TSTP Solution File: TOP004-1 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : TOP004-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 21:26:57 EDT 2022
% Result : Unsatisfiable 0.21s 0.49s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 115
% Syntax : Number of formulae : 914 ( 33 unt; 0 def)
% Number of atoms : 2963 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 3890 (1841 ~;2049 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 22 usr; 1 prp; 0-4 aty)
% Number of functors : 37 ( 37 usr; 3 con; 0-5 aty)
% Number of variables : 2942 ( 253 sgn1083 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
% Start CNF derivation
% End CNF derivation
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X15,X13,X1,X2,X14] :
( ~ limit_point(X15,X13,X1,X2)
| ~ neighborhood(X14,X15,X1,X2)
| ~ eq_p(f15(X15,X13,X1,X2,X14),X15) ),
file('<stdin>',limit_point_66) ).
fof(c_0_1,axiom,
! [X15,X13,X1,X2,X14] :
( ~ limit_point(X15,X13,X1,X2)
| ~ neighborhood(X14,X15,X1,X2)
| element_of_set(f15(X15,X13,X1,X2,X14),intersection_of_sets(X14,X13)) ),
file('<stdin>',limit_point_65) ).
fof(c_0_2,axiom,
! [X13,X1,X6,X22,X23] :
( ~ basis(X1,X6)
| ~ element_of_set(X13,X1)
| ~ element_of_collection(X23,X6)
| ~ element_of_collection(X22,X6)
| ~ element_of_set(X13,intersection_of_sets(X23,X22))
| subset_sets(f6(X1,X6,X13,X23,X22),intersection_of_sets(X23,X22)) ),
file('<stdin>',basis_for_topology_31) ).
fof(c_0_3,axiom,
! [X13,X1,X6,X22,X23] :
( ~ basis(X1,X6)
| ~ element_of_set(X13,X1)
| ~ element_of_collection(X23,X6)
| ~ element_of_collection(X22,X6)
| ~ element_of_set(X13,intersection_of_sets(X23,X22))
| element_of_set(X13,f6(X1,X6,X13,X23,X22)) ),
file('<stdin>',basis_for_topology_29) ).
fof(c_0_4,axiom,
! [X13,X1,X6,X22,X23] :
( ~ basis(X1,X6)
| ~ element_of_set(X13,X1)
| ~ element_of_collection(X23,X6)
| ~ element_of_collection(X22,X6)
| ~ element_of_set(X13,intersection_of_sets(X23,X22))
| element_of_collection(f6(X1,X6,X13,X23,X22),X6) ),
file('<stdin>',basis_for_topology_30) ).
fof(c_0_5,axiom,
! [X15,X13,X1,X2,X16] :
( limit_point(X15,X13,X1,X2)
| ~ topological_space(X1,X2)
| ~ subset_sets(X13,X1)
| ~ element_of_set(X16,intersection_of_sets(f16(X15,X13,X1,X2),X13))
| eq_p(X16,X15) ),
file('<stdin>',limit_point_68) ).
fof(c_0_6,axiom,
! [X13,X1,X2,X14] :
( ~ element_of_collection(X14,subspace_topology(X1,X2,X13))
| equal_sets(X14,intersection_of_sets(X13,f12(X1,X2,X13,X14))) ),
file('<stdin>',subspace_topology_45) ).
fof(c_0_7,axiom,
! [X11,X12,X1,X2] :
( ~ hausdorff(X1,X2)
| ~ element_of_set(X12,X1)
| ~ element_of_set(X11,X1)
| eq_p(X12,X11)
| disjoint_s(f17(X1,X2,X12,X11),f18(X1,X2,X12,X11)) ),
file('<stdin>',hausdorff_76) ).
fof(c_0_8,axiom,
! [X15,X13,X1,X2] :
( limit_point(X15,X13,X1,X2)
| ~ topological_space(X1,X2)
| ~ subset_sets(X13,X1)
| neighborhood(f16(X15,X13,X1,X2),X15,X1,X2) ),
file('<stdin>',limit_point_67) ).
fof(c_0_9,axiom,
! [X13,X1,X2,X14] :
( element_of_set(X14,closure(X13,X1,X2))
| ~ topological_space(X1,X2)
| ~ subset_sets(X13,X1)
| ~ element_of_set(X14,f14(X13,X1,X2,X14)) ),
file('<stdin>',closure_58) ).
fof(c_0_10,axiom,
! [X1,X2,X9,X10] :
( hausdorff(X1,X2)
| ~ topological_space(X1,X2)
| ~ neighborhood(X10,f19(X1,X2),X1,X2)
| ~ neighborhood(X9,f20(X1,X2),X1,X2)
| ~ disjoint_s(X10,X9) ),
file('<stdin>',hausdorff_80) ).
fof(c_0_11,axiom,
! [X11,X12,X1,X2] :
( ~ hausdorff(X1,X2)
| ~ element_of_set(X12,X1)
| ~ element_of_set(X11,X1)
| eq_p(X12,X11)
| neighborhood(f17(X1,X2,X12,X11),X12,X1,X2) ),
file('<stdin>',hausdorff_74) ).
fof(c_0_12,axiom,
! [X11,X12,X1,X2] :
( ~ hausdorff(X1,X2)
| ~ element_of_set(X12,X1)
| ~ element_of_set(X11,X1)
| eq_p(X12,X11)
| neighborhood(f18(X1,X2,X12,X11),X11,X1,X2) ),
file('<stdin>',hausdorff_75) ).
fof(c_0_13,axiom,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,interior(X13,X1,X2))
| open(f13(X13,X1,X2,X14),X1,X2) ),
file('<stdin>',interior_51) ).
fof(c_0_14,axiom,
! [X13,X1,X2,X14] :
( element_of_set(X14,closure(X13,X1,X2))
| ~ topological_space(X1,X2)
| ~ subset_sets(X13,X1)
| closed(f14(X13,X1,X2,X14),X1,X2) ),
file('<stdin>',closure_57) ).
fof(c_0_15,axiom,
! [X13,X1,X2,X14] :
( ~ element_of_collection(X14,subspace_topology(X1,X2,X13))
| element_of_collection(f12(X1,X2,X13,X14),X2) ),
file('<stdin>',subspace_topology_44) ).
fof(c_0_16,axiom,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,interior(X13,X1,X2))
| element_of_set(X14,f13(X13,X1,X2,X14)) ),
file('<stdin>',interior_49) ).
fof(c_0_17,axiom,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,interior(X13,X1,X2))
| subset_sets(f13(X13,X1,X2,X14),X13) ),
file('<stdin>',interior_50) ).
fof(c_0_18,axiom,
! [X13,X1,X2,X14] :
( element_of_set(X14,closure(X13,X1,X2))
| ~ topological_space(X1,X2)
| ~ subset_sets(X13,X1)
| subset_sets(X13,f14(X13,X1,X2,X14)) ),
file('<stdin>',closure_56) ).
fof(c_0_19,axiom,
! [X13,X1,X2,X14] :
( element_of_set(X14,boundary(X13,X1,X2))
| ~ topological_space(X1,X2)
| ~ element_of_set(X14,closure(X13,X1,X2))
| ~ element_of_set(X14,closure(relative_complement_sets(X13,X1),X1,X2)) ),
file('<stdin>',boundary_72) ).
fof(c_0_20,axiom,
! [X13,X1,X2,X14] :
( ~ neighborhood(X14,X13,X1,X2)
| open(X14,X1,X2) ),
file('<stdin>',neighborhood_60) ).
fof(c_0_21,axiom,
! [X1,X2] :
( topological_space(X1,X2)
| ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2) ),
file('<stdin>',topological_space_17) ).
fof(c_0_22,axiom,
! [X1,X2,X7,X8] :
( ~ separation(X8,X7,X1,X2)
| equal_sets(union_of_sets(X8,X7),X1) ),
file('<stdin>',separation_86) ).
fof(c_0_23,axiom,
! [X1,X2,X7,X8] :
( separation(X8,X7,X1,X2)
| ~ topological_space(X1,X2)
| equal_sets(X8,empty_set)
| equal_sets(X7,empty_set)
| ~ element_of_collection(X8,X2)
| ~ element_of_collection(X7,X2)
| ~ equal_sets(union_of_sets(X8,X7),X1)
| ~ disjoint_s(X8,X7) ),
file('<stdin>',separation_88) ).
fof(c_0_24,axiom,
! [X1,X2,X7,X8] :
( ~ connected_space(X1,X2)
| ~ separation(X8,X7,X1,X2) ),
file('<stdin>',connected_space_90) ).
fof(c_0_25,axiom,
! [X1,X2,X7,X8] :
( ~ separation(X8,X7,X1,X2)
| ~ equal_sets(X8,empty_set) ),
file('<stdin>',separation_82) ).
fof(c_0_26,axiom,
! [X1,X2,X7,X8] :
( ~ separation(X8,X7,X1,X2)
| ~ equal_sets(X7,empty_set) ),
file('<stdin>',separation_83) ).
fof(c_0_27,axiom,
! [X13,X1,X2,X14] :
( ~ neighborhood(X14,X13,X1,X2)
| topological_space(X1,X2) ),
file('<stdin>',neighborhood_59) ).
fof(c_0_28,axiom,
! [X13,X1,X2,X14] :
( ~ neighborhood(X14,X13,X1,X2)
| element_of_set(X13,X14) ),
file('<stdin>',neighborhood_61) ).
fof(c_0_29,axiom,
! [X15,X13,X1,X2] :
( ~ limit_point(X15,X13,X1,X2)
| topological_space(X1,X2) ),
file('<stdin>',limit_point_63) ).
fof(c_0_30,axiom,
! [X15,X13,X1,X2] :
( ~ limit_point(X15,X13,X1,X2)
| subset_sets(X13,X1) ),
file('<stdin>',limit_point_64) ).
fof(c_0_31,axiom,
! [X1,X2,X7,X8] :
( ~ separation(X8,X7,X1,X2)
| topological_space(X1,X2) ),
file('<stdin>',separation_81) ).
fof(c_0_32,axiom,
! [X1,X2,X7,X8] :
( ~ separation(X8,X7,X1,X2)
| element_of_collection(X8,X2) ),
file('<stdin>',separation_84) ).
fof(c_0_33,axiom,
! [X1,X2,X7,X8] :
( ~ separation(X8,X7,X1,X2)
| element_of_collection(X7,X2) ),
file('<stdin>',separation_85) ).
fof(c_0_34,axiom,
! [X1,X2,X7,X8] :
( ~ separation(X8,X7,X1,X2)
| disjoint_s(X8,X7) ),
file('<stdin>',separation_87) ).
fof(c_0_35,axiom,
! [X13,X1,X2,X14] :
( neighborhood(X14,X13,X1,X2)
| ~ topological_space(X1,X2)
| ~ open(X14,X1,X2)
| ~ element_of_set(X13,X14) ),
file('<stdin>',neighborhood_62) ).
fof(c_0_36,axiom,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,boundary(X13,X1,X2))
| element_of_set(X14,closure(relative_complement_sets(X13,X1),X1,X2)) ),
file('<stdin>',boundary_71) ).
fof(c_0_37,axiom,
! [X1,X6,X21] :
( basis(X1,X6)
| ~ equal_sets(union_of_members(X6),X1)
| ~ element_of_set(f7(X1,X6),X21)
| ~ element_of_collection(X21,X6)
| ~ subset_sets(X21,intersection_of_sets(f8(X1,X6),f9(X1,X6))) ),
file('<stdin>',basis_for_topology_36) ).
fof(c_0_38,axiom,
! [X1,X2] :
( topological_space(X1,X2)
| ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| subset_collections(f5(X1,X2),X2) ),
file('<stdin>',topological_space_16) ).
fof(c_0_39,axiom,
! [X1,X2] :
( connected_space(X1,X2)
| ~ topological_space(X1,X2)
| separation(f21(X1,X2),f22(X1,X2),X1,X2) ),
file('<stdin>',connected_space_91) ).
fof(c_0_40,axiom,
! [X13,X1,X2,X17,X14] :
( ~ element_of_set(X14,closure(X13,X1,X2))
| ~ subset_sets(X13,X17)
| ~ closed(X17,X1,X2)
| element_of_set(X14,X17) ),
file('<stdin>',closure_55) ).
fof(c_0_41,axiom,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,boundary(X13,X1,X2))
| element_of_set(X14,closure(X13,X1,X2)) ),
file('<stdin>',boundary_70) ).
fof(c_0_42,axiom,
! [X13,X1,X2,X18,X14] :
( element_of_set(X14,interior(X13,X1,X2))
| ~ topological_space(X1,X2)
| ~ subset_sets(X13,X1)
| ~ element_of_set(X14,X18)
| ~ subset_sets(X18,X13)
| ~ open(X18,X1,X2) ),
file('<stdin>',interior_52) ).
fof(c_0_43,axiom,
! [X1,X2,X3] :
( connected_set(X3,X1,X2)
| ~ topological_space(X1,X2)
| ~ subset_sets(X3,X1)
| ~ connected_space(X3,subspace_topology(X1,X2,X3)) ),
file('<stdin>',connected_set_95) ).
fof(c_0_44,axiom,
! [X1,X2,X3] :
( compact_set(X3,X1,X2)
| ~ topological_space(X1,X2)
| ~ subset_sets(X3,X1)
| ~ compact_space(X3,subspace_topology(X1,X2,X3)) ),
file('<stdin>',compact_set_109) ).
fof(c_0_45,axiom,
! [X1,X2,X5] :
( ~ compact_space(X1,X2)
| ~ open_covering(X5,X1,X2)
| open_covering(f23(X1,X2,X5),X1,X2) ),
file('<stdin>',compact_space_103) ).
fof(c_0_46,axiom,
! [X13,X1,X2,X19,X14] :
( element_of_collection(X14,subspace_topology(X1,X2,X13))
| ~ topological_space(X1,X2)
| ~ subset_sets(X13,X1)
| ~ element_of_collection(X19,X2)
| ~ equal_sets(X14,intersection_of_sets(X13,X19)) ),
file('<stdin>',subspace_topology_46) ).
fof(c_0_47,axiom,
! [X1,X2] :
( topological_space(X1,X2)
| ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| element_of_collection(f3(X1,X2),X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2) ),
file('<stdin>',topological_space_13) ).
fof(c_0_48,axiom,
! [X1,X2] :
( topological_space(X1,X2)
| ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| element_of_collection(f4(X1,X2),X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2) ),
file('<stdin>',topological_space_15) ).
fof(c_0_49,axiom,
! [X1,X2,X5] :
( ~ compact_space(X1,X2)
| ~ open_covering(X5,X1,X2)
| subset_collections(f23(X1,X2,X5),X5) ),
file('<stdin>',compact_space_102) ).
fof(c_0_50,axiom,
! [X1,X2,X5] :
( ~ compact_space(X1,X2)
| ~ open_covering(X5,X1,X2)
| finite(f23(X1,X2,X5)) ),
file('<stdin>',compact_space_101) ).
fof(c_0_51,axiom,
! [X1,X6] :
( basis(X1,X6)
| ~ equal_sets(union_of_members(X6),X1)
| element_of_set(f7(X1,X6),intersection_of_sets(f8(X1,X6),f9(X1,X6))) ),
file('<stdin>',basis_for_topology_35) ).
fof(c_0_52,axiom,
! [X1,X2,X3] :
( ~ connected_set(X3,X1,X2)
| connected_space(X3,subspace_topology(X1,X2,X3)) ),
file('<stdin>',connected_set_94) ).
fof(c_0_53,axiom,
! [X1,X2,X3] :
( ~ compact_set(X3,X1,X2)
| compact_space(X3,subspace_topology(X1,X2,X3)) ),
file('<stdin>',compact_set_108) ).
fof(c_0_54,axiom,
! [X13,X1,X2,X14] :
( ~ element_of_collection(X14,subspace_topology(X1,X2,X13))
| topological_space(X1,X2) ),
file('<stdin>',subspace_topology_42) ).
fof(c_0_55,axiom,
! [X13,X1,X2,X14] :
( ~ element_of_collection(X14,subspace_topology(X1,X2,X13))
| subset_sets(X13,X1) ),
file('<stdin>',subspace_topology_43) ).
fof(c_0_56,axiom,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,interior(X13,X1,X2))
| topological_space(X1,X2) ),
file('<stdin>',interior_47) ).
fof(c_0_57,axiom,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,interior(X13,X1,X2))
| subset_sets(X13,X1) ),
file('<stdin>',interior_48) ).
fof(c_0_58,axiom,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,closure(X13,X1,X2))
| topological_space(X1,X2) ),
file('<stdin>',closure_53) ).
fof(c_0_59,axiom,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,closure(X13,X1,X2))
| subset_sets(X13,X1) ),
file('<stdin>',closure_54) ).
fof(c_0_60,axiom,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,boundary(X13,X1,X2))
| topological_space(X1,X2) ),
file('<stdin>',boundary_69) ).
fof(c_0_61,axiom,
! [X1,X2,X14] :
( closed(X14,X1,X2)
| ~ topological_space(X1,X2)
| ~ open(relative_complement_sets(X14,X1),X1,X2) ),
file('<stdin>',closed_set_23) ).
fof(c_0_62,axiom,
! [X1,X2,X4] :
( compact_space(X1,X2)
| ~ topological_space(X1,X2)
| ~ finite(X4)
| ~ subset_collections(X4,f24(X1,X2))
| ~ open_covering(X4,X1,X2) ),
file('<stdin>',compact_space_105) ).
fof(c_0_63,axiom,
! [X1,X6,X14] :
( ~ element_of_collection(X14,top_of_basis(X6))
| ~ element_of_set(X1,X14)
| element_of_set(X1,f10(X6,X14,X1)) ),
file('<stdin>',topology_generated_37) ).
fof(c_0_64,axiom,
! [X1,X6,X14] :
( ~ element_of_collection(X14,top_of_basis(X6))
| ~ element_of_set(X1,X14)
| element_of_collection(f10(X6,X14,X1),X6) ),
file('<stdin>',topology_generated_38) ).
fof(c_0_65,axiom,
! [X1,X6,X14] :
( ~ element_of_collection(X14,top_of_basis(X6))
| ~ element_of_set(X1,X14)
| subset_sets(f10(X6,X14,X1),X14) ),
file('<stdin>',topology_generated_39) ).
fof(c_0_66,axiom,
! [X1,X2] :
( topological_space(X1,X2)
| ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| element_of_collection(f3(X1,X2),X2)
| subset_collections(f5(X1,X2),X2) ),
file('<stdin>',topological_space_12) ).
fof(c_0_67,axiom,
! [X1,X2] :
( topological_space(X1,X2)
| ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| element_of_collection(f4(X1,X2),X2)
| subset_collections(f5(X1,X2),X2) ),
file('<stdin>',topological_space_14) ).
fof(c_0_68,axiom,
! [X1,X2,X14] :
( ~ closed(X14,X1,X2)
| open(relative_complement_sets(X14,X1),X1,X2) ),
file('<stdin>',closed_set_22) ).
fof(c_0_69,axiom,
! [X1,X2] :
( hausdorff(X1,X2)
| ~ topological_space(X1,X2)
| ~ eq_p(f19(X1,X2),f20(X1,X2)) ),
file('<stdin>',hausdorff_79) ).
fof(c_0_70,axiom,
! [X1,X2,X6] :
( open_covering(X6,X1,X2)
| ~ topological_space(X1,X2)
| ~ subset_collections(X6,X2)
| ~ equal_sets(union_of_members(X6),X1) ),
file('<stdin>',open_covering_99) ).
fof(c_0_71,axiom,
! [X6,X20,X14] :
( element_of_collection(X14,top_of_basis(X6))
| ~ element_of_set(f11(X6,X14),X20)
| ~ element_of_collection(X20,X6)
| ~ subset_sets(X20,X14) ),
file('<stdin>',topology_generated_41) ).
fof(c_0_72,axiom,
! [X1,X2,X24] :
( finer(X2,X24,X1)
| ~ topological_space(X1,X2)
| ~ topological_space(X1,X24)
| ~ subset_collections(X24,X2) ),
file('<stdin>',finer_topology_27) ).
fof(c_0_73,axiom,
! [X1,X2] :
( compact_space(X1,X2)
| ~ topological_space(X1,X2)
| open_covering(f24(X1,X2),X1,X2) ),
file('<stdin>',compact_space_104) ).
fof(c_0_74,axiom,
! [X15,X13,X1,X2] :
( ~ topological_space(X1,X2)
| ~ element_of_collection(X13,X2)
| ~ element_of_collection(X15,X2)
| element_of_collection(intersection_of_sets(X13,X15),X2) ),
file('<stdin>',topological_space_10) ).
fof(c_0_75,axiom,
! [X1,X2,X6] :
( ~ open_covering(X6,X1,X2)
| equal_sets(union_of_members(X6),X1) ),
file('<stdin>',open_covering_98) ).
fof(c_0_76,axiom,
! [X1,X2,X14] :
( ~ open(X14,X1,X2)
| topological_space(X1,X2) ),
file('<stdin>',open_set_18) ).
fof(c_0_77,axiom,
! [X1,X2,X14] :
( ~ open(X14,X1,X2)
| element_of_collection(X14,X2) ),
file('<stdin>',open_set_19) ).
fof(c_0_78,axiom,
! [X1,X2,X14] :
( ~ closed(X14,X1,X2)
| topological_space(X1,X2) ),
file('<stdin>',closed_set_21) ).
fof(c_0_79,axiom,
! [X1,X2,X24] :
( ~ finer(X2,X24,X1)
| topological_space(X1,X2) ),
file('<stdin>',finer_topology_24) ).
fof(c_0_80,axiom,
! [X1,X2,X24] :
( ~ finer(X2,X24,X1)
| topological_space(X1,X24) ),
file('<stdin>',finer_topology_25) ).
fof(c_0_81,axiom,
! [X1,X2,X24] :
( ~ finer(X2,X24,X1)
| subset_collections(X24,X2) ),
file('<stdin>',finer_topology_26) ).
fof(c_0_82,axiom,
! [X1,X2,X3] :
( ~ connected_set(X3,X1,X2)
| topological_space(X1,X2) ),
file('<stdin>',connected_set_92) ).
fof(c_0_83,axiom,
! [X1,X2,X3] :
( ~ connected_set(X3,X1,X2)
| subset_sets(X3,X1) ),
file('<stdin>',connected_set_93) ).
fof(c_0_84,axiom,
! [X1,X2,X6] :
( ~ open_covering(X6,X1,X2)
| topological_space(X1,X2) ),
file('<stdin>',open_covering_96) ).
fof(c_0_85,axiom,
! [X1,X2,X6] :
( ~ open_covering(X6,X1,X2)
| subset_collections(X6,X2) ),
file('<stdin>',open_covering_97) ).
fof(c_0_86,axiom,
! [X1,X2,X3] :
( ~ compact_set(X3,X1,X2)
| topological_space(X1,X2) ),
file('<stdin>',compact_set_106) ).
fof(c_0_87,axiom,
! [X1,X2,X3] :
( ~ compact_set(X3,X1,X2)
| subset_sets(X3,X1) ),
file('<stdin>',compact_set_107) ).
fof(c_0_88,axiom,
! [X1,X2,X14] :
( open(X14,X1,X2)
| ~ topological_space(X1,X2)
| ~ element_of_collection(X14,X2) ),
file('<stdin>',open_set_20) ).
fof(c_0_89,axiom,
! [X1,X6] :
( basis(X1,X6)
| ~ equal_sets(union_of_members(X6),X1)
| element_of_set(f7(X1,X6),X1) ),
file('<stdin>',basis_for_topology_32) ).
fof(c_0_90,axiom,
! [X1,X6] :
( basis(X1,X6)
| ~ equal_sets(union_of_members(X6),X1)
| element_of_collection(f8(X1,X6),X6) ),
file('<stdin>',basis_for_topology_33) ).
fof(c_0_91,axiom,
! [X1,X6] :
( basis(X1,X6)
| ~ equal_sets(union_of_members(X6),X1)
| element_of_collection(f9(X1,X6),X6) ),
file('<stdin>',basis_for_topology_34) ).
fof(c_0_92,axiom,
! [X6,X14] :
( element_of_set(X14,intersection_of_members(X6))
| ~ element_of_set(X14,f2(X6,X14)) ),
file('<stdin>',intersection_of_members_6) ).
fof(c_0_93,axiom,
! [X1,X2] :
( hausdorff(X1,X2)
| ~ topological_space(X1,X2)
| element_of_set(f19(X1,X2),X1) ),
file('<stdin>',hausdorff_77) ).
fof(c_0_94,axiom,
! [X1,X2] :
( hausdorff(X1,X2)
| ~ topological_space(X1,X2)
| element_of_set(f20(X1,X2),X1) ),
file('<stdin>',hausdorff_78) ).
fof(c_0_95,axiom,
! [X6,X14] :
( ~ element_of_set(X14,union_of_members(X6))
| element_of_set(X14,f1(X6,X14)) ),
file('<stdin>',union_of_members_1) ).
fof(c_0_96,axiom,
! [X6,X14] :
( ~ element_of_set(X14,union_of_members(X6))
| element_of_collection(f1(X6,X14),X6) ),
file('<stdin>',union_of_members_2) ).
fof(c_0_97,axiom,
! [X6,X3,X14] :
( ~ element_of_set(X14,intersection_of_members(X6))
| ~ element_of_collection(X3,X6)
| element_of_set(X14,X3) ),
file('<stdin>',intersection_of_members_4) ).
fof(c_0_98,axiom,
! [X6,X25,X14] :
( element_of_set(X14,union_of_members(X6))
| ~ element_of_set(X14,X25)
| ~ element_of_collection(X25,X6) ),
file('<stdin>',union_of_members_3) ).
fof(c_0_99,axiom,
! [X1,X2,X6] :
( ~ topological_space(X1,X2)
| ~ subset_collections(X6,X2)
| element_of_collection(union_of_members(X6),X2) ),
file('<stdin>',topological_space_11) ).
fof(c_0_100,axiom,
! [X6,X14] :
( element_of_set(X14,intersection_of_members(X6))
| element_of_collection(f2(X6,X14),X6) ),
file('<stdin>',intersection_of_members_5) ).
