TSTP Solution File: TOP011-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : TOP011-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 0.68s 0.88s
% Output : Saturation 0.68s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 80)
% Comments :
%------------------------------------------------------------------------------
cnf(1771,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)],[501,1700]),
[iquote('4:Res:501.2,1700.1')] ).
cnf(1772,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)],[500,1700]),
[iquote('4:Res:500.2,1700.1')] ).
cnf(1773,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)],[499,1700]),
[iquote('4:Res:499.2,1700.1')] ).
cnf(1774,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)],[498,1700]),
[iquote('4:Res:498.2,1700.1')] ).
cnf(1757,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)],[501,1698]),
[iquote('4:Res:501.2,1698.1')] ).
cnf(1758,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)],[500,1698]),
[iquote('4:Res:500.2,1698.1')] ).
cnf(1759,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)],[499,1698]),
[iquote('4:Res:499.2,1698.1')] ).
cnf(1760,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)],[498,1698]),
[iquote('4:Res:498.2,1698.1')] ).
cnf(1743,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)],[501,1682]),
[iquote('4:Res:501.2,1682.1')] ).
cnf(1744,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)],[500,1682]),
[iquote('4:Res:500.2,1682.1')] ).
cnf(1745,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)],[499,1682]),
[iquote('4:Res:499.2,1682.1')] ).
cnf(1746,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)],[498,1682]),
[iquote('4:Res:498.2,1682.1')] ).
cnf(1729,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)],[501,1652]),
[iquote('4:Res:501.2,1652.1')] ).
cnf(1730,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)],[500,1652]),
[iquote('4:Res:500.2,1652.1')] ).
cnf(1731,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)],[499,1652]),
[iquote('4:Res:499.2,1652.1')] ).
cnf(1732,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)],[498,1652]),
[iquote('4:Res:498.2,1652.1')] ).
cnf(1689,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)],[501,1636]),
[iquote('4:Res:501.2,1636.1')] ).
cnf(1690,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)],[500,1636]),
[iquote('4:Res:500.2,1636.1')] ).
cnf(1691,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)],[499,1636]),
[iquote('4:Res:499.2,1636.1')] ).
cnf(1692,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)],[498,1636]),
[iquote('4:Res:498.2,1636.1')] ).
cnf(1673,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)],[501,1612]),
[iquote('4:Res:501.2,1612.1')] ).
cnf(1674,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)],[500,1612]),
[iquote('4:Res:500.2,1612.1')] ).
cnf(1675,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)],[499,1612]),
[iquote('4:Res:499.2,1612.1')] ).
cnf(1676,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)],[498,1612]),
[iquote('4:Res:498.2,1612.1')] ).
cnf(1659,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)],[501,1610]),
[iquote('4:Res:501.2,1610.1')] ).
cnf(1660,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)],[500,1610]),
[iquote('4:Res:500.2,1610.1')] ).
cnf(1661,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)],[499,1610]),
[iquote('4:Res:499.2,1610.1')] ).
cnf(1662,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)],[498,1610]),
[iquote('4:Res:498.2,1610.1')] ).
cnf(1643,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)],[501,1608]),
[iquote('4:Res:501.2,1608.1')] ).
cnf(1701,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)],[383,1433]),
[iquote('4:Res:383.1,1433.0')] ).
cnf(1644,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)],[500,1608]),
[iquote('4:Res:500.2,1608.1')] ).
cnf(1645,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)],[499,1608]),
[iquote('4:Res:499.2,1608.1')] ).
cnf(1646,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)],[498,1608]),
[iquote('4:Res:498.2,1608.1')] ).
cnf(1769,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)],[497,1700]),
[iquote('4:Res:497.2,1700.1')] ).
cnf(1699,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)],[383,1424]),
[iquote('4:Res:383.1,1424.0')] ).
cnf(1770,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)],[496,1700]),
[iquote('4:Res:496.2,1700.1')] ).
cnf(1755,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)],[497,1698]),
[iquote('4:Res:497.2,1698.1')] ).
cnf(1756,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)],[496,1698]),
[iquote('4:Res:496.2,1698.1')] ).
cnf(1741,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)],[497,1682]),
[iquote('4:Res:497.2,1682.1')] ).
cnf(1683,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)],[383,1415]),
[iquote('4:Res:383.1,1415.0')] ).
cnf(1742,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)],[496,1682]),
[iquote('4:Res:496.2,1682.1')] ).
cnf(1727,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)],[497,1652]),
[iquote('4:Res:497.2,1652.1')] ).
cnf(1728,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)],[496,1652]),
[iquote('4:Res:496.2,1652.1')] ).
cnf(1599,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)],[501,1592]),
[iquote('4:Res:501.2,1592.1')] ).
cnf(1653,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)],[383,1406]),
[iquote('4:Res:383.1,1406.0')] ).
cnf(1600,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)],[500,1592]),
[iquote('4:Res:500.2,1592.1')] ).
cnf(1601,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)],[499,1592]),
[iquote('4:Res:499.2,1592.1')] ).
cnf(1602,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)],[498,1592]),
[iquote('4:Res:498.2,1592.1')] ).
cnf(1583,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)],[501,1576]),
[iquote('4:Res:501.2,1576.1')] ).
cnf(1593,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)],[383,1276]),
[iquote('4:Res:383.1,1276.0')] ).
cnf(1584,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)],[500,1576]),
[iquote('4:Res:500.2,1576.1')] ).
cnf(1585,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)],[499,1576]),
[iquote('4:Res:499.2,1576.1')] ).
cnf(1586,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)],[498,1576]),
[iquote('4:Res:498.2,1576.1')] ).
cnf(1687,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)],[497,1636]),
[iquote('4:Res:497.2,1636.1')] ).
cnf(1577,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)],[383,1267]),
[iquote('4:Res:383.1,1267.0')] ).
cnf(1688,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)],[496,1636]),
[iquote('4:Res:496.2,1636.1')] ).
cnf(1671,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)],[497,1612]),
[iquote('4:Res:497.2,1612.1')] ).
cnf(1672,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)],[496,1612]),
[iquote('4:Res:496.2,1612.1')] ).
cnf(1657,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)],[497,1610]),
[iquote('4:Res:497.2,1610.1')] ).
cnf(1529,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)],[383,1126]),
[iquote('4:Res:383.1,1126.0')] ).
cnf(1658,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)],[496,1610]),
[iquote('4:Res:496.2,1610.1')] ).
cnf(1641,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)],[497,1608]),
[iquote('4:Res:497.2,1608.1')] ).
cnf(1642,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)],[496,1608]),
[iquote('4:Res:496.2,1608.1')] ).
cnf(1567,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)],[501,1560]),
[iquote('4:Res:501.2,1560.1')] ).
cnf(1513,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)],[383,1117]),
[iquote('4:Res:383.1,1117.0')] ).
cnf(1568,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)],[500,1560]),
[iquote('4:Res:500.2,1560.1')] ).
cnf(1569,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)],[499,1560]),
[iquote('4:Res:499.2,1560.1')] ).
cnf(1570,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)],[498,1560]),
[iquote('4:Res:498.2,1560.1')] ).
cnf(1551,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)],[501,1544]),
[iquote('4:Res:501.2,1544.1')] ).
cnf(1637,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)],[383,1388]),
[iquote('4:Res:383.1,1388.0')] ).
cnf(1552,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)],[500,1544]),
[iquote('4:Res:500.2,1544.1')] ).
cnf(1553,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)],[499,1544]),
[iquote('4:Res:499.2,1544.1')] ).
cnf(1554,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)],[498,1544]),
[iquote('4:Res:498.2,1544.1')] ).
cnf(1779,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)],[1775,419]),
[iquote('4:MRR:1775.0,419.1')] ).
cnf(1613,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)],[383,1376]),
[iquote('4:Res:383.1,1376.0')] ).
cnf(1778,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)],[1776,432]),
[iquote('4:MRR:1776.0,432.1')] ).
cnf(1765,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)],[1761,419]),
[iquote('4:MRR:1761.0,419.1')] ).
cnf(1764,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)],[1762,432]),
[iquote('4:MRR:1762.0,432.1')] ).
cnf(1751,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)],[1747,419]),
[iquote('4:MRR:1747.0,419.1')] ).
cnf(1611,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)],[383,1364]),
[iquote('4:Res:383.1,1364.0')] ).
cnf(1750,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)],[1748,432]),
[iquote('4:MRR:1748.0,432.1')] ).
cnf(1737,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)],[1733,419]),
[iquote('4:MRR:1733.0,419.1')] ).
cnf(1736,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)],[1734,432]),
[iquote('4:MRR:1734.0,432.1')] ).
cnf(1535,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)],[501,1528]),
[iquote('4:Res:501.2,1528.1')] ).
cnf(1609,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)],[383,1352]),
[iquote('4:Res:383.1,1352.0')] ).
cnf(1536,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)],[500,1528]),
[iquote('4:Res:500.2,1528.1')] ).
cnf(1537,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)],[499,1528]),
[iquote('4:Res:499.2,1528.1')] ).
cnf(1538,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)],[498,1528]),
[iquote('4:Res:498.2,1528.1')] ).
cnf(1519,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)],[501,1512]),
[iquote('4:Res:501.2,1512.1')] ).
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(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)],[383,1060]),
[iquote('4:Res:383.1,1060.0')] ).
cnf(1520,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)],[500,1512]),
[iquote('4:Res:500.2,1512.1')] ).
cnf(1521,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)],[499,1512]),
[iquote('4:Res:499.2,1512.1')] ).
cnf(1522,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)],[498,1512]),
[iquote('4:Res:498.2,1512.1')] ).
cnf(1777,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)],[1768,376]),
[iquote('4:MRR:1768.0,376.1')] ).
cnf(1700,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)],[373,1433]),
[iquote('4:Res:373.1,1433.0')] ).
cnf(1697,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)],[1693,419]),
[iquote('4:MRR:1693.0,419.1')] ).
cnf(1696,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)],[1694,432]),
[iquote('4:MRR:1694.0,432.1')] ).
cnf(1681,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)],[1677,419]),
[iquote('4:MRR:1677.0,419.1')] ).
cnf(1763,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)],[1754,376]),
[iquote('4:MRR:1754.0,376.1')] ).
cnf(1698,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)],[373,1424]),
[iquote('4:Res:373.1,1424.0')] ).
cnf(1680,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)],[1678,432]),
[iquote('4:MRR:1678.0,432.1')] ).
cnf(1667,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)],[1663,419]),
[iquote('4:MRR:1663.0,419.1')] ).
cnf(1666,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)],[1664,432]),
[iquote('4:MRR:1664.0,432.1')] ).
cnf(1749,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)],[1740,376]),
[iquote('4:MRR:1740.0,376.1')] ).
cnf(1682,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)],[373,1415]),
[iquote('4:Res:373.1,1415.0')] ).
cnf(1735,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)],[1726,376]),
[iquote('4:MRR:1726.0,376.1')] ).
cnf(1652,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)],[373,1406]),
[iquote('4:Res:373.1,1406.0')] ).
