TSTP Solution File: TOP015-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : TOP015-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 21:34:57 EDT 2022
% Result : Satisfiable 0.11s 0.45s
% Output : Saturation 0.11s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 114)
% Comments :
%------------------------------------------------------------------------------
cnf(1352,plain,
( ~ element_of_set(u,f16(v,w,x,y))
| ~ limit_point(u,z,x1,x2)
| ~ limit_point(v,z,x,y)
| ~ hausdorff(intersection_of_sets(f16(v,w,x,y),z),x3)
| limit_point(v,w,x,y)
| eq(f15(u,z,x1,x2,f16(v,w,x,y)),f15(v,z,x,y,f16(v,w,x,y))) ),
inference(res,[status(thm),theory(equality)],[578,1351]),
[iquote('6:Res:578.1,1351.0')] ).
cnf(1354,plain,
( ~ limit_point(u,v,w,x)
| ~ hausdorff(intersection_of_sets(f16(u,y,w,x),v),z)
| limit_point(u,y,w,x)
| eq(f15(u,v,w,x,f16(u,y,w,x)),f15(u,v,w,x,f16(u,y,w,x))) ),
inference(obv,[status(thm),theory(equality)],[1353]),
[iquote('6:Obv:1353.3')] ).
cnf(1351,plain,
( ~ neighborhood(f16(u,v,w,x),y,z,x1)
| ~ limit_point(y,x2,z,x1)
| ~ limit_point(u,x2,w,x)
| ~ hausdorff(intersection_of_sets(f16(u,v,w,x),x2),x3)
| limit_point(u,v,w,x)
| eq(f15(y,x2,z,x1,f16(u,v,w,x)),f15(u,x2,w,x,f16(u,v,w,x))) ),
inference(res,[status(thm),theory(equality)],[68,1221]),
[iquote('6:Res:68.2,1221.1')] ).
cnf(1349,plain,
( ~ limit_point(u,v,w,x)
| ~ hausdorff(intersection_of_sets(f16(u,y,w,x),v),z)
| hausdorff(intersection_of_sets(f16(u,y,w,x),v),x1)
| limit_point(u,y,w,x)
| eq(f20(intersection_of_sets(f16(u,y,w,x),v),x1),f15(u,v,w,x,f16(u,y,w,x))) ),
inference(res,[status(thm),theory(equality)],[471,1221]),
[iquote('6:Res:471.1,1221.1')] ).
cnf(1350,plain,
( ~ limit_point(u,v,w,x)
| ~ hausdorff(intersection_of_sets(f16(u,y,w,x),v),z)
| hausdorff(intersection_of_sets(f16(u,y,w,x),v),x1)
| limit_point(u,y,w,x)
| eq(f19(intersection_of_sets(f16(u,y,w,x),v),x1),f15(u,v,w,x,f16(u,y,w,x))) ),
inference(res,[status(thm),theory(equality)],[472,1221]),
[iquote('6:Res:472.1,1221.1')] ).
cnf(1346,plain,
( ~ limit_point(u,v,w,x)
| ~ hausdorff(intersection_of_sets(f16(u,y,w,x),v),z)
| limit_point(u,y,w,x)
| hausdorff(intersection_of_sets(f16(u,y,w,x),v),x1)
| eq(f15(u,v,w,x,f16(u,y,w,x)),f19(intersection_of_sets(f16(u,y,w,x),v),x1)) ),
inference(res,[status(thm),theory(equality)],[587,908]),
[iquote('6:Res:587.1,908.0')] ).
cnf(1340,plain,
( ~ limit_point(u,v,w,x)
| ~ hausdorff(intersection_of_sets(f16(u,y,w,x),v),z)
| limit_point(u,y,w,x)
| hausdorff(intersection_of_sets(f16(u,y,w,x),v),x1)
| eq(f15(u,v,w,x,f16(u,y,w,x)),f20(intersection_of_sets(f16(u,y,w,x),v),x1)) ),
inference(res,[status(thm),theory(equality)],[587,887]),
[iquote('6:Res:587.1,887.0')] ).
cnf(1239,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ neighborhood(z,x1,x2,x3)
| ~ limit_point(x1,x4,x2,x3)
| ~ hausdorff(interior(x5,x6,x7),x8)
| eq(f15(v,y,w,x,u),f15(x1,x4,x2,x3,z)) ),
inference(res,[status(thm),theory(equality)],[743,913]),
[iquote('6:Res:743.2,913.2')] ).
cnf(1221,plain,
( ~ limit_point(u,v,w,x)
| ~ element_of_set(y,intersection_of_sets(f16(u,z,w,x),v))
| ~ hausdorff(intersection_of_sets(f16(u,z,w,x),v),x1)
| limit_point(u,z,w,x)
| eq(y,f15(u,v,w,x,f16(u,z,w,x))) ),
inference(res,[status(thm),theory(equality)],[587,866]),
[iquote('6:Res:587.1,866.0')] ).
cnf(1207,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ hausdorff(f6(v,y,u,w,x),z)
| hausdorff(f6(v,y,u,w,x),x1)
| eq(f20(f6(v,y,u,w,x),x1),u) ),
inference(res,[status(thm),theory(equality)],[471,853]),
[iquote('6:Res:471.1,853.2')] ).
cnf(1208,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ hausdorff(f6(v,y,u,w,x),z)
| hausdorff(f6(v,y,u,w,x),x1)
| eq(f19(f6(v,y,u,w,x),x1),u) ),
inference(res,[status(thm),theory(equality)],[472,853]),
[iquote('6:Res:472.1,853.2')] ).
cnf(895,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ hausdorff(f6(v,y,u,w,x),z)
| hausdorff(f6(v,y,u,w,x),x1)
| eq(u,f19(f6(v,y,u,w,x),x1)) ),
inference(res,[status(thm),theory(equality)],[606,855]),
[iquote('6:Res:606.2,855.0')] ).
