%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU388+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:44:15 AM UTC 2026
% Result : Theorem 1.50s 0.57s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 22
% Syntax : Number of formulae : 279 ( 128 unt; 0 typ; 0 def)
% Number of atoms : 2382 ( 733 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 4290 (1126 ~; 736 |; 53 &;2315 @)
% ( 13 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 68 usr; 8 con; 0-3 aty)
% Number of variables : 598 ( 0 ^; 583 !; 15 ?; 598 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_2_0_yellow19,type,
a_2_0_yellow19: $i > $i > $i ).
thf(tp_antisymmetric_relstr,type,
antisymmetric_relstr: $i > $o ).
thf(tp_boole_POSet,type,
boole_POSet: $i > $i ).
thf(tp_boolean_relstr,type,
boolean_relstr: $i > $o ).
thf(tp_boundary_set,type,
boundary_set: $i > $i > $o ).
thf(tp_bounded_relstr,type,
bounded_relstr: $i > $o ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_cast_as_carrier_subset,type,
cast_as_carrier_subset: $i > $i ).
thf(tp_closed_subset,type,
closed_subset: $i > $i > $o ).
thf(tp_complemented_relstr,type,
complemented_relstr: $i > $o ).
thf(tp_complete_relstr,type,
complete_relstr: $i > $o ).
thf(tp_connected_relstr,type,
connected_relstr: $i > $o ).
thf(tp_dense,type,
dense: $i > $i > $o ).
thf(tp_directed_relstr,type,
directed_relstr: $i > $o ).
thf(tp_directed_subset,type,
directed_subset: $i > $i > $o ).
thf(tp_distributive_relstr,type,
distributive_relstr: $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_carrier,type,
empty_carrier: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_filtered_subset,type,
filtered_subset: $i > $i > $o ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_heyting_relstr,type,
heyting_relstr: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_join_complete_relstr,type,
join_complete_relstr: $i > $o ).
thf(tp_lower_bounded_relstr,type,
lower_bounded_relstr: $i > $o ).
thf(tp_lower_relstr_subset,type,
lower_relstr_subset: $i > $i > $o ).
thf(tp_neighborhood_system,type,
neighborhood_system: $i > $i > $i ).
thf(tp_nowhere_dense,type,
nowhere_dense: $i > $i > $o ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_open_subset,type,
open_subset: $i > $i > $o ).
thf(tp_point_neighbourhood,type,
point_neighbourhood: $i > $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_reflexive_relstr,type,
reflexive_relstr: $i > $o ).
thf(tp_rel_str,type,
rel_str: $i > $o ).
thf(tp_rel_str_of,type,
rel_str_of: $i > $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SY47,type,
sK5_SY47: $i > $i ).
thf(tp_sK6_SY57,type,
sK6_SY57: $i ).
thf(tp_sK7_SY59,type,
sK7_SY59: $i > $i > $i ).
thf(tp_sK8_SY60,type,
sK8_SY60: $i > $i > $i ).
thf(tp_sK9_SY62,type,
sK9_SY62: $i > $i > $i > $i ).
thf(tp_strict_rel_str,type,
strict_rel_str: $i > $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_the_InternalRel,type,
the_InternalRel: $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_top_str,type,
top_str: $i > $o ).
thf(tp_topological_space,type,
topological_space: $i > $o ).
thf(tp_transitive_relstr,type,
transitive_relstr: $i > $o ).
thf(tp_trivial_carrier,type,
trivial_carrier: $i > $o ).
thf(tp_up_complete_relstr,type,
up_complete_relstr: $i > $o ).
thf(tp_upper_bounded_relstr,type,
upper_bounded_relstr: $i > $o ).
thf(tp_upper_relstr_subset,type,
upper_relstr_subset: $i > $i > $o ).
thf(tp_v1_membered,type,
v1_membered: $i > $o ).
thf(tp_v1_yellow_3,type,
v1_yellow_3: $i > $o ).
thf(tp_v2_membered,type,
v2_membered: $i > $o ).
thf(tp_v3_membered,type,
v3_membered: $i > $o ).
thf(tp_v4_membered,type,
v4_membered: $i > $o ).
thf(tp_v5_membered,type,
v5_membered: $i > $o ).
thf(tp_with_infima_relstr,type,
with_infima_relstr: $i > $o ).
thf(tp_with_suprema_relstr,type,
with_suprema_relstr: $i > $o ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(24,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( topological_space @ B )
& ( top_str @ B )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( in @ A @ ( a_2_0_yellow19 @ B @ C ) )
<=> ? [D: $i] :
( ( point_neighbourhood @ D @ B @ C )
& ( A = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_yellow19) ).
thf(70,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ? [C: $i] : ( point_neighbourhood @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_connsp_2) ).
thf(74,axiom,
? [A: $i] : ( top_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(76,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(79,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(80,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( point_neighbourhood @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( the_carrier @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_connsp_2) ).
thf(82,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(83,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(86,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(88,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(90,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(92,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( neighborhood_system @ A @ B )
= ( a_2_0_yellow19 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_yellow19) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(119,conjecture,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( neighborhood_system @ A @ B ) )
<=> ( point_neighbourhood @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_yellow19) ).
thf(120,negated_conjecture,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( neighborhood_system @ A @ B ) )
<=> ( point_neighbourhood @ C @ A @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[119]) ).
thf(121,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( neighborhood_system @ A @ B ) )
<=> ( point_neighbourhood @ C @ A @ B ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[120]) ).
thf(122,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(123,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(124,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(125,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(126,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(127,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(128,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( topological_space @ B )
& ( top_str @ B )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( in @ A @ ( a_2_0_yellow19 @ B @ C ) )
<=> ? [D: $i] :
( ( point_neighbourhood @ D @ B @ C )
& ( A = D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(129,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(130,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ? [C: $i] : ( point_neighbourhood @ C @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(131,plain,
( ( ? [A: $i] : ( top_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(132,plain,
$true = $true,
inference(unfold_def,[status(thm)],[76]) ).
thf(133,plain,
$true = $true,
inference(unfold_def,[status(thm)],[79]) ).
thf(134,plain,
$true = $true,
inference(unfold_def,[status(thm)],[80]) ).
