%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : TOP016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 2.67s 0.78s
% Output : Saturation 1.90s
% 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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Vt] :
( equal_sets(union_of_members(Vt),X)
| ~ topological_space(X,Vt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Vt] :
( element_of_collection(empty_set,Vt)
| ~ topological_space(X,Vt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Vt] :
( element_of_collection(X,Vt)
| ~ topological_space(X,Vt) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U,X,Vt] :
( topological_space(X,Vt)
| ~ open(U,X,Vt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [U,X,Vt] :
( element_of_collection(U,Vt)
| ~ open(U,X,Vt) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [U,X,Vt] :
( topological_space(X,Vt)
| ~ closed(U,X,Vt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [U,X,Vt] :
( open(relative_complement_sets(U,X),X,Vt)
| ~ closed(U,X,Vt) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Vt,Vs,X] :
( topological_space(X,Vt)
| ~ finer(Vt,Vs,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [Vt,Vs,X] :
( topological_space(X,Vs)
| ~ finer(Vt,Vs,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [Vt,Vs,X] :
( subset_collections(Vs,Vt)
| ~ finer(Vt,Vs,X) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X,Vf] :
( equal_sets(union_of_members(Vf),X)
| ~ basis(X,Vf) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [U,Y,X,Vt] :
( topological_space(X,Vt)
| ~ neighborhood(U,Y,X,Vt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [U,Y,X,Vt] :
( open(U,X,Vt)
| ~ neighborhood(U,Y,X,Vt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [U,Y,X,Vt] :
( element_of_set(Y,U)
| ~ neighborhood(U,Y,X,Vt) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f63,axiom,
! [Z,Y,X,Vt] :
( topological_space(X,Vt)
| ~ limit_point(Z,Y,X,Vt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,axiom,
! [Z,Y,X,Vt] :
( subset_sets(Y,X)
| ~ limit_point(Z,Y,X,Vt) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [X,Vt] :
( topological_space(X,Vt)
| ~ hausdorff(X,Vt) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [Va1,Va2,X,Vt] :
( topological_space(X,Vt)
| ~ separation(Va1,Va2,X,Vt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,axiom,
! [Va1,Va2,X,Vt] :
( ~ equal_sets(Va1,empty_set)
| ~ separation(Va1,Va2,X,Vt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [Va1,Va2,X,Vt] :
( ~ equal_sets(Va2,empty_set)
| ~ separation(Va1,Va2,X,Vt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [Va1,Va2,X,Vt] :
( element_of_collection(Va1,Vt)
| ~ separation(Va1,Va2,X,Vt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [Va1,Va2,X,Vt] :
( element_of_collection(Va2,Vt)
| ~ separation(Va1,Va2,X,Vt) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f87,axiom,
! [Va1,Va2,X,Vt] :
( disjoint_s(Va1,Va2)
| ~ separation(Va1,Va2,X,Vt) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f89,axiom,
! [X,Vt] :
( topological_space(X,Vt)
| ~ connected_space(X,Vt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f90,axiom,
! [X,Vt,Va1,Va2] :
( ~ separation(Va1,Va2,X,Vt)
| ~ connected_space(X,Vt) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f92,axiom,
! [Va,X,Vt] :
( topological_space(X,Vt)
| ~ connected_set(Va,X,Vt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,axiom,
! [Va,X,Vt] :
( subset_sets(Va,X)
| ~ connected_set(Va,X,Vt) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f96,axiom,
! [Vf,X,Vt] :
( topological_space(X,Vt)
| ~ open_covering(Vf,X,Vt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,axiom,
! [Vf,X,Vt] :
( subset_collections(Vf,Vt)
| ~ open_covering(Vf,X,Vt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f98,axiom,
! [Vf,X,Vt] :
( equal_sets(union_of_members(Vf),X)
| ~ open_covering(Vf,X,Vt) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [X,Vt] :
( topological_space(X,Vt)
| ~ compact_space(X,Vt) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f106,axiom,
! [Va,X,Vt] :
( topological_space(X,Vt)
| ~ compact_set(Va,X,Vt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f107,axiom,
! [Va,X,Vt] :
( subset_sets(Va,X)
| ~ compact_set(Va,X,Vt) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f110,negated_conjecture,
topological_space(cx,ct),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f111,negated_conjecture,
subset_sets(a,cx),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f112,negated_conjecture,
~ equal_sets(union_of_sets(interior(a,cx,ct),boundary(a,cx,ct)),closure(a,cx,ct)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f113,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(f114,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(f115,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(f116,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)],[f115]) ).
fof(f117,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(f118,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)],[f117]) ).
fof(f119,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(f120,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(f121,plain,
! [X0,X1] :
( equal_sets(union_of_members(X1),X0)
| ~ topological_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f122,plain,
! [Vt] :
( element_of_collection(empty_set,Vt)
| ! [X] : ~ topological_space(X,Vt) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f123,plain,
! [X0,X1] :
( element_of_collection(empty_set,X1)
| ~ topological_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f124,plain,
! [X0,X1] :
( element_of_collection(X0,X1)
| ~ topological_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f125,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(f126,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)],[f125]) ).
fof(f127,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(f128,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)],[f127]) ).
fof(f129,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(f130,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(f131,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(f132,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(f133,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(f134,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(f135,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [U] : ~ open(U,X,Vt) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f136,plain,
! [X0,X1,X2] :
( topological_space(X1,X2)
| ~ open(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
! [U,Vt] :
( element_of_collection(U,Vt)
| ! [X] : ~ open(U,X,Vt) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f138,plain,
! [X0,X1,X2] :
( element_of_collection(X0,X2)
| ~ open(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f139,plain,
! [U,Vt] :
( ~ element_of_collection(U,Vt)
| ! [X] :
( ~ topological_space(X,Vt)
| open(U,X,Vt) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f140,plain,
! [X0,X1,X2] :
( ~ element_of_collection(X0,X2)
| ~ topological_space(X1,X2)
| open(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f141,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [U] : ~ closed(U,X,Vt) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f142,plain,
! [X0,X1,X2] :
( topological_space(X1,X2)
| ~ closed(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f143,plain,
! [X0,X1,X2] :
( open(relative_complement_sets(X0,X1),X1,X2)
| ~ closed(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f144,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(f145,plain,
! [Vt,X] :
( topological_space(X,Vt)
| ! [Vs] : ~ finer(Vt,Vs,X) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f146,plain,
! [X0,X1,X2] :
( topological_space(X2,X0)
| ~ finer(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f147,plain,
! [Vs,X] :
( topological_space(X,Vs)
| ! [Vt] : ~ finer(Vt,Vs,X) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f148,plain,
! [X0,X1,X2] :
( topological_space(X2,X1)
| ~ finer(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f149,plain,
! [Vt,Vs] :
( subset_collections(Vs,Vt)
| ! [X] : ~ finer(Vt,Vs,X) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f150,plain,
! [X0,X1,X2] :
( subset_collections(X1,X0)
| ~ finer(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f151,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(f152,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)],[f151]) ).
fof(f153,plain,
! [X0,X1] :
( equal_sets(union_of_members(X1),X0)
| ~ basis(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f154,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(f155,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(f156,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(f157,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(f158,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(f159,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(f160,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(f161,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(f162,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(f163,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(f164,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(f165,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(f166,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(f167,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)],[f166]) ).
fof(f168,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [U,Y] : ~ element_of_collection(U,subspace_topology(X,Vt,Y)) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f169,plain,
! [X0,X1,X2,X3] :
( topological_space(X1,X2)
| ~ element_of_collection(X0,subspace_topology(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f170,plain,
! [X,Y] :
( subset_sets(Y,X)
| ! [U,Vt] : ~ element_of_collection(U,subspace_topology(X,Vt,Y)) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f171,plain,
! [X0,X1,X2,X3] :
( subset_sets(X3,X1)
| ~ element_of_collection(X0,subspace_topology(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f172,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(f173,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(f174,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(f175,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)],[f174]) ).
fof(f176,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [U,Y] : ~ element_of_set(U,interior(Y,X,Vt)) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f177,plain,
! [X0,X1,X2,X3] :
( topological_space(X2,X3)
| ~ element_of_set(X0,interior(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f178,plain,
! [Y,X] :
( subset_sets(Y,X)
| ! [U,Vt] : ~ element_of_set(U,interior(Y,X,Vt)) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f179,plain,
! [X0,X1,X2,X3] :
( subset_sets(X1,X2)
| ~ element_of_set(X0,interior(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f180,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(f181,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(f182,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(f183,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(f184,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)],[f183]) ).
fof(f185,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [U,Y] : ~ element_of_set(U,closure(Y,X,Vt)) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f186,plain,
! [X0,X1,X2,X3] :
( topological_space(X2,X3)
| ~ element_of_set(X0,closure(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f187,plain,
! [Y,X] :
( subset_sets(Y,X)
| ! [U,Vt] : ~ element_of_set(U,closure(Y,X,Vt)) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f188,plain,
! [X0,X1,X2,X3] :
( subset_sets(X1,X2)
| ~ element_of_set(X0,closure(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f189,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(f190,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)],[f189]) ).
fof(f191,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(f192,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(f193,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(f194,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [U,Y] : ~ neighborhood(U,Y,X,Vt) ),
inference(miniscoping,[status(thm)],[f59]) ).
fof(f195,plain,
! [X0,X1,X2,X3] :
( topological_space(X2,X3)
| ~ neighborhood(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f196,plain,
! [U,X,Vt] :
( open(U,X,Vt)
| ! [Y] : ~ neighborhood(U,Y,X,Vt) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f197,plain,
! [X0,X1,X2,X3] :
( open(X0,X2,X3)
| ~ neighborhood(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f198,plain,
! [U,Y] :
( element_of_set(Y,U)
| ! [X,Vt] : ~ neighborhood(U,Y,X,Vt) ),
inference(miniscoping,[status(thm)],[f61]) ).
fof(f199,plain,
! [X0,X1,X2,X3] :
( element_of_set(X1,X0)
| ~ neighborhood(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f200,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(f201,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)],[f200]) ).
fof(f202,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [Z,Y] : ~ limit_point(Z,Y,X,Vt) ),
inference(miniscoping,[status(thm)],[f63]) ).
fof(f203,plain,
! [X0,X1,X2,X3] :
( topological_space(X2,X3)
| ~ limit_point(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f204,plain,
! [Y,X] :
( subset_sets(Y,X)
| ! [Z,Vt] : ~ limit_point(Z,Y,X,Vt) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f205,plain,
! [X0,X1,X2,X3] :
( subset_sets(X1,X2)
| ~ limit_point(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f206,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(f207,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(f208,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(f209,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(f210,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)],[f209]) ).
fof(f211,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [U,Y] : ~ element_of_set(U,boundary(Y,X,Vt)) ),
inference(miniscoping,[status(thm)],[f69]) ).
fof(f212,plain,
! [X0,X1,X2,X3] :
( topological_space(X2,X3)
| ~ element_of_set(X0,boundary(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f213,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(f214,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(f215,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(f216,plain,
! [X0,X1] :
( topological_space(X0,X1)
| ~ hausdorff(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f217,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(f218,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(f219,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(f220,plain,
! [X0,X1] :
( element_of_set(f19(X0,X1),X0)
| ~ topological_space(X0,X1)
| hausdorff(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f221,plain,
! [X0,X1] :
( element_of_set(f20(X0,X1),X0)
| ~ topological_space(X0,X1)
| hausdorff(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f222,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(f223,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(f224,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)],[f223]) ).
fof(f225,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [Va1,Va2] : ~ separation(Va1,Va2,X,Vt) ),
inference(miniscoping,[status(thm)],[f81]) ).
fof(f226,plain,
! [X0,X1,X2,X3] :
( topological_space(X2,X3)
| ~ separation(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f225]) ).
fof(f227,plain,
! [Va1] :
( ~ equal_sets(Va1,empty_set)
| ! [Va2,X,Vt] : ~ separation(Va1,Va2,X,Vt) ),
inference(miniscoping,[status(thm)],[f82]) ).
fof(f228,plain,
! [X0,X1,X2,X3] :
( ~ equal_sets(X0,empty_set)
| ~ separation(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f227]) ).
fof(f229,plain,
! [Va2] :
( ~ equal_sets(Va2,empty_set)
| ! [Va1,X,Vt] : ~ separation(Va1,Va2,X,Vt) ),
inference(miniscoping,[status(thm)],[f83]) ).
fof(f230,plain,
! [X0,X1,X2,X3] :
( ~ equal_sets(X1,empty_set)
| ~ separation(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f231,plain,
! [Va1,Vt] :
( element_of_collection(Va1,Vt)
| ! [Va2,X] : ~ separation(Va1,Va2,X,Vt) ),
inference(miniscoping,[status(thm)],[f84]) ).
fof(f232,plain,
! [X0,X1,X2,X3] :
( element_of_collection(X0,X3)
| ~ separation(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f233,plain,
! [Va2,Vt] :
( element_of_collection(Va2,Vt)
| ! [Va1,X] : ~ separation(Va1,Va2,X,Vt) ),
inference(miniscoping,[status(thm)],[f85]) ).
fof(f234,plain,
! [X0,X1,X2,X3] :
( element_of_collection(X1,X3)
| ~ separation(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f233]) ).
fof(f235,plain,
! [Va1,Va2,X] :
( equal_sets(union_of_sets(Va1,Va2),X)
| ! [Vt] : ~ separation(Va1,Va2,X,Vt) ),
inference(miniscoping,[status(thm)],[f86]) ).
fof(f236,plain,
! [X0,X1,X2,X3] :
( equal_sets(union_of_sets(X0,X1),X2)
| ~ separation(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f235]) ).
fof(f237,plain,
! [Va1,Va2] :
( disjoint_s(Va1,Va2)
| ! [X,Vt] : ~ separation(Va1,Va2,X,Vt) ),
inference(miniscoping,[status(thm)],[f87]) ).
fof(f238,plain,
! [X0,X1,X2,X3] :
( disjoint_s(X0,X1)
| ~ separation(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f237]) ).
fof(f239,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(f240,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)],[f239]) ).
fof(f241,plain,
! [X0,X1] :
( topological_space(X0,X1)
| ~ connected_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f242,plain,
! [X,Vt] :
( ! [Va1,Va2] : ~ separation(Va1,Va2,X,Vt)
| ~ connected_space(X,Vt) ),
inference(miniscoping,[status(thm)],[f90]) ).
fof(f243,plain,
! [X0,X1,X2,X3] :
( ~ separation(X2,X3,X0,X1)
| ~ connected_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f242]) ).
fof(f244,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(f245,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [Va] : ~ connected_set(Va,X,Vt) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f246,plain,
! [X0,X1,X2] :
( topological_space(X1,X2)
| ~ connected_set(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f245]) ).
fof(f247,plain,
! [Va,X] :
( subset_sets(Va,X)
| ! [Vt] : ~ connected_set(Va,X,Vt) ),
inference(miniscoping,[status(thm)],[f93]) ).
fof(f248,plain,
! [X0,X1,X2] :
( subset_sets(X0,X1)
| ~ connected_set(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f247]) ).
fof(f249,plain,
! [X0,X1,X2] :
( connected_space(X0,subspace_topology(X1,X2,X0))
| ~ connected_set(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f250,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(f251,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [Vf] : ~ open_covering(Vf,X,Vt) ),
inference(miniscoping,[status(thm)],[f96]) ).
fof(f252,plain,
! [X0,X1,X2] :
( topological_space(X1,X2)
| ~ open_covering(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f251]) ).
fof(f253,plain,
! [Vf,Vt] :
( subset_collections(Vf,Vt)
| ! [X] : ~ open_covering(Vf,X,Vt) ),
inference(miniscoping,[status(thm)],[f97]) ).
fof(f254,plain,
! [X0,X1,X2] :
( subset_collections(X0,X2)
| ~ open_covering(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f255,plain,
! [Vf,X] :
( equal_sets(union_of_members(Vf),X)
| ! [Vt] : ~ open_covering(Vf,X,Vt) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f256,plain,
! [X0,X1,X2] :
( equal_sets(union_of_members(X0),X1)
| ~ open_covering(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f257,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(f258,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)],[f257]) ).
fof(f259,plain,
! [X0,X1] :
( topological_space(X0,X1)
| ~ compact_space(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f260,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(f261,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(f262,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(f263,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(f264,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(f265,plain,
! [X,Vt] :
( topological_space(X,Vt)
| ! [Va] : ~ compact_set(Va,X,Vt) ),
inference(miniscoping,[status(thm)],[f106]) ).
fof(f266,plain,
! [X0,X1,X2] :
( topological_space(X1,X2)
| ~ compact_set(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f265]) ).
fof(f267,plain,
! [Va,X] :
( subset_sets(Va,X)
| ! [Vt] : ~ compact_set(Va,X,Vt) ),
inference(miniscoping,[status(thm)],[f107]) ).
fof(f268,plain,
! [X0,X1,X2] :
( subset_sets(X0,X1)
| ~ compact_set(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f269,plain,
! [X0,X1,X2] :
( compact_space(X0,subspace_topology(X1,X2,X0))
| ~ compact_set(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f270,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(f271,plain,
topological_space(cx,ct),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f272,plain,
subset_sets(a,cx),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f273,plain,
~ equal_sets(union_of_sets(interior(a,cx,ct),boundary(a,cx,ct)),closure(a,cx,ct)),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f274,plain,
element_of_collection(cx,ct),
inference(resolution,[status(thm)],[f124,f271]) ).
fof(f275,plain,
element_of_collection(empty_set,ct),
inference(resolution,[status(thm)],[f123,f271]) ).
fof(f276,plain,
equal_sets(union_of_members(ct),cx),
inference(resolution,[status(thm)],[f121,f271]) ).
fof(f277,plain,
! [X0] :
( ~ element_of_collection(X0,ct)
| open(X0,cx,ct) ),
inference(resolution,[status(thm)],[f140,f271]) ).
fof(f278,plain,
open(empty_set,cx,ct),
inference(resolution,[status(thm)],[f277,f275]) ).
fof(f279,plain,
open(cx,cx,ct),
inference(resolution,[status(thm)],[f277,f274]) ).
fof(f281,plain,
! [X0,X1] :
( ~ subset_sets(empty_set,X1)
| ~ element_of_set(X0,empty_set)
| ~ subset_sets(X1,cx)
| ~ topological_space(cx,ct)
| element_of_set(X0,interior(X1,cx,ct)) ),
inference(resolution,[status(thm)],[f278,f184]) ).
fof(f282,definition,
! [X0,X1] :
( sQ0_spl
<=> ( ~ subset_sets(empty_set,X1)
| ~ element_of_set(X0,empty_set)
| ~ subset_sets(X1,cx)
| element_of_set(X0,interior(X1,cx,ct)) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f283,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ subset_sets(empty_set,X1)
| ~ element_of_set(X0,empty_set)
| ~ subset_sets(X1,cx)
| element_of_set(X0,interior(X1,cx,ct)) ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f285,definition,
( sQ1_spl
<=> topological_space(cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( sQ1_spl
| ~ topological_space(cx,ct) ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f288,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f281,f282,f285]) ).
fof(f290,plain,
! [X0,X1] :
( ~ subset_sets(cx,X1)
| ~ element_of_set(X0,cx)
| ~ subset_sets(X1,cx)
| ~ topological_space(cx,ct)
| element_of_set(X0,interior(X1,cx,ct)) ),
inference(resolution,[status(thm)],[f279,f184]) ).
fof(f291,definition,
! [X0,X1] :
( sQ2_spl
<=> ( ~ subset_sets(cx,X1)
| ~ element_of_set(X0,cx)
| ~ subset_sets(X1,cx)
| element_of_set(X0,interior(X1,cx,ct)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f292,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ subset_sets(cx,X1)
| ~ element_of_set(X0,cx)
| ~ subset_sets(X1,cx)
| element_of_set(X0,interior(X1,cx,ct)) ),
inference(component_clause,[status(thm)],[f291]) ).
