TSTP Solution File: TOP010-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : TOP010-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 0.80s 1.03s
% Output : Saturation 0.80s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 80)
% Comments :
%------------------------------------------------------------------------------
cnf(1896,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f19(boundary(z,x1,x2),x3),u)
| hausdorff(boundary(x4,x5,x6),x7)
| eq(f19(boundary(x4,x5,x6),x7),w)
| eq(f15(u,x,x8,x9,v),f15(w,x,x10,x11,v)) ),
inference(res,[status(thm),theory(equality)],[626,1825]),
[iquote('3:Res:626.2,1825.1')] ).
cnf(1897,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f19(closure(z,x1,x2),x3),u)
| hausdorff(boundary(x4,x5,x6),x7)
| eq(f19(boundary(x4,x5,x6),x7),w)
| eq(f15(u,x,x8,x9,v),f15(w,x,x10,x11,v)) ),
inference(res,[status(thm),theory(equality)],[625,1825]),
[iquote('3:Res:625.2,1825.1')] ).
cnf(1898,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f20(boundary(z,x1,x2),x3),u)
| hausdorff(boundary(x4,x5,x6),x7)
| eq(f19(boundary(x4,x5,x6),x7),w)
| eq(f15(u,x,x8,x9,v),f15(w,x,x10,x11,v)) ),
inference(res,[status(thm),theory(equality)],[624,1825]),
[iquote('3:Res:624.2,1825.1')] ).
cnf(1899,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f20(closure(z,x1,x2),x3),u)
| hausdorff(boundary(x4,x5,x6),x7)
| eq(f19(boundary(x4,x5,x6),x7),w)
| eq(f15(u,x,x8,x9,v),f15(w,x,x10,x11,v)) ),
inference(res,[status(thm),theory(equality)],[623,1825]),
[iquote('3:Res:623.2,1825.1')] ).
cnf(1882,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f19(boundary(z,x1,x2),x3),u)
| hausdorff(closure(x4,x5,x6),x7)
| eq(f19(closure(x4,x5,x6),x7),w)
| eq(f15(u,x,x8,x9,v),f15(w,x,x10,x11,v)) ),
inference(res,[status(thm),theory(equality)],[626,1823]),
[iquote('3:Res:626.2,1823.1')] ).
cnf(1883,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f19(closure(z,x1,x2),x3),u)
| hausdorff(closure(x4,x5,x6),x7)
| eq(f19(closure(x4,x5,x6),x7),w)
| eq(f15(u,x,x8,x9,v),f15(w,x,x10,x11,v)) ),
inference(res,[status(thm),theory(equality)],[625,1823]),
[iquote('3:Res:625.2,1823.1')] ).
cnf(1884,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f20(boundary(z,x1,x2),x3),u)
| hausdorff(closure(x4,x5,x6),x7)
| eq(f19(closure(x4,x5,x6),x7),w)
| eq(f15(u,x,x8,x9,v),f15(w,x,x10,x11,v)) ),
inference(res,[status(thm),theory(equality)],[624,1823]),
[iquote('3:Res:624.2,1823.1')] ).
cnf(1885,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f20(closure(z,x1,x2),x3),u)
| hausdorff(closure(x4,x5,x6),x7)
| eq(f19(closure(x4,x5,x6),x7),w)
| eq(f15(u,x,x8,x9,v),f15(w,x,x10,x11,v)) ),
inference(res,[status(thm),theory(equality)],[623,1823]),
[iquote('3:Res:623.2,1823.1')] ).
cnf(1868,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f19(boundary(z,x1,x2),x3),u)
| hausdorff(boundary(x4,x5,x6),x7)
| eq(f20(boundary(x4,x5,x6),x7),w)
| eq(f15(u,x,x8,x9,v),f15(w,x,x10,x11,v)) ),
inference(res,[status(thm),theory(equality)],[626,1807]),
[iquote('3:Res:626.2,1807.1')] ).
cnf(1869,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f19(closure(z,x1,x2),x3),u)
| hausdorff(boundary(x4,x5,x6),x7)
| eq(f20(boundary(x4,x5,x6),x7),w)
| eq(f15(u,x,x8,x9,v),f15(w,x,x10,x11,v)) ),
inference(res,[status(thm),theory(equality)],[625,1807]),
[iquote('3:Res:625.2,1807.1')] ).
cnf(1870,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f20(boundary(z,x1,x2),x3),u)
| hausdorff(boundary(x4,x5,x6),x7)
| eq(f20(boundary(x4,x5,x6),x7),w)
| eq(f15(u,x,x8,x9,v),f15(w,x,x10,x11,v)) ),
inference(res,[status(thm),theory(equality)],[624,1807]),
[iquote('3:Res:624.2,1807.1')] ).
cnf(1871,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f20(closure(z,x1,x2),x3),u)
| hausdorff(boundary(x4,x5,x6),x7)
| eq(f20(boundary(x4,x5,x6),x7),w)
| eq(f15(u,x,x8,x9,v),f15(w,x,x10,x11,v)) ),
inference(res,[status(thm),theory(equality)],[623,1807]),
[iquote('3:Res:623.2,1807.1')] ).
cnf(1854,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f19(boundary(z,x1,x2),x3),u)
| hausdorff(closure(x4,x5,x6),x7)
| eq(f20(closure(x4,x5,x6),x7),w)
| eq(f15(u,x,x8,x9,v),f15(w,x,x10,x11,v)) ),
inference(res,[status(thm),theory(equality)],[626,1777]),
[iquote('3:Res:626.2,1777.1')] ).
cnf(1855,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f19(closure(z,x1,x2),x3),u)
| hausdorff(closure(x4,x5,x6),x7)
| eq(f20(closure(x4,x5,x6),x7),w)
| eq(f15(u,x,x8,x9,v),f15(w,x,x10,x11,v)) ),
inference(res,[status(thm),theory(equality)],[625,1777]),
[iquote('3:Res:625.2,1777.1')] ).
cnf(1856,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f20(boundary(z,x1,x2),x3),u)
| hausdorff(closure(x4,x5,x6),x7)
| eq(f20(closure(x4,x5,x6),x7),w)
| eq(f15(u,x,x8,x9,v),f15(w,x,x10,x11,v)) ),
inference(res,[status(thm),theory(equality)],[624,1777]),
[iquote('3:Res:624.2,1777.1')] ).
cnf(1857,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f20(closure(z,x1,x2),x3),u)
| hausdorff(closure(x4,x5,x6),x7)
| eq(f20(closure(x4,x5,x6),x7),w)
| eq(f15(u,x,x8,x9,v),f15(w,x,x10,x11,v)) ),
inference(res,[status(thm),theory(equality)],[623,1777]),
[iquote('3:Res:623.2,1777.1')] ).
cnf(1814,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f19(boundary(x1,x2,x3),x4),u)
| hausdorff(boundary(x5,x6,x7),x8)
| eq(f19(boundary(x5,x6,x7),x8),w)
| eq(f15(u,x9,x10,x11,v),f15(w,x12,x13,x14,x)) ),
inference(res,[status(thm),theory(equality)],[626,1761]),
[iquote('3:Res:626.2,1761.1')] ).
cnf(1815,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f19(closure(x1,x2,x3),x4),u)
| hausdorff(boundary(x5,x6,x7),x8)
| eq(f19(boundary(x5,x6,x7),x8),w)
| eq(f15(u,x9,x10,x11,v),f15(w,x12,x13,x14,x)) ),
inference(res,[status(thm),theory(equality)],[625,1761]),
[iquote('3:Res:625.2,1761.1')] ).
cnf(1816,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f20(boundary(x1,x2,x3),x4),u)
| hausdorff(boundary(x5,x6,x7),x8)
| eq(f19(boundary(x5,x6,x7),x8),w)
| eq(f15(u,x9,x10,x11,v),f15(w,x12,x13,x14,x)) ),
inference(res,[status(thm),theory(equality)],[624,1761]),
[iquote('3:Res:624.2,1761.1')] ).
cnf(1817,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f20(closure(x1,x2,x3),x4),u)
| hausdorff(boundary(x5,x6,x7),x8)
| eq(f19(boundary(x5,x6,x7),x8),w)
| eq(f15(u,x9,x10,x11,v),f15(w,x12,x13,x14,x)) ),
inference(res,[status(thm),theory(equality)],[623,1761]),
[iquote('3:Res:623.2,1761.1')] ).
cnf(1798,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f19(boundary(x1,x2,x3),x4),u)
| hausdorff(closure(x5,x6,x7),x8)
| eq(f19(closure(x5,x6,x7),x8),w)
| eq(f15(u,x9,x10,x11,v),f15(w,x12,x13,x14,x)) ),
inference(res,[status(thm),theory(equality)],[626,1737]),
[iquote('3:Res:626.2,1737.1')] ).
cnf(1799,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f19(closure(x1,x2,x3),x4),u)
| hausdorff(closure(x5,x6,x7),x8)
| eq(f19(closure(x5,x6,x7),x8),w)
| eq(f15(u,x9,x10,x11,v),f15(w,x12,x13,x14,x)) ),
inference(res,[status(thm),theory(equality)],[625,1737]),
[iquote('3:Res:625.2,1737.1')] ).
cnf(1800,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f20(boundary(x1,x2,x3),x4),u)
| hausdorff(closure(x5,x6,x7),x8)
| eq(f19(closure(x5,x6,x7),x8),w)
| eq(f15(u,x9,x10,x11,v),f15(w,x12,x13,x14,x)) ),
inference(res,[status(thm),theory(equality)],[624,1737]),
[iquote('3:Res:624.2,1737.1')] ).
cnf(1801,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f20(closure(x1,x2,x3),x4),u)
| hausdorff(closure(x5,x6,x7),x8)
| eq(f19(closure(x5,x6,x7),x8),w)
| eq(f15(u,x9,x10,x11,v),f15(w,x12,x13,x14,x)) ),
inference(res,[status(thm),theory(equality)],[623,1737]),
[iquote('3:Res:623.2,1737.1')] ).
cnf(1784,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f19(boundary(x1,x2,x3),x4),u)
| hausdorff(boundary(x5,x6,x7),x8)
| eq(f20(boundary(x5,x6,x7),x8),w)
| eq(f15(u,x9,x10,x11,v),f15(w,x12,x13,x14,x)) ),
inference(res,[status(thm),theory(equality)],[626,1735]),
[iquote('3:Res:626.2,1735.1')] ).
cnf(1785,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f19(closure(x1,x2,x3),x4),u)
| hausdorff(boundary(x5,x6,x7),x8)
| eq(f20(boundary(x5,x6,x7),x8),w)
| eq(f15(u,x9,x10,x11,v),f15(w,x12,x13,x14,x)) ),
inference(res,[status(thm),theory(equality)],[625,1735]),
[iquote('3:Res:625.2,1735.1')] ).
cnf(1786,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f20(boundary(x1,x2,x3),x4),u)
| hausdorff(boundary(x5,x6,x7),x8)
| eq(f20(boundary(x5,x6,x7),x8),w)
| eq(f15(u,x9,x10,x11,v),f15(w,x12,x13,x14,x)) ),
inference(res,[status(thm),theory(equality)],[624,1735]),
[iquote('3:Res:624.2,1735.1')] ).
cnf(1787,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f20(closure(x1,x2,x3),x4),u)
| hausdorff(boundary(x5,x6,x7),x8)
| eq(f20(boundary(x5,x6,x7),x8),w)
| eq(f15(u,x9,x10,x11,v),f15(w,x12,x13,x14,x)) ),
inference(res,[status(thm),theory(equality)],[623,1735]),
[iquote('3:Res:623.2,1735.1')] ).
cnf(1768,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f19(boundary(x1,x2,x3),x4),u)
| hausdorff(closure(x5,x6,x7),x8)
| eq(f20(closure(x5,x6,x7),x8),w)
| eq(f15(u,x9,x10,x11,v),f15(w,x12,x13,x14,x)) ),
inference(res,[status(thm),theory(equality)],[626,1733]),
[iquote('3:Res:626.2,1733.1')] ).
cnf(1769,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f19(closure(x1,x2,x3),x4),u)
| hausdorff(closure(x5,x6,x7),x8)
| eq(f20(closure(x5,x6,x7),x8),w)
| eq(f15(u,x9,x10,x11,v),f15(w,x12,x13,x14,x)) ),
inference(res,[status(thm),theory(equality)],[625,1733]),
[iquote('3:Res:625.2,1733.1')] ).
cnf(1770,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f20(boundary(x1,x2,x3),x4),u)
| hausdorff(closure(x5,x6,x7),x8)
| eq(f20(closure(x5,x6,x7),x8),w)
| eq(f15(u,x9,x10,x11,v),f15(w,x12,x13,x14,x)) ),
inference(res,[status(thm),theory(equality)],[624,1733]),
[iquote('3:Res:624.2,1733.1')] ).
cnf(1771,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f20(closure(x1,x2,x3),x4),u)
| hausdorff(closure(x5,x6,x7),x8)
| eq(f20(closure(x5,x6,x7),x8),w)
| eq(f15(u,x9,x10,x11,v),f15(w,x12,x13,x14,x)) ),
inference(res,[status(thm),theory(equality)],[623,1733]),
[iquote('3:Res:623.2,1733.1')] ).
cnf(1894,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f19(intersection_of_members(z),x1),u)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f19(boundary(x2,x3,x4),x5),w)
| eq(f15(u,x,x6,x7,v),f15(w,x,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[622,1825]),
[iquote('3:Res:622.2,1825.1')] ).
cnf(1826,plain,
( ~ limit_point(u,v,w,x)
| ~ element_of_set(y,f16(u,z,w,x))
| ~ hausdorff(intersection_of_sets(f16(u,z,w,x),v),x1)
| limit_point(u,z,w,x)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f19(boundary(x2,x3,x4),x5),y)
| eq(f15(u,v,w,x,f16(u,z,w,x)),f15(y,v,x6,x7,f16(u,z,w,x))) ),
inference(res,[status(thm),theory(equality)],[493,1558]),
[iquote('3:Res:493.1,1558.0')] ).
cnf(1895,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f20(intersection_of_members(z),x1),u)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f19(boundary(x2,x3,x4),x5),w)
| eq(f15(u,x,x6,x7,v),f15(w,x,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[621,1825]),
[iquote('3:Res:621.2,1825.1')] ).
cnf(1880,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f19(intersection_of_members(z),x1),u)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f19(closure(x2,x3,x4),x5),w)
| eq(f15(u,x,x6,x7,v),f15(w,x,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[622,1823]),
[iquote('3:Res:622.2,1823.1')] ).
cnf(1881,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f20(intersection_of_members(z),x1),u)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f19(closure(x2,x3,x4),x5),w)
| eq(f15(u,x,x6,x7,v),f15(w,x,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[621,1823]),
[iquote('3:Res:621.2,1823.1')] ).
cnf(1866,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f19(intersection_of_members(z),x1),u)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f20(boundary(x2,x3,x4),x5),w)
| eq(f15(u,x,x6,x7,v),f15(w,x,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[622,1807]),
[iquote('3:Res:622.2,1807.1')] ).
cnf(1824,plain,
( ~ limit_point(u,v,w,x)
| ~ element_of_set(y,f16(u,z,w,x))
| ~ hausdorff(intersection_of_sets(f16(u,z,w,x),v),x1)
| limit_point(u,z,w,x)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f19(closure(x2,x3,x4),x5),y)
| eq(f15(u,v,w,x,f16(u,z,w,x)),f15(y,v,x6,x7,f16(u,z,w,x))) ),
inference(res,[status(thm),theory(equality)],[493,1549]),
[iquote('3:Res:493.1,1549.0')] ).
cnf(1867,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f20(intersection_of_members(z),x1),u)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f20(boundary(x2,x3,x4),x5),w)
| eq(f15(u,x,x6,x7,v),f15(w,x,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[621,1807]),
[iquote('3:Res:621.2,1807.1')] ).
cnf(1852,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f19(intersection_of_members(z),x1),u)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f20(closure(x2,x3,x4),x5),w)
| eq(f15(u,x,x6,x7,v),f15(w,x,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[622,1777]),
[iquote('3:Res:622.2,1777.1')] ).
cnf(1853,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f20(intersection_of_members(z),x1),u)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f20(closure(x2,x3,x4),x5),w)
| eq(f15(u,x,x6,x7,v),f15(w,x,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[621,1777]),
[iquote('3:Res:621.2,1777.1')] ).
cnf(1724,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f19(boundary(z,x1,x2),x3),u)
| hausdorff(intersection_of_members(x4),x5)
| eq(f19(intersection_of_members(x4),x5),w)
| eq(f15(u,x,x6,x7,v),f15(w,x,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[626,1717]),
[iquote('3:Res:626.2,1717.1')] ).
cnf(1808,plain,
( ~ limit_point(u,v,w,x)
| ~ element_of_set(y,f16(u,z,w,x))
| ~ hausdorff(intersection_of_sets(f16(u,z,w,x),v),x1)
| limit_point(u,z,w,x)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f20(boundary(x2,x3,x4),x5),y)
| eq(f15(u,v,w,x,f16(u,z,w,x)),f15(y,v,x6,x7,f16(u,z,w,x))) ),
inference(res,[status(thm),theory(equality)],[493,1540]),
[iquote('3:Res:493.1,1540.0')] ).
cnf(1725,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f19(closure(z,x1,x2),x3),u)
| hausdorff(intersection_of_members(x4),x5)
| eq(f19(intersection_of_members(x4),x5),w)
| eq(f15(u,x,x6,x7,v),f15(w,x,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[625,1717]),
[iquote('3:Res:625.2,1717.1')] ).
cnf(1726,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f20(boundary(z,x1,x2),x3),u)
| hausdorff(intersection_of_members(x4),x5)
| eq(f19(intersection_of_members(x4),x5),w)
| eq(f15(u,x,x6,x7,v),f15(w,x,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[624,1717]),
[iquote('3:Res:624.2,1717.1')] ).
cnf(1727,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f20(closure(z,x1,x2),x3),u)
| hausdorff(intersection_of_members(x4),x5)
| eq(f19(intersection_of_members(x4),x5),w)
| eq(f15(u,x,x6,x7,v),f15(w,x,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[623,1717]),
[iquote('3:Res:623.2,1717.1')] ).
cnf(1708,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f19(boundary(z,x1,x2),x3),u)
| hausdorff(intersection_of_members(x4),x5)
| eq(f20(intersection_of_members(x4),x5),w)
| eq(f15(u,x,x6,x7,v),f15(w,x,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[626,1701]),
[iquote('3:Res:626.2,1701.1')] ).
cnf(1778,plain,
( ~ limit_point(u,v,w,x)
| ~ element_of_set(y,f16(u,z,w,x))
| ~ hausdorff(intersection_of_sets(f16(u,z,w,x),v),x1)
| limit_point(u,z,w,x)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f20(closure(x2,x3,x4),x5),y)
| eq(f15(u,v,w,x,f16(u,z,w,x)),f15(y,v,x6,x7,f16(u,z,w,x))) ),
inference(res,[status(thm),theory(equality)],[493,1531]),
[iquote('3:Res:493.1,1531.0')] ).
cnf(1709,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f19(closure(z,x1,x2),x3),u)
| hausdorff(intersection_of_members(x4),x5)
| eq(f20(intersection_of_members(x4),x5),w)
| eq(f15(u,x,x6,x7,v),f15(w,x,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[625,1701]),
[iquote('3:Res:625.2,1701.1')] ).
cnf(1710,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f20(boundary(z,x1,x2),x3),u)
| hausdorff(intersection_of_members(x4),x5)
| eq(f20(intersection_of_members(x4),x5),w)
| eq(f15(u,x,x6,x7,v),f15(w,x,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[624,1701]),
[iquote('3:Res:624.2,1701.1')] ).
cnf(1711,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f20(closure(z,x1,x2),x3),u)
| hausdorff(intersection_of_members(x4),x5)
| eq(f20(intersection_of_members(x4),x5),w)
| eq(f15(u,x,x6,x7,v),f15(w,x,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[623,1701]),
[iquote('3:Res:623.2,1701.1')] ).
cnf(1812,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f19(intersection_of_members(x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f19(boundary(x3,x4,x5),x6),w)
| eq(f15(u,x7,x8,x9,v),f15(w,x10,x11,x12,x)) ),
inference(res,[status(thm),theory(equality)],[622,1761]),
[iquote('3:Res:622.2,1761.1')] ).
cnf(1718,plain,
( ~ limit_point(u,v,w,x)
| ~ element_of_set(y,f16(u,z,w,x))
| ~ hausdorff(intersection_of_sets(f16(u,z,w,x),v),x1)
| limit_point(u,z,w,x)
| hausdorff(intersection_of_members(x2),x3)
| eq(f19(intersection_of_members(x2),x3),y)
| eq(f15(u,v,w,x,f16(u,z,w,x)),f15(y,v,x4,x5,f16(u,z,w,x))) ),
inference(res,[status(thm),theory(equality)],[493,1401]),
[iquote('3:Res:493.1,1401.0')] ).
cnf(1813,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f20(intersection_of_members(x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f19(boundary(x3,x4,x5),x6),w)
| eq(f15(u,x7,x8,x9,v),f15(w,x10,x11,x12,x)) ),
inference(res,[status(thm),theory(equality)],[621,1761]),
[iquote('3:Res:621.2,1761.1')] ).
cnf(1796,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f19(intersection_of_members(x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f19(closure(x3,x4,x5),x6),w)
| eq(f15(u,x7,x8,x9,v),f15(w,x10,x11,x12,x)) ),
inference(res,[status(thm),theory(equality)],[622,1737]),
[iquote('3:Res:622.2,1737.1')] ).
cnf(1797,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f20(intersection_of_members(x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f19(closure(x3,x4,x5),x6),w)
| eq(f15(u,x7,x8,x9,v),f15(w,x10,x11,x12,x)) ),
inference(res,[status(thm),theory(equality)],[621,1737]),
[iquote('3:Res:621.2,1737.1')] ).
cnf(1782,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f19(intersection_of_members(x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f20(boundary(x3,x4,x5),x6),w)
| eq(f15(u,x7,x8,x9,v),f15(w,x10,x11,x12,x)) ),
inference(res,[status(thm),theory(equality)],[622,1735]),
[iquote('3:Res:622.2,1735.1')] ).
cnf(1702,plain,
( ~ limit_point(u,v,w,x)
| ~ element_of_set(y,f16(u,z,w,x))
| ~ hausdorff(intersection_of_sets(f16(u,z,w,x),v),x1)
| limit_point(u,z,w,x)
| hausdorff(intersection_of_members(x2),x3)
| eq(f20(intersection_of_members(x2),x3),y)
| eq(f15(u,v,w,x,f16(u,z,w,x)),f15(y,v,x4,x5,f16(u,z,w,x))) ),
inference(res,[status(thm),theory(equality)],[493,1376]),
[iquote('3:Res:493.1,1376.0')] ).
cnf(1783,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f20(intersection_of_members(x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f20(boundary(x3,x4,x5),x6),w)
| eq(f15(u,x7,x8,x9,v),f15(w,x10,x11,x12,x)) ),
inference(res,[status(thm),theory(equality)],[621,1735]),
[iquote('3:Res:621.2,1735.1')] ).
cnf(1766,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f19(intersection_of_members(x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f20(closure(x3,x4,x5),x6),w)
| eq(f15(u,x7,x8,x9,v),f15(w,x10,x11,x12,x)) ),
inference(res,[status(thm),theory(equality)],[622,1733]),
[iquote('3:Res:622.2,1733.1')] ).
cnf(1767,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f20(intersection_of_members(x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f20(closure(x3,x4,x5),x6),w)
| eq(f15(u,x7,x8,x9,v),f15(w,x10,x11,x12,x)) ),
inference(res,[status(thm),theory(equality)],[621,1733]),
[iquote('3:Res:621.2,1733.1')] ).
cnf(1692,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f19(boundary(x1,x2,x3),x4),u)
| hausdorff(intersection_of_members(x5),x6)
| eq(f19(intersection_of_members(x5),x6),w)
| eq(f15(u,x7,x8,x9,v),f15(w,x10,x11,x12,x)) ),
inference(res,[status(thm),theory(equality)],[626,1685]),
[iquote('3:Res:626.2,1685.1')] ).
cnf(1640,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(closure(x1,x2,x3),x4)
| eq(f15(u,v,w,x,f16(u,y,w,x)),f15(f20(closure(x1,x2,x3),x4),v,x5,x6,f16(u,y,w,x))) ),
inference(res,[status(thm),theory(equality)],[493,1251]),
[iquote('3:Res:493.1,1251.0')] ).
