TSTP Solution File: TOP010-1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : TOP010-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n010.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 : 300s
% DateTime : Fri Sep 1 05:57:14 EDT 2023
% Result : Satisfiable 4.11s 1.18s
% Output : Saturation 4.11s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(c_49,negated_conjecture,
finer(ct1,ct2,cx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',problem_5_123) ).
cnf(c_50,negated_conjecture,
subset_sets(a,cx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',problem_5_124) ).
cnf(c_51,negated_conjecture,
~ finer(subspace_topology(cx,ct1,a),subspace_topology(cx,ct2,a),cx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',problem_5_125) ).
cnf(c_52,plain,
( ~ element_of_set(X0,union_of_members(X1))
| element_of_set(X0,f1(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',union_of_members_1) ).
cnf(c_53,plain,
( ~ element_of_set(X0,union_of_members(X1))
| element_of_collection(f1(X1,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',union_of_members_2) ).
cnf(c_54,plain,
( ~ element_of_set(X0,X1)
| ~ element_of_collection(X1,X2)
| element_of_set(X0,union_of_members(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',union_of_members_3) ).
cnf(c_55,plain,
( ~ element_of_set(X0,intersection_of_members(X1))
| ~ element_of_collection(X2,X1)
| element_of_set(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',intersection_of_members_4) ).
cnf(c_56,plain,
( element_of_collection(f2(X0,X1),X0)
| element_of_set(X1,intersection_of_members(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',intersection_of_members_5) ).
cnf(c_57,plain,
( ~ element_of_set(X0,f2(X1,X0))
| element_of_set(X0,intersection_of_members(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',intersection_of_members_6) ).
cnf(c_58,plain,
( ~ topological_space(X0,X1)
| equal_sets(union_of_members(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',topological_space_7) ).
cnf(c_59,plain,
( ~ topological_space(X0,X1)
| element_of_collection(empty_set,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',topological_space_8) ).
cnf(c_60,plain,
( ~ topological_space(X0,X1)
| element_of_collection(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',topological_space_9) ).
cnf(c_61,plain,
( ~ element_of_collection(X0,X1)
| ~ element_of_collection(X2,X1)
| ~ topological_space(X3,X1)
| element_of_collection(intersection_of_sets(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',topological_space_10) ).
cnf(c_62,plain,
( ~ topological_space(X0,X1)
| ~ subset_collections(X2,X1)
| element_of_collection(union_of_members(X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',topological_space_11) ).
cnf(c_63,plain,
( ~ equal_sets(union_of_members(X0),X1)
| ~ element_of_collection(X1,X0)
| ~ element_of_collection(empty_set,X0)
| element_of_collection(f3(X1,X0),X0)
| subset_collections(f5(X1,X0),X0)
| topological_space(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',topological_space_12) ).
cnf(c_64,plain,
( ~ element_of_collection(union_of_members(f5(X0,X1)),X1)
| ~ equal_sets(union_of_members(X1),X0)
| ~ element_of_collection(X0,X1)
| ~ element_of_collection(empty_set,X1)
| element_of_collection(f3(X0,X1),X1)
| topological_space(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',topological_space_13) ).
cnf(c_65,plain,
( ~ equal_sets(union_of_members(X0),X1)
| ~ element_of_collection(X1,X0)
| ~ element_of_collection(empty_set,X0)
| element_of_collection(f4(X1,X0),X0)
| subset_collections(f5(X1,X0),X0)
| topological_space(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',topological_space_14) ).
cnf(c_66,plain,
( ~ element_of_collection(union_of_members(f5(X0,X1)),X1)
| ~ equal_sets(union_of_members(X1),X0)
| ~ element_of_collection(X0,X1)
| ~ element_of_collection(empty_set,X1)
| element_of_collection(f4(X0,X1),X1)
| topological_space(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',topological_space_15) ).
cnf(c_67,plain,
( ~ element_of_collection(intersection_of_sets(f3(X0,X1),f4(X0,X1)),X1)
| ~ equal_sets(union_of_members(X1),X0)
| ~ element_of_collection(X0,X1)
| ~ element_of_collection(empty_set,X1)
| subset_collections(f5(X0,X1),X1)
| topological_space(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',topological_space_16) ).
cnf(c_68,plain,
( ~ element_of_collection(intersection_of_sets(f3(X0,X1),f4(X0,X1)),X1)
| ~ element_of_collection(union_of_members(f5(X0,X1)),X1)
| ~ equal_sets(union_of_members(X1),X0)
| ~ element_of_collection(X0,X1)
| ~ element_of_collection(empty_set,X1)
| topological_space(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',topological_space_17) ).
cnf(c_69,plain,
( ~ open(X0,X1,X2)
| topological_space(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',open_set_18) ).
cnf(c_70,plain,
( ~ open(X0,X1,X2)
| element_of_collection(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',open_set_19) ).
cnf(c_71,plain,
( ~ element_of_collection(X0,X1)
| ~ topological_space(X2,X1)
| open(X0,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',open_set_20) ).
cnf(c_72,plain,
( ~ closed(X0,X1,X2)
| topological_space(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',closed_set_21) ).
cnf(c_73,plain,
( ~ closed(X0,X1,X2)
| open(relative_complement_sets(X0,X1),X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',closed_set_22) ).
cnf(c_74,plain,
( ~ open(relative_complement_sets(X0,X1),X1,X2)
| ~ topological_space(X1,X2)
| closed(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',closed_set_23) ).
cnf(c_75,plain,
( ~ finer(X0,X1,X2)
| topological_space(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',finer_topology_24) ).
cnf(c_76,plain,
( ~ finer(X0,X1,X2)
| topological_space(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',finer_topology_25) ).
cnf(c_77,plain,
( ~ finer(X0,X1,X2)
| subset_collections(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',finer_topology_26) ).
cnf(c_78,plain,
( ~ topological_space(X0,X1)
| ~ topological_space(X0,X2)
| ~ subset_collections(X2,X1)
| finer(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',finer_topology_27) ).
cnf(c_79,plain,
( ~ basis(X0,X1)
| equal_sets(union_of_members(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',basis_for_topology_28) ).
cnf(c_80,plain,
( ~ element_of_set(X0,intersection_of_sets(X1,X2))
| ~ element_of_set(X0,X3)
| ~ element_of_collection(X1,X4)
| ~ element_of_collection(X2,X4)
| ~ basis(X3,X4)
| element_of_set(X0,f6(X3,X4,X0,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',basis_for_topology_29) ).
cnf(c_81,plain,
( ~ element_of_set(X0,intersection_of_sets(X1,X2))
| ~ element_of_set(X0,X3)
| ~ element_of_collection(X1,X4)
| ~ element_of_collection(X2,X4)
| ~ basis(X3,X4)
| element_of_collection(f6(X3,X4,X0,X1,X2),X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',basis_for_topology_30) ).
