%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : TOP004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:52:26 AM UTC 2026
% Result : Unsatisfiable 6.20s 3.12s
% Output : Refutation 6.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 113
% Syntax : Number of formulae : 227 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 681 ( 0 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 3076 ( 412 ~; 454 |; 0 &;2210 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 59 usr; 4 con; 0-5 aty)
% Number of variables : 722 ( 0 ^; 722 !; 0 ?; 722 :)
% Comments :
%------------------------------------------------------------------------------
thf(basis_decl,type,
basis: $i > $i > $o ).
thf(cx_decl,type,
cx: $i ).
thf(f_decl,type,
f: $i ).
thf(element_of_collection_decl,type,
element_of_collection: $i > $i > $o ).
thf(top_of_basis_decl,type,
top_of_basis: $i > $i ).
thf(intersection_of_sets_decl,type,
intersection_of_sets: $i > $i > $i ).
thf(compact_space_decl,type,
compact_space: $i > $i > $o ).
thf(open_covering_decl,type,
open_covering: $i > $i > $i > $o ).
thf(finite_decl,type,
finite: $i > $o ).
thf(f23_decl,type,
f23: $i > $i > $i > $i ).
thf(topological_space_decl,type,
topological_space: $i > $i > $o ).
thf(subset_collections_decl,type,
subset_collections: $i > $i > $o ).
thf(f24_decl,type,
f24: $i > $i > $i ).
thf(element_of_set_decl,type,
element_of_set: $i > $i > $o ).
thf(boundary_decl,type,
boundary: $i > $i > $i > $i ).
thf(closure_decl,type,
closure: $i > $i > $i > $i ).
thf(relative_complement_sets_decl,type,
relative_complement_sets: $i > $i > $i ).
thf(compact_set_decl,type,
compact_set: $i > $i > $i > $o ).
thf(subspace_topology_decl,type,
subspace_topology: $i > $i > $i > $i ).
thf(closed_decl,type,
closed: $i > $i > $i > $o ).
thf(open_decl,type,
open: $i > $i > $i > $o ).
thf(connected_set_decl,type,
connected_set: $i > $i > $i > $o ).
thf(connected_space_decl,type,
connected_space: $i > $i > $o ).
thf(interior_decl,type,
interior: $i > $i > $i > $i ).
thf(f13_decl,type,
f13: $i > $i > $i > $i > $i ).
thf(equal_sets_decl,type,
equal_sets: $i > $i > $o ).
thf(union_of_members_decl,type,
union_of_members: $i > $i ).
thf(limit_point_decl,type,
limit_point: $i > $i > $i > $i > $o ).
thf(neighborhood_decl,type,
neighborhood: $i > $i > $i > $i > $o ).
thf(eq_p_decl,type,
eq_p: $i > $i > $o ).
thf(f15_decl,type,
f15: $i > $i > $i > $i > $i > $i ).
thf(subset_sets_decl,type,
subset_sets: $i > $i > $o ).
thf(intersection_of_members_decl,type,
intersection_of_members: $i > $i ).
thf(f2_decl,type,
f2: $i > $i > $i ).
thf(separation_decl,type,
separation: $i > $i > $i > $i > $o ).
thf(disjoint_s_decl,type,
disjoint_s: $i > $i > $o ).
thf(hausdorff_decl,type,
hausdorff: $i > $i > $o ).
thf(f19_decl,type,
f19: $i > $i > $i ).
thf(f20_decl,type,
f20: $i > $i > $i ).
thf(finer_decl,type,
finer: $i > $i > $i > $o ).
thf(f1_decl,type,
f1: $i > $i > $i ).
thf(f14_decl,type,
f14: $i > $i > $i > $i > $i ).
thf(f16_decl,type,
f16: $i > $i > $i > $i > $i ).
thf(f21_decl,type,
f21: $i > $i > $i ).
thf(f22_decl,type,
f22: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(union_of_sets_decl,type,
union_of_sets: $i > $i > $i ).
thf(f17_decl,type,
f17: $i > $i > $i > $i > $i ).
thf(f18_decl,type,
f18: $i > $i > $i > $i > $i ).
thf(f8_decl,type,
f8: $i > $i > $i ).
thf(f10_decl,type,
f10: $i > $i > $i > $i ).
thf(f7_decl,type,
f7: $i > $i > $i ).
thf(f3_decl,type,
f3: $i > $i > $i ).
thf(f5_decl,type,
f5: $i > $i > $i ).
thf(f6_decl,type,
f6: $i > $i > $i > $i > $i > $i ).
thf(f4_decl,type,
f4: $i > $i > $i ).
thf(f11_decl,type,
f11: $i > $i > $i ).
thf(f9_decl,type,
f9: $i > $i > $i ).
thf(f12_decl,type,
f12: $i > $i > $i > $i > $i ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ f2 ) @ ( A @ element_of_set ) )
| ( B @ intersection_of_members @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_members_6) ).
thf(153,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ f2 ) @ ( A @ element_of_set ) )
| ( B @ intersection_of_members @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ element_of_collection ) )
| ~ ( B @ ( A @ topological_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topological_space_9) ).
thf(333,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ element_of_collection ) )
| ~ ( B @ ( A @ topological_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ f18 ) ) ) @ ( D @ ( C @ ( B @ ( A @ f17 ) ) ) @ disjoint_s ) )
| ( D @ ( C @ eq_p ) )
| ~ ( A @ ( D @ element_of_set ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ hausdorff ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hausdorff_76) ).
