topological_space(X,Vt)
| limit_point(Z,Y,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,axiom,
! [U,Y,X,Vt] :
( topological_space(X,Vt)
| ~ element_of_set(U,boundary(Y,X,Vt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f70,axiom,
! [U,Y,X,Vt] :
( element_of_set(U,closure(Y,X,Vt))
| ~ element_of_set(U,boundary(Y,X,Vt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,axiom,
! [U,Y,X,Vt] :
( element_of_set(U,closure(relative_complement_sets(Y,X),X,Vt))
| ~ element_of_set(U,boundary(Y,X,Vt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f72,axiom,
! [U,Y,X,Vt] :
( ~ element_of_set(U,closure(relative_complement_sets(Y,X),X,Vt))
| ~ element_of_set(U,closure(Y,X,Vt))
| ~ topological_space(X,Vt)
| element_of_set(U,boundary(Y,X,Vt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [X,Vt] :
( topological_space(X,Vt)
| ~ hausdorff(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [X,Vt,X_1,X_2] :
( neighborhood(f17(X,Vt,X_1,X_2),X_1,X,Vt)
| eq_p(X_1,X_2)
| ~ element_of_set(X_2,X)
| ~ element_of_set(X_1,X)
| ~ hausdorff(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f75,axiom,
! [X,Vt,X_1,X_2] :
( neighborhood(f18(X,Vt,X_1,X_2),X_2,X,Vt)
| eq_p(X_1,X_2)
| ~ element_of_set(X_2,X)
| ~ element_of_set(X_1,X)
| ~ hausdorff(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f76,axiom,
! [X,Vt,X_1,X_2] :
( disjoint_s(f17(X,Vt,X_1,X_2),f18(X,Vt,X_1,X_2))
| eq_p(X_1,X_2)
| ~ element_of_set(X_2,X)
| ~ element_of_set(X_1,X)
| ~ hausdorff(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f77,axiom,
! [X,Vt] :
( element_of_set(f19(X,Vt),X)
| ~ topological_space(X,Vt)
| hausdorff(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [X,Vt] :
( element_of_set(f20(X,Vt),X)
| ~ topological_space(X,Vt)
| hausdorff(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f79,axiom,
! [X,Vt] :
( ~ eq_p(f19(X,Vt),f20(X,Vt))
| ~ topological_space(X,Vt)
| hausdorff(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [X,Vt,Uu19,Uu20] :
( ~ disjoint_s(Uu19,Uu20)
| ~ neighborhood(Uu20,f20(X,Vt),X,Vt)
| ~ neighborhood(Uu19,f19(X,Vt),X,Vt)
| ~ topological_space(X,Vt)
| hausdorff(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [Va1,Va2,X,Vt] :
( topological_space(X,Vt)
| ~ separation(Va1,Va2,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f82,axiom,
! [Va1,Va2,X,Vt] :
( ~ equal_sets(Va1,empty_set)
| ~ separation(Va1,Va2,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [Va1,Va2,X,Vt] :
( ~ equal_sets(Va2,empty_set)
| ~ separation(Va1,Va2,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [Va1,Va2,X,Vt] :
( element_of_collection(Va1,Vt)
| ~ separation(Va1,Va2,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [Va1,Va2,X,Vt] :
( element_of_collection(Va2,Vt)
| ~ separation(Va1,Va2,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [Va1,Va2,X,Vt] :
( equal_sets(union_of_sets(Va1,Va2),X)
| ~ separation(Va1,Va2,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f87,axiom,
! [Va1,Va2,X,Vt] :
( disjoint_s(Va1,Va2)
| ~ separation(Va1,Va2,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f88,axiom,
! [Va1,Va2,X,Vt] :
( ~ disjoint_s(Va1,Va2)
| ~ equal_sets(union_of_sets(Va1,Va2),X)
| ~ element_of_collection(Va2,Vt)
| ~ element_of_collection(Va1,Vt)
| equal_sets(Va2,empty_set)
| equal_sets(Va1,empty_set)
| ~ topological_space(X,Vt)
| separation(Va1,Va2,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f89,axiom,
! [X,Vt] :
( topological_space(X,Vt)
| ~ connected_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f90,axiom,
! [X,Vt,Va1,Va2] :
( ~ separation(Va1,Va2,X,Vt)
| ~ connected_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f91,axiom,
! [X,Vt] :
( separation(f21(X,Vt),f22(X,Vt),X,Vt)
| ~ topological_space(X,Vt)
| connected_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f92,axiom,
! [Va,X,Vt] :
( topological_space(X,Vt)
| ~ connected_set(Va,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,axiom,
! [Va,X,Vt] :
( subset_sets(Va,X)
| ~ connected_set(Va,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,axiom,
! [Va,X,Vt] :
( connected_space(Va,subspace_topology(X,Vt,Va))
| ~ connected_set(Va,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,axiom,
! [Va,X,Vt] :
( ~ connected_space(Va,subspace_topology(X,Vt,Va))
| ~ subset_sets(Va,X)
| ~ topological_space(X,Vt)
| connected_set(Va,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,axiom,
! [Vf,X,Vt] :
( topological_space(X,Vt)
| ~ open_covering(Vf,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,axiom,
! [Vf,X,Vt] :
( subset_collections(Vf,Vt)
| ~ open_covering(Vf,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f98,axiom,
! [Vf,X,Vt] :
( equal_sets(union_of_members(Vf),X)
| ~ open_covering(Vf,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f99,axiom,
! [Vf,X,Vt] :
( ~ equal_sets(union_of_members(Vf),X)
| ~ subset_collections(Vf,Vt)
| ~ topological_space(X,Vt)
| open_covering(Vf,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [X,Vt] :
( topological_space(X,Vt)
| ~ compact_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f101,axiom,
! [X,Vt,Vf1] :
( finite(f23(X,Vt,Vf1))
| ~ open_covering(Vf1,X,Vt)
| ~ compact_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f102,axiom,
! [X,Vt,Vf1] :
( subset_collections(f23(X,Vt,Vf1),Vf1)
| ~ open_covering(Vf1,X,Vt)
| ~ compact_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f103,axiom,
! [X,Vt,Vf1] :
( open_covering(f23(X,Vt,Vf1),X,Vt)
| ~ open_covering(Vf1,X,Vt)
| ~ compact_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f104,axiom,
! [X,Vt] :
( open_covering(f24(X,Vt),X,Vt)
| ~ topological_space(X,Vt)
| compact_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f105,axiom,
! [X,Vt,Uu24] :
( ~ open_covering(Uu24,X,Vt)
| ~ subset_collections(Uu24,f24(X,Vt))
| ~ finite(Uu24)
| ~ topological_space(X,Vt)
| compact_space(X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f106,axiom,
! [Va,X,Vt] :
( topological_space(X,Vt)
| ~ compact_set(Va,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f107,axiom,
! [Va,X,Vt] :
( subset_sets(Va,X)
| ~ compact_set(Va,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f108,axiom,
! [Va,X,Vt] :
( compact_space(Va,subspace_topology(X,Vt,Va))
| ~ compact_set(Va,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f109,axiom,
! [Va,X,Vt] :
( ~ compact_space(Va,subspace_topology(X,Vt,Va))
| ~ subset_sets(Va,X)
| ~ topological_space(X,Vt)
| compact_set(Va,X,Vt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f110,negated_conjecture,
topological_space(cx,ct),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f111,negated_conjecture,
subset_sets(a,cx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f112,negated_conjecture,
( open(a,cx,ct)
| equal_sets(boundary(a,cx,ct),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
( closed(a,cx,ct)
| equal_sets(boundary(a,cx,ct),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
( ~ closed(a,cx,ct)
| ~ open(a,cx,ct)
| ~ equal_sets(boundary(a,cx,ct),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f115,plain,
! [X0,X1] :
( element_of_set(X0,f1(X1,X0))
| ~ element_of_set(X0,union_of_members(X1)) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f116,plain,
! [X0,X1] :
( element_of_collection(f1(X1,X0),X1)
| ~ element_of_set(X0,union_of_members(X1)) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f117,plain,
! [Vf,Uu1] :
( ~ element_of_collection(Uu1,Vf)
| ! [U] :
( ~ element_of_set(U,Uu1)
| element_of_set(U,union_of_members(Vf)) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ~ element_of_collection(X2,X1)
| ~ element_of_set(X0,X2)
| element_of_set(X0,union_of_members(X1)) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f119,plain,
! [U,Va] :
( element_of_set(U,Va)
| ! [Vf] :
( ~ element_of_collection(Va,Vf)
| ~ element_of_set(U,intersection_of_members(Vf)) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f120,plain,
! [X0,X1,X2] :
( element_of_set(X0,X2)
| ~ element_of_collection(X2,X1)
| ~ element_of_set(X0,intersection_of_members(X1)) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [X0,X1] :
( element_of_collection(f2(X1,X0),X1)
| element_of_set(X0,intersection_of_members(X1)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f122,plain,
! [X0,X1] :
( ~ element_of_set(X0,f2(X1,X0))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f123,plain,
! [X0,X1] :
( equal_sets(union_of_members(X1),X0)
| ~ topological_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f124,plain,
! [Vt] :
( element_of_collection(empty_set,Vt)
| ! [X] : ~ topological_space(X,Vt) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f125,plain,
! [X0,X1] :
( element_of_collection(empty_set,X1)
| ~ topological_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
! [X0,X1] :
( element_of_collection(X0,X1)
| ~ topological_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f127,plain,
! [Vt,Y,Z] :
( element_of_collection(intersection_of_sets(Y,Z),Vt)
| ~ element_of_collection(Z,Vt)
| ~ element_of_collection(Y,Vt)
| ! [X] : ~ topological_space(X,Vt) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f128,plain,
! [X0,X1,X2,X3] :
( element_of_collection(intersection_of_sets(X2,X3),X1)
| ~ element_of_collection(X3,X1)
| ~ element_of_collection(X2,X1)
| ~ topological_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [Vt,Vf] :
( element_of_collection(union_of_members(Vf),Vt)
| ~ subset_collections(Vf,Vt)
| ! [X] : ~ topological_space(X,Vt) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f130,plain,
! [X0,X1,X2] :
( element_of_collection(union_of_members(X2),X1)
| ~ subset_collections(X2,X1)
| ~ topological_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( subset_collections(f5(X0,X1),X1)
| element_of_collection(f3(X0,X1),X1)
| ~ element_of_collection(X0,X1)
| ~ element_of_collection(empty_set,X1)
| ~ equal_sets(union_of_members(X1),X0)
| topological_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f132,plain,
! [X0,X1] :
( ~ element_of_collection(union_of_members(f5(X0,X1)),X1)
| element_of_collection(f3(X0,X1),X1)
| ~ element_of_collection(X0,X1)
| ~ element_of_collection(empty_set,X1)
| ~ equal_sets(union_of_members(X1),X0)
| topological_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f133,plain,
! [X0,X1] :
( subset_collections(f5(X0,X1),X1)
| element_of_collection(f4(X0,X1),X1)
| ~ element_of_collection(X0,X1)
| ~ element_of_collection(empty_set,X1)
| ~ equal_sets(union_of_members(X1),X0)
| topological_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f134,plain,
! [X0,X1] :
( ~ element_of_collection(union_of_members(f5(X0,X1)),X1)
| element_of_collection(f4(X0,X1),X1)
| ~ element_of_collection(X0,X1)
| ~ element_of_collection(empty_set,X1)
| ~ equal_sets(union_of_members(X1),X0)
| topological_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f135,plain,
! [X0,X1] :
( subset_collections(f5(X0,X1),X1)
| ~ element_of_collection(intersection_of_sets(f3(X0,X1),f4(X0,X1)),X1)
| ~ element_of_collection(X0,X1)
| ~ element_of_collection(empty_set,X1)
| ~ equal_sets(union_of_members(X1),X0)
| topological_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f136,plain,
! [X0,X1] :
( ~ element_of_collection(union_of_members(f5(X0,X1)),X1)
| ~ element_of_collection(intersection_of_sets(f3(X0,X1),f4(X0,X1)),X1)
| ~ element_of_collection(X0,X1)
| ~ element_of_collection(empty_set,X1)
| ~ equal_sets(union_of_members(X1),X0)
| topological_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f137,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [U] : ~ open(U,X,Vt) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f138,plain,
! [X0,X1,X2] :
( topological_space(X1,X2)
| ~ open(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f139,plain,
! [U,Vt] :
( element_of_collection(U,Vt)
| ! [X] : ~ open(U,X,Vt) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f140,plain,
! [X0,X1,X2] :
( element_of_collection(X0,X2)
| ~ open(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f141,plain,
! [U,Vt] :
( ~ element_of_collection(U,Vt)
| ! [X] :
( ~ topological_space(X,Vt)
| open(U,X,Vt) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ~ element_of_collection(X0,X2)
| ~ topological_space(X1,X2)
| open(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f143,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [U] : ~ closed(U,X,Vt) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f144,plain,
! [X0,X1,X2] :
( topological_space(X1,X2)
| ~ closed(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f145,plain,
! [X0,X1,X2] :
( open(relative_complement_sets(X0,X1),X1,X2)
| ~ closed(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f146,plain,
! [X0,X1,X2] :
( ~ open(relative_complement_sets(X0,X1),X1,X2)
| ~ topological_space(X1,X2)
| closed(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f147,plain,
! [Vt,X] :
( topological_space(X,Vt)
| ! [Vs] : ~ finer(Vt,Vs,X) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f148,plain,
! [X0,X1,X2] :
( topological_space(X2,X0)
| ~ finer(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f149,plain,
! [Vs,X] :
( topological_space(X,Vs)
| ! [Vt] : ~ finer(Vt,Vs,X) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f150,plain,
! [X0,X1,X2] :
( topological_space(X2,X1)
| ~ finer(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f151,plain,
! [Vt,Vs] :
( subset_collections(Vs,Vt)
| ! [X] : ~ finer(Vt,Vs,X) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f152,plain,
! [X0,X1,X2] :
( subset_collections(X1,X0)
| ~ finer(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f153,plain,
! [Vt,Vs] :
( ~ subset_collections(Vs,Vt)
| ! [X] :
( ~ topological_space(X,Vs)
| ~ topological_space(X,Vt)
| finer(Vt,Vs,X) ) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f154,plain,
! [X0,X1,X2] :
( ~ subset_collections(X1,X0)
| ~ topological_space(X2,X1)
| ~ topological_space(X2,X0)
| finer(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f155,plain,
! [X0,X1] :
( equal_sets(union_of_members(X1),X0)
| ~ basis(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f156,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(X2,f6(X0,X1,X2,X3,X4))
| ~ element_of_set(X2,intersection_of_sets(X3,X4))
| ~ element_of_collection(X4,X1)
| ~ element_of_collection(X3,X1)
| ~ element_of_set(X2,X0)
| ~ basis(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f157,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(f6(X0,X1,X2,X3,X4),X1)
| ~ element_of_set(X2,intersection_of_sets(X3,X4))
| ~ element_of_collection(X4,X1)
| ~ element_of_collection(X3,X1)
| ~ element_of_set(X2,X0)
| ~ basis(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f158,plain,
! [X0,X1,X2,X3,X4] :
( subset_sets(f6(X0,X1,X2,X3,X4),intersection_of_sets(X3,X4))
| ~ element_of_set(X2,intersection_of_sets(X3,X4))
| ~ element_of_collection(X4,X1)
| ~ element_of_collection(X3,X1)
| ~ element_of_set(X2,X0)
| ~ basis(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f159,plain,
! [X0,X1] :
( element_of_set(f7(X0,X1),X0)
| ~ equal_sets(union_of_members(X1),X0)
| basis(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f160,plain,
! [X0,X1] :
( element_of_collection(f8(X0,X1),X1)
| ~ equal_sets(union_of_members(X1),X0)
| basis(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f161,plain,
! [X0,X1] :
( element_of_collection(f9(X0,X1),X1)
| ~ equal_sets(union_of_members(X1),X0)
| basis(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f162,plain,
! [X0,X1] :
( 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) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f163,plain,
! [X0,X1,X2] :
( ~ subset_sets(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)))
| ~ element_of_collection(X2,X1)
| ~ element_of_set(f7(X0,X1),X2)
| ~ equal_sets(union_of_members(X1),X0)
| basis(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f164,plain,
! [X0,X1,X2] :
( element_of_set(X2,f10(X1,X0,X2))
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f165,plain,
! [X0,X1,X2] :
( element_of_collection(f10(X1,X0,X2),X1)
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f166,plain,
! [X0,X1,X2] :
( subset_sets(f10(X1,X0,X2),X0)
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f167,plain,
! [X0,X1] :
( element_of_set(f11(X1,X0),X0)
| element_of_collection(X0,top_of_basis(X1)) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f168,plain,
! [U,Uu11] :
( ~ subset_sets(Uu11,U)
| ! [Vf] :
( ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f169,plain,
! [X0,X1,X2] :
( ~ subset_sets(X2,X0)
| ~ element_of_collection(X2,X1)
| ~ element_of_set(f11(X1,X0),X2)
| element_of_collection(X0,top_of_basis(X1)) ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f170,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [U,Y] : ~ element_of_collection(U,subspace_topology(X,Vt,Y)) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f171,plain,
! [X0,X1,X2,X3] :
( topological_space(X1,X2)
| ~ element_of_collection(X0,subspace_topology(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f172,plain,
! [X,Y] :
( subset_sets(Y,X)
| ! [U,Vt] : ~ element_of_collection(U,subspace_topology(X,Vt,Y)) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f173,plain,
! [X0,X1,X2,X3] :
( subset_sets(X3,X1)
| ~ element_of_collection(X0,subspace_topology(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f174,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f12(X1,X2,X3,X0),X2)
| ~ element_of_collection(X0,subspace_topology(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f175,plain,
! [X0,X1,X2,X3] :
( equal_sets(X0,intersection_of_sets(X3,f12(X1,X2,X3,X0)))
| ~ element_of_collection(X0,subspace_topology(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f176,plain,
! [U,Y,Uu12] :
( ~ equal_sets(U,intersection_of_sets(Y,Uu12))
| ! [Vt] :
( ~ element_of_collection(Uu12,Vt)
| ! [X] :
( ~ subset_sets(Y,X)
| ~ topological_space(X,Vt)
| element_of_collection(U,subspace_topology(X,Vt,Y)) ) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f177,plain,
! [X0,X1,X2,X3,X4] :
( ~ equal_sets(X0,intersection_of_sets(X3,X4))
| ~ element_of_collection(X4,X2)
| ~ subset_sets(X3,X1)
| ~ topological_space(X1,X2)
| element_of_collection(X0,subspace_topology(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f178,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [U,Y] : ~ element_of_set(U,interior(Y,X,Vt)) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f179,plain,
! [X0,X1,X2,X3] :
( topological_space(X2,X3)
| ~ element_of_set(X0,interior(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f180,plain,
! [Y,X] :
( subset_sets(Y,X)
| ! [U,Vt] : ~ element_of_set(U,interior(Y,X,Vt)) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f181,plain,
! [X0,X1,X2,X3] :
( subset_sets(X1,X2)
| ~ element_of_set(X0,interior(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f182,plain,
! [X0,X1,X2,X3] :
( element_of_set(X0,f13(X1,X2,X3,X0))
| ~ element_of_set(X0,interior(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f183,plain,
! [X0,X1,X2,X3] :
( subset_sets(f13(X1,X2,X3,X0),X1)
| ~ element_of_set(X0,interior(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f184,plain,
! [X0,X1,X2,X3] :
( open(f13(X1,X2,X3,X0),X2,X3)
| ~ element_of_set(X0,interior(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f185,plain,
! [X,Vt,Uu13] :
( ~ open(Uu13,X,Vt)
| ! [Y] :
( ~ subset_sets(Uu13,Y)
| ! [U] :
( ~ element_of_set(U,Uu13)
| ~ subset_sets(Y,X)
| ~ topological_space(X,Vt)
| element_of_set(U,interior(Y,X,Vt)) ) ) ),
inference(miniscoping,[status(thm)],[f52]) ).
fof(f186,plain,
! [X0,X1,X2,X3,X4] :
( ~ open(X4,X2,X3)
| ~ subset_sets(X4,X1)
| ~ element_of_set(X0,X4)
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| element_of_set(X0,interior(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f187,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [U,Y] : ~ element_of_set(U,closure(Y,X,Vt)) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f188,plain,
! [X0,X1,X2,X3] :
( topological_space(X2,X3)
| ~ element_of_set(X0,closure(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f189,plain,
! [Y,X] :
( subset_sets(Y,X)
| ! [U,Vt] : ~ element_of_set(U,closure(Y,X,Vt)) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f190,plain,
! [X0,X1,X2,X3] :
( subset_sets(X1,X2)
| ~ element_of_set(X0,closure(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f191,plain,
! [U,V] :
( element_of_set(U,V)
| ! [X,Vt] :
( ~ closed(V,X,Vt)
| ! [Y] :
( ~ subset_sets(Y,V)
| ~ element_of_set(U,closure(Y,X,Vt)) ) ) ),
inference(miniscoping,[status(thm)],[f55]) ).
fof(f192,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(X0,X4)
| ~ closed(X4,X2,X3)
| ~ subset_sets(X1,X4)
| ~ element_of_set(X0,closure(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f193,plain,
! [X0,X1,X2,X3] :
( subset_sets(X1,f14(X1,X2,X3,X0))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| element_of_set(X0,closure(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f194,plain,
! [X0,X1,X2,X3] :
( closed(f14(X1,X2,X3,X0),X2,X3)
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| element_of_set(X0,closure(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f195,plain,
! [X0,X1,X2,X3] :
( ~ element_of_set(X0,f14(X1,X2,X3,X0))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| element_of_set(X0,closure(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f196,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [U,Y] : ~ neighborhood(U,Y,X,Vt) ),
inference(miniscoping,[status(thm)],[f59]) ).
fof(f197,plain,
! [X0,X1,X2,X3] :
( topological_space(X2,X3)
| ~ neighborhood(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f198,plain,
! [U,X,Vt] :
( open(U,X,Vt)
| ! [Y] : ~ neighborhood(U,Y,X,Vt) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f199,plain,
! [X0,X1,X2,X3] :
( open(X0,X2,X3)
| ~ neighborhood(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f200,plain,
! [U,Y] :
( element_of_set(Y,U)
| ! [X,Vt] : ~ neighborhood(U,Y,X,Vt) ),
inference(miniscoping,[status(thm)],[f61]) ).
fof(f201,plain,
! [X0,X1,X2,X3] :
( element_of_set(X1,X0)
| ~ neighborhood(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f202,plain,
! [U,Y] :
( ~ element_of_set(Y,U)
| ! [X,Vt] :
( ~ open(U,X,Vt)
| ~ topological_space(X,Vt)
| neighborhood(U,Y,X,Vt) ) ),
inference(miniscoping,[status(thm)],[f62]) ).
fof(f203,plain,
! [X0,X1,X2,X3] :
( ~ element_of_set(X1,X0)
| ~ open(X0,X2,X3)
| ~ topological_space(X2,X3)
| neighborhood(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f204,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [Z,Y] : ~ limit_point(Z,Y,X,Vt) ),
inference(miniscoping,[status(thm)],[f63]) ).
fof(f205,plain,
! [X0,X1,X2,X3] :
( topological_space(X2,X3)
| ~ limit_point(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f206,plain,
! [Y,X] :
( subset_sets(Y,X)
| ! [Z,Vt] : ~ limit_point(Z,Y,X,Vt) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f207,plain,
! [X0,X1,X2,X3] :
( subset_sets(X1,X2)
| ~ limit_point(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f206]) ).
fof(f208,plain,
! [X0,X1,X2,X3,X4] :
( 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) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f209,plain,
! [X0,X1,X2,X3,X4] :
( ~ eq_p(f15(X0,X1,X2,X3,X4),X0)
| ~ neighborhood(X4,X0,X2,X3)
| ~ limit_point(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f210,plain,
! [X0,X1,X2,X3] :
( neighborhood(f16(X0,X1,X2,X3),X0,X2,X3)
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| limit_point(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f211,plain,
! [Z,Uu16] :
( eq_p(Uu16,Z)
| ! [Y,X,Vt] :
( ~ element_of_set(Uu16,intersection_of_sets(f16(Z,Y,X,Vt),Y))
| ~ subset_sets(Y,X)
| ~ topological_space(X,Vt)
| limit_point(Z,Y,X,Vt) ) ),
inference(miniscoping,[status(thm)],[f68]) ).
fof(f212,plain,
! [X0,X1,X2,X3,X4] :
( eq_p(X4,X0)
| ~ element_of_set(X4,intersection_of_sets(f16(X0,X1,X2,X3),X1))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| limit_point(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f213,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [U,Y] : ~ element_of_set(U,boundary(Y,X,Vt)) ),
inference(miniscoping,[status(thm)],[f69]) ).
fof(f214,plain,
! [X0,X1,X2,X3] :
( topological_space(X2,X3)
| ~ element_of_set(X0,boundary(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f215,plain,
! [X0,X1,X2,X3] :
( element_of_set(X0,closure(X1,X2,X3))
| ~ element_of_set(X0,boundary(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f216,plain,
! [X0,X1,X2,X3] :
( element_of_set(X0,closure(relative_complement_sets(X1,X2),X2,X3))
| ~ element_of_set(X0,boundary(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f217,plain,
! [X0,X1,X2,X3] :
( ~ element_of_set(X0,closure(relative_complement_sets(X1,X2),X2,X3))
| ~ element_of_set(X0,closure(X1,X2,X3))
| ~ topological_space(X2,X3)
| element_of_set(X0,boundary(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f218,plain,
! [X0,X1] :
( topological_space(X0,X1)
| ~ hausdorff(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f219,plain,
! [X0,X1,X2,X3] :
( neighborhood(f17(X0,X1,X2,X3),X2,X0,X1)
| eq_p(X2,X3)
| ~ element_of_set(X3,X0)
| ~ element_of_set(X2,X0)
| ~ hausdorff(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f220,plain,
! [X0,X1,X2,X3] :
( neighborhood(f18(X0,X1,X2,X3),X3,X0,X1)
| eq_p(X2,X3)
| ~ element_of_set(X3,X0)
| ~ element_of_set(X2,X0)
| ~ hausdorff(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f221,plain,
! [X0,X1,X2,X3] :
( disjoint_s(f17(X0,X1,X2,X3),f18(X0,X1,X2,X3))
| eq_p(X2,X3)
| ~ element_of_set(X3,X0)
| ~ element_of_set(X2,X0)
| ~ hausdorff(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f222,plain,
! [X0,X1] :
( element_of_set(f19(X0,X1),X0)
| ~ topological_space(X0,X1)
| hausdorff(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f223,plain,
! [X0,X1] :
( element_of_set(f20(X0,X1),X0)
| ~ topological_space(X0,X1)
| hausdorff(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f224,plain,
! [X0,X1] :
( ~ eq_p(f19(X0,X1),f20(X0,X1))
| ~ topological_space(X0,X1)
| hausdorff(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f225,plain,
! [Uu19,Uu20] :
( ~ disjoint_s(Uu19,Uu20)
| ! [X,Vt] :
( ~ neighborhood(Uu20,f20(X,Vt),X,Vt)
| ~ neighborhood(Uu19,f19(X,Vt),X,Vt)
| ~ topological_space(X,Vt)
| hausdorff(X,Vt) ) ),
inference(miniscoping,[status(thm)],[f80]) ).
fof(f226,plain,
! [X0,X1,X2,X3] :
( ~ disjoint_s(X2,X3)
| ~ neighborhood(X3,f20(X0,X1),X0,X1)
| ~ neighborhood(X2,f19(X0,X1),X0,X1)
| ~ topological_space(X0,X1)
| hausdorff(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f225]) ).
fof(f227,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [Va1,Va2] : ~ separation(Va1,Va2,X,Vt) ),
inference(miniscoping,[status(thm)],[f81]) ).
fof(f228,plain,
! [X0,X1,X2,X3] :
( topological_space(X2,X3)
| ~ separation(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f227]) ).
fof(f229,plain,
! [Va1] :
( ~ equal_sets(Va1,empty_set)
| ! [Va2,X,Vt] : ~ separation(Va1,Va2,X,Vt) ),
inference(miniscoping,[status(thm)],[f82]) ).
fof(f230,plain,
! [X0,X1,X2,X3] :
( ~ equal_sets(X0,empty_set)
| ~ separation(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f231,plain,
! [Va2] :
( ~ equal_sets(Va2,empty_set)
| ! [Va1,X,Vt] : ~ separation(Va1,Va2,X,Vt) ),
inference(miniscoping,[status(thm)],[f83]) ).
fof(f232,plain,
! [X0,X1,X2,X3] :
( ~ equal_sets(X1,empty_set)
| ~ separation(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f233,plain,
! [Va1,Vt] :
( element_of_collection(Va1,Vt)
| ! [Va2,X] : ~ separation(Va1,Va2,X,Vt) ),
inference(miniscoping,[status(thm)],[f84]) ).
fof(f234,plain,
! [X0,X1,X2,X3] :
( element_of_collection(X0,X3)
| ~ separation(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f233]) ).
fof(f235,plain,
! [Va2,Vt] :
( element_of_collection(Va2,Vt)
| ! [Va1,X] : ~ separation(Va1,Va2,X,Vt) ),
inference(miniscoping,[status(thm)],[f85]) ).
fof(f236,plain,
! [X0,X1,X2,X3] :
( element_of_collection(X1,X3)
| ~ separation(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f235]) ).
fof(f237,plain,
! [Va1,Va2,X] :
( equal_sets(union_of_sets(Va1,Va2),X)
| ! [Vt] : ~ separation(Va1,Va2,X,Vt) ),
inference(miniscoping,[status(thm)],[f86]) ).
fof(f238,plain,
! [X0,X1,X2,X3] :
( equal_sets(union_of_sets(X0,X1),X2)
| ~ separation(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f237]) ).
fof(f239,plain,
! [Va1,Va2] :
( disjoint_s(Va1,Va2)
| ! [X,Vt] : ~ separation(Va1,Va2,X,Vt) ),
inference(miniscoping,[status(thm)],[f87]) ).
fof(f240,plain,
! [X0,X1,X2,X3] :
( disjoint_s(X0,X1)
| ~ separation(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f239]) ).
fof(f241,plain,
! [Va1,Va2] :
( ~ disjoint_s(Va1,Va2)
| ! [X] :
( ~ equal_sets(union_of_sets(Va1,Va2),X)
| ! [Vt] :
( ~ element_of_collection(Va2,Vt)
| ~ element_of_collection(Va1,Vt)
| equal_sets(Va2,empty_set)
| equal_sets(Va1,empty_set)
| ~ topological_space(X,Vt)
| separation(Va1,Va2,X,Vt) ) ) ),
inference(miniscoping,[status(thm)],[f88]) ).
fof(f242,plain,
! [X0,X1,X2,X3] :
( ~ disjoint_s(X0,X1)
| ~ equal_sets(union_of_sets(X0,X1),X2)
| ~ element_of_collection(X1,X3)
| ~ element_of_collection(X0,X3)
| equal_sets(X1,empty_set)
| equal_sets(X0,empty_set)
| ~ topological_space(X2,X3)
| separation(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f241]) ).
fof(f243,plain,
! [X0,X1] :
( topological_space(X0,X1)
| ~ connected_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f244,plain,
! [X,Vt] :
( ! [Va1,Va2] : ~ separation(Va1,Va2,X,Vt)
| ~ connected_space(X,Vt) ),
inference(miniscoping,[status(thm)],[f90]) ).
fof(f245,plain,
! [X0,X1,X2,X3] :
( ~ separation(X2,X3,X0,X1)
| ~ connected_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f246,plain,
! [X0,X1] :
( separation(f21(X0,X1),f22(X0,X1),X0,X1)
| ~ topological_space(X0,X1)
| connected_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f247,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [Va] : ~ connected_set(Va,X,Vt) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f248,plain,
! [X0,X1,X2] :
( topological_space(X1,X2)
| ~ connected_set(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f247]) ).
fof(f249,plain,
! [Va,X] :
( subset_sets(Va,X)
| ! [Vt] : ~ connected_set(Va,X,Vt) ),
inference(miniscoping,[status(thm)],[f93]) ).
fof(f250,plain,
! [X0,X1,X2] :
( subset_sets(X0,X1)
| ~ connected_set(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f249]) ).
fof(f251,plain,
! [X0,X1,X2] :
( connected_space(X0,subspace_topology(X1,X2,X0))
| ~ connected_set(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f252,plain,
! [X0,X1,X2] :
( ~ connected_space(X0,subspace_topology(X1,X2,X0))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| connected_set(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f253,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [Vf] : ~ open_covering(Vf,X,Vt) ),
inference(miniscoping,[status(thm)],[f96]) ).
fof(f254,plain,
! [X0,X1,X2] :
( topological_space(X1,X2)
| ~ open_covering(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f255,plain,
! [Vf,Vt] :
( subset_collections(Vf,Vt)
| ! [X] : ~ open_covering(Vf,X,Vt) ),
inference(miniscoping,[status(thm)],[f97]) ).
fof(f256,plain,
! [X0,X1,X2] :
( subset_collections(X0,X2)
| ~ open_covering(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f257,plain,
! [Vf,X] :
( equal_sets(union_of_members(Vf),X)
| ! [Vt] : ~ open_covering(Vf,X,Vt) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f258,plain,
! [X0,X1,X2] :
( equal_sets(union_of_members(X0),X1)
| ~ open_covering(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f257]) ).
fof(f259,plain,
! [Vf,X] :
( ~ equal_sets(union_of_members(Vf),X)
| ! [Vt] :
( ~ subset_collections(Vf,Vt)
| ~ topological_space(X,Vt)
| open_covering(Vf,X,Vt) ) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f260,plain,
! [X0,X1,X2] :
( ~ equal_sets(union_of_members(X0),X1)
| ~ subset_collections(X0,X2)
| ~ topological_space(X1,X2)
| open_covering(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f259]) ).
fof(f261,plain,
! [X0,X1] :
( topological_space(X0,X1)
| ~ compact_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f262,plain,
! [X0,X1,X2] :
( finite(f23(X0,X1,X2))
| ~ open_covering(X2,X0,X1)
| ~ compact_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f263,plain,
! [X0,X1,X2] :
( subset_collections(f23(X0,X1,X2),X2)
| ~ open_covering(X2,X0,X1)
| ~ compact_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f264,plain,
! [X0,X1,X2] :
( open_covering(f23(X0,X1,X2),X0,X1)
| ~ open_covering(X2,X0,X1)
| ~ compact_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f265,plain,
! [X0,X1] :
( open_covering(f24(X0,X1),X0,X1)
| ~ topological_space(X0,X1)
| compact_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f266,plain,
! [X0,X1,X2] :
( ~ open_covering(X2,X0,X1)
| ~ subset_collections(X2,f24(X0,X1))
| ~ finite(X2)
| ~ topological_space(X0,X1)
| compact_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f267,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [Va] : ~ compact_set(Va,X,Vt) ),
inference(miniscoping,[status(thm)],[f106]) ).
fof(f268,plain,
! [X0,X1,X2] :
( topological_space(X1,X2)
| ~ compact_set(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f269,plain,
! [Va,X] :
( subset_sets(Va,X)
| ! [Vt] : ~ compact_set(Va,X,Vt) ),
inference(miniscoping,[status(thm)],[f107]) ).
fof(f270,plain,
! [X0,X1,X2] :
( subset_sets(X0,X1)
| ~ compact_set(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f271,plain,
! [X0,X1,X2] :
( compact_space(X0,subspace_topology(X1,X2,X0))
| ~ compact_set(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f272,plain,
! [X0,X1,X2] :
( ~ compact_space(X0,subspace_topology(X1,X2,X0))
| ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| compact_set(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f273,plain,
topological_space(cx,ct),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f274,plain,
subset_sets(a,cx),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f275,plain,
( open(a,cx,ct)
| equal_sets(boundary(a,cx,ct),empty_set) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f276,plain,
( closed(a,cx,ct)
| equal_sets(boundary(a,cx,ct),empty_set) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f277,plain,
( ~ closed(a,cx,ct)
| ~ open(a,cx,ct)
| ~ equal_sets(boundary(a,cx,ct),empty_set) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f278,definition,
( sQ0_spl
<=> equal_sets(boundary(a,cx,ct),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f279,plain,
( ~ sQ0_spl
| equal_sets(boundary(a,cx,ct),empty_set) ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f280,plain,
( sQ0_spl
| ~ equal_sets(boundary(a,cx,ct),empty_set) ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f281,definition,
( sQ1_spl
<=> open(a,cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f282,plain,
( ~ sQ1_spl
| open(a,cx,ct) ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f283,plain,
( sQ1_spl
| ~ open(a,cx,ct) ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f284,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f275,f278,f281]) ).
fof(f285,definition,
( sQ2_spl
<=> closed(a,cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f286,plain,
( ~ sQ2_spl
| closed(a,cx,ct) ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f288,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f276,f278,f285]) ).
fof(f289,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f277,f278,f281,f285]) ).
fof(f290,plain,
element_of_collection(cx,ct),
inference(resolution,[status(thm)],[f126,f273]) ).
fof(f291,plain,
element_of_collection(empty_set,ct),
inference(resolution,[status(thm)],[f125,f273]) ).
fof(f292,plain,
! [X0] :
( ~ element_of_set(X0,empty_set)
| element_of_set(X0,union_of_members(ct)) ),
inference(resolution,[status(thm)],[f118,f291]) ).
fof(f293,plain,
! [X0] :
( ~ element_of_set(X0,cx)
| element_of_set(X0,union_of_members(ct)) ),
inference(resolution,[status(thm)],[f118,f290]) ).
fof(f294,plain,
! [X0,X1,X2] :
( ~ element_of_set(X2,f2(X1,X0))
| element_of_set(X2,union_of_members(X1))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f121,f118]) ).
fof(f295,plain,
! [X0,X1] :
( element_of_collection(f1(X0,f11(X1,union_of_members(X0))),X0)
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f167,f116]) ).
fof(f296,plain,
! [X0,X1] :
( element_of_set(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)) ),
inference(resolution,[status(thm)],[f167,f115]) ).
fof(f297,plain,
( element_of_set(f19(cx,ct),cx)
| hausdorff(cx,ct) ),
inference(resolution,[status(thm)],[f222,f273]) ).
fof(f298,definition,
( sQ3_spl
<=> hausdorff(cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f299,plain,
( ~ sQ3_spl
| hausdorff(cx,ct) ),
inference(component_clause,[status(thm)],[f298]) ).
fof(f301,definition,
( sQ4_spl
<=> element_of_set(f19(cx,ct),cx) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f304,plain,
( sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f297,f298,f301]) ).
fof(f305,plain,
( element_of_set(f20(cx,ct),cx)
| hausdorff(cx,ct) ),
inference(resolution,[status(thm)],[f223,f273]) ).
fof(f306,definition,
( sQ5_spl
<=> element_of_set(f20(cx,ct),cx) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f309,plain,
( sQ5_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f305,f298,f306]) ).
fof(f310,plain,
( open_covering(f24(cx,ct),cx,ct)
| compact_space(cx,ct) ),
inference(resolution,[status(thm)],[f265,f273]) ).
fof(f311,definition,
( sQ6_spl
<=> compact_space(cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f312,plain,
( ~ sQ6_spl
| compact_space(cx,ct) ),
inference(component_clause,[status(thm)],[f311]) ).
fof(f313,plain,
( sQ6_spl
| ~ compact_space(cx,ct) ),
inference(component_clause,[status(thm)],[f311]) ).
fof(f314,definition,
( sQ7_spl
<=> open_covering(f24(cx,ct),cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( ~ sQ7_spl
| open_covering(f24(cx,ct),cx,ct) ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f317,plain,
( sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f310,f311,f314]) ).
fof(f318,plain,
! [X0,X1,X2] :
( element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(f11(X2,f2(X1,X0)),union_of_members(X1))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f294,f167]) ).
fof(f319,plain,
( separation(f21(cx,ct),f22(cx,ct),cx,ct)
| connected_space(cx,ct) ),
inference(resolution,[status(thm)],[f246,f273]) ).
fof(f320,definition,
( sQ8_spl
<=> connected_space(cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f321,plain,
( ~ sQ8_spl
| connected_space(cx,ct) ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,definition,
( sQ9_spl
<=> separation(f21(cx,ct),f22(cx,ct),cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f326,plain,
( sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f319,f320,f323]) ).
fof(f327,plain,
! [X0,X1,X2] :
( ~ element_of_set(X2,f1(X0,f11(X1,union_of_members(X0))))
| element_of_set(X2,union_of_members(X0))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f295,f118]) ).
fof(f328,plain,
! [X0,X1] :
( subset_sets(X1,f14(X1,cx,ct,X0))
| ~ subset_sets(X1,cx)
| element_of_set(X0,closure(X1,cx,ct)) ),
inference(resolution,[status(thm)],[f193,f273]) ).
fof(f329,plain,
! [X0] :
( subset_sets(a,f14(a,cx,ct,X0))
| element_of_set(X0,closure(a,cx,ct)) ),
inference(resolution,[status(thm)],[f328,f274]) ).
fof(f330,plain,
! [X0,X1] :
( neighborhood(f16(X0,X1,cx,ct),X0,cx,ct)
| ~ subset_sets(X1,cx)
| limit_point(X0,X1,cx,ct) ),
inference(resolution,[status(thm)],[f210,f273]) ).
fof(f331,plain,
! [X0] :
( neighborhood(f16(X0,a,cx,ct),X0,cx,ct)
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f330,f274]) ).
fof(f332,plain,
! [X0,X1] :
( closed(f14(X1,cx,ct,X0),cx,ct)
| ~ subset_sets(X1,cx)
| element_of_set(X0,closure(X1,cx,ct)) ),
inference(resolution,[status(thm)],[f194,f273]) ).
fof(f333,plain,
! [X0] :
( closed(f14(a,cx,ct,X0),cx,ct)
| element_of_set(X0,closure(a,cx,ct)) ),
inference(resolution,[status(thm)],[f332,f274]) ).
fof(f334,plain,
! [X0] :
( topological_space(cx,ct)
| element_of_set(X0,closure(a,cx,ct)) ),
inference(resolution,[status(thm)],[f333,f144]) ).
fof(f335,definition,
! [X0] :
( sQ10_spl
<=> element_of_set(X0,closure(a,cx,ct)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f336,plain,
! [X0] :
( ~ sQ10_spl
| element_of_set(X0,closure(a,cx,ct)) ),
inference(component_clause,[status(thm)],[f335]) ).
fof(f338,definition,
( sQ11_spl
<=> topological_space(cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f341,plain,
( sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f334,f335,f338]) ).
fof(f343,plain,
! [X0,X1,X2] :
( element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_set(f11(X2,f1(X0,f11(X1,union_of_members(X0)))),union_of_members(X0))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f327,f167]) ).
fof(f345,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(intersection_of_sets(f16(X0,X1,X2,X3),X1),top_of_basis(X4))
| eq_p(f11(X4,intersection_of_sets(f16(X0,X1,X2,X3),X1)),X0)
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| limit_point(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f212,f167]) ).
fof(f346,plain,
! [X0,X1,X2] :
( element_of_collection(intersection_of_sets(f16(X0,X1,cx,ct),X1),top_of_basis(X2))
| eq_p(f11(X2,intersection_of_sets(f16(X0,X1,cx,ct),X1)),X0)
| ~ subset_sets(X1,cx)
| limit_point(X0,X1,cx,ct) ),
inference(resolution,[status(thm)],[f345,f273]) ).