cnf(1651,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)],[1647,419]),
[iquote('4:MRR:1647.0,419.1')] ).
cnf(1650,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)],[1648,432]),
[iquote('4:MRR:1648.0,432.1')] ).
cnf(1561,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)],[383,1150]),
[iquote('4:Res:383.1,1150.0')] ).
cnf(1545,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)],[383,1138]),
[iquote('4:Res:383.1,1138.0')] ).
cnf(1503,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)],[501,1496]),
[iquote('4:Res:501.2,1496.1')] ).
cnf(1504,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)],[500,1496]),
[iquote('4:Res:500.2,1496.1')] ).
cnf(1505,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)],[499,1496]),
[iquote('4:Res:499.2,1496.1')] ).
cnf(1466,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)],[373,1397]),
[iquote('4:Res:373.1,1397.0')] ).
cnf(1506,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)],[498,1496]),
[iquote('4:Res:498.2,1496.1')] ).
cnf(1487,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)],[501,1480]),
[iquote('4:Res:501.2,1480.1')] ).
cnf(1488,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)],[500,1480]),
[iquote('4:Res:500.2,1480.1')] ).
cnf(1489,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)],[499,1480]),
[iquote('4:Res:499.2,1480.1')] ).
cnf(1433,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)],[68,1043]),
[iquote('4:Res:68.2,1043.1')] ).
cnf(1490,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)],[498,1480]),
[iquote('4:Res:498.2,1480.1')] ).
cnf(1597,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)],[497,1592]),
[iquote('4:Res:497.2,1592.1')] ).
cnf(1598,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)],[496,1592]),
[iquote('4:Res:496.2,1592.1')] ).
cnf(1581,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)],[497,1576]),
[iquote('4:Res:497.2,1576.1')] ).
cnf(1424,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)],[68,1044]),
[iquote('4:Res:68.2,1044.1')] ).
cnf(1582,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)],[496,1576]),
[iquote('4:Res:496.2,1576.1')] ).
cnf(1695,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)],[1686,376]),
[iquote('4:MRR:1686.0,376.1')] ).
cnf(1636,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)],[373,1388]),
[iquote('4:Res:373.1,1388.0')] ).
cnf(1679,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)],[1670,376]),
[iquote('4:MRR:1670.0,376.1')] ).
cnf(1415,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)],[68,1045]),
[iquote('4:Res:68.2,1045.1')] ).
cnf(1612,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)],[373,1376]),
[iquote('4:Res:373.1,1376.0')] ).
cnf(1665,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)],[1656,376]),
[iquote('4:MRR:1656.0,376.1')] ).
cnf(1610,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)],[373,1364]),
[iquote('4:Res:373.1,1364.0')] ).
cnf(1649,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)],[1640,376]),
[iquote('4:MRR:1640.0,376.1')] ).
cnf(1406,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)],[68,1046]),
[iquote('4:Res:68.2,1046.1')] ).
cnf(1608,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)],[373,1352]),
[iquote('4:Res:373.1,1352.0')] ).
cnf(1565,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)],[497,1560]),
[iquote('4:Res:497.2,1560.1')] ).
cnf(1566,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)],[496,1560]),
[iquote('4:Res:496.2,1560.1')] ).
cnf(1549,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)],[497,1544]),
[iquote('4:Res:497.2,1544.1')] ).
cnf(1388,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)],[517,993]),
[iquote('4:Res:517.2,993.1')] ).
cnf(1550,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)],[496,1544]),
[iquote('4:Res:496.2,1544.1')] ).
cnf(1497,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)],[383,1037]),
[iquote('4:Res:383.1,1037.0')] ).
cnf(1481,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)],[383,1025]),
[iquote('4:Res:383.1,1025.0')] ).
cnf(1607,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)],[1603,419]),
[iquote('4:MRR:1603.0,419.1')] ).
cnf(1376,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)],[517,994]),
[iquote('4:Res:517.2,994.1')] ).
cnf(1606,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)],[1604,432]),
[iquote('4:MRR:1604.0,432.1')] ).
cnf(1591,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)],[1587,419]),
[iquote('4:MRR:1587.0,419.1')] ).
cnf(1590,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)],[1588,432]),
[iquote('4:MRR:1588.0,432.1')] ).
cnf(1533,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)],[497,1528]),
[iquote('4:Res:497.2,1528.1')] ).
cnf(1364,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)],[517,995]),
[iquote('4:Res:517.2,995.1')] ).
cnf(1534,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)],[496,1528]),
[iquote('4:Res:496.2,1528.1')] ).
cnf(1517,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)],[497,1512]),
[iquote('4:Res:497.2,1512.1')] ).
cnf(1518,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)],[496,1512]),
[iquote('4:Res:496.2,1512.1')] ).
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(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)],[501,1450]),
[iquote('4:Res:501.2,1450.1')] ).
cnf(1352,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)],[517,996]),
[iquote('4:Res:517.2,996.1')] ).
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(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)],[500,1450]),
[iquote('4:Res:500.2,1450.1')] ).
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(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)],[499,1450]),
[iquote('4:Res:499.2,1450.1')] ).
cnf(1605,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)],[1596,376]),
[iquote('4:MRR:1596.0,376.1')] ).
cnf(1592,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)],[373,1276]),
[iquote('4:Res:373.1,1276.0')] ).
cnf(1276,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)],[68,1041]),
[iquote('4:Res:68.2,1041.1')] ).
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(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)],[498,1450]),
[iquote('4:Res:498.2,1450.1')] ).
cnf(1589,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)],[1580,376]),
[iquote('4:MRR:1580.0,376.1')] ).
cnf(1576,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)],[373,1267]),
[iquote('4:Res:373.1,1267.0')] ).
cnf(1575,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)],[1571,419]),
[iquote('4:MRR:1571.0,419.1')] ).
cnf(1267,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)],[68,1042]),
[iquote('4:Res:68.2,1042.1')] ).
cnf(1574,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)],[1572,432]),
[iquote('4:MRR:1572.0,432.1')] ).
cnf(1559,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)],[1555,419]),
[iquote('4:MRR:1555.0,419.1')] ).
cnf(1573,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)],[1564,376]),
[iquote('4:MRR:1564.0,376.1')] ).
cnf(1560,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)],[373,1150]),
[iquote('4:Res:373.1,1150.0')] ).
cnf(1150,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)],[517,991]),
[iquote('4:Res:517.2,991.1')] ).
cnf(1558,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)],[1556,432]),
[iquote('4:MRR:1556.0,432.1')] ).
cnf(1557,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)],[1548,376]),
[iquote('4:MRR:1548.0,376.1')] ).
cnf(1544,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)],[373,1138]),
[iquote('4:Res:373.1,1138.0')] ).
cnf(1138,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)],[517,992]),
[iquote('4:Res:517.2,992.1')] ).
cnf(1429,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)],[419,1043]),
[iquote('4:Res:419.1,1043.1')] ).
cnf(1430,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)],[432,1043]),
[iquote('4:Res:432.1,1043.1')] ).
cnf(1431,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)],[420,1043]),
[iquote('4:Res:420.1,1043.1')] ).
cnf(1432,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)],[433,1043]),
[iquote('4:Res:433.1,1043.1')] ).
cnf(1420,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)],[419,1044]),
[iquote('4:Res:419.1,1044.1')] ).
cnf(1421,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)],[432,1044]),
[iquote('4:Res:432.1,1044.1')] ).
cnf(1422,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)],[420,1044]),
[iquote('4:Res:420.1,1044.1')] ).
cnf(1423,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)],[433,1044]),
[iquote('4:Res:433.1,1044.1')] ).
cnf(1411,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)],[419,1045]),
[iquote('4:Res:419.1,1045.1')] ).
cnf(1412,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)],[432,1045]),
[iquote('4:Res:432.1,1045.1')] ).
cnf(1413,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)],[420,1045]),
[iquote('4:Res:420.1,1045.1')] ).
cnf(1414,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)],[433,1045]),
[iquote('4:Res:433.1,1045.1')] ).
cnf(1402,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)],[419,1046]),
[iquote('4:Res:419.1,1046.1')] ).
cnf(1403,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)],[432,1046]),
[iquote('4:Res:432.1,1046.1')] ).
cnf(1404,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)],[420,1046]),
[iquote('4:Res:420.1,1046.1')] ).
cnf(1405,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)],[433,1046]),
[iquote('4:Res:433.1,1046.1')] ).
cnf(1332,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)],[501,1311]),
[iquote('4:Res:501.2,1311.1')] ).
cnf(1333,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)],[500,1311]),
[iquote('4:Res:500.2,1311.1')] ).
cnf(1334,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)],[499,1311]),
[iquote('4:Res:499.2,1311.1')] ).
cnf(1335,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)],[498,1311]),
[iquote('4:Res:498.2,1311.1')] ).
cnf(1318,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)],[501,1281]),
[iquote('4:Res:501.2,1281.1')] ).
cnf(1319,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)],[500,1281]),
[iquote('4:Res:500.2,1281.1')] ).
cnf(1320,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)],[499,1281]),
[iquote('4:Res:499.2,1281.1')] ).
cnf(1321,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)],[498,1281]),
[iquote('4:Res:498.2,1281.1')] ).
cnf(1302,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)],[501,1279]),
[iquote('4:Res:501.2,1279.1')] ).
cnf(1303,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)],[500,1279]),
[iquote('4:Res:500.2,1279.1')] ).
cnf(1304,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)],[499,1279]),
[iquote('4:Res:499.2,1279.1')] ).
cnf(1305,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)],[498,1279]),
[iquote('4:Res:498.2,1279.1')] ).
cnf(1288,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)],[501,1277]),
[iquote('4:Res:501.2,1277.1')] ).
cnf(1289,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)],[500,1277]),
[iquote('4:Res:500.2,1277.1')] ).
cnf(1290,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)],[499,1277]),
[iquote('4:Res:499.2,1277.1')] ).
cnf(1501,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)],[497,1496]),
[iquote('4:Res:497.2,1496.1')] ).
cnf(1502,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)],[496,1496]),
[iquote('4:Res:496.2,1496.1')] ).
cnf(1485,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)],[497,1480]),
[iquote('4:Res:497.2,1480.1')] ).
cnf(1486,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)],[496,1480]),
[iquote('4:Res:496.2,1480.1')] ).
cnf(1291,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)],[498,1277]),
[iquote('4:Res:498.2,1277.1')] ).
cnf(1441,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)],[501,1434]),
[iquote('4:Res:501.2,1434.1')] ).
cnf(1442,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)],[500,1434]),
[iquote('4:Res:500.2,1434.1')] ).
cnf(1443,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)],[499,1434]),
[iquote('4:Res:499.2,1434.1')] ).
cnf(1444,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)],[498,1434]),
[iquote('4:Res:498.2,1434.1')] ).
cnf(1468,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)],[1467]),
[iquote('4:Obv:1467.3')] ).
cnf(1543,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)],[1539,419]),
[iquote('4:MRR:1539.0,419.1')] ).
cnf(1542,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)],[1540,432]),
[iquote('4:MRR:1540.0,432.1')] ).