thf(135,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( point_neighbourhood @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( the_carrier @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(136,plain,
$true = $true,
inference(unfold_def,[status(thm)],[82]) ).
thf(137,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(138,plain,
$true = $true,
inference(unfold_def,[status(thm)],[86]) ).
thf(139,plain,
$true = $true,
inference(unfold_def,[status(thm)],[88]) ).
thf(140,plain,
$true = $true,
inference(unfold_def,[status(thm)],[90]) ).
thf(141,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( neighborhood_system @ A @ B )
= ( a_2_0_yellow19 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(142,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(143,plain,
( ( ( ~ ( empty_carrier @ sK1_A )
& ( topological_space @ sK1_A )
& ( top_str @ sK1_A ) )
=> ! [SY34: $i] :
( ( element @ SY34 @ ( the_carrier @ sK1_A ) )
=> ! [SY35: $i] :
( ( in @ SY35 @ ( neighborhood_system @ sK1_A @ SY34 ) )
<=> ( point_neighbourhood @ SY35 @ sK1_A @ SY34 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[121]) ).
thf(144,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[143]) ).
thf(145,plain,
( ( topological_space @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[143]) ).
thf(146,plain,
( ( top_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[143]) ).
thf(147,plain,
( ( ! [SY34: $i] :
( ( element @ SY34 @ ( the_carrier @ sK1_A ) )
=> ! [SY35: $i] :
( ( in @ SY35 @ ( neighborhood_system @ sK1_A @ SY34 ) )
<=> ( point_neighbourhood @ SY35 @ sK1_A @ SY34 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[143]) ).
thf(148,plain,
( ( ~ ! [SY34: $i] :
( ( element @ SY34 @ ( the_carrier @ sK1_A ) )
=> ! [SY35: $i] :
( ( in @ SY35 @ ( neighborhood_system @ sK1_A @ SY34 ) )
<=> ( point_neighbourhood @ SY35 @ sK1_A @ SY34 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[147]) ).
thf(149,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(150,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( neighborhood_system @ A @ B )
= ( a_2_0_yellow19 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(151,plain,
$true = $true,
inference(copy,[status(thm)],[140]) ).
thf(152,plain,
$true = $true,
inference(copy,[status(thm)],[139]) ).
thf(153,plain,
$true = $true,
inference(copy,[status(thm)],[138]) ).
thf(154,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(155,plain,
$true = $true,
inference(copy,[status(thm)],[136]) ).
thf(156,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ! [C: $i] :
( ( point_neighbourhood @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( the_carrier @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(157,plain,
$true = $true,
inference(copy,[status(thm)],[134]) ).
thf(158,plain,
$true = $true,
inference(copy,[status(thm)],[133]) ).
thf(159,plain,
$true = $true,
inference(copy,[status(thm)],[132]) ).
thf(160,plain,
( ( ? [A: $i] : ( top_str @ A ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(161,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ? [C: $i] : ( point_neighbourhood @ C @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(162,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(163,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( topological_space @ B )
& ( top_str @ B )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( in @ A @ ( a_2_0_yellow19 @ B @ C ) )
<=> ? [D: $i] :
( ( point_neighbourhood @ D @ B @ C )
& ( A = D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(164,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(165,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(166,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(167,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(168,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(169,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(170,plain,
( ( top_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(171,plain,
( ( topological_space @ sK1_A )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(172,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(173,plain,
( ( ~ ! [SY34: $i] :
( ( element @ SY34 @ ( the_carrier @ sK1_A ) )
=> ! [SY35: $i] :
( ( in @ SY35 @ ( neighborhood_system @ sK1_A @ SY34 ) )
<=> ( point_neighbourhood @ SY35 @ sK1_A @ SY34 ) ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(174,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(175,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX1 )
| ~ ( topological_space @ SX1 ) )
| ~ ( top_str @ SX1 ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX1 ) ) )
| ~ ( ~ ( ~ ( in @ SX0 @ ( a_2_0_yellow19 @ SX1 @ SX2 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( point_neighbourhood @ SX3 @ SX1 @ SX2 )
| ( SX0 != SX3 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( point_neighbourhood @ SX3 @ SX1 @ SX2 )
| ( SX0 != SX3 ) )
| ( in @ SX0 @ ( a_2_0_yellow19 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(176,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ! [SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( neighborhood_system @ sK1_A @ SX0 ) )
| ( point_neighbourhood @ SX1 @ sK1_A @ SX0 ) )
| ~ ( ~ ( point_neighbourhood @ SX1 @ sK1_A @ SX0 )
| ( in @ SX1 @ ( neighborhood_system @ sK1_A @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(177,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(178,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(179,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( topological_space @ SX0 ) )
| ~ ( top_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ! [SX2: $i] :
( ~ ( point_neighbourhood @ SX2 @ SX0 @ SX1 )
| ( element @ SX2 @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(180,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(181,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(182,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(183,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(184,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(185,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( topological_space @ SX0 ) )
| ~ ( top_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ~ ! [SX2: $i] :
~ ( point_neighbourhood @ SX2 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(186,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( topological_space @ SX0 ) )
| ~ ( top_str @ SX0 ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ( ( neighborhood_system @ SX0 @ SX1 )
= ( a_2_0_yellow19 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(187,plain,
( ( ~ ! [SX0: $i] :
~ ( top_str @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(188,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(189,plain,