cnf(874,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ hausdorff(f6(v,y,u,w,x),z)
| hausdorff(f6(v,y,u,w,x),x1)
| eq(u,f20(f6(v,y,u,w,x),x1)) ),
inference(res,[status(thm),theory(equality)],[606,854]),
[iquote('6:Res:606.2,854.0')] ).
cnf(1345,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ hausdorff(intersection_of_sets(v,w),z)
| hausdorff(intersection_of_sets(v,w),x1)
| eq(f15(u,w,x,y,v),f19(intersection_of_sets(v,w),x1)) ),
inference(res,[status(thm),theory(equality)],[578,908]),
[iquote('6:Res:578.1,908.0')] ).
cnf(908,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(intersection_of_sets(u,y),z)
| hausdorff(intersection_of_sets(u,y),x1)
| eq(f15(v,y,w,x,u),f19(intersection_of_sets(u,y),x1)) ),
inference(res,[status(thm),theory(equality)],[68,855]),
[iquote('6:Res:68.2,855.0')] ).
cnf(1330,plain,
( ~ limit_point(u,v,w,x)
| ~ hausdorff(union_of_members(y),z)
| limit_point(u,x1,w,x)
| limit_point(x2,x3,x4,x5)
| eq(f15(u,v,w,x,f16(u,x1,w,x)),x2) ),
inference(res,[status(thm),theory(equality)],[587,1004]),
[iquote('6:Res:587.1,1004.0')] ).
cnf(1339,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ hausdorff(intersection_of_sets(v,w),z)
| hausdorff(intersection_of_sets(v,w),x1)
| eq(f15(u,w,x,y,v),f20(intersection_of_sets(v,w),x1)) ),
inference(res,[status(thm),theory(equality)],[578,887]),
[iquote('6:Res:578.1,887.0')] ).
cnf(887,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(intersection_of_sets(u,y),z)
| hausdorff(intersection_of_sets(u,y),x1)
| eq(f15(v,y,w,x,u),f20(intersection_of_sets(u,y),x1)) ),
inference(res,[status(thm),theory(equality)],[68,854]),
[iquote('6:Res:68.2,854.0')] ).
cnf(1326,plain,
( ~ limit_point(u,v,w,x)
| ~ hausdorff(union_of_members(y),z)
| limit_point(u,x1,w,x)
| hausdorff(x2,x3)
| eq(f15(u,v,w,x,f16(u,x1,w,x)),f19(x2,x3)) ),
inference(res,[status(thm),theory(equality)],[587,948]),
[iquote('6:Res:587.1,948.0')] ).
cnf(1322,plain,
( ~ limit_point(u,v,w,x)
| ~ hausdorff(union_of_members(y),z)
| limit_point(u,x1,w,x)
| hausdorff(x2,x3)
| eq(f15(u,v,w,x,f16(u,x1,w,x)),f20(x2,x3)) ),
inference(res,[status(thm),theory(equality)],[587,936]),
[iquote('6:Res:587.1,936.0')] ).
cnf(1197,plain,
( ~ limit_point(u,v,w,x)
| ~ element_of_set(y,union_of_members(z))
| ~ hausdorff(union_of_members(z),x1)
| limit_point(u,x2,w,x)
| eq(y,f15(u,v,w,x,f16(u,x2,w,x))) ),
inference(res,[status(thm),theory(equality)],[587,867]),
[iquote('6:Res:587.1,867.0')] ).
cnf(1230,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(interior(z,x1,x2),x3)
| limit_point(x4,x5,x6,x7)
| eq(x4,f15(v,y,w,x,u)) ),
inference(res,[status(thm),theory(equality)],[678,913]),
[iquote('6:Res:678.1,913.2')] ).
cnf(1177,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(interior(z,x1,x2),x3)
| limit_point(x4,x5,x6,x7)
| eq(f15(v,y,w,x,u),x4) ),
inference(res,[status(thm),theory(equality)],[743,849]),
[iquote('6:Res:743.2,849.0')] ).
cnf(1233,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(interior(z,x1,x2),x3)
| hausdorff(x4,x5)
| eq(f20(x4,x5),f15(v,y,w,x,u)) ),
inference(res,[status(thm),theory(equality)],[642,913]),
[iquote('6:Res:642.1,913.2')] ).
cnf(1234,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(interior(z,x1,x2),x3)
| hausdorff(x4,x5)
| eq(f19(x4,x5),f15(v,y,w,x,u)) ),
inference(res,[status(thm),theory(equality)],[643,913]),
[iquote('6:Res:643.1,913.2')] ).
cnf(1167,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(interior(z,x1,x2),x3)
| hausdorff(x4,x5)
| eq(f15(v,y,w,x,u),f20(x4,x5)) ),
inference(res,[status(thm),theory(equality)],[743,860]),
[iquote('6:Res:743.2,860.0')] ).
cnf(1157,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(interior(z,x1,x2),x3)
| hausdorff(x4,x5)
| eq(f15(v,y,w,x,u),f19(x4,x5)) ),
inference(res,[status(thm),theory(equality)],[743,861]),
[iquote('6:Res:743.2,861.0')] ).
cnf(1187,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(f13(v,w,x,u),y)
| hausdorff(f13(v,w,x,u),z)
| eq(f20(f13(v,w,x,u),z),u) ),
inference(res,[status(thm),theory(equality)],[471,850]),
[iquote('6:Res:471.1,850.1')] ).
cnf(1188,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(f13(v,w,x,u),y)
| hausdorff(f13(v,w,x,u),z)
| eq(f19(f13(v,w,x,u),z),u) ),
inference(res,[status(thm),theory(equality)],[472,850]),
[iquote('6:Res:472.1,850.1')] ).
cnf(892,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(f13(v,w,x,u),y)
| hausdorff(f13(v,w,x,u),z)
| eq(u,f19(f13(v,w,x,u),z)) ),
inference(res,[status(thm),theory(equality)],[52,855]),
[iquote('6:Res:52.1,855.0')] ).