cnf(1541,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)],[1532,376]),
[iquote('4:MRR:1532.0,376.1')] ).
cnf(1528,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)],[373,1126]),
[iquote('4:Res:373.1,1126.0')] ).
cnf(1126,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)],[68,1051]),
[iquote('4:Res:68.2,1051.0')] ).
cnf(1527,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)],[1523,419]),
[iquote('4:MRR:1523.0,419.1')] ).
cnf(1526,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)],[1524,432]),
[iquote('4:MRR:1524.0,432.1')] ).
cnf(1525,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)],[1516,376]),
[iquote('4:MRR:1516.0,376.1')] ).
cnf(1512,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)],[373,1117]),
[iquote('4:Res:373.1,1117.0')] ).
cnf(1117,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)],[68,1050]),
[iquote('4:Res:68.2,1050.0')] ).
cnf(1511,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)],[1507,419]),
[iquote('4:MRR:1507.0,419.1')] ).
cnf(1510,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)],[1508,432]),
[iquote('4:MRR:1508.0,432.1')] ).
cnf(1509,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)],[1500,376]),
[iquote('4:MRR:1500.0,376.1')] ).
cnf(1496,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)],[373,1037]),
[iquote('4:Res:373.1,1037.0')] ).
cnf(1037,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)],[517,1001]),
[iquote('4:Res:517.2,1001.0')] ).
cnf(1495,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)],[1491,419]),
[iquote('4:MRR:1491.0,419.1')] ).
cnf(1494,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)],[1492,432]),
[iquote('4:MRR:1492.0,432.1')] ).
cnf(1493,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)],[1484,376]),
[iquote('4:MRR:1484.0,376.1')] ).
cnf(1480,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)],[373,1025]),
[iquote('4:Res:373.1,1025.0')] ).
cnf(1025,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)],[517,1000]),
[iquote('4:Res:517.2,1000.0')] ).
cnf(1425,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)],[304,1043]),
[iquote('4:Res:304.1,1043.1')] ).
cnf(1426,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)],[305,1043]),
[iquote('4:Res:305.1,1043.1')] ).
cnf(1416,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)],[304,1044]),
[iquote('4:Res:304.1,1044.1')] ).
cnf(1417,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)],[305,1044]),
[iquote('4:Res:305.1,1044.1')] ).
cnf(1407,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)],[304,1045]),
[iquote('4:Res:304.1,1045.1')] ).
cnf(1408,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)],[305,1045]),
[iquote('4:Res:305.1,1045.1')] ).
cnf(1398,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)],[304,1046]),
[iquote('4:Res:304.1,1046.1')] ).
cnf(1399,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)],[305,1046]),
[iquote('4:Res:305.1,1046.1')] ).
cnf(1250,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)],[501,1243]),
[iquote('4:Res:501.2,1243.1')] ).
cnf(1251,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)],[500,1243]),
[iquote('4:Res:500.2,1243.1')] ).
cnf(1252,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)],[499,1243]),
[iquote('4:Res:499.2,1243.1')] ).
cnf(1253,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)],[498,1243]),
[iquote('4:Res:498.2,1243.1')] ).
cnf(1212,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)],[501,1205]),
[iquote('4:Res:501.2,1205.1')] ).
cnf(1213,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)],[500,1205]),
[iquote('4:Res:500.2,1205.1')] ).
cnf(1214,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)],[499,1205]),
[iquote('4:Res:499.2,1205.1')] ).
cnf(1215,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)],[498,1205]),
[iquote('4:Res:498.2,1205.1')] ).
cnf(1435,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)],[383,1013]),
[iquote('4:Res:383.1,1013.0')] ).
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(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)],[497,1450]),
[iquote('4:Res:497.2,1450.1')] ).
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(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)],[496,1450]),
[iquote('4:Res:496.2,1450.1')] ).
cnf(1397,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)],[68,975]),
[iquote('4:Res:68.2,975.1')] ).
cnf(1427,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)],[376,1043]),
[iquote('4:Res:376.1,1043.1')] ).
cnf(1428,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)],[377,1043]),
[iquote('4:Res:377.1,1043.1')] ).
cnf(1418,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)],[376,1044]),
[iquote('4:Res:376.1,1044.1')] ).
cnf(1419,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)],[377,1044]),
[iquote('4:Res:377.1,1044.1')] ).
cnf(1389,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)],[304,975]),
[iquote('4:Res:304.1,975.1')] ).
cnf(1409,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)],[376,1045]),
[iquote('4:Res:376.1,1045.1')] ).
cnf(1410,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)],[377,1045]),
[iquote('4:Res:377.1,1045.1')] ).
cnf(1400,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)],[376,1046]),
[iquote('4:Res:376.1,1046.1')] ).
cnf(1401,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)],[377,1046]),
[iquote('4:Res:377.1,1046.1')] ).
cnf(1390,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)],[305,975]),
[iquote('4:Res:305.1,975.1')] ).
cnf(1330,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)],[497,1311]),
[iquote('4:Res:497.2,1311.1')] ).
cnf(1331,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)],[496,1311]),
[iquote('4:Res:496.2,1311.1')] ).
cnf(1316,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)],[497,1281]),
[iquote('4:Res:497.2,1281.1')] ).
cnf(1317,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)],[496,1281]),
[iquote('4:Res:496.2,1281.1')] ).
cnf(1244,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)],[383,681]),
[iquote('4:Res:383.1,681.0')] ).
cnf(1300,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)],[497,1279]),
[iquote('4:Res:497.2,1279.1')] ).
cnf(1301,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)],[496,1279]),
[iquote('4:Res:496.2,1279.1')] ).
cnf(1286,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)],[497,1277]),
[iquote('4:Res:497.2,1277.1')] ).
cnf(1287,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)],[496,1277]),
[iquote('4:Res:496.2,1277.1')] ).
cnf(1206,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)],[383,660]),
[iquote('4:Res:383.1,660.0')] ).
cnf(1272,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)],[419,1041]),
[iquote('4:Res:419.1,1041.1')] ).
cnf(1273,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)],[432,1041]),
[iquote('4:Res:432.1,1041.1')] ).
cnf(1274,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)],[420,1041]),
[iquote('4:Res:420.1,1041.1')] ).
cnf(1275,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)],[433,1041]),
[iquote('4:Res:433.1,1041.1')] ).
cnf(1393,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)],[419,975]),
[iquote('4:Res:419.1,975.1')] ).
cnf(1263,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)],[419,1042]),
[iquote('4:Res:419.1,1042.1')] ).
cnf(1264,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)],[432,1042]),
[iquote('4:Res:432.1,1042.1')] ).
cnf(1265,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)],[420,1042]),
[iquote('4:Res:420.1,1042.1')] ).
cnf(1266,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)],[433,1042]),
[iquote('4:Res:433.1,1042.1')] ).
cnf(1394,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)],[432,975]),
[iquote('4:Res:432.1,975.1')] ).
cnf(1174,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)],[501,1167]),
[iquote('4:Res:501.2,1167.1')] ).
cnf(1175,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)],[500,1167]),
[iquote('4:Res:500.2,1167.1')] ).
cnf(1176,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)],[499,1167]),
[iquote('4:Res:499.2,1167.1')] ).
cnf(1177,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)],[498,1167]),
[iquote('4:Res:498.2,1167.1')] ).
cnf(1395,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)],[420,975]),
[iquote('4:Res:420.1,975.1')] ).
cnf(1158,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)],[501,1151]),
[iquote('4:Res:501.2,1151.1')] ).
cnf(1159,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)],[500,1151]),
[iquote('4:Res:500.2,1151.1')] ).
cnf(1160,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)],[499,1151]),
[iquote('4:Res:499.2,1151.1')] ).
cnf(1161,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)],[498,1151]),
[iquote('4:Res:498.2,1151.1')] ).
cnf(1396,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)],[433,975]),
[iquote('4:Res:433.1,975.1')] ).
cnf(1439,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)],[497,1434]),
[iquote('4:Res:497.2,1434.1')] ).
cnf(1440,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)],[496,1434]),
[iquote('4:Res:496.2,1434.1')] ).
cnf(1465,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)],[1461,419]),
[iquote('4:MRR:1461.0,419.1')] ).
cnf(1464,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)],[1462,432]),
[iquote('4:MRR:1462.0,432.1')] ).
cnf(1312,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)],[383,903]),
[iquote('4:Res:383.1,903.0')] ).
cnf(1463,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)],[1454,376]),
[iquote('4:MRR:1454.0,376.1')] ).
cnf(1450,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)],[373,1060]),
[iquote('4:Res:373.1,1060.0')] ).
cnf(1060,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)],[68,1049]),
[iquote('4:Res:68.2,1049.0')] ).
cnf(1449,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)],[1445,419]),
[iquote('4:MRR:1445.0,419.1')] ).
cnf(1282,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)],[383,881]),
[iquote('4:Res:383.1,881.0')] ).
cnf(1448,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)],[1446,432]),
[iquote('4:MRR:1446.0,432.1')] ).
cnf(1447,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)],[1438,376]),
[iquote('4:MRR:1438.0,376.1')] ).
cnf(1434,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)],[373,1013]),
[iquote('4:Res:373.1,1013.0')] ).
cnf(1013,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)],[517,999]),
[iquote('4:Res:517.2,999.0')] ).
cnf(1280,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)],[383,859]),
[iquote('4:Res:383.1,859.0')] ).
cnf(1268,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)],[304,1041]),
[iquote('4:Res:304.1,1041.1')] ).
cnf(1269,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)],[305,1041]),
[iquote('4:Res:305.1,1041.1')] ).
cnf(1259,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)],[304,1042]),
[iquote('4:Res:304.1,1042.1')] ).
cnf(1260,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)],[305,1042]),
[iquote('4:Res:305.1,1042.1')] ).
cnf(1278,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)],[383,837]),
[iquote('4:Res:383.1,837.0')] ).
cnf(1248,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)],[497,1243]),
[iquote('4:Res:497.2,1243.1')] ).
cnf(1249,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)],[496,1243]),
[iquote('4:Res:496.2,1243.1')] ).
cnf(1210,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)],[497,1205]),
[iquote('4:Res:497.2,1205.1')] ).
cnf(1211,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)],[496,1205]),
[iquote('4:Res:496.2,1205.1')] ).
cnf(1391,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)],[376,975]),
[iquote('4:Res:376.1,975.1')] ).
cnf(1377,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)],[458,993]),
[iquote('4:Res:458.1,993.1')] ).
cnf(1365,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)],[458,994]),
[iquote('4:Res:458.1,994.1')] ).
cnf(1353,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)],[458,995]),
[iquote('4:Res:458.1,995.1')] ).
cnf(1341,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)],[458,996]),
[iquote('4:Res:458.1,996.1')] ).
cnf(1392,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)],[377,975]),
[iquote('4:Res:377.1,975.1')] ).
cnf(1340,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)],[1336,419]),
[iquote('4:MRR:1336.0,419.1')] ).
cnf(1339,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)],[1337,432]),
[iquote('4:MRR:1337.0,432.1')] ).
cnf(1326,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)],[1322,419]),
[iquote('4:MRR:1322.0,419.1')] ).