thf(249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ f18 ) ) ) @ ( D @ ( C @ ( B @ ( A @ f17 ) ) ) @ disjoint_s ) )
| ( D @ ( C @ eq_p ) )
| ~ ( A @ ( D @ element_of_set ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ hausdorff ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(2,negated_conjecture,
! [A: $i] : ( f @ top_of_basis @ ( A @ element_of_collection ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1d_2) ).
thf(115,plain,
! [A: $i] : ( f @ top_of_basis @ ( A @ element_of_collection ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ union_of_sets ) @ equal_sets ) )
| ~ ( D @ ( C @ ( B @ ( A @ separation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',separation_86) ).
thf(217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ union_of_sets ) @ equal_sets ) )
| ~ ( D @ ( C @ ( B @ ( A @ separation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty_set @ ( A @ equal_sets ) )
| ~ ( D @ ( C @ ( B @ ( A @ separation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',separation_82) ).
thf(247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty_set @ ( A @ equal_sets ) )
| ~ ( D @ ( C @ ( B @ ( A @ separation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(80,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( E @ eq_p ) )
| ~ ( B @ ( D @ ( C @ ( B @ ( A @ f16 ) ) ) @ intersection_of_sets ) @ ( E @ element_of_set ) )
| ~ ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ ( A @ limit_point ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',limit_point_68) ).
thf(269,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( E @ eq_p ) )
| ~ ( B @ ( D @ ( C @ ( B @ ( A @ f16 ) ) ) @ intersection_of_sets ) @ ( E @ element_of_set ) )
| ~ ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ ( A @ limit_point ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ subset_collections ) )
| ~ ( C @ ( B @ ( A @ finer ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finer_topology_26) ).
thf(185,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ subset_collections ) )
| ~ ( C @ ( B @ ( A @ finer ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ intersection_of_sets ) @ element_of_collection ) )
| ~ ( B @ ( D @ element_of_collection ) )
| ~ ( B @ ( C @ element_of_collection ) )
| ~ ( B @ ( A @ topological_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topological_space_10) ).
thf(301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ intersection_of_sets ) @ element_of_collection ) )
| ~ ( B @ ( D @ element_of_collection ) )
| ~ ( B @ ( C @ element_of_collection ) )
| ~ ( B @ ( A @ topological_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ disjoint_s ) )
| ~ ( C @ ( B @ ( A @ union_of_sets ) @ equal_sets ) )
| ~ ( D @ ( B @ element_of_collection ) )
| ~ ( D @ ( A @ element_of_collection ) )
| ( empty_set @ ( B @ equal_sets ) )
| ( empty_set @ ( A @ equal_sets ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ ( A @ separation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',separation_88) ).
thf(257,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ disjoint_s ) )
| ~ ( C @ ( B @ ( A @ union_of_sets ) @ equal_sets ) )
| ~ ( D @ ( B @ element_of_collection ) )
| ~ ( D @ ( A @ element_of_collection ) )
| ( empty_set @ ( B @ equal_sets ) )
| ( empty_set @ ( A @ equal_sets ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ ( A @ separation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( C @ ( B @ relative_complement_sets ) @ closure ) ) @ ( A @ element_of_set ) )
| ~ ( D @ ( C @ ( B @ boundary ) ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boundary_71) ).
thf(125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( C @ ( B @ relative_complement_sets ) @ closure ) ) @ ( A @ element_of_set ) )
| ~ ( D @ ( C @ ( B @ boundary ) ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ disjoint_s ) )
| ~ ( D @ ( C @ ( B @ ( A @ separation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',separation_87) ).
thf(157,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ disjoint_s ) )
| ~ ( D @ ( C @ ( B @ ( A @ separation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ union_of_members @ equal_sets ) )
| ~ ( B @ ( A @ topological_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topological_space_7) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ union_of_members @ equal_sets ) )
| ~ ( B @ ( A @ topological_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ f11 ) @ element_of_set ) )
| ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_40) ).
thf(325,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ f11 ) @ element_of_set ) )
| ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ f5 ) @ union_of_members @ element_of_collection ) )
| ( B @ ( B @ ( A @ f4 ) @ element_of_collection ) )
| ~ ( B @ ( A @ element_of_collection ) )
| ~ ( B @ ( empty_set @ element_of_collection ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ topological_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topological_space_15) ).
thf(289,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ f5 ) @ union_of_members @ element_of_collection ) )
| ( B @ ( B @ ( A @ f4 ) @ element_of_collection ) )
| ~ ( B @ ( A @ element_of_collection ) )
| ~ ( B @ ( empty_set @ element_of_collection ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ topological_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(76,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ intersection_of_sets ) @ ( E @ ( D @ ( C @ ( B @ ( A @ f15 ) ) ) ) @ element_of_set ) )
| ~ ( D @ ( C @ ( A @ ( E @ neighborhood ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ limit_point ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',limit_point_65) ).
thf(261,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ intersection_of_sets ) @ ( E @ ( D @ ( C @ ( B @ ( A @ f15 ) ) ) ) @ element_of_set ) )
| ~ ( D @ ( C @ ( A @ ( E @ neighborhood ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ limit_point ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ element_of_set ) )
| ~ ( D @ ( C @ ( A @ open ) ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ ( A @ neighborhood ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',neighborhood_62) ).
thf(179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ element_of_set ) )
| ~ ( D @ ( C @ ( A @ open ) ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ ( A @ neighborhood ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ element_of_collection ) )
| ~ ( D @ ( C @ ( B @ ( A @ separation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',separation_84) ).