fof(f347,plain,
! [X0,X1] :
( element_of_collection(intersection_of_sets(f16(X0,a,cx,ct),a),top_of_basis(X1))
| eq_p(f11(X1,intersection_of_sets(f16(X0,a,cx,ct),a)),X0)
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f346,f274]) ).
fof(f348,plain,
! [X0,X1,X2] :
( element_of_collection(f1(X1,f11(X2,f2(X1,X0))),X1)
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f318,f116]) ).
fof(f349,plain,
! [X0,X1,X2] :
( element_of_set(f11(X2,f2(X1,X0)),f1(X1,f11(X2,f2(X1,X0))))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f318,f115]) ).
fof(f350,plain,
! [X0,X1,X2,X3] :
( ~ element_of_set(X3,f1(X1,f11(X2,f2(X1,X0))))
| element_of_set(X3,union_of_members(X1))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f348,f118]) ).
fof(f352,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f1(X1,f11(X2,f2(X1,X0))),top_of_basis(X3))
| element_of_set(f11(X3,f1(X1,f11(X2,f2(X1,X0)))),union_of_members(X1))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f350,f167]) ).
fof(f354,plain,
! [X0,X1,X2] :
( element_of_collection(f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))),X0)
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f343,f116]) ).
fof(f355,plain,
! [X0,X1,X2] :
( element_of_set(f11(X2,f1(X0,f11(X1,union_of_members(X0)))),f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f343,f115]) ).
fof(f356,plain,
! [X0,X1,X2,X3] :
( ~ element_of_set(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))
| element_of_set(X3,union_of_members(X0))
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f354,f118]) ).
fof(f357,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))),top_of_basis(X3))
| element_of_set(f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0)))))),union_of_members(X0))
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f356,f167]) ).
fof(f358,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))),X1)
| element_of_collection(f1(X1,f11(X2,f2(X1,X0))),top_of_basis(X3))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f352,f116]) ).
fof(f359,plain,
! [X0,X1,X2,X3] :
( element_of_set(f11(X3,f1(X1,f11(X2,f2(X1,X0)))),f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))
| element_of_collection(f1(X1,f11(X2,f2(X1,X0))),top_of_basis(X3))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f352,f115]) ).
fof(f360,plain,
! [X0,X1,X2,X3,X4] :
( ~ element_of_set(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))
| element_of_set(X4,union_of_members(X1))
| element_of_collection(f1(X1,f11(X2,f2(X1,X0))),top_of_basis(X3))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f358,f118]) ).
fof(f363,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))),top_of_basis(X4))
| element_of_set(f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0)))))),union_of_members(X1))
| element_of_collection(f1(X1,f11(X2,f2(X1,X0))),top_of_basis(X3))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f360,f167]) ).
fof(f366,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))),X0)
| element_of_collection(f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f357,f116]) ).
fof(f367,plain,
! [X0,X1,X2,X3] :
( element_of_set(f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0)))))),f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))
| element_of_collection(f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f357,f115]) ).
fof(f368,plain,
! [X0,X1,X2,X3,X4] :
( ~ element_of_set(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))
| element_of_set(X4,union_of_members(X0))
| element_of_collection(f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f366,f118]) ).
fof(f369,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))),top_of_basis(X4))
| element_of_set(f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0)))))))),union_of_members(X0))
| element_of_collection(f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f368,f167]) ).
fof(f370,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))),X1)
| element_of_collection(f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))),top_of_basis(X4))
| element_of_collection(f1(X1,f11(X2,f2(X1,X0))),top_of_basis(X3))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f363,f116]) ).
fof(f371,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0)))))),f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))))
| element_of_collection(f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))),top_of_basis(X4))
| element_of_collection(f1(X1,f11(X2,f2(X1,X0))),top_of_basis(X3))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f363,f115]) ).
fof(f372,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ element_of_set(X5,f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))))
| element_of_set(X5,union_of_members(X1))
| element_of_collection(f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))),top_of_basis(X4))
| element_of_collection(f1(X1,f11(X2,f2(X1,X0))),top_of_basis(X3))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f370,f118]) ).
fof(f373,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_collection(f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))),top_of_basis(X5))
| element_of_set(f11(X5,f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0)))))))),union_of_members(X1))
| element_of_collection(f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))),top_of_basis(X4))
| element_of_collection(f1(X1,f11(X2,f2(X1,X0))),top_of_basis(X3))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f372,f167]) ).
fof(f378,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))),X0)
| element_of_collection(f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))),top_of_basis(X4))
| element_of_collection(f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f369,f116]) ).
fof(f379,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0)))))))),f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))))
| element_of_collection(f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))),top_of_basis(X4))
| element_of_collection(f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f369,f115]) ).
fof(f380,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ element_of_set(X5,f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))))
| element_of_set(X5,union_of_members(X0))
| element_of_collection(f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))),top_of_basis(X4))
| element_of_collection(f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f378,f118]) ).
fof(f381,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_collection(f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))),top_of_basis(X5))
| element_of_set(f11(X5,f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0)))))))))),union_of_members(X0))
| element_of_collection(f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))),top_of_basis(X4))
| element_of_collection(f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f380,f167]) ).
fof(f382,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_collection(f1(X1,f11(X5,f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))))),X1)
| element_of_collection(f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))),top_of_basis(X5))
| element_of_collection(f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))),top_of_basis(X4))
| element_of_collection(f1(X1,f11(X2,f2(X1,X0))),top_of_basis(X3))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f373,f116]) ).
fof(f383,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_set(f11(X5,f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0)))))))),f1(X1,f11(X5,f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))))))
| element_of_collection(f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))),top_of_basis(X5))
| element_of_collection(f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))),top_of_basis(X4))
| element_of_collection(f1(X1,f11(X2,f2(X1,X0))),top_of_basis(X3))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f373,f115]) ).
fof(f386,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_collection(f1(X0,f11(X5,f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))))),X0)
| element_of_collection(f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))),top_of_basis(X5))
| element_of_collection(f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))),top_of_basis(X4))
| element_of_collection(f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f381,f116]) ).
fof(f387,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_set(f11(X5,f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0)))))))))),f1(X0,f11(X5,f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))))))
| element_of_collection(f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))),top_of_basis(X5))
| element_of_collection(f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))),top_of_basis(X4))
| element_of_collection(f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f381,f115]) ).
fof(f388,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ element_of_set(X6,f1(X1,f11(X5,f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))))))
| element_of_set(X6,union_of_members(X1))
| element_of_collection(f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))),top_of_basis(X5))
| element_of_collection(f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))),top_of_basis(X4))
| element_of_collection(f1(X1,f11(X2,f2(X1,X0))),top_of_basis(X3))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f382,f118]) ).
fof(f389,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ element_of_set(X6,f1(X0,f11(X5,f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))))))
| element_of_set(X6,union_of_members(X0))
| element_of_collection(f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))),top_of_basis(X5))
| element_of_collection(f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))),top_of_basis(X4))
| element_of_collection(f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f386,f118]) ).
fof(f391,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( element_of_collection(f1(X1,f11(X5,f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))))),top_of_basis(X6))
| element_of_set(f11(X6,f1(X1,f11(X5,f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0)))))))))),union_of_members(X1))
| element_of_collection(f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))),top_of_basis(X5))
| element_of_collection(f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))),top_of_basis(X4))
| element_of_collection(f1(X1,f11(X2,f2(X1,X0))),top_of_basis(X3))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f388,f167]) ).
fof(f394,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( element_of_collection(f1(X0,f11(X5,f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))))),top_of_basis(X6))
| element_of_set(f11(X6,f1(X0,f11(X5,f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0)))))))))))),union_of_members(X0))
| element_of_collection(f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))),top_of_basis(X5))
| element_of_collection(f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))),top_of_basis(X4))
| element_of_collection(f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f389,f167]) ).
fof(f396,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( element_of_collection(f1(X1,f11(X6,f1(X1,f11(X5,f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))))))),X1)
| element_of_collection(f1(X1,f11(X5,f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))))),top_of_basis(X6))
| element_of_collection(f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))),top_of_basis(X5))
| element_of_collection(f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))),top_of_basis(X4))
| element_of_collection(f1(X1,f11(X2,f2(X1,X0))),top_of_basis(X3))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f391,f116]) ).
fof(f397,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( element_of_set(f11(X6,f1(X1,f11(X5,f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0)))))))))),f1(X1,f11(X6,f1(X1,f11(X5,f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))))))))
| element_of_collection(f1(X1,f11(X5,f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))))),top_of_basis(X6))
| element_of_collection(f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))),top_of_basis(X5))
| element_of_collection(f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))),top_of_basis(X4))
| element_of_collection(f1(X1,f11(X2,f2(X1,X0))),top_of_basis(X3))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f391,f115]) ).
fof(f398,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( element_of_collection(f1(X0,f11(X6,f1(X0,f11(X5,f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))))))),X0)
| element_of_collection(f1(X0,f11(X5,f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))))),top_of_basis(X6))
| element_of_collection(f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))),top_of_basis(X5))
| element_of_collection(f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))),top_of_basis(X4))
| element_of_collection(f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f394,f116]) ).
fof(f399,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( element_of_set(f11(X6,f1(X0,f11(X5,f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0)))))))))))),f1(X0,f11(X6,f1(X0,f11(X5,f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))))))))
| element_of_collection(f1(X0,f11(X5,f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))))),top_of_basis(X6))
| element_of_collection(f1(X0,f11(X4,f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))))),top_of_basis(X5))
| element_of_collection(f1(X0,f11(X3,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))),top_of_basis(X4))
| element_of_collection(f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X1,union_of_members(X0))),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f394,f115]) ).
fof(f400,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ element_of_set(X7,f1(X1,f11(X6,f1(X1,f11(X5,f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))))))))
| element_of_set(X7,union_of_members(X1))
| element_of_collection(f1(X1,f11(X5,f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))))),top_of_basis(X6))
| element_of_collection(f1(X1,f11(X4,f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))))),top_of_basis(X5))
| element_of_collection(f1(X1,f11(X3,f1(X1,f11(X2,f2(X1,X0))))),top_of_basis(X4))
| element_of_collection(f1(X1,f11(X2,f2(X1,X0))),top_of_basis(X3))
| element_of_collection(f2(X1,X0),top_of_basis(X2))
| element_of_set(X0,intersection_of_members(X1)) ),
inference(resolution,[status(thm)],[f396,f118]) ).
fof(f401,plain,
! [X0,X1] :
( ~ sQ3_spl
| disjoint_s(f17(cx,ct,X0,X1),f18(cx,ct,X0,X1))
| eq_p(X0,X1)
| ~ element_of_set(X1,cx)
| ~ element_of_set(X0,cx) ),
inference(resolution,[status(thm)],[f299,f221]) ).
fof(f402,plain,
! [X0,X1] :
( ~ sQ3_spl
| neighborhood(f18(cx,ct,X0,X1),X1,cx,ct)
| eq_p(X0,X1)
| ~ element_of_set(X1,cx)
| ~ element_of_set(X0,cx) ),
inference(resolution,[status(thm)],[f299,f220]) ).
fof(f403,plain,
! [X0,X1] :
( ~ sQ3_spl
| neighborhood(f17(cx,ct,X0,X1),X0,cx,ct)
| eq_p(X0,X1)
| ~ element_of_set(X1,cx)
| ~ element_of_set(X0,cx) ),
inference(resolution,[status(thm)],[f299,f219]) ).
fof(f407,plain,
! [X0] :
( limit_point(X0,a,cx,ct)
| open(f16(X0,a,cx,ct),cx,ct) ),
inference(resolution,[status(thm)],[f199,f331]) ).
fof(f408,plain,
! [X0,X1,X2,X3] :
( element_of_collection(boundary(X2,X0,X1),top_of_basis(X3))
| topological_space(X0,X1) ),
inference(resolution,[status(thm)],[f214,f167]) ).
fof(f409,plain,
! [X0] :
( element_of_collection(empty_set,top_of_basis(X0))
| element_of_set(f11(X0,empty_set),union_of_members(ct)) ),
inference(resolution,[status(thm)],[f292,f167]) ).
fof(f410,plain,
! [X0] :
( ~ element_of_collection(X0,ct)
| open(X0,cx,ct) ),
inference(resolution,[status(thm)],[f142,f273]) ).
fof(f411,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(closure(X0,X2,X3),top_of_basis(X4))
| element_of_set(f11(X4,closure(X0,X2,X3)),X1)
| ~ closed(X1,X2,X3)
| ~ subset_sets(X0,X1) ),
inference(resolution,[status(thm)],[f192,f167]) ).
fof(f412,plain,
! [X0,X1] :
( ~ sQ10_spl
| element_of_set(X1,X0)
| ~ closed(X0,cx,ct)
| ~ subset_sets(a,X0) ),
inference(resolution,[status(thm)],[f192,f336]) ).
fof(f413,plain,
! [X0,X1,X2] :
( element_of_collection(intersection_of_members(X1),top_of_basis(X2))
| element_of_set(f11(X2,intersection_of_members(X1)),X0)
| ~ element_of_collection(X0,X1) ),
inference(resolution,[status(thm)],[f120,f167]) ).
fof(f414,plain,
equal_sets(union_of_members(ct),cx),
inference(resolution,[status(thm)],[f123,f273]) ).
fof(f415,plain,
! [X0] :
( element_of_collection(f1(ct,f11(X0,empty_set)),ct)
| element_of_collection(empty_set,top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f409,f116]) ).
fof(f416,plain,
! [X0] :
( element_of_set(f11(X0,empty_set),f1(ct,f11(X0,empty_set)))
| element_of_collection(empty_set,top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f409,f115]) ).
fof(f417,plain,
! [X0,X1] :
( ~ element_of_set(X1,f1(ct,f11(X0,empty_set)))
| element_of_set(X1,union_of_members(ct))
| element_of_collection(empty_set,top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f415,f118]) ).
fof(f418,plain,
! [X0] :
( element_of_collection(f16(X0,a,cx,ct),ct)
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f407,f140]) ).
fof(f419,plain,
! [X0] :
( topological_space(cx,ct)
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f407,f138]) ).
fof(f420,definition,
! [X0] :
( sQ12_spl
<=> limit_point(X0,a,cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f423,plain,
( sQ11_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f419,f420,f338]) ).
fof(f424,plain,
! [X0,X1] :
( ~ element_of_set(X1,f16(X0,a,cx,ct))
| element_of_set(X1,union_of_members(ct))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f418,f118]) ).
fof(f426,plain,
! [X0,X1] :
( element_of_collection(f1(ct,f11(X0,empty_set)),top_of_basis(X1))
| element_of_set(f11(X1,f1(ct,f11(X0,empty_set))),union_of_members(ct))
| element_of_collection(empty_set,top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f417,f167]) ).
fof(f430,plain,
! [X0,X1] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X1))
| disjoint_s(f17(cx,ct,f11(X1,cx),X0),f18(cx,ct,f11(X1,cx),X0))
| eq_p(f11(X1,cx),X0)
| ~ element_of_set(X0,cx) ),
inference(resolution,[status(thm)],[f401,f167]) ).
fof(f431,plain,
! [X0,X1] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X1))
| neighborhood(f18(cx,ct,f11(X1,cx),X0),X0,cx,ct)
| eq_p(f11(X1,cx),X0)
| ~ element_of_set(X0,cx) ),
inference(resolution,[status(thm)],[f402,f167]) ).
fof(f432,plain,
! [X0,X1] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X1))
| neighborhood(f17(cx,ct,f11(X1,cx),X0),f11(X1,cx),cx,ct)
| eq_p(f11(X1,cx),X0)
| ~ element_of_set(X0,cx) ),
inference(resolution,[status(thm)],[f403,f167]) ).
fof(f433,plain,
! [X0,X1] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X1))
| element_of_collection(cx,top_of_basis(X0))
| disjoint_s(f17(cx,ct,f11(X0,cx),f11(X1,cx)),f18(cx,ct,f11(X0,cx),f11(X1,cx)))
| eq_p(f11(X0,cx),f11(X1,cx)) ),
inference(resolution,[status(thm)],[f430,f167]) ).
fof(f435,plain,
! [X0,X1] :
( element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| element_of_set(f11(X1,f16(X0,a,cx,ct)),union_of_members(ct))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f424,f167]) ).
fof(f436,plain,
! [X0,X1,X2,X3] :
( element_of_set(X0,closure(a,cx,ct))
| element_of_collection(closure(a,X1,X2),top_of_basis(X3))
| element_of_set(f11(X3,closure(a,X1,X2)),f14(a,cx,ct,X0))
| ~ closed(f14(a,cx,ct,X0),X1,X2) ),
inference(resolution,[status(thm)],[f411,f329]) ).
fof(f437,plain,
! [X0,X1,X2] :
( element_of_collection(closure(a,X0,X1),top_of_basis(X2))
| element_of_set(f11(X2,closure(a,X0,X1)),cx)
| ~ closed(cx,X0,X1) ),
inference(resolution,[status(thm)],[f411,f274]) ).
fof(f438,plain,
! [X0,X1] :
( element_of_collection(f1(ct,f11(X1,f1(ct,f11(X0,empty_set)))),ct)
| element_of_collection(f1(ct,f11(X0,empty_set)),top_of_basis(X1))
| element_of_collection(empty_set,top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f426,f116]) ).
fof(f439,plain,
! [X0,X1] :
( element_of_set(f11(X1,f1(ct,f11(X0,empty_set))),f1(ct,f11(X1,f1(ct,f11(X0,empty_set)))))
| element_of_collection(f1(ct,f11(X0,empty_set)),top_of_basis(X1))
| element_of_collection(empty_set,top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f426,f115]) ).
fof(f440,plain,
! [X0,X1] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X1))
| element_of_collection(cx,top_of_basis(X0))
| neighborhood(f18(cx,ct,f11(X0,cx),f11(X1,cx)),f11(X1,cx),cx,ct)
| eq_p(f11(X0,cx),f11(X1,cx)) ),
inference(resolution,[status(thm)],[f431,f167]) ).
fof(f441,plain,
! [X0,X1] :
( element_of_collection(f1(ct,f11(X1,f16(X0,a,cx,ct))),ct)
| element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f435,f116]) ).
fof(f442,plain,
! [X0,X1] :
( element_of_set(f11(X1,f16(X0,a,cx,ct)),f1(ct,f11(X1,f16(X0,a,cx,ct))))
| element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f435,f115]) ).
fof(f443,plain,
! [X0,X1,X2] :
( ~ element_of_set(X2,f1(ct,f11(X1,f1(ct,f11(X0,empty_set)))))
| element_of_set(X2,union_of_members(ct))
| element_of_collection(f1(ct,f11(X0,empty_set)),top_of_basis(X1))
| element_of_collection(empty_set,top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f438,f118]) ).
fof(f444,plain,
! [X0,X1] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X1))
| element_of_collection(cx,top_of_basis(X0))
| neighborhood(f17(cx,ct,f11(X0,cx),f11(X1,cx)),f11(X0,cx),cx,ct)
| eq_p(f11(X0,cx),f11(X1,cx)) ),
inference(resolution,[status(thm)],[f432,f167]) ).
fof(f445,plain,
! [X0,X1,X2] :
( ~ element_of_set(X2,f1(ct,f11(X1,f16(X0,a,cx,ct))))
| element_of_set(X2,union_of_members(ct))
| element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f441,f118]) ).
fof(f446,plain,
! [X0,X1,X2] :
( element_of_collection(f1(ct,f11(X1,f1(ct,f11(X0,empty_set)))),top_of_basis(X2))
| element_of_set(f11(X2,f1(ct,f11(X1,f1(ct,f11(X0,empty_set))))),union_of_members(ct))
| element_of_collection(f1(ct,f11(X0,empty_set)),top_of_basis(X1))
| element_of_collection(empty_set,top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f443,f167]) ).
fof(f447,plain,
! [X0,X1,X2] :
( element_of_collection(f1(ct,f11(X1,f16(X0,a,cx,ct))),top_of_basis(X2))
| element_of_set(f11(X2,f1(ct,f11(X1,f16(X0,a,cx,ct)))),union_of_members(ct))
| element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f445,f167]) ).
fof(f450,plain,
! [X0,X1] :
( ~ sQ3_spl
| open(f18(cx,ct,f11(X0,cx),f11(X1,cx)),cx,ct)
| element_of_collection(cx,top_of_basis(X1))
| element_of_collection(cx,top_of_basis(X0))
| eq_p(f11(X0,cx),f11(X1,cx)) ),
inference(resolution,[status(thm)],[f440,f199]) ).
fof(f451,plain,
! [X0,X1] :
( ~ sQ3_spl
| element_of_collection(f18(cx,ct,f11(X0,cx),f11(X1,cx)),ct)
| element_of_collection(cx,top_of_basis(X1))
| element_of_collection(cx,top_of_basis(X0))
| eq_p(f11(X0,cx),f11(X1,cx)) ),
inference(resolution,[status(thm)],[f450,f140]) ).
fof(f452,plain,
! [X0,X1] :
( ~ sQ3_spl
| topological_space(cx,ct)
| element_of_collection(cx,top_of_basis(X1))
| element_of_collection(cx,top_of_basis(X0))
| eq_p(f11(X0,cx),f11(X1,cx)) ),
inference(resolution,[status(thm)],[f450,f138]) ).
fof(f453,definition,
! [X0,X1] :
( sQ13_spl
<=> ( element_of_collection(cx,top_of_basis(X1))
| element_of_collection(cx,top_of_basis(X0))
| eq_p(f11(X0,cx),f11(X1,cx)) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( ~ sQ3_spl
| sQ11_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f452,f453,f338,f298]) ).
fof(f457,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ element_of_set(X2,f18(cx,ct,f11(X0,cx),f11(X1,cx)))
| element_of_set(X2,union_of_members(ct))
| element_of_collection(cx,top_of_basis(X1))
| element_of_collection(cx,top_of_basis(X0))
| eq_p(f11(X0,cx),f11(X1,cx)) ),
inference(resolution,[status(thm)],[f451,f118]) ).
fof(f458,plain,
! [X0,X1] :
( element_of_set(X1,closure(a,cx,ct))
| element_of_set(X1,closure(a,cx,ct))
| element_of_collection(closure(a,cx,ct),top_of_basis(X0))
| element_of_set(f11(X0,closure(a,cx,ct)),f14(a,cx,ct,X1)) ),
inference(resolution,[status(thm)],[f436,f333]) ).
fof(f459,plain,
! [X0,X1] :
( element_of_set(X1,closure(a,cx,ct))
| element_of_collection(closure(a,cx,ct),top_of_basis(X0))
| element_of_set(f11(X0,closure(a,cx,ct)),f14(a,cx,ct,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f458]) ).
fof(f460,plain,
! [X0,X1] :
( ~ sQ3_spl
| open(f17(cx,ct,f11(X0,cx),f11(X1,cx)),cx,ct)
| element_of_collection(cx,top_of_basis(X1))
| element_of_collection(cx,top_of_basis(X0))
| eq_p(f11(X0,cx),f11(X1,cx)) ),
inference(resolution,[status(thm)],[f444,f199]) ).
fof(f461,plain,
! [X0,X1] :
( ~ sQ3_spl
| element_of_collection(f17(cx,ct,f11(X0,cx),f11(X1,cx)),ct)
| element_of_collection(cx,top_of_basis(X1))
| element_of_collection(cx,top_of_basis(X0))
| eq_p(f11(X0,cx),f11(X1,cx)) ),
inference(resolution,[status(thm)],[f460,f140]) ).
fof(f464,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ element_of_set(X2,f17(cx,ct,f11(X0,cx),f11(X1,cx)))
| element_of_set(X2,union_of_members(ct))
| element_of_collection(cx,top_of_basis(X1))
| element_of_collection(cx,top_of_basis(X0))
| eq_p(f11(X0,cx),f11(X1,cx)) ),
inference(resolution,[status(thm)],[f461,f118]) ).
fof(f467,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| element_of_collection(f18(cx,ct,f11(X0,cx),f11(X1,cx)),top_of_basis(X2))
| element_of_set(f11(X2,f18(cx,ct,f11(X0,cx),f11(X1,cx))),union_of_members(ct))
| element_of_collection(cx,top_of_basis(X1))
| element_of_collection(cx,top_of_basis(X0))
| eq_p(f11(X0,cx),f11(X1,cx)) ),
inference(resolution,[status(thm)],[f457,f167]) ).
fof(f468,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X2))
| element_of_collection(cx,top_of_basis(X1))
| eq_p(f11(X1,cx),f11(X2,cx))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(ct)),f17(cx,ct,f11(X1,cx),f11(X2,cx))) ),
inference(resolution,[status(thm)],[f413,f461]) ).
fof(f469,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X2))
| element_of_collection(cx,top_of_basis(X1))
| eq_p(f11(X1,cx),f11(X2,cx))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(ct)),f18(cx,ct,f11(X1,cx),f11(X2,cx))) ),
inference(resolution,[status(thm)],[f413,f451]) ).
fof(f470,plain,
! [X0,X1,X2,X3,X4] :
( topological_space(X3,X4)
| element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(top_of_basis(X1))),boundary(X2,X3,X4)) ),
inference(resolution,[status(thm)],[f413,f408]) ).
fof(f471,plain,
! [X0,X1] :
( limit_point(X1,a,cx,ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(ct)),f16(X1,a,cx,ct)) ),
inference(resolution,[status(thm)],[f413,f418]) ).
fof(f472,plain,
! [X0,X1,X2] :
( element_of_collection(f16(X2,a,cx,ct),top_of_basis(X1))
| limit_point(X2,a,cx,ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(ct)),f1(ct,f11(X1,f16(X2,a,cx,ct)))) ),
inference(resolution,[status(thm)],[f413,f441]) ).
fof(f473,plain,
! [X0,X1,X2] :
( element_of_collection(f1(ct,f11(X2,empty_set)),top_of_basis(X1))
| element_of_collection(empty_set,top_of_basis(X2))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(ct)),f1(ct,f11(X1,f1(ct,f11(X2,empty_set))))) ),
inference(resolution,[status(thm)],[f413,f438]) ).
fof(f474,plain,
! [X0,X1] :
( element_of_collection(empty_set,top_of_basis(X1))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(ct)),f1(ct,f11(X1,empty_set))) ),
inference(resolution,[status(thm)],[f413,f415]) ).
fof(f475,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( element_of_collection(f1(X1,f11(X3,f1(X1,f11(X4,f1(X1,f11(X5,f1(X1,f11(X6,f2(X1,X7))))))))),top_of_basis(X2))
| element_of_collection(f1(X1,f11(X4,f1(X1,f11(X5,f1(X1,f11(X6,f2(X1,X7))))))),top_of_basis(X3))
| element_of_collection(f1(X1,f11(X5,f1(X1,f11(X6,f2(X1,X7))))),top_of_basis(X4))
| element_of_collection(f1(X1,f11(X6,f2(X1,X7))),top_of_basis(X5))
| element_of_collection(f2(X1,X7),top_of_basis(X6))
| element_of_set(X7,intersection_of_members(X1))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),f1(X1,f11(X2,f1(X1,f11(X3,f1(X1,f11(X4,f1(X1,f11(X5,f1(X1,f11(X6,f2(X1,X7)))))))))))) ),
inference(resolution,[status(thm)],[f413,f396]) ).
fof(f476,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( element_of_collection(f1(X1,f11(X3,f1(X1,f11(X4,f1(X1,f11(X5,f1(X1,f11(X6,union_of_members(X1))))))))),top_of_basis(X2))
| element_of_collection(f1(X1,f11(X4,f1(X1,f11(X5,f1(X1,f11(X6,union_of_members(X1))))))),top_of_basis(X3))
| element_of_collection(f1(X1,f11(X5,f1(X1,f11(X6,union_of_members(X1))))),top_of_basis(X4))
| element_of_collection(f1(X1,f11(X6,union_of_members(X1))),top_of_basis(X5))
| element_of_collection(union_of_members(X1),top_of_basis(X6))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),f1(X1,f11(X2,f1(X1,f11(X3,f1(X1,f11(X4,f1(X1,f11(X5,f1(X1,f11(X6,union_of_members(X1)))))))))))) ),
inference(resolution,[status(thm)],[f413,f386]) ).
fof(f477,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( element_of_collection(f1(X1,f11(X3,f1(X1,f11(X4,f1(X1,f11(X5,f2(X1,X6))))))),top_of_basis(X2))
| element_of_collection(f1(X1,f11(X4,f1(X1,f11(X5,f2(X1,X6))))),top_of_basis(X3))
| element_of_collection(f1(X1,f11(X5,f2(X1,X6))),top_of_basis(X4))
| element_of_collection(f2(X1,X6),top_of_basis(X5))
| element_of_set(X6,intersection_of_members(X1))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),f1(X1,f11(X2,f1(X1,f11(X3,f1(X1,f11(X4,f1(X1,f11(X5,f2(X1,X6)))))))))) ),
inference(resolution,[status(thm)],[f413,f382]) ).
fof(f478,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_collection(f1(X1,f11(X3,f1(X1,f11(X4,f1(X1,f11(X5,union_of_members(X1))))))),top_of_basis(X2))
| element_of_collection(f1(X1,f11(X4,f1(X1,f11(X5,union_of_members(X1))))),top_of_basis(X3))
| element_of_collection(f1(X1,f11(X5,union_of_members(X1))),top_of_basis(X4))
| element_of_collection(union_of_members(X1),top_of_basis(X5))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),f1(X1,f11(X2,f1(X1,f11(X3,f1(X1,f11(X4,f1(X1,f11(X5,union_of_members(X1)))))))))) ),
inference(resolution,[status(thm)],[f413,f378]) ).
fof(f479,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_collection(f1(X1,f11(X3,f1(X1,f11(X4,f2(X1,X5))))),top_of_basis(X2))
| element_of_collection(f1(X1,f11(X4,f2(X1,X5))),top_of_basis(X3))
| element_of_collection(f2(X1,X5),top_of_basis(X4))
| element_of_set(X5,intersection_of_members(X1))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),f1(X1,f11(X2,f1(X1,f11(X3,f1(X1,f11(X4,f2(X1,X5)))))))) ),
inference(resolution,[status(thm)],[f413,f370]) ).
fof(f480,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(f1(X1,f11(X3,f1(X1,f11(X4,union_of_members(X1))))),top_of_basis(X2))
| element_of_collection(f1(X1,f11(X4,union_of_members(X1))),top_of_basis(X3))
| element_of_collection(union_of_members(X1),top_of_basis(X4))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),f1(X1,f11(X2,f1(X1,f11(X3,f1(X1,f11(X4,union_of_members(X1)))))))) ),
inference(resolution,[status(thm)],[f413,f366]) ).
fof(f481,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(f1(X1,f11(X3,f2(X1,X4))),top_of_basis(X2))
| element_of_collection(f2(X1,X4),top_of_basis(X3))
| element_of_set(X4,intersection_of_members(X1))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),f1(X1,f11(X2,f1(X1,f11(X3,f2(X1,X4)))))) ),
inference(resolution,[status(thm)],[f413,f358]) ).
fof(f482,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f1(X1,f11(X3,union_of_members(X1))),top_of_basis(X2))
| element_of_collection(union_of_members(X1),top_of_basis(X3))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),f1(X1,f11(X2,f1(X1,f11(X3,union_of_members(X1)))))) ),
inference(resolution,[status(thm)],[f413,f354]) ).
fof(f483,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f2(X1,X3),top_of_basis(X2))
| element_of_set(X3,intersection_of_members(X1))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),f1(X1,f11(X2,f2(X1,X3)))) ),
inference(resolution,[status(thm)],[f413,f348]) ).
fof(f484,plain,
! [X0,X1,X2] :
( element_of_collection(union_of_members(X1),top_of_basis(X2))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),f1(X1,f11(X2,union_of_members(X1)))) ),
inference(resolution,[status(thm)],[f413,f295]) ).
fof(f485,plain,
! [X0,X1,X2] :
( element_of_set(X2,intersection_of_members(X1))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),f2(X1,X2)) ),
inference(resolution,[status(thm)],[f413,f121]) ).
fof(f486,plain,
! [X0] :
( element_of_collection(intersection_of_members(ct),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(ct)),empty_set) ),
inference(resolution,[status(thm)],[f413,f291]) ).
fof(f487,plain,
! [X0] :
( element_of_collection(intersection_of_members(ct),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(ct)),cx) ),
inference(resolution,[status(thm)],[f413,f290]) ).
fof(f488,plain,
! [X0,X1,X2,X3] :
( topological_space(X2,X3)
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f470,f214]) ).
fof(f489,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(intersection_of_members(top_of_basis(X3)),top_of_basis(X2))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X3))),intersection_of_members(top_of_basis(X4)))
| topological_space(X0,X1) ),
inference(resolution,[status(thm)],[f488,f413]) ).
fof(f490,plain,
! [X0,X1,X2,X3,X4] :
( ~ element_of_set(X2,intersection_of_members(top_of_basis(X4)))
| element_of_set(X2,union_of_members(top_of_basis(X3)))
| topological_space(X0,X1) ),
inference(resolution,[status(thm)],[f488,f118]) ).
fof(f491,plain,
! [X0,X1,X2,X3] :
( equal_sets(union_of_members(X2),X3)
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f488,f123]) ).
fof(f492,plain,
! [X0,X1,X2,X3,X4] :
( ~ element_of_collection(X2,X4)
| open(X2,X3,X4)
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f488,f142]) ).
fof(f493,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( element_of_collection(intersection_of_sets(f16(X2,X3,X4,X5),X3),top_of_basis(X6))
| eq_p(f11(X6,intersection_of_sets(f16(X2,X3,X4,X5),X3)),X2)
| ~ subset_sets(X3,X4)
| limit_point(X2,X3,X4,X5)
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f488,f345]) ).
fof(f494,plain,
! [X0,X1,X2,X3,X4,X5] :
( closed(f14(X3,X4,X5,X2),X4,X5)
| ~ subset_sets(X3,X4)
| element_of_set(X2,closure(X3,X4,X5))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f488,f194]) ).
fof(f495,plain,
! [X0,X1,X2,X3,X4,X5] :
( neighborhood(f16(X2,X3,X4,X5),X2,X4,X5)
| ~ subset_sets(X3,X4)
| limit_point(X2,X3,X4,X5)
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f488,f210]) ).
fof(f496,plain,
! [X0,X1,X2,X3,X4,X5] :
( subset_sets(X3,f14(X3,X4,X5,X2))
| ~ subset_sets(X3,X4)
| element_of_set(X2,closure(X3,X4,X5))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f488,f193]) ).
fof(f497,plain,
! [X0,X1,X2,X3] :
( separation(f21(X2,X3),f22(X2,X3),X2,X3)
| connected_space(X2,X3)
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f488,f246]) ).
fof(f498,plain,
! [X0,X1,X2,X3] :
( open_covering(f24(X2,X3),X2,X3)
| compact_space(X2,X3)
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f488,f265]) ).
fof(f499,plain,
! [X0,X1,X2,X3] :
( element_of_set(f20(X2,X3),X2)
| hausdorff(X2,X3)
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f488,f223]) ).
fof(f500,plain,
! [X0,X1,X2,X3] :
( element_of_set(f19(X2,X3),X2)
| hausdorff(X2,X3)
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f488,f222]) ).
fof(f501,plain,
! [X0,X1,X2] :
( element_of_collection(empty_set,X2)
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f488,f125]) ).
fof(f502,plain,
! [X0,X1,X2,X3] :
( element_of_collection(X2,X3)
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f488,f126]) ).
fof(f503,definition,
! [X0,X1] :
( sQ14_spl
<=> topological_space(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f504,plain,
! [X0,X1] :
( ~ sQ14_spl
| topological_space(X0,X1) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,definition,
! [X2,X3,X4] :
( sQ15_spl
<=> ( element_of_collection(intersection_of_members(top_of_basis(X3)),top_of_basis(X2))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X3))),intersection_of_members(top_of_basis(X4))) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f507,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(top_of_basis(X1))),intersection_of_members(top_of_basis(X2))) ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f509,plain,
( sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f489,f503,f506]) ).
fof(f510,definition,
! [X2,X3,X4] :
( sQ16_spl
<=> ( ~ element_of_set(X2,intersection_of_members(top_of_basis(X4)))
| element_of_set(X2,union_of_members(top_of_basis(X3))) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f511,plain,
! [X0,X1,X2] :
( ~ sQ16_spl
| ~ element_of_set(X0,intersection_of_members(top_of_basis(X2)))
| element_of_set(X0,union_of_members(top_of_basis(X1))) ),
inference(component_clause,[status(thm)],[f510]) ).
fof(f513,plain,
( sQ16_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f490,f503,f510]) ).
fof(f514,definition,
! [X0,X1] :
( sQ17_spl
<=> element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f515,plain,
! [X0,X1] :
( ~ sQ17_spl
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(component_clause,[status(thm)],[f514]) ).
fof(f517,definition,
! [X2,X3] :
( sQ18_spl
<=> equal_sets(union_of_members(X2),X3) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f520,plain,
( sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f491,f514,f517]) ).
fof(f521,definition,
! [X2,X3,X4] :
( sQ19_spl
<=> ( ~ element_of_collection(X2,X4)
| open(X2,X3,X4) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( sQ19_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f492,f514,f521]) ).
fof(f525,definition,
! [X2,X3,X4,X5,X6] :
( sQ20_spl
<=> ( element_of_collection(intersection_of_sets(f16(X2,X3,X4,X5),X3),top_of_basis(X6))
| eq_p(f11(X6,intersection_of_sets(f16(X2,X3,X4,X5),X3)),X2)
| ~ subset_sets(X3,X4)
| limit_point(X2,X3,X4,X5) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f528,plain,
( sQ20_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f493,f514,f525]) ).
fof(f529,definition,
! [X2,X3,X4,X5] :
( sQ21_spl
<=> ( closed(f14(X3,X4,X5,X2),X4,X5)
| ~ subset_sets(X3,X4)
| element_of_set(X2,closure(X3,X4,X5)) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f532,plain,
( sQ21_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f494,f514,f529]) ).
fof(f533,definition,
! [X2,X3,X4,X5] :
( sQ22_spl
<=> ( neighborhood(f16(X2,X3,X4,X5),X2,X4,X5)
| ~ subset_sets(X3,X4)
| limit_point(X2,X3,X4,X5) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f536,plain,
( sQ22_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f495,f514,f533]) ).
fof(f537,definition,
! [X2,X3,X4,X5] :
( sQ23_spl
<=> ( subset_sets(X3,f14(X3,X4,X5,X2))
| ~ subset_sets(X3,X4)
| element_of_set(X2,closure(X3,X4,X5)) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f540,plain,
( sQ23_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f496,f514,f537]) ).
fof(f541,definition,
! [X2,X3] :
( sQ24_spl
<=> ( separation(f21(X2,X3),f22(X2,X3),X2,X3)
| connected_space(X2,X3) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f544,plain,
( sQ24_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f497,f514,f541]) ).
fof(f545,definition,
! [X2,X3] :
( sQ25_spl
<=> ( open_covering(f24(X2,X3),X2,X3)
| compact_space(X2,X3) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f548,plain,
( sQ25_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f498,f514,f545]) ).
fof(f549,definition,
! [X2,X3] :
( sQ26_spl
<=> ( element_of_set(f20(X2,X3),X2)
| hausdorff(X2,X3) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f552,plain,
( sQ26_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f499,f514,f549]) ).
fof(f553,definition,
! [X2,X3] :
( sQ27_spl
<=> ( element_of_set(f19(X2,X3),X2)
| hausdorff(X2,X3) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f556,plain,
( sQ27_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f500,f514,f553]) ).
fof(f557,definition,
! [X2] :
( sQ28_spl
<=> element_of_collection(empty_set,X2) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f560,plain,
( sQ28_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f501,f514,f557]) ).
fof(f561,definition,
! [X2,X3] :
( sQ29_spl
<=> element_of_collection(X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f564,plain,
( sQ29_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f502,f514,f561]) ).
fof(f565,plain,
! [X0] :
( element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f486,f292]) ).
fof(f566,plain,
! [X0,X1] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X1))
| neighborhood(f17(cx,ct,f11(X1,cx),f11(X0,intersection_of_members(ct))),f11(X1,cx),cx,ct)
| eq_p(f11(X1,cx),f11(X0,intersection_of_members(ct)))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f487,f432]) ).
fof(f567,plain,
! [X0,X1] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X1))
| neighborhood(f18(cx,ct,f11(X1,cx),f11(X0,intersection_of_members(ct))),f11(X0,intersection_of_members(ct)),cx,ct)
| eq_p(f11(X1,cx),f11(X0,intersection_of_members(ct)))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f487,f431]) ).
fof(f568,plain,
! [X0,X1] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X1))
| disjoint_s(f17(cx,ct,f11(X1,cx),f11(X0,intersection_of_members(ct))),f18(cx,ct,f11(X1,cx),f11(X0,intersection_of_members(ct))))
| eq_p(f11(X1,cx),f11(X0,intersection_of_members(ct)))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f487,f430]) ).
fof(f569,plain,
! [X0,X1] :
( ~ sQ3_spl
| neighborhood(f17(cx,ct,f11(X0,intersection_of_members(ct)),X1),f11(X0,intersection_of_members(ct)),cx,ct)
| eq_p(f11(X0,intersection_of_members(ct)),X1)
| ~ element_of_set(X1,cx)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f487,f403]) ).
fof(f570,plain,
! [X0,X1] :
( ~ sQ3_spl
| neighborhood(f18(cx,ct,f11(X0,intersection_of_members(ct)),X1),X1,cx,ct)
| eq_p(f11(X0,intersection_of_members(ct)),X1)
| ~ element_of_set(X1,cx)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f487,f402]) ).
fof(f571,plain,
! [X0,X1] :
( ~ sQ3_spl
| disjoint_s(f17(cx,ct,f11(X0,intersection_of_members(ct)),X1),f18(cx,ct,f11(X0,intersection_of_members(ct)),X1))
| eq_p(f11(X0,intersection_of_members(ct)),X1)
| ~ element_of_set(X1,cx)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f487,f401]) ).
fof(f572,plain,
! [X0] :
( element_of_collection(f1(ct,f11(X0,intersection_of_members(ct))),ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f565,f116]) ).
fof(f573,plain,
! [X0] :
( element_of_set(f11(X0,intersection_of_members(ct)),f1(ct,f11(X0,intersection_of_members(ct))))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f565,f115]) ).
fof(f574,plain,
! [X0,X1] :
( element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| element_of_set(f11(X1,intersection_of_members(ct)),f1(ct,f11(X0,intersection_of_members(ct))))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f572,f413]) ).
fof(f575,plain,
! [X0,X1] :
( ~ element_of_set(X1,f1(ct,f11(X0,intersection_of_members(ct))))
| element_of_set(X1,union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f572,f118]) ).
fof(f577,plain,
! [X0,X1,X2] :
( element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_set(X2,intersection_of_members(X0))
| element_of_set(X2,intersection_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f485,f294]) ).
fof(f579,plain,
! [X0,X1,X2] :
( element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_set(X2,intersection_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f577]) ).
