TSTP Solution File: SEU388+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU388+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:11:24 EDT 2022
% Result : Theorem 16.63s 16.86s
% Output : CNFRefutation 16.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 145
% Syntax : Number of formulae : 877 ( 387 unt; 85 typ; 0 def)
% Number of atoms : 5823 (1557 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 9494 (1807 ~;1745 |; 222 &;5588 @)
% ( 12 <=>; 120 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 100 ( 100 >; 0 *; 0 +; 0 <<)
% Number of symbols : 88 ( 85 usr; 13 con; 0-3 aty)
% Number of variables : 1198 ( 0 ^1154 !; 44 ?;1198 :)
% 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_sK10_B,type,
sK10_B: $i > $i ).
thf(tp_sK11_B,type,
sK11_B: $i > $i ).
thf(tp_sK12_A,type,
sK12_A: $i ).
thf(tp_sK13_A,type,
sK13_A: $i ).
thf(tp_sK14_A,type,
sK14_A: $i ).
thf(tp_sK15_A,type,
sK15_A: $i ).
thf(tp_sK16_A,type,
sK16_A: $i ).
thf(tp_sK17_C,type,
sK17_C: $i > $i > $i ).
thf(tp_sK18_B,type,
sK18_B: $i > $i ).
thf(tp_sK19_A,type,
sK19_A: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_B,type,
sK20_B: $i > $i ).
thf(tp_sK21_B,type,
sK21_B: $i > $i ).
thf(tp_sK22_B,type,
sK22_B: $i > $i ).
thf(tp_sK23_D,type,
sK23_D: $i > $i > $i > $i ).
thf(tp_sK24_B,type,
sK24_B: $i > $i ).
thf(tp_sK25_C,type,
sK25_C: $i > $i > $i ).
thf(tp_sK26_A,type,
sK26_A: $i ).
thf(tp_sK2_SY103,type,
sK2_SY103: $i ).
thf(tp_sK3_SY105,type,
sK3_SY105: $i ).
thf(tp_sK4_B,type,
sK4_B: $i > $i ).
thf(tp_sK5_B,type,
sK5_B: $i > $i ).
thf(tp_sK6_B,type,
sK6_B: $i > $i ).
thf(tp_sK7_B,type,
sK7_B: $i > $i ).
thf(tp_sK8_B,type,
sK8_B: $i > $i ).
thf(tp_sK9_B,type,
sK9_B: $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(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(10,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(15,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( closed_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_pre_topc) ).
thf(16,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( closed_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(18,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(21,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(22,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_waybel_7) ).
thf(23,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_tops_1) ).
thf(24,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(26,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(28,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_waybel_7) ).
thf(30,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tops_1) ).
thf(31,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(32,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(37,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tops_1) ).
thf(38,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(39,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(41,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_yellow19) ).
thf(48,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( dense @ ( cast_as_carrier_subset @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_tops_1) ).
thf(51,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ( ( open_subset @ ( cast_as_carrier_subset @ A ) @ A )
& ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_tops_1) ).
thf(54,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_pre_topc) ).
thf(55,axiom,
! [A: $i] :
( ( ( with_infima_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_waybel_0) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(59,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_yellow_0) ).
thf(61,axiom,
! [A: $i] :
( ( ( with_suprema_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_waybel_0) ).
thf(62,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pre_topc) ).
thf(64,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(65,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(70,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',existence_m1_connsp_2) ).
thf(73,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(74,axiom,
? [A: $i] : ( top_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(75,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
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/sandbox2/benchmark/theBenchmark.p',dt_m1_connsp_2) ).
thf(83,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(84,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(87,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ( element @ ( neighborhood_system @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow19) ).