cnf(1325,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)],[1323,432]),
[iquote('4:MRR:1323.0,432.1')] ).
cnf(1168,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)],[383,755]),
[iquote('4:Res:383.1,755.0')] ).
cnf(1310,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)],[1306,419]),
[iquote('4:MRR:1306.0,419.1')] ).
cnf(1309,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)],[1307,432]),
[iquote('4:MRR:1307.0,432.1')] ).
cnf(1296,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)],[1292,419]),
[iquote('4:MRR:1292.0,419.1')] ).
cnf(1295,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)],[1293,432]),
[iquote('4:MRR:1293.0,432.1')] ).
cnf(1152,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)],[383,733]),
[iquote('4:Res:383.1,733.0')] ).
cnf(1122,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)],[419,1051]),
[iquote('4:Res:419.1,1051.0')] ).
cnf(1123,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)],[432,1051]),
[iquote('4:Res:432.1,1051.0')] ).
cnf(1124,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)],[420,1051]),
[iquote('4:Res:420.1,1051.0')] ).
cnf(1125,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)],[433,1051]),
[iquote('4:Res:433.1,1051.0')] ).
cnf(1043,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)],[501,974]),
[iquote('4:Res:501.2,974.1')] ).
cnf(1113,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)],[419,1050]),
[iquote('4:Res:419.1,1050.0')] ).
cnf(1114,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)],[432,1050]),
[iquote('4:Res:432.1,1050.0')] ).
cnf(1115,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)],[420,1050]),
[iquote('4:Res:420.1,1050.0')] ).
cnf(1116,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)],[433,1050]),
[iquote('4:Res:433.1,1050.0')] ).
cnf(1044,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)],[500,974]),
[iquote('4:Res:500.2,974.1')] ).
cnf(1100,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)],[501,1093]),
[iquote('4:Res:501.2,1093.1')] ).
cnf(1101,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)],[500,1093]),
[iquote('4:Res:500.2,1093.1')] ).
cnf(1102,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)],[499,1093]),
[iquote('4:Res:499.2,1093.1')] ).
cnf(1103,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)],[498,1093]),
[iquote('4:Res:498.2,1093.1')] ).
cnf(1045,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)],[499,974]),
[iquote('4:Res:499.2,974.1')] ).
cnf(1380,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)],[402,993]),
[iquote('4:Res:402.1,993.1')] ).
cnf(1381,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)],[404,993]),
[iquote('4:Res:404.1,993.1')] ).
cnf(1368,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)],[402,994]),
[iquote('4:Res:402.1,994.1')] ).
cnf(1369,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)],[404,994]),
[iquote('4:Res:404.1,994.1')] ).
cnf(1046,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)],[498,974]),
[iquote('4:Res:498.2,974.1')] ).
cnf(1356,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)],[402,995]),
[iquote('4:Res:402.1,995.1')] ).
cnf(1357,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)],[404,995]),
[iquote('4:Res:404.1,995.1')] ).
cnf(1344,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)],[402,996]),
[iquote('4:Res:402.1,996.1')] ).
cnf(1345,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)],[404,996]),
[iquote('4:Res:404.1,996.1')] ).
cnf(987,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)],[516,685]),
[iquote('4:Res:516.2,685.2')] ).
cnf(1084,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)],[501,1077]),
[iquote('4:Res:501.2,1077.1')] ).
cnf(1085,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)],[500,1077]),
[iquote('4:Res:500.2,1077.1')] ).
cnf(1086,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)],[499,1077]),
[iquote('4:Res:499.2,1077.1')] ).
cnf(1087,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)],[498,1077]),
[iquote('4:Res:498.2,1077.1')] ).
cnf(975,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)],[383,639]),
[iquote('4:Res:383.1,639.0')] ).
cnf(1068,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)],[501,1061]),
[iquote('4:Res:501.2,1061.1')] ).
cnf(1069,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)],[500,1061]),
[iquote('4:Res:500.2,1061.1')] ).
cnf(1070,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)],[499,1061]),
[iquote('4:Res:499.2,1061.1')] ).
cnf(1071,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)],[498,1061]),
[iquote('4:Res:498.2,1061.1')] ).
cnf(965,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)],[304,626]),
[iquote('4:Res:304.1,626.2')] ).
cnf(993,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)],[501,962]),
[iquote('4:Res:501.2,962.1')] ).
cnf(994,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)],[500,962]),
[iquote('4:Res:500.2,962.1')] ).
cnf(995,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)],[499,962]),
[iquote('4:Res:499.2,962.1')] ).
cnf(996,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)],[498,962]),
[iquote('4:Res:498.2,962.1')] ).
cnf(966,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)],[305,626]),
[iquote('4:Res:305.1,626.2')] ).
cnf(1338,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)],[1329,376]),
[iquote('4:MRR:1329.0,376.1')] ).
cnf(1311,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)],[373,903]),
[iquote('4:Res:373.1,903.0')] ).
cnf(1324,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)],[1315,376]),
[iquote('4:MRR:1315.0,376.1')] ).
cnf(1281,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)],[373,881]),
[iquote('4:Res:373.1,881.0')] ).
cnf(903,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)],[68,635]),
[iquote('4:Res:68.2,635.0')] ).
cnf(1308,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)],[1299,376]),
[iquote('4:MRR:1299.0,376.1')] ).
cnf(1279,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)],[373,859]),
[iquote('4:Res:373.1,859.0')] ).
cnf(1294,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)],[1285,376]),
[iquote('4:MRR:1285.0,376.1')] ).
cnf(1277,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)],[373,837]),
[iquote('4:Res:373.1,837.0')] ).
cnf(881,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)],[68,636]),
[iquote('4:Res:68.2,636.0')] ).
cnf(1270,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)],[376,1041]),
[iquote('4:Res:376.1,1041.1')] ).
cnf(1271,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)],[377,1041]),
[iquote('4:Res:377.1,1041.1')] ).
cnf(1261,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)],[376,1042]),
[iquote('4:Res:376.1,1042.1')] ).
cnf(1262,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)],[377,1042]),
[iquote('4:Res:377.1,1042.1')] ).
cnf(859,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)],[68,637]),
[iquote('4:Res:68.2,637.0')] ).
cnf(1172,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)],[497,1167]),
[iquote('4:Res:497.2,1167.1')] ).
cnf(1173,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)],[496,1167]),
[iquote('4:Res:496.2,1167.1')] ).
cnf(1156,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)],[497,1151]),
[iquote('4:Res:497.2,1151.1')] ).
cnf(1157,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)],[496,1151]),
[iquote('4:Res:496.2,1151.1')] ).
cnf(837,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)],[68,638]),
[iquote('4:Res:68.2,638.0')] ).
cnf(1258,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)],[1254,419]),
[iquote('4:MRR:1254.0,419.1')] ).
cnf(1257,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)],[1255,432]),
[iquote('4:MRR:1255.0,432.1')] ).
cnf(1220,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)],[1216,419]),
[iquote('4:MRR:1216.0,419.1')] ).
cnf(1219,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)],[1217,432]),
[iquote('4:MRR:1217.0,432.1')] ).
cnf(668,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)],[396,628]),
[iquote('4:Res:396.2,628.0')] ).
cnf(1118,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)],[304,1051]),
[iquote('4:Res:304.1,1051.0')] ).
cnf(1119,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)],[305,1051]),
[iquote('4:Res:305.1,1051.0')] ).
cnf(1109,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)],[304,1050]),
[iquote('4:Res:304.1,1050.0')] ).
cnf(1110,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)],[305,1050]),
[iquote('4:Res:305.1,1050.0')] ).
cnf(647,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)],[396,627]),
[iquote('4:Res:396.2,627.0')] ).
cnf(1041,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)],[497,974]),
[iquote('4:Res:497.2,974.1')] ).
cnf(1042,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)],[496,974]),
[iquote('4:Res:496.2,974.1')] ).
cnf(1256,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)],[1247,376]),
[iquote('4:MRR:1247.0,376.1')] ).
cnf(1243,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)],[373,681]),
[iquote('4:Res:373.1,681.0')] ).
cnf(681,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)],[68,628]),
[iquote('4:Res:68.2,628.0')] ).
cnf(1094,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)],[383,769]),
[iquote('4:Res:383.1,769.0')] ).
cnf(1078,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)],[383,713]),
[iquote('4:Res:383.1,713.0')] ).
cnf(1218,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)],[1209,376]),
[iquote('4:MRR:1209.0,376.1')] ).
cnf(1205,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)],[373,660]),
[iquote('4:Res:373.1,660.0')] ).
cnf(660,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)],[68,627]),
[iquote('4:Res:68.2,627.0')] ).
cnf(1062,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)],[383,699]),
[iquote('4:Res:383.1,699.0')] ).
cnf(963,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)],[383,640]),
[iquote('4:Res:383.1,640.0')] ).
cnf(969,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)],[419,626]),
[iquote('4:Res:419.1,626.2')] ).
cnf(970,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)],[432,626]),
[iquote('4:Res:432.1,626.2')] ).
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(f19(closure(x1,x2,x3),x4),u) ),
inference(res,[status(thm),theory(equality)],[420,626]),
[iquote('4:Res:420.1,626.2')] ).
cnf(972,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)],[433,626]),
[iquote('4:Res:433.1,626.2')] ).
cnf(890,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)],[396,635]),
[iquote('4:Res:396.2,635.0')] ).
cnf(868,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)],[396,636]),
[iquote('4:Res:396.2,636.0')] ).
cnf(846,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)],[396,637]),
[iquote('4:Res:396.2,637.0')] ).
cnf(824,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)],[396,638]),
[iquote('4:Res:396.2,638.0')] ).
cnf(1182,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)],[1178,419]),
[iquote('4:MRR:1178.0,419.1')] ).
cnf(1181,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)],[1179,432]),
[iquote('4:MRR:1179.0,432.1')] ).
cnf(1180,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)],[1171,376]),
[iquote('4:MRR:1171.0,376.1')] ).
cnf(1167,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)],[373,755]),
[iquote('4:Res:373.1,755.0')] ).
cnf(755,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)],[68,632]),
[iquote('4:Res:68.2,632.0')] ).
cnf(1166,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)],[1162,419]),
[iquote('4:MRR:1162.0,419.1')] ).
cnf(1165,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)],[1163,432]),
[iquote('4:MRR:1163.0,432.1')] ).
cnf(1164,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)],[1155,376]),
[iquote('4:MRR:1155.0,376.1')] ).
cnf(1151,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)],[373,733]),
[iquote('4:Res:373.1,733.0')] ).
cnf(733,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)],[68,631]),
[iquote('4:Res:68.2,631.0')] ).
cnf(976,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)],[457,685]),
[iquote('4:Res:457.1,685.2')] ).
cnf(1139,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)],[458,991]),
[iquote('4:Res:458.1,991.1')] ).
cnf(1127,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)],[458,992]),
[iquote('4:Res:458.1,992.1')] ).
cnf(1120,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)],[376,1051]),
[iquote('4:Res:376.1,1051.0')] ).