fof(c_0_101,axiom,
! [X6,X14] :
( element_of_collection(X14,top_of_basis(X6))
| element_of_set(f11(X6,X14),X14) ),
file('<stdin>',topology_generated_40) ).
fof(c_0_102,axiom,
! [X1,X2] :
( ~ topological_space(X1,X2)
| equal_sets(union_of_members(X2),X1) ),
file('<stdin>',topological_space_7) ).
fof(c_0_103,axiom,
! [X1,X6] :
( ~ basis(X1,X6)
| equal_sets(union_of_members(X6),X1) ),
file('<stdin>',basis_for_topology_28) ).
fof(c_0_104,axiom,
! [X1,X2] :
( ~ topological_space(X1,X2)
| element_of_collection(X1,X2) ),
file('<stdin>',topological_space_9) ).
fof(c_0_105,axiom,
! [X1,X2] :
( ~ hausdorff(X1,X2)
| topological_space(X1,X2) ),
file('<stdin>',hausdorff_73) ).
fof(c_0_106,axiom,
! [X1,X2] :
( ~ connected_space(X1,X2)
| topological_space(X1,X2) ),
file('<stdin>',connected_space_89) ).
fof(c_0_107,axiom,
! [X1,X2] :
( ~ compact_space(X1,X2)
| topological_space(X1,X2) ),
file('<stdin>',compact_space_100) ).
fof(c_0_108,axiom,
! [X1,X2] :
( ~ topological_space(X1,X2)
| element_of_collection(empty_set,X2) ),
file('<stdin>',topological_space_8) ).
fof(c_0_109,plain,
! [X15,X13,X1,X2,X14] :
( ~ limit_point(X15,X13,X1,X2)
| ~ neighborhood(X14,X15,X1,X2)
| ~ eq_p(f15(X15,X13,X1,X2,X14),X15) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_110,plain,
! [X15,X13,X1,X2,X14] :
( ~ limit_point(X15,X13,X1,X2)
| ~ neighborhood(X14,X15,X1,X2)
| element_of_set(f15(X15,X13,X1,X2,X14),intersection_of_sets(X14,X13)) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_111,plain,
! [X13,X1,X6,X22,X23] :
( ~ basis(X1,X6)
| ~ element_of_set(X13,X1)
| ~ element_of_collection(X23,X6)
| ~ element_of_collection(X22,X6)
| ~ element_of_set(X13,intersection_of_sets(X23,X22))
| subset_sets(f6(X1,X6,X13,X23,X22),intersection_of_sets(X23,X22)) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_112,plain,
! [X13,X1,X6,X22,X23] :
( ~ basis(X1,X6)
| ~ element_of_set(X13,X1)
| ~ element_of_collection(X23,X6)
| ~ element_of_collection(X22,X6)
| ~ element_of_set(X13,intersection_of_sets(X23,X22))
| element_of_set(X13,f6(X1,X6,X13,X23,X22)) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_113,plain,
! [X13,X1,X6,X22,X23] :
( ~ basis(X1,X6)
| ~ element_of_set(X13,X1)
| ~ element_of_collection(X23,X6)
| ~ element_of_collection(X22,X6)
| ~ element_of_set(X13,intersection_of_sets(X23,X22))
| element_of_collection(f6(X1,X6,X13,X23,X22),X6) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_114,plain,
! [X15,X13,X1,X2,X16] :
( limit_point(X15,X13,X1,X2)
| ~ topological_space(X1,X2)
| ~ subset_sets(X13,X1)
| ~ element_of_set(X16,intersection_of_sets(f16(X15,X13,X1,X2),X13))
| eq_p(X16,X15) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_115,plain,
! [X13,X1,X2,X14] :
( ~ element_of_collection(X14,subspace_topology(X1,X2,X13))
| equal_sets(X14,intersection_of_sets(X13,f12(X1,X2,X13,X14))) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_116,plain,
! [X11,X12,X1,X2] :
( ~ hausdorff(X1,X2)
| ~ element_of_set(X12,X1)
| ~ element_of_set(X11,X1)
| eq_p(X12,X11)
| disjoint_s(f17(X1,X2,X12,X11),f18(X1,X2,X12,X11)) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_117,plain,
! [X15,X13,X1,X2] :
( limit_point(X15,X13,X1,X2)
| ~ topological_space(X1,X2)
| ~ subset_sets(X13,X1)
| neighborhood(f16(X15,X13,X1,X2),X15,X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_118,plain,
! [X13,X1,X2,X14] :
( element_of_set(X14,closure(X13,X1,X2))
| ~ topological_space(X1,X2)
| ~ subset_sets(X13,X1)
| ~ element_of_set(X14,f14(X13,X1,X2,X14)) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_119,plain,
! [X1,X2,X9,X10] :
( hausdorff(X1,X2)
| ~ topological_space(X1,X2)
| ~ neighborhood(X10,f19(X1,X2),X1,X2)
| ~ neighborhood(X9,f20(X1,X2),X1,X2)
| ~ disjoint_s(X10,X9) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_120,plain,
! [X11,X12,X1,X2] :
( ~ hausdorff(X1,X2)
| ~ element_of_set(X12,X1)
| ~ element_of_set(X11,X1)
| eq_p(X12,X11)
| neighborhood(f17(X1,X2,X12,X11),X12,X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_121,plain,
! [X11,X12,X1,X2] :
( ~ hausdorff(X1,X2)
| ~ element_of_set(X12,X1)
| ~ element_of_set(X11,X1)
| eq_p(X12,X11)
| neighborhood(f18(X1,X2,X12,X11),X11,X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_122,plain,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,interior(X13,X1,X2))
| open(f13(X13,X1,X2,X14),X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_123,plain,
! [X13,X1,X2,X14] :
( element_of_set(X14,closure(X13,X1,X2))
| ~ topological_space(X1,X2)
| ~ subset_sets(X13,X1)
| closed(f14(X13,X1,X2,X14),X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_124,plain,
! [X13,X1,X2,X14] :
( ~ element_of_collection(X14,subspace_topology(X1,X2,X13))
| element_of_collection(f12(X1,X2,X13,X14),X2) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_125,plain,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,interior(X13,X1,X2))
| element_of_set(X14,f13(X13,X1,X2,X14)) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_126,plain,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,interior(X13,X1,X2))
| subset_sets(f13(X13,X1,X2,X14),X13) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_127,plain,
! [X13,X1,X2,X14] :
( element_of_set(X14,closure(X13,X1,X2))
| ~ topological_space(X1,X2)
| ~ subset_sets(X13,X1)
| subset_sets(X13,f14(X13,X1,X2,X14)) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_128,plain,
! [X13,X1,X2,X14] :
( element_of_set(X14,boundary(X13,X1,X2))
| ~ topological_space(X1,X2)
| ~ element_of_set(X14,closure(X13,X1,X2))
| ~ element_of_set(X14,closure(relative_complement_sets(X13,X1),X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_129,plain,
! [X13,X1,X2,X14] :
( ~ neighborhood(X14,X13,X1,X2)
| open(X14,X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_130,plain,
! [X1,X2] :
( topological_space(X1,X2)
| ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_131,plain,
! [X1,X2,X7,X8] :
( ~ separation(X8,X7,X1,X2)
| equal_sets(union_of_sets(X8,X7),X1) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_132,plain,
! [X1,X2,X7,X8] :
( separation(X8,X7,X1,X2)
| ~ topological_space(X1,X2)
| equal_sets(X8,empty_set)
| equal_sets(X7,empty_set)
| ~ element_of_collection(X8,X2)
| ~ element_of_collection(X7,X2)
| ~ equal_sets(union_of_sets(X8,X7),X1)
| ~ disjoint_s(X8,X7) ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_133,plain,
! [X1,X2,X7,X8] :
( ~ connected_space(X1,X2)
| ~ separation(X8,X7,X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_134,plain,
! [X1,X2,X7,X8] :
( ~ separation(X8,X7,X1,X2)
| ~ equal_sets(X8,empty_set) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_135,plain,
! [X1,X2,X7,X8] :
( ~ separation(X8,X7,X1,X2)
| ~ equal_sets(X7,empty_set) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_136,plain,
! [X13,X1,X2,X14] :
( ~ neighborhood(X14,X13,X1,X2)
| topological_space(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_137,plain,
! [X13,X1,X2,X14] :
( ~ neighborhood(X14,X13,X1,X2)
| element_of_set(X13,X14) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_138,plain,
! [X15,X13,X1,X2] :
( ~ limit_point(X15,X13,X1,X2)
| topological_space(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_139,plain,
! [X15,X13,X1,X2] :
( ~ limit_point(X15,X13,X1,X2)
| subset_sets(X13,X1) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_140,plain,
! [X1,X2,X7,X8] :
( ~ separation(X8,X7,X1,X2)
| topological_space(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_141,plain,
! [X1,X2,X7,X8] :
( ~ separation(X8,X7,X1,X2)
| element_of_collection(X8,X2) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_142,plain,
! [X1,X2,X7,X8] :
( ~ separation(X8,X7,X1,X2)
| element_of_collection(X7,X2) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_143,plain,
! [X1,X2,X7,X8] :
( ~ separation(X8,X7,X1,X2)
| disjoint_s(X8,X7) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_144,plain,
! [X13,X1,X2,X14] :
( neighborhood(X14,X13,X1,X2)
| ~ topological_space(X1,X2)
| ~ open(X14,X1,X2)
| ~ element_of_set(X13,X14) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_145,plain,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,boundary(X13,X1,X2))
| element_of_set(X14,closure(relative_complement_sets(X13,X1),X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_146,plain,
! [X1,X6,X21] :
( basis(X1,X6)
| ~ equal_sets(union_of_members(X6),X1)
| ~ element_of_set(f7(X1,X6),X21)
| ~ element_of_collection(X21,X6)
| ~ subset_sets(X21,intersection_of_sets(f8(X1,X6),f9(X1,X6))) ),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_147,plain,
! [X1,X2] :
( topological_space(X1,X2)
| ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| subset_collections(f5(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_148,plain,
! [X1,X2] :
( connected_space(X1,X2)
| ~ topological_space(X1,X2)
| separation(f21(X1,X2),f22(X1,X2),X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_149,plain,
! [X13,X1,X2,X17,X14] :
( ~ element_of_set(X14,closure(X13,X1,X2))
| ~ subset_sets(X13,X17)
| ~ closed(X17,X1,X2)
| element_of_set(X14,X17) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_150,plain,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,boundary(X13,X1,X2))
| element_of_set(X14,closure(X13,X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_151,plain,
! [X13,X1,X2,X18,X14] :
( element_of_set(X14,interior(X13,X1,X2))
| ~ topological_space(X1,X2)
| ~ subset_sets(X13,X1)
| ~ element_of_set(X14,X18)
| ~ subset_sets(X18,X13)
| ~ open(X18,X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_152,plain,
! [X1,X2,X3] :
( connected_set(X3,X1,X2)
| ~ topological_space(X1,X2)
| ~ subset_sets(X3,X1)
| ~ connected_space(X3,subspace_topology(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_153,plain,
! [X1,X2,X3] :
( compact_set(X3,X1,X2)
| ~ topological_space(X1,X2)
| ~ subset_sets(X3,X1)
| ~ compact_space(X3,subspace_topology(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_154,plain,
! [X1,X2,X5] :
( ~ compact_space(X1,X2)
| ~ open_covering(X5,X1,X2)
| open_covering(f23(X1,X2,X5),X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_155,plain,
! [X13,X1,X2,X19,X14] :
( element_of_collection(X14,subspace_topology(X1,X2,X13))
| ~ topological_space(X1,X2)
| ~ subset_sets(X13,X1)
| ~ element_of_collection(X19,X2)
| ~ equal_sets(X14,intersection_of_sets(X13,X19)) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_156,plain,
! [X1,X2] :
( topological_space(X1,X2)
| ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| element_of_collection(f3(X1,X2),X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2) ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_157,plain,
! [X1,X2] :
( topological_space(X1,X2)
| ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| element_of_collection(f4(X1,X2),X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_158,plain,
! [X1,X2,X5] :
( ~ compact_space(X1,X2)
| ~ open_covering(X5,X1,X2)
| subset_collections(f23(X1,X2,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_159,plain,
! [X1,X2,X5] :
( ~ compact_space(X1,X2)
| ~ open_covering(X5,X1,X2)
| finite(f23(X1,X2,X5)) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_160,plain,
! [X1,X6] :
( basis(X1,X6)
| ~ equal_sets(union_of_members(X6),X1)
| element_of_set(f7(X1,X6),intersection_of_sets(f8(X1,X6),f9(X1,X6))) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_161,plain,
! [X1,X2,X3] :
( ~ connected_set(X3,X1,X2)
| connected_space(X3,subspace_topology(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_162,plain,
! [X1,X2,X3] :
( ~ compact_set(X3,X1,X2)
| compact_space(X3,subspace_topology(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_163,plain,
! [X13,X1,X2,X14] :
( ~ element_of_collection(X14,subspace_topology(X1,X2,X13))
| topological_space(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_164,plain,
! [X13,X1,X2,X14] :
( ~ element_of_collection(X14,subspace_topology(X1,X2,X13))
| subset_sets(X13,X1) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_165,plain,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,interior(X13,X1,X2))
| topological_space(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_166,plain,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,interior(X13,X1,X2))
| subset_sets(X13,X1) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_167,plain,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,closure(X13,X1,X2))
| topological_space(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_168,plain,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,closure(X13,X1,X2))
| subset_sets(X13,X1) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_169,plain,
! [X13,X1,X2,X14] :
( ~ element_of_set(X14,boundary(X13,X1,X2))
| topological_space(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_170,plain,
! [X1,X2,X14] :
( closed(X14,X1,X2)
| ~ topological_space(X1,X2)
| ~ open(relative_complement_sets(X14,X1),X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_171,plain,
! [X1,X2,X4] :
( compact_space(X1,X2)
| ~ topological_space(X1,X2)
| ~ finite(X4)
| ~ subset_collections(X4,f24(X1,X2))
| ~ open_covering(X4,X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_172,plain,
! [X1,X6,X14] :
( ~ element_of_collection(X14,top_of_basis(X6))
| ~ element_of_set(X1,X14)
| element_of_set(X1,f10(X6,X14,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_173,plain,
! [X1,X6,X14] :
( ~ element_of_collection(X14,top_of_basis(X6))
| ~ element_of_set(X1,X14)
| element_of_collection(f10(X6,X14,X1),X6) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_174,plain,
! [X1,X6,X14] :
( ~ element_of_collection(X14,top_of_basis(X6))
| ~ element_of_set(X1,X14)
| subset_sets(f10(X6,X14,X1),X14) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_175,plain,
! [X1,X2] :
( topological_space(X1,X2)
| ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| element_of_collection(f3(X1,X2),X2)
| subset_collections(f5(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_176,plain,
! [X1,X2] :
( topological_space(X1,X2)
| ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| element_of_collection(f4(X1,X2),X2)
| subset_collections(f5(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_177,plain,
! [X1,X2,X14] :
( ~ closed(X14,X1,X2)
| open(relative_complement_sets(X14,X1),X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_178,plain,
! [X1,X2] :
( hausdorff(X1,X2)
| ~ topological_space(X1,X2)
| ~ eq_p(f19(X1,X2),f20(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_179,plain,
! [X1,X2,X6] :
( open_covering(X6,X1,X2)
| ~ topological_space(X1,X2)
| ~ subset_collections(X6,X2)
| ~ equal_sets(union_of_members(X6),X1) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_180,plain,
! [X6,X20,X14] :
( element_of_collection(X14,top_of_basis(X6))
| ~ element_of_set(f11(X6,X14),X20)
| ~ element_of_collection(X20,X6)
| ~ subset_sets(X20,X14) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_181,plain,
! [X1,X2,X24] :
( finer(X2,X24,X1)
| ~ topological_space(X1,X2)
| ~ topological_space(X1,X24)
| ~ subset_collections(X24,X2) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_182,plain,
! [X1,X2] :
( compact_space(X1,X2)
| ~ topological_space(X1,X2)
| open_covering(f24(X1,X2),X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_183,plain,
! [X15,X13,X1,X2] :
( ~ topological_space(X1,X2)
| ~ element_of_collection(X13,X2)
| ~ element_of_collection(X15,X2)
| element_of_collection(intersection_of_sets(X13,X15),X2) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_184,plain,
! [X1,X2,X6] :
( ~ open_covering(X6,X1,X2)
| equal_sets(union_of_members(X6),X1) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_185,plain,
! [X1,X2,X14] :
( ~ open(X14,X1,X2)
| topological_space(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_186,plain,
! [X1,X2,X14] :
( ~ open(X14,X1,X2)
| element_of_collection(X14,X2) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_187,plain,
! [X1,X2,X14] :
( ~ closed(X14,X1,X2)
| topological_space(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_188,plain,
! [X1,X2,X24] :
( ~ finer(X2,X24,X1)
| topological_space(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_189,plain,
! [X1,X2,X24] :
( ~ finer(X2,X24,X1)
| topological_space(X1,X24) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_190,plain,
! [X1,X2,X24] :
( ~ finer(X2,X24,X1)
| subset_collections(X24,X2) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_191,plain,
! [X1,X2,X3] :
( ~ connected_set(X3,X1,X2)
| topological_space(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_192,plain,
! [X1,X2,X3] :
( ~ connected_set(X3,X1,X2)
| subset_sets(X3,X1) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_193,plain,
! [X1,X2,X6] :
( ~ open_covering(X6,X1,X2)
| topological_space(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_194,plain,
! [X1,X2,X6] :
( ~ open_covering(X6,X1,X2)
| subset_collections(X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_195,plain,
! [X1,X2,X3] :
( ~ compact_set(X3,X1,X2)
| topological_space(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_196,plain,
! [X1,X2,X3] :
( ~ compact_set(X3,X1,X2)
| subset_sets(X3,X1) ),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_197,plain,
! [X1,X2,X14] :
( open(X14,X1,X2)
| ~ topological_space(X1,X2)
| ~ element_of_collection(X14,X2) ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_198,plain,
! [X1,X6] :
( basis(X1,X6)
| ~ equal_sets(union_of_members(X6),X1)
| element_of_set(f7(X1,X6),X1) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_199,plain,
! [X1,X6] :
( basis(X1,X6)
| ~ equal_sets(union_of_members(X6),X1)
| element_of_collection(f8(X1,X6),X6) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_200,plain,
! [X1,X6] :
( basis(X1,X6)
| ~ equal_sets(union_of_members(X6),X1)
| element_of_collection(f9(X1,X6),X6) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_201,plain,
! [X6,X14] :
( element_of_set(X14,intersection_of_members(X6))
| ~ element_of_set(X14,f2(X6,X14)) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_202,plain,
! [X1,X2] :
( hausdorff(X1,X2)
| ~ topological_space(X1,X2)
| element_of_set(f19(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_203,plain,
! [X1,X2] :
( hausdorff(X1,X2)
| ~ topological_space(X1,X2)
| element_of_set(f20(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_204,plain,
! [X6,X14] :
( ~ element_of_set(X14,union_of_members(X6))
| element_of_set(X14,f1(X6,X14)) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_205,plain,
! [X6,X14] :
( ~ element_of_set(X14,union_of_members(X6))
| element_of_collection(f1(X6,X14),X6) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_206,plain,
! [X6,X3,X14] :
( ~ element_of_set(X14,intersection_of_members(X6))
| ~ element_of_collection(X3,X6)
| element_of_set(X14,X3) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_207,plain,
! [X6,X25,X14] :
( element_of_set(X14,union_of_members(X6))
| ~ element_of_set(X14,X25)
| ~ element_of_collection(X25,X6) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_208,plain,
! [X1,X2,X6] :
( ~ topological_space(X1,X2)
| ~ subset_collections(X6,X2)
| element_of_collection(union_of_members(X6),X2) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_209,axiom,
! [X6,X14] :
( element_of_set(X14,intersection_of_members(X6))
| element_of_collection(f2(X6,X14),X6) ),
c_0_100 ).
fof(c_0_210,axiom,
! [X6,X14] :
( element_of_collection(X14,top_of_basis(X6))
| element_of_set(f11(X6,X14),X14) ),
c_0_101 ).
fof(c_0_211,plain,
! [X1,X2] :
( ~ topological_space(X1,X2)
| equal_sets(union_of_members(X2),X1) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_212,plain,
! [X1,X6] :
( ~ basis(X1,X6)
| equal_sets(union_of_members(X6),X1) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_213,plain,
! [X1,X2] :
( ~ topological_space(X1,X2)
| element_of_collection(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_214,plain,
! [X1,X2] :
( ~ hausdorff(X1,X2)
| topological_space(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_215,plain,
! [X1,X2] :
( ~ connected_space(X1,X2)
| topological_space(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_216,plain,
! [X1,X2] :
( ~ compact_space(X1,X2)
| topological_space(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_217,plain,
! [X1,X2] :
( ~ topological_space(X1,X2)
| element_of_collection(empty_set,X2) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_218,plain,
! [X16,X17,X18,X19,X20] :
( ~ limit_point(X16,X17,X18,X19)
| ~ neighborhood(X20,X16,X18,X19)
| ~ eq_p(f15(X16,X17,X18,X19,X20),X16) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_109])])]) ).
fof(c_0_219,plain,
! [X16,X17,X18,X19,X20] :
( ~ limit_point(X16,X17,X18,X19)
| ~ neighborhood(X20,X16,X18,X19)
| element_of_set(f15(X16,X17,X18,X19,X20),intersection_of_sets(X20,X17)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_110])])]) ).
fof(c_0_220,plain,
! [X24,X25,X26,X27,X28] :
( ~ basis(X25,X26)
| ~ element_of_set(X24,X25)
| ~ element_of_collection(X28,X26)
| ~ element_of_collection(X27,X26)
| ~ element_of_set(X24,intersection_of_sets(X28,X27))
| subset_sets(f6(X25,X26,X24,X28,X27),intersection_of_sets(X28,X27)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_111])])]) ).
fof(c_0_221,plain,
! [X24,X25,X26,X27,X28] :
( ~ basis(X25,X26)
| ~ element_of_set(X24,X25)
| ~ element_of_collection(X28,X26)
| ~ element_of_collection(X27,X26)
| ~ element_of_set(X24,intersection_of_sets(X28,X27))
| element_of_set(X24,f6(X25,X26,X24,X28,X27)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_112])])]) ).
fof(c_0_222,plain,
! [X24,X25,X26,X27,X28] :
( ~ basis(X25,X26)
| ~ element_of_set(X24,X25)
| ~ element_of_collection(X28,X26)
| ~ element_of_collection(X27,X26)
| ~ element_of_set(X24,intersection_of_sets(X28,X27))
| element_of_collection(f6(X25,X26,X24,X28,X27),X26) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_113])])]) ).
fof(c_0_223,plain,
! [X17,X18,X19,X20,X21] :
( limit_point(X17,X18,X19,X20)
| ~ topological_space(X19,X20)
| ~ subset_sets(X18,X19)
| ~ element_of_set(X21,intersection_of_sets(f16(X17,X18,X19,X20),X18))
| eq_p(X21,X17) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_114])])]) ).
fof(c_0_224,plain,
! [X15,X16,X17,X18] :
( ~ element_of_collection(X18,subspace_topology(X16,X17,X15))
| equal_sets(X18,intersection_of_sets(X15,f12(X16,X17,X15,X18))) ),
inference(variable_rename,[status(thm)],[c_0_115]) ).
fof(c_0_225,plain,
! [X13,X14,X15,X16] :
( ~ hausdorff(X15,X16)
| ~ element_of_set(X14,X15)
| ~ element_of_set(X13,X15)
| eq_p(X14,X13)
| disjoint_s(f17(X15,X16,X14,X13),f18(X15,X16,X14,X13)) ),
inference(variable_rename,[status(thm)],[c_0_116]) ).
fof(c_0_226,plain,
! [X16,X17,X18,X19] :
( limit_point(X16,X17,X18,X19)
| ~ topological_space(X18,X19)
| ~ subset_sets(X17,X18)
| neighborhood(f16(X16,X17,X18,X19),X16,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_117]) ).
fof(c_0_227,plain,
! [X15,X16,X17,X18] :
( element_of_set(X18,closure(X15,X16,X17))
| ~ topological_space(X16,X17)
| ~ subset_sets(X15,X16)
| ~ element_of_set(X18,f14(X15,X16,X17,X18)) ),
inference(variable_rename,[status(thm)],[c_0_118]) ).
fof(c_0_228,plain,
! [X11,X12,X13,X14] :
( hausdorff(X11,X12)
| ~ topological_space(X11,X12)
| ~ neighborhood(X14,f19(X11,X12),X11,X12)
| ~ neighborhood(X13,f20(X11,X12),X11,X12)
| ~ disjoint_s(X14,X13) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_119])])]) ).
fof(c_0_229,plain,
! [X13,X14,X15,X16] :
( ~ hausdorff(X15,X16)
| ~ element_of_set(X14,X15)
| ~ element_of_set(X13,X15)
| eq_p(X14,X13)
| neighborhood(f17(X15,X16,X14,X13),X14,X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_120]) ).
fof(c_0_230,plain,
! [X13,X14,X15,X16] :
( ~ hausdorff(X15,X16)
| ~ element_of_set(X14,X15)
| ~ element_of_set(X13,X15)
| eq_p(X14,X13)
| neighborhood(f18(X15,X16,X14,X13),X13,X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_121]) ).
fof(c_0_231,plain,
! [X15,X16,X17,X18] :
( ~ element_of_set(X18,interior(X15,X16,X17))
| open(f13(X15,X16,X17,X18),X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_122]) ).
fof(c_0_232,plain,
! [X15,X16,X17,X18] :
( element_of_set(X18,closure(X15,X16,X17))
| ~ topological_space(X16,X17)
| ~ subset_sets(X15,X16)
| closed(f14(X15,X16,X17,X18),X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_123]) ).
fof(c_0_233,plain,
! [X15,X16,X17,X18] :
( ~ element_of_collection(X18,subspace_topology(X16,X17,X15))
| element_of_collection(f12(X16,X17,X15,X18),X17) ),
inference(variable_rename,[status(thm)],[c_0_124]) ).
