TSTP Solution File: TOP018-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : TOP018-1 : 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 0.19s 0.49s
% Output : Saturation 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 688)
% Comments :
%------------------------------------------------------------------------------
cnf(697,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)],[575,689]),
[iquote('1:Res:575.4,689.0')] ).
cnf(701,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)],[643,689]),
[iquote('1:Res:643.4,689.0')] ).
cnf(696,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)],[418,689]),
[iquote('1:Res:418.2,689.0')] ).
cnf(695,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)],[493,689]),
[iquote('1:Res:493.1,689.0')] ).
cnf(694,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)],[373,689]),
[iquote('1:Res:373.1,689.0')] ).
cnf(709,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)],[693,448]),
[iquote('1:MRR:693.0,448.1')] ).
cnf(708,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)],[691,424]),
[iquote('1:MRR:691.0,424.1')] ).
cnf(707,plain,
( ~ hausdorff(interior(u,v,w),x)
| hausdorff(y,z) ),
inference(mrr,[status(thm)],[706,449]),
[iquote('1:MRR:706.0,449.1')] ).
cnf(705,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(w,x) ),
inference(mrr,[status(thm)],[704,426]),
[iquote('1:MRR:704.0,426.1')] ).
cnf(703,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w) ),
inference(mrr,[status(thm)],[702,327]),
[iquote('1:MRR:702.0,327.1')] ).
cnf(689,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)],[688,332]),
[iquote('1:MRR:688.3,332.0')] ).
cnf(686,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)],[685]),
[iquote('1:Obv:685.7')] ).
cnf(659,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)],[643,549]),
[iquote('1:Res:643.4,549.0')] ).
cnf(654,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)],[575,549]),
[iquote('1:Res:575.4,549.0')] ).
cnf(657,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)],[643,565]),
[iquote('1:Res:643.4,565.0')] ).
cnf(652,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)],[575,565]),
[iquote('1:Res:575.4,565.0')] ).
cnf(658,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)],[643,564]),
[iquote('1:Res:643.4,564.0')] ).
cnf(557,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)],[418,549]),
[iquote('1:Res:418.2,549.0')] ).
cnf(653,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)],[575,564]),
[iquote('1:Res:575.4,564.0')] ).
cnf(681,plain,
( ~ element_of_set(u,b)
| limit_point(u,a,v,w) ),
inference(res,[status(thm),theory(equality)],[2,680]),
[iquote('1:Res:2.1,680.0')] ).
cnf(680,plain,
( ~ limit_point(u,v,w,x)
| limit_point(u,v,y,z) ),
inference(mrr,[status(thm)],[678,493]),
[iquote('1:MRR:678.0,493.1')] ).
cnf(538,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)],[68,410]),
[iquote('1:Res:68.2,410.0')] ).
cnf(634,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)],[418,565]),
[iquote('1:Res:418.2,565.0')] ).
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)],[418,564]),
[iquote('1:Res:418.2,564.0')] ).
cnf(556,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)],[493,549]),
[iquote('1:Res:493.1,549.0')] ).
cnf(675,plain,
( ~ subset_collections(u,f24(v,u))
| ~ compact_space(w,f24(v,u))
| compact_space(v,u) ),
inference(res,[status(thm),theory(equality)],[397,674]),
[iquote('1:Res:397.1,674.1')] ).
cnf(547,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)],[405,118]),
[iquote('1:Res:405.1,118.1')] ).
cnf(674,plain,
( ~ compact_space(u,f24(v,w))
| ~ open_covering(w,u,f24(v,w))
| compact_space(v,w) ),
inference(obv,[status(thm),theory(equality)],[673]),
[iquote('1:Obv:673.1')] ).
cnf(672,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)],[397,512]),
[iquote('1:Res:397.1,512.2')] ).
cnf(512,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)],[510,104]),
[iquote('0:MRR:510.0,104.2')] ).
cnf(517,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)],[326,410]),
[iquote('1:Res:326.1,410.0')] ).
cnf(518,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)],[327,410]),
[iquote('1:Res:327.1,410.0')] ).
cnf(669,plain,
( ~ compact_set(u,v,w)
| compact_space(x,subspace_topology(v,w,u)) ),
inference(res,[status(thm),theory(equality)],[111,668]),
[iquote('1:Res:111.1,668.0')] ).
cnf(668,plain,
( ~ compact_space(u,v)
| compact_space(w,v) ),
inference(mrr,[status(thm)],[667,329]),
[iquote('1:MRR:667.0,329.1')] ).