cnf(871,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(f13(v,w,x,u),y)
| hausdorff(f13(v,w,x,u),z)
| eq(u,f20(f13(v,w,x,u),z)) ),
inference(res,[status(thm),theory(equality)],[52,854]),
[iquote('6:Res:52.1,854.0')] ).
cnf(1329,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ hausdorff(union_of_members(z),x1)
| limit_point(x2,x3,x4,x5)
| eq(f15(u,w,x,y,v),x2) ),
inference(res,[status(thm),theory(equality)],[578,1004]),
[iquote('6:Res:578.1,1004.0')] ).
cnf(1004,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(union_of_members(z),x1)
| limit_point(x2,x3,x4,x5)
| eq(f15(v,y,w,x,u),x2) ),
inference(res,[status(thm),theory(equality)],[744,847]),
[iquote('6:Res:744.2,847.0')] ).
cnf(1325,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ hausdorff(union_of_members(z),x1)
| hausdorff(x2,x3)
| eq(f15(u,w,x,y,v),f19(x2,x3)) ),
inference(res,[status(thm),theory(equality)],[578,948]),
[iquote('6:Res:578.1,948.0')] ).
cnf(948,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(union_of_members(z),x1)
| hausdorff(x2,x3)
| eq(f15(v,y,w,x,u),f19(x2,x3)) ),
inference(res,[status(thm),theory(equality)],[744,857]),
[iquote('6:Res:744.2,857.0')] ).
cnf(1321,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ hausdorff(union_of_members(z),x1)
| hausdorff(x2,x3)
| eq(f15(u,w,x,y,v),f20(x2,x3)) ),
inference(res,[status(thm),theory(equality)],[578,936]),
[iquote('6:Res:578.1,936.0')] ).
cnf(936,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(union_of_members(z),x1)
| hausdorff(x2,x3)
| eq(f15(v,y,w,x,u),f20(x2,x3)) ),
inference(res,[status(thm),theory(equality)],[744,856]),
[iquote('6:Res:744.2,856.0')] ).
cnf(1220,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ element_of_set(z,intersection_of_sets(v,w))
| ~ hausdorff(intersection_of_sets(v,w),x1)
| eq(z,f15(u,w,x,y,v)) ),
inference(res,[status(thm),theory(equality)],[578,866]),
[iquote('6:Res:578.1,866.0')] ).
cnf(1179,plain,
( ~ hausdorff(f16(u,v,w,x),y)
| hausdorff(f16(u,v,w,x),z)
| limit_point(u,v,w,x)
| eq(f20(f16(u,v,w,x),z),u) ),
inference(res,[status(thm),theory(equality)],[471,852]),
[iquote('6:Res:471.1,852.0')] ).
cnf(1180,plain,
( ~ hausdorff(f16(u,v,w,x),y)
| hausdorff(f16(u,v,w,x),z)
| limit_point(u,v,w,x)
| eq(f19(f16(u,v,w,x),z),u) ),
inference(res,[status(thm),theory(equality)],[472,852]),
[iquote('6:Res:472.1,852.0')] ).
cnf(894,plain,
( ~ hausdorff(f16(u,v,w,x),y)
| limit_point(u,v,w,x)
| hausdorff(f16(u,v,w,x),z)
| eq(u,f19(f16(u,v,w,x),z)) ),
inference(res,[status(thm),theory(equality)],[677,855]),
[iquote('6:Res:677.1,855.0')] ).
cnf(1314,plain,
hausdorff(closure(u,v,w),x),
inference(obv,[status(thm),theory(equality)],[1313]),
[iquote('6:Obv:1313.1')] ).
cnf(873,plain,
( ~ hausdorff(f16(u,v,w,x),y)
| limit_point(u,v,w,x)
| hausdorff(f16(u,v,w,x),z)
| eq(u,f20(f16(u,v,w,x),z)) ),
inference(res,[status(thm),theory(equality)],[677,854]),
[iquote('6:Res:677.1,854.0')] ).
cnf(1297,plain,
hausdorff(boundary(u,v,w),x),
inference(obv,[status(thm),theory(equality)],[1296]),
[iquote('6:Obv:1296.1')] ).
cnf(1196,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ element_of_set(z,union_of_members(x1))
| ~ hausdorff(union_of_members(x1),x2)
| eq(z,f15(u,w,x,y,v)) ),
inference(res,[status(thm),theory(equality)],[578,867]),
[iquote('6:Res:578.1,867.0')] ).
cnf(1061,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| hausdorff(f10(w,v,u),y)
| eq(f20(f10(w,v,u),y),u) ),
inference(res,[status(thm),theory(equality)],[471,851]),
[iquote('6:Res:471.1,851.1')] ).
cnf(1062,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| hausdorff(f10(w,v,u),y)
| eq(f19(f10(w,v,u),y),u) ),
inference(res,[status(thm),theory(equality)],[472,851]),
[iquote('6:Res:472.1,851.1')] ).
cnf(893,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| hausdorff(f10(w,v,u),y)
| eq(u,f19(f10(w,v,u),y)) ),
inference(res,[status(thm),theory(equality)],[538,855]),
[iquote('6:Res:538.1,855.0')] ).
cnf(872,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| hausdorff(f10(w,v,u),y)
| eq(u,f20(f10(w,v,u),y)) ),
inference(res,[status(thm),theory(equality)],[538,854]),
[iquote('6:Res:538.1,854.0')] ).
cnf(913,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ element_of_set(z,interior(x1,x2,x3))
| ~ hausdorff(interior(x1,x2,x3),x4)
| eq(z,f15(v,y,w,x,u)) ),
inference(res,[status(thm),theory(equality)],[743,846]),
[iquote('6:Res:743.2,846.0')] ).