fof(f294,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f290,f291,f285]) ).
fof(f295,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f287,f271]) ).
fof(f296,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f295]) ).
fof(f297,plain,
! [X0] :
( ~ element_of_set(X0,empty_set)
| element_of_set(X0,union_of_members(ct)) ),
inference(resolution,[status(thm)],[f116,f275]) ).
fof(f298,plain,
! [X0] :
( ~ element_of_set(X0,cx)
| element_of_set(X0,union_of_members(ct)) ),
inference(resolution,[status(thm)],[f116,f274]) ).
fof(f299,plain,
! [X0,X1] :
( element_of_collection(intersection_of_sets(X0,X1),ct)
| ~ element_of_collection(X1,ct)
| ~ element_of_collection(X0,ct) ),
inference(resolution,[status(thm)],[f126,f271]) ).
fof(f300,plain,
! [X0] :
( open(f2(ct,X0),cx,ct)
| element_of_set(X0,intersection_of_members(ct)) ),
inference(resolution,[status(thm)],[f119,f277]) ).
fof(f301,plain,
! [X0,X1,X2,X3] :
( subset_sets(X3,X1)
| element_of_set(X0,intersection_of_members(subspace_topology(X1,X2,X3))) ),
inference(resolution,[status(thm)],[f119,f171]) ).
fof(f302,plain,
! [X0,X1,X2,X3] :
( topological_space(X1,X2)
| element_of_set(X0,intersection_of_members(subspace_topology(X1,X2,X3))) ),
inference(resolution,[status(thm)],[f119,f169]) ).
fof(f303,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)],[f119,f116]) ).
fof(f305,plain,
! [X0,X1,X2] :
( ~ subset_sets(f2(ct,X0),X2)
| ~ element_of_set(X1,f2(ct,X0))
| ~ subset_sets(X2,cx)
| ~ topological_space(cx,ct)
| element_of_set(X1,interior(X2,cx,ct))
| element_of_set(X0,intersection_of_members(ct)) ),
inference(resolution,[status(thm)],[f300,f184]) ).
fof(f306,definition,
! [X0,X1,X2] :
( sQ3_spl
<=> ( ~ subset_sets(f2(ct,X0),X2)
| ~ element_of_set(X1,f2(ct,X0))
| ~ subset_sets(X2,cx)
| element_of_set(X1,interior(X2,cx,ct))
| element_of_set(X0,intersection_of_members(ct)) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f307,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ subset_sets(f2(ct,X0),X2)
| ~ element_of_set(X1,f2(ct,X0))
| ~ subset_sets(X2,cx)
| element_of_set(X1,interior(X2,cx,ct))
| element_of_set(X0,intersection_of_members(ct)) ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f309,plain,
( ~ sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f305,f306,f285]) ).
fof(f310,plain,
! [X0,X1,X2] :
( element_of_set(f11(X1,intersection_of_members(X0)),X2)
| ~ element_of_collection(X2,X0)
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f165,f118]) ).
fof(f311,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)],[f165,f114]) ).
fof(f312,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)],[f165,f113]) ).
fof(f313,plain,
! [X0,X1,X2,X3] :
( element_of_set(f11(X3,boundary(X0,X1,X2)),closure(X0,X1,X2))
| element_of_collection(boundary(X0,X1,X2),top_of_basis(X3)) ),
inference(resolution,[status(thm)],[f165,f213]) ).
fof(f314,plain,
! [X0,X1,X2,X3] :
( topological_space(X1,X2)
| element_of_collection(boundary(X0,X1,X2),top_of_basis(X3)) ),
inference(resolution,[status(thm)],[f165,f212]) ).
fof(f315,plain,
! [X0,X1,X2,X3] :
( subset_sets(X0,X1)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X3)) ),
inference(resolution,[status(thm)],[f165,f188]) ).
fof(f316,plain,
! [X0,X1,X2,X3] :
( topological_space(X1,X2)
| element_of_collection(closure(X0,X1,X2),top_of_basis(X3)) ),
inference(resolution,[status(thm)],[f165,f186]) ).
fof(f317,plain,
! [X0,X1,X2,X3] :
( subset_sets(X0,X1)
| element_of_collection(interior(X0,X1,X2),top_of_basis(X3)) ),
inference(resolution,[status(thm)],[f165,f179]) ).
fof(f318,plain,
! [X0,X1,X2,X3] :
( topological_space(X1,X2)
| element_of_collection(interior(X0,X1,X2),top_of_basis(X3)) ),
inference(resolution,[status(thm)],[f165,f177]) ).
fof(f324,plain,
! [X0,X1,X2,X3] :
( subset_sets(X0,X1)
| element_of_collection(boundary(X0,X1,X2),top_of_basis(X3)) ),
inference(resolution,[status(thm)],[f313,f188]) ).
fof(f326,plain,
! [X0,X1,X2,X3,X4] :
( ~ element_of_set(X2,boundary(X0,X1,X4))
| element_of_set(X2,union_of_members(top_of_basis(X3)))
| subset_sets(X0,X1) ),
inference(resolution,[status(thm)],[f324,f116]) ).
fof(f330,plain,
( element_of_set(f19(cx,ct),cx)
| hausdorff(cx,ct) ),
inference(resolution,[status(thm)],[f220,f271]) ).
fof(f331,definition,
( sQ4_spl
<=> hausdorff(cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( ~ sQ4_spl
| hausdorff(cx,ct) ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f334,definition,
( sQ5_spl
<=> element_of_set(f19(cx,ct),cx) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f337,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f330,f331,f334]) ).
fof(f338,plain,
( element_of_set(f20(cx,ct),cx)
| hausdorff(cx,ct) ),
inference(resolution,[status(thm)],[f221,f271]) ).
fof(f339,definition,
( sQ6_spl
<=> element_of_set(f20(cx,ct),cx) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f342,plain,
( sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f338,f331,f339]) ).
fof(f343,plain,
( open_covering(f24(cx,ct),cx,ct)
| compact_space(cx,ct) ),
inference(resolution,[status(thm)],[f263,f271]) ).
fof(f344,definition,
( sQ7_spl
<=> compact_space(cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f345,plain,
( ~ sQ7_spl
| compact_space(cx,ct) ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f346,plain,
( sQ7_spl
| ~ compact_space(cx,ct) ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f347,definition,
( sQ8_spl
<=> open_covering(f24(cx,ct),cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f348,plain,
( ~ sQ8_spl
| open_covering(f24(cx,ct),cx,ct) ),
inference(component_clause,[status(thm)],[f347]) ).
fof(f350,plain,
( sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f343,f344,f347]) ).
fof(f351,plain,
( element_of_set(f7(cx,ct),cx)
| basis(cx,ct) ),
inference(resolution,[status(thm)],[f157,f276]) ).
fof(f352,definition,
( sQ9_spl
<=> basis(cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( ~ sQ9_spl
| basis(cx,ct) ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f355,definition,
( sQ10_spl
<=> element_of_set(f7(cx,ct),cx) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f358,plain,
( sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f351,f352,f355]) ).
fof(f359,plain,
( element_of_collection(f8(cx,ct),ct)
| basis(cx,ct) ),
inference(resolution,[status(thm)],[f158,f276]) ).
fof(f360,definition,
( sQ11_spl
<=> element_of_collection(f8(cx,ct),ct) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( sQ11_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f359,f352,f360]) ).
fof(f364,plain,
( element_of_collection(f9(cx,ct),ct)
| basis(cx,ct) ),
inference(resolution,[status(thm)],[f159,f276]) ).
fof(f365,definition,
( sQ12_spl
<=> element_of_collection(f9(cx,ct),ct) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f368,plain,
( sQ12_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f364,f352,f365]) ).
fof(f369,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)],[f303,f165]) ).
fof(f370,plain,
( separation(f21(cx,ct),f22(cx,ct),cx,ct)
| connected_space(cx,ct) ),
inference(resolution,[status(thm)],[f244,f271]) ).
fof(f371,definition,
( sQ13_spl
<=> connected_space(cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f372,plain,
( ~ sQ13_spl
| connected_space(cx,ct) ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f374,definition,
( sQ14_spl
<=> separation(f21(cx,ct),f22(cx,ct),cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f377,plain,
( sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f370,f371,f374]) ).
fof(f378,plain,
! [X0] :
( open(f1(ct,f11(X0,union_of_members(ct))),cx,ct)
| element_of_collection(union_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f311,f277]) ).
fof(f379,plain,
! [X0,X1,X2,X3] :
( subset_sets(X2,X0)
| element_of_collection(union_of_members(subspace_topology(X0,X1,X2)),top_of_basis(X3)) ),
inference(resolution,[status(thm)],[f311,f171]) ).
fof(f380,plain,
! [X0,X1,X2,X3] :
( topological_space(X0,X1)
| element_of_collection(union_of_members(subspace_topology(X0,X1,X2)),top_of_basis(X3)) ),
inference(resolution,[status(thm)],[f311,f169]) ).
fof(f381,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)],[f311,f116]) ).
fof(f383,plain,
! [X0,X1,X2] :
( ~ subset_sets(f1(ct,f11(X0,union_of_members(ct))),X2)
| ~ element_of_set(X1,f1(ct,f11(X0,union_of_members(ct))))
| ~ subset_sets(X2,cx)
| ~ topological_space(cx,ct)
| element_of_set(X1,interior(X2,cx,ct))
| element_of_collection(union_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f378,f184]) ).
fof(f384,definition,
! [X0,X1,X2] :
( sQ15_spl
<=> ( ~ subset_sets(f1(ct,f11(X0,union_of_members(ct))),X2)
| ~ element_of_set(X1,f1(ct,f11(X0,union_of_members(ct))))
| ~ subset_sets(X2,cx)
| element_of_set(X1,interior(X2,cx,ct))
| element_of_collection(union_of_members(ct),top_of_basis(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f385,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ subset_sets(f1(ct,f11(X0,union_of_members(ct))),X2)
| ~ element_of_set(X1,f1(ct,f11(X0,union_of_members(ct))))
| ~ subset_sets(X2,cx)
| element_of_set(X1,interior(X2,cx,ct))
| element_of_collection(union_of_members(ct),top_of_basis(X0)) ),
inference(component_clause,[status(thm)],[f384]) ).
fof(f387,plain,
( ~ sQ1_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f383,f384,f285]) ).
fof(f402,plain,
! [X0,X1,X2,X3,X4] :
( ~ element_of_set(X2,union_of_members(subspace_topology(X1,X4,X0)))
| element_of_set(X2,union_of_members(top_of_basis(X3)))
| subset_sets(X0,X1) ),
inference(resolution,[status(thm)],[f379,f116]) ).
fof(f403,plain,
! [X0,X1,X2,X3,X4] :
( ~ element_of_set(X2,union_of_members(subspace_topology(X0,X1,X4)))
| element_of_set(X2,union_of_members(top_of_basis(X3)))
| topological_space(X0,X1) ),
inference(resolution,[status(thm)],[f380,f116]) ).
fof(f406,plain,
! [X0,X1,X2] :
( element_of_collection(union_of_members(X0),top_of_basis(X2))
| element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X2,union_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f310,f311]) ).
fof(f407,plain,
! [X0,X1,X2,X3,X4] :
( topological_space(X3,X4)
| element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),interior(X2,X3,X4))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f310,f318]) ).
fof(f408,plain,
! [X0,X1,X2,X3,X4] :
( subset_sets(X2,X3)
| element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),interior(X2,X3,X4))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f310,f317]) ).
fof(f413,plain,
! [X0,X1,X2] :
( element_of_set(X2,intersection_of_members(X0))
| element_of_set(f11(X1,intersection_of_members(X0)),f2(X0,X2))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f310,f119]) ).
fof(f414,plain,
! [X0] :
( element_of_set(f11(X0,intersection_of_members(ct)),empty_set)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f310,f275]) ).
fof(f415,plain,
! [X0] :
( element_of_set(f11(X0,intersection_of_members(ct)),cx)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f310,f274]) ).
fof(f416,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)],[f407,f177]) ).
fof(f417,plain,
! [X0,X1,X2,X3] :
( subset_sets(X2,X3)
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f408,f179]) ).
fof(f421,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(f11(X3,intersection_of_members(top_of_basis(X2))),intersection_of_members(top_of_basis(X4)))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| topological_space(X0,X1) ),
inference(resolution,[status(thm)],[f416,f310]) ).
fof(f422,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)],[f416,f116]) ).
fof(f423,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)],[f416,f244]) ).
fof(f424,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)],[f416,f263]) ).
fof(f425,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)],[f416,f221]) ).
fof(f426,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)],[f416,f220]) ).
fof(f427,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(intersection_of_sets(X2,X4),X3)
| ~ element_of_collection(X4,X3)
| ~ element_of_collection(X2,X3)
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f416,f126]) ).
fof(f428,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)],[f416,f140]) ).
fof(f429,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)],[f416,f121]) ).
fof(f430,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)],[f416,f123]) ).
fof(f431,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)],[f416,f124]) ).
fof(f432,definition,
! [X0,X1] :
( sQ20_spl
<=> topological_space(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f433,plain,
! [X0,X1] :
( ~ sQ20_spl
| topological_space(X0,X1) ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f435,definition,
! [X2,X3,X4] :
( sQ21_spl
<=> ( element_of_set(f11(X3,intersection_of_members(top_of_basis(X2))),intersection_of_members(top_of_basis(X4)))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f436,plain,
! [X0,X1,X2] :
( ~ sQ21_spl
| element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),intersection_of_members(top_of_basis(X2)))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,plain,
( sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f421,f432,f435]) ).
fof(f439,definition,
! [X2,X3,X4] :
( sQ22_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,[sQ22_spl])],[split_symbol_definition]) ).
fof(f440,plain,
! [X0,X1,X2] :
( ~ sQ22_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)],[f439]) ).
fof(f442,plain,
( sQ22_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f422,f432,f439]) ).
fof(f443,definition,
! [X0,X1] :
( sQ23_spl
<=> element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f444,plain,
! [X0,X1] :
( ~ sQ23_spl
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,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(f449,plain,
( sQ24_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f423,f443,f446]) ).
fof(f450,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(f453,plain,
( sQ25_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f424,f443,f450]) ).
fof(f454,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(f457,plain,
( sQ26_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f425,f443,f454]) ).
fof(f458,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(f461,plain,
( sQ27_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f426,f443,f458]) ).
fof(f462,definition,
! [X2,X3,X4] :
( sQ28_spl
<=> ( element_of_collection(intersection_of_sets(X2,X4),X3)
| ~ element_of_collection(X4,X3)
| ~ element_of_collection(X2,X3) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( sQ28_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f427,f443,f462]) ).
fof(f466,definition,
! [X2,X3,X4] :
( sQ29_spl
<=> ( ~ element_of_collection(X2,X4)
| open(X2,X3,X4) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f469,plain,
( sQ29_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f428,f443,f466]) ).
fof(f470,definition,
! [X2,X3] :
( sQ30_spl
<=> equal_sets(union_of_members(X2),X3) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f473,plain,
( sQ30_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f429,f443,f470]) ).
fof(f474,definition,
! [X2] :
( sQ31_spl
<=> element_of_collection(empty_set,X2) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( sQ31_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f430,f443,f474]) ).
fof(f478,definition,
! [X2,X3] :
( sQ32_spl
<=> element_of_collection(X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f481,plain,
( sQ32_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f431,f443,f478]) ).
fof(f482,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(f11(X3,intersection_of_members(top_of_basis(X2))),intersection_of_members(top_of_basis(X4)))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| subset_sets(X0,X1) ),
inference(resolution,[status(thm)],[f417,f310]) ).
fof(f483,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)))
| subset_sets(X0,X1) ),
inference(resolution,[status(thm)],[f417,f116]) ).
fof(f484,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ15_spl
| ~ element_of_set(X3,f1(ct,f11(X2,union_of_members(ct))))
| ~ subset_sets(X4,cx)
| element_of_set(X3,interior(X4,cx,ct))
| element_of_collection(union_of_members(ct),top_of_basis(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f417,f385]) ).
fof(f485,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ3_spl
| ~ element_of_set(X3,f2(ct,X2))
| ~ subset_sets(X4,cx)
| element_of_set(X3,interior(X4,cx,ct))
| element_of_set(X2,intersection_of_members(ct))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f417,f307]) ).
fof(f486,definition,
! [X0,X1] :
( sQ33_spl
<=> subset_sets(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f487,plain,
! [X0,X1] :
( ~ sQ33_spl
| subset_sets(X0,X1) ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f489,plain,
( sQ21_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f482,f486,f435]) ).
fof(f490,plain,
( sQ22_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f483,f486,f439]) ).
fof(f491,definition,
! [X2,X3,X4] :
( sQ34_spl
<=> ( ~ element_of_set(X3,f1(ct,f11(X2,union_of_members(ct))))
| ~ subset_sets(X4,cx)
| element_of_set(X3,interior(X4,cx,ct))
| element_of_collection(union_of_members(ct),top_of_basis(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f494,plain,
( ~ sQ15_spl
| sQ34_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f484,f443,f491,f384]) ).
fof(f495,definition,
! [X2,X3,X4] :
( sQ35_spl
<=> ( ~ element_of_set(X3,f2(ct,X2))
| ~ subset_sets(X4,cx)
| element_of_set(X3,interior(X4,cx,ct))
| element_of_set(X2,intersection_of_members(ct)) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( ~ sQ3_spl
| sQ35_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f485,f443,f495,f306]) ).
fof(f501,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)],[f191,f271]) ).
fof(f502,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_collection(intersection_of_members(top_of_basis(X4)),top_of_basis(X5))
| subset_sets(X1,f14(X1,X2,X3,X0))
| ~ subset_sets(X1,X2)
| element_of_set(X0,closure(X1,X2,X3)) ),
inference(resolution,[status(thm)],[f191,f416]) ).
fof(f503,definition,
! [X0,X1,X2,X3] :
( sQ36_spl
<=> ( subset_sets(X1,f14(X1,X2,X3,X0))
| ~ subset_sets(X1,X2)
| element_of_set(X0,closure(X1,X2,X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f506,plain,
( sQ23_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f502,f503,f443]) ).
fof(f507,plain,
! [X0] :
( subset_sets(a,f14(a,cx,ct,X0))
| element_of_set(X0,closure(a,cx,ct)) ),
inference(resolution,[status(thm)],[f501,f272]) ).
fof(f508,plain,
! [X0,X1,X2,X3] :
( element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| subset_sets(X1,f14(X1,cx,ct,X0))
| element_of_set(X0,closure(X1,cx,ct)) ),
inference(resolution,[status(thm)],[f501,f417]) ).
fof(f509,definition,
! [X0,X1] :
( sQ37_spl
<=> ( subset_sets(X1,f14(X1,cx,ct,X0))
| element_of_set(X0,closure(X1,cx,ct)) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f512,plain,
( sQ23_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f508,f509,f443]) ).
fof(f513,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)],[f208,f271]) ).
fof(f514,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_collection(intersection_of_members(top_of_basis(X4)),top_of_basis(X5))
| neighborhood(f16(X0,X1,X2,X3),X0,X2,X3)
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f208,f416]) ).
fof(f515,definition,
! [X0,X1,X2,X3] :
( sQ38_spl
<=> ( neighborhood(f16(X0,X1,X2,X3),X0,X2,X3)
| ~ subset_sets(X1,X2)
| limit_point(X0,X1,X2,X3) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f518,plain,
( sQ23_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f514,f515,f443]) ).