cnf(663,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)],[397,511]),
[iquote('1:Res:397.1,511.2')] ).
cnf(511,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)],[508,104]),
[iquote('0:MRR:508.0,104.2')] ).
cnf(555,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)],[373,549]),
[iquote('1:Res:373.1,549.0')] ).
cnf(536,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)],[68,403]),
[iquote('1:Res:68.2,403.0')] ).
cnf(643,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)],[77,64]),
[iquote('0:Res:77.4,64.0')] ).
cnf(539,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)],[377,529]),
[iquote('1:Res:377.0,529.1')] ).
cnf(575,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)],[78,64]),
[iquote('0:Res:78.4,64.0')] ).
cnf(537,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)],[68,368]),
[iquote('1:Res:68.2,368.0')] ).
cnf(633,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)],[493,565]),
[iquote('1:Res:493.1,565.0')] ).
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)],[493,564]),
[iquote('1:Res:493.1,564.0')] ).
cnf(574,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)],[554,449]),
[iquote('1:MRR:554.0,449.1')] ).
cnf(529,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)],[419,93]),
[iquote('1:Res:419.4,93.1')] ).
cnf(632,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)],[373,565]),
[iquote('1:Res:373.1,565.0')] ).
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)],[373,564]),
[iquote('1:Res:373.1,564.0')] ).
cnf(569,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(f1(x,f19(u,v)),w)
| hausdorff(u,v) ),
inference(mrr,[status(thm)],[552,426]),
[iquote('1:MRR:552.0,426.1')] ).
cnf(568,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(interior(x,y,z),w)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[561]),
[iquote('1:Obv:561.2')] ).
cnf(79,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('TOP018-1.p',unknown),
[] ).
cnf(642,plain,
( ~ disjoint_s(union_of_members(u),f13(v,w,x,f20(y,z)))
| hausdorff(y,z) ),
inference(mrr,[status(thm)],[631,448]),
[iquote('1:MRR:631.0,448.1')] ).
cnf(641,plain,
( ~ disjoint_s(union_of_members(u),f1(v,f20(w,x)))
| hausdorff(w,x) ),
inference(mrr,[status(thm)],[629,424]),
[iquote('1:MRR:629.0,424.1')] ).
cnf(640,plain,
( ~ disjoint_s(union_of_members(u),interior(v,w,x))
| hausdorff(y,z) ),
inference(obv,[status(thm),theory(equality)],[637]),
[iquote('1:Obv:637.1')] ).
cnf(639,plain,
( ~ disjoint_s(union_of_members(u),union_of_members(v))
| hausdorff(w,x) ),
inference(obv,[status(thm),theory(equality)],[636]),
[iquote('1:Obv:636.1')] ).
cnf(77,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('TOP018-1.p',unknown),
[] ).
cnf(638,plain,
( ~ disjoint_s(union_of_members(u),v)
| hausdorff(v,w) ),
inference(obv,[status(thm),theory(equality)],[635]),
[iquote('1:Obv:635.1')] ).
cnf(565,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(union_of_members(x),w)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[559]),
[iquote('1:Obv:559.2')] ).
cnf(622,plain,
( ~ disjoint_s(u,f13(v,w,x,f20(u,y)))
| hausdorff(u,y) ),
inference(mrr,[status(thm)],[611,448]),
[iquote('1:MRR:611.0,448.1')] ).
cnf(621,plain,
( ~ disjoint_s(u,f1(v,f20(u,w)))
| hausdorff(u,w) ),
inference(mrr,[status(thm)],[609,424]),
[iquote('1:MRR:609.0,424.1')] ).
cnf(419,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)],[349,324]),
[iquote('1:MRR:349.1,349.2,324.0,324.0')] ).
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(564,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(u,w)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[558]),
[iquote('1:Obv:558.2')] ).
cnf(336,plain,
( connected_space(u,v)
| separation(f21(u,v),f22(u,v),u,v) ),
inference(mrr,[status(thm)],[94,322]),
[iquote('1:MRR:94.0,322.0')] ).
cnf(463,plain,
( connected_space(u,v)
| equal_sets(union_of_sets(f21(u,v),f22(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[336,89]),
[iquote('1:Res:336.1,89.0')] ).
cnf(89,axiom,
( ~ separation(u,v,w,x)
| equal_sets(union_of_sets(u,v),w) ),
file('TOP018-1.p',unknown),
[] ).
cnf(401,plain,
( ~ connected_space(u,subspace_topology(v,w,u))
| connected_set(u,v,w) ),
inference(mrr,[status(thm)],[343,370]),
[iquote('1:MRR:343.0,370.0')] ).
