TSTP Solution File: TOP019-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : TOP019-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 21:34:58 EDT 2022
% Result : Satisfiable 0.20s 0.48s
% Output : Saturation 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 681)
% Comments :
%------------------------------------------------------------------------------
cnf(690,plain,
( ~ element_of_set(f20(u,v),w)
| ~ element_of_set(x,w)
| ~ hausdorff(w,y)
| ~ element_of_set(f19(u,v),f18(w,y,x,f20(u,v)))
| ~ hausdorff(f18(w,y,x,f20(u,v)),z)
| eq(x,f20(u,v))
| hausdorff(u,v) ),
inference(res,[status(thm),theory(equality)],[571,682]),
[iquote('1:Res:571.4,682.0')] ).
cnf(694,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(f20(w,x),v)
| ~ hausdorff(v,y)
| ~ element_of_set(f19(w,x),f17(v,y,f20(w,x),u))
| ~ hausdorff(f17(v,y,f20(w,x),u),z)
| eq(f20(w,x),u)
| hausdorff(w,x) ),
inference(res,[status(thm),theory(equality)],[623,682]),
[iquote('1:Res:623.4,682.0')] ).
cnf(689,plain,
( ~ element_of_set(f20(u,v),w)
| ~ element_of_set(f20(u,v),intersection_of_sets(x,y))
| ~ element_of_set(f19(u,v),f6(w,z,f20(u,v),x,y))
| ~ hausdorff(f6(w,z,f20(u,v),x,y),x1)
| hausdorff(u,v) ),
inference(res,[status(thm),theory(equality)],[413,682]),
[iquote('1:Res:413.2,682.0')] ).
cnf(688,plain,
( ~ element_of_set(f19(u,v),f16(f20(u,v),w,x,y))
| ~ hausdorff(f16(f20(u,v),w,x,y),z)
| limit_point(f20(u,v),w,x,y)
| hausdorff(u,v) ),
inference(res,[status(thm),theory(equality)],[467,682]),
[iquote('1:Res:467.1,682.0')] ).
cnf(687,plain,
( ~ element_of_set(f20(u,v),w)
| ~ element_of_set(f19(u,v),f10(x,w,f20(u,v)))
| ~ hausdorff(f10(x,w,f20(u,v)),y)
| hausdorff(u,v) ),
inference(res,[status(thm),theory(equality)],[368,682]),
[iquote('1:Res:368.1,682.0')] ).
cnf(702,plain,
( ~ element_of_set(f19(u,v),f13(w,x,y,f20(u,v)))
| ~ hausdorff(f13(w,x,y,f20(u,v)),z)
| hausdorff(u,v) ),
inference(mrr,[status(thm)],[686,443]),
[iquote('1:MRR:686.0,443.1')] ).
cnf(701,plain,
( ~ element_of_set(f19(u,v),f1(w,f20(u,v)))
| ~ hausdorff(f1(w,f20(u,v)),x)
| hausdorff(u,v) ),
inference(mrr,[status(thm)],[684,419]),
[iquote('1:MRR:684.0,419.1')] ).
cnf(700,plain,
( ~ hausdorff(interior(u,v,w),x)
| hausdorff(y,z) ),
inference(mrr,[status(thm)],[699,444]),
[iquote('1:MRR:699.0,444.1')] ).
cnf(698,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(w,x) ),
inference(mrr,[status(thm)],[697,421]),
[iquote('1:MRR:697.0,421.1')] ).
cnf(696,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w) ),
inference(mrr,[status(thm)],[695,323]),
[iquote('1:MRR:695.0,323.1')] ).
cnf(682,plain,
( ~ element_of_set(f20(u,v),w)
| ~ element_of_set(f19(u,v),w)
| ~ hausdorff(w,x)
| hausdorff(u,v) ),
inference(mrr,[status(thm)],[681,328]),
[iquote('1:MRR:681.3,328.0')] ).
cnf(679,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(f19(w,x),v)
| ~ hausdorff(v,y)
| ~ element_of_set(f20(w,x),f18(v,y,f19(w,x),u))
| eq(f19(w,x),u)
| hausdorff(w,x) ),
inference(obv,[status(thm),theory(equality)],[678]),
[iquote('1:Obv:678.7')] ).