( ( empty_carrier @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(190,plain,
! [SV1: $i] :
( ( ! [SY36: $i] :
( ~ ( in @ SV1 @ SY36 )
| ~ ( in @ SY36 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(191,plain,
! [SV2: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SY37 )
| ~ ( topological_space @ SY37 ) )
| ~ ( top_str @ SY37 ) )
| ~ ( element @ SY38 @ ( the_carrier @ SY37 ) ) )
| ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SY37 @ SY38 ) )
| ~ ! [SY39: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY39 @ SY37 @ SY38 )
| ( SV2 != SY39 ) ) )
| ~ ( ~ ~ ! [SY40: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY40 @ SY37 @ SY38 )
| ( SV2 != SY40 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SY37 @ SY38 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(192,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ! [SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( neighborhood_system @ sK1_A @ SX0 ) )
| ( point_neighbourhood @ SX1 @ sK1_A @ SX0 ) )
| ~ ( ~ ( point_neighbourhood @ SX1 @ sK1_A @ SX0 )
| ( in @ SX1 @ ( neighborhood_system @ sK1_A @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(193,plain,
! [SV3: $i] :
( ( ~ ( top_str @ SV3 )
| ( one_sorted_str @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(194,plain,
! [SV4: $i] :
( ( ! [SY41: $i] :
( ~ ( in @ SV4 @ SY41 )
| ( element @ SV4 @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(195,plain,
! [SV5: $i] :
( ( ! [SY42: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( topological_space @ SV5 ) )
| ~ ( top_str @ SV5 ) )
| ~ ( element @ SY42 @ ( the_carrier @ SV5 ) ) )
| ! [SY43: $i] :
( ~ ( point_neighbourhood @ SY43 @ SV5 @ SY42 )
| ( element @ SY43 @ ( powerset @ ( the_carrier @ SV5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(196,plain,
! [SV6: $i] :
( ( ! [SY44: $i] :
( ~ ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SV6 )
| ( in @ SY45 @ SY44 ) )
| ~ ( ~ ( in @ SY45 @ SY44 )
| ( in @ SY45 @ SV6 ) ) )
| ( SV6 = SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(197,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(198,plain,
! [SV7: $i] :
( ( ! [SY46: $i] :
( ~ ( element @ SV7 @ SY46 )
| ( empty @ SY46 )
| ( in @ SV7 @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(199,plain,
! [SV8: $i] :
( ( ~ ! [SY47: $i] :
~ ( element @ SY47 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(200,plain,
! [SV9: $i] :
( ( ! [SY48: $i] :
~ ~ ( ~ ( in @ SV9 @ SY48 )
| ~ ( empty @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(201,plain,
! [SV10: $i] :
( ( ! [SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( topological_space @ SV10 ) )
| ~ ( top_str @ SV10 ) )
| ~ ( element @ SY49 @ ( the_carrier @ SV10 ) ) )
| ~ ! [SY50: $i] :
~ ( point_neighbourhood @ SY50 @ SV10 @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(202,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( topological_space @ SV11 ) )
| ~ ( top_str @ SV11 ) )
| ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV11 ) )
| ( ( neighborhood_system @ SV11 @ SY51 )
= ( a_2_0_yellow19 @ SV11 @ SY51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(203,plain,
( ( ! [SX0: $i] :
~ ( top_str @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(204,plain,
! [SV12: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ~ ( ~ ( in @ SV12 @ SY52 )
| ~ ( element @ SY52 @ ( powerset @ SY53 ) ) )
| ( element @ SV12 @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(205,plain,
! [SV13: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV13 )
| ~ ( in @ SV13 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(206,plain,
! [SV2: $i,SV14: $i] :
( ( ! [SY54: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV14 )
| ~ ( topological_space @ SV14 ) )
| ~ ( top_str @ SV14 ) )
| ~ ( element @ SY54 @ ( the_carrier @ SV14 ) ) )
| ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SY54 ) )
| ~ ! [SY55: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY55 @ SV14 @ SY54 )
| ( SV2 != SY55 ) ) )
| ~ ( ~ ~ ! [SY56: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY56 @ SV14 @ SY54 )
| ( SV2 != SY56 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SY54 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(207,plain,
( ( ~ ( element @ sK2_SX0 @ ( the_carrier @ sK1_A ) )
| ! [SY57: $i] :
~ ( ~ ( ~ ( in @ SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) )
| ( point_neighbourhood @ SY57 @ sK1_A @ sK2_SX0 ) )
| ~ ( ~ ( point_neighbourhood @ SY57 @ sK1_A @ sK2_SX0 )
| ( in @ SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[192]) ).
thf(208,plain,
! [SV3: $i] :
( ( ( ~ ( top_str @ SV3 ) )
= $true )
| ( ( one_sorted_str @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(209,plain,
! [SV15: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ SV15 )
| ( element @ SV4 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(210,plain,
! [SV16: $i,SV5: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( topological_space @ SV5 ) )
| ~ ( top_str @ SV5 ) )
| ~ ( element @ SV16 @ ( the_carrier @ SV5 ) ) )
| ! [SY58: $i] :
( ~ ( point_neighbourhood @ SY58 @ SV5 @ SV16 )
| ( element @ SY58 @ ( powerset @ ( the_carrier @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(211,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ! [SY59: $i] :
~ ( ~ ( ~ ( in @ SY59 @ SV6 )
| ( in @ SY59 @ SV17 ) )
| ~ ( ~ ( in @ SY59 @ SV17 )
| ( in @ SY59 @ SV6 ) ) )
| ( SV6 = SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(212,plain,
( ( ~ ~ ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[197]) ).
thf(213,plain,
! [SV18: $i,SV7: $i] :
( ( ~ ( element @ SV7 @ SV18 )
| ( empty @ SV18 )
| ( in @ SV7 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(214,plain,
! [SV8: $i] :
( ( ! [SY47: $i] :
~ ( element @ SY47 @ SV8 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(215,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ~ ( ~ ( in @ SV9 @ SV19 )
| ~ ( empty @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(216,plain,
! [SV20: $i,SV10: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( topological_space @ SV10 ) )
| ~ ( top_str @ SV10 ) )
| ~ ( element @ SV20 @ ( the_carrier @ SV10 ) ) )
| ~ ! [SY60: $i] :
~ ( point_neighbourhood @ SY60 @ SV10 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(217,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( topological_space @ SV11 ) )
| ~ ( top_str @ SV11 ) ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV11 ) )
| ( ( neighborhood_system @ SV11 @ SY51 )
= ( a_2_0_yellow19 @ SV11 @ SY51 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(218,plain,
( ( ~ ( top_str @ sK4_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[203]) ).