cnf(c_82,plain,
( ~ element_of_set(X0,intersection_of_sets(X1,X2))
| ~ element_of_set(X0,X3)
| ~ element_of_collection(X1,X4)
| ~ element_of_collection(X2,X4)
| ~ basis(X3,X4)
| subset_sets(f6(X3,X4,X0,X1,X2),intersection_of_sets(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',basis_for_topology_31) ).
cnf(c_83,plain,
( ~ equal_sets(union_of_members(X0),X1)
| element_of_set(f7(X1,X0),X1)
| basis(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',basis_for_topology_32) ).
cnf(c_84,plain,
( ~ equal_sets(union_of_members(X0),X1)
| element_of_collection(f8(X1,X0),X0)
| basis(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',basis_for_topology_33) ).
cnf(c_85,plain,
( ~ equal_sets(union_of_members(X0),X1)
| element_of_collection(f9(X1,X0),X0)
| basis(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',basis_for_topology_34) ).
cnf(c_86,plain,
( ~ equal_sets(union_of_members(X0),X1)
| element_of_set(f7(X1,X0),intersection_of_sets(f8(X1,X0),f9(X1,X0)))
| basis(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',basis_for_topology_35) ).
cnf(c_87,plain,
( ~ subset_sets(X0,intersection_of_sets(f8(X1,X2),f9(X1,X2)))
| ~ element_of_set(f7(X1,X2),X0)
| ~ equal_sets(union_of_members(X2),X1)
| ~ element_of_collection(X0,X2)
| basis(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',basis_for_topology_36) ).
cnf(c_88,plain,
( ~ element_of_collection(X0,top_of_basis(X1))
| ~ element_of_set(X2,X0)
| element_of_set(X2,f10(X1,X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',topology_generated_37) ).
cnf(c_89,plain,
( ~ element_of_collection(X0,top_of_basis(X1))
| ~ element_of_set(X2,X0)
| element_of_collection(f10(X1,X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',topology_generated_38) ).
cnf(c_90,plain,
( ~ element_of_collection(X0,top_of_basis(X1))
| ~ element_of_set(X2,X0)
| subset_sets(f10(X1,X0,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',topology_generated_39) ).
cnf(c_91,plain,
( element_of_set(f11(X0,X1),X1)
| element_of_collection(X1,top_of_basis(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',topology_generated_40) ).
cnf(c_92,plain,
( ~ element_of_set(f11(X0,X1),X2)
| ~ subset_sets(X2,X1)
| ~ element_of_collection(X2,X0)
| element_of_collection(X1,top_of_basis(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',topology_generated_41) ).
cnf(c_93,plain,
( ~ element_of_collection(X0,subspace_topology(X1,X2,X3))
| topological_space(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',subspace_topology_42) ).
cnf(c_94,plain,
( ~ element_of_collection(X0,subspace_topology(X1,X2,X3))
| subset_sets(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',subspace_topology_43) ).
cnf(c_95,plain,
( ~ element_of_collection(X0,subspace_topology(X1,X2,X3))
| element_of_collection(f12(X1,X2,X3,X0),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',subspace_topology_44) ).
cnf(c_96,plain,
( ~ element_of_collection(X0,subspace_topology(X1,X2,X3))
| equal_sets(X0,intersection_of_sets(X3,f12(X1,X2,X3,X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',subspace_topology_45) ).
cnf(c_97,plain,
( ~ equal_sets(X0,intersection_of_sets(X1,X2))
| ~ subset_sets(X1,X3)
| ~ element_of_collection(X2,X4)
| ~ topological_space(X3,X4)
| element_of_collection(X0,subspace_topology(X3,X4,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',subspace_topology_46) ).
cnf(c_98,plain,
( ~ element_of_set(X0,interior(X1,X2,X3))
| topological_space(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',interior_47) ).
cnf(c_99,plain,
( ~ element_of_set(X0,interior(X1,X2,X3))
| subset_sets(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',interior_48) ).
cnf(c_100,plain,
( ~ element_of_set(X0,interior(X1,X2,X3))
| element_of_set(X0,f13(X1,X2,X3,X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',interior_49) ).
cnf(c_101,plain,
( ~ element_of_set(X0,interior(X1,X2,X3))
| subset_sets(f13(X1,X2,X3,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',interior_50) ).
cnf(c_102,plain,
( ~ element_of_set(X0,interior(X1,X2,X3))
| open(f13(X1,X2,X3,X0),X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',interior_51) ).
cnf(c_103,plain,
( ~ open(X0,X1,X2)
| ~ subset_sets(X0,X3)
| ~ subset_sets(X3,X1)
| ~ element_of_set(X4,X0)
| ~ topological_space(X1,X2)
| element_of_set(X4,interior(X3,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',interior_52) ).
cnf(c_104,plain,
( ~ element_of_set(X0,closure(X1,X2,X3))
| topological_space(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',closure_53) ).
cnf(c_105,plain,
( ~ element_of_set(X0,closure(X1,X2,X3))
| subset_sets(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',closure_54) ).
cnf(c_106,plain,
( ~ element_of_set(X0,closure(X1,X2,X3))
| ~ closed(X4,X2,X3)
| ~ subset_sets(X1,X4)
| element_of_set(X0,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',closure_55) ).
cnf(c_107,plain,
( ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| subset_sets(X0,f14(X0,X1,X2,X3))
| element_of_set(X3,closure(X0,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',closure_56) ).
cnf(c_108,plain,
( ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| closed(f14(X0,X1,X2,X3),X1,X2)
| element_of_set(X3,closure(X0,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',closure_57) ).
cnf(c_109,plain,
( ~ element_of_set(X0,f14(X1,X2,X3,X0))
| ~ subset_sets(X1,X2)
| ~ topological_space(X2,X3)
| element_of_set(X0,closure(X1,X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',closure_58) ).
cnf(c_110,plain,
( ~ neighborhood(X0,X1,X2,X3)
| topological_space(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',neighborhood_59) ).
cnf(c_111,plain,
( ~ neighborhood(X0,X1,X2,X3)
| open(X0,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',neighborhood_60) ).
cnf(c_112,plain,
( ~ neighborhood(X0,X1,X2,X3)
| element_of_set(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',neighborhood_61) ).
cnf(c_113,plain,
( ~ open(X0,X1,X2)
| ~ element_of_set(X3,X0)
| ~ topological_space(X1,X2)
| neighborhood(X0,X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',neighborhood_62) ).
cnf(c_114,plain,
( ~ limit_point(X0,X1,X2,X3)
| topological_space(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',limit_point_63) ).
cnf(c_115,plain,
( ~ limit_point(X0,X1,X2,X3)
| subset_sets(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',limit_point_64) ).