cnf(654,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(f19(w,x),v)
| ~ hausdorff(v,y)
| ~ element_of_set(f20(w,x),z)
| ~ disjoint_s(f17(v,y,f19(w,x),u),z)
| eq(f19(w,x),u)
| hausdorff(w,x) ),
inference(res,[status(thm),theory(equality)],[623,544]),
[iquote('1:Res:623.4,544.0')] ).
cnf(649,plain,
( ~ element_of_set(f19(u,v),w)
| ~ element_of_set(x,w)
| ~ hausdorff(w,y)
| ~ element_of_set(f20(u,v),z)
| ~ disjoint_s(f18(w,y,x,f19(u,v)),z)
| eq(x,f19(u,v))
| hausdorff(u,v) ),
inference(res,[status(thm),theory(equality)],[571,544]),
[iquote('1:Res:571.4,544.0')] ).
cnf(652,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(f20(w,x),v)
| ~ hausdorff(v,y)
| ~ disjoint_s(union_of_members(z),f17(v,y,f20(w,x),u))
| eq(f20(w,x),u)
| hausdorff(w,x) ),
inference(res,[status(thm),theory(equality)],[623,560]),
[iquote('1:Res:623.4,560.0')] ).
cnf(552,plain,
( ~ element_of_set(f19(u,v),w)
| ~ element_of_set(f19(u,v),intersection_of_sets(x,y))
| ~ element_of_set(f20(u,v),z)
| ~ disjoint_s(f6(w,x1,f19(u,v),x,y),z)
| hausdorff(u,v) ),
inference(res,[status(thm),theory(equality)],[413,544]),
[iquote('1:Res:413.2,544.0')] ).
cnf(647,plain,
( ~ element_of_set(f20(u,v),w)
| ~ element_of_set(x,w)
| ~ hausdorff(w,y)
| ~ disjoint_s(union_of_members(z),f18(w,y,x,f20(u,v)))
| eq(x,f20(u,v))
| hausdorff(u,v) ),
inference(res,[status(thm),theory(equality)],[571,560]),
[iquote('1:Res:571.4,560.0')] ).
cnf(653,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(f20(w,x),v)
| ~ hausdorff(v,y)
| ~ disjoint_s(w,f17(v,y,f20(w,x),u))
| eq(f20(w,x),u)
| hausdorff(w,x) ),
inference(res,[status(thm),theory(equality)],[623,559]),
[iquote('1:Res:623.4,559.0')] ).
cnf(675,plain,
( ~ limit_point(u,v,w,x)
| limit_point(u,v,y,z) ),
inference(mrr,[status(thm)],[673,467]),
[iquote('1:MRR:673.0,467.1')] ).
cnf(533,plain,
( ~ neighborhood(f16(u,v,w,x),y,z,x1)
| ~ limit_point(y,v,z,x1)
| eq(f15(y,v,z,x1,f16(u,v,w,x)),u)
| limit_point(u,v,w,x) ),
inference(res,[status(thm),theory(equality)],[67,405]),
[iquote('1:Res:67.2,405.0')] ).
cnf(648,plain,
( ~ element_of_set(f20(u,v),w)
| ~ element_of_set(x,w)
| ~ hausdorff(w,y)
| ~ disjoint_s(u,f18(w,y,x,f20(u,v)))
| eq(x,f20(u,v))
| hausdorff(u,v) ),
inference(res,[status(thm),theory(equality)],[571,559]),
[iquote('1:Res:571.4,559.0')] ).
cnf(632,plain,
( ~ element_of_set(f20(u,v),w)
| ~ element_of_set(f20(u,v),intersection_of_sets(x,y))
| ~ disjoint_s(union_of_members(z),f6(w,x1,f20(u,v),x,y))
| hausdorff(u,v) ),
inference(res,[status(thm),theory(equality)],[413,560]),
[iquote('1:Res:413.2,560.0')] ).
cnf(614,plain,
( ~ element_of_set(f20(u,v),w)
| ~ element_of_set(f20(u,v),intersection_of_sets(x,y))
| ~ disjoint_s(u,f6(w,z,f20(u,v),x,y))
| hausdorff(u,v) ),
inference(res,[status(thm),theory(equality)],[413,559]),
[iquote('1:Res:413.2,559.0')] ).