thf(219,plain,
! [SV21: $i,SV12: $i] :
( ( ! [SY61: $i] :
( ~ ~ ( ~ ( in @ SV12 @ SV21 )
| ~ ( element @ SV21 @ ( powerset @ SY61 ) ) )
| ( element @ SV12 @ SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(220,plain,
! [SV13: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV13 ) )
= $true )
| ( ( ~ ( in @ SV13 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(221,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV14 )
| ~ ( topological_space @ SV14 ) )
| ~ ( top_str @ SV14 ) )
| ~ ( element @ SV22 @ ( the_carrier @ SV14 ) ) )
| ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
| ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(222,plain,
( ( ~ ( element @ sK2_SX0 @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(223,plain,
( ( ! [SY57: $i] :
~ ( ~ ( ~ ( in @ SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) )
| ( point_neighbourhood @ SY57 @ sK1_A @ sK2_SX0 ) )
| ~ ( ~ ( point_neighbourhood @ SY57 @ sK1_A @ sK2_SX0 )
| ( in @ SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(224,plain,
! [SV3: $i] :
( ( ( top_str @ SV3 )
= $false )
| ( ( one_sorted_str @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(225,plain,
! [SV15: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV15 ) )
= $true )
| ( ( element @ SV4 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(226,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( topological_space @ SV5 ) )
| ~ ( top_str @ SV5 ) )
| ~ ( element @ SV16 @ ( the_carrier @ SV5 ) ) ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( point_neighbourhood @ SY58 @ SV5 @ SV16 )
| ( element @ SY58 @ ( powerset @ ( the_carrier @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(227,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ! [SY59: $i] :
~ ( ~ ( ~ ( in @ SY59 @ SV6 )
| ( in @ SY59 @ SV17 ) )
| ~ ( ~ ( in @ SY59 @ SV17 )
| ( in @ SY59 @ SV6 ) ) ) )
= $true )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(228,plain,
( ( ~ ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(229,plain,
! [SV18: $i,SV7: $i] :
( ( ( ~ ( element @ SV7 @ SV18 ) )
= $true )
| ( ( ( empty @ SV18 )
| ( in @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(230,plain,
! [SV8: $i] :
( ( ~ ( element @ ( sK5_SY47 @ SV8 ) @ SV8 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[214]) ).
thf(231,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ( ~ ( in @ SV9 @ SV19 )
| ~ ( empty @ SV19 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(232,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( topological_space @ SV10 ) )
| ~ ( top_str @ SV10 ) )
| ~ ( element @ SV20 @ ( the_carrier @ SV10 ) ) ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ( point_neighbourhood @ SY60 @ SV10 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(233,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( topological_space @ SV11 ) )
| ~ ( top_str @ SV11 ) ) )
= $false )
| ( ( ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV11 ) )
| ( ( neighborhood_system @ SV11 @ SY51 )
= ( a_2_0_yellow19 @ SV11 @ SY51 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(234,plain,
( ( top_str @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(235,plain,
! [SV23: $i,SV21: $i,SV12: $i] :
( ( ~ ~ ( ~ ( in @ SV12 @ SV21 )
| ~ ( element @ SV21 @ ( powerset @ SV23 ) ) )
| ( element @ SV12 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(236,plain,
! [SV13: $i,SV1: $i] :
( ( ( in @ SV1 @ SV13 )
= $false )
| ( ( ~ ( in @ SV13 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(237,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV14 )
| ~ ( topological_space @ SV14 ) )
| ~ ( top_str @ SV14 ) )
| ~ ( element @ SV22 @ ( the_carrier @ SV14 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
| ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(238,plain,
( ( element @ sK2_SX0 @ ( the_carrier @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(239,plain,
( ( ~ ( ~ ( ~ ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) )
| ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 ) )
| ~ ( ~ ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 )
| ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[223]) ).
thf(240,plain,
! [SV15: $i,SV4: $i] :
( ( ( in @ SV4 @ SV15 )
= $false )
| ( ( element @ SV4 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(241,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( topological_space @ SV5 ) )
| ~ ( top_str @ SV5 ) )
| ~ ( element @ SV16 @ ( the_carrier @ SV5 ) ) ) )
= $false )
| ( ( ! [SY58: $i] :
( ~ ( point_neighbourhood @ SY58 @ SV5 @ SV16 )
| ( element @ SY58 @ ( powerset @ ( the_carrier @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(242,plain,
! [SV17: $i,SV6: $i] :
( ( ( ! [SY59: $i] :
~ ( ~ ( ~ ( in @ SY59 @ SV6 )
| ( in @ SY59 @ SV17 ) )
| ~ ( ~ ( in @ SY59 @ SV17 )
| ( in @ SY59 @ SV6 ) ) ) )
= $false )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(243,plain,
( ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(244,plain,
! [SV18: $i,SV7: $i] :
( ( ( element @ SV7 @ SV18 )
= $false )
| ( ( ( empty @ SV18 )
| ( in @ SV7 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(245,plain,
! [SV8: $i] :
( ( element @ ( sK5_SY47 @ SV8 ) @ SV8 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(246,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ( in @ SV9 @ SV19 )
| ~ ( empty @ SV19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(247,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( topological_space @ SV10 ) )
| ~ ( top_str @ SV10 ) )
| ~ ( element @ SV20 @ ( the_carrier @ SV10 ) ) ) )
= $false )
| ( ( ~ ! [SY60: $i] :
~ ( point_neighbourhood @ SY60 @ SV10 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(248,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( topological_space @ SV11 ) )
| ~ ( top_str @ SV11 ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV11 ) )
| ( ( neighborhood_system @ SV11 @ SY51 )
= ( a_2_0_yellow19 @ SV11 @ SY51 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(249,plain,
! [SV23: $i,SV21: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( in @ SV12 @ SV21 )
| ~ ( element @ SV21 @ ( powerset @ SV23 ) ) ) )
= $true )
| ( ( element @ SV12 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(250,plain,
! [SV1: $i,SV13: $i] :
( ( ( in @ SV13 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(251,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV14 )
| ~ ( topological_space @ SV14 ) )
| ~ ( top_str @ SV14 ) )
| ~ ( element @ SV22 @ ( the_carrier @ SV14 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
| ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(252,plain,
( ( ~ ( ~ ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) )
| ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 ) )
| ~ ( ~ ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 )
| ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(253,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( topological_space @ SV5 ) )
| ~ ( top_str @ SV5 ) )
| ~ ( element @ SV16 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( point_neighbourhood @ SY58 @ SV5 @ SV16 )
| ( element @ SY58 @ ( powerset @ ( the_carrier @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(254,plain,
! [SV6: $i,SV17: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 )
| ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 ) )
| ~ ( ~ ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 )
| ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 ) ) ) )
= $false )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[242]) ).