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/sandbox2/benchmark/theBenchmark.p',d1_yellow19) ).
thf(101,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( nowhere_dense @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_tops_1) ).
thf(103,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( boundary_set @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_tops_1) ).
thf(104,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( with_infima_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(105,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(106,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow_0) ).
thf(107,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_tops_1) ).
thf(109,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(110,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( with_suprema_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattice3) ).
thf(111,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/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/sandbox2/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] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(123,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(124,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(125,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( closed_subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(126,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(127,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(128,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(129,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(130,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(131,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(132,plain,
( ( ! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(133,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(134,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(135,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(136,plain,
( ( ! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ( ( open_subset @ ( cast_as_carrier_subset @ A ) @ A )
& ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(137,plain,
( ( ! [A: $i] :
( ( ( with_infima_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(138,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(139,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(140,plain,
( ( ! [A: $i] :
( ( ( with_suprema_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(141,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(142,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(143,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(144,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(145,plain,
( ( ? [A: $i] : ( rel_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(146,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(147,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(148,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ( element @ ( neighborhood_system @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(149,plain,
( ( ! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( nowhere_dense @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(150,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( boundary_set @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(151,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(152,plain,
( ( ! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(153,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(154,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(155,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(156,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(157,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(158,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(159,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(160,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(161,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(162,plain,
( ( ! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( closed_subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(163,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(164,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(165,plain,
( ( ! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(166,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(167,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(168,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( dense @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(169,plain,
( ( ! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(170,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(171,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(172,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(173,plain,
( ( ? [A: $i] : ( top_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(174,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(175,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(176,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(177,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( with_infima_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(178,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(179,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( with_suprema_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(180,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(181,plain,
( ( ( ~ ( empty_carrier @ sK1_A )
& ( topological_space @ sK1_A )
& ( top_str @ sK1_A ) )
=> ! [SY103: $i] :
( ( element @ SY103 @ ( the_carrier @ sK1_A ) )
=> ! [SY104: $i] :
( ( in @ SY104 @ ( neighborhood_system @ sK1_A @ SY103 ) )
<=> ( point_neighbourhood @ SY104 @ sK1_A @ SY103 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[121]) ).
thf(182,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[181]) ).
thf(183,plain,
( ( topological_space @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[181]) ).
thf(184,plain,
( ( top_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[181]) ).
thf(185,plain,
( ( ! [SY103: $i] :
( ( element @ SY103 @ ( the_carrier @ sK1_A ) )
=> ! [SY104: $i] :
( ( in @ SY104 @ ( neighborhood_system @ sK1_A @ SY103 ) )
<=> ( point_neighbourhood @ SY104 @ sK1_A @ SY103 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[181]) ).
thf(186,plain,
( ( ~ ! [SY103: $i] :
( ( element @ SY103 @ ( the_carrier @ sK1_A ) )
=> ! [SY104: $i] :
( ( in @ SY104 @ ( neighborhood_system @ sK1_A @ SY103 ) )
<=> ( point_neighbourhood @ SY104 @ sK1_A @ SY103 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[185]) ).
thf(187,plain,
( ( ( element @ sK2_SY103 @ ( the_carrier @ sK1_A ) )
& ( ~ ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ~ ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) )
& ( ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[186]) ).
thf(188,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[122]) ).
thf(189,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[123]) ).
thf(190,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[124]) ).
thf(191,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( topological_space @ A )
| ~ ( top_str @ A )
| ( ( element @ ( sK4_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK4_B @ A ) )
& ( closed_subset @ ( sK4_B @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[125]) ).
thf(192,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( ( element @ ( sK5_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK5_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[126]) ).
thf(193,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK6_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK6_B @ A ) )
& ( finite @ ( sK6_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[127]) ).
thf(194,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( element @ ( sK7_B @ A ) @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ~ ( empty @ ( sK7_B @ A ) )
& ( finite @ ( sK7_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[128]) ).
thf(195,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( topological_space @ A )
| ~ ( top_str @ A )
| ( ( element @ ( sK8_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK8_B @ A ) )
& ( open_subset @ ( sK8_B @ A ) @ A )
& ( closed_subset @ ( sK8_B @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[129]) ).
thf(196,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK9_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK9_B @ A ) )
& ( finite @ ( sK9_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[130]) ).
thf(197,plain,
( ( ! [A: $i] :
( ( element @ ( sK10_B @ A ) @ ( powerset @ ( powerset @ A ) ) )
& ~ ( empty @ ( sK10_B @ A ) )
& ( finite @ ( sK10_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[131]) ).
thf(198,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ~ ( topological_space @ A )
| ( ( element @ ( sK11_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ ( sK11_B @ A ) @ A )
& ( closed_subset @ ( sK11_B @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[132]) ).
thf(199,plain,
( ( ~ ( empty @ sK12_A )
& ( relation @ sK12_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[133]) ).