fof(c_0_234,plain,
! [X15,X16,X17,X18] :
( ~ element_of_set(X18,interior(X15,X16,X17))
| element_of_set(X18,f13(X15,X16,X17,X18)) ),
inference(variable_rename,[status(thm)],[c_0_125]) ).
fof(c_0_235,plain,
! [X15,X16,X17,X18] :
( ~ element_of_set(X18,interior(X15,X16,X17))
| subset_sets(f13(X15,X16,X17,X18),X15) ),
inference(variable_rename,[status(thm)],[c_0_126]) ).
fof(c_0_236,plain,
! [X15,X16,X17,X18] :
( element_of_set(X18,closure(X15,X16,X17))
| ~ topological_space(X16,X17)
| ~ subset_sets(X15,X16)
| subset_sets(X15,f14(X15,X16,X17,X18)) ),
inference(variable_rename,[status(thm)],[c_0_127]) ).
fof(c_0_237,plain,
! [X15,X16,X17,X18] :
( element_of_set(X18,boundary(X15,X16,X17))
| ~ topological_space(X16,X17)
| ~ element_of_set(X18,closure(X15,X16,X17))
| ~ element_of_set(X18,closure(relative_complement_sets(X15,X16),X16,X17)) ),
inference(variable_rename,[status(thm)],[c_0_128]) ).
fof(c_0_238,plain,
! [X15,X16,X17,X18] :
( ~ neighborhood(X18,X15,X16,X17)
| open(X18,X16,X17) ),
inference(variable_rename,[status(thm)],[c_0_129]) ).
fof(c_0_239,plain,
! [X3,X4] :
( topological_space(X3,X4)
| ~ equal_sets(union_of_members(X4),X3)
| ~ element_of_collection(empty_set,X4)
| ~ element_of_collection(X3,X4)
| ~ element_of_collection(intersection_of_sets(f3(X3,X4),f4(X3,X4)),X4)
| ~ element_of_collection(union_of_members(f5(X3,X4)),X4) ),
inference(variable_rename,[status(thm)],[c_0_130]) ).
fof(c_0_240,plain,
! [X9,X10,X11,X12] :
( ~ separation(X12,X11,X9,X10)
| equal_sets(union_of_sets(X12,X11),X9) ),
inference(variable_rename,[status(thm)],[c_0_131]) ).
fof(c_0_241,plain,
! [X9,X10,X11,X12] :
( separation(X12,X11,X9,X10)
| ~ topological_space(X9,X10)
| equal_sets(X12,empty_set)
| equal_sets(X11,empty_set)
| ~ element_of_collection(X12,X10)
| ~ element_of_collection(X11,X10)
| ~ equal_sets(union_of_sets(X12,X11),X9)
| ~ disjoint_s(X12,X11) ),
inference(variable_rename,[status(thm)],[c_0_132]) ).
fof(c_0_242,plain,
! [X9,X10,X11,X12] :
( ~ connected_space(X9,X10)
| ~ separation(X12,X11,X9,X10) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_133])])]) ).
fof(c_0_243,plain,
! [X9,X10,X11,X12] :
( ~ separation(X12,X11,X9,X10)
| ~ equal_sets(X12,empty_set) ),
inference(variable_rename,[status(thm)],[c_0_134]) ).
fof(c_0_244,plain,
! [X9,X10,X11,X12] :
( ~ separation(X12,X11,X9,X10)
| ~ equal_sets(X11,empty_set) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_135])])]) ).
fof(c_0_245,plain,
! [X15,X16,X17,X18] :
( ~ neighborhood(X18,X15,X16,X17)
| topological_space(X16,X17) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_136])])]) ).
fof(c_0_246,plain,
! [X15,X16,X17,X18] :
( ~ neighborhood(X18,X15,X16,X17)
| element_of_set(X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_137]) ).
fof(c_0_247,plain,
! [X16,X17,X18,X19] :
( ~ limit_point(X16,X17,X18,X19)
| topological_space(X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_138]) ).
fof(c_0_248,plain,
! [X16,X17,X18,X19] :
( ~ limit_point(X16,X17,X18,X19)
| subset_sets(X17,X18) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_139])])]) ).
fof(c_0_249,plain,
! [X9,X10,X11,X12] :
( ~ separation(X12,X11,X9,X10)
| topological_space(X9,X10) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_140])])]) ).
fof(c_0_250,plain,
! [X9,X10,X11,X12] :
( ~ separation(X12,X11,X9,X10)
| element_of_collection(X12,X10) ),
inference(variable_rename,[status(thm)],[c_0_141]) ).
fof(c_0_251,plain,
! [X9,X10,X11,X12] :
( ~ separation(X12,X11,X9,X10)
| element_of_collection(X11,X10) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_142])])]) ).
fof(c_0_252,plain,
! [X9,X10,X11,X12] :
( ~ separation(X12,X11,X9,X10)
| disjoint_s(X12,X11) ),
inference(variable_rename,[status(thm)],[c_0_143]) ).
fof(c_0_253,plain,
! [X15,X16,X17,X18] :
( neighborhood(X18,X15,X16,X17)
| ~ topological_space(X16,X17)
| ~ open(X18,X16,X17)
| ~ element_of_set(X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_144]) ).
fof(c_0_254,plain,
! [X15,X16,X17,X18] :
( ~ element_of_set(X18,boundary(X15,X16,X17))
| element_of_set(X18,closure(relative_complement_sets(X15,X16),X16,X17)) ),
inference(variable_rename,[status(thm)],[c_0_145]) ).
fof(c_0_255,plain,
! [X22,X23,X24] :
( basis(X22,X23)
| ~ equal_sets(union_of_members(X23),X22)
| ~ element_of_set(f7(X22,X23),X24)
| ~ element_of_collection(X24,X23)
| ~ subset_sets(X24,intersection_of_sets(f8(X22,X23),f9(X22,X23))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_146])])]) ).
fof(c_0_256,plain,
! [X3,X4] :
( topological_space(X3,X4)
| ~ equal_sets(union_of_members(X4),X3)
| ~ element_of_collection(empty_set,X4)
| ~ element_of_collection(X3,X4)
| ~ element_of_collection(intersection_of_sets(f3(X3,X4),f4(X3,X4)),X4)
| subset_collections(f5(X3,X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_147]) ).
fof(c_0_257,plain,
! [X3,X4] :
( connected_space(X3,X4)
| ~ topological_space(X3,X4)
| separation(f21(X3,X4),f22(X3,X4),X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_148]) ).
fof(c_0_258,plain,
! [X18,X19,X20,X21,X22] :
( ~ element_of_set(X22,closure(X18,X19,X20))
| ~ subset_sets(X18,X21)
| ~ closed(X21,X19,X20)
| element_of_set(X22,X21) ),
inference(variable_rename,[status(thm)],[c_0_149]) ).
fof(c_0_259,plain,
! [X15,X16,X17,X18] :
( ~ element_of_set(X18,boundary(X15,X16,X17))
| element_of_set(X18,closure(X15,X16,X17)) ),
inference(variable_rename,[status(thm)],[c_0_150]) ).
fof(c_0_260,plain,
! [X19,X20,X21,X22,X23] :
( element_of_set(X23,interior(X19,X20,X21))
| ~ topological_space(X20,X21)
| ~ subset_sets(X19,X20)
| ~ element_of_set(X23,X22)
| ~ subset_sets(X22,X19)
| ~ open(X22,X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_151]) ).
fof(c_0_261,plain,
! [X4,X5,X6] :
( connected_set(X6,X4,X5)
| ~ topological_space(X4,X5)
| ~ subset_sets(X6,X4)
| ~ connected_space(X6,subspace_topology(X4,X5,X6)) ),
inference(variable_rename,[status(thm)],[c_0_152]) ).
fof(c_0_262,plain,
! [X4,X5,X6] :
( compact_set(X6,X4,X5)
| ~ topological_space(X4,X5)
| ~ subset_sets(X6,X4)
| ~ compact_space(X6,subspace_topology(X4,X5,X6)) ),
inference(variable_rename,[status(thm)],[c_0_153]) ).
fof(c_0_263,plain,
! [X6,X7,X8] :
( ~ compact_space(X6,X7)
| ~ open_covering(X8,X6,X7)
| open_covering(f23(X6,X7,X8),X6,X7) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_154])])]) ).
fof(c_0_264,plain,
! [X20,X21,X22,X23,X24] :
( element_of_collection(X24,subspace_topology(X21,X22,X20))
| ~ topological_space(X21,X22)
| ~ subset_sets(X20,X21)
| ~ element_of_collection(X23,X22)
| ~ equal_sets(X24,intersection_of_sets(X20,X23)) ),
inference(variable_rename,[status(thm)],[c_0_155]) ).
fof(c_0_265,plain,
! [X3,X4] :
( topological_space(X3,X4)
| ~ equal_sets(union_of_members(X4),X3)
| ~ element_of_collection(empty_set,X4)
| ~ element_of_collection(X3,X4)
| element_of_collection(f3(X3,X4),X4)
| ~ element_of_collection(union_of_members(f5(X3,X4)),X4) ),
inference(variable_rename,[status(thm)],[c_0_156]) ).
fof(c_0_266,plain,
! [X3,X4] :
( topological_space(X3,X4)
| ~ equal_sets(union_of_members(X4),X3)
| ~ element_of_collection(empty_set,X4)
| ~ element_of_collection(X3,X4)
| element_of_collection(f4(X3,X4),X4)
| ~ element_of_collection(union_of_members(f5(X3,X4)),X4) ),
inference(variable_rename,[status(thm)],[c_0_157]) ).
fof(c_0_267,plain,
! [X6,X7,X8] :
( ~ compact_space(X6,X7)
| ~ open_covering(X8,X6,X7)
| subset_collections(f23(X6,X7,X8),X8) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_158])])]) ).
fof(c_0_268,plain,
! [X6,X7,X8] :
( ~ compact_space(X6,X7)
| ~ open_covering(X8,X6,X7)
| finite(f23(X6,X7,X8)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_159])])]) ).
fof(c_0_269,plain,
! [X7,X8] :
( basis(X7,X8)
| ~ equal_sets(union_of_members(X8),X7)
| element_of_set(f7(X7,X8),intersection_of_sets(f8(X7,X8),f9(X7,X8))) ),
inference(variable_rename,[status(thm)],[c_0_160]) ).
fof(c_0_270,plain,
! [X4,X5,X6] :
( ~ connected_set(X6,X4,X5)
| connected_space(X6,subspace_topology(X4,X5,X6)) ),
inference(variable_rename,[status(thm)],[c_0_161]) ).
fof(c_0_271,plain,
! [X4,X5,X6] :
( ~ compact_set(X6,X4,X5)
| compact_space(X6,subspace_topology(X4,X5,X6)) ),
inference(variable_rename,[status(thm)],[c_0_162]) ).
fof(c_0_272,plain,
! [X15,X16,X17,X18] :
( ~ element_of_collection(X18,subspace_topology(X16,X17,X15))
| topological_space(X16,X17) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_163])])]) ).
fof(c_0_273,plain,
! [X15,X16,X17,X18] :
( ~ element_of_collection(X18,subspace_topology(X16,X17,X15))
| subset_sets(X15,X16) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_164])])]) ).
fof(c_0_274,plain,
! [X15,X16,X17,X18] :
( ~ element_of_set(X18,interior(X15,X16,X17))
| topological_space(X16,X17) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_165])])]) ).
fof(c_0_275,plain,
! [X15,X16,X17,X18] :
( ~ element_of_set(X18,interior(X15,X16,X17))
| subset_sets(X15,X16) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_166])])]) ).
fof(c_0_276,plain,
! [X15,X16,X17,X18] :
( ~ element_of_set(X18,closure(X15,X16,X17))
| topological_space(X16,X17) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_167])])]) ).
fof(c_0_277,plain,
! [X15,X16,X17,X18] :
( ~ element_of_set(X18,closure(X15,X16,X17))
| subset_sets(X15,X16) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_168])])]) ).
fof(c_0_278,plain,
! [X15,X16,X17,X18] :
( ~ element_of_set(X18,boundary(X15,X16,X17))
| topological_space(X16,X17) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_169])])]) ).
fof(c_0_279,plain,
! [X15,X16,X17] :
( closed(X17,X15,X16)
| ~ topological_space(X15,X16)
| ~ open(relative_complement_sets(X17,X15),X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_170]) ).
fof(c_0_280,plain,
! [X5,X6,X7] :
( compact_space(X5,X6)
| ~ topological_space(X5,X6)
| ~ finite(X7)
| ~ subset_collections(X7,f24(X5,X6))
| ~ open_covering(X7,X5,X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_171])])]) ).
fof(c_0_281,plain,
! [X15,X16,X17] :
( ~ element_of_collection(X17,top_of_basis(X16))
| ~ element_of_set(X15,X17)
| element_of_set(X15,f10(X16,X17,X15)) ),
inference(variable_rename,[status(thm)],[c_0_172]) ).
fof(c_0_282,plain,
! [X15,X16,X17] :
( ~ element_of_collection(X17,top_of_basis(X16))
| ~ element_of_set(X15,X17)
| element_of_collection(f10(X16,X17,X15),X16) ),
inference(variable_rename,[status(thm)],[c_0_173]) ).
fof(c_0_283,plain,
! [X15,X16,X17] :
( ~ element_of_collection(X17,top_of_basis(X16))
| ~ element_of_set(X15,X17)
| subset_sets(f10(X16,X17,X15),X17) ),
inference(variable_rename,[status(thm)],[c_0_174]) ).
fof(c_0_284,plain,
! [X3,X4] :
( topological_space(X3,X4)
| ~ equal_sets(union_of_members(X4),X3)
| ~ element_of_collection(empty_set,X4)
| ~ element_of_collection(X3,X4)
| element_of_collection(f3(X3,X4),X4)
| subset_collections(f5(X3,X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_175]) ).
fof(c_0_285,plain,
! [X3,X4] :
( topological_space(X3,X4)
| ~ equal_sets(union_of_members(X4),X3)
| ~ element_of_collection(empty_set,X4)
| ~ element_of_collection(X3,X4)
| element_of_collection(f4(X3,X4),X4)
| subset_collections(f5(X3,X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_176]) ).
fof(c_0_286,plain,
! [X15,X16,X17] :
( ~ closed(X17,X15,X16)
| open(relative_complement_sets(X17,X15),X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_177]) ).
fof(c_0_287,plain,
! [X3,X4] :
( hausdorff(X3,X4)
| ~ topological_space(X3,X4)
| ~ eq_p(f19(X3,X4),f20(X3,X4)) ),
inference(variable_rename,[status(thm)],[c_0_178]) ).
fof(c_0_288,plain,
! [X7,X8,X9] :
( open_covering(X9,X7,X8)
| ~ topological_space(X7,X8)
| ~ subset_collections(X9,X8)
| ~ equal_sets(union_of_members(X9),X7) ),
inference(variable_rename,[status(thm)],[c_0_179]) ).
fof(c_0_289,plain,
! [X21,X22,X23] :
( element_of_collection(X23,top_of_basis(X21))
| ~ element_of_set(f11(X21,X23),X22)
| ~ element_of_collection(X22,X21)
| ~ subset_sets(X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_180]) ).
fof(c_0_290,plain,
! [X25,X26,X27] :
( finer(X26,X27,X25)
| ~ topological_space(X25,X26)
| ~ topological_space(X25,X27)
| ~ subset_collections(X27,X26) ),
inference(variable_rename,[status(thm)],[c_0_181]) ).
fof(c_0_291,plain,
! [X3,X4] :
( compact_space(X3,X4)
| ~ topological_space(X3,X4)
| open_covering(f24(X3,X4),X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_182]) ).
fof(c_0_292,plain,
! [X16,X17,X18,X19] :
( ~ topological_space(X18,X19)
| ~ element_of_collection(X17,X19)
| ~ element_of_collection(X16,X19)
| element_of_collection(intersection_of_sets(X17,X16),X19) ),
inference(variable_rename,[status(thm)],[c_0_183]) ).
fof(c_0_293,plain,
! [X7,X8,X9] :
( ~ open_covering(X9,X7,X8)
| equal_sets(union_of_members(X9),X7) ),
inference(variable_rename,[status(thm)],[c_0_184]) ).
fof(c_0_294,plain,
! [X15,X16,X17] :
( ~ open(X17,X15,X16)
| topological_space(X15,X16) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_185])])]) ).
fof(c_0_295,plain,
! [X15,X16,X17] :
( ~ open(X17,X15,X16)
| element_of_collection(X17,X16) ),
inference(variable_rename,[status(thm)],[c_0_186]) ).
fof(c_0_296,plain,
! [X15,X16,X17] :
( ~ closed(X17,X15,X16)
| topological_space(X15,X16) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_187])])]) ).
fof(c_0_297,plain,
! [X25,X26,X27] :
( ~ finer(X26,X27,X25)
| topological_space(X25,X26) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_188])])]) ).
fof(c_0_298,plain,
! [X25,X26,X27] :
( ~ finer(X26,X27,X25)
| topological_space(X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_189]) ).
fof(c_0_299,plain,
! [X25,X26,X27] :
( ~ finer(X26,X27,X25)
| subset_collections(X27,X26) ),
inference(variable_rename,[status(thm)],[c_0_190]) ).
fof(c_0_300,plain,
! [X4,X5,X6] :
( ~ connected_set(X6,X4,X5)
| topological_space(X4,X5) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_191])])]) ).
fof(c_0_301,plain,
! [X4,X5,X6] :
( ~ connected_set(X6,X4,X5)
| subset_sets(X6,X4) ),
inference(variable_rename,[status(thm)],[c_0_192]) ).
fof(c_0_302,plain,
! [X7,X8,X9] :
( ~ open_covering(X9,X7,X8)
| topological_space(X7,X8) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_193])])]) ).
fof(c_0_303,plain,
! [X7,X8,X9] :
( ~ open_covering(X9,X7,X8)
| subset_collections(X9,X8) ),
inference(variable_rename,[status(thm)],[c_0_194]) ).
fof(c_0_304,plain,
! [X4,X5,X6] :
( ~ compact_set(X6,X4,X5)
| topological_space(X4,X5) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_195])])]) ).
fof(c_0_305,plain,
! [X4,X5,X6] :
( ~ compact_set(X6,X4,X5)
| subset_sets(X6,X4) ),
inference(variable_rename,[status(thm)],[c_0_196]) ).
fof(c_0_306,plain,
! [X15,X16,X17] :
( open(X17,X15,X16)
| ~ topological_space(X15,X16)
| ~ element_of_collection(X17,X16) ),
inference(variable_rename,[status(thm)],[c_0_197]) ).
fof(c_0_307,plain,
! [X7,X8] :
( basis(X7,X8)
| ~ equal_sets(union_of_members(X8),X7)
| element_of_set(f7(X7,X8),X7) ),
inference(variable_rename,[status(thm)],[c_0_198]) ).
fof(c_0_308,plain,
! [X7,X8] :
( basis(X7,X8)
| ~ equal_sets(union_of_members(X8),X7)
| element_of_collection(f8(X7,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_199]) ).
fof(c_0_309,plain,
! [X7,X8] :
( basis(X7,X8)
| ~ equal_sets(union_of_members(X8),X7)
| element_of_collection(f9(X7,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_200]) ).
fof(c_0_310,plain,
! [X15,X16] :
( element_of_set(X16,intersection_of_members(X15))
| ~ element_of_set(X16,f2(X15,X16)) ),
inference(variable_rename,[status(thm)],[c_0_201]) ).
fof(c_0_311,plain,
! [X3,X4] :
( hausdorff(X3,X4)
| ~ topological_space(X3,X4)
| element_of_set(f19(X3,X4),X3) ),
inference(variable_rename,[status(thm)],[c_0_202]) ).
fof(c_0_312,plain,
! [X3,X4] :
( hausdorff(X3,X4)
| ~ topological_space(X3,X4)
| element_of_set(f20(X3,X4),X3) ),
inference(variable_rename,[status(thm)],[c_0_203]) ).
fof(c_0_313,plain,
! [X15,X16] :
( ~ element_of_set(X16,union_of_members(X15))
| element_of_set(X16,f1(X15,X16)) ),
inference(variable_rename,[status(thm)],[c_0_204]) ).
fof(c_0_314,plain,
! [X15,X16] :
( ~ element_of_set(X16,union_of_members(X15))
| element_of_collection(f1(X15,X16),X15) ),
inference(variable_rename,[status(thm)],[c_0_205]) ).
fof(c_0_315,plain,
! [X15,X16,X17] :
( ~ element_of_set(X17,intersection_of_members(X15))
| ~ element_of_collection(X16,X15)
| element_of_set(X17,X16) ),
inference(variable_rename,[status(thm)],[c_0_206]) ).
fof(c_0_316,plain,
! [X26,X27,X28] :
( element_of_set(X28,union_of_members(X26))
| ~ element_of_set(X28,X27)
| ~ element_of_collection(X27,X26) ),
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_317,plain,
! [X7,X8,X9] :
( ~ topological_space(X7,X8)
| ~ subset_collections(X9,X8)
| element_of_collection(union_of_members(X9),X8) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_208])])]) ).
fof(c_0_318,plain,
! [X15,X16] :
( element_of_set(X16,intersection_of_members(X15))
| element_of_collection(f2(X15,X16),X15) ),
inference(variable_rename,[status(thm)],[c_0_209]) ).
fof(c_0_319,plain,
! [X15,X16] :
( element_of_collection(X16,top_of_basis(X15))
| element_of_set(f11(X15,X16),X16) ),
inference(variable_rename,[status(thm)],[c_0_210]) ).
fof(c_0_320,plain,
! [X3,X4] :
( ~ topological_space(X3,X4)
| equal_sets(union_of_members(X4),X3) ),
inference(variable_rename,[status(thm)],[c_0_211]) ).
fof(c_0_321,plain,
! [X7,X8] :
( ~ basis(X7,X8)
| equal_sets(union_of_members(X8),X7) ),
inference(variable_rename,[status(thm)],[c_0_212]) ).
fof(c_0_322,plain,
! [X3,X4] :
( ~ topological_space(X3,X4)
| element_of_collection(X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_213]) ).
fof(c_0_323,plain,
! [X3,X4] :
( ~ hausdorff(X3,X4)
| topological_space(X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_214]) ).
fof(c_0_324,plain,
! [X3,X4] :
( ~ connected_space(X3,X4)
| topological_space(X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_215]) ).
fof(c_0_325,plain,
! [X3,X4] :
( ~ compact_space(X3,X4)
| topological_space(X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_216]) ).
fof(c_0_326,plain,
! [X3,X4] :
( ~ topological_space(X3,X4)
| element_of_collection(empty_set,X4) ),
inference(variable_rename,[status(thm)],[c_0_217]) ).
cnf(c_0_327,plain,
( ~ eq_p(f15(X1,X2,X3,X4,X5),X1)
| ~ neighborhood(X5,X1,X3,X4)
| ~ limit_point(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_218]) ).
cnf(c_0_328,plain,
( element_of_set(f15(X1,X2,X3,X4,X5),intersection_of_sets(X5,X2))
| ~ neighborhood(X5,X1,X3,X4)
| ~ limit_point(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_219]) ).
cnf(c_0_329,plain,
( subset_sets(f6(X1,X2,X3,X4,X5),intersection_of_sets(X4,X5))
| ~ element_of_set(X3,intersection_of_sets(X4,X5))
| ~ element_of_collection(X5,X2)
| ~ element_of_collection(X4,X2)
| ~ element_of_set(X3,X1)
| ~ basis(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_220]) ).
cnf(c_0_330,plain,
( element_of_set(X1,f6(X2,X3,X1,X4,X5))
| ~ element_of_set(X1,intersection_of_sets(X4,X5))
| ~ element_of_collection(X5,X3)
| ~ element_of_collection(X4,X3)
| ~ element_of_set(X1,X2)
| ~ basis(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_221]) ).
cnf(c_0_331,plain,
( element_of_collection(f6(X1,X2,X3,X4,X5),X2)
| ~ element_of_set(X3,intersection_of_sets(X4,X5))
| ~ element_of_collection(X5,X2)
| ~ element_of_collection(X4,X2)
| ~ element_of_set(X3,X1)
| ~ basis(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_222]) ).
cnf(c_0_332,plain,
( eq_p(X1,X2)
| limit_point(X2,X3,X4,X5)
| ~ element_of_set(X1,intersection_of_sets(f16(X2,X3,X4,X5),X3))
| ~ subset_sets(X3,X4)
| ~ topological_space(X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_223]) ).
cnf(c_0_333,plain,
( equal_sets(X1,intersection_of_sets(X2,f12(X3,X4,X2,X1)))
| ~ element_of_collection(X1,subspace_topology(X3,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_224]) ).
cnf(c_0_334,plain,
( disjoint_s(f17(X1,X2,X3,X4),f18(X1,X2,X3,X4))
| eq_p(X3,X4)
| ~ element_of_set(X4,X1)
| ~ element_of_set(X3,X1)
| ~ hausdorff(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_225]) ).
cnf(c_0_335,plain,
( neighborhood(f16(X1,X2,X3,X4),X1,X3,X4)
| limit_point(X1,X2,X3,X4)
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_336,plain,
( element_of_set(X1,closure(X2,X3,X4))
| ~ element_of_set(X1,f14(X2,X3,X4,X1))
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_227]) ).
cnf(c_0_337,plain,
( hausdorff(X3,X4)
| ~ disjoint_s(X1,X2)
| ~ neighborhood(X2,f20(X3,X4),X3,X4)
| ~ neighborhood(X1,f19(X3,X4),X3,X4)
| ~ topological_space(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_338,plain,
( neighborhood(f17(X1,X2,X3,X4),X3,X1,X2)
| eq_p(X3,X4)
| ~ element_of_set(X4,X1)
| ~ element_of_set(X3,X1)
| ~ hausdorff(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_339,plain,
( neighborhood(f18(X1,X2,X3,X4),X4,X1,X2)
| eq_p(X3,X4)
| ~ element_of_set(X4,X1)
| ~ element_of_set(X3,X1)
| ~ hausdorff(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_340,plain,
( open(f13(X1,X2,X3,X4),X2,X3)
| ~ element_of_set(X4,interior(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_231]) ).