cnf(c_116,plain,
( ~ neighborhood(X0,X1,X2,X3)
| ~ limit_point(X1,X4,X2,X3)
| element_of_set(f15(X1,X4,X2,X3,X0),intersection_of_sets(X0,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',limit_point_65) ).
cnf(c_117,plain,
( ~ eq_p(f15(X0,X1,X2,X3,X4),X0)
| ~ neighborhood(X4,X0,X2,X3)
| ~ limit_point(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',limit_point_66) ).
cnf(c_118,plain,
( ~ subset_sets(X0,X1)
| ~ topological_space(X1,X2)
| neighborhood(f16(X3,X0,X1,X2),X3,X1,X2)
| limit_point(X3,X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',limit_point_67) ).
cnf(c_119,plain,
( ~ element_of_set(X0,intersection_of_sets(f16(X1,X2,X3,X4),X2))
| ~ subset_sets(X2,X3)
| ~ topological_space(X3,X4)
| limit_point(X1,X2,X3,X4)
| eq_p(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',limit_point_68) ).
cnf(c_120,plain,
( ~ element_of_set(X0,boundary(X1,X2,X3))
| topological_space(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',boundary_69) ).
cnf(c_121,plain,
( ~ element_of_set(X0,boundary(X1,X2,X3))
| element_of_set(X0,closure(X1,X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',boundary_70) ).
cnf(c_122,plain,
( ~ element_of_set(X0,boundary(X1,X2,X3))
| element_of_set(X0,closure(relative_complement_sets(X1,X2),X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',boundary_71) ).
cnf(c_123,plain,
( ~ element_of_set(X0,closure(relative_complement_sets(X1,X2),X2,X3))
| ~ element_of_set(X0,closure(X1,X2,X3))
| ~ topological_space(X2,X3)
| element_of_set(X0,boundary(X1,X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',boundary_72) ).
cnf(c_124,plain,
( ~ hausdorff(X0,X1)
| topological_space(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',hausdorff_73) ).
cnf(c_125,plain,
( ~ element_of_set(X0,X1)
| ~ element_of_set(X2,X1)
| ~ hausdorff(X1,X3)
| neighborhood(f17(X1,X3,X0,X2),X0,X1,X3)
| eq_p(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',hausdorff_74) ).
cnf(c_126,plain,
( ~ element_of_set(X0,X1)
| ~ element_of_set(X2,X1)
| ~ hausdorff(X1,X3)
| neighborhood(f18(X1,X3,X0,X2),X2,X1,X3)
| eq_p(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',hausdorff_75) ).
cnf(c_127,plain,
( ~ element_of_set(X0,X1)
| ~ element_of_set(X2,X1)
| ~ hausdorff(X1,X3)
| disjoint_s(f17(X1,X3,X0,X2),f18(X1,X3,X0,X2))
| eq_p(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',hausdorff_76) ).
cnf(c_128,plain,
( ~ topological_space(X0,X1)
| element_of_set(f19(X0,X1),X0)
| hausdorff(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',hausdorff_77) ).
cnf(c_129,plain,
( ~ topological_space(X0,X1)
| element_of_set(f20(X0,X1),X0)
| hausdorff(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',hausdorff_78) ).
cnf(c_130,plain,
( ~ eq_p(f19(X0,X1),f20(X0,X1))
| ~ topological_space(X0,X1)
| hausdorff(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',hausdorff_79) ).
cnf(c_131,plain,
( ~ neighborhood(X0,f19(X1,X2),X1,X2)
| ~ neighborhood(X3,f20(X1,X2),X1,X2)
| ~ topological_space(X1,X2)
| ~ disjoint_s(X0,X3)
| hausdorff(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',hausdorff_80) ).
cnf(c_132,plain,
( ~ separation(X0,X1,X2,X3)
| topological_space(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',separation_81) ).
cnf(c_133,plain,
( ~ separation(X0,X1,X2,X3)
| ~ equal_sets(X0,empty_set) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',separation_82) ).
cnf(c_134,plain,
( ~ separation(X0,X1,X2,X3)
| ~ equal_sets(X1,empty_set) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',separation_83) ).
cnf(c_135,plain,
( ~ separation(X0,X1,X2,X3)
| element_of_collection(X0,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',separation_84) ).
cnf(c_136,plain,
( ~ separation(X0,X1,X2,X3)
| element_of_collection(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',separation_85) ).
cnf(c_137,plain,
( ~ separation(X0,X1,X2,X3)
| equal_sets(union_of_sets(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',separation_86) ).
cnf(c_138,plain,
( ~ separation(X0,X1,X2,X3)
| disjoint_s(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',separation_87) ).
cnf(c_139,plain,
( ~ equal_sets(union_of_sets(X0,X1),X2)
| ~ element_of_collection(X0,X3)
| ~ element_of_collection(X1,X3)
| ~ topological_space(X2,X3)
| ~ disjoint_s(X0,X1)
| separation(X0,X1,X2,X3)
| equal_sets(X0,empty_set)
| equal_sets(X1,empty_set) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',separation_88) ).
cnf(c_141,plain,
( ~ separation(X0,X1,X2,X3)
| ~ connected_space(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',connected_space_90) ).
cnf(c_142,plain,
( ~ topological_space(X0,X1)
| separation(f21(X0,X1),f22(X0,X1),X0,X1)
| connected_space(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',connected_space_91) ).
cnf(c_147,plain,
( ~ open_covering(X0,X1,X2)
| topological_space(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',open_covering_96) ).
cnf(c_148,plain,
( ~ open_covering(X0,X1,X2)
| subset_collections(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',open_covering_97) ).
cnf(c_149,plain,
( ~ open_covering(X0,X1,X2)
| equal_sets(union_of_members(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',open_covering_98) ).
cnf(c_150,plain,
( ~ equal_sets(union_of_members(X0),X1)
| ~ topological_space(X1,X2)
| ~ subset_collections(X0,X2)
| open_covering(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',open_covering_99) ).
cnf(c_151,plain,
( ~ compact_space(X0,X1)
| topological_space(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',compact_space_100) ).
cnf(c_152,plain,
( ~ open_covering(X0,X1,X2)
| ~ compact_space(X1,X2)
| finite(f23(X1,X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',compact_space_101) ).
cnf(c_153,plain,
( ~ open_covering(X0,X1,X2)
| ~ compact_space(X1,X2)
| subset_collections(f23(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',compact_space_102) ).
cnf(c_154,plain,
( ~ open_covering(X0,X1,X2)
| ~ compact_space(X1,X2)
| open_covering(f23(X1,X2,X0),X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',compact_space_103) ).
cnf(c_155,plain,
( ~ topological_space(X0,X1)
| open_covering(f24(X0,X1),X0,X1)
| compact_space(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',compact_space_104) ).
cnf(c_156,plain,
( ~ subset_collections(X0,f24(X1,X2))
| ~ open_covering(X0,X1,X2)
| ~ topological_space(X1,X2)
| ~ finite(X0)
| compact_space(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/TOP001-0.ax',compact_space_105) ).