cnf(551,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(f16(f19(u,v),x,y,z),w)
| limit_point(f19(u,v),x,y,z)
| hausdorff(u,v) ),
inference(res,[status(thm),theory(equality)],[467,544]),
[iquote('1:Res:467.1,544.0')] ).
cnf(542,plain,
( ~ disjoint_s(u,f16(f20(v,w),x,v,w))
| ~ neighborhood(u,f19(v,w),v,w)
| limit_point(f20(v,w),x,v,w)
| hausdorff(v,w) ),
inference(res,[status(thm),theory(equality)],[400,117]),
[iquote('1:Res:400.1,117.1')] ).
cnf(670,plain,
( ~ subset_collections(u,f24(v,u))
| ~ compact_space(w,f24(v,u))
| compact_space(v,u) ),
inference(res,[status(thm),theory(equality)],[392,669]),
[iquote('1:Res:392.1,669.1')] ).
cnf(669,plain,
( ~ compact_space(u,f24(v,w))
| ~ open_covering(w,u,f24(v,w))
| compact_space(v,w) ),
inference(obv,[status(thm),theory(equality)],[668]),
[iquote('1:Obv:668.1')] ).
cnf(667,plain,
( ~ subset_collections(f23(u,f24(v,w),x),w)
| ~ compact_space(u,f24(v,w))
| ~ open_covering(x,u,f24(v,w))
| compact_space(v,w) ),
inference(res,[status(thm),theory(equality)],[392,507]),
[iquote('1:Res:392.1,507.2')] ).
cnf(507,plain,
( ~ compact_space(u,f24(v,w))
| ~ open_covering(x,u,f24(v,w))
| ~ open_covering(f23(u,f24(v,w),x),v,w)
| compact_space(v,w) ),
inference(mrr,[status(thm)],[506,103]),
[iquote('0:MRR:506.0,103.2')] ).
cnf(512,plain,
( hausdorff(intersection_of_sets(f16(u,v,w,x),v),y)
| eq(f20(intersection_of_sets(f16(u,v,w,x),v),y),u)
| limit_point(u,v,w,x) ),
inference(res,[status(thm),theory(equality)],[322,405]),
[iquote('1:Res:322.1,405.0')] ).
cnf(664,plain,
( ~ compact_set(u,v,w)
| compact_space(x,subspace_topology(v,w,u)) ),
inference(res,[status(thm),theory(equality)],[110,663]),
[iquote('1:Res:110.1,663.0')] ).
cnf(663,plain,
( ~ compact_space(u,v)
| compact_space(w,v) ),
inference(mrr,[status(thm)],[662,325]),
[iquote('1:MRR:662.0,325.1')] ).
cnf(658,plain,
( ~ subset_collections(f23(u,v,f24(w,x)),x)
| ~ compact_space(u,v)
| ~ open_covering(f24(w,x),u,v)
| compact_space(w,x) ),
inference(res,[status(thm),theory(equality)],[392,505]),
[iquote('1:Res:392.1,505.2')] ).
cnf(513,plain,
( hausdorff(intersection_of_sets(f16(u,v,w,x),v),y)
| eq(f19(intersection_of_sets(f16(u,v,w,x),v),y),u)
| limit_point(u,v,w,x) ),
inference(res,[status(thm),theory(equality)],[323,405]),
[iquote('1:Res:323.1,405.0')] ).
cnf(505,plain,
( ~ compact_space(u,v)
| ~ open_covering(f24(w,x),u,v)
| ~ open_covering(f23(u,v,f24(w,x)),w,x)
| compact_space(w,x) ),
inference(mrr,[status(thm)],[504,103]),
[iquote('0:MRR:504.0,103.2')] ).
cnf(550,plain,
( ~ element_of_set(f19(u,v),w)
| ~ element_of_set(f20(u,v),x)
| ~ disjoint_s(f10(y,w,f19(u,v)),x)
| hausdorff(u,v) ),
inference(res,[status(thm),theory(equality)],[368,544]),
[iquote('1:Res:368.1,544.0')] ).
cnf(531,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| element_of_set(f15(v,y,w,x,u),interior(z,x1,x2)) ),
inference(res,[status(thm),theory(equality)],[67,398]),
[iquote('1:Res:67.2,398.0')] ).