fof(f580,plain,
! [X0,X1,X2,X3] :
( element_of_set(X3,X2)
| ~ element_of_collection(X2,X0)
| element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f579,f120]) ).
fof(f581,plain,
! [X0,X1,X2] :
( element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),X0)
| element_of_set(X2,intersection_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f579,f116]) ).
fof(f582,plain,
! [X0,X1,X2] :
( element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_set(X2,intersection_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f579,f115]) ).
fof(f583,plain,
! [X0,X1,X2,X3] :
( element_of_set(X3,X2)
| ~ element_of_collection(X2,X0)
| element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),X0)
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f581,f120]) ).
fof(f584,plain,
! [X0,X1,X2,X3] :
( element_of_collection(intersection_of_members(X0),top_of_basis(X3))
| element_of_set(f11(X3,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_set(X2,intersection_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f581,f413]) ).
fof(f585,plain,
! [X0,X1,X2,X3] :
( ~ element_of_set(X3,f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_set(X3,union_of_members(X0))
| element_of_set(X2,intersection_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f581,f118]) ).
fof(f586,plain,
! [X0,X1,X2,X3,X4,X5] :
( topological_space(X4,X5)
| element_of_set(X2,intersection_of_members(top_of_basis(X3)))
| element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),union_of_members(top_of_basis(X0)))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f580,f488]) ).
fof(f587,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X3))
| element_of_collection(cx,top_of_basis(X2))
| eq_p(f11(X2,cx),f11(X3,cx))
| element_of_set(X1,f17(cx,ct,f11(X2,cx),f11(X3,cx)))
| element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f580,f461]) ).
fof(f588,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X3))
| element_of_collection(cx,top_of_basis(X2))
| eq_p(f11(X2,cx),f11(X3,cx))
| element_of_set(X1,f18(cx,ct,f11(X2,cx),f11(X3,cx)))
| element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f580,f451]) ).
fof(f589,plain,
! [X0,X1,X2,X3,X4,X5] :
( topological_space(X4,X5)
| element_of_set(X2,boundary(X3,X4,X5))
| element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),union_of_members(top_of_basis(X0)))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f580,f408]) ).
fof(f590,plain,
! [X0,X1,X2] :
( limit_point(X2,a,cx,ct)
| element_of_set(X1,f16(X2,a,cx,ct))
| element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f580,f418]) ).
fof(f591,plain,
! [X0,X1,X2] :
( element_of_collection(intersection_of_members(ct),top_of_basis(X2))
| element_of_set(X1,f1(ct,f11(X2,intersection_of_members(ct))))
| element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f580,f572]) ).
fof(f592,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f16(X3,a,cx,ct),top_of_basis(X2))
| limit_point(X3,a,cx,ct)
| element_of_set(X1,f1(ct,f11(X2,f16(X3,a,cx,ct))))
| element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f580,f441]) ).
fof(f593,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f1(ct,f11(X3,empty_set)),top_of_basis(X2))
| element_of_collection(empty_set,top_of_basis(X3))
| element_of_set(X1,f1(ct,f11(X2,f1(ct,f11(X3,empty_set)))))
| element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f580,f438]) ).
fof(f594,plain,
! [X0,X1,X2] :
( element_of_collection(empty_set,top_of_basis(X2))
| element_of_set(X1,f1(ct,f11(X2,empty_set)))
| element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f580,f415]) ).
fof(f597,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( element_of_collection(f1(X0,f11(X4,f1(X0,f11(X5,f1(X0,f11(X6,f1(X0,f11(X7,union_of_members(X0))))))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X5,f1(X0,f11(X6,f1(X0,f11(X7,union_of_members(X0))))))),top_of_basis(X4))
| element_of_collection(f1(X0,f11(X6,f1(X0,f11(X7,union_of_members(X0))))),top_of_basis(X5))
| element_of_collection(f1(X0,f11(X7,union_of_members(X0))),top_of_basis(X6))
| element_of_collection(union_of_members(X0),top_of_basis(X7))
| element_of_set(X2,f1(X0,f11(X3,f1(X0,f11(X4,f1(X0,f11(X5,f1(X0,f11(X6,f1(X0,f11(X7,union_of_members(X0))))))))))))
| element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f580,f386]) ).
fof(f599,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( element_of_collection(f1(X0,f11(X4,f1(X0,f11(X5,f1(X0,f11(X6,union_of_members(X0))))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X5,f1(X0,f11(X6,union_of_members(X0))))),top_of_basis(X4))
| element_of_collection(f1(X0,f11(X6,union_of_members(X0))),top_of_basis(X5))
| element_of_collection(union_of_members(X0),top_of_basis(X6))
| element_of_set(X2,f1(X0,f11(X3,f1(X0,f11(X4,f1(X0,f11(X5,f1(X0,f11(X6,union_of_members(X0))))))))))
| element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f580,f378]) ).
fof(f601,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_collection(f1(X0,f11(X4,f1(X0,f11(X5,union_of_members(X0))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X5,union_of_members(X0))),top_of_basis(X4))
| element_of_collection(union_of_members(X0),top_of_basis(X5))
| element_of_set(X2,f1(X0,f11(X3,f1(X0,f11(X4,f1(X0,f11(X5,union_of_members(X0))))))))
| element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f580,f366]) ).
fof(f603,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(f1(X0,f11(X4,union_of_members(X0))),top_of_basis(X3))
| element_of_collection(union_of_members(X0),top_of_basis(X4))
| element_of_set(X2,f1(X0,f11(X3,f1(X0,f11(X4,union_of_members(X0))))))
| element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f580,f354]) ).
fof(f605,plain,
! [X0,X1,X2,X3] :
( element_of_collection(union_of_members(X0),top_of_basis(X3))
| element_of_set(X2,f1(X0,f11(X3,union_of_members(X0))))
| element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f580,f295]) ).
fof(f607,plain,
! [X0,X1] :
( element_of_set(X1,empty_set)
| element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f580,f291]) ).
fof(f608,plain,
! [X0,X1] :
( element_of_set(X1,cx)
| element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f580,f290]) ).
fof(f609,definition,
! [X0,X1] :
( sQ30_spl
<=> ( element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),union_of_members(top_of_basis(X0)))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f610,plain,
! [X0,X1] :
( ~ sQ30_spl
| element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),union_of_members(top_of_basis(X0)))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(component_clause,[status(thm)],[f609]) ).
fof(f612,definition,
! [X2,X3] :
( sQ31_spl
<=> element_of_set(X2,intersection_of_members(top_of_basis(X3))) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( sQ14_spl
| sQ31_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f586,f609,f612,f503]) ).
fof(f616,definition,
! [X0] :
( sQ32_spl
<=> ( element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f619,definition,
! [X1,X2,X3] :
( sQ33_spl
<=> ( element_of_collection(cx,top_of_basis(X3))
| element_of_collection(cx,top_of_basis(X2))
| eq_p(f11(X2,cx),f11(X3,cx))
| element_of_set(X1,f17(cx,ct,f11(X2,cx),f11(X3,cx))) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f622,plain,
( ~ sQ3_spl
| sQ33_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f587,f616,f619,f298]) ).
fof(f623,definition,
! [X1,X2,X3] :
( sQ34_spl
<=> ( element_of_collection(cx,top_of_basis(X3))
| element_of_collection(cx,top_of_basis(X2))
| eq_p(f11(X2,cx),f11(X3,cx))
| element_of_set(X1,f18(cx,ct,f11(X2,cx),f11(X3,cx))) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f626,plain,
( ~ sQ3_spl
| sQ34_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f588,f616,f623,f298]) ).
fof(f627,definition,
! [X2,X3,X4,X5] :
( sQ35_spl
<=> ( topological_space(X4,X5)
| element_of_set(X2,boundary(X3,X4,X5)) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f630,plain,
( sQ35_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f589,f609,f627]) ).
fof(f631,definition,
! [X1,X2] :
( sQ36_spl
<=> ( limit_point(X2,a,cx,ct)
| element_of_set(X1,f16(X2,a,cx,ct)) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f634,plain,
( sQ36_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f590,f616,f631]) ).
fof(f635,definition,
! [X1,X2] :
( sQ37_spl
<=> ( element_of_collection(intersection_of_members(ct),top_of_basis(X2))
| element_of_set(X1,f1(ct,f11(X2,intersection_of_members(ct)))) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f638,plain,
( sQ37_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f591,f616,f635]) ).
fof(f639,definition,
! [X1,X2,X3] :
( sQ38_spl
<=> ( element_of_collection(f16(X3,a,cx,ct),top_of_basis(X2))
| limit_point(X3,a,cx,ct)
| element_of_set(X1,f1(ct,f11(X2,f16(X3,a,cx,ct)))) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f642,plain,
( sQ38_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f592,f616,f639]) ).
fof(f643,definition,
! [X1,X2,X3] :
( sQ39_spl
<=> ( element_of_collection(f1(ct,f11(X3,empty_set)),top_of_basis(X2))
| element_of_collection(empty_set,top_of_basis(X3))
| element_of_set(X1,f1(ct,f11(X2,f1(ct,f11(X3,empty_set))))) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f646,plain,
( sQ39_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f593,f616,f643]) ).
fof(f647,definition,
! [X1,X2] :
( sQ40_spl
<=> ( element_of_collection(empty_set,top_of_basis(X2))
| element_of_set(X1,f1(ct,f11(X2,empty_set))) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f650,plain,
( sQ40_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f594,f616,f647]) ).
fof(f651,definition,
! [X1] :
( sQ41_spl
<=> element_of_set(X1,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f654,plain,
( sQ41_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f607,f616,f651]) ).
fof(f655,definition,
! [X1] :
( sQ42_spl
<=> element_of_set(X1,cx) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f658,plain,
( sQ42_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f608,f616,f655]) ).
fof(f659,plain,
! [X0,X1] :
( ~ sQ30_spl
| element_of_collection(f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))),top_of_basis(X0))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f610,f116]) ).
fof(f660,plain,
! [X0,X1] :
( ~ sQ30_spl
| element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f610,f115]) ).
fof(f661,plain,
! [X0,X1,X2,X3,X4,X5] :
( topological_space(X4,X5)
| element_of_set(X2,intersection_of_members(top_of_basis(X3)))
| element_of_collection(f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))),top_of_basis(X0))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f583,f488]) ).
fof(f662,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X3))
| element_of_collection(cx,top_of_basis(X2))
| eq_p(f11(X2,cx),f11(X3,cx))
| element_of_set(X1,f17(cx,ct,f11(X2,cx),f11(X3,cx)))
| element_of_collection(f1(ct,f11(X0,intersection_of_members(ct))),ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f583,f461]) ).
fof(f663,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X3))
| element_of_collection(cx,top_of_basis(X2))
| eq_p(f11(X2,cx),f11(X3,cx))
| element_of_set(X1,f18(cx,ct,f11(X2,cx),f11(X3,cx)))
| element_of_collection(f1(ct,f11(X0,intersection_of_members(ct))),ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f583,f451]) ).
fof(f664,plain,
! [X0,X1,X2,X3,X4,X5] :
( topological_space(X4,X5)
| element_of_set(X2,boundary(X3,X4,X5))
| element_of_collection(f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))),top_of_basis(X0))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f583,f408]) ).
fof(f665,plain,
! [X0,X1,X2] :
( limit_point(X2,a,cx,ct)
| element_of_set(X1,f16(X2,a,cx,ct))
| element_of_collection(f1(ct,f11(X0,intersection_of_members(ct))),ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f583,f418]) ).
fof(f666,plain,
! [X0,X1,X2] :
( element_of_collection(intersection_of_members(ct),top_of_basis(X2))
| element_of_set(X1,f1(ct,f11(X2,intersection_of_members(ct))))
| element_of_collection(f1(ct,f11(X0,intersection_of_members(ct))),ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f583,f572]) ).
fof(f667,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f16(X3,a,cx,ct),top_of_basis(X2))
| limit_point(X3,a,cx,ct)
| element_of_set(X1,f1(ct,f11(X2,f16(X3,a,cx,ct))))
| element_of_collection(f1(ct,f11(X0,intersection_of_members(ct))),ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f583,f441]) ).
fof(f668,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f1(ct,f11(X3,empty_set)),top_of_basis(X2))
| element_of_collection(empty_set,top_of_basis(X3))
| element_of_set(X1,f1(ct,f11(X2,f1(ct,f11(X3,empty_set)))))
| element_of_collection(f1(ct,f11(X0,intersection_of_members(ct))),ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f583,f438]) ).
fof(f669,plain,
! [X0,X1,X2] :
( element_of_collection(empty_set,top_of_basis(X2))
| element_of_set(X1,f1(ct,f11(X2,empty_set)))
| element_of_collection(f1(ct,f11(X0,intersection_of_members(ct))),ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f583,f415]) ).
fof(f672,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( element_of_collection(f1(X0,f11(X4,f1(X0,f11(X5,f1(X0,f11(X6,f1(X0,f11(X7,union_of_members(X0))))))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X5,f1(X0,f11(X6,f1(X0,f11(X7,union_of_members(X0))))))),top_of_basis(X4))
| element_of_collection(f1(X0,f11(X6,f1(X0,f11(X7,union_of_members(X0))))),top_of_basis(X5))
| element_of_collection(f1(X0,f11(X7,union_of_members(X0))),top_of_basis(X6))
| element_of_collection(union_of_members(X0),top_of_basis(X7))
| element_of_set(X2,f1(X0,f11(X3,f1(X0,f11(X4,f1(X0,f11(X5,f1(X0,f11(X6,f1(X0,f11(X7,union_of_members(X0))))))))))))
| element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),X0)
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f583,f386]) ).
fof(f674,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( element_of_collection(f1(X0,f11(X4,f1(X0,f11(X5,f1(X0,f11(X6,union_of_members(X0))))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X5,f1(X0,f11(X6,union_of_members(X0))))),top_of_basis(X4))
| element_of_collection(f1(X0,f11(X6,union_of_members(X0))),top_of_basis(X5))
| element_of_collection(union_of_members(X0),top_of_basis(X6))
| element_of_set(X2,f1(X0,f11(X3,f1(X0,f11(X4,f1(X0,f11(X5,f1(X0,f11(X6,union_of_members(X0))))))))))
| element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),X0)
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f583,f378]) ).
fof(f676,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_collection(f1(X0,f11(X4,f1(X0,f11(X5,union_of_members(X0))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X5,union_of_members(X0))),top_of_basis(X4))
| element_of_collection(union_of_members(X0),top_of_basis(X5))
| element_of_set(X2,f1(X0,f11(X3,f1(X0,f11(X4,f1(X0,f11(X5,union_of_members(X0))))))))
| element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),X0)
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f583,f366]) ).
fof(f678,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(f1(X0,f11(X4,union_of_members(X0))),top_of_basis(X3))
| element_of_collection(union_of_members(X0),top_of_basis(X4))
| element_of_set(X2,f1(X0,f11(X3,f1(X0,f11(X4,union_of_members(X0))))))
| element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),X0)
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f583,f354]) ).
fof(f680,plain,
! [X0,X1,X2,X3] :
( element_of_collection(union_of_members(X0),top_of_basis(X3))
| element_of_set(X2,f1(X0,f11(X3,union_of_members(X0))))
| element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),X0)
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f583,f295]) ).
fof(f682,plain,
! [X0,X1] :
( element_of_set(X1,empty_set)
| element_of_collection(f1(ct,f11(X0,intersection_of_members(ct))),ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f583,f291]) ).
fof(f683,plain,
! [X0,X1] :
( element_of_set(X1,cx)
| element_of_collection(f1(ct,f11(X0,intersection_of_members(ct))),ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f583,f290]) ).
fof(f684,definition,
! [X0,X1] :
( sQ43_spl
<=> ( element_of_collection(f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))),top_of_basis(X0))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f685,plain,
! [X0,X1] :
( ~ sQ43_spl
| element_of_collection(f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))),top_of_basis(X0))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(component_clause,[status(thm)],[f684]) ).
fof(f687,plain,
( sQ14_spl
| sQ31_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f661,f684,f612,f503]) ).
fof(f688,definition,
! [X0] :
( sQ44_spl
<=> ( element_of_collection(f1(ct,f11(X0,intersection_of_members(ct))),ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f691,plain,
( ~ sQ3_spl
| sQ33_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f662,f688,f619,f298]) ).
fof(f692,plain,
( ~ sQ3_spl
| sQ34_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f663,f688,f623,f298]) ).
fof(f693,plain,
( sQ35_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f664,f684,f627]) ).
fof(f694,plain,
( sQ36_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f665,f688,f631]) ).
fof(f695,plain,
( sQ37_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f666,f688,f635]) ).
fof(f696,plain,
( sQ38_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f667,f688,f639]) ).
fof(f697,plain,
( sQ39_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f668,f688,f643]) ).
fof(f698,plain,
( sQ40_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f669,f688,f647]) ).
fof(f699,plain,
( sQ41_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f682,f688,f651]) ).
fof(f700,plain,
( sQ42_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f683,f688,f655]) ).
fof(f703,plain,
! [X0,X1,X2] :
( ~ sQ30_spl
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X2))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X0))),f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f659,f413]) ).
fof(f704,plain,
! [X0,X1,X2] :
( ~ sQ30_spl
| ~ element_of_set(X2,f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))))
| element_of_set(X2,union_of_members(top_of_basis(X0)))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f659,f118]) ).
fof(f706,plain,
! [X0,X1] :
( element_of_collection(f1(ct,f11(X0,intersection_of_members(ct))),top_of_basis(X1))
| element_of_set(f11(X1,f1(ct,f11(X0,intersection_of_members(ct)))),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f575,f167]) ).
fof(f708,plain,
! [X0,X1,X2,X3] :
( element_of_set(X3,X2)
| ~ element_of_collection(X2,X0)
| element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f582,f120]) ).
fof(f709,plain,
! [X0,X1] :
( element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0))
| element_of_set(X1,intersection_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f582,f575]) ).
fof(f710,definition,
! [X0] :
( sQ45_spl
<=> ( element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f713,definition,
! [X1] :
( sQ46_spl
<=> element_of_set(X1,intersection_of_members(ct)) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f716,plain,
( sQ46_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f709,f710,f713]) ).
fof(f720,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),top_of_basis(X3))
| element_of_set(f11(X3,f1(X0,f11(X1,intersection_of_members(X0)))),union_of_members(X0))
| element_of_set(X2,intersection_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f585,f167]) ).
fof(f723,plain,
! [X0,X1,X2] :
( element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(union_of_members(X0),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X2))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f484,f327]) ).
fof(f724,plain,
! [X0,X1,X2] :
( element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(union_of_members(X0),top_of_basis(X2))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f723]) ).
fof(f725,plain,
! [X0,X1,X2] :
( element_of_collection(f4(X0,top_of_basis(X1)),top_of_basis(X1))
| ~ element_of_collection(X0,top_of_basis(X1))
| ~ element_of_collection(empty_set,top_of_basis(X1))
| ~ equal_sets(union_of_members(top_of_basis(X1)),X0)
| topological_space(X0,top_of_basis(X1))
| element_of_set(f11(X2,intersection_of_members(f5(X0,top_of_basis(X1)))),union_of_members(f5(X0,top_of_basis(X1))))
| element_of_collection(intersection_of_members(f5(X0,top_of_basis(X1))),top_of_basis(X2)) ),
inference(resolution,[status(thm)],[f724,f134]) ).
fof(f726,plain,
! [X0,X1,X2] :
( element_of_collection(f3(X0,top_of_basis(X1)),top_of_basis(X1))
| ~ element_of_collection(X0,top_of_basis(X1))
| ~ element_of_collection(empty_set,top_of_basis(X1))
| ~ equal_sets(union_of_members(top_of_basis(X1)),X0)
| topological_space(X0,top_of_basis(X1))
| element_of_set(f11(X2,intersection_of_members(f5(X0,top_of_basis(X1)))),union_of_members(f5(X0,top_of_basis(X1))))
| element_of_collection(intersection_of_members(f5(X0,top_of_basis(X1))),top_of_basis(X2)) ),
inference(resolution,[status(thm)],[f724,f132]) ).
fof(f727,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(X4,union_of_members(X0))
| element_of_collection(f1(top_of_basis(X2),f11(X3,intersection_of_members(top_of_basis(X2)))),top_of_basis(X2))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f724,f583]) ).
fof(f728,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(X4,union_of_members(X0))
| element_of_set(f11(X3,intersection_of_members(top_of_basis(X2))),union_of_members(top_of_basis(X2)))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f724,f580]) ).
fof(f729,plain,
! [X0,X1,X2,X3] :
( element_of_collection(intersection_of_members(top_of_basis(X3)),top_of_basis(X2))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X3))),union_of_members(X0))
| element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f724,f413]) ).
fof(f730,plain,
! [X0,X1,X2,X3] :
( ~ element_of_set(X2,union_of_members(X0))
| element_of_set(X2,union_of_members(top_of_basis(X3)))
| element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f724,f118]) ).
fof(f731,plain,
! [X0,X1,X2] :
( element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),X0)
| element_of_collection(union_of_members(X0),top_of_basis(X2))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f724,f116]) ).
fof(f732,plain,
! [X0,X1,X2] :
( element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(union_of_members(X0),top_of_basis(X2))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f724,f115]) ).
fof(f733,definition,
! [X0,X1,X4] :
( sQ47_spl
<=> ( element_of_set(X4,union_of_members(X0))
| element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f736,plain,
( sQ43_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f727,f733,f684]) ).
fof(f737,plain,
( sQ30_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f728,f733,f609]) ).
fof(f738,plain,
! [X0,X1,X2] :
( element_of_collection(f4(X0,top_of_basis(X1)),top_of_basis(X1))
| ~ element_of_collection(X0,top_of_basis(X1))
| ~ element_of_collection(empty_set,top_of_basis(X1))
| ~ equal_sets(union_of_members(top_of_basis(X1)),X0)
| topological_space(X0,top_of_basis(X1))
| element_of_collection(f1(f5(X0,top_of_basis(X1)),f11(X2,intersection_of_members(f5(X0,top_of_basis(X1))))),f5(X0,top_of_basis(X1)))
| element_of_collection(intersection_of_members(f5(X0,top_of_basis(X1))),top_of_basis(X2)) ),
inference(resolution,[status(thm)],[f731,f134]) ).
fof(f739,plain,
! [X0,X1,X2] :
( element_of_collection(f3(X0,top_of_basis(X1)),top_of_basis(X1))
| ~ element_of_collection(X0,top_of_basis(X1))
| ~ element_of_collection(empty_set,top_of_basis(X1))
| ~ equal_sets(union_of_members(top_of_basis(X1)),X0)
| topological_space(X0,top_of_basis(X1))
| element_of_collection(f1(f5(X0,top_of_basis(X1)),f11(X2,intersection_of_members(f5(X0,top_of_basis(X1))))),f5(X0,top_of_basis(X1)))
| element_of_collection(intersection_of_members(f5(X0,top_of_basis(X1))),top_of_basis(X2)) ),
inference(resolution,[status(thm)],[f731,f132]) ).
fof(f740,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(X4,union_of_members(X0))
| element_of_collection(f1(top_of_basis(X2),f11(X3,intersection_of_members(top_of_basis(X2)))),top_of_basis(X2))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),X0)
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f731,f583]) ).
fof(f741,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(X4,union_of_members(X0))
| element_of_set(f11(X3,intersection_of_members(top_of_basis(X2))),union_of_members(top_of_basis(X2)))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),X0)
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f731,f580]) ).
fof(f742,plain,
! [X0,X1,X2,X3] :
( element_of_collection(intersection_of_members(top_of_basis(X3)),top_of_basis(X2))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X3))),union_of_members(X0))
| element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),X0)
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f731,f413]) ).
fof(f743,plain,
! [X0,X1,X2,X3] :
( ~ element_of_set(X2,union_of_members(X0))
| element_of_set(X2,union_of_members(top_of_basis(X3)))
| element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),X0)
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f731,f118]) ).
fof(f746,plain,
! [X0,X1,X2,X3] :
( element_of_collection(intersection_of_members(X0),top_of_basis(X3))
| element_of_set(f11(X3,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(union_of_members(X0),top_of_basis(X2))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f731,f413]) ).
fof(f747,plain,
! [X0,X1,X2,X3] :
( ~ element_of_set(X3,f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_set(X3,union_of_members(X0))
| element_of_collection(union_of_members(X0),top_of_basis(X2))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f731,f118]) ).
fof(f748,definition,
! [X0,X1,X4] :
( sQ48_spl
<=> ( element_of_set(X4,union_of_members(X0))
| element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),X0)
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f751,plain,
( sQ43_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f740,f748,f684]) ).
fof(f752,plain,
( sQ30_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f741,f748,f609]) ).
fof(f755,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(f1(X3,f11(X4,intersection_of_members(X3))),X3)
| element_of_collection(intersection_of_members(X3),top_of_basis(X4))
| element_of_set(X2,union_of_members(X3))
| element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f708,f731]) ).
fof(f756,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(f11(X4,intersection_of_members(X3)),union_of_members(X3))
| element_of_collection(intersection_of_members(X3),top_of_basis(X4))
| element_of_set(X2,union_of_members(X3))
| element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f708,f724]) ).
fof(f757,plain,
! [X0,X1,X2,X3,X4,X5] :
( topological_space(X4,X5)
| element_of_set(X2,intersection_of_members(top_of_basis(X3)))
| element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f708,f488]) ).
fof(f758,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X3))
| element_of_collection(cx,top_of_basis(X2))
| eq_p(f11(X2,cx),f11(X3,cx))
| element_of_set(X1,f17(cx,ct,f11(X2,cx),f11(X3,cx)))
| element_of_set(f11(X0,intersection_of_members(ct)),f1(ct,f11(X0,intersection_of_members(ct))))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f708,f461]) ).
fof(f759,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X3))
| element_of_collection(cx,top_of_basis(X2))
| eq_p(f11(X2,cx),f11(X3,cx))
| element_of_set(X1,f18(cx,ct,f11(X2,cx),f11(X3,cx)))
| element_of_set(f11(X0,intersection_of_members(ct)),f1(ct,f11(X0,intersection_of_members(ct))))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f708,f451]) ).
fof(f760,plain,
! [X0,X1,X2,X3,X4,X5] :
( topological_space(X4,X5)
| element_of_set(X2,boundary(X3,X4,X5))
| element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f708,f408]) ).
fof(f761,plain,
! [X0,X1,X2] :
( limit_point(X2,a,cx,ct)
| element_of_set(X1,f16(X2,a,cx,ct))
| element_of_set(f11(X0,intersection_of_members(ct)),f1(ct,f11(X0,intersection_of_members(ct))))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f708,f418]) ).
fof(f763,plain,
! [X0,X1,X2] :
( element_of_collection(intersection_of_members(ct),top_of_basis(X2))
| element_of_set(X1,f1(ct,f11(X2,intersection_of_members(ct))))
| element_of_set(f11(X0,intersection_of_members(ct)),f1(ct,f11(X0,intersection_of_members(ct))))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f708,f572]) ).
fof(f764,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f16(X3,a,cx,ct),top_of_basis(X2))
| limit_point(X3,a,cx,ct)
| element_of_set(X1,f1(ct,f11(X2,f16(X3,a,cx,ct))))
| element_of_set(f11(X0,intersection_of_members(ct)),f1(ct,f11(X0,intersection_of_members(ct))))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f708,f441]) ).
fof(f765,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f1(ct,f11(X3,empty_set)),top_of_basis(X2))
| element_of_collection(empty_set,top_of_basis(X3))
| element_of_set(X1,f1(ct,f11(X2,f1(ct,f11(X3,empty_set)))))
| element_of_set(f11(X0,intersection_of_members(ct)),f1(ct,f11(X0,intersection_of_members(ct))))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f708,f438]) ).
fof(f766,plain,
! [X0,X1,X2] :
( element_of_collection(empty_set,top_of_basis(X2))
| element_of_set(X1,f1(ct,f11(X2,empty_set)))
| element_of_set(f11(X0,intersection_of_members(ct)),f1(ct,f11(X0,intersection_of_members(ct))))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f708,f415]) ).
fof(f767,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(union_of_members(X0),top_of_basis(X4))
| element_of_collection(intersection_of_members(X0),top_of_basis(X3))
| element_of_set(X2,f1(X0,f11(X3,intersection_of_members(X0))))
| element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f708,f731]) ).
fof(f770,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( element_of_collection(f1(X0,f11(X4,f1(X0,f11(X5,f1(X0,f11(X6,f1(X0,f11(X7,union_of_members(X0))))))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X5,f1(X0,f11(X6,f1(X0,f11(X7,union_of_members(X0))))))),top_of_basis(X4))
| element_of_collection(f1(X0,f11(X6,f1(X0,f11(X7,union_of_members(X0))))),top_of_basis(X5))
| element_of_collection(f1(X0,f11(X7,union_of_members(X0))),top_of_basis(X6))
| element_of_collection(union_of_members(X0),top_of_basis(X7))
| element_of_set(X2,f1(X0,f11(X3,f1(X0,f11(X4,f1(X0,f11(X5,f1(X0,f11(X6,f1(X0,f11(X7,union_of_members(X0))))))))))))
| element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f708,f386]) ).
fof(f772,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( element_of_collection(f1(X0,f11(X4,f1(X0,f11(X5,f1(X0,f11(X6,union_of_members(X0))))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X5,f1(X0,f11(X6,union_of_members(X0))))),top_of_basis(X4))
| element_of_collection(f1(X0,f11(X6,union_of_members(X0))),top_of_basis(X5))
| element_of_collection(union_of_members(X0),top_of_basis(X6))
| element_of_set(X2,f1(X0,f11(X3,f1(X0,f11(X4,f1(X0,f11(X5,f1(X0,f11(X6,union_of_members(X0))))))))))
| element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f708,f378]) ).
fof(f774,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_collection(f1(X0,f11(X4,f1(X0,f11(X5,union_of_members(X0))))),top_of_basis(X3))
| element_of_collection(f1(X0,f11(X5,union_of_members(X0))),top_of_basis(X4))
| element_of_collection(union_of_members(X0),top_of_basis(X5))
| element_of_set(X2,f1(X0,f11(X3,f1(X0,f11(X4,f1(X0,f11(X5,union_of_members(X0))))))))
| element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f708,f366]) ).
fof(f776,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(f1(X0,f11(X4,union_of_members(X0))),top_of_basis(X3))
| element_of_collection(union_of_members(X0),top_of_basis(X4))
| element_of_set(X2,f1(X0,f11(X3,f1(X0,f11(X4,union_of_members(X0))))))
| element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f708,f354]) ).
fof(f778,plain,
! [X0,X1,X2,X3] :
( element_of_collection(union_of_members(X0),top_of_basis(X3))
| element_of_set(X2,f1(X0,f11(X3,union_of_members(X0))))
| element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f708,f295]) ).
fof(f780,plain,
! [X0,X1] :
( element_of_set(X1,empty_set)
| element_of_set(f11(X0,intersection_of_members(ct)),f1(ct,f11(X0,intersection_of_members(ct))))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f708,f291]) ).
fof(f781,plain,
! [X0,X1] :
( element_of_set(X1,cx)
| element_of_set(f11(X0,intersection_of_members(ct)),f1(ct,f11(X0,intersection_of_members(ct))))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f708,f290]) ).
fof(f782,definition,
! [X0,X1] :
( sQ49_spl
<=> ( element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f783,plain,
! [X0,X1] :
( ~ sQ49_spl
| element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(component_clause,[status(thm)],[f782]) ).
fof(f785,plain,
( sQ48_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f755,f782,f748]) ).
fof(f786,plain,
( sQ47_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f756,f782,f733]) ).
fof(f787,plain,
( sQ14_spl
| sQ31_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f757,f782,f612,f503]) ).
fof(f788,definition,
! [X0] :
( sQ50_spl
<=> ( element_of_set(f11(X0,intersection_of_members(ct)),f1(ct,f11(X0,intersection_of_members(ct))))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f791,plain,
( ~ sQ3_spl
| sQ33_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f758,f788,f619,f298]) ).
fof(f792,plain,
( ~ sQ3_spl
| sQ34_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f759,f788,f623,f298]) ).
fof(f793,plain,
( sQ35_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f760,f782,f627]) ).
fof(f794,plain,
( sQ36_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f761,f788,f631]) ).
fof(f795,plain,
( sQ37_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f763,f788,f635]) ).
fof(f796,plain,
( sQ38_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f764,f788,f639]) ).
fof(f797,plain,
( sQ39_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f765,f788,f643]) ).
fof(f798,plain,
( sQ40_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f766,f788,f647]) ).
fof(f799,plain,
( sQ41_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f780,f788,f651]) ).
fof(f800,plain,
( sQ42_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f781,f788,f655]) ).
fof(f802,plain,
! [X0,X1,X2] :
( element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| element_of_set(f11(X1,intersection_of_members(ct)),union_of_members(top_of_basis(X2)))
| element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f730,f565]) ).
fof(f805,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f16(X2,a,cx,ct),top_of_basis(X1))
| limit_point(X2,a,cx,ct)
| element_of_set(f11(X1,f16(X2,a,cx,ct)),union_of_members(top_of_basis(X3)))
| element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f730,f435]) ).
fof(f806,plain,
! [X0,X1,X2] :
( element_of_collection(empty_set,top_of_basis(X1))
| element_of_set(f11(X1,empty_set),union_of_members(top_of_basis(X2)))
| element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f730,f409]) ).
fof(f807,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f1(ct,f11(X2,empty_set)),top_of_basis(X1))
| element_of_collection(empty_set,top_of_basis(X2))
| element_of_set(f11(X1,f1(ct,f11(X2,empty_set))),union_of_members(top_of_basis(X3)))
| element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f730,f426]) ).
fof(f819,definition,
! [X1,X2] :
( sQ51_spl
<=> ( element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| element_of_set(f11(X1,intersection_of_members(ct)),union_of_members(top_of_basis(X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f822,plain,
( sQ51_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f802,f616,f819]) ).
fof(f823,definition,
! [X1,X2,X3] :
( sQ52_spl
<=> ( element_of_collection(f16(X2,a,cx,ct),top_of_basis(X1))
| limit_point(X2,a,cx,ct)
| element_of_set(f11(X1,f16(X2,a,cx,ct)),union_of_members(top_of_basis(X3))) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f826,plain,
( sQ52_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f805,f616,f823]) ).
fof(f827,definition,
! [X1,X2] :
( sQ53_spl
<=> ( element_of_collection(empty_set,top_of_basis(X1))
| element_of_set(f11(X1,empty_set),union_of_members(top_of_basis(X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f830,plain,
( sQ53_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f806,f616,f827]) ).
fof(f831,definition,
! [X1,X2,X3] :
( sQ54_spl
<=> ( element_of_collection(f1(ct,f11(X2,empty_set)),top_of_basis(X1))
| element_of_collection(empty_set,top_of_basis(X2))
| element_of_set(f11(X1,f1(ct,f11(X2,empty_set))),union_of_members(top_of_basis(X3))) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f834,plain,
( sQ54_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f807,f616,f831]) ).
fof(f835,plain,
! [X0,X1] :
( ~ sQ3_spl
| element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| neighborhood(f17(cx,ct,f11(X0,intersection_of_members(ct)),f11(X1,intersection_of_members(ct))),f11(X0,intersection_of_members(ct)),cx,ct)
| eq_p(f11(X0,intersection_of_members(ct)),f11(X1,intersection_of_members(ct)))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f569,f487]) ).
fof(f836,plain,
! [X0,X1] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X1))
| neighborhood(f17(cx,ct,f11(X0,intersection_of_members(ct)),f11(X1,cx)),f11(X0,intersection_of_members(ct)),cx,ct)
| eq_p(f11(X0,intersection_of_members(ct)),f11(X1,cx))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f569,f167]) ).
fof(f837,plain,
! [X0,X1] :
( ~ sQ3_spl
| element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| neighborhood(f18(cx,ct,f11(X0,intersection_of_members(ct)),f11(X1,intersection_of_members(ct))),f11(X1,intersection_of_members(ct)),cx,ct)
| eq_p(f11(X0,intersection_of_members(ct)),f11(X1,intersection_of_members(ct)))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f570,f487]) ).
fof(f838,plain,
! [X0,X1] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X1))
| neighborhood(f18(cx,ct,f11(X0,intersection_of_members(ct)),f11(X1,cx)),f11(X1,cx),cx,ct)
| eq_p(f11(X0,intersection_of_members(ct)),f11(X1,cx))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f570,f167]) ).
fof(f839,plain,
! [X0,X1] :
( ~ sQ3_spl
| element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| disjoint_s(f17(cx,ct,f11(X0,intersection_of_members(ct)),f11(X1,intersection_of_members(ct))),f18(cx,ct,f11(X0,intersection_of_members(ct)),f11(X1,intersection_of_members(ct))))
| eq_p(f11(X0,intersection_of_members(ct)),f11(X1,intersection_of_members(ct)))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f571,f487]) ).
fof(f840,plain,
! [X0,X1] :
( ~ sQ3_spl
| element_of_collection(cx,top_of_basis(X1))
| disjoint_s(f17(cx,ct,f11(X0,intersection_of_members(ct)),f11(X1,cx)),f18(cx,ct,f11(X0,intersection_of_members(ct)),f11(X1,cx)))
| eq_p(f11(X0,intersection_of_members(ct)),f11(X1,cx))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f571,f167]) ).
fof(f843,plain,
! [X0,X1] :
( ~ sQ3_spl
| open(f17(cx,ct,f11(X1,cx),f11(X0,intersection_of_members(ct))),cx,ct)
| element_of_collection(cx,top_of_basis(X1))
| eq_p(f11(X1,cx),f11(X0,intersection_of_members(ct)))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f566,f199]) ).
fof(f844,plain,
! [X0,X1] :
( ~ sQ3_spl
| open(f18(cx,ct,f11(X1,cx),f11(X0,intersection_of_members(ct))),cx,ct)
| element_of_collection(cx,top_of_basis(X1))
| eq_p(f11(X1,cx),f11(X0,intersection_of_members(ct)))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f567,f199]) ).
fof(f845,plain,
! [X0,X1,X2,X3] :
( element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),union_of_members(top_of_basis(X3)))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X0))),union_of_members(top_of_basis(X0)))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f729,f730]) ).
fof(f847,plain,
! [X0,X1] :
( element_of_collection(f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))),top_of_basis(X0))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f729,f116]) ).
fof(f848,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),X0)
| element_of_collection(intersection_of_members(top_of_basis(X3)),top_of_basis(X2))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X3))),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f729,f116]) ).
fof(f849,plain,
! [X0,X1] :
( element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f729,f115]) ).
fof(f850,plain,
! [X0,X1,X2,X3] :
( element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(top_of_basis(X3)),top_of_basis(X2))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X3))),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f729,f115]) ).
fof(f851,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_set(f11(X3,intersection_of_members(top_of_basis(X2))),union_of_members(top_of_basis(X5)))
| element_of_set(f11(X4,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X4))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f729,f730]) ).
fof(f852,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f1(X0,f11(X3,intersection_of_members(top_of_basis(X2)))),X0)
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f729,f116]) ).
fof(f853,plain,
! [X0,X1,X2,X3] :
( element_of_set(f11(X3,intersection_of_members(top_of_basis(X2))),f1(X0,f11(X3,intersection_of_members(top_of_basis(X2)))))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f729,f115]) ).
fof(f854,plain,
! [X0,X1,X2,X3] :
( element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),union_of_members(top_of_basis(X3)))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X0))),union_of_members(top_of_basis(X0)))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f845]) ).
fof(f855,plain,
! [X0,X1] :
( element_of_collection(f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))),top_of_basis(X0))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f847]) ).
fof(f856,plain,
! [X0,X1] :
( element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),f1(top_of_basis(X0),f11(X1,intersection_of_members(top_of_basis(X0)))))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f849]) ).
fof(f857,definition,
! [X0,X1,X4] :
( sQ55_spl
<=> ( element_of_set(f11(X4,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X4))
| element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f858,plain,
! [X0,X1,X2] :
( ~ sQ55_spl
| element_of_set(f11(X2,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X2))
| element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(component_clause,[status(thm)],[f857]) ).
fof(f860,definition,
! [X2,X3,X5] :
( sQ56_spl
<=> ( element_of_set(f11(X3,intersection_of_members(top_of_basis(X2))),union_of_members(top_of_basis(X5)))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f863,plain,
( sQ56_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f851,f857,f860]) ).
fof(f864,plain,
! [X0,X1,X2] :
( element_of_collection(f4(X0,top_of_basis(X1)),top_of_basis(X1))
| ~ element_of_collection(X0,top_of_basis(X1))
| ~ element_of_collection(empty_set,top_of_basis(X1))
| ~ equal_sets(union_of_members(top_of_basis(X1)),X0)
| topological_space(X0,top_of_basis(X1))
| element_of_set(f11(X2,intersection_of_members(f5(X0,top_of_basis(X1)))),f1(f5(X0,top_of_basis(X1)),f11(X2,intersection_of_members(f5(X0,top_of_basis(X1))))))
| element_of_collection(intersection_of_members(f5(X0,top_of_basis(X1))),top_of_basis(X2)) ),
inference(resolution,[status(thm)],[f732,f134]) ).
fof(f865,plain,
! [X0,X1,X2] :
( element_of_collection(f3(X0,top_of_basis(X1)),top_of_basis(X1))
| ~ element_of_collection(X0,top_of_basis(X1))
| ~ element_of_collection(empty_set,top_of_basis(X1))
| ~ equal_sets(union_of_members(top_of_basis(X1)),X0)
| topological_space(X0,top_of_basis(X1))
| element_of_set(f11(X2,intersection_of_members(f5(X0,top_of_basis(X1)))),f1(f5(X0,top_of_basis(X1)),f11(X2,intersection_of_members(f5(X0,top_of_basis(X1))))))
| element_of_collection(intersection_of_members(f5(X0,top_of_basis(X1))),top_of_basis(X2)) ),
inference(resolution,[status(thm)],[f732,f132]) ).
fof(f866,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(X4,union_of_members(X0))
| element_of_set(f11(X3,intersection_of_members(top_of_basis(X2))),f1(top_of_basis(X2),f11(X3,intersection_of_members(top_of_basis(X2)))))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f732,f708]) ).
fof(f867,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(X4,union_of_members(X0))
| element_of_collection(f1(top_of_basis(X2),f11(X3,intersection_of_members(top_of_basis(X2)))),top_of_basis(X2))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f732,f583]) ).
fof(f868,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(X4,union_of_members(X0))
| element_of_set(f11(X3,intersection_of_members(top_of_basis(X2))),union_of_members(top_of_basis(X2)))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f732,f580]) ).
fof(f869,plain,
! [X0,X1,X2,X3] :
( element_of_collection(intersection_of_members(top_of_basis(X3)),top_of_basis(X2))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X3))),union_of_members(X0))
| element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f732,f413]) ).
fof(f870,plain,
! [X0,X1,X2,X3] :
( ~ element_of_set(X2,union_of_members(X0))
| element_of_set(X2,union_of_members(top_of_basis(X3)))
| element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f732,f118]) ).
fof(f871,plain,
! [X0,X1] :
( element_of_set(f11(X0,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0))
| element_of_collection(union_of_members(ct),top_of_basis(X1))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f732,f575]) ).
fof(f873,definition,
! [X0,X1,X4] :
( sQ57_spl
<=> ( element_of_set(X4,union_of_members(X0))
| element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f876,plain,
( sQ49_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f866,f873,f782]) ).