cnf(c_266,plain,
( ~ element_of_set(X3,X0)
| ~ open(X0,X1,X2)
| neighborhood(X0,X3,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_113,c_69,c_113]) ).
cnf(c_267,plain,
( ~ open(X0,X1,X2)
| ~ element_of_set(X3,X0)
| neighborhood(X0,X3,X1,X2) ),
inference(renaming,[status(thm)],[c_266]) ).
cnf(c_269,plain,
( ~ open_covering(X0,X1,X2)
| ~ subset_collections(X0,f24(X1,X2))
| ~ finite(X0)
| compact_space(X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_156,c_147,c_156]) ).
cnf(c_270,plain,
( ~ subset_collections(X0,f24(X1,X2))
| ~ open_covering(X0,X1,X2)
| ~ finite(X0)
| compact_space(X1,X2) ),
inference(renaming,[status(thm)],[c_269]) ).
cnf(c_272,plain,
( ~ element_of_set(X0,closure(X1,X2,X3))
| ~ element_of_set(X0,closure(relative_complement_sets(X1,X2),X2,X3))
| element_of_set(X0,boundary(X1,X2,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_123,c_104,c_123]) ).
cnf(c_273,plain,
( ~ element_of_set(X0,closure(relative_complement_sets(X1,X2),X2,X3))
| ~ element_of_set(X0,closure(X1,X2,X3))
| element_of_set(X0,boundary(X1,X2,X3)) ),
inference(renaming,[status(thm)],[c_272]) ).
cnf(c_275,plain,
( ~ element_of_set(X4,X0)
| ~ subset_sets(X3,X1)
| ~ subset_sets(X0,X3)
| ~ open(X0,X1,X2)
| element_of_set(X4,interior(X3,X1,X2)) ),
inference(global_subsumption_just,[status(thm)],[c_103,c_69,c_103]) ).
cnf(c_276,plain,
( ~ open(X0,X1,X2)
| ~ subset_sets(X0,X3)
| ~ subset_sets(X3,X1)
| ~ element_of_set(X4,X0)
| element_of_set(X4,interior(X3,X1,X2)) ),
inference(renaming,[status(thm)],[c_275]) ).
cnf(c_312,plain,
( ~ open(relative_complement_sets(X0,X1),X1,X2)
| closed(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_74,c_69]) ).
cnf(c_374,plain,
( ~ neighborhood(X0,f19(X1,X2),X1,X2)
| ~ neighborhood(X3,f20(X1,X2),X1,X2)
| ~ disjoint_s(X0,X3)
| hausdorff(X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_131,c_110]) ).
cnf(c_973,plain,
( ~ separation(X0,X1,X2,X3)
| ~ topological_space(X2,X3)
| separation(f21(X2,X3),f22(X2,X3),X2,X3) ),
inference(resolution,[status(thm)],[c_142,c_141]) ).
cnf(c_975,plain,
( ~ separation(X0,X1,X2,X3)
| separation(f21(X2,X3),f22(X2,X3),X2,X3) ),
inference(global_subsumption_just,[status(thm)],[c_973,c_132,c_973]) ).
cnf(c_989,plain,
subset_collections(ct2,ct1),
inference(resolution,[status(thm)],[c_49,c_77]) ).
cnf(c_993,plain,
topological_space(cx,ct2),
inference(resolution,[status(thm)],[c_49,c_76]) ).
cnf(c_997,plain,
topological_space(cx,ct1),
inference(resolution,[status(thm)],[c_49,c_75]) ).
cnf(c_1001,plain,
( ~ subset_collections(subspace_topology(cx,ct2,a),subspace_topology(cx,ct1,a))
| ~ topological_space(cx,subspace_topology(cx,ct1,a))
| ~ topological_space(cx,subspace_topology(cx,ct2,a)) ),
inference(resolution,[status(thm)],[c_51,c_78]) ).
cnf(c_3033,plain,
( closed(X0,X1,X2)
| ~ open(relative_complement_sets(X0,X1),X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_312]) ).
cnf(c_3034,plain,
( ~ open(relative_complement_sets(X0,X1),X1,X2)
| closed(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_3033]) ).
cnf(c_3161,plain,
( ~ separation(X0,X1,X2,X3)
| separation(f21(X2,X3),f22(X2,X3),X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_975]) ).
cnf(c_5944,plain,
( ~ subset_collections(subspace_topology(cx,ct2,a),subspace_topology(cx,ct1,a))
| ~ topological_space(cx,subspace_topology(cx,ct1,a))
| ~ topological_space(cx,subspace_topology(cx,ct2,a)) ),
inference(subtyping,[status(esa)],[c_1001]) ).
cnf(c_5945,plain,
topological_space(cx,ct1),
inference(subtyping,[status(esa)],[c_997]) ).
cnf(c_5946,plain,
topological_space(cx,ct2),
inference(subtyping,[status(esa)],[c_993]) ).
cnf(c_5947,plain,
subset_collections(ct2,ct1),
inference(subtyping,[status(esa)],[c_989]) ).
cnf(c_5948,plain,
( ~ separation(X0_14,X1_14,X2_14,X0_13)
| separation(f21(X2_14,X0_13),f22(X2_14,X0_13),X2_14,X0_13) ),
inference(subtyping,[status(esa)],[c_3161]) ).
cnf(c_5949,plain,
( ~ neighborhood(X0_14,f20(X1_14,X0_13),X1_14,X0_13)
| ~ neighborhood(X2_14,f19(X1_14,X0_13),X1_14,X0_13)
| ~ disjoint_s(X2_14,X0_14)
| hausdorff(X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_374]) ).
cnf(c_5950,plain,
( ~ open(relative_complement_sets(X0_14,X1_14),X1_14,X0_13)
| closed(X0_14,X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_3034]) ).
cnf(c_5951,plain,
( ~ open(X0_14,X1_14,X0_13)
| ~ subset_sets(X0_14,X2_14)
| ~ subset_sets(X2_14,X1_14)
| ~ element_of_set(X0_15,X0_14)
| element_of_set(X0_15,interior(X2_14,X1_14,X0_13)) ),
inference(subtyping,[status(esa)],[c_276]) ).
cnf(c_5952,plain,
( ~ element_of_set(X0_15,closure(relative_complement_sets(X0_14,X1_14),X1_14,X0_13))
| ~ element_of_set(X0_15,closure(X0_14,X1_14,X0_13))
| element_of_set(X0_15,boundary(X0_14,X1_14,X0_13)) ),
inference(subtyping,[status(esa)],[c_273]) ).
cnf(c_5953,plain,
( ~ subset_collections(X0_13,f24(X0_14,X1_13))
| ~ open_covering(X0_13,X0_14,X1_13)
| ~ finite(X0_13)
| compact_space(X0_14,X1_13) ),
inference(subtyping,[status(esa)],[c_270]) ).