cnf(623,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(v,x)
| eq(w,u)
| element_of_set(w,f17(v,x,w,u)) ),
inference(res,[status(thm),theory(equality)],[76,63]),
[iquote('0:Res:76.4,63.0')] ).
cnf(571,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(v,x)
| eq(w,u)
| element_of_set(u,f18(v,x,w,u)) ),
inference(res,[status(thm),theory(equality)],[77,63]),
[iquote('0:Res:77.4,63.0')] ).
cnf(534,plain,
( ~ disjoint_s(u,v)
| ~ connected_space(intersection_of_sets(w,f12(x,y,w,union_of_sets(u,v))),z)
| equal_sets(v,empty_set)
| equal_sets(u,empty_set) ),
inference(res,[status(thm),theory(equality)],[372,524]),
[iquote('1:Res:372.0,524.1')] ).
cnf(631,plain,
( ~ disjoint_s(union_of_members(u),f16(f20(v,w),x,y,z))
| limit_point(f20(v,w),x,y,z)
| hausdorff(v,w) ),
inference(res,[status(thm),theory(equality)],[467,560]),
[iquote('1:Res:467.1,560.0')] ).
cnf(613,plain,
( ~ disjoint_s(u,f16(f20(u,v),w,x,y))
| limit_point(f20(u,v),w,x,y)
| hausdorff(u,v) ),
inference(res,[status(thm),theory(equality)],[467,559]),
[iquote('1:Res:467.1,559.0')] ).
cnf(569,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(f13(x,y,z,f19(u,v)),w)
| hausdorff(u,v) ),
inference(mrr,[status(thm)],[549,444]),
[iquote('1:MRR:549.0,444.1')] ).
cnf(532,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| element_of_set(f15(v,y,w,x,u),union_of_members(z)) ),
inference(res,[status(thm),theory(equality)],[67,363]),
[iquote('1:Res:67.2,363.0')] ).
cnf(630,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(union_of_members(x),f10(y,w,f20(u,v)))
| hausdorff(u,v) ),
inference(res,[status(thm),theory(equality)],[368,560]),
[iquote('1:Res:368.1,560.0')] ).
cnf(612,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(u,f10(x,w,f20(u,v)))
| hausdorff(u,v) ),
inference(res,[status(thm),theory(equality)],[368,559]),
[iquote('1:Res:368.1,559.0')] ).
cnf(564,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(f1(x,f19(u,v)),w)
| hausdorff(u,v) ),
inference(mrr,[status(thm)],[547,421]),
[iquote('1:MRR:547.0,421.1')] ).
cnf(563,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(interior(x,y,z),w)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[556]),
[iquote('1:Obv:556.2')] ).
cnf(524,plain,
( ~ disjoint_s(u,v)
| ~ equal_sets(union_of_sets(u,v),w)
| ~ connected_space(w,x)
| equal_sets(v,empty_set)
| equal_sets(u,empty_set) ),
inference(res,[status(thm),theory(equality)],[414,92]),
[iquote('1:Res:414.4,92.1')] ).
cnf(640,plain,
( ~ disjoint_s(union_of_members(u),f13(v,w,x,f20(y,z)))
| hausdorff(y,z) ),
inference(mrr,[status(thm)],[629,443]),
[iquote('1:MRR:629.0,443.1')] ).
cnf(639,plain,
( ~ disjoint_s(union_of_members(u),f1(v,f20(w,x)))
| hausdorff(w,x) ),
inference(mrr,[status(thm)],[627,419]),
[iquote('1:MRR:627.0,419.1')] ).
cnf(638,plain,
( ~ disjoint_s(union_of_members(u),interior(v,w,x))
| hausdorff(y,z) ),
inference(obv,[status(thm),theory(equality)],[635]),
[iquote('1:Obv:635.1')] ).
cnf(637,plain,
( ~ disjoint_s(union_of_members(u),union_of_members(v))
| hausdorff(w,x) ),
inference(obv,[status(thm),theory(equality)],[634]),
[iquote('1:Obv:634.1')] ).
cnf(78,axiom,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(v,x)
| eq(w,u)
| disjoint_s(f17(v,x,w,u),f18(v,x,w,u)) ),
file('TOP019-1.p',unknown),
[] ).