cnf(c_0_341,plain,
( closed(f14(X1,X2,X3,X4),X2,X3)
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_232]) ).
cnf(c_0_342,plain,
( element_of_collection(f12(X1,X2,X3,X4),X2)
| ~ element_of_collection(X4,subspace_topology(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_343,plain,
( element_of_set(X1,f13(X2,X3,X4,X1))
| ~ element_of_set(X1,interior(X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_234]) ).
cnf(c_0_344,plain,
( subset_sets(f13(X1,X2,X3,X4),X1)
| ~ element_of_set(X4,interior(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_235]) ).
cnf(c_0_345,plain,
( subset_sets(X1,f14(X1,X2,X3,X4))
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_236]) ).
cnf(c_0_346,plain,
( element_of_set(X1,boundary(X2,X3,X4))
| ~ element_of_set(X1,closure(relative_complement_sets(X2,X3),X3,X4))
| ~ element_of_set(X1,closure(X2,X3,X4))
| ~ topological_space(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_347,plain,
( open(X1,X2,X3)
| ~ neighborhood(X1,X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_348,plain,
( topological_space(X1,X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_349,plain,
( equal_sets(union_of_sets(X1,X2),X3)
| ~ separation(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_240]) ).
cnf(c_0_350,plain,
( equal_sets(X2,empty_set)
| equal_sets(X1,empty_set)
| separation(X1,X2,X3,X4)
| ~ disjoint_s(X1,X2)
| ~ equal_sets(union_of_sets(X1,X2),X3)
| ~ element_of_collection(X2,X4)
| ~ element_of_collection(X1,X4)
| ~ topological_space(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
cnf(c_0_351,plain,
( ~ separation(X1,X2,X3,X4)
| ~ connected_space(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_352,plain,
( ~ equal_sets(X1,empty_set)
| ~ separation(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_243]) ).
cnf(c_0_353,plain,
( ~ equal_sets(X1,empty_set)
| ~ separation(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
cnf(c_0_354,plain,
( topological_space(X1,X2)
| ~ neighborhood(X3,X4,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_245]) ).
cnf(c_0_355,plain,
( element_of_set(X1,X2)
| ~ neighborhood(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
cnf(c_0_356,plain,
( topological_space(X1,X2)
| ~ limit_point(X3,X4,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_247]) ).
cnf(c_0_357,plain,
( subset_sets(X1,X2)
| ~ limit_point(X3,X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_248]) ).
cnf(c_0_358,plain,
( topological_space(X1,X2)
| ~ separation(X3,X4,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_249]) ).
cnf(c_0_359,plain,
( element_of_collection(X1,X2)
| ~ separation(X1,X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_250]) ).
cnf(c_0_360,plain,
( element_of_collection(X1,X2)
| ~ separation(X3,X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_251]) ).
cnf(c_0_361,plain,
( disjoint_s(X1,X2)
| ~ separation(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_252]) ).
cnf(c_0_362,plain,
( neighborhood(X2,X1,X3,X4)
| ~ element_of_set(X1,X2)
| ~ open(X2,X3,X4)
| ~ topological_space(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_253]) ).
cnf(c_0_363,plain,
( element_of_set(X1,closure(relative_complement_sets(X2,X3),X3,X4))
| ~ element_of_set(X1,boundary(X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_254]) ).
cnf(c_0_364,plain,
( basis(X2,X3)
| ~ subset_sets(X1,intersection_of_sets(f8(X2,X3),f9(X2,X3)))
| ~ element_of_collection(X1,X3)
| ~ element_of_set(f7(X2,X3),X1)
| ~ equal_sets(union_of_members(X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_255]) ).
cnf(c_0_365,plain,
( subset_collections(f5(X1,X2),X2)
| topological_space(X1,X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_256]) ).
cnf(c_0_366,plain,
( separation(f21(X1,X2),f22(X1,X2),X1,X2)
| connected_space(X1,X2)
| ~ topological_space(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_257]) ).
cnf(c_0_367,plain,
( element_of_set(X1,X2)
| ~ closed(X2,X3,X4)
| ~ subset_sets(X5,X2)
| ~ element_of_set(X1,closure(X5,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_258]) ).
cnf(c_0_368,plain,
( element_of_set(X1,closure(X2,X3,X4))
| ~ element_of_set(X1,boundary(X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_259]) ).
cnf(c_0_369,plain,
( element_of_set(X5,interior(X4,X2,X3))
| ~ open(X1,X2,X3)
| ~ subset_sets(X1,X4)
| ~ element_of_set(X5,X1)
| ~ subset_sets(X4,X2)
| ~ topological_space(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_260]) ).
cnf(c_0_370,plain,
( connected_set(X1,X2,X3)
| ~ connected_space(X1,subspace_topology(X2,X3,X1))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_371,plain,
( compact_set(X1,X2,X3)
| ~ compact_space(X1,subspace_topology(X2,X3,X1))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_262]) ).
cnf(c_0_372,plain,
( open_covering(f23(X1,X2,X3),X1,X2)
| ~ open_covering(X3,X1,X2)
| ~ compact_space(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_263]) ).
cnf(c_0_373,plain,
( element_of_collection(X1,subspace_topology(X5,X4,X2))
| ~ equal_sets(X1,intersection_of_sets(X2,X3))
| ~ element_of_collection(X3,X4)
| ~ subset_sets(X2,X5)
| ~ topological_space(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_264]) ).
cnf(c_0_374,plain,
( element_of_collection(f3(X1,X2),X2)
| topological_space(X1,X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_265]) ).
cnf(c_0_375,plain,
( element_of_collection(f4(X1,X2),X2)
| topological_space(X1,X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_266]) ).
cnf(c_0_376,plain,
( subset_collections(f23(X1,X2,X3),X3)
| ~ open_covering(X3,X1,X2)
| ~ compact_space(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_377,plain,
( finite(f23(X1,X2,X3))
| ~ open_covering(X3,X1,X2)
| ~ compact_space(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_268]) ).
cnf(c_0_378,plain,
( element_of_set(f7(X1,X2),intersection_of_sets(f8(X1,X2),f9(X1,X2)))
| basis(X1,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_379,plain,
( connected_space(X1,subspace_topology(X2,X3,X1))
| ~ connected_set(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_380,plain,
( compact_space(X1,subspace_topology(X2,X3,X1))
| ~ compact_set(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_381,plain,
( topological_space(X1,X2)
| ~ element_of_collection(X3,subspace_topology(X1,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_272]) ).
cnf(c_0_382,plain,
( subset_sets(X1,X2)
| ~ element_of_collection(X3,subspace_topology(X2,X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_383,plain,
( topological_space(X1,X2)
| ~ element_of_set(X3,interior(X4,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_384,plain,
( subset_sets(X1,X2)
| ~ element_of_set(X3,interior(X1,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_385,plain,
( topological_space(X1,X2)
| ~ element_of_set(X3,closure(X4,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_386,plain,
( subset_sets(X1,X2)
| ~ element_of_set(X3,closure(X1,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_387,plain,
( topological_space(X1,X2)
| ~ element_of_set(X3,boundary(X4,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_388,plain,
( closed(X1,X2,X3)
| ~ open(relative_complement_sets(X1,X2),X2,X3)
| ~ topological_space(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_389,plain,
( compact_space(X2,X3)
| ~ open_covering(X1,X2,X3)
| ~ subset_collections(X1,f24(X2,X3))
| ~ finite(X1)
| ~ topological_space(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_390,plain,
( element_of_set(X1,f10(X2,X3,X1))
| ~ element_of_set(X1,X3)
| ~ element_of_collection(X3,top_of_basis(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_391,plain,
( element_of_collection(f10(X1,X2,X3),X1)
| ~ element_of_set(X3,X2)
| ~ element_of_collection(X2,top_of_basis(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_282]) ).
cnf(c_0_392,plain,
( subset_sets(f10(X1,X2,X3),X2)
| ~ element_of_set(X3,X2)
| ~ element_of_collection(X2,top_of_basis(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_393,plain,
( subset_collections(f5(X1,X2),X2)
| element_of_collection(f3(X1,X2),X2)
| topological_space(X1,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
cnf(c_0_394,plain,
( subset_collections(f5(X1,X2),X2)
| element_of_collection(f4(X1,X2),X2)
| topological_space(X1,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_395,plain,
( open(relative_complement_sets(X1,X2),X2,X3)
| ~ closed(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_286]) ).
cnf(c_0_396,plain,
( hausdorff(X1,X2)
| ~ eq_p(f19(X1,X2),f20(X1,X2))
| ~ topological_space(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_397,plain,
( open_covering(X1,X2,X3)
| ~ equal_sets(union_of_members(X1),X2)
| ~ subset_collections(X1,X3)
| ~ topological_space(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_288]) ).
cnf(c_0_398,plain,
( element_of_collection(X2,top_of_basis(X3))
| ~ subset_sets(X1,X2)
| ~ element_of_collection(X1,X3)
| ~ element_of_set(f11(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_289]) ).
cnf(c_0_399,plain,
( finer(X2,X1,X3)
| ~ subset_collections(X1,X2)
| ~ topological_space(X3,X1)
| ~ topological_space(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_400,plain,
( open_covering(f24(X1,X2),X1,X2)
| compact_space(X1,X2)
| ~ topological_space(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_291]) ).
cnf(c_0_401,plain,
( element_of_collection(intersection_of_sets(X1,X2),X3)
| ~ element_of_collection(X2,X3)
| ~ element_of_collection(X1,X3)
| ~ topological_space(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_292]) ).
cnf(c_0_402,plain,
( equal_sets(union_of_members(X1),X2)
| ~ open_covering(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
cnf(c_0_403,plain,
( topological_space(X1,X2)
| ~ open(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_404,plain,
( element_of_collection(X1,X2)
| ~ open(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_405,plain,
( topological_space(X1,X2)
| ~ closed(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_406,plain,
( topological_space(X1,X2)
| ~ finer(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_297]) ).
cnf(c_0_407,plain,
( topological_space(X1,X2)
| ~ finer(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_298]) ).
cnf(c_0_408,plain,
( subset_collections(X1,X2)
| ~ finer(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_409,plain,
( topological_space(X1,X2)
| ~ connected_set(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_300]) ).
cnf(c_0_410,plain,
( subset_sets(X1,X2)
| ~ connected_set(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_411,plain,
( topological_space(X1,X2)
| ~ open_covering(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_302]) ).
cnf(c_0_412,plain,
( subset_collections(X1,X2)
| ~ open_covering(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
cnf(c_0_413,plain,
( topological_space(X1,X2)
| ~ compact_set(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_304]) ).
cnf(c_0_414,plain,
( subset_sets(X1,X2)
| ~ compact_set(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_305]) ).
cnf(c_0_415,plain,
( open(X1,X3,X2)
| ~ element_of_collection(X1,X2)
| ~ topological_space(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_306]) ).
cnf(c_0_416,plain,
( element_of_set(f7(X1,X2),X1)
| basis(X1,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_307]) ).
cnf(c_0_417,plain,
( element_of_collection(f8(X1,X2),X2)
| basis(X1,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_418,plain,
( element_of_collection(f9(X1,X2),X2)
| basis(X1,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_309]) ).
cnf(c_0_419,plain,
( element_of_set(X1,intersection_of_members(X2))
| ~ element_of_set(X1,f2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_310]) ).
cnf(c_0_420,plain,
( element_of_set(f19(X1,X2),X1)
| hausdorff(X1,X2)
| ~ topological_space(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
cnf(c_0_421,plain,
( element_of_set(f20(X1,X2),X1)
| hausdorff(X1,X2)
| ~ topological_space(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_312]) ).
cnf(c_0_422,plain,
( element_of_set(X1,f1(X2,X1))
| ~ element_of_set(X1,union_of_members(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_313]) ).
cnf(c_0_423,plain,
( element_of_collection(f1(X1,X2),X1)
| ~ element_of_set(X2,union_of_members(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
cnf(c_0_424,plain,
( element_of_set(X1,X2)
| ~ element_of_collection(X2,X3)
| ~ element_of_set(X1,intersection_of_members(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_425,plain,
( element_of_set(X3,union_of_members(X2))
| ~ element_of_collection(X1,X2)
| ~ element_of_set(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
cnf(c_0_426,plain,
( element_of_collection(union_of_members(X1),X2)
| ~ subset_collections(X1,X2)
| ~ topological_space(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_427,plain,
( element_of_collection(f2(X1,X2),X1)
| element_of_set(X2,intersection_of_members(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_428,plain,
( element_of_set(f11(X1,X2),X2)
| element_of_collection(X2,top_of_basis(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
cnf(c_0_429,plain,
( equal_sets(union_of_members(X1),X2)
| ~ topological_space(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_430,plain,
( equal_sets(union_of_members(X1),X2)
| ~ basis(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_431,plain,
( element_of_collection(X1,X2)
| ~ topological_space(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_432,plain,
( topological_space(X1,X2)
| ~ hausdorff(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_323]) ).
cnf(c_0_433,plain,
( topological_space(X1,X2)
| ~ connected_space(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_324]) ).
cnf(c_0_434,plain,
( topological_space(X1,X2)
| ~ compact_space(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_435,plain,
( element_of_collection(empty_set,X1)
| ~ topological_space(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_436,plain,
( ~ eq_p(f15(X1,X2,X3,X4,X5),X1)
| ~ neighborhood(X5,X1,X3,X4)
| ~ limit_point(X1,X2,X3,X4) ),
c_0_327,
[final] ).
cnf(c_0_437,plain,
( element_of_set(f15(X1,X2,X3,X4,X5),intersection_of_sets(X5,X2))
| ~ neighborhood(X5,X1,X3,X4)
| ~ limit_point(X1,X2,X3,X4) ),
c_0_328,
[final] ).
cnf(c_0_438,plain,
( subset_sets(f6(X1,X2,X3,X4,X5),intersection_of_sets(X4,X5))
| ~ element_of_set(X3,intersection_of_sets(X4,X5))
| ~ element_of_collection(X5,X2)
| ~ element_of_collection(X4,X2)
| ~ element_of_set(X3,X1)
| ~ basis(X1,X2) ),
c_0_329,
[final] ).
cnf(c_0_439,plain,
( element_of_set(X1,f6(X2,X3,X1,X4,X5))
| ~ element_of_set(X1,intersection_of_sets(X4,X5))
| ~ element_of_collection(X5,X3)
| ~ element_of_collection(X4,X3)
| ~ element_of_set(X1,X2)
| ~ basis(X2,X3) ),
c_0_330,
[final] ).
cnf(c_0_440,plain,
( element_of_collection(f6(X1,X2,X3,X4,X5),X2)
| ~ element_of_set(X3,intersection_of_sets(X4,X5))
| ~ element_of_collection(X5,X2)
| ~ element_of_collection(X4,X2)
| ~ element_of_set(X3,X1)
| ~ basis(X1,X2) ),
c_0_331,
[final] ).
cnf(c_0_441,plain,
( eq_p(X1,X2)
| limit_point(X2,X3,X4,X5)
| ~ element_of_set(X1,intersection_of_sets(f16(X2,X3,X4,X5),X3))
| ~ subset_sets(X3,X4)
| ~ topological_space(X4,X5) ),
c_0_332,
[final] ).
cnf(c_0_442,plain,
( equal_sets(X1,intersection_of_sets(X2,f12(X3,X4,X2,X1)))
| ~ element_of_collection(X1,subspace_topology(X3,X4,X2)) ),
c_0_333,
[final] ).
cnf(c_0_443,plain,
( disjoint_s(f17(X1,X2,X3,X4),f18(X1,X2,X3,X4))
| eq_p(X3,X4)
| ~ element_of_set(X4,X1)
| ~ element_of_set(X3,X1)
| ~ hausdorff(X1,X2) ),
c_0_334,
[final] ).
cnf(c_0_444,plain,
( neighborhood(f16(X1,X2,X3,X4),X1,X3,X4)
| limit_point(X1,X2,X3,X4)
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4) ),
c_0_335,
[final] ).
cnf(c_0_445,plain,
( element_of_set(X1,closure(X2,X3,X4))
| ~ element_of_set(X1,f14(X2,X3,X4,X1))
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4) ),
c_0_336,
[final] ).
cnf(c_0_446,plain,
( hausdorff(X3,X4)
| ~ disjoint_s(X1,X2)
| ~ neighborhood(X2,f20(X3,X4),X3,X4)
| ~ neighborhood(X1,f19(X3,X4),X3,X4)
| ~ topological_space(X3,X4) ),
c_0_337,
[final] ).
cnf(c_0_447,plain,
( neighborhood(f17(X1,X2,X3,X4),X3,X1,X2)
| eq_p(X3,X4)
| ~ element_of_set(X4,X1)
| ~ element_of_set(X3,X1)
| ~ hausdorff(X1,X2) ),
c_0_338,
[final] ).
cnf(c_0_448,plain,
( neighborhood(f18(X1,X2,X3,X4),X4,X1,X2)
| eq_p(X3,X4)
| ~ element_of_set(X4,X1)
| ~ element_of_set(X3,X1)
| ~ hausdorff(X1,X2) ),
c_0_339,
[final] ).
cnf(c_0_449,plain,
( open(f13(X1,X2,X3,X4),X2,X3)
| ~ element_of_set(X4,interior(X1,X2,X3)) ),
c_0_340,
[final] ).
cnf(c_0_450,plain,
( closed(f14(X1,X2,X3,X4),X2,X3)
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ),
c_0_341,
[final] ).
cnf(c_0_451,plain,
( element_of_collection(f12(X1,X2,X3,X4),X2)
| ~ element_of_collection(X4,subspace_topology(X1,X2,X3)) ),
c_0_342,
[final] ).
cnf(c_0_452,plain,
( element_of_set(X1,f13(X2,X3,X4,X1))
| ~ element_of_set(X1,interior(X2,X3,X4)) ),
c_0_343,
[final] ).
cnf(c_0_453,plain,
( subset_sets(f13(X1,X2,X3,X4),X1)
| ~ element_of_set(X4,interior(X1,X2,X3)) ),
c_0_344,
[final] ).
cnf(c_0_454,plain,
( subset_sets(X1,f14(X1,X2,X3,X4))
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ),
c_0_345,
[final] ).
cnf(c_0_455,plain,
( element_of_set(X1,boundary(X2,X3,X4))
| ~ element_of_set(X1,closure(relative_complement_sets(X2,X3),X3,X4))
| ~ element_of_set(X1,closure(X2,X3,X4))
| ~ topological_space(X3,X4) ),
c_0_346,
[final] ).
cnf(c_0_456,plain,
( open(X1,X2,X3)
| ~ neighborhood(X1,X4,X2,X3) ),
c_0_347,
[final] ).
cnf(c_0_457,plain,
( topological_space(X1,X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
c_0_348,
[final] ).
cnf(c_0_458,plain,
( equal_sets(union_of_sets(X1,X2),X3)
| ~ separation(X1,X2,X3,X4) ),
c_0_349,
[final] ).
cnf(c_0_459,plain,
( equal_sets(X2,empty_set)
| equal_sets(X1,empty_set)
| separation(X1,X2,X3,X4)
| ~ disjoint_s(X1,X2)
| ~ equal_sets(union_of_sets(X1,X2),X3)
| ~ element_of_collection(X2,X4)
| ~ element_of_collection(X1,X4)
| ~ topological_space(X3,X4) ),
c_0_350,
[final] ).
cnf(c_0_460,plain,
( ~ separation(X1,X2,X3,X4)
| ~ connected_space(X3,X4) ),
c_0_351,
[final] ).
cnf(c_0_461,plain,
( ~ equal_sets(X1,empty_set)
| ~ separation(X1,X2,X3,X4) ),
c_0_352,
[final] ).
cnf(c_0_462,plain,
( ~ equal_sets(X1,empty_set)
| ~ separation(X2,X1,X3,X4) ),
c_0_353,
[final] ).
cnf(c_0_463,plain,
( topological_space(X1,X2)
| ~ neighborhood(X3,X4,X1,X2) ),
c_0_354,
[final] ).
cnf(c_0_464,plain,
( element_of_set(X1,X2)
| ~ neighborhood(X2,X1,X3,X4) ),
c_0_355,
[final] ).
cnf(c_0_465,plain,
( topological_space(X1,X2)
| ~ limit_point(X3,X4,X1,X2) ),
c_0_356,
[final] ).
cnf(c_0_466,plain,
( subset_sets(X1,X2)
| ~ limit_point(X3,X1,X2,X4) ),
c_0_357,
[final] ).
cnf(c_0_467,plain,
( topological_space(X1,X2)
| ~ separation(X3,X4,X1,X2) ),
c_0_358,
[final] ).
cnf(c_0_468,plain,
( element_of_collection(X1,X2)
| ~ separation(X1,X3,X4,X2) ),
c_0_359,
[final] ).
cnf(c_0_469,plain,
( element_of_collection(X1,X2)
| ~ separation(X3,X1,X4,X2) ),
c_0_360,
[final] ).
cnf(c_0_470,plain,
( disjoint_s(X1,X2)
| ~ separation(X1,X2,X3,X4) ),
c_0_361,
[final] ).
cnf(c_0_471,plain,
( neighborhood(X2,X1,X3,X4)
| ~ element_of_set(X1,X2)
| ~ open(X2,X3,X4)
| ~ topological_space(X3,X4) ),
c_0_362,
[final] ).
cnf(c_0_472,plain,
( element_of_set(X1,closure(relative_complement_sets(X2,X3),X3,X4))
| ~ element_of_set(X1,boundary(X2,X3,X4)) ),
c_0_363,
[final] ).
cnf(c_0_473,plain,
( basis(X2,X3)
| ~ subset_sets(X1,intersection_of_sets(f8(X2,X3),f9(X2,X3)))
| ~ element_of_collection(X1,X3)
| ~ element_of_set(f7(X2,X3),X1)
| ~ equal_sets(union_of_members(X3),X2) ),
c_0_364,
[final] ).
cnf(c_0_474,plain,
( subset_collections(f5(X1,X2),X2)
| topological_space(X1,X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
c_0_365,
[final] ).
cnf(c_0_475,plain,
( separation(f21(X1,X2),f22(X1,X2),X1,X2)
| connected_space(X1,X2)
| ~ topological_space(X1,X2) ),
c_0_366,
[final] ).
cnf(c_0_476,plain,
( element_of_set(X1,X2)
| ~ closed(X2,X3,X4)
| ~ subset_sets(X5,X2)
| ~ element_of_set(X1,closure(X5,X3,X4)) ),
c_0_367,
[final] ).
cnf(c_0_477,plain,
( element_of_set(X1,closure(X2,X3,X4))
| ~ element_of_set(X1,boundary(X2,X3,X4)) ),
c_0_368,
[final] ).
cnf(c_0_478,plain,
( element_of_set(X5,interior(X4,X2,X3))
| ~ open(X1,X2,X3)
| ~ subset_sets(X1,X4)
| ~ element_of_set(X5,X1)
| ~ subset_sets(X4,X2)
| ~ topological_space(X2,X3) ),
c_0_369,
[final] ).
cnf(c_0_479,plain,
( connected_set(X1,X2,X3)
| ~ connected_space(X1,subspace_topology(X2,X3,X1))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ),
c_0_370,
[final] ).
cnf(c_0_480,plain,
( compact_set(X1,X2,X3)
| ~ compact_space(X1,subspace_topology(X2,X3,X1))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ),
c_0_371,
[final] ).
cnf(c_0_481,plain,
( open_covering(f23(X1,X2,X3),X1,X2)
| ~ open_covering(X3,X1,X2)
| ~ compact_space(X1,X2) ),
c_0_372,
[final] ).
cnf(c_0_482,plain,
( element_of_collection(X1,subspace_topology(X5,X4,X2))
| ~ equal_sets(X1,intersection_of_sets(X2,X3))
| ~ element_of_collection(X3,X4)
| ~ subset_sets(X2,X5)
| ~ topological_space(X5,X4) ),
c_0_373,
[final] ).
cnf(c_0_483,plain,
( element_of_collection(f3(X1,X2),X2)
| topological_space(X1,X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
c_0_374,
[final] ).
cnf(c_0_484,plain,
( element_of_collection(f4(X1,X2),X2)
| topological_space(X1,X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
c_0_375,
[final] ).
cnf(c_0_485,plain,
( subset_collections(f23(X1,X2,X3),X3)
| ~ open_covering(X3,X1,X2)
| ~ compact_space(X1,X2) ),
c_0_376,
[final] ).
cnf(c_0_486,plain,
( finite(f23(X1,X2,X3))
| ~ open_covering(X3,X1,X2)
| ~ compact_space(X1,X2) ),
c_0_377,
[final] ).
cnf(c_0_487,plain,
( element_of_set(f7(X1,X2),intersection_of_sets(f8(X1,X2),f9(X1,X2)))
| basis(X1,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
c_0_378,
[final] ).
cnf(c_0_488,plain,
( connected_space(X1,subspace_topology(X2,X3,X1))
| ~ connected_set(X1,X2,X3) ),
c_0_379,
[final] ).
cnf(c_0_489,plain,
( compact_space(X1,subspace_topology(X2,X3,X1))
| ~ compact_set(X1,X2,X3) ),
c_0_380,
[final] ).
cnf(c_0_490,plain,
( topological_space(X1,X2)
| ~ element_of_collection(X3,subspace_topology(X1,X2,X4)) ),
c_0_381,
[final] ).
cnf(c_0_491,plain,
( subset_sets(X1,X2)
| ~ element_of_collection(X3,subspace_topology(X2,X4,X1)) ),
c_0_382,
[final] ).
cnf(c_0_492,plain,
( topological_space(X1,X2)
| ~ element_of_set(X3,interior(X4,X1,X2)) ),
c_0_383,
[final] ).
cnf(c_0_493,plain,
( subset_sets(X1,X2)
| ~ element_of_set(X3,interior(X1,X2,X4)) ),
c_0_384,
[final] ).
cnf(c_0_494,plain,
( topological_space(X1,X2)
| ~ element_of_set(X3,closure(X4,X1,X2)) ),
c_0_385,
[final] ).