cnf(465,plain,
( connected_space(u,v)
| disjoint_s(f21(u,v),f22(u,v)) ),
inference(res,[status(thm),theory(equality)],[336,90]),
[iquote('1:Res:336.1,90.0')] ).
cnf(93,axiom,
( ~ connected_space(u,v)
| ~ separation(w,x,u,v) ),
file('TOP018-1.p',unknown),
[] ).
cnf(86,axiom,
( ~ equal_sets(u,empty_set)
| ~ separation(v,u,w,x) ),
file('TOP018-1.p',unknown),
[] ).
cnf(85,axiom,
( ~ equal_sets(u,empty_set)
| ~ separation(u,v,w,x) ),
file('TOP018-1.p',unknown),
[] ).
cnf(466,plain,
( ~ equal_sets(f22(u,v),empty_set)
| connected_space(u,v) ),
inference(res,[status(thm),theory(equality)],[336,86]),
[iquote('1:Res:336.1,86.1')] ).
cnf(464,plain,
( ~ equal_sets(f21(u,v),empty_set)
| connected_space(u,v) ),
inference(res,[status(thm),theory(equality)],[336,85]),
[iquote('1:Res:336.1,85.1')] ).
cnf(90,axiom,
( ~ separation(u,v,w,x)
| disjoint_s(u,v) ),
file('TOP018-1.p',unknown),
[] ).
cnf(543,plain,
( ~ connected_set(u,v,w)
| connected_space(u,x) ),
inference(res,[status(thm),theory(equality)],[97,541]),
[iquote('1:Res:97.1,541.0')] ).
cnf(541,plain,
( ~ connected_space(u,v)
| connected_space(u,w) ),
inference(mrr,[status(thm)],[540,465,466,464]),
[iquote('1:MRR:540.0,540.3,540.4,465.1,466.0,464.0')] ).
cnf(542,plain,
connected_space(a,u),
inference(res,[status(thm),theory(equality)],[119,541]),
[iquote('1:Res:119.0,541.0')] ).
cnf(599,plain,
hausdorff(boundary(u,v,w),x),
inference(spt,[],[597,590]),
[iquote('4:Spt:597.0,590.1')] ).
cnf(591,plain,
hausdorff(closure(u,v,w),x),
inference(spt,[],[589]),
[iquote('3:Spt:589.1')] ).
cnf(586,plain,
hausdorff(intersection_of_members(u),v),
inference(spt,[],[584,578]),
[iquote('2:Spt:584.0,578.1')] ).
cnf(78,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('TOP018-1.p',unknown),
[] ).
cnf(549,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)],[395,546]),
[iquote('1:Res:395.1,546.2')] ).
cnf(546,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)],[395,118]),
[iquote('1:Res:395.1,118.1')] ).
cnf(545,plain,
connected_set(a,u,v),
inference(res,[status(thm),theory(equality)],[542,401]),
[iquote('1:Res:542.0,401.0')] ).
cnf(118,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)],[83,62]),
[iquote('0:MRR:83.0,62.1')] ).
cnf(68,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('TOP018-1.p',unknown),
[] ).
cnf(69,axiom,
( ~ eq(f15(u,v,w,x,y),u)
| ~ neighborhood(y,u,w,x)
| ~ limit_point(u,v,w,x) ),
file('TOP018-1.p',unknown),
[] ).
cnf(410,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)],[348,370]),
[iquote('1:MRR:348.0,370.0')] ).
cnf(418,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)],[374,412]),
[iquote('1:MRR:374.1,412.0')] ).
cnf(115,plain,
( ~ finite(u)
| ~ subset_collections(u,f24(v,w))
| ~ open_covering(u,v,w)
| compact_space(v,w) ),
inference(mrr,[status(thm)],[108,99]),
[iquote('0:MRR:108.1,99.1')] ).
cnf(507,plain,
( ~ compact_space(u,v)
| ~ open_covering(w,u,v)
| subset_collections(f23(u,v,w),v) ),
inference(res,[status(thm),theory(equality)],[106,100]),
[iquote('0:Res:106.2,100.0')] ).
cnf(106,axiom,
( ~ compact_space(u,v)
| ~ open_covering(w,u,v)
| open_covering(f23(u,v,w),u,v) ),
file('TOP018-1.p',unknown),
[] ).
cnf(494,plain,
( limit_point(u,v,w,x)
| element_of_set(u,interior(y,z,x1)) ),
inference(res,[status(thm),theory(equality)],[493,403]),
[iquote('1:Res:493.1,403.0')] ).