cnf(c_5954,plain,
( ~ open(X0_14,X1_14,X0_13)
| ~ element_of_set(X0_15,X0_14)
| neighborhood(X0_14,X0_15,X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_267]) ).
cnf(c_5955,plain,
( ~ topological_space(X0_14,X0_13)
| open_covering(f24(X0_14,X0_13),X0_14,X0_13)
| compact_space(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_155]) ).
cnf(c_5956,plain,
( ~ open_covering(X0_13,X0_14,X1_13)
| ~ compact_space(X0_14,X1_13)
| open_covering(f23(X0_14,X1_13,X0_13),X0_14,X1_13) ),
inference(subtyping,[status(esa)],[c_154]) ).
cnf(c_5957,plain,
( ~ open_covering(X0_13,X0_14,X1_13)
| ~ compact_space(X0_14,X1_13)
| subset_collections(f23(X0_14,X1_13,X0_13),X0_13) ),
inference(subtyping,[status(esa)],[c_153]) ).
cnf(c_5958,plain,
( ~ open_covering(X0_13,X0_14,X1_13)
| ~ compact_space(X0_14,X1_13)
| finite(f23(X0_14,X1_13,X0_13)) ),
inference(subtyping,[status(esa)],[c_152]) ).
cnf(c_5959,plain,
( ~ compact_space(X0_14,X0_13)
| topological_space(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_151]) ).
cnf(c_5960,plain,
( ~ equal_sets(union_of_members(X0_13),X0_14)
| ~ topological_space(X0_14,X1_13)
| ~ subset_collections(X0_13,X1_13)
| open_covering(X0_13,X0_14,X1_13) ),
inference(subtyping,[status(esa)],[c_150]) ).
cnf(c_5961,plain,
( ~ open_covering(X0_13,X0_14,X1_13)
| equal_sets(union_of_members(X0_13),X0_14) ),
inference(subtyping,[status(esa)],[c_149]) ).
cnf(c_5962,plain,
( ~ open_covering(X0_13,X0_14,X1_13)
| subset_collections(X0_13,X1_13) ),
inference(subtyping,[status(esa)],[c_148]) ).
cnf(c_5963,plain,
( ~ open_covering(X0_13,X0_14,X1_13)
| topological_space(X0_14,X1_13) ),
inference(subtyping,[status(esa)],[c_147]) ).
cnf(c_5964,plain,
( ~ equal_sets(union_of_sets(X0_14,X1_14),X2_14)
| ~ element_of_collection(X0_14,X0_13)
| ~ element_of_collection(X1_14,X0_13)
| ~ topological_space(X2_14,X0_13)
| ~ disjoint_s(X0_14,X1_14)
| separation(X0_14,X1_14,X2_14,X0_13)
| equal_sets(X0_14,empty_set)
| equal_sets(X1_14,empty_set) ),
inference(subtyping,[status(esa)],[c_139]) ).
cnf(c_5965,plain,
( ~ separation(X0_14,X1_14,X2_14,X0_13)
| disjoint_s(X0_14,X1_14) ),
inference(subtyping,[status(esa)],[c_138]) ).
cnf(c_5966,plain,
( ~ separation(X0_14,X1_14,X2_14,X0_13)
| equal_sets(union_of_sets(X0_14,X1_14),X2_14) ),
inference(subtyping,[status(esa)],[c_137]) ).
cnf(c_5967,plain,
( ~ separation(X0_14,X1_14,X2_14,X0_13)
| element_of_collection(X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_136]) ).
cnf(c_5968,plain,
( ~ separation(X0_14,X1_14,X2_14,X0_13)
| element_of_collection(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_135]) ).
cnf(c_5969,plain,
( ~ separation(X0_14,X1_14,X2_14,X0_13)
| ~ equal_sets(X1_14,empty_set) ),
inference(subtyping,[status(esa)],[c_134]) ).
cnf(c_5970,plain,
( ~ separation(X0_14,X1_14,X2_14,X0_13)
| ~ equal_sets(X0_14,empty_set) ),
inference(subtyping,[status(esa)],[c_133]) ).
cnf(c_5971,plain,
( ~ separation(X0_14,X1_14,X2_14,X0_13)
| topological_space(X2_14,X0_13) ),
inference(subtyping,[status(esa)],[c_132]) ).
cnf(c_5972,plain,
( ~ eq_p(f19(X0_14,X0_13),f20(X0_14,X0_13))
| ~ topological_space(X0_14,X0_13)
| hausdorff(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_130]) ).
cnf(c_5973,plain,
( ~ topological_space(X0_14,X0_13)
| element_of_set(f20(X0_14,X0_13),X0_14)
| hausdorff(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_129]) ).
cnf(c_5974,plain,
( ~ topological_space(X0_14,X0_13)
| element_of_set(f19(X0_14,X0_13),X0_14)
| hausdorff(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_128]) ).
cnf(c_5975,plain,
( ~ element_of_set(X0_15,X0_14)
| ~ element_of_set(X1_15,X0_14)
| ~ hausdorff(X0_14,X0_13)
| disjoint_s(f17(X0_14,X0_13,X0_15,X1_15),f18(X0_14,X0_13,X0_15,X1_15))
| eq_p(X0_15,X1_15) ),
inference(subtyping,[status(esa)],[c_127]) ).
cnf(c_5976,plain,
( ~ element_of_set(X0_15,X0_14)
| ~ element_of_set(X1_15,X0_14)
| ~ hausdorff(X0_14,X0_13)
| neighborhood(f18(X0_14,X0_13,X0_15,X1_15),X1_15,X0_14,X0_13)
| eq_p(X0_15,X1_15) ),
inference(subtyping,[status(esa)],[c_126]) ).
cnf(c_5977,plain,
( ~ element_of_set(X0_15,X0_14)
| ~ element_of_set(X1_15,X0_14)
| ~ hausdorff(X0_14,X0_13)
| neighborhood(f17(X0_14,X0_13,X0_15,X1_15),X0_15,X0_14,X0_13)
| eq_p(X0_15,X1_15) ),
inference(subtyping,[status(esa)],[c_125]) ).
cnf(c_5978,plain,
( ~ hausdorff(X0_14,X0_13)
| topological_space(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_124]) ).
cnf(c_5979,plain,
( ~ element_of_set(X0_15,boundary(X0_14,X1_14,X0_13))
| element_of_set(X0_15,closure(relative_complement_sets(X0_14,X1_14),X1_14,X0_13)) ),
inference(subtyping,[status(esa)],[c_122]) ).
cnf(c_5980,plain,
( ~ element_of_set(X0_15,boundary(X0_14,X1_14,X0_13))
| element_of_set(X0_15,closure(X0_14,X1_14,X0_13)) ),
inference(subtyping,[status(esa)],[c_121]) ).