cnf(636,plain,
( ~ disjoint_s(union_of_members(u),v)
| hausdorff(v,w) ),
inference(obv,[status(thm),theory(equality)],[633]),
[iquote('1:Obv:633.1')] ).
cnf(560,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(union_of_members(x),w)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[554]),
[iquote('1:Obv:554.2')] ).
cnf(622,plain,
( ~ disjoint_s(u,f13(v,w,x,f20(u,y)))
| hausdorff(u,y) ),
inference(mrr,[status(thm)],[611,443]),
[iquote('1:MRR:611.0,443.1')] ).
cnf(621,plain,
( ~ disjoint_s(u,f1(v,f20(u,w)))
| hausdorff(u,w) ),
inference(mrr,[status(thm)],[609,419]),
[iquote('1:MRR:609.0,419.1')] ).
cnf(76,axiom,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(v,x)
| eq(w,u)
| neighborhood(f17(v,x,w,u),w,v,x) ),
file('TOP019-1.p',unknown),
[] ).
cnf(620,plain,
( ~ disjoint_s(u,interior(v,w,x))
| hausdorff(u,y) ),
inference(obv,[status(thm),theory(equality)],[617]),
[iquote('1:Obv:617.1')] ).
cnf(619,plain,
( ~ disjoint_s(u,union_of_members(v))
| hausdorff(u,w) ),
inference(obv,[status(thm),theory(equality)],[616]),
[iquote('1:Obv:616.1')] ).
cnf(618,plain,
( ~ disjoint_s(u,u)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[615]),
[iquote('1:Obv:615.1')] ).
cnf(559,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(u,w)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[553]),
[iquote('1:Obv:553.2')] ).
cnf(414,plain,
( ~ disjoint_s(u,v)
| ~ equal_sets(union_of_sets(u,v),w)
| equal_sets(v,empty_set)
| equal_sets(u,empty_set)
| separation(u,v,w,x) ),
inference(mrr,[status(thm)],[345,320]),
[iquote('1:MRR:345.1,345.2,320.0,320.0')] ).
cnf(332,plain,
( connected_space(u,v)
| separation(f21(u,v),f22(u,v),u,v) ),
inference(mrr,[status(thm)],[93,318]),
[iquote('1:MRR:93.0,318.0')] ).
cnf(460,plain,
( connected_space(u,v)
| equal_sets(union_of_sets(f21(u,v),f22(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[332,88]),
[iquote('1:Res:332.1,88.0')] ).
cnf(88,axiom,
( ~ separation(u,v,w,x)
| equal_sets(union_of_sets(u,v),w) ),
file('TOP019-1.p',unknown),
[] ).
cnf(396,plain,
( ~ connected_space(u,subspace_topology(v,w,u))
| connected_set(u,v,w) ),
inference(mrr,[status(thm)],[339,365]),
[iquote('1:MRR:339.0,365.0')] ).
cnf(92,axiom,
( ~ connected_space(u,v)
| ~ separation(w,x,u,v) ),
file('TOP019-1.p',unknown),
[] ).
cnf(462,plain,
( connected_space(u,v)
| disjoint_s(f21(u,v),f22(u,v)) ),
inference(res,[status(thm),theory(equality)],[332,89]),
[iquote('1:Res:332.1,89.0')] ).
cnf(85,axiom,
( ~ equal_sets(u,empty_set)
| ~ separation(v,u,w,x) ),
file('TOP019-1.p',unknown),
[] ).
cnf(596,plain,
hausdorff(boundary(u,v,w),x),
inference(spt,[],[585]),
[iquote('4:Spt:585.1')] ).
cnf(463,plain,
( ~ equal_sets(f22(u,v),empty_set)
| connected_space(u,v) ),
inference(res,[status(thm),theory(equality)],[332,85]),
[iquote('1:Res:332.1,85.1')] ).
cnf(84,axiom,
( ~ equal_sets(u,empty_set)
| ~ separation(u,v,w,x) ),
file('TOP019-1.p',unknown),
[] ).
cnf(461,plain,
( ~ equal_sets(f21(u,v),empty_set)
| connected_space(u,v) ),
inference(res,[status(thm),theory(equality)],[332,84]),
[iquote('1:Res:332.1,84.1')] ).
