TSTP Solution File: TOP011-1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : TOP011-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n028.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 2.28s 1.14s
% Output : Saturation 2.28s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(c_49,negated_conjecture,
( element_of_set(cu,top_of_basis(f))
| subset_collections(g,f) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',problem_6_126) ).
cnf(c_50,negated_conjecture,
( element_of_set(cu,top_of_basis(f))
| equal_sets(cu,union_of_members(g)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',problem_6_127) ).
cnf(c_51,negated_conjecture,
( ~ equal_sets(cu,union_of_members(X0))
| ~ element_of_set(cu,top_of_basis(f))
| ~ subset_collections(X0,f) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',problem_6_128) ).
cnf(c_52,plain,
( ~ element_of_set(X0,union_of_members(X1))
| element_of_set(X0,f1(X1,X0)) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',topological_space_8) ).
cnf(c_60,plain,
( ~ topological_space(X0,X1)
| element_of_collection(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',topological_space_10) ).
cnf(c_62,plain,
( ~ subset_collections(X0,X1)
| ~ topological_space(X2,X1)
| element_of_collection(union_of_members(X0),X1) ),
file('/export/starexec/sandbox/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)
| subset_collections(f5(X1,X0),X0)
| element_of_collection(f3(X1,X0),X0)
| topological_space(X1,X0) ),
file('/export/starexec/sandbox/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/sandbox/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)
| subset_collections(f5(X1,X0),X0)
| element_of_collection(f4(X1,X0),X0)
| topological_space(X1,X0) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',topological_space_17) ).
cnf(c_69,plain,
( ~ open(X0,X1,X2)
| topological_space(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',open_set_18) ).
cnf(c_70,plain,
( ~ open(X0,X1,X2)
| element_of_collection(X0,X2) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',open_set_20) ).
cnf(c_72,plain,
( ~ closed(X0,X1,X2)
| topological_space(X1,X2) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',closed_set_23) ).
cnf(c_75,plain,
( ~ finer(X0,X1,X2)
| topological_space(X2,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',finer_topology_24) ).
cnf(c_76,plain,
( ~ finer(X0,X1,X2)
| topological_space(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',finer_topology_25) ).
cnf(c_77,plain,
( ~ finer(X0,X1,X2)
| subset_collections(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',finer_topology_26) ).
cnf(c_78,plain,
( ~ subset_collections(X0,X1)
| ~ topological_space(X2,X0)
| ~ topological_space(X2,X1)
| finer(X1,X0,X2) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',topology_generated_40) ).
cnf(c_92,plain,
( ~ element_of_set(f11(X0,X1),X2)
| ~ element_of_collection(X2,X0)
| ~ subset_sets(X2,X1)
| element_of_collection(X1,top_of_basis(X0)) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',subspace_topology_45) ).
cnf(c_97,plain,
( ~ equal_sets(X0,intersection_of_sets(X1,X2))
| ~ element_of_collection(X2,X3)
| ~ topological_space(X4,X3)
| ~ subset_sets(X1,X4)
| element_of_collection(X0,subspace_topology(X4,X3,X1)) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',interior_51) ).
cnf(c_103,plain,
( ~ open(X0,X1,X2)
| ~ element_of_set(X3,X0)
| ~ topological_space(X1,X2)
| ~ subset_sets(X0,X4)
| ~ subset_sets(X4,X1)
| element_of_set(X3,interior(X4,X1,X2)) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',closure_55) ).
cnf(c_107,plain,
( ~ topological_space(X0,X1)
| ~ subset_sets(X2,X0)
| subset_sets(X2,f14(X2,X0,X1,X3))
| element_of_set(X3,closure(X2,X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',closure_56) ).
cnf(c_108,plain,
( ~ topological_space(X0,X1)
| ~ subset_sets(X2,X0)
| closed(f14(X2,X0,X1,X3),X0,X1)
| element_of_set(X3,closure(X2,X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',closure_57) ).