fof(f877,plain,
( sQ43_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f867,f873,f684]) ).
fof(f878,plain,
( sQ30_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f868,f873,f609]) ).
fof(f879,definition,
! [X1] :
( sQ58_spl
<=> element_of_collection(union_of_members(ct),top_of_basis(X1)) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f882,plain,
( sQ58_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f871,f710,f879]) ).
fof(f884,plain,
! [X0,X1] :
( ~ sQ3_spl
| open(f17(cx,ct,f11(X0,intersection_of_members(ct)),f11(X1,intersection_of_members(ct))),cx,ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| eq_p(f11(X0,intersection_of_members(ct)),f11(X1,intersection_of_members(ct)))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f835,f199]) ).
fof(f885,plain,
( element_of_set(f7(cx,ct),intersection_of_sets(f8(cx,ct),f9(cx,ct)))
| basis(cx,ct) ),
inference(resolution,[status(thm)],[f414,f162]) ).
fof(f886,plain,
( subset_collections(f5(cx,ct),ct)
| element_of_collection(f4(cx,ct),ct)
| ~ element_of_collection(cx,ct)
| ~ element_of_collection(empty_set,ct)
| topological_space(cx,ct) ),
inference(resolution,[status(thm)],[f414,f133]) ).
fof(f887,plain,
( subset_collections(f5(cx,ct),ct)
| element_of_collection(f3(cx,ct),ct)
| ~ element_of_collection(cx,ct)
| ~ element_of_collection(empty_set,ct)
| topological_space(cx,ct) ),
inference(resolution,[status(thm)],[f414,f131]) ).
fof(f888,plain,
( element_of_collection(f9(cx,ct),ct)
| basis(cx,ct) ),
inference(resolution,[status(thm)],[f414,f161]) ).
fof(f889,plain,
( element_of_collection(f8(cx,ct),ct)
| basis(cx,ct) ),
inference(resolution,[status(thm)],[f414,f160]) ).
fof(f890,plain,
( element_of_set(f7(cx,ct),cx)
| basis(cx,ct) ),
inference(resolution,[status(thm)],[f414,f159]) ).
fof(f891,definition,
( sQ59_spl
<=> basis(cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f892,plain,
( ~ sQ59_spl
| basis(cx,ct) ),
inference(component_clause,[status(thm)],[f891]) ).
fof(f894,definition,
( sQ60_spl
<=> element_of_set(f7(cx,ct),intersection_of_sets(f8(cx,ct),f9(cx,ct))) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f897,plain,
( sQ60_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f885,f891,f894]) ).
fof(f898,definition,
( sQ61_spl
<=> element_of_collection(empty_set,ct) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f901,definition,
( sQ62_spl
<=> element_of_collection(cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f904,definition,
( sQ63_spl
<=> element_of_collection(f4(cx,ct),ct) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f907,definition,
( sQ64_spl
<=> subset_collections(f5(cx,ct),ct) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f910,plain,
( sQ64_spl
| sQ63_spl
| ~ sQ62_spl
| ~ sQ61_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f886,f338,f898,f901,f904,f907]) ).
fof(f911,definition,
( sQ65_spl
<=> element_of_collection(f3(cx,ct),ct) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f914,plain,
( sQ64_spl
| sQ65_spl
| ~ sQ62_spl
| ~ sQ61_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f887,f338,f898,f901,f911,f907]) ).
fof(f915,definition,
( sQ66_spl
<=> element_of_collection(f9(cx,ct),ct) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f918,plain,
( sQ66_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f888,f891,f915]) ).
fof(f919,definition,
( sQ67_spl
<=> element_of_collection(f8(cx,ct),ct) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f922,plain,
( sQ67_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f889,f891,f919]) ).
fof(f923,definition,
( sQ68_spl
<=> element_of_set(f7(cx,ct),cx) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f926,plain,
( sQ68_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f890,f891,f923]) ).
fof(f930,plain,
! [X0] :
( element_of_collection(intersection_of_members(ct),top_of_basis(X0))
| open(f1(ct,f11(X0,intersection_of_members(ct))),cx,ct) ),
inference(resolution,[status(thm)],[f410,f572]) ).
fof(f931,plain,
! [X0,X1] :
( element_of_collection(f16(X1,a,cx,ct),top_of_basis(X0))
| limit_point(X1,a,cx,ct)
| open(f1(ct,f11(X0,f16(X1,a,cx,ct))),cx,ct) ),
inference(resolution,[status(thm)],[f410,f441]) ).
fof(f932,plain,
! [X0,X1] :
( element_of_collection(f1(ct,f11(X1,empty_set)),top_of_basis(X0))
| element_of_collection(empty_set,top_of_basis(X1))
| open(f1(ct,f11(X0,f1(ct,f11(X1,empty_set)))),cx,ct) ),
inference(resolution,[status(thm)],[f410,f438]) ).
fof(f933,plain,
! [X0] :
( element_of_collection(empty_set,top_of_basis(X0))
| open(f1(ct,f11(X0,empty_set)),cx,ct) ),
inference(resolution,[status(thm)],[f410,f415]) ).
fof(f934,plain,
! [X0,X1] :
( element_of_collection(union_of_members(ct),top_of_basis(X1))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0))
| open(f1(ct,f11(X0,intersection_of_members(ct))),cx,ct) ),
inference(resolution,[status(thm)],[f410,f731]) ).
fof(f935,plain,
! [X0,X1] :
( element_of_set(X1,intersection_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0))
| open(f1(ct,f11(X0,intersection_of_members(ct))),cx,ct) ),
inference(resolution,[status(thm)],[f410,f581]) ).
fof(f936,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_collection(f1(ct,f11(X1,f1(ct,f11(X2,f1(ct,f11(X3,f1(ct,f11(X4,f2(ct,X5))))))))),top_of_basis(X0))
| element_of_collection(f1(ct,f11(X2,f1(ct,f11(X3,f1(ct,f11(X4,f2(ct,X5))))))),top_of_basis(X1))
| element_of_collection(f1(ct,f11(X3,f1(ct,f11(X4,f2(ct,X5))))),top_of_basis(X2))
| element_of_collection(f1(ct,f11(X4,f2(ct,X5))),top_of_basis(X3))
| element_of_collection(f2(ct,X5),top_of_basis(X4))
| element_of_set(X5,intersection_of_members(ct))
| open(f1(ct,f11(X0,f1(ct,f11(X1,f1(ct,f11(X2,f1(ct,f11(X3,f1(ct,f11(X4,f2(ct,X5))))))))))),cx,ct) ),
inference(resolution,[status(thm)],[f410,f396]) ).
fof(f937,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(f1(ct,f11(X1,f1(ct,f11(X2,f1(ct,f11(X3,f1(ct,f11(X4,union_of_members(ct))))))))),top_of_basis(X0))
| element_of_collection(f1(ct,f11(X2,f1(ct,f11(X3,f1(ct,f11(X4,union_of_members(ct))))))),top_of_basis(X1))
| element_of_collection(f1(ct,f11(X3,f1(ct,f11(X4,union_of_members(ct))))),top_of_basis(X2))
| element_of_collection(f1(ct,f11(X4,union_of_members(ct))),top_of_basis(X3))
| element_of_collection(union_of_members(ct),top_of_basis(X4))
| open(f1(ct,f11(X0,f1(ct,f11(X1,f1(ct,f11(X2,f1(ct,f11(X3,f1(ct,f11(X4,union_of_members(ct))))))))))),cx,ct) ),
inference(resolution,[status(thm)],[f410,f386]) ).
fof(f938,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(f1(ct,f11(X1,f1(ct,f11(X2,f1(ct,f11(X3,f2(ct,X4))))))),top_of_basis(X0))
| element_of_collection(f1(ct,f11(X2,f1(ct,f11(X3,f2(ct,X4))))),top_of_basis(X1))
| element_of_collection(f1(ct,f11(X3,f2(ct,X4))),top_of_basis(X2))
| element_of_collection(f2(ct,X4),top_of_basis(X3))
| element_of_set(X4,intersection_of_members(ct))
| open(f1(ct,f11(X0,f1(ct,f11(X1,f1(ct,f11(X2,f1(ct,f11(X3,f2(ct,X4))))))))),cx,ct) ),
inference(resolution,[status(thm)],[f410,f382]) ).
fof(f939,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f1(ct,f11(X1,f1(ct,f11(X2,f1(ct,f11(X3,union_of_members(ct))))))),top_of_basis(X0))
| element_of_collection(f1(ct,f11(X2,f1(ct,f11(X3,union_of_members(ct))))),top_of_basis(X1))
| element_of_collection(f1(ct,f11(X3,union_of_members(ct))),top_of_basis(X2))
| element_of_collection(union_of_members(ct),top_of_basis(X3))
| open(f1(ct,f11(X0,f1(ct,f11(X1,f1(ct,f11(X2,f1(ct,f11(X3,union_of_members(ct))))))))),cx,ct) ),
inference(resolution,[status(thm)],[f410,f378]) ).
fof(f940,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f1(ct,f11(X1,f1(ct,f11(X2,f2(ct,X3))))),top_of_basis(X0))
| element_of_collection(f1(ct,f11(X2,f2(ct,X3))),top_of_basis(X1))
| element_of_collection(f2(ct,X3),top_of_basis(X2))
| element_of_set(X3,intersection_of_members(ct))
| open(f1(ct,f11(X0,f1(ct,f11(X1,f1(ct,f11(X2,f2(ct,X3))))))),cx,ct) ),
inference(resolution,[status(thm)],[f410,f370]) ).
fof(f941,plain,
! [X0,X1,X2] :
( element_of_collection(f1(ct,f11(X1,f1(ct,f11(X2,union_of_members(ct))))),top_of_basis(X0))
| element_of_collection(f1(ct,f11(X2,union_of_members(ct))),top_of_basis(X1))
| element_of_collection(union_of_members(ct),top_of_basis(X2))
| open(f1(ct,f11(X0,f1(ct,f11(X1,f1(ct,f11(X2,union_of_members(ct))))))),cx,ct) ),
inference(resolution,[status(thm)],[f410,f366]) ).
fof(f942,plain,
! [X0,X1,X2] :
( element_of_collection(f1(ct,f11(X1,f2(ct,X2))),top_of_basis(X0))
| element_of_collection(f2(ct,X2),top_of_basis(X1))
| element_of_set(X2,intersection_of_members(ct))
| open(f1(ct,f11(X0,f1(ct,f11(X1,f2(ct,X2))))),cx,ct) ),
inference(resolution,[status(thm)],[f410,f358]) ).
fof(f943,plain,
! [X0,X1] :
( element_of_collection(f1(ct,f11(X1,union_of_members(ct))),top_of_basis(X0))
| element_of_collection(union_of_members(ct),top_of_basis(X1))
| open(f1(ct,f11(X0,f1(ct,f11(X1,union_of_members(ct))))),cx,ct) ),
inference(resolution,[status(thm)],[f410,f354]) ).
fof(f944,plain,
! [X0,X1] :
( element_of_collection(f2(ct,X1),top_of_basis(X0))
| element_of_set(X1,intersection_of_members(ct))
| open(f1(ct,f11(X0,f2(ct,X1))),cx,ct) ),
inference(resolution,[status(thm)],[f410,f348]) ).
fof(f945,plain,
! [X0] :
( element_of_collection(union_of_members(ct),top_of_basis(X0))
| open(f1(ct,f11(X0,union_of_members(ct))),cx,ct) ),
inference(resolution,[status(thm)],[f410,f295]) ).
fof(f946,plain,
! [X0] :
( element_of_set(X0,intersection_of_members(ct))
| open(f2(ct,X0),cx,ct) ),
inference(resolution,[status(thm)],[f410,f121]) ).
fof(f947,plain,
open(empty_set,cx,ct),
inference(resolution,[status(thm)],[f410,f291]) ).
fof(f948,plain,
open(cx,cx,ct),
inference(resolution,[status(thm)],[f410,f290]) ).
fof(f949,definition,
! [X0] :
( sQ69_spl
<=> ( element_of_collection(intersection_of_members(ct),top_of_basis(X0))
| open(f1(ct,f11(X0,intersection_of_members(ct))),cx,ct) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f950,plain,
! [X0] :
( ~ sQ69_spl
| element_of_collection(intersection_of_members(ct),top_of_basis(X0))
| open(f1(ct,f11(X0,intersection_of_members(ct))),cx,ct) ),
inference(component_clause,[status(thm)],[f949]) ).
fof(f952,plain,
( sQ58_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f934,f949,f879]) ).
fof(f953,plain,
( sQ46_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f935,f949,f713]) ).
fof(f954,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ disjoint_s(X0,X1)
| ~ equal_sets(union_of_sets(X0,X1),X2)
| ~ element_of_collection(X1,X3)
| ~ element_of_collection(X0,X3)
| equal_sets(X1,empty_set)
| equal_sets(X0,empty_set)
| separation(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f242,f504]) ).
fof(f955,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| eq_p(X4,X0)
| ~ element_of_set(X4,intersection_of_sets(f16(X0,X1,X2,X3),X1))
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f212,f504]) ).
fof(f956,plain,
! [X0,X1] :
( ~ sQ14_spl
| equal_sets(union_of_members(X0),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f123,f504]) ).
fof(f957,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ element_of_collection(X0,X2)
| open(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f142,f504]) ).
fof(f959,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| closed(f14(X1,X2,X3,X0),X2,X3)
| ~ subset_sets(X1,X2)
| element_of_set(X0,closure(X1,X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[f194,f504]) ).
fof(f960,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| neighborhood(f16(X0,X1,X2,X3),X0,X2,X3)
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f210,f504]) ).
fof(f961,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| subset_sets(X1,f14(X1,X2,X3,X0))
| ~ subset_sets(X1,X2)
| element_of_set(X0,closure(X1,X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[f193,f504]) ).
fof(f962,plain,
! [X0,X1] :
( ~ sQ14_spl
| separation(f21(X0,X1),f22(X0,X1),X0,X1)
| connected_space(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f246,f504]) ).
fof(f963,plain,
! [X0,X1] :
( ~ sQ14_spl
| open_covering(f24(X0,X1),X0,X1)
| compact_space(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f265,f504]) ).
fof(f964,plain,
! [X0,X1] :
( ~ sQ14_spl
| element_of_set(f20(X0,X1),X0)
| hausdorff(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f223,f504]) ).
fof(f965,plain,
! [X0,X1] :
( ~ sQ14_spl
| element_of_set(f19(X0,X1),X0)
| hausdorff(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f222,f504]) ).
fof(f967,plain,
! [X0,X1] :
( ~ sQ14_spl
| element_of_collection(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f126,f504]) ).
fof(f968,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(X0,X2)
| ~ element_of_set(X0,intersection_of_members(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f120,f967]) ).
fof(f969,plain,
! [X0] :
( ~ sQ14_spl
| open(X0,cx,ct) ),
inference(backward_subsumption_resolution,[status(thm)],[f410,f967]) ).
fof(f970,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ element_of_set(X0,X2)
| element_of_set(X0,union_of_members(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f118,f967]) ).
fof(f971,plain,
! [X0,X1] :
( ~ sQ14_spl
| element_of_set(f7(X0,X1),intersection_of_sets(f8(X0,X1),f9(X0,X1)))
| basis(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f162,f956]) ).
fof(f972,plain,
! [X0,X1] :
( ~ sQ14_spl
| element_of_set(f7(X0,X1),X0)
| basis(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f159,f956]) ).
fof(f973,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ element_of_set(X1,X0)
| ~ open(X0,X2,X3)
| neighborhood(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f203,f504]) ).
fof(f975,plain,
( sQ1_spl
| ~ sQ14_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f283,f969]) ).
fof(f976,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ element_of_set(X1,X0)
| neighborhood(X0,X1,cx,ct) ),
inference(resolution,[status(thm)],[f969,f973]) ).
fof(f977,plain,
( sQ1_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f975]) ).
fof(f978,plain,
( sQ14_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f488,f514,f503]) ).
fof(f979,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(f20(boundary(X0,X1,X2),X3),closure(X0,X1,X2))
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f964,f215]) ).
fof(f980,plain,
! [X0,X1] :
( ~ sQ14_spl
| element_of_set(f20(f16(X0,a,cx,ct),X1),union_of_members(ct))
| limit_point(X0,a,cx,ct)
| hausdorff(f16(X0,a,cx,ct),X1) ),
inference(resolution,[status(thm)],[f964,f424]) ).
fof(f981,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f20(cx,X0),X1),f20(cx,X0),cx,ct)
| eq_p(f20(cx,X0),X1)
| ~ element_of_set(X1,cx)
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f964,f403]) ).
fof(f982,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f20(cx,X0),X1),X1,cx,ct)
| eq_p(f20(cx,X0),X1)
| ~ element_of_set(X1,cx)
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f964,f402]) ).
fof(f983,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f20(cx,X0),X1),f18(cx,ct,f20(cx,X0),X1))
| eq_p(f20(cx,X0),X1)
| ~ element_of_set(X1,cx)
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f964,f401]) ).
fof(f984,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f20(closure(X0,X1,X2),X3),X4)
| ~ closed(X4,X1,X2)
| ~ subset_sets(X0,X4)
| hausdorff(closure(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f964,f192]) ).
fof(f985,plain,
! [X0] :
( ~ sQ14_spl
| element_of_set(f20(empty_set,X0),union_of_members(ct))
| hausdorff(empty_set,X0) ),
inference(resolution,[status(thm)],[f964,f292]) ).
fof(f986,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f20(f2(X0,X1),X2),union_of_members(X0))
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2) ),
inference(resolution,[status(thm)],[f964,f294]) ).
fof(f987,plain,
! [X0,X1] :
( ~ sQ14_spl
| element_of_set(f20(union_of_members(X0),X1),f1(X0,f20(union_of_members(X0),X1)))
| hausdorff(union_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f964,f115]) ).
fof(f988,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(f19(boundary(X0,X1,X2),X3),closure(X0,X1,X2))
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f965,f215]) ).
fof(f989,plain,
! [X0,X1] :
( ~ sQ14_spl
| element_of_set(f19(f16(X0,a,cx,ct),X1),union_of_members(ct))
| limit_point(X0,a,cx,ct)
| hausdorff(f16(X0,a,cx,ct),X1) ),
inference(resolution,[status(thm)],[f965,f424]) ).
fof(f990,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f19(cx,X0),X1),f19(cx,X0),cx,ct)
| eq_p(f19(cx,X0),X1)
| ~ element_of_set(X1,cx)
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f965,f403]) ).
fof(f991,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f19(cx,X0),X1),X1,cx,ct)
| eq_p(f19(cx,X0),X1)
| ~ element_of_set(X1,cx)
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f965,f402]) ).
fof(f992,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f19(cx,X0),X1),f18(cx,ct,f19(cx,X0),X1))
| eq_p(f19(cx,X0),X1)
| ~ element_of_set(X1,cx)
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f965,f401]) ).
fof(f993,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f19(closure(X0,X1,X2),X3),X4)
| ~ closed(X4,X1,X2)
| ~ subset_sets(X0,X4)
| hausdorff(closure(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f965,f192]) ).
fof(f994,plain,
! [X0] :
( ~ sQ14_spl
| element_of_set(f19(empty_set,X0),union_of_members(ct))
| hausdorff(empty_set,X0) ),
inference(resolution,[status(thm)],[f965,f292]) ).
fof(f995,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f19(f2(X0,X1),X2),union_of_members(X0))
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2) ),
inference(resolution,[status(thm)],[f965,f294]) ).
fof(f996,plain,
! [X0,X1] :
( ~ sQ14_spl
| element_of_set(f19(union_of_members(X0),X1),f1(X0,f19(union_of_members(X0),X1)))
| hausdorff(union_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f965,f115]) ).
fof(f997,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(f7(boundary(X0,X1,X2),X3),closure(X0,X1,X2))
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f972,f215]) ).
fof(f998,plain,
! [X0,X1] :
( ~ sQ14_spl
| element_of_set(f7(f16(X0,a,cx,ct),X1),union_of_members(ct))
| limit_point(X0,a,cx,ct)
| basis(f16(X0,a,cx,ct),X1) ),
inference(resolution,[status(thm)],[f972,f424]) ).
fof(f999,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f7(cx,X0),X1),f7(cx,X0),cx,ct)
| eq_p(f7(cx,X0),X1)
| ~ element_of_set(X1,cx)
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f972,f403]) ).
fof(f1000,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f7(cx,X0),X1),X1,cx,ct)
| eq_p(f7(cx,X0),X1)
| ~ element_of_set(X1,cx)
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f972,f402]) ).
fof(f1001,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f7(cx,X0),X1),f18(cx,ct,f7(cx,X0),X1))
| eq_p(f7(cx,X0),X1)
| ~ element_of_set(X1,cx)
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f972,f401]) ).
fof(f1002,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f7(closure(X0,X1,X2),X3),X4)
| ~ closed(X4,X1,X2)
| ~ subset_sets(X0,X4)
| basis(closure(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f972,f192]) ).
fof(f1003,plain,
! [X0] :
( ~ sQ14_spl
| element_of_set(f7(empty_set,X0),union_of_members(ct))
| basis(empty_set,X0) ),
inference(resolution,[status(thm)],[f972,f292]) ).
fof(f1004,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f7(f2(X0,X1),X2),union_of_members(X0))
| element_of_set(X1,intersection_of_members(X0))
| basis(f2(X0,X1),X2) ),
inference(resolution,[status(thm)],[f972,f294]) ).
fof(f1005,plain,
! [X0,X1] :
( ~ sQ14_spl
| element_of_set(f7(union_of_members(X0),X1),f1(X0,f7(union_of_members(X0),X1)))
| basis(union_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f972,f115]) ).
fof(f1006,plain,
! [X0,X1] :
( ~ sQ14_spl
| subset_collections(f24(X0,X1),X1)
| compact_space(X0,X1) ),
inference(resolution,[status(thm)],[f963,f256]) ).
fof(f1007,plain,
! [X0] :
( ~ sQ14_spl
| element_of_set(f20(empty_set,X0),f1(ct,f20(empty_set,X0)))
| hausdorff(empty_set,X0) ),
inference(resolution,[status(thm)],[f985,f115]) ).
fof(f1008,plain,
! [X0] :
( ~ sQ14_spl
| element_of_set(f19(empty_set,X0),f1(ct,f19(empty_set,X0)))
| hausdorff(empty_set,X0) ),
inference(resolution,[status(thm)],[f994,f115]) ).
fof(f1009,plain,
! [X0] :
( ~ sQ14_spl
| element_of_set(f7(empty_set,X0),f1(ct,f7(empty_set,X0)))
| basis(empty_set,X0) ),
inference(resolution,[status(thm)],[f1003,f115]) ).
fof(f1011,plain,
! [X0,X1] :
( ~ sQ14_spl
| neighborhood(f16(X0,a,cx,X1),X0,cx,X1)
| limit_point(X0,a,cx,X1) ),
inference(resolution,[status(thm)],[f960,f274]) ).
fof(f1013,plain,
! [X0,X1] :
( ~ sQ14_spl
| subset_sets(a,f14(a,cx,X1,X0))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f961,f274]) ).
fof(f1014,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ disjoint_s(X0,X1)
| ~ equal_sets(union_of_sets(X0,X1),X2)
| ~ element_of_collection(X1,X3)
| equal_sets(X1,empty_set)
| equal_sets(X0,empty_set)
| separation(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f954,f967]) ).
fof(f1015,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| basis(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4)
| eq_p(f7(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4),X0)
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f955,f972]) ).
fof(f1016,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4)
| eq_p(f19(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4),X0)
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f955,f965]) ).
fof(f1017,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4)
| eq_p(f20(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4),X0)
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f955,f964]) ).
fof(f1019,plain,
! [X0,X1] :
( ~ sQ14_spl
| closed(f14(a,cx,X1,X0),cx,X1)
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f959,f274]) ).
fof(f1020,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f20(boundary(X0,X1,X2),X3),X4)
| ~ closed(X4,X1,X2)
| ~ subset_sets(X0,X4)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f979,f192]) ).
fof(f1022,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f20(closure(a,X0,X1),X2),cx)
| ~ closed(cx,X0,X1)
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f984,f274]) ).
fof(f1023,plain,
! [X0,X1] :
( ~ sQ14_spl
| open(f16(X0,a,cx,X1),cx,X1)
| limit_point(X0,a,cx,X1) ),
inference(resolution,[status(thm)],[f1011,f199]) ).
fof(f1024,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f20(closure(a,X2,X3),X4),f14(a,cx,X1,X0))
| ~ closed(f14(a,cx,X1,X0),X2,X3)
| hausdorff(closure(a,X2,X3),X4)
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1013,f984]) ).
fof(f1026,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| subset_sets(a,f14(a,f14(a,cx,X1,X0),X3,X2))
| element_of_set(X2,closure(a,f14(a,cx,X1,X0),X3))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1013,f961]) ).
fof(f1027,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| neighborhood(f16(X2,a,f14(a,cx,X1,X0),X3),X2,f14(a,cx,X1,X0),X3)
| limit_point(X2,a,f14(a,cx,X1,X0),X3)
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1013,f960]) ).
fof(f1028,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f19(boundary(X0,X1,X2),X3),X4)
| ~ closed(X4,X1,X2)
| ~ subset_sets(X0,X4)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f988,f192]) ).
fof(f1029,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f7(boundary(X0,X1,X2),X3),X4)
| ~ closed(X4,X1,X2)
| ~ subset_sets(X0,X4)
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f997,f192]) ).
fof(f1030,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ element_of_set(X1,X0)
| ~ open(X0,X2,X3)
| neighborhood(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f203,f504]) ).
fof(f1031,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| limit_point(X0,a,cx,X1)
| ~ element_of_set(X2,f16(X0,a,cx,X1))
| neighborhood(f16(X0,a,cx,X1),X2,cx,X1) ),
inference(resolution,[status(thm)],[f1030,f1023]) ).
fof(f1033,plain,
( ~ sQ2_spl
| open(relative_complement_sets(a,cx),cx,ct) ),
inference(resolution,[status(thm)],[f145,f286]) ).
fof(f1034,plain,
! [X0,X1] :
( ~ sQ14_spl
| element_of_set(X1,closure(a,cx,X0))
| open(relative_complement_sets(f14(a,cx,X0,X1),cx),cx,X0) ),
inference(resolution,[status(thm)],[f145,f1019]) ).
fof(f1035,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ open(relative_complement_sets(X0,X1),X1,X2)
| closed(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f146,f504]) ).
fof(f1036,plain,
! [X0] :
( ~ sQ14_spl
| closed(X0,cx,ct) ),
inference(resolution,[status(thm)],[f1035,f969]) ).
fof(f1037,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ subset_collections(X1,X0)
| ~ topological_space(X2,X1)
| finer(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f154,f504]) ).
fof(f1038,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| compact_space(X1,X0)
| ~ topological_space(X2,f24(X1,X0))
| finer(X0,f24(X1,X0),X2) ),
inference(resolution,[status(thm)],[f1037,f1006]) ).
fof(f1039,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| compact_space(X1,X0)
| finer(X0,f24(X1,X0),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1038,f504]) ).
fof(f1041,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ element_of_set(X2,relative_complement_sets(f14(a,cx,X1,X0),cx))
| neighborhood(relative_complement_sets(f14(a,cx,X1,X0),cx),X2,cx,X1)
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1034,f1030]) ).
fof(f1042,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(f16(X0,a,cx,X1),X2)
| limit_point(X0,a,cx,X1)
| neighborhood(f16(X0,a,cx,X1),f7(f16(X0,a,cx,X1),X2),cx,X1) ),
inference(resolution,[status(thm)],[f1031,f972]) ).
fof(f1043,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(f16(X0,a,cx,X1),X2)
| limit_point(X0,a,cx,X1)
| neighborhood(f16(X0,a,cx,X1),f19(f16(X0,a,cx,X1),X2),cx,X1) ),
inference(resolution,[status(thm)],[f1031,f965]) ).
fof(f1044,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(f16(X0,a,cx,X1),X2)
| limit_point(X0,a,cx,X1)
| neighborhood(f16(X0,a,cx,X1),f20(f16(X0,a,cx,X1),X2),cx,X1) ),
inference(resolution,[status(thm)],[f1031,f964]) ).
fof(f1048,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f20(closure(a,X4,X5),X6),f14(a,f14(a,cx,X1,X0),X3,X2))
| ~ closed(f14(a,f14(a,cx,X1,X0),X3,X2),X4,X5)
| hausdorff(closure(a,X4,X5),X6)
| element_of_set(X2,closure(a,f14(a,cx,X1,X0),X3))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1026,f984]) ).
fof(f1050,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| subset_sets(a,f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4))
| element_of_set(X4,closure(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5))
| element_of_set(X2,closure(a,f14(a,cx,X1,X0),X3))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1026,f961]) ).
fof(f1051,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| neighborhood(f16(X4,a,f14(a,f14(a,cx,X1,X0),X3,X2),X5),X4,f14(a,f14(a,cx,X1,X0),X3,X2),X5)
| limit_point(X4,a,f14(a,f14(a,cx,X1,X0),X3,X2),X5)
| element_of_set(X2,closure(a,f14(a,cx,X1,X0),X3))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1026,f960]) ).
fof(f1054,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f20(f2(X0,X1),X2),f1(X0,f20(f2(X0,X1),X2)))
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2) ),
inference(resolution,[status(thm)],[f986,f115]) ).
fof(f1055,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f19(f2(X0,X1),X2),f1(X0,f19(f2(X0,X1),X2)))
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2) ),
inference(resolution,[status(thm)],[f995,f115]) ).
fof(f1056,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f7(f2(X0,X1),X2),f1(X0,f7(f2(X0,X1),X2)))
| element_of_set(X1,intersection_of_members(X0))
| basis(f2(X0,X1),X2) ),
inference(resolution,[status(thm)],[f1004,f115]) ).
fof(f1057,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X6,closure(a,f14(a,cx,X3,X4),X5))
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f19(closure(a,X0,X1),X2),f14(a,f14(a,cx,X3,X4),X5,X6))
| ~ closed(f14(a,f14(a,cx,X3,X4),X5,X6),X0,X1)
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f993,f1026]) ).
fof(f1058,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f19(closure(a,X0,X1),X2),f14(a,cx,X3,X4))
| ~ closed(f14(a,cx,X3,X4),X0,X1)
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f993,f1013]) ).
fof(f1059,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f19(closure(a,X0,X1),X2),cx)
| ~ closed(cx,X0,X1)
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f993,f274]) ).
fof(f1060,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X6,closure(a,f14(a,cx,X3,X4),X5))
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f7(closure(a,X0,X1),X2),f14(a,f14(a,cx,X3,X4),X5,X6))
| ~ closed(f14(a,f14(a,cx,X3,X4),X5,X6),X0,X1)
| basis(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1002,f1026]) ).
fof(f1061,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f7(closure(a,X0,X1),X2),f14(a,cx,X3,X4))
| ~ closed(f14(a,cx,X3,X4),X0,X1)
| basis(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1002,f1013]) ).
fof(f1062,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f7(closure(a,X0,X1),X2),cx)
| ~ closed(cx,X0,X1)
| basis(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1002,f274]) ).
fof(f1063,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X6,closure(a,f14(a,cx,X3,X4),X5))
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f20(boundary(a,X0,X1),X2),f14(a,f14(a,cx,X3,X4),X5,X6))
| ~ closed(f14(a,f14(a,cx,X3,X4),X5,X6),X0,X1)
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1020,f1026]) ).
fof(f1064,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f20(boundary(a,X0,X1),X2),f14(a,cx,X3,X4))
| ~ closed(f14(a,cx,X3,X4),X0,X1)
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1020,f1013]) ).
fof(f1065,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f20(boundary(a,X0,X1),X2),cx)
| ~ closed(cx,X0,X1)
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1020,f274]) ).
fof(f1066,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X6,closure(a,f14(a,cx,X3,X4),X5))
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f19(boundary(a,X0,X1),X2),f14(a,f14(a,cx,X3,X4),X5,X6))
| ~ closed(f14(a,f14(a,cx,X3,X4),X5,X6),X0,X1)
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1028,f1026]) ).
fof(f1067,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f19(boundary(a,X0,X1),X2),f14(a,cx,X3,X4))
| ~ closed(f14(a,cx,X3,X4),X0,X1)
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1028,f1013]) ).
fof(f1068,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f19(boundary(a,X0,X1),X2),cx)
| ~ closed(cx,X0,X1)
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1028,f274]) ).
fof(f1069,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X6,closure(a,f14(a,cx,X3,X4),X5))
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f7(boundary(a,X0,X1),X2),f14(a,f14(a,cx,X3,X4),X5,X6))
| ~ closed(f14(a,f14(a,cx,X3,X4),X5,X6),X0,X1)
| basis(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1029,f1026]) ).
fof(f1070,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f7(boundary(a,X0,X1),X2),f14(a,cx,X3,X4))
| ~ closed(f14(a,cx,X3,X4),X0,X1)
| basis(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1029,f1013]) ).
fof(f1071,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f7(boundary(a,X0,X1),X2),cx)
| ~ closed(cx,X0,X1)
| basis(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1029,f274]) ).
fof(f1072,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,f14(a,cx,X1,X2),X3))
| element_of_set(X2,closure(a,cx,X1))
| basis(intersection_of_sets(f16(X0,a,f14(a,f14(a,cx,X1,X2),X3,X4),X5),a),X6)
| eq_p(f7(intersection_of_sets(f16(X0,a,f14(a,f14(a,cx,X1,X2),X3,X4),X5),a),X6),X0)
| limit_point(X0,a,f14(a,f14(a,cx,X1,X2),X3,X4),X5) ),
inference(resolution,[status(thm)],[f1015,f1026]) ).
fof(f1073,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X2,closure(a,cx,X1))
| basis(intersection_of_sets(f16(X0,a,f14(a,cx,X1,X2),X3),a),X4)
| eq_p(f7(intersection_of_sets(f16(X0,a,f14(a,cx,X1,X2),X3),a),X4),X0)
| limit_point(X0,a,f14(a,cx,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1015,f1013]) ).
fof(f1074,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(intersection_of_sets(f16(X0,a,cx,X1),a),X2)
| eq_p(f7(intersection_of_sets(f16(X0,a,cx,X1),a),X2),X0)
| limit_point(X0,a,cx,X1) ),
inference(resolution,[status(thm)],[f1015,f274]) ).
fof(f1075,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,f14(a,cx,X1,X2),X3))
| element_of_set(X2,closure(a,cx,X1))
| hausdorff(intersection_of_sets(f16(X0,a,f14(a,f14(a,cx,X1,X2),X3,X4),X5),a),X6)
| eq_p(f19(intersection_of_sets(f16(X0,a,f14(a,f14(a,cx,X1,X2),X3,X4),X5),a),X6),X0)
| limit_point(X0,a,f14(a,f14(a,cx,X1,X2),X3,X4),X5) ),
inference(resolution,[status(thm)],[f1016,f1026]) ).
fof(f1076,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X2,closure(a,cx,X1))
| hausdorff(intersection_of_sets(f16(X0,a,f14(a,cx,X1,X2),X3),a),X4)
| eq_p(f19(intersection_of_sets(f16(X0,a,f14(a,cx,X1,X2),X3),a),X4),X0)
| limit_point(X0,a,f14(a,cx,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1016,f1013]) ).
fof(f1077,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X0,a,cx,X1),a),X2)
| eq_p(f19(intersection_of_sets(f16(X0,a,cx,X1),a),X2),X0)
| limit_point(X0,a,cx,X1) ),
inference(resolution,[status(thm)],[f1016,f274]) ).
fof(f1078,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,f14(a,cx,X1,X2),X3))
| element_of_set(X2,closure(a,cx,X1))
| hausdorff(intersection_of_sets(f16(X0,a,f14(a,f14(a,cx,X1,X2),X3,X4),X5),a),X6)
| eq_p(f20(intersection_of_sets(f16(X0,a,f14(a,f14(a,cx,X1,X2),X3,X4),X5),a),X6),X0)
| limit_point(X0,a,f14(a,f14(a,cx,X1,X2),X3,X4),X5) ),
inference(resolution,[status(thm)],[f1017,f1026]) ).
fof(f1079,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X2,closure(a,cx,X1))
| hausdorff(intersection_of_sets(f16(X0,a,f14(a,cx,X1,X2),X3),a),X4)
| eq_p(f20(intersection_of_sets(f16(X0,a,f14(a,cx,X1,X2),X3),a),X4),X0)
| limit_point(X0,a,f14(a,cx,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1017,f1013]) ).
fof(f1080,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X0,a,cx,X1),a),X2)
| eq_p(f20(intersection_of_sets(f16(X0,a,cx,X1),a),X2),X0)
| limit_point(X0,a,cx,X1) ),
inference(resolution,[status(thm)],[f1017,f274]) ).
fof(f1081,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(X2,closure(a,cx,X0))
| element_of_set(X2,closure(a,cx,X0))
| element_of_set(f19(closure(a,cx,X0),X1),f14(a,cx,X0,X2))
| hausdorff(closure(a,cx,X0),X1) ),
inference(resolution,[status(thm)],[f1058,f1019]) ).
fof(f1082,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(X2,closure(a,cx,X0))
| element_of_set(f19(closure(a,cx,X0),X1),f14(a,cx,X0,X2))
| hausdorff(closure(a,cx,X0),X1) ),
inference(duplicate_literals_removal,[status(thm)],[f1081]) ).
fof(f1083,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(X2,closure(a,cx,X0))
| element_of_set(X2,closure(a,cx,X0))
| element_of_set(f7(closure(a,cx,X0),X1),f14(a,cx,X0,X2))
| basis(closure(a,cx,X0),X1) ),
inference(resolution,[status(thm)],[f1061,f1019]) ).
fof(f1084,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(X2,closure(a,cx,X0))
| element_of_set(f7(closure(a,cx,X0),X1),f14(a,cx,X0,X2))
| basis(closure(a,cx,X0),X1) ),
inference(duplicate_literals_removal,[status(thm)],[f1083]) ).
fof(f1085,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(X2,closure(a,cx,X1))
| element_of_set(f7(closure(a,cx,ct),X0),f14(a,cx,X1,X2))
| basis(closure(a,cx,ct),X0) ),
inference(resolution,[status(thm)],[f1036,f1061]) ).
fof(f1086,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(X2,closure(a,cx,X1))
| element_of_set(f19(closure(a,cx,ct),X0),f14(a,cx,X1,X2))
| hausdorff(closure(a,cx,ct),X0) ),
inference(resolution,[status(thm)],[f1036,f1058]) ).
fof(f1087,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f20(closure(a,cx,ct),X2),f14(a,cx,X1,X0))
| hausdorff(closure(a,cx,ct),X2)
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1036,f1024]) ).
fof(f1095,plain,
! [X0] :
( ~ sQ14_spl
| basis(cx,X0)
| element_of_set(f7(cx,X0),union_of_members(ct)) ),
inference(resolution,[status(thm)],[f293,f972]) ).
fof(f1096,plain,
! [X0] :
( ~ sQ14_spl
| hausdorff(cx,X0)
| element_of_set(f19(cx,X0),union_of_members(ct)) ),
inference(resolution,[status(thm)],[f293,f965]) ).
fof(f1097,plain,
! [X0] :
( ~ sQ14_spl
| hausdorff(cx,X0)
| element_of_set(f20(cx,X0),union_of_members(ct)) ),
inference(resolution,[status(thm)],[f293,f964]) ).
fof(f1098,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| closed(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f1035,f1100]) ).
fof(f1099,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ element_of_set(X1,X0)
| neighborhood(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f1030,f1100]) ).
fof(f1100,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| open(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f957,f967]) ).
fof(f1101,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f7(boundary(X0,X1,X2),X3),X4)
| ~ subset_sets(X0,X4)
| basis(boundary(X0,X1,X2),X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f1029,f1098]) ).
fof(f1102,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f19(boundary(X0,X1,X2),X3),X4)
| ~ subset_sets(X0,X4)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f1028,f1098]) ).
fof(f1103,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f20(boundary(X0,X1,X2),X3),X4)
| ~ subset_sets(X0,X4)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f1020,f1098]) ).
fof(f1104,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f7(closure(X0,X1,X2),X3),X4)
| ~ subset_sets(X0,X4)
| basis(closure(X0,X1,X2),X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f1002,f1098]) ).
fof(f1105,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f19(closure(X0,X1,X2),X3),X4)
| ~ subset_sets(X0,X4)
| hausdorff(closure(X0,X1,X2),X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f993,f1098]) ).
fof(f1106,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f20(closure(X0,X1,X2),X3),X4)
| ~ subset_sets(X0,X4)
| hausdorff(closure(X0,X1,X2),X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f984,f1098]) ).
fof(f1107,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X0,X4)
| ~ subset_sets(X1,X4)
| ~ element_of_set(X0,closure(X1,X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[f192,f1098]) ).
fof(f1108,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f7(closure(a,X0,X1),X2),f14(a,cx,X3,X4))
| basis(closure(a,X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f1061,f1098]) ).
fof(f1109,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f19(closure(a,X0,X1),X2),f14(a,cx,X3,X4))
| hausdorff(closure(a,X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f1058,f1098]) ).
fof(f1110,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f20(closure(a,X2,X3),X4),f14(a,cx,X1,X0))
| hausdorff(closure(a,X2,X3),X4)
| element_of_set(X0,closure(a,cx,X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f1024,f1098]) ).
fof(f1111,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f7(boundary(a,X0,X1),X2),cx)
| basis(boundary(a,X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f1071,f1098]) ).
fof(f1112,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f19(boundary(a,X0,X1),X2),cx)
| hausdorff(boundary(a,X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f1068,f1098]) ).
fof(f1113,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f20(boundary(a,X0,X1),X2),cx)
| hausdorff(boundary(a,X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f1065,f1098]) ).
fof(f1114,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f7(closure(a,X0,X1),X2),cx)
| basis(closure(a,X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f1062,f1098]) ).
fof(f1115,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f19(closure(a,X0,X1),X2),cx)
| hausdorff(closure(a,X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f1059,f1098]) ).
fof(f1116,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f20(closure(a,X0,X1),X2),cx)
| hausdorff(closure(a,X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f1022,f1098]) ).
fof(f1117,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X2,f6(X0,X1,X2,X4,X3))
| ~ element_of_set(X2,intersection_of_sets(X4,X3))
| ~ element_of_collection(X3,X1)
| ~ element_of_set(X2,X0)
| ~ basis(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f967]) ).
fof(f1118,plain,
! [X0,X1,X2] :
( ~ sQ59_spl
| ~ sQ14_spl
| element_of_set(X0,f6(cx,ct,X0,X2,X1))
| ~ element_of_set(X0,intersection_of_sets(X2,X1))
| ~ element_of_collection(X1,ct)
| ~ element_of_set(X0,cx) ),
inference(resolution,[status(thm)],[f1117,f892]) ).
fof(f1119,plain,
! [X0,X1,X2] :
( ~ sQ59_spl
| ~ sQ14_spl
| element_of_set(X0,f6(cx,ct,X0,X1,X2))
| ~ element_of_set(X0,intersection_of_sets(X1,X2))
| ~ element_of_set(X0,cx) ),
inference(forward_subsumption_resolution,[status(thm)],[f1118,f967]) ).