thf(321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ element_of_collection ) )
| ~ ( D @ ( C @ ( B @ ( A @ separation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ ( A @ f23 ) ) @ open_covering ) ) )
| ~ ( B @ ( A @ ( C @ open_covering ) ) )
| ~ ( B @ ( A @ compact_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compact_space_103) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ ( A @ f23 ) ) @ open_covering ) ) )
| ~ ( B @ ( A @ ( C @ open_covering ) ) )
| ~ ( B @ ( A @ compact_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ topological_space ) )
| ~ ( C @ ( B @ ( A @ open_covering ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_covering_96) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ topological_space ) )
| ~ ( C @ ( B @ ( A @ open_covering ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ ( D @ ( C @ ( B @ ( A @ f18 ) ) ) @ neighborhood ) ) ) )
| ( D @ ( C @ eq_p ) )
| ~ ( A @ ( D @ element_of_set ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ hausdorff ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hausdorff_75) ).
thf(253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ ( D @ ( C @ ( B @ ( A @ f18 ) ) ) @ neighborhood ) ) ) )
| ( D @ ( C @ eq_p ) )
| ~ ( A @ ( D @ element_of_set ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ hausdorff ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ subset_sets ) )
| ~ ( C @ ( B @ ( A @ connected_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connected_set_93) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ subset_sets ) )
| ~ ( C @ ( B @ ( A @ connected_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ element_of_set ) )
| ~ ( D @ ( C @ ( B @ ( A @ neighborhood ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',neighborhood_61) ).
thf(221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ element_of_set ) )
| ~ ( D @ ( C @ ( B @ ( A @ neighborhood ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ union_of_members @ element_of_collection ) )
| ~ ( B @ ( C @ subset_collections ) )
| ~ ( B @ ( A @ topological_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topological_space_11) ).
thf(293,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ union_of_members @ element_of_collection ) )
| ~ ( B @ ( C @ subset_collections ) )
| ~ ( B @ ( A @ topological_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ subspace_topology ) ) @ ( A @ connected_space ) )
| ~ ( C @ ( B @ ( A @ connected_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connected_set_94) ).
thf(133,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ subspace_topology ) ) @ ( A @ connected_space ) )
| ~ ( C @ ( B @ ( A @ connected_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(78,axiom,
! [B: $i,A: $i] :
( ( B @ ( empty_set @ element_of_collection ) )
| ~ ( B @ ( A @ topological_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topological_space_8) ).
thf(265,plain,
! [B: $i,A: $i] :
( ( B @ ( empty_set @ element_of_collection ) )
| ~ ( B @ ( A @ topological_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(3,negated_conjecture,
! [A: $i] : ( f @ top_of_basis @ ( A @ element_of_collection ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1d_3) ).
thf(116,plain,
! [A: $i] : ( f @ top_of_basis @ ( A @ element_of_collection ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ topological_space ) )
| ~ ( D @ ( C @ ( B @ ( A @ neighborhood ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',neighborhood_59) ).
thf(243,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ topological_space ) )
| ~ ( D @ ( C @ ( B @ ( A @ neighborhood ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( B @ f10 ) ) @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_38) ).
thf(307,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( B @ f10 ) ) @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ ( B @ f14 ) ) ) @ ( B @ subset_sets ) )
| ~ ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ closure ) ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_56) ).
thf(233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ ( B @ f14 ) ) ) @ ( B @ subset_sets ) )
| ~ ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ closure ) ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(4,negated_conjecture,
! [B: $i,A: $i] :
~ ( f @ top_of_basis @ ( B @ ( A @ intersection_of_sets ) @ element_of_collection ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1d_4) ).
thf(117,plain,
! [B: $i,A: $i] :
~ ( f @ top_of_basis @ ( B @ ( A @ intersection_of_sets ) @ element_of_collection ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ topological_space ) )
| ~ ( C @ ( B @ ( A @ connected_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connected_set_92) ).
thf(201,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ topological_space ) )
| ~ ( C @ ( B @ ( A @ connected_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ topological_space ) )
| ~ ( D @ ( C @ ( B @ subspace_topology ) ) @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subspace_topology_42) ).
thf(297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ topological_space ) )
| ~ ( D @ ( C @ ( B @ subspace_topology ) ) @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ subset_sets ) )
| ~ ( C @ ( B @ ( A @ compact_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compact_set_107) ).
thf(165,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ subset_sets ) )
| ~ ( C @ ( B @ ( A @ compact_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(83,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ element_of_collection ) )
| ~ ( C @ ( B @ ( A @ open ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_set_19) ).
thf(275,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ element_of_collection ) )
| ~ ( C @ ( B @ ( A @ open ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ f23 ) ) @ subset_collections ) )
| ~ ( B @ ( A @ ( C @ open_covering ) ) )
| ~ ( B @ ( A @ compact_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compact_space_102) ).
thf(137,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ f23 ) ) @ subset_collections ) )
| ~ ( B @ ( A @ ( C @ open_covering ) ) )
| ~ ( B @ ( A @ compact_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ topological_space ) )
| ~ ( D @ ( C @ ( B @ boundary ) ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boundary_69) ).
thf(229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ topological_space ) )
| ~ ( D @ ( C @ ( B @ boundary ) ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ topological_space ) )
| ~ ( D @ ( C @ ( B @ ( A @ separation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',separation_81) ).
thf(197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ topological_space ) )
| ~ ( D @ ( C @ ( B @ ( A @ separation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ f2 ) @ element_of_collection ) )
| ( B @ intersection_of_members @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_members_5) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ f2 ) @ element_of_collection ) )
| ( B @ intersection_of_members @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(88,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ element_of_collection ) )
| ~ ( D @ ( C @ ( B @ ( A @ separation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',separation_85) ).