cnf(941,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)],[516,622]),
[iquote('4:Res:516.2,622.0')] ).
cnf(1121,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)],[377,1051]),
[iquote('4:Res:377.1,1051.0')] ).
cnf(1111,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)],[376,1050]),
[iquote('4:Res:376.1,1050.0')] ).
cnf(1112,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)],[377,1050]),
[iquote('4:Res:377.1,1050.0')] ).
cnf(1098,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)],[497,1093]),
[iquote('4:Res:497.2,1093.1')] ).
cnf(981,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)],[426,685]),
[iquote('4:Res:426.1,685.2')] ).
cnf(1099,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)],[496,1093]),
[iquote('4:Res:496.2,1093.1')] ).
cnf(1056,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)],[419,1049]),
[iquote('4:Res:419.1,1049.0')] ).
cnf(1057,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)],[432,1049]),
[iquote('4:Res:432.1,1049.0')] ).
cnf(1058,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)],[420,1049]),
[iquote('4:Res:420.1,1049.0')] ).
cnf(982,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)],[427,685]),
[iquote('4:Res:427.1,685.2')] ).
cnf(1059,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)],[433,1049]),
[iquote('4:Res:433.1,1049.0')] ).
cnf(1142,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)],[402,991]),
[iquote('4:Res:402.1,991.1')] ).
cnf(1143,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)],[404,991]),
[iquote('4:Res:404.1,991.1')] ).
cnf(1130,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)],[402,992]),
[iquote('4:Res:402.1,992.1')] ).
cnf(929,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)],[516,633]),
[iquote('4:Res:516.2,633.0')] ).
cnf(1131,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)],[404,992]),
[iquote('4:Res:404.1,992.1')] ).
cnf(1082,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)],[497,1077]),
[iquote('4:Res:497.2,1077.1')] ).
cnf(1083,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)],[496,1077]),
[iquote('4:Res:496.2,1077.1')] ).
cnf(1066,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)],[497,1061]),
[iquote('4:Res:497.2,1061.1')] ).
cnf(917,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)],[516,634]),
[iquote('4:Res:516.2,634.0')] ).
cnf(1067,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)],[496,1061]),
[iquote('4:Res:496.2,1061.1')] ).
cnf(991,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)],[497,962]),
[iquote('4:Res:497.2,962.1')] ).
cnf(992,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)],[496,962]),
[iquote('4:Res:496.2,962.1')] ).
cnf(953,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)],[304,623]),
[iquote('4:Res:304.1,623.1')] ).
cnf(954,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)],[305,623]),
[iquote('4:Res:305.1,623.1')] ).
cnf(665,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)],[52,628]),
[iquote('4:Res:52.1,628.0')] ).
cnf(1051,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)],[1047,419]),
[iquote('4:MRR:1047.0,419.1')] ).
cnf(1050,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)],[1048,432]),
[iquote('4:MRR:1048.0,432.1')] ).
cnf(1052,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)],[304,1049]),
[iquote('4:Res:304.1,1049.0')] ).
cnf(644,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)],[52,627]),
[iquote('4:Res:52.1,627.0')] ).
cnf(1108,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)],[1104,419]),
[iquote('4:MRR:1104.0,419.1')] ).
cnf(1107,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)],[1105,432]),
[iquote('4:MRR:1105.0,432.1')] ).
cnf(1106,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)],[1097,376]),
[iquote('4:MRR:1097.0,376.1')] ).
cnf(1093,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)],[373,769]),
[iquote('4:Res:373.1,769.0')] ).
cnf(769,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)],[517,620]),
[iquote('4:Res:517.2,620.0')] ).
cnf(1092,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)],[1088,419]),
[iquote('4:MRR:1088.0,419.1')] ).
cnf(1091,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)],[1089,432]),
[iquote('4:MRR:1089.0,432.1')] ).
cnf(1090,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)],[1081,376]),
[iquote('4:MRR:1081.0,376.1')] ).
cnf(1077,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)],[373,713]),
[iquote('4:Res:373.1,713.0')] ).
cnf(713,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)],[517,630]),
[iquote('4:Res:517.2,630.0')] ).
cnf(1076,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)],[1072,419]),
[iquote('4:MRR:1072.0,419.1')] ).
cnf(1075,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)],[1073,432]),
[iquote('4:MRR:1073.0,432.1')] ).
cnf(1074,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)],[1065,376]),
[iquote('4:MRR:1065.0,376.1')] ).
cnf(1061,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)],[373,699]),
[iquote('4:Res:373.1,699.0')] ).
cnf(699,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)],[517,629]),
[iquote('4:Res:517.2,629.0')] ).
cnf(1053,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)],[305,1049]),
[iquote('4:Res:305.1,1049.0')] ).
cnf(1054,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)],[376,1049]),
[iquote('4:Res:376.1,1049.0')] ).
cnf(1055,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)],[377,1049]),
[iquote('4:Res:377.1,1049.0')] ).
cnf(1049,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)],[1040,376]),
[iquote('4:MRR:1040.0,376.1')] ).
cnf(974,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)],[373,639]),
[iquote('4:Res:373.1,639.0')] ).
cnf(943,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)],[304,625]),
[iquote('4:Res:304.1,625.0')] ).
cnf(944,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)],[305,625]),
[iquote('4:Res:305.1,625.0')] ).
cnf(1026,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)],[458,1001]),
[iquote('4:Res:458.1,1001.0')] ).
cnf(1014,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)],[458,1000]),
[iquote('4:Res:458.1,1000.0')] ).
cnf(667,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)],[456,628]),
[iquote('4:Res:456.1,628.0')] ).
cnf(1029,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)],[402,1001]),
[iquote('4:Res:402.1,1001.0')] ).
cnf(1030,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)],[404,1001]),
[iquote('4:Res:404.1,1001.0')] ).
cnf(1017,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)],[402,1000]),
[iquote('4:Res:402.1,1000.0')] ).
cnf(1018,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)],[404,1000]),
[iquote('4:Res:404.1,1000.0')] ).
cnf(646,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)],[456,627]),
[iquote('4:Res:456.1,627.0')] ).
cnf(957,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)],[419,623]),
[iquote('4:Res:419.1,623.1')] ).
cnf(958,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)],[432,623]),
[iquote('4:Res:432.1,623.1')] ).
cnf(959,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)],[420,623]),
[iquote('4:Res:420.1,623.1')] ).
cnf(960,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)],[433,623]),
[iquote('4:Res:433.1,623.1')] ).
cnf(887,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)],[52,635]),
[iquote('4:Res:52.1,635.0')] ).
cnf(899,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)],[419,635]),
[iquote('4:Res:419.1,635.0')] ).
cnf(900,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)],[432,635]),
[iquote('4:Res:432.1,635.0')] ).
cnf(901,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)],[420,635]),
[iquote('4:Res:420.1,635.0')] ).
cnf(902,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)],[433,635]),
[iquote('4:Res:433.1,635.0')] ).
cnf(865,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)],[52,636]),
[iquote('4:Res:52.1,636.0')] ).
cnf(877,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)],[419,636]),
[iquote('4:Res:419.1,636.0')] ).
cnf(878,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)],[432,636]),
[iquote('4:Res:432.1,636.0')] ).
cnf(879,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)],[420,636]),
[iquote('4:Res:420.1,636.0')] ).
cnf(880,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)],[433,636]),
[iquote('4:Res:433.1,636.0')] ).
cnf(843,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)],[52,637]),
[iquote('4:Res:52.1,637.0')] ).
cnf(855,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)],[419,637]),
[iquote('4:Res:419.1,637.0')] ).
cnf(856,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)],[432,637]),
[iquote('4:Res:432.1,637.0')] ).
cnf(857,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)],[420,637]),
[iquote('4:Res:420.1,637.0')] ).
cnf(858,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)],[433,637]),
[iquote('4:Res:433.1,637.0')] ).
cnf(821,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)],[52,638]),
[iquote('4:Res:52.1,638.0')] ).
cnf(833,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)],[419,638]),
[iquote('4:Res:419.1,638.0')] ).
cnf(834,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)],[432,638]),
[iquote('4:Res:432.1,638.0')] ).
cnf(835,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)],[420,638]),
[iquote('4:Res:420.1,638.0')] ).
cnf(1001,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)],[997,419]),
[iquote('4:MRR:997.0,419.1')] ).
cnf(836,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)],[433,638]),
[iquote('4:Res:433.1,638.0')] ).
cnf(1000,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)],[998,432]),
[iquote('4:MRR:998.0,432.1')] ).
cnf(967,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)],[376,626]),
[iquote('4:Res:376.1,626.2')] ).
cnf(968,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)],[377,626]),
[iquote('4:Res:377.1,626.2')] ).
cnf(742,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)],[396,632]),
[iquote('4:Res:396.2,632.0')] ).
cnf(720,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)],[396,631]),
[iquote('4:Res:396.2,631.0')] ).
cnf(1002,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)],[458,999]),
[iquote('4:Res:458.1,999.0')] ).
cnf(1005,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)],[402,999]),
[iquote('4:Res:402.1,999.0')] ).
cnf(1006,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)],[404,999]),
[iquote('4:Res:404.1,999.0')] ).
cnf(999,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)],[990,376]),
[iquote('4:MRR:990.0,376.1')] ).
cnf(962,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)],[373,640]),
[iquote('4:Res:373.1,640.0')] ).
cnf(889,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)],[456,635]),
[iquote('4:Res:456.1,635.0')] ).
cnf(867,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)],[456,636]),
[iquote('4:Res:456.1,636.0')] ).
cnf(845,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)],[456,637]),
[iquote('4:Res:456.1,637.0')] ).
cnf(823,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)],[456,638]),
[iquote('4:Res:456.1,638.0')] ).
cnf(888,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)],[351,635]),
[iquote('4:Res:351.1,635.0')] ).
cnf(866,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)],[351,636]),
[iquote('4:Res:351.1,636.0')] ).
cnf(844,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)],[351,637]),
[iquote('4:Res:351.1,637.0')] ).
cnf(822,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)],[351,638]),
[iquote('4:Res:351.1,638.0')] ).
cnf(809,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)],[304,624]),
[iquote('4:Res:304.1,624.1')] ).
cnf(810,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)],[305,624]),
[iquote('4:Res:305.1,624.1')] ).
cnf(813,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)],[419,624]),
[iquote('4:Res:419.1,624.1')] ).
cnf(814,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)],[432,624]),
[iquote('4:Res:432.1,624.1')] ).
cnf(815,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)],[420,624]),
[iquote('4:Res:420.1,624.1')] ).
cnf(816,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)],[433,624]),
[iquote('4:Res:433.1,624.1')] ).
cnf(666,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)],[351,628]),
[iquote('4:Res:351.1,628.0')] ).
cnf(645,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)],[351,627]),
[iquote('4:Res:351.1,627.0')] ).
cnf(955,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)],[376,623]),
[iquote('4:Res:376.1,623.1')] ).
cnf(956,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)],[377,623]),
[iquote('4:Res:377.1,623.1')] ).
cnf(885,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)],[4,635]),
[iquote('4:Res:4.1,635.0')] ).