cnf(c_0_495,plain,
( subset_sets(X1,X2)
| ~ element_of_set(X3,closure(X1,X2,X4)) ),
c_0_386,
[final] ).
cnf(c_0_496,plain,
( topological_space(X1,X2)
| ~ element_of_set(X3,boundary(X4,X1,X2)) ),
c_0_387,
[final] ).
cnf(c_0_497,plain,
( closed(X1,X2,X3)
| ~ open(relative_complement_sets(X1,X2),X2,X3)
| ~ topological_space(X2,X3) ),
c_0_388,
[final] ).
cnf(c_0_498,plain,
( compact_space(X2,X3)
| ~ open_covering(X1,X2,X3)
| ~ subset_collections(X1,f24(X2,X3))
| ~ finite(X1)
| ~ topological_space(X2,X3) ),
c_0_389,
[final] ).
cnf(c_0_499,plain,
( element_of_set(X1,f10(X2,X3,X1))
| ~ element_of_set(X1,X3)
| ~ element_of_collection(X3,top_of_basis(X2)) ),
c_0_390,
[final] ).
cnf(c_0_500,plain,
( element_of_collection(f10(X1,X2,X3),X1)
| ~ element_of_set(X3,X2)
| ~ element_of_collection(X2,top_of_basis(X1)) ),
c_0_391,
[final] ).
cnf(c_0_501,plain,
( subset_sets(f10(X1,X2,X3),X2)
| ~ element_of_set(X3,X2)
| ~ element_of_collection(X2,top_of_basis(X1)) ),
c_0_392,
[final] ).
cnf(c_0_502,plain,
( subset_collections(f5(X1,X2),X2)
| element_of_collection(f3(X1,X2),X2)
| topological_space(X1,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
c_0_393,
[final] ).
cnf(c_0_503,plain,
( subset_collections(f5(X1,X2),X2)
| element_of_collection(f4(X1,X2),X2)
| topological_space(X1,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
c_0_394,
[final] ).
cnf(c_0_504,plain,
( open(relative_complement_sets(X1,X2),X2,X3)
| ~ closed(X1,X2,X3) ),
c_0_395,
[final] ).
cnf(c_0_505,plain,
( hausdorff(X1,X2)
| ~ eq_p(f19(X1,X2),f20(X1,X2))
| ~ topological_space(X1,X2) ),
c_0_396,
[final] ).
cnf(c_0_506,plain,
( open_covering(X1,X2,X3)
| ~ equal_sets(union_of_members(X1),X2)
| ~ subset_collections(X1,X3)
| ~ topological_space(X2,X3) ),
c_0_397,
[final] ).
cnf(c_0_507,plain,
( element_of_collection(X2,top_of_basis(X3))
| ~ subset_sets(X1,X2)
| ~ element_of_collection(X1,X3)
| ~ element_of_set(f11(X3,X2),X1) ),
c_0_398,
[final] ).
cnf(c_0_508,plain,
( finer(X2,X1,X3)
| ~ subset_collections(X1,X2)
| ~ topological_space(X3,X1)
| ~ topological_space(X3,X2) ),
c_0_399,
[final] ).
cnf(c_0_509,plain,
( open_covering(f24(X1,X2),X1,X2)
| compact_space(X1,X2)
| ~ topological_space(X1,X2) ),
c_0_400,
[final] ).
cnf(c_0_510,plain,
( element_of_collection(intersection_of_sets(X1,X2),X3)
| ~ element_of_collection(X2,X3)
| ~ element_of_collection(X1,X3)
| ~ topological_space(X4,X3) ),
c_0_401,
[final] ).
cnf(c_0_511,plain,
( equal_sets(union_of_members(X1),X2)
| ~ open_covering(X1,X2,X3) ),
c_0_402,
[final] ).
cnf(c_0_512,plain,
( topological_space(X1,X2)
| ~ open(X3,X1,X2) ),
c_0_403,
[final] ).
cnf(c_0_513,plain,
( element_of_collection(X1,X2)
| ~ open(X1,X3,X2) ),
c_0_404,
[final] ).
cnf(c_0_514,plain,
( topological_space(X1,X2)
| ~ closed(X3,X1,X2) ),
c_0_405,
[final] ).
cnf(c_0_515,plain,
( topological_space(X1,X2)
| ~ finer(X2,X3,X1) ),
c_0_406,
[final] ).
cnf(c_0_516,plain,
( topological_space(X1,X2)
| ~ finer(X3,X2,X1) ),
c_0_407,
[final] ).
cnf(c_0_517,plain,
( subset_collections(X1,X2)
| ~ finer(X2,X1,X3) ),
c_0_408,
[final] ).
cnf(c_0_518,plain,
( topological_space(X1,X2)
| ~ connected_set(X3,X1,X2) ),
c_0_409,
[final] ).
cnf(c_0_519,plain,
( subset_sets(X1,X2)
| ~ connected_set(X1,X2,X3) ),
c_0_410,
[final] ).
cnf(c_0_520,plain,
( topological_space(X1,X2)
| ~ open_covering(X3,X1,X2) ),
c_0_411,
[final] ).
cnf(c_0_521,plain,
( subset_collections(X1,X2)
| ~ open_covering(X1,X3,X2) ),
c_0_412,
[final] ).
cnf(c_0_522,plain,
( topological_space(X1,X2)
| ~ compact_set(X3,X1,X2) ),
c_0_413,
[final] ).
cnf(c_0_523,plain,
( subset_sets(X1,X2)
| ~ compact_set(X1,X2,X3) ),
c_0_414,
[final] ).
cnf(c_0_524,plain,
( open(X1,X3,X2)
| ~ element_of_collection(X1,X2)
| ~ topological_space(X3,X2) ),
c_0_415,
[final] ).
cnf(c_0_525,plain,
( element_of_set(f7(X1,X2),X1)
| basis(X1,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
c_0_416,
[final] ).
cnf(c_0_526,plain,
( element_of_collection(f8(X1,X2),X2)
| basis(X1,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
c_0_417,
[final] ).
cnf(c_0_527,plain,
( element_of_collection(f9(X1,X2),X2)
| basis(X1,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
c_0_418,
[final] ).
cnf(c_0_528,plain,
( element_of_set(X1,intersection_of_members(X2))
| ~ element_of_set(X1,f2(X2,X1)) ),
c_0_419,
[final] ).
cnf(c_0_529,plain,
( element_of_set(f19(X1,X2),X1)
| hausdorff(X1,X2)
| ~ topological_space(X1,X2) ),
c_0_420,
[final] ).
cnf(c_0_530,plain,
( element_of_set(f20(X1,X2),X1)
| hausdorff(X1,X2)
| ~ topological_space(X1,X2) ),
c_0_421,
[final] ).
cnf(c_0_531,plain,
( element_of_set(X1,f1(X2,X1))
| ~ element_of_set(X1,union_of_members(X2)) ),
c_0_422,
[final] ).
cnf(c_0_532,plain,
( element_of_collection(f1(X1,X2),X1)
| ~ element_of_set(X2,union_of_members(X1)) ),
c_0_423,
[final] ).
cnf(c_0_533,plain,
( element_of_set(X1,X2)
| ~ element_of_collection(X2,X3)
| ~ element_of_set(X1,intersection_of_members(X3)) ),
c_0_424,
[final] ).
cnf(c_0_534,plain,
( element_of_set(X3,union_of_members(X2))
| ~ element_of_collection(X1,X2)
| ~ element_of_set(X3,X1) ),
c_0_425,
[final] ).
cnf(c_0_535,plain,
( element_of_collection(union_of_members(X1),X2)
| ~ subset_collections(X1,X2)
| ~ topological_space(X3,X2) ),
c_0_426,
[final] ).
cnf(c_0_536,plain,
( element_of_collection(f2(X1,X2),X1)
| element_of_set(X2,intersection_of_members(X1)) ),
c_0_427,
[final] ).
cnf(c_0_537,plain,
( element_of_set(f11(X1,X2),X2)
| element_of_collection(X2,top_of_basis(X1)) ),
c_0_428,
[final] ).
cnf(c_0_538,plain,
( equal_sets(union_of_members(X1),X2)
| ~ topological_space(X2,X1) ),
c_0_429,
[final] ).
cnf(c_0_539,plain,
( equal_sets(union_of_members(X1),X2)
| ~ basis(X2,X1) ),
c_0_430,
[final] ).
cnf(c_0_540,plain,
( element_of_collection(X1,X2)
| ~ topological_space(X1,X2) ),
c_0_431,
[final] ).
cnf(c_0_541,plain,
( topological_space(X1,X2)
| ~ hausdorff(X1,X2) ),
c_0_432,
[final] ).
cnf(c_0_542,plain,
( topological_space(X1,X2)
| ~ connected_space(X1,X2) ),
c_0_433,
[final] ).
cnf(c_0_543,plain,
( topological_space(X1,X2)
| ~ compact_space(X1,X2) ),
c_0_434,
[final] ).
cnf(c_0_544,plain,
( element_of_collection(empty_set,X1)
| ~ topological_space(X2,X1) ),
c_0_435,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_436_0,axiom,
( ~ eq_p(f15(X1,X2,X3,X4,X5),X1)
| ~ neighborhood(X5,X1,X3,X4)
| ~ limit_point(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_436]) ).
cnf(c_0_436_1,axiom,
( ~ neighborhood(X5,X1,X3,X4)
| ~ eq_p(f15(X1,X2,X3,X4,X5),X1)
| ~ limit_point(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_436]) ).
cnf(c_0_436_2,axiom,
( ~ limit_point(X1,X2,X3,X4)
| ~ neighborhood(X5,X1,X3,X4)
| ~ eq_p(f15(X1,X2,X3,X4,X5),X1) ),
inference(literals_permutation,[status(thm)],[c_0_436]) ).
cnf(c_0_437_0,axiom,
( element_of_set(f15(X1,X2,X3,X4,X5),intersection_of_sets(X5,X2))
| ~ neighborhood(X5,X1,X3,X4)
| ~ limit_point(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_437]) ).
cnf(c_0_437_1,axiom,
( ~ neighborhood(X5,X1,X3,X4)
| element_of_set(f15(X1,X2,X3,X4,X5),intersection_of_sets(X5,X2))
| ~ limit_point(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_437]) ).
cnf(c_0_437_2,axiom,
( ~ limit_point(X1,X2,X3,X4)
| ~ neighborhood(X5,X1,X3,X4)
| element_of_set(f15(X1,X2,X3,X4,X5),intersection_of_sets(X5,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_437]) ).
cnf(c_0_438_0,axiom,
( subset_sets(f6(X1,X2,X3,X4,X5),intersection_of_sets(X4,X5))
| ~ element_of_set(X3,intersection_of_sets(X4,X5))
| ~ element_of_collection(X5,X2)
| ~ element_of_collection(X4,X2)
| ~ element_of_set(X3,X1)
| ~ basis(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_438]) ).
cnf(c_0_438_1,axiom,
( ~ element_of_set(X3,intersection_of_sets(X4,X5))
| subset_sets(f6(X1,X2,X3,X4,X5),intersection_of_sets(X4,X5))
| ~ element_of_collection(X5,X2)
| ~ element_of_collection(X4,X2)
| ~ element_of_set(X3,X1)
| ~ basis(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_438]) ).
cnf(c_0_438_2,axiom,
( ~ element_of_collection(X5,X2)
| ~ element_of_set(X3,intersection_of_sets(X4,X5))
| subset_sets(f6(X1,X2,X3,X4,X5),intersection_of_sets(X4,X5))
| ~ element_of_collection(X4,X2)
| ~ element_of_set(X3,X1)
| ~ basis(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_438]) ).
cnf(c_0_438_3,axiom,
( ~ element_of_collection(X4,X2)
| ~ element_of_collection(X5,X2)
| ~ element_of_set(X3,intersection_of_sets(X4,X5))
| subset_sets(f6(X1,X2,X3,X4,X5),intersection_of_sets(X4,X5))
| ~ element_of_set(X3,X1)
| ~ basis(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_438]) ).
cnf(c_0_438_4,axiom,
( ~ element_of_set(X3,X1)
| ~ element_of_collection(X4,X2)
| ~ element_of_collection(X5,X2)
| ~ element_of_set(X3,intersection_of_sets(X4,X5))
| subset_sets(f6(X1,X2,X3,X4,X5),intersection_of_sets(X4,X5))
| ~ basis(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_438]) ).
cnf(c_0_438_5,axiom,
( ~ basis(X1,X2)
| ~ element_of_set(X3,X1)
| ~ element_of_collection(X4,X2)
| ~ element_of_collection(X5,X2)
| ~ element_of_set(X3,intersection_of_sets(X4,X5))
| subset_sets(f6(X1,X2,X3,X4,X5),intersection_of_sets(X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_438]) ).
cnf(c_0_439_0,axiom,
( element_of_set(X1,f6(X2,X3,X1,X4,X5))
| ~ element_of_set(X1,intersection_of_sets(X4,X5))
| ~ element_of_collection(X5,X3)
| ~ element_of_collection(X4,X3)
| ~ element_of_set(X1,X2)
| ~ basis(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_439]) ).
cnf(c_0_439_1,axiom,
( ~ element_of_set(X1,intersection_of_sets(X4,X5))
| element_of_set(X1,f6(X2,X3,X1,X4,X5))
| ~ element_of_collection(X5,X3)
| ~ element_of_collection(X4,X3)
| ~ element_of_set(X1,X2)
| ~ basis(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_439]) ).
cnf(c_0_439_2,axiom,
( ~ element_of_collection(X5,X3)
| ~ element_of_set(X1,intersection_of_sets(X4,X5))
| element_of_set(X1,f6(X2,X3,X1,X4,X5))
| ~ element_of_collection(X4,X3)
| ~ element_of_set(X1,X2)
| ~ basis(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_439]) ).
cnf(c_0_439_3,axiom,
( ~ element_of_collection(X4,X3)
| ~ element_of_collection(X5,X3)
| ~ element_of_set(X1,intersection_of_sets(X4,X5))
| element_of_set(X1,f6(X2,X3,X1,X4,X5))
| ~ element_of_set(X1,X2)
| ~ basis(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_439]) ).
cnf(c_0_439_4,axiom,
( ~ element_of_set(X1,X2)
| ~ element_of_collection(X4,X3)
| ~ element_of_collection(X5,X3)
| ~ element_of_set(X1,intersection_of_sets(X4,X5))
| element_of_set(X1,f6(X2,X3,X1,X4,X5))
| ~ basis(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_439]) ).
cnf(c_0_439_5,axiom,
( ~ basis(X2,X3)
| ~ element_of_set(X1,X2)
| ~ element_of_collection(X4,X3)
| ~ element_of_collection(X5,X3)
| ~ element_of_set(X1,intersection_of_sets(X4,X5))
| element_of_set(X1,f6(X2,X3,X1,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_439]) ).
cnf(c_0_440_0,axiom,
( element_of_collection(f6(X1,X2,X3,X4,X5),X2)
| ~ element_of_set(X3,intersection_of_sets(X4,X5))
| ~ element_of_collection(X5,X2)
| ~ element_of_collection(X4,X2)
| ~ element_of_set(X3,X1)
| ~ basis(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_440]) ).
cnf(c_0_440_1,axiom,
( ~ element_of_set(X3,intersection_of_sets(X4,X5))
| element_of_collection(f6(X1,X2,X3,X4,X5),X2)
| ~ element_of_collection(X5,X2)
| ~ element_of_collection(X4,X2)
| ~ element_of_set(X3,X1)
| ~ basis(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_440]) ).
cnf(c_0_440_2,axiom,
( ~ element_of_collection(X5,X2)
| ~ element_of_set(X3,intersection_of_sets(X4,X5))
| element_of_collection(f6(X1,X2,X3,X4,X5),X2)
| ~ element_of_collection(X4,X2)
| ~ element_of_set(X3,X1)
| ~ basis(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_440]) ).
cnf(c_0_440_3,axiom,
( ~ element_of_collection(X4,X2)
| ~ element_of_collection(X5,X2)
| ~ element_of_set(X3,intersection_of_sets(X4,X5))
| element_of_collection(f6(X1,X2,X3,X4,X5),X2)
| ~ element_of_set(X3,X1)
| ~ basis(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_440]) ).
cnf(c_0_440_4,axiom,
( ~ element_of_set(X3,X1)
| ~ element_of_collection(X4,X2)
| ~ element_of_collection(X5,X2)
| ~ element_of_set(X3,intersection_of_sets(X4,X5))
| element_of_collection(f6(X1,X2,X3,X4,X5),X2)
| ~ basis(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_440]) ).
cnf(c_0_440_5,axiom,
( ~ basis(X1,X2)
| ~ element_of_set(X3,X1)
| ~ element_of_collection(X4,X2)
| ~ element_of_collection(X5,X2)
| ~ element_of_set(X3,intersection_of_sets(X4,X5))
| element_of_collection(f6(X1,X2,X3,X4,X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_440]) ).
cnf(c_0_441_0,axiom,
( eq_p(X1,X2)
| limit_point(X2,X3,X4,X5)
| ~ element_of_set(X1,intersection_of_sets(f16(X2,X3,X4,X5),X3))
| ~ subset_sets(X3,X4)
| ~ topological_space(X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_441]) ).
cnf(c_0_441_1,axiom,
( limit_point(X2,X3,X4,X5)
| eq_p(X1,X2)
| ~ element_of_set(X1,intersection_of_sets(f16(X2,X3,X4,X5),X3))
| ~ subset_sets(X3,X4)
| ~ topological_space(X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_441]) ).
cnf(c_0_441_2,axiom,
( ~ element_of_set(X1,intersection_of_sets(f16(X2,X3,X4,X5),X3))
| limit_point(X2,X3,X4,X5)
| eq_p(X1,X2)
| ~ subset_sets(X3,X4)
| ~ topological_space(X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_441]) ).
cnf(c_0_441_3,axiom,
( ~ subset_sets(X3,X4)
| ~ element_of_set(X1,intersection_of_sets(f16(X2,X3,X4,X5),X3))
| limit_point(X2,X3,X4,X5)
| eq_p(X1,X2)
| ~ topological_space(X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_441]) ).
cnf(c_0_441_4,axiom,
( ~ topological_space(X4,X5)
| ~ subset_sets(X3,X4)
| ~ element_of_set(X1,intersection_of_sets(f16(X2,X3,X4,X5),X3))
| limit_point(X2,X3,X4,X5)
| eq_p(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_441]) ).
cnf(c_0_442_0,axiom,
( equal_sets(X1,intersection_of_sets(X2,f12(X3,X4,X2,X1)))
| ~ element_of_collection(X1,subspace_topology(X3,X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_442]) ).
cnf(c_0_442_1,axiom,
( ~ element_of_collection(X1,subspace_topology(X3,X4,X2))
| equal_sets(X1,intersection_of_sets(X2,f12(X3,X4,X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_442]) ).
cnf(c_0_443_0,axiom,
( disjoint_s(f17(X1,X2,X3,X4),f18(X1,X2,X3,X4))
| eq_p(X3,X4)
| ~ element_of_set(X4,X1)
| ~ element_of_set(X3,X1)
| ~ hausdorff(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_443]) ).
cnf(c_0_443_1,axiom,
( eq_p(X3,X4)
| disjoint_s(f17(X1,X2,X3,X4),f18(X1,X2,X3,X4))
| ~ element_of_set(X4,X1)
| ~ element_of_set(X3,X1)
| ~ hausdorff(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_443]) ).
cnf(c_0_443_2,axiom,
( ~ element_of_set(X4,X1)
| eq_p(X3,X4)
| disjoint_s(f17(X1,X2,X3,X4),f18(X1,X2,X3,X4))
| ~ element_of_set(X3,X1)
| ~ hausdorff(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_443]) ).
cnf(c_0_443_3,axiom,
( ~ element_of_set(X3,X1)
| ~ element_of_set(X4,X1)
| eq_p(X3,X4)
| disjoint_s(f17(X1,X2,X3,X4),f18(X1,X2,X3,X4))
| ~ hausdorff(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_443]) ).
cnf(c_0_443_4,axiom,
( ~ hausdorff(X1,X2)
| ~ element_of_set(X3,X1)
| ~ element_of_set(X4,X1)
| eq_p(X3,X4)
| disjoint_s(f17(X1,X2,X3,X4),f18(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_443]) ).
cnf(c_0_444_0,axiom,
( neighborhood(f16(X1,X2,X3,X4),X1,X3,X4)
| limit_point(X1,X2,X3,X4)
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_444]) ).
cnf(c_0_444_1,axiom,
( limit_point(X1,X2,X3,X4)
| neighborhood(f16(X1,X2,X3,X4),X1,X3,X4)
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_444]) ).
cnf(c_0_444_2,axiom,
( ~ subset_sets(X2,X3)
| limit_point(X1,X2,X3,X4)
| neighborhood(f16(X1,X2,X3,X4),X1,X3,X4)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_444]) ).
cnf(c_0_444_3,axiom,
( ~ topological_space(X3,X4)
| ~ subset_sets(X2,X3)
| limit_point(X1,X2,X3,X4)
| neighborhood(f16(X1,X2,X3,X4),X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_444]) ).
cnf(c_0_445_0,axiom,
( element_of_set(X1,closure(X2,X3,X4))
| ~ element_of_set(X1,f14(X2,X3,X4,X1))
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_445]) ).
cnf(c_0_445_1,axiom,
( ~ element_of_set(X1,f14(X2,X3,X4,X1))
| element_of_set(X1,closure(X2,X3,X4))
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_445]) ).
cnf(c_0_445_2,axiom,
( ~ subset_sets(X2,X3)
| ~ element_of_set(X1,f14(X2,X3,X4,X1))
| element_of_set(X1,closure(X2,X3,X4))
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_445]) ).
cnf(c_0_445_3,axiom,
( ~ topological_space(X3,X4)
| ~ subset_sets(X2,X3)
| ~ element_of_set(X1,f14(X2,X3,X4,X1))
| element_of_set(X1,closure(X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_445]) ).
cnf(c_0_446_0,axiom,
( hausdorff(X3,X4)
| ~ disjoint_s(X1,X2)
| ~ neighborhood(X2,f20(X3,X4),X3,X4)
| ~ neighborhood(X1,f19(X3,X4),X3,X4)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_446]) ).
cnf(c_0_446_1,axiom,
( ~ disjoint_s(X1,X2)
| hausdorff(X3,X4)
| ~ neighborhood(X2,f20(X3,X4),X3,X4)
| ~ neighborhood(X1,f19(X3,X4),X3,X4)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_446]) ).
cnf(c_0_446_2,axiom,
( ~ neighborhood(X2,f20(X3,X4),X3,X4)
| ~ disjoint_s(X1,X2)
| hausdorff(X3,X4)
| ~ neighborhood(X1,f19(X3,X4),X3,X4)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_446]) ).
cnf(c_0_446_3,axiom,
( ~ neighborhood(X1,f19(X3,X4),X3,X4)
| ~ neighborhood(X2,f20(X3,X4),X3,X4)
| ~ disjoint_s(X1,X2)
| hausdorff(X3,X4)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_446]) ).
cnf(c_0_446_4,axiom,
( ~ topological_space(X3,X4)
| ~ neighborhood(X1,f19(X3,X4),X3,X4)
| ~ neighborhood(X2,f20(X3,X4),X3,X4)
| ~ disjoint_s(X1,X2)
| hausdorff(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_446]) ).
cnf(c_0_447_0,axiom,
( neighborhood(f17(X1,X2,X3,X4),X3,X1,X2)
| eq_p(X3,X4)
| ~ element_of_set(X4,X1)
| ~ element_of_set(X3,X1)
| ~ hausdorff(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_447]) ).
cnf(c_0_447_1,axiom,
( eq_p(X3,X4)
| neighborhood(f17(X1,X2,X3,X4),X3,X1,X2)
| ~ element_of_set(X4,X1)
| ~ element_of_set(X3,X1)
| ~ hausdorff(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_447]) ).
cnf(c_0_447_2,axiom,
( ~ element_of_set(X4,X1)
| eq_p(X3,X4)
| neighborhood(f17(X1,X2,X3,X4),X3,X1,X2)
| ~ element_of_set(X3,X1)
| ~ hausdorff(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_447]) ).
cnf(c_0_447_3,axiom,
( ~ element_of_set(X3,X1)
| ~ element_of_set(X4,X1)
| eq_p(X3,X4)
| neighborhood(f17(X1,X2,X3,X4),X3,X1,X2)
| ~ hausdorff(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_447]) ).
cnf(c_0_447_4,axiom,
( ~ hausdorff(X1,X2)
| ~ element_of_set(X3,X1)
| ~ element_of_set(X4,X1)
| eq_p(X3,X4)
| neighborhood(f17(X1,X2,X3,X4),X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_447]) ).
cnf(c_0_448_0,axiom,
( neighborhood(f18(X1,X2,X3,X4),X4,X1,X2)
| eq_p(X3,X4)
| ~ element_of_set(X4,X1)
| ~ element_of_set(X3,X1)
| ~ hausdorff(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_448]) ).
cnf(c_0_448_1,axiom,
( eq_p(X3,X4)
| neighborhood(f18(X1,X2,X3,X4),X4,X1,X2)
| ~ element_of_set(X4,X1)
| ~ element_of_set(X3,X1)
| ~ hausdorff(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_448]) ).
cnf(c_0_448_2,axiom,
( ~ element_of_set(X4,X1)
| eq_p(X3,X4)
| neighborhood(f18(X1,X2,X3,X4),X4,X1,X2)
| ~ element_of_set(X3,X1)
| ~ hausdorff(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_448]) ).
cnf(c_0_448_3,axiom,
( ~ element_of_set(X3,X1)
| ~ element_of_set(X4,X1)
| eq_p(X3,X4)
| neighborhood(f18(X1,X2,X3,X4),X4,X1,X2)
| ~ hausdorff(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_448]) ).
cnf(c_0_448_4,axiom,
( ~ hausdorff(X1,X2)
| ~ element_of_set(X3,X1)
| ~ element_of_set(X4,X1)
| eq_p(X3,X4)
| neighborhood(f18(X1,X2,X3,X4),X4,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_448]) ).