fof(f1123,plain,
! [X0] :
( ~ sQ14_spl
| element_of_set(f7(cx,X0),f1(ct,f7(cx,X0)))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1095,f115]) ).
fof(f1124,plain,
! [X0] :
( ~ sQ14_spl
| element_of_set(f19(cx,X0),f1(ct,f19(cx,X0)))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f1096,f115]) ).
fof(f1125,plain,
! [X0] :
( ~ sQ14_spl
| element_of_set(f20(cx,X0),f1(ct,f20(cx,X0)))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f1097,f115]) ).
fof(f1126,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f7(boundary(a,X0,X1),X2),union_of_members(ct))
| basis(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1111,f293]) ).
fof(f1127,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f7(boundary(a,X0,X1),X2),X3),f7(boundary(a,X0,X1),X2),cx,ct)
| eq_p(f7(boundary(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| basis(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1111,f403]) ).
fof(f1128,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f7(boundary(a,X0,X1),X2),X3),X3,cx,ct)
| eq_p(f7(boundary(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| basis(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1111,f402]) ).
fof(f1129,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f7(boundary(a,X0,X1),X2),X3),f18(cx,ct,f7(boundary(a,X0,X1),X2),X3))
| eq_p(f7(boundary(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| basis(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1111,f401]) ).
fof(f1130,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f19(boundary(a,X0,X1),X2),union_of_members(ct))
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1112,f293]) ).
fof(f1131,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f19(boundary(a,X0,X1),X2),X3),f19(boundary(a,X0,X1),X2),cx,ct)
| eq_p(f19(boundary(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1112,f403]) ).
fof(f1132,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f19(boundary(a,X0,X1),X2),X3),X3,cx,ct)
| eq_p(f19(boundary(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1112,f402]) ).
fof(f1133,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f19(boundary(a,X0,X1),X2),X3),f18(cx,ct,f19(boundary(a,X0,X1),X2),X3))
| eq_p(f19(boundary(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1112,f401]) ).
fof(f1134,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f7(closure(a,X0,X1),X2),union_of_members(ct))
| basis(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1114,f293]) ).
fof(f1135,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f7(closure(a,X0,X1),X2),X3),f7(closure(a,X0,X1),X2),cx,ct)
| eq_p(f7(closure(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| basis(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1114,f403]) ).
fof(f1136,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f7(closure(a,X0,X1),X2),X3),X3,cx,ct)
| eq_p(f7(closure(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| basis(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1114,f402]) ).
fof(f1137,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f7(closure(a,X0,X1),X2),X3),f18(cx,ct,f7(closure(a,X0,X1),X2),X3))
| eq_p(f7(closure(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| basis(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1114,f401]) ).
fof(f1138,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f20(boundary(a,X0,X1),X2),union_of_members(ct))
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1113,f293]) ).
fof(f1139,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f20(boundary(a,X0,X1),X2),X3),f20(boundary(a,X0,X1),X2),cx,ct)
| eq_p(f20(boundary(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1113,f403]) ).
fof(f1140,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f20(boundary(a,X0,X1),X2),X3),X3,cx,ct)
| eq_p(f20(boundary(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1113,f402]) ).
fof(f1141,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f20(boundary(a,X0,X1),X2),X3),f18(cx,ct,f20(boundary(a,X0,X1),X2),X3))
| eq_p(f20(boundary(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1113,f401]) ).
fof(f1142,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f19(closure(a,X0,X1),X2),union_of_members(ct))
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1115,f293]) ).
fof(f1143,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f19(closure(a,X0,X1),X2),X3),f19(closure(a,X0,X1),X2),cx,ct)
| eq_p(f19(closure(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1115,f403]) ).
fof(f1144,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f19(closure(a,X0,X1),X2),X3),X3,cx,ct)
| eq_p(f19(closure(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1115,f402]) ).
fof(f1145,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f19(closure(a,X0,X1),X2),X3),f18(cx,ct,f19(closure(a,X0,X1),X2),X3))
| eq_p(f19(closure(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1115,f401]) ).
fof(f1146,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f20(closure(a,X0,X1),X2),union_of_members(ct))
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1116,f293]) ).
fof(f1147,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f20(closure(a,X0,X1),X2),X3),f20(closure(a,X0,X1),X2),cx,ct)
| eq_p(f20(closure(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1116,f403]) ).
fof(f1148,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f20(closure(a,X0,X1),X2),X3),X3,cx,ct)
| eq_p(f20(closure(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1116,f402]) ).
fof(f1149,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f20(closure(a,X0,X1),X2),X3),f18(cx,ct,f20(closure(a,X0,X1),X2),X3))
| eq_p(f20(closure(a,X0,X1),X2),X3)
| ~ element_of_set(X3,cx)
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1116,f401]) ).
fof(f1150,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X6,closure(a,f14(a,cx,X3,X4),X5))
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f7(boundary(a,X0,X1),X2),f14(a,f14(a,cx,X3,X4),X5,X6))
| basis(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1101,f1026]) ).
fof(f1151,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f7(boundary(a,X0,X1),X2),f14(a,cx,X3,X4))
| basis(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1101,f1013]) ).
fof(f1153,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X6,closure(a,f14(a,cx,X3,X4),X5))
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f19(boundary(a,X0,X1),X2),f14(a,f14(a,cx,X3,X4),X5,X6))
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1102,f1026]) ).
fof(f1154,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f19(boundary(a,X0,X1),X2),f14(a,cx,X3,X4))
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1102,f1013]) ).
fof(f1156,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X6,closure(a,f14(a,cx,X3,X4),X5))
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f20(boundary(a,X0,X1),X2),f14(a,f14(a,cx,X3,X4),X5,X6))
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1103,f1026]) ).
fof(f1157,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f20(boundary(a,X0,X1),X2),f14(a,cx,X3,X4))
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1103,f1013]) ).
fof(f1159,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X6,closure(a,f14(a,cx,X3,X4),X5))
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f7(closure(a,X0,X1),X2),f14(a,f14(a,cx,X3,X4),X5,X6))
| basis(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1104,f1026]) ).
fof(f1162,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X6,closure(a,f14(a,cx,X3,X4),X5))
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f19(closure(a,X0,X1),X2),f14(a,f14(a,cx,X3,X4),X5,X6))
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1105,f1026]) ).
fof(f1165,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X6,closure(a,f14(a,cx,X3,X4),X5))
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f20(closure(a,X0,X1),X2),f14(a,f14(a,cx,X3,X4),X5,X6))
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1106,f1026]) ).
fof(f1168,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f7(boundary(a,X0,X1),X2),f1(ct,f7(boundary(a,X0,X1),X2)))
| basis(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1126,f115]) ).
fof(f1169,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f19(boundary(a,X0,X1),X2),f1(ct,f19(boundary(a,X0,X1),X2)))
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1130,f115]) ).
fof(f1170,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f7(closure(a,X0,X1),X2),f1(ct,f7(closure(a,X0,X1),X2)))
| basis(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1134,f115]) ).
fof(f1171,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f20(boundary(a,X0,X1),X2),f1(ct,f20(boundary(a,X0,X1),X2)))
| hausdorff(boundary(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1138,f115]) ).
fof(f1172,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f19(closure(a,X0,X1),X2),f1(ct,f19(closure(a,X0,X1),X2)))
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1142,f115]) ).
fof(f1173,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f20(closure(a,X0,X1),X2),f1(ct,f20(closure(a,X0,X1),X2)))
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1146,f115]) ).
fof(f1174,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(closure(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f20(cx,X0),f7(closure(a,X1,X2),X3)),f20(cx,X0),cx,ct)
| eq_p(f20(cx,X0),f7(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f981,f1114]) ).
fof(f1175,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(boundary(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f20(cx,X0),f7(boundary(a,X1,X2),X3)),f20(cx,X0),cx,ct)
| eq_p(f20(cx,X0),f7(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f981,f1111]) ).
fof(f1176,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(cx,X1)
| neighborhood(f17(cx,ct,f20(cx,X0),f7(cx,X1)),f20(cx,X0),cx,ct)
| eq_p(f20(cx,X0),f7(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f981,f972]) ).
fof(f1177,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f20(cx,X0),f19(closure(a,X1,X2),X3)),f20(cx,X0),cx,ct)
| eq_p(f20(cx,X0),f19(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f981,f1115]) ).
fof(f1178,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f20(cx,X0),f19(boundary(a,X1,X2),X3)),f20(cx,X0),cx,ct)
| eq_p(f20(cx,X0),f19(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f981,f1112]) ).
fof(f1179,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| neighborhood(f17(cx,ct,f20(cx,X0),f19(cx,X1)),f20(cx,X0),cx,ct)
| eq_p(f20(cx,X0),f19(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f981,f965]) ).
fof(f1180,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f20(cx,X0),f20(closure(a,X1,X2),X3)),f20(cx,X0),cx,ct)
| eq_p(f20(cx,X0),f20(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f981,f1116]) ).
fof(f1181,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f20(cx,X0),f20(boundary(a,X1,X2),X3)),f20(cx,X0),cx,ct)
| eq_p(f20(cx,X0),f20(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f981,f1113]) ).
fof(f1182,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| neighborhood(f17(cx,ct,f20(cx,X0),f20(cx,X1)),f20(cx,X0),cx,ct)
| eq_p(f20(cx,X0),f20(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f981,f964]) ).
fof(f1183,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(closure(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f20(cx,X0),f7(closure(a,X1,X2),X3)),f7(closure(a,X1,X2),X3),cx,ct)
| eq_p(f20(cx,X0),f7(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f982,f1114]) ).
fof(f1184,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(boundary(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f20(cx,X0),f7(boundary(a,X1,X2),X3)),f7(boundary(a,X1,X2),X3),cx,ct)
| eq_p(f20(cx,X0),f7(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f982,f1111]) ).
fof(f1185,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(cx,X1)
| neighborhood(f18(cx,ct,f20(cx,X0),f7(cx,X1)),f7(cx,X1),cx,ct)
| eq_p(f20(cx,X0),f7(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f982,f972]) ).
fof(f1186,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f20(cx,X0),f19(closure(a,X1,X2),X3)),f19(closure(a,X1,X2),X3),cx,ct)
| eq_p(f20(cx,X0),f19(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f982,f1115]) ).
fof(f1187,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f20(cx,X0),f19(boundary(a,X1,X2),X3)),f19(boundary(a,X1,X2),X3),cx,ct)
| eq_p(f20(cx,X0),f19(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f982,f1112]) ).
fof(f1188,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| neighborhood(f18(cx,ct,f20(cx,X0),f19(cx,X1)),f19(cx,X1),cx,ct)
| eq_p(f20(cx,X0),f19(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f982,f965]) ).
fof(f1189,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f20(cx,X0),f20(closure(a,X1,X2),X3)),f20(closure(a,X1,X2),X3),cx,ct)
| eq_p(f20(cx,X0),f20(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f982,f1116]) ).
fof(f1190,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f20(cx,X0),f20(boundary(a,X1,X2),X3)),f20(boundary(a,X1,X2),X3),cx,ct)
| eq_p(f20(cx,X0),f20(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f982,f1113]) ).
fof(f1191,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| neighborhood(f18(cx,ct,f20(cx,X0),f20(cx,X1)),f20(cx,X1),cx,ct)
| eq_p(f20(cx,X0),f20(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f982,f964]) ).
fof(f1192,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(closure(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f20(cx,X0),f7(closure(a,X1,X2),X3)),f18(cx,ct,f20(cx,X0),f7(closure(a,X1,X2),X3)))
| eq_p(f20(cx,X0),f7(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f983,f1114]) ).
fof(f1193,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(boundary(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f20(cx,X0),f7(boundary(a,X1,X2),X3)),f18(cx,ct,f20(cx,X0),f7(boundary(a,X1,X2),X3)))
| eq_p(f20(cx,X0),f7(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f983,f1111]) ).
fof(f1194,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(cx,X1)
| disjoint_s(f17(cx,ct,f20(cx,X0),f7(cx,X1)),f18(cx,ct,f20(cx,X0),f7(cx,X1)))
| eq_p(f20(cx,X0),f7(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f983,f972]) ).
fof(f1195,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f20(cx,X0),f19(closure(a,X1,X2),X3)),f18(cx,ct,f20(cx,X0),f19(closure(a,X1,X2),X3)))
| eq_p(f20(cx,X0),f19(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f983,f1115]) ).
fof(f1196,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f20(cx,X0),f19(boundary(a,X1,X2),X3)),f18(cx,ct,f20(cx,X0),f19(boundary(a,X1,X2),X3)))
| eq_p(f20(cx,X0),f19(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f983,f1112]) ).
fof(f1197,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| disjoint_s(f17(cx,ct,f20(cx,X0),f19(cx,X1)),f18(cx,ct,f20(cx,X0),f19(cx,X1)))
| eq_p(f20(cx,X0),f19(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f983,f965]) ).
fof(f1198,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f20(cx,X0),f20(closure(a,X1,X2),X3)),f18(cx,ct,f20(cx,X0),f20(closure(a,X1,X2),X3)))
| eq_p(f20(cx,X0),f20(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f983,f1116]) ).
fof(f1199,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f20(cx,X0),f20(boundary(a,X1,X2),X3)),f18(cx,ct,f20(cx,X0),f20(boundary(a,X1,X2),X3)))
| eq_p(f20(cx,X0),f20(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f983,f1113]) ).
fof(f1200,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| disjoint_s(f17(cx,ct,f20(cx,X0),f20(cx,X1)),f18(cx,ct,f20(cx,X0),f20(cx,X1)))
| eq_p(f20(cx,X0),f20(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f983,f964]) ).
fof(f1201,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(closure(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f19(cx,X0),f7(closure(a,X1,X2),X3)),f19(cx,X0),cx,ct)
| eq_p(f19(cx,X0),f7(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f990,f1114]) ).
fof(f1202,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(boundary(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f19(cx,X0),f7(boundary(a,X1,X2),X3)),f19(cx,X0),cx,ct)
| eq_p(f19(cx,X0),f7(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f990,f1111]) ).
fof(f1203,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(cx,X1)
| neighborhood(f17(cx,ct,f19(cx,X0),f7(cx,X1)),f19(cx,X0),cx,ct)
| eq_p(f19(cx,X0),f7(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f990,f972]) ).
fof(f1204,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f19(cx,X0),f19(closure(a,X1,X2),X3)),f19(cx,X0),cx,ct)
| eq_p(f19(cx,X0),f19(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f990,f1115]) ).
fof(f1205,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f19(cx,X0),f19(boundary(a,X1,X2),X3)),f19(cx,X0),cx,ct)
| eq_p(f19(cx,X0),f19(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f990,f1112]) ).
fof(f1206,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| neighborhood(f17(cx,ct,f19(cx,X0),f19(cx,X1)),f19(cx,X0),cx,ct)
| eq_p(f19(cx,X0),f19(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f990,f965]) ).
fof(f1207,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f19(cx,X0),f20(closure(a,X1,X2),X3)),f19(cx,X0),cx,ct)
| eq_p(f19(cx,X0),f20(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f990,f1116]) ).
fof(f1208,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f19(cx,X0),f20(boundary(a,X1,X2),X3)),f19(cx,X0),cx,ct)
| eq_p(f19(cx,X0),f20(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f990,f1113]) ).
fof(f1209,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| neighborhood(f17(cx,ct,f19(cx,X0),f20(cx,X1)),f19(cx,X0),cx,ct)
| eq_p(f19(cx,X0),f20(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f990,f964]) ).
fof(f1210,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(closure(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f19(cx,X0),f7(closure(a,X1,X2),X3)),f7(closure(a,X1,X2),X3),cx,ct)
| eq_p(f19(cx,X0),f7(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f991,f1114]) ).
fof(f1211,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(boundary(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f19(cx,X0),f7(boundary(a,X1,X2),X3)),f7(boundary(a,X1,X2),X3),cx,ct)
| eq_p(f19(cx,X0),f7(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f991,f1111]) ).
fof(f1212,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(cx,X1)
| neighborhood(f18(cx,ct,f19(cx,X0),f7(cx,X1)),f7(cx,X1),cx,ct)
| eq_p(f19(cx,X0),f7(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f991,f972]) ).
fof(f1213,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f19(cx,X0),f19(closure(a,X1,X2),X3)),f19(closure(a,X1,X2),X3),cx,ct)
| eq_p(f19(cx,X0),f19(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f991,f1115]) ).
fof(f1214,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f19(cx,X0),f19(boundary(a,X1,X2),X3)),f19(boundary(a,X1,X2),X3),cx,ct)
| eq_p(f19(cx,X0),f19(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f991,f1112]) ).
fof(f1215,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| neighborhood(f18(cx,ct,f19(cx,X0),f19(cx,X1)),f19(cx,X1),cx,ct)
| eq_p(f19(cx,X0),f19(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f991,f965]) ).
fof(f1216,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f19(cx,X0),f20(closure(a,X1,X2),X3)),f20(closure(a,X1,X2),X3),cx,ct)
| eq_p(f19(cx,X0),f20(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f991,f1116]) ).
fof(f1217,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f19(cx,X0),f20(boundary(a,X1,X2),X3)),f20(boundary(a,X1,X2),X3),cx,ct)
| eq_p(f19(cx,X0),f20(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f991,f1113]) ).
fof(f1218,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| neighborhood(f18(cx,ct,f19(cx,X0),f20(cx,X1)),f20(cx,X1),cx,ct)
| eq_p(f19(cx,X0),f20(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f991,f964]) ).
fof(f1219,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(closure(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f19(cx,X0),f7(closure(a,X1,X2),X3)),f18(cx,ct,f19(cx,X0),f7(closure(a,X1,X2),X3)))
| eq_p(f19(cx,X0),f7(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f992,f1114]) ).
fof(f1220,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(boundary(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f19(cx,X0),f7(boundary(a,X1,X2),X3)),f18(cx,ct,f19(cx,X0),f7(boundary(a,X1,X2),X3)))
| eq_p(f19(cx,X0),f7(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f992,f1111]) ).
fof(f1221,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(cx,X1)
| disjoint_s(f17(cx,ct,f19(cx,X0),f7(cx,X1)),f18(cx,ct,f19(cx,X0),f7(cx,X1)))
| eq_p(f19(cx,X0),f7(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f992,f972]) ).
fof(f1222,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f19(cx,X0),f19(closure(a,X1,X2),X3)),f18(cx,ct,f19(cx,X0),f19(closure(a,X1,X2),X3)))
| eq_p(f19(cx,X0),f19(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f992,f1115]) ).
fof(f1223,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f19(cx,X0),f19(boundary(a,X1,X2),X3)),f18(cx,ct,f19(cx,X0),f19(boundary(a,X1,X2),X3)))
| eq_p(f19(cx,X0),f19(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f992,f1112]) ).
fof(f1224,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| disjoint_s(f17(cx,ct,f19(cx,X0),f19(cx,X1)),f18(cx,ct,f19(cx,X0),f19(cx,X1)))
| eq_p(f19(cx,X0),f19(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f992,f965]) ).
fof(f1225,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f19(cx,X0),f20(closure(a,X1,X2),X3)),f18(cx,ct,f19(cx,X0),f20(closure(a,X1,X2),X3)))
| eq_p(f19(cx,X0),f20(closure(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f992,f1116]) ).
fof(f1226,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f19(cx,X0),f20(boundary(a,X1,X2),X3)),f18(cx,ct,f19(cx,X0),f20(boundary(a,X1,X2),X3)))
| eq_p(f19(cx,X0),f20(boundary(a,X1,X2),X3))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f992,f1113]) ).
fof(f1227,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| disjoint_s(f17(cx,ct,f19(cx,X0),f20(cx,X1)),f18(cx,ct,f19(cx,X0),f20(cx,X1)))
| eq_p(f19(cx,X0),f20(cx,X1))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f992,f964]) ).
fof(f1228,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(closure(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f7(cx,X0),f7(closure(a,X1,X2),X3)),f7(cx,X0),cx,ct)
| eq_p(f7(cx,X0),f7(closure(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f999,f1114]) ).
fof(f1229,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(boundary(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f7(cx,X0),f7(boundary(a,X1,X2),X3)),f7(cx,X0),cx,ct)
| eq_p(f7(cx,X0),f7(boundary(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f999,f1111]) ).
fof(f1230,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(cx,X1)
| neighborhood(f17(cx,ct,f7(cx,X0),f7(cx,X1)),f7(cx,X0),cx,ct)
| eq_p(f7(cx,X0),f7(cx,X1))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f999,f972]) ).
fof(f1231,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f7(cx,X0),f19(closure(a,X1,X2),X3)),f7(cx,X0),cx,ct)
| eq_p(f7(cx,X0),f19(closure(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f999,f1115]) ).
fof(f1232,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f7(cx,X0),f19(boundary(a,X1,X2),X3)),f7(cx,X0),cx,ct)
| eq_p(f7(cx,X0),f19(boundary(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f999,f1112]) ).
fof(f1233,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| neighborhood(f17(cx,ct,f7(cx,X0),f19(cx,X1)),f7(cx,X0),cx,ct)
| eq_p(f7(cx,X0),f19(cx,X1))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f999,f965]) ).
fof(f1234,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f7(cx,X0),f20(closure(a,X1,X2),X3)),f7(cx,X0),cx,ct)
| eq_p(f7(cx,X0),f20(closure(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f999,f1116]) ).
fof(f1235,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| neighborhood(f17(cx,ct,f7(cx,X0),f20(boundary(a,X1,X2),X3)),f7(cx,X0),cx,ct)
| eq_p(f7(cx,X0),f20(boundary(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f999,f1113]) ).
fof(f1236,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| neighborhood(f17(cx,ct,f7(cx,X0),f20(cx,X1)),f7(cx,X0),cx,ct)
| eq_p(f7(cx,X0),f20(cx,X1))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f999,f964]) ).
fof(f1237,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(closure(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f7(cx,X0),f7(closure(a,X1,X2),X3)),f7(closure(a,X1,X2),X3),cx,ct)
| eq_p(f7(cx,X0),f7(closure(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1000,f1114]) ).
fof(f1238,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(boundary(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f7(cx,X0),f7(boundary(a,X1,X2),X3)),f7(boundary(a,X1,X2),X3),cx,ct)
| eq_p(f7(cx,X0),f7(boundary(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1000,f1111]) ).
fof(f1239,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(cx,X1)
| neighborhood(f18(cx,ct,f7(cx,X0),f7(cx,X1)),f7(cx,X1),cx,ct)
| eq_p(f7(cx,X0),f7(cx,X1))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1000,f972]) ).
fof(f1240,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f7(cx,X0),f19(closure(a,X1,X2),X3)),f19(closure(a,X1,X2),X3),cx,ct)
| eq_p(f7(cx,X0),f19(closure(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1000,f1115]) ).
fof(f1241,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f7(cx,X0),f19(boundary(a,X1,X2),X3)),f19(boundary(a,X1,X2),X3),cx,ct)
| eq_p(f7(cx,X0),f19(boundary(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1000,f1112]) ).
fof(f1242,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| neighborhood(f18(cx,ct,f7(cx,X0),f19(cx,X1)),f19(cx,X1),cx,ct)
| eq_p(f7(cx,X0),f19(cx,X1))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1000,f965]) ).
fof(f1243,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f7(cx,X0),f20(closure(a,X1,X2),X3)),f20(closure(a,X1,X2),X3),cx,ct)
| eq_p(f7(cx,X0),f20(closure(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1000,f1116]) ).
fof(f1244,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| neighborhood(f18(cx,ct,f7(cx,X0),f20(boundary(a,X1,X2),X3)),f20(boundary(a,X1,X2),X3),cx,ct)
| eq_p(f7(cx,X0),f20(boundary(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1000,f1113]) ).
fof(f1245,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| neighborhood(f18(cx,ct,f7(cx,X0),f20(cx,X1)),f20(cx,X1),cx,ct)
| eq_p(f7(cx,X0),f20(cx,X1))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1000,f964]) ).
fof(f1246,plain,
! [X0,X1] :
( ~ sQ14_spl
| element_of_set(f20(f16(X0,a,cx,ct),X1),f1(ct,f20(f16(X0,a,cx,ct),X1)))
| limit_point(X0,a,cx,ct)
| hausdorff(f16(X0,a,cx,ct),X1) ),
inference(resolution,[status(thm)],[f980,f115]) ).
fof(f1247,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(closure(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f7(cx,X0),f7(closure(a,X1,X2),X3)),f18(cx,ct,f7(cx,X0),f7(closure(a,X1,X2),X3)))
| eq_p(f7(cx,X0),f7(closure(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1001,f1114]) ).
fof(f1248,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(boundary(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f7(cx,X0),f7(boundary(a,X1,X2),X3)),f18(cx,ct,f7(cx,X0),f7(boundary(a,X1,X2),X3)))
| eq_p(f7(cx,X0),f7(boundary(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1001,f1111]) ).
fof(f1249,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| basis(cx,X1)
| disjoint_s(f17(cx,ct,f7(cx,X0),f7(cx,X1)),f18(cx,ct,f7(cx,X0),f7(cx,X1)))
| eq_p(f7(cx,X0),f7(cx,X1))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1001,f972]) ).
fof(f1250,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f7(cx,X0),f19(closure(a,X1,X2),X3)),f18(cx,ct,f7(cx,X0),f19(closure(a,X1,X2),X3)))
| eq_p(f7(cx,X0),f19(closure(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1001,f1115]) ).
fof(f1251,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f7(cx,X0),f19(boundary(a,X1,X2),X3)),f18(cx,ct,f7(cx,X0),f19(boundary(a,X1,X2),X3)))
| eq_p(f7(cx,X0),f19(boundary(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1001,f1112]) ).
fof(f1252,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| disjoint_s(f17(cx,ct,f7(cx,X0),f19(cx,X1)),f18(cx,ct,f7(cx,X0),f19(cx,X1)))
| eq_p(f7(cx,X0),f19(cx,X1))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1001,f965]) ).
fof(f1253,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(closure(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f7(cx,X0),f20(closure(a,X1,X2),X3)),f18(cx,ct,f7(cx,X0),f20(closure(a,X1,X2),X3)))
| eq_p(f7(cx,X0),f20(closure(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1001,f1116]) ).
fof(f1254,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(boundary(a,X1,X2),X3)
| disjoint_s(f17(cx,ct,f7(cx,X0),f20(boundary(a,X1,X2),X3)),f18(cx,ct,f7(cx,X0),f20(boundary(a,X1,X2),X3)))
| eq_p(f7(cx,X0),f20(boundary(a,X1,X2),X3))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1001,f1113]) ).
fof(f1255,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ3_spl
| hausdorff(cx,X1)
| disjoint_s(f17(cx,ct,f7(cx,X0),f20(cx,X1)),f18(cx,ct,f7(cx,X0),f20(cx,X1)))
| eq_p(f7(cx,X0),f20(cx,X1))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1001,f964]) ).
fof(f1256,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(relative_complement_sets(f14(a,cx,X1,X0),cx),X2)
| neighborhood(relative_complement_sets(f14(a,cx,X1,X0),cx),f7(relative_complement_sets(f14(a,cx,X1,X0),cx),X2),cx,X1)
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1041,f972]) ).
fof(f1257,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(relative_complement_sets(f14(a,cx,X1,X0),cx),X2)
| neighborhood(relative_complement_sets(f14(a,cx,X1,X0),cx),f19(relative_complement_sets(f14(a,cx,X1,X0),cx),X2),cx,X1)
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1041,f965]) ).
fof(f1258,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(relative_complement_sets(f14(a,cx,X1,X0),cx),X2)
| neighborhood(relative_complement_sets(f14(a,cx,X1,X0),cx),f20(relative_complement_sets(f14(a,cx,X1,X0),cx),X2),cx,X1)
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1041,f964]) ).
fof(f1259,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f20(closure(a,X4,X5),X6),f14(a,f14(a,cx,X1,X0),X3,X2))
| hausdorff(closure(a,X4,X5),X6)
| element_of_set(X2,closure(a,f14(a,cx,X1,X0),X3))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1048,f1098]) ).
fof(f1260,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| element_of_set(f20(closure(a,X6,X7),X8),f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4))
| hausdorff(closure(a,X6,X7),X8)
| element_of_set(X4,closure(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5))
| element_of_set(X2,closure(a,f14(a,cx,X1,X0),X3))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1050,f1106]) ).
fof(f1261,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| element_of_set(f19(closure(a,X6,X7),X8),f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4))
| hausdorff(closure(a,X6,X7),X8)
| element_of_set(X4,closure(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5))
| element_of_set(X2,closure(a,f14(a,cx,X1,X0),X3))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1050,f1105]) ).
fof(f1262,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| element_of_set(f7(closure(a,X6,X7),X8),f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4))
| basis(closure(a,X6,X7),X8)
| element_of_set(X4,closure(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5))
| element_of_set(X2,closure(a,f14(a,cx,X1,X0),X3))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1050,f1104]) ).
fof(f1263,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| element_of_set(f20(boundary(a,X6,X7),X8),f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4))
| hausdorff(boundary(a,X6,X7),X8)
| element_of_set(X4,closure(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5))
| element_of_set(X2,closure(a,f14(a,cx,X1,X0),X3))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1050,f1103]) ).
fof(f1264,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| element_of_set(f19(boundary(a,X6,X7),X8),f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4))
| hausdorff(boundary(a,X6,X7),X8)
| element_of_set(X4,closure(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5))
| element_of_set(X2,closure(a,f14(a,cx,X1,X0),X3))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1050,f1102]) ).
fof(f1265,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| element_of_set(f7(boundary(a,X6,X7),X8),f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4))
| basis(boundary(a,X6,X7),X8)
| element_of_set(X4,closure(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5))
| element_of_set(X2,closure(a,f14(a,cx,X1,X0),X3))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1050,f1101]) ).
fof(f1266,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X6,a,f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4),X7),a),X8)
| eq_p(f20(intersection_of_sets(f16(X6,a,f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4),X7),a),X8),X6)
| limit_point(X6,a,f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4),X7)
| element_of_set(X4,closure(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5))
| element_of_set(X2,closure(a,f14(a,cx,X1,X0),X3))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1050,f1017]) ).
fof(f1267,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X6,a,f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4),X7),a),X8)
| eq_p(f19(intersection_of_sets(f16(X6,a,f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4),X7),a),X8),X6)
| limit_point(X6,a,f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4),X7)
| element_of_set(X4,closure(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5))
| element_of_set(X2,closure(a,f14(a,cx,X1,X0),X3))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1050,f1016]) ).
fof(f1268,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| basis(intersection_of_sets(f16(X6,a,f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4),X7),a),X8)
| eq_p(f7(intersection_of_sets(f16(X6,a,f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4),X7),a),X8),X6)
| limit_point(X6,a,f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4),X7)
| element_of_set(X4,closure(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5))
| element_of_set(X2,closure(a,f14(a,cx,X1,X0),X3))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1050,f1015]) ).
fof(f1269,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| subset_sets(a,f14(a,f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4),X7,X6))
| element_of_set(X6,closure(a,f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4),X7))
| element_of_set(X4,closure(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5))
| element_of_set(X2,closure(a,f14(a,cx,X1,X0),X3))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1050,f961]) ).
fof(f1270,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| neighborhood(f16(X6,a,f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4),X7),X6,f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4),X7)
| limit_point(X6,a,f14(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5,X4),X7)
| element_of_set(X4,closure(a,f14(a,f14(a,cx,X1,X0),X3,X2),X5))
| element_of_set(X2,closure(a,f14(a,cx,X1,X0),X3))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(resolution,[status(thm)],[f1050,f960]) ).
fof(f1271,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(closure(a,X0,X1),X2)
| neighborhood(f1(ct,f7(closure(a,X0,X1),X2)),f7(closure(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1170]) ).
fof(f1272,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(closure(a,X0,X1),X2)
| neighborhood(union_of_members(ct),f7(closure(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1134]) ).
fof(f1273,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(closure(a,X0,X1),X2)
| neighborhood(cx,f7(closure(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1114]) ).
fof(f1274,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X1,closure(a,cx,X0))
| basis(closure(a,X2,X3),X4)
| neighborhood(f14(a,cx,X0,X1),f7(closure(a,X2,X3),X4),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1108]) ).
fof(f1275,plain,
! [X0] :
( ~ sQ14_spl
| basis(cx,X0)
| neighborhood(f1(ct,f7(cx,X0)),f7(cx,X0),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1123]) ).
fof(f1276,plain,
! [X0] :
( ~ sQ14_spl
| basis(cx,X0)
| neighborhood(union_of_members(ct),f7(cx,X0),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1095]) ).
fof(f1277,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| basis(f2(X0,X1),X2)
| neighborhood(f1(X0,f7(f2(X0,X1),X2)),f7(f2(X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1056]) ).
fof(f1278,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| basis(f2(X0,X1),X2)
| neighborhood(union_of_members(X0),f7(f2(X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1004]) ).
fof(f1279,plain,
! [X0,X1] :
( ~ sQ14_spl
| basis(union_of_members(X0),X1)
| neighborhood(f1(X0,f7(union_of_members(X0),X1)),f7(union_of_members(X0),X1),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1005]) ).
fof(f1280,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X1,closure(a,cx,X0))
| basis(boundary(a,X2,X3),X4)
| neighborhood(f14(a,cx,X0,X1),f7(boundary(a,X2,X3),X4),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1151]) ).
fof(f1281,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(boundary(a,X0,X1),X2)
| neighborhood(f1(ct,f7(boundary(a,X0,X1),X2)),f7(boundary(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1168]) ).
fof(f1282,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(boundary(a,X0,X1),X2)
| neighborhood(union_of_members(ct),f7(boundary(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1126]) ).
fof(f1283,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(boundary(a,X0,X1),X2)
| neighborhood(cx,f7(boundary(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1111]) ).
fof(f1284,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(boundary(X0,X1,X2),X3)
| neighborhood(closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3),cx,ct) ),
inference(resolution,[status(thm)],[f976,f997]) ).
fof(f1285,plain,
! [X0] :
( ~ sQ14_spl
| basis(empty_set,X0)
| neighborhood(f1(ct,f7(empty_set,X0)),f7(empty_set,X0),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1009]) ).
fof(f1286,plain,
! [X0] :
( ~ sQ14_spl
| basis(empty_set,X0)
| neighborhood(union_of_members(ct),f7(empty_set,X0),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1003]) ).
fof(f1287,plain,
! [X0,X1] :
( ~ sQ14_spl
| basis(X0,X1)
| neighborhood(intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1),cx,ct) ),
inference(resolution,[status(thm)],[f976,f971]) ).
fof(f1289,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| neighborhood(f1(ct,f19(closure(a,X0,X1),X2)),f19(closure(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1172]) ).
fof(f1290,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| neighborhood(union_of_members(ct),f19(closure(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1142]) ).
fof(f1291,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| neighborhood(cx,f19(closure(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1115]) ).
fof(f1292,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X1,closure(a,cx,X0))
| hausdorff(closure(a,X2,X3),X4)
| neighborhood(f14(a,cx,X0,X1),f19(closure(a,X2,X3),X4),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1109]) ).
fof(f1293,plain,
! [X0] :
( ~ sQ14_spl
| hausdorff(cx,X0)
| neighborhood(f1(ct,f19(cx,X0)),f19(cx,X0),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1124]) ).
fof(f1294,plain,
! [X0] :
( ~ sQ14_spl
| hausdorff(cx,X0)
| neighborhood(union_of_members(ct),f19(cx,X0),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1096]) ).
fof(f1295,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2)
| neighborhood(f1(X0,f19(f2(X0,X1),X2)),f19(f2(X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1055]) ).
fof(f1296,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2)
| neighborhood(union_of_members(X0),f19(f2(X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f995]) ).
fof(f1297,plain,
! [X0,X1] :
( ~ sQ14_spl
| hausdorff(union_of_members(X0),X1)
| neighborhood(f1(X0,f19(union_of_members(X0),X1)),f19(union_of_members(X0),X1),cx,ct) ),
inference(resolution,[status(thm)],[f976,f996]) ).
fof(f1298,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X1,closure(a,cx,X0))
| hausdorff(boundary(a,X2,X3),X4)
| neighborhood(f14(a,cx,X0,X1),f19(boundary(a,X2,X3),X4),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1154]) ).
fof(f1299,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| neighborhood(f1(ct,f19(boundary(a,X0,X1),X2)),f19(boundary(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1169]) ).
fof(f1300,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| neighborhood(union_of_members(ct),f19(boundary(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1130]) ).
fof(f1301,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| neighborhood(cx,f19(boundary(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1112]) ).
fof(f1302,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(boundary(X0,X1,X2),X3)
| neighborhood(closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3),cx,ct) ),
inference(resolution,[status(thm)],[f976,f988]) ).
fof(f1303,plain,
! [X0] :
( ~ sQ14_spl
| hausdorff(empty_set,X0)
| neighborhood(f1(ct,f19(empty_set,X0)),f19(empty_set,X0),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1008]) ).
fof(f1304,plain,
! [X0] :
( ~ sQ14_spl
| hausdorff(empty_set,X0)
| neighborhood(union_of_members(ct),f19(empty_set,X0),cx,ct) ),
inference(resolution,[status(thm)],[f976,f994]) ).
fof(f1306,plain,
! [X0,X1] :
( ~ sQ14_spl
| limit_point(X0,a,cx,ct)
| hausdorff(f16(X0,a,cx,ct),X1)
| neighborhood(union_of_members(ct),f20(f16(X0,a,cx,ct),X1),cx,ct) ),
inference(resolution,[status(thm)],[f976,f980]) ).
fof(f1307,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| neighborhood(f1(ct,f20(closure(a,X0,X1),X2)),f20(closure(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1173]) ).
fof(f1308,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| neighborhood(union_of_members(ct),f20(closure(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1146]) ).
fof(f1309,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| neighborhood(cx,f20(closure(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1116]) ).
fof(f1310,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(closure(a,X4,X5),X6)
| element_of_set(X3,closure(a,f14(a,cx,X0,X1),X2))
| element_of_set(X1,closure(a,cx,X0))
| neighborhood(f14(a,f14(a,cx,X0,X1),X2,X3),f20(closure(a,X4,X5),X6),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1259]) ).
fof(f1311,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(closure(a,X2,X3),X4)
| element_of_set(X1,closure(a,cx,X0))
| neighborhood(f14(a,cx,X0,X1),f20(closure(a,X2,X3),X4),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1110]) ).
fof(f1312,plain,
! [X0] :
( ~ sQ14_spl
| hausdorff(cx,X0)
| neighborhood(f1(ct,f20(cx,X0)),f20(cx,X0),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1125]) ).
fof(f1313,plain,
! [X0] :
( ~ sQ14_spl
| hausdorff(cx,X0)
| neighborhood(union_of_members(ct),f20(cx,X0),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1097]) ).
fof(f1314,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2)
| neighborhood(f1(X0,f20(f2(X0,X1),X2)),f20(f2(X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1054]) ).
fof(f1315,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2)
| neighborhood(union_of_members(X0),f20(f2(X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f986]) ).
fof(f1316,plain,
! [X0,X1] :
( ~ sQ14_spl
| hausdorff(union_of_members(X0),X1)
| neighborhood(f1(X0,f20(union_of_members(X0),X1)),f20(union_of_members(X0),X1),cx,ct) ),
inference(resolution,[status(thm)],[f976,f987]) ).
fof(f1317,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X1,closure(a,cx,X0))
| hausdorff(boundary(a,X2,X3),X4)
| neighborhood(f14(a,cx,X0,X1),f20(boundary(a,X2,X3),X4),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1157]) ).
fof(f1318,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| neighborhood(f1(ct,f20(boundary(a,X0,X1),X2)),f20(boundary(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1171]) ).
fof(f1319,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| neighborhood(union_of_members(ct),f20(boundary(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1138]) ).
fof(f1320,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| neighborhood(cx,f20(boundary(a,X0,X1),X2),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1113]) ).
fof(f1321,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(boundary(X0,X1,X2),X3)
| neighborhood(closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3),cx,ct) ),
inference(resolution,[status(thm)],[f976,f979]) ).
fof(f1322,plain,
! [X0] :
( ~ sQ14_spl
| hausdorff(empty_set,X0)
| neighborhood(f1(ct,f20(empty_set,X0)),f20(empty_set,X0),cx,ct) ),
inference(resolution,[status(thm)],[f976,f1007]) ).
fof(f1323,plain,
! [X0] :
( ~ sQ14_spl
| hausdorff(empty_set,X0)
| neighborhood(union_of_members(ct),f20(empty_set,X0),cx,ct) ),
inference(resolution,[status(thm)],[f976,f985]) ).
fof(f1325,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(intersection_of_members(X0),X1)
| element_of_set(f7(intersection_of_members(X0),X1),X2) ),
inference(resolution,[status(thm)],[f968,f972]) ).
fof(f1326,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(intersection_of_members(X0),X1)
| element_of_set(f19(intersection_of_members(X0),X1),X2) ),
inference(resolution,[status(thm)],[f968,f965]) ).
fof(f1327,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(intersection_of_members(X0),X1)
| element_of_set(f20(intersection_of_members(X0),X1),X2) ),
inference(resolution,[status(thm)],[f968,f964]) ).
fof(f1328,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(closure(a,X0,X1),X2)
| element_of_set(f7(closure(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1170]) ).
fof(f1329,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(closure(a,X0,X1),X2)
| element_of_set(f7(closure(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1134]) ).
fof(f1330,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(closure(a,X0,X1),X2)
| element_of_set(f7(closure(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1114]) ).
fof(f1331,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,cx,X5))
| basis(closure(a,X0,X1),X2)
| element_of_set(f7(closure(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1108]) ).
fof(f1332,plain,
! [X0,X1] :
( ~ sQ14_spl
| basis(cx,X0)
| element_of_set(f7(cx,X0),union_of_members(X1)) ),
inference(resolution,[status(thm)],[f970,f1123]) ).
fof(f1334,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| basis(f2(X0,X1),X2)
| element_of_set(f7(f2(X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1056]) ).
fof(f1335,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| basis(f2(X0,X1),X2)
| element_of_set(f7(f2(X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1004]) ).
fof(f1337,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,cx,X5))
| basis(boundary(a,X0,X1),X2)
| element_of_set(f7(boundary(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1151]) ).
fof(f1338,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(boundary(a,X0,X1),X2)
| element_of_set(f7(boundary(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1168]) ).
fof(f1339,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(boundary(a,X0,X1),X2)
| element_of_set(f7(boundary(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1126]) ).
fof(f1340,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(boundary(a,X0,X1),X2)
| element_of_set(f7(boundary(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1111]) ).
fof(f1342,plain,
! [X0,X1] :
( ~ sQ14_spl
| basis(empty_set,X0)
| element_of_set(f7(empty_set,X0),union_of_members(X1)) ),
inference(resolution,[status(thm)],[f970,f1009]) ).
fof(f1344,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(X0,X1)
| element_of_set(f7(X0,X1),union_of_members(X2)) ),
inference(resolution,[status(thm)],[f970,f971]) ).
fof(f1346,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(f19(closure(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1172]) ).
fof(f1347,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(f19(closure(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1142]) ).
fof(f1348,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(f19(closure(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1115]) ).
fof(f1349,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,cx,X5))
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(f19(closure(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1109]) ).