fof(f519,plain,
! [X0] :
( neighborhood(f16(X0,a,cx,ct),X0,cx,ct)
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f513,f272]) ).
fof(f520,plain,
! [X0,X1,X2,X3] :
( element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| neighborhood(f16(X0,X1,cx,ct),X0,cx,ct)
| limit_point(X0,X1,cx,ct) ),
inference(resolution,[status(thm)],[f513,f417]) ).
fof(f521,definition,
! [X0,X1] :
( sQ39_spl
<=> ( neighborhood(f16(X0,X1,cx,ct),X0,cx,ct)
| limit_point(X0,X1,cx,ct) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( sQ23_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f520,f521,f443]) ).
fof(f525,plain,
! [X0] :
( open(f16(X0,a,cx,ct),cx,ct)
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f519,f197]) ).
fof(f526,plain,
! [X0] :
( element_of_set(X0,f16(X0,a,cx,ct))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f519,f199]) ).
fof(f527,plain,
! [X0] :
( topological_space(cx,ct)
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f519,f195]) ).
fof(f528,definition,
! [X0] :
( sQ40_spl
<=> limit_point(X0,a,cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f529,plain,
! [X0] :
( ~ sQ40_spl
| limit_point(X0,a,cx,ct) ),
inference(component_clause,[status(thm)],[f528]) ).
fof(f531,plain,
( sQ1_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f527,f528,f285]) ).
fof(f532,plain,
! [X0] :
( element_of_collection(f16(X0,a,cx,ct),ct)
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f525,f138]) ).
fof(f533,plain,
! [X0,X1,X2] :
( ~ subset_sets(f16(X0,a,cx,ct),X2)
| ~ element_of_set(X1,f16(X0,a,cx,ct))
| ~ subset_sets(X2,cx)
| ~ topological_space(cx,ct)
| element_of_set(X1,interior(X2,cx,ct))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f525,f184]) ).
fof(f534,definition,
! [X0,X1,X2] :
( sQ41_spl
<=> ( ~ subset_sets(f16(X0,a,cx,ct),X2)
| ~ element_of_set(X1,f16(X0,a,cx,ct))
| ~ subset_sets(X2,cx)
| element_of_set(X1,interior(X2,cx,ct))
| limit_point(X0,a,cx,ct) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f535,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| ~ subset_sets(f16(X0,a,cx,ct),X2)
| ~ element_of_set(X1,f16(X0,a,cx,ct))
| ~ subset_sets(X2,cx)
| element_of_set(X1,interior(X2,cx,ct))
| limit_point(X0,a,cx,ct) ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f537,plain,
( ~ sQ1_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f533,f534,f285]) ).
fof(f539,plain,
! [X0,X1] :
( element_of_set(f11(X1,intersection_of_members(ct)),f16(X0,a,cx,ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f532,f310]) ).
fof(f540,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)],[f532,f116]) ).
fof(f541,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)],[f540,f165]) ).
fof(f542,plain,
! [X0] :
( limit_point(X0,a,cx,ct)
| element_of_set(X0,union_of_members(ct))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f540,f526]) ).
fof(f543,plain,
! [X0] :
( element_of_set(X0,union_of_members(ct))
| limit_point(X0,a,cx,ct) ),
inference(duplicate_literals_removal,[status(thm)],[f542]) ).
fof(f544,plain,
! [X0] :
( subset_sets(a,cx)
| element_of_set(X0,union_of_members(ct)) ),
inference(resolution,[status(thm)],[f543,f205]) ).
fof(f545,plain,
! [X0] :
( topological_space(cx,ct)
| element_of_set(X0,union_of_members(ct)) ),
inference(resolution,[status(thm)],[f543,f203]) ).
fof(f546,definition,
! [X0] :
( sQ42_spl
<=> element_of_set(X0,union_of_members(ct)) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f547,plain,
! [X0] :
( ~ sQ42_spl
| element_of_set(X0,union_of_members(ct)) ),
inference(component_clause,[status(thm)],[f546]) ).
fof(f549,definition,
( sQ43_spl
<=> subset_sets(a,cx) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f552,plain,
( sQ43_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f544,f546,f549]) ).
fof(f553,plain,
( sQ1_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f545,f546,f285]) ).
fof(f554,plain,
! [X0,X1] :
( element_of_set(f11(X1,intersection_of_members(ct)),union_of_members(ct))
| limit_point(X0,a,cx,ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f539,f540]) ).
fof(f555,definition,
! [X0] :
( sQ44_spl
<=> ( limit_point(X0,a,cx,ct)
| limit_point(X0,a,cx,ct) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f556,plain,
! [X0] :
( ~ sQ44_spl
| limit_point(X0,a,cx,ct)
| limit_point(X0,a,cx,ct) ),
inference(component_clause,[status(thm)],[f555]) ).
fof(f558,definition,
! [X1] :
( sQ45_spl
<=> ( element_of_set(f11(X1,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f559,plain,
! [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)) ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f561,plain,
( sQ45_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f554,f555,f558]) ).
fof(f562,plain,
! [X0] :
( ~ sQ44_spl
| limit_point(X0,a,cx,ct) ),
inference(duplicate_literals_removal,[status(thm)],[f556]) ).
fof(f563,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)],[f541,f114]) ).
fof(f564,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)],[f541,f113]) ).
fof(f565,plain,
! [X0,X1] :
( open(f1(ct,f11(X1,f16(X0,a,cx,ct))),cx,ct)
| element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f563,f277]) ).
fof(f566,plain,
! [X0,X1,X2] :
( element_of_set(f11(X2,intersection_of_members(ct)),f1(ct,f11(X1,f16(X0,a,cx,ct))))
| element_of_collection(intersection_of_members(ct),top_of_basis(X2))
| element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f563,f310]) ).
fof(f567,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)],[f563,f116]) ).
fof(f569,plain,
! [X0,X1,X2,X3] :
( ~ subset_sets(f1(ct,f11(X1,f16(X0,a,cx,ct))),X3)
| ~ element_of_set(X2,f1(ct,f11(X1,f16(X0,a,cx,ct))))
| ~ subset_sets(X3,cx)
| ~ topological_space(cx,ct)
| element_of_set(X2,interior(X3,cx,ct))
| element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f565,f184]) ).
fof(f570,definition,
! [X0,X1,X2,X3] :
( sQ46_spl
<=> ( ~ subset_sets(f1(ct,f11(X1,f16(X0,a,cx,ct))),X3)
| ~ element_of_set(X2,f1(ct,f11(X1,f16(X0,a,cx,ct))))
| ~ subset_sets(X3,cx)
| element_of_set(X2,interior(X3,cx,ct))
| element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f571,plain,
! [X0,X1,X2,X3] :
( ~ sQ46_spl
| ~ subset_sets(f1(ct,f11(X1,f16(X0,a,cx,ct))),X3)
| ~ element_of_set(X2,f1(ct,f11(X1,f16(X0,a,cx,ct))))
| ~ subset_sets(X3,cx)
| element_of_set(X2,interior(X3,cx,ct))
| element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ),
inference(component_clause,[status(thm)],[f570]) ).
fof(f573,plain,
( ~ sQ1_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f569,f570,f285]) ).
fof(f574,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ41_spl
| element_of_collection(intersection_of_members(top_of_basis(X3)),top_of_basis(X4))
| ~ element_of_set(X1,f16(X0,a,cx,ct))
| ~ subset_sets(X2,cx)
| element_of_set(X1,interior(X2,cx,ct))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f535,f417]) ).
fof(f575,definition,
! [X0,X1,X2] :
( sQ47_spl
<=> ( ~ element_of_set(X1,f16(X0,a,cx,ct))
| ~ subset_sets(X2,cx)
| element_of_set(X1,interior(X2,cx,ct))
| limit_point(X0,a,cx,ct) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f578,plain,
( ~ sQ41_spl
| sQ23_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f574,f575,f443,f534]) ).
fof(f580,plain,
! [X0,X1,X2] :
( element_of_collection(intersection_of_members(ct),top_of_basis(X2))
| element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct)
| element_of_set(f11(X2,intersection_of_members(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)],[f567,f566]) ).
fof(f581,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)],[f567,f165]) ).
fof(f583,definition,
! [X0,X1] :
( sQ48_spl
<=> ( element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct)
| element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f584,plain,
! [X0,X1] :
( ~ sQ48_spl
| element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct)
| element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ),
inference(component_clause,[status(thm)],[f583]) ).
fof(f586,plain,
( sQ45_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f580,f583,f558]) ).
fof(f587,plain,
! [X0] :
( ~ sQ45_spl
| 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)],[f559,f114]) ).
fof(f588,plain,
! [X0] :
( ~ sQ45_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)) ),
inference(resolution,[status(thm)],[f559,f113]) ).
fof(f589,plain,
! [X0] :
( ~ sQ45_spl
| open(f1(ct,f11(X0,intersection_of_members(ct))),cx,ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f587,f277]) ).
fof(f590,plain,
! [X0,X1] :
( ~ sQ45_spl
| 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(X1))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f587,f310]) ).
fof(f591,plain,
! [X0,X1] :
( ~ sQ45_spl
| ~ 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)],[f587,f116]) ).
fof(f593,plain,
! [X0,X1,X2] :
( ~ sQ45_spl
| ~ subset_sets(f1(ct,f11(X0,intersection_of_members(ct))),X2)
| ~ element_of_set(X1,f1(ct,f11(X0,intersection_of_members(ct))))
| ~ subset_sets(X2,cx)
| ~ topological_space(cx,ct)
| element_of_set(X1,interior(X2,cx,ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f589,f184]) ).
fof(f594,definition,
! [X0,X1,X2] :
( sQ49_spl
<=> ( ~ subset_sets(f1(ct,f11(X0,intersection_of_members(ct))),X2)
| ~ element_of_set(X1,f1(ct,f11(X0,intersection_of_members(ct))))
| ~ subset_sets(X2,cx)
| element_of_set(X1,interior(X2,cx,ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f595,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| ~ subset_sets(f1(ct,f11(X0,intersection_of_members(ct))),X2)
| ~ element_of_set(X1,f1(ct,f11(X0,intersection_of_members(ct))))
| ~ subset_sets(X2,cx)
| element_of_set(X1,interior(X2,cx,ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(component_clause,[status(thm)],[f594]) ).
fof(f597,plain,
( ~ sQ45_spl
| ~ sQ1_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f593,f594,f285,f558]) ).
fof(f598,plain,
! [X0,X1] :
( ~ sQ48_spl
| element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ),
inference(duplicate_literals_removal,[status(thm)],[f584]) ).
fof(f599,plain,
! [X0,X1,X2] :
( ~ sQ48_spl
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X1))),f16(X0,a,cx,ct))
| element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X2))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f598,f310]) ).
fof(f600,plain,
! [X0,X1,X2] :
( ~ sQ48_spl
| ~ element_of_set(X1,f16(X0,a,cx,ct))
| element_of_set(X1,union_of_members(top_of_basis(X2)))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f598,f116]) ).
fof(f601,plain,
! [X0,X1,X2] :
( ~ sQ48_spl
| element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct)
| element_of_set(f11(X1,intersection_of_members(ct)),union_of_members(top_of_basis(X2)))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f600,f539]) ).
fof(f603,plain,
! [X0,X1] :
( ~ sQ48_spl
| limit_point(X0,a,cx,ct)
| element_of_set(X0,union_of_members(top_of_basis(X1)))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f600,f526]) ).
fof(f604,definition,
! [X1,X2] :
( sQ50_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,[sQ50_spl])],[split_symbol_definition]) ).
fof(f607,plain,
( ~ sQ48_spl
| sQ50_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f601,f555,f604,f583]) ).
fof(f608,plain,
! [X0,X1] :
( ~ sQ48_spl
| element_of_set(X0,union_of_members(top_of_basis(X1)))
| limit_point(X0,a,cx,ct) ),
inference(duplicate_literals_removal,[status(thm)],[f603]) ).
fof(f619,plain,
! [X0,X1] :
( open(f1(ct,f11(X1,f16(X0,a,cx,ct))),cx,ct)
| element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f563,f277]) ).
fof(f620,plain,
! [X0,X1,X2] :
( element_of_set(f11(X2,intersection_of_members(ct)),f1(ct,f11(X1,f16(X0,a,cx,ct))))
| element_of_collection(intersection_of_members(ct),top_of_basis(X2))
| element_of_collection(f16(X0,a,cx,ct),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f563,f310]) ).
fof(f621,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)],[f563,f116]) ).
fof(f624,plain,
! [X0,X1] :
( ~ sQ45_spl
| 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)],[f591,f165]) ).
fof(f631,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)],[f567,f165]) ).
fof(f638,plain,
( element_of_set(f7(cx,ct),intersection_of_sets(f8(cx,ct),f9(cx,ct)))
| basis(cx,ct) ),
inference(resolution,[status(thm)],[f160,f276]) ).
fof(f639,definition,
( sQ52_spl
<=> element_of_set(f7(cx,ct),intersection_of_sets(f8(cx,ct),f9(cx,ct))) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f642,plain,
( sQ52_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f638,f352,f639]) ).
fof(f643,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)],[f192,f271]) ).
fof(f644,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_collection(intersection_of_members(top_of_basis(X4)),top_of_basis(X5))
| closed(f14(X1,X2,X3,X0),X2,X3)
| ~ subset_sets(X1,X2)
| element_of_set(X0,closure(X1,X2,X3)) ),
inference(resolution,[status(thm)],[f192,f416]) ).
fof(f645,definition,
! [X0,X1,X2,X3] :
( sQ53_spl
<=> ( closed(f14(X1,X2,X3,X0),X2,X3)
| ~ subset_sets(X1,X2)
| element_of_set(X0,closure(X1,X2,X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f648,plain,
( sQ23_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f644,f645,f443]) ).
fof(f649,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)],[f413,f303]) ).
fof(f651,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)],[f649]) ).
fof(f653,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)],[f651,f118]) ).
fof(f656,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)],[f651,f114]) ).
fof(f657,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)],[f651,f113]) ).
fof(f658,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)],[f656,f118]) ).
fof(f659,plain,
! [X0,X1] :
( open(f1(ct,f11(X0,intersection_of_members(ct))),cx,ct)
| element_of_set(X1,intersection_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f656,f277]) ).
fof(f662,plain,
! [X0,X1,X2,X3] :
( element_of_set(f11(X3,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X3))
| element_of_set(X2,intersection_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f656,f310]) ).
fof(f663,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)],[f656,f116]) ).
fof(f664,definition,
! [X0] :
( sQ54_spl
<=> ( open(f1(ct,f11(X0,intersection_of_members(ct))),cx,ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f665,plain,
! [X0] :
( ~ sQ54_spl
| open(f1(ct,f11(X0,intersection_of_members(ct))),cx,ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(component_clause,[status(thm)],[f664]) ).
fof(f667,definition,
! [X1] :
( sQ55_spl
<=> element_of_set(X1,intersection_of_members(ct)) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f668,plain,
! [X0] :
( ~ sQ55_spl
| element_of_set(X0,intersection_of_members(ct)) ),
inference(component_clause,[status(thm)],[f667]) ).
fof(f670,plain,
( sQ55_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f659,f664,f667]) ).
fof(f673,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)],[f369,f114]) ).
fof(f674,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)],[f369,f113]) ).
fof(f675,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)],[f653,f532]) ).
fof(f676,plain,
! [X0,X1,X2,X3,X4,X5] :
( subset_sets(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)],[f653,f417]) ).
fof(f677,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)],[f653,f416]) ).
fof(f678,plain,
! [X0,X1,X2,X3,X4,X5] :
( topological_space(X3,X4)
| element_of_set(X2,union_of_members(subspace_topology(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)],[f653,f380]) ).
fof(f679,plain,
! [X0,X1,X2,X3,X4,X5] :
( subset_sets(X5,X3)
| element_of_set(X2,union_of_members(subspace_topology(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)],[f653,f379]) ).
fof(f680,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)],[f653,f563]) ).
fof(f683,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)],[f653,f311]) ).
fof(f684,plain,
! [X0,X1,X2,X3,X4,X5] :
( topological_space(X4,X5)
| element_of_set(X2,interior(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)],[f653,f318]) ).
fof(f685,plain,
! [X0,X1,X2,X3,X4,X5] :
( subset_sets(X3,X4)
| element_of_set(X2,interior(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)],[f653,f317]) ).
fof(f686,plain,
! [X0,X1,X2,X3,X4,X5] :
( topological_space(X4,X5)
| element_of_set(X2,closure(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)],[f653,f316]) ).
fof(f687,plain,
! [X0,X1,X2,X3,X4,X5] :
( subset_sets(X3,X4)
| element_of_set(X2,closure(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)],[f653,f315]) ).
fof(f688,plain,
! [X0,X1,X2,X3,X4,X5] :
( subset_sets(X3,X4)
| 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)],[f653,f324]) ).
fof(f689,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)],[f653,f314]) ).
fof(f691,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)],[f653,f275]) ).
fof(f692,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)],[f653,f274]) ).
fof(f693,definition,
! [X1,X2] :
( sQ56_spl
<=> ( limit_point(X2,a,cx,ct)
| element_of_set(X1,f16(X2,a,cx,ct)) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f694,plain,
! [X0,X1] :
( ~ sQ56_spl
| limit_point(X1,a,cx,ct)
| element_of_set(X0,f16(X1,a,cx,ct)) ),
inference(component_clause,[status(thm)],[f693]) ).
fof(f696,plain,
( sQ56_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f675,f558,f693]) ).
fof(f697,definition,
! [X0,X1] :
( sQ57_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,[sQ57_spl])],[split_symbol_definition]) ).
fof(f698,plain,
! [X0,X1] :
( ~ sQ57_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)],[f697]) ).
fof(f700,definition,
! [X2,X3] :
( sQ58_spl
<=> element_of_set(X2,intersection_of_members(top_of_basis(X3))) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f701,plain,
! [X0,X1] :
( ~ sQ58_spl
| element_of_set(X0,intersection_of_members(top_of_basis(X1))) ),
inference(component_clause,[status(thm)],[f700]) ).
fof(f703,plain,
( sQ33_spl
| sQ58_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f676,f697,f700,f486]) ).
fof(f704,plain,
( sQ20_spl
| sQ58_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f677,f697,f700,f432]) ).
fof(f705,definition,
! [X2,X3,X4,X5] :
( sQ59_spl
<=> ( topological_space(X3,X4)
| element_of_set(X2,union_of_members(subspace_topology(X3,X4,X5))) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f706,plain,
! [X0,X1,X2,X3] :
( ~ sQ59_spl
| topological_space(X1,X2)
| element_of_set(X0,union_of_members(subspace_topology(X1,X2,X3))) ),
inference(component_clause,[status(thm)],[f705]) ).
fof(f708,plain,
( sQ59_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f678,f697,f705]) ).
fof(f709,definition,
! [X2,X3,X4,X5] :
( sQ60_spl
<=> ( subset_sets(X5,X3)
| element_of_set(X2,union_of_members(subspace_topology(X3,X4,X5))) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f710,plain,
! [X0,X1,X2,X3] :
( ~ sQ60_spl
| subset_sets(X3,X1)
| element_of_set(X0,union_of_members(subspace_topology(X1,X2,X3))) ),
inference(component_clause,[status(thm)],[f709]) ).
fof(f712,plain,
( sQ60_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f679,f697,f709]) ).
fof(f713,definition,
! [X1,X2,X3] :
( sQ61_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,[sQ61_spl])],[split_symbol_definition]) ).
fof(f714,plain,
! [X0,X1,X2] :
( ~ sQ61_spl
| element_of_collection(f16(X2,a,cx,ct),top_of_basis(X1))
| limit_point(X2,a,cx,ct)
| element_of_set(X0,f1(ct,f11(X1,f16(X2,a,cx,ct)))) ),
inference(component_clause,[status(thm)],[f713]) ).