thf(255,plain,
( ( ~ ( one_sorted_str @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(256,plain,
( ( ~ ~ ( empty_carrier @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(257,plain,
! [SV7: $i,SV18: $i] :
( ( ( empty @ SV18 )
= $true )
| ( ( in @ SV7 @ SV18 )
= $true )
| ( ( element @ SV7 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(258,plain,
! [SV19: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV19 ) )
= $true )
| ( ( ~ ( empty @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(259,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( topological_space @ SV10 ) )
| ~ ( top_str @ SV10 ) )
| ~ ( element @ SV20 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ( point_neighbourhood @ SY60 @ SV10 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(260,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( topological_space @ SV11 ) ) )
= $true )
| ( ( ~ ( top_str @ SV11 ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV11 ) )
| ( ( neighborhood_system @ SV11 @ SY51 )
= ( a_2_0_yellow19 @ SV11 @ SY51 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(261,plain,
! [SV23: $i,SV21: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ SV12 @ SV21 )
| ~ ( element @ SV21 @ ( powerset @ SV23 ) ) ) )
= $false )
| ( ( element @ SV12 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(262,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV14 )
| ~ ( topological_space @ SV14 ) )
| ~ ( top_str @ SV14 ) )
| ~ ( element @ SV22 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
| ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(263,plain,
( ( ( ~ ( ~ ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) )
| ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 ) ) )
= $true )
| ( ( ~ ( ~ ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 )
| ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(264,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( topological_space @ SV5 ) )
| ~ ( top_str @ SV5 ) ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( point_neighbourhood @ SY58 @ SV5 @ SV16 )
| ( element @ SY58 @ ( powerset @ ( the_carrier @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(265,plain,
! [SV6: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 )
| ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 ) )
| ~ ( ~ ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 )
| ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(266,plain,
( ( one_sorted_str @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(267,plain,
( ( ~ ( empty_carrier @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(268,plain,
! [SV19: $i,SV9: $i] :
( ( ( in @ SV9 @ SV19 )
= $false )
| ( ( ~ ( empty @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(269,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( topological_space @ SV10 ) )
| ~ ( top_str @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV20 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ( point_neighbourhood @ SY60 @ SV10 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(270,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( topological_space @ SV11 ) ) )
= $false )
| ( ( ~ ( top_str @ SV11 ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV11 ) )
| ( ( neighborhood_system @ SV11 @ SY51 )
= ( a_2_0_yellow19 @ SV11 @ SY51 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(271,plain,
! [SV23: $i,SV21: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV21 )
| ~ ( element @ SV21 @ ( powerset @ SV23 ) ) )
= $true )
| ( ( element @ SV12 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(272,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV14 )
| ~ ( topological_space @ SV14 ) )
| ~ ( top_str @ SV14 ) ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
| ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(273,plain,
( ( ( ~ ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) )
| ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 ) )
= $false )
| ( ( ~ ( ~ ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 )
| ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(274,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( topological_space @ SV5 ) )
| ~ ( top_str @ SV5 ) ) )
= $false )
| ( ( ~ ( element @ SV16 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( point_neighbourhood @ SY58 @ SV5 @ SV16 )
| ( element @ SY58 @ ( powerset @ ( the_carrier @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(275,plain,
! [SV6: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 )
| ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 )
| ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(276,plain,
( ( empty_carrier @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(277,plain,
! [SV9: $i,SV19: $i] :
( ( ( empty @ SV19 )
= $false )
| ( ( in @ SV9 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(278,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( topological_space @ SV10 ) )
| ~ ( top_str @ SV10 ) ) )
= $false )
| ( ( ~ ( element @ SV20 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ( point_neighbourhood @ SY60 @ SV10 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(279,plain,
! [SV11: $i] :
( ( ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( topological_space @ SV11 ) )
= $true )
| ( ( ~ ( top_str @ SV11 ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV11 ) )
| ( ( neighborhood_system @ SV11 @ SY51 )
= ( a_2_0_yellow19 @ SV11 @ SY51 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(280,plain,
! [SV23: $i,SV21: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV21 ) )
= $true )
| ( ( ~ ( element @ SV21 @ ( powerset @ SV23 ) ) )
= $true )
| ( ( element @ SV12 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(281,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV14 )
| ~ ( topological_space @ SV14 ) )
| ~ ( top_str @ SV14 ) ) )
= $false )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
| ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(282,plain,
( ( ( ~ ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) ) )
= $false )
| ( ( ~ ( ~ ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 )
| ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(283,plain,
( ( ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 )
= $false )
| ( ( ~ ( ~ ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 )
| ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(284,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( topological_space @ SV5 ) )
| ~ ( top_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( point_neighbourhood @ SY58 @ SV5 @ SV16 )
| ( element @ SY58 @ ( powerset @ ( the_carrier @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(285,plain,
! [SV6: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 )
| ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 )
| ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(286,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( topological_space @ SV10 ) )
| ~ ( top_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV20 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ( point_neighbourhood @ SY60 @ SV10 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(287,plain,
! [SV11: $i] :
( ( ( ~ ~ ( empty_carrier @ SV11 ) )
= $true )
| ( ( ~ ( topological_space @ SV11 ) )
= $true )
| ( ( ~ ( top_str @ SV11 ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV11 ) )
| ( ( neighborhood_system @ SV11 @ SY51 )
= ( a_2_0_yellow19 @ SV11 @ SY51 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(288,plain,
! [SV23: $i,SV21: $i,SV12: $i] :
( ( ( in @ SV12 @ SV21 )
= $false )
| ( ( ~ ( element @ SV21 @ ( powerset @ SV23 ) ) )
= $true )
| ( ( element @ SV12 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(289,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV14 )
| ~ ( topological_space @ SV14 ) )
| ~ ( top_str @ SV14 ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
| ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(290,plain,
( ( ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) )
= $true )
| ( ( ~ ( ~ ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 )
| ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(291,plain,
( ( ( ~ ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 )
| ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) ) )
= $false )
| ( ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(292,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( topological_space @ SV5 ) ) )