thf(285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ element_of_collection ) )
| ~ ( D @ ( C @ ( B @ ( A @ separation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(104,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ ( C @ ( B @ f12 ) ) ) @ element_of_collection ) )
| ~ ( D @ ( C @ ( B @ subspace_topology ) ) @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subspace_topology_44) ).
thf(317,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ ( C @ ( B @ f12 ) ) ) @ element_of_collection ) )
| ~ ( D @ ( C @ ( B @ subspace_topology ) ) @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ topological_space ) )
| ~ ( B @ ( A @ compact_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compact_space_100) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ topological_space ) )
| ~ ( B @ ( A @ compact_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ f24 ) @ open_covering ) ) )
| ~ ( B @ ( A @ topological_space ) )
| ( B @ ( A @ compact_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compact_space_104) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ f24 ) @ open_covering ) ) )
| ~ ( B @ ( A @ topological_space ) )
| ( B @ ( A @ compact_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ topological_space ) )
| ~ ( B @ ( A @ hausdorff ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hausdorff_73) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ topological_space ) )
| ~ ( B @ ( A @ hausdorff ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ subset_collections ) )
| ~ ( C @ ( B @ ( A @ open_covering ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_covering_97) ).
thf(193,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ subset_collections ) )
| ~ ( C @ ( B @ ( A @ open_covering ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ f20 ) @ element_of_set ) )
| ~ ( B @ ( A @ topological_space ) )
| ( B @ ( A @ hausdorff ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hausdorff_78) ).
thf(173,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ f20 ) @ element_of_set ) )
| ~ ( B @ ( A @ topological_space ) )
| ( B @ ( A @ hausdorff ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ subspace_topology ) ) @ ( A @ compact_space ) )
| ~ ( C @ ( B @ ( A @ compact_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compact_set_108) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ subspace_topology ) ) @ ( A @ compact_space ) )
| ~ ( C @ ( B @ ( A @ compact_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ topological_space ) )
| ~ ( D @ ( C @ ( B @ closure ) ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_53) ).
thf(237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ topological_space ) )
| ~ ( D @ ( C @ ( B @ closure ) ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ ( B @ interior ) ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interior_48) ).
thf(205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ ( B @ interior ) ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ ( B @ f12 ) ) ) @ ( D @ intersection_of_sets ) @ ( A @ equal_sets ) )
| ~ ( D @ ( C @ ( B @ subspace_topology ) ) @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subspace_topology_45) ).
thf(311,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ ( B @ f12 ) ) ) @ ( D @ intersection_of_sets ) @ ( A @ equal_sets ) )
| ~ ( D @ ( C @ ( B @ subspace_topology ) ) @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ subspace_topology ) ) @ ( A @ connected_space ) )
| ~ ( B @ ( A @ subset_sets ) )
| ~ ( C @ ( B @ topological_space ) )
| ( C @ ( B @ ( A @ connected_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connected_set_95) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ subspace_topology ) ) @ ( A @ connected_space ) )
| ~ ( B @ ( A @ subset_sets ) )
| ~ ( C @ ( B @ topological_space ) )
| ( C @ ( B @ ( A @ connected_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ f7 ) @ element_of_set ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ basis ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_32) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ f7 ) @ element_of_set ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ basis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ topological_space ) )
| ~ ( B @ ( A @ connected_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connected_space_89) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ topological_space ) )
| ~ ( B @ ( A @ connected_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( D @ ( C @ ( B @ f13 ) ) ) @ open ) ) )
| ~ ( D @ ( C @ ( B @ interior ) ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interior_51) ).
thf(191,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( D @ ( C @ ( B @ f13 ) ) ) @ open ) ) )
| ~ ( D @ ( C @ ( B @ interior ) ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(91,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ f6 ) ) ) ) @ element_of_collection ) )
| ~ ( E @ ( D @ intersection_of_sets ) @ ( C @ element_of_set ) )
| ~ ( B @ ( E @ element_of_collection ) )
| ~ ( B @ ( D @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ basis ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_30) ).
thf(291,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ f6 ) ) ) ) @ element_of_collection ) )
| ~ ( E @ ( D @ intersection_of_sets ) @ ( C @ element_of_set ) )
| ~ ( B @ ( E @ element_of_collection ) )
| ~ ( B @ ( D @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ basis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f5 ) @ subset_collections ) )
| ( B @ ( B @ ( A @ f3 ) @ element_of_collection ) )
| ~ ( B @ ( A @ element_of_collection ) )
| ~ ( B @ ( empty_set @ element_of_collection ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ topological_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topological_space_12) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f5 ) @ subset_collections ) )
| ( B @ ( B @ ( A @ f3 ) @ element_of_collection ) )
| ~ ( B @ ( A @ element_of_collection ) )
| ~ ( B @ ( empty_set @ element_of_collection ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ topological_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f8 ) @ element_of_collection ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ basis ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_33) ).
thf(259,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f8 ) @ element_of_collection ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ basis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f5 ) @ subset_collections ) )
| ( B @ ( B @ ( A @ f4 ) @ element_of_collection ) )
| ~ ( B @ ( A @ element_of_collection ) )
| ~ ( B @ ( empty_set @ element_of_collection ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ topological_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topological_space_14) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f5 ) @ subset_collections ) )
| ( B @ ( B @ ( A @ f4 ) @ element_of_collection ) )
| ~ ( B @ ( A @ element_of_collection ) )
| ~ ( B @ ( empty_set @ element_of_collection ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ topological_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ f9 ) @ ( B @ ( A @ f8 ) @ intersection_of_sets ) @ ( C @ subset_sets ) )
| ~ ( B @ ( C @ element_of_collection ) )
| ~ ( C @ ( B @ ( A @ f7 ) @ element_of_set ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ basis ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_36) ).