fof(f716,plain,
( sQ61_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f680,f558,f713]) ).
fof(f717,definition,
! [X1,X2] :
( sQ62_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,[sQ62_spl])],[split_symbol_definition]) ).
fof(f718,plain,
! [X0,X1] :
( ~ sQ62_spl
| element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| element_of_set(X0,f1(ct,f11(X1,intersection_of_members(ct)))) ),
inference(component_clause,[status(thm)],[f717]) ).
fof(f721,definition,
! [X2,X3,X4,X5] :
( sQ63_spl
<=> ( topological_space(X4,X5)
| element_of_set(X2,interior(X3,X4,X5)) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f722,plain,
! [X0,X1,X2,X3] :
( ~ sQ63_spl
| topological_space(X2,X3)
| element_of_set(X0,interior(X1,X2,X3)) ),
inference(component_clause,[status(thm)],[f721]) ).
fof(f724,plain,
( sQ63_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f684,f697,f721]) ).
fof(f725,definition,
! [X2,X3,X4,X5] :
( sQ64_spl
<=> ( subset_sets(X3,X4)
| element_of_set(X2,interior(X3,X4,X5)) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f726,plain,
! [X0,X1,X2,X3] :
( ~ sQ64_spl
| subset_sets(X1,X2)
| element_of_set(X0,interior(X1,X2,X3)) ),
inference(component_clause,[status(thm)],[f725]) ).
fof(f728,plain,
( sQ64_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f685,f697,f725]) ).
fof(f729,definition,
! [X2,X3,X4,X5] :
( sQ65_spl
<=> ( topological_space(X4,X5)
| element_of_set(X2,closure(X3,X4,X5)) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f730,plain,
! [X0,X1,X2,X3] :
( ~ sQ65_spl
| topological_space(X2,X3)
| element_of_set(X0,closure(X1,X2,X3)) ),
inference(component_clause,[status(thm)],[f729]) ).
fof(f732,plain,
( sQ65_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f686,f697,f729]) ).
fof(f733,definition,
! [X2,X3,X4,X5] :
( sQ66_spl
<=> ( subset_sets(X3,X4)
| element_of_set(X2,closure(X3,X4,X5)) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f734,plain,
! [X0,X1,X2,X3] :
( ~ sQ66_spl
| subset_sets(X1,X2)
| element_of_set(X0,closure(X1,X2,X3)) ),
inference(component_clause,[status(thm)],[f733]) ).
fof(f736,plain,
( sQ66_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f687,f697,f733]) ).
fof(f737,definition,
! [X2,X3,X4,X5] :
( sQ67_spl
<=> ( subset_sets(X3,X4)
| element_of_set(X2,boundary(X3,X4,X5)) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f738,plain,
! [X0,X1,X2,X3] :
( ~ sQ67_spl
| subset_sets(X1,X2)
| element_of_set(X0,boundary(X1,X2,X3)) ),
inference(component_clause,[status(thm)],[f737]) ).
fof(f740,plain,
( sQ67_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f688,f697,f737]) ).
fof(f741,definition,
! [X2,X3,X4,X5] :
( sQ68_spl
<=> ( topological_space(X4,X5)
| element_of_set(X2,boundary(X3,X4,X5)) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f742,plain,
! [X0,X1,X2,X3] :
( ~ sQ68_spl
| topological_space(X2,X3)
| element_of_set(X0,boundary(X1,X2,X3)) ),
inference(component_clause,[status(thm)],[f741]) ).
fof(f744,plain,
( sQ68_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f689,f697,f741]) ).
fof(f745,definition,
! [X1] :
( sQ69_spl
<=> element_of_set(X1,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f746,plain,
! [X0] :
( ~ sQ69_spl
| element_of_set(X0,empty_set) ),
inference(component_clause,[status(thm)],[f745]) ).
fof(f748,plain,
( sQ69_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f691,f558,f745]) ).
fof(f749,definition,
! [X1] :
( sQ70_spl
<=> element_of_set(X1,cx) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f750,plain,
! [X0] :
( ~ sQ70_spl
| element_of_set(X0,cx) ),
inference(component_clause,[status(thm)],[f749]) ).
fof(f752,plain,
( sQ70_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f692,f558,f749]) ).
fof(f753,plain,
! [X0,X1] :
( ~ sQ48_spl
| subset_sets(a,cx)
| element_of_set(X0,union_of_members(top_of_basis(X1))) ),
inference(resolution,[status(thm)],[f608,f205]) ).
fof(f754,plain,
! [X0,X1] :
( ~ sQ48_spl
| topological_space(cx,ct)
| element_of_set(X0,union_of_members(top_of_basis(X1))) ),
inference(resolution,[status(thm)],[f608,f203]) ).
fof(f755,plain,
! [X0,X1] :
( ~ sQ48_spl
| element_of_collection(f1(top_of_basis(X1),X0),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f608,f114]) ).
fof(f756,plain,
! [X0,X1] :
( ~ sQ48_spl
| element_of_set(X0,f1(top_of_basis(X1),X0))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f608,f113]) ).
fof(f757,definition,
! [X0,X1] :
( sQ71_spl
<=> element_of_set(X0,union_of_members(top_of_basis(X1))) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f758,plain,
! [X0,X1] :
( ~ sQ71_spl
| element_of_set(X0,union_of_members(top_of_basis(X1))) ),
inference(component_clause,[status(thm)],[f757]) ).
fof(f760,plain,
( ~ sQ48_spl
| sQ43_spl
| sQ71_spl ),
inference(split_clause,[status(thm)],[f753,f757,f549,f583]) ).
fof(f761,plain,
( ~ sQ48_spl
| sQ1_spl
| sQ71_spl ),
inference(split_clause,[status(thm)],[f754,f757,f285,f583]) ).
fof(f762,plain,
! [X0,X1,X2,X3] :
( ~ sQ48_spl
| element_of_set(X3,f1(top_of_basis(X1),X0))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X1))),union_of_members(top_of_basis(X1)))
| element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X2))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f755,f653]) ).
fof(f763,plain,
! [X0,X1,X2] :
( ~ sQ48_spl
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X1))),f1(top_of_basis(X1),X0))
| element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X2))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f755,f310]) ).
fof(f764,plain,
! [X0,X1,X2] :
( ~ sQ48_spl
| ~ element_of_set(X1,f1(top_of_basis(X2),X0))
| element_of_set(X1,union_of_members(top_of_basis(X2)))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f755,f116]) ).
fof(f765,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| ~ sQ56_spl
| ~ subset_sets(f16(X0,a,cx,ct),X2)
| ~ subset_sets(X2,cx)
| element_of_set(X1,interior(X2,cx,ct))
| limit_point(X0,a,cx,ct) ),
inference(backward_subsumption_resolution,[status(thm)],[f535,f694]) ).
fof(f766,plain,
! [X0,X1] :
( ~ sQ56_spl
| element_of_set(X1,union_of_members(ct))
| limit_point(X0,a,cx,ct) ),
inference(backward_subsumption_resolution,[status(thm)],[f540,f694]) ).
fof(f767,plain,
( ~ sQ56_spl
| sQ42_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f766,f528,f546,f693]) ).
fof(f768,plain,
! [X0,X1,X2,X3] :
( ~ sQ48_spl
| element_of_set(X3,f16(X0,a,cx,ct))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X1))),union_of_members(top_of_basis(X1)))
| element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X2))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f598,f653]) ).
fof(f769,plain,
! [X0,X1,X2] :
( ~ sQ48_spl
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X1))),f16(X0,a,cx,ct))
| element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X2))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f598,f310]) ).
fof(f770,plain,
! [X0,X1,X2] :
( ~ sQ48_spl
| ~ element_of_set(X1,f16(X0,a,cx,ct))
| element_of_set(X1,union_of_members(top_of_basis(X2)))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f598,f116]) ).
fof(f771,plain,
( ~ sQ48_spl
| sQ57_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f768,f693,f697,f583]) ).
fof(f772,plain,
! [X0,X1,X2] :
( ~ sQ48_spl
| ~ sQ56_spl
| element_of_set(X1,union_of_members(top_of_basis(X2)))
| limit_point(X0,a,cx,ct) ),
inference(forward_subsumption_resolution,[status(thm)],[f770,f694]) ).
fof(f775,plain,
! [X0,X1,X2] :
( ~ sQ48_spl
| ~ sQ56_spl
| element_of_collection(f1(top_of_basis(X1),X2),top_of_basis(X1))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f772,f114]) ).
fof(f776,plain,
! [X0,X1,X2] :
( ~ sQ48_spl
| ~ sQ56_spl
| element_of_set(X1,f1(top_of_basis(X2),X1))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f772,f113]) ).
fof(f779,definition,
! [X1,X2] :
( sQ72_spl
<=> element_of_collection(f1(top_of_basis(X1),X2),top_of_basis(X1)) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f782,plain,
( ~ sQ48_spl
| ~ sQ56_spl
| sQ72_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f775,f528,f779,f693,f583]) ).
fof(f783,definition,
! [X1,X2] :
( sQ73_spl
<=> element_of_set(X1,f1(top_of_basis(X2),X1)) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f786,plain,
( ~ sQ48_spl
| ~ sQ56_spl
| sQ73_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f776,f528,f783,f693,f583]) ).
fof(f787,plain,
! [X0,X1] :
( ~ sQ57_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)],[f698,f114]) ).
fof(f788,plain,
! [X0,X1] :
( ~ sQ57_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)],[f698,f113]) ).
fof(f789,plain,
! [X0] :
( ~ sQ54_spl
| 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)],[f665,f138]) ).
fof(f790,plain,
! [X0,X1,X2] :
( ~ sQ54_spl
| ~ subset_sets(f1(ct,f11(X0,intersection_of_members(ct))),X2)
| ~ element_of_set(X1,f1(ct,f11(X0,intersection_of_members(ct))))
| ~ subset_sets(X2,cx)
| ~ topological_space(cx,ct)
| element_of_set(X1,interior(X2,cx,ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f665,f184]) ).
fof(f791,plain,
( ~ sQ54_spl
| ~ sQ1_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f790,f594,f285,f664]) ).
fof(f792,plain,
! [X0,X1,X2,X3] :
( ~ sQ48_spl
| limit_point(X3,a,cx,ct)
| element_of_set(X2,f16(X3,a,cx,ct))
| 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)],[f658,f598]) ).
fof(f793,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)],[f658,f532]) ).
fof(f794,plain,
! [X0,X1,X2,X3,X4,X5] :
( subset_sets(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)],[f658,f417]) ).
fof(f795,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)],[f658,f416]) ).
fof(f796,plain,
! [X0,X1,X2,X3,X4,X5] :
( topological_space(X3,X4)
| element_of_set(X2,union_of_members(subspace_topology(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)],[f658,f380]) ).
fof(f797,plain,
! [X0,X1,X2,X3,X4,X5] :
( subset_sets(X5,X3)
| element_of_set(X2,union_of_members(subspace_topology(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)],[f658,f379]) ).
fof(f798,plain,
! [X0,X1,X2,X3] :
( ~ sQ48_spl
| limit_point(X3,a,cx,ct)
| element_of_set(X2,f1(top_of_basis(X0),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)],[f658,f755]) ).
fof(f800,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)],[f658,f311]) ).
fof(f801,plain,
! [X0,X1,X2,X3,X4,X5] :
( topological_space(X4,X5)
| element_of_set(X2,interior(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)],[f658,f318]) ).
fof(f802,plain,
! [X0,X1,X2,X3,X4,X5] :
( subset_sets(X3,X4)
| element_of_set(X2,interior(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)],[f658,f317]) ).
fof(f803,plain,
! [X0,X1,X2,X3,X4,X5] :
( topological_space(X4,X5)
| element_of_set(X2,closure(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)],[f658,f316]) ).
fof(f804,plain,
! [X0,X1,X2,X3,X4,X5] :
( subset_sets(X3,X4)
| element_of_set(X2,closure(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)],[f658,f315]) ).
fof(f805,plain,
! [X0,X1,X2,X3,X4,X5] :
( subset_sets(X3,X4)
| 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)],[f658,f324]) ).
fof(f806,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)],[f658,f314]) ).
fof(f808,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)],[f658,f275]) ).
fof(f809,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)],[f658,f274]) ).
fof(f810,definition,
! [X0,X1] :
( sQ74_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,[sQ74_spl])],[split_symbol_definition]) ).
fof(f811,plain,
! [X0,X1] :
( ~ sQ74_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)],[f810]) ).
fof(f813,plain,
( ~ sQ48_spl
| sQ56_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f792,f810,f693,f583]) ).
fof(f814,definition,
! [X0] :
( sQ75_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,[sQ75_spl])],[split_symbol_definition]) ).
fof(f815,plain,
! [X0] :
( ~ sQ75_spl
| element_of_collection(f1(ct,f11(X0,intersection_of_members(ct))),ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(component_clause,[status(thm)],[f814]) ).
fof(f817,plain,
( sQ56_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f793,f814,f693]) ).
fof(f818,plain,
( sQ33_spl
| sQ58_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f794,f810,f700,f486]) ).
fof(f819,plain,
( sQ20_spl
| sQ58_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f795,f810,f700,f432]) ).
fof(f820,plain,
( sQ59_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f796,f810,f705]) ).
fof(f821,plain,
( sQ60_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f797,f810,f709]) ).
fof(f822,plain,
( sQ63_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f801,f810,f721]) ).
fof(f823,plain,
( sQ64_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f802,f810,f725]) ).
fof(f824,plain,
( sQ65_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f803,f810,f729]) ).
fof(f825,plain,
( sQ66_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f804,f810,f733]) ).
fof(f826,plain,
( sQ67_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f805,f810,f737]) ).
fof(f827,plain,
( sQ68_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f806,f810,f741]) ).
fof(f828,plain,
( sQ69_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f808,f814,f745]) ).
fof(f829,plain,
( sQ70_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f809,f814,f749]) ).
fof(f830,plain,
! [X0,X1] :
( open(f1(ct,f11(X1,f2(ct,X0))),cx,ct)
| element_of_collection(f2(ct,X0),top_of_basis(X1))
| element_of_set(X0,intersection_of_members(ct)) ),
inference(resolution,[status(thm)],[f673,f277]) ).
fof(f835,plain,
! [X0,X1,X2,X3] :
( element_of_set(f11(X3,intersection_of_members(X1)),f1(X1,f11(X2,f2(X1,X0))))
| element_of_collection(intersection_of_members(X1),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)],[f673,f310]) ).
fof(f836,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)],[f673,f116]) ).
fof(f839,plain,
! [X0,X1,X2] :
( ~ sQ57_spl
| 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(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f787,f310]) ).
fof(f840,plain,
! [X0,X1,X2] :
( ~ sQ57_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)],[f787,f116]) ).
fof(f841,plain,
! [X0] :
( closed(f14(a,cx,ct,X0),cx,ct)
| element_of_set(X0,closure(a,cx,ct)) ),
inference(resolution,[status(thm)],[f643,f272]) ).
fof(f842,plain,
! [X0,X1,X2,X3] :
( element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| closed(f14(X1,cx,ct,X0),cx,ct)
| element_of_set(X0,closure(X1,cx,ct)) ),
inference(resolution,[status(thm)],[f643,f417]) ).
fof(f843,definition,
! [X0,X1] :
( sQ76_spl
<=> ( closed(f14(X1,cx,ct,X0),cx,ct)
| element_of_set(X0,closure(X1,cx,ct)) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f846,plain,
( sQ23_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f842,f843,f443]) ).
fof(f847,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)],[f210,f165]) ).
fof(f848,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)],[f657,f118]) ).
fof(f849,plain,
! [X0,X1,X2,X3] :
( ~ sQ48_spl
| limit_point(X3,a,cx,ct)
| element_of_set(X2,f16(X3,a,cx,ct))
| 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)],[f848,f598]) ).
fof(f850,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)],[f848,f532]) ).
fof(f851,plain,
! [X0,X1,X2,X3,X4,X5] :
( subset_sets(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)],[f848,f417]) ).
fof(f852,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)],[f848,f416]) ).
fof(f853,plain,
! [X0,X1,X2,X3,X4,X5] :
( topological_space(X3,X4)
| element_of_set(X2,union_of_members(subspace_topology(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)],[f848,f380]) ).
fof(f854,plain,
! [X0,X1,X2,X3,X4,X5] :
( subset_sets(X5,X3)
| element_of_set(X2,union_of_members(subspace_topology(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)],[f848,f379]) ).
fof(f856,plain,
! [X0,X1,X2,X3] :
( ~ sQ48_spl
| limit_point(X3,a,cx,ct)
| element_of_set(X2,f1(top_of_basis(X0),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)],[f848,f755]) ).
fof(f859,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)],[f848,f311]) ).
fof(f860,plain,
! [X0,X1,X2,X3,X4,X5] :
( topological_space(X4,X5)
| element_of_set(X2,interior(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)],[f848,f318]) ).
fof(f861,plain,
! [X0,X1,X2,X3,X4,X5] :
( subset_sets(X3,X4)
| element_of_set(X2,interior(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)],[f848,f317]) ).
fof(f862,plain,
! [X0,X1,X2,X3,X4,X5] :
( topological_space(X4,X5)
| element_of_set(X2,closure(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)],[f848,f316]) ).
fof(f863,plain,
! [X0,X1,X2,X3,X4,X5] :
( subset_sets(X3,X4)
| element_of_set(X2,closure(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)],[f848,f315]) ).
fof(f864,plain,
! [X0,X1,X2,X3,X4,X5] :
( subset_sets(X3,X4)
| 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)],[f848,f324]) ).
fof(f865,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)],[f848,f314]) ).
fof(f867,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)],[f848,f275]) ).
fof(f868,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)],[f848,f274]) ).
fof(f869,definition,
! [X0,X1] :
( sQ77_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,[sQ77_spl])],[split_symbol_definition]) ).
fof(f870,plain,
! [X0,X1] :
( ~ sQ77_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)],[f869]) ).
fof(f872,plain,
( ~ sQ48_spl
| sQ56_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f849,f869,f693,f583]) ).
fof(f873,definition,
! [X0] :
( sQ78_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,[sQ78_spl])],[split_symbol_definition]) ).
fof(f874,plain,
! [X0] :
( ~ sQ78_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)) ),
inference(component_clause,[status(thm)],[f873]) ).
fof(f876,plain,
( sQ56_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f850,f873,f693]) ).
fof(f877,plain,
( sQ33_spl
| sQ58_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f851,f869,f700,f486]) ).
fof(f878,plain,
( sQ20_spl
| sQ58_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f852,f869,f700,f432]) ).
fof(f879,plain,
( sQ59_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f853,f869,f705]) ).
fof(f880,plain,
( sQ60_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f854,f869,f709]) ).
fof(f881,plain,
( sQ63_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f860,f869,f721]) ).
fof(f882,plain,
( sQ64_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f861,f869,f725]) ).
fof(f883,plain,
( sQ65_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f862,f869,f729]) ).
fof(f884,plain,
( sQ66_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f863,f869,f733]) ).
fof(f885,plain,
( sQ67_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f864,f869,f737]) ).
fof(f886,plain,
( sQ68_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f865,f869,f741]) ).
fof(f887,plain,
( sQ69_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f867,f873,f745]) ).
fof(f888,plain,
( sQ70_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f868,f873,f749]) ).
fof(f890,plain,
! [X0,X1,X2,X3] :
( ~ subset_sets(f1(ct,f11(X1,f2(ct,X0))),X3)
| ~ element_of_set(X2,f1(ct,f11(X1,f2(ct,X0))))
| ~ subset_sets(X3,cx)
| ~ topological_space(cx,ct)
| element_of_set(X2,interior(X3,cx,ct))
| element_of_collection(f2(ct,X0),top_of_basis(X1))
| element_of_set(X0,intersection_of_members(ct)) ),
inference(resolution,[status(thm)],[f830,f184]) ).