cnf(c_0_449_0,axiom,
( open(f13(X1,X2,X3,X4),X2,X3)
| ~ element_of_set(X4,interior(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_449]) ).
cnf(c_0_449_1,axiom,
( ~ element_of_set(X4,interior(X1,X2,X3))
| open(f13(X1,X2,X3,X4),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_449]) ).
cnf(c_0_450_0,axiom,
( closed(f14(X1,X2,X3,X4),X2,X3)
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_450]) ).
cnf(c_0_450_1,axiom,
( element_of_set(X4,closure(X1,X2,X3))
| closed(f14(X1,X2,X3,X4),X2,X3)
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_450]) ).
cnf(c_0_450_2,axiom,
( ~ subset_sets(X1,X2)
| element_of_set(X4,closure(X1,X2,X3))
| closed(f14(X1,X2,X3,X4),X2,X3)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_450]) ).
cnf(c_0_450_3,axiom,
( ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| element_of_set(X4,closure(X1,X2,X3))
| closed(f14(X1,X2,X3,X4),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_450]) ).
cnf(c_0_451_0,axiom,
( element_of_collection(f12(X1,X2,X3,X4),X2)
| ~ element_of_collection(X4,subspace_topology(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_451]) ).
cnf(c_0_451_1,axiom,
( ~ element_of_collection(X4,subspace_topology(X1,X2,X3))
| element_of_collection(f12(X1,X2,X3,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_451]) ).
cnf(c_0_452_0,axiom,
( element_of_set(X1,f13(X2,X3,X4,X1))
| ~ element_of_set(X1,interior(X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_452]) ).
cnf(c_0_452_1,axiom,
( ~ element_of_set(X1,interior(X2,X3,X4))
| element_of_set(X1,f13(X2,X3,X4,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_452]) ).
cnf(c_0_453_0,axiom,
( subset_sets(f13(X1,X2,X3,X4),X1)
| ~ element_of_set(X4,interior(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_453]) ).
cnf(c_0_453_1,axiom,
( ~ element_of_set(X4,interior(X1,X2,X3))
| subset_sets(f13(X1,X2,X3,X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_453]) ).
cnf(c_0_454_0,axiom,
( subset_sets(X1,f14(X1,X2,X3,X4))
| element_of_set(X4,closure(X1,X2,X3))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_454]) ).
cnf(c_0_454_1,axiom,
( element_of_set(X4,closure(X1,X2,X3))
| subset_sets(X1,f14(X1,X2,X3,X4))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_454]) ).
cnf(c_0_454_2,axiom,
( ~ subset_sets(X1,X2)
| element_of_set(X4,closure(X1,X2,X3))
| subset_sets(X1,f14(X1,X2,X3,X4))
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_454]) ).
cnf(c_0_454_3,axiom,
( ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| element_of_set(X4,closure(X1,X2,X3))
| subset_sets(X1,f14(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_454]) ).
cnf(c_0_455_0,axiom,
( element_of_set(X1,boundary(X2,X3,X4))
| ~ element_of_set(X1,closure(relative_complement_sets(X2,X3),X3,X4))
| ~ element_of_set(X1,closure(X2,X3,X4))
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_455]) ).
cnf(c_0_455_1,axiom,
( ~ element_of_set(X1,closure(relative_complement_sets(X2,X3),X3,X4))
| element_of_set(X1,boundary(X2,X3,X4))
| ~ element_of_set(X1,closure(X2,X3,X4))
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_455]) ).
cnf(c_0_455_2,axiom,
( ~ element_of_set(X1,closure(X2,X3,X4))
| ~ element_of_set(X1,closure(relative_complement_sets(X2,X3),X3,X4))
| element_of_set(X1,boundary(X2,X3,X4))
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_455]) ).
cnf(c_0_455_3,axiom,
( ~ topological_space(X3,X4)
| ~ element_of_set(X1,closure(X2,X3,X4))
| ~ element_of_set(X1,closure(relative_complement_sets(X2,X3),X3,X4))
| element_of_set(X1,boundary(X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_455]) ).
cnf(c_0_456_0,axiom,
( open(X1,X2,X3)
| ~ neighborhood(X1,X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_456]) ).
cnf(c_0_456_1,axiom,
( ~ neighborhood(X1,X4,X2,X3)
| open(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_456]) ).
cnf(c_0_457_0,axiom,
( topological_space(X1,X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_457]) ).
cnf(c_0_457_1,axiom,
( ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| topological_space(X1,X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_457]) ).
cnf(c_0_457_2,axiom,
( ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| topological_space(X1,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_457]) ).
cnf(c_0_457_3,axiom,
( ~ element_of_collection(X1,X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| topological_space(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_457]) ).
cnf(c_0_457_4,axiom,
( ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| topological_space(X1,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_457]) ).
cnf(c_0_457_5,axiom,
( ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_457]) ).
cnf(c_0_458_0,axiom,
( equal_sets(union_of_sets(X1,X2),X3)
| ~ separation(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_458]) ).
cnf(c_0_458_1,axiom,
( ~ separation(X1,X2,X3,X4)
| equal_sets(union_of_sets(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_458]) ).
cnf(c_0_459_0,axiom,
( equal_sets(X2,empty_set)
| equal_sets(X1,empty_set)
| separation(X1,X2,X3,X4)
| ~ disjoint_s(X1,X2)
| ~ equal_sets(union_of_sets(X1,X2),X3)
| ~ element_of_collection(X2,X4)
| ~ element_of_collection(X1,X4)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_459]) ).
cnf(c_0_459_1,axiom,
( equal_sets(X1,empty_set)
| equal_sets(X2,empty_set)
| separation(X1,X2,X3,X4)
| ~ disjoint_s(X1,X2)
| ~ equal_sets(union_of_sets(X1,X2),X3)
| ~ element_of_collection(X2,X4)
| ~ element_of_collection(X1,X4)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_459]) ).
cnf(c_0_459_2,axiom,
( separation(X1,X2,X3,X4)
| equal_sets(X1,empty_set)
| equal_sets(X2,empty_set)
| ~ disjoint_s(X1,X2)
| ~ equal_sets(union_of_sets(X1,X2),X3)
| ~ element_of_collection(X2,X4)
| ~ element_of_collection(X1,X4)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_459]) ).
cnf(c_0_459_3,axiom,
( ~ disjoint_s(X1,X2)
| separation(X1,X2,X3,X4)
| equal_sets(X1,empty_set)
| equal_sets(X2,empty_set)
| ~ equal_sets(union_of_sets(X1,X2),X3)
| ~ element_of_collection(X2,X4)
| ~ element_of_collection(X1,X4)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_459]) ).
cnf(c_0_459_4,axiom,
( ~ equal_sets(union_of_sets(X1,X2),X3)
| ~ disjoint_s(X1,X2)
| separation(X1,X2,X3,X4)
| equal_sets(X1,empty_set)
| equal_sets(X2,empty_set)
| ~ element_of_collection(X2,X4)
| ~ element_of_collection(X1,X4)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_459]) ).
cnf(c_0_459_5,axiom,
( ~ element_of_collection(X2,X4)
| ~ equal_sets(union_of_sets(X1,X2),X3)
| ~ disjoint_s(X1,X2)
| separation(X1,X2,X3,X4)
| equal_sets(X1,empty_set)
| equal_sets(X2,empty_set)
| ~ element_of_collection(X1,X4)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_459]) ).
cnf(c_0_459_6,axiom,
( ~ element_of_collection(X1,X4)
| ~ element_of_collection(X2,X4)
| ~ equal_sets(union_of_sets(X1,X2),X3)
| ~ disjoint_s(X1,X2)
| separation(X1,X2,X3,X4)
| equal_sets(X1,empty_set)
| equal_sets(X2,empty_set)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_459]) ).
cnf(c_0_459_7,axiom,
( ~ topological_space(X3,X4)
| ~ element_of_collection(X1,X4)
| ~ element_of_collection(X2,X4)
| ~ equal_sets(union_of_sets(X1,X2),X3)
| ~ disjoint_s(X1,X2)
| separation(X1,X2,X3,X4)
| equal_sets(X1,empty_set)
| equal_sets(X2,empty_set) ),
inference(literals_permutation,[status(thm)],[c_0_459]) ).
cnf(c_0_460_0,axiom,
( ~ separation(X1,X2,X3,X4)
| ~ connected_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_460]) ).
cnf(c_0_460_1,axiom,
( ~ connected_space(X3,X4)
| ~ separation(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_460]) ).
cnf(c_0_461_0,axiom,
( ~ equal_sets(X1,empty_set)
| ~ separation(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_461]) ).
cnf(c_0_461_1,axiom,
( ~ separation(X1,X2,X3,X4)
| ~ equal_sets(X1,empty_set) ),
inference(literals_permutation,[status(thm)],[c_0_461]) ).
cnf(c_0_462_0,axiom,
( ~ equal_sets(X1,empty_set)
| ~ separation(X2,X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_462]) ).
cnf(c_0_462_1,axiom,
( ~ separation(X2,X1,X3,X4)
| ~ equal_sets(X1,empty_set) ),
inference(literals_permutation,[status(thm)],[c_0_462]) ).
cnf(c_0_463_0,axiom,
( topological_space(X1,X2)
| ~ neighborhood(X3,X4,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_463]) ).
cnf(c_0_463_1,axiom,
( ~ neighborhood(X3,X4,X1,X2)
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_463]) ).
cnf(c_0_464_0,axiom,
( element_of_set(X1,X2)
| ~ neighborhood(X2,X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_464]) ).
cnf(c_0_464_1,axiom,
( ~ neighborhood(X2,X1,X3,X4)
| element_of_set(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_464]) ).
cnf(c_0_465_0,axiom,
( topological_space(X1,X2)
| ~ limit_point(X3,X4,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_465]) ).
cnf(c_0_465_1,axiom,
( ~ limit_point(X3,X4,X1,X2)
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_465]) ).
cnf(c_0_466_0,axiom,
( subset_sets(X1,X2)
| ~ limit_point(X3,X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_466]) ).
cnf(c_0_466_1,axiom,
( ~ limit_point(X3,X1,X2,X4)
| subset_sets(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_466]) ).
cnf(c_0_467_0,axiom,
( topological_space(X1,X2)
| ~ separation(X3,X4,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_467]) ).
cnf(c_0_467_1,axiom,
( ~ separation(X3,X4,X1,X2)
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_467]) ).
cnf(c_0_468_0,axiom,
( element_of_collection(X1,X2)
| ~ separation(X1,X3,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_468]) ).
cnf(c_0_468_1,axiom,
( ~ separation(X1,X3,X4,X2)
| element_of_collection(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_468]) ).
cnf(c_0_469_0,axiom,
( element_of_collection(X1,X2)
| ~ separation(X3,X1,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_469]) ).
cnf(c_0_469_1,axiom,
( ~ separation(X3,X1,X4,X2)
| element_of_collection(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_469]) ).
cnf(c_0_470_0,axiom,
( disjoint_s(X1,X2)
| ~ separation(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_470]) ).
cnf(c_0_470_1,axiom,
( ~ separation(X1,X2,X3,X4)
| disjoint_s(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_470]) ).
cnf(c_0_471_0,axiom,
( neighborhood(X2,X1,X3,X4)
| ~ element_of_set(X1,X2)
| ~ open(X2,X3,X4)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_471]) ).
cnf(c_0_471_1,axiom,
( ~ element_of_set(X1,X2)
| neighborhood(X2,X1,X3,X4)
| ~ open(X2,X3,X4)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_471]) ).
cnf(c_0_471_2,axiom,
( ~ open(X2,X3,X4)
| ~ element_of_set(X1,X2)
| neighborhood(X2,X1,X3,X4)
| ~ topological_space(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_471]) ).
cnf(c_0_471_3,axiom,
( ~ topological_space(X3,X4)
| ~ open(X2,X3,X4)
| ~ element_of_set(X1,X2)
| neighborhood(X2,X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_471]) ).
cnf(c_0_472_0,axiom,
( element_of_set(X1,closure(relative_complement_sets(X2,X3),X3,X4))
| ~ element_of_set(X1,boundary(X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_472]) ).
cnf(c_0_472_1,axiom,
( ~ element_of_set(X1,boundary(X2,X3,X4))
| element_of_set(X1,closure(relative_complement_sets(X2,X3),X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_472]) ).
cnf(c_0_473_0,axiom,
( basis(X2,X3)
| ~ subset_sets(X1,intersection_of_sets(f8(X2,X3),f9(X2,X3)))
| ~ element_of_collection(X1,X3)
| ~ element_of_set(f7(X2,X3),X1)
| ~ equal_sets(union_of_members(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_473]) ).
cnf(c_0_473_1,axiom,
( ~ subset_sets(X1,intersection_of_sets(f8(X2,X3),f9(X2,X3)))
| basis(X2,X3)
| ~ element_of_collection(X1,X3)
| ~ element_of_set(f7(X2,X3),X1)
| ~ equal_sets(union_of_members(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_473]) ).
cnf(c_0_473_2,axiom,
( ~ element_of_collection(X1,X3)
| ~ subset_sets(X1,intersection_of_sets(f8(X2,X3),f9(X2,X3)))
| basis(X2,X3)
| ~ element_of_set(f7(X2,X3),X1)
| ~ equal_sets(union_of_members(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_473]) ).
cnf(c_0_473_3,axiom,
( ~ element_of_set(f7(X2,X3),X1)
| ~ element_of_collection(X1,X3)
| ~ subset_sets(X1,intersection_of_sets(f8(X2,X3),f9(X2,X3)))
| basis(X2,X3)
| ~ equal_sets(union_of_members(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_473]) ).
cnf(c_0_473_4,axiom,
( ~ equal_sets(union_of_members(X3),X2)
| ~ element_of_set(f7(X2,X3),X1)
| ~ element_of_collection(X1,X3)
| ~ subset_sets(X1,intersection_of_sets(f8(X2,X3),f9(X2,X3)))
| basis(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_473]) ).
cnf(c_0_474_0,axiom,
( subset_collections(f5(X1,X2),X2)
| topological_space(X1,X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_474]) ).
cnf(c_0_474_1,axiom,
( topological_space(X1,X2)
| subset_collections(f5(X1,X2),X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_474]) ).
cnf(c_0_474_2,axiom,
( ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| topological_space(X1,X2)
| subset_collections(f5(X1,X2),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_474]) ).
cnf(c_0_474_3,axiom,
( ~ element_of_collection(X1,X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| topological_space(X1,X2)
| subset_collections(f5(X1,X2),X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_474]) ).
cnf(c_0_474_4,axiom,
( ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| topological_space(X1,X2)
| subset_collections(f5(X1,X2),X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_474]) ).
cnf(c_0_474_5,axiom,
( ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(intersection_of_sets(f3(X1,X2),f4(X1,X2)),X2)
| topological_space(X1,X2)
| subset_collections(f5(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_474]) ).
cnf(c_0_475_0,axiom,
( separation(f21(X1,X2),f22(X1,X2),X1,X2)
| connected_space(X1,X2)
| ~ topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_475]) ).
cnf(c_0_475_1,axiom,
( connected_space(X1,X2)
| separation(f21(X1,X2),f22(X1,X2),X1,X2)
| ~ topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_475]) ).
cnf(c_0_475_2,axiom,
( ~ topological_space(X1,X2)
| connected_space(X1,X2)
| separation(f21(X1,X2),f22(X1,X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_475]) ).
cnf(c_0_476_0,axiom,
( element_of_set(X1,X2)
| ~ closed(X2,X3,X4)
| ~ subset_sets(X5,X2)
| ~ element_of_set(X1,closure(X5,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_476]) ).
cnf(c_0_476_1,axiom,
( ~ closed(X2,X3,X4)
| element_of_set(X1,X2)
| ~ subset_sets(X5,X2)
| ~ element_of_set(X1,closure(X5,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_476]) ).
cnf(c_0_476_2,axiom,
( ~ subset_sets(X5,X2)
| ~ closed(X2,X3,X4)
| element_of_set(X1,X2)
| ~ element_of_set(X1,closure(X5,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_476]) ).
cnf(c_0_476_3,axiom,
( ~ element_of_set(X1,closure(X5,X3,X4))
| ~ subset_sets(X5,X2)
| ~ closed(X2,X3,X4)
| element_of_set(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_476]) ).
cnf(c_0_477_0,axiom,
( element_of_set(X1,closure(X2,X3,X4))
| ~ element_of_set(X1,boundary(X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_477]) ).
cnf(c_0_477_1,axiom,
( ~ element_of_set(X1,boundary(X2,X3,X4))
| element_of_set(X1,closure(X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_477]) ).
cnf(c_0_478_0,axiom,
( element_of_set(X5,interior(X4,X2,X3))
| ~ open(X1,X2,X3)
| ~ subset_sets(X1,X4)
| ~ element_of_set(X5,X1)
| ~ subset_sets(X4,X2)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_478]) ).
cnf(c_0_478_1,axiom,
( ~ open(X1,X2,X3)
| element_of_set(X5,interior(X4,X2,X3))
| ~ subset_sets(X1,X4)
| ~ element_of_set(X5,X1)
| ~ subset_sets(X4,X2)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_478]) ).
cnf(c_0_478_2,axiom,
( ~ subset_sets(X1,X4)
| ~ open(X1,X2,X3)
| element_of_set(X5,interior(X4,X2,X3))
| ~ element_of_set(X5,X1)
| ~ subset_sets(X4,X2)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_478]) ).
cnf(c_0_478_3,axiom,
( ~ element_of_set(X5,X1)
| ~ subset_sets(X1,X4)
| ~ open(X1,X2,X3)
| element_of_set(X5,interior(X4,X2,X3))
| ~ subset_sets(X4,X2)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_478]) ).
cnf(c_0_478_4,axiom,
( ~ subset_sets(X4,X2)
| ~ element_of_set(X5,X1)
| ~ subset_sets(X1,X4)
| ~ open(X1,X2,X3)
| element_of_set(X5,interior(X4,X2,X3))
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_478]) ).
cnf(c_0_478_5,axiom,
( ~ topological_space(X2,X3)
| ~ subset_sets(X4,X2)
| ~ element_of_set(X5,X1)
| ~ subset_sets(X1,X4)
| ~ open(X1,X2,X3)
| element_of_set(X5,interior(X4,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_478]) ).
cnf(c_0_479_0,axiom,
( connected_set(X1,X2,X3)
| ~ connected_space(X1,subspace_topology(X2,X3,X1))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_479]) ).
cnf(c_0_479_1,axiom,
( ~ connected_space(X1,subspace_topology(X2,X3,X1))
| connected_set(X1,X2,X3)
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_479]) ).
cnf(c_0_479_2,axiom,
( ~ subset_sets(X1,X2)
| ~ connected_space(X1,subspace_topology(X2,X3,X1))
| connected_set(X1,X2,X3)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_479]) ).
cnf(c_0_479_3,axiom,
( ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| ~ connected_space(X1,subspace_topology(X2,X3,X1))
| connected_set(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_479]) ).
cnf(c_0_480_0,axiom,
( compact_set(X1,X2,X3)
| ~ compact_space(X1,subspace_topology(X2,X3,X1))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_480]) ).
cnf(c_0_480_1,axiom,
( ~ compact_space(X1,subspace_topology(X2,X3,X1))
| compact_set(X1,X2,X3)
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_480]) ).
cnf(c_0_480_2,axiom,
( ~ subset_sets(X1,X2)
| ~ compact_space(X1,subspace_topology(X2,X3,X1))
| compact_set(X1,X2,X3)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_480]) ).
cnf(c_0_480_3,axiom,
( ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| ~ compact_space(X1,subspace_topology(X2,X3,X1))
| compact_set(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_480]) ).
cnf(c_0_481_0,axiom,
( open_covering(f23(X1,X2,X3),X1,X2)
| ~ open_covering(X3,X1,X2)
| ~ compact_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_481]) ).
cnf(c_0_481_1,axiom,
( ~ open_covering(X3,X1,X2)
| open_covering(f23(X1,X2,X3),X1,X2)
| ~ compact_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_481]) ).
cnf(c_0_481_2,axiom,
( ~ compact_space(X1,X2)
| ~ open_covering(X3,X1,X2)
| open_covering(f23(X1,X2,X3),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_481]) ).
cnf(c_0_482_0,axiom,
( element_of_collection(X1,subspace_topology(X5,X4,X2))
| ~ equal_sets(X1,intersection_of_sets(X2,X3))
| ~ element_of_collection(X3,X4)
| ~ subset_sets(X2,X5)
| ~ topological_space(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_482]) ).
cnf(c_0_482_1,axiom,
( ~ equal_sets(X1,intersection_of_sets(X2,X3))
| element_of_collection(X1,subspace_topology(X5,X4,X2))
| ~ element_of_collection(X3,X4)
| ~ subset_sets(X2,X5)
| ~ topological_space(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_482]) ).
cnf(c_0_482_2,axiom,
( ~ element_of_collection(X3,X4)
| ~ equal_sets(X1,intersection_of_sets(X2,X3))
| element_of_collection(X1,subspace_topology(X5,X4,X2))
| ~ subset_sets(X2,X5)
| ~ topological_space(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_482]) ).
cnf(c_0_482_3,axiom,
( ~ subset_sets(X2,X5)
| ~ element_of_collection(X3,X4)
| ~ equal_sets(X1,intersection_of_sets(X2,X3))
| element_of_collection(X1,subspace_topology(X5,X4,X2))
| ~ topological_space(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_482]) ).
cnf(c_0_482_4,axiom,
( ~ topological_space(X5,X4)
| ~ subset_sets(X2,X5)
| ~ element_of_collection(X3,X4)
| ~ equal_sets(X1,intersection_of_sets(X2,X3))
| element_of_collection(X1,subspace_topology(X5,X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_482]) ).
cnf(c_0_483_0,axiom,
( element_of_collection(f3(X1,X2),X2)
| topological_space(X1,X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_483]) ).
cnf(c_0_483_1,axiom,
( topological_space(X1,X2)
| element_of_collection(f3(X1,X2),X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_483]) ).
cnf(c_0_483_2,axiom,
( ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| topological_space(X1,X2)
| element_of_collection(f3(X1,X2),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_483]) ).
cnf(c_0_483_3,axiom,
( ~ element_of_collection(X1,X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| topological_space(X1,X2)
| element_of_collection(f3(X1,X2),X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_483]) ).
cnf(c_0_483_4,axiom,
( ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| topological_space(X1,X2)
| element_of_collection(f3(X1,X2),X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_483]) ).
cnf(c_0_483_5,axiom,
( ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| topological_space(X1,X2)
| element_of_collection(f3(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_483]) ).
cnf(c_0_484_0,axiom,
( element_of_collection(f4(X1,X2),X2)
| topological_space(X1,X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_484]) ).
cnf(c_0_484_1,axiom,
( topological_space(X1,X2)
| element_of_collection(f4(X1,X2),X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_484]) ).
cnf(c_0_484_2,axiom,
( ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| topological_space(X1,X2)
| element_of_collection(f4(X1,X2),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_484]) ).
cnf(c_0_484_3,axiom,
( ~ element_of_collection(X1,X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| topological_space(X1,X2)
| element_of_collection(f4(X1,X2),X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_484]) ).
cnf(c_0_484_4,axiom,
( ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| topological_space(X1,X2)
| element_of_collection(f4(X1,X2),X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_484]) ).
cnf(c_0_484_5,axiom,
( ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(union_of_members(f5(X1,X2)),X2)
| topological_space(X1,X2)
| element_of_collection(f4(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_484]) ).
cnf(c_0_485_0,axiom,
( subset_collections(f23(X1,X2,X3),X3)
| ~ open_covering(X3,X1,X2)
| ~ compact_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_485]) ).
cnf(c_0_485_1,axiom,
( ~ open_covering(X3,X1,X2)
| subset_collections(f23(X1,X2,X3),X3)
| ~ compact_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_485]) ).
cnf(c_0_485_2,axiom,
( ~ compact_space(X1,X2)
| ~ open_covering(X3,X1,X2)
| subset_collections(f23(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_485]) ).
cnf(c_0_486_0,axiom,
( finite(f23(X1,X2,X3))
| ~ open_covering(X3,X1,X2)
| ~ compact_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_486]) ).
cnf(c_0_486_1,axiom,
( ~ open_covering(X3,X1,X2)
| finite(f23(X1,X2,X3))
| ~ compact_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_486]) ).
cnf(c_0_486_2,axiom,
( ~ compact_space(X1,X2)
| ~ open_covering(X3,X1,X2)
| finite(f23(X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_486]) ).
cnf(c_0_487_0,axiom,
( element_of_set(f7(X1,X2),intersection_of_sets(f8(X1,X2),f9(X1,X2)))
| basis(X1,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_487]) ).
cnf(c_0_487_1,axiom,
( basis(X1,X2)
| element_of_set(f7(X1,X2),intersection_of_sets(f8(X1,X2),f9(X1,X2)))
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_487]) ).
cnf(c_0_487_2,axiom,
( ~ equal_sets(union_of_members(X2),X1)
| basis(X1,X2)
| element_of_set(f7(X1,X2),intersection_of_sets(f8(X1,X2),f9(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_487]) ).
cnf(c_0_488_0,axiom,
( connected_space(X1,subspace_topology(X2,X3,X1))
| ~ connected_set(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_488]) ).
cnf(c_0_488_1,axiom,
( ~ connected_set(X1,X2,X3)
| connected_space(X1,subspace_topology(X2,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_488]) ).
cnf(c_0_489_0,axiom,
( compact_space(X1,subspace_topology(X2,X3,X1))
| ~ compact_set(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_489]) ).
cnf(c_0_489_1,axiom,
( ~ compact_set(X1,X2,X3)
| compact_space(X1,subspace_topology(X2,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_489]) ).
cnf(c_0_490_0,axiom,
( topological_space(X1,X2)
| ~ element_of_collection(X3,subspace_topology(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_490]) ).
cnf(c_0_490_1,axiom,
( ~ element_of_collection(X3,subspace_topology(X1,X2,X4))
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_490]) ).
cnf(c_0_491_0,axiom,
( subset_sets(X1,X2)
| ~ element_of_collection(X3,subspace_topology(X2,X4,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_491]) ).