cnf(495,plain,
( limit_point(u,v,w,x)
| element_of_set(u,union_of_members(y)) ),
inference(res,[status(thm),theory(equality)],[493,368]),
[iquote('1:Res:493.1,368.0')] ).
cnf(493,plain,
( limit_point(u,v,w,x)
| element_of_set(u,f16(u,v,w,x)) ),
inference(res,[status(thm),theory(equality)],[405,64]),
[iquote('1:Res:405.1,64.0')] ).
cnf(405,plain,
( limit_point(u,v,w,x)
| neighborhood(f16(u,v,w,x),u,w,x) ),
inference(mrr,[status(thm)],[345,370]),
[iquote('1:MRR:345.0,370.0')] ).
cnf(406,plain,
( ~ element_of_set(u,f14(v,w,x,u))
| element_of_set(u,closure(v,w,x)) ),
inference(mrr,[status(thm)],[346,370]),
[iquote('1:MRR:346.0,370.0')] ).
cnf(449,plain,
( hausdorff(u,v)
| element_of_set(f19(u,v),interior(w,x,y)) ),
inference(res,[status(thm),theory(equality)],[327,403]),
[iquote('1:Res:327.1,403.0')] ).
cnf(448,plain,
( hausdorff(u,v)
| element_of_set(f20(u,v),interior(w,x,y)) ),
inference(res,[status(thm),theory(equality)],[326,403]),
[iquote('1:Res:326.1,403.0')] ).
cnf(400,plain,
( ~ compact_space(u,subspace_topology(v,w,u))
| compact_set(u,v,w) ),
inference(mrr,[status(thm)],[342,370]),
[iquote('1:MRR:342.0,370.0')] ).
cnf(440,plain,
( ~ element_of_set(u,boundary(v,w,x))
| element_of_set(u,y) ),
inference(res,[status(thm),theory(equality)],[73,402]),
[iquote('1:Res:73.1,402.0')] ).
cnf(332,plain,
( ~ eq(f19(u,v),f20(u,v))
| hausdorff(u,v) ),
inference(mrr,[status(thm)],[82,322]),
[iquote('1:MRR:82.0,322.0')] ).
cnf(403,plain,
( ~ element_of_set(u,v)
| element_of_set(u,interior(w,x,y)) ),
inference(mrr,[status(thm)],[385,393]),
[iquote('1:MRR:385.1,393.0')] ).
cnf(402,plain,
( ~ element_of_set(u,closure(v,w,x))
| element_of_set(u,y) ),
inference(mrr,[status(thm)],[384,394]),
[iquote('1:MRR:384.1,394.0')] ).
cnf(373,plain,
( ~ element_of_set(u,v)
| element_of_set(u,f10(w,v,u)) ),
inference(mrr,[status(thm)],[40,324]),
[iquote('1:MRR:40.1,324.0')] ).
cnf(395,plain,
( ~ element_of_set(u,v)
| neighborhood(v,u,w,x) ),
inference(mrr,[status(thm)],[114,393]),
[iquote('1:MRR:114.1,393.0')] ).
cnf(377,plain,
equal_sets(u,intersection_of_sets(v,f12(w,x,v,u))),
inference(mrr,[status(thm)],[48,324]),
[iquote('1:MRR:48.0,324.0')] ).
cnf(426,plain,
( hausdorff(u,v)
| element_of_set(f19(u,v),union_of_members(w)) ),
inference(res,[status(thm),theory(equality)],[327,368]),
[iquote('1:Res:327.1,368.0')] ).
cnf(424,plain,
( hausdorff(u,v)
| element_of_set(f20(u,v),union_of_members(w)) ),
inference(res,[status(thm),theory(equality)],[326,368]),
[iquote('1:Res:326.1,368.0')] ).
cnf(328,plain,
( compact_space(u,v)
| open_covering(f24(u,v),u,v) ),
inference(mrr,[status(thm)],[107,322]),
[iquote('1:MRR:107.0,322.0')] ).
cnf(397,plain,
( ~ subset_collections(u,v)
| open_covering(u,w,v) ),
inference(mrr,[status(thm)],[358,325]),
[iquote('1:MRR:358.1,325.0')] ).
cnf(357,plain,
( ~ subset_collections(u,v)
| finer(v,u,w) ),
inference(mrr,[status(thm)],[30,322]),
[iquote('1:MRR:30.1,30.2,322.0')] ).