fof(f891,definition,
! [X0,X1,X2,X3] :
( sQ79_spl
<=> ( ~ subset_sets(f1(ct,f11(X1,f2(ct,X0))),X3)
| ~ element_of_set(X2,f1(ct,f11(X1,f2(ct,X0))))
| ~ subset_sets(X3,cx)
| element_of_set(X2,interior(X3,cx,ct))
| element_of_collection(f2(ct,X0),top_of_basis(X1))
| element_of_set(X0,intersection_of_members(ct)) ) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f892,plain,
! [X0,X1,X2,X3] :
( ~ sQ79_spl
| ~ subset_sets(f1(ct,f11(X1,f2(ct,X0))),X3)
| ~ element_of_set(X2,f1(ct,f11(X1,f2(ct,X0))))
| ~ subset_sets(X3,cx)
| element_of_set(X2,interior(X3,cx,ct))
| element_of_collection(f2(ct,X0),top_of_basis(X1))
| element_of_set(X0,intersection_of_members(ct)) ),
inference(component_clause,[status(thm)],[f891]) ).
fof(f894,plain,
( ~ sQ1_spl
| sQ79_spl ),
inference(split_clause,[status(thm)],[f890,f891,f285]) ).
fof(f895,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ41_spl
| ~ sQ56_spl
| element_of_collection(intersection_of_members(top_of_basis(X3)),top_of_basis(X4))
| ~ subset_sets(X2,cx)
| element_of_set(X1,interior(X2,cx,ct))
| limit_point(X0,a,cx,ct) ),
inference(resolution,[status(thm)],[f765,f417]) ).
fof(f896,definition,
! [X1,X2] :
( sQ80_spl
<=> ( ~ subset_sets(X2,cx)
| element_of_set(X1,interior(X2,cx,ct)) ) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f899,plain,
( ~ sQ41_spl
| ~ sQ56_spl
| sQ23_spl
| sQ80_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f895,f528,f896,f443,f693,f534]) ).
fof(f900,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(X4,X3)
| ~ element_of_collection(X3,X0)
| element_of_set(f11(X2,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X2))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f662,f118]) ).
fof(f904,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(union_of_members(X0),top_of_basis(X3))
| element_of_set(X2,f1(X0,f11(X3,union_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f683,f113]) ).
fof(f905,plain,
! [X0,X1,X2] :
( open(f1(ct,f11(X0,intersection_of_members(ct))),cx,ct)
| element_of_collection(union_of_members(ct),top_of_basis(X2))
| element_of_set(X1,f1(ct,f11(X2,union_of_members(ct))))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f800,f277]) ).
fof(f908,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_set(X5,f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_set(f11(X4,intersection_of_members(X0)),f1(X0,f11(X4,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X4))
| 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(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f800,f848]) ).
fof(f911,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(f11(X4,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X4))
| 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(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f800,f310]) ).
fof(f912,plain,
! [X0,X1,X2,X3,X4] :
( ~ element_of_set(X4,f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_set(X4,union_of_members(X0))
| 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(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f800,f116]) ).
fof(f913,definition,
! [X1,X2] :
( sQ81_spl
<=> ( element_of_collection(union_of_members(ct),top_of_basis(X2))
| element_of_set(X1,f1(ct,f11(X2,union_of_members(ct)))) ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f914,plain,
! [X0,X1] :
( ~ sQ81_spl
| element_of_collection(union_of_members(ct),top_of_basis(X1))
| element_of_set(X0,f1(ct,f11(X1,union_of_members(ct)))) ),
inference(component_clause,[status(thm)],[f913]) ).
fof(f916,plain,
( sQ81_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f905,f664,f913]) ).
fof(f918,plain,
! [X0,X1,X2] :
( ~ sQ54_spl
| element_of_set(X2,f1(ct,f11(X0,intersection_of_members(ct))))
| element_of_set(f11(X1,intersection_of_members(ct)),f1(ct,f11(X1,intersection_of_members(ct))))
| element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f789,f848]) ).
fof(f919,plain,
! [X0,X1,X2] :
( ~ sQ54_spl
| element_of_set(X2,f1(ct,f11(X0,intersection_of_members(ct))))
| element_of_collection(f1(ct,f11(X1,intersection_of_members(ct))),ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f789,f658]) ).
fof(f920,plain,
! [X0,X1,X2] :
( ~ sQ54_spl
| element_of_set(X2,f1(ct,f11(X0,intersection_of_members(ct))))
| element_of_set(f11(X1,intersection_of_members(ct)),union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f789,f653]) ).
fof(f921,plain,
! [X0,X1] :
( ~ sQ54_spl
| 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(X1))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f789,f310]) ).
fof(f922,plain,
! [X0,X1] :
( ~ sQ54_spl
| ~ 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)],[f789,f116]) ).
fof(f923,plain,
( ~ sQ54_spl
| sQ78_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f918,f717,f873,f664]) ).
fof(f924,plain,
( ~ sQ54_spl
| sQ75_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f919,f717,f814,f664]) ).
fof(f925,plain,
( ~ sQ54_spl
| sQ45_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f920,f717,f558,f664]) ).
fof(f929,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ48_spl
| limit_point(X4,a,cx,ct)
| element_of_set(X3,f16(X4,a,cx,ct))
| 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(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f900,f598]) ).
fof(f930,plain,
! [X0,X1,X2,X3] :
( limit_point(X3,a,cx,ct)
| element_of_set(X2,f16(X3,a,cx,ct))
| 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(X1))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f900,f532]) ).
fof(f931,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( subset_sets(X5,X6)
| element_of_set(X3,intersection_of_members(top_of_basis(X4)))
| 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(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f900,f417]) ).
fof(f932,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( topological_space(X5,X6)
| element_of_set(X3,intersection_of_members(top_of_basis(X4)))
| 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(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f900,f416]) ).
fof(f933,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( topological_space(X4,X5)
| element_of_set(X3,union_of_members(subspace_topology(X4,X5,X6)))
| 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(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f900,f380]) ).
fof(f934,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( subset_sets(X6,X4)
| element_of_set(X3,union_of_members(subspace_topology(X4,X5,X6)))
| 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(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f900,f379]) ).
fof(f935,plain,
! [X0,X1,X2,X3] :
( ~ sQ54_spl
| element_of_collection(intersection_of_members(ct),top_of_basis(X3))
| element_of_set(X2,f1(ct,f11(X3,intersection_of_members(ct))))
| 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(X1))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f900,f789]) ).
fof(f936,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ57_spl
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X4))
| element_of_set(X3,f1(top_of_basis(X0),f11(X4,intersection_of_members(top_of_basis(X0)))))
| 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(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f900,f787]) ).
fof(f937,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ48_spl
| limit_point(X4,a,cx,ct)
| element_of_set(X3,f1(top_of_basis(X0),X4))
| 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(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f900,f755]) ).
fof(f939,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( element_of_collection(union_of_members(X0),top_of_basis(X6))
| element_of_set(X5,f1(X0,f11(X6,union_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X4))
| element_of_set(X3,f1(X0,f11(X4,intersection_of_members(X0))))
| element_of_set(f11(X2,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X2))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f900,f800]) ).
fof(f941,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(union_of_members(X0),top_of_basis(X4))
| element_of_set(X3,f1(X0,f11(X4,union_of_members(X0))))
| element_of_set(f11(X2,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X2))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f900,f311]) ).
fof(f942,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( topological_space(X5,X6)
| element_of_set(X3,interior(X4,X5,X6))
| 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(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f900,f318]) ).
fof(f943,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( subset_sets(X4,X5)
| element_of_set(X3,interior(X4,X5,X6))
| 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(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f900,f317]) ).
fof(f944,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( topological_space(X5,X6)
| element_of_set(X3,closure(X4,X5,X6))
| 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(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f900,f316]) ).
fof(f945,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( subset_sets(X4,X5)
| element_of_set(X3,closure(X4,X5,X6))
| 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(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f900,f315]) ).
fof(f946,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( subset_sets(X4,X5)
| element_of_set(X3,boundary(X4,X5,X6))
| 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(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f900,f324]) ).
fof(f947,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( topological_space(X5,X6)
| element_of_set(X3,boundary(X4,X5,X6))
| 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(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f900,f314]) ).
fof(f949,plain,
! [X0,X1,X2] :
( element_of_set(X2,empty_set)
| 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(X1))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f900,f275]) ).
fof(f950,plain,
! [X0,X1,X2] :
( element_of_set(X2,cx)
| 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(X1))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f900,f274]) ).
fof(f951,definition,
! [X0,X1,X2] :
( sQ82_spl
<=> ( 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(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f952,plain,
! [X0,X1,X2] :
( ~ sQ82_spl
| 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(X2))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(component_clause,[status(thm)],[f951]) ).
fof(f954,plain,
( ~ sQ48_spl
| sQ56_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f929,f951,f693,f583]) ).
fof(f955,definition,
! [X0,X1] :
( sQ83_spl
<=> ( 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(X1))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f956,plain,
! [X0,X1] :
( ~ sQ83_spl
| 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(X1))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(component_clause,[status(thm)],[f955]) ).
fof(f958,plain,
( sQ56_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f930,f955,f693]) ).
fof(f959,plain,
( sQ33_spl
| sQ58_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f931,f951,f700,f486]) ).
fof(f960,plain,
( sQ20_spl
| sQ58_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f932,f951,f700,f432]) ).
fof(f961,plain,
( sQ59_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f933,f951,f705]) ).
fof(f962,plain,
( sQ60_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f934,f951,f709]) ).
fof(f963,plain,
( ~ sQ54_spl
| sQ62_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f935,f955,f717,f664]) ).
fof(f964,plain,
( sQ63_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f942,f951,f721]) ).
fof(f965,plain,
( sQ64_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f943,f951,f725]) ).
fof(f966,plain,
( sQ65_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f944,f951,f729]) ).
fof(f967,plain,
( sQ66_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f945,f951,f733]) ).
fof(f968,plain,
( sQ67_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f946,f951,f737]) ).
fof(f969,plain,
( sQ68_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f947,f951,f741]) ).
fof(f970,plain,
( sQ69_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f949,f955,f745]) ).
fof(f971,plain,
( sQ70_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f950,f955,f749]) ).
fof(f972,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ sQ81_spl
| ~ subset_sets(f1(ct,f11(X0,union_of_members(ct))),X2)
| ~ subset_sets(X2,cx)
| element_of_set(X1,interior(X2,cx,ct))
| element_of_collection(union_of_members(ct),top_of_basis(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f385,f914]) ).
fof(f973,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ15_spl
| ~ sQ81_spl
| element_of_collection(intersection_of_members(top_of_basis(X3)),top_of_basis(X4))
| ~ subset_sets(X2,cx)
| element_of_set(X1,interior(X2,cx,ct))
| element_of_collection(union_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f972,f417]) ).
fof(f974,definition,
! [X0] :
( sQ84_spl
<=> element_of_collection(union_of_members(ct),top_of_basis(X0)) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f975,plain,
! [X0] :
( ~ sQ84_spl
| element_of_collection(union_of_members(ct),top_of_basis(X0)) ),
inference(component_clause,[status(thm)],[f974]) ).
fof(f977,plain,
( ~ sQ15_spl
| ~ sQ81_spl
| sQ23_spl
| sQ80_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f973,f974,f896,f443,f913,f384]) ).
fof(f979,plain,
! [X0,X1,X2] :
( ~ sQ48_spl
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X2))
| limit_point(f11(X1,union_of_members(top_of_basis(X0))),a,cx,ct)
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X0))),union_of_members(top_of_basis(X0)))
| element_of_collection(union_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f381,f763]) ).
fof(f980,plain,
! [X0,X1,X2] :
( element_of_collection(union_of_members(X0),top_of_basis(X1))
| element_of_collection(intersection_of_members(X0),top_of_basis(X2))
| element_of_set(f11(X2,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f381,f406]) ).
fof(f981,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)],[f381,f165]) ).
fof(f982,plain,
! [X0,X1] :
( ~ sQ81_spl
| element_of_collection(union_of_members(ct),top_of_basis(X0))
| element_of_set(X1,union_of_members(ct))
| element_of_collection(union_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f381,f914]) ).
fof(f987,plain,
! [X0,X1,X2] :
( element_of_collection(intersection_of_members(X0),top_of_basis(X2))
| element_of_set(f11(X2,intersection_of_members(X0)),union_of_members(X0))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f980]) ).
fof(f988,definition,
! [X0] :
( sQ85_spl
<=> ( element_of_collection(union_of_members(ct),top_of_basis(X0))
| element_of_collection(union_of_members(ct),top_of_basis(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f991,plain,
( ~ sQ81_spl
| sQ42_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f982,f988,f546,f913]) ).
fof(f994,plain,
! [X0,X1,X2] :
( element_of_collection(f3(X1,top_of_basis(X2)),top_of_basis(X2))
| ~ element_of_collection(X1,top_of_basis(X2))
| ~ element_of_collection(empty_set,top_of_basis(X2))
| ~ equal_sets(union_of_members(top_of_basis(X2)),X1)
| topological_space(X1,top_of_basis(X2))
| element_of_collection(intersection_of_members(f5(X1,top_of_basis(X2))),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(f5(X1,top_of_basis(X2)))),union_of_members(f5(X1,top_of_basis(X2)))) ),
inference(resolution,[status(thm)],[f987,f130]) ).
fof(f995,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_set(X5,union_of_members(X1))
| element_of_set(f11(X4,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(X4))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X1)) ),
inference(resolution,[status(thm)],[f987,f900]) ).
fof(f996,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(X4,union_of_members(X1))
| 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_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X1)) ),
inference(resolution,[status(thm)],[f987,f848]) ).
fof(f997,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(X4,union_of_members(X1))
| 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(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X1)) ),
inference(resolution,[status(thm)],[f987,f658]) ).
fof(f998,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(X4,union_of_members(X1))
| 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(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X1)) ),
inference(resolution,[status(thm)],[f987,f653]) ).
fof(f999,plain,
! [X0,X1,X2,X3] :
( element_of_set(f11(X3,intersection_of_members(top_of_basis(X2))),union_of_members(X1))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X1)) ),
inference(resolution,[status(thm)],[f987,f310]) ).
fof(f1000,plain,
! [X0,X1,X2,X3] :
( ~ element_of_set(X2,union_of_members(X1))
| element_of_set(X2,union_of_members(top_of_basis(X3)))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X1)) ),
inference(resolution,[status(thm)],[f987,f116]) ).
fof(f1003,plain,
! [X0,X1,X2] :
( element_of_collection(f1(X0,f11(X2,intersection_of_members(X0))),X0)
| element_of_collection(intersection_of_members(X0),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f987,f114]) ).
fof(f1004,plain,
! [X0,X1,X2] :
( element_of_set(f11(X2,intersection_of_members(X0)),f1(X0,f11(X2,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f987,f113]) ).
fof(f1005,definition,
! [X0,X1,X5] :
( sQ86_spl
<=> ( element_of_set(X5,union_of_members(X1))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1006,plain,
! [X0,X1,X2] :
( ~ sQ86_spl
| element_of_set(X2,union_of_members(X1))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X1)) ),
inference(component_clause,[status(thm)],[f1005]) ).
fof(f1008,plain,
( sQ82_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f995,f1005,f951]) ).
fof(f1009,plain,
( sQ77_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f996,f1005,f869]) ).
fof(f1010,plain,
( sQ74_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f997,f1005,f810]) ).
fof(f1011,plain,
( sQ57_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f998,f1005,f697]) ).
fof(f1012,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)],[f1003,f130]) ).
fof(f1013,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_set(X5,union_of_members(X0))
| element_of_set(f11(X4,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(X4))
| 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)],[f1003,f900]) ).
fof(f1014,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_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)],[f1003,f848]) ).
fof(f1015,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)],[f1003,f658]) ).
fof(f1016,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)],[f1003,f653]) ).
fof(f1017,plain,
! [X0,X1,X2,X3] :
( element_of_set(f11(X3,intersection_of_members(top_of_basis(X2))),union_of_members(X0))
| 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)],[f1003,f310]) ).
fof(f1018,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)],[f1003,f116]) ).
fof(f1019,plain,
! [X0,X1] :
( open(f1(ct,f11(X1,intersection_of_members(ct))),cx,ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| element_of_collection(union_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f1003,f277]) ).
fof(f1022,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_set(X5,f1(X0,f11(X2,intersection_of_members(X0))))
| element_of_set(f11(X4,intersection_of_members(X0)),f1(X0,f11(X3,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X4))
| element_of_collection(intersection_of_members(X0),top_of_basis(X3))
| element_of_collection(intersection_of_members(X0),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f1003,f900]) ).
fof(f1023,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(X4,f1(X0,f11(X2,intersection_of_members(X0))))
| element_of_set(f11(X3,intersection_of_members(X0)),f1(X0,f11(X3,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X3))
| element_of_collection(intersection_of_members(X0),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f1003,f848]) ).
fof(f1026,plain,
! [X0,X1,X2,X3] :
( element_of_set(f11(X3,intersection_of_members(X0)),f1(X0,f11(X2,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X3))
| element_of_collection(intersection_of_members(X0),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f1003,f310]) ).
fof(f1027,plain,
! [X0,X1,X2,X3] :
( ~ element_of_set(X3,f1(X0,f11(X2,intersection_of_members(X0))))
| element_of_set(X3,union_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X2))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f1003,f116]) ).
fof(f1028,definition,
! [X0,X1,X5] :
( sQ87_spl
<=> ( element_of_set(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)) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1029,plain,
! [X0,X1,X2] :
( ~ sQ87_spl
| element_of_set(X2,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(component_clause,[status(thm)],[f1028]) ).
fof(f1031,plain,
( sQ82_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f1013,f1028,f951]) ).
fof(f1032,plain,
( sQ77_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f1014,f1028,f869]) ).
fof(f1033,plain,
( sQ74_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f1015,f1028,f810]) ).
fof(f1034,plain,
( sQ57_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f1016,f1028,f697]) ).
fof(f1035,plain,
( sQ54_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f1019,f974,f664]) ).
fof(f1036,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| ~ sQ62_spl
| ~ subset_sets(f1(ct,f11(X0,intersection_of_members(ct))),X2)
| ~ subset_sets(X2,cx)
| element_of_set(X1,interior(X2,cx,ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f595,f718]) ).
fof(f1037,plain,
! [X0,X1] :
( ~ sQ54_spl
| ~ sQ62_spl
| element_of_set(X1,union_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f922,f718]) ).
fof(f1038,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ54_spl
| ~ sQ62_spl
| element_of_set(X4,intersection_of_members(ct))
| element_of_set(f11(X3,intersection_of_members(top_of_basis(X1))),f1(top_of_basis(X1),f11(X2,intersection_of_members(top_of_basis(X1)))))
| element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X3))
| element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X2))
| element_of_set(X0,union_of_members(ct)) ),
inference(resolution,[status(thm)],[f1037,f900]) ).
fof(f1039,plain,
! [X0,X1,X2,X3] :
( ~ sQ54_spl
| ~ sQ62_spl
| element_of_set(X3,intersection_of_members(ct))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X1))),f1(top_of_basis(X1),f11(X2,intersection_of_members(top_of_basis(X1)))))
| element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X2))
| element_of_set(X0,union_of_members(ct)) ),
inference(resolution,[status(thm)],[f1037,f848]) ).
fof(f1040,plain,
! [X0,X1,X2,X3] :
( ~ sQ54_spl
| ~ sQ62_spl
| element_of_set(X3,intersection_of_members(ct))
| element_of_collection(f1(top_of_basis(X1),f11(X2,intersection_of_members(top_of_basis(X1)))),top_of_basis(X1))
| element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X2))
| element_of_set(X0,union_of_members(ct)) ),
inference(resolution,[status(thm)],[f1037,f658]) ).