cnf(c_5981,plain,
( ~ element_of_set(X0_15,boundary(X0_14,X1_14,X0_13))
| topological_space(X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_120]) ).
cnf(c_5982,plain,
( ~ element_of_set(X0_15,intersection_of_sets(f16(X1_15,X0_14,X1_14,X0_13),X0_14))
| ~ subset_sets(X0_14,X1_14)
| ~ topological_space(X1_14,X0_13)
| limit_point(X1_15,X0_14,X1_14,X0_13)
| eq_p(X0_15,X1_15) ),
inference(subtyping,[status(esa)],[c_119]) ).
cnf(c_5983,plain,
( ~ subset_sets(X0_14,X1_14)
| ~ topological_space(X1_14,X0_13)
| neighborhood(f16(X0_15,X0_14,X1_14,X0_13),X0_15,X1_14,X0_13)
| limit_point(X0_15,X0_14,X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_118]) ).
cnf(c_5984,plain,
( ~ eq_p(f15(X0_15,X0_14,X1_14,X0_13,X2_14),X0_15)
| ~ neighborhood(X2_14,X0_15,X1_14,X0_13)
| ~ limit_point(X0_15,X0_14,X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_117]) ).
cnf(c_5985,plain,
( ~ neighborhood(X0_14,X0_15,X1_14,X0_13)
| ~ limit_point(X0_15,X2_14,X1_14,X0_13)
| element_of_set(f15(X0_15,X2_14,X1_14,X0_13,X0_14),intersection_of_sets(X0_14,X2_14)) ),
inference(subtyping,[status(esa)],[c_116]) ).
cnf(c_5986,plain,
( ~ limit_point(X0_15,X0_14,X1_14,X0_13)
| subset_sets(X0_14,X1_14) ),
inference(subtyping,[status(esa)],[c_115]) ).
cnf(c_5987,plain,
( ~ limit_point(X0_15,X0_14,X1_14,X0_13)
| topological_space(X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_114]) ).
cnf(c_5988,plain,
( ~ neighborhood(X0_14,X0_15,X1_14,X0_13)
| element_of_set(X0_15,X0_14) ),
inference(subtyping,[status(esa)],[c_112]) ).
cnf(c_5989,plain,
( ~ neighborhood(X0_14,X0_15,X1_14,X0_13)
| open(X0_14,X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_111]) ).
cnf(c_5990,plain,
( ~ neighborhood(X0_14,X0_15,X1_14,X0_13)
| topological_space(X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_110]) ).
cnf(c_5991,plain,
( ~ element_of_set(X0_15,f14(X0_14,X1_14,X0_13,X0_15))
| ~ subset_sets(X0_14,X1_14)
| ~ topological_space(X1_14,X0_13)
| element_of_set(X0_15,closure(X0_14,X1_14,X0_13)) ),
inference(subtyping,[status(esa)],[c_109]) ).
cnf(c_5992,plain,
( ~ subset_sets(X0_14,X1_14)
| ~ topological_space(X1_14,X0_13)
| closed(f14(X0_14,X1_14,X0_13,X0_15),X1_14,X0_13)
| element_of_set(X0_15,closure(X0_14,X1_14,X0_13)) ),
inference(subtyping,[status(esa)],[c_108]) ).
cnf(c_5993,plain,
( ~ subset_sets(X0_14,X1_14)
| ~ topological_space(X1_14,X0_13)
| subset_sets(X0_14,f14(X0_14,X1_14,X0_13,X0_15))
| element_of_set(X0_15,closure(X0_14,X1_14,X0_13)) ),
inference(subtyping,[status(esa)],[c_107]) ).
cnf(c_5994,plain,
( ~ element_of_set(X0_15,closure(X0_14,X1_14,X0_13))
| ~ closed(X2_14,X1_14,X0_13)
| ~ subset_sets(X0_14,X2_14)
| element_of_set(X0_15,X2_14) ),
inference(subtyping,[status(esa)],[c_106]) ).
cnf(c_5995,plain,
( ~ element_of_set(X0_15,closure(X0_14,X1_14,X0_13))
| subset_sets(X0_14,X1_14) ),
inference(subtyping,[status(esa)],[c_105]) ).
cnf(c_5996,plain,
( ~ element_of_set(X0_15,closure(X0_14,X1_14,X0_13))
| topological_space(X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_104]) ).
cnf(c_5997,plain,
( ~ element_of_set(X0_15,interior(X0_14,X1_14,X0_13))
| open(f13(X0_14,X1_14,X0_13,X0_15),X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_102]) ).
cnf(c_5998,plain,
( ~ element_of_set(X0_15,interior(X0_14,X1_14,X0_13))
| subset_sets(f13(X0_14,X1_14,X0_13,X0_15),X0_14) ),
inference(subtyping,[status(esa)],[c_101]) ).
cnf(c_5999,plain,
( ~ element_of_set(X0_15,interior(X0_14,X1_14,X0_13))
| element_of_set(X0_15,f13(X0_14,X1_14,X0_13,X0_15)) ),
inference(subtyping,[status(esa)],[c_100]) ).
cnf(c_6000,plain,
( ~ element_of_set(X0_15,interior(X0_14,X1_14,X0_13))
| subset_sets(X0_14,X1_14) ),
inference(subtyping,[status(esa)],[c_99]) ).
cnf(c_6001,plain,
( ~ element_of_set(X0_15,interior(X0_14,X1_14,X0_13))
| topological_space(X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_98]) ).
cnf(c_6002,plain,
( ~ equal_sets(X0_14,intersection_of_sets(X1_14,X2_14))
| ~ subset_sets(X1_14,X3_14)
| ~ element_of_collection(X2_14,X0_13)
| ~ topological_space(X3_14,X0_13)
| element_of_collection(X0_14,subspace_topology(X3_14,X0_13,X1_14)) ),
inference(subtyping,[status(esa)],[c_97]) ).
cnf(c_6003,plain,
( ~ element_of_collection(X0_14,subspace_topology(X1_14,X0_13,X2_14))
| equal_sets(X0_14,intersection_of_sets(X2_14,f12(X1_14,X0_13,X2_14,X0_14))) ),
inference(subtyping,[status(esa)],[c_96]) ).
cnf(c_6004,plain,
( ~ element_of_collection(X0_14,subspace_topology(X1_14,X0_13,X2_14))
| element_of_collection(f12(X1_14,X0_13,X2_14,X0_14),X0_13) ),
inference(subtyping,[status(esa)],[c_95]) ).
cnf(c_6005,plain,
( ~ element_of_collection(X0_14,subspace_topology(X1_14,X0_13,X2_14))
| subset_sets(X2_14,X1_14) ),
inference(subtyping,[status(esa)],[c_94]) ).
cnf(c_6006,plain,
( ~ element_of_collection(X0_14,subspace_topology(X1_14,X0_13,X2_14))
| topological_space(X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_93]) ).