thf(200,plain,
( ( ( empty @ sK13_A )
& ( relation @ sK13_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[134]) ).
thf(201,plain,
( ( ~ ( empty @ sK14_A )
& ( finite @ sK14_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[135]) ).
thf(202,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ~ ( topological_space @ A )
| ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) )
& ! [A: $i] :
( ~ ( top_str @ A )
| ~ ( topological_space @ A )
| ( open_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[136]) ).
thf(203,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_infima_relstr @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_infima_relstr @ A )
| ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[137]) ).
thf(204,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[138]) ).
thf(205,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( rel_str @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[139]) ).
thf(206,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_suprema_relstr @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_suprema_relstr @ A )
| ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[140]) ).
thf(207,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[141]) ).
thf(208,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ A )
| ~ ( finite @ B )
| ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[143]) ).
thf(209,plain,
( ( one_sorted_str @ sK15_A )
= $true ),
inference(extcnf_combined,[status(esa)],[144]) ).
thf(210,plain,
( ( rel_str @ sK16_A )
= $true ),
inference(extcnf_combined,[status(esa)],[145]) ).
thf(211,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[146]) ).
thf(212,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[147]) ).
thf(213,plain,
( ( ! [A: $i,B: $i] :
( ( empty_carrier @ A )
| ~ ( topological_space @ A )
| ~ ( top_str @ A )
| ~ ( element @ B @ ( the_carrier @ A ) )
| ( element @ ( neighborhood_system @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[148]) ).
thf(214,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ~ ( topological_space @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( empty @ B )
| ( nowhere_dense @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(215,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( empty @ B )
| ( boundary_set @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[150]) ).
thf(216,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( complete_relstr @ A )
| ~ ( empty_carrier @ A ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( complete_relstr @ A )
| ( with_suprema_relstr @ A ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( complete_relstr @ A )
| ( with_infima_relstr @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[151]) ).
thf(217,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ~ ( topological_space @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( empty @ B )
| ( closed_subset @ B @ A ) )
& ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( empty @ B )
| ( open_subset @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[152]) ).
thf(218,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[153]) ).
thf(219,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[154]) ).
thf(220,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[155]) ).
thf(221,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[156]) ).
thf(222,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[157]) ).
thf(223,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[158]) ).
thf(224,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK17_C @ B @ A ) @ A )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( in @ ( sK17_C @ B @ A ) @ A )
| ( in @ ( sK17_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[159]) ).
thf(225,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[160]) ).
thf(226,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[161]) ).
thf(227,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ~ ( topological_space @ A )
| ( ( closed_subset @ ( sK18_B @ A ) @ A )
& ( element @ ( sK18_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[162]) ).
thf(228,plain,
( ( ( one_sorted_str @ sK19_A )
& ~ ( empty_carrier @ sK19_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[163]) ).
thf(229,plain,
( ( ! [A: $i] :
( ( element @ ( sK20_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK20_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[164]) ).
thf(230,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ~ ( topological_space @ A )
| ( ( element @ ( sK21_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ ( sK21_B @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[165]) ).
thf(231,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK22_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK22_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[166]) ).
thf(232,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( empty_carrier @ B )
| ~ ( topological_space @ B )
| ~ ( top_str @ B )
| ~ ( element @ C @ ( the_carrier @ B ) )
| ! [D: $i] :
( ( A != D )
| ~ ( point_neighbourhood @ D @ B @ C ) )
| ( in @ A @ ( a_2_0_yellow19 @ B @ C ) ) )
& ! [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 ) )
| ( ( A
= ( sK23_D @ C @ B @ A ) )
& ( point_neighbourhood @ ( sK23_D @ C @ B @ A ) @ B @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[167]) ).
thf(233,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ( dense @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[168]) ).
thf(234,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ~ ( topological_space @ A )
| ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[169]) ).
thf(235,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[170]) ).
thf(236,plain,
( ( ! [A: $i] : ( element @ ( sK24_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[171]) ).
thf(237,plain,
( ( ! [A: $i,B: $i] :
( ( empty_carrier @ A )
| ~ ( topological_space @ A )
| ~ ( top_str @ A )
| ~ ( element @ B @ ( the_carrier @ A ) )
| ( point_neighbourhood @ ( sK25_C @ B @ A ) @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[172]) ).