cnf(866,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ element_of_set(z,intersection_of_sets(u,y))
| ~ hausdorff(intersection_of_sets(u,y),x1)
| eq(z,f15(v,y,w,x,u)) ),
inference(res,[status(thm),theory(equality)],[68,846]),
[iquote('6:Res:68.2,846.0')] ).
cnf(1213,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ hausdorff(f6(v,y,u,w,x),z)
| eq(u,u) ),
inference(obv,[status(thm),theory(equality)],[1206]),
[iquote('6:Obv:1206.1')] ).
cnf(853,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ element_of_set(y,f6(v,z,u,w,x))
| ~ hausdorff(f6(v,z,u,w,x),x1)
| eq(y,u) ),
inference(res,[status(thm),theory(equality)],[606,846]),
[iquote('6:Res:606.2,846.0')] ).
cnf(867,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ element_of_set(z,union_of_members(x1))
| ~ hausdorff(union_of_members(x1),x2)
| eq(z,f15(v,y,w,x,u)) ),
inference(res,[status(thm),theory(equality)],[744,846]),
[iquote('6:Res:744.2,846.0')] ).
cnf(1041,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| hausdorff(f1(v,u),x)
| eq(f20(f1(v,u),x),u) ),
inference(res,[status(thm),theory(equality)],[471,848]),
[iquote('6:Res:471.1,848.1')] ).
cnf(1042,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| hausdorff(f1(v,u),x)
| eq(f19(f1(v,u),x),u) ),
inference(res,[status(thm),theory(equality)],[472,848]),
[iquote('6:Res:472.1,848.1')] ).
cnf(1193,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(f13(v,w,x,u),y)
| eq(u,u) ),
inference(obv,[status(thm),theory(equality)],[1186]),
[iquote('6:Obv:1186.0')] ).
cnf(850,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ element_of_set(y,f13(v,w,x,u))
| ~ hausdorff(f13(v,w,x,u),z)
| eq(y,u) ),
inference(res,[status(thm),theory(equality)],[52,846]),
[iquote('6:Res:52.1,846.0')] ).
cnf(890,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| hausdorff(f1(v,u),x)
| eq(u,f19(f1(v,u),x)) ),
inference(res,[status(thm),theory(equality)],[4,855]),
[iquote('6:Res:4.1,855.0')] ).
cnf(869,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| hausdorff(f1(v,u),x)
| eq(u,f20(f1(v,u),x)) ),
inference(res,[status(thm),theory(equality)],[4,854]),
[iquote('6:Res:4.1,854.0')] ).
cnf(1168,plain,
( ~ hausdorff(interior(u,v,w),x)
| limit_point(y,z,x1,x2)
| limit_point(x3,x4,x5,x6)
| eq(y,x3) ),
inference(res,[status(thm),theory(equality)],[678,849]),
[iquote('6:Res:678.1,849.0')] ).
cnf(1185,plain,
( ~ hausdorff(f16(u,v,w,x),y)
| limit_point(u,v,w,x)
| eq(u,u) ),
inference(obv,[status(thm),theory(equality)],[1178]),
[iquote('6:Obv:1178.1')] ).
cnf(852,plain,
( ~ element_of_set(u,f16(v,w,x,y))
| ~ hausdorff(f16(v,w,x,y),z)
| limit_point(v,w,x,y)
| eq(u,v) ),
inference(res,[status(thm),theory(equality)],[677,846]),
[iquote('6:Res:677.1,846.0')] ).
cnf(1171,plain,
( ~ hausdorff(interior(u,v,w),x)
| hausdorff(y,z)
| limit_point(x1,x2,x3,x4)
| eq(f20(y,z),x1) ),
inference(res,[status(thm),theory(equality)],[642,849]),
[iquote('6:Res:642.1,849.0')] ).
cnf(1172,plain,
( ~ hausdorff(interior(u,v,w),x)
| hausdorff(y,z)
| limit_point(x1,x2,x3,x4)
| eq(f19(y,z),x1) ),
inference(res,[status(thm),theory(equality)],[643,849]),
[iquote('6:Res:643.1,849.0')] ).
cnf(849,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(interior(v,w,x),y)
| limit_point(z,x1,x2,x3)
| eq(u,z) ),
inference(res,[status(thm),theory(equality)],[678,846]),
[iquote('6:Res:678.1,846.0')] ).
cnf(1158,plain,
( ~ hausdorff(interior(u,v,w),x)
| limit_point(y,z,x1,x2)
| hausdorff(x3,x4)
| eq(y,f20(x3,x4)) ),
inference(res,[status(thm),theory(equality)],[678,860]),
[iquote('6:Res:678.1,860.0')] ).
cnf(817,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)],[606,767]),
[iquote('4:Res:606.2,767.0')] ).
cnf(1161,plain,
( ~ hausdorff(interior(u,v,w),x)
| hausdorff(y,z)
| hausdorff(x1,x2)
| eq(f20(y,z),f20(x1,x2)) ),
inference(res,[status(thm),theory(equality)],[642,860]),
[iquote('6:Res:642.1,860.0')] ).
cnf(1162,plain,
( ~ hausdorff(interior(u,v,w),x)
| hausdorff(y,z)
| hausdorff(x1,x2)
| eq(f19(y,z),f20(x1,x2)) ),
inference(res,[status(thm),theory(equality)],[643,860]),
[iquote('6:Res:643.1,860.0')] ).
cnf(860,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(interior(v,w,x),y)
| hausdorff(z,x1)
| eq(u,f20(z,x1)) ),
inference(res,[status(thm),theory(equality)],[642,846]),
[iquote('6:Res:642.1,846.0')] ).
cnf(1148,plain,
( ~ hausdorff(interior(u,v,w),x)
| limit_point(y,z,x1,x2)
| hausdorff(x3,x4)
| eq(y,f19(x3,x4)) ),
inference(res,[status(thm),theory(equality)],[678,861]),
[iquote('6:Res:678.1,861.0')] ).