thf(335,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ f9 ) @ ( B @ ( A @ f8 ) @ intersection_of_sets ) @ ( C @ subset_sets ) )
| ~ ( B @ ( C @ element_of_collection ) )
| ~ ( C @ ( B @ ( A @ f7 ) @ element_of_set ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ basis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ topological_space ) )
| ~ ( C @ ( B @ ( A @ finer ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finer_topology_25) ).
thf(181,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ topological_space ) )
| ~ ( C @ ( B @ ( A @ finer ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ f20 ) @ ( B @ ( A @ f19 ) @ eq_p ) )
| ~ ( B @ ( A @ topological_space ) )
| ( B @ ( A @ hausdorff ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hausdorff_79) ).
thf(159,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ f20 ) @ ( B @ ( A @ f19 ) @ eq_p ) )
| ~ ( B @ ( A @ topological_space ) )
| ( B @ ( A @ hausdorff ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ open ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ neighborhood ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',neighborhood_60) ).
thf(187,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ open ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ neighborhood ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( D @ ( C @ ( B @ ( A @ f17 ) ) ) @ neighborhood ) ) ) )
| ( D @ ( C @ eq_p ) )
| ~ ( A @ ( D @ element_of_set ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ hausdorff ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hausdorff_74) ).
thf(219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( D @ ( C @ ( B @ ( A @ f17 ) ) ) @ neighborhood ) ) ) )
| ( D @ ( C @ eq_p ) )
| ~ ( A @ ( D @ element_of_set ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ hausdorff ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ disjoint_s ) )
| ~ ( B @ ( A @ ( B @ ( A @ f20 ) @ ( D @ neighborhood ) ) ) )
| ~ ( B @ ( A @ ( B @ ( A @ f19 ) @ ( C @ neighborhood ) ) ) )
| ~ ( B @ ( A @ topological_space ) )
| ( B @ ( A @ hausdorff ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hausdorff_80) ).
thf(245,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ disjoint_s ) )
| ~ ( B @ ( A @ ( B @ ( A @ f20 ) @ ( D @ neighborhood ) ) ) )
| ~ ( B @ ( A @ ( B @ ( A @ f19 ) @ ( C @ neighborhood ) ) ) )
| ~ ( B @ ( A @ topological_space ) )
| ( B @ ( A @ hausdorff ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ subset_sets ) )
| ~ ( B @ ( C @ element_of_collection ) )
| ~ ( C @ ( A @ ( B @ f11 ) @ element_of_set ) )
| ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_41) ).
thf(303,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ subset_sets ) )
| ~ ( B @ ( C @ element_of_collection ) )
| ~ ( C @ ( A @ ( B @ f11 ) @ element_of_set ) )
| ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ element_of_collection ) )
| ~ ( C @ ( B @ topological_space ) )
| ( C @ ( B @ ( A @ open ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_set_20) ).
thf(271,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ element_of_collection ) )
| ~ ( C @ ( B @ topological_space ) )
| ( C @ ( B @ ( A @ open ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ f1 ) @ element_of_collection ) )
| ~ ( B @ union_of_members @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_members_2) ).
thf(323,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ f1 ) @ element_of_collection ) )
| ~ ( B @ union_of_members @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty_set @ ( B @ equal_sets ) )
| ~ ( D @ ( C @ ( B @ ( A @ separation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',separation_83) ).
thf(213,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty_set @ ( B @ equal_sets ) )
| ~ ( D @ ( C @ ( B @ ( A @ separation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( B @ f14 ) ) ) @ ( A @ element_of_set ) )
| ~ ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ closure ) ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_58) ).
thf(251,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( B @ f14 ) ) ) @ ( A @ element_of_set ) )
| ~ ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ closure ) ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ ( B @ closure ) ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_54) ).
thf(155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ ( B @ closure ) ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(57,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ element_of_set ) )
| ~ ( D @ ( C @ ( E @ closed ) ) )
| ~ ( E @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ ( B @ closure ) ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_55) ).
thf(223,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ element_of_set ) )
| ~ ( D @ ( C @ ( E @ closed ) ) )
| ~ ( E @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ ( B @ closure ) ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ ( B @ f13 ) ) ) @ ( A @ element_of_set ) )
| ~ ( D @ ( C @ ( B @ interior ) ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interior_49) ).
thf(135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ ( B @ f13 ) ) ) @ ( A @ element_of_set ) )
| ~ ( D @ ( C @ ( B @ interior ) ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f5 ) @ subset_collections ) )
| ~ ( B @ ( B @ ( A @ f4 ) @ ( B @ ( A @ f3 ) @ intersection_of_sets ) @ element_of_collection ) )
| ~ ( B @ ( A @ element_of_collection ) )
| ~ ( B @ ( empty_set @ element_of_collection ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ topological_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topological_space_16) ).
thf(299,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f5 ) @ subset_collections ) )
| ~ ( B @ ( B @ ( A @ f4 ) @ ( B @ ( A @ f3 ) @ intersection_of_sets ) @ element_of_collection ) )
| ~ ( B @ ( A @ element_of_collection ) )
| ~ ( B @ ( empty_set @ element_of_collection ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ topological_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ f10 ) ) @ ( C @ element_of_set ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_37) ).
thf(267,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ f10 ) ) @ ( C @ element_of_set ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ topological_space ) )
| ~ ( D @ ( C @ ( B @ interior ) ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interior_47) ).