cnf(329,plain,
( compact_space(u,v)
| subset_collections(f24(u,v),v) ),
inference(mrr,[status(thm)],[227,322]),
[iquote('1:MRR:227.0,322.0')] ).
cnf(327,plain,
( hausdorff(u,v)
| element_of_set(f19(u,v),u) ),
inference(mrr,[status(thm)],[80,322]),
[iquote('1:MRR:80.0,322.0')] ).
cnf(326,plain,
( hausdorff(u,v)
| element_of_set(f20(u,v),u) ),
inference(mrr,[status(thm)],[81,322]),
[iquote('1:MRR:81.0,322.0')] ).
cnf(369,plain,
( ~ element_of_set(u,intersection_of_members(v))
| element_of_set(u,w) ),
inference(mrr,[status(thm)],[7,324]),
[iquote('1:MRR:7.0,324.0')] ).
cnf(368,plain,
( ~ element_of_set(u,v)
| element_of_set(u,union_of_members(w)) ),
inference(mrr,[status(thm)],[6,324]),
[iquote('1:MRR:6.0,324.0')] ).
cnf(394,plain,
closed(u,v,w),
inference(mrr,[status(thm)],[113,393]),
[iquote('1:MRR:113.0,393.0')] ).
cnf(393,plain,
open(u,v,w),
inference(mrr,[status(thm)],[334,324]),
[iquote('1:MRR:334.0,324.0')] ).
cnf(325,plain,
equal_sets(union_of_members(u),v),
inference(mrr,[status(thm)],[10,322]),
[iquote('1:MRR:10.0,322.0')] ).
cnf(412,plain,
basis(u,v),
inference(mrr,[status(thm)],[387,411]),
[iquote('1:MRR:387.1,411.0')] ).
cnf(370,plain,
subset_sets(u,v),
inference(mrr,[status(thm)],[46,324]),
[iquote('1:MRR:46.0,324.0')] ).
cnf(324,plain,
element_of_collection(u,v),
inference(mrr,[status(thm)],[12,322]),
[iquote('1:MRR:12.0,322.0')] ).
cnf(322,plain,
topological_space(u,v),
inference(spt,[],[320]),
[iquote('1:Spt:320.1')] ).
cnf(105,axiom,
( ~ compact_space(u,v)
| ~ open_covering(w,u,v)
| subset_collections(f23(u,v,w),w) ),
file('TOP018-1.p',unknown),
[] ).
cnf(52,axiom,
( ~ element_of_set(u,interior(v,w,x))
| element_of_set(u,f13(v,w,x,u)) ),
file('TOP018-1.p',unknown),
[] ).
cnf(104,axiom,
( ~ compact_space(u,v)
| ~ open_covering(w,u,v)
| finite(f23(u,v,w)) ),
file('TOP018-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ element_of_set(u,f2(v,u))
| element_of_set(u,intersection_of_members(v)) ),
file('TOP018-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ element_of_set(u,union_of_members(v))
| element_of_set(u,f1(v,u)) ),
file('TOP018-1.p',unknown),
[] ).
cnf(64,axiom,
( ~ neighborhood(u,v,w,x)
| element_of_set(v,u) ),
file('TOP018-1.p',unknown),
[] ).
cnf(100,axiom,
( ~ open_covering(u,v,w)
| subset_collections(u,w) ),
file('TOP018-1.p',unknown),
[] ).
cnf(29,axiom,
( ~ finer(u,v,w)
| subset_collections(v,u) ),
file('TOP018-1.p',unknown),
[] ).
cnf(3,axiom,
~ connected_set(union_of_sets(a,b),cx,ct),
file('TOP018-1.p',unknown),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : TOP018-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n022.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 : 600
% 0.12/0.34 % DateTime : Sun May 29 08:19:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.49
% 0.19/0.49 SPASS V 3.9
% 0.19/0.49 SPASS beiseite: Completion found.
% 0.19/0.49 % SZS status CounterSatisfiable
% 0.19/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 SPASS derived 524 clauses, backtracked 36 clauses, performed 4 splits and kept 441 clauses.
% 0.19/0.49 SPASS allocated 76395 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.19/0.49 0:00:00.04 for the input.
% 0.19/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.49 0:00:00.01 for inferences.
% 0.19/0.49 0:00:00.00 for the backtracking.
% 0.19/0.49 0:00:00.06 for the reduction.
% 0.19/0.49
% 0.19/0.49
% 0.19/0.49 The saturated set of worked-off clauses is :
% 0.19/0.49 % SZS output start Saturation
% See solution above
%------------------------------------------------------------------------------