cnf(895,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)],[376,635]),
[iquote('4:Res:376.1,635.0')] ).
cnf(896,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)],[377,635]),
[iquote('4:Res:377.1,635.0')] ).
cnf(863,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)],[4,636]),
[iquote('4:Res:4.1,636.0')] ).
cnf(873,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)],[376,636]),
[iquote('4:Res:376.1,636.0')] ).
cnf(874,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)],[377,636]),
[iquote('4:Res:377.1,636.0')] ).
cnf(841,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)],[4,637]),
[iquote('4:Res:4.1,637.0')] ).
cnf(851,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)],[376,637]),
[iquote('4:Res:376.1,637.0')] ).
cnf(852,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)],[377,637]),
[iquote('4:Res:377.1,637.0')] ).
cnf(819,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)],[4,638]),
[iquote('4:Res:4.1,638.0')] ).
cnf(829,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)],[376,638]),
[iquote('4:Res:376.1,638.0')] ).
cnf(830,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)],[377,638]),
[iquote('4:Res:377.1,638.0')] ).
cnf(791,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)],[419,621]),
[iquote('4:Res:419.1,621.1')] ).
cnf(792,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)],[432,621]),
[iquote('4:Res:432.1,621.1')] ).
cnf(793,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)],[420,621]),
[iquote('4:Res:420.1,621.1')] ).
cnf(794,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)],[433,621]),
[iquote('4:Res:433.1,621.1')] ).
cnf(739,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)],[52,632]),
[iquote('4:Res:52.1,632.0')] ).
cnf(751,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)],[419,632]),
[iquote('4:Res:419.1,632.0')] ).
cnf(752,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)],[432,632]),
[iquote('4:Res:432.1,632.0')] ).
cnf(753,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)],[420,632]),
[iquote('4:Res:420.1,632.0')] ).
cnf(754,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)],[433,632]),
[iquote('4:Res:433.1,632.0')] ).
cnf(717,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)],[52,631]),
[iquote('4:Res:52.1,631.0')] ).
cnf(729,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)],[419,631]),
[iquote('4:Res:419.1,631.0')] ).
cnf(730,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)],[432,631]),
[iquote('4:Res:432.1,631.0')] ).
cnf(731,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)],[420,631]),
[iquote('4:Res:420.1,631.0')] ).
cnf(732,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)],[433,631]),
[iquote('4:Res:433.1,631.0')] ).
cnf(891,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)],[304,635]),
[iquote('4:Res:304.1,635.0')] ).
cnf(892,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)],[305,635]),
[iquote('4:Res:305.1,635.0')] ).
cnf(869,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)],[304,636]),
[iquote('4:Res:304.1,636.0')] ).
cnf(870,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)],[305,636]),
[iquote('4:Res:305.1,636.0')] ).
cnf(847,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)],[304,637]),
[iquote('4:Res:304.1,637.0')] ).
cnf(685,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)],[516,619]),
[iquote('4:Res:516.2,619.0')] ).
cnf(848,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)],[305,637]),
[iquote('4:Res:305.1,637.0')] ).
cnf(825,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)],[304,638]),
[iquote('4:Res:304.1,638.0')] ).
cnf(826,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)],[305,638]),
[iquote('4:Res:305.1,638.0')] ).
cnf(741,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)],[456,632]),
[iquote('4:Res:456.1,632.0')] ).
cnf(639,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)],[68,619]),
[iquote('4:Res:68.2,619.0')] ).
cnf(719,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)],[456,631]),
[iquote('4:Res:456.1,631.0')] ).
cnf(677,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)],[419,628]),
[iquote('4:Res:419.1,628.0')] ).
cnf(678,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)],[432,628]),
[iquote('4:Res:432.1,628.0')] ).
cnf(973,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)],[964]),
[iquote('4:Obv:964.1')] ).
cnf(626,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)],[396,619]),
[iquote('4:Res:396.2,619.0')] ).
cnf(679,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)],[420,628]),
[iquote('4:Res:420.1,628.0')] ).
cnf(680,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)],[433,628]),
[iquote('4:Res:433.1,628.0')] ).
cnf(656,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)],[419,627]),
[iquote('4:Res:419.1,627.0')] ).
cnf(657,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)],[432,627]),
[iquote('4:Res:432.1,627.0')] ).
cnf(640,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)],[517,619]),
[iquote('4:Res:517.2,619.0')] ).
cnf(658,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)],[420,627]),
[iquote('4:Res:420.1,627.0')] ).
cnf(659,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)],[433,627]),
[iquote('4:Res:433.1,627.0')] ).
cnf(787,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)],[304,621]),
[iquote('4:Res:304.1,621.1')] ).
cnf(961,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)],[952]),
[iquote('4:Obv:952.0')] ).
cnf(623,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)],[52,619]),
[iquote('4:Res:52.1,619.0')] ).
cnf(788,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)],[305,621]),
[iquote('4:Res:305.1,621.1')] ).
cnf(663,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)],[4,628]),
[iquote('4:Res:4.1,628.0')] ).
cnf(642,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)],[4,627]),
[iquote('4:Res:4.1,627.0')] ).
cnf(951,plain,
( ~ hausdorff(f16(u,v,w,x),y)
| limit_point(u,v,w,x)
| eq(u,u) ),
inference(obv,[status(thm),theory(equality)],[942]),
[iquote('4:Obv:942.1')] ).
cnf(625,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)],[456,619]),
[iquote('4:Res:456.1,619.0')] ).
cnf(930,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)],[457,622]),
[iquote('4:Res:457.1,622.0')] ).
cnf(935,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)],[426,622]),
[iquote('4:Res:426.1,622.0')] ).
cnf(936,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)],[427,622]),
[iquote('4:Res:427.1,622.0')] ).
cnf(918,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)],[457,633]),
[iquote('4:Res:457.1,633.0')] ).
cnf(622,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)],[457,619]),
[iquote('4:Res:457.1,619.0')] ).
cnf(906,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)],[457,634]),
[iquote('4:Res:457.1,634.0')] ).
cnf(923,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)],[426,633]),
[iquote('4:Res:426.1,633.0')] ).
cnf(924,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)],[427,633]),
[iquote('4:Res:427.1,633.0')] ).
cnf(911,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)],[426,634]),
[iquote('4:Res:426.1,634.0')] ).
cnf(633,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)],[426,619]),
[iquote('4:Res:426.1,619.0')] ).
cnf(912,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)],[427,634]),
[iquote('4:Res:427.1,634.0')] ).
cnf(634,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)],[427,619]),
[iquote('4:Res:427.1,619.0')] ).
cnf(635,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)],[419,619]),
[iquote('4:Res:419.1,619.0')] ).
cnf(636,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)],[432,619]),
[iquote('4:Res:432.1,619.0')] ).
cnf(590,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)],[396,540]),
[iquote('2:Res:396.2,540.0')] ).
cnf(637,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)],[420,619]),
[iquote('4:Res:420.1,619.0')] ).
cnf(638,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)],[433,619]),
[iquote('4:Res:433.1,619.0')] ).
cnf(566,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)],[396,539]),
[iquote('2:Res:396.2,539.0')] ).
cnf(589,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)],[456,540]),
[iquote('2:Res:456.1,540.0')] ).
cnf(811,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)],[376,624]),
[iquote('4:Res:376.1,624.1')] ).
cnf(532,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)],[396,524]),
[iquote('2:Res:396.2,524.0')] ).
cnf(812,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)],[377,624]),
[iquote('4:Res:377.1,624.1')] ).
cnf(817,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(f10(w,v,u),x)
| eq(u,u) ),
inference(obv,[status(thm),theory(equality)],[808]),
[iquote('4:Obv:808.0')] ).
cnf(624,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)],[351,619]),
[iquote('4:Res:351.1,619.0')] ).
cnf(740,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)],[351,632]),
[iquote('4:Res:351.1,632.0')] ).
cnf(531,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)],[456,524]),
[iquote('2:Res:456.1,524.0')] ).
cnf(718,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)],[351,631]),
[iquote('4:Res:351.1,631.0')] ).
cnf(789,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)],[376,621]),
[iquote('4:Res:376.1,621.1')] ).
cnf(807,plain,
( ~ subset_collections(u,f24(v,u))
| ~ compact_space(w,f24(v,u))
| compact_space(v,u) ),
inference(res,[status(thm),theory(equality)],[375,806]),
[iquote('2:Res:375.1,806.1')] ).
cnf(806,plain,
( ~ compact_space(u,f24(v,w))
| ~ open_covering(w,u,f24(v,w))
| compact_space(v,w) ),
inference(obv,[status(thm),theory(equality)],[805]),
[iquote('2:Obv:805.1')] ).
cnf(804,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)],[375,489]),
[iquote('2:Res:375.1,489.2')] ).
cnf(790,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)],[377,621]),
[iquote('4:Res:377.1,621.1')] ).
cnf(737,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)],[4,632]),
[iquote('4:Res:4.1,632.0')] ).
cnf(747,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)],[376,632]),
[iquote('4:Res:376.1,632.0')] ).
cnf(748,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)],[377,632]),
[iquote('4:Res:377.1,632.0')] ).
cnf(530,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)],[351,524]),
[iquote('2:Res:351.1,524.0')] ).
cnf(715,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)],[4,631]),
[iquote('4:Res:4.1,631.0')] ).
cnf(725,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)],[376,631]),
[iquote('4:Res:376.1,631.0')] ).
cnf(726,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)],[377,631]),
[iquote('4:Res:377.1,631.0')] ).
cnf(565,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)],[456,539]),
[iquote('2:Res:456.1,539.0')] ).
cnf(489,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)],[487,104]),
[iquote('0:MRR:487.0,104.2')] ).
cnf(801,plain,
( ~ compact_set(u,v,w)
| compact_space(x,subspace_topology(v,w,u)) ),
inference(res,[status(thm),theory(equality)],[111,800]),
[iquote('2:Res:111.1,800.0')] ).
cnf(800,plain,
( ~ compact_space(u,v)
| compact_space(w,v) ),
inference(mrr,[status(thm)],[799,307]),
[iquote('2:MRR:799.0,307.1')] ).
cnf(795,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ hausdorff(f1(v,u),w)
| eq(u,u) ),
inference(obv,[status(thm),theory(equality)],[786]),
[iquote('4:Obv:786.0')] ).
cnf(701,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)],[375,488]),
[iquote('2:Res:375.1,488.2')] ).
cnf(621,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)],[4,619]),
[iquote('4:Res:4.1,619.0')] ).
cnf(549,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)],[529,427]),
[iquote('2:MRR:529.0,427.1')] ).
cnf(744,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)],[305,632]),
[iquote('4:Res:305.1,632.0')] ).
cnf(774,plain,
( ~ limit_point(u,v,w,x)
| limit_point(u,v,y,z) ),
inference(mrr,[status(thm)],[772,456]),
[iquote('2:MRR:772.0,456.1')] ).
cnf(743,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)],[304,632]),
[iquote('4:Res:304.1,632.0')] ).
cnf(722,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)],[305,631]),
[iquote('4:Res:305.1,631.0')] ).