cnf(1693,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f19(closure(x1,x2,x3),x4),u)
| hausdorff(intersection_of_members(x5),x6)
| eq(f19(intersection_of_members(x5),x6),w)
| eq(f15(u,x7,x8,x9,v),f15(w,x10,x11,x12,x)) ),
inference(res,[status(thm),theory(equality)],[625,1685]),
[iquote('3:Res:625.2,1685.1')] ).
cnf(1694,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f20(boundary(x1,x2,x3),x4),u)
| hausdorff(intersection_of_members(x5),x6)
| eq(f19(intersection_of_members(x5),x6),w)
| eq(f15(u,x7,x8,x9,v),f15(w,x10,x11,x12,x)) ),
inference(res,[status(thm),theory(equality)],[624,1685]),
[iquote('3:Res:624.2,1685.1')] ).
cnf(1695,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f20(closure(x1,x2,x3),x4),u)
| hausdorff(intersection_of_members(x5),x6)
| eq(f19(intersection_of_members(x5),x6),w)
| eq(f15(u,x7,x8,x9,v),f15(w,x10,x11,x12,x)) ),
inference(res,[status(thm),theory(equality)],[623,1685]),
[iquote('3:Res:623.2,1685.1')] ).
cnf(1676,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f19(boundary(x1,x2,x3),x4),u)
| hausdorff(intersection_of_members(x5),x6)
| eq(f20(intersection_of_members(x5),x6),w)
| eq(f15(u,x7,x8,x9,v),f15(w,x10,x11,x12,x)) ),
inference(res,[status(thm),theory(equality)],[626,1669]),
[iquote('3:Res:626.2,1669.1')] ).
cnf(1638,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(boundary(x1,x2,x3),x4)
| eq(f15(u,v,w,x,f16(u,y,w,x)),f15(f20(boundary(x1,x2,x3),x4),v,x5,x6,f16(u,y,w,x))) ),
inference(res,[status(thm),theory(equality)],[493,1242]),
[iquote('3:Res:493.1,1242.0')] ).
cnf(1677,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f19(closure(x1,x2,x3),x4),u)
| hausdorff(intersection_of_members(x5),x6)
| eq(f20(intersection_of_members(x5),x6),w)
| eq(f15(u,x7,x8,x9,v),f15(w,x10,x11,x12,x)) ),
inference(res,[status(thm),theory(equality)],[625,1669]),
[iquote('3:Res:625.2,1669.1')] ).
cnf(1678,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f20(boundary(x1,x2,x3),x4),u)
| hausdorff(intersection_of_members(x5),x6)
| eq(f20(intersection_of_members(x5),x6),w)
| eq(f15(u,x7,x8,x9,v),f15(w,x10,x11,x12,x)) ),
inference(res,[status(thm),theory(equality)],[624,1669]),
[iquote('3:Res:624.2,1669.1')] ).
cnf(1679,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f20(closure(x1,x2,x3),x4),u)
| hausdorff(intersection_of_members(x5),x6)
| eq(f20(intersection_of_members(x5),x6),w)
| eq(f15(u,x7,x8,x9,v),f15(w,x10,x11,x12,x)) ),
inference(res,[status(thm),theory(equality)],[623,1669]),
[iquote('3:Res:623.2,1669.1')] ).
cnf(1904,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f19(boundary(x3,x4,x5),x6),u)
| eq(f15(f20(closure(y,z,x1),x2),w,x7,x8,v),f15(u,w,x9,x10,v)) ),
inference(mrr,[status(thm)],[1900,544]),
[iquote('3:MRR:1900.0,544.1')] ).
cnf(1762,plain,
( ~ limit_point(u,v,w,x)
| ~ element_of_set(y,z)
| ~ hausdorff(union_of_members(x1),x2)
| limit_point(u,x3,w,x)
| hausdorff(boundary(x4,x5,x6),x7)
| eq(f19(boundary(x4,x5,x6),x7),y)
| eq(f15(u,v,w,x,f16(u,x3,w,x)),f15(y,x8,x9,x10,z)) ),
inference(res,[status(thm),theory(equality)],[493,1513]),
[iquote('3:Res:493.1,1513.0')] ).
cnf(1903,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f19(boundary(x3,x4,x5),x6),u)
| eq(f15(f20(boundary(y,z,x1),x2),w,x7,x8,v),f15(u,w,x9,x10,v)) ),
inference(mrr,[status(thm)],[1901,557]),
[iquote('3:MRR:1901.0,557.1')] ).
cnf(1890,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f19(closure(x3,x4,x5),x6),u)
| eq(f15(f20(closure(y,z,x1),x2),w,x7,x8,v),f15(u,w,x9,x10,v)) ),
inference(mrr,[status(thm)],[1886,544]),
[iquote('3:MRR:1886.0,544.1')] ).
cnf(1889,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f19(closure(x3,x4,x5),x6),u)
| eq(f15(f20(boundary(y,z,x1),x2),w,x7,x8,v),f15(u,w,x9,x10,v)) ),
inference(mrr,[status(thm)],[1887,557]),
[iquote('3:MRR:1887.0,557.1')] ).
cnf(1876,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f20(boundary(x3,x4,x5),x6),u)
| eq(f15(f20(closure(y,z,x1),x2),w,x7,x8,v),f15(u,w,x9,x10,v)) ),
inference(mrr,[status(thm)],[1872,544]),
[iquote('3:MRR:1872.0,544.1')] ).
cnf(1738,plain,
( ~ limit_point(u,v,w,x)
| ~ element_of_set(y,z)
| ~ hausdorff(union_of_members(x1),x2)
| limit_point(u,x3,w,x)
| hausdorff(closure(x4,x5,x6),x7)
| eq(f19(closure(x4,x5,x6),x7),y)
| eq(f15(u,v,w,x,f16(u,x3,w,x)),f15(y,x8,x9,x10,z)) ),
inference(res,[status(thm),theory(equality)],[493,1501]),
[iquote('3:Res:493.1,1501.0')] ).
cnf(1875,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f20(boundary(x3,x4,x5),x6),u)
| eq(f15(f20(boundary(y,z,x1),x2),w,x7,x8,v),f15(u,w,x9,x10,v)) ),
inference(mrr,[status(thm)],[1873,557]),
[iquote('3:MRR:1873.0,557.1')] ).
cnf(1862,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f20(closure(x3,x4,x5),x6),u)
| eq(f15(f20(closure(y,z,x1),x2),w,x7,x8,v),f15(u,w,x9,x10,v)) ),
inference(mrr,[status(thm)],[1858,544]),
[iquote('3:MRR:1858.0,544.1')] ).
cnf(1861,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f20(closure(x3,x4,x5),x6),u)
| eq(f15(f20(boundary(y,z,x1),x2),w,x7,x8,v),f15(u,w,x9,x10,v)) ),
inference(mrr,[status(thm)],[1859,557]),
[iquote('3:MRR:1859.0,557.1')] ).
cnf(1660,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f15(f20(closure(x3,x4,x5),x6),w,x9,x10,v)) ),
inference(res,[status(thm),theory(equality)],[626,1639]),
[iquote('3:Res:626.2,1639.1')] ).
cnf(1736,plain,
( ~ limit_point(u,v,w,x)
| ~ element_of_set(y,z)
| ~ hausdorff(union_of_members(x1),x2)
| limit_point(u,x3,w,x)
| hausdorff(boundary(x4,x5,x6),x7)
| eq(f20(boundary(x4,x5,x6),x7),y)
| eq(f15(u,v,w,x,f16(u,x3,w,x)),f15(y,x8,x9,x10,z)) ),
inference(res,[status(thm),theory(equality)],[493,1489]),
[iquote('3:Res:493.1,1489.0')] ).
cnf(1661,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f15(f20(closure(x3,x4,x5),x6),w,x9,x10,v)) ),
inference(res,[status(thm),theory(equality)],[625,1639]),
[iquote('3:Res:625.2,1639.1')] ).
cnf(1662,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f15(f20(closure(x3,x4,x5),x6),w,x9,x10,v)) ),
inference(res,[status(thm),theory(equality)],[624,1639]),
[iquote('3:Res:624.2,1639.1')] ).
cnf(1663,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f15(f20(closure(x3,x4,x5),x6),w,x9,x10,v)) ),
inference(res,[status(thm),theory(equality)],[623,1639]),
[iquote('3:Res:623.2,1639.1')] ).
cnf(1646,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f15(f20(boundary(x3,x4,x5),x6),w,x9,x10,v)) ),
inference(res,[status(thm),theory(equality)],[626,1637]),
[iquote('3:Res:626.2,1637.1')] ).
cnf(1734,plain,
( ~ limit_point(u,v,w,x)
| ~ element_of_set(y,z)
| ~ hausdorff(union_of_members(x1),x2)
| limit_point(u,x3,w,x)
| hausdorff(closure(x4,x5,x6),x7)
| eq(f20(closure(x4,x5,x6),x7),y)
| eq(f15(u,v,w,x,f16(u,x3,w,x)),f15(y,x8,x9,x10,z)) ),
inference(res,[status(thm),theory(equality)],[493,1477]),
[iquote('3:Res:493.1,1477.0')] ).
cnf(1647,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f15(f20(boundary(x3,x4,x5),x6),w,x9,x10,v)) ),
inference(res,[status(thm),theory(equality)],[625,1637]),
[iquote('3:Res:625.2,1637.1')] ).
cnf(1648,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f15(f20(boundary(x3,x4,x5),x6),w,x9,x10,v)) ),
inference(res,[status(thm),theory(equality)],[624,1637]),
[iquote('3:Res:624.2,1637.1')] ).
cnf(1649,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f15(f20(boundary(x3,x4,x5),x6),w,x9,x10,v)) ),
inference(res,[status(thm),theory(equality)],[623,1637]),
[iquote('3:Res:623.2,1637.1')] ).
cnf(1902,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f19(boundary(x1,x2,x3),x4),u)
| eq(f15(f20(intersection_of_members(y),z),w,x5,x6,v),f15(u,w,x7,x8,v)) ),
inference(mrr,[status(thm)],[1893,486]),
[iquote('3:MRR:1893.0,486.1')] ).
cnf(1576,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_members(x1),x2)
| eq(f15(u,v,w,x,f16(u,y,w,x)),f15(f20(intersection_of_members(x1),x2),v,x3,x4,f16(u,y,w,x))) ),
inference(res,[status(thm),theory(equality)],[493,1187]),
[iquote('3:Res:493.1,1187.0')] ).
cnf(1825,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ element_of_set(z,v)
| ~ hausdorff(intersection_of_sets(v,w),x1)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f19(boundary(x2,x3,x4),x5),z)
| eq(f15(u,w,x,y,v),f15(z,w,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[481,1558]),
[iquote('3:Res:481.1,1558.0')] ).
cnf(1822,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f19(boundary(x3,x4,x5),x6),u)
| eq(f15(f20(closure(y,z,x1),x2),x7,x8,x9,x10),f15(u,x11,x12,x13,v)) ),
inference(mrr,[status(thm)],[1818,544]),
[iquote('3:MRR:1818.0,544.1')] ).
cnf(1821,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f19(boundary(x3,x4,x5),x6),u)
| eq(f15(f20(boundary(y,z,x1),x2),x7,x8,x9,x10),f15(u,x11,x12,x13,v)) ),
inference(mrr,[status(thm)],[1819,557]),
[iquote('3:MRR:1819.0,557.1')] ).
cnf(1888,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f19(closure(x1,x2,x3),x4),u)
| eq(f15(f20(intersection_of_members(y),z),w,x5,x6,v),f15(u,w,x7,x8,v)) ),
inference(mrr,[status(thm)],[1879,486]),
[iquote('3:MRR:1879.0,486.1')] ).
cnf(1823,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ element_of_set(z,v)
| ~ hausdorff(intersection_of_sets(v,w),x1)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f19(closure(x2,x3,x4),x5),z)
| eq(f15(u,w,x,y,v),f15(z,w,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[481,1549]),
[iquote('3:Res:481.1,1549.0')] ).
cnf(1806,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f19(closure(x3,x4,x5),x6),u)
| eq(f15(f20(closure(y,z,x1),x2),x7,x8,x9,x10),f15(u,x11,x12,x13,v)) ),
inference(mrr,[status(thm)],[1802,544]),
[iquote('3:MRR:1802.0,544.1')] ).
cnf(1805,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f19(closure(x3,x4,x5),x6),u)
| eq(f15(f20(boundary(y,z,x1),x2),x7,x8,x9,x10),f15(u,x11,x12,x13,v)) ),
inference(mrr,[status(thm)],[1803,557]),
[iquote('3:MRR:1803.0,557.1')] ).
cnf(1792,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f20(boundary(x3,x4,x5),x6),u)
| eq(f15(f20(closure(y,z,x1),x2),x7,x8,x9,x10),f15(u,x11,x12,x13,v)) ),
inference(mrr,[status(thm)],[1788,544]),
[iquote('3:MRR:1788.0,544.1')] ).
cnf(1874,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f20(boundary(x1,x2,x3),x4),u)
| eq(f15(f20(intersection_of_members(y),z),w,x5,x6,v),f15(u,w,x7,x8,v)) ),
inference(mrr,[status(thm)],[1865,486]),
[iquote('3:MRR:1865.0,486.1')] ).
cnf(1807,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ element_of_set(z,v)
| ~ hausdorff(intersection_of_sets(v,w),x1)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f20(boundary(x2,x3,x4),x5),z)
| eq(f15(u,w,x,y,v),f15(z,w,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[481,1540]),
[iquote('3:Res:481.1,1540.0')] ).
cnf(1791,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f20(boundary(x3,x4,x5),x6),u)
| eq(f15(f20(boundary(y,z,x1),x2),x7,x8,x9,x10),f15(u,x11,x12,x13,v)) ),
inference(mrr,[status(thm)],[1789,557]),
[iquote('3:MRR:1789.0,557.1')] ).
cnf(1776,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f20(closure(x3,x4,x5),x6),u)
| eq(f15(f20(closure(y,z,x1),x2),x7,x8,x9,x10),f15(u,x11,x12,x13,v)) ),
inference(mrr,[status(thm)],[1772,544]),
[iquote('3:MRR:1772.0,544.1')] ).
cnf(1775,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f20(closure(x3,x4,x5),x6),u)
| eq(f15(f20(boundary(y,z,x1),x2),x7,x8,x9,x10),f15(u,x11,x12,x13,v)) ),
inference(mrr,[status(thm)],[1773,557]),
[iquote('3:MRR:1773.0,557.1')] ).
cnf(1860,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f20(closure(x1,x2,x3),x4),u)
| eq(f15(f20(intersection_of_members(y),z),w,x5,x6,v),f15(u,w,x7,x8,v)) ),
inference(mrr,[status(thm)],[1851,486]),
[iquote('3:MRR:1851.0,486.1')] ).
cnf(1777,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ element_of_set(z,v)
| ~ hausdorff(intersection_of_sets(v,w),x1)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f20(closure(x2,x3,x4),x5),z)
| eq(f15(u,w,x,y,v),f15(z,w,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[481,1531]),
[iquote('3:Res:481.1,1531.0')] ).
cnf(1686,plain,
( ~ limit_point(u,v,w,x)
| ~ element_of_set(y,z)
| ~ hausdorff(union_of_members(x1),x2)
| limit_point(u,x3,w,x)
| hausdorff(intersection_of_members(x4),x5)
| eq(f19(intersection_of_members(x4),x5),y)
| eq(f15(u,v,w,x,f16(u,x3,w,x)),f15(y,x6,x7,x8,z)) ),
inference(res,[status(thm),theory(equality)],[493,1275]),
[iquote('3:Res:493.1,1275.0')] ).
cnf(1670,plain,
( ~ limit_point(u,v,w,x)
| ~ element_of_set(y,z)
| ~ hausdorff(union_of_members(x1),x2)
| limit_point(u,x3,w,x)
| hausdorff(intersection_of_members(x4),x5)
| eq(f20(intersection_of_members(x4),x5),y)
| eq(f15(u,v,w,x,f16(u,x3,w,x)),f15(y,x6,x7,x8,z)) ),
inference(res,[status(thm),theory(equality)],[493,1263]),
[iquote('3:Res:493.1,1263.0')] ).
cnf(1628,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f15(u,x7,x8,x9,v),f15(f20(closure(x3,x4,x5),x6),x10,x11,x12,x13)) ),
inference(res,[status(thm),theory(equality)],[626,1607]),
[iquote('3:Res:626.2,1607.1')] ).
cnf(1629,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f15(u,x7,x8,x9,v),f15(f20(closure(x3,x4,x5),x6),x10,x11,x12,x13)) ),
inference(res,[status(thm),theory(equality)],[625,1607]),
[iquote('3:Res:625.2,1607.1')] ).
cnf(1591,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)],[481,1522]),
[iquote('3:Res:481.1,1522.0')] ).
cnf(1630,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f15(u,x7,x8,x9,v),f15(f20(closure(x3,x4,x5),x6),x10,x11,x12,x13)) ),
inference(res,[status(thm),theory(equality)],[624,1607]),
[iquote('3:Res:624.2,1607.1')] ).
cnf(1631,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f15(u,x7,x8,x9,v),f15(f20(closure(x3,x4,x5),x6),x10,x11,x12,x13)) ),
inference(res,[status(thm),theory(equality)],[623,1607]),
[iquote('3:Res:623.2,1607.1')] ).
cnf(1614,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f15(u,x7,x8,x9,v),f15(f20(boundary(x3,x4,x5),x6),x10,x11,x12,x13)) ),
inference(res,[status(thm),theory(equality)],[626,1605]),
[iquote('3:Res:626.2,1605.1')] ).
cnf(1615,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f15(u,x7,x8,x9,v),f15(f20(boundary(x3,x4,x5),x6),x10,x11,x12,x13)) ),
inference(res,[status(thm),theory(equality)],[625,1605]),
[iquote('3:Res:625.2,1605.1')] ).
cnf(1558,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ element_of_set(z,u)
| ~ hausdorff(intersection_of_sets(u,y),x1)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f19(boundary(x2,x3,x4),x5),z)
| eq(f15(v,y,w,x,u),f15(z,y,x6,x7,u)) ),
inference(res,[status(thm),theory(equality)],[68,1168]),
[iquote('3:Res:68.2,1168.1')] ).
cnf(1616,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f15(u,x7,x8,x9,v),f15(f20(boundary(x3,x4,x5),x6),x10,x11,x12,x13)) ),
inference(res,[status(thm),theory(equality)],[624,1605]),
[iquote('3:Res:624.2,1605.1')] ).
cnf(1617,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f15(u,x7,x8,x9,v),f15(f20(boundary(x3,x4,x5),x6),x10,x11,x12,x13)) ),
inference(res,[status(thm),theory(equality)],[623,1605]),
[iquote('3:Res:623.2,1605.1')] ).
cnf(1722,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f19(intersection_of_members(z),x1),u)
| hausdorff(intersection_of_members(x2),x3)
| eq(f19(intersection_of_members(x2),x3),w)
| eq(f15(u,x,x4,x5,v),f15(w,x,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[622,1717]),
[iquote('3:Res:622.2,1717.1')] ).
cnf(1723,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f20(intersection_of_members(z),x1),u)
| hausdorff(intersection_of_members(x2),x3)
| eq(f19(intersection_of_members(x2),x3),w)
| eq(f15(u,x,x4,x5,v),f15(w,x,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[621,1717]),
[iquote('3:Res:621.2,1717.1')] ).
cnf(1549,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ element_of_set(z,u)
| ~ hausdorff(intersection_of_sets(u,y),x1)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f19(closure(x2,x3,x4),x5),z)
| eq(f15(v,y,w,x,u),f15(z,y,x6,x7,u)) ),
inference(res,[status(thm),theory(equality)],[68,1169]),
[iquote('3:Res:68.2,1169.1')] ).
cnf(1706,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f19(intersection_of_members(z),x1),u)
| hausdorff(intersection_of_members(x2),x3)
| eq(f20(intersection_of_members(x2),x3),w)
| eq(f15(u,x,x4,x5,v),f15(w,x,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[622,1701]),
[iquote('3:Res:622.2,1701.1')] ).
cnf(1707,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f20(intersection_of_members(z),x1),u)
| hausdorff(intersection_of_members(x2),x3)
| eq(f20(intersection_of_members(x2),x3),w)
| eq(f15(u,x,x4,x5,v),f15(w,x,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[621,1701]),
[iquote('3:Res:621.2,1701.1')] ).
cnf(1820,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f19(boundary(x1,x2,x3),x4),u)
| eq(f15(f20(intersection_of_members(y),z),x5,x6,x7,x8),f15(u,x9,x10,x11,v)) ),
inference(mrr,[status(thm)],[1811,486]),
[iquote('3:MRR:1811.0,486.1')] ).
cnf(1761,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ element_of_set(z,x1)
| ~ hausdorff(union_of_members(x2),x3)
| hausdorff(boundary(x4,x5,x6),x7)
| eq(f19(boundary(x4,x5,x6),x7),z)
| eq(f15(u,w,x,y,v),f15(z,x8,x9,x10,x1)) ),
inference(res,[status(thm),theory(equality)],[481,1513]),
[iquote('3:Res:481.1,1513.0')] ).
cnf(1540,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ element_of_set(z,u)
| ~ hausdorff(intersection_of_sets(u,y),x1)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f20(boundary(x2,x3,x4),x5),z)
| eq(f15(v,y,w,x,u),f15(z,y,x6,x7,u)) ),
inference(res,[status(thm),theory(equality)],[68,1170]),
[iquote('3:Res:68.2,1170.1')] ).
cnf(1804,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f19(closure(x1,x2,x3),x4),u)
| eq(f15(f20(intersection_of_members(y),z),x5,x6,x7,x8),f15(u,x9,x10,x11,v)) ),
inference(mrr,[status(thm)],[1795,486]),
[iquote('3:MRR:1795.0,486.1')] ).
cnf(1737,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ element_of_set(z,x1)
| ~ hausdorff(union_of_members(x2),x3)
| hausdorff(closure(x4,x5,x6),x7)
| eq(f19(closure(x4,x5,x6),x7),z)
| eq(f15(u,w,x,y,v),f15(z,x8,x9,x10,x1)) ),
inference(res,[status(thm),theory(equality)],[481,1501]),
[iquote('3:Res:481.1,1501.0')] ).
cnf(1790,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f20(boundary(x1,x2,x3),x4),u)
| eq(f15(f20(intersection_of_members(y),z),x5,x6,x7,x8),f15(u,x9,x10,x11,v)) ),
inference(mrr,[status(thm)],[1781,486]),
[iquote('3:MRR:1781.0,486.1')] ).
cnf(1735,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ element_of_set(z,x1)
| ~ hausdorff(union_of_members(x2),x3)
| hausdorff(boundary(x4,x5,x6),x7)
| eq(f20(boundary(x4,x5,x6),x7),z)
| eq(f15(u,w,x,y,v),f15(z,x8,x9,x10,x1)) ),
inference(res,[status(thm),theory(equality)],[481,1489]),
[iquote('3:Res:481.1,1489.0')] ).
cnf(1531,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ element_of_set(z,u)
| ~ hausdorff(intersection_of_sets(u,y),x1)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f20(closure(x2,x3,x4),x5),z)
| eq(f15(v,y,w,x,u),f15(z,y,x6,x7,u)) ),
inference(res,[status(thm),theory(equality)],[68,1171]),
[iquote('3:Res:68.2,1171.1')] ).
cnf(1774,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f20(closure(x1,x2,x3),x4),u)
| eq(f15(f20(intersection_of_members(y),z),x5,x6,x7,x8),f15(u,x9,x10,x11,v)) ),
inference(mrr,[status(thm)],[1765,486]),
[iquote('3:MRR:1765.0,486.1')] ).
cnf(1733,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ element_of_set(z,x1)
| ~ hausdorff(union_of_members(x2),x3)
| hausdorff(closure(x4,x5,x6),x7)
| eq(f20(closure(x4,x5,x6),x7),z)
| eq(f15(u,w,x,y,v),f15(z,x8,x9,x10,x1)) ),
inference(res,[status(thm),theory(equality)],[481,1477]),
[iquote('3:Res:481.1,1477.0')] ).
cnf(1690,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f19(intersection_of_members(x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f19(intersection_of_members(x3),x4),w)
| eq(f15(u,x5,x6,x7,v),f15(w,x8,x9,x10,x)) ),
inference(res,[status(thm),theory(equality)],[622,1685]),
[iquote('3:Res:622.2,1685.1')] ).
cnf(1691,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f20(intersection_of_members(x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f19(intersection_of_members(x3),x4),w)
| eq(f15(u,x5,x6,x7,v),f15(w,x8,x9,x10,x)) ),
inference(res,[status(thm),theory(equality)],[621,1685]),
[iquote('3:Res:621.2,1685.1')] ).