fof(f1041,plain,
! [X0,X1,X2,X3] :
( ~ sQ54_spl
| ~ sQ62_spl
| element_of_set(X3,intersection_of_members(ct))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X1))),union_of_members(top_of_basis(X1)))
| element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X2))
| element_of_set(X0,union_of_members(ct)) ),
inference(resolution,[status(thm)],[f1037,f653]) ).
fof(f1042,plain,
! [X0,X1,X2] :
( ~ sQ54_spl
| ~ sQ62_spl
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X1))),intersection_of_members(ct))
| element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X2))
| element_of_set(X0,union_of_members(ct)) ),
inference(resolution,[status(thm)],[f1037,f310]) ).
fof(f1043,plain,
! [X0,X1,X2] :
( ~ sQ54_spl
| ~ sQ62_spl
| ~ element_of_set(X1,intersection_of_members(ct))
| element_of_set(X1,union_of_members(top_of_basis(X2)))
| element_of_set(X0,union_of_members(ct)) ),
inference(resolution,[status(thm)],[f1037,f116]) ).
fof(f1044,plain,
! [X0,X1] :
( ~ sQ54_spl
| ~ sQ62_spl
| element_of_collection(f1(ct,X1),ct)
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f1037,f114]) ).
fof(f1045,plain,
! [X0,X1] :
( ~ sQ54_spl
| ~ sQ62_spl
| element_of_set(X1,f1(ct,X1))
| element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f1037,f113]) ).
fof(f1046,plain,
( ~ sQ54_spl
| ~ sQ62_spl
| sQ55_spl
| sQ82_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f1038,f546,f951,f667,f717,f664]) ).
fof(f1047,plain,
( ~ sQ54_spl
| ~ sQ62_spl
| sQ55_spl
| sQ77_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f1039,f546,f869,f667,f717,f664]) ).
fof(f1048,plain,
( ~ sQ54_spl
| ~ sQ62_spl
| sQ55_spl
| sQ74_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f1040,f546,f810,f667,f717,f664]) ).
fof(f1049,plain,
( ~ sQ54_spl
| ~ sQ62_spl
| sQ55_spl
| sQ57_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f1041,f546,f697,f667,f717,f664]) ).
fof(f1050,definition,
! [X1,X2] :
( sQ88_spl
<=> ( element_of_set(f11(X2,intersection_of_members(top_of_basis(X1))),intersection_of_members(ct))
| element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1053,plain,
( ~ sQ54_spl
| ~ sQ62_spl
| sQ88_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f1042,f546,f1050,f717,f664]) ).
fof(f1054,definition,
! [X1,X2] :
( sQ89_spl
<=> ( ~ element_of_set(X1,intersection_of_members(ct))
| element_of_set(X1,union_of_members(top_of_basis(X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f1057,plain,
( ~ sQ54_spl
| ~ sQ62_spl
| sQ89_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f1043,f546,f1054,f717,f664]) ).
fof(f1058,definition,
! [X0] :
( sQ90_spl
<=> element_of_collection(intersection_of_members(ct),top_of_basis(X0)) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1061,definition,
! [X1] :
( sQ91_spl
<=> element_of_collection(f1(ct,X1),ct) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1064,plain,
( ~ sQ54_spl
| ~ sQ62_spl
| sQ91_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f1044,f1058,f1061,f717,f664]) ).
fof(f1065,definition,
! [X1] :
( sQ92_spl
<=> element_of_set(X1,f1(ct,X1)) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1068,plain,
( ~ sQ54_spl
| ~ sQ62_spl
| sQ92_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f1045,f1058,f1065,f717,f664]) ).
fof(f1071,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)],[f1004,f130]) ).
fof(f1072,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_set(X5,union_of_members(X0))
| element_of_set(f11(X4,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(X4))
| 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)],[f1004,f900]) ).
fof(f1073,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)],[f1004,f848]) ).
fof(f1074,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)],[f1004,f658]) ).
fof(f1075,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)],[f1004,f653]) ).
fof(f1076,plain,
! [X0,X1,X2,X3] :
( element_of_set(f11(X3,intersection_of_members(top_of_basis(X2))),union_of_members(X0))
| 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)],[f1004,f310]) ).
fof(f1077,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)],[f1004,f116]) ).
fof(f1078,definition,
! [X0,X1,X5] :
( sQ93_spl
<=> ( element_of_set(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)) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1079,plain,
! [X0,X1,X2] :
( ~ sQ93_spl
| element_of_set(X2,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(component_clause,[status(thm)],[f1078]) ).
fof(f1081,plain,
( sQ82_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f1072,f1078,f951]) ).
fof(f1082,plain,
( sQ77_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f1073,f1078,f869]) ).
fof(f1083,plain,
( sQ74_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f1074,f1078,f810]) ).
fof(f1084,plain,
( sQ57_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f1075,f1078,f697]) ).
fof(f1090,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ48_spl
| ~ sQ56_spl
| limit_point(X4,a,cx,ct)
| element_of_set(X2,union_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)],[f1018,f772]) ).
fof(f1091,plain,
( ~ sQ48_spl
| ~ sQ56_spl
| sQ40_spl
| sQ71_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f1090,f810,f757,f528,f693,f583]) ).
fof(f1097,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)],[f981,f114]) ).
fof(f1098,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)],[f981,f113]) ).
fof(f1099,plain,
! [X0,X1] :
( open(f1(ct,f11(X1,f1(ct,f11(X0,union_of_members(ct))))),cx,ct)
| element_of_collection(f1(ct,f11(X0,union_of_members(ct))),top_of_basis(X1))
| element_of_collection(union_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f1097,f277]) ).
fof(f1102,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_set(X5,f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))
| element_of_set(f11(X4,intersection_of_members(X0)),f1(X0,f11(X3,intersection_of_members(X0))))
| element_of_collection(intersection_of_members(X0),top_of_basis(X4))
| element_of_collection(intersection_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)],[f1097,f900]) ).
fof(f1106,plain,
! [X0,X1,X2,X3] :
( element_of_set(f11(X3,intersection_of_members(X0)),f1(X0,f11(X2,f1(X0,f11(X1,union_of_members(X0))))))
| element_of_collection(intersection_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)],[f1097,f310]) ).
fof(f1107,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)],[f1097,f116]) ).
fof(f1109,plain,
! [X0,X1,X2,X3] :
( ~ subset_sets(f1(ct,f11(X1,f1(ct,f11(X0,union_of_members(ct))))),X3)
| ~ element_of_set(X2,f1(ct,f11(X1,f1(ct,f11(X0,union_of_members(ct))))))
| ~ subset_sets(X3,cx)
| ~ topological_space(cx,ct)
| element_of_set(X2,interior(X3,cx,ct))
| element_of_collection(f1(ct,f11(X0,union_of_members(ct))),top_of_basis(X1))
| element_of_collection(union_of_members(ct),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[f1099,f184]) ).
fof(f1110,definition,
! [X0,X1,X2,X3] :
( sQ94_spl
<=> ( ~ subset_sets(f1(ct,f11(X1,f1(ct,f11(X0,union_of_members(ct))))),X3)
| ~ element_of_set(X2,f1(ct,f11(X1,f1(ct,f11(X0,union_of_members(ct))))))
| ~ subset_sets(X3,cx)
| element_of_set(X2,interior(X3,cx,ct))
| element_of_collection(f1(ct,f11(X0,union_of_members(ct))),top_of_basis(X1))
| element_of_collection(union_of_members(ct),top_of_basis(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1111,plain,
! [X0,X1,X2,X3] :
( ~ sQ94_spl
| ~ subset_sets(f1(ct,f11(X1,f1(ct,f11(X0,union_of_members(ct))))),X3)
| ~ element_of_set(X2,f1(ct,f11(X1,f1(ct,f11(X0,union_of_members(ct))))))
| ~ subset_sets(X3,cx)
| element_of_set(X2,interior(X3,cx,ct))
| element_of_collection(f1(ct,f11(X0,union_of_members(ct))),top_of_basis(X1))
| element_of_collection(union_of_members(ct),top_of_basis(X0)) ),
inference(component_clause,[status(thm)],[f1110]) ).
fof(f1113,plain,
( ~ sQ1_spl
| sQ94_spl ),
inference(split_clause,[status(thm)],[f1109,f1110,f285]) ).
fof(f1116,plain,
! [X0,X1,X2,X3] :
( ~ sQ48_spl
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X3))
| limit_point(f11(X1,intersection_of_members(top_of_basis(X0))),a,cx,ct)
| element_of_set(f11(X3,intersection_of_members(top_of_basis(X0))),union_of_members(top_of_basis(X0)))
| element_of_set(X2,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)],[f663,f763]) ).
fof(f1120,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)],[f663,f165]) ).
fof(f1121,plain,
! [X0,X1,X2] :
( ~ sQ48_spl
| limit_point(f11(X1,intersection_of_members(top_of_basis(X0))),a,cx,ct)
| element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),union_of_members(top_of_basis(X0)))
| element_of_set(X2,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)],[f663,f756]) ).
fof(f1127,plain,
! [X0,X1,X2,X3,X4] :
( element_of_set(X4,X3)
| ~ element_of_collection(X3,X0)
| element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),top_of_basis(X2))
| element_of_set(f11(X2,f1(X0,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)],[f1120,f118]) ).
fof(f1131,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f1(X0,f11(X3,f1(X0,f11(X1,intersection_of_members(X0))))),X0)
| element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),top_of_basis(X3))
| element_of_set(X2,intersection_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f1120,f114]) ).
fof(f1132,plain,
! [X0,X1,X2,X3] :
( element_of_set(f11(X3,f1(X0,f11(X1,intersection_of_members(X0)))),f1(X0,f11(X3,f1(X0,f11(X1,intersection_of_members(X0))))))
| element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),top_of_basis(X3))
| element_of_set(X2,intersection_of_members(X0))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f1120,f113]) ).
fof(f1138,plain,
! [X0,X1,X2] :
( 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))
| 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)) ),
inference(resolution,[status(thm)],[f132,f1004]) ).
fof(f1139,plain,
! [X0,X1,X2] :
( 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))
| 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)) ),
inference(resolution,[status(thm)],[f132,f1003]) ).
fof(f1140,plain,
! [X0,X1,X2] :
( element_of_collection(intersection_of_members(f5(X0,top_of_basis(X1))),top_of_basis(X2))
| 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(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)) ),
inference(resolution,[status(thm)],[f132,f987]) ).
fof(f1141,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)],[f847,f271]) ).
fof(f1142,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( element_of_collection(intersection_of_members(top_of_basis(X5)),top_of_basis(X6))
| 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)
| limit_point(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f847,f416]) ).
fof(f1143,definition,
! [X0,X1,X2,X3,X4] :
( sQ96_spl
<=> ( 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)
| limit_point(X0,X1,X2,X3) ) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f1146,plain,
( sQ23_spl
| sQ96_spl ),
inference(split_clause,[status(thm)],[f1142,f1143,f443]) ).
fof(f1147,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)],[f1141,f272]) ).
fof(f1148,plain,
! [X0,X1,X2,X3,X4] :
( element_of_collection(intersection_of_members(top_of_basis(X3)),top_of_basis(X4))
| 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)
| limit_point(X0,X1,cx,ct) ),
inference(resolution,[status(thm)],[f1141,f417]) ).
fof(f1149,definition,
! [X0,X1,X2] :
( sQ97_spl
<=> ( 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)
| limit_point(X0,X1,cx,ct) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1152,plain,
( sQ23_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f1148,f1149,f443]) ).
fof(f1156,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)],[f836,f165]) ).
fof(f1162,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_collection(f1(top_of_basis(X0),f11(X2,intersection_of_members(top_of_basis(X0)))),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)],[f999,f1018]) ).
fof(f1163,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_set(f11(X1,intersection_of_members(X0)),union_of_members(top_of_basis(X5)))
| element_of_collection(f1(X0,f11(X4,intersection_of_members(X0))),X0)
| element_of_collection(intersection_of_members(X0),top_of_basis(X4))
| element_of_set(f11(X3,intersection_of_members(top_of_basis(X2))),union_of_members(X0))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f999,f1018]) ).
fof(f1164,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)],[f999,f114]) ).
fof(f1165,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f1(X0,f11(X1,intersection_of_members(X0))),X0)
| element_of_set(f11(X3,intersection_of_members(top_of_basis(X2))),union_of_members(X0))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f999,f114]) ).
fof(f1166,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)],[f999,f113]) ).
fof(f1167,plain,
! [X0,X1,X2,X3] :
( element_of_set(f11(X1,intersection_of_members(X0)),f1(X0,f11(X1,intersection_of_members(X0))))
| element_of_set(f11(X3,intersection_of_members(top_of_basis(X2))),union_of_members(X0))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| element_of_collection(intersection_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f999,f113]) ).
fof(f1168,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( element_of_set(f11(X5,intersection_of_members(top_of_basis(X4))),union_of_members(top_of_basis(X6)))
| topological_space(X1,X2)
| element_of_collection(intersection_of_members(top_of_basis(X4)),top_of_basis(X5))
| element_of_collection(intersection_of_members(subspace_topology(X1,X2,X3)),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(subspace_topology(X1,X2,X3))),union_of_members(subspace_topology(X1,X2,X3))) ),
inference(resolution,[status(thm)],[f999,f403]) ).
fof(f1169,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( element_of_set(f11(X5,intersection_of_members(top_of_basis(X4))),union_of_members(top_of_basis(X6)))
| subset_sets(X3,X1)
| element_of_collection(intersection_of_members(top_of_basis(X4)),top_of_basis(X5))
| element_of_collection(intersection_of_members(subspace_topology(X1,X2,X3)),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(subspace_topology(X1,X2,X3))),union_of_members(subspace_topology(X1,X2,X3))) ),
inference(resolution,[status(thm)],[f999,f402]) ).
fof(f1170,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_collection(f1(X1,f11(X4,intersection_of_members(X1))),X1)
| element_of_collection(intersection_of_members(X1),top_of_basis(X4))
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X1)) ),
inference(resolution,[status(thm)],[f999,f1018]) ).
fof(f1171,plain,
! [X0,X1,X2,X3] :
( element_of_collection(f1(X1,f11(X3,intersection_of_members(top_of_basis(X2)))),X1)
| element_of_collection(intersection_of_members(top_of_basis(X2)),top_of_basis(X3))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X1)) ),
inference(resolution,[status(thm)],[f999,f114]) ).
fof(f1172,plain,
! [X0,X1,X2,X3] :
( element_of_set(f11(X3,intersection_of_members(top_of_basis(X2))),f1(X1,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_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X1)) ),
inference(resolution,[status(thm)],[f999,f113]) ).
fof(f1173,plain,
! [X0,X1] :
( element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X0))
| 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))),union_of_members(top_of_basis(X1))) ),
inference(factoring,[status(thm)],[f999]) ).
fof(f1174,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_collection(f1(top_of_basis(X0),f11(X2,intersection_of_members(top_of_basis(X0)))),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)],[f1162]) ).
fof(f1175,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)],[f1164]) ).
fof(f1176,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)],[f1166]) ).
fof(f1177,definition,
! [X0,X1,X2,X3] :
( sQ98_spl
<=> ( topological_space(X1,X2)
| element_of_collection(intersection_of_members(subspace_topology(X1,X2,X3)),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(subspace_topology(X1,X2,X3))),union_of_members(subspace_topology(X1,X2,X3))) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1180,definition,
! [X4,X5,X6] :
( sQ99_spl
<=> ( element_of_set(f11(X5,intersection_of_members(top_of_basis(X4))),union_of_members(top_of_basis(X6)))
| element_of_collection(intersection_of_members(top_of_basis(X4)),top_of_basis(X5)) ) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1181,plain,
! [X0,X1,X2] :
( ~ sQ99_spl
| element_of_set(f11(X1,intersection_of_members(top_of_basis(X0))),union_of_members(top_of_basis(X2)))
| element_of_collection(intersection_of_members(top_of_basis(X0)),top_of_basis(X1)) ),
inference(component_clause,[status(thm)],[f1180]) ).
fof(f1183,plain,
( sQ99_spl
| sQ98_spl ),
inference(split_clause,[status(thm)],[f1168,f1177,f1180]) ).
fof(f1184,definition,
! [X0,X1,X2,X3] :
( sQ100_spl
<=> ( subset_sets(X3,X1)
| element_of_collection(intersection_of_members(subspace_topology(X1,X2,X3)),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(subspace_topology(X1,X2,X3))),union_of_members(subspace_topology(X1,X2,X3))) ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1187,plain,
( sQ99_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f1169,f1184,f1180]) ).
fof(f1188,definition,
! [X0,X1,X4] :
( sQ101_spl
<=> ( element_of_collection(f1(X1,f11(X4,intersection_of_members(X1))),X1)
| element_of_collection(intersection_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)),union_of_members(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1191,plain,
( sQ99_spl
| sQ101_spl ),
inference(split_clause,[status(thm)],[f1170,f1188,f1180]) ).
fof(f1192,plain,
! [X0,X1] :
( 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))),union_of_members(top_of_basis(X1))) ),
inference(duplicate_literals_removal,[status(thm)],[f1173]) ).
fof(f1197,plain,
! [X0,X1,X2,X3] :
( element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X2))
| element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X2))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X1))),union_of_members(top_of_basis(X3)))
| 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))),union_of_members(top_of_basis(X1))) ),
inference(resolution,[status(thm)],[f1000,f999]) ).
fof(f1198,plain,
! [X0,X1,X2,X3,X4,X5] :
( element_of_collection(intersection_of_members(top_of_basis(X3)),top_of_basis(X2))
| element_of_collection(intersection_of_members(X1),top_of_basis(X5))
| element_of_set(f11(X5,intersection_of_members(X1)),union_of_members(X1))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X3))),union_of_members(top_of_basis(X4)))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X1)) ),
inference(resolution,[status(thm)],[f1000,f999]) ).
fof(f1199,plain,
! [X0,X1,X2,X3] :
( element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X2))
| element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X2))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X1))),union_of_members(top_of_basis(X3)))
| 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))),union_of_members(top_of_basis(X1))) ),
inference(resolution,[status(thm)],[f1000,f999]) ).
fof(f1204,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ48_spl
| ~ sQ56_spl
| limit_point(X4,a,cx,ct)
| element_of_set(X2,union_of_members(top_of_basis(X3)))
| 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))),union_of_members(top_of_basis(X1))) ),
inference(resolution,[status(thm)],[f1000,f772]) ).
fof(f1205,plain,
! [X0,X1,X2,X3] :
( element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X2))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X1))),union_of_members(top_of_basis(X3)))
| 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))),union_of_members(top_of_basis(X1))) ),
inference(duplicate_literals_removal,[status(thm)],[f1197]) ).
fof(f1206,definition,
! [X0,X1,X5] :
( sQ102_spl
<=> ( element_of_collection(intersection_of_members(X1),top_of_basis(X5))
| element_of_set(f11(X5,intersection_of_members(X1)),union_of_members(X1))
| element_of_collection(intersection_of_members(X1),top_of_basis(X0))
| element_of_set(f11(X0,intersection_of_members(X1)),union_of_members(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1209,plain,
( sQ99_spl
| sQ102_spl ),
inference(split_clause,[status(thm)],[f1198,f1206,f1180]) ).
fof(f1210,plain,
! [X0,X1,X2,X3] :
( element_of_collection(intersection_of_members(top_of_basis(X1)),top_of_basis(X2))
| element_of_set(f11(X2,intersection_of_members(top_of_basis(X1))),union_of_members(top_of_basis(X3)))
| 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))),union_of_members(top_of_basis(X1))) ),
inference(duplicate_literals_removal,[status(thm)],[f1199]) ).