= $true )
| ( ( ~ ( top_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( point_neighbourhood @ SY58 @ SV5 @ SV16 )
| ( element @ SY58 @ ( powerset @ ( the_carrier @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(293,plain,
! [SV6: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 )
| ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(294,plain,
! [SV6: $i,SV17: $i] :
( ( ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 )
| ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(295,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( topological_space @ SV10 ) ) )
= $true )
| ( ( ~ ( top_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV20 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ( point_neighbourhood @ SY60 @ SV10 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(296,plain,
! [SV11: $i] :
( ( ( ~ ( empty_carrier @ SV11 ) )
= $false )
| ( ( ~ ( topological_space @ SV11 ) )
= $true )
| ( ( ~ ( top_str @ SV11 ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV11 ) )
| ( ( neighborhood_system @ SV11 @ SY51 )
= ( a_2_0_yellow19 @ SV11 @ SY51 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(297,plain,
! [SV12: $i,SV23: $i,SV21: $i] :
( ( ( element @ SV21 @ ( powerset @ SV23 ) )
= $false )
| ( ( in @ SV12 @ SV21 )
= $false )
| ( ( element @ SV12 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(298,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV14 )
| ~ ( topological_space @ SV14 ) ) )
= $true )
| ( ( ~ ( top_str @ SV14 ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
| ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(299,plain,
( ( ( ~ ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 )
| ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) ) )
= $false )
| ( ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(300,plain,
( ( ( ~ ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 ) )
= $false )
| ( ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(301,plain,
( ( ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) )
= $false )
| ( ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(302,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( topological_space @ SV5 ) ) )
= $false )
| ( ( ~ ( top_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( point_neighbourhood @ SY58 @ SV5 @ SV16 )
| ( element @ SY58 @ ( powerset @ ( the_carrier @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(303,plain,
! [SV6: $i,SV17: $i] :
( ( ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 )
| ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(304,plain,
! [SV6: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 )
| ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 ) )
= $false )
| ( ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 )
= $false )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(305,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( topological_space @ SV10 ) ) )
= $false )
| ( ( ~ ( top_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV20 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ( point_neighbourhood @ SY60 @ SV10 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(306,plain,
! [SV11: $i] :
( ( ( empty_carrier @ SV11 )
= $true )
| ( ( ~ ( topological_space @ SV11 ) )
= $true )
| ( ( ~ ( top_str @ SV11 ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV11 ) )
| ( ( neighborhood_system @ SV11 @ SY51 )
= ( a_2_0_yellow19 @ SV11 @ SY51 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(307,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV14 )
| ~ ( topological_space @ SV14 ) ) )
= $false )
| ( ( ~ ( top_str @ SV14 ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
| ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(308,plain,
( ( ( ~ ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 ) )
= $false )
| ( ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(309,plain,
( ( ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) )
= $false )
| ( ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(310,plain,
( ( ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 )
= $true )
| ( ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(311,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( topological_space @ SV5 ) )
= $true )
| ( ( ~ ( top_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( point_neighbourhood @ SY58 @ SV5 @ SV16 )
| ( element @ SY58 @ ( powerset @ ( the_carrier @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(312,plain,
! [SV6: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 )
| ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 ) )
= $false )
| ( ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(313,plain,
! [SV6: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 ) )
= $false )
| ( ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 )
= $false )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[304]) ).
thf(314,plain,
! [SV6: $i,SV17: $i] :
( ( ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 )
= $false )
| ( ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 )
= $false )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[304]) ).
thf(315,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( topological_space @ SV10 ) )
= $true )
| ( ( ~ ( top_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV20 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ( point_neighbourhood @ SY60 @ SV10 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(316,plain,
! [SV11: $i] :
( ( ( topological_space @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( ~ ( top_str @ SV11 ) )
= $true )
| ( ( ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV11 ) )
| ( ( neighborhood_system @ SV11 @ SY51 )
= ( a_2_0_yellow19 @ SV11 @ SY51 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(317,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( ~ ~ ( empty_carrier @ SV14 )
| ~ ( topological_space @ SV14 ) )
= $true )
| ( ( ~ ( top_str @ SV14 ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
| ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(318,plain,
( ( ( point_neighbourhood @ sK6_SY57 @ sK1_A @ sK2_SX0 )
= $true )
| ( ( in @ sK6_SY57 @ ( neighborhood_system @ sK1_A @ sK2_SX0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(319,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ~ ( empty_carrier @ SV5 ) )
= $true )
| ( ( ~ ( topological_space @ SV5 ) )
= $true )
| ( ( ~ ( top_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( point_neighbourhood @ SY58 @ SV5 @ SV16 )
| ( element @ SY58 @ ( powerset @ ( the_carrier @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(320,plain,
! [SV6: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 ) )
= $false )
| ( ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(321,plain,
! [SV6: $i,SV17: $i] :
( ( ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 )
= $false )
| ( ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(322,plain,
! [SV6: $i,SV17: $i] :
( ( ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 )
= $true )
| ( ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 )
= $false )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(323,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ~ ( empty_carrier @ SV10 ) )
= $true )
| ( ( ~ ( topological_space @ SV10 ) )
= $true )
| ( ( ~ ( top_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV20 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ( point_neighbourhood @ SY60 @ SV10 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(324,plain,
! [SV11: $i] :
( ( ( top_str @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( topological_space @ SV11 )
= $false )
| ( ( ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV11 ) )
| ( ( neighborhood_system @ SV11 @ SY51 )
= ( a_2_0_yellow19 @ SV11 @ SY51 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(325,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( ~ ~ ( empty_carrier @ SV14 ) )
= $true )
| ( ( ~ ( topological_space @ SV14 ) )
= $true )
| ( ( ~ ( top_str @ SV14 ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
| ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(326,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( empty_carrier @ SV5 ) )
= $false )
| ( ( ~ ( topological_space @ SV5 ) )
= $true )
| ( ( ~ ( top_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( point_neighbourhood @ SY58 @ SV5 @ SV16 )