cnf(1513,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ element_of_set(z,x1)
| ~ hausdorff(union_of_members(x2),x3)
| hausdorff(boundary(x4,x5,x6),x7)
| eq(f19(boundary(x4,x5,x6),x7),z)
| eq(f15(v,y,w,x,u),f15(z,x8,x9,x10,x1)) ),
inference(res,[status(thm),theory(equality)],[643,1118]),
[iquote('3:Res:643.2,1118.1')] ).
cnf(1674,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f19(intersection_of_members(x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f20(intersection_of_members(x3),x4),w)
| eq(f15(u,x5,x6,x7,v),f15(w,x8,x9,x10,x)) ),
inference(res,[status(thm),theory(equality)],[622,1669]),
[iquote('3:Res:622.2,1669.1')] ).
cnf(1675,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,x)
| ~ hausdorff(union_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f20(intersection_of_members(x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f20(intersection_of_members(x3),x4),w)
| eq(f15(u,x5,x6,x7,v),f15(w,x8,x9,x10,x)) ),
inference(res,[status(thm),theory(equality)],[621,1669]),
[iquote('3:Res:621.2,1669.1')] ).
cnf(1608,plain,
( ~ limit_point(u,v,w,x)
| ~ hausdorff(union_of_members(y),z)
| limit_point(u,x1,w,x)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f15(u,v,w,x,f16(u,x1,w,x)),f15(f20(closure(x2,x3,x4),x5),x6,x7,x8,x9)) ),
inference(res,[status(thm),theory(equality)],[493,1162]),
[iquote('3:Res:493.1,1162.0')] ).
cnf(1606,plain,
( ~ limit_point(u,v,w,x)
| ~ hausdorff(union_of_members(y),z)
| limit_point(u,x1,w,x)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f15(u,v,w,x,f16(u,x1,w,x)),f15(f20(boundary(x2,x3,x4),x5),x6,x7,x8,x9)) ),
inference(res,[status(thm),theory(equality)],[493,1150]),
[iquote('3:Res:493.1,1150.0')] ).
cnf(1501,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ element_of_set(z,x1)
| ~ hausdorff(union_of_members(x2),x3)
| hausdorff(closure(x4,x5,x6),x7)
| eq(f19(closure(x4,x5,x6),x7),z)
| eq(f15(v,y,w,x,u),f15(z,x8,x9,x10,x1)) ),
inference(res,[status(thm),theory(equality)],[643,1119]),
[iquote('3:Res:643.2,1119.1')] ).
cnf(1732,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f19(intersection_of_members(x3),x4),u)
| eq(f15(f20(closure(y,z,x1),x2),w,x5,x6,v),f15(u,w,x7,x8,v)) ),
inference(mrr,[status(thm)],[1728,544]),
[iquote('3:MRR:1728.0,544.1')] ).
cnf(1731,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f19(intersection_of_members(x3),x4),u)
| eq(f15(f20(boundary(y,z,x1),x2),w,x5,x6,v),f15(u,w,x7,x8,v)) ),
inference(mrr,[status(thm)],[1729,557]),
[iquote('3:MRR:1729.0,557.1')] ).
cnf(1716,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f20(intersection_of_members(x3),x4),u)
| eq(f15(f20(closure(y,z,x1),x2),w,x5,x6,v),f15(u,w,x7,x8,v)) ),
inference(mrr,[status(thm)],[1712,544]),
[iquote('3:MRR:1712.0,544.1')] ).
cnf(1715,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f20(intersection_of_members(x3),x4),u)
| eq(f15(f20(boundary(y,z,x1),x2),w,x5,x6,v),f15(u,w,x7,x8,v)) ),
inference(mrr,[status(thm)],[1713,557]),
[iquote('3:MRR:1713.0,557.1')] ).
cnf(1489,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ element_of_set(z,x1)
| ~ hausdorff(union_of_members(x2),x3)
| hausdorff(boundary(x4,x5,x6),x7)
| eq(f20(boundary(x4,x5,x6),x7),z)
| eq(f15(v,y,w,x,u),f15(z,x8,x9,x10,x1)) ),
inference(res,[status(thm),theory(equality)],[643,1120]),
[iquote('3:Res:643.2,1120.1')] ).
cnf(1658,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f15(u,w,x5,x6,v),f15(f20(closure(x1,x2,x3),x4),w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[622,1639]),
[iquote('3:Res:622.2,1639.1')] ).
cnf(1659,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f15(u,w,x5,x6,v),f15(f20(closure(x1,x2,x3),x4),w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[621,1639]),
[iquote('3:Res:621.2,1639.1')] ).
cnf(1644,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f15(u,w,x5,x6,v),f15(f20(boundary(x1,x2,x3),x4),w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[622,1637]),
[iquote('3:Res:622.2,1637.1')] ).
cnf(1645,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f15(u,w,x5,x6,v),f15(f20(boundary(x1,x2,x3),x4),w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[621,1637]),
[iquote('3:Res:621.2,1637.1')] ).
cnf(1477,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ element_of_set(z,x1)
| ~ hausdorff(union_of_members(x2),x3)
| hausdorff(closure(x4,x5,x6),x7)
| eq(f20(closure(x4,x5,x6),x7),z)
| eq(f15(v,y,w,x,u),f15(z,x8,x9,x10,x1)) ),
inference(res,[status(thm),theory(equality)],[643,1121]),
[iquote('3:Res:643.2,1121.1')] ).
cnf(1582,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f15(u,w,x5,x6,v),f15(f20(intersection_of_members(x3),x4),w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[626,1575]),
[iquote('3:Res:626.2,1575.1')] ).
cnf(1583,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f15(u,w,x5,x6,v),f15(f20(intersection_of_members(x3),x4),w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[625,1575]),
[iquote('3:Res:625.2,1575.1')] ).
cnf(1730,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f19(intersection_of_members(x1),x2),u)
| eq(f15(f20(intersection_of_members(y),z),w,x3,x4,v),f15(u,w,x5,x6,v)) ),
inference(mrr,[status(thm)],[1721,486]),
[iquote('3:MRR:1721.0,486.1')] ).
cnf(1717,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ element_of_set(z,v)
| ~ hausdorff(intersection_of_sets(v,w),x1)
| hausdorff(intersection_of_members(x2),x3)
| eq(f19(intersection_of_members(x2),x3),z)
| eq(f15(u,w,x,y,v),f15(z,w,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[481,1401]),
[iquote('3:Res:481.1,1401.0')] ).
cnf(1401,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ element_of_set(z,u)
| ~ hausdorff(intersection_of_sets(u,y),x1)
| hausdorff(intersection_of_members(x2),x3)
| eq(f19(intersection_of_members(x2),x3),z)
| eq(f15(v,y,w,x,u),f15(z,y,x4,x5,u)) ),
inference(res,[status(thm),theory(equality)],[68,1166]),
[iquote('3:Res:68.2,1166.1')] ).
cnf(1584,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f15(u,w,x5,x6,v),f15(f20(intersection_of_members(x3),x4),w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[624,1575]),
[iquote('3:Res:624.2,1575.1')] ).
cnf(1585,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f15(u,w,x5,x6,v),f15(f20(intersection_of_members(x3),x4),w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[623,1575]),
[iquote('3:Res:623.2,1575.1')] ).
cnf(1714,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f20(intersection_of_members(x1),x2),u)
| eq(f15(f20(intersection_of_members(y),z),w,x3,x4,v),f15(u,w,x5,x6,v)) ),
inference(mrr,[status(thm)],[1705,486]),
[iquote('3:MRR:1705.0,486.1')] ).
cnf(1701,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ element_of_set(z,v)
| ~ hausdorff(intersection_of_sets(v,w),x1)
| hausdorff(intersection_of_members(x2),x3)
| eq(f20(intersection_of_members(x2),x3),z)
| eq(f15(u,w,x,y,v),f15(z,w,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[481,1376]),
[iquote('3:Res:481.1,1376.0')] ).
cnf(1376,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ element_of_set(z,u)
| ~ hausdorff(intersection_of_sets(u,y),x1)
| hausdorff(intersection_of_members(x2),x3)
| eq(f20(intersection_of_members(x2),x3),z)
| eq(f15(v,y,w,x,u),f15(z,y,x4,x5,u)) ),
inference(res,[status(thm),theory(equality)],[68,1167]),
[iquote('3:Res:68.2,1167.1')] ).
cnf(1700,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f19(intersection_of_members(x3),x4),u)
| eq(f15(f20(closure(y,z,x1),x2),x5,x6,x7,x8),f15(u,x9,x10,x11,v)) ),
inference(mrr,[status(thm)],[1696,544]),
[iquote('3:MRR:1696.0,544.1')] ).
cnf(1699,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f19(intersection_of_members(x3),x4),u)
| eq(f15(f20(boundary(y,z,x1),x2),x5,x6,x7,x8),f15(u,x9,x10,x11,v)) ),
inference(mrr,[status(thm)],[1697,557]),
[iquote('3:MRR:1697.0,557.1')] ).
cnf(1698,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f19(intersection_of_members(x1),x2),u)
| eq(f15(f20(intersection_of_members(y),z),x3,x4,x5,x6),f15(u,x7,x8,x9,v)) ),
inference(mrr,[status(thm)],[1689,486]),
[iquote('3:MRR:1689.0,486.1')] ).
cnf(1685,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ element_of_set(z,x1)
| ~ hausdorff(union_of_members(x2),x3)
| hausdorff(intersection_of_members(x4),x5)
| eq(f19(intersection_of_members(x4),x5),z)
| eq(f15(u,w,x,y,v),f15(z,x6,x7,x8,x1)) ),
inference(res,[status(thm),theory(equality)],[481,1275]),
[iquote('3:Res:481.1,1275.0')] ).
cnf(1275,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ element_of_set(z,x1)
| ~ hausdorff(union_of_members(x2),x3)
| hausdorff(intersection_of_members(x4),x5)
| eq(f19(intersection_of_members(x4),x5),z)
| eq(f15(v,y,w,x,u),f15(z,x6,x7,x8,x1)) ),
inference(res,[status(thm),theory(equality)],[643,1116]),
[iquote('3:Res:643.2,1116.1')] ).
cnf(1684,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f20(intersection_of_members(x3),x4),u)
| eq(f15(f20(closure(y,z,x1),x2),x5,x6,x7,x8),f15(u,x9,x10,x11,v)) ),
inference(mrr,[status(thm)],[1680,544]),
[iquote('3:MRR:1680.0,544.1')] ).
cnf(1683,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f20(intersection_of_members(x3),x4),u)
| eq(f15(f20(boundary(y,z,x1),x2),x5,x6,x7,x8),f15(u,x9,x10,x11,v)) ),
inference(mrr,[status(thm)],[1681,557]),
[iquote('3:MRR:1681.0,557.1')] ).
cnf(1682,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f20(intersection_of_members(x1),x2),u)
| eq(f15(f20(intersection_of_members(y),z),x3,x4,x5,x6),f15(u,x7,x8,x9,v)) ),
inference(mrr,[status(thm)],[1673,486]),
[iquote('3:MRR:1673.0,486.1')] ).
cnf(1669,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ element_of_set(z,x1)
| ~ hausdorff(union_of_members(x2),x3)
| hausdorff(intersection_of_members(x4),x5)
| eq(f20(intersection_of_members(x4),x5),z)
| eq(f15(u,w,x,y,v),f15(z,x6,x7,x8,x1)) ),
inference(res,[status(thm),theory(equality)],[481,1263]),
[iquote('3:Res:481.1,1263.0')] ).
cnf(1263,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ element_of_set(z,x1)
| ~ hausdorff(union_of_members(x2),x3)
| hausdorff(intersection_of_members(x4),x5)
| eq(f20(intersection_of_members(x4),x5),z)
| eq(f15(v,y,w,x,u),f15(z,x6,x7,x8,x1)) ),
inference(res,[status(thm),theory(equality)],[643,1117]),
[iquote('3:Res:643.2,1117.1')] ).
cnf(1554,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f19(boundary(x3,x4,x5),x6),u)
| eq(f20(closure(y,z,x1),x2),f15(u,w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[544,1168]),
[iquote('3:Res:544.1,1168.1')] ).
cnf(1555,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f19(boundary(x3,x4,x5),x6),u)
| eq(f20(boundary(y,z,x1),x2),f15(u,w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[557,1168]),
[iquote('3:Res:557.1,1168.1')] ).
cnf(1556,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f19(boundary(x3,x4,x5),x6),u)
| eq(f19(closure(y,z,x1),x2),f15(u,w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[545,1168]),
[iquote('3:Res:545.1,1168.1')] ).
cnf(1557,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f19(boundary(x3,x4,x5),x6),u)
| eq(f19(boundary(y,z,x1),x2),f15(u,w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[558,1168]),
[iquote('3:Res:558.1,1168.1')] ).
cnf(1545,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f19(closure(x3,x4,x5),x6),u)
| eq(f20(closure(y,z,x1),x2),f15(u,w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[544,1169]),
[iquote('3:Res:544.1,1169.1')] ).
cnf(1546,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f19(closure(x3,x4,x5),x6),u)
| eq(f20(boundary(y,z,x1),x2),f15(u,w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[557,1169]),
[iquote('3:Res:557.1,1169.1')] ).
cnf(1547,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f19(closure(x3,x4,x5),x6),u)
| eq(f19(closure(y,z,x1),x2),f15(u,w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[545,1169]),
[iquote('3:Res:545.1,1169.1')] ).
cnf(1548,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f19(closure(x3,x4,x5),x6),u)
| eq(f19(boundary(y,z,x1),x2),f15(u,w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[558,1169]),
[iquote('3:Res:558.1,1169.1')] ).
cnf(1536,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f20(boundary(x3,x4,x5),x6),u)
| eq(f20(closure(y,z,x1),x2),f15(u,w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[544,1170]),
[iquote('3:Res:544.1,1170.1')] ).
cnf(1537,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f20(boundary(x3,x4,x5),x6),u)
| eq(f20(boundary(y,z,x1),x2),f15(u,w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[557,1170]),
[iquote('3:Res:557.1,1170.1')] ).
cnf(1538,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f20(boundary(x3,x4,x5),x6),u)
| eq(f19(closure(y,z,x1),x2),f15(u,w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[545,1170]),
[iquote('3:Res:545.1,1170.1')] ).
cnf(1539,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f20(boundary(x3,x4,x5),x6),u)
| eq(f19(boundary(y,z,x1),x2),f15(u,w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[558,1170]),
[iquote('3:Res:558.1,1170.1')] ).
cnf(1527,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f20(closure(x3,x4,x5),x6),u)
| eq(f20(closure(y,z,x1),x2),f15(u,w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[544,1171]),
[iquote('3:Res:544.1,1171.1')] ).
cnf(1528,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f20(closure(x3,x4,x5),x6),u)
| eq(f20(boundary(y,z,x1),x2),f15(u,w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[557,1171]),
[iquote('3:Res:557.1,1171.1')] ).
cnf(1529,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f20(closure(x3,x4,x5),x6),u)
| eq(f19(closure(y,z,x1),x2),f15(u,w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[545,1171]),
[iquote('3:Res:545.1,1171.1')] ).
cnf(1530,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f20(closure(x3,x4,x5),x6),u)
| eq(f19(boundary(y,z,x1),x2),f15(u,w,x7,x8,v)) ),
inference(res,[status(thm),theory(equality)],[558,1171]),
[iquote('3:Res:558.1,1171.1')] ).
cnf(1457,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f20(closure(x3,x4,x5),x6)) ),
inference(res,[status(thm),theory(equality)],[626,1450]),
[iquote('3:Res:626.2,1450.1')] ).
cnf(1458,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f20(closure(x3,x4,x5),x6)) ),
inference(res,[status(thm),theory(equality)],[625,1450]),
[iquote('3:Res:625.2,1450.1')] ).
cnf(1459,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f20(closure(x3,x4,x5),x6)) ),
inference(res,[status(thm),theory(equality)],[624,1450]),
[iquote('3:Res:624.2,1450.1')] ).
cnf(1460,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f20(closure(x3,x4,x5),x6)) ),
inference(res,[status(thm),theory(equality)],[623,1450]),
[iquote('3:Res:623.2,1450.1')] ).
cnf(1441,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f20(boundary(x3,x4,x5),x6)) ),
inference(res,[status(thm),theory(equality)],[626,1420]),
[iquote('3:Res:626.2,1420.1')] ).
cnf(1442,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f20(boundary(x3,x4,x5),x6)) ),
inference(res,[status(thm),theory(equality)],[625,1420]),
[iquote('3:Res:625.2,1420.1')] ).
cnf(1443,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f20(boundary(x3,x4,x5),x6)) ),
inference(res,[status(thm),theory(equality)],[624,1420]),
[iquote('3:Res:624.2,1420.1')] ).
cnf(1444,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f20(boundary(x3,x4,x5),x6)) ),
inference(res,[status(thm),theory(equality)],[623,1420]),
[iquote('3:Res:623.2,1420.1')] ).
cnf(1427,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f19(closure(x3,x4,x5),x6)) ),
inference(res,[status(thm),theory(equality)],[626,1404]),
[iquote('3:Res:626.2,1404.1')] ).
cnf(1428,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f19(closure(x3,x4,x5),x6)) ),
inference(res,[status(thm),theory(equality)],[625,1404]),
[iquote('3:Res:625.2,1404.1')] ).
cnf(1429,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f19(closure(x3,x4,x5),x6)) ),
inference(res,[status(thm),theory(equality)],[624,1404]),
[iquote('3:Res:624.2,1404.1')] ).
cnf(1430,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f19(closure(x3,x4,x5),x6)) ),
inference(res,[status(thm),theory(equality)],[623,1404]),
[iquote('3:Res:623.2,1404.1')] ).
cnf(1411,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f19(boundary(x3,x4,x5),x6)) ),
inference(res,[status(thm),theory(equality)],[626,1402]),
[iquote('3:Res:626.2,1402.1')] ).
cnf(1412,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f19(boundary(x3,x4,x5),x6)) ),
inference(res,[status(thm),theory(equality)],[625,1402]),
[iquote('3:Res:625.2,1402.1')] ).
cnf(1626,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f15(u,x5,x6,x7,v),f15(f20(closure(x1,x2,x3),x4),x8,x9,x10,x11)) ),
inference(res,[status(thm),theory(equality)],[622,1607]),
[iquote('3:Res:622.2,1607.1')] ).
cnf(1627,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f15(u,x5,x6,x7,v),f15(f20(closure(x1,x2,x3),x4),x8,x9,x10,x11)) ),
inference(res,[status(thm),theory(equality)],[621,1607]),
[iquote('3:Res:621.2,1607.1')] ).
cnf(1612,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f15(u,x5,x6,x7,v),f15(f20(boundary(x1,x2,x3),x4),x8,x9,x10,x11)) ),
inference(res,[status(thm),theory(equality)],[622,1605]),
[iquote('3:Res:622.2,1605.1')] ).
cnf(1613,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f15(u,x5,x6,x7,v),f15(f20(boundary(x1,x2,x3),x4),x8,x9,x10,x11)) ),
inference(res,[status(thm),theory(equality)],[621,1605]),
[iquote('3:Res:621.2,1605.1')] ).
cnf(1413,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f19(boundary(x3,x4,x5),x6)) ),
inference(res,[status(thm),theory(equality)],[624,1402]),
[iquote('3:Res:624.2,1402.1')] ).
cnf(1566,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f15(u,x5,x6,x7,v),f15(f20(intersection_of_members(x3),x4),x8,x9,x10,x11)) ),
inference(res,[status(thm),theory(equality)],[626,1559]),
[iquote('3:Res:626.2,1559.1')] ).
cnf(1567,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f15(u,x5,x6,x7,v),f15(f20(intersection_of_members(x3),x4),x8,x9,x10,x11)) ),
inference(res,[status(thm),theory(equality)],[625,1559]),
[iquote('3:Res:625.2,1559.1')] ).
cnf(1568,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f15(u,x5,x6,x7,v),f15(f20(intersection_of_members(x3),x4),x8,x9,x10,x11)) ),
inference(res,[status(thm),theory(equality)],[624,1559]),
[iquote('3:Res:624.2,1559.1')] ).
cnf(1569,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f15(u,x5,x6,x7,v),f15(f20(intersection_of_members(x3),x4),x8,x9,x10,x11)) ),
inference(res,[status(thm),theory(equality)],[623,1559]),
[iquote('3:Res:623.2,1559.1')] ).
cnf(1414,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f15(u,w,x7,x8,v),f19(boundary(x3,x4,x5),x6)) ),
inference(res,[status(thm),theory(equality)],[623,1402]),
[iquote('3:Res:623.2,1402.1')] ).
cnf(1668,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(closure(x,y,z),x1)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f15(f20(closure(x,y,z),x1),v,x6,x7,u),f15(f20(closure(x2,x3,x4),x5),v,x8,x9,u)) ),
inference(mrr,[status(thm)],[1664,544]),
[iquote('3:MRR:1664.0,544.1')] ).
cnf(1667,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(boundary(x,y,z),x1)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f15(f20(boundary(x,y,z),x1),v,x6,x7,u),f15(f20(closure(x2,x3,x4),x5),v,x8,x9,u)) ),
inference(mrr,[status(thm)],[1665,557]),
[iquote('3:MRR:1665.0,557.1')] ).
cnf(1654,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(closure(x,y,z),x1)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f15(f20(closure(x,y,z),x1),v,x6,x7,u),f15(f20(boundary(x2,x3,x4),x5),v,x8,x9,u)) ),
inference(mrr,[status(thm)],[1650,544]),
[iquote('3:MRR:1650.0,544.1')] ).
cnf(1653,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(boundary(x,y,z),x1)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f15(f20(boundary(x,y,z),x1),v,x6,x7,u),f15(f20(boundary(x2,x3,x4),x5),v,x8,x9,u)) ),
inference(mrr,[status(thm)],[1651,557]),
[iquote('3:MRR:1651.0,557.1')] ).
cnf(1593,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)],[1592]),
[iquote('3:Obv:1592.3')] ).
cnf(1666,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_members(x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f15(f20(intersection_of_members(x),y),v,x4,x5,u),f15(f20(closure(z,x1,x2),x3),v,x6,x7,u)) ),
inference(mrr,[status(thm)],[1657,486]),
[iquote('3:MRR:1657.0,486.1')] ).
cnf(1639,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ hausdorff(intersection_of_sets(v,w),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f15(u,w,x,y,v),f15(f20(closure(x1,x2,x3),x4),w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[481,1251]),
[iquote('3:Res:481.1,1251.0')] ).
cnf(1652,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_members(x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f15(f20(intersection_of_members(x),y),v,x4,x5,u),f15(f20(boundary(z,x1,x2),x3),v,x6,x7,u)) ),
inference(mrr,[status(thm)],[1643,486]),
[iquote('3:MRR:1643.0,486.1')] ).
cnf(1637,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ hausdorff(intersection_of_sets(v,w),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f15(u,w,x,y,v),f15(f20(boundary(x1,x2,x3),x4),w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[481,1242]),
[iquote('3:Res:481.1,1242.0')] ).
cnf(1251,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(intersection_of_sets(u,y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f15(v,y,w,x,u),f15(f20(closure(x1,x2,x3),x4),y,x5,x6,u)) ),
inference(res,[status(thm),theory(equality)],[68,1176]),
[iquote('3:Res:68.2,1176.0')] ).
cnf(1636,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(closure(w,x,y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f15(f20(closure(w,x,y),z),x5,x6,x7,x8),f15(f20(closure(x1,x2,x3),x4),x9,x10,x11,x12)) ),
inference(mrr,[status(thm)],[1632,544]),
[iquote('3:MRR:1632.0,544.1')] ).
cnf(1635,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f15(f20(boundary(w,x,y),z),x5,x6,x7,x8),f15(f20(closure(x1,x2,x3),x4),x9,x10,x11,x12)) ),
inference(mrr,[status(thm)],[1633,557]),
[iquote('3:MRR:1633.0,557.1')] ).
cnf(1622,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(closure(w,x,y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f15(f20(closure(w,x,y),z),x5,x6,x7,x8),f15(f20(boundary(x1,x2,x3),x4),x9,x10,x11,x12)) ),
inference(mrr,[status(thm)],[1618,544]),
[iquote('3:MRR:1618.0,544.1')] ).
cnf(1621,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f15(f20(boundary(w,x,y),z),x5,x6,x7,x8),f15(f20(boundary(x1,x2,x3),x4),x9,x10,x11,x12)) ),
inference(mrr,[status(thm)],[1619,557]),
[iquote('3:MRR:1619.0,557.1')] ).