thf(241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ topological_space ) )
| ~ ( D @ ( C @ ( B @ interior ) ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ f19 ) @ element_of_set ) )
| ~ ( B @ ( A @ topological_space ) )
| ( B @ ( A @ hausdorff ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hausdorff_77) ).
thf(167,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ f19 ) @ element_of_set ) )
| ~ ( B @ ( A @ topological_space ) )
| ( B @ ( A @ hausdorff ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ ( B @ ( A @ limit_point ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',limit_point_64) ).
thf(255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ ( B @ ( A @ limit_point ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ subset_collections ) )
| ~ ( B @ ( C @ topological_space ) )
| ~ ( A @ ( C @ topological_space ) )
| ( C @ ( B @ ( A @ finer ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finer_topology_27) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ subset_collections ) )
| ~ ( B @ ( C @ topological_space ) )
| ~ ( A @ ( C @ topological_space ) )
| ( C @ ( B @ ( A @ finer ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ open_covering ) ) )
| ~ ( B @ ( A @ f24 ) @ ( C @ subset_collections ) )
| ~ ( C @ finite )
| ~ ( B @ ( A @ topological_space ) )
| ( B @ ( A @ compact_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compact_space_105) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ open_covering ) ) )
| ~ ( B @ ( A @ f24 ) @ ( C @ subset_collections ) )
| ~ ( C @ finite )
| ~ ( B @ ( A @ topological_space ) )
| ( B @ ( A @ compact_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ f15 ) ) ) ) @ eq_p ) )
| ~ ( D @ ( C @ ( A @ ( E @ neighborhood ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ limit_point ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',limit_point_66) ).
thf(145,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ f15 ) ) ) ) @ eq_p ) )
| ~ ( D @ ( C @ ( A @ ( E @ neighborhood ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ limit_point ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ f10 ) ) @ subset_sets ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_39) ).
thf(295,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ f10 ) ) @ subset_sets ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ f5 ) @ union_of_members @ element_of_collection ) )
| ( B @ ( B @ ( A @ f3 ) @ element_of_collection ) )
| ~ ( B @ ( A @ element_of_collection ) )
| ~ ( B @ ( empty_set @ element_of_collection ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ topological_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topological_space_13) ).
thf(327,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ f5 ) @ union_of_members @ element_of_collection ) )
| ( B @ ( B @ ( A @ f3 ) @ element_of_collection ) )
| ~ ( B @ ( A @ element_of_collection ) )
| ~ ( B @ ( empty_set @ element_of_collection ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ topological_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(77,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ intersection_of_sets ) @ ( A @ equal_sets ) )
| ~ ( C @ ( E @ element_of_collection ) )
| ~ ( B @ ( D @ subset_sets ) )
| ~ ( C @ ( B @ topological_space ) )
| ( D @ ( C @ ( B @ subspace_topology ) ) @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subspace_topology_46) ).
thf(263,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ intersection_of_sets ) @ ( A @ equal_sets ) )
| ~ ( C @ ( E @ element_of_collection ) )
| ~ ( B @ ( D @ subset_sets ) )
| ~ ( C @ ( B @ topological_space ) )
| ( D @ ( C @ ( B @ subspace_topology ) ) @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(45,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( D @ ( C @ ( B @ ( A @ f16 ) ) ) @ neighborhood ) ) ) )
| ~ ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ ( A @ limit_point ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',limit_point_67) ).
thf(199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( D @ ( C @ ( B @ ( A @ f16 ) ) ) @ neighborhood ) ) ) )
| ~ ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ ( A @ limit_point ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(34,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ open ) ) )
| ~ ( B @ ( E @ subset_sets ) )
| ~ ( E @ ( A @ element_of_set ) )
| ~ ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ interior ) ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interior_52) ).
thf(177,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ open ) ) )
| ~ ( B @ ( E @ subset_sets ) )
| ~ ( E @ ( A @ element_of_set ) )
| ~ ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ interior ) ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ f5 ) @ union_of_members @ element_of_collection ) )
| ~ ( B @ ( B @ ( A @ f4 ) @ ( B @ ( A @ f3 ) @ intersection_of_sets ) @ element_of_collection ) )
| ~ ( B @ ( A @ element_of_collection ) )
| ~ ( B @ ( empty_set @ element_of_collection ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ topological_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topological_space_17) ).
thf(331,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ f5 ) @ union_of_members @ element_of_collection ) )
| ~ ( B @ ( B @ ( A @ f4 ) @ ( B @ ( A @ f3 ) @ intersection_of_sets ) @ element_of_collection ) )
| ~ ( B @ ( A @ element_of_collection ) )
| ~ ( B @ ( empty_set @ element_of_collection ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ topological_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( C @ ( B @ relative_complement_sets ) @ closure ) ) @ ( A @ element_of_set ) )
| ~ ( D @ ( C @ ( B @ closure ) ) @ ( A @ element_of_set ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ boundary ) ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boundary_72) ).
thf(127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( C @ ( B @ relative_complement_sets ) @ closure ) ) @ ( A @ element_of_set ) )
| ~ ( D @ ( C @ ( B @ closure ) ) @ ( A @ element_of_set ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ boundary ) ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( D @ ( C @ ( B @ f14 ) ) ) @ closed ) ) )
| ~ ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ closure ) ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_57) ).