cnf(721,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)],[304,631]),
[iquote('4:Res:304.1,631.0')] ).
cnf(674,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)],[377,628]),
[iquote('4:Res:377.1,628.0')] ).
cnf(518,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)],[68,388]),
[iquote('2:Res:68.2,388.0')] ).
cnf(673,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)],[376,628]),
[iquote('4:Res:376.1,628.0')] ).
cnf(653,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)],[377,627]),
[iquote('4:Res:377.1,627.0')] ).
cnf(652,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)],[376,627]),
[iquote('4:Res:376.1,627.0')] ).
cnf(758,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)],[458,620]),
[iquote('4:Res:458.1,620.0')] ).
cnf(523,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)],[383,118]),
[iquote('2:Res:383.1,118.1')] ).
cnf(762,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)],[404,620]),
[iquote('4:Res:404.1,620.0')] ).
cnf(761,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)],[402,620]),
[iquote('4:Res:402.1,620.0')] ).
cnf(702,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)],[458,630]),
[iquote('4:Res:458.1,630.0')] ).
cnf(688,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)],[458,629]),
[iquote('4:Res:458.1,629.0')] ).
cnf(494,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)],[304,388]),
[iquote('2:Res:304.1,388.0')] ).
cnf(706,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)],[404,630]),
[iquote('4:Res:404.1,630.0')] ).
cnf(705,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)],[402,630]),
[iquote('4:Res:402.1,630.0')] ).
cnf(692,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)],[404,629]),
[iquote('4:Res:404.1,629.0')] ).
cnf(691,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)],[402,629]),
[iquote('4:Res:402.1,629.0')] ).
cnf(495,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)],[305,388]),
[iquote('2:Res:305.1,388.0')] ).
cnf(620,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)],[458,619]),
[iquote('4:Res:458.1,619.0')] ).
cnf(632,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)],[377,619]),
[iquote('4:Res:377.1,619.0')] ).
cnf(631,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)],[376,619]),
[iquote('4:Res:376.1,619.0')] ).
cnf(630,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)],[404,619]),
[iquote('4:Res:404.1,619.0')] ).
cnf(488,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)],[485,104]),
[iquote('0:MRR:485.0,104.2')] ).
cnf(629,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)],[402,619]),
[iquote('4:Res:402.1,619.0')] ).
cnf(670,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(u,x)
| eq(f19(u,w),f19(u,x)) ),
inference(res,[status(thm),theory(equality)],[305,628]),
[iquote('4:Res:305.1,628.0')] ).
cnf(669,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(u,x)
| eq(f20(u,w),f19(u,x)) ),
inference(res,[status(thm),theory(equality)],[304,628]),
[iquote('4:Res:304.1,628.0')] ).
cnf(649,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(u,x)
| eq(f19(u,w),f20(u,x)) ),
inference(res,[status(thm),theory(equality)],[305,627]),
[iquote('4:Res:305.1,627.0')] ).
cnf(516,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)],[68,381]),
[iquote('2:Res:68.2,381.0')] ).
cnf(648,plain,
( ~ hausdorff(u,v)
| hausdorff(u,w)
| hausdorff(u,x)
| eq(f20(u,w),f20(u,x)) ),
inference(res,[status(thm),theory(equality)],[304,627]),
[iquote('4:Res:304.1,627.0')] ).
cnf(628,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(v,w)
| hausdorff(v,x)
| eq(u,f19(v,x)) ),
inference(res,[status(thm),theory(equality)],[305,619]),
[iquote('4:Res:305.1,619.0')] ).
cnf(627,plain,
( ~ element_of_set(u,v)
| ~ hausdorff(v,w)
| hausdorff(v,x)
| eq(u,f20(v,x)) ),
inference(res,[status(thm),theory(equality)],[304,619]),
[iquote('4:Res:304.1,619.0')] ).
cnf(619,plain,
( ~ element_of_set(u,v)
| ~ element_of_set(w,v)
| ~ hausdorff(v,x)
| eq(w,u) ),
inference(spt,[],[608]),
[iquote('4:Spt:608.0,608.1,608.2,608.3')] ).
cnf(588,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)],[351,540]),
[iquote('2:Res:351.1,540.0')] ).
cnf(564,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)],[351,539]),
[iquote('2:Res:351.1,539.0')] ).
cnf(544,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(f1(x,f19(u,v)),w)
| hausdorff(u,v) ),
inference(mrr,[status(thm)],[527,404]),
[iquote('2:MRR:527.0,404.1')] ).
cnf(543,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(interior(x,y,z),w)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[536]),
[iquote('2:Obv:536.2')] ).
cnf(604,plain,
( ~ disjoint_s(union_of_members(u),f13(v,w,x,f20(y,z)))
| hausdorff(y,z) ),
inference(mrr,[status(thm)],[587,426]),
[iquote('2:MRR:587.0,426.1')] ).
cnf(603,plain,
( ~ disjoint_s(union_of_members(u),f1(v,f20(w,x)))
| hausdorff(w,x) ),
inference(mrr,[status(thm)],[585,402]),
[iquote('2:MRR:585.0,402.1')] ).
cnf(600,plain,
( ~ disjoint_s(union_of_members(u),interior(v,w,x))
| hausdorff(y,z) ),
inference(obv,[status(thm),theory(equality)],[594]),
[iquote('2:Obv:594.1')] ).
cnf(598,plain,
( ~ disjoint_s(union_of_members(u),union_of_members(v))
| hausdorff(w,x) ),
inference(obv,[status(thm),theory(equality)],[592]),
[iquote('2:Obv:592.1')] ).
cnf(597,plain,
( ~ disjoint_s(union_of_members(u),v)
| hausdorff(v,w) ),
inference(obv,[status(thm),theory(equality)],[591]),
[iquote('2:Obv:591.1')] ).
cnf(540,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(union_of_members(x),w)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[534]),
[iquote('2:Obv:534.2')] ).
cnf(580,plain,
( ~ disjoint_s(u,f13(v,w,x,f20(u,y)))
| hausdorff(u,y) ),
inference(mrr,[status(thm)],[563,426]),
[iquote('2:MRR:563.0,426.1')] ).
cnf(577,plain,
( ~ disjoint_s(u,f1(v,f20(u,w)))
| hausdorff(u,w) ),
inference(mrr,[status(thm)],[561,402]),
[iquote('2:MRR:561.0,402.1')] ).
cnf(576,plain,
( ~ disjoint_s(u,interior(v,w,x))
| hausdorff(u,y) ),
inference(obv,[status(thm),theory(equality)],[570]),
[iquote('2:Obv:570.1')] ).
cnf(574,plain,
( ~ disjoint_s(u,union_of_members(v))
| hausdorff(u,w) ),
inference(obv,[status(thm),theory(equality)],[568]),
[iquote('2:Obv:568.1')] ).
cnf(573,plain,
( ~ disjoint_s(u,u)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[567]),
[iquote('2:Obv:567.1')] ).
cnf(539,plain,
( ~ element_of_set(f20(u,v),w)
| ~ disjoint_s(u,w)
| hausdorff(u,v) ),
inference(obv,[status(thm),theory(equality)],[533]),
[iquote('2:Obv:533.2')] ).
cnf(548,plain,
( ~ disjoint_s(u,v)
| hausdorff(closure(w,x,y),z) ),
inference(mrr,[status(thm)],[547,419]),
[iquote('2:MRR:547.0,419.1')] ).
cnf(546,plain,
( ~ disjoint_s(u,v)
| hausdorff(boundary(w,x,y),z) ),
inference(mrr,[status(thm)],[545,432]),
[iquote('2:MRR:545.0,432.1')] ).
cnf(555,plain,
( ~ disjoint_s(u,v)
| equal_sets(v,empty_set)
| equal_sets(u,empty_set) ),
inference(mrr,[status(thm)],[513,551]),
[iquote('3:MRR:513.1,551.0')] ).
cnf(552,plain,
~ separation(u,v,w,x),
inference(mrr,[status(thm)],[93,551]),
[iquote('3:MRR:93.0,551.0')] ).
cnf(553,plain,
connected_set(u,v,w),
inference(mrr,[status(thm)],[379,551]),
[iquote('3:MRR:379.0,551.0')] ).
cnf(551,plain,
connected_space(u,v),
inference(spt,[],[550]),
[iquote('3:Spt:550.0')] ).
cnf(542,plain,
( ~ disjoint_s(u,v)
| hausdorff(intersection_of_members(w),x) ),
inference(mrr,[status(thm)],[541,376]),
[iquote('2:MRR:541.0,376.1')] ).
cnf(524,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)],[373,522]),
[iquote('2:Res:373.1,522.2')] ).
cnf(522,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)],[373,118]),
[iquote('2:Res:373.1,118.1')] ).
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(517,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)],[68,346]),
[iquote('2:Res:68.2,346.0')] ).
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('TOP011-1.p',unknown),
[] ).
cnf(512,plain,
( limit_point(f20(boundary(u,v,w),x),y,z,x1)
| hausdorff(boundary(u,v,w),x) ),
inference(obv,[status(thm),theory(equality)],[511]),
[iquote('2:Obv:511.0')] ).
cnf(501,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)],[433,388]),
[iquote('2:Res:433.1,388.0')] ).
cnf(510,plain,
( limit_point(f20(closure(u,v,w),x),y,z,x1)
| hausdorff(closure(u,v,w),x) ),
inference(obv,[status(thm),theory(equality)],[509]),
[iquote('2:Obv:509.0')] ).
cnf(69,axiom,
( ~ eq(f15(u,v,w,x,y),u)
| ~ neighborhood(y,u,w,x)
| ~ limit_point(u,v,w,x) ),
file('TOP011-1.p',unknown),
[] ).
cnf(500,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)],[420,388]),
[iquote('2:Res:420.1,388.0')] ).
cnf(499,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)],[432,388]),
[iquote('2:Res:432.1,388.0')] ).
cnf(498,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)],[419,388]),
[iquote('2:Res:419.1,388.0')] ).
cnf(503,plain,
( limit_point(f20(intersection_of_members(u),v),w,x,y)
| hausdorff(intersection_of_members(u),v) ),
inference(obv,[status(thm),theory(equality)],[502]),
[iquote('2:Obv:502.0')] ).
cnf(497,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)],[377,388]),
[iquote('2:Res:377.1,388.0')] ).
cnf(496,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)],[376,388]),
[iquote('2:Res:376.1,388.0')] ).
cnf(388,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)],[327,348]),
[iquote('2:MRR:327.0,348.0')] ).
cnf(396,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)],[352,390]),
[iquote('2:MRR:352.1,390.0')] ).