cnf(1242,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(intersection_of_sets(u,y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f15(v,y,w,x,u),f15(f20(boundary(x1,x2,x3),x4),y,x5,x6,u)) ),
inference(res,[status(thm),theory(equality)],[68,1175]),
[iquote('3:Res:68.2,1175.0')] ).
cnf(1634,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f15(f20(intersection_of_members(w),x),x3,x4,x5,x6),f15(f20(closure(y,z,x1),x2),x7,x8,x9,x10)) ),
inference(mrr,[status(thm)],[1625,486]),
[iquote('3:MRR:1625.0,486.1')] ).
cnf(1607,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ hausdorff(union_of_members(z),x1)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f15(u,w,x,y,v),f15(f20(closure(x2,x3,x4),x5),x6,x7,x8,x9)) ),
inference(res,[status(thm),theory(equality)],[481,1162]),
[iquote('3:Res:481.1,1162.0')] ).
cnf(1620,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f15(f20(intersection_of_members(w),x),x3,x4,x5,x6),f15(f20(boundary(y,z,x1),x2),x7,x8,x9,x10)) ),
inference(mrr,[status(thm)],[1611,486]),
[iquote('3:MRR:1611.0,486.1')] ).
cnf(1605,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ hausdorff(union_of_members(z),x1)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f15(u,w,x,y,v),f15(f20(boundary(x2,x3,x4),x5),x6,x7,x8,x9)) ),
inference(res,[status(thm),theory(equality)],[481,1150]),
[iquote('3:Res:481.1,1150.0')] ).
cnf(1162,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(union_of_members(z),x1)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f15(v,y,w,x,u),f15(f20(closure(x2,x3,x4),x5),x6,x7,x8,x9)) ),
inference(res,[status(thm),theory(equality)],[643,1126]),
[iquote('3:Res:643.2,1126.0')] ).
cnf(1150,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(union_of_members(z),x1)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f15(v,y,w,x,u),f15(f20(boundary(x2,x3,x4),x5),x6,x7,x8,x9)) ),
inference(res,[status(thm),theory(equality)],[643,1125]),
[iquote('3:Res:643.2,1125.0')] ).
cnf(1550,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_sets(v,w),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f19(boundary(z,x1,x2),x3),u)
| eq(f20(intersection_of_sets(v,w),y),f15(u,w,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[394,1168]),
[iquote('3:Res:394.1,1168.1')] ).
cnf(1551,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_sets(v,w),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f19(boundary(z,x1,x2),x3),u)
| eq(f19(intersection_of_sets(v,w),y),f15(u,w,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[395,1168]),
[iquote('3:Res:395.1,1168.1')] ).
cnf(1541,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_sets(v,w),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f19(closure(z,x1,x2),x3),u)
| eq(f20(intersection_of_sets(v,w),y),f15(u,w,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[394,1169]),
[iquote('3:Res:394.1,1169.1')] ).
cnf(1542,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_sets(v,w),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f19(closure(z,x1,x2),x3),u)
| eq(f19(intersection_of_sets(v,w),y),f15(u,w,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[395,1169]),
[iquote('3:Res:395.1,1169.1')] ).
cnf(1532,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_sets(v,w),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f20(boundary(z,x1,x2),x3),u)
| eq(f20(intersection_of_sets(v,w),y),f15(u,w,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[394,1170]),
[iquote('3:Res:394.1,1170.1')] ).
cnf(1533,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_sets(v,w),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f20(boundary(z,x1,x2),x3),u)
| eq(f19(intersection_of_sets(v,w),y),f15(u,w,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[395,1170]),
[iquote('3:Res:395.1,1170.1')] ).
cnf(1523,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_sets(v,w),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f20(closure(z,x1,x2),x3),u)
| eq(f20(intersection_of_sets(v,w),y),f15(u,w,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[394,1171]),
[iquote('3:Res:394.1,1171.1')] ).
cnf(1524,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_sets(v,w),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f20(closure(z,x1,x2),x3),u)
| eq(f19(intersection_of_sets(v,w),y),f15(u,w,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[395,1171]),
[iquote('3:Res:395.1,1171.1')] ).
cnf(1384,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u)
| hausdorff(intersection_of_sets(v,w),x3)
| eq(f15(u,w,x4,x5,v),f19(intersection_of_sets(v,w),x3)) ),
inference(res,[status(thm),theory(equality)],[626,1377]),
[iquote('3:Res:626.2,1377.1')] ).
cnf(1385,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u)
| hausdorff(intersection_of_sets(v,w),x3)
| eq(f15(u,w,x4,x5,v),f19(intersection_of_sets(v,w),x3)) ),
inference(res,[status(thm),theory(equality)],[625,1377]),
[iquote('3:Res:625.2,1377.1')] ).
cnf(1386,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u)
| hausdorff(intersection_of_sets(v,w),x3)
| eq(f15(u,w,x4,x5,v),f19(intersection_of_sets(v,w),x3)) ),
inference(res,[status(thm),theory(equality)],[624,1377]),
[iquote('3:Res:624.2,1377.1')] ).
cnf(1387,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u)
| hausdorff(intersection_of_sets(v,w),x3)
| eq(f15(u,w,x4,x5,v),f19(intersection_of_sets(v,w),x3)) ),
inference(res,[status(thm),theory(equality)],[623,1377]),
[iquote('3:Res:623.2,1377.1')] ).
cnf(1348,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u)
| hausdorff(intersection_of_sets(v,w),x3)
| eq(f15(u,w,x4,x5,v),f20(intersection_of_sets(v,w),x3)) ),
inference(res,[status(thm),theory(equality)],[626,1341]),
[iquote('3:Res:626.2,1341.1')] ).
cnf(1349,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u)
| hausdorff(intersection_of_sets(v,w),x3)
| eq(f15(u,w,x4,x5,v),f20(intersection_of_sets(v,w),x3)) ),
inference(res,[status(thm),theory(equality)],[625,1341]),
[iquote('3:Res:625.2,1341.1')] ).
cnf(1350,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u)
| hausdorff(intersection_of_sets(v,w),x3)
| eq(f15(u,w,x4,x5,v),f20(intersection_of_sets(v,w),x3)) ),
inference(res,[status(thm),theory(equality)],[624,1341]),
[iquote('3:Res:624.2,1341.1')] ).
cnf(1351,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u)
| hausdorff(intersection_of_sets(v,w),x3)
| eq(f15(u,w,x4,x5,v),f20(intersection_of_sets(v,w),x3)) ),
inference(res,[status(thm),theory(equality)],[623,1341]),
[iquote('3:Res:623.2,1341.1')] ).
cnf(1560,plain,
( ~ limit_point(u,v,w,x)
| ~ hausdorff(union_of_members(y),z)
| limit_point(u,x1,w,x)
| hausdorff(intersection_of_members(x2),x3)
| eq(f15(u,v,w,x,f16(u,x1,w,x)),f15(f20(intersection_of_members(x2),x3),x4,x5,x6,x7)) ),
inference(res,[status(thm),theory(equality)],[493,1138]),
[iquote('3:Res:493.1,1138.0')] ).
cnf(1580,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u)
| hausdorff(intersection_of_members(x1),x2)
| eq(f15(u,w,x3,x4,v),f15(f20(intersection_of_members(x1),x2),w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[622,1575]),
[iquote('3:Res:622.2,1575.1')] ).
cnf(1522,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)],[68,1100]),
[iquote('3:Res:68.2,1100.1')] ).
cnf(1581,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u)
| hausdorff(intersection_of_members(x1),x2)
| eq(f15(u,w,x3,x4,v),f15(f20(intersection_of_members(x1),x2),w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[621,1575]),
[iquote('3:Res:621.2,1575.1')] ).
cnf(1552,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f19(boundary(x1,x2,x3),x4),u)
| eq(f20(intersection_of_members(y),z),f15(u,w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[486,1168]),
[iquote('3:Res:486.1,1168.1')] ).
cnf(1553,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f19(boundary(x1,x2,x3),x4),u)
| eq(f19(intersection_of_members(y),z),f15(u,w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[487,1168]),
[iquote('3:Res:487.1,1168.1')] ).
cnf(1543,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f19(closure(x1,x2,x3),x4),u)
| eq(f20(intersection_of_members(y),z),f15(u,w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[486,1169]),
[iquote('3:Res:486.1,1169.1')] ).
cnf(1514,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)],[394,1100]),
[iquote('3:Res:394.1,1100.1')] ).
cnf(1544,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f19(closure(x1,x2,x3),x4),u)
| eq(f19(intersection_of_members(y),z),f15(u,w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[487,1169]),
[iquote('3:Res:487.1,1169.1')] ).
cnf(1534,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f20(boundary(x1,x2,x3),x4),u)
| eq(f20(intersection_of_members(y),z),f15(u,w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[486,1170]),
[iquote('3:Res:486.1,1170.1')] ).
cnf(1535,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f20(boundary(x1,x2,x3),x4),u)
| eq(f19(intersection_of_members(y),z),f15(u,w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[487,1170]),
[iquote('3:Res:487.1,1170.1')] ).
cnf(1525,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f20(closure(x1,x2,x3),x4),u)
| eq(f20(intersection_of_members(y),z),f15(u,w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[486,1171]),
[iquote('3:Res:486.1,1171.1')] ).
cnf(1515,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)],[395,1100]),
[iquote('3:Res:395.1,1100.1')] ).
cnf(1526,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f20(closure(x1,x2,x3),x4),u)
| eq(f19(intersection_of_members(y),z),f15(u,w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[487,1171]),
[iquote('3:Res:487.1,1171.1')] ).
cnf(1455,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f15(u,w,x5,x6,v),f20(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[622,1450]),
[iquote('3:Res:622.2,1450.1')] ).
cnf(1456,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f15(u,w,x5,x6,v),f20(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[621,1450]),
[iquote('3:Res:621.2,1450.1')] ).
cnf(1439,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f15(u,w,x5,x6,v),f20(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[622,1420]),
[iquote('3:Res:622.2,1420.1')] ).
cnf(1378,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)],[493,810]),
[iquote('3:Res:493.1,810.0')] ).
cnf(1440,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f15(u,w,x5,x6,v),f20(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[621,1420]),
[iquote('3:Res:621.2,1420.1')] ).
cnf(1425,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f15(u,w,x5,x6,v),f19(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[622,1404]),
[iquote('3:Res:622.2,1404.1')] ).
cnf(1426,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f15(u,w,x5,x6,v),f19(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[621,1404]),
[iquote('3:Res:621.2,1404.1')] ).
cnf(1409,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f15(u,w,x5,x6,v),f19(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[622,1402]),
[iquote('3:Res:622.2,1402.1')] ).
cnf(1342,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)],[493,788]),
[iquote('3:Res:493.1,788.0')] ).
cnf(1410,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f15(u,w,x5,x6,v),f19(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[621,1402]),
[iquote('3:Res:621.2,1402.1')] ).
cnf(1397,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f19(intersection_of_members(x3),x4),u)
| eq(f20(closure(y,z,x1),x2),f15(u,w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[544,1166]),
[iquote('3:Res:544.1,1166.1')] ).
cnf(1398,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f19(intersection_of_members(x3),x4),u)
| eq(f20(boundary(y,z,x1),x2),f15(u,w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[557,1166]),
[iquote('3:Res:557.1,1166.1')] ).
cnf(1399,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f19(intersection_of_members(x3),x4),u)
| eq(f19(closure(y,z,x1),x2),f15(u,w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[545,1166]),
[iquote('3:Res:545.1,1166.1')] ).
cnf(1518,plain,
( ~ limit_point(u,v,w,x)
| ~ hausdorff(intersection_of_sets(f16(u,y,w,x),v),z)
| hausdorff(closure(x1,x2,x3),x4)
| limit_point(u,y,w,x)
| eq(f20(closure(x1,x2,x3),x4),f15(u,v,w,x,f16(u,y,w,x))) ),
inference(res,[status(thm),theory(equality)],[544,1100]),
[iquote('3:Res:544.1,1100.1')] ).
cnf(1400,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f19(intersection_of_members(x3),x4),u)
| eq(f19(boundary(y,z,x1),x2),f15(u,w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[558,1166]),
[iquote('3:Res:558.1,1166.1')] ).
cnf(1372,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f20(intersection_of_members(x3),x4),u)
| eq(f20(closure(y,z,x1),x2),f15(u,w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[544,1167]),
[iquote('3:Res:544.1,1167.1')] ).
cnf(1373,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f20(intersection_of_members(x3),x4),u)
| eq(f20(boundary(y,z,x1),x2),f15(u,w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[557,1167]),
[iquote('3:Res:557.1,1167.1')] ).
cnf(1374,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f20(intersection_of_members(x3),x4),u)
| eq(f19(closure(y,z,x1),x2),f15(u,w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[545,1167]),
[iquote('3:Res:545.1,1167.1')] ).
cnf(1519,plain,
( ~ limit_point(u,v,w,x)
| ~ hausdorff(intersection_of_sets(f16(u,y,w,x),v),z)
| hausdorff(boundary(x1,x2,x3),x4)
| limit_point(u,y,w,x)
| eq(f20(boundary(x1,x2,x3),x4),f15(u,v,w,x,f16(u,y,w,x))) ),
inference(res,[status(thm),theory(equality)],[557,1100]),
[iquote('3:Res:557.1,1100.1')] ).
cnf(1375,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f20(intersection_of_members(x3),x4),u)
| eq(f19(boundary(y,z,x1),x2),f15(u,w,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[558,1167]),
[iquote('3:Res:558.1,1167.1')] ).
cnf(1299,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f15(u,w,x5,x6,v),f19(intersection_of_members(x3),x4)) ),
inference(res,[status(thm),theory(equality)],[626,1278]),
[iquote('3:Res:626.2,1278.1')] ).
cnf(1300,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f15(u,w,x5,x6,v),f19(intersection_of_members(x3),x4)) ),
inference(res,[status(thm),theory(equality)],[625,1278]),
[iquote('3:Res:625.2,1278.1')] ).
cnf(1301,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f15(u,w,x5,x6,v),f19(intersection_of_members(x3),x4)) ),
inference(res,[status(thm),theory(equality)],[624,1278]),
[iquote('3:Res:624.2,1278.1')] ).
cnf(1520,plain,
( ~ limit_point(u,v,w,x)
| ~ hausdorff(intersection_of_sets(f16(u,y,w,x),v),z)
| hausdorff(closure(x1,x2,x3),x4)
| limit_point(u,y,w,x)
| eq(f19(closure(x1,x2,x3),x4),f15(u,v,w,x,f16(u,y,w,x))) ),
inference(res,[status(thm),theory(equality)],[545,1100]),
[iquote('3:Res:545.1,1100.1')] ).
cnf(1302,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f15(u,w,x5,x6,v),f19(intersection_of_members(x3),x4)) ),
inference(res,[status(thm),theory(equality)],[623,1278]),
[iquote('3:Res:623.2,1278.1')] ).
cnf(1285,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f15(u,w,x5,x6,v),f20(intersection_of_members(x3),x4)) ),
inference(res,[status(thm),theory(equality)],[626,1276]),
[iquote('3:Res:626.2,1276.1')] ).
cnf(1286,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f15(u,w,x5,x6,v),f20(intersection_of_members(x3),x4)) ),
inference(res,[status(thm),theory(equality)],[625,1276]),
[iquote('3:Res:625.2,1276.1')] ).
cnf(1287,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f15(u,w,x5,x6,v),f20(intersection_of_members(x3),x4)) ),
inference(res,[status(thm),theory(equality)],[624,1276]),
[iquote('3:Res:624.2,1276.1')] ).
cnf(1521,plain,
( ~ limit_point(u,v,w,x)
| ~ hausdorff(intersection_of_sets(f16(u,y,w,x),v),z)
| hausdorff(boundary(x1,x2,x3),x4)
| limit_point(u,y,w,x)
| eq(f19(boundary(x1,x2,x3),x4),f15(u,v,w,x,f16(u,y,w,x))) ),
inference(res,[status(thm),theory(equality)],[558,1100]),
[iquote('3:Res:558.1,1100.1')] ).
cnf(1288,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u)
| hausdorff(intersection_of_members(x3),x4)
| eq(f15(u,w,x5,x6,v),f20(intersection_of_members(x3),x4)) ),
inference(res,[status(thm),theory(equality)],[623,1276]),
[iquote('3:Res:623.2,1276.1')] ).
cnf(1564,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u)
| hausdorff(intersection_of_members(x1),x2)
| eq(f15(u,x3,x4,x5,v),f15(f20(intersection_of_members(x1),x2),x6,x7,x8,x9)) ),
inference(res,[status(thm),theory(equality)],[622,1559]),
[iquote('3:Res:622.2,1559.1')] ).
cnf(1565,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u)
| hausdorff(intersection_of_members(x1),x2)
| eq(f15(u,x3,x4,x5,v),f15(f20(intersection_of_members(x1),x2),x6,x7,x8,x9)) ),
inference(res,[status(thm),theory(equality)],[621,1559]),
[iquote('3:Res:621.2,1559.1')] ).
cnf(1590,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(closure(x,y,z),x1)
| hausdorff(intersection_of_members(x2),x3)
| eq(f15(f20(closure(x,y,z),x1),v,x4,x5,u),f15(f20(intersection_of_members(x2),x3),v,x6,x7,u)) ),
inference(mrr,[status(thm)],[1586,544]),
[iquote('3:MRR:1586.0,544.1')] ).
cnf(1451,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(closure(x1,x2,x3),x4)
| eq(f15(u,v,w,x,f16(u,y,w,x)),f20(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[493,1028]),
[iquote('3:Res:493.1,1028.0')] ).
cnf(1589,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(boundary(x,y,z),x1)
| hausdorff(intersection_of_members(x2),x3)
| eq(f15(f20(boundary(x,y,z),x1),v,x4,x5,u),f15(f20(intersection_of_members(x2),x3),v,x6,x7,u)) ),
inference(mrr,[status(thm)],[1587,557]),
[iquote('3:MRR:1587.0,557.1')] ).
cnf(1588,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_members(x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f15(f20(intersection_of_members(x),y),v,x2,x3,u),f15(f20(intersection_of_members(z),x1),v,x4,x5,u)) ),
inference(mrr,[status(thm)],[1579,486]),
[iquote('3:MRR:1579.0,486.1')] ).
cnf(1575,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ hausdorff(intersection_of_sets(v,w),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f15(u,w,x,y,v),f15(f20(intersection_of_members(x1),x2),w,x3,x4,v)) ),
inference(res,[status(thm),theory(equality)],[481,1187]),
[iquote('3:Res:481.1,1187.0')] ).
cnf(1187,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(intersection_of_sets(u,y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f15(v,y,w,x,u),f15(f20(intersection_of_members(x1),x2),y,x3,x4,u)) ),
inference(res,[status(thm),theory(equality)],[68,1174]),
[iquote('3:Res:68.2,1174.0')] ).
cnf(1421,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(boundary(x1,x2,x3),x4)
| eq(f15(u,v,w,x,f16(u,y,w,x)),f20(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[493,1006]),
[iquote('3:Res:493.1,1006.0')] ).
cnf(1574,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(closure(w,x,y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f15(f20(closure(w,x,y),z),x3,x4,x5,x6),f15(f20(intersection_of_members(x1),x2),x7,x8,x9,x10)) ),
inference(mrr,[status(thm)],[1570,544]),
[iquote('3:MRR:1570.0,544.1')] ).
cnf(1573,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f15(f20(boundary(w,x,y),z),x3,x4,x5,x6),f15(f20(intersection_of_members(x1),x2),x7,x8,x9,x10)) ),
inference(mrr,[status(thm)],[1571,557]),
[iquote('3:MRR:1571.0,557.1')] ).
cnf(1572,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f15(f20(intersection_of_members(w),x),x1,x2,x3,x4),f15(f20(intersection_of_members(y),z),x5,x6,x7,x8)) ),
inference(mrr,[status(thm)],[1563,486]),
[iquote('3:MRR:1563.0,486.1')] ).
cnf(1559,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ hausdorff(union_of_members(z),x1)
| hausdorff(intersection_of_members(x2),x3)
| eq(f15(u,w,x,y,v),f15(f20(intersection_of_members(x2),x3),x4,x5,x6,x7)) ),
inference(res,[status(thm),theory(equality)],[481,1138]),
[iquote('3:Res:481.1,1138.0')] ).
cnf(1405,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(closure(x1,x2,x3),x4)
| eq(f15(u,v,w,x,f16(u,y,w,x)),f19(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[493,984]),
[iquote('3:Res:493.1,984.0')] ).
cnf(1138,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(union_of_members(z),x1)
| hausdorff(intersection_of_members(x2),x3)
| eq(f15(v,y,w,x,u),f15(f20(intersection_of_members(x2),x3),x4,x5,x6,x7)) ),
inference(res,[status(thm),theory(equality)],[643,1124]),
[iquote('3:Res:643.2,1124.0')] ).
cnf(1393,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_sets(v,w),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f19(intersection_of_members(z),x1),u)
| eq(f20(intersection_of_sets(v,w),y),f15(u,w,x2,x3,v)) ),
inference(res,[status(thm),theory(equality)],[394,1166]),
[iquote('3:Res:394.1,1166.1')] ).
cnf(1394,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_sets(v,w),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f19(intersection_of_members(z),x1),u)
| eq(f19(intersection_of_sets(v,w),y),f15(u,w,x2,x3,v)) ),
inference(res,[status(thm),theory(equality)],[395,1166]),
[iquote('3:Res:395.1,1166.1')] ).
cnf(1382,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u)
| hausdorff(intersection_of_sets(v,w),x1)
| eq(f15(u,w,x2,x3,v),f19(intersection_of_sets(v,w),x1)) ),
inference(res,[status(thm),theory(equality)],[622,1377]),
[iquote('3:Res:622.2,1377.1')] ).
cnf(1403,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(boundary(x1,x2,x3),x4)
| eq(f15(u,v,w,x,f16(u,y,w,x)),f19(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[493,962]),
[iquote('3:Res:493.1,962.0')] ).
cnf(1383,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u)
| hausdorff(intersection_of_sets(v,w),x1)
| eq(f15(u,w,x2,x3,v),f19(intersection_of_sets(v,w),x1)) ),
inference(res,[status(thm),theory(equality)],[621,1377]),
[iquote('3:Res:621.2,1377.1')] ).
cnf(1368,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_sets(v,w),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f20(intersection_of_members(z),x1),u)
| eq(f20(intersection_of_sets(v,w),y),f15(u,w,x2,x3,v)) ),
inference(res,[status(thm),theory(equality)],[394,1167]),
[iquote('3:Res:394.1,1167.1')] ).
cnf(1369,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_sets(v,w),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f20(intersection_of_members(z),x1),u)
| eq(f19(intersection_of_sets(v,w),y),f15(u,w,x2,x3,v)) ),
inference(res,[status(thm),theory(equality)],[395,1167]),
[iquote('3:Res:395.1,1167.1')] ).
cnf(1346,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u)
| hausdorff(intersection_of_sets(v,w),x1)
| eq(f15(u,w,x2,x3,v),f20(intersection_of_sets(v,w),x1)) ),
inference(res,[status(thm),theory(equality)],[622,1341]),
[iquote('3:Res:622.2,1341.1')] ).
cnf(1516,plain,
( ~ limit_point(u,v,w,x)
| ~ hausdorff(intersection_of_sets(f16(u,y,w,x),v),z)
| hausdorff(intersection_of_members(x1),x2)
| limit_point(u,y,w,x)
| eq(f20(intersection_of_members(x1),x2),f15(u,v,w,x,f16(u,y,w,x))) ),
inference(res,[status(thm),theory(equality)],[486,1100]),
[iquote('3:Res:486.1,1100.1')] ).
cnf(1347,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u)
| hausdorff(intersection_of_sets(v,w),x1)
| eq(f15(u,w,x2,x3,v),f20(intersection_of_sets(v,w),x1)) ),
inference(res,[status(thm),theory(equality)],[621,1341]),
[iquote('3:Res:621.2,1341.1')] ).
cnf(1502,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| limit_point(y,z,x1,x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f19(boundary(x3,x4,x5),x6),u)
| eq(y,f15(u,x7,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[583,1118]),
[iquote('3:Res:583.1,1118.1')] ).
cnf(1490,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| limit_point(y,z,x1,x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f19(closure(x3,x4,x5),x6),u)
| eq(y,f15(u,x7,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[583,1119]),
[iquote('3:Res:583.1,1119.1')] ).