cnf(c_6007,plain,
( ~ element_of_set(f11(X0_13,X0_14),X1_14)
| ~ subset_sets(X1_14,X0_14)
| ~ element_of_collection(X1_14,X0_13)
| element_of_collection(X0_14,top_of_basis(X0_13)) ),
inference(subtyping,[status(esa)],[c_92]) ).
cnf(c_6008,plain,
( element_of_set(f11(X0_13,X0_14),X0_14)
| element_of_collection(X0_14,top_of_basis(X0_13)) ),
inference(subtyping,[status(esa)],[c_91]) ).
cnf(c_6009,plain,
( ~ element_of_collection(X0_14,top_of_basis(X0_13))
| ~ element_of_set(X0_15,X0_14)
| subset_sets(f10(X0_13,X0_14,X0_15),X0_14) ),
inference(subtyping,[status(esa)],[c_90]) ).
cnf(c_6010,plain,
( ~ element_of_collection(X0_14,top_of_basis(X0_13))
| ~ element_of_set(X0_15,X0_14)
| element_of_collection(f10(X0_13,X0_14,X0_15),X0_13) ),
inference(subtyping,[status(esa)],[c_89]) ).
cnf(c_6011,plain,
( ~ element_of_collection(X0_14,top_of_basis(X0_13))
| ~ element_of_set(X0_15,X0_14)
| element_of_set(X0_15,f10(X0_13,X0_14,X0_15)) ),
inference(subtyping,[status(esa)],[c_88]) ).
cnf(c_6012,plain,
( ~ subset_sets(X0_14,intersection_of_sets(f8(X1_14,X0_13),f9(X1_14,X0_13)))
| ~ element_of_set(f7(X1_14,X0_13),X0_14)
| ~ equal_sets(union_of_members(X0_13),X1_14)
| ~ element_of_collection(X0_14,X0_13)
| basis(X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_87]) ).
cnf(c_6013,plain,
( ~ equal_sets(union_of_members(X0_13),X0_14)
| element_of_set(f7(X0_14,X0_13),intersection_of_sets(f8(X0_14,X0_13),f9(X0_14,X0_13)))
| basis(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_86]) ).
cnf(c_6014,plain,
( ~ equal_sets(union_of_members(X0_13),X0_14)
| element_of_collection(f9(X0_14,X0_13),X0_13)
| basis(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_85]) ).
cnf(c_6015,plain,
( ~ equal_sets(union_of_members(X0_13),X0_14)
| element_of_collection(f8(X0_14,X0_13),X0_13)
| basis(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_84]) ).
cnf(c_6016,plain,
( ~ equal_sets(union_of_members(X0_13),X0_14)
| element_of_set(f7(X0_14,X0_13),X0_14)
| basis(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_83]) ).
cnf(c_6017,plain,
( ~ element_of_set(X0_15,intersection_of_sets(X0_14,X1_14))
| ~ element_of_set(X0_15,X2_14)
| ~ element_of_collection(X0_14,X0_13)
| ~ element_of_collection(X1_14,X0_13)
| ~ basis(X2_14,X0_13)
| subset_sets(f6(X2_14,X0_13,X0_15,X0_14,X1_14),intersection_of_sets(X0_14,X1_14)) ),
inference(subtyping,[status(esa)],[c_82]) ).
cnf(c_6018,plain,
( ~ element_of_set(X0_15,intersection_of_sets(X0_14,X1_14))
| ~ element_of_set(X0_15,X2_14)
| ~ element_of_collection(X0_14,X0_13)
| ~ element_of_collection(X1_14,X0_13)
| ~ basis(X2_14,X0_13)
| element_of_collection(f6(X2_14,X0_13,X0_15,X0_14,X1_14),X0_13) ),
inference(subtyping,[status(esa)],[c_81]) ).
cnf(c_6019,plain,
( ~ element_of_set(X0_15,intersection_of_sets(X0_14,X1_14))
| ~ element_of_set(X0_15,X2_14)
| ~ element_of_collection(X0_14,X0_13)
| ~ element_of_collection(X1_14,X0_13)
| ~ basis(X2_14,X0_13)
| element_of_set(X0_15,f6(X2_14,X0_13,X0_15,X0_14,X1_14)) ),
inference(subtyping,[status(esa)],[c_80]) ).
cnf(c_6020,plain,
( ~ basis(X0_14,X0_13)
| equal_sets(union_of_members(X0_13),X0_14) ),
inference(subtyping,[status(esa)],[c_79]) ).
cnf(c_6021,plain,
( ~ closed(X0_14,X1_14,X0_13)
| open(relative_complement_sets(X0_14,X1_14),X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_73]) ).
cnf(c_6022,plain,
( ~ closed(X0_14,X1_14,X0_13)
| topological_space(X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_72]) ).
cnf(c_6023,plain,
( ~ element_of_collection(X0_14,X0_13)
| ~ topological_space(X1_14,X0_13)
| open(X0_14,X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_71]) ).
cnf(c_6024,plain,
( ~ open(X0_14,X1_14,X0_13)
| element_of_collection(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_70]) ).
cnf(c_6025,plain,
( ~ open(X0_14,X1_14,X0_13)
| topological_space(X1_14,X0_13) ),
inference(subtyping,[status(esa)],[c_69]) ).
cnf(c_6026,plain,
( ~ element_of_collection(intersection_of_sets(f3(X0_14,X0_13),f4(X0_14,X0_13)),X0_13)
| ~ element_of_collection(union_of_members(f5(X0_14,X0_13)),X0_13)
| ~ equal_sets(union_of_members(X0_13),X0_14)
| ~ element_of_collection(X0_14,X0_13)
| ~ element_of_collection(empty_set,X0_13)
| topological_space(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_68]) ).
cnf(c_6027,plain,
( ~ element_of_collection(intersection_of_sets(f3(X0_14,X0_13),f4(X0_14,X0_13)),X0_13)
| ~ equal_sets(union_of_members(X0_13),X0_14)
| ~ element_of_collection(X0_14,X0_13)
| ~ element_of_collection(empty_set,X0_13)
| subset_collections(f5(X0_14,X0_13),X0_13)
| topological_space(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_67]) ).
cnf(c_6028,plain,
( ~ element_of_collection(union_of_members(f5(X0_14,X0_13)),X0_13)
| ~ equal_sets(union_of_members(X0_13),X0_14)
| ~ element_of_collection(X0_14,X0_13)
| ~ element_of_collection(empty_set,X0_13)
| element_of_collection(f4(X0_14,X0_13),X0_13)
| topological_space(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_66]) ).
cnf(c_6029,plain,
( ~ equal_sets(union_of_members(X0_13),X0_14)
| ~ element_of_collection(X0_14,X0_13)
| ~ element_of_collection(empty_set,X0_13)
| element_of_collection(f4(X0_14,X0_13),X0_13)
| subset_collections(f5(X0_14,X0_13),X0_13)
| topological_space(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_65]) ).