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(484,plain,
( ~ compact_space(u,v)
| ~ open_covering(w,u,v)
| subset_collections(f23(u,v,w),v) ),
inference(res,[status(thm),theory(equality)],[106,100]),
[iquote('0:Res:106.2,100.0')] ).
cnf(106,axiom,
( ~ compact_space(u,v)
| ~ open_covering(w,u,v)
| open_covering(f23(u,v,w),u,v) ),
file('TOP011-1.p',unknown),
[] ).
cnf(433,plain,
( hausdorff(boundary(u,v,w),x)
| element_of_set(f19(boundary(u,v,w),x),y) ),
inference(res,[status(thm),theory(equality)],[305,418]),
[iquote('2:Res:305.1,418.0')] ).
cnf(432,plain,
( hausdorff(boundary(u,v,w),x)
| element_of_set(f20(boundary(u,v,w),x),y) ),
inference(res,[status(thm),theory(equality)],[304,418]),
[iquote('2:Res:304.1,418.0')] ).
cnf(105,axiom,
( ~ compact_space(u,v)
| ~ open_covering(w,u,v)
| subset_collections(f23(u,v,w),w) ),
file('TOP011-1.p',unknown),
[] ).
cnf(420,plain,
( hausdorff(closure(u,v,w),x)
| element_of_set(f19(closure(u,v,w),x),y) ),
inference(res,[status(thm),theory(equality)],[305,380]),
[iquote('2:Res:305.1,380.0')] ).
cnf(457,plain,
( limit_point(u,v,w,x)
| element_of_set(u,interior(y,z,x1)) ),
inference(res,[status(thm),theory(equality)],[456,381]),
[iquote('2:Res:456.1,381.0')] ).
cnf(458,plain,
( limit_point(u,v,w,x)
| element_of_set(u,union_of_members(y)) ),
inference(res,[status(thm),theory(equality)],[456,346]),
[iquote('2:Res:456.1,346.0')] ).
cnf(456,plain,
( limit_point(u,v,w,x)
| element_of_set(u,f16(u,v,w,x)) ),
inference(res,[status(thm),theory(equality)],[383,64]),
[iquote('2:Res:383.1,64.0')] ).
cnf(383,plain,
( limit_point(u,v,w,x)
| neighborhood(f16(u,v,w,x),u,w,x) ),
inference(mrr,[status(thm)],[324,348]),
[iquote('2:MRR:324.0,348.0')] ).
cnf(419,plain,
( hausdorff(closure(u,v,w),x)
| element_of_set(f20(closure(u,v,w),x),y) ),
inference(res,[status(thm),theory(equality)],[304,380]),
[iquote('2:Res:304.1,380.0')] ).
cnf(384,plain,
( ~ element_of_set(u,f14(v,w,x,u))
| element_of_set(u,closure(v,w,x)) ),
inference(mrr,[status(thm)],[325,348]),
[iquote('2:MRR:325.0,348.0')] ).
cnf(427,plain,
( hausdorff(u,v)
| element_of_set(f19(u,v),interior(w,x,y)) ),
inference(res,[status(thm),theory(equality)],[305,381]),
[iquote('2:Res:305.1,381.0')] ).
cnf(426,plain,
( hausdorff(u,v)
| element_of_set(f20(u,v),interior(w,x,y)) ),
inference(res,[status(thm),theory(equality)],[304,381]),
[iquote('2:Res:304.1,381.0')] ).
cnf(378,plain,
( ~ compact_space(u,subspace_topology(v,w,u))
| compact_set(u,v,w) ),
inference(mrr,[status(thm)],[321,348]),
[iquote('2:MRR:321.0,348.0')] ).
cnf(310,plain,
( ~ eq(f19(u,v),f20(u,v))
| hausdorff(u,v) ),
inference(mrr,[status(thm)],[82,300]),
[iquote('2:MRR:82.0,300.0')] ).
cnf(418,plain,
( ~ element_of_set(u,boundary(v,w,x))
| element_of_set(u,y) ),
inference(res,[status(thm),theory(equality)],[73,380]),
[iquote('2:Res:73.1,380.0')] ).
cnf(381,plain,
( ~ element_of_set(u,v)
| element_of_set(u,interior(w,x,y)) ),
inference(mrr,[status(thm)],[363,371]),
[iquote('2:MRR:363.1,371.0')] ).
cnf(380,plain,
( ~ element_of_set(u,closure(v,w,x))
| element_of_set(u,y) ),
inference(mrr,[status(thm)],[362,372]),
[iquote('2:MRR:362.1,372.0')] ).
cnf(351,plain,
( ~ element_of_set(u,v)
| element_of_set(u,f10(w,v,u)) ),
inference(mrr,[status(thm)],[40,302]),
[iquote('2:MRR:40.1,302.0')] ).
cnf(377,plain,
( hausdorff(intersection_of_members(u),v)
| element_of_set(f19(intersection_of_members(u),v),w) ),
inference(mrr,[status(thm)],[320,302]),
[iquote('2:MRR:320.0,302.0')] ).
cnf(376,plain,
( hausdorff(intersection_of_members(u),v)
| element_of_set(f20(intersection_of_members(u),v),w) ),
inference(mrr,[status(thm)],[319,302]),
[iquote('2:MRR:319.0,302.0')] ).
cnf(373,plain,
( ~ element_of_set(u,v)
| neighborhood(v,u,w,x) ),
inference(mrr,[status(thm)],[114,371]),
[iquote('2:MRR:114.1,371.0')] ).
cnf(355,plain,
equal_sets(u,intersection_of_sets(v,f12(w,x,v,u))),
inference(mrr,[status(thm)],[48,302]),
[iquote('2:MRR:48.0,302.0')] ).
cnf(306,plain,
( compact_space(u,v)
| open_covering(f24(u,v),u,v) ),
inference(mrr,[status(thm)],[107,300]),
[iquote('2:MRR:107.0,300.0')] ).
cnf(404,plain,
( hausdorff(u,v)
| element_of_set(f19(u,v),union_of_members(w)) ),
inference(res,[status(thm),theory(equality)],[305,346]),
[iquote('2:Res:305.1,346.0')] ).
cnf(402,plain,
( hausdorff(u,v)
| element_of_set(f20(u,v),union_of_members(w)) ),
inference(res,[status(thm),theory(equality)],[304,346]),
[iquote('2:Res:304.1,346.0')] ).
cnf(375,plain,
( ~ subset_collections(u,v)
| open_covering(u,w,v) ),
inference(mrr,[status(thm)],[336,303]),
[iquote('2:MRR:336.1,303.0')] ).
cnf(335,plain,
( ~ subset_collections(u,v)
| finer(v,u,w) ),
inference(mrr,[status(thm)],[30,300]),
[iquote('2:MRR:30.1,30.2,300.0')] ).
cnf(307,plain,
( compact_space(u,v)
| subset_collections(f24(u,v),v) ),
inference(mrr,[status(thm)],[206,300]),
[iquote('2:MRR:206.0,300.0')] ).
cnf(305,plain,
( hausdorff(u,v)
| element_of_set(f19(u,v),u) ),
inference(mrr,[status(thm)],[80,300]),
[iquote('2:MRR:80.0,300.0')] ).
cnf(304,plain,
( hausdorff(u,v)
| element_of_set(f20(u,v),u) ),
inference(mrr,[status(thm)],[81,300]),
[iquote('2:MRR:81.0,300.0')] ).
cnf(347,plain,
( ~ element_of_set(u,intersection_of_members(v))
| element_of_set(u,w) ),
inference(mrr,[status(thm)],[7,302]),
[iquote('2:MRR:7.0,302.0')] ).
cnf(346,plain,
( ~ element_of_set(u,v)
| element_of_set(u,union_of_members(w)) ),
inference(mrr,[status(thm)],[6,302]),
[iquote('2:MRR:6.0,302.0')] ).
cnf(372,plain,
closed(u,v,w),
inference(mrr,[status(thm)],[113,371]),
[iquote('2:MRR:113.0,371.0')] ).
cnf(371,plain,
open(u,v,w),
inference(mrr,[status(thm)],[312,302]),
[iquote('2:MRR:312.0,302.0')] ).
cnf(303,plain,
equal_sets(union_of_members(u),v),
inference(mrr,[status(thm)],[10,300]),
[iquote('2:MRR:10.0,300.0')] ).
cnf(390,plain,
basis(u,v),
inference(mrr,[status(thm)],[365,389]),
[iquote('2:MRR:365.1,389.0')] ).
cnf(348,plain,
subset_sets(u,v),
inference(mrr,[status(thm)],[46,302]),
[iquote('2:MRR:46.0,302.0')] ).
cnf(302,plain,
element_of_collection(u,v),
inference(mrr,[status(thm)],[12,300]),
[iquote('2:MRR:12.0,300.0')] ).
cnf(300,plain,
topological_space(u,v),
inference(spt,[],[299]),
[iquote('2:Spt:299.1')] ).
cnf(52,axiom,
( ~ element_of_set(u,interior(v,w,x))
| element_of_set(u,f13(v,w,x,u)) ),
file('TOP011-1.p',unknown),
[] ).
cnf(104,axiom,
( ~ compact_space(u,v)
| ~ open_covering(w,u,v)
| finite(f23(u,v,w)) ),
file('TOP011-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ element_of_set(u,f2(v,u))
| element_of_set(u,intersection_of_members(v)) ),
file('TOP011-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ element_of_set(u,union_of_members(v))
| element_of_set(u,f1(v,u)) ),
file('TOP011-1.p',unknown),
[] ).
cnf(64,axiom,
( ~ neighborhood(u,v,w,x)
| element_of_set(v,u) ),
file('TOP011-1.p',unknown),
[] ).
cnf(100,axiom,
( ~ open_covering(u,v,w)
| subset_collections(u,w) ),
file('TOP011-1.p',unknown),
[] ).
cnf(29,axiom,
( ~ finer(u,v,w)
| subset_collections(v,u) ),
file('TOP011-1.p',unknown),
[] ).
cnf(122,plain,
equal_sets(cu,union_of_members(g)),
inference(mrr,[status(thm)],[2,120]),
[iquote('1:MRR:2.1,120.0')] ).
cnf(121,plain,
subset_collections(g,f),
inference(mrr,[status(thm)],[1,120]),
[iquote('1:MRR:1.1,120.0')] ).
cnf(120,plain,
~ element_of_set(cu,top_of_basis(f)),
inference(spt,[],[3]),
[iquote('1:Spt:3.2')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09 % Problem : TOP011-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.10 % Command : run_spass %d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Sun May 29 06:41:11 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.68/0.88
% 0.68/0.88 SPASS V 3.9
% 0.68/0.88 SPASS beiseite: Completion found.
% 0.68/0.88 % SZS status CounterSatisfiable
% 0.68/0.88 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.68/0.88 SPASS derived 1546 clauses, backtracked 0 clauses, performed 4 splits and kept 1089 clauses.
% 0.68/0.88 SPASS allocated 78063 KBytes.
% 0.68/0.88 SPASS spent 0:00:00.59 on the problem.
% 0.68/0.88 0:00:00.02 for the input.
% 0.68/0.88 0:00:00.00 for the FLOTTER CNF translation.
% 0.68/0.88 0:00:00.06 for inferences.
% 0.68/0.88 0:00:00.00 for the backtracking.
% 0.68/0.88 0:00:00.46 for the reduction.
% 0.68/0.88
% 0.68/0.88
% 0.68/0.88 The saturated set of worked-off clauses is :
% 0.68/0.88 % SZS output start Saturation
% See solution above
%------------------------------------------------------------------------------