cnf(c_109,plain,
( ~ element_of_set(X0,f14(X1,X2,X3,X0))
| ~ topological_space(X2,X3)
| ~ subset_sets(X1,X2)
| element_of_set(X0,closure(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',closure_58) ).
cnf(c_110,plain,
( ~ neighborhood(X0,X1,X2,X3)
| topological_space(X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',neighborhood_59) ).
cnf(c_111,plain,
( ~ neighborhood(X0,X1,X2,X3)
| open(X0,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',neighborhood_60) ).
cnf(c_112,plain,
( ~ neighborhood(X0,X1,X2,X3)
| element_of_set(X1,X0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',neighborhood_62) ).
cnf(c_114,plain,
( ~ limit_point(X0,X1,X2,X3)
| topological_space(X2,X3) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',limit_point_66) ).
cnf(c_118,plain,
( ~ topological_space(X0,X1)
| ~ subset_sets(X2,X0)
| neighborhood(f16(X3,X2,X0,X1),X3,X0,X1)
| limit_point(X3,X2,X0,X1) ),
file('/export/starexec/sandbox/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))
| ~ topological_space(X3,X4)
| ~ subset_sets(X2,X3)
| limit_point(X1,X2,X3,X4)
| eq_p(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',boundary_72) ).
cnf(c_124,plain,
( ~ hausdorff(X0,X1)
| topological_space(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',hausdorff_80) ).
cnf(c_132,plain,
( ~ separation(X0,X1,X2,X3)
| topological_space(X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',separation_81) ).
cnf(c_133,plain,
( ~ separation(X0,X1,X2,X3)
| ~ equal_sets(X0,empty_set) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',separation_82) ).
cnf(c_134,plain,
( ~ separation(X0,X1,X2,X3)
| ~ equal_sets(X1,empty_set) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',separation_83) ).
cnf(c_135,plain,
( ~ separation(X0,X1,X2,X3)
| element_of_collection(X0,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',separation_84) ).
cnf(c_136,plain,
( ~ separation(X0,X1,X2,X3)
| element_of_collection(X1,X3) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',separation_86) ).
cnf(c_138,plain,
( ~ separation(X0,X1,X2,X3)
| disjoint_s(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',separation_88) ).
cnf(c_140,plain,
( ~ connected_space(X0,X1)
| topological_space(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',connected_space_89) ).
cnf(c_141,plain,
( ~ separation(X0,X1,X2,X3)
| ~ connected_space(X2,X3) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',connected_space_91) ).
cnf(c_143,plain,
( ~ connected_set(X0,X1,X2)
| topological_space(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',connected_set_92) ).
cnf(c_144,plain,
( ~ connected_set(X0,X1,X2)
| subset_sets(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',connected_set_93) ).
cnf(c_145,plain,
( ~ connected_set(X0,X1,X2)
| connected_space(X0,subspace_topology(X1,X2,X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',connected_set_94) ).
cnf(c_146,plain,
( ~ connected_space(X0,subspace_topology(X1,X2,X0))
| ~ topological_space(X1,X2)
| ~ subset_sets(X0,X1)
| connected_set(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',connected_set_95) ).
cnf(c_147,plain,
( ~ open_covering(X0,X1,X2)
| topological_space(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',open_covering_96) ).
cnf(c_148,plain,
( ~ open_covering(X0,X1,X2)
| subset_collections(X0,X2) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',open_covering_98) ).
cnf(c_150,plain,
( ~ equal_sets(union_of_members(X0),X1)
| ~ subset_collections(X0,X2)
| ~ topological_space(X1,X2)
| open_covering(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',open_covering_99) ).
cnf(c_151,plain,
( ~ compact_space(X0,X1)
| topological_space(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/TOP001-0.ax',compact_space_105) ).
cnf(c_157,plain,
( ~ compact_set(X0,X1,X2)
| topological_space(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',compact_set_106) ).
cnf(c_158,plain,
( ~ compact_set(X0,X1,X2)
| subset_sets(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',compact_set_107) ).
cnf(c_159,plain,
( ~ compact_set(X0,X1,X2)
| compact_space(X0,subspace_topology(X1,X2,X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',compact_set_108) ).