cnf(538,plain,
( ~ connected_set(u,v,w)
| connected_space(u,x) ),
inference(res,[status(thm),theory(equality)],[96,536]),
[iquote('1:Res:96.1,536.0')] ).
cnf(536,plain,
( ~ connected_space(u,v)
| connected_space(u,w) ),
inference(mrr,[status(thm)],[535,462,463,461]),
[iquote('1:MRR:535.0,535.3,535.4,462.1,463.0,461.0')] ).
cnf(537,plain,
connected_space(a,u),
inference(res,[status(thm),theory(equality)],[118,536]),
[iquote('1:Res:118.0,536.0')] ).
cnf(89,axiom,
( ~ separation(u,v,w,x)
| disjoint_s(u,v) ),
file('TOP019-1.p',unknown),
[] ).
cnf(593,plain,
hausdorff(closure(u,v,w),x),
inference(spt,[],[591,584]),
[iquote('3:Spt:591.0,584.1')] ).
cnf(581,plain,
hausdorff(intersection_of_members(u),v),
inference(spt,[],[579,570]),
[iquote('2:Spt:579.0,570.1')] ).
cnf(77,axiom,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(v,x)
| eq(w,u)
| neighborhood(f18(v,x,w,u),u,v,x) ),
file('TOP019-1.p',unknown),
[] ).
cnf(544,plain,
( ~ element_of_set(f19(u,v),w)
| ~ element_of_set(f20(u,v),x)
| ~ disjoint_s(w,x)
| hausdorff(u,v) ),
inference(res,[status(thm),theory(equality)],[390,541]),
[iquote('1:Res:390.1,541.2')] ).
cnf(541,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(x,w)
| ~ neighborhood(x,f19(u,v),u,v)
| hausdorff(u,v) ),
inference(res,[status(thm),theory(equality)],[390,117]),
[iquote('1:Res:390.1,117.1')] ).
cnf(117,plain,
( ~ disjoint_s(u,v)
| ~ neighborhood(v,f20(w,x),w,x)
| ~ neighborhood(u,f19(w,x),w,x)
| hausdorff(w,x) ),
inference(mrr,[status(thm)],[82,61]),
[iquote('0:MRR:82.0,61.1')] ).
cnf(540,plain,
connected_set(a,u,v),
inference(res,[status(thm),theory(equality)],[537,396]),
[iquote('1:Res:537.0,396.0')] ).
cnf(67,axiom,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| element_of_set(f15(v,y,w,x,u),intersection_of_sets(u,y)) ),
file('TOP019-1.p',unknown),
[] ).
cnf(68,axiom,
( ~ eq(f15(u,v,w,x,y),u)
| ~ neighborhood(y,u,w,x)
| ~ limit_point(u,v,w,x) ),
file('TOP019-1.p',unknown),
[] ).
cnf(405,plain,
( ~ element_of_set(u,intersection_of_sets(f16(v,w,x,y),w))
| eq(u,v)
| limit_point(v,w,x,y) ),
inference(mrr,[status(thm)],[344,365]),
[iquote('1:MRR:344.0,365.0')] ).
cnf(413,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| element_of_set(u,f6(v,y,u,w,x)) ),
inference(mrr,[status(thm)],[369,407]),
[iquote('1:MRR:369.1,407.0')] ).
cnf(502,plain,
( ~ compact_space(u,v)
| ~ open_covering(w,u,v)
| subset_collections(f23(u,v,w),v) ),
inference(res,[status(thm),theory(equality)],[105,99]),
[iquote('0:Res:105.2,99.0')] ).
cnf(114,plain,
( ~ finite(u)
| ~ subset_collections(u,f24(v,w))
| ~ open_covering(u,v,w)
| compact_space(v,w) ),
inference(mrr,[status(thm)],[107,98]),
[iquote('0:MRR:107.1,98.1')] ).
cnf(105,axiom,
( ~ compact_space(u,v)
| ~ open_covering(w,u,v)
| open_covering(f23(u,v,w),u,v) ),
file('TOP019-1.p',unknown),
[] ).
cnf(104,axiom,
( ~ compact_space(u,v)
| ~ open_covering(w,u,v)
| subset_collections(f23(u,v,w),w) ),
file('TOP019-1.p',unknown),
[] ).