cnf(c_0_491_1,axiom,
( ~ element_of_collection(X3,subspace_topology(X2,X4,X1))
| subset_sets(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_491]) ).
cnf(c_0_492_0,axiom,
( topological_space(X1,X2)
| ~ element_of_set(X3,interior(X4,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_492]) ).
cnf(c_0_492_1,axiom,
( ~ element_of_set(X3,interior(X4,X1,X2))
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_492]) ).
cnf(c_0_493_0,axiom,
( subset_sets(X1,X2)
| ~ element_of_set(X3,interior(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_493]) ).
cnf(c_0_493_1,axiom,
( ~ element_of_set(X3,interior(X1,X2,X4))
| subset_sets(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_493]) ).
cnf(c_0_494_0,axiom,
( topological_space(X1,X2)
| ~ element_of_set(X3,closure(X4,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_494]) ).
cnf(c_0_494_1,axiom,
( ~ element_of_set(X3,closure(X4,X1,X2))
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_494]) ).
cnf(c_0_495_0,axiom,
( subset_sets(X1,X2)
| ~ element_of_set(X3,closure(X1,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_495]) ).
cnf(c_0_495_1,axiom,
( ~ element_of_set(X3,closure(X1,X2,X4))
| subset_sets(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_495]) ).
cnf(c_0_496_0,axiom,
( topological_space(X1,X2)
| ~ element_of_set(X3,boundary(X4,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_496]) ).
cnf(c_0_496_1,axiom,
( ~ element_of_set(X3,boundary(X4,X1,X2))
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_496]) ).
cnf(c_0_497_0,axiom,
( closed(X1,X2,X3)
| ~ open(relative_complement_sets(X1,X2),X2,X3)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_497]) ).
cnf(c_0_497_1,axiom,
( ~ open(relative_complement_sets(X1,X2),X2,X3)
| closed(X1,X2,X3)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_497]) ).
cnf(c_0_497_2,axiom,
( ~ topological_space(X2,X3)
| ~ open(relative_complement_sets(X1,X2),X2,X3)
| closed(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_497]) ).
cnf(c_0_498_0,axiom,
( compact_space(X2,X3)
| ~ open_covering(X1,X2,X3)
| ~ subset_collections(X1,f24(X2,X3))
| ~ finite(X1)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_498]) ).
cnf(c_0_498_1,axiom,
( ~ open_covering(X1,X2,X3)
| compact_space(X2,X3)
| ~ subset_collections(X1,f24(X2,X3))
| ~ finite(X1)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_498]) ).
cnf(c_0_498_2,axiom,
( ~ subset_collections(X1,f24(X2,X3))
| ~ open_covering(X1,X2,X3)
| compact_space(X2,X3)
| ~ finite(X1)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_498]) ).
cnf(c_0_498_3,axiom,
( ~ finite(X1)
| ~ subset_collections(X1,f24(X2,X3))
| ~ open_covering(X1,X2,X3)
| compact_space(X2,X3)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_498]) ).
cnf(c_0_498_4,axiom,
( ~ topological_space(X2,X3)
| ~ finite(X1)
| ~ subset_collections(X1,f24(X2,X3))
| ~ open_covering(X1,X2,X3)
| compact_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_498]) ).
cnf(c_0_499_0,axiom,
( element_of_set(X1,f10(X2,X3,X1))
| ~ element_of_set(X1,X3)
| ~ element_of_collection(X3,top_of_basis(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_499]) ).
cnf(c_0_499_1,axiom,
( ~ element_of_set(X1,X3)
| element_of_set(X1,f10(X2,X3,X1))
| ~ element_of_collection(X3,top_of_basis(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_499]) ).
cnf(c_0_499_2,axiom,
( ~ element_of_collection(X3,top_of_basis(X2))
| ~ element_of_set(X1,X3)
| element_of_set(X1,f10(X2,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_499]) ).
cnf(c_0_500_0,axiom,
( element_of_collection(f10(X1,X2,X3),X1)
| ~ element_of_set(X3,X2)
| ~ element_of_collection(X2,top_of_basis(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_500]) ).
cnf(c_0_500_1,axiom,
( ~ element_of_set(X3,X2)
| element_of_collection(f10(X1,X2,X3),X1)
| ~ element_of_collection(X2,top_of_basis(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_500]) ).
cnf(c_0_500_2,axiom,
( ~ element_of_collection(X2,top_of_basis(X1))
| ~ element_of_set(X3,X2)
| element_of_collection(f10(X1,X2,X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_500]) ).
cnf(c_0_501_0,axiom,
( subset_sets(f10(X1,X2,X3),X2)
| ~ element_of_set(X3,X2)
| ~ element_of_collection(X2,top_of_basis(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_501]) ).
cnf(c_0_501_1,axiom,
( ~ element_of_set(X3,X2)
| subset_sets(f10(X1,X2,X3),X2)
| ~ element_of_collection(X2,top_of_basis(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_501]) ).
cnf(c_0_501_2,axiom,
( ~ element_of_collection(X2,top_of_basis(X1))
| ~ element_of_set(X3,X2)
| subset_sets(f10(X1,X2,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_501]) ).
cnf(c_0_502_0,axiom,
( subset_collections(f5(X1,X2),X2)
| element_of_collection(f3(X1,X2),X2)
| topological_space(X1,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_502]) ).
cnf(c_0_502_1,axiom,
( element_of_collection(f3(X1,X2),X2)
| subset_collections(f5(X1,X2),X2)
| topological_space(X1,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_502]) ).
cnf(c_0_502_2,axiom,
( topological_space(X1,X2)
| element_of_collection(f3(X1,X2),X2)
| subset_collections(f5(X1,X2),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_502]) ).
cnf(c_0_502_3,axiom,
( ~ element_of_collection(X1,X2)
| topological_space(X1,X2)
| element_of_collection(f3(X1,X2),X2)
| subset_collections(f5(X1,X2),X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_502]) ).
cnf(c_0_502_4,axiom,
( ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| topological_space(X1,X2)
| element_of_collection(f3(X1,X2),X2)
| subset_collections(f5(X1,X2),X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_502]) ).
cnf(c_0_502_5,axiom,
( ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| topological_space(X1,X2)
| element_of_collection(f3(X1,X2),X2)
| subset_collections(f5(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_502]) ).
cnf(c_0_503_0,axiom,
( subset_collections(f5(X1,X2),X2)
| element_of_collection(f4(X1,X2),X2)
| topological_space(X1,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_503]) ).
cnf(c_0_503_1,axiom,
( element_of_collection(f4(X1,X2),X2)
| subset_collections(f5(X1,X2),X2)
| topological_space(X1,X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_503]) ).
cnf(c_0_503_2,axiom,
( topological_space(X1,X2)
| element_of_collection(f4(X1,X2),X2)
| subset_collections(f5(X1,X2),X2)
| ~ element_of_collection(X1,X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_503]) ).
cnf(c_0_503_3,axiom,
( ~ element_of_collection(X1,X2)
| topological_space(X1,X2)
| element_of_collection(f4(X1,X2),X2)
| subset_collections(f5(X1,X2),X2)
| ~ element_of_collection(empty_set,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_503]) ).
cnf(c_0_503_4,axiom,
( ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| topological_space(X1,X2)
| element_of_collection(f4(X1,X2),X2)
| subset_collections(f5(X1,X2),X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_503]) ).
cnf(c_0_503_5,axiom,
( ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(empty_set,X2)
| ~ element_of_collection(X1,X2)
| topological_space(X1,X2)
| element_of_collection(f4(X1,X2),X2)
| subset_collections(f5(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_503]) ).
cnf(c_0_504_0,axiom,
( open(relative_complement_sets(X1,X2),X2,X3)
| ~ closed(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_504]) ).
cnf(c_0_504_1,axiom,
( ~ closed(X1,X2,X3)
| open(relative_complement_sets(X1,X2),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_504]) ).
cnf(c_0_505_0,axiom,
( hausdorff(X1,X2)
| ~ eq_p(f19(X1,X2),f20(X1,X2))
| ~ topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_505]) ).
cnf(c_0_505_1,axiom,
( ~ eq_p(f19(X1,X2),f20(X1,X2))
| hausdorff(X1,X2)
| ~ topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_505]) ).
cnf(c_0_505_2,axiom,
( ~ topological_space(X1,X2)
| ~ eq_p(f19(X1,X2),f20(X1,X2))
| hausdorff(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_505]) ).
cnf(c_0_506_0,axiom,
( open_covering(X1,X2,X3)
| ~ equal_sets(union_of_members(X1),X2)
| ~ subset_collections(X1,X3)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_506]) ).
cnf(c_0_506_1,axiom,
( ~ equal_sets(union_of_members(X1),X2)
| open_covering(X1,X2,X3)
| ~ subset_collections(X1,X3)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_506]) ).
cnf(c_0_506_2,axiom,
( ~ subset_collections(X1,X3)
| ~ equal_sets(union_of_members(X1),X2)
| open_covering(X1,X2,X3)
| ~ topological_space(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_506]) ).
cnf(c_0_506_3,axiom,
( ~ topological_space(X2,X3)
| ~ subset_collections(X1,X3)
| ~ equal_sets(union_of_members(X1),X2)
| open_covering(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_506]) ).
cnf(c_0_507_0,axiom,
( element_of_collection(X2,top_of_basis(X3))
| ~ subset_sets(X1,X2)
| ~ element_of_collection(X1,X3)
| ~ element_of_set(f11(X3,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_507]) ).
cnf(c_0_507_1,axiom,
( ~ subset_sets(X1,X2)
| element_of_collection(X2,top_of_basis(X3))
| ~ element_of_collection(X1,X3)
| ~ element_of_set(f11(X3,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_507]) ).
cnf(c_0_507_2,axiom,
( ~ element_of_collection(X1,X3)
| ~ subset_sets(X1,X2)
| element_of_collection(X2,top_of_basis(X3))
| ~ element_of_set(f11(X3,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_507]) ).
cnf(c_0_507_3,axiom,
( ~ element_of_set(f11(X3,X2),X1)
| ~ element_of_collection(X1,X3)
| ~ subset_sets(X1,X2)
| element_of_collection(X2,top_of_basis(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_507]) ).
cnf(c_0_508_0,axiom,
( finer(X2,X1,X3)
| ~ subset_collections(X1,X2)
| ~ topological_space(X3,X1)
| ~ topological_space(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_508]) ).
cnf(c_0_508_1,axiom,
( ~ subset_collections(X1,X2)
| finer(X2,X1,X3)
| ~ topological_space(X3,X1)
| ~ topological_space(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_508]) ).
cnf(c_0_508_2,axiom,
( ~ topological_space(X3,X1)
| ~ subset_collections(X1,X2)
| finer(X2,X1,X3)
| ~ topological_space(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_508]) ).
cnf(c_0_508_3,axiom,
( ~ topological_space(X3,X2)
| ~ topological_space(X3,X1)
| ~ subset_collections(X1,X2)
| finer(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_508]) ).
cnf(c_0_509_0,axiom,
( open_covering(f24(X1,X2),X1,X2)
| compact_space(X1,X2)
| ~ topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_509]) ).
cnf(c_0_509_1,axiom,
( compact_space(X1,X2)
| open_covering(f24(X1,X2),X1,X2)
| ~ topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_509]) ).
cnf(c_0_509_2,axiom,
( ~ topological_space(X1,X2)
| compact_space(X1,X2)
| open_covering(f24(X1,X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_509]) ).
cnf(c_0_510_0,axiom,
( element_of_collection(intersection_of_sets(X1,X2),X3)
| ~ element_of_collection(X2,X3)
| ~ element_of_collection(X1,X3)
| ~ topological_space(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_510]) ).
cnf(c_0_510_1,axiom,
( ~ element_of_collection(X2,X3)
| element_of_collection(intersection_of_sets(X1,X2),X3)
| ~ element_of_collection(X1,X3)
| ~ topological_space(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_510]) ).
cnf(c_0_510_2,axiom,
( ~ element_of_collection(X1,X3)
| ~ element_of_collection(X2,X3)
| element_of_collection(intersection_of_sets(X1,X2),X3)
| ~ topological_space(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_510]) ).
cnf(c_0_510_3,axiom,
( ~ topological_space(X4,X3)
| ~ element_of_collection(X1,X3)
| ~ element_of_collection(X2,X3)
| element_of_collection(intersection_of_sets(X1,X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_510]) ).
cnf(c_0_511_0,axiom,
( equal_sets(union_of_members(X1),X2)
| ~ open_covering(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_511]) ).
cnf(c_0_511_1,axiom,
( ~ open_covering(X1,X2,X3)
| equal_sets(union_of_members(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_511]) ).
cnf(c_0_512_0,axiom,
( topological_space(X1,X2)
| ~ open(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_512]) ).
cnf(c_0_512_1,axiom,
( ~ open(X3,X1,X2)
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_512]) ).
cnf(c_0_513_0,axiom,
( element_of_collection(X1,X2)
| ~ open(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_513]) ).
cnf(c_0_513_1,axiom,
( ~ open(X1,X3,X2)
| element_of_collection(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_513]) ).
cnf(c_0_514_0,axiom,
( topological_space(X1,X2)
| ~ closed(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_514]) ).
cnf(c_0_514_1,axiom,
( ~ closed(X3,X1,X2)
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_514]) ).
cnf(c_0_515_0,axiom,
( topological_space(X1,X2)
| ~ finer(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_515]) ).
cnf(c_0_515_1,axiom,
( ~ finer(X2,X3,X1)
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_515]) ).
cnf(c_0_516_0,axiom,
( topological_space(X1,X2)
| ~ finer(X3,X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_516]) ).
cnf(c_0_516_1,axiom,
( ~ finer(X3,X2,X1)
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_516]) ).
cnf(c_0_517_0,axiom,
( subset_collections(X1,X2)
| ~ finer(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_517]) ).
cnf(c_0_517_1,axiom,
( ~ finer(X2,X1,X3)
| subset_collections(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_517]) ).
cnf(c_0_518_0,axiom,
( topological_space(X1,X2)
| ~ connected_set(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_518]) ).
cnf(c_0_518_1,axiom,
( ~ connected_set(X3,X1,X2)
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_518]) ).
cnf(c_0_519_0,axiom,
( subset_sets(X1,X2)
| ~ connected_set(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_519]) ).
cnf(c_0_519_1,axiom,
( ~ connected_set(X1,X2,X3)
| subset_sets(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_519]) ).
cnf(c_0_520_0,axiom,
( topological_space(X1,X2)
| ~ open_covering(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_520]) ).
cnf(c_0_520_1,axiom,
( ~ open_covering(X3,X1,X2)
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_520]) ).
cnf(c_0_521_0,axiom,
( subset_collections(X1,X2)
| ~ open_covering(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_521]) ).
cnf(c_0_521_1,axiom,
( ~ open_covering(X1,X3,X2)
| subset_collections(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_521]) ).
cnf(c_0_522_0,axiom,
( topological_space(X1,X2)
| ~ compact_set(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_522]) ).
cnf(c_0_522_1,axiom,
( ~ compact_set(X3,X1,X2)
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_522]) ).
cnf(c_0_523_0,axiom,
( subset_sets(X1,X2)
| ~ compact_set(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_523]) ).
cnf(c_0_523_1,axiom,
( ~ compact_set(X1,X2,X3)
| subset_sets(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_523]) ).
cnf(c_0_524_0,axiom,
( open(X1,X3,X2)
| ~ element_of_collection(X1,X2)
| ~ topological_space(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_524]) ).
cnf(c_0_524_1,axiom,
( ~ element_of_collection(X1,X2)
| open(X1,X3,X2)
| ~ topological_space(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_524]) ).
cnf(c_0_524_2,axiom,
( ~ topological_space(X3,X2)
| ~ element_of_collection(X1,X2)
| open(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_524]) ).
cnf(c_0_525_0,axiom,
( element_of_set(f7(X1,X2),X1)
| basis(X1,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_525]) ).
cnf(c_0_525_1,axiom,
( basis(X1,X2)
| element_of_set(f7(X1,X2),X1)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_525]) ).
cnf(c_0_525_2,axiom,
( ~ equal_sets(union_of_members(X2),X1)
| basis(X1,X2)
| element_of_set(f7(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_525]) ).
cnf(c_0_526_0,axiom,
( element_of_collection(f8(X1,X2),X2)
| basis(X1,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_526]) ).
cnf(c_0_526_1,axiom,
( basis(X1,X2)
| element_of_collection(f8(X1,X2),X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_526]) ).
cnf(c_0_526_2,axiom,
( ~ equal_sets(union_of_members(X2),X1)
| basis(X1,X2)
| element_of_collection(f8(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_526]) ).
cnf(c_0_527_0,axiom,
( element_of_collection(f9(X1,X2),X2)
| basis(X1,X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_527]) ).
cnf(c_0_527_1,axiom,
( basis(X1,X2)
| element_of_collection(f9(X1,X2),X2)
| ~ equal_sets(union_of_members(X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_527]) ).
cnf(c_0_527_2,axiom,
( ~ equal_sets(union_of_members(X2),X1)
| basis(X1,X2)
| element_of_collection(f9(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_527]) ).
cnf(c_0_528_0,axiom,
( element_of_set(X1,intersection_of_members(X2))
| ~ element_of_set(X1,f2(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_528]) ).
cnf(c_0_528_1,axiom,
( ~ element_of_set(X1,f2(X2,X1))
| element_of_set(X1,intersection_of_members(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_528]) ).
cnf(c_0_529_0,axiom,
( element_of_set(f19(X1,X2),X1)
| hausdorff(X1,X2)
| ~ topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_529]) ).
cnf(c_0_529_1,axiom,
( hausdorff(X1,X2)
| element_of_set(f19(X1,X2),X1)
| ~ topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_529]) ).
cnf(c_0_529_2,axiom,
( ~ topological_space(X1,X2)
| hausdorff(X1,X2)
| element_of_set(f19(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_529]) ).
cnf(c_0_530_0,axiom,
( element_of_set(f20(X1,X2),X1)
| hausdorff(X1,X2)
| ~ topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_530]) ).
cnf(c_0_530_1,axiom,
( hausdorff(X1,X2)
| element_of_set(f20(X1,X2),X1)
| ~ topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_530]) ).
cnf(c_0_530_2,axiom,
( ~ topological_space(X1,X2)
| hausdorff(X1,X2)
| element_of_set(f20(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_530]) ).
cnf(c_0_531_0,axiom,
( element_of_set(X1,f1(X2,X1))
| ~ element_of_set(X1,union_of_members(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_531]) ).
cnf(c_0_531_1,axiom,
( ~ element_of_set(X1,union_of_members(X2))
| element_of_set(X1,f1(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_531]) ).
cnf(c_0_532_0,axiom,
( element_of_collection(f1(X1,X2),X1)
| ~ element_of_set(X2,union_of_members(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_532]) ).
cnf(c_0_532_1,axiom,
( ~ element_of_set(X2,union_of_members(X1))
| element_of_collection(f1(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_532]) ).
cnf(c_0_533_0,axiom,
( element_of_set(X1,X2)
| ~ element_of_collection(X2,X3)
| ~ element_of_set(X1,intersection_of_members(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_533]) ).
cnf(c_0_533_1,axiom,
( ~ element_of_collection(X2,X3)
| element_of_set(X1,X2)
| ~ element_of_set(X1,intersection_of_members(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_533]) ).
cnf(c_0_533_2,axiom,
( ~ element_of_set(X1,intersection_of_members(X3))
| ~ element_of_collection(X2,X3)
| element_of_set(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_533]) ).
cnf(c_0_534_0,axiom,
( element_of_set(X3,union_of_members(X2))
| ~ element_of_collection(X1,X2)
| ~ element_of_set(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_534]) ).
cnf(c_0_534_1,axiom,
( ~ element_of_collection(X1,X2)
| element_of_set(X3,union_of_members(X2))
| ~ element_of_set(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_534]) ).
cnf(c_0_534_2,axiom,
( ~ element_of_set(X3,X1)
| ~ element_of_collection(X1,X2)
| element_of_set(X3,union_of_members(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_534]) ).
cnf(c_0_535_0,axiom,
( element_of_collection(union_of_members(X1),X2)
| ~ subset_collections(X1,X2)
| ~ topological_space(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_535]) ).
cnf(c_0_535_1,axiom,
( ~ subset_collections(X1,X2)
| element_of_collection(union_of_members(X1),X2)
| ~ topological_space(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_535]) ).
cnf(c_0_535_2,axiom,
( ~ topological_space(X3,X2)
| ~ subset_collections(X1,X2)
| element_of_collection(union_of_members(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_535]) ).
cnf(c_0_536_0,axiom,
( element_of_collection(f2(X1,X2),X1)
| element_of_set(X2,intersection_of_members(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_536]) ).
cnf(c_0_536_1,axiom,
( element_of_set(X2,intersection_of_members(X1))
| element_of_collection(f2(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_536]) ).
cnf(c_0_537_0,axiom,
( element_of_set(f11(X1,X2),X2)
| element_of_collection(X2,top_of_basis(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_537]) ).
cnf(c_0_537_1,axiom,
( element_of_collection(X2,top_of_basis(X1))
| element_of_set(f11(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_537]) ).
cnf(c_0_538_0,axiom,
( equal_sets(union_of_members(X1),X2)
| ~ topological_space(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_538]) ).
cnf(c_0_538_1,axiom,
( ~ topological_space(X2,X1)
| equal_sets(union_of_members(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_538]) ).
cnf(c_0_539_0,axiom,
( equal_sets(union_of_members(X1),X2)
| ~ basis(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_539]) ).
cnf(c_0_539_1,axiom,
( ~ basis(X2,X1)
| equal_sets(union_of_members(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_539]) ).
cnf(c_0_540_0,axiom,
( element_of_collection(X1,X2)
| ~ topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_540]) ).
cnf(c_0_540_1,axiom,
( ~ topological_space(X1,X2)
| element_of_collection(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_540]) ).
cnf(c_0_541_0,axiom,
( topological_space(X1,X2)
| ~ hausdorff(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_541]) ).
cnf(c_0_541_1,axiom,
( ~ hausdorff(X1,X2)
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_541]) ).
cnf(c_0_542_0,axiom,
( topological_space(X1,X2)
| ~ connected_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_542]) ).
cnf(c_0_542_1,axiom,
( ~ connected_space(X1,X2)
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_542]) ).
cnf(c_0_543_0,axiom,
( topological_space(X1,X2)
| ~ compact_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_543]) ).
cnf(c_0_543_1,axiom,
( ~ compact_space(X1,X2)
| topological_space(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_543]) ).
cnf(c_0_544_0,axiom,
( element_of_collection(empty_set,X1)
| ~ topological_space(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_544]) ).
cnf(c_0_544_1,axiom,
( ~ topological_space(X2,X1)
| element_of_collection(empty_set,X1) ),
inference(literals_permutation,[status(thm)],[c_0_544]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,negated_conjecture,
! [X2,X1] : ~ element_of_collection(intersection_of_sets(X1,X2),top_of_basis(f)),
file('<stdin>',lemma_1d_4) ).
fof(c_0_1_002,negated_conjecture,
! [X2] : element_of_collection(X2,top_of_basis(f)),
file('<stdin>',lemma_1d_3) ).
fof(c_0_2_003,negated_conjecture,
! [X1] : element_of_collection(X1,top_of_basis(f)),
file('<stdin>',lemma_1d_2) ).
fof(c_0_3_004,negated_conjecture,
basis(cx,f),
file('<stdin>',lemma_1d_1) ).
fof(c_0_4_005,negated_conjecture,
! [X2,X1] : ~ element_of_collection(intersection_of_sets(X1,X2),top_of_basis(f)),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_5_006,negated_conjecture,
! [X2] : element_of_collection(X2,top_of_basis(f)),
c_0_1 ).
fof(c_0_6_007,negated_conjecture,
! [X1] : element_of_collection(X1,top_of_basis(f)),
c_0_2 ).
fof(c_0_7_008,negated_conjecture,
basis(cx,f),
c_0_3 ).
fof(c_0_8_009,negated_conjecture,
! [X3,X4] : ~ element_of_collection(intersection_of_sets(X4,X3),top_of_basis(f)),
inference(variable_rename,[status(thm)],[c_0_4]) ).
fof(c_0_9_010,negated_conjecture,
! [X3] : element_of_collection(X3,top_of_basis(f)),
inference(variable_rename,[status(thm)],[c_0_5]) ).
fof(c_0_10_011,negated_conjecture,
! [X2] : element_of_collection(X2,top_of_basis(f)),
inference(variable_rename,[status(thm)],[c_0_6]) ).
fof(c_0_11_012,negated_conjecture,
basis(cx,f),
c_0_7 ).
cnf(c_0_12_013,negated_conjecture,
~ element_of_collection(intersection_of_sets(X1,X2),top_of_basis(f)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13_014,negated_conjecture,
element_of_collection(X1,top_of_basis(f)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14_015,negated_conjecture,
element_of_collection(X1,top_of_basis(f)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15_016,negated_conjecture,
basis(cx,f),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16_017,negated_conjecture,
~ element_of_collection(intersection_of_sets(X1,X2),top_of_basis(f)),
c_0_12,
[final] ).
cnf(c_0_17_018,negated_conjecture,
element_of_collection(X1,top_of_basis(f)),
c_0_13,
[final] ).
cnf(c_0_18_019,negated_conjecture,
element_of_collection(X1,top_of_basis(f)),
c_0_14,
[final] ).
cnf(c_0_19_020,negated_conjecture,
basis(cx,f),
c_0_15,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_336,negated_conjecture,
~ element_of_collection(intersection_of_sets(X0,X1),top_of_basis(f)),
file('/export/starexec/sandbox/tmp/iprover_modulo_b0664e.p',c_0_16) ).
cnf(c_447,negated_conjecture,
~ element_of_collection(intersection_of_sets(X0,X1),top_of_basis(f)),
inference(copy,[status(esa)],[c_336]) ).
cnf(c_463,negated_conjecture,
~ element_of_collection(intersection_of_sets(X0,X1),top_of_basis(f)),
inference(copy,[status(esa)],[c_447]) ).
cnf(c_468,negated_conjecture,
~ element_of_collection(intersection_of_sets(X0,X1),top_of_basis(f)),
inference(copy,[status(esa)],[c_463]) ).
cnf(c_469,negated_conjecture,
~ element_of_collection(intersection_of_sets(X0,X1),top_of_basis(f)),
inference(copy,[status(esa)],[c_468]) ).
cnf(c_1483,negated_conjecture,
~ element_of_collection(intersection_of_sets(X0,X1),top_of_basis(f)),
inference(copy,[status(esa)],[c_469]) ).
cnf(c_337,negated_conjecture,
element_of_collection(X0,top_of_basis(f)),
file('/export/starexec/sandbox/tmp/iprover_modulo_b0664e.p',c_0_17) ).
cnf(c_449,negated_conjecture,
element_of_collection(X0,top_of_basis(f)),
inference(copy,[status(esa)],[c_337]) ).
cnf(c_464,negated_conjecture,
element_of_collection(X0,top_of_basis(f)),
inference(copy,[status(esa)],[c_449]) ).
cnf(c_467,negated_conjecture,
element_of_collection(X0,top_of_basis(f)),
inference(copy,[status(esa)],[c_464]) ).
cnf(c_470,negated_conjecture,
element_of_collection(X0,top_of_basis(f)),
inference(copy,[status(esa)],[c_467]) ).
cnf(c_1485,negated_conjecture,
element_of_collection(X0,top_of_basis(f)),
inference(copy,[status(esa)],[c_470]) ).
cnf(c_1504,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1483,c_1485]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : TOP004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : iprover_modulo %s %d
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun May 29 14:27:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running in mono-core mode
% 0.21/0.42 % Orienting using strategy Equiv(ClausalAll)
% 0.21/0.42 % Orientation found
% 0.21/0.42 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_f1e78d.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_b0664e.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_3a2c17 | grep -v "SZS"
% 0.21/0.44
% 0.21/0.44 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.21/0.44
% 0.21/0.44 %
% 0.21/0.44 % ------ iProver source info
% 0.21/0.44
% 0.21/0.44 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.21/0.44 % git: non_committed_changes: true
% 0.21/0.44 % git: last_make_outside_of_git: true
% 0.21/0.44
% 0.21/0.44 %
% 0.21/0.44 % ------ Input Options
% 0.21/0.44
% 0.21/0.44 % --out_options all
% 0.21/0.44 % --tptp_safe_out true
% 0.21/0.44 % --problem_path ""
% 0.21/0.44 % --include_path ""
% 0.21/0.44 % --clausifier .//eprover
% 0.21/0.44 % --clausifier_options --tstp-format
% 0.21/0.44 % --stdin false
% 0.21/0.44 % --dbg_backtrace false
% 0.21/0.44 % --dbg_dump_prop_clauses false
% 0.21/0.44 % --dbg_dump_prop_clauses_file -
% 0.21/0.44 % --dbg_out_stat false
% 0.21/0.44
% 0.21/0.44 % ------ General Options
% 0.21/0.44
% 0.21/0.44 % --fof false
% 0.21/0.44 % --time_out_real 150.