cnf(c_160,plain,
( ~ compact_space(X0,subspace_topology(X1,X2,X0))
| ~ topological_space(X1,X2)
| ~ subset_sets(X0,X1)
| compact_set(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/TOP001-0.ax',compact_set_109) ).
cnf(c_267,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_268,plain,
( ~ open(X0,X1,X2)
| ~ element_of_set(X3,X0)
| neighborhood(X0,X3,X1,X2) ),
inference(renaming,[status(thm)],[c_267]) ).
cnf(c_270,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_271,plain,
( ~ subset_collections(X0,f24(X1,X2))
| ~ open_covering(X0,X1,X2)
| ~ finite(X0)
| compact_space(X1,X2) ),
inference(renaming,[status(thm)],[c_270]) ).
cnf(c_273,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_274,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_273]) ).
cnf(c_276,plain,
( ~ element_of_set(X3,X0)
| ~ open(X0,X1,X2)
| ~ subset_sets(X0,X4)
| ~ subset_sets(X4,X1)
| element_of_set(X3,interior(X4,X1,X2)) ),
inference(global_subsumption_just,[status(thm)],[c_103,c_69,c_103]) ).
cnf(c_277,plain,
( ~ open(X0,X1,X2)
| ~ element_of_set(X3,X0)
| ~ subset_sets(X0,X4)
| ~ subset_sets(X4,X1)
| element_of_set(X3,interior(X4,X1,X2)) ),
inference(renaming,[status(thm)],[c_276]) ).
cnf(c_315,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_377,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]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : TOP011-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 23:30:53 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.28/1.14 % SZS status Started for theBenchmark.p
% 2.28/1.14 % SZS status Satisfiable for theBenchmark.p
% 2.28/1.14
% 2.28/1.14 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.28/1.14
% 2.28/1.14 ------ iProver source info
% 2.28/1.14
% 2.28/1.14 git: date: 2023-05-31 18:12:56 +0000
% 2.28/1.14 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.28/1.14 git: non_committed_changes: false
% 2.28/1.14 git: last_make_outside_of_git: false
% 2.28/1.14
% 2.28/1.14 ------ Parsing...successful
% 2.28/1.14
% 2.28/1.14
% 2.28/1.14
% 2.28/1.14 ------ Preprocessing... sf_s rm: 112 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e
% 2.28/1.14
% 2.28/1.14 ------ Preprocessing...------ preprocesses with Option_epr_horn
% 2.28/1.14 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.28/1.14 ------ Proving...
% 2.28/1.14 ------ Problem Properties
% 2.28/1.14
% 2.28/1.14
% 2.28/1.14 clauses 0
% 2.28/1.14 conjectures 0
% 2.28/1.14 EPR 0
% 2.28/1.14 Horn 0
% 2.28/1.14 unary 0
% 2.28/1.14 binary 0
% 2.28/1.14 lits 0
% 2.28/1.14 lits eq 0
% 2.28/1.14 fd_pure 0
% 2.28/1.14 fd_pseudo 0
% 2.28/1.14 fd_cond 0
% 2.28/1.14 fd_pseudo_cond 0
% 2.28/1.14 AC symbols 0
% 2.28/1.14
% 2.28/1.14 ------ Schedule EPR Horn non eq is on
% 2.28/1.14
% 2.28/1.14 ------ no conjectures: strip conj schedule
% 2.28/1.14
% 2.28/1.14 ------ no equalities: superposition off
% 2.28/1.14
% 2.28/1.14 ------ Option_epr_horn stripped conjectures Time Limit: Unbounded
% 2.28/1.14
% 2.28/1.14
% 2.28/1.14
% 2.28/1.14
% 2.28/1.14 % SZS status Satisfiable for theBenchmark.p
% 2.28/1.14
% 2.28/1.14 % SZS output start Saturation for theBenchmark.p
% See solution above
% 2.28/1.14
% 2.28/1.14
%------------------------------------------------------------------------------