thf(238,plain,
( ( top_str @ sK26_A )
= $true ),
inference(extcnf_combined,[status(esa)],[173]) ).
thf(239,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(extcnf_combined,[status(esa)],[174]) ).
thf(240,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[175]) ).
thf(241,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(extcnf_combined,[status(esa)],[176]) ).
thf(242,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_infima_relstr @ A )
| ~ ( empty_carrier @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[177]) ).
thf(243,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[178]) ).
thf(244,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_suprema_relstr @ A )
| ~ ( empty_carrier @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[179]) ).
thf(245,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[180]) ).
thf(246,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(247,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_suprema_relstr @ A )
| ~ ( empty_carrier @ A ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(248,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(249,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_infima_relstr @ A )
| ~ ( empty_carrier @ A ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(250,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)],[241]) ).
thf(251,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(252,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)],[239]) ).
thf(253,plain,
( ( top_str @ sK26_A )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(254,plain,
( ( ! [A: $i,B: $i] :
( ( empty_carrier @ A )
| ~ ( topological_space @ A )
| ~ ( top_str @ A )
| ~ ( element @ B @ ( the_carrier @ A ) )
| ( point_neighbourhood @ ( sK25_C @ B @ A ) @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(255,plain,
( ( ! [A: $i] : ( element @ ( sK24_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(256,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(257,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ~ ( topological_space @ A )
| ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(258,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ( dense @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(259,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( empty_carrier @ B )
| ~ ( topological_space @ B )
| ~ ( top_str @ B )
| ~ ( element @ C @ ( the_carrier @ B ) )
| ! [D: $i] :
( ( A != D )
| ~ ( point_neighbourhood @ D @ B @ C ) )
| ( in @ A @ ( a_2_0_yellow19 @ B @ C ) ) )
& ! [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 ) )
| ( ( A
= ( sK23_D @ C @ B @ A ) )
& ( point_neighbourhood @ ( sK23_D @ C @ B @ A ) @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(260,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK22_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK22_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(261,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ~ ( topological_space @ A )
| ( ( element @ ( sK21_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ ( sK21_B @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(262,plain,
( ( ! [A: $i] :
( ( element @ ( sK20_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK20_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(263,plain,
( ( ( one_sorted_str @ sK19_A )
& ~ ( empty_carrier @ sK19_A ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(264,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ~ ( topological_space @ A )
| ( ( closed_subset @ ( sK18_B @ A ) @ A )
& ( element @ ( sK18_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(265,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(266,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(267,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK17_C @ B @ A ) @ A )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( in @ ( sK17_C @ B @ A ) @ A )
| ( in @ ( sK17_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(268,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(269,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(270,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(271,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(272,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(273,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(274,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ~ ( topological_space @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( empty @ B )
| ( closed_subset @ B @ A ) )
& ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( empty @ B )
| ( open_subset @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(275,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( complete_relstr @ A )
| ~ ( empty_carrier @ A ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( complete_relstr @ A )
| ( with_suprema_relstr @ A ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( complete_relstr @ A )
| ( with_infima_relstr @ A ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(276,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( empty @ B )
| ( boundary_set @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(277,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ~ ( topological_space @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( empty @ B )
| ( nowhere_dense @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(278,plain,
( ( ! [A: $i,B: $i] :
( ( empty_carrier @ A )
| ~ ( topological_space @ A )
| ~ ( top_str @ A )
| ~ ( element @ B @ ( the_carrier @ A ) )
| ( element @ ( neighborhood_system @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(279,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(280,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(281,plain,
( ( rel_str @ sK16_A )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(282,plain,
( ( one_sorted_str @ sK15_A )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(283,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ A )
| ~ ( finite @ B )
| ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(284,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(285,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(286,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_suprema_relstr @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_suprema_relstr @ A )
| ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(287,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( rel_str @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(288,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(289,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_infima_relstr @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_infima_relstr @ A )
| ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(290,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ~ ( topological_space @ A )
| ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) )