thf(175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( D @ ( C @ ( B @ f14 ) ) ) @ closed ) ) )
| ~ ( C @ ( B @ subset_sets ) )
| ~ ( D @ ( C @ topological_space ) )
| ( D @ ( C @ ( B @ closure ) ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ union_of_members @ equal_sets ) )
| ~ ( C @ ( B @ ( A @ open_covering ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_covering_98) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ union_of_members @ equal_sets ) )
| ~ ( C @ ( B @ ( A @ open_covering ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ subspace_topology ) ) @ ( A @ compact_space ) )
| ~ ( B @ ( A @ subset_sets ) )
| ~ ( C @ ( B @ topological_space ) )
| ( C @ ( B @ ( A @ compact_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compact_set_109) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ subspace_topology ) ) @ ( A @ compact_space ) )
| ~ ( B @ ( A @ subset_sets ) )
| ~ ( C @ ( B @ topological_space ) )
| ( C @ ( B @ ( A @ compact_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ union_of_members @ equal_sets ) )
| ~ ( C @ ( A @ subset_collections ) )
| ~ ( C @ ( B @ topological_space ) )
| ( C @ ( B @ ( A @ open_covering ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_covering_99) ).
thf(203,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ union_of_members @ equal_sets ) )
| ~ ( C @ ( A @ subset_collections ) )
| ~ ( C @ ( B @ topological_space ) )
| ( C @ ( B @ ( A @ open_covering ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f9 ) @ element_of_collection ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ basis ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_34) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f9 ) @ element_of_collection ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ basis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(1,negated_conjecture,
f @ ( cx @ basis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1d_1) ).
thf(114,plain,
f @ ( cx @ basis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ f1 ) @ ( A @ element_of_set ) )
| ~ ( B @ union_of_members @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_members_1) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ f1 ) @ ( A @ element_of_set ) )
| ~ ( B @ union_of_members @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ closure ) ) @ ( A @ element_of_set ) )
| ~ ( D @ ( C @ ( B @ boundary ) ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boundary_70) ).
thf(139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ closure ) ) @ ( A @ element_of_set ) )
| ~ ( D @ ( C @ ( B @ boundary ) ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f23 ) ) @ finite )
| ~ ( B @ ( A @ ( C @ open_covering ) ) )
| ~ ( B @ ( A @ compact_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compact_space_101) ).
thf(119,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f23 ) ) @ finite )
| ~ ( B @ ( A @ ( C @ open_covering ) ) )
| ~ ( B @ ( A @ compact_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ separation ) ) ) )
| ~ ( B @ ( A @ connected_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connected_space_90) ).
thf(235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( C @ separation ) ) ) )
| ~ ( B @ ( A @ connected_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ f22 ) @ ( B @ ( A @ f21 ) @ separation ) ) ) )
| ~ ( B @ ( A @ topological_space ) )
| ( B @ ( A @ connected_space ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connected_space_91) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ f22 ) @ ( B @ ( A @ f21 ) @ separation ) ) ) )
| ~ ( B @ ( A @ topological_space ) )
| ( B @ ( A @ connected_space ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(89,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ intersection_of_sets ) @ ( E @ ( D @ ( C @ ( B @ ( A @ f6 ) ) ) ) @ subset_sets ) )
| ~ ( E @ ( D @ intersection_of_sets ) @ ( C @ element_of_set ) )
| ~ ( B @ ( E @ element_of_collection ) )
| ~ ( B @ ( D @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ basis ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_31) ).
thf(287,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ intersection_of_sets ) @ ( E @ ( D @ ( C @ ( B @ ( A @ f6 ) ) ) ) @ subset_sets ) )
| ~ ( E @ ( D @ intersection_of_sets ) @ ( C @ element_of_set ) )
| ~ ( B @ ( E @ element_of_collection ) )
| ~ ( B @ ( D @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ basis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ topological_space ) )
| ~ ( C @ ( B @ ( A @ closed ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed_set_21) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ topological_space ) )
| ~ ( C @ ( B @ ( A @ closed ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(103,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ f6 ) ) ) ) @ ( C @ element_of_set ) )
| ~ ( E @ ( D @ intersection_of_sets ) @ ( C @ element_of_set ) )
| ~ ( B @ ( E @ element_of_collection ) )
| ~ ( B @ ( D @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ basis ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_29) ).
thf(315,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ f6 ) ) ) ) @ ( C @ element_of_set ) )
| ~ ( E @ ( D @ intersection_of_sets ) @ ( C @ element_of_set ) )
| ~ ( B @ ( E @ element_of_collection ) )
| ~ ( B @ ( D @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ basis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( B @ ( A @ relative_complement_sets ) @ open ) ) )
| ~ ( C @ ( B @ topological_space ) )
| ( C @ ( B @ ( A @ closed ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed_set_23) ).
thf(183,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( B @ ( A @ relative_complement_sets ) @ open ) ) )
| ~ ( C @ ( B @ topological_space ) )
| ( C @ ( B @ ( A @ closed ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ element_of_set ) )
| ~ ( B @ ( C @ element_of_collection ) )
| ~ ( B @ intersection_of_members @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_members_4) ).
thf(273,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ element_of_set ) )
| ~ ( B @ ( C @ element_of_collection ) )
| ~ ( B @ intersection_of_members @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ element_of_collection ) )
| ~ ( C @ ( A @ element_of_set ) )
| ( B @ union_of_members @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_members_3) ).
thf(305,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ element_of_collection ) )
| ~ ( C @ ( A @ element_of_set ) )
| ( B @ union_of_members @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(65,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ topological_space ) )
| ~ ( D @ ( C @ ( B @ ( A @ limit_point ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',limit_point_63) ).
thf(239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ topological_space ) )
| ~ ( D @ ( C @ ( B @ ( A @ limit_point ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ ( C @ ( B @ f13 ) ) ) @ subset_sets ) )
| ~ ( D @ ( C @ ( B @ interior ) ) @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interior_50) ).