cnf(1478,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| limit_point(y,z,x1,x2)
| hausdorff(boundary(x3,x4,x5),x6)
| eq(f20(boundary(x3,x4,x5),x6),u)
| eq(y,f15(u,x7,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[583,1120]),
[iquote('3:Res:583.1,1120.1')] ).
cnf(1517,plain,
( ~ limit_point(u,v,w,x)
| ~ hausdorff(intersection_of_sets(f16(u,y,w,x),v),z)
| hausdorff(intersection_of_members(x1),x2)
| limit_point(u,y,w,x)
| eq(f19(intersection_of_members(x1),x2),f15(u,v,w,x,f16(u,y,w,x))) ),
inference(res,[status(thm),theory(equality)],[487,1100]),
[iquote('3:Res:487.1,1100.1')] ).
cnf(1466,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| limit_point(y,z,x1,x2)
| hausdorff(closure(x3,x4,x5),x6)
| eq(f20(closure(x3,x4,x5),x6),u)
| eq(y,f15(u,x7,x8,x9,v)) ),
inference(res,[status(thm),theory(equality)],[583,1121]),
[iquote('3:Res:583.1,1121.1')] ).
cnf(1465,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(closure(x,y,z),x1)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f15(f20(closure(x,y,z),x1),v,x6,x7,u),f20(closure(x2,x3,x4),x5)) ),
inference(mrr,[status(thm)],[1461,544]),
[iquote('3:MRR:1461.0,544.1')] ).
cnf(1464,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(boundary(x,y,z),x1)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f15(f20(boundary(x,y,z),x1),v,x6,x7,u),f20(closure(x2,x3,x4),x5)) ),
inference(mrr,[status(thm)],[1462,557]),
[iquote('3:MRR:1462.0,557.1')] ).
cnf(1449,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(closure(x,y,z),x1)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f15(f20(closure(x,y,z),x1),v,x6,x7,u),f20(boundary(x2,x3,x4),x5)) ),
inference(mrr,[status(thm)],[1445,544]),
[iquote('3:MRR:1445.0,544.1')] ).
cnf(1279,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_members(x1),x2)
| eq(f15(u,v,w,x,f16(u,y,w,x)),f19(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[493,880]),
[iquote('3:Res:493.1,880.0')] ).
cnf(1448,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(boundary(x,y,z),x1)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f15(f20(boundary(x,y,z),x1),v,x6,x7,u),f20(boundary(x2,x3,x4),x5)) ),
inference(mrr,[status(thm)],[1446,557]),
[iquote('3:MRR:1446.0,557.1')] ).
cnf(1435,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(closure(x,y,z),x1)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f15(f20(closure(x,y,z),x1),v,x6,x7,u),f19(closure(x2,x3,x4),x5)) ),
inference(mrr,[status(thm)],[1431,544]),
[iquote('3:MRR:1431.0,544.1')] ).
cnf(1434,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(boundary(x,y,z),x1)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f15(f20(boundary(x,y,z),x1),v,x6,x7,u),f19(closure(x2,x3,x4),x5)) ),
inference(mrr,[status(thm)],[1432,557]),
[iquote('3:MRR:1432.0,557.1')] ).
cnf(1419,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(closure(x,y,z),x1)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f15(f20(closure(x,y,z),x1),v,x6,x7,u),f19(boundary(x2,x3,x4),x5)) ),
inference(mrr,[status(thm)],[1415,544]),
[iquote('3:MRR:1415.0,544.1')] ).
cnf(1277,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_members(x1),x2)
| eq(f15(u,v,w,x,f16(u,y,w,x)),f20(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[493,858]),
[iquote('3:Res:493.1,858.0')] ).
cnf(1418,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(boundary(x,y,z),x1)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f15(f20(boundary(x,y,z),x1),v,x6,x7,u),f19(boundary(x2,x3,x4),x5)) ),
inference(mrr,[status(thm)],[1416,557]),
[iquote('3:MRR:1416.0,557.1')] ).
cnf(1247,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(closure(x,y,z),x1)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f20(closure(x,y,z),x1),f15(f20(closure(x2,x3,x4),x5),v,x6,x7,u)) ),
inference(res,[status(thm),theory(equality)],[544,1176]),
[iquote('3:Res:544.1,1176.0')] ).
cnf(1248,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(boundary(x,y,z),x1)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f20(boundary(x,y,z),x1),f15(f20(closure(x2,x3,x4),x5),v,x6,x7,u)) ),
inference(res,[status(thm),theory(equality)],[557,1176]),
[iquote('3:Res:557.1,1176.0')] ).
cnf(1249,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(closure(x,y,z),x1)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f19(closure(x,y,z),x1),f15(f20(closure(x2,x3,x4),x5),v,x6,x7,u)) ),
inference(res,[status(thm),theory(equality)],[545,1176]),
[iquote('3:Res:545.1,1176.0')] ).
cnf(1168,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,intersection_of_sets(v,x))
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f19(boundary(z,x1,x2),x3),u)
| eq(w,f15(u,x,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[626,1099]),
[iquote('3:Res:626.2,1099.1')] ).
cnf(1250,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(boundary(x,y,z),x1)
| hausdorff(closure(x2,x3,x4),x5)
| eq(f19(boundary(x,y,z),x1),f15(f20(closure(x2,x3,x4),x5),v,x6,x7,u)) ),
inference(res,[status(thm),theory(equality)],[558,1176]),
[iquote('3:Res:558.1,1176.0')] ).
cnf(1238,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(closure(x,y,z),x1)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f20(closure(x,y,z),x1),f15(f20(boundary(x2,x3,x4),x5),v,x6,x7,u)) ),
inference(res,[status(thm),theory(equality)],[544,1175]),
[iquote('3:Res:544.1,1175.0')] ).
cnf(1239,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(boundary(x,y,z),x1)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f20(boundary(x,y,z),x1),f15(f20(boundary(x2,x3,x4),x5),v,x6,x7,u)) ),
inference(res,[status(thm),theory(equality)],[557,1175]),
[iquote('3:Res:557.1,1175.0')] ).
cnf(1240,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(closure(x,y,z),x1)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f19(closure(x,y,z),x1),f15(f20(boundary(x2,x3,x4),x5),v,x6,x7,u)) ),
inference(res,[status(thm),theory(equality)],[545,1175]),
[iquote('3:Res:545.1,1175.0')] ).
cnf(1169,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,intersection_of_sets(v,x))
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f19(closure(z,x1,x2),x3),u)
| eq(w,f15(u,x,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[625,1099]),
[iquote('3:Res:625.2,1099.1')] ).
cnf(1241,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(boundary(x,y,z),x1)
| hausdorff(boundary(x2,x3,x4),x5)
| eq(f19(boundary(x,y,z),x1),f15(f20(boundary(x2,x3,x4),x5),v,x6,x7,u)) ),
inference(res,[status(thm),theory(equality)],[558,1175]),
[iquote('3:Res:558.1,1175.0')] ).
cnf(1225,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u)
| limit_point(x3,x4,x5,x6)
| eq(f15(u,x7,x8,x9,v),x3) ),
inference(res,[status(thm),theory(equality)],[626,1218]),
[iquote('3:Res:626.2,1218.1')] ).
cnf(1226,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u)
| limit_point(x3,x4,x5,x6)
| eq(f15(u,x7,x8,x9,v),x3) ),
inference(res,[status(thm),theory(equality)],[625,1218]),
[iquote('3:Res:625.2,1218.1')] ).
cnf(1227,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u)
| limit_point(x3,x4,x5,x6)
| eq(f15(u,x7,x8,x9,v),x3) ),
inference(res,[status(thm),theory(equality)],[624,1218]),
[iquote('3:Res:624.2,1218.1')] ).
cnf(1170,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,intersection_of_sets(v,x))
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f20(boundary(z,x1,x2),x3),u)
| eq(w,f15(u,x,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[624,1099]),
[iquote('3:Res:624.2,1099.1')] ).
cnf(1228,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u)
| limit_point(x3,x4,x5,x6)
| eq(f15(u,x7,x8,x9,v),x3) ),
inference(res,[status(thm),theory(equality)],[623,1218]),
[iquote('3:Res:623.2,1218.1')] ).
cnf(1505,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(y,z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f19(boundary(x1,x2,x3),x4),u)
| eq(f20(y,z),f15(u,x5,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[521,1118]),
[iquote('3:Res:521.1,1118.1')] ).
cnf(1506,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(y,z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f19(boundary(x1,x2,x3),x4),u)
| eq(f19(y,z),f15(u,x5,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[523,1118]),
[iquote('3:Res:523.1,1118.1')] ).
cnf(1493,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(y,z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f19(closure(x1,x2,x3),x4),u)
| eq(f20(y,z),f15(u,x5,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[521,1119]),
[iquote('3:Res:521.1,1119.1')] ).
cnf(1171,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,intersection_of_sets(v,x))
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f20(closure(z,x1,x2),x3),u)
| eq(w,f15(u,x,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[623,1099]),
[iquote('3:Res:623.2,1099.1')] ).
cnf(1494,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(y,z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f19(closure(x1,x2,x3),x4),u)
| eq(f19(y,z),f15(u,x5,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[523,1119]),
[iquote('3:Res:523.1,1119.1')] ).
cnf(1481,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(y,z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f20(boundary(x1,x2,x3),x4),u)
| eq(f20(y,z),f15(u,x5,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[521,1120]),
[iquote('3:Res:521.1,1120.1')] ).
cnf(1482,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(y,z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f20(boundary(x1,x2,x3),x4),u)
| eq(f19(y,z),f15(u,x5,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[523,1120]),
[iquote('3:Res:523.1,1120.1')] ).
cnf(1469,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(y,z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f20(closure(x1,x2,x3),x4),u)
| eq(f20(y,z),f15(u,x5,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[521,1121]),
[iquote('3:Res:521.1,1121.1')] ).
cnf(1112,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)],[642,766]),
[iquote('3:Res:642.2,766.2')] ).
cnf(1470,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(y,z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f20(closure(x1,x2,x3),x4),u)
| eq(f19(y,z),f15(u,x5,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[523,1121]),
[iquote('3:Res:523.1,1121.1')] ).
cnf(1209,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u)
| hausdorff(x3,x4)
| eq(f15(u,x5,x6,x7,v),f19(x3,x4)) ),
inference(res,[status(thm),theory(equality)],[626,1202]),
[iquote('3:Res:626.2,1202.1')] ).
cnf(1210,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u)
| hausdorff(x3,x4)
| eq(f15(u,x5,x6,x7,v),f19(x3,x4)) ),
inference(res,[status(thm),theory(equality)],[625,1202]),
[iquote('3:Res:625.2,1202.1')] ).
cnf(1211,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u)
| hausdorff(x3,x4)
| eq(f15(u,x5,x6,x7,v),f19(x3,x4)) ),
inference(res,[status(thm),theory(equality)],[624,1202]),
[iquote('3:Res:624.2,1202.1')] ).
cnf(1100,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)],[493,764]),
[iquote('3:Res:493.1,764.0')] ).
cnf(1212,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u)
| hausdorff(x3,x4)
| eq(f15(u,x5,x6,x7,v),f19(x3,x4)) ),
inference(res,[status(thm),theory(equality)],[623,1202]),
[iquote('3:Res:623.2,1202.1')] ).
cnf(1193,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u)
| hausdorff(x3,x4)
| eq(f15(u,x5,x6,x7,v),f20(x3,x4)) ),
inference(res,[status(thm),theory(equality)],[626,1177]),
[iquote('3:Res:626.2,1177.1')] ).
cnf(1194,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u)
| hausdorff(x3,x4)
| eq(f15(u,x5,x6,x7,v),f20(x3,x4)) ),
inference(res,[status(thm),theory(equality)],[625,1177]),
[iquote('3:Res:625.2,1177.1')] ).
cnf(1195,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u)
| hausdorff(x3,x4)
| eq(f15(u,x5,x6,x7,v),f20(x3,x4)) ),
inference(res,[status(thm),theory(equality)],[624,1177]),
[iquote('3:Res:624.2,1177.1')] ).
cnf(1090,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)],[394,751]),
[iquote('3:Res:394.1,751.2')] ).
cnf(1196,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u)
| hausdorff(x3,x4)
| eq(f15(u,x5,x6,x7,v),f20(x3,x4)) ),
inference(res,[status(thm),theory(equality)],[623,1177]),
[iquote('3:Res:623.2,1177.1')] ).
cnf(1118,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,union_of_members(x))
| ~ hausdorff(union_of_members(x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f19(boundary(z,x1,x2),x3),u)
| eq(w,f15(u,x4,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[626,1087]),
[iquote('3:Res:626.2,1087.1')] ).
cnf(1119,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,union_of_members(x))
| ~ hausdorff(union_of_members(x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f19(closure(z,x1,x2),x3),u)
| eq(w,f15(u,x4,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[625,1087]),
[iquote('3:Res:625.2,1087.1')] ).
cnf(1120,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,union_of_members(x))
| ~ hausdorff(union_of_members(x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f20(boundary(z,x1,x2),x3),u)
| eq(w,f15(u,x4,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[624,1087]),
[iquote('3:Res:624.2,1087.1')] ).
cnf(1091,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)],[395,751]),
[iquote('3:Res:395.1,751.2')] ).
cnf(1121,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,union_of_members(x))
| ~ hausdorff(union_of_members(x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f20(closure(z,x1,x2),x3),u)
| eq(w,f15(u,x4,x5,x6,v)) ),
inference(res,[status(thm),theory(equality)],[623,1087]),
[iquote('3:Res:623.2,1087.1')] ).
cnf(1463,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_members(x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f15(f20(intersection_of_members(x),y),v,x4,x5,u),f20(closure(z,x1,x2),x3)) ),
inference(mrr,[status(thm)],[1454,486]),
[iquote('3:MRR:1454.0,486.1')] ).
cnf(1450,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ hausdorff(intersection_of_sets(v,w),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f15(u,w,x,y,v),f20(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[481,1028]),
[iquote('3:Res:481.1,1028.0')] ).
cnf(1447,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_members(x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f15(f20(intersection_of_members(x),y),v,x4,x5,u),f20(boundary(z,x1,x2),x3)) ),
inference(mrr,[status(thm)],[1438,486]),
[iquote('3:MRR:1438.0,486.1')] ).
cnf(1028,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(intersection_of_sets(u,y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f15(v,y,w,x,u),f20(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[68,760]),
[iquote('3:Res:68.2,760.0')] ).
cnf(1420,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ hausdorff(intersection_of_sets(v,w),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f15(u,w,x,y,v),f20(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[481,1006]),
[iquote('3:Res:481.1,1006.0')] ).
cnf(1433,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_members(x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f15(f20(intersection_of_members(x),y),v,x4,x5,u),f19(closure(z,x1,x2),x3)) ),
inference(mrr,[status(thm)],[1424,486]),
[iquote('3:MRR:1424.0,486.1')] ).
cnf(1404,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ hausdorff(intersection_of_sets(v,w),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f15(u,w,x,y,v),f19(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[481,984]),
[iquote('3:Res:481.1,984.0')] ).
cnf(1417,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_members(x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f15(f20(intersection_of_members(x),y),v,x4,x5,u),f19(boundary(z,x1,x2),x3)) ),
inference(mrr,[status(thm)],[1408,486]),
[iquote('3:MRR:1408.0,486.1')] ).
cnf(1006,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(intersection_of_sets(u,y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f15(v,y,w,x,u),f20(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[68,761]),
[iquote('3:Res:68.2,761.0')] ).
cnf(1402,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ hausdorff(intersection_of_sets(v,w),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f15(u,w,x,y,v),f19(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[481,962]),
[iquote('3:Res:481.1,962.0')] ).
cnf(1395,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f19(intersection_of_members(x1),x2),u)
| eq(f20(intersection_of_members(y),z),f15(u,w,x3,x4,v)) ),
inference(res,[status(thm),theory(equality)],[486,1166]),
[iquote('3:Res:486.1,1166.1')] ).
cnf(1396,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f19(intersection_of_members(x1),x2),u)
| eq(f19(intersection_of_members(y),z),f15(u,w,x3,x4,v)) ),
inference(res,[status(thm),theory(equality)],[487,1166]),
[iquote('3:Res:487.1,1166.1')] ).
cnf(1370,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f20(intersection_of_members(x1),x2),u)
| eq(f20(intersection_of_members(y),z),f15(u,w,x3,x4,v)) ),
inference(res,[status(thm),theory(equality)],[486,1167]),
[iquote('3:Res:486.1,1167.1')] ).
cnf(984,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(intersection_of_sets(u,y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f15(v,y,w,x,u),f19(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[68,762]),
[iquote('3:Res:68.2,762.0')] ).
cnf(1371,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f20(intersection_of_members(x1),x2),u)
| eq(f19(intersection_of_members(y),z),f15(u,w,x3,x4,v)) ),
inference(res,[status(thm),theory(equality)],[487,1167]),
[iquote('3:Res:487.1,1167.1')] ).
cnf(1297,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u)
| hausdorff(intersection_of_members(x1),x2)
| eq(f15(u,w,x3,x4,v),f19(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[622,1278]),
[iquote('3:Res:622.2,1278.1')] ).
cnf(1298,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u)
| hausdorff(intersection_of_members(x1),x2)
| eq(f15(u,w,x3,x4,v),f19(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[621,1278]),
[iquote('3:Res:621.2,1278.1')] ).
cnf(1283,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u)
| hausdorff(intersection_of_members(x1),x2)
| eq(f15(u,w,x3,x4,v),f20(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[622,1276]),
[iquote('3:Res:622.2,1276.1')] ).
cnf(962,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(intersection_of_sets(u,y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f15(v,y,w,x,u),f19(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[68,763]),
[iquote('3:Res:68.2,763.0')] ).
cnf(1284,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u)
| hausdorff(intersection_of_members(x1),x2)
| eq(f15(u,w,x3,x4,v),f20(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[621,1276]),
[iquote('3:Res:621.2,1276.1')] ).
cnf(1392,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(closure(x,y,z),x1)
| hausdorff(intersection_of_sets(u,v),x2)
| eq(f15(f20(closure(x,y,z),x1),v,x3,x4,u),f19(intersection_of_sets(u,v),x2)) ),
inference(mrr,[status(thm)],[1388,544]),
[iquote('3:MRR:1388.0,544.1')] ).
cnf(1391,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(boundary(x,y,z),x1)
| hausdorff(intersection_of_sets(u,v),x2)
| eq(f15(f20(boundary(x,y,z),x1),v,x3,x4,u),f19(intersection_of_sets(u,v),x2)) ),
inference(mrr,[status(thm)],[1389,557]),
[iquote('3:MRR:1389.0,557.1')] ).
cnf(1356,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(closure(x,y,z),x1)
| hausdorff(intersection_of_sets(u,v),x2)
| eq(f15(f20(closure(x,y,z),x1),v,x3,x4,u),f20(intersection_of_sets(u,v),x2)) ),
inference(mrr,[status(thm)],[1352,544]),
[iquote('3:MRR:1352.0,544.1')] ).
cnf(797,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)],[514,753]),
[iquote('3:Res:514.2,753.0')] ).
cnf(1355,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(boundary(x,y,z),x1)
| hausdorff(intersection_of_sets(u,v),x2)
| eq(f15(f20(boundary(x,y,z),x1),v,x3,x4,u),f20(intersection_of_sets(u,v),x2)) ),
inference(mrr,[status(thm)],[1353,557]),
[iquote('3:MRR:1353.0,557.1')] ).
cnf(1243,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_sets(u,v),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(intersection_of_sets(u,v),x),f15(f20(closure(y,z,x1),x2),v,x3,x4,u)) ),
inference(res,[status(thm),theory(equality)],[394,1176]),
[iquote('3:Res:394.1,1176.0')] ).
cnf(1244,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_sets(u,v),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(intersection_of_sets(u,v),x),f15(f20(closure(y,z,x1),x2),v,x3,x4,u)) ),
inference(res,[status(thm),theory(equality)],[395,1176]),
[iquote('3:Res:395.1,1176.0')] ).
cnf(1234,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_sets(u,v),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(intersection_of_sets(u,v),x),f15(f20(boundary(y,z,x1),x2),v,x3,x4,u)) ),
inference(res,[status(thm),theory(equality)],[394,1175]),
[iquote('3:Res:394.1,1175.0')] ).
cnf(775,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)],[514,752]),
[iquote('3:Res:514.2,752.0')] ).
cnf(1235,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_sets(u,v),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(intersection_of_sets(u,v),x),f15(f20(boundary(y,z,x1),x2),v,x3,x4,u)) ),
inference(res,[status(thm),theory(equality)],[395,1175]),
[iquote('3:Res:395.1,1175.0')] ).
cnf(1166,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,intersection_of_sets(v,x))
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f19(intersection_of_members(z),x1),u)
| eq(w,f15(u,x,x2,x3,v)) ),
inference(res,[status(thm),theory(equality)],[622,1099]),
[iquote('3:Res:622.2,1099.1')] ).
cnf(1390,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_members(x),y)
| hausdorff(intersection_of_sets(u,v),z)
| eq(f15(f20(intersection_of_members(x),y),v,x1,x2,u),f19(intersection_of_sets(u,v),z)) ),
inference(mrr,[status(thm)],[1381,486]),
[iquote('3:MRR:1381.0,486.1')] ).
cnf(1377,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)],[481,810]),
[iquote('3:Res:481.1,810.0')] ).
cnf(810,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)],[68,753]),
[iquote('3:Res:68.2,753.0')] ).
cnf(1167,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,intersection_of_sets(v,x))
| ~ hausdorff(intersection_of_sets(v,x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f20(intersection_of_members(z),x1),u)
| eq(w,f15(u,x,x2,x3,v)) ),
inference(res,[status(thm),theory(equality)],[621,1099]),
[iquote('3:Res:621.2,1099.1')] ).
cnf(1219,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)],[493,894]),
[iquote('3:Res:493.1,894.0')] ).
cnf(1354,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_members(x),y)
| hausdorff(intersection_of_sets(u,v),z)
| eq(f15(f20(intersection_of_members(x),y),v,x1,x2,u),f20(intersection_of_sets(u,v),z)) ),
inference(mrr,[status(thm)],[1345,486]),
[iquote('3:MRR:1345.0,486.1')] ).
cnf(1341,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)],[481,788]),
[iquote('3:Res:481.1,788.0')] ).
cnf(788,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)],[68,752]),
[iquote('3:Res:68.2,752.0')] ).
cnf(1203,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)],[493,838]),
[iquote('3:Res:493.1,838.0')] ).
cnf(1178,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)],[493,826]),
[iquote('3:Res:493.1,826.0')] ).
cnf(1088,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)],[493,765]),
[iquote('3:Res:493.1,765.0')] ).
cnf(1094,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ hausdorff(f6(v,y,u,w,x),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f20(closure(x1,x2,x3),x4),u) ),
inference(res,[status(thm),theory(equality)],[544,751]),
[iquote('3:Res:544.1,751.2')] ).
cnf(1095,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ hausdorff(f6(v,y,u,w,x),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f20(boundary(x1,x2,x3),x4),u) ),
inference(res,[status(thm),theory(equality)],[557,751]),
[iquote('3:Res:557.1,751.2')] ).
cnf(1096,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ hausdorff(f6(v,y,u,w,x),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f19(closure(x1,x2,x3),x4),u) ),
inference(res,[status(thm),theory(equality)],[545,751]),
[iquote('3:Res:545.1,751.2')] ).
cnf(1097,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ hausdorff(f6(v,y,u,w,x),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f19(boundary(x1,x2,x3),x4),u) ),
inference(res,[status(thm),theory(equality)],[558,751]),
[iquote('3:Res:558.1,751.2')] ).
cnf(1015,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ hausdorff(f6(v,y,u,w,x),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(u,f20(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[514,760]),
[iquote('3:Res:514.2,760.0')] ).
cnf(993,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ hausdorff(f6(v,y,u,w,x),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(u,f20(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[514,761]),
[iquote('3:Res:514.2,761.0')] ).
cnf(971,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ hausdorff(f6(v,y,u,w,x),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(u,f19(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[514,762]),
[iquote('3:Res:514.2,762.0')] ).
cnf(1307,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(closure(x,y,z),x1)
| hausdorff(intersection_of_members(x2),x3)
| eq(f15(f20(closure(x,y,z),x1),v,x4,x5,u),f19(intersection_of_members(x2),x3)) ),
inference(mrr,[status(thm)],[1303,544]),
[iquote('3:MRR:1303.0,544.1')] ).
cnf(1306,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(boundary(x,y,z),x1)
| hausdorff(intersection_of_members(x2),x3)
| eq(f15(f20(boundary(x,y,z),x1),v,x4,x5,u),f19(intersection_of_members(x2),x3)) ),
inference(mrr,[status(thm)],[1304,557]),
[iquote('3:MRR:1304.0,557.1')] ).