cnf(793,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)],[606,766]),
[iquote('4:Res:606.2,766.0')] ).
cnf(1151,plain,
( ~ hausdorff(interior(u,v,w),x)
| hausdorff(y,z)
| hausdorff(x1,x2)
| eq(f20(y,z),f19(x1,x2)) ),
inference(res,[status(thm),theory(equality)],[642,861]),
[iquote('6:Res:642.1,861.0')] ).
cnf(1152,plain,
( ~ hausdorff(interior(u,v,w),x)
| hausdorff(y,z)
| hausdorff(x1,x2)
| eq(f19(y,z),f19(x1,x2)) ),
inference(res,[status(thm),theory(equality)],[643,861]),
[iquote('6:Res:643.1,861.0')] ).
cnf(861,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(interior(v,w,x),y)
| hausdorff(z,x1)
| eq(u,f19(z,x1)) ),
inference(res,[status(thm),theory(equality)],[643,846]),
[iquote('6:Res:643.1,846.0')] ).
cnf(759,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)],[606,751]),
[iquote('4:Res:606.2,751.0')] ).
cnf(816,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)],[677,767]),
[iquote('4:Res:677.1,767.0')] ).
cnf(758,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)],[677,751]),
[iquote('4:Res:677.1,751.0')] ).
cnf(1067,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| eq(u,u) ),
inference(obv,[status(thm),theory(equality)],[1060]),
[iquote('6:Obv:1060.0')] ).
cnf(851,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,f10(x,v,u))
| ~ hausdorff(f10(x,v,u),y)
| eq(w,u) ),
inference(res,[status(thm),theory(equality)],[538,846]),
[iquote('6:Res:538.1,846.0')] ).
cnf(1059,plain,
( ~ subset_collections(u,f24(v,u))
| ~ compact_space(w,f24(v,u))
| compact_space(v,u) ),
inference(res,[status(thm),theory(equality)],[579,1058]),
[iquote('4:Res:579.1,1058.1')] ).
cnf(1058,plain,
( ~ compact_space(u,f24(v,w))
| ~ open_covering(w,u,f24(v,w))
| compact_space(v,w) ),
inference(obv,[status(thm),theory(equality)],[1057]),
[iquote('4:Obv:1057.1')] ).
cnf(1038,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)],[579,712]),
[iquote('4:Res:579.1,712.2')] ).
cnf(1052,plain,
hausdorff(intersection_of_members(u),v),
inference(obv,[status(thm),theory(equality)],[1051]),
[iquote('6:Obv:1051.1')] ).
cnf(792,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)],[677,766]),
[iquote('4:Res:677.1,766.0')] ).
cnf(757,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)],[538,751]),
[iquote('4:Res:538.1,751.0')] ).
cnf(1049,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| eq(u,u) ),
inference(obv,[status(thm),theory(equality)],[1040]),
[iquote('6:Obv:1040.0')] ).
cnf(848,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ element_of_set(w,f1(v,u))
| ~ hausdorff(f1(v,u),x)
| eq(w,u) ),
inference(res,[status(thm),theory(equality)],[4,846]),
[iquote('6:Res:4.1,846.0')] ).
cnf(776,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)],[756,643]),
[iquote('4:MRR:756.0,643.1')] ).
cnf(712,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)],[710,104]),
[iquote('0:MRR:710.0,104.2')] ).
cnf(1034,plain,
( ~ compact_set(u,v,w)
| compact_space(x,subspace_topology(v,w,u)) ),
inference(res,[status(thm),theory(equality)],[111,1032]),
[iquote('4:Res:111.1,1032.0')] ).
cnf(1033,plain,
compact_space(u,ct),
inference(res,[status(thm),theory(equality)],[188,1032]),
[iquote('4:Res:188.0,1032.0')] ).
cnf(1032,plain,
( ~ compact_space(u,v)
| compact_space(w,v) ),
inference(mrr,[status(thm)],[1031,474]),
[iquote('4:MRR:1031.0,474.1')] ).
cnf(922,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)],[579,711]),
[iquote('4:Res:579.1,711.2')] ).
cnf(1013,plain,
( ~ limit_point(u,v,w,x)
| limit_point(u,v,y,z) ),
inference(mrr,[status(thm)],[1011,677]),
[iquote('4:MRR:1011.0,677.1')] ).
cnf(745,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)],[68,595]),
[iquote('4:Res:68.2,595.0')] ).
cnf(993,plain,
( ~ hausdorff(union_of_members(u),v)
| limit_point(w,x,y,z)
| limit_point(x1,x2,x3,x4)
| eq(w,x1) ),
inference(res,[status(thm),theory(equality)],[679,847]),
[iquote('6:Res:679.1,847.0')] ).
cnf(997,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(w,x)
| limit_point(y,z,x1,x2)
| eq(f19(w,x),y) ),
inference(res,[status(thm),theory(equality)],[616,847]),
[iquote('6:Res:616.1,847.0')] ).
cnf(996,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(w,x)
| limit_point(y,z,x1,x2)
| eq(f20(w,x),y) ),
inference(res,[status(thm),theory(equality)],[613,847]),
[iquote('6:Res:613.1,847.0')] ).
cnf(937,plain,
( ~ hausdorff(union_of_members(u),v)
| limit_point(w,x,y,z)
| hausdorff(x1,x2)
| eq(w,f19(x1,x2)) ),
inference(res,[status(thm),theory(equality)],[679,857]),
[iquote('6:Res:679.1,857.0')] ).
cnf(750,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)],[587,118]),
[iquote('4:Res:587.1,118.1')] ).
cnf(925,plain,
( ~ hausdorff(union_of_members(u),v)
| limit_point(w,x,y,z)
| hausdorff(x1,x2)
| eq(w,f20(x1,x2)) ),
inference(res,[status(thm),theory(equality)],[679,856]),
[iquote('6:Res:679.1,856.0')] ).