| ( element @ SY58 @ ( powerset @ ( the_carrier @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(327,plain,
! [SV6: $i,SV17: $i] :
( ( ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV17 )
= $true )
| ( ( in @ ( sK7_SY59 @ SV17 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(328,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ( empty_carrier @ SV10 ) )
= $false )
| ( ( ~ ( topological_space @ SV10 ) )
= $true )
| ( ( ~ ( top_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV20 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ( point_neighbourhood @ SY60 @ SV10 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(329,plain,
! [SV11: $i,SV24: $i] :
( ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) )
| ( ( neighborhood_system @ SV11 @ SV24 )
= ( a_2_0_yellow19 @ SV11 @ SV24 ) ) )
= $true )
| ( ( topological_space @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( top_str @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(330,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( ~ ( empty_carrier @ SV14 ) )
= $false )
| ( ( ~ ( topological_space @ SV14 ) )
= $true )
| ( ( ~ ( top_str @ SV14 ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
| ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(331,plain,
! [SV16: $i,SV5: $i] :
( ( ( empty_carrier @ SV5 )
= $true )
| ( ( ~ ( topological_space @ SV5 ) )
= $true )
| ( ( ~ ( top_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( point_neighbourhood @ SY58 @ SV5 @ SV16 )
| ( element @ SY58 @ ( powerset @ ( the_carrier @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(332,plain,
! [SV20: $i,SV10: $i] :
( ( ( empty_carrier @ SV10 )
= $true )
| ( ( ~ ( topological_space @ SV10 ) )
= $true )
| ( ( ~ ( top_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV20 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ( point_neighbourhood @ SY60 @ SV10 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(333,plain,
! [SV11: $i,SV24: $i] :
( ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ( neighborhood_system @ SV11 @ SV24 )
= ( a_2_0_yellow19 @ SV11 @ SV24 ) )
= $true )
| ( ( topological_space @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( top_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(334,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( empty_carrier @ SV14 )
= $true )
| ( ( ~ ( topological_space @ SV14 ) )
= $true )
| ( ( ~ ( top_str @ SV14 ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
| ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(335,plain,
! [SV16: $i,SV5: $i] :
( ( ( topological_space @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( ~ ( top_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( point_neighbourhood @ SY58 @ SV5 @ SV16 )
| ( element @ SY58 @ ( powerset @ ( the_carrier @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(336,plain,
! [SV20: $i,SV10: $i] :
( ( ( topological_space @ SV10 )
= $false )
| ( ( empty_carrier @ SV10 )
= $true )
| ( ( ~ ( top_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV20 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ( point_neighbourhood @ SY60 @ SV10 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(337,plain,
! [SV11: $i,SV24: $i] :
( ( ( element @ SV24 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( ( neighborhood_system @ SV11 @ SV24 )
= ( a_2_0_yellow19 @ SV11 @ SV24 ) )
= $true )
| ( ( topological_space @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( top_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(338,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( topological_space @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( ~ ( top_str @ SV14 ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
| ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(339,plain,
! [SV16: $i,SV5: $i] :
( ( ( top_str @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( topological_space @ SV5 )
= $false )
| ( ( ~ ( element @ SV16 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( point_neighbourhood @ SY58 @ SV5 @ SV16 )
| ( element @ SY58 @ ( powerset @ ( the_carrier @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(340,plain,
! [SV20: $i,SV10: $i] :
( ( ( top_str @ SV10 )
= $false )
| ( ( empty_carrier @ SV10 )
= $true )
| ( ( topological_space @ SV10 )
= $false )
| ( ( ~ ( element @ SV20 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ( point_neighbourhood @ SY60 @ SV10 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(341,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
| ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(342,plain,
! [SV5: $i,SV16: $i] :
( ( ( element @ SV16 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( topological_space @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( top_str @ SV5 )
= $false )
| ( ( ! [SY58: $i] :
( ~ ( point_neighbourhood @ SY58 @ SV5 @ SV16 )
| ( element @ SY58 @ ( powerset @ ( the_carrier @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(343,plain,
! [SV10: $i,SV20: $i] :
( ( ( element @ SV20 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( empty_carrier @ SV10 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( ~ ! [SY60: $i] :
~ ( point_neighbourhood @ SY60 @ SV10 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(344,plain,
! [SV2: $i,SV14: $i,SV22: $i] :
( ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( topological_space @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( top_str @ SV14 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
| ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(345,plain,
! [SV16: $i,SV5: $i,SV25: $i] :
( ( ( ~ ( point_neighbourhood @ SV25 @ SV5 @ SV16 )
| ( element @ SV25 @ ( powerset @ ( the_carrier @ SV5 ) ) ) )
= $true )
| ( ( top_str @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( topological_space @ SV5 )
= $false )
| ( ( element @ SV16 @ ( the_carrier @ SV5 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(346,plain,
! [SV20: $i,SV10: $i] :
( ( ( ! [SY60: $i] :
~ ( point_neighbourhood @ SY60 @ SV10 @ SV20 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( empty_carrier @ SV10 )
= $true )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV20 @ ( the_carrier @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(347,plain,
! [SV22: $i,SV14: $i,SV2: $i] :
( ( ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
| ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) )
= $false )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(348,plain,
! [SV16: $i,SV5: $i,SV25: $i] :
( ( ( ~ ( point_neighbourhood @ SV25 @ SV5 @ SV16 ) )
= $true )
| ( ( element @ SV25 @ ( powerset @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( top_str @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( topological_space @ SV5 )
= $false )
| ( ( element @ SV16 @ ( the_carrier @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(349,plain,
! [SV10: $i,SV20: $i] :
( ( ( ~ ( point_neighbourhood @ ( sK8_SY60 @ SV20 @ SV10 ) @ SV10 @ SV20 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( empty_carrier @ SV10 )
= $true )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV20 @ ( the_carrier @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[346]) ).
thf(350,plain,
! [SV22: $i,SV14: $i,SV2: $i] :
( ( ( ~ ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) ) )
= $false )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(351,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) ) )
= $false )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(352,plain,
! [SV16: $i,SV5: $i,SV25: $i] :
( ( ( point_neighbourhood @ SV25 @ SV5 @ SV16 )
= $false )
| ( ( element @ SV25 @ ( powerset @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( top_str @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( topological_space @ SV5 )
= $false )
| ( ( element @ SV16 @ ( the_carrier @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(353,plain,
! [SV10: $i,SV20: $i] :
( ( ( point_neighbourhood @ ( sK8_SY60 @ SV20 @ SV10 ) @ SV10 @ SV20 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( empty_carrier @ SV10 )
= $true )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV20 @ ( the_carrier @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(354,plain,
! [SV22: $i,SV14: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
= $true )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[350]) ).