cnf(1293,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(closure(x,y,z),x1)
| hausdorff(intersection_of_members(x2),x3)
| eq(f15(f20(closure(x,y,z),x1),v,x4,x5,u),f20(intersection_of_members(x2),x3)) ),
inference(mrr,[status(thm)],[1289,544]),
[iquote('3:MRR:1289.0,544.1')] ).
cnf(1292,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(boundary(x,y,z),x1)
| hausdorff(intersection_of_members(x2),x3)
| eq(f15(f20(boundary(x,y,z),x1),v,x4,x5,u),f20(intersection_of_members(x2),x3)) ),
inference(mrr,[status(thm)],[1290,557]),
[iquote('3:MRR:1290.0,557.1')] ).
cnf(949,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ hausdorff(f6(v,y,u,w,x),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(u,f19(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[514,763]),
[iquote('3:Res:514.2,763.0')] ).
cnf(1305,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_members(x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f15(f20(intersection_of_members(x),y),v,x2,x3,u),f19(intersection_of_members(z),x1)) ),
inference(mrr,[status(thm)],[1296,486]),
[iquote('3:MRR:1296.0,486.1')] ).
cnf(1278,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ hausdorff(intersection_of_sets(v,w),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f15(u,w,x,y,v),f19(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[481,880]),
[iquote('3:Res:481.1,880.0')] ).
cnf(1291,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_members(x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f15(f20(intersection_of_members(x),y),v,x2,x3,u),f20(intersection_of_members(z),x1)) ),
inference(mrr,[status(thm)],[1282,486]),
[iquote('3:MRR:1282.0,486.1')] ).
cnf(1276,plain,
( ~ element_of_set(u,v)
| ~ limit_point(u,w,x,y)
| ~ hausdorff(intersection_of_sets(v,w),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f15(u,w,x,y,v),f20(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[481,858]),
[iquote('3:Res:481.1,858.0')] ).
cnf(880,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(intersection_of_sets(u,y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f15(v,y,w,x,u),f19(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[68,757]),
[iquote('3:Res:68.2,757.0')] ).
cnf(858,plain,
( ~ neighborhood(u,v,w,x)
| ~ limit_point(v,y,w,x)
| ~ hausdorff(intersection_of_sets(u,y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f15(v,y,w,x,u),f20(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[68,756]),
[iquote('3:Res:68.2,756.0')] ).
cnf(1101,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)],[582,766]),
[iquote('3:Res:582.1,766.2')] ).
cnf(1264,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| limit_point(y,z,x1,x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f19(intersection_of_members(x3),x4),u)
| eq(y,f15(u,x5,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[583,1116]),
[iquote('3:Res:583.1,1116.1')] ).
cnf(1252,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| limit_point(y,z,x1,x2)
| hausdorff(intersection_of_members(x3),x4)
| eq(f20(intersection_of_members(x3),x4),u)
| eq(y,f15(u,x5,x6,x7,v)) ),
inference(res,[status(thm),theory(equality)],[583,1117]),
[iquote('3:Res:583.1,1117.1')] ).
cnf(1066,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)],[642,747]),
[iquote('3:Res:642.2,747.0')] ).
cnf(1245,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_members(x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f20(intersection_of_members(x),y),f15(f20(closure(z,x1,x2),x3),v,x4,x5,u)) ),
inference(res,[status(thm),theory(equality)],[486,1176]),
[iquote('3:Res:486.1,1176.0')] ).
cnf(1246,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_members(x),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f19(intersection_of_members(x),y),f15(f20(closure(z,x1,x2),x3),v,x4,x5,u)) ),
inference(res,[status(thm),theory(equality)],[487,1176]),
[iquote('3:Res:487.1,1176.0')] ).
cnf(1236,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_members(x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f20(intersection_of_members(x),y),f15(f20(boundary(z,x1,x2),x3),v,x4,x5,u)) ),
inference(res,[status(thm),theory(equality)],[486,1175]),
[iquote('3:Res:486.1,1175.0')] ).
cnf(1237,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_members(x),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f19(intersection_of_members(x),y),f15(f20(boundary(z,x1,x2),x3),v,x4,x5,u)) ),
inference(res,[status(thm),theory(equality)],[487,1175]),
[iquote('3:Res:487.1,1175.0')] ).
cnf(1106,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)],[551,766]),
[iquote('3:Res:551.1,766.2')] ).
cnf(1223,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u)
| limit_point(x1,x2,x3,x4)
| eq(f15(u,x5,x6,x7,v),x1) ),
inference(res,[status(thm),theory(equality)],[622,1218]),
[iquote('3:Res:622.2,1218.1')] ).
cnf(1224,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u)
| limit_point(x1,x2,x3,x4)
| eq(f15(u,x5,x6,x7,v),x1) ),
inference(res,[status(thm),theory(equality)],[621,1218]),
[iquote('3:Res:621.2,1218.1')] ).
cnf(1183,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(closure(x,y,z),x1)
| hausdorff(intersection_of_members(x2),x3)
| eq(f20(closure(x,y,z),x1),f15(f20(intersection_of_members(x2),x3),v,x4,x5,u)) ),
inference(res,[status(thm),theory(equality)],[544,1174]),
[iquote('3:Res:544.1,1174.0')] ).
cnf(1184,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(boundary(x,y,z),x1)
| hausdorff(intersection_of_members(x2),x3)
| eq(f20(boundary(x,y,z),x1),f15(f20(intersection_of_members(x2),x3),v,x4,x5,u)) ),
inference(res,[status(thm),theory(equality)],[557,1174]),
[iquote('3:Res:557.1,1174.0')] ).
cnf(1107,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)],[552,766]),
[iquote('3:Res:552.1,766.2')] ).
cnf(1185,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(closure(x,y,z),x1)
| hausdorff(intersection_of_members(x2),x3)
| eq(f19(closure(x,y,z),x1),f15(f20(intersection_of_members(x2),x3),v,x4,x5,u)) ),
inference(res,[status(thm),theory(equality)],[545,1174]),
[iquote('3:Res:545.1,1174.0')] ).
cnf(1186,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(boundary(x,y,z),x1)
| hausdorff(intersection_of_members(x2),x3)
| eq(f19(boundary(x,y,z),x1),f15(f20(intersection_of_members(x2),x3),v,x4,x5,u)) ),
inference(res,[status(thm),theory(equality)],[558,1174]),
[iquote('3:Res:558.1,1174.0')] ).
cnf(1267,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(y,z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f19(intersection_of_members(x1),x2),u)
| eq(f20(y,z),f15(u,x3,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[521,1116]),
[iquote('3:Res:521.1,1116.1')] ).
cnf(1268,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(y,z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f19(intersection_of_members(x1),x2),u)
| eq(f19(y,z),f15(u,x3,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[523,1116]),
[iquote('3:Res:523.1,1116.1')] ).
cnf(1054,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)],[642,758]),
[iquote('3:Res:642.2,758.0')] ).
cnf(1255,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(y,z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f20(intersection_of_members(x1),x2),u)
| eq(f20(y,z),f15(u,x3,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[521,1117]),
[iquote('3:Res:521.1,1117.1')] ).
cnf(1256,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(y,z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f20(intersection_of_members(x1),x2),u)
| eq(f19(y,z),f15(u,x3,x4,x5,v)) ),
inference(res,[status(thm),theory(equality)],[523,1117]),
[iquote('3:Res:523.1,1117.1')] ).
cnf(1207,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u)
| hausdorff(x1,x2)
| eq(f15(u,x3,x4,x5,v),f19(x1,x2)) ),
inference(res,[status(thm),theory(equality)],[622,1202]),
[iquote('3:Res:622.2,1202.1')] ).
cnf(1208,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u)
| hausdorff(x1,x2)
| eq(f15(u,x3,x4,x5,v),f19(x1,x2)) ),
inference(res,[status(thm),theory(equality)],[621,1202]),
[iquote('3:Res:621.2,1202.1')] ).
cnf(1042,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)],[642,759]),
[iquote('3:Res:642.2,759.0')] ).
cnf(1191,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u)
| hausdorff(x1,x2)
| eq(f15(u,x3,x4,x5,v),f20(x1,x2)) ),
inference(res,[status(thm),theory(equality)],[622,1177]),
[iquote('3:Res:622.2,1177.1')] ).
cnf(1192,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(union_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u)
| hausdorff(x1,x2)
| eq(f15(u,x3,x4,x5,v),f20(x1,x2)) ),
inference(res,[status(thm),theory(equality)],[621,1177]),
[iquote('3:Res:621.2,1177.1')] ).
cnf(1116,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,union_of_members(x))
| ~ hausdorff(union_of_members(x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f19(intersection_of_members(z),x1),u)
| eq(w,f15(u,x2,x3,x4,v)) ),
inference(res,[status(thm),theory(equality)],[622,1087]),
[iquote('3:Res:622.2,1087.1')] ).
cnf(1117,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,union_of_members(x))
| ~ hausdorff(union_of_members(x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f20(intersection_of_members(z),x1),u)
| eq(w,f15(u,x2,x3,x4,v)) ),
inference(res,[status(thm),theory(equality)],[621,1087]),
[iquote('3:Res:621.2,1087.1')] ).
cnf(1078,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)],[394,748]),
[iquote('3:Res:394.1,748.1')] ).
cnf(1079,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)],[395,748]),
[iquote('3:Res:395.1,748.1')] ).
cnf(1176,plain,
( ~ element_of_set(u,intersection_of_sets(v,w))
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(u,f15(f20(closure(y,z,x1),x2),w,x3,x4,v)) ),
inference(mrr,[status(thm)],[1172,544]),
[iquote('3:MRR:1172.0,544.1')] ).
cnf(1175,plain,
( ~ element_of_set(u,intersection_of_sets(v,w))
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(u,f15(f20(boundary(y,z,x1),x2),w,x3,x4,v)) ),
inference(mrr,[status(thm)],[1173,557]),
[iquote('3:MRR:1173.0,557.1')] ).
cnf(1179,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_sets(u,v),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_sets(u,v),x),f15(f20(intersection_of_members(y),z),v,x1,x2,u)) ),
inference(res,[status(thm),theory(equality)],[394,1174]),
[iquote('3:Res:394.1,1174.0')] ).
cnf(794,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)],[52,753]),
[iquote('3:Res:52.1,753.0')] ).
cnf(1180,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_sets(u,v),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_sets(u,v),x),f15(f20(intersection_of_members(y),z),v,x1,x2,u)) ),
inference(res,[status(thm),theory(equality)],[395,1174]),
[iquote('3:Res:395.1,1174.0')] ).
cnf(1233,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(closure(w,x,y),z)
| limit_point(x1,x2,x3,x4)
| eq(f15(f20(closure(w,x,y),z),x5,x6,x7,x8),x1) ),
inference(mrr,[status(thm)],[1229,544]),
[iquote('3:MRR:1229.0,544.1')] ).
cnf(1232,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(boundary(w,x,y),z)
| limit_point(x1,x2,x3,x4)
| eq(f15(f20(boundary(w,x,y),z),x5,x6,x7,x8),x1) ),
inference(mrr,[status(thm)],[1230,557]),
[iquote('3:MRR:1230.0,557.1')] ).
cnf(1217,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(closure(w,x,y),z)
| hausdorff(x1,x2)
| eq(f15(f20(closure(w,x,y),z),x3,x4,x5,x6),f19(x1,x2)) ),
inference(mrr,[status(thm)],[1213,544]),
[iquote('3:MRR:1213.0,544.1')] ).
cnf(772,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)],[52,752]),
[iquote('3:Res:52.1,752.0')] ).
cnf(1216,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(x1,x2)
| eq(f15(f20(boundary(w,x,y),z),x3,x4,x5,x6),f19(x1,x2)) ),
inference(mrr,[status(thm)],[1214,557]),
[iquote('3:MRR:1214.0,557.1')] ).
cnf(1201,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(closure(w,x,y),z)
| hausdorff(x1,x2)
| eq(f15(f20(closure(w,x,y),z),x3,x4,x5,x6),f20(x1,x2)) ),
inference(mrr,[status(thm)],[1197,544]),
[iquote('3:MRR:1197.0,544.1')] ).
cnf(1231,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(intersection_of_members(w),x)
| limit_point(y,z,x1,x2)
| eq(f15(f20(intersection_of_members(w),x),x3,x4,x5,x6),y) ),
inference(mrr,[status(thm)],[1222,486]),
[iquote('3:MRR:1222.0,486.1')] ).
cnf(1218,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)],[481,894]),
[iquote('3:Res:481.1,894.0')] ).
cnf(894,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)],[643,745]),
[iquote('3:Res:643.2,745.0')] ).
cnf(1200,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(x1,x2)
| eq(f15(f20(boundary(w,x,y),z),x3,x4,x5,x6),f20(x1,x2)) ),
inference(mrr,[status(thm)],[1198,557]),
[iquote('3:MRR:1198.0,557.1')] ).
cnf(1215,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(y,z)
| eq(f15(f20(intersection_of_members(w),x),x1,x2,x3,x4),f19(y,z)) ),
inference(mrr,[status(thm)],[1206,486]),
[iquote('3:MRR:1206.0,486.1')] ).
cnf(1202,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)],[481,838]),
[iquote('3:Res:481.1,838.0')] ).
cnf(1199,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(y,z)
| eq(f15(f20(intersection_of_members(w),x),x1,x2,x3,x4),f20(y,z)) ),
inference(mrr,[status(thm)],[1190,486]),
[iquote('3:MRR:1190.0,486.1')] ).
cnf(838,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)],[643,755]),
[iquote('3:Res:643.2,755.0')] ).
cnf(1177,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)],[481,826]),
[iquote('3:Res:481.1,826.0')] ).
cnf(1181,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_members(x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f20(intersection_of_members(x),y),f15(f20(intersection_of_members(z),x1),v,x2,x3,u)) ),
inference(res,[status(thm),theory(equality)],[486,1174]),
[iquote('3:Res:486.1,1174.0')] ).
cnf(1182,plain,
( ~ hausdorff(intersection_of_sets(u,v),w)
| hausdorff(intersection_of_members(x),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f19(intersection_of_members(x),y),f15(f20(intersection_of_members(z),x1),v,x2,x3,u)) ),
inference(res,[status(thm),theory(equality)],[487,1174]),
[iquote('3:Res:487.1,1174.0')] ).
cnf(1174,plain,
( ~ element_of_set(u,intersection_of_sets(v,w))
| ~ hausdorff(intersection_of_sets(v,w),x)
| hausdorff(intersection_of_members(y),z)
| eq(u,f15(f20(intersection_of_members(y),z),w,x1,x2,v)) ),
inference(mrr,[status(thm)],[1165,486]),
[iquote('3:MRR:1165.0,486.1')] ).
cnf(826,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)],[643,754]),
[iquote('3:Res:643.2,754.0')] ).
cnf(1099,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)],[481,764]),
[iquote('3:Res:481.1,764.0')] ).
cnf(1068,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)],[394,750]),
[iquote('3:Res:394.1,750.0')] ).
cnf(1069,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)],[395,750]),
[iquote('3:Res:395.1,750.0')] ).
cnf(1151,plain,
( ~ hausdorff(union_of_members(u),v)
| limit_point(w,x,y,z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(w,f15(f20(closure(x1,x2,x3),x4),x5,x6,x7,x8)) ),
inference(res,[status(thm),theory(equality)],[583,1126]),
[iquote('3:Res:583.1,1126.0')] ).
cnf(796,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)],[581,753]),
[iquote('3:Res:581.1,753.0')] ).
cnf(1139,plain,
( ~ hausdorff(union_of_members(u),v)
| limit_point(w,x,y,z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(w,f15(f20(boundary(x1,x2,x3),x4),x5,x6,x7,x8)) ),
inference(res,[status(thm),theory(equality)],[583,1125]),
[iquote('3:Res:583.1,1125.0')] ).
cnf(1154,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(w,x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(w,x),f15(f20(closure(y,z,x1),x2),x3,x4,x5,x6)) ),
inference(res,[status(thm),theory(equality)],[521,1126]),
[iquote('3:Res:521.1,1126.0')] ).
cnf(1155,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(w,x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(w,x),f15(f20(closure(y,z,x1),x2),x3,x4,x5,x6)) ),
inference(res,[status(thm),theory(equality)],[523,1126]),
[iquote('3:Res:523.1,1126.0')] ).
cnf(1142,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(w,x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(w,x),f15(f20(boundary(y,z,x1),x2),x3,x4,x5,x6)) ),
inference(res,[status(thm),theory(equality)],[521,1125]),
[iquote('3:Res:521.1,1125.0')] ).
cnf(774,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)],[581,752]),
[iquote('3:Res:581.1,752.0')] ).
cnf(1143,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(w,x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(w,x),f15(f20(boundary(y,z,x1),x2),x3,x4,x5,x6)) ),
inference(res,[status(thm),theory(equality)],[523,1125]),
[iquote('3:Res:523.1,1125.0')] ).
cnf(1082,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(f13(v,w,x,u),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f20(closure(z,x1,x2),x3),u) ),
inference(res,[status(thm),theory(equality)],[544,748]),
[iquote('3:Res:544.1,748.1')] ).
cnf(1083,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(f13(v,w,x,u),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f20(boundary(z,x1,x2),x3),u) ),
inference(res,[status(thm),theory(equality)],[557,748]),
[iquote('3:Res:557.1,748.1')] ).
cnf(1084,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(f13(v,w,x,u),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(f19(closure(z,x1,x2),x3),u) ),
inference(res,[status(thm),theory(equality)],[545,748]),
[iquote('3:Res:545.1,748.1')] ).
cnf(1085,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(f13(v,w,x,u),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(f19(boundary(z,x1,x2),x3),u) ),
inference(res,[status(thm),theory(equality)],[558,748]),
[iquote('3:Res:558.1,748.1')] ).
cnf(1012,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(f13(v,w,x,u),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(u,f20(closure(z,x1,x2),x3)) ),
inference(res,[status(thm),theory(equality)],[52,760]),
[iquote('3:Res:52.1,760.0')] ).
cnf(1024,plain,
( ~ hausdorff(u,v)
| hausdorff(closure(w,x,y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f20(closure(w,x,y),z),f20(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[544,760]),
[iquote('3:Res:544.1,760.0')] ).
cnf(1025,plain,
( ~ hausdorff(u,v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f20(boundary(w,x,y),z),f20(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[557,760]),
[iquote('3:Res:557.1,760.0')] ).
cnf(1026,plain,
( ~ hausdorff(u,v)
| hausdorff(closure(w,x,y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f19(closure(w,x,y),z),f20(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[545,760]),
[iquote('3:Res:545.1,760.0')] ).
cnf(1027,plain,
( ~ hausdorff(u,v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f19(boundary(w,x,y),z),f20(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[558,760]),
[iquote('3:Res:558.1,760.0')] ).
cnf(990,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(f13(v,w,x,u),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(u,f20(boundary(z,x1,x2),x3)) ),
inference(res,[status(thm),theory(equality)],[52,761]),
[iquote('3:Res:52.1,761.0')] ).
cnf(1002,plain,
( ~ hausdorff(u,v)
| hausdorff(closure(w,x,y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f20(closure(w,x,y),z),f20(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[544,761]),
[iquote('3:Res:544.1,761.0')] ).
cnf(1003,plain,
( ~ hausdorff(u,v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f20(boundary(w,x,y),z),f20(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[557,761]),
[iquote('3:Res:557.1,761.0')] ).
cnf(1004,plain,
( ~ hausdorff(u,v)
| hausdorff(closure(w,x,y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f19(closure(w,x,y),z),f20(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[545,761]),
[iquote('3:Res:545.1,761.0')] ).
cnf(1005,plain,
( ~ hausdorff(u,v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f19(boundary(w,x,y),z),f20(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[558,761]),
[iquote('3:Res:558.1,761.0')] ).
cnf(968,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(f13(v,w,x,u),y)
| hausdorff(closure(z,x1,x2),x3)
| eq(u,f19(closure(z,x1,x2),x3)) ),
inference(res,[status(thm),theory(equality)],[52,762]),
[iquote('3:Res:52.1,762.0')] ).
cnf(980,plain,
( ~ hausdorff(u,v)
| hausdorff(closure(w,x,y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f20(closure(w,x,y),z),f19(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[544,762]),
[iquote('3:Res:544.1,762.0')] ).
cnf(981,plain,
( ~ hausdorff(u,v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f20(boundary(w,x,y),z),f19(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[557,762]),
[iquote('3:Res:557.1,762.0')] ).
cnf(982,plain,
( ~ hausdorff(u,v)
| hausdorff(closure(w,x,y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f19(closure(w,x,y),z),f19(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[545,762]),
[iquote('3:Res:545.1,762.0')] ).
cnf(983,plain,
( ~ hausdorff(u,v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(closure(x1,x2,x3),x4)
| eq(f19(boundary(w,x,y),z),f19(closure(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[558,762]),
[iquote('3:Res:558.1,762.0')] ).
cnf(946,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(f13(v,w,x,u),y)
| hausdorff(boundary(z,x1,x2),x3)
| eq(u,f19(boundary(z,x1,x2),x3)) ),
inference(res,[status(thm),theory(equality)],[52,763]),
[iquote('3:Res:52.1,763.0')] ).
cnf(958,plain,
( ~ hausdorff(u,v)
| hausdorff(closure(w,x,y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f20(closure(w,x,y),z),f19(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[544,763]),
[iquote('3:Res:544.1,763.0')] ).
cnf(959,plain,
( ~ hausdorff(u,v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f20(boundary(w,x,y),z),f19(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[557,763]),
[iquote('3:Res:557.1,763.0')] ).
cnf(960,plain,
( ~ hausdorff(u,v)
| hausdorff(closure(w,x,y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f19(closure(w,x,y),z),f19(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[545,763]),
[iquote('3:Res:545.1,763.0')] ).
cnf(961,plain,
( ~ hausdorff(u,v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(boundary(x1,x2,x3),x4)
| eq(f19(boundary(w,x,y),z),f19(boundary(x1,x2,x3),x4)) ),
inference(res,[status(thm),theory(equality)],[558,763]),
[iquote('3:Res:558.1,763.0')] ).
cnf(1126,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(union_of_members(v),w)
| hausdorff(closure(x,y,z),x1)
| eq(u,f15(f20(closure(x,y,z),x1),x2,x3,x4,x5)) ),
inference(mrr,[status(thm)],[1122,544]),
[iquote('3:MRR:1122.0,544.1')] ).
cnf(1125,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(union_of_members(v),w)
| hausdorff(boundary(x,y,z),x1)
| eq(u,f15(f20(boundary(x,y,z),x1),x2,x3,x4,x5)) ),
inference(mrr,[status(thm)],[1123,557]),
[iquote('3:MRR:1123.0,557.1')] ).
cnf(1092,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ hausdorff(f6(v,y,u,w,x),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f20(intersection_of_members(x1),x2),u) ),
inference(res,[status(thm),theory(equality)],[486,751]),
[iquote('3:Res:486.1,751.2')] ).
cnf(1093,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ hausdorff(f6(v,y,u,w,x),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f19(intersection_of_members(x1),x2),u) ),
inference(res,[status(thm),theory(equality)],[487,751]),
[iquote('3:Res:487.1,751.2')] ).
cnf(867,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ hausdorff(f6(v,y,u,w,x),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(u,f19(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[514,757]),
[iquote('3:Res:514.2,757.0')] ).
cnf(1127,plain,
( ~ hausdorff(union_of_members(u),v)
| limit_point(w,x,y,z)
| hausdorff(intersection_of_members(x1),x2)
| eq(w,f15(f20(intersection_of_members(x1),x2),x3,x4,x5,x6)) ),
inference(res,[status(thm),theory(equality)],[583,1124]),
[iquote('3:Res:583.1,1124.0')] ).
cnf(1130,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(w,x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(w,x),f15(f20(intersection_of_members(y),z),x1,x2,x3,x4)) ),
inference(res,[status(thm),theory(equality)],[521,1124]),
[iquote('3:Res:521.1,1124.0')] ).
cnf(1131,plain,
( ~ hausdorff(union_of_members(u),v)
| hausdorff(w,x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(w,x),f15(f20(intersection_of_members(y),z),x1,x2,x3,x4)) ),
inference(res,[status(thm),theory(equality)],[523,1124]),
[iquote('3:Res:523.1,1124.0')] ).
cnf(1124,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(union_of_members(v),w)
| hausdorff(intersection_of_members(x),y)
| eq(u,f15(f20(intersection_of_members(x),y),z,x1,x2,x3)) ),
inference(mrr,[status(thm)],[1115,486]),
[iquote('3:MRR:1115.0,486.1')] ).