fof(f1211,plain,
( ~ sQ48_spl
| ~ sQ56_spl
| sQ40_spl
| sQ71_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f1204,f697,f757,f528,f693,f583]) ).
fof(f1212,plain,
! [X0,X1] :
( ~ sQ4_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)],[f332,f219]) ).
fof(f1213,plain,
! [X0,X1] :
( ~ sQ4_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)],[f332,f218]) ).
fof(f1214,plain,
! [X0,X1] :
( ~ sQ4_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)],[f332,f217]) ).
fof(f1216,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ70_spl
| disjoint_s(f17(cx,ct,X1,X0),f18(cx,ct,X1,X0))
| eq_p(X1,X0)
| ~ element_of_set(X0,cx) ),
inference(forward_subsumption_resolution,[status(thm)],[f1212,f750]) ).
fof(f1217,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ70_spl
| neighborhood(f18(cx,ct,X1,X0),X0,cx,ct)
| eq_p(X1,X0)
| ~ element_of_set(X0,cx) ),
inference(forward_subsumption_resolution,[status(thm)],[f1213,f750]) ).
fof(f1218,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ70_spl
| neighborhood(f17(cx,ct,X1,X0),X1,cx,ct)
| eq_p(X1,X0)
| ~ element_of_set(X0,cx) ),
inference(forward_subsumption_resolution,[status(thm)],[f1214,f750]) ).
fof(f1222,plain,
! [X0,X1] :
( limit_point(X1,a,cx,ct)
| element_of_collection(intersection_of_sets(f16(X1,a,cx,ct),X0),ct)
| ~ element_of_collection(X0,ct) ),
inference(resolution,[status(thm)],[f299,f532]) ).
fof(f1223,plain,
! [X0,X1,X2] :
( 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))
| element_of_collection(intersection_of_sets(f1(ct,f11(X1,f1(ct,f11(X2,union_of_members(ct))))),X0),ct)
| ~ element_of_collection(X0,ct) ),
inference(resolution,[status(thm)],[f299,f1097]) ).
fof(f1224,plain,
! [X0,X1,X2] :
( element_of_collection(f2(ct,X2),top_of_basis(X1))
| element_of_set(X2,intersection_of_members(ct))
| element_of_collection(intersection_of_sets(f1(ct,f11(X1,f2(ct,X2))),X0),ct)
| ~ element_of_collection(X0,ct) ),
inference(resolution,[status(thm)],[f299,f673]) ).
fof(f1225,plain,
! [X0,X1,X2] :
( element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| element_of_collection(union_of_members(ct),top_of_basis(X2))
| element_of_collection(intersection_of_sets(f1(ct,f11(X1,intersection_of_members(ct))),X0),ct)
| ~ element_of_collection(X0,ct) ),
inference(resolution,[status(thm)],[f299,f1003]) ).
fof(f1226,plain,
! [X0,X1,X2] :
( element_of_set(X2,intersection_of_members(ct))
| element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| element_of_collection(intersection_of_sets(f1(ct,f11(X1,intersection_of_members(ct))),X0),ct)
| ~ element_of_collection(X0,ct) ),
inference(resolution,[status(thm)],[f299,f656]) ).
fof(f1227,plain,
! [X0,X1] :
( element_of_collection(union_of_members(ct),top_of_basis(X1))
| element_of_collection(intersection_of_sets(f1(ct,f11(X1,union_of_members(ct))),X0),ct)
| ~ element_of_collection(X0,ct) ),
inference(resolution,[status(thm)],[f299,f311]) ).
fof(f1228,plain,
! [X0,X1] :
( element_of_set(X1,intersection_of_members(ct))
| element_of_collection(intersection_of_sets(f2(ct,X1),X0),ct)
| ~ element_of_collection(X0,ct) ),
inference(resolution,[status(thm)],[f299,f119]) ).
fof(f1229,plain,
! [X0] :
( element_of_collection(intersection_of_sets(empty_set,X0),ct)
| ~ element_of_collection(X0,ct) ),
inference(resolution,[status(thm)],[f299,f275]) ).
fof(f1230,plain,
! [X0] :
( element_of_collection(intersection_of_sets(cx,X0),ct)
| ~ element_of_collection(X0,ct) ),
inference(resolution,[status(thm)],[f299,f274]) ).
fof(f1231,definition,
! [X0,X1] :
( sQ103_spl
<=> ( element_of_collection(intersection_of_members(ct),top_of_basis(X1))
| element_of_collection(intersection_of_sets(f1(ct,f11(X1,intersection_of_members(ct))),X0),ct)
| ~ element_of_collection(X0,ct) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1234,plain,
( sQ84_spl
| sQ103_spl ),
inference(split_clause,[status(thm)],[f1225,f1231,f974]) ).
fof(f1235,plain,
( sQ55_spl
| sQ103_spl ),
inference(split_clause,[status(thm)],[f1226,f1231,f667]) ).
fof(f1236,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ20_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)],[f210,f433]) ).
fof(f1237,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_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)],[f240,f433]) ).
fof(f1238,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ20_spl
| ~ open(X4,X2,X3)
| ~ subset_sets(X4,X1)
| ~ element_of_set(X0,X4)
| ~ subset_sets(X1,X2)
| element_of_set(X0,interior(X1,X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[f184,f433]) ).
fof(f1239,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ20_spl
| 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)
| limit_point(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f847,f433]) ).
fof(f1240,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_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)],[f192,f433]) ).
fof(f1241,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_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)],[f208,f433]) ).
fof(f1242,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_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)],[f191,f433]) ).
fof(f1243,plain,
! [X0,X1] :
( ~ sQ20_spl
| separation(f21(X0,X1),f22(X0,X1),X0,X1)
| connected_space(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f244,f433]) ).
fof(f1244,plain,
! [X0,X1] :
( ~ sQ20_spl
| open_covering(f24(X0,X1),X0,X1)
| compact_space(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f263,f433]) ).
fof(f1245,plain,
! [X0,X1] :
( ~ sQ20_spl
| element_of_set(f20(X0,X1),X0)
| hausdorff(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f221,f433]) ).
fof(f1246,plain,
! [X0,X1] :
( ~ sQ20_spl
| element_of_set(f19(X0,X1),X0)
| hausdorff(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f220,f433]) ).
fof(f1248,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| ~ element_of_collection(X0,X2)
| open(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f140,f433]) ).
fof(f1249,plain,
! [X0,X1] :
( ~ sQ20_spl
| equal_sets(union_of_members(X0),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f121,f433]) ).
fof(f1251,plain,
! [X0,X1] :
( ~ sQ20_spl
| element_of_collection(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f124,f433]) ).
fof(f1252,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ sQ81_spl
| ~ sQ33_spl
| ~ subset_sets(f1(ct,f11(X0,union_of_members(ct))),X2)
| element_of_set(X1,interior(X2,cx,ct))
| element_of_collection(union_of_members(ct),top_of_basis(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f972,f487]) ).
fof(f1253,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| ~ sQ56_spl
| ~ sQ33_spl
| ~ subset_sets(f16(X0,a,cx,ct),X2)
| element_of_set(X1,interior(X2,cx,ct))
| limit_point(X0,a,cx,ct) ),
inference(backward_subsumption_resolution,[status(thm)],[f765,f487]) ).
fof(f1254,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ33_spl
| ~ subset_sets(f2(ct,X0),X2)
| ~ element_of_set(X1,f2(ct,X0))
| element_of_set(X1,interior(X2,cx,ct))
| element_of_set(X0,intersection_of_members(ct)) ),
inference(backward_subsumption_resolution,[status(thm)],[f307,f487]) ).
fof(f1255,plain,
! [X0,X1,X2] :
( ~ sQ33_spl
| 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)
| limit_point(X0,X1,cx,ct) ),
inference(backward_subsumption_resolution,[status(thm)],[f1141,f487]) ).
fof(f1256,plain,
! [X0,X1] :
( ~ sQ33_spl
| closed(f14(X1,cx,ct,X0),cx,ct)
| element_of_set(X0,closure(X1,cx,ct)) ),
inference(backward_subsumption_resolution,[status(thm)],[f643,f487]) ).
fof(f1257,plain,
! [X0,X1] :
( ~ sQ33_spl
| neighborhood(f16(X0,X1,cx,ct),X0,cx,ct)
| limit_point(X0,X1,cx,ct) ),
inference(backward_subsumption_resolution,[status(thm)],[f513,f487]) ).
fof(f1258,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ sQ81_spl
| ~ sQ33_spl
| element_of_set(X1,interior(X2,cx,ct))
| element_of_collection(union_of_members(ct),top_of_basis(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1252,f487]) ).
fof(f1259,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| ~ sQ56_spl
| ~ sQ33_spl
| element_of_set(X1,interior(X2,cx,ct))
| limit_point(X0,a,cx,ct) ),
inference(forward_subsumption_resolution,[status(thm)],[f1253,f487]) ).
fof(f1260,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ33_spl
| ~ element_of_set(X1,f2(ct,X0))
| element_of_set(X1,interior(X2,cx,ct))
| element_of_set(X0,intersection_of_members(ct)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1254,f487]) ).
fof(f1261,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| element_of_set(X0,X2)
| ~ element_of_set(X0,intersection_of_members(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f118,f1251]) ).
fof(f1262,plain,
! [X0] :
( ~ sQ20_spl
| open(X0,cx,ct) ),
inference(backward_subsumption_resolution,[status(thm)],[f277,f1251]) ).
fof(f1263,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| ~ element_of_set(X0,X2)
| element_of_set(X0,union_of_members(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f116,f1251]) ).
fof(f1264,plain,
! [X0,X1] :
( ~ sQ20_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)],[f160,f1249]) ).
fof(f1265,plain,
! [X0,X1] :
( ~ sQ20_spl
| element_of_set(f7(X0,X1),X0)
| basis(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f157,f1249]) ).
fof(f1266,plain,
! [X0] :
( ~ sQ42_spl
| element_of_set(X0,f1(ct,X0)) ),
inference(resolution,[status(thm)],[f547,f113]) ).
fof(f1267,plain,
! [X0,X1] :
( ~ sQ71_spl
| element_of_set(X0,f1(top_of_basis(X1),X0)) ),
inference(resolution,[status(thm)],[f758,f113]) ).
fof(f1268,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ20_spl
| ~ sQ33_spl
| ~ open(X4,X2,X3)
| ~ subset_sets(X4,X1)
| ~ element_of_set(X0,X4)
| element_of_set(X0,interior(X1,X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1238,f487]) ).
fof(f1269,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| ~ sQ33_spl
| ~ subset_sets(X2,X1)
| ~ element_of_set(X0,X2)
| element_of_set(X0,interior(X1,cx,ct)) ),
inference(resolution,[status(thm)],[f1268,f1262]) ).
fof(f1270,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| ~ sQ33_spl
| ~ element_of_set(X0,X2)
| element_of_set(X0,interior(X1,cx,ct)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1269,f487]) ).
fof(f1271,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ20_spl
| ~ sQ33_spl
| ~ subset_sets(X4,X1)
| ~ element_of_set(X0,X4)
| element_of_set(X0,interior(X1,X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[f1268,f1272]) ).
fof(f1272,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| open(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1248,f1251]) ).
fof(f1273,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ20_spl
| ~ sQ33_spl
| ~ element_of_set(X0,X4)
| element_of_set(X0,interior(X1,X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1271,f487]) ).
fof(f1274,plain,
! [X0,X1] :
( ~ sQ55_spl
| ~ sQ20_spl
| element_of_set(X0,X1) ),
inference(resolution,[status(thm)],[f1261,f668]) ).
fof(f1275,plain,
! [X0,X1,X2,X3] :
( ~ sQ55_spl
| ~ sQ20_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)],[f219,f1274]) ).
fof(f1278,plain,
! [X0,X1,X2,X3] :
( ~ sQ55_spl
| ~ sQ20_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)],[f1275,f1274]) ).
fof(f1283,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ55_spl
| ~ sQ20_spl
| disjoint_s(f17(cx,ct,X0,X1),f18(cx,ct,X0,X1))
| eq_p(X0,X1) ),
inference(resolution,[status(thm)],[f1278,f332]) ).
fof(f1285,plain,
! [X0,X1] :
( ~ sQ20_spl
| subset_collections(f24(X0,X1),X1)
| compact_space(X0,X1) ),
inference(resolution,[status(thm)],[f1244,f254]) ).
fof(f1286,plain,
! [X0,X1] :
( ~ sQ20_spl
| equal_sets(union_of_sets(f21(X0,X1),f22(X0,X1)),X0)
| connected_space(X0,X1) ),
inference(resolution,[status(thm)],[f1243,f236]) ).
fof(f1287,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_spl
| ~ sQ33_spl
| neighborhood(f16(X0,X1,X2,X3),X0,X2,X3)
| limit_point(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1241,f487]) ).
fof(f1288,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ20_spl
| ~ sQ33_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(forward_subsumption_resolution,[status(thm)],[f1236,f487]) ).
fof(f1289,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ55_spl
| ~ sQ20_spl
| ~ sQ33_spl
| eq_p(X4,X0)
| limit_point(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f1288,f1274]) ).
fof(f1290,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_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)],[f1237,f1251]) ).
fof(f1291,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| connected_space(X0,X1)
| ~ 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) ),
inference(resolution,[status(thm)],[f1290,f1286]) ).
fof(f1292,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| connected_space(X0,X1)
| ~ disjoint_s(f21(X0,X1),f22(X0,X1))
| equal_sets(f22(X0,X1),empty_set)
| equal_sets(f21(X0,X1),empty_set)
| separation(f21(X0,X1),f22(X0,X1),X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1291,f1251]) ).
fof(f1293,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| ~ open(relative_complement_sets(X0,X1),X1,X2)
| closed(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f144,f433]) ).
fof(f1294,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| closed(X0,X1,X2) ),
inference(resolution,[status(thm)],[f1293,f1272]) ).
fof(f1295,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ eq_p(f19(X0,X1),f20(X0,X1))
| hausdorff(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f222,f433]) ).
fof(f1296,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ55_spl
| ~ sQ20_spl
| ~ sQ33_spl
| limit_point(f20(X0,X1),X2,X3,X4)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1295,f1289]) ).
fof(f1298,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_spl
| equal_sets(X0,intersection_of_sets(X1,f12(X2,X3,X1,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f1251]) ).
fof(f1299,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ20_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)],[f1298,f1290]) ).
fof(f1300,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ20_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)],[f1299,f1251]) ).
fof(f1301,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ4_spl
| ~ sQ55_spl
| ~ sQ20_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)],[f1300,f1283]) ).
fof(f1304,plain,
! [X0,X1] :
( ~ sQ20_spl
| connected_space(X0,X1)
| disjoint_s(f21(X0,X1),f22(X0,X1)) ),
inference(resolution,[status(thm)],[f238,f1243]) ).
fof(f1305,plain,
! [X0,X1,X2] :
( ~ sQ20_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),X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f1292,f1304]) ).
fof(f1306,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ20_spl
| 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)
| connected_space(X0,X1) ),
inference(resolution,[status(thm)],[f1304,f1300]) ).
fof(f1311,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ4_spl
| ~ sQ55_spl
| ~ sQ20_spl
| eq_p(X3,X4)
| equal_sets(f18(cx,ct,X3,X4),empty_set)
| equal_sets(f17(cx,ct,X3,X4),empty_set)
| ~ connected_space(intersection_of_sets(X0,f12(X1,X2,X0,union_of_sets(f17(cx,ct,X3,X4),f18(cx,ct,X3,X4)))),X5) ),
inference(resolution,[status(thm)],[f243,f1301]) ).
fof(f1312,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ20_spl
| equal_sets(f22(X3,X4),empty_set)
| equal_sets(f21(X3,X4),empty_set)
| connected_space(X3,X4)
| ~ connected_space(intersection_of_sets(X0,f12(X1,X2,X0,union_of_sets(f21(X3,X4),f22(X3,X4)))),X5) ),
inference(resolution,[status(thm)],[f243,f1306]) ).
fof(f1313,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| connected_space(X0,X2)
| equal_sets(f22(X0,X2),empty_set)
| equal_sets(f21(X0,X2),empty_set)
| ~ connected_space(X0,X1) ),
inference(resolution,[status(thm)],[f243,f1305]) ).
fof(f1315,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ20_spl
| connected_space(cx,X0)
| equal_sets(f22(cx,X0),empty_set)
| equal_sets(f21(cx,X0),empty_set) ),
inference(resolution,[status(thm)],[f1313,f372]) ).
fof(f1316,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_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)],[f224,f433]) ).
fof(f1317,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_spl
| ~ sQ33_spl
| limit_point(f20(X0,X1),X3,X0,X1)
| ~ disjoint_s(X2,f16(f20(X0,X1),X3,X0,X1))
| ~ neighborhood(X2,f19(X0,X1),X0,X1)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1316,f1287]) ).
fof(f1331,plain,
! [X0,X1] :
( ~ sQ20_spl
| connected_space(X0,X1)
| ~ equal_sets(f21(X0,X1),empty_set) ),
inference(resolution,[status(thm)],[f228,f1243]) ).
fof(f1332,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ20_spl
| connected_space(cx,X0)
| equal_sets(f22(cx,X0),empty_set) ),
inference(backward_subsumption_resolution,[status(thm)],[f1315,f1331]) ).
fof(f1333,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ20_spl
| equal_sets(f22(X3,X4),empty_set)
| connected_space(X3,X4)
| ~ connected_space(intersection_of_sets(X0,f12(X1,X2,X0,union_of_sets(f21(X3,X4),f22(X3,X4)))),X5) ),
inference(backward_subsumption_resolution,[status(thm)],[f1312,f1331]) ).
fof(f1334,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| connected_space(X0,X2)
| equal_sets(f22(X0,X2),empty_set)
| ~ connected_space(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f1313,f1331]) ).
fof(f1335,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ20_spl
| 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)
| connected_space(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f1306,f1331]) ).
fof(f1336,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| connected_space(X0,X1)
| equal_sets(f22(X0,X1),empty_set)
| separation(f21(X0,X1),f22(X0,X1),X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f1305,f1331]) ).
fof(f1349,plain,
! [X0,X1] :
( ~ sQ20_spl
| connected_space(X0,X1)
| ~ equal_sets(f22(X0,X1),empty_set) ),
inference(resolution,[status(thm)],[f230,f1243]) ).
fof(f1350,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ20_spl
| connected_space(X3,X4)
| ~ connected_space(intersection_of_sets(X0,f12(X1,X2,X0,union_of_sets(f21(X3,X4),f22(X3,X4)))),X5) ),
inference(backward_subsumption_resolution,[status(thm)],[f1333,f1349]) ).
fof(f1351,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ20_spl
| 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)
| connected_space(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f1335,f1349]) ).
fof(f1352,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| connected_space(X0,X1)
| separation(f21(X0,X1),f22(X0,X1),X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f1336,f1349]) ).
fof(f1353,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| connected_space(X0,X2)
| ~ connected_space(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f1334,f1349]) ).
fof(f1354,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ20_spl
| connected_space(cx,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f1332,f1349]) ).
fof(f1366,plain,
! [X0,X1,X2] :
( ~ sQ20_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)],[f161,f1249]) ).
fof(f1367,plain,
! [X0,X1,X2] :
( ~ sQ33_spl
| ~ sQ20_spl
| ~ element_of_collection(X2,X1)
| ~ element_of_set(f7(X0,X1),X2)
| basis(X0,X1) ),
inference(resolution,[status(thm)],[f1366,f487]) ).
fof(f1368,plain,
! [X0,X1,X2] :
( ~ sQ33_spl
| ~ sQ20_spl
| ~ sQ55_spl
| ~ element_of_collection(X2,X1)
| basis(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1367,f1274]) ).