% 0.21/0.44 % --time_out_prep_mult 0.2
% 0.21/0.44 % --time_out_virtual -1.
% 0.21/0.44 % --schedule none
% 0.21/0.44 % --ground_splitting input
% 0.21/0.44 % --splitting_nvd 16
% 0.21/0.44 % --non_eq_to_eq false
% 0.21/0.44 % --prep_gs_sim true
% 0.21/0.44 % --prep_unflatten false
% 0.21/0.44 % --prep_res_sim true
% 0.21/0.44 % --prep_upred true
% 0.21/0.44 % --res_sim_input true
% 0.21/0.44 % --clause_weak_htbl true
% 0.21/0.44 % --gc_record_bc_elim false
% 0.21/0.44 % --symbol_type_check false
% 0.21/0.44 % --clausify_out false
% 0.21/0.44 % --large_theory_mode false
% 0.21/0.44 % --prep_sem_filter none
% 0.21/0.44 % --prep_sem_filter_out false
% 0.21/0.44 % --preprocessed_out false
% 0.21/0.44 % --sub_typing false
% 0.21/0.44 % --brand_transform false
% 0.21/0.44 % --pure_diseq_elim true
% 0.21/0.44 % --min_unsat_core false
% 0.21/0.44 % --pred_elim true
% 0.21/0.44 % --add_important_lit false
% 0.21/0.44 % --soft_assumptions false
% 0.21/0.44 % --reset_solvers false
% 0.21/0.44 % --bc_imp_inh []
% 0.21/0.44 % --conj_cone_tolerance 1.5
% 0.21/0.44 % --prolific_symb_bound 500
% 0.21/0.44 % --lt_threshold 2000
% 0.21/0.44
% 0.21/0.44 % ------ SAT Options
% 0.21/0.44
% 0.21/0.44 % --sat_mode false
% 0.21/0.44 % --sat_fm_restart_options ""
% 0.21/0.44 % --sat_gr_def false
% 0.21/0.44 % --sat_epr_types true
% 0.21/0.44 % --sat_non_cyclic_types false
% 0.21/0.44 % --sat_finite_models false
% 0.21/0.44 % --sat_fm_lemmas false
% 0.21/0.44 % --sat_fm_prep false
% 0.21/0.44 % --sat_fm_uc_incr true
% 0.21/0.44 % --sat_out_model small
% 0.21/0.44 % --sat_out_clauses false
% 0.21/0.44
% 0.21/0.44 % ------ QBF Options
% 0.21/0.44
% 0.21/0.44 % --qbf_mode false
% 0.21/0.44 % --qbf_elim_univ true
% 0.21/0.44 % --qbf_sk_in true
% 0.21/0.44 % --qbf_pred_elim true
% 0.21/0.44 % --qbf_split 32
% 0.21/0.44
% 0.21/0.44 % ------ BMC1 Options
% 0.21/0.44
% 0.21/0.44 % --bmc1_incremental false
% 0.21/0.44 % --bmc1_axioms reachable_all
% 0.21/0.44 % --bmc1_min_bound 0
% 0.21/0.44 % --bmc1_max_bound -1
% 0.21/0.44 % --bmc1_max_bound_default -1
% 0.21/0.44 % --bmc1_symbol_reachability true
% 0.21/0.44 % --bmc1_property_lemmas false
% 0.21/0.44 % --bmc1_k_induction false
% 0.21/0.44 % --bmc1_non_equiv_states false
% 0.21/0.44 % --bmc1_deadlock false
% 0.21/0.44 % --bmc1_ucm false
% 0.21/0.44 % --bmc1_add_unsat_core none
% 0.21/0.44 % --bmc1_unsat_core_children false
% 0.21/0.44 % --bmc1_unsat_core_extrapolate_axioms false
% 0.21/0.44 % --bmc1_out_stat full
% 0.21/0.44 % --bmc1_ground_init false
% 0.21/0.44 % --bmc1_pre_inst_next_state false
% 0.21/0.44 % --bmc1_pre_inst_state false
% 0.21/0.44 % --bmc1_pre_inst_reach_state false
% 0.21/0.44 % --bmc1_out_unsat_core false
% 0.21/0.44 % --bmc1_aig_witness_out false
% 0.21/0.44 % --bmc1_verbose false
% 0.21/0.44 % --bmc1_dump_clauses_tptp false
% 0.21/0.48 % --bmc1_dump_unsat_core_tptp false
% 0.21/0.48 % --bmc1_dump_file -
% 0.21/0.48 % --bmc1_ucm_expand_uc_limit 128
% 0.21/0.48 % --bmc1_ucm_n_expand_iterations 6
% 0.21/0.48 % --bmc1_ucm_extend_mode 1
% 0.21/0.48 % --bmc1_ucm_init_mode 2
% 0.21/0.48 % --bmc1_ucm_cone_mode none
% 0.21/0.48 % --bmc1_ucm_reduced_relation_type 0
% 0.21/0.48 % --bmc1_ucm_relax_model 4
% 0.21/0.48 % --bmc1_ucm_full_tr_after_sat true
% 0.21/0.48 % --bmc1_ucm_expand_neg_assumptions false
% 0.21/0.48 % --bmc1_ucm_layered_model none
% 0.21/0.48 % --bmc1_ucm_max_lemma_size 10
% 0.21/0.48
% 0.21/0.48 % ------ AIG Options
% 0.21/0.48
% 0.21/0.48 % --aig_mode false
% 0.21/0.48
% 0.21/0.48 % ------ Instantiation Options
% 0.21/0.48
% 0.21/0.48 % --instantiation_flag true
% 0.21/0.48 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.21/0.48 % --inst_solver_per_active 750
% 0.21/0.48 % --inst_solver_calls_frac 0.5
% 0.21/0.48 % --inst_passive_queue_type priority_queues
% 0.21/0.48 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.21/0.48 % --inst_passive_queues_freq [25;2]
% 0.21/0.48 % --inst_dismatching true
% 0.21/0.48 % --inst_eager_unprocessed_to_passive true
% 0.21/0.48 % --inst_prop_sim_given true
% 0.21/0.48 % --inst_prop_sim_new false
% 0.21/0.48 % --inst_orphan_elimination true
% 0.21/0.48 % --inst_learning_loop_flag true
% 0.21/0.48 % --inst_learning_start 3000
% 0.21/0.48 % --inst_learning_factor 2
% 0.21/0.48 % --inst_start_prop_sim_after_learn 3
% 0.21/0.48 % --inst_sel_renew solver
% 0.21/0.48 % --inst_lit_activity_flag true
% 0.21/0.48 % --inst_out_proof true
% 0.21/0.48
% 0.21/0.48 % ------ Resolution Options
% 0.21/0.48
% 0.21/0.48 % --resolution_flag true
% 0.21/0.48 % --res_lit_sel kbo_max
% 0.21/0.48 % --res_to_prop_solver none
% 0.21/0.48 % --res_prop_simpl_new false
% 0.21/0.48 % --res_prop_simpl_given false
% 0.21/0.48 % --res_passive_queue_type priority_queues
% 0.21/0.48 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.21/0.48 % --res_passive_queues_freq [15;5]
% 0.21/0.48 % --res_forward_subs full
% 0.21/0.48 % --res_backward_subs full
% 0.21/0.48 % --res_forward_subs_resolution true
% 0.21/0.48 % --res_backward_subs_resolution true
% 0.21/0.48 % --res_orphan_elimination false
% 0.21/0.48 % --res_time_limit 1000.
% 0.21/0.48 % --res_out_proof true
% 0.21/0.48 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_f1e78d.s
% 0.21/0.48 % --modulo true
% 0.21/0.48
% 0.21/0.48 % ------ Combination Options
% 0.21/0.48
% 0.21/0.48 % --comb_res_mult 1000
% 0.21/0.48 % --comb_inst_mult 300
% 0.21/0.48 % ------
% 0.21/0.48
% 0.21/0.48 % ------ Parsing...% successful
% 0.21/0.48
% 0.21/0.48 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 0.21/0.48
% 0.21/0.48 % ------ Proving...
% 0.21/0.48 % ------ Problem Properties
% 0.21/0.48
% 0.21/0.48 %
% 0.21/0.48 % EPR false
% 0.21/0.48 % Horn false
% 0.21/0.48 % Has equality false
% 0.21/0.48
% 0.21/0.48 % % ------ Input Options Time Limit: Unbounded
% 0.21/0.48
% 0.21/0.48
% 0.21/0.48 % % ------ Current options:
% 0.21/0.48
% 0.21/0.48 % ------ Input Options
% 0.21/0.48
% 0.21/0.48 % --out_options all
% 0.21/0.48 % --tptp_safe_out true
% 0.21/0.48 % --problem_path ""
% 0.21/0.48 % --include_path ""
% 0.21/0.48 % --clausifier .//eprover
% 0.21/0.48 % --clausifier_options --tstp-format
% 0.21/0.48 % --stdin false
% 0.21/0.48 % --dbg_backtrace false
% 0.21/0.48 % --dbg_dump_prop_clauses false
% 0.21/0.48 % --dbg_dump_prop_clauses_file -
% 0.21/0.48 % --dbg_out_stat false
% 0.21/0.48
% 0.21/0.48 % ------ General Options
% 0.21/0.48
% 0.21/0.48 % --fof false
% 0.21/0.48 % --time_out_real 150.
% 0.21/0.48 % --time_out_prep_mult 0.2
% 0.21/0.48 % --time_out_virtual -1.
% 0.21/0.48 % --schedule none
% 0.21/0.48 % --ground_splitting input
% 0.21/0.48 % --splitting_nvd 16
% 0.21/0.48 % --non_eq_to_eq false
% 0.21/0.48 % --prep_gs_sim true
% 0.21/0.48 % --prep_unflatten false
% 0.21/0.48 % --prep_res_sim true
% 0.21/0.48 % --prep_upred true
% 0.21/0.48 % --res_sim_input true
% 0.21/0.48 % --clause_weak_htbl true
% 0.21/0.48 % --gc_record_bc_elim false
% 0.21/0.48 % --symbol_type_check false
% 0.21/0.48 % --clausify_out false
% 0.21/0.48 % --large_theory_mode false
% 0.21/0.48 % --prep_sem_filter none
% 0.21/0.48 % --prep_sem_filter_out false
% 0.21/0.48 % --preprocessed_out false
% 0.21/0.48 % --sub_typing false
% 0.21/0.48 % --brand_transform false
% 0.21/0.48 % --pure_diseq_elim true
% 0.21/0.48 % --min_unsat_core false
% 0.21/0.48 % --pred_elim true
% 0.21/0.48 % --add_important_lit false
% 0.21/0.48 % --soft_assumptions false
% 0.21/0.48 % --reset_solvers false
% 0.21/0.48 % --bc_imp_inh []
% 0.21/0.48 % --conj_cone_tolerance 1.5
% 0.21/0.48 % --prolific_symb_bound 500
% 0.21/0.48 % --lt_threshold 2000
% 0.21/0.48
% 0.21/0.48 % ------ SAT Options
% 0.21/0.48
% 0.21/0.48 % --sat_mode false
% 0.21/0.48 % --sat_fm_restart_options ""
% 0.21/0.48 % --sat_gr_def false
% 0.21/0.48 % --sat_epr_types true
% 0.21/0.48 % --sat_non_cyclic_types false
% 0.21/0.48 % --sat_finite_models false
% 0.21/0.48 % --sat_fm_lemmas false
% 0.21/0.48 % --sat_fm_prep false
% 0.21/0.48 % --sat_fm_uc_incr true
% 0.21/0.48 % --sat_out_model small
% 0.21/0.48 % --sat_out_clauses false
% 0.21/0.48
% 0.21/0.48 % ------ QBF Options
% 0.21/0.48
% 0.21/0.48 % --qbf_mode false
% 0.21/0.48 % --qbf_elim_univ true
% 0.21/0.48 % --qbf_sk_in true
% 0.21/0.48 % --qbf_pred_elim true
% 0.21/0.48 % --qbf_split 32
% 0.21/0.48
% 0.21/0.48 % ------ BMC1 Options
% 0.21/0.48
% 0.21/0.48 % --bmc1_incremental false
% 0.21/0.48 % --bmc1_axioms reachable_all
% 0.21/0.48 % --bmc1_min_bound 0
% 0.21/0.48 % --bmc1_max_bound -1
% 0.21/0.48 % --bmc1_max_bound_default -1
% 0.21/0.48 % --bmc1_symbol_reachability true
% 0.21/0.48 % --bmc1_property_lemmas false
% 0.21/0.48 % --bmc1_k_induction false
% 0.21/0.48 % --bmc1_non_equiv_states false
% 0.21/0.48 % --bmc1_deadlock false
% 0.21/0.48 % --bmc1_ucm false
% 0.21/0.48 % --bmc1_add_unsat_core none
% 0.21/0.48 % --bmc1_unsat_core_children false
% 0.21/0.48 % --bmc1_unsat_core_extrapolate_axioms false
% 0.21/0.48 % --bmc1_out_stat full
% 0.21/0.48 % --bmc1_ground_init false
% 0.21/0.48 % --bmc1_pre_inst_next_state false
% 0.21/0.48 % --bmc1_pre_inst_state false
% 0.21/0.48 % --bmc1_pre_inst_reach_state false
% 0.21/0.48 % --bmc1_out_unsat_core false
% 0.21/0.48 % --bmc1_aig_witness_out false
% 0.21/0.48 % --bmc1_verbose false
% 0.21/0.48 % --bmc1_dump_clauses_tptp false
% 0.21/0.48 % --bmc1_dump_unsat_core_tptp false
% 0.21/0.48 % --bmc1_dump_file -
% 0.21/0.48 % --bmc1_ucm_expand_uc_limit 128
% 0.21/0.48 % --bmc1_ucm_n_expand_iterations 6
% 0.21/0.48 % --bmc1_ucm_extend_mode 1
% 0.21/0.48 % --bmc1_ucm_init_mode 2
% 0.21/0.48 % --bmc1_ucm_cone_mode none
% 0.21/0.48 % --bmc1_ucm_reduced_relation_type 0
% 0.21/0.48 % --bmc1_ucm_relax_model 4
% 0.21/0.48 % --bmc1_ucm_full_tr_after_sat true
% 0.21/0.48 % --bmc1_ucm_expand_neg_assumptions false
% 0.21/0.48 % --bmc1_ucm_layered_model none
% 0.21/0.48 % --bmc1_ucm_max_lemma_size 10
% 0.21/0.48
% 0.21/0.48 % ------ AIG Options
% 0.21/0.48
% 0.21/0.48 % --aig_mode false
% 0.21/0.48
% 0.21/0.48 % ------ Instantiation Options
% 0.21/0.48
% 0.21/0.48 % --instantiation_flag true
% 0.21/0.48 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.21/0.48 % --inst_solver_per_active 750
% 0.21/0.48 % --inst_solver_calls_frac 0.5
% 0.21/0.48 % --inst_passive_queue_type priority_queues
% 0.21/0.48 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.21/0.48 % --inst_passive_queues_freq [25;2]
% 0.21/0.48 % --inst_dismatching true
% 0.21/0.48 % --inst_eager_unprocessed_to_passive true
% 0.21/0.48 % --inst_prop_sim_given true
% 0.21/0.48 % --inst_prop_sim_new false
% 0.21/0.48 % --inst_orphan_elimination true
% 0.21/0.48 % --inst_learning_loop_flag true
% 0.21/0.48 % --inst_learning_start 3000
% 0.21/0.48 % --inst_learning_factor 2
% 0.21/0.48 % --inst_start_prop_sim_after_learn 3
% 0.21/0.48 % --inst_sel_renew solver
% 0.21/0.48 % --inst_lit_activity_flag true
% 0.21/0.48 % --inst_out_proof true
% 0.21/0.48
% 0.21/0.48 % ------ Resolution Options
% 0.21/0.48
% 0.21/0.48 % --resolution_flag true
% 0.21/0.48 % --res_lit_sel kbo_max
% 0.21/0.48 % --res_to_prop_solver none
% 0.21/0.48 % --res_prop_simpl_new false
% 0.21/0.48 % --res_prop_simpl_given false
% 0.21/0.48 % --res_passive_queue_type priority_queues
% 0.21/0.48 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.21/0.48 % --res_passive_queues_freq [15;5]
% 0.21/0.48 % --res_forward_subs full
% 0.21/0.48 % --res_backward_subs full
% 0.21/0.48 % --res_forward_subs_resolution true
% 0.21/0.48 % --res_backward_subs_resolution true
% 0.21/0.49 % --res_orphan_elimination false
% 0.21/0.49 % --res_time_limit 1000.
% 0.21/0.49 % --res_out_proof true
% 0.21/0.49 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_f1e78d.s
% 0.21/0.49 % --modulo true
% 0.21/0.49
% 0.21/0.49 % ------ Combination Options
% 0.21/0.49
% 0.21/0.49 % --comb_res_mult 1000
% 0.21/0.49 % --comb_inst_mult 300
% 0.21/0.49 % ------
% 0.21/0.49
% 0.21/0.49
% 0.21/0.49
% 0.21/0.49 % ------ Proving...
% 0.21/0.49 %
% 0.21/0.49
% 0.21/0.49
% 0.21/0.49 % Resolution empty clause
% 0.21/0.49
% 0.21/0.49 % ------ Statistics
% 0.21/0.49
% 0.21/0.49 % ------ General
% 0.21/0.49
% 0.21/0.49 % num_of_input_clauses: 340
% 0.21/0.49 % num_of_input_neg_conjectures: 4
% 0.21/0.49 % num_of_splits: 0
% 0.21/0.49 % num_of_split_atoms: 0
% 0.21/0.49 % num_of_sem_filtered_clauses: 0
% 0.21/0.49 % num_of_subtypes: 0
% 0.21/0.49 % monotx_restored_types: 0
% 0.21/0.49 % sat_num_of_epr_types: 0
% 0.21/0.49 % sat_num_of_non_cyclic_types: 0
% 0.21/0.49 % sat_guarded_non_collapsed_types: 0
% 0.21/0.49 % is_epr: 0
% 0.21/0.49 % is_horn: 0
% 0.21/0.49 % has_eq: 0
% 0.21/0.49 % num_pure_diseq_elim: 0
% 0.21/0.49 % simp_replaced_by: 0
% 0.21/0.49 % res_preprocessed: 8
% 0.21/0.49 % prep_upred: 0
% 0.21/0.49 % prep_unflattend: 0
% 0.21/0.49 % pred_elim_cands: 0
% 0.21/0.49 % pred_elim: 0
% 0.21/0.49 % pred_elim_cl: 0
% 0.21/0.49 % pred_elim_cycles: 0
% 0.21/0.49 % forced_gc_time: 0
% 0.21/0.49 % gc_basic_clause_elim: 0
% 0.21/0.49 % parsing_time: 0.018
% 0.21/0.49 % sem_filter_time: 0.
% 0.21/0.49 % pred_elim_time: 0.
% 0.21/0.49 % out_proof_time: 0.
% 0.21/0.49 % monotx_time: 0.
% 0.21/0.49 % subtype_inf_time: 0.
% 0.21/0.49 % unif_index_cands_time: 0.
% 0.21/0.49 % unif_index_add_time: 0.
% 0.21/0.49 % total_time: 0.06
% 0.21/0.49 % num_of_symbols: 84
% 0.21/0.49 % num_of_terms: 826
% 0.21/0.49
% 0.21/0.49 % ------ Propositional Solver
% 0.21/0.49
% 0.21/0.49 % prop_solver_calls: 1
% 0.21/0.49 % prop_fast_solver_calls: 11
% 0.21/0.49 % prop_num_of_clauses: 300
% 0.21/0.49 % prop_preprocess_simplified: 1106
% 0.21/0.49 % prop_fo_subsumed: 0
% 0.21/0.49 % prop_solver_time: 0.
% 0.21/0.49 % prop_fast_solver_time: 0.
% 0.21/0.49 % prop_unsat_core_time: 0.
% 0.21/0.49
% 0.21/0.49 % ------ QBF
% 0.21/0.49
% 0.21/0.49 % qbf_q_res: 0
% 0.21/0.49 % qbf_num_tautologies: 0
% 0.21/0.49 % qbf_prep_cycles: 0
% 0.21/0.49
% 0.21/0.49 % ------ BMC1
% 0.21/0.49
% 0.21/0.49 % bmc1_current_bound: -1
% 0.21/0.49 % bmc1_last_solved_bound: -1
% 0.21/0.49 % bmc1_unsat_core_size: -1
% 0.21/0.49 % bmc1_unsat_core_parents_size: -1
% 0.21/0.49 % bmc1_merge_next_fun: 0
% 0.21/0.49 % bmc1_unsat_core_clauses_time: 0.
% 0.21/0.49
% 0.21/0.49 % ------ Instantiation
% 0.21/0.49
% 0.21/0.49 % inst_num_of_clauses: 339
% 0.21/0.49 % inst_num_in_passive: 0
% 0.21/0.49 % inst_num_in_active: 0
% 0.21/0.49 % inst_num_in_unprocessed: 339
% 0.21/0.49 % inst_num_of_loops: 0
% 0.21/0.49 % inst_num_of_learning_restarts: 0
% 0.21/0.49 % inst_num_moves_active_passive: 0
% 0.21/0.49 % inst_lit_activity: 0
% 0.21/0.49 % inst_lit_activity_moves: 0
% 0.21/0.49 % inst_num_tautologies: 0
% 0.21/0.49 % inst_num_prop_implied: 0
% 0.21/0.49 % inst_num_existing_simplified: 0
% 0.21/0.49 % inst_num_eq_res_simplified: 0
% 0.21/0.49 % inst_num_child_elim: 0
% 0.21/0.49 % inst_num_of_dismatching_blockings: 0
% 0.21/0.49 % inst_num_of_non_proper_insts: 0
% 0.21/0.49 % inst_num_of_duplicates: 0
% 0.21/0.49 % inst_inst_num_from_inst_to_res: 0
% 0.21/0.49 % inst_dismatching_checking_time: 0.
% 0.21/0.49
% 0.21/0.49 % ------ Resolution
% 0.21/0.49
% 0.21/0.49 % res_num_of_clauses: 392
% 0.21/0.49 % res_num_in_passive: 5
% 0.21/0.49 % res_num_in_active: 122
% 0.21/0.49 % res_num_of_loops: 3
% 0.21/0.49 % res_forward_subset_subsumed: 216
% 0.21/0.49 % res_backward_subset_subsumed: 0
% 0.21/0.49 % res_forward_subsumed: 0
% 0.21/0.49 % res_backward_subsumed: 0
% 0.21/0.49 % res_forward_subsumption_resolution: 1
% 0.21/0.49 % res_backward_subsumption_resolution: 0
% 0.21/0.49 % res_clause_to_clause_subsumption: 1
% 0.21/0.49 % res_orphan_elimination: 0
% 0.21/0.49 % res_tautology_del: 0
% 0.21/0.49 % res_num_eq_res_simplified: 0
% 0.21/0.49 % res_num_sel_changes: 0
% 0.21/0.49 % res_moves_from_active_to_pass: 0
% 0.21/0.49
% 0.21/0.49 % Status Unsatisfiable
% 0.21/0.49 % SZS status Unsatisfiable
% 0.21/0.49 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------