cnf(941,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(w,x)
| hausdorff(y,z)
| eq(f19(w,x),f19(y,z)) ),
inference(res,[status(thm),theory(equality)],[616,857]),
[iquote('6:Res:616.1,857.0')] ).
cnf(940,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(w,x)
| hausdorff(y,z)
| eq(f20(w,x),f19(y,z)) ),
inference(res,[status(thm),theory(equality)],[613,857]),
[iquote('6:Res:613.1,857.0')] ).
cnf(929,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(w,x)
| hausdorff(y,z)
| eq(f19(w,x),f20(y,z)) ),
inference(res,[status(thm),theory(equality)],[616,856]),
[iquote('6:Res:616.1,856.0')] ).
cnf(717,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)],[471,595]),
[iquote('4:Res:471.1,595.0')] ).
cnf(928,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(w,x)
| hausdorff(y,z)
| eq(f20(w,x),f20(y,z)) ),
inference(res,[status(thm),theory(equality)],[613,856]),
[iquote('6:Res:613.1,856.0')] ).
cnf(847,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(union_of_members(v),w)
| limit_point(x,y,z,x1)
| eq(u,x) ),
inference(res,[status(thm),theory(equality)],[679,846]),
[iquote('6:Res:679.1,846.0')] ).
cnf(718,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)],[472,595]),
[iquote('4:Res:472.1,595.0')] ).
cnf(857,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(union_of_members(v),w)
| hausdorff(x,y)
| eq(u,f19(x,y)) ),
inference(res,[status(thm),theory(equality)],[616,846]),
[iquote('6:Res:616.1,846.0')] ).
cnf(856,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(union_of_members(v),w)
| hausdorff(x,y)
| eq(u,f20(x,y)) ),
inference(res,[status(thm),theory(equality)],[613,846]),
[iquote('6:Res:613.1,846.0')] ).
cnf(897,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(u,x)
| eq(f19(u,w),f19(u,x)) ),
inference(res,[status(thm),theory(equality)],[472,855]),
[iquote('6:Res:472.1,855.0')] ).
cnf(896,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(u,x)
| eq(f20(u,w),f19(u,x)) ),
inference(res,[status(thm),theory(equality)],[471,855]),
[iquote('6:Res:471.1,855.0')] ).
cnf(711,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)],[708,104]),
[iquote('0:MRR:708.0,104.2')] ).
cnf(918,plain,
hausdorff(cx,u),
inference(obv,[status(thm),theory(equality)],[917]),
[iquote('6:Obv:917.1')] ).
cnf(876,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(u,x)
| eq(f19(u,w),f20(u,x)) ),
inference(res,[status(thm),theory(equality)],[472,854]),
[iquote('6:Res:472.1,854.0')] ).
cnf(743,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)],[68,585]),
[iquote('4:Res:68.2,585.0')] ).
cnf(875,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(u,x)
| eq(f20(u,w),f20(u,x)) ),
inference(res,[status(thm),theory(equality)],[471,854]),
[iquote('6:Res:471.1,854.0')] ).
cnf(855,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(v,w)
| hausdorff(v,x)
| eq(u,f19(v,x)) ),
inference(res,[status(thm),theory(equality)],[472,846]),
[iquote('6:Res:472.1,846.0')] ).
cnf(854,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(v,w)
| hausdorff(v,x)
| eq(u,f20(v,x)) ),
inference(res,[status(thm),theory(equality)],[471,846]),
[iquote('6:Res:471.1,846.0')] ).
cnf(846,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(v,x)
| eq(w,u) ),
inference(spt,[],[835]),
[iquote('6:Spt:835.0,835.1,835.2,835.3')] ).
cnf(815,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)],[538,767]),
[iquote('4:Res:538.1,767.0')] ).
cnf(791,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)],[538,766]),
[iquote('4:Res:538.1,766.0')] ).
cnf(771,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(f1(x,f19(u,v)),w)
| hausdorff(u,v) ),
inference(mrr,[status(thm)],[754,616]),
[iquote('4:MRR:754.0,616.1')] ).
cnf(770,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(interior(x,y,z),w)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[763]),
[iquote('4:Obv:763.2')] ).
cnf(831,plain,
( ~ disjoint_s(union_of_members(u),f13(v,w,x,f20(y,z)))
| hausdorff(y,z) ),
inference(mrr,[status(thm)],[814,642]),
[iquote('4:MRR:814.0,642.1')] ).
cnf(830,plain,
( ~ disjoint_s(union_of_members(u),f1(v,f20(w,x)))
| hausdorff(w,x) ),
inference(mrr,[status(thm)],[812,613]),
[iquote('4:MRR:812.0,613.1')] ).
cnf(827,plain,
( ~ disjoint_s(union_of_members(u),interior(v,w,x))
| hausdorff(y,z) ),
inference(obv,[status(thm),theory(equality)],[821]),
[iquote('4:Obv:821.1')] ).
cnf(825,plain,
( ~ disjoint_s(union_of_members(u),union_of_members(v))
| hausdorff(w,x) ),
inference(obv,[status(thm),theory(equality)],[819]),
[iquote('4:Obv:819.1')] ).
cnf(824,plain,
( ~ disjoint_s(union_of_members(u),v)
| hausdorff(v,w) ),
inference(obv,[status(thm),theory(equality)],[818]),
[iquote('4:Obv:818.1')] ).
cnf(767,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(union_of_members(x),w)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[761]),
[iquote('4:Obv:761.2')] ).
cnf(807,plain,
( ~ disjoint_s(u,f13(v,w,x,f20(u,y)))
| hausdorff(u,y) ),
inference(mrr,[status(thm)],[790,642]),
[iquote('4:MRR:790.0,642.1')] ).
cnf(804,plain,
( ~ disjoint_s(u,f1(v,f20(u,w)))
| hausdorff(u,w) ),
inference(mrr,[status(thm)],[788,613]),
[iquote('4:MRR:788.0,613.1')] ).