fof(f1350,plain,
! [X0,X1] :
( ~ sQ14_spl
| hausdorff(cx,X0)
| element_of_set(f19(cx,X0),union_of_members(X1)) ),
inference(resolution,[status(thm)],[f970,f1124]) ).
fof(f1352,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2)
| element_of_set(f19(f2(X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1055]) ).
fof(f1353,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2)
| element_of_set(f19(f2(X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f995]) ).
fof(f1355,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,cx,X5))
| hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f19(boundary(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1154]) ).
fof(f1356,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f19(boundary(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1169]) ).
fof(f1357,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f19(boundary(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1130]) ).
fof(f1358,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f19(boundary(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1112]) ).
fof(f1362,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(X0,X1)
| element_of_set(f19(X0,X1),union_of_members(X2)) ),
inference(resolution,[status(thm)],[f970,f965]) ).
fof(f1363,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| limit_point(X0,a,cx,ct)
| hausdorff(f16(X0,a,cx,ct),X1)
| element_of_set(f20(f16(X0,a,cx,ct),X1),union_of_members(X2)) ),
inference(resolution,[status(thm)],[f970,f980]) ).
fof(f1364,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(f20(closure(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1173]) ).
fof(f1365,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(f20(closure(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1146]) ).
fof(f1366,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(f20(closure(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1116]) ).
fof(f1367,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(X6,closure(a,f14(a,cx,X5,X4),X7))
| element_of_set(X4,closure(a,cx,X5))
| element_of_set(f20(closure(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1259]) ).
fof(f1368,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(X4,closure(a,cx,X5))
| element_of_set(f20(closure(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1110]) ).
fof(f1371,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2)
| element_of_set(f20(f2(X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1054]) ).
fof(f1372,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2)
| element_of_set(f20(f2(X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f986]) ).
fof(f1374,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(X4,closure(a,cx,X5))
| hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f20(boundary(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1157]) ).
fof(f1375,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f20(boundary(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1171]) ).
fof(f1376,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f20(boundary(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1138]) ).
fof(f1377,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f20(boundary(a,X0,X1),X2),union_of_members(X3)) ),
inference(resolution,[status(thm)],[f970,f1113]) ).
fof(f1381,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(X0,X1)
| element_of_set(f20(X0,X1),union_of_members(X2)) ),
inference(resolution,[status(thm)],[f970,f964]) ).
fof(f1382,definition,
! [X0,X1,X2,X3] :
( sQ70_spl
<=> ( basis(closure(a,X0,X1),X2)
| element_of_set(f7(closure(a,X0,X1),X2),union_of_members(X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1385,definition,
! [X4,X5] :
( sQ71_spl
<=> element_of_set(X4,closure(a,cx,X5)) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1386,plain,
! [X0,X1] :
( ~ sQ71_spl
| element_of_set(X0,closure(a,cx,X1)) ),
inference(component_clause,[status(thm)],[f1385]) ).
fof(f1388,plain,
( ~ sQ14_spl
| sQ71_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f1331,f1382,f1385,f503]) ).
fof(f1389,definition,
! [X0,X1,X2,X3] :
( sQ72_spl
<=> ( basis(boundary(a,X0,X1),X2)
| element_of_set(f7(boundary(a,X0,X1),X2),union_of_members(X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1392,plain,
( ~ sQ14_spl
| sQ71_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f1337,f1389,f1385,f503]) ).
fof(f1393,definition,
! [X0,X1,X2,X3] :
( sQ73_spl
<=> ( hausdorff(closure(a,X0,X1),X2)
| element_of_set(f19(closure(a,X0,X1),X2),union_of_members(X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1394,plain,
! [X0,X1,X2,X3] :
( ~ sQ73_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(f19(closure(a,X0,X1),X2),union_of_members(X3)) ),
inference(component_clause,[status(thm)],[f1393]) ).
fof(f1396,plain,
( ~ sQ14_spl
| sQ71_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f1349,f1393,f1385,f503]) ).
fof(f1397,definition,
! [X0,X1,X2,X3] :
( sQ74_spl
<=> ( hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f19(boundary(a,X0,X1),X2),union_of_members(X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1400,plain,
( ~ sQ14_spl
| sQ71_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f1355,f1397,f1385,f503]) ).
fof(f1401,definition,
! [X0,X1,X2,X3] :
( sQ75_spl
<=> ( hausdorff(closure(a,X0,X1),X2)
| element_of_set(f20(closure(a,X0,X1),X2),union_of_members(X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1402,plain,
! [X0,X1,X2,X3] :
( ~ sQ75_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(f20(closure(a,X0,X1),X2),union_of_members(X3)) ),
inference(component_clause,[status(thm)],[f1401]) ).
fof(f1404,definition,
! [X4,X5,X6,X7] :
( sQ76_spl
<=> ( element_of_set(X6,closure(a,f14(a,cx,X5,X4),X7))
| element_of_set(X4,closure(a,cx,X5)) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1405,plain,
! [X0,X1,X2,X3] :
( ~ sQ76_spl
| element_of_set(X2,closure(a,f14(a,cx,X1,X0),X3))
| element_of_set(X0,closure(a,cx,X1)) ),
inference(component_clause,[status(thm)],[f1404]) ).
fof(f1407,plain,
( ~ sQ14_spl
| sQ76_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f1367,f1401,f1404,f503]) ).
fof(f1408,plain,
( ~ sQ14_spl
| sQ71_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f1368,f1401,f1385,f503]) ).
fof(f1409,definition,
! [X0,X1,X2,X3] :
( sQ77_spl
<=> ( hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f20(boundary(a,X0,X1),X2),union_of_members(X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1412,plain,
( ~ sQ14_spl
| sQ71_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f1374,f1409,f1385,f503]) ).
fof(f1413,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| basis(closure(a,X0,X1),X2)
| neighborhood(f1(ct,f7(closure(a,X0,X1),X2)),f7(closure(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1170]) ).
fof(f1414,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| basis(closure(a,X0,X1),X2)
| neighborhood(union_of_members(ct),f7(closure(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1134]) ).
fof(f1415,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| basis(closure(a,X0,X1),X2)
| neighborhood(cx,f7(closure(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1114]) ).
fof(f1416,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X1,closure(a,cx,X0))
| basis(closure(a,X2,X3),X4)
| neighborhood(f14(a,cx,X0,X1),f7(closure(a,X2,X3),X4),X5,X6) ),
inference(resolution,[status(thm)],[f1099,f1108]) ).
fof(f1417,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(cx,X0)
| neighborhood(f1(ct,f7(cx,X0)),f7(cx,X0),X1,X2) ),
inference(resolution,[status(thm)],[f1099,f1123]) ).
fof(f1419,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| basis(f2(X0,X1),X2)
| neighborhood(f1(X0,f7(f2(X0,X1),X2)),f7(f2(X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1056]) ).
fof(f1420,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| basis(f2(X0,X1),X2)
| neighborhood(union_of_members(X0),f7(f2(X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1004]) ).
fof(f1421,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(union_of_members(X0),X1)
| neighborhood(f1(X0,f7(union_of_members(X0),X1)),f7(union_of_members(X0),X1),X2,X3) ),
inference(resolution,[status(thm)],[f1099,f1005]) ).
fof(f1422,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X1,closure(a,cx,X0))
| basis(boundary(a,X2,X3),X4)
| neighborhood(f14(a,cx,X0,X1),f7(boundary(a,X2,X3),X4),X5,X6) ),
inference(resolution,[status(thm)],[f1099,f1151]) ).
fof(f1423,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| basis(boundary(a,X0,X1),X2)
| neighborhood(f1(ct,f7(boundary(a,X0,X1),X2)),f7(boundary(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1168]) ).
fof(f1424,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| basis(boundary(a,X0,X1),X2)
| neighborhood(union_of_members(ct),f7(boundary(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1126]) ).
fof(f1425,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| basis(boundary(a,X0,X1),X2)
| neighborhood(cx,f7(boundary(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1111]) ).
fof(f1426,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| basis(boundary(X0,X1,X2),X3)
| neighborhood(closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3),X4,X5) ),
inference(resolution,[status(thm)],[f1099,f997]) ).
fof(f1427,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(empty_set,X0)
| neighborhood(f1(ct,f7(empty_set,X0)),f7(empty_set,X0),X1,X2) ),
inference(resolution,[status(thm)],[f1099,f1009]) ).
fof(f1429,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(X0,X1)
| neighborhood(intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f1099,f971]) ).
fof(f1430,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(X0,X1)
| neighborhood(X0,f7(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f1099,f972]) ).
fof(f1431,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| neighborhood(f1(ct,f19(closure(a,X0,X1),X2)),f19(closure(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1172]) ).
fof(f1432,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| neighborhood(union_of_members(ct),f19(closure(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1142]) ).
fof(f1433,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| neighborhood(cx,f19(closure(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1115]) ).
fof(f1434,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X1,closure(a,cx,X0))
| hausdorff(closure(a,X2,X3),X4)
| neighborhood(f14(a,cx,X0,X1),f19(closure(a,X2,X3),X4),X5,X6) ),
inference(resolution,[status(thm)],[f1099,f1109]) ).
fof(f1435,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(cx,X0)
| neighborhood(f1(ct,f19(cx,X0)),f19(cx,X0),X1,X2) ),
inference(resolution,[status(thm)],[f1099,f1124]) ).
fof(f1437,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2)
| neighborhood(f1(X0,f19(f2(X0,X1),X2)),f19(f2(X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1055]) ).
fof(f1438,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2)
| neighborhood(union_of_members(X0),f19(f2(X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f995]) ).
fof(f1439,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(union_of_members(X0),X1)
| neighborhood(f1(X0,f19(union_of_members(X0),X1)),f19(union_of_members(X0),X1),X2,X3) ),
inference(resolution,[status(thm)],[f1099,f996]) ).
fof(f1440,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X1,closure(a,cx,X0))
| hausdorff(boundary(a,X2,X3),X4)
| neighborhood(f14(a,cx,X0,X1),f19(boundary(a,X2,X3),X4),X5,X6) ),
inference(resolution,[status(thm)],[f1099,f1154]) ).
fof(f1441,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| neighborhood(f1(ct,f19(boundary(a,X0,X1),X2)),f19(boundary(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1169]) ).
fof(f1442,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| neighborhood(union_of_members(ct),f19(boundary(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1130]) ).
fof(f1443,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| neighborhood(cx,f19(boundary(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1112]) ).
fof(f1444,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| hausdorff(boundary(X0,X1,X2),X3)
| neighborhood(closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3),X4,X5) ),
inference(resolution,[status(thm)],[f1099,f988]) ).
fof(f1445,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(empty_set,X0)
| neighborhood(f1(ct,f19(empty_set,X0)),f19(empty_set,X0),X1,X2) ),
inference(resolution,[status(thm)],[f1099,f1008]) ).
fof(f1447,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(X0,X1)
| neighborhood(X0,f19(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f1099,f965]) ).
fof(f1448,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| limit_point(X0,a,cx,ct)
| hausdorff(f16(X0,a,cx,ct),X1)
| neighborhood(union_of_members(ct),f20(f16(X0,a,cx,ct),X1),X2,X3) ),
inference(resolution,[status(thm)],[f1099,f980]) ).
fof(f1449,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| neighborhood(f1(ct,f20(closure(a,X0,X1),X2)),f20(closure(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1173]) ).
fof(f1450,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| neighborhood(union_of_members(ct),f20(closure(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1146]) ).
fof(f1451,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| neighborhood(cx,f20(closure(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1116]) ).
fof(f1452,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| hausdorff(closure(a,X4,X5),X6)
| element_of_set(X3,closure(a,f14(a,cx,X0,X1),X2))
| element_of_set(X1,closure(a,cx,X0))
| neighborhood(f14(a,f14(a,cx,X0,X1),X2,X3),f20(closure(a,X4,X5),X6),X7,X8) ),
inference(resolution,[status(thm)],[f1099,f1259]) ).
fof(f1453,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(closure(a,X2,X3),X4)
| element_of_set(X1,closure(a,cx,X0))
| neighborhood(f14(a,cx,X0,X1),f20(closure(a,X2,X3),X4),X5,X6) ),
inference(resolution,[status(thm)],[f1099,f1110]) ).
fof(f1454,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(cx,X0)
| neighborhood(f1(ct,f20(cx,X0)),f20(cx,X0),X1,X2) ),
inference(resolution,[status(thm)],[f1099,f1125]) ).
fof(f1456,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2)
| neighborhood(f1(X0,f20(f2(X0,X1),X2)),f20(f2(X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1054]) ).
fof(f1457,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2)
| neighborhood(union_of_members(X0),f20(f2(X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f986]) ).
fof(f1458,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(union_of_members(X0),X1)
| neighborhood(f1(X0,f20(union_of_members(X0),X1)),f20(union_of_members(X0),X1),X2,X3) ),
inference(resolution,[status(thm)],[f1099,f987]) ).
fof(f1459,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X1,closure(a,cx,X0))
| hausdorff(boundary(a,X2,X3),X4)
| neighborhood(f14(a,cx,X0,X1),f20(boundary(a,X2,X3),X4),X5,X6) ),
inference(resolution,[status(thm)],[f1099,f1157]) ).
fof(f1460,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| neighborhood(f1(ct,f20(boundary(a,X0,X1),X2)),f20(boundary(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1171]) ).
fof(f1461,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| neighborhood(union_of_members(ct),f20(boundary(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1138]) ).
fof(f1462,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| neighborhood(cx,f20(boundary(a,X0,X1),X2),X3,X4) ),
inference(resolution,[status(thm)],[f1099,f1113]) ).
fof(f1463,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| hausdorff(boundary(X0,X1,X2),X3)
| neighborhood(closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3),X4,X5) ),
inference(resolution,[status(thm)],[f1099,f979]) ).
fof(f1464,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(empty_set,X0)
| neighborhood(f1(ct,f20(empty_set,X0)),f20(empty_set,X0),X1,X2) ),
inference(resolution,[status(thm)],[f1099,f1007]) ).
fof(f1466,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(X0,X1)
| neighborhood(X0,f20(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f1099,f964]) ).
fof(f1473,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| limit_point(X0,a,f14(a,f14(a,cx,X1,X2),X3,X4),X5)
| element_of_set(X4,closure(a,f14(a,cx,X1,X2),X3))
| element_of_set(X2,closure(a,cx,X1))
| element_of_set(X0,f16(X0,a,f14(a,f14(a,cx,X1,X2),X3,X4),X5)) ),
inference(resolution,[status(thm)],[f201,f1051]) ).
fof(f1474,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| limit_point(X0,a,f14(a,cx,X1,X2),X3)
| element_of_set(X2,closure(a,cx,X1))
| element_of_set(X0,f16(X0,a,f14(a,cx,X1,X2),X3)) ),
inference(resolution,[status(thm)],[f201,f1027]) ).
fof(f1475,plain,
! [X0,X1] :
( ~ sQ14_spl
| limit_point(X0,a,cx,X1)
| element_of_set(X0,f16(X0,a,cx,X1)) ),
inference(resolution,[status(thm)],[f201,f1011]) ).
fof(f1476,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ subset_sets(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)))
| ~ element_of_collection(X2,X1)
| ~ element_of_set(f7(X0,X1),X2)
| basis(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f163,f956]) ).
fof(f1477,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(X0,f10(X2,X1,X0))
| ~ element_of_set(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f164,f967]) ).
fof(f1478,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(closure(a,X0,X1),X2)
| element_of_set(f7(closure(a,X0,X1),X2),f10(X3,f1(ct,f7(closure(a,X0,X1),X2)),f7(closure(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1170]) ).
fof(f1479,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(closure(a,X0,X1),X2)
| element_of_set(f7(closure(a,X0,X1),X2),f10(X3,union_of_members(ct),f7(closure(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1134]) ).
fof(f1480,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(closure(a,X0,X1),X2)
| element_of_set(f7(closure(a,X0,X1),X2),f10(X3,cx,f7(closure(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1114]) ).
fof(f1481,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(X5,closure(a,cx,X4))
| basis(closure(a,X0,X1),X2)
| element_of_set(f7(closure(a,X0,X1),X2),f10(X3,f14(a,cx,X4,X5),f7(closure(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1108]) ).
fof(f1482,plain,
! [X0,X1] :
( ~ sQ14_spl
| basis(cx,X0)
| element_of_set(f7(cx,X0),f10(X1,f1(ct,f7(cx,X0)),f7(cx,X0))) ),
inference(resolution,[status(thm)],[f1477,f1123]) ).
fof(f1483,plain,
! [X0,X1] :
( ~ sQ14_spl
| basis(cx,X0)
| element_of_set(f7(cx,X0),f10(X1,union_of_members(ct),f7(cx,X0))) ),
inference(resolution,[status(thm)],[f1477,f1095]) ).
fof(f1484,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| basis(f2(X0,X1),X2)
| element_of_set(f7(f2(X0,X1),X2),f10(X3,f1(X0,f7(f2(X0,X1),X2)),f7(f2(X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1056]) ).
fof(f1485,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| basis(f2(X0,X1),X2)
| element_of_set(f7(f2(X0,X1),X2),f10(X3,union_of_members(X0),f7(f2(X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1004]) ).
fof(f1486,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(union_of_members(X0),X1)
| element_of_set(f7(union_of_members(X0),X1),f10(X2,f1(X0,f7(union_of_members(X0),X1)),f7(union_of_members(X0),X1))) ),
inference(resolution,[status(thm)],[f1477,f1005]) ).
fof(f1487,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(X5,closure(a,cx,X4))
| basis(boundary(a,X0,X1),X2)
| element_of_set(f7(boundary(a,X0,X1),X2),f10(X3,f14(a,cx,X4,X5),f7(boundary(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1151]) ).
fof(f1488,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(boundary(a,X0,X1),X2)
| element_of_set(f7(boundary(a,X0,X1),X2),f10(X3,f1(ct,f7(boundary(a,X0,X1),X2)),f7(boundary(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1168]) ).
fof(f1489,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(boundary(a,X0,X1),X2)
| element_of_set(f7(boundary(a,X0,X1),X2),f10(X3,union_of_members(ct),f7(boundary(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1126]) ).
fof(f1490,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(boundary(a,X0,X1),X2)
| element_of_set(f7(boundary(a,X0,X1),X2),f10(X3,cx,f7(boundary(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1111]) ).
fof(f1491,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| basis(boundary(X0,X1,X2),X3)
| element_of_set(f7(boundary(X0,X1,X2),X3),f10(X4,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3))) ),
inference(resolution,[status(thm)],[f1477,f997]) ).
fof(f1492,plain,
! [X0,X1] :
( ~ sQ14_spl
| basis(empty_set,X0)
| element_of_set(f7(empty_set,X0),f10(X1,f1(ct,f7(empty_set,X0)),f7(empty_set,X0))) ),
inference(resolution,[status(thm)],[f1477,f1009]) ).
fof(f1493,plain,
! [X0,X1] :
( ~ sQ14_spl
| basis(empty_set,X0)
| element_of_set(f7(empty_set,X0),f10(X1,union_of_members(ct),f7(empty_set,X0))) ),
inference(resolution,[status(thm)],[f1477,f1003]) ).
fof(f1494,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(X0,X1)
| element_of_set(f7(X0,X1),f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1))) ),
inference(resolution,[status(thm)],[f1477,f971]) ).
fof(f1495,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(X0,X1)
| element_of_set(f7(X0,X1),f10(X2,X0,f7(X0,X1))) ),
inference(resolution,[status(thm)],[f1477,f972]) ).
fof(f1496,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(f19(closure(a,X0,X1),X2),f10(X3,f1(ct,f19(closure(a,X0,X1),X2)),f19(closure(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1172]) ).
fof(f1497,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(f19(closure(a,X0,X1),X2),f10(X3,union_of_members(ct),f19(closure(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1142]) ).
fof(f1498,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(f19(closure(a,X0,X1),X2),f10(X3,cx,f19(closure(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1115]) ).
fof(f1499,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(X5,closure(a,cx,X4))
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(f19(closure(a,X0,X1),X2),f10(X3,f14(a,cx,X4,X5),f19(closure(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1109]) ).
fof(f1500,plain,
! [X0,X1] :
( ~ sQ14_spl
| hausdorff(cx,X0)
| element_of_set(f19(cx,X0),f10(X1,f1(ct,f19(cx,X0)),f19(cx,X0))) ),
inference(resolution,[status(thm)],[f1477,f1124]) ).
fof(f1501,plain,
! [X0,X1] :
( ~ sQ14_spl
| hausdorff(cx,X0)
| element_of_set(f19(cx,X0),f10(X1,union_of_members(ct),f19(cx,X0))) ),
inference(resolution,[status(thm)],[f1477,f1096]) ).
fof(f1502,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2)
| element_of_set(f19(f2(X0,X1),X2),f10(X3,f1(X0,f19(f2(X0,X1),X2)),f19(f2(X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1055]) ).
fof(f1503,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2)
| element_of_set(f19(f2(X0,X1),X2),f10(X3,union_of_members(X0),f19(f2(X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f995]) ).
fof(f1504,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(union_of_members(X0),X1)
| element_of_set(f19(union_of_members(X0),X1),f10(X2,f1(X0,f19(union_of_members(X0),X1)),f19(union_of_members(X0),X1))) ),
inference(resolution,[status(thm)],[f1477,f996]) ).
fof(f1505,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(X5,closure(a,cx,X4))
| hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f19(boundary(a,X0,X1),X2),f10(X3,f14(a,cx,X4,X5),f19(boundary(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1154]) ).
fof(f1506,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f19(boundary(a,X0,X1),X2),f10(X3,f1(ct,f19(boundary(a,X0,X1),X2)),f19(boundary(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1169]) ).
fof(f1507,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f19(boundary(a,X0,X1),X2),f10(X3,union_of_members(ct),f19(boundary(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1130]) ).
fof(f1508,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f19(boundary(a,X0,X1),X2),f10(X3,cx,f19(boundary(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1112]) ).
fof(f1509,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f19(boundary(X0,X1,X2),X3),f10(X4,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3))) ),
inference(resolution,[status(thm)],[f1477,f988]) ).
fof(f1510,plain,
! [X0,X1] :
( ~ sQ14_spl
| hausdorff(empty_set,X0)
| element_of_set(f19(empty_set,X0),f10(X1,f1(ct,f19(empty_set,X0)),f19(empty_set,X0))) ),
inference(resolution,[status(thm)],[f1477,f1008]) ).
fof(f1511,plain,
! [X0,X1] :
( ~ sQ14_spl
| hausdorff(empty_set,X0)
| element_of_set(f19(empty_set,X0),f10(X1,union_of_members(ct),f19(empty_set,X0))) ),
inference(resolution,[status(thm)],[f1477,f994]) ).
fof(f1512,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(X0,X1)
| element_of_set(f19(X0,X1),f10(X2,X0,f19(X0,X1))) ),
inference(resolution,[status(thm)],[f1477,f965]) ).
fof(f1513,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| limit_point(X0,a,cx,ct)
| hausdorff(f16(X0,a,cx,ct),X1)
| element_of_set(f20(f16(X0,a,cx,ct),X1),f10(X2,union_of_members(ct),f20(f16(X0,a,cx,ct),X1))) ),
inference(resolution,[status(thm)],[f1477,f980]) ).
fof(f1514,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(f20(closure(a,X0,X1),X2),f10(X3,f1(ct,f20(closure(a,X0,X1),X2)),f20(closure(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1173]) ).
fof(f1515,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(f20(closure(a,X0,X1),X2),f10(X3,union_of_members(ct),f20(closure(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1146]) ).
fof(f1516,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(f20(closure(a,X0,X1),X2),f10(X3,cx,f20(closure(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1116]) ).
fof(f1517,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(X7,closure(a,f14(a,cx,X4,X5),X6))
| element_of_set(X5,closure(a,cx,X4))
| element_of_set(f20(closure(a,X0,X1),X2),f10(X3,f14(a,f14(a,cx,X4,X5),X6,X7),f20(closure(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1259]) ).
fof(f1518,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| hausdorff(closure(a,X0,X1),X2)
| element_of_set(X5,closure(a,cx,X4))
| element_of_set(f20(closure(a,X0,X1),X2),f10(X3,f14(a,cx,X4,X5),f20(closure(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1110]) ).
fof(f1519,plain,
! [X0,X1] :
( ~ sQ14_spl
| hausdorff(cx,X0)
| element_of_set(f20(cx,X0),f10(X1,f1(ct,f20(cx,X0)),f20(cx,X0))) ),
inference(resolution,[status(thm)],[f1477,f1125]) ).
fof(f1520,plain,
! [X0,X1] :
( ~ sQ14_spl
| hausdorff(cx,X0)
| element_of_set(f20(cx,X0),f10(X1,union_of_members(ct),f20(cx,X0))) ),
inference(resolution,[status(thm)],[f1477,f1097]) ).
fof(f1521,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2)
| element_of_set(f20(f2(X0,X1),X2),f10(X3,f1(X0,f20(f2(X0,X1),X2)),f20(f2(X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1054]) ).
fof(f1522,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(X1,intersection_of_members(X0))
| hausdorff(f2(X0,X1),X2)
| element_of_set(f20(f2(X0,X1),X2),f10(X3,union_of_members(X0),f20(f2(X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f986]) ).
fof(f1523,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(union_of_members(X0),X1)
| element_of_set(f20(union_of_members(X0),X1),f10(X2,f1(X0,f20(union_of_members(X0),X1)),f20(union_of_members(X0),X1))) ),
inference(resolution,[status(thm)],[f1477,f987]) ).
fof(f1524,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(X5,closure(a,cx,X4))
| hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f20(boundary(a,X0,X1),X2),f10(X3,f14(a,cx,X4,X5),f20(boundary(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1157]) ).
fof(f1525,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f20(boundary(a,X0,X1),X2),f10(X3,f1(ct,f20(boundary(a,X0,X1),X2)),f20(boundary(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1171]) ).
fof(f1526,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f20(boundary(a,X0,X1),X2),f10(X3,union_of_members(ct),f20(boundary(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1138]) ).
fof(f1527,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(boundary(a,X0,X1),X2)
| element_of_set(f20(boundary(a,X0,X1),X2),f10(X3,cx,f20(boundary(a,X0,X1),X2))) ),
inference(resolution,[status(thm)],[f1477,f1113]) ).
fof(f1528,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(boundary(X0,X1,X2),X3)
| element_of_set(f20(boundary(X0,X1,X2),X3),f10(X4,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3))) ),
inference(resolution,[status(thm)],[f1477,f979]) ).
fof(f1529,plain,
! [X0,X1] :
( ~ sQ14_spl
| hausdorff(empty_set,X0)
| element_of_set(f20(empty_set,X0),f10(X1,f1(ct,f20(empty_set,X0)),f20(empty_set,X0))) ),
inference(resolution,[status(thm)],[f1477,f1007]) ).
fof(f1530,plain,
! [X0,X1] :
( ~ sQ14_spl
| hausdorff(empty_set,X0)
| element_of_set(f20(empty_set,X0),f10(X1,union_of_members(ct),f20(empty_set,X0))) ),
inference(resolution,[status(thm)],[f1477,f985]) ).
fof(f1531,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(X0,X1)
| element_of_set(f20(X0,X1),f10(X2,X0,f20(X0,X1))) ),
inference(resolution,[status(thm)],[f1477,f964]) ).
fof(f1535,plain,
! [X0,X1] :
( ~ sQ14_spl
| element_of_set(f7(cx,X0),f1(X1,f7(cx,X0)))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1332,f115]) ).
fof(f1536,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f7(cx,X0),f10(X1,union_of_members(X2),f7(cx,X0)))
| basis(cx,X0) ),
inference(resolution,[status(thm)],[f1332,f1477]) ).
fof(f1539,plain,
! [X0,X1] :
( ~ sQ14_spl
| element_of_set(f7(empty_set,X0),f1(X1,f7(empty_set,X0)))
| basis(empty_set,X0) ),
inference(resolution,[status(thm)],[f1342,f115]) ).
fof(f1540,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f7(empty_set,X0),f10(X1,union_of_members(X2),f7(empty_set,X0)))
| basis(empty_set,X0) ),
inference(resolution,[status(thm)],[f1342,f1477]) ).
fof(f1543,plain,
! [X0,X1] :
( ~ sQ14_spl
| element_of_set(f19(cx,X0),f1(X1,f19(cx,X0)))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f1350,f115]) ).
fof(f1544,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f19(cx,X0),f10(X1,union_of_members(X2),f19(cx,X0)))
| hausdorff(cx,X0) ),
inference(resolution,[status(thm)],[f1350,f1477]) ).
fof(f1547,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(X0,f10(X2,f16(X0,a,cx,X1),X0))
| limit_point(X0,a,cx,X1) ),
inference(resolution,[status(thm)],[f1475,f1477]) ).
fof(f1548,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| neighborhood(f16(X0,a,cx,X1),X0,X2,X3)
| limit_point(X0,a,cx,X1) ),
inference(resolution,[status(thm)],[f1475,f1099]) ).
fof(f1549,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(X0,union_of_members(X2))
| limit_point(X0,a,cx,X1) ),
inference(resolution,[status(thm)],[f1475,f970]) ).
fof(f1550,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X6,closure(a,f14(a,cx,X3,X4),X5))
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f19(closure(a,X0,X1),X2),f14(a,f14(a,cx,X3,X4),X5,X6))
| hausdorff(closure(a,X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1057,f1098]) ).
fof(f1551,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f19(closure(a,X0,X1),X2),f10(X7,f14(a,f14(a,cx,X4,X3),X6,X5),f19(closure(a,X0,X1),X2)))
| element_of_set(X5,closure(a,f14(a,cx,X4,X3),X6))
| element_of_set(X3,closure(a,cx,X4))
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1550,f1477]) ).
fof(f1552,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| neighborhood(f14(a,f14(a,cx,X4,X3),X6,X5),f19(closure(a,X0,X1),X2),X7,X8)
| element_of_set(X5,closure(a,f14(a,cx,X4,X3),X6))
| element_of_set(X3,closure(a,cx,X4))
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1550,f1099]) ).
fof(f1553,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f19(closure(a,X0,X1),X2),union_of_members(X7))
| element_of_set(X5,closure(a,f14(a,cx,X4,X3),X6))
| element_of_set(X3,closure(a,cx,X4))
| hausdorff(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1550,f970]) ).
fof(f1554,plain,
( ~ sQ14_spl
| sQ76_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f1553,f1393,f1404,f503]) ).
fof(f1555,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(X6,closure(a,f14(a,cx,X3,X4),X5))
| element_of_set(X4,closure(a,cx,X3))
| element_of_set(f7(closure(a,X0,X1),X2),f14(a,f14(a,cx,X3,X4),X5,X6))
| basis(closure(a,X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1060,f1098]) ).
fof(f1556,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f7(closure(a,X0,X1),X2),f10(X7,f14(a,f14(a,cx,X4,X3),X6,X5),f7(closure(a,X0,X1),X2)))
| element_of_set(X5,closure(a,f14(a,cx,X4,X3),X6))
| element_of_set(X3,closure(a,cx,X4))
| basis(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1555,f1477]) ).
fof(f1557,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| neighborhood(f14(a,f14(a,cx,X4,X3),X6,X5),f7(closure(a,X0,X1),X2),X7,X8)
| element_of_set(X5,closure(a,f14(a,cx,X4,X3),X6))
| element_of_set(X3,closure(a,cx,X4))
| basis(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1555,f1099]) ).
fof(f1558,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f7(closure(a,X0,X1),X2),union_of_members(X7))
| element_of_set(X5,closure(a,f14(a,cx,X4,X3),X6))
| element_of_set(X3,closure(a,cx,X4))
| basis(closure(a,X0,X1),X2) ),
inference(resolution,[status(thm)],[f1555,f970]) ).
fof(f1559,plain,
( ~ sQ14_spl
| sQ76_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f1558,f1382,f1404,f503]) ).
fof(f1560,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f7(X0,X1),f1(X2,f7(X0,X1)))
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1344,f115]) ).
fof(f1561,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(f7(X0,X1),f10(X2,union_of_members(X3),f7(X0,X1)))
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1344,f1477]) ).
fof(f1562,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(union_of_members(X2),f7(X0,X1),X3,X4)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1344,f1099]) ).
fof(f1564,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f19(X0,X1),f1(X2,f19(X0,X1)))
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1362,f115]) ).
fof(f1565,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(f19(X0,X1),f10(X2,union_of_members(X3),f19(X0,X1)))
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1362,f1477]) ).
fof(f1566,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(union_of_members(X2),f19(X0,X1),X3,X4)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1362,f1099]) ).
fof(f1568,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(f20(X0,X1),f1(X2,f20(X0,X1)))
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1381,f115]) ).
fof(f1569,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(f20(X0,X1),f10(X2,union_of_members(X3),f20(X0,X1)))
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1381,f1477]) ).
fof(f1570,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(union_of_members(X2),f20(X0,X1),X3,X4)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1381,f1099]) ).
fof(f1575,plain,
! [X0,X1] :
( ~ sQ14_spl
| subset_sets(a,cx)
| element_of_set(X0,union_of_members(X1)) ),
inference(resolution,[status(thm)],[f1549,f207]) ).
fof(f1576,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| element_of_set(X0,f1(X2,X0))
| limit_point(X0,a,cx,X1) ),
inference(resolution,[status(thm)],[f1549,f115]) ).
fof(f1577,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(X0,f10(X2,union_of_members(X3),X0))
| limit_point(X0,a,cx,X1) ),
inference(resolution,[status(thm)],[f1549,f1477]) ).
fof(f1578,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(union_of_members(X2),X0,X3,X4)
| limit_point(X0,a,cx,X1) ),
inference(resolution,[status(thm)],[f1549,f1099]) ).
fof(f1580,definition,
! [X0,X1] :
( sQ78_spl
<=> element_of_set(X0,union_of_members(X1)) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1581,plain,
! [X0,X1] :
( ~ sQ78_spl
| element_of_set(X0,union_of_members(X1)) ),
inference(component_clause,[status(thm)],[f1580]) ).
fof(f1583,definition,
( sQ79_spl
<=> subset_sets(a,cx) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1586,plain,
( ~ sQ14_spl
| sQ79_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f1575,f1580,f1583,f503]) ).
fof(f1589,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| eq_p(f7(intersection_of_members(X0),X1),X2)
| ~ subset_sets(X3,X4)
| limit_point(X2,X3,X4,X5)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1325,f955]) ).
fof(f1591,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f7(cx,X2),f7(intersection_of_members(X0),X1)),f18(cx,ct,f7(cx,X2),f7(intersection_of_members(X0),X1)))
| eq_p(f7(cx,X2),f7(intersection_of_members(X0),X1))
| basis(cx,X2)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1325,f1001]) ).
fof(f1592,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f7(cx,X2),f7(intersection_of_members(X0),X1)),f7(intersection_of_members(X0),X1),cx,ct)
| eq_p(f7(cx,X2),f7(intersection_of_members(X0),X1))
| basis(cx,X2)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1325,f1000]) ).
fof(f1593,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f7(cx,X2),f7(intersection_of_members(X0),X1)),f7(cx,X2),cx,ct)
| eq_p(f7(cx,X2),f7(intersection_of_members(X0),X1))
| basis(cx,X2)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1325,f999]) ).
fof(f1594,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f19(cx,X2),f7(intersection_of_members(X0),X1)),f18(cx,ct,f19(cx,X2),f7(intersection_of_members(X0),X1)))
| eq_p(f19(cx,X2),f7(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1325,f992]) ).
fof(f1595,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f19(cx,X2),f7(intersection_of_members(X0),X1)),f7(intersection_of_members(X0),X1),cx,ct)
| eq_p(f19(cx,X2),f7(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1325,f991]) ).
fof(f1596,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f19(cx,X2),f7(intersection_of_members(X0),X1)),f19(cx,X2),cx,ct)
| eq_p(f19(cx,X2),f7(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1325,f990]) ).
fof(f1597,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f20(cx,X2),f7(intersection_of_members(X0),X1)),f18(cx,ct,f20(cx,X2),f7(intersection_of_members(X0),X1)))
| eq_p(f20(cx,X2),f7(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1325,f983]) ).
fof(f1598,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f20(cx,X2),f7(intersection_of_members(X0),X1)),f7(intersection_of_members(X0),X1),cx,ct)
| eq_p(f20(cx,X2),f7(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1325,f982]) ).
fof(f1599,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f20(cx,X2),f7(intersection_of_members(X0),X1)),f20(cx,X2),cx,ct)
| eq_p(f20(cx,X2),f7(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1325,f981]) ).
fof(f1600,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f7(intersection_of_members(X0),X1),X2),f7(intersection_of_members(X0),X1),cx,ct)
| eq_p(f7(intersection_of_members(X0),X1),X2)
| ~ element_of_set(X2,cx)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1325,f403]) ).
fof(f1601,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f7(intersection_of_members(X0),X1),X2),X2,cx,ct)
| eq_p(f7(intersection_of_members(X0),X1),X2)
| ~ element_of_set(X2,cx)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1325,f402]) ).
fof(f1602,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f7(intersection_of_members(X0),X1),X2),f18(cx,ct,f7(intersection_of_members(X0),X1),X2))
| eq_p(f7(intersection_of_members(X0),X1),X2)
| ~ element_of_set(X2,cx)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1325,f401]) ).
fof(f1606,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(X2,f7(intersection_of_members(X0),X1),X3,X4)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1325,f1099]) ).
fof(f1610,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| eq_p(f19(intersection_of_members(X0),X1),X2)
| ~ subset_sets(X3,X4)
| limit_point(X2,X3,X4,X5)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1326,f955]) ).
fof(f1612,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f7(cx,X2),f19(intersection_of_members(X0),X1)),f18(cx,ct,f7(cx,X2),f19(intersection_of_members(X0),X1)))
| eq_p(f7(cx,X2),f19(intersection_of_members(X0),X1))
| basis(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1326,f1001]) ).
fof(f1613,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f7(cx,X2),f19(intersection_of_members(X0),X1)),f19(intersection_of_members(X0),X1),cx,ct)
| eq_p(f7(cx,X2),f19(intersection_of_members(X0),X1))
| basis(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1326,f1000]) ).
fof(f1614,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f7(cx,X2),f19(intersection_of_members(X0),X1)),f7(cx,X2),cx,ct)
| eq_p(f7(cx,X2),f19(intersection_of_members(X0),X1))
| basis(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1326,f999]) ).
fof(f1615,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f19(cx,X2),f19(intersection_of_members(X0),X1)),f18(cx,ct,f19(cx,X2),f19(intersection_of_members(X0),X1)))
| eq_p(f19(cx,X2),f19(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1326,f992]) ).
fof(f1616,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f19(cx,X2),f19(intersection_of_members(X0),X1)),f19(intersection_of_members(X0),X1),cx,ct)
| eq_p(f19(cx,X2),f19(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1326,f991]) ).
fof(f1617,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f19(cx,X2),f19(intersection_of_members(X0),X1)),f19(cx,X2),cx,ct)
| eq_p(f19(cx,X2),f19(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1326,f990]) ).
fof(f1618,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f20(cx,X2),f19(intersection_of_members(X0),X1)),f18(cx,ct,f20(cx,X2),f19(intersection_of_members(X0),X1)))
| eq_p(f20(cx,X2),f19(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1326,f983]) ).
fof(f1619,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f20(cx,X2),f19(intersection_of_members(X0),X1)),f19(intersection_of_members(X0),X1),cx,ct)
| eq_p(f20(cx,X2),f19(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1326,f982]) ).
fof(f1620,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f20(cx,X2),f19(intersection_of_members(X0),X1)),f20(cx,X2),cx,ct)
| eq_p(f20(cx,X2),f19(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1326,f981]) ).
fof(f1621,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f19(intersection_of_members(X0),X1),X2),f19(intersection_of_members(X0),X1),cx,ct)
| eq_p(f19(intersection_of_members(X0),X1),X2)
| ~ element_of_set(X2,cx)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1326,f403]) ).
fof(f1622,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f19(intersection_of_members(X0),X1),X2),X2,cx,ct)
| eq_p(f19(intersection_of_members(X0),X1),X2)
| ~ element_of_set(X2,cx)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1326,f402]) ).
fof(f1623,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f19(intersection_of_members(X0),X1),X2),f18(cx,ct,f19(intersection_of_members(X0),X1),X2))
| eq_p(f19(intersection_of_members(X0),X1),X2)
| ~ element_of_set(X2,cx)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1326,f401]) ).
fof(f1627,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(X2,f19(intersection_of_members(X0),X1),X3,X4)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1326,f1099]) ).
fof(f1631,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| eq_p(f20(intersection_of_members(X0),X1),X2)
| ~ subset_sets(X3,X4)
| limit_point(X2,X3,X4,X5)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1327,f955]) ).
fof(f1633,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f7(cx,X2),f20(intersection_of_members(X0),X1)),f18(cx,ct,f7(cx,X2),f20(intersection_of_members(X0),X1)))
| eq_p(f7(cx,X2),f20(intersection_of_members(X0),X1))
| basis(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1327,f1001]) ).
fof(f1634,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f7(cx,X2),f20(intersection_of_members(X0),X1)),f20(intersection_of_members(X0),X1),cx,ct)
| eq_p(f7(cx,X2),f20(intersection_of_members(X0),X1))
| basis(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1327,f1000]) ).
fof(f1635,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f7(cx,X2),f20(intersection_of_members(X0),X1)),f7(cx,X2),cx,ct)
| eq_p(f7(cx,X2),f20(intersection_of_members(X0),X1))
| basis(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1327,f999]) ).
fof(f1636,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f19(cx,X2),f20(intersection_of_members(X0),X1)),f18(cx,ct,f19(cx,X2),f20(intersection_of_members(X0),X1)))
| eq_p(f19(cx,X2),f20(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1327,f992]) ).
fof(f1637,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f19(cx,X2),f20(intersection_of_members(X0),X1)),f20(intersection_of_members(X0),X1),cx,ct)
| eq_p(f19(cx,X2),f20(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1327,f991]) ).
fof(f1638,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f19(cx,X2),f20(intersection_of_members(X0),X1)),f19(cx,X2),cx,ct)
| eq_p(f19(cx,X2),f20(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1327,f990]) ).
fof(f1639,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f20(cx,X2),f20(intersection_of_members(X0),X1)),f18(cx,ct,f20(cx,X2),f20(intersection_of_members(X0),X1)))
| eq_p(f20(cx,X2),f20(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1327,f983]) ).
fof(f1640,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f20(cx,X2),f20(intersection_of_members(X0),X1)),f20(intersection_of_members(X0),X1),cx,ct)
| eq_p(f20(cx,X2),f20(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1327,f982]) ).
fof(f1641,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f20(cx,X2),f20(intersection_of_members(X0),X1)),f20(cx,X2),cx,ct)
| eq_p(f20(cx,X2),f20(intersection_of_members(X0),X1))
| hausdorff(cx,X2)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1327,f981]) ).
fof(f1642,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f17(cx,ct,f20(intersection_of_members(X0),X1),X2),f20(intersection_of_members(X0),X1),cx,ct)
| eq_p(f20(intersection_of_members(X0),X1),X2)
| ~ element_of_set(X2,cx)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1327,f403]) ).
fof(f1643,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| neighborhood(f18(cx,ct,f20(intersection_of_members(X0),X1),X2),X2,cx,ct)
| eq_p(f20(intersection_of_members(X0),X1),X2)
| ~ element_of_set(X2,cx)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1327,f402]) ).