fof(f1369,plain,
! [X0,X1] :
( ~ sQ33_spl
| ~ sQ20_spl
| ~ sQ55_spl
| basis(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1368,f1251]) ).
fof(f1370,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| ~ subset_collections(X1,X0)
| ~ topological_space(X2,X1)
| finer(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f152,f433]) ).
fof(f1371,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| compact_space(X1,X0)
| ~ topological_space(X2,f24(X1,X0))
| finer(X0,f24(X1,X0),X2) ),
inference(resolution,[status(thm)],[f1370,f1285]) ).
fof(f1372,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| compact_space(X1,X0)
| finer(X0,f24(X1,X0),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1371,f433]) ).
fof(f1375,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_spl
| ~ element_of_set(X1,X0)
| ~ open(X0,X2,X3)
| neighborhood(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f201,f433]) ).
fof(f1376,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_spl
| ~ element_of_set(X1,X0)
| neighborhood(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f1375,f1272]) ).
fof(f1377,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_spl
| ~ sQ55_spl
| neighborhood(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1376,f1274]) ).
fof(f1378,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_spl
| ~ sQ55_spl
| ~ disjoint_s(X3,X2)
| ~ neighborhood(X2,f20(X0,X1),X0,X1)
| hausdorff(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f1316,f1377]) ).
fof(f1379,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_spl
| ~ sQ55_spl
| ~ disjoint_s(X2,X3)
| hausdorff(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1378,f1377]) ).
fof(f1380,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_spl
| ~ sQ55_spl
| connected_space(X2,X3)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1379,f1304]) ).
fof(f1381,plain,
! [X0,X1,X2,X3] :
( ~ sQ4_spl
| ~ sQ55_spl
| ~ sQ20_spl
| eq_p(X2,X3)
| hausdorff(X0,X1) ),
inference(resolution,[status(thm)],[f1379,f1283]) ).
fof(f1382,definition,
! [X0,X1] :
( sQ106_spl
<=> hausdorff(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1383,plain,
! [X0,X1] :
( ~ sQ106_spl
| hausdorff(X0,X1) ),
inference(component_clause,[status(thm)],[f1382]) ).
fof(f1385,definition,
! [X2,X3] :
( sQ107_spl
<=> connected_space(X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1388,plain,
( ~ sQ20_spl
| ~ sQ55_spl
| sQ107_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f1380,f1382,f1385,f667,f432]) ).
fof(f1389,definition,
! [X2,X3] :
( sQ108_spl
<=> eq_p(X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1392,plain,
( ~ sQ4_spl
| ~ sQ55_spl
| ~ sQ20_spl
| sQ108_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f1381,f1382,f1389,f432,f667,f331]) ).
fof(f1393,plain,
! [X0,X1,X2,X3] :
( ~ sQ55_spl
| ~ sQ20_spl
| ~ sQ106_spl
| disjoint_s(f17(X2,X3,X0,X1),f18(X2,X3,X0,X1))
| eq_p(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f1278,f1383]) ).
fof(f1394,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ20_spl
| ~ sQ55_spl
| ~ sQ106_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)],[f1393,f1300]) ).
fof(f1397,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ20_spl
| ~ sQ55_spl
| ~ sQ106_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)],[f1394,f243]) ).
fof(f1400,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| ~ equal_sets(union_of_members(X0),X1)
| ~ subset_collections(X0,X2)
| open_covering(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f258,f433]) ).
fof(f1401,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| ~ subset_collections(X0,X2)
| open_covering(X0,X1,X2) ),
inference(resolution,[status(thm)],[f1400,f1249]) ).
fof(f1403,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| compact_space(X0,X1)
| open_covering(f24(X0,X1),X2,X1) ),
inference(resolution,[status(thm)],[f1401,f1285]) ).
fof(f1404,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| subset_collections(f23(X2,X1,f24(X0,X1)),f24(X0,X1))
| ~ compact_space(X2,X1)
| compact_space(X0,X1) ),
inference(resolution,[status(thm)],[f1403,f261]) ).
fof(f1405,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| open_covering(f23(X2,X1,f24(X0,X1)),X2,X1)
| ~ compact_space(X2,X1)
| compact_space(X0,X1) ),
inference(resolution,[status(thm)],[f1403,f262]) ).
fof(f1406,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| finite(f23(X2,X1,f24(X0,X1)))
| ~ compact_space(X2,X1)
| compact_space(X0,X1) ),
inference(resolution,[status(thm)],[f1403,f260]) ).
fof(f1408,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ20_spl
| finite(f23(cx,ct,f24(X0,ct)))
| compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f1406,f345]) ).
fof(f1409,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ20_spl
| open_covering(f23(cx,ct,f24(X0,ct)),cx,ct)
| compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f1405,f345]) ).
fof(f1410,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ20_spl
| subset_collections(f23(cx,ct,f24(X0,ct)),f24(X0,ct))
| compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f1404,f345]) ).
fof(f1411,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ20_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)],[f1409,f261]) ).
fof(f1412,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ20_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)],[f1409,f262]) ).
fof(f1413,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ20_spl
| finite(f23(cx,ct,f23(cx,ct,f24(X0,ct))))
| ~ compact_space(cx,ct)
| compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f1409,f260]) ).
fof(f1414,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ20_spl
| subset_collections(f23(cx,ct,f24(X0,ct)),ct)
| compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f1409,f254]) ).
fof(f1415,definition,
! [X0] :
( sQ109_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,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1416,plain,
! [X0] :
( ~ sQ109_spl
| subset_collections(f23(cx,ct,f23(cx,ct,f24(X0,ct))),f23(cx,ct,f24(X0,ct)))
| compact_space(X0,ct) ),
inference(component_clause,[status(thm)],[f1415]) ).
fof(f1418,plain,
( ~ sQ20_spl
| ~ sQ7_spl
| sQ109_spl ),
inference(split_clause,[status(thm)],[f1411,f1415,f344,f432]) ).
fof(f1419,definition,
! [X0] :
( sQ110_spl
<=> ( open_covering(f23(cx,ct,f23(cx,ct,f24(X0,ct))),cx,ct)
| compact_space(X0,ct) ) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1420,plain,
! [X0] :
( ~ sQ110_spl
| open_covering(f23(cx,ct,f23(cx,ct,f24(X0,ct))),cx,ct)
| compact_space(X0,ct) ),
inference(component_clause,[status(thm)],[f1419]) ).
fof(f1422,plain,
( ~ sQ20_spl
| ~ sQ7_spl
| sQ110_spl ),
inference(split_clause,[status(thm)],[f1412,f1419,f344,f432]) ).
fof(f1423,definition,
! [X0] :
( sQ111_spl
<=> ( finite(f23(cx,ct,f23(cx,ct,f24(X0,ct))))
| compact_space(X0,ct) ) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1424,plain,
! [X0] :
( ~ sQ111_spl
| finite(f23(cx,ct,f23(cx,ct,f24(X0,ct))))
| compact_space(X0,ct) ),
inference(component_clause,[status(thm)],[f1423]) ).
fof(f1426,plain,
( ~ sQ20_spl
| ~ sQ7_spl
| sQ111_spl ),
inference(split_clause,[status(thm)],[f1413,f1423,f344,f432]) ).
fof(f1427,plain,
! [X0,X1,X2] :
( ~ sQ33_spl
| ~ element_of_collection(X2,X1)
| ~ element_of_set(f7(X0,X1),X2)
| ~ equal_sets(union_of_members(X1),X0)
| basis(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f161,f487]) ).
fof(f1428,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ33_spl
| ~ equal_sets(X0,intersection_of_sets(X3,X4))
| ~ element_of_collection(X4,X2)
| ~ topological_space(X1,X2)
| element_of_collection(X0,subspace_topology(X1,X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f175,f487]) ).
fof(f1429,plain,
! [X0,X1,X2,X3] :
( ~ sQ33_spl
| ~ element_of_set(X0,f14(X1,X2,X3,X0))
| ~ topological_space(X2,X3)
| element_of_set(X0,closure(X1,X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f193,f487]) ).
fof(f1430,plain,
! [X0,X1,X2] :
( ~ sQ33_spl
| ~ element_of_collection(X2,X1)
| ~ element_of_set(f11(X1,X0),X2)
| element_of_collection(X0,top_of_basis(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f167,f487]) ).
fof(f1431,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ sQ33_spl
| ~ subset_sets(cx,X1)
| ~ element_of_set(X0,cx)
| element_of_set(X0,interior(X1,cx,ct)) ),
inference(forward_subsumption_resolution,[status(thm)],[f292,f487]) ).
fof(f1432,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ33_spl
| ~ subset_sets(empty_set,X1)
| ~ element_of_set(X0,empty_set)
| element_of_set(X0,interior(X1,cx,ct)) ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f487]) ).
fof(f1433,plain,
! [X0,X1,X2,X3] :
( ~ sQ94_spl
| ~ sQ33_spl
| ~ subset_sets(f1(ct,f11(X1,f1(ct,f11(X0,union_of_members(ct))))),X3)
| ~ element_of_set(X2,f1(ct,f11(X1,f1(ct,f11(X0,union_of_members(ct))))))
| element_of_set(X2,interior(X3,cx,ct))
| element_of_collection(f1(ct,f11(X0,union_of_members(ct))),top_of_basis(X1))
| element_of_collection(union_of_members(ct),top_of_basis(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1111,f487]) ).
fof(f1434,plain,
! [X0,X1,X2,X3] :
( ~ sQ79_spl
| ~ sQ33_spl
| ~ subset_sets(f1(ct,f11(X1,f2(ct,X0))),X3)
| ~ element_of_set(X2,f1(ct,f11(X1,f2(ct,X0))))
| element_of_set(X2,interior(X3,cx,ct))
| element_of_collection(f2(ct,X0),top_of_basis(X1))
| element_of_set(X0,intersection_of_members(ct)) ),
inference(forward_subsumption_resolution,[status(thm)],[f892,f487]) ).
fof(f1435,definition,
! [X1,X2] :
( sQ112_spl
<=> element_of_set(X1,interior(X2,cx,ct)) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1438,plain,
( ~ sQ15_spl
| ~ sQ81_spl
| ~ sQ33_spl
| sQ112_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f1258,f974,f1435,f486,f913,f384]) ).
fof(f1439,plain,
! [X0,X1,X2,X3] :
( ~ sQ106_spl
| disjoint_s(f17(X1,X3,X0,X2),f18(X1,X3,X0,X2))
| eq_p(X0,X2)
| ~ element_of_set(X2,X1)
| ~ element_of_set(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f219,f1383]) ).
fof(f1440,plain,
! [X0,X1,X2,X3] :
( ~ sQ106_spl
| neighborhood(f18(X1,X3,X0,X2),X2,X1,X3)
| eq_p(X0,X2)
| ~ element_of_set(X2,X1)
| ~ element_of_set(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f218,f1383]) ).
fof(f1441,plain,
! [X0,X1,X2,X3] :
( ~ sQ106_spl
| neighborhood(f17(X1,X3,X0,X2),X0,X1,X3)
| eq_p(X0,X2)
| ~ element_of_set(X2,X1)
| ~ element_of_set(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f217,f1383]) ).
fof(f1442,plain,
! [X0,X1] :
( ~ sQ106_spl
| topological_space(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f216,f1383]) ).
fof(f1443,plain,
( sQ20_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f416,f443,f432]) ).
fof(f1444,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ33_spl
| eq_p(X4,X0)
| ~ element_of_set(X4,intersection_of_sets(f16(X0,X1,X2,X3),X1))
| ~ topological_space(X2,X3)
| limit_point(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f487]) ).
fof(f1445,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ33_spl
| ~ open(X4,X2,X3)
| ~ subset_sets(X4,X1)
| ~ element_of_set(X0,X4)
| ~ topological_space(X2,X3)
| element_of_set(X0,interior(X1,X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f487]) ).
fof(f1446,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ33_spl
| 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)
| ~ topological_space(X2,X3)
| limit_point(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f847,f487]) ).
fof(f1447,plain,
! [X0,X1,X2,X3] :
( ~ sQ33_spl
| closed(f14(X1,X2,X3,X0),X2,X3)
| ~ topological_space(X2,X3)
| element_of_set(X0,closure(X1,X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f487]) ).
fof(f1448,plain,
! [X0,X1,X2,X3] :
( ~ sQ33_spl
| neighborhood(f16(X0,X1,X2,X3),X0,X2,X3)
| ~ topological_space(X2,X3)
| limit_point(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f208,f487]) ).
fof(f1449,plain,
! [X0,X1,X2,X3] :
( ~ sQ106_spl
| neighborhood(f17(X0,X3,f11(X1,X0),X2),f11(X1,X0),X0,X3)
| eq_p(f11(X1,X0),X2)
| ~ element_of_set(X2,X0)
| element_of_collection(X0,top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f165,f1441]) ).
fof(f1450,plain,
! [X0,X1,X2,X3] :
( ~ sQ106_spl
| neighborhood(f18(X0,X3,f11(X1,X0),X2),X2,X0,X3)
| eq_p(f11(X1,X0),X2)
| ~ element_of_set(X2,X0)
| element_of_collection(X0,top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f165,f1440]) ).
fof(f1451,plain,
! [X0,X1,X2,X3] :
( ~ sQ106_spl
| disjoint_s(f17(X0,X3,f11(X1,X0),X2),f18(X0,X3,f11(X1,X0),X2))
| eq_p(f11(X1,X0),X2)
| ~ element_of_set(X2,X0)
| element_of_collection(X0,top_of_basis(X1)) ),
inference(resolution,[status(thm)],[f165,f1439]) ).
fof(f1482,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_spl
| ~ disjoint_s(X0,X1)
| ~ equal_sets(union_of_sets(X0,X1),X2)
| equal_sets(X1,empty_set)
| equal_sets(X0,empty_set)
| separation(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1290,f1251]) ).
fof(f1487,plain,
( ~ sQ8_spl
| subset_collections(f23(cx,ct,f24(cx,ct)),f24(cx,ct))
| ~ compact_space(cx,ct) ),
inference(resolution,[status(thm)],[f348,f261]) ).
fof(f1488,plain,
( ~ sQ8_spl
| open_covering(f23(cx,ct,f24(cx,ct)),cx,ct)
| ~ compact_space(cx,ct) ),
inference(resolution,[status(thm)],[f348,f262]) ).
fof(f1489,plain,
( ~ sQ8_spl
| finite(f23(cx,ct,f24(cx,ct)))
| ~ compact_space(cx,ct) ),
inference(resolution,[status(thm)],[f348,f260]) ).
fof(f1490,plain,
( ~ sQ8_spl
| subset_collections(f24(cx,ct),ct) ),
inference(resolution,[status(thm)],[f348,f254]) ).
fof(f1491,definition,
( sQ113_spl
<=> subset_collections(f23(cx,ct,f24(cx,ct)),f24(cx,ct)) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f1494,plain,
( ~ sQ8_spl
| sQ113_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1487,f344,f1491,f347]) ).
fof(f1495,definition,
( sQ114_spl
<=> open_covering(f23(cx,ct,f24(cx,ct)),cx,ct) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1498,plain,
( ~ sQ8_spl
| sQ114_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1488,f344,f1495,f347]) ).
fof(f1499,definition,
( sQ115_spl
<=> finite(f23(cx,ct,f24(cx,ct))) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f1502,plain,
( ~ sQ8_spl
| sQ115_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1489,f344,f1499,f347]) ).
fof(f1503,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ8_spl
| open_covering(f24(cx,ct),X0,ct) ),
inference(resolution,[status(thm)],[f1490,f1401]) ).
fof(f1504,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ8_spl
| subset_collections(f23(X0,ct,f24(cx,ct)),f24(cx,ct))
| ~ compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f1503,f261]) ).
fof(f1505,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ8_spl
| open_covering(f23(X0,ct,f24(cx,ct)),X0,ct)
| ~ compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f1503,f262]) ).
fof(f1506,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ8_spl
| finite(f23(X0,ct,f24(cx,ct)))
| ~ compact_space(X0,ct) ),
inference(resolution,[status(thm)],[f1503,f260]) ).
fof(f1509,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| ~ sQ106_spl
| ~ subset_collections(X1,X0)
| finer(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1370,f1442]) ).
fof(f1510,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ20_spl
| ~ sQ106_spl
| finer(ct,f24(cx,ct),X0) ),
inference(resolution,[status(thm)],[f1509,f1490]) ).
fof(f1513,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ20_spl
| ~ sQ55_spl
| ~ eq_p(f15(X0,X1,X2,X3,X4),X0)
| ~ limit_point(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f207,f1377]) ).
fof(f1514,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ55_spl
| ~ sQ20_spl
| ~ sQ33_spl
| limit_point(X0,X4,X5,X6)
| ~ limit_point(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f1513,f1289]) ).
fof(f1515,plain,
! [X0,X1,X2,X3] :
( ~ sQ44_spl
| ~ sQ55_spl
| ~ sQ20_spl
| ~ sQ33_spl
| limit_point(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f1514,f562]) ).
fof(f1517,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ20_spl
| ~ sQ55_spl
| ~ sQ44_spl
| ~ sQ33_spl
| ~ eq_p(f15(X0,X1,X2,X3,X4),X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f1513,f1515]) ).
fof(f1518,plain,
! [X0,X1,X2] :
( ~ sQ106_spl
| ~ connected_space(X0,subspace_topology(X1,X2,X0))
| ~ subset_sets(X0,X1)
| connected_set(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f250,f1442]) ).
fof(f1519,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ20_spl
| ~ sQ106_spl
| ~ subset_sets(cx,X0)
| connected_set(cx,X0,X1) ),
inference(resolution,[status(thm)],[f1518,f1354]) ).
fof(f1520,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ20_spl
| ~ sQ106_spl
| ~ sQ33_spl
| connected_set(cx,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1519,f487]) ).
fof(f1521,plain,
! [X0,X1,X2] :
( ~ sQ106_spl
| ~ open_covering(X2,X0,X1)
| ~ subset_collections(X2,f24(X0,X1))
| ~ finite(X2)
| compact_space(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f264,f1442]) ).
fof(f1522,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| ~ sQ106_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)],[f1521,f1285]) ).
fof(f1524,plain,
! [X0,X1,X2] :
( ~ sQ106_spl
| ~ compact_space(X0,subspace_topology(X1,X2,X0))
| ~ subset_sets(X0,X1)
| compact_set(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f270,f1442]) ).
fof(model,axiom,
( sQ0_spl
| sQ1_spl
| sQ2_spl
| sQ3_spl
| sQ4_spl
| ~ sQ7_spl
| sQ8_spl
| sQ9_spl
| sQ13_spl
| sQ15_spl
| sQ20_spl
| sQ23_spl
| sQ33_spl
| sQ40_spl
| sQ41_spl
| sQ42_spl
| sQ44_spl
| ~ sQ45_spl
| sQ46_spl
| sQ48_spl
| ~ sQ54_spl
| sQ55_spl
| sQ56_spl
| sQ57_spl
| sQ61_spl
| sQ69_spl
| sQ70_spl
| sQ71_spl
| sQ74_spl
| sQ77_spl
| sQ79_spl
| sQ81_spl
| sQ82_spl
| sQ84_spl
| sQ94_spl
| sQ99_spl
| sQ106_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 12:38:52 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 2.67/0.78 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 2.67/0.78 % SZS output start Saturation for theBenchmark
% See solution above
% 1.90/0.80 % Elapsed time: 0.441509 seconds
% 1.90/0.80 % CPU time: 3.117335 seconds
% 1.90/0.80 % Total memory used: 68.669 MB
% 1.90/0.80 % Net memory used: 60.931 MB
%------------------------------------------------------------------------------