cnf(803,plain,
( ~ disjoint_s(u,interior(v,w,x))
| hausdorff(u,y) ),
inference(obv,[status(thm),theory(equality)],[797]),
[iquote('4:Obv:797.1')] ).
cnf(801,plain,
( ~ disjoint_s(u,union_of_members(v))
| hausdorff(u,w) ),
inference(obv,[status(thm),theory(equality)],[795]),
[iquote('4:Obv:795.1')] ).
cnf(800,plain,
( ~ disjoint_s(u,u)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[794]),
[iquote('4:Obv:794.1')] ).
cnf(766,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(u,w)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[760]),
[iquote('4:Obv:760.2')] ).
cnf(782,plain,
( ~ disjoint_s(u,v)
| equal_sets(v,empty_set)
| equal_sets(u,empty_set) ),
inference(mrr,[status(thm)],[737,778]),
[iquote('5:MRR:737.1,778.0')] ).
cnf(779,plain,
~ separation(u,v,w,x),
inference(mrr,[status(thm)],[93,778]),
[iquote('5:MRR:93.0,778.0')] ).
cnf(780,plain,
connected_set(u,v,w),
inference(mrr,[status(thm)],[583,778]),
[iquote('5:MRR:583.0,778.0')] ).
cnf(778,plain,
connected_space(u,v),
inference(spt,[],[777]),
[iquote('5:Spt:777.0')] ).
cnf(751,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)],[578,749]),
[iquote('4:Res:578.1,749.2')] ).
cnf(749,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)],[578,118]),
[iquote('4:Res:578.1,118.1')] ).
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(744,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)],[68,470]),
[iquote('4:Res:68.2,470.0')] ).
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('TOP015-1.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('TOP015-1.p',unknown),
[] ).
cnf(595,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)],[504,482]),
[iquote('4:MRR:504.0,482.0')] ).
cnf(606,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)],[540,597]),
[iquote('4:MRR:540.1,597.0')] ).
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(700,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('TOP015-1.p',unknown),
[] ).
cnf(678,plain,
( limit_point(u,v,w,x)
| element_of_set(u,interior(y,z,x1)) ),
inference(res,[status(thm),theory(equality)],[677,585]),
[iquote('4:Res:677.1,585.0')] ).
cnf(680,plain,
( ~ element_of_set(u,boundary(v,w,x))
| element_of_set(u,y) ),
inference(res,[status(thm),theory(equality)],[74,584]),
[iquote('4:Res:74.1,584.0')] ).
cnf(679,plain,
( limit_point(u,v,w,x)
| element_of_set(u,union_of_members(y)) ),
inference(res,[status(thm),theory(equality)],[677,470]),
[iquote('4:Res:677.1,470.0')] ).
cnf(677,plain,
( limit_point(u,v,w,x)
| element_of_set(u,f16(u,v,w,x)) ),
inference(res,[status(thm),theory(equality)],[587,64]),
[iquote('4:Res:587.1,64.0')] ).
cnf(587,plain,
( limit_point(u,v,w,x)
| neighborhood(f16(u,v,w,x),u,w,x) ),
inference(mrr,[status(thm)],[501,482]),
[iquote('4:MRR:501.0,482.0')] ).
cnf(588,plain,
( ~ element_of_set(u,f14(v,w,x,u))
| element_of_set(u,closure(v,w,x)) ),
inference(mrr,[status(thm)],[502,482]),
[iquote('4:MRR:502.0,482.0')] ).
cnf(643,plain,
( hausdorff(u,v)
| element_of_set(f19(u,v),interior(w,x,y)) ),
inference(res,[status(thm),theory(equality)],[472,585]),
[iquote('4:Res:472.1,585.0')] ).
cnf(642,plain,
( hausdorff(u,v)
| element_of_set(f20(u,v),interior(w,x,y)) ),
inference(res,[status(thm),theory(equality)],[471,585]),
[iquote('4:Res:471.1,585.0')] ).
cnf(582,plain,
( ~ compact_space(u,subspace_topology(v,w,u))
| compact_set(u,v,w) ),
inference(mrr,[status(thm)],[498,482]),
[iquote('4:MRR:498.0,482.0')] ).
cnf(477,plain,
( ~ eq(f19(u,v),f20(u,v))
| hausdorff(u,v) ),
inference(mrr,[status(thm)],[82,465]),
[iquote('4:MRR:82.0,465.0')] ).
cnf(585,plain,
( ~ element_of_set(u,v)
| element_of_set(u,interior(w,x,y)) ),
inference(mrr,[status(thm)],[560,577]),
[iquote('4:MRR:560.1,577.0')] ).
cnf(584,plain,
( ~ element_of_set(u,closure(v,w,x))
| element_of_set(u,y) ),
inference(mrr,[status(thm)],[559,481]),
[iquote('4:MRR:559.1,481.0')] ).
cnf(538,plain,
( ~ element_of_set(u,v)
| element_of_set(u,f10(w,v,u)) ),
inference(mrr,[status(thm)],[40,468]),
[iquote('4:MRR:40.1,468.0')] ).
cnf(578,plain,
( ~ element_of_set(u,v)
| neighborhood(v,u,w,x) ),
inference(mrr,[status(thm)],[114,577]),
[iquote('4:MRR:114.1,577.0')] ).
cnf(543,plain,
equal_sets(u,intersection_of_sets(v,f12(w,x,v,u))),
inference(mrr,[status(thm)],[48,468]),
[iquote('4:MRR:48.0,468.0')] ).
cnf(616,plain,
( hausdorff(u,v)
| element_of_set(f19(u,v),union_of_members(w)) ),
inference(res,[status(thm),theory(equality)],[472,470]),
[iquote('4:Res:472.1,470.0')] ).