cnf(468,plain,
( limit_point(u,v,w,x)
| element_of_set(u,interior(y,z,x1)) ),
inference(res,[status(thm),theory(equality)],[467,398]),
[iquote('1:Res:467.1,398.0')] ).
cnf(469,plain,
( limit_point(u,v,w,x)
| element_of_set(u,union_of_members(y)) ),
inference(res,[status(thm),theory(equality)],[467,363]),
[iquote('1:Res:467.1,363.0')] ).
cnf(467,plain,
( limit_point(u,v,w,x)
| element_of_set(u,f16(u,v,w,x)) ),
inference(res,[status(thm),theory(equality)],[400,63]),
[iquote('1:Res:400.1,63.0')] ).
cnf(400,plain,
( limit_point(u,v,w,x)
| neighborhood(f16(u,v,w,x),u,w,x) ),
inference(mrr,[status(thm)],[341,365]),
[iquote('1:MRR:341.0,365.0')] ).
cnf(401,plain,
( ~ element_of_set(u,f14(v,w,x,u))
| element_of_set(u,closure(v,w,x)) ),
inference(mrr,[status(thm)],[342,365]),
[iquote('1:MRR:342.0,365.0')] ).
cnf(444,plain,
( hausdorff(u,v)
| element_of_set(f19(u,v),interior(w,x,y)) ),
inference(res,[status(thm),theory(equality)],[323,398]),
[iquote('1:Res:323.1,398.0')] ).
cnf(443,plain,
( hausdorff(u,v)
| element_of_set(f20(u,v),interior(w,x,y)) ),
inference(res,[status(thm),theory(equality)],[322,398]),
[iquote('1:Res:322.1,398.0')] ).
cnf(395,plain,
( ~ compact_space(u,subspace_topology(v,w,u))
| compact_set(u,v,w) ),
inference(mrr,[status(thm)],[338,365]),
[iquote('1:MRR:338.0,365.0')] ).
cnf(328,plain,
( ~ eq(f19(u,v),f20(u,v))
| hausdorff(u,v) ),
inference(mrr,[status(thm)],[81,318]),
[iquote('1:MRR:81.0,318.0')] ).
cnf(435,plain,
( ~ element_of_set(u,boundary(v,w,x))
| element_of_set(u,y) ),
inference(res,[status(thm),theory(equality)],[72,397]),
[iquote('1:Res:72.1,397.0')] ).
cnf(398,plain,
( ~ element_of_set(u,v)
| element_of_set(u,interior(w,x,y)) ),
inference(mrr,[status(thm)],[380,388]),
[iquote('1:MRR:380.1,388.0')] ).
cnf(397,plain,
( ~ element_of_set(u,closure(v,w,x))
| element_of_set(u,y) ),
inference(mrr,[status(thm)],[379,389]),
[iquote('1:MRR:379.1,389.0')] ).
cnf(368,plain,
( ~ element_of_set(u,v)
| element_of_set(u,f10(w,v,u)) ),
inference(mrr,[status(thm)],[39,320]),
[iquote('1:MRR:39.1,320.0')] ).
cnf(390,plain,
( ~ element_of_set(u,v)
| neighborhood(v,u,w,x) ),
inference(mrr,[status(thm)],[113,388]),
[iquote('1:MRR:113.1,388.0')] ).
cnf(372,plain,
equal_sets(u,intersection_of_sets(v,f12(w,x,v,u))),
inference(mrr,[status(thm)],[47,320]),
[iquote('1:MRR:47.0,320.0')] ).
cnf(324,plain,
( compact_space(u,v)
| open_covering(f24(u,v),u,v) ),
inference(mrr,[status(thm)],[106,318]),
[iquote('1:MRR:106.0,318.0')] ).
cnf(421,plain,
( hausdorff(u,v)
| element_of_set(f19(u,v),union_of_members(w)) ),
inference(res,[status(thm),theory(equality)],[323,363]),
[iquote('1:Res:323.1,363.0')] ).
cnf(419,plain,
( hausdorff(u,v)
| element_of_set(f20(u,v),union_of_members(w)) ),
inference(res,[status(thm),theory(equality)],[322,363]),
[iquote('1:Res:322.1,363.0')] ).
cnf(392,plain,
( ~ subset_collections(u,v)
| open_covering(u,w,v) ),
inference(mrr,[status(thm)],[353,321]),
[iquote('1:MRR:353.1,321.0')] ).