& ! [A: $i] :
( ~ ( top_str @ A )
| ~ ( topological_space @ A )
| ( open_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(291,plain,
( ( ~ ( empty @ sK14_A )
& ( finite @ sK14_A ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(292,plain,
( ( ( empty @ sK13_A )
& ( relation @ sK13_A ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(293,plain,
( ( ~ ( empty @ sK12_A )
& ( relation @ sK12_A ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(294,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ~ ( topological_space @ A )
| ( ( element @ ( sK11_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ ( sK11_B @ A ) @ A )
& ( closed_subset @ ( sK11_B @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(295,plain,
( ( ! [A: $i] :
( ( element @ ( sK10_B @ A ) @ ( powerset @ ( powerset @ A ) ) )
& ~ ( empty @ ( sK10_B @ A ) )
& ( finite @ ( sK10_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(296,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK9_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK9_B @ A ) )
& ( finite @ ( sK9_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(297,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( topological_space @ A )
| ~ ( top_str @ A )
| ( ( element @ ( sK8_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK8_B @ A ) )
& ( open_subset @ ( sK8_B @ A ) @ A )
& ( closed_subset @ ( sK8_B @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(298,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( element @ ( sK7_B @ A ) @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ~ ( empty @ ( sK7_B @ A ) )
& ( finite @ ( sK7_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(299,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK6_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK6_B @ A ) )
& ( finite @ ( sK6_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(300,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( ( element @ ( sK5_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK5_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(301,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( topological_space @ A )
| ~ ( top_str @ A )
| ( ( element @ ( sK4_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK4_B @ A ) )
& ( closed_subset @ ( sK4_B @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(302,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(303,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(304,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(305,plain,
( ( top_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(306,plain,
( ( topological_space @ sK1_A )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(307,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(308,plain,
( ( ( element @ sK2_SY103 @ ( the_carrier @ sK1_A ) )
& ( ~ ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ~ ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) )
& ( ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(309,plain,
( ( ~ ( ~ ( one_sorted_str @ sK19_A )
| ~ ~ ( empty_carrier @ sK19_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(310,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ~ ( topological_space @ SX0 )
| ( closed_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ~ ( topological_space @ SX0 )
| ( open_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(311,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK22_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK22_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(312,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(313,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ~ ( ~ ( element @ ( sK5_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(314,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(315,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK6_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK6_B @ SX0 ) ) )
| ~ ( finite @ ( sK6_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(316,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ~ ( topological_space @ SX0 )
| ~ ( ~ ( element @ ( sK21_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ( open_subset @ ( sK21_B @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(317,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK7_B @ SX0 ) @ ( powerset @ ( powerset @ ( the_carrier @ SX0 ) ) ) )
| ~ ~ ( empty @ ( sK7_B @ SX0 ) ) )
| ~ ( finite @ ( sK7_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(318,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ~ ( topological_space @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ( empty @ SX1 )
| ( closed_subset @ SX1 @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ( empty @ SX1 )
| ( open_subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(319,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( empty_carrier @ SX1 )
| ~ ( topological_space @ SX1 )
| ~ ( top_str @ SX1 )
| ~ ( element @ SX2 @ ( the_carrier @ SX1 ) )
| ! [SX3: $i] :
( ( SX0 != SX3 )
| ~ ( point_neighbourhood @ SX3 @ SX1 @ SX2 ) )
| ( in @ SX0 @ ( a_2_0_yellow19 @ SX1 @ SX2 ) ) )
| ~ ! [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 ) )
| ~ ( ( SX0
!= ( sK23_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( point_neighbourhood @ ( sK23_D @ SX2 @ SX1 @ SX0 ) @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(320,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK9_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK9_B @ SX0 ) ) )
| ~ ( finite @ ( sK9_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(321,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_suprema_relstr @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_infima_relstr @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(322,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( topological_space @ SX0 )
| ~ ( top_str @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK4_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ~ ( empty @ ( sK4_B @ SX0 ) ) )
| ~ ( closed_subset @ ( sK4_B @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(323,plain,
( ( ~ ( ~ ~ ( empty @ sK12_A )
| ~ ( relation @ sK12_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(324,plain,
( ( ~ ( ~ ( element @ sK2_SY103 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( ~ ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ~ ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) )
| ~ ( ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(325,plain,
( ( ~ ( ~ ~ ( empty @ sK14_A )
| ~ ( finite @ sK14_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(326,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ~ ( topological_space @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK11_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ( open_subset @ ( sK11_B @ SX0 ) @ SX0 ) )
| ~ ( closed_subset @ ( sK