cnf(845,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(u,intersection_of_sets(w,x))
| ~ hausdorff(f6(v,y,u,w,x),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(u,f20(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[514,756]),
[iquote('3:Res:514.2,756.0')] ).
cnf(1087,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)],[481,765]),
[iquote('3:Res:481.1,765.0')] ).
cnf(1014,plain,
( ~ hausdorff(f16(u,v,w,x),y)
| limit_point(u,v,w,x)
| hausdorff(closure(z,x1,x2),x3)
| eq(u,f20(closure(z,x1,x2),x3)) ),
inference(res,[status(thm),theory(equality)],[581,760]),
[iquote('3:Res:581.1,760.0')] ).
cnf(992,plain,
( ~ hausdorff(f16(u,v,w,x),y)
| limit_point(u,v,w,x)
| hausdorff(boundary(z,x1,x2),x3)
| eq(u,f20(boundary(z,x1,x2),x3)) ),
inference(res,[status(thm),theory(equality)],[581,761]),
[iquote('3:Res:581.1,761.0')] ).
cnf(970,plain,
( ~ hausdorff(f16(u,v,w,x),y)
| limit_point(u,v,w,x)
| hausdorff(closure(z,x1,x2),x3)
| eq(u,f19(closure(z,x1,x2),x3)) ),
inference(res,[status(thm),theory(equality)],[581,762]),
[iquote('3:Res:581.1,762.0')] ).
cnf(948,plain,
( ~ hausdorff(f16(u,v,w,x),y)
| limit_point(u,v,w,x)
| hausdorff(boundary(z,x1,x2),x3)
| eq(u,f19(boundary(z,x1,x2),x3)) ),
inference(res,[status(thm),theory(equality)],[581,763]),
[iquote('3:Res:581.1,763.0')] ).
cnf(1013,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| hausdorff(closure(y,z,x1),x2)
| eq(u,f20(closure(y,z,x1),x2)) ),
inference(res,[status(thm),theory(equality)],[453,760]),
[iquote('3:Res:453.1,760.0')] ).
cnf(991,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(u,f20(boundary(y,z,x1),x2)) ),
inference(res,[status(thm),theory(equality)],[453,761]),
[iquote('3:Res:453.1,761.0')] ).
cnf(969,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| hausdorff(closure(y,z,x1),x2)
| eq(u,f19(closure(y,z,x1),x2)) ),
inference(res,[status(thm),theory(equality)],[453,762]),
[iquote('3:Res:453.1,762.0')] ).
cnf(947,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(u,f19(boundary(y,z,x1),x2)) ),
inference(res,[status(thm),theory(equality)],[453,763]),
[iquote('3:Res:453.1,763.0')] ).
cnf(934,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)],[394,749]),
[iquote('3:Res:394.1,749.1')] ).
cnf(935,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)],[395,749]),
[iquote('3:Res:395.1,749.1')] ).
cnf(938,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(closure(y,z,x1),x2),u) ),
inference(res,[status(thm),theory(equality)],[544,749]),
[iquote('3:Res:544.1,749.1')] ).
cnf(939,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(boundary(y,z,x1),x2),u) ),
inference(res,[status(thm),theory(equality)],[557,749]),
[iquote('3:Res:557.1,749.1')] ).
cnf(940,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(closure(y,z,x1),x2),u) ),
inference(res,[status(thm),theory(equality)],[545,749]),
[iquote('3:Res:545.1,749.1')] ).
cnf(941,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(boundary(y,z,x1),x2),u) ),
inference(res,[status(thm),theory(equality)],[558,749]),
[iquote('3:Res:558.1,749.1')] ).
cnf(795,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)],[453,753]),
[iquote('3:Res:453.1,753.0')] ).
cnf(773,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)],[453,752]),
[iquote('3:Res:453.1,752.0')] ).
cnf(1080,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(f13(v,w,x,u),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f20(intersection_of_members(z),x1),u) ),
inference(res,[status(thm),theory(equality)],[486,748]),
[iquote('3:Res:486.1,748.1')] ).
cnf(1081,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(f13(v,w,x,u),y)
| hausdorff(intersection_of_members(z),x1)
| eq(f19(intersection_of_members(z),x1),u) ),
inference(res,[status(thm),theory(equality)],[487,748]),
[iquote('3:Res:487.1,748.1')] ).
cnf(1010,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| hausdorff(closure(x,y,z),x1)
| eq(u,f20(closure(x,y,z),x1)) ),
inference(res,[status(thm),theory(equality)],[4,760]),
[iquote('3:Res:4.1,760.0')] ).
cnf(1020,plain,
( ~ hausdorff(u,v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(intersection_of_members(w),x),f20(closure(y,z,x1),x2)) ),
inference(res,[status(thm),theory(equality)],[486,760]),
[iquote('3:Res:486.1,760.0')] ).
cnf(1021,plain,
( ~ hausdorff(u,v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(intersection_of_members(w),x),f20(closure(y,z,x1),x2)) ),
inference(res,[status(thm),theory(equality)],[487,760]),
[iquote('3:Res:487.1,760.0')] ).
cnf(988,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| hausdorff(boundary(x,y,z),x1)
| eq(u,f20(boundary(x,y,z),x1)) ),
inference(res,[status(thm),theory(equality)],[4,761]),
[iquote('3:Res:4.1,761.0')] ).
cnf(998,plain,
( ~ hausdorff(u,v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(intersection_of_members(w),x),f20(boundary(y,z,x1),x2)) ),
inference(res,[status(thm),theory(equality)],[486,761]),
[iquote('3:Res:486.1,761.0')] ).
cnf(999,plain,
( ~ hausdorff(u,v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(intersection_of_members(w),x),f20(boundary(y,z,x1),x2)) ),
inference(res,[status(thm),theory(equality)],[487,761]),
[iquote('3:Res:487.1,761.0')] ).
cnf(966,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| hausdorff(closure(x,y,z),x1)
| eq(u,f19(closure(x,y,z),x1)) ),
inference(res,[status(thm),theory(equality)],[4,762]),
[iquote('3:Res:4.1,762.0')] ).
cnf(976,plain,
( ~ hausdorff(u,v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f20(intersection_of_members(w),x),f19(closure(y,z,x1),x2)) ),
inference(res,[status(thm),theory(equality)],[486,762]),
[iquote('3:Res:486.1,762.0')] ).
cnf(977,plain,
( ~ hausdorff(u,v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(closure(y,z,x1),x2)
| eq(f19(intersection_of_members(w),x),f19(closure(y,z,x1),x2)) ),
inference(res,[status(thm),theory(equality)],[487,762]),
[iquote('3:Res:487.1,762.0')] ).
cnf(944,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| hausdorff(boundary(x,y,z),x1)
| eq(u,f19(boundary(x,y,z),x1)) ),
inference(res,[status(thm),theory(equality)],[4,763]),
[iquote('3:Res:4.1,763.0')] ).
cnf(954,plain,
( ~ hausdorff(u,v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f20(intersection_of_members(w),x),f19(boundary(y,z,x1),x2)) ),
inference(res,[status(thm),theory(equality)],[486,763]),
[iquote('3:Res:486.1,763.0')] ).
cnf(955,plain,
( ~ hausdorff(u,v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(boundary(y,z,x1),x2)
| eq(f19(intersection_of_members(w),x),f19(boundary(y,z,x1),x2)) ),
inference(res,[status(thm),theory(equality)],[487,763]),
[iquote('3:Res:487.1,763.0')] ).
cnf(925,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| hausdorff(closure(x,y,z),x1)
| eq(f20(closure(x,y,z),x1),u) ),
inference(res,[status(thm),theory(equality)],[544,746]),
[iquote('3:Res:544.1,746.1')] ).
cnf(926,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| hausdorff(boundary(x,y,z),x1)
| eq(f20(boundary(x,y,z),x1),u) ),
inference(res,[status(thm),theory(equality)],[557,746]),
[iquote('3:Res:557.1,746.1')] ).
cnf(927,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| hausdorff(closure(x,y,z),x1)
| eq(f19(closure(x,y,z),x1),u) ),
inference(res,[status(thm),theory(equality)],[545,746]),
[iquote('3:Res:545.1,746.1')] ).
cnf(928,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| hausdorff(boundary(x,y,z),x1)
| eq(f19(boundary(x,y,z),x1),u) ),
inference(res,[status(thm),theory(equality)],[558,746]),
[iquote('3:Res:558.1,746.1')] ).
cnf(864,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(f13(v,w,x,u),y)
| hausdorff(intersection_of_members(z),x1)
| eq(u,f19(intersection_of_members(z),x1)) ),
inference(res,[status(thm),theory(equality)],[52,757]),
[iquote('3:Res:52.1,757.0')] ).
cnf(876,plain,
( ~ hausdorff(u,v)
| hausdorff(closure(w,x,y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f20(closure(w,x,y),z),f19(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[544,757]),
[iquote('3:Res:544.1,757.0')] ).
cnf(877,plain,
( ~ hausdorff(u,v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f20(boundary(w,x,y),z),f19(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[557,757]),
[iquote('3:Res:557.1,757.0')] ).
cnf(878,plain,
( ~ hausdorff(u,v)
| hausdorff(closure(w,x,y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f19(closure(w,x,y),z),f19(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[545,757]),
[iquote('3:Res:545.1,757.0')] ).
cnf(879,plain,
( ~ hausdorff(u,v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f19(boundary(w,x,y),z),f19(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[558,757]),
[iquote('3:Res:558.1,757.0')] ).
cnf(842,plain,
( ~ element_of_set(u,interior(v,w,x))
| ~ hausdorff(f13(v,w,x,u),y)
| hausdorff(intersection_of_members(z),x1)
| eq(u,f20(intersection_of_members(z),x1)) ),
inference(res,[status(thm),theory(equality)],[52,756]),
[iquote('3:Res:52.1,756.0')] ).
cnf(854,plain,
( ~ hausdorff(u,v)
| hausdorff(closure(w,x,y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f20(closure(w,x,y),z),f20(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[544,756]),
[iquote('3:Res:544.1,756.0')] ).
cnf(855,plain,
( ~ hausdorff(u,v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f20(boundary(w,x,y),z),f20(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[557,756]),
[iquote('3:Res:557.1,756.0')] ).
cnf(856,plain,
( ~ hausdorff(u,v)
| hausdorff(closure(w,x,y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f19(closure(w,x,y),z),f20(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[545,756]),
[iquote('3:Res:545.1,756.0')] ).
cnf(857,plain,
( ~ hausdorff(u,v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(intersection_of_members(x1),x2)
| eq(f19(boundary(w,x,y),z),f20(intersection_of_members(x1),x2)) ),
inference(res,[status(thm),theory(equality)],[558,756]),
[iquote('3:Res:558.1,756.0')] ).
cnf(1016,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(closure(x,y,z),x1)
| eq(f20(u,w),f20(closure(x,y,z),x1)) ),
inference(res,[status(thm),theory(equality)],[394,760]),
[iquote('3:Res:394.1,760.0')] ).
cnf(1017,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(closure(x,y,z),x1)
| eq(f19(u,w),f20(closure(x,y,z),x1)) ),
inference(res,[status(thm),theory(equality)],[395,760]),
[iquote('3:Res:395.1,760.0')] ).
cnf(994,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(boundary(x,y,z),x1)
| eq(f20(u,w),f20(boundary(x,y,z),x1)) ),
inference(res,[status(thm),theory(equality)],[394,761]),
[iquote('3:Res:394.1,761.0')] ).
cnf(995,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(boundary(x,y,z),x1)
| eq(f19(u,w),f20(boundary(x,y,z),x1)) ),
inference(res,[status(thm),theory(equality)],[395,761]),
[iquote('3:Res:395.1,761.0')] ).
cnf(766,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)],[642,744]),
[iquote('3:Res:642.2,744.0')] ).
cnf(972,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(closure(x,y,z),x1)
| eq(f20(u,w),f19(closure(x,y,z),x1)) ),
inference(res,[status(thm),theory(equality)],[394,762]),
[iquote('3:Res:394.1,762.0')] ).
cnf(973,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(closure(x,y,z),x1)
| eq(f19(u,w),f19(closure(x,y,z),x1)) ),
inference(res,[status(thm),theory(equality)],[395,762]),
[iquote('3:Res:395.1,762.0')] ).
cnf(950,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(boundary(x,y,z),x1)
| eq(f20(u,w),f19(boundary(x,y,z),x1)) ),
inference(res,[status(thm),theory(equality)],[394,763]),
[iquote('3:Res:394.1,763.0')] ).
cnf(951,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(boundary(x,y,z),x1)
| eq(f19(u,w),f19(boundary(x,y,z),x1)) ),
inference(res,[status(thm),theory(equality)],[395,763]),
[iquote('3:Res:395.1,763.0')] ).
cnf(764,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)],[68,744]),
[iquote('3:Res:68.2,744.0')] ).
cnf(866,plain,
( ~ hausdorff(f16(u,v,w,x),y)
| limit_point(u,v,w,x)
| hausdorff(intersection_of_members(z),x1)
| eq(u,f19(intersection_of_members(z),x1)) ),
inference(res,[status(thm),theory(equality)],[581,757]),
[iquote('3:Res:581.1,757.0')] ).
cnf(844,plain,
( ~ hausdorff(f16(u,v,w,x),y)
| limit_point(u,v,w,x)
| hausdorff(intersection_of_members(z),x1)
| eq(u,f20(intersection_of_members(z),x1)) ),
inference(res,[status(thm),theory(equality)],[581,756]),
[iquote('3:Res:581.1,756.0')] ).
cnf(806,plain,
( ~ hausdorff(u,v)
| hausdorff(closure(w,x,y),z)
| hausdorff(u,x1)
| eq(f20(closure(w,x,y),z),f19(u,x1)) ),
inference(res,[status(thm),theory(equality)],[544,753]),
[iquote('3:Res:544.1,753.0')] ).
cnf(1098,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)],[1089]),
[iquote('3:Obv:1089.1')] ).
cnf(751,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)],[514,744]),
[iquote('3:Res:514.2,744.0')] ).
cnf(807,plain,
( ~ hausdorff(u,v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(u,x1)
| eq(f20(boundary(w,x,y),z),f19(u,x1)) ),
inference(res,[status(thm),theory(equality)],[557,753]),
[iquote('3:Res:557.1,753.0')] ).
cnf(808,plain,
( ~ hausdorff(u,v)
| hausdorff(closure(w,x,y),z)
| hausdorff(u,x1)
| eq(f19(closure(w,x,y),z),f19(u,x1)) ),
inference(res,[status(thm),theory(equality)],[545,753]),
[iquote('3:Res:545.1,753.0')] ).
cnf(809,plain,
( ~ hausdorff(u,v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(u,x1)
| eq(f19(boundary(w,x,y),z),f19(u,x1)) ),
inference(res,[status(thm),theory(equality)],[558,753]),
[iquote('3:Res:558.1,753.0')] ).
cnf(784,plain,
( ~ hausdorff(u,v)
| hausdorff(closure(w,x,y),z)
| hausdorff(u,x1)
| eq(f20(closure(w,x,y),z),f20(u,x1)) ),
inference(res,[status(thm),theory(equality)],[544,752]),
[iquote('3:Res:544.1,752.0')] ).
cnf(765,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)],[643,744]),
[iquote('3:Res:643.2,744.0')] ).
cnf(785,plain,
( ~ hausdorff(u,v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(u,x1)
| eq(f20(boundary(w,x,y),z),f20(u,x1)) ),
inference(res,[status(thm),theory(equality)],[557,752]),
[iquote('3:Res:557.1,752.0')] ).
cnf(786,plain,
( ~ hausdorff(u,v)
| hausdorff(closure(w,x,y),z)
| hausdorff(u,x1)
| eq(f19(closure(w,x,y),z),f20(u,x1)) ),
inference(res,[status(thm),theory(equality)],[545,752]),
[iquote('3:Res:545.1,752.0')] ).
cnf(787,plain,
( ~ hausdorff(u,v)
| hausdorff(boundary(w,x,y),z)
| hausdorff(u,x1)
| eq(f19(boundary(w,x,y),z),f20(u,x1)) ),
inference(res,[status(thm),theory(equality)],[558,752]),
[iquote('3:Res:558.1,752.0')] ).
cnf(1086,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)],[1077]),
[iquote('3:Obv:1077.0')] ).
cnf(748,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)],[52,744]),
[iquote('3:Res:52.1,744.0')] ).
cnf(921,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)],[394,746]),
[iquote('3:Res:394.1,746.1')] ).
cnf(922,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)],[395,746]),
[iquote('3:Res:395.1,746.1')] ).
cnf(792,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)],[4,753]),
[iquote('3:Res:4.1,753.0')] ).
cnf(1076,plain,
( ~ hausdorff(f16(u,v,w,x),y)
| limit_point(u,v,w,x)
| eq(u,u) ),
inference(obv,[status(thm),theory(equality)],[1067]),
[iquote('3:Obv:1067.1')] ).
cnf(750,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)],[581,744]),
[iquote('3:Res:581.1,744.0')] ).
cnf(770,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)],[4,752]),
[iquote('3:Res:4.1,752.0')] ).
cnf(1055,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)],[582,747]),
[iquote('3:Res:582.1,747.0')] ).
cnf(1060,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)],[551,747]),
[iquote('3:Res:551.1,747.0')] ).
cnf(1061,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)],[552,747]),
[iquote('3:Res:552.1,747.0')] ).
cnf(747,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)],[582,744]),
[iquote('3:Res:582.1,744.0')] ).
cnf(1043,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)],[582,758]),
[iquote('3:Res:582.1,758.0')] ).
cnf(1031,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)],[582,759]),
[iquote('3:Res:582.1,759.0')] ).
cnf(1048,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)],[551,758]),
[iquote('3:Res:551.1,758.0')] ).
cnf(1049,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)],[552,758]),
[iquote('3:Res:552.1,758.0')] ).
cnf(758,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)],[551,744]),
[iquote('3:Res:551.1,744.0')] ).
cnf(1036,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)],[551,759]),
[iquote('3:Res:551.1,759.0')] ).
cnf(1037,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)],[552,759]),
[iquote('3:Res:552.1,759.0')] ).
cnf(759,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)],[552,744]),
[iquote('3:Res:552.1,744.0')] ).
cnf(760,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(v,w)
| hausdorff(closure(x,y,z),x1)
| eq(u,f20(closure(x,y,z),x1)) ),
inference(res,[status(thm),theory(equality)],[544,744]),
[iquote('3:Res:544.1,744.0')] ).
cnf(719,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)],[514,668]),
[iquote('1:Res:514.2,668.0')] ).
cnf(761,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(v,w)
| hausdorff(boundary(x,y,z),x1)
| eq(u,f20(boundary(x,y,z),x1)) ),
inference(res,[status(thm),theory(equality)],[557,744]),
[iquote('3:Res:557.1,744.0')] ).
cnf(762,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(v,w)
| hausdorff(closure(x,y,z),x1)
| eq(u,f19(closure(x,y,z),x1)) ),
inference(res,[status(thm),theory(equality)],[545,744]),
[iquote('3:Res:545.1,744.0')] ).
cnf(763,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(v,w)
| hausdorff(boundary(x,y,z),x1)
| eq(u,f19(boundary(x,y,z),x1)) ),
inference(res,[status(thm),theory(equality)],[558,744]),
[iquote('3:Res:558.1,744.0')] ).
cnf(694,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)],[514,667]),
[iquote('1:Res:514.2,667.0')] ).
cnf(936,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(y),z),u) ),
inference(res,[status(thm),theory(equality)],[486,749]),
[iquote('3:Res:486.1,749.1')] ).
cnf(718,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)],[581,668]),
[iquote('1:Res:581.1,668.0')] ).
cnf(937,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(y),z),u) ),
inference(res,[status(thm),theory(equality)],[487,749]),
[iquote('3:Res:487.1,749.1')] ).
cnf(942,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| eq(u,u) ),
inference(obv,[status(thm),theory(equality)],[933]),
[iquote('3:Obv:933.0')] ).
cnf(749,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)],[453,744]),
[iquote('3:Res:453.1,744.0')] ).
cnf(865,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| hausdorff(intersection_of_members(y),z)
| eq(u,f19(intersection_of_members(y),z)) ),
inference(res,[status(thm),theory(equality)],[453,757]),
[iquote('3:Res:453.1,757.0')] ).
cnf(660,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)],[514,651]),
[iquote('1:Res:514.2,651.0')] ).
cnf(843,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| hausdorff(intersection_of_members(y),z)
| eq(u,f20(intersection_of_members(y),z)) ),
inference(res,[status(thm),theory(equality)],[453,756]),
[iquote('3:Res:453.1,756.0')] ).
cnf(923,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| hausdorff(intersection_of_members(x),y)
| eq(f20(intersection_of_members(x),y),u) ),
inference(res,[status(thm),theory(equality)],[486,746]),
[iquote('3:Res:486.1,746.1')] ).
cnf(924,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| hausdorff(intersection_of_members(x),y)
| eq(f19(intersection_of_members(x),y),u) ),
inference(res,[status(thm),theory(equality)],[487,746]),
[iquote('3:Res:487.1,746.1')] ).
cnf(862,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| hausdorff(intersection_of_members(x),y)
| eq(u,f19(intersection_of_members(x),y)) ),
inference(res,[status(thm),theory(equality)],[4,757]),
[iquote('3:Res:4.1,757.0')] ).
cnf(659,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)],[581,651]),
[iquote('1:Res:581.1,651.0')] ).
cnf(872,plain,
( ~ hausdorff(u,v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(w),x),f19(intersection_of_members(y),z)) ),
inference(res,[status(thm),theory(equality)],[486,757]),
[iquote('3:Res:486.1,757.0')] ).
cnf(873,plain,
( ~ hausdorff(u,v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(w),x),f19(intersection_of_members(y),z)) ),
inference(res,[status(thm),theory(equality)],[487,757]),
[iquote('3:Res:487.1,757.0')] ).
cnf(932,plain,
( ~ subset_collections(u,f24(v,u))
| ~ compact_space(w,f24(v,u))
| compact_space(v,u) ),
inference(res,[status(thm),theory(equality)],[485,931]),
[iquote('1:Res:485.1,931.1')] ).
cnf(931,plain,
( ~ compact_space(u,f24(v,w))
| ~ open_covering(w,u,f24(v,w))
| compact_space(v,w) ),
inference(obv,[status(thm),theory(equality)],[930]),
[iquote('1:Obv:930.1')] ).
cnf(919,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)],[485,614]),
[iquote('1:Res:485.1,614.2')] ).
cnf(840,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| hausdorff(intersection_of_members(x),y)
| eq(u,f20(intersection_of_members(x),y)) ),
inference(res,[status(thm),theory(equality)],[4,756]),
[iquote('3:Res:4.1,756.0')] ).
cnf(850,plain,
( ~ hausdorff(u,v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f20(intersection_of_members(w),x),f20(intersection_of_members(y),z)) ),
inference(res,[status(thm),theory(equality)],[486,756]),
[iquote('3:Res:486.1,756.0')] ).
cnf(851,plain,
( ~ hausdorff(u,v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(intersection_of_members(y),z)
| eq(f19(intersection_of_members(w),x),f20(intersection_of_members(y),z)) ),
inference(res,[status(thm),theory(equality)],[487,756]),
[iquote('3:Res:487.1,756.0')] ).
cnf(693,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)],[581,667]),
[iquote('1:Res:581.1,667.0')] ).
cnf(658,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)],[453,651]),
[iquote('1:Res:453.1,651.0')] ).
cnf(929,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| eq(u,u) ),
inference(obv,[status(thm),theory(equality)],[920]),
[iquote('3:Obv:920.0')] ).
cnf(746,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)],[4,744]),
[iquote('3:Res:4.1,744.0')] ).
cnf(677,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)],[657,552]),
[iquote('1:MRR:657.0,552.1')] ).
cnf(869,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(intersection_of_members(x),y)
| eq(f19(u,w),f19(intersection_of_members(x),y)) ),
inference(res,[status(thm),theory(equality)],[395,757]),
[iquote('3:Res:395.1,757.0')] ).
cnf(614,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)],[612,104]),
[iquote('0:MRR:612.0,104.2')] ).
cnf(868,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(intersection_of_members(x),y)
| eq(f20(u,w),f19(intersection_of_members(x),y)) ),
inference(res,[status(thm),theory(equality)],[394,757]),
[iquote('3:Res:394.1,757.0')] ).