fof(f1644,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ14_spl
| disjoint_s(f17(cx,ct,f20(intersection_of_members(X0),X1),X2),f18(cx,ct,f20(intersection_of_members(X0),X1),X2))
| eq_p(f20(intersection_of_members(X0),X1),X2)
| ~ element_of_set(X2,cx)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1327,f401]) ).
fof(f1648,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(X2,f20(intersection_of_members(X0),X1),X3,X4)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1327,f1099]) ).
fof(f1651,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(f7(X0,X1),f10(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)))
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1494,f1477]) ).
fof(f1652,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1),X3,X4)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1494,f1099]) ).
fof(f1654,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(f7(X0,X1),f10(X2,f10(X3,X0,f7(X0,X1)),f7(X0,X1)))
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1495,f1477]) ).
fof(f1655,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(f10(X2,X0,f7(X0,X1)),f7(X0,X1),X3,X4)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1495,f1099]) ).
fof(f1657,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(f19(X0,X1),f10(X2,f10(X3,X0,f19(X0,X1)),f19(X0,X1)))
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1512,f1477]) ).
fof(f1658,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(f10(X2,X0,f19(X0,X1)),f19(X0,X1),X3,X4)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1512,f1099]) ).
fof(f1660,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(f20(X0,X1),f10(X2,f10(X3,X0,f20(X0,X1)),f20(X0,X1)))
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1531,f1477]) ).
fof(f1661,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(f10(X2,X0,f20(X0,X1)),f20(X0,X1),X3,X4)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1531,f1099]) ).
fof(f1666,plain,
! [X0,X1] :
( ~ sQ14_spl
| subset_sets(a,cx)
| element_of_set(X0,f1(X1,X0)) ),
inference(resolution,[status(thm)],[f1576,f207]) ).
fof(f1667,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(X0,f10(X2,f1(X3,X0),X0))
| limit_point(X0,a,cx,X1) ),
inference(resolution,[status(thm)],[f1576,f1477]) ).
fof(f1668,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(f1(X2,X0),X0,X3,X4)
| limit_point(X0,a,cx,X1) ),
inference(resolution,[status(thm)],[f1576,f1099]) ).
fof(f1670,definition,
! [X0,X1] :
( sQ80_spl
<=> element_of_set(X0,f1(X1,X0)) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1673,plain,
( ~ sQ14_spl
| sQ79_spl
| sQ80_spl ),
inference(split_clause,[status(thm)],[f1666,f1670,f1583,f503]) ).
fof(f1674,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| subset_sets(a,cx)
| neighborhood(union_of_members(X0),X1,X2,X3) ),
inference(resolution,[status(thm)],[f1578,f207]) ).
fof(f1676,definition,
! [X0,X1,X2,X3] :
( sQ81_spl
<=> neighborhood(union_of_members(X0),X1,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1679,plain,
( ~ sQ14_spl
| sQ79_spl
| sQ81_spl ),
inference(split_clause,[status(thm)],[f1674,f1676,f1583,f503]) ).
fof(f1680,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(f7(X0,X1),f10(X2,f1(X3,f7(X0,X1)),f7(X0,X1)))
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1560,f1477]) ).
fof(f1681,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(f1(X2,f7(X0,X1)),f7(X0,X1),X3,X4)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1560,f1099]) ).
fof(f1683,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(f19(X0,X1),f10(X2,f1(X3,f19(X0,X1)),f19(X0,X1)))
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1564,f1477]) ).
fof(f1684,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(f1(X2,f19(X0,X1)),f19(X0,X1),X3,X4)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1564,f1099]) ).
fof(f1686,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(f20(X0,X1),f10(X2,f1(X3,f20(X0,X1)),f20(X0,X1)))
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1568,f1477]) ).
fof(f1687,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(f1(X2,f20(X0,X1)),f20(X0,X1),X3,X4)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1568,f1099]) ).
fof(f1692,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| subset_sets(a,cx)
| neighborhood(f1(X0,X1),X1,X2,X3) ),
inference(resolution,[status(thm)],[f1668,f207]) ).
fof(f1694,definition,
! [X0,X1,X2,X3] :
( sQ82_spl
<=> neighborhood(f1(X0,X1),X1,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1697,plain,
( ~ sQ14_spl
| sQ79_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f1692,f1694,f1583,f503]) ).
fof(f1704,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(f7(union_of_members(X0),X1),f10(X2,f10(X3,f1(X0,f7(union_of_members(X0),X1)),f7(union_of_members(X0),X1)),f7(union_of_members(X0),X1)))
| basis(union_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1486,f1477]) ).
fof(f1705,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(f10(X2,f1(X0,f7(union_of_members(X0),X1)),f7(union_of_members(X0),X1)),f7(union_of_members(X0),X1),X3,X4)
| basis(union_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1486,f1099]) ).
fof(f1707,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f7(boundary(X0,X1,X2),X3),f10(X4,f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),f7(boundary(X0,X1,X2),X3)))
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1491,f1477]) ).
fof(f1708,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| neighborhood(f10(X4,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),f7(boundary(X0,X1,X2),X3),X5,X6)
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1491,f1099]) ).
fof(f1710,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| element_of_set(f19(union_of_members(X0),X1),f10(X2,f10(X3,f1(X0,f19(union_of_members(X0),X1)),f19(union_of_members(X0),X1)),f19(union_of_members(X0),X1)))
| hausdorff(union_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1504,f1477]) ).
fof(f1711,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(f10(X2,f1(X0,f19(union_of_members(X0),X1)),f19(union_of_members(X0),X1)),f19(union_of_members(X0),X1),X3,X4)
| hausdorff(union_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1504,f1099]) ).
fof(f1713,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f19(boundary(X0,X1,X2),X3),f10(X4,f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),f19(boundary(X0,X1,X2),X3)))
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1509,f1477]) ).
fof(f1714,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| neighborhood(f10(X4,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),f19(boundary(X0,X1,X2),X3),X5,X6)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1509,f1099]) ).
fof(f1716,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ71_spl
| element_of_set(X1,X0)
| ~ subset_sets(a,X0) ),
inference(resolution,[status(thm)],[f1386,f1107]) ).
fof(f1719,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ71_spl
| element_of_set(X0,union_of_members(X1)) ),
inference(resolution,[status(thm)],[f1386,f970]) ).
fof(f1720,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ71_spl
| element_of_set(X0,f1(X1,X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f115,f1719]) ).
fof(f1723,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ sQ71_spl
| element_of_set(X0,f10(X1,f1(X2,X0),X0)) ),
inference(resolution,[status(thm)],[f1720,f1477]) ).
fof(f1726,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ71_spl
| element_of_set(X0,cx) ),
inference(resolution,[status(thm)],[f1716,f274]) ).
fof(f1729,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ71_spl
| disjoint_s(f17(cx,ct,X0,X1),f18(cx,ct,X0,X1))
| eq_p(X0,X1)
| ~ element_of_set(X0,cx) ),
inference(backward_subsumption_resolution,[status(thm)],[f401,f1726]) ).
fof(f1733,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ71_spl
| disjoint_s(f17(cx,ct,f19(cx,X0),X1),f18(cx,ct,f19(cx,X0),X1))
| eq_p(f19(cx,X0),X1)
| hausdorff(cx,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f992,f1726]) ).
fof(f1735,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ71_spl
| neighborhood(f17(cx,ct,f19(cx,X0),X1),f19(cx,X0),cx,ct)
| eq_p(f19(cx,X0),X1)
| hausdorff(cx,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f990,f1726]) ).
fof(f1736,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ71_spl
| disjoint_s(f17(cx,ct,f20(cx,X0),X1),f18(cx,ct,f20(cx,X0),X1))
| eq_p(f20(cx,X0),X1)
| hausdorff(cx,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f983,f1726]) ).
fof(f1738,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ71_spl
| neighborhood(f17(cx,ct,f20(cx,X0),X1),f20(cx,X0),cx,ct)
| eq_p(f20(cx,X0),X1)
| hausdorff(cx,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f981,f1726]) ).
fof(f1743,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ71_spl
| disjoint_s(f17(cx,ct,X0,X1),f18(cx,ct,X0,X1))
| eq_p(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1729,f1726]) ).
fof(f1750,plain,
! [X0,X1] :
( ~ sQ14_spl
| connected_space(X0,X1)
| disjoint_s(f21(X0,X1),f22(X0,X1)) ),
inference(resolution,[status(thm)],[f240,f962]) ).
fof(f1754,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| subset_sets(f10(X2,X1,X0),X1)
| ~ element_of_set(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f166,f967]) ).
fof(f1755,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(intersection_of_members(X2),X3)
| subset_sets(f10(X0,X1,f7(intersection_of_members(X2),X3)),X1) ),
inference(resolution,[status(thm)],[f1754,f1325]) ).
fof(f1757,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| basis(boundary(X1,X2,X3),X4)
| subset_sets(f10(X0,closure(X1,X2,X3),f7(boundary(X1,X2,X3),X4)),closure(X1,X2,X3)) ),
inference(resolution,[status(thm)],[f1754,f997]) ).
fof(f1758,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(X2,X3)
| subset_sets(f10(X0,f10(X1,intersection_of_sets(f8(X2,X3),f9(X2,X3)),f7(X2,X3)),f7(X2,X3)),f10(X1,intersection_of_sets(f8(X2,X3),f9(X2,X3)),f7(X2,X3))) ),
inference(resolution,[status(thm)],[f1754,f1494]) ).
fof(f1759,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| basis(X2,X3)
| subset_sets(f10(X0,f10(X1,X2,f7(X2,X3)),f7(X2,X3)),f10(X1,X2,f7(X2,X3))) ),
inference(resolution,[status(thm)],[f1754,f1495]) ).
fof(f1760,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(X1,X2)
| subset_sets(f10(X0,intersection_of_sets(f8(X1,X2),f9(X1,X2)),f7(X1,X2)),intersection_of_sets(f8(X1,X2),f9(X1,X2))) ),
inference(resolution,[status(thm)],[f1754,f971]) ).
fof(f1761,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| basis(X1,X2)
| subset_sets(f10(X0,X1,f7(X1,X2)),X1) ),
inference(resolution,[status(thm)],[f1754,f972]) ).
fof(f1762,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(intersection_of_members(X2),X3)
| subset_sets(f10(X0,X1,f19(intersection_of_members(X2),X3)),X1) ),
inference(resolution,[status(thm)],[f1754,f1326]) ).
fof(f1764,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(boundary(X1,X2,X3),X4)
| subset_sets(f10(X0,closure(X1,X2,X3),f19(boundary(X1,X2,X3),X4)),closure(X1,X2,X3)) ),
inference(resolution,[status(thm)],[f1754,f988]) ).
fof(f1765,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(X2,X3)
| subset_sets(f10(X0,f10(X1,X2,f19(X2,X3)),f19(X2,X3)),f10(X1,X2,f19(X2,X3))) ),
inference(resolution,[status(thm)],[f1754,f1512]) ).
fof(f1766,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(X1,X2)
| subset_sets(f10(X0,X1,f19(X1,X2)),X1) ),
inference(resolution,[status(thm)],[f1754,f965]) ).
fof(f1767,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| hausdorff(intersection_of_members(X2),X3)
| subset_sets(f10(X0,X1,f20(intersection_of_members(X2),X3)),X1) ),
inference(resolution,[status(thm)],[f1754,f1327]) ).
fof(f1768,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(boundary(X1,X2,X3),X4)
| subset_sets(f10(X0,closure(X1,X2,X3),f20(boundary(X1,X2,X3),X4)),closure(X1,X2,X3)) ),
inference(resolution,[status(thm)],[f1754,f979]) ).
fof(f1770,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| hausdorff(X1,X2)
| subset_sets(f10(X0,X1,f20(X1,X2)),X1) ),
inference(resolution,[status(thm)],[f1754,f964]) ).
fof(f1773,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ71_spl
| subset_sets(f10(X0,f10(X1,f1(X2,X3),X3),X3),f10(X1,f1(X2,X3),X3)) ),
inference(resolution,[status(thm)],[f1754,f1723]) ).
fof(f1776,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ sQ71_spl
| subset_sets(f10(X0,f1(X1,X2),X2),f1(X1,X2)) ),
inference(resolution,[status(thm)],[f1754,f1720]) ).
fof(f1789,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ element_of_collection(f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2)),X1)
| ~ element_of_set(f7(X0,X1),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2)))
| basis(X0,X1)
| basis(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2) ),
inference(resolution,[status(thm)],[f1761,f1476]) ).
fof(f1790,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f20(closure(f10(X2,X0,f7(X0,X1)),X3,X4),X5),X0)
| hausdorff(closure(f10(X2,X0,f7(X0,X1)),X3,X4),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1761,f1106]) ).
fof(f1791,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f19(closure(f10(X2,X0,f7(X0,X1)),X3,X4),X5),X0)
| hausdorff(closure(f10(X2,X0,f7(X0,X1)),X3,X4),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1761,f1105]) ).
fof(f1792,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f7(closure(f10(X2,X0,f7(X0,X1)),X3,X4),X5),X0)
| basis(closure(f10(X2,X0,f7(X0,X1)),X3,X4),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1761,f1104]) ).
fof(f1793,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f20(boundary(f10(X2,X0,f7(X0,X1)),X3,X4),X5),X0)
| hausdorff(boundary(f10(X2,X0,f7(X0,X1)),X3,X4),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1761,f1103]) ).
fof(f1794,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f19(boundary(f10(X2,X0,f7(X0,X1)),X3,X4),X5),X0)
| hausdorff(boundary(f10(X2,X0,f7(X0,X1)),X3,X4),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1761,f1102]) ).
fof(f1795,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f7(boundary(f10(X2,X0,f7(X0,X1)),X3,X4),X5),X0)
| basis(boundary(f10(X2,X0,f7(X0,X1)),X3,X4),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1761,f1101]) ).
fof(f1796,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,X0,f7(X0,X1)),X0,X4),f10(X3,X0,f7(X0,X1))),X5)
| eq_p(f20(intersection_of_sets(f16(X2,f10(X3,X0,f7(X0,X1)),X0,X4),f10(X3,X0,f7(X0,X1))),X5),X2)
| limit_point(X2,f10(X3,X0,f7(X0,X1)),X0,X4)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1761,f1017]) ).
fof(f1797,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,X0,f7(X0,X1)),X0,X4),f10(X3,X0,f7(X0,X1))),X5)
| eq_p(f19(intersection_of_sets(f16(X2,f10(X3,X0,f7(X0,X1)),X0,X4),f10(X3,X0,f7(X0,X1))),X5),X2)
| limit_point(X2,f10(X3,X0,f7(X0,X1)),X0,X4)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1761,f1016]) ).
fof(f1798,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| basis(intersection_of_sets(f16(X2,f10(X3,X0,f7(X0,X1)),X0,X4),f10(X3,X0,f7(X0,X1))),X5)
| eq_p(f7(intersection_of_sets(f16(X2,f10(X3,X0,f7(X0,X1)),X0,X4),f10(X3,X0,f7(X0,X1))),X5),X2)
| limit_point(X2,f10(X3,X0,f7(X0,X1)),X0,X4)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1761,f1015]) ).
fof(f1799,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| subset_sets(f10(X3,X0,f7(X0,X1)),f14(f10(X3,X0,f7(X0,X1)),X0,X4,X2))
| element_of_set(X2,closure(f10(X3,X0,f7(X0,X1)),X0,X4))
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1761,f961]) ).
fof(f1800,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(f16(X2,f10(X3,X0,f7(X0,X1)),X0,X4),X2,X0,X4)
| limit_point(X2,f10(X3,X0,f7(X0,X1)),X0,X4)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1761,f960]) ).
fof(f1801,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ element_of_set(f7(X0,X1),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2)))
| basis(X0,X1)
| basis(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1789,f967]) ).
fof(f1802,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ element_of_collection(f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f19(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2)),X1)
| ~ element_of_set(f7(X0,X1),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f19(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2)))
| basis(X0,X1)
| hausdorff(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2) ),
inference(resolution,[status(thm)],[f1766,f1476]) ).
fof(f1803,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f20(closure(f10(X2,X0,f19(X0,X1)),X3,X4),X5),X0)
| hausdorff(closure(f10(X2,X0,f19(X0,X1)),X3,X4),X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1766,f1106]) ).
fof(f1804,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f19(closure(f10(X2,X0,f19(X0,X1)),X3,X4),X5),X0)
| hausdorff(closure(f10(X2,X0,f19(X0,X1)),X3,X4),X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1766,f1105]) ).
fof(f1805,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f7(closure(f10(X2,X0,f19(X0,X1)),X3,X4),X5),X0)
| basis(closure(f10(X2,X0,f19(X0,X1)),X3,X4),X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1766,f1104]) ).
fof(f1806,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f20(boundary(f10(X2,X0,f19(X0,X1)),X3,X4),X5),X0)
| hausdorff(boundary(f10(X2,X0,f19(X0,X1)),X3,X4),X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1766,f1103]) ).
fof(f1807,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f19(boundary(f10(X2,X0,f19(X0,X1)),X3,X4),X5),X0)
| hausdorff(boundary(f10(X2,X0,f19(X0,X1)),X3,X4),X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1766,f1102]) ).
fof(f1808,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f7(boundary(f10(X2,X0,f19(X0,X1)),X3,X4),X5),X0)
| basis(boundary(f10(X2,X0,f19(X0,X1)),X3,X4),X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1766,f1101]) ).
fof(f1809,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,X0,f19(X0,X1)),X0,X4),f10(X3,X0,f19(X0,X1))),X5)
| eq_p(f20(intersection_of_sets(f16(X2,f10(X3,X0,f19(X0,X1)),X0,X4),f10(X3,X0,f19(X0,X1))),X5),X2)
| limit_point(X2,f10(X3,X0,f19(X0,X1)),X0,X4)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1766,f1017]) ).
fof(f1810,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,X0,f19(X0,X1)),X0,X4),f10(X3,X0,f19(X0,X1))),X5)
| eq_p(f19(intersection_of_sets(f16(X2,f10(X3,X0,f19(X0,X1)),X0,X4),f10(X3,X0,f19(X0,X1))),X5),X2)
| limit_point(X2,f10(X3,X0,f19(X0,X1)),X0,X4)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1766,f1016]) ).
fof(f1811,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| basis(intersection_of_sets(f16(X2,f10(X3,X0,f19(X0,X1)),X0,X4),f10(X3,X0,f19(X0,X1))),X5)
| eq_p(f7(intersection_of_sets(f16(X2,f10(X3,X0,f19(X0,X1)),X0,X4),f10(X3,X0,f19(X0,X1))),X5),X2)
| limit_point(X2,f10(X3,X0,f19(X0,X1)),X0,X4)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1766,f1015]) ).
fof(f1812,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| subset_sets(f10(X3,X0,f19(X0,X1)),f14(f10(X3,X0,f19(X0,X1)),X0,X4,X2))
| element_of_set(X2,closure(f10(X3,X0,f19(X0,X1)),X0,X4))
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1766,f961]) ).
fof(f1813,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(f16(X2,f10(X3,X0,f19(X0,X1)),X0,X4),X2,X0,X4)
| limit_point(X2,f10(X3,X0,f19(X0,X1)),X0,X4)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1766,f960]) ).
fof(f1814,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ element_of_set(f7(X0,X1),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f19(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2)))
| basis(X0,X1)
| hausdorff(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1802,f967]) ).
fof(f1815,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ element_of_collection(f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f20(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2)),X1)
| ~ element_of_set(f7(X0,X1),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f20(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2)))
| basis(X0,X1)
| hausdorff(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2) ),
inference(resolution,[status(thm)],[f1770,f1476]) ).
fof(f1816,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f20(closure(f10(X2,X0,f20(X0,X1)),X3,X4),X5),X0)
| hausdorff(closure(f10(X2,X0,f20(X0,X1)),X3,X4),X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1770,f1106]) ).
fof(f1817,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f19(closure(f10(X2,X0,f20(X0,X1)),X3,X4),X5),X0)
| hausdorff(closure(f10(X2,X0,f20(X0,X1)),X3,X4),X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1770,f1105]) ).
fof(f1818,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f7(closure(f10(X2,X0,f20(X0,X1)),X3,X4),X5),X0)
| basis(closure(f10(X2,X0,f20(X0,X1)),X3,X4),X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1770,f1104]) ).
fof(f1819,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f20(boundary(f10(X2,X0,f20(X0,X1)),X3,X4),X5),X0)
| hausdorff(boundary(f10(X2,X0,f20(X0,X1)),X3,X4),X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1770,f1103]) ).
fof(f1820,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f19(boundary(f10(X2,X0,f20(X0,X1)),X3,X4),X5),X0)
| hausdorff(boundary(f10(X2,X0,f20(X0,X1)),X3,X4),X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1770,f1102]) ).
fof(f1821,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f7(boundary(f10(X2,X0,f20(X0,X1)),X3,X4),X5),X0)
| basis(boundary(f10(X2,X0,f20(X0,X1)),X3,X4),X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1770,f1101]) ).
fof(f1822,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,X0,f20(X0,X1)),X0,X4),f10(X3,X0,f20(X0,X1))),X5)
| eq_p(f20(intersection_of_sets(f16(X2,f10(X3,X0,f20(X0,X1)),X0,X4),f10(X3,X0,f20(X0,X1))),X5),X2)
| limit_point(X2,f10(X3,X0,f20(X0,X1)),X0,X4)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1770,f1017]) ).
fof(f1823,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,X0,f20(X0,X1)),X0,X4),f10(X3,X0,f20(X0,X1))),X5)
| eq_p(f19(intersection_of_sets(f16(X2,f10(X3,X0,f20(X0,X1)),X0,X4),f10(X3,X0,f20(X0,X1))),X5),X2)
| limit_point(X2,f10(X3,X0,f20(X0,X1)),X0,X4)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1770,f1016]) ).
fof(f1824,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| basis(intersection_of_sets(f16(X2,f10(X3,X0,f20(X0,X1)),X0,X4),f10(X3,X0,f20(X0,X1))),X5)
| eq_p(f7(intersection_of_sets(f16(X2,f10(X3,X0,f20(X0,X1)),X0,X4),f10(X3,X0,f20(X0,X1))),X5),X2)
| limit_point(X2,f10(X3,X0,f20(X0,X1)),X0,X4)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1770,f1015]) ).
fof(f1825,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| subset_sets(f10(X3,X0,f20(X0,X1)),f14(f10(X3,X0,f20(X0,X1)),X0,X4,X2))
| element_of_set(X2,closure(f10(X3,X0,f20(X0,X1)),X0,X4))
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1770,f961]) ).
fof(f1826,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(f16(X2,f10(X3,X0,f20(X0,X1)),X0,X4),X2,X0,X4)
| limit_point(X2,f10(X3,X0,f20(X0,X1)),X0,X4)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1770,f960]) ).
fof(f1827,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ element_of_set(f7(X0,X1),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f20(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2)))
| basis(X0,X1)
| hausdorff(intersection_of_sets(f8(X0,X1),f9(X0,X1)),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1815,f967]) ).
fof(f1828,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| ~ element_of_collection(f10(X4,intersection_of_sets(f8(X2,X3),f9(X2,X3)),f7(intersection_of_members(X0),X1)),X3)
| ~ element_of_set(f7(X2,X3),f10(X4,intersection_of_sets(f8(X2,X3),f9(X2,X3)),f7(intersection_of_members(X0),X1)))
| basis(X2,X3)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1755,f1476]) ).
fof(f1829,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f20(closure(f10(X2,X3,f7(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| hausdorff(closure(f10(X2,X3,f7(intersection_of_members(X0),X1)),X4,X5),X6)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1755,f1106]) ).
fof(f1830,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f19(closure(f10(X2,X3,f7(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| hausdorff(closure(f10(X2,X3,f7(intersection_of_members(X0),X1)),X4,X5),X6)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1755,f1105]) ).
fof(f1831,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f7(closure(f10(X2,X3,f7(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| basis(closure(f10(X2,X3,f7(intersection_of_members(X0),X1)),X4,X5),X6)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1755,f1104]) ).
fof(f1832,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f20(boundary(f10(X2,X3,f7(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| hausdorff(boundary(f10(X2,X3,f7(intersection_of_members(X0),X1)),X4,X5),X6)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1755,f1103]) ).
fof(f1833,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f19(boundary(f10(X2,X3,f7(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| hausdorff(boundary(f10(X2,X3,f7(intersection_of_members(X0),X1)),X4,X5),X6)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1755,f1102]) ).
fof(f1834,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f7(boundary(f10(X2,X3,f7(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| basis(boundary(f10(X2,X3,f7(intersection_of_members(X0),X1)),X4,X5),X6)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1755,f1101]) ).
fof(f1835,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,X4,f7(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f7(intersection_of_members(X0),X1))),X6)
| eq_p(f20(intersection_of_sets(f16(X2,f10(X3,X4,f7(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f7(intersection_of_members(X0),X1))),X6),X2)
| limit_point(X2,f10(X3,X4,f7(intersection_of_members(X0),X1)),X4,X5)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1755,f1017]) ).
fof(f1836,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,X4,f7(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f7(intersection_of_members(X0),X1))),X6)
| eq_p(f19(intersection_of_sets(f16(X2,f10(X3,X4,f7(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f7(intersection_of_members(X0),X1))),X6),X2)
| limit_point(X2,f10(X3,X4,f7(intersection_of_members(X0),X1)),X4,X5)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1755,f1016]) ).
fof(f1837,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| basis(intersection_of_sets(f16(X2,f10(X3,X4,f7(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f7(intersection_of_members(X0),X1))),X6)
| eq_p(f7(intersection_of_sets(f16(X2,f10(X3,X4,f7(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f7(intersection_of_members(X0),X1))),X6),X2)
| limit_point(X2,f10(X3,X4,f7(intersection_of_members(X0),X1)),X4,X5)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1755,f1015]) ).
fof(f1838,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| subset_sets(f10(X3,X4,f7(intersection_of_members(X0),X1)),f14(f10(X3,X4,f7(intersection_of_members(X0),X1)),X4,X5,X2))
| element_of_set(X2,closure(f10(X3,X4,f7(intersection_of_members(X0),X1)),X4,X5))
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1755,f961]) ).
fof(f1839,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| neighborhood(f16(X2,f10(X3,X4,f7(intersection_of_members(X0),X1)),X4,X5),X2,X4,X5)
| limit_point(X2,f10(X3,X4,f7(intersection_of_members(X0),X1)),X4,X5)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1755,f960]) ).
fof(f1840,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| ~ element_of_set(f7(X2,X3),f10(X4,intersection_of_sets(f8(X2,X3),f9(X2,X3)),f7(intersection_of_members(X0),X1)))
| basis(X2,X3)
| basis(intersection_of_members(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1828,f967]) ).
fof(f1841,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| ~ element_of_collection(f10(X4,intersection_of_sets(f8(X2,X3),f9(X2,X3)),f19(intersection_of_members(X0),X1)),X3)
| ~ element_of_set(f7(X2,X3),f10(X4,intersection_of_sets(f8(X2,X3),f9(X2,X3)),f19(intersection_of_members(X0),X1)))
| basis(X2,X3)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1762,f1476]) ).
fof(f1842,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f20(closure(f10(X2,X3,f19(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| hausdorff(closure(f10(X2,X3,f19(intersection_of_members(X0),X1)),X4,X5),X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1762,f1106]) ).
fof(f1843,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f19(closure(f10(X2,X3,f19(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| hausdorff(closure(f10(X2,X3,f19(intersection_of_members(X0),X1)),X4,X5),X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1762,f1105]) ).
fof(f1844,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f7(closure(f10(X2,X3,f19(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| basis(closure(f10(X2,X3,f19(intersection_of_members(X0),X1)),X4,X5),X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1762,f1104]) ).
fof(f1845,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f20(boundary(f10(X2,X3,f19(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| hausdorff(boundary(f10(X2,X3,f19(intersection_of_members(X0),X1)),X4,X5),X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1762,f1103]) ).
fof(f1846,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f19(boundary(f10(X2,X3,f19(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| hausdorff(boundary(f10(X2,X3,f19(intersection_of_members(X0),X1)),X4,X5),X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1762,f1102]) ).
fof(f1847,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f7(boundary(f10(X2,X3,f19(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| basis(boundary(f10(X2,X3,f19(intersection_of_members(X0),X1)),X4,X5),X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1762,f1101]) ).
fof(f1848,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,X4,f19(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f19(intersection_of_members(X0),X1))),X6)
| eq_p(f20(intersection_of_sets(f16(X2,f10(X3,X4,f19(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f19(intersection_of_members(X0),X1))),X6),X2)
| limit_point(X2,f10(X3,X4,f19(intersection_of_members(X0),X1)),X4,X5)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1762,f1017]) ).
fof(f1849,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,X4,f19(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f19(intersection_of_members(X0),X1))),X6)
| eq_p(f19(intersection_of_sets(f16(X2,f10(X3,X4,f19(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f19(intersection_of_members(X0),X1))),X6),X2)
| limit_point(X2,f10(X3,X4,f19(intersection_of_members(X0),X1)),X4,X5)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1762,f1016]) ).
fof(f1850,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| basis(intersection_of_sets(f16(X2,f10(X3,X4,f19(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f19(intersection_of_members(X0),X1))),X6)
| eq_p(f7(intersection_of_sets(f16(X2,f10(X3,X4,f19(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f19(intersection_of_members(X0),X1))),X6),X2)
| limit_point(X2,f10(X3,X4,f19(intersection_of_members(X0),X1)),X4,X5)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1762,f1015]) ).
fof(f1851,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| subset_sets(f10(X3,X4,f19(intersection_of_members(X0),X1)),f14(f10(X3,X4,f19(intersection_of_members(X0),X1)),X4,X5,X2))
| element_of_set(X2,closure(f10(X3,X4,f19(intersection_of_members(X0),X1)),X4,X5))
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1762,f961]) ).
fof(f1852,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| neighborhood(f16(X2,f10(X3,X4,f19(intersection_of_members(X0),X1)),X4,X5),X2,X4,X5)
| limit_point(X2,f10(X3,X4,f19(intersection_of_members(X0),X1)),X4,X5)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1762,f960]) ).
fof(f1853,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| ~ element_of_set(f7(X2,X3),f10(X4,intersection_of_sets(f8(X2,X3),f9(X2,X3)),f19(intersection_of_members(X0),X1)))
| basis(X2,X3)
| hausdorff(intersection_of_members(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1841,f967]) ).
fof(f1854,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| ~ element_of_collection(f10(X4,intersection_of_sets(f8(X2,X3),f9(X2,X3)),f20(intersection_of_members(X0),X1)),X3)
| ~ element_of_set(f7(X2,X3),f10(X4,intersection_of_sets(f8(X2,X3),f9(X2,X3)),f20(intersection_of_members(X0),X1)))
| basis(X2,X3)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1767,f1476]) ).
fof(f1855,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f20(closure(f10(X2,X3,f20(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| hausdorff(closure(f10(X2,X3,f20(intersection_of_members(X0),X1)),X4,X5),X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1767,f1106]) ).
fof(f1856,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f19(closure(f10(X2,X3,f20(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| hausdorff(closure(f10(X2,X3,f20(intersection_of_members(X0),X1)),X4,X5),X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1767,f1105]) ).
fof(f1857,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f7(closure(f10(X2,X3,f20(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| basis(closure(f10(X2,X3,f20(intersection_of_members(X0),X1)),X4,X5),X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1767,f1104]) ).
fof(f1858,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f20(boundary(f10(X2,X3,f20(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| hausdorff(boundary(f10(X2,X3,f20(intersection_of_members(X0),X1)),X4,X5),X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1767,f1103]) ).
fof(f1859,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f19(boundary(f10(X2,X3,f20(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| hausdorff(boundary(f10(X2,X3,f20(intersection_of_members(X0),X1)),X4,X5),X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1767,f1102]) ).
fof(f1860,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f7(boundary(f10(X2,X3,f20(intersection_of_members(X0),X1)),X4,X5),X6),X3)
| basis(boundary(f10(X2,X3,f20(intersection_of_members(X0),X1)),X4,X5),X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1767,f1101]) ).
fof(f1861,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,X4,f20(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f20(intersection_of_members(X0),X1))),X6)
| eq_p(f20(intersection_of_sets(f16(X2,f10(X3,X4,f20(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f20(intersection_of_members(X0),X1))),X6),X2)
| limit_point(X2,f10(X3,X4,f20(intersection_of_members(X0),X1)),X4,X5)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1767,f1017]) ).
fof(f1862,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,X4,f20(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f20(intersection_of_members(X0),X1))),X6)
| eq_p(f19(intersection_of_sets(f16(X2,f10(X3,X4,f20(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f20(intersection_of_members(X0),X1))),X6),X2)
| limit_point(X2,f10(X3,X4,f20(intersection_of_members(X0),X1)),X4,X5)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1767,f1016]) ).
fof(f1863,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| basis(intersection_of_sets(f16(X2,f10(X3,X4,f20(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f20(intersection_of_members(X0),X1))),X6)
| eq_p(f7(intersection_of_sets(f16(X2,f10(X3,X4,f20(intersection_of_members(X0),X1)),X4,X5),f10(X3,X4,f20(intersection_of_members(X0),X1))),X6),X2)
| limit_point(X2,f10(X3,X4,f20(intersection_of_members(X0),X1)),X4,X5)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1767,f1015]) ).
fof(f1864,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| subset_sets(f10(X3,X4,f20(intersection_of_members(X0),X1)),f14(f10(X3,X4,f20(intersection_of_members(X0),X1)),X4,X5,X2))
| element_of_set(X2,closure(f10(X3,X4,f20(intersection_of_members(X0),X1)),X4,X5))
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1767,f961]) ).
fof(f1865,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| neighborhood(f16(X2,f10(X3,X4,f20(intersection_of_members(X0),X1)),X4,X5),X2,X4,X5)
| limit_point(X2,f10(X3,X4,f20(intersection_of_members(X0),X1)),X4,X5)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1767,f960]) ).
fof(f1866,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| ~ element_of_set(f7(X2,X3),f10(X4,intersection_of_sets(f8(X2,X3),f9(X2,X3)),f20(intersection_of_members(X0),X1)))
| basis(X2,X3)
| hausdorff(intersection_of_members(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1854,f967]) ).
fof(f1873,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ element_of_collection(f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X1)
| ~ element_of_set(f7(X0,X1),f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)))
| basis(X0,X1)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1760,f1476]) ).
fof(f1874,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f20(closure(f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X3,X4),X5),intersection_of_sets(f8(X0,X1),f9(X0,X1)))
| hausdorff(closure(f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X3,X4),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1760,f1106]) ).
fof(f1875,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f19(closure(f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X3,X4),X5),intersection_of_sets(f8(X0,X1),f9(X0,X1)))
| hausdorff(closure(f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X3,X4),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1760,f1105]) ).
fof(f1876,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f7(closure(f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X3,X4),X5),intersection_of_sets(f8(X0,X1),f9(X0,X1)))
| basis(closure(f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X3,X4),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1760,f1104]) ).
fof(f1877,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f20(boundary(f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X3,X4),X5),intersection_of_sets(f8(X0,X1),f9(X0,X1)))
| hausdorff(boundary(f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X3,X4),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1760,f1103]) ).
fof(f1878,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f19(boundary(f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X3,X4),X5),intersection_of_sets(f8(X0,X1),f9(X0,X1)))
| hausdorff(boundary(f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X3,X4),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1760,f1102]) ).
fof(f1879,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f7(boundary(f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X3,X4),X5),intersection_of_sets(f8(X0,X1),f9(X0,X1)))
| basis(boundary(f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X3,X4),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1760,f1101]) ).
fof(f1880,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),intersection_of_sets(f8(X0,X1),f9(X0,X1)),X4),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1))),X5)
| eq_p(f20(intersection_of_sets(f16(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),intersection_of_sets(f8(X0,X1),f9(X0,X1)),X4),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1))),X5),X2)
| limit_point(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),intersection_of_sets(f8(X0,X1),f9(X0,X1)),X4)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1760,f1017]) ).
fof(f1881,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),intersection_of_sets(f8(X0,X1),f9(X0,X1)),X4),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1))),X5)
| eq_p(f19(intersection_of_sets(f16(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),intersection_of_sets(f8(X0,X1),f9(X0,X1)),X4),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1))),X5),X2)
| limit_point(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),intersection_of_sets(f8(X0,X1),f9(X0,X1)),X4)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1760,f1016]) ).
fof(f1882,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| basis(intersection_of_sets(f16(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),intersection_of_sets(f8(X0,X1),f9(X0,X1)),X4),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1))),X5)
| eq_p(f7(intersection_of_sets(f16(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),intersection_of_sets(f8(X0,X1),f9(X0,X1)),X4),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1))),X5),X2)
| limit_point(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),intersection_of_sets(f8(X0,X1),f9(X0,X1)),X4)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1760,f1015]) ).
fof(f1883,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| subset_sets(f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f14(f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),intersection_of_sets(f8(X0,X1),f9(X0,X1)),X4,X2))
| element_of_set(X2,closure(f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),intersection_of_sets(f8(X0,X1),f9(X0,X1)),X4))
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1760,f961]) ).
fof(f1884,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| neighborhood(f16(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),intersection_of_sets(f8(X0,X1),f9(X0,X1)),X4),X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),X4)
| limit_point(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),intersection_of_sets(f8(X0,X1),f9(X0,X1)),X4)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1760,f960]) ).
fof(f1885,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ element_of_collection(f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X1)
| ~ element_of_set(f7(X0,X1),f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)))
| basis(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f1873]) ).
fof(f1886,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ element_of_collection(f10(X2,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X1)
| basis(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1885,f1494]) ).
fof(f1887,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| subset_sets(f10(X4,f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),f20(boundary(X0,X1,X2),X3)),f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)))
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1528,f1754]) ).
fof(f1888,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| element_of_set(f20(boundary(X0,X1,X2),X3),f10(X4,f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),f20(boundary(X0,X1,X2),X3)))
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1528,f1477]) ).
fof(f1889,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| neighborhood(f10(X4,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),f20(boundary(X0,X1,X2),X3),X5,X6)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1528,f1099]) ).
fof(f1890,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| basis(X4,X5)
| eq_p(f7(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,intersection_of_sets(f8(X4,X5),f9(X4,X5)),f7(X4,X5)),intersection_of_sets(f8(X4,X5),f9(X4,X5)),X6)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1589,f1760]) ).
fof(f1891,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| hausdorff(intersection_of_members(X5),X6)
| eq_p(f7(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f20(intersection_of_members(X5),X6)),X4,X7)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1589,f1767]) ).
fof(f1892,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(X4,X5)
| eq_p(f7(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f20(X4,X5)),X4,X6)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1589,f1770]) ).
fof(f1893,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| hausdorff(intersection_of_members(X5),X6)
| eq_p(f7(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f19(intersection_of_members(X5),X6)),X4,X7)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1589,f1762]) ).
fof(f1894,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(X4,X5)
| eq_p(f7(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f19(X4,X5)),X4,X6)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1589,f1766]) ).
fof(f1895,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| basis(intersection_of_members(X5),X6)
| eq_p(f7(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f7(intersection_of_members(X5),X6)),X4,X7)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1589,f1755]) ).
fof(f1896,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| basis(X4,X5)
| eq_p(f7(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f7(X4,X5)),X4,X6)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1589,f1761]) ).
fof(f1897,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| eq_p(f7(intersection_of_members(X0),X1),X2)
| limit_point(X2,a,cx,X3)
| basis(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1589,f274]) ).
fof(f1898,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| basis(X4,X5)
| eq_p(f19(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,intersection_of_sets(f8(X4,X5),f9(X4,X5)),f7(X4,X5)),intersection_of_sets(f8(X4,X5),f9(X4,X5)),X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1610,f1760]) ).
fof(f1899,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| hausdorff(intersection_of_members(X5),X6)
| eq_p(f19(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f20(intersection_of_members(X5),X6)),X4,X7)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1610,f1767]) ).
fof(f1900,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(X4,X5)
| eq_p(f19(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f20(X4,X5)),X4,X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1610,f1770]) ).
fof(f1901,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| hausdorff(intersection_of_members(X5),X6)
| eq_p(f19(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f19(intersection_of_members(X5),X6)),X4,X7)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1610,f1762]) ).
fof(f1902,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(X4,X5)
| eq_p(f19(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f19(X4,X5)),X4,X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1610,f1766]) ).
fof(f1903,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| basis(intersection_of_members(X5),X6)
| eq_p(f19(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f7(intersection_of_members(X5),X6)),X4,X7)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1610,f1755]) ).
fof(f1904,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| basis(X4,X5)
| eq_p(f19(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f7(X4,X5)),X4,X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1610,f1761]) ).
fof(f1905,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| eq_p(f19(intersection_of_members(X0),X1),X2)
| limit_point(X2,a,cx,X3)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1610,f274]) ).
fof(f1912,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| basis(X4,X5)
| eq_p(f20(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,intersection_of_sets(f8(X4,X5),f9(X4,X5)),f7(X4,X5)),intersection_of_sets(f8(X4,X5),f9(X4,X5)),X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1631,f1760]) ).
fof(f1913,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| hausdorff(intersection_of_members(X5),X6)
| eq_p(f20(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f20(intersection_of_members(X5),X6)),X4,X7)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1631,f1767]) ).
fof(f1914,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(X4,X5)
| eq_p(f20(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f20(X4,X5)),X4,X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1631,f1770]) ).
fof(f1915,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| hausdorff(intersection_of_members(X5),X6)
| eq_p(f20(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f19(intersection_of_members(X5),X6)),X4,X7)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1631,f1762]) ).
fof(f1916,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(X4,X5)
| eq_p(f20(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f19(X4,X5)),X4,X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1631,f1766]) ).
fof(f1917,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| basis(intersection_of_members(X5),X6)
| eq_p(f20(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f7(intersection_of_members(X5),X6)),X4,X7)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1631,f1755]) ).
fof(f1918,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| basis(X4,X5)
| eq_p(f20(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,X4,f7(X4,X5)),X4,X6)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1631,f1761]) ).
fof(f1919,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| eq_p(f20(intersection_of_members(X0),X1),X2)
| limit_point(X2,a,cx,X3)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1631,f274]) ).
fof(f1920,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| subset_sets(f10(X2,f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)))
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1651,f1754]) ).
fof(f1921,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f7(X0,X1),f10(X2,f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f7(X0,X1)))
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1651,f1477]) ).
fof(f1922,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| neighborhood(f10(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f7(X0,X1),X4,X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1651,f1099]) ).
fof(f1924,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| subset_sets(f10(X2,f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1)))
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1654,f1754]) ).
fof(f1925,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f7(X0,X1),f10(X2,f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1)),f7(X0,X1)))
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1654,f1477]) ).
fof(f1926,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| neighborhood(f10(X2,f10(X3,X0,f7(X0,X1)),f7(X0,X1)),f7(X0,X1),X4,X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1654,f1099]) ).
fof(f1927,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| subset_sets(f10(X2,f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1)),f19(X0,X1)),f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1)))
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1657,f1754]) ).
fof(f1928,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f19(X0,X1),f10(X2,f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1)),f19(X0,X1)))
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1657,f1477]) ).
fof(f1929,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| neighborhood(f10(X2,f10(X3,X0,f19(X0,X1)),f19(X0,X1)),f19(X0,X1),X4,X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1657,f1099]) ).