cnf(325,plain,
( compact_space(u,v)
| subset_collections(f24(u,v),v) ),
inference(mrr,[status(thm)],[224,318]),
[iquote('1:MRR:224.0,318.0')] ).
cnf(352,plain,
( ~ subset_collections(u,v)
| finer(v,u,w) ),
inference(mrr,[status(thm)],[29,318]),
[iquote('1:MRR:29.1,29.2,318.0')] ).
cnf(323,plain,
( hausdorff(u,v)
| element_of_set(f19(u,v),u) ),
inference(mrr,[status(thm)],[79,318]),
[iquote('1:MRR:79.0,318.0')] ).
cnf(322,plain,
( hausdorff(u,v)
| element_of_set(f20(u,v),u) ),
inference(mrr,[status(thm)],[80,318]),
[iquote('1:MRR:80.0,318.0')] ).
cnf(364,plain,
( ~ element_of_set(u,intersection_of_members(v))
| element_of_set(u,w) ),
inference(mrr,[status(thm)],[6,320]),
[iquote('1:MRR:6.0,320.0')] ).
cnf(363,plain,
( ~ element_of_set(u,v)
| element_of_set(u,union_of_members(w)) ),
inference(mrr,[status(thm)],[5,320]),
[iquote('1:MRR:5.0,320.0')] ).
cnf(389,plain,
closed(u,v,w),
inference(mrr,[status(thm)],[112,388]),
[iquote('1:MRR:112.0,388.0')] ).
cnf(388,plain,
open(u,v,w),
inference(mrr,[status(thm)],[330,320]),
[iquote('1:MRR:330.0,320.0')] ).
cnf(321,plain,
equal_sets(union_of_members(u),v),
inference(mrr,[status(thm)],[9,318]),
[iquote('1:MRR:9.0,318.0')] ).
cnf(407,plain,
basis(u,v),
inference(mrr,[status(thm)],[382,406]),
[iquote('1:MRR:382.1,406.0')] ).
cnf(365,plain,
subset_sets(u,v),
inference(mrr,[status(thm)],[45,320]),
[iquote('1:MRR:45.0,320.0')] ).
cnf(320,plain,
element_of_collection(u,v),
inference(mrr,[status(thm)],[11,318]),
[iquote('1:MRR:11.0,318.0')] ).
cnf(318,plain,
topological_space(u,v),
inference(spt,[],[317]),
[iquote('1:Spt:317.1')] ).
cnf(51,axiom,
( ~ element_of_set(u,interior(v,w,x))
| element_of_set(u,f13(v,w,x,u)) ),
file('TOP019-1.p',unknown),
[] ).
cnf(103,axiom,
( ~ compact_space(u,v)
| ~ open_covering(w,u,v)
| finite(f23(u,v,w)) ),
file('TOP019-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ element_of_set(u,f2(v,u))
| element_of_set(u,intersection_of_members(v)) ),
file('TOP019-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ element_of_set(u,union_of_members(v))
| element_of_set(u,f1(v,u)) ),
file('TOP019-1.p',unknown),
[] ).
cnf(63,axiom,
( ~ neighborhood(u,v,w,x)
| element_of_set(v,u) ),
file('TOP019-1.p',unknown),
[] ).
cnf(99,axiom,
( ~ open_covering(u,v,w)
| subset_collections(u,w) ),
file('TOP019-1.p',unknown),
[] ).
cnf(28,axiom,
( ~ finer(u,v,w)
| subset_collections(v,u) ),
file('TOP019-1.p',unknown),
[] ).
cnf(2,axiom,
~ connected_set(closure(a,cx,ct),cx,ct),
file('TOP019-1.p',unknown),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : TOP019-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun May 29 04:38:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Completion found.
% 0.20/0.48 % SZS status CounterSatisfiable
% 0.20/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 518 clauses, backtracked 37 clauses, performed 4 splits and kept 439 clauses.
% 0.20/0.48 SPASS allocated 76388 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.48 0:00:00.04 for the input.
% 0.20/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.01 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.05 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 The saturated set of worked-off clauses is :
% 0.20/0.48 % SZS output start Saturation
% See solution above
%------------------------------------------------------------------------------