cnf(c_6030,plain,
( ~ element_of_collection(union_of_members(f5(X0_14,X0_13)),X0_13)
| ~ equal_sets(union_of_members(X0_13),X0_14)
| ~ element_of_collection(X0_14,X0_13)
| ~ element_of_collection(empty_set,X0_13)
| element_of_collection(f3(X0_14,X0_13),X0_13)
| topological_space(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_64]) ).
cnf(c_6031,plain,
( ~ equal_sets(union_of_members(X0_13),X0_14)
| ~ element_of_collection(X0_14,X0_13)
| ~ element_of_collection(empty_set,X0_13)
| element_of_collection(f3(X0_14,X0_13),X0_13)
| subset_collections(f5(X0_14,X0_13),X0_13)
| topological_space(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_63]) ).
cnf(c_6032,plain,
( ~ topological_space(X0_14,X0_13)
| ~ subset_collections(X1_13,X0_13)
| element_of_collection(union_of_members(X1_13),X0_13) ),
inference(subtyping,[status(esa)],[c_62]) ).
cnf(c_6033,plain,
( ~ element_of_collection(X0_14,X0_13)
| ~ element_of_collection(X1_14,X0_13)
| ~ topological_space(X2_14,X0_13)
| element_of_collection(intersection_of_sets(X0_14,X1_14),X0_13) ),
inference(subtyping,[status(esa)],[c_61]) ).
cnf(c_6034,plain,
( ~ topological_space(X0_14,X0_13)
| element_of_collection(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_60]) ).
cnf(c_6035,plain,
( ~ topological_space(X0_14,X0_13)
| element_of_collection(empty_set,X0_13) ),
inference(subtyping,[status(esa)],[c_59]) ).
cnf(c_6036,plain,
( ~ topological_space(X0_14,X0_13)
| equal_sets(union_of_members(X0_13),X0_14) ),
inference(subtyping,[status(esa)],[c_58]) ).
cnf(c_6037,plain,
( ~ element_of_set(X0_15,f2(X0_13,X0_15))
| element_of_set(X0_15,intersection_of_members(X0_13)) ),
inference(subtyping,[status(esa)],[c_57]) ).
cnf(c_6038,plain,
( element_of_collection(f2(X0_13,X0_15),X0_13)
| element_of_set(X0_15,intersection_of_members(X0_13)) ),
inference(subtyping,[status(esa)],[c_56]) ).
cnf(c_6039,plain,
( ~ element_of_set(X0_15,intersection_of_members(X0_13))
| ~ element_of_collection(X0_14,X0_13)
| element_of_set(X0_15,X0_14) ),
inference(subtyping,[status(esa)],[c_55]) ).
cnf(c_6040,plain,
( ~ element_of_set(X0_15,X0_14)
| ~ element_of_collection(X0_14,X0_13)
| element_of_set(X0_15,union_of_members(X0_13)) ),
inference(subtyping,[status(esa)],[c_54]) ).
cnf(c_6041,plain,
( ~ element_of_set(X0_15,union_of_members(X0_13))
| element_of_collection(f1(X0_13,X0_15),X0_13) ),
inference(subtyping,[status(esa)],[c_53]) ).
cnf(c_6042,plain,
( ~ element_of_set(X0_15,union_of_members(X0_13))
| element_of_set(X0_15,f1(X0_13,X0_15)) ),
inference(subtyping,[status(esa)],[c_52]) ).
cnf(c_6043,negated_conjecture,
subset_sets(a,cx),
inference(subtyping,[status(esa)],[c_50]) ).
cnf(c_6162,plain,
( ~ separation(X0_14,X1_14,X2_14,X0_13)
| ~ equal_sets(f22(X2_14,X0_13),empty_set) ),
inference(resolution,[status(thm)],[c_5969,c_5948]) ).
cnf(c_6172,plain,
( ~ separation(X0_14,X1_14,X2_14,X0_13)
| ~ equal_sets(f21(X2_14,X0_13),empty_set) ),
inference(resolution,[status(thm)],[c_5970,c_5948]) ).
cnf(c_6254,plain,
( ~ open_covering(subspace_topology(cx,ct2,a),X0_14,subspace_topology(cx,ct1,a))
| ~ topological_space(cx,subspace_topology(cx,ct1,a))
| ~ topological_space(cx,subspace_topology(cx,ct2,a)) ),
inference(resolution,[status(thm)],[c_5944,c_5962]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : TOP010-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.15 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 22:58:50 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.23/0.49 Running first-order theorem proving
% 0.23/0.49 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.11/1.18 % SZS status Started for theBenchmark.p
% 4.11/1.18 % SZS status Satisfiable for theBenchmark.p
% 4.11/1.18
% 4.11/1.18 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 4.11/1.18
% 4.11/1.18 ------ iProver source info
% 4.11/1.18
% 4.11/1.18 git: date: 2023-05-31 18:12:56 +0000
% 4.11/1.18 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 4.11/1.18 git: non_committed_changes: false
% 4.11/1.18 git: last_make_outside_of_git: false
% 4.11/1.18
% 4.11/1.18 ------ Parsing...successful
% 4.11/1.18
% 4.11/1.18
% 4.11/1.18
% 4.11/1.18 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e
% 4.11/1.18
% 4.11/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.11/1.18 ------ Proving...
% 4.11/1.18 ------ Problem Properties
% 4.11/1.18
% 4.11/1.18
% 4.11/1.18 clauses 100
% 4.11/1.18 conjectures 1
% 4.11/1.18 EPR 26
% 4.11/1.18 Horn 78
% 4.11/1.18 unary 4
% 4.11/1.18 binary 46
% 4.11/1.18 lits 302
% 4.11/1.18 lits eq 0
% 4.11/1.18 fd_pure 0
% 4.11/1.18 fd_pseudo 0
% 4.11/1.18 fd_cond 0
% 4.11/1.18 fd_pseudo_cond 0
% 4.11/1.18 AC symbols 0
% 4.11/1.18
% 4.11/1.18 ------ Input Options Time Limit: Unbounded
% 4.11/1.18
% 4.11/1.18
% 4.11/1.18 ------
% 4.11/1.18 Current options:
% 4.11/1.18 ------
% 4.11/1.18
% 4.11/1.18
% 4.11/1.18
% 4.11/1.18
% 4.11/1.18 ------ Proving...
% 4.11/1.18
% 4.11/1.18
% 4.11/1.18 % SZS status Satisfiable for theBenchmark.p
% 4.11/1.18
% 4.11/1.18 % SZS output start Saturation for theBenchmark.p
% See solution above
% 4.11/1.18
% 4.11/1.19
%------------------------------------------------------------------------------