cnf(473,plain,
( compact_space(u,v)
| open_covering(f24(u,v),u,v) ),
inference(mrr,[status(thm)],[107,465]),
[iquote('4:MRR:107.0,465.0')] ).
cnf(613,plain,
( hausdorff(u,v)
| element_of_set(f20(u,v),union_of_members(w)) ),
inference(res,[status(thm),theory(equality)],[471,470]),
[iquote('4:Res:471.1,470.0')] ).
cnf(579,plain,
( ~ subset_collections(u,v)
| open_covering(u,w,v) ),
inference(mrr,[status(thm)],[516,469]),
[iquote('4:MRR:516.1,469.0')] ).
cnf(474,plain,
( compact_space(u,v)
| subset_collections(f24(u,v),v) ),
inference(mrr,[status(thm)],[308,465]),
[iquote('4:MRR:308.0,465.0')] ).
cnf(515,plain,
( ~ subset_collections(u,v)
| finer(v,u,w) ),
inference(mrr,[status(thm)],[30,465]),
[iquote('4:MRR:30.1,30.2,465.0')] ).
cnf(472,plain,
( hausdorff(u,v)
| element_of_set(f19(u,v),u) ),
inference(mrr,[status(thm)],[80,465]),
[iquote('4:MRR:80.0,465.0')] ).
cnf(471,plain,
( hausdorff(u,v)
| element_of_set(f20(u,v),u) ),
inference(mrr,[status(thm)],[81,465]),
[iquote('4:MRR:81.0,465.0')] ).
cnf(534,plain,
( ~ element_of_set(u,intersection_of_members(v))
| element_of_set(u,w) ),
inference(mrr,[status(thm)],[7,468]),
[iquote('4:MRR:7.0,468.0')] ).
cnf(470,plain,
( ~ element_of_set(u,v)
| element_of_set(u,union_of_members(w)) ),
inference(mrr,[status(thm)],[238,465]),
[iquote('4:MRR:238.0,465.0')] ).
cnf(577,plain,
open(u,v,w),
inference(mrr,[status(thm)],[479,468]),
[iquote('4:MRR:479.0,468.0')] ).
cnf(481,plain,
closed(u,v,w),
inference(mrr,[status(thm)],[329,465]),
[iquote('4:MRR:329.0,329.1,465.0')] ).
cnf(469,plain,
equal_sets(union_of_members(u),v),
inference(mrr,[status(thm)],[10,465]),
[iquote('4:MRR:10.0,465.0')] ).
cnf(597,plain,
basis(u,v),
inference(mrr,[status(thm)],[565,596]),
[iquote('4:MRR:565.1,596.0')] ).
cnf(482,plain,
subset_sets(u,v),
inference(mrr,[status(thm)],[190,465]),
[iquote('4:MRR:190.0,465.0')] ).
cnf(468,plain,
element_of_collection(u,v),
inference(mrr,[status(thm)],[12,465]),
[iquote('4:MRR:12.0,465.0')] ).
cnf(465,plain,
topological_space(u,v),
inference(spt,[],[464]),
[iquote('4:Spt:464.1')] ).
cnf(105,axiom,
( ~ compact_space(u,v)
| ~ open_covering(w,u,v)
| subset_collections(f23(u,v,w),w) ),
file('TOP015-1.p',unknown),
[] ).
cnf(52,axiom,
( ~ element_of_set(u,interior(v,w,x))
| element_of_set(u,f13(v,w,x,u)) ),
file('TOP015-1.p',unknown),
[] ).
cnf(104,axiom,
( ~ compact_space(u,v)
| ~ open_covering(w,u,v)
| finite(f23(u,v,w)) ),
file('TOP015-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal_sets(intersection_of_sets(interior(a,cx,ct),boundary(a,cx,ct)),empty_set),
file('TOP015-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ element_of_set(u,f2(v,u))
| element_of_set(u,intersection_of_members(v)) ),
file('TOP015-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ element_of_set(u,union_of_members(v))
| element_of_set(u,f1(v,u)) ),
file('TOP015-1.p',unknown),
[] ).
cnf(64,axiom,
( ~ neighborhood(u,v,w,x)
| element_of_set(v,u) ),
file('TOP015-1.p',unknown),
[] ).
cnf(100,axiom,
( ~ open_covering(u,v,w)
| subset_collections(u,w) ),
file('TOP015-1.p',unknown),
[] ).
cnf(29,axiom,
( ~ finer(u,v,w)
| subset_collections(v,u) ),
file('TOP015-1.p',unknown),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.07 % Problem : TOP015-1 : TPTP v8.1.0. Released v1.0.0.
% 0.01/0.07 % Command : run_spass %d %s
% 0.08/0.25 % Computer : n026.cluster.edu
% 0.08/0.25 % Model : x86_64 x86_64
% 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.25 % Memory : 8042.1875MB
% 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 600
% 0.08/0.25 % DateTime : Sun May 29 12:07:24 EDT 2022
% 0.08/0.25 % CPUTime :
% 0.11/0.45
% 0.11/0.45 SPASS V 3.9
% 0.11/0.45 SPASS beiseite: Completion found.
% 0.11/0.45 % SZS status CounterSatisfiable
% 0.11/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.45 SPASS derived 1148 clauses, backtracked 0 clauses, performed 6 splits and kept 778 clauses.
% 0.11/0.45 SPASS allocated 77171 KBytes.
% 0.11/0.45 SPASS spent 0:00:00.20 on the problem.
% 0.11/0.45 0:00:00.03 for the input.
% 0.11/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.11/0.45 0:00:00.02 for inferences.
% 0.11/0.45 0:00:00.00 for the backtracking.
% 0.11/0.45 0:00:00.12 for the reduction.
% 0.11/0.45
% 0.11/0.45
% 0.11/0.45 The saturated set of worked-off clauses is :
% 0.11/0.45 % SZS output start Saturation
% See solution above
%------------------------------------------------------------------------------