fof(f1930,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| subset_sets(f10(X2,f10(X3,f10(X4,X0,f20(X0,X1)),f20(X0,X1)),f20(X0,X1)),f10(X3,f10(X4,X0,f20(X0,X1)),f20(X0,X1)))
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1660,f1754]) ).
fof(f1931,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f20(X0,X1),f10(X2,f10(X3,f10(X4,X0,f20(X0,X1)),f20(X0,X1)),f20(X0,X1)))
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1660,f1477]) ).
fof(f1932,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| neighborhood(f10(X2,f10(X3,X0,f20(X0,X1)),f20(X0,X1)),f20(X0,X1),X4,X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1660,f1099]) ).
fof(f1933,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| eq_p(f20(intersection_of_members(X4),X5),X6)
| limit_point(X6,f10(X7,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X8)
| hausdorff(intersection_of_members(X4),X5)
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1757,f1631]) ).
fof(f1934,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| eq_p(f19(intersection_of_members(X4),X5),X6)
| limit_point(X6,f10(X7,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X8)
| hausdorff(intersection_of_members(X4),X5)
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1757,f1610]) ).
fof(f1935,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| eq_p(f7(intersection_of_members(X4),X5),X6)
| limit_point(X6,f10(X7,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X8)
| basis(intersection_of_members(X4),X5)
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1757,f1589]) ).
fof(f1936,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f20(closure(f10(X4,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| hausdorff(closure(f10(X4,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),X5,X6),X7)
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1757,f1106]) ).
fof(f1937,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f19(closure(f10(X4,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| hausdorff(closure(f10(X4,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),X5,X6),X7)
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1757,f1105]) ).
fof(f1938,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f7(closure(f10(X4,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| basis(closure(f10(X4,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),X5,X6),X7)
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1757,f1104]) ).
fof(f1939,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f20(boundary(f10(X4,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| hausdorff(boundary(f10(X4,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),X5,X6),X7)
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1757,f1103]) ).
fof(f1940,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f19(boundary(f10(X4,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| hausdorff(boundary(f10(X4,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),X5,X6),X7)
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1757,f1102]) ).
fof(f1941,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f7(boundary(f10(X4,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| basis(boundary(f10(X4,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),X5,X6),X7)
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1757,f1101]) ).
fof(f1942,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3))),X7)
| eq_p(f20(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3))),X7),X4)
| limit_point(X4,f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6)
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1757,f1017]) ).
fof(f1943,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3))),X7)
| eq_p(f19(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3))),X7),X4)
| limit_point(X4,f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6)
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1757,f1016]) ).
fof(f1944,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| basis(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3))),X7)
| eq_p(f7(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3))),X7),X4)
| limit_point(X4,f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6)
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1757,f1015]) ).
fof(f1945,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| subset_sets(f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),f14(f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6,X4))
| element_of_set(X4,closure(f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6))
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1757,f961]) ).
fof(f1946,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| neighborhood(f16(X4,f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),X4,closure(X0,X1,X2),X6)
| limit_point(X4,f10(X5,closure(X0,X1,X2),f7(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6)
| basis(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1757,f960]) ).
fof(f1947,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| eq_p(f20(intersection_of_members(X2),X3),X4)
| limit_point(X4,f10(X5,f10(X6,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X6,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X7)
| hausdorff(intersection_of_members(X2),X3)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1758,f1631]) ).
fof(f1948,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| eq_p(f19(intersection_of_members(X2),X3),X4)
| limit_point(X4,f10(X5,f10(X6,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X6,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X7)
| hausdorff(intersection_of_members(X2),X3)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1758,f1610]) ).
fof(f1949,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| eq_p(f7(intersection_of_members(X2),X3),X4)
| limit_point(X4,f10(X5,f10(X6,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X6,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X7)
| basis(intersection_of_members(X2),X3)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1758,f1589]) ).
fof(f1950,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f20(closure(f10(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),X4,X5),X6),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)))
| hausdorff(closure(f10(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),X4,X5),X6)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1758,f1106]) ).
fof(f1951,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f19(closure(f10(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),X4,X5),X6),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)))
| hausdorff(closure(f10(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),X4,X5),X6)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1758,f1105]) ).
fof(f1952,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f7(closure(f10(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),X4,X5),X6),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)))
| basis(closure(f10(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),X4,X5),X6)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1758,f1104]) ).
fof(f1953,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f20(boundary(f10(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),X4,X5),X6),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)))
| hausdorff(boundary(f10(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),X4,X5),X6)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1758,f1103]) ).
fof(f1954,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f19(boundary(f10(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),X4,X5),X6),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)))
| hausdorff(boundary(f10(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),X4,X5),X6)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1758,f1102]) ).
fof(f1955,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f7(boundary(f10(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),X4,X5),X6),f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)))
| basis(boundary(f10(X2,f10(X3,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),X4,X5),X6)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1758,f1101]) ).
fof(f1956,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X5),f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1))),X6)
| eq_p(f20(intersection_of_sets(f16(X2,f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X5),f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1))),X6),X2)
| limit_point(X2,f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1758,f1017]) ).
fof(f1957,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X5),f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1))),X6)
| eq_p(f19(intersection_of_sets(f16(X2,f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X5),f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1))),X6),X2)
| limit_point(X2,f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1758,f1016]) ).
fof(f1958,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| basis(intersection_of_sets(f16(X2,f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X5),f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1))),X6)
| eq_p(f7(intersection_of_sets(f16(X2,f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X5),f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1))),X6),X2)
| limit_point(X2,f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1758,f1015]) ).
fof(f1959,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| subset_sets(f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f14(f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X5,X2))
| element_of_set(X2,closure(f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X5))
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1758,f961]) ).
fof(f1960,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| neighborhood(f16(X2,f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X5),X2,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X5)
| limit_point(X2,f10(X3,f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),f7(X0,X1)),f10(X4,intersection_of_sets(f8(X0,X1),f9(X0,X1)),f7(X0,X1)),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1758,f960]) ).
fof(f1961,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| eq_p(f20(intersection_of_members(X2),X3),X4)
| limit_point(X4,f10(X5,f10(X6,X0,f7(X0,X1)),f7(X0,X1)),f10(X6,X0,f7(X0,X1)),X7)
| hausdorff(intersection_of_members(X2),X3)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1759,f1631]) ).
fof(f1962,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| eq_p(f19(intersection_of_members(X2),X3),X4)
| limit_point(X4,f10(X5,f10(X6,X0,f7(X0,X1)),f7(X0,X1)),f10(X6,X0,f7(X0,X1)),X7)
| hausdorff(intersection_of_members(X2),X3)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1759,f1610]) ).
fof(f1963,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| eq_p(f7(intersection_of_members(X2),X3),X4)
| limit_point(X4,f10(X5,f10(X6,X0,f7(X0,X1)),f7(X0,X1)),f10(X6,X0,f7(X0,X1)),X7)
| basis(intersection_of_members(X2),X3)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1759,f1589]) ).
fof(f1964,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f20(closure(f10(X2,f10(X3,X0,f7(X0,X1)),f7(X0,X1)),X4,X5),X6),f10(X3,X0,f7(X0,X1)))
| hausdorff(closure(f10(X2,f10(X3,X0,f7(X0,X1)),f7(X0,X1)),X4,X5),X6)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1759,f1106]) ).
fof(f1965,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f19(closure(f10(X2,f10(X3,X0,f7(X0,X1)),f7(X0,X1)),X4,X5),X6),f10(X3,X0,f7(X0,X1)))
| hausdorff(closure(f10(X2,f10(X3,X0,f7(X0,X1)),f7(X0,X1)),X4,X5),X6)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1759,f1105]) ).
fof(f1966,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f7(closure(f10(X2,f10(X3,X0,f7(X0,X1)),f7(X0,X1)),X4,X5),X6),f10(X3,X0,f7(X0,X1)))
| basis(closure(f10(X2,f10(X3,X0,f7(X0,X1)),f7(X0,X1)),X4,X5),X6)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1759,f1104]) ).
fof(f1967,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f20(boundary(f10(X2,f10(X3,X0,f7(X0,X1)),f7(X0,X1)),X4,X5),X6),f10(X3,X0,f7(X0,X1)))
| hausdorff(boundary(f10(X2,f10(X3,X0,f7(X0,X1)),f7(X0,X1)),X4,X5),X6)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1759,f1103]) ).
fof(f1968,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f19(boundary(f10(X2,f10(X3,X0,f7(X0,X1)),f7(X0,X1)),X4,X5),X6),f10(X3,X0,f7(X0,X1)))
| hausdorff(boundary(f10(X2,f10(X3,X0,f7(X0,X1)),f7(X0,X1)),X4,X5),X6)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1759,f1102]) ).
fof(f1969,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f7(boundary(f10(X2,f10(X3,X0,f7(X0,X1)),f7(X0,X1)),X4,X5),X6),f10(X3,X0,f7(X0,X1)))
| basis(boundary(f10(X2,f10(X3,X0,f7(X0,X1)),f7(X0,X1)),X4,X5),X6)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1759,f1101]) ).
fof(f1970,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1)),f10(X4,X0,f7(X0,X1)),X5),f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1))),X6)
| eq_p(f20(intersection_of_sets(f16(X2,f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1)),f10(X4,X0,f7(X0,X1)),X5),f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1))),X6),X2)
| limit_point(X2,f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1)),f10(X4,X0,f7(X0,X1)),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1759,f1017]) ).
fof(f1971,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1)),f10(X4,X0,f7(X0,X1)),X5),f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1))),X6)
| eq_p(f19(intersection_of_sets(f16(X2,f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1)),f10(X4,X0,f7(X0,X1)),X5),f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1))),X6),X2)
| limit_point(X2,f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1)),f10(X4,X0,f7(X0,X1)),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1759,f1016]) ).
fof(f1972,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| basis(intersection_of_sets(f16(X2,f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1)),f10(X4,X0,f7(X0,X1)),X5),f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1))),X6)
| eq_p(f7(intersection_of_sets(f16(X2,f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1)),f10(X4,X0,f7(X0,X1)),X5),f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1))),X6),X2)
| limit_point(X2,f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1)),f10(X4,X0,f7(X0,X1)),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1759,f1015]) ).
fof(f1973,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| subset_sets(f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1)),f14(f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1)),f10(X4,X0,f7(X0,X1)),X5,X2))
| element_of_set(X2,closure(f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1)),f10(X4,X0,f7(X0,X1)),X5))
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1759,f961]) ).
fof(f1974,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| neighborhood(f16(X2,f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1)),f10(X4,X0,f7(X0,X1)),X5),X2,f10(X4,X0,f7(X0,X1)),X5)
| limit_point(X2,f10(X3,f10(X4,X0,f7(X0,X1)),f7(X0,X1)),f10(X4,X0,f7(X0,X1)),X5)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1759,f960]) ).
fof(f1975,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| eq_p(f20(intersection_of_members(X4),X5),X6)
| limit_point(X6,f10(X7,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X8)
| hausdorff(intersection_of_members(X4),X5)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1764,f1631]) ).
fof(f1976,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| eq_p(f19(intersection_of_members(X4),X5),X6)
| limit_point(X6,f10(X7,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X8)
| hausdorff(intersection_of_members(X4),X5)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1764,f1610]) ).
fof(f1977,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| eq_p(f7(intersection_of_members(X4),X5),X6)
| limit_point(X6,f10(X7,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X8)
| basis(intersection_of_members(X4),X5)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1764,f1589]) ).
fof(f1978,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f20(closure(f10(X4,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| hausdorff(closure(f10(X4,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),X5,X6),X7)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1764,f1106]) ).
fof(f1979,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f19(closure(f10(X4,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| hausdorff(closure(f10(X4,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),X5,X6),X7)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1764,f1105]) ).
fof(f1980,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f7(closure(f10(X4,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| basis(closure(f10(X4,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),X5,X6),X7)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1764,f1104]) ).
fof(f1981,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f20(boundary(f10(X4,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| hausdorff(boundary(f10(X4,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),X5,X6),X7)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1764,f1103]) ).
fof(f1982,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f19(boundary(f10(X4,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| hausdorff(boundary(f10(X4,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),X5,X6),X7)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1764,f1102]) ).
fof(f1983,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f7(boundary(f10(X4,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| basis(boundary(f10(X4,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),X5,X6),X7)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1764,f1101]) ).
fof(f1984,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3))),X7)
| eq_p(f20(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3))),X7),X4)
| limit_point(X4,f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1764,f1017]) ).
fof(f1985,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3))),X7)
| eq_p(f19(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3))),X7),X4)
| limit_point(X4,f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1764,f1016]) ).
fof(f1986,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| basis(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3))),X7)
| eq_p(f7(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3))),X7),X4)
| limit_point(X4,f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1764,f1015]) ).
fof(f1987,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| subset_sets(f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),f14(f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6,X4))
| element_of_set(X4,closure(f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6))
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1764,f961]) ).
fof(f1988,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| neighborhood(f16(X4,f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),X4,closure(X0,X1,X2),X6)
| limit_point(X4,f10(X5,closure(X0,X1,X2),f19(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1764,f960]) ).
fof(f1989,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| eq_p(f20(intersection_of_members(X2),X3),X4)
| limit_point(X4,f10(X5,f10(X6,X0,f19(X0,X1)),f19(X0,X1)),f10(X6,X0,f19(X0,X1)),X7)
| hausdorff(intersection_of_members(X2),X3)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1765,f1631]) ).
fof(f1990,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| eq_p(f19(intersection_of_members(X2),X3),X4)
| limit_point(X4,f10(X5,f10(X6,X0,f19(X0,X1)),f19(X0,X1)),f10(X6,X0,f19(X0,X1)),X7)
| hausdorff(intersection_of_members(X2),X3)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1765,f1610]) ).
fof(f1991,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| eq_p(f7(intersection_of_members(X2),X3),X4)
| limit_point(X4,f10(X5,f10(X6,X0,f19(X0,X1)),f19(X0,X1)),f10(X6,X0,f19(X0,X1)),X7)
| basis(intersection_of_members(X2),X3)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1765,f1589]) ).
fof(f1992,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f20(closure(f10(X2,f10(X3,X0,f19(X0,X1)),f19(X0,X1)),X4,X5),X6),f10(X3,X0,f19(X0,X1)))
| hausdorff(closure(f10(X2,f10(X3,X0,f19(X0,X1)),f19(X0,X1)),X4,X5),X6)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1765,f1106]) ).
fof(f1993,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f19(closure(f10(X2,f10(X3,X0,f19(X0,X1)),f19(X0,X1)),X4,X5),X6),f10(X3,X0,f19(X0,X1)))
| hausdorff(closure(f10(X2,f10(X3,X0,f19(X0,X1)),f19(X0,X1)),X4,X5),X6)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1765,f1105]) ).
fof(f1994,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f7(closure(f10(X2,f10(X3,X0,f19(X0,X1)),f19(X0,X1)),X4,X5),X6),f10(X3,X0,f19(X0,X1)))
| basis(closure(f10(X2,f10(X3,X0,f19(X0,X1)),f19(X0,X1)),X4,X5),X6)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1765,f1104]) ).
fof(f1995,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f20(boundary(f10(X2,f10(X3,X0,f19(X0,X1)),f19(X0,X1)),X4,X5),X6),f10(X3,X0,f19(X0,X1)))
| hausdorff(boundary(f10(X2,f10(X3,X0,f19(X0,X1)),f19(X0,X1)),X4,X5),X6)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1765,f1103]) ).
fof(f1996,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f19(boundary(f10(X2,f10(X3,X0,f19(X0,X1)),f19(X0,X1)),X4,X5),X6),f10(X3,X0,f19(X0,X1)))
| hausdorff(boundary(f10(X2,f10(X3,X0,f19(X0,X1)),f19(X0,X1)),X4,X5),X6)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1765,f1102]) ).
fof(f1997,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| element_of_set(f7(boundary(f10(X2,f10(X3,X0,f19(X0,X1)),f19(X0,X1)),X4,X5),X6),f10(X3,X0,f19(X0,X1)))
| basis(boundary(f10(X2,f10(X3,X0,f19(X0,X1)),f19(X0,X1)),X4,X5),X6)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1765,f1101]) ).
fof(f1998,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1)),f10(X4,X0,f19(X0,X1)),X5),f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1))),X6)
| eq_p(f20(intersection_of_sets(f16(X2,f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1)),f10(X4,X0,f19(X0,X1)),X5),f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1))),X6),X2)
| limit_point(X2,f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1)),f10(X4,X0,f19(X0,X1)),X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1765,f1017]) ).
fof(f1999,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X2,f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1)),f10(X4,X0,f19(X0,X1)),X5),f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1))),X6)
| eq_p(f19(intersection_of_sets(f16(X2,f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1)),f10(X4,X0,f19(X0,X1)),X5),f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1))),X6),X2)
| limit_point(X2,f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1)),f10(X4,X0,f19(X0,X1)),X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1765,f1016]) ).
fof(f2000,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| basis(intersection_of_sets(f16(X2,f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1)),f10(X4,X0,f19(X0,X1)),X5),f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1))),X6)
| eq_p(f7(intersection_of_sets(f16(X2,f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1)),f10(X4,X0,f19(X0,X1)),X5),f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1))),X6),X2)
| limit_point(X2,f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1)),f10(X4,X0,f19(X0,X1)),X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1765,f1015]) ).
fof(f2001,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| subset_sets(f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1)),f14(f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1)),f10(X4,X0,f19(X0,X1)),X5,X2))
| element_of_set(X2,closure(f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1)),f10(X4,X0,f19(X0,X1)),X5))
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1765,f961]) ).
fof(f2002,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| neighborhood(f16(X2,f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1)),f10(X4,X0,f19(X0,X1)),X5),X2,f10(X4,X0,f19(X0,X1)),X5)
| limit_point(X2,f10(X3,f10(X4,X0,f19(X0,X1)),f19(X0,X1)),f10(X4,X0,f19(X0,X1)),X5)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1765,f960]) ).
fof(f2003,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| eq_p(f20(intersection_of_members(X4),X5),X6)
| limit_point(X6,f10(X7,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X8)
| hausdorff(intersection_of_members(X4),X5)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1768,f1631]) ).
fof(f2004,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| eq_p(f19(intersection_of_members(X4),X5),X6)
| limit_point(X6,f10(X7,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X8)
| hausdorff(intersection_of_members(X4),X5)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1768,f1610]) ).
fof(f2005,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ14_spl
| eq_p(f7(intersection_of_members(X4),X5),X6)
| limit_point(X6,f10(X7,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X8)
| basis(intersection_of_members(X4),X5)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1768,f1589]) ).
fof(f2006,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f20(closure(f10(X4,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| hausdorff(closure(f10(X4,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),X5,X6),X7)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1768,f1106]) ).
fof(f2007,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f19(closure(f10(X4,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| hausdorff(closure(f10(X4,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),X5,X6),X7)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1768,f1105]) ).
fof(f2008,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f7(closure(f10(X4,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| basis(closure(f10(X4,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),X5,X6),X7)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1768,f1104]) ).
fof(f2009,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f20(boundary(f10(X4,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| hausdorff(boundary(f10(X4,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),X5,X6),X7)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1768,f1103]) ).
fof(f2010,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f19(boundary(f10(X4,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| hausdorff(boundary(f10(X4,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),X5,X6),X7)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1768,f1102]) ).
fof(f2011,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| element_of_set(f7(boundary(f10(X4,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),X5,X6),X7),closure(X0,X1,X2))
| basis(boundary(f10(X4,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),X5,X6),X7)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1768,f1101]) ).
fof(f2012,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3))),X7)
| eq_p(f20(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3))),X7),X4)
| limit_point(X4,f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1768,f1017]) ).
fof(f2013,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3))),X7)
| eq_p(f19(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3))),X7),X4)
| limit_point(X4,f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1768,f1016]) ).
fof(f2014,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| basis(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3))),X7)
| eq_p(f7(intersection_of_sets(f16(X4,f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3))),X7),X4)
| limit_point(X4,f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1768,f1015]) ).
fof(f2015,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| subset_sets(f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),f14(f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6,X4))
| element_of_set(X4,closure(f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6))
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1768,f961]) ).
fof(f2016,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| neighborhood(f16(X4,f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6),X4,closure(X0,X1,X2),X6)
| limit_point(X4,f10(X5,closure(X0,X1,X2),f20(boundary(X0,X1,X2),X3)),closure(X0,X1,X2),X6)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f1768,f960]) ).
fof(f2038,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| ~ sQ71_spl
| element_of_set(f20(boundary(f10(X0,f1(X1,X2),X2),X3,X4),X5),f1(X1,X2))
| hausdorff(boundary(f10(X0,f1(X1,X2),X2),X3,X4),X5) ),
inference(resolution,[status(thm)],[f1776,f1103]) ).
fof(f2039,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| ~ sQ71_spl
| element_of_set(f19(boundary(f10(X0,f1(X1,X2),X2),X3,X4),X5),f1(X1,X2))
| hausdorff(boundary(f10(X0,f1(X1,X2),X2),X3,X4),X5) ),
inference(resolution,[status(thm)],[f1776,f1102]) ).
fof(f2066,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| ~ sQ71_spl
| eq_p(f20(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,f10(X4,f1(X5,X6),X6),X6),f10(X4,f1(X5,X6),X6),X7)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1773,f1631]) ).
fof(f2067,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| ~ sQ71_spl
| eq_p(f19(intersection_of_members(X0),X1),X2)
| limit_point(X2,f10(X3,f10(X4,f1(X5,X6),X6),X6),f10(X4,f1(X5,X6),X6),X7)
| hausdorff(intersection_of_members(X0),X1) ),
inference(resolution,[status(thm)],[f1773,f1610]) ).
fof(f2069,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| ~ sQ71_spl
| element_of_set(f20(closure(f10(X0,f10(X1,f1(X2,X3),X3),X3),X4,X5),X6),f10(X1,f1(X2,X3),X3))
| hausdorff(closure(f10(X0,f10(X1,f1(X2,X3),X3),X3),X4,X5),X6) ),
inference(resolution,[status(thm)],[f1773,f1106]) ).
fof(f2070,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| ~ sQ71_spl
| element_of_set(f19(closure(f10(X0,f10(X1,f1(X2,X3),X3),X3),X4,X5),X6),f10(X1,f1(X2,X3),X3))
| hausdorff(closure(f10(X0,f10(X1,f1(X2,X3),X3),X3),X4,X5),X6) ),
inference(resolution,[status(thm)],[f1773,f1105]) ).
fof(f2072,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| ~ sQ71_spl
| element_of_set(f20(boundary(f10(X0,f10(X1,f1(X2,X3),X3),X3),X4,X5),X6),f10(X1,f1(X2,X3),X3))
| hausdorff(boundary(f10(X0,f10(X1,f1(X2,X3),X3),X3),X4,X5),X6) ),
inference(resolution,[status(thm)],[f1773,f1103]) ).
fof(f2073,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| ~ sQ71_spl
| element_of_set(f19(boundary(f10(X0,f10(X1,f1(X2,X3),X3),X3),X4,X5),X6),f10(X1,f1(X2,X3),X3))
| hausdorff(boundary(f10(X0,f10(X1,f1(X2,X3),X3),X3),X4,X5),X6) ),
inference(resolution,[status(thm)],[f1773,f1102]) ).
fof(f2080,plain,
! [X0,X1] :
( ~ sQ14_spl
| connected_space(X0,X1)
| ~ equal_sets(f21(X0,X1),empty_set) ),
inference(resolution,[status(thm)],[f230,f962]) ).
fof(f2081,plain,
! [X0,X1] :
( ~ sQ14_spl
| connected_space(X0,X1)
| ~ equal_sets(f22(X0,X1),empty_set) ),
inference(resolution,[status(thm)],[f232,f962]) ).
fof(f2082,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(X0,X4)
| ~ element_of_set(X0,closure(X1,X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[f1107,f2099]) ).
fof(f2083,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| eq_p(X4,X0)
| ~ element_of_set(X4,intersection_of_sets(f16(X0,X1,X2,X3),X1))
| limit_point(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f955,f2099]) ).
fof(f2084,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ71_spl
| element_of_set(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f1716,f2099]) ).
fof(f2085,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ element_of_collection(X2,X1)
| ~ element_of_set(f7(X0,X1),X2)
| basis(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f1476,f2099]) ).
fof(f2086,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| eq_p(f20(intersection_of_members(X0),X1),X2)
| limit_point(X2,X3,X4,X5)
| hausdorff(intersection_of_members(X0),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f1631,f2099]) ).
fof(f2087,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| eq_p(f19(intersection_of_members(X0),X1),X2)
| limit_point(X2,X3,X4,X5)
| hausdorff(intersection_of_members(X0),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f1610,f2099]) ).
fof(f2088,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| eq_p(f7(intersection_of_members(X0),X1),X2)
| limit_point(X2,X3,X4,X5)
| basis(intersection_of_members(X0),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f1589,f2099]) ).
fof(f2089,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f20(closure(X0,X1,X2),X3),X4)
| hausdorff(closure(X0,X1,X2),X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f1106,f2099]) ).
fof(f2090,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f19(closure(X0,X1,X2),X3),X4)
| hausdorff(closure(X0,X1,X2),X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f1105,f2099]) ).
fof(f2091,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f7(closure(X0,X1,X2),X3),X4)
| basis(closure(X0,X1,X2),X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f1104,f2099]) ).
fof(f2092,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f20(boundary(X0,X1,X2),X3),X4)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f1103,f2099]) ).
fof(f2093,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f19(boundary(X0,X1,X2),X3),X4)
| hausdorff(boundary(X0,X1,X2),X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f1102,f2099]) ).
fof(f2094,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| element_of_set(f7(boundary(X0,X1,X2),X3),X4)
| basis(boundary(X0,X1,X2),X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f1101,f2099]) ).
fof(f2095,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4)
| eq_p(f20(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4),X0)
| limit_point(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f1017,f2099]) ).
fof(f2096,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| hausdorff(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4)
| eq_p(f19(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4),X0)
| limit_point(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f1016,f2099]) ).
fof(f2097,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| basis(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4)
| eq_p(f7(intersection_of_sets(f16(X0,X1,X2,X3),X1),X4),X0)
| limit_point(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f1015,f2099]) ).
fof(f2098,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| neighborhood(f16(X0,X1,X2,X3),X0,X2,X3)
| limit_point(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f960,f2099]) ).
fof(f2099,plain,
! [X0,X1] :
( ~ sQ14_spl
| subset_sets(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f967]) ).
fof(f2100,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ element_of_set(f7(X0,X1),X2)
| basis(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2085,f967]) ).
fof(f2101,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ71_spl
| disjoint_s(f17(X0,X1,X2,X3),f18(X0,X1,X2,X3))
| eq_p(X2,X3)
| ~ element_of_set(X2,X0)
| ~ hausdorff(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f221,f2084]) ).
fof(f2104,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ71_spl
| neighborhood(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f1099,f2084]) ).
fof(f2105,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ71_spl
| disjoint_s(f17(X0,X1,X2,X3),f18(X0,X1,X2,X3))
| eq_p(X2,X3)
| ~ hausdorff(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2101,f2084]) ).
fof(f2108,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| equal_sets(X0,intersection_of_sets(X1,f12(X2,X3,X1,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f175,f967]) ).
fof(f2109,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| ~ disjoint_s(X0,X1)
| ~ element_of_collection(X1,X5)
| equal_sets(X1,empty_set)
| equal_sets(X0,empty_set)
| separation(X0,X1,intersection_of_sets(X2,f12(X3,X4,X2,union_of_sets(X0,X1))),X5) ),
inference(resolution,[status(thm)],[f2108,f1014]) ).
fof(f2110,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| ~ disjoint_s(X0,X1)
| equal_sets(X1,empty_set)
| equal_sets(X0,empty_set)
| separation(X0,X1,intersection_of_sets(X2,f12(X3,X4,X2,union_of_sets(X0,X1))),X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f2109,f967]) ).
fof(f2112,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| ~ sQ71_spl
| eq_p(X4,X0)
| limit_point(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2083,f2084]) ).
fof(f2113,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| connected_space(X0,X1)
| equal_sets(f22(X0,X1),empty_set)
| equal_sets(f21(X0,X1),empty_set)
| separation(f21(X0,X1),f22(X0,X1),intersection_of_sets(X2,f12(X3,X4,X2,union_of_sets(f21(X0,X1),f22(X0,X1)))),X5) ),
inference(resolution,[status(thm)],[f2110,f1750]) ).
fof(f2114,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ71_spl
| eq_p(X0,X1)
| equal_sets(f18(cx,ct,X0,X1),empty_set)
| equal_sets(f17(cx,ct,X0,X1),empty_set)
| separation(f17(cx,ct,X0,X1),f18(cx,ct,X0,X1),intersection_of_sets(X2,f12(X3,X4,X2,union_of_sets(f17(cx,ct,X0,X1),f18(cx,ct,X0,X1)))),X5) ),
inference(resolution,[status(thm)],[f2110,f1743]) ).
fof(f2118,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ71_spl
| basis(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2100,f2084]) ).
fof(f2119,plain,
! [X0,X1] :
( ~ sQ14_spl
| connected_space(X0,X1)
| equal_sets(union_of_sets(f21(X0,X1),f22(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f238,f962]) ).
fof(f2120,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ disjoint_s(f21(X0,X1),f22(X0,X1))
| ~ element_of_collection(f22(X0,X1),X2)
| equal_sets(f22(X0,X1),empty_set)
| equal_sets(f21(X0,X1),empty_set)
| separation(f21(X0,X1),f22(X0,X1),X0,X2)
| connected_space(X0,X1) ),
inference(resolution,[status(thm)],[f2119,f1014]) ).
fof(f2121,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ disjoint_s(f21(X0,X1),f22(X0,X1))
| ~ element_of_collection(f22(X0,X1),X2)
| equal_sets(f22(X0,X1),empty_set)
| separation(f21(X0,X1),f22(X0,X1),X0,X2)
| connected_space(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2120,f2080]) ).
fof(f2124,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| ~ sQ71_spl
| ~ eq_p(f15(X0,X1,X2,X3,X4),X0)
| ~ limit_point(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f209,f2104]) ).
fof(f2125,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ14_spl
| ~ sQ71_spl
| limit_point(X0,X4,X5,X6)
| ~ limit_point(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f2124,f2112]) ).
fof(f2126,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| connected_space(X0,X1)
| equal_sets(f22(X0,X1),empty_set)
| separation(f21(X0,X1),f22(X0,X1),intersection_of_sets(X2,f12(X3,X4,X2,union_of_sets(f21(X0,X1),f22(X0,X1)))),X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f2113,f2080]) ).
fof(f2130,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| ~ connected_space(intersection_of_sets(X2,f12(X3,X4,X2,union_of_sets(f21(X0,X1),f22(X0,X1)))),X5)
| connected_space(X0,X1)
| equal_sets(f22(X0,X1),empty_set) ),
inference(resolution,[status(thm)],[f2126,f245]) ).
fof(f2132,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ14_spl
| ~ connected_space(intersection_of_sets(X2,f12(X3,X4,X2,union_of_sets(f21(X0,X1),f22(X0,X1)))),X5)
| connected_space(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2130,f2081]) ).
fof(f2133,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ disjoint_s(f21(X0,X1),f22(X0,X1))
| ~ element_of_collection(f22(X0,X1),X2)
| separation(f21(X0,X1),f22(X0,X1),X0,X2)
| connected_space(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2121,f2081]) ).
fof(f2134,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| connected_space(X0,X1)
| ~ element_of_collection(f22(X0,X1),X2)
| separation(f21(X0,X1),f22(X0,X1),X0,X2)
| connected_space(X0,X1) ),
inference(resolution,[status(thm)],[f2133,f1750]) ).
fof(f2135,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ element_of_collection(f22(X0,X1),X2)
| separation(f21(X0,X1),f22(X0,X1),X0,X2)
| connected_space(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f2134]) ).
fof(f2136,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| separation(f21(X0,X1),f22(X0,X1),X0,X2)
| connected_space(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2135,f967]) ).
fof(f2140,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ connected_space(X0,X2)
| connected_space(X0,X1) ),
inference(resolution,[status(thm)],[f2136,f245]) ).
fof(f2143,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| connected_space(cx,X0) ),
inference(resolution,[status(thm)],[f2140,f321]) ).
fof(f2145,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ eq_p(f19(X0,X1),f20(X0,X1))
| hausdorff(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f224,f504]) ).
fof(f2146,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ14_spl
| ~ sQ71_spl
| limit_point(f20(X0,X1),X2,X3,X4)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f2145,f2112]) ).
fof(f2148,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ equal_sets(union_of_members(X0),X1)
| ~ subset_collections(X0,X2)
| open_covering(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f260,f504]) ).
fof(f2149,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ subset_collections(X0,X2)
| open_covering(X0,X1,X2) ),
inference(resolution,[status(thm)],[f2148,f956]) ).
fof(f2151,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| compact_space(X0,X1)
| open_covering(f24(X0,X1),X2,X1) ),
inference(resolution,[status(thm)],[f2149,f1006]) ).
fof(f2152,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ connected_space(X0,subspace_topology(X1,X2,X0))
| ~ subset_sets(X0,X1)
| connected_set(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f252,f504]) ).
fof(f2153,plain,
! [X0,X1] :
( ~ sQ8_spl
| ~ sQ14_spl
| ~ subset_sets(cx,X0)
| connected_set(cx,X0,X1) ),
inference(resolution,[status(thm)],[f2152,f2143]) ).
fof(f2154,plain,
! [X0,X1] :
( ~ sQ8_spl
| ~ sQ14_spl
| connected_set(cx,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2153,f2099]) ).
fof(f2156,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ compact_space(X0,subspace_topology(X1,X2,X0))
| ~ subset_sets(X0,X1)
| compact_set(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f272,f504]) ).
fof(f2157,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ open_covering(X2,X0,X1)
| ~ subset_collections(X2,f24(X0,X1))
| ~ finite(X2)
| compact_space(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f266,f504]) ).
fof(f2158,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| compact_space(X2,f24(X0,X1))
| ~ open_covering(f24(X2,f24(X0,X1)),X0,X1)
| ~ finite(f24(X2,f24(X0,X1)))
| compact_space(X0,X1) ),
inference(resolution,[status(thm)],[f2157,f1006]) ).
fof(f2159,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ disjoint_s(X2,X3)
| ~ neighborhood(X3,f20(X0,X1),X0,X1)
| ~ neighborhood(X2,f19(X0,X1),X0,X1)
| hausdorff(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f226,f504]) ).
fof(f2160,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ71_spl
| ~ disjoint_s(X2,X3)
| ~ neighborhood(X2,f19(X0,X1),X0,X1)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f2159,f2104]) ).
fof(f2161,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ71_spl
| ~ disjoint_s(X2,X3)
| hausdorff(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2160,f2104]) ).
fof(f2162,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ71_spl
| connected_space(X2,X3)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f2161,f1750]) ).
fof(f2163,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ71_spl
| eq_p(X2,X3)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f2161,f1743]) ).
fof(f2164,definition,
! [X0,X1] :
( sQ83_spl
<=> hausdorff(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f2165,plain,
! [X0,X1] :
( ~ sQ83_spl
| hausdorff(X0,X1) ),
inference(component_clause,[status(thm)],[f2164]) ).
fof(f2167,definition,
! [X2,X3] :
( sQ84_spl
<=> connected_space(X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f2170,plain,
( ~ sQ14_spl
| ~ sQ71_spl
| sQ84_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f2162,f2164,f2167,f1385,f503]) ).
fof(f2171,definition,
! [X2,X3] :
( sQ85_spl
<=> eq_p(X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f2174,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ71_spl
| sQ85_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f2163,f2164,f2171,f1385,f503,f298]) ).
fof(f2175,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| ~ sQ71_spl
| ~ sQ83_spl
| disjoint_s(f17(X2,X3,X0,X1),f18(X2,X3,X0,X1))
| eq_p(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f2105,f2165]) ).
fof(f2176,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| ~ sQ71_spl
| ~ sQ83_spl
| equal_sets(f18(X2,X3,X0,X1),empty_set)
| equal_sets(f17(X2,X3,X0,X1),empty_set)
| separation(f17(X2,X3,X0,X1),f18(X2,X3,X0,X1),intersection_of_sets(X4,f12(X5,X6,X4,union_of_sets(f17(X2,X3,X0,X1),f18(X2,X3,X0,X1)))),X7)
| eq_p(X0,X1) ),
inference(resolution,[status(thm)],[f2175,f2110]) ).
fof(f2180,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ14_spl
| ~ sQ71_spl
| ~ sQ83_spl
| ~ connected_space(intersection_of_sets(X4,f12(X5,X6,X4,union_of_sets(f17(X2,X3,X0,X1),f18(X2,X3,X0,X1)))),X7)
| equal_sets(f18(X2,X3,X0,X1),empty_set)
| equal_sets(f17(X2,X3,X0,X1),empty_set)
| eq_p(X0,X1) ),
inference(resolution,[status(thm)],[f2176,f245]) ).
fof(f2182,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| open_covering(f23(X2,X1,f24(X0,X1)),X2,X1)
| ~ compact_space(X2,X1)
| compact_space(X0,X1) ),
inference(resolution,[status(thm)],[f2151,f264]) ).
fof(f2183,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| subset_collections(f23(X2,X1,f24(X0,X1)),f24(X0,X1))
| ~ compact_space(X2,X1)
| compact_space(X0,X1) ),
inference(resolution,[status(thm)],[f2151,f263]) ).
fof(f2184,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| finite(f23(X2,X1,f24(X0,X1)))
| ~ compact_space(X2,X1)
| compact_space(X0,X1) ),
inference(resolution,[status(thm)],[f2151,f262]) ).
fof(f2186,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ14_spl
| finite(f23(cx,ct,f24(X0,ct)))
| compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f2184,f312]) ).
fof(f2187,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ14_spl
| open_covering(f23(cx,ct,f24(X0,ct)),cx,ct)
| compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f2182,f312]) ).
fof(f2188,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ14_spl
| subset_collections(f23(cx,ct,f24(X0,ct)),f24(X0,ct))
| compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f2183,f312]) ).
fof(f2189,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ14_spl
| open_covering(f23(cx,ct,f23(cx,ct,f24(X0,ct))),cx,ct)
| ~ compact_space(cx,ct)
| compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f2187,f264]) ).
fof(f2190,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ14_spl
| subset_collections(f23(cx,ct,f23(cx,ct,f24(X0,ct))),f23(cx,ct,f24(X0,ct)))
| ~ compact_space(cx,ct)
| compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f2187,f263]) ).
fof(f2191,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ14_spl
| finite(f23(cx,ct,f23(cx,ct,f24(X0,ct))))
| ~ compact_space(cx,ct)
| compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f2187,f262]) ).
fof(f2192,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ14_spl
| subset_collections(f23(cx,ct,f24(X0,ct)),ct)
| compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f2187,f256]) ).
fof(f2193,definition,
! [X0] :
( sQ86_spl
<=> ( open_covering(f23(cx,ct,f23(cx,ct,f24(X0,ct))),cx,ct)
| compact_space(X0,ct) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f2196,plain,
( ~ sQ14_spl
| ~ sQ6_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f2189,f2193,f311,f503]) ).
fof(f2197,definition,
! [X0] :
( sQ87_spl
<=> ( subset_collections(f23(cx,ct,f23(cx,ct,f24(X0,ct))),f23(cx,ct,f24(X0,ct)))
| compact_space(X0,ct) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f2200,plain,
( ~ sQ14_spl
| ~ sQ6_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f2190,f2197,f311,f503]) ).
fof(f2201,definition,
! [X0] :
( sQ88_spl
<=> ( finite(f23(cx,ct,f23(cx,ct,f24(X0,ct))))
| compact_space(X0,ct) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f2204,plain,
( ~ sQ14_spl
| ~ sQ6_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f2191,f2201,f311,f503]) ).
fof(f2205,plain,
( ~ sQ7_spl
| open_covering(f23(cx,ct,f24(cx,ct)),cx,ct)
| ~ compact_space(cx,ct) ),
inference(resolution,[status(thm)],[f315,f264]) ).
fof(f2206,plain,
( ~ sQ7_spl
| subset_collections(f23(cx,ct,f24(cx,ct)),f24(cx,ct))
| ~ compact_space(cx,ct) ),
inference(resolution,[status(thm)],[f315,f263]) ).
fof(f2207,plain,
( ~ sQ7_spl
| finite(f23(cx,ct,f24(cx,ct)))
| ~ compact_space(cx,ct) ),
inference(resolution,[status(thm)],[f315,f262]) ).
fof(f2208,plain,
( ~ sQ7_spl
| subset_collections(f24(cx,ct),ct) ),
inference(resolution,[status(thm)],[f315,f256]) ).
fof(f2209,definition,
( sQ89_spl
<=> open_covering(f23(cx,ct,f24(cx,ct)),cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f2212,plain,
( ~ sQ7_spl
| sQ89_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f2205,f311,f2209,f314]) ).
fof(f2213,definition,
( sQ90_spl
<=> subset_collections(f23(cx,ct,f24(cx,ct)),f24(cx,ct)) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f2216,plain,
( ~ sQ7_spl
| sQ90_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f2206,f311,f2213,f314]) ).
fof(f2217,definition,
( sQ91_spl
<=> finite(f23(cx,ct,f24(cx,ct))) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f2220,plain,
( ~ sQ7_spl
| sQ91_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f2207,f311,f2217,f314]) ).
fof(f2221,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ7_spl
| open_covering(f24(cx,ct),X0,ct) ),
inference(resolution,[status(thm)],[f2208,f2149]) ).
fof(f2222,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ7_spl
| ~ topological_space(X0,f24(cx,ct))
| finer(ct,f24(cx,ct),X0) ),
inference(resolution,[status(thm)],[f2208,f1037]) ).
fof(f2223,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ7_spl
| finer(ct,f24(cx,ct),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2222,f504]) ).
fof(f2224,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ7_spl
| open_covering(f23(X0,ct,f24(cx,ct)),X0,ct)
| ~ compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f2221,f264]) ).
fof(f2225,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ7_spl
| subset_collections(f23(X0,ct,f24(cx,ct)),f24(cx,ct))
| ~ compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f2221,f263]) ).
fof(f2226,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ7_spl
| finite(f23(X0,ct,f24(cx,ct)))
| ~ compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f2221,f262]) ).
fof(model,axiom,
( ~ sQ0_spl
| sQ1_spl
| sQ2_spl
| sQ3_spl
| ~ sQ6_spl
| sQ7_spl
| sQ8_spl
| sQ11_spl
| sQ14_spl
| sQ17_spl
| sQ30_spl
| sQ32_spl
| sQ43_spl
| sQ44_spl
| sQ45_spl
| sQ49_spl
| sQ50_spl
| sQ55_spl
| sQ59_spl
| sQ69_spl
| sQ71_spl
| sQ76_spl
| sQ79_spl
| sQ83_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP017-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 12:41:33 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.72 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 0.10/0.72 % SZS output start Saturation for theBenchmark
% See solution above
% 0.36/0.78 % Elapsed time: 0.394153 seconds
% 0.36/0.78 % CPU time: 2.686310 seconds
% 0.36/0.78 % Total memory used: 55.642 MB
% 0.36/0.78 % Net memory used: 51.757 MB
%------------------------------------------------------------------------------