thf(355,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) )
| ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) )
= $true )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(356,plain,
! [SV22: $i,SV14: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) ) )
= $true )
| ( ( ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
= $true )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(357,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) ) )
= $true )
| ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $true )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(358,plain,
! [SV22: $i,SV14: $i,SV2: $i] :
( ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $false )
| ( ( ~ ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
= $true )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(359,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( ~ ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) ) )
= $false )
| ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $true )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(360,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( ! [SY62: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY62 @ SV14 @ SV22 )
| ( SV2 != SY62 ) ) )
= $false )
| ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $false )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(361,plain,
! [SV2: $i,SV22: $i,SV14: $i] :
( ( ( ! [SY63: $i] :
~ ~ ( ~ ( point_neighbourhood @ SY63 @ SV14 @ SV22 )
| ( SV2 != SY63 ) ) )
= $true )
| ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $true )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(362,plain,
! [SV14: $i,SV22: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( point_neighbourhood @ ( sK9_SY62 @ SV2 @ SV22 @ SV14 ) @ SV14 @ SV22 )
| ( SV2
!= ( sK9_SY62 @ SV2 @ SV22 @ SV14 ) ) ) )
= $false )
| ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $false )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[360]) ).
thf(363,plain,
! [SV2: $i,SV22: $i,SV14: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( point_neighbourhood @ SV26 @ SV14 @ SV22 )
| ( SV2 != SV26 ) ) )
= $true )
| ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $true )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(364,plain,
! [SV14: $i,SV22: $i,SV2: $i] :
( ( ( ~ ( ~ ( point_neighbourhood @ ( sK9_SY62 @ SV2 @ SV22 @ SV14 ) @ SV14 @ SV22 )
| ( SV2
!= ( sK9_SY62 @ SV2 @ SV22 @ SV14 ) ) ) )
= $true )
| ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $false )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(365,plain,
! [SV2: $i,SV22: $i,SV14: $i,SV26: $i] :
( ( ( ~ ( ~ ( point_neighbourhood @ SV26 @ SV14 @ SV22 )
| ( SV2 != SV26 ) ) )
= $false )
| ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $true )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(366,plain,
! [SV14: $i,SV22: $i,SV2: $i] :
( ( ( ~ ( point_neighbourhood @ ( sK9_SY62 @ SV2 @ SV22 @ SV14 ) @ SV14 @ SV22 )
| ( SV2
!= ( sK9_SY62 @ SV2 @ SV22 @ SV14 ) ) )
= $false )
| ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $false )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(367,plain,
! [SV2: $i,SV22: $i,SV14: $i,SV26: $i] :
( ( ( ~ ( point_neighbourhood @ SV26 @ SV14 @ SV22 )
| ( SV2 != SV26 ) )
= $true )
| ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $true )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(368,plain,
! [SV14: $i,SV22: $i,SV2: $i] :
( ( ( ~ ( point_neighbourhood @ ( sK9_SY62 @ SV2 @ SV22 @ SV14 ) @ SV14 @ SV22 ) )
= $false )
| ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $false )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[366]) ).
thf(369,plain,
! [SV14: $i,SV22: $i,SV2: $i] :
( ( ( SV2
!= ( sK9_SY62 @ SV2 @ SV22 @ SV14 ) )
= $false )
| ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $false )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[366]) ).
thf(370,plain,
! [SV2: $i,SV22: $i,SV14: $i,SV26: $i] :
( ( ( ~ ( point_neighbourhood @ SV26 @ SV14 @ SV22 ) )
= $true )
| ( ( SV2 != SV26 )
= $true )
| ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $true )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(371,plain,
! [SV14: $i,SV22: $i,SV2: $i] :
( ( ( point_neighbourhood @ ( sK9_SY62 @ SV2 @ SV22 @ SV14 ) @ SV14 @ SV22 )
= $true )
| ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $false )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(372,plain,
! [SV14: $i,SV22: $i,SV2: $i] :
( ( ( SV2
= ( sK9_SY62 @ SV2 @ SV22 @ SV14 ) )
= $true )
| ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $false )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(373,plain,
! [SV2: $i,SV22: $i,SV14: $i,SV26: $i] :
( ( ( point_neighbourhood @ SV26 @ SV14 @ SV22 )
= $false )
| ( ( SV2 != SV26 )
= $true )
| ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $true )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(374,plain,
! [SV22: $i,SV14: $i,SV26: $i,SV2: $i] :
( ( ( SV2 = SV26 )
= $false )
| ( ( point_neighbourhood @ SV26 @ SV14 @ SV22 )
= $false )
| ( ( in @ SV2 @ ( a_2_0_yellow19 @ SV14 @ SV22 ) )
= $true )
| ( ( top_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( topological_space @ SV14 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(375,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[151,374,372,371,353,352,337,327,322,321,318,314,310,309,301,297,277,276,266,257,250,245,240,238,234,224,189,171,170,159,158,157,155,153,152]) ).
thf(376,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[375]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU388+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 15:21:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.50/0.57
% 1.50/0.57 No.of.Axioms: 21
% 1.50/0.57
% 1.50/0.57 Length.of.Defs: 0
% 1.50/0.57
% 1.50/0.57 Contains.Choice.Funs: false
% 1.50/0.57 .........
% 1.50/0.57
% 1.50/0.57 ********************************
% 1.50/0.57 * All subproblems solved! *
% 1.50/0.57 ********************************
% 1.50/0.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:24,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:375,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.50/0.57
% 1.50/0.57 %**** Beginning of derivation protocol ****
% 1.50/0.57 % SZS output start CNFRefutation
% See solution above
% 0.51/0.57
% 0.51/0.57 %**** End of derivation protocol ****
% 0.51/0.57 %**** no. of clauses in derivation: 279 ****
% 0.51/0.57 %**** clause counter: 375 ****
% 0.51/0.57
% 0.51/0.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:24,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:375,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------