thf(195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ ( C @ ( B @ f13 ) ) ) @ subset_sets ) )
| ~ ( D @ ( C @ ( B @ interior ) ) @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ union_of_members @ equal_sets ) )
| ~ ( B @ ( A @ basis ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_28) ).
thf(283,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ union_of_members @ equal_sets ) )
| ~ ( B @ ( A @ basis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ ( A @ relative_complement_sets ) @ open ) ) )
| ~ ( C @ ( B @ ( A @ closed ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed_set_22) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ ( A @ relative_complement_sets ) @ open ) ) )
| ~ ( C @ ( B @ ( A @ closed ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ topological_space ) )
| ~ ( C @ ( B @ ( A @ finer ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finer_topology_24) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ topological_space ) )
| ~ ( C @ ( B @ ( A @ finer ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ subset_sets ) )
| ~ ( D @ ( C @ ( B @ subspace_topology ) ) @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subspace_topology_43) ).
thf(277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ subset_sets ) )
| ~ ( D @ ( C @ ( B @ subspace_topology ) ) @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ topological_space ) )
| ~ ( C @ ( B @ ( A @ compact_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compact_set_106) ).
thf(227,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ topological_space ) )
| ~ ( C @ ( B @ ( A @ compact_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f9 ) @ ( B @ ( A @ f8 ) @ intersection_of_sets ) @ ( B @ ( A @ f7 ) @ element_of_set ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ basis ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_35) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f9 ) @ ( B @ ( A @ f8 ) @ intersection_of_sets ) @ ( B @ ( A @ f7 ) @ element_of_set ) )
| ~ ( A @ ( B @ union_of_members @ equal_sets ) )
| ( B @ ( A @ basis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ topological_space ) )
| ~ ( C @ ( B @ ( A @ open ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_set_18) ).
thf(215,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ topological_space ) )
| ~ ( C @ ( B @ ( A @ open ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(337,plain,
$false,
inference(e,[status(thm)],[153,333,249,115,217,247,269,185,301,257,125,157,189,325,289,261,179,321,121,211,253,147,221,293,133,265,116,243,307,233,117,201,297,165,275,137,229,197,329,285,317,169,141,225,193,173,129,237,205,311,161,279,149,191,291,281,259,313,335,181,159,187,219,245,303,271,323,213,251,155,223,135,299,267,241,167,255,209,123,145,295,327,263,199,177,331,127,175,143,231,203,319,114,171,139,119,235,207,287,151,315,183,273,305,239,195,283,131,163,277,227,309,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.41 % Computer : n013.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 20:29:22 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.86/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.35/1.26 % [INFO] Parsing done (244ms).
% 1.35/1.27 % [INFO] Running in sequential loop mode.
% 2.27/1.66 % [INFO] eprover registered as external prover.
% 2.27/1.67 % [INFO] Scanning for conjecture ...
% 2.47/1.79 % [INFO] Found a conjecture (or negated_conjecture) and 109 axioms. Running axiom selection ...
% 2.85/1.92 % [INFO] Axiom selection finished. Selected 109 axioms (removed 0 axioms).
% 3.25/2.04 % [INFO] Problem is propositional (TPTP CNF).
% 3.25/2.05 % [INFO] Type checking passed.
% 3.25/2.05 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.20/3.12 % External prover 'e' found a proof!
% 6.20/3.12 % [INFO] Killing All external provers ...
% 6.20/3.12 % Time passed: 2555ms (effective reasoning time: 1841ms)
% 6.20/3.12 % Axioms used in derivation (109): hausdorff_74, topology_generated_40, topological_space_9, compact_set_109, finer_topology_27, topological_space_7, separation_86, intersection_of_members_5, basis_for_topology_28, boundary_72, topological_space_15, neighborhood_60, open_set_20, hausdorff_79, topological_space_14, interior_48, hausdorff_78, connected_set_92, open_set_19, basis_for_topology_35, topology_generated_37, compact_space_104, finer_topology_24, limit_point_66, open_covering_98, separation_82, compact_space_100, limit_point_63, closure_55, interior_52, closed_set_23, boundary_71, interior_47, union_of_members_3, topological_space_10, closure_56, separation_87, closed_set_21, basis_for_topology_29, neighborhood_62, connected_space_91, subspace_topology_42, hausdorff_77, subspace_topology_45, topological_space_8, topological_space_13, hausdorff_73, basis_for_topology_36, connected_set_93, open_covering_97, compact_space_103, basis_for_topology_32, compact_set_108, separation_83, intersection_of_members_4, hausdorff_80, connected_space_89, limit_point_65, open_covering_96, topological_space_12, limit_point_64, topology_generated_39, separation_84, basis_for_topology_33, closed_set_22, closure_57, topological_space_17, open_covering_99, subspace_topology_43, finer_topology_25, limit_point_68, connected_space_90, finer_topology_26, closure_53, connected_set_94, union_of_members_2, hausdorff_76, basis_for_topology_31, compact_space_102, compact_set_107, intersection_of_members_6, open_set_18, topological_space_16, topological_space_11, interior_49, compact_space_105, subspace_topology_44, closure_58, interior_50, compact_set_106, boundary_69, topology_generated_38, neighborhood_61, separation_85, connected_set_95, neighborhood_59, boundary_70, subspace_topology_46, basis_for_topology_30, separation_81, limit_point_67, union_of_members_1, compact_space_101, separation_88, topology_generated_41, closure_54, interior_51, basis_for_topology_34, hausdorff_75
% 6.20/3.12 % No. of inferences in proof: 227
% 6.20/3.12 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2555 ms resp. 1841 ms w/o parsing
% 6.84/3.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.84/3.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------