cnf(916,plain,
( ~ compact_set(u,v,w)
| compact_space(x,subspace_topology(v,w,u)) ),
inference(res,[status(thm),theory(equality)],[111,915]),
[iquote('1:Res:111.1,915.0')] ).
cnf(915,plain,
( ~ compact_space(u,v)
| compact_space(w,v) ),
inference(mrr,[status(thm)],[914,397]),
[iquote('1:MRR:914.0,397.1')] ).
cnf(814,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)],[485,613]),
[iquote('1:Res:485.1,613.2')] ).
cnf(847,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(intersection_of_members(x),y)
| eq(f19(u,w),f20(intersection_of_members(x),y)) ),
inference(res,[status(thm),theory(equality)],[395,756]),
[iquote('3:Res:395.1,756.0')] ).
cnf(846,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(intersection_of_members(x),y)
| eq(f20(u,w),f20(intersection_of_members(x),y)) ),
inference(res,[status(thm),theory(equality)],[394,756]),
[iquote('3:Res:394.1,756.0')] ).
cnf(803,plain,
( ~ hausdorff(u,v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(u,y)
| eq(f19(intersection_of_members(w),x),f19(u,y)) ),
inference(res,[status(thm),theory(equality)],[487,753]),
[iquote('3:Res:487.1,753.0')] ).
cnf(899,plain,
( ~ limit_point(u,v,w,x)
| limit_point(u,v,y,z) ),
inference(mrr,[status(thm)],[897,581]),
[iquote('1:MRR:897.0,581.1')] ).
cnf(802,plain,
( ~ hausdorff(u,v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(u,y)
| eq(f20(intersection_of_members(w),x),f19(u,y)) ),
inference(res,[status(thm),theory(equality)],[486,753]),
[iquote('3:Res:486.1,753.0')] ).
cnf(781,plain,
( ~ hausdorff(u,v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(u,y)
| eq(f19(intersection_of_members(w),x),f20(u,y)) ),
inference(res,[status(thm),theory(equality)],[487,752]),
[iquote('3:Res:487.1,752.0')] ).
cnf(780,plain,
( ~ hausdorff(u,v)
| hausdorff(intersection_of_members(w),x)
| hausdorff(u,y)
| eq(f20(intersection_of_members(w),x),f20(u,y)) ),
inference(res,[status(thm),theory(equality)],[486,752]),
[iquote('3:Res:486.1,752.0')] ).
cnf(717,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)],[453,668]),
[iquote('1:Res:453.1,668.0')] ).
cnf(644,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)],[68,504]),
[iquote('1:Res:68.2,504.0')] ).
cnf(883,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)],[583,745]),
[iquote('3:Res:583.1,745.0')] ).
cnf(887,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)],[523,745]),
[iquote('3:Res:523.1,745.0')] ).
cnf(886,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)],[521,745]),
[iquote('3:Res:521.1,745.0')] ).
cnf(827,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)],[583,755]),
[iquote('3:Res:583.1,755.0')] ).
cnf(648,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)],[493,118]),
[iquote('1:Res:493.1,118.1')] ).
cnf(815,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)],[583,754]),
[iquote('3:Res:583.1,754.0')] ).
cnf(831,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)],[523,755]),
[iquote('3:Res:523.1,755.0')] ).
cnf(830,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)],[521,755]),
[iquote('3:Res:521.1,755.0')] ).
cnf(819,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)],[523,754]),
[iquote('3:Res:523.1,754.0')] ).
cnf(619,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)],[394,504]),
[iquote('1:Res:394.1,504.0')] ).
cnf(818,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)],[521,754]),
[iquote('3:Res:521.1,754.0')] ).
cnf(745,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)],[583,744]),
[iquote('3:Res:583.1,744.0')] ).
cnf(757,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(v,w)
| hausdorff(intersection_of_members(x),y)
| eq(u,f19(intersection_of_members(x),y)) ),
inference(res,[status(thm),theory(equality)],[487,744]),
[iquote('3:Res:487.1,744.0')] ).
cnf(756,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(v,w)
| hausdorff(intersection_of_members(x),y)
| eq(u,f20(intersection_of_members(x),y)) ),
inference(res,[status(thm),theory(equality)],[486,744]),
[iquote('3:Res:486.1,744.0')] ).
cnf(620,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)],[395,504]),
[iquote('1:Res:395.1,504.0')] ).
cnf(755,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)],[523,744]),
[iquote('3:Res:523.1,744.0')] ).
cnf(754,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)],[521,744]),
[iquote('3:Res:521.1,744.0')] ).
cnf(799,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(u,x)
| eq(f19(u,w),f19(u,x)) ),
inference(res,[status(thm),theory(equality)],[395,753]),
[iquote('3:Res:395.1,753.0')] ).
cnf(798,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(u,x)
| eq(f20(u,w),f19(u,x)) ),
inference(res,[status(thm),theory(equality)],[394,753]),
[iquote('3:Res:394.1,753.0')] ).
cnf(613,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)],[610,104]),
[iquote('0:MRR:610.0,104.2')] ).
cnf(777,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(u,x)
| eq(f19(u,w),f20(u,x)) ),
inference(res,[status(thm),theory(equality)],[395,752]),
[iquote('3:Res:395.1,752.0')] ).
cnf(776,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(u,x)
| eq(f20(u,w),f20(u,x)) ),
inference(res,[status(thm),theory(equality)],[394,752]),
[iquote('3:Res:394.1,752.0')] ).
cnf(753,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(v,w)
| hausdorff(v,x)
| eq(u,f19(v,x)) ),
inference(res,[status(thm),theory(equality)],[395,744]),
[iquote('3:Res:395.1,744.0')] ).
cnf(752,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(v,w)
| hausdorff(v,x)
| eq(u,f20(v,x)) ),
inference(res,[status(thm),theory(equality)],[394,744]),
[iquote('3:Res:394.1,744.0')] ).
cnf(642,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)],[68,491]),
[iquote('1:Res:68.2,491.0')] ).
cnf(744,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(v,x)
| eq(w,u) ),
inference(spt,[],[712]),
[iquote('3:Spt:712.0,712.1,712.2,712.3')] ).
cnf(692,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)],[453,667]),
[iquote('1:Res:453.1,667.0')] ).
cnf(672,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(f1(x,f19(u,v)),w)
| hausdorff(u,v) ),
inference(mrr,[status(thm)],[655,523]),
[iquote('1:MRR:655.0,523.1')] ).
cnf(671,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(interior(x,y,z),w)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[664]),
[iquote('1:Obv:664.2')] ).
cnf(733,plain,
( ~ disjoint_s(union_of_members(u),f13(v,w,x,f20(y,z)))
| hausdorff(y,z) ),
inference(mrr,[status(thm)],[716,551]),
[iquote('1:MRR:716.0,551.1')] ).
cnf(732,plain,
( ~ disjoint_s(union_of_members(u),f1(v,f20(w,x)))
| hausdorff(w,x) ),
inference(mrr,[status(thm)],[714,521]),
[iquote('1:MRR:714.0,521.1')] ).
cnf(729,plain,
( ~ disjoint_s(union_of_members(u),interior(v,w,x))
| hausdorff(y,z) ),
inference(obv,[status(thm),theory(equality)],[723]),
[iquote('1:Obv:723.1')] ).
cnf(727,plain,
( ~ disjoint_s(union_of_members(u),union_of_members(v))
| hausdorff(w,x) ),
inference(obv,[status(thm),theory(equality)],[721]),
[iquote('1:Obv:721.1')] ).
cnf(726,plain,
( ~ disjoint_s(union_of_members(u),v)
| hausdorff(v,w) ),
inference(obv,[status(thm),theory(equality)],[720]),
[iquote('1:Obv:720.1')] ).
cnf(668,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(union_of_members(x),w)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[662]),
[iquote('1:Obv:662.2')] ).
cnf(708,plain,
( ~ disjoint_s(u,f13(v,w,x,f20(u,y)))
| hausdorff(u,y) ),
inference(mrr,[status(thm)],[691,551]),
[iquote('1:MRR:691.0,551.1')] ).
cnf(705,plain,
( ~ disjoint_s(u,f1(v,f20(u,w)))
| hausdorff(u,w) ),
inference(mrr,[status(thm)],[689,521]),
[iquote('1:MRR:689.0,521.1')] ).
cnf(704,plain,
( ~ disjoint_s(u,interior(v,w,x))
| hausdorff(u,y) ),
inference(obv,[status(thm),theory(equality)],[698]),
[iquote('1:Obv:698.1')] ).
cnf(702,plain,
( ~ disjoint_s(u,union_of_members(v))
| hausdorff(u,w) ),
inference(obv,[status(thm),theory(equality)],[696]),
[iquote('1:Obv:696.1')] ).
cnf(701,plain,
( ~ disjoint_s(u,u)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[695]),
[iquote('1:Obv:695.1')] ).
cnf(667,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(u,w)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[661]),
[iquote('1:Obv:661.2')] ).
cnf(676,plain,
( ~ disjoint_s(u,v)
| hausdorff(closure(w,x,y),z) ),
inference(mrr,[status(thm)],[675,544]),
[iquote('1:MRR:675.0,544.1')] ).
cnf(674,plain,
( ~ disjoint_s(u,v)
| hausdorff(boundary(w,x,y),z) ),
inference(mrr,[status(thm)],[673,557]),
[iquote('1:MRR:673.0,557.1')] ).
cnf(683,plain,
( ~ disjoint_s(u,v)
| equal_sets(v,empty_set)
| equal_sets(u,empty_set) ),
inference(mrr,[status(thm)],[638,679]),
[iquote('2:MRR:638.1,679.0')] ).
cnf(680,plain,
~ separation(u,v,w,x),
inference(mrr,[status(thm)],[93,679]),
[iquote('2:MRR:93.0,679.0')] ).
cnf(681,plain,
connected_set(u,v,w),
inference(mrr,[status(thm)],[489,679]),
[iquote('2:MRR:489.0,679.0')] ).
cnf(679,plain,
connected_space(u,v),
inference(spt,[],[678]),
[iquote('2:Spt:678.0')] ).
cnf(670,plain,
( ~ disjoint_s(u,v)
| hausdorff(intersection_of_members(w),x) ),
inference(mrr,[status(thm)],[669,486]),
[iquote('1:MRR:669.0,486.1')] ).
cnf(651,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)],[481,647]),
[iquote('1:Res:481.1,647.2')] ).
cnf(647,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)],[481,118]),
[iquote('1:Res:481.1,118.1')] ).
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(643,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)],[68,448]),
[iquote('1:Res:68.2,448.0')] ).
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('TOP010-1.p',unknown),
[] ).
cnf(637,plain,
( limit_point(f20(boundary(u,v,w),x),y,z,x1)
| hausdorff(boundary(u,v,w),x) ),
inference(obv,[status(thm),theory(equality)],[636]),
[iquote('1:Obv:636.0')] ).
cnf(626,plain,
( hausdorff(boundary(u,v,w),x)
| eq(f19(boundary(u,v,w),x),y)
| limit_point(y,z,x1,x2) ),
inference(res,[status(thm),theory(equality)],[558,504]),
[iquote('1:Res:558.1,504.0')] ).
cnf(69,axiom,
( ~ eq(f15(u,v,w,x,y),u)
| ~ neighborhood(y,u,w,x)
| ~ limit_point(u,v,w,x) ),
file('TOP010-1.p',unknown),
[] ).
cnf(635,plain,
( limit_point(f20(closure(u,v,w),x),y,z,x1)
| hausdorff(closure(u,v,w),x) ),
inference(obv,[status(thm),theory(equality)],[634]),
[iquote('1:Obv:634.0')] ).
cnf(625,plain,
( hausdorff(closure(u,v,w),x)
| eq(f19(closure(u,v,w),x),y)
| limit_point(y,z,x1,x2) ),
inference(res,[status(thm),theory(equality)],[545,504]),
[iquote('1:Res:545.1,504.0')] ).
cnf(624,plain,
( hausdorff(boundary(u,v,w),x)
| eq(f20(boundary(u,v,w),x),y)
| limit_point(y,z,x1,x2) ),
inference(res,[status(thm),theory(equality)],[557,504]),
[iquote('1:Res:557.1,504.0')] ).
cnf(623,plain,
( hausdorff(closure(u,v,w),x)
| eq(f20(closure(u,v,w),x),y)
| limit_point(y,z,x1,x2) ),
inference(res,[status(thm),theory(equality)],[544,504]),
[iquote('1:Res:544.1,504.0')] ).
cnf(628,plain,
( limit_point(f20(intersection_of_members(u),v),w,x,y)
| hausdorff(intersection_of_members(u),v) ),
inference(obv,[status(thm),theory(equality)],[627]),
[iquote('1:Obv:627.0')] ).
cnf(622,plain,
( hausdorff(intersection_of_members(u),v)
| eq(f19(intersection_of_members(u),v),w)
| limit_point(w,x,y,z) ),
inference(res,[status(thm),theory(equality)],[487,504]),
[iquote('1:Res:487.1,504.0')] ).
cnf(621,plain,
( hausdorff(intersection_of_members(u),v)
| eq(f20(intersection_of_members(u),v),w)
| limit_point(w,x,y,z) ),
inference(res,[status(thm),theory(equality)],[486,504]),
[iquote('1:Res:486.1,504.0')] ).
cnf(504,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)],[416,450]),
[iquote('1:MRR:416.0,450.0')] ).
cnf(514,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)],[455,506]),
[iquote('1:MRR:455.1,506.0')] ).
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(595,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(558,plain,
( hausdorff(boundary(u,v,w),x)
| element_of_set(f19(boundary(u,v,w),x),y) ),
inference(res,[status(thm),theory(equality)],[395,542]),
[iquote('1:Res:395.1,542.0')] ).
cnf(557,plain,
( hausdorff(boundary(u,v,w),x)
| element_of_set(f20(boundary(u,v,w),x),y) ),
inference(res,[status(thm),theory(equality)],[394,542]),
[iquote('1:Res:394.1,542.0')] ).
cnf(106,axiom,
( ~ compact_space(u,v)
| ~ open_covering(w,u,v)
| open_covering(f23(u,v,w),u,v) ),
file('TOP010-1.p',unknown),
[] ).
cnf(545,plain,
( hausdorff(closure(u,v,w),x)
| element_of_set(f19(closure(u,v,w),x),y) ),
inference(res,[status(thm),theory(equality)],[395,490]),
[iquote('1:Res:395.1,490.0')] ).
cnf(582,plain,
( limit_point(u,v,w,x)
| element_of_set(u,interior(y,z,x1)) ),
inference(res,[status(thm),theory(equality)],[581,491]),
[iquote('1:Res:581.1,491.0')] ).
cnf(583,plain,
( limit_point(u,v,w,x)
| element_of_set(u,union_of_members(y)) ),
inference(res,[status(thm),theory(equality)],[581,448]),
[iquote('1:Res:581.1,448.0')] ).
cnf(581,plain,
( limit_point(u,v,w,x)
| element_of_set(u,f16(u,v,w,x)) ),
inference(res,[status(thm),theory(equality)],[493,64]),
[iquote('1:Res:493.1,64.0')] ).
cnf(493,plain,
( limit_point(u,v,w,x)
| neighborhood(f16(u,v,w,x),u,w,x) ),
inference(mrr,[status(thm)],[413,450]),
[iquote('1:MRR:413.0,450.0')] ).
cnf(544,plain,
( hausdorff(closure(u,v,w),x)
| element_of_set(f20(closure(u,v,w),x),y) ),
inference(res,[status(thm),theory(equality)],[394,490]),
[iquote('1:Res:394.1,490.0')] ).
cnf(494,plain,
( ~ element_of_set(u,f14(v,w,x,u))
| element_of_set(u,closure(v,w,x)) ),
inference(mrr,[status(thm)],[414,450]),
[iquote('1:MRR:414.0,450.0')] ).
cnf(552,plain,
( hausdorff(u,v)
| element_of_set(f19(u,v),interior(w,x,y)) ),
inference(res,[status(thm),theory(equality)],[395,491]),
[iquote('1:Res:395.1,491.0')] ).
cnf(551,plain,
( hausdorff(u,v)
| element_of_set(f20(u,v),interior(w,x,y)) ),
inference(res,[status(thm),theory(equality)],[394,491]),
[iquote('1:Res:394.1,491.0')] ).
cnf(488,plain,
( ~ compact_space(u,subspace_topology(v,w,u))
| compact_set(u,v,w) ),
inference(mrr,[status(thm)],[410,450]),
[iquote('1:MRR:410.0,450.0')] ).
cnf(400,plain,
( ~ eq(f19(u,v),f20(u,v))
| hausdorff(u,v) ),
inference(mrr,[status(thm)],[82,388]),
[iquote('1:MRR:82.0,388.0')] ).
cnf(542,plain,
( ~ element_of_set(u,boundary(v,w,x))
| element_of_set(u,y) ),
inference(res,[status(thm),theory(equality)],[73,490]),
[iquote('1:Res:73.1,490.0')] ).
cnf(491,plain,
( ~ element_of_set(u,v)
| element_of_set(u,interior(w,x,y)) ),
inference(mrr,[status(thm)],[467,479]),
[iquote('1:MRR:467.1,479.0')] ).
cnf(490,plain,
( ~ element_of_set(u,closure(v,w,x))
| element_of_set(u,y) ),
inference(mrr,[status(thm)],[466,480]),
[iquote('1:MRR:466.1,480.0')] ).
cnf(487,plain,
( hausdorff(intersection_of_members(u),v)
| element_of_set(f19(intersection_of_members(u),v),w) ),
inference(mrr,[status(thm)],[409,392]),
[iquote('1:MRR:409.0,392.0')] ).
cnf(486,plain,
( hausdorff(intersection_of_members(u),v)
| element_of_set(f20(intersection_of_members(u),v),w) ),
inference(mrr,[status(thm)],[408,392]),
[iquote('1:MRR:408.0,392.0')] ).
cnf(437,plain,
~ subset_collections(subspace_topology(cx,ct2,a),subspace_topology(cx,ct1,a)),
inference(mrr,[status(thm)],[134,388]),
[iquote('1:MRR:134.1,134.0,388.0')] ).
cnf(453,plain,
( ~ element_of_set(u,v)
| element_of_set(u,f10(w,v,u)) ),
inference(mrr,[status(thm)],[40,392]),
[iquote('1:MRR:40.1,392.0')] ).
cnf(481,plain,
( ~ element_of_set(u,v)
| neighborhood(v,u,w,x) ),
inference(mrr,[status(thm)],[114,479]),
[iquote('1:MRR:114.1,479.0')] ).
cnf(458,plain,
equal_sets(u,intersection_of_sets(v,f12(w,x,v,u))),
inference(mrr,[status(thm)],[48,392]),
[iquote('1:MRR:48.0,392.0')] ).
cnf(523,plain,
( hausdorff(u,v)
| element_of_set(f19(u,v),union_of_members(w)) ),
inference(res,[status(thm),theory(equality)],[395,448]),
[iquote('1:Res:395.1,448.0')] ).
cnf(521,plain,
( hausdorff(u,v)
| element_of_set(f20(u,v),union_of_members(w)) ),
inference(res,[status(thm),theory(equality)],[394,448]),
[iquote('1:Res:394.1,448.0')] ).
cnf(396,plain,
( compact_space(u,v)
| open_covering(f24(u,v),u,v) ),
inference(mrr,[status(thm)],[107,388]),
[iquote('1:MRR:107.0,388.0')] ).
cnf(485,plain,
( ~ subset_collections(u,v)
| open_covering(u,w,v) ),
inference(mrr,[status(thm)],[430,393]),
[iquote('1:MRR:430.1,393.0')] ).
cnf(429,plain,
( ~ subset_collections(u,v)
| finer(v,u,w) ),
inference(mrr,[status(thm)],[30,388]),
[iquote('1:MRR:30.1,30.2,388.0')] ).
cnf(397,plain,
( compact_space(u,v)
| subset_collections(f24(u,v),v) ),
inference(mrr,[status(thm)],[232,388]),
[iquote('1:MRR:232.0,388.0')] ).
cnf(395,plain,
( hausdorff(u,v)
| element_of_set(f19(u,v),u) ),
inference(mrr,[status(thm)],[80,388]),
[iquote('1:MRR:80.0,388.0')] ).
cnf(394,plain,
( hausdorff(u,v)
| element_of_set(f20(u,v),u) ),
inference(mrr,[status(thm)],[81,388]),
[iquote('1:MRR:81.0,388.0')] ).
cnf(449,plain,
( ~ element_of_set(u,intersection_of_members(v))
| element_of_set(u,w) ),
inference(mrr,[status(thm)],[7,392]),
[iquote('1:MRR:7.0,392.0')] ).
cnf(448,plain,
( ~ element_of_set(u,v)
| element_of_set(u,union_of_members(w)) ),
inference(mrr,[status(thm)],[6,392]),
[iquote('1:MRR:6.0,392.0')] ).
cnf(480,plain,
closed(u,v,w),
inference(mrr,[status(thm)],[113,479]),
[iquote('1:MRR:113.0,479.0')] ).
cnf(479,plain,
open(u,v,w),
inference(mrr,[status(thm)],[402,392]),
[iquote('1:MRR:402.0,392.0')] ).
cnf(393,plain,
equal_sets(union_of_members(u),v),
inference(mrr,[status(thm)],[10,388]),
[iquote('1:MRR:10.0,388.0')] ).
cnf(506,plain,
basis(u,v),
inference(mrr,[status(thm)],[471,505]),
[iquote('1:MRR:471.1,505.0')] ).
cnf(450,plain,
subset_sets(u,v),
inference(mrr,[status(thm)],[46,392]),
[iquote('1:MRR:46.0,392.0')] ).
cnf(392,plain,
element_of_collection(u,v),
inference(mrr,[status(thm)],[12,388]),
[iquote('1:MRR:12.0,388.0')] ).
cnf(388,plain,
topological_space(u,v),
inference(spt,[],[385]),
[iquote('1:Spt:385.1')] ).
cnf(105,axiom,
( ~ compact_space(u,v)
| ~ open_covering(w,u,v)
| subset_collections(f23(u,v,w),w) ),
file('TOP010-1.p',unknown),
[] ).
cnf(52,axiom,
( ~ element_of_set(u,interior(v,w,x))
| element_of_set(u,f13(v,w,x,u)) ),
file('TOP010-1.p',unknown),
[] ).
cnf(104,axiom,
( ~ compact_space(u,v)
| ~ open_covering(w,u,v)
| finite(f23(u,v,w)) ),
file('TOP010-1.p',unknown),
[] ).
cnf(3,axiom,
~ finer(subspace_topology(cx,ct1,a),subspace_topology(cx,ct2,a),cx),
file('TOP010-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ element_of_set(u,f2(v,u))
| element_of_set(u,intersection_of_members(v)) ),
file('TOP010-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ element_of_set(u,union_of_members(v))
| element_of_set(u,f1(v,u)) ),
file('TOP010-1.p',unknown),
[] ).
cnf(64,axiom,
( ~ neighborhood(u,v,w,x)
| element_of_set(v,u) ),
file('TOP010-1.p',unknown),
[] ).
cnf(100,axiom,
( ~ open_covering(u,v,w)
| subset_collections(u,w) ),
file('TOP010-1.p',unknown),
[] ).
cnf(29,axiom,
( ~ finer(u,v,w)
| subset_collections(v,u) ),
file('TOP010-1.p',unknown),
[] ).
cnf(1,axiom,
finer(ct1,ct2,cx),
file('TOP010-1.p',unknown),
[] ).
cnf(133,plain,
subset_collections(ct2,ct1),
inference(res,[status(thm),theory(equality)],[1,29]),
[iquote('0:Res:1.0,29.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : TOP010-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun May 29 05:49:27 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.80/1.03
% 0.80/1.03 SPASS V 3.9
% 0.80/1.03 SPASS beiseite: Completion found.
% 0.80/1.03 % SZS status CounterSatisfiable
% 0.80/1.03 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.80/1.03 SPASS derived 1655 clauses, backtracked 0 clauses, performed 3 splits and kept 1155 clauses.
% 0.80/1.03 SPASS allocated 78191 KBytes.
% 0.80/1.03 SPASS spent 0:00:00.68 on the problem.
% 0.80/1.03 0:00:00.04 for the input.
% 0.80/1.03 0:00:00.00 for the FLOTTER CNF translation.
% 0.80/1.03 0:00:00.07 for inferences.
% 0.80/1.03 0:00:00.00 for the backtracking.
% 0.80/1.03 0:00:00.51 for the reduction.
% 0.80/1.03
% 0.80/1.03
% 0.80/1.03 The saturated set of worked-off clauses is :
% 0.80/1.03 % SZS output start Saturation
% See solution above
%------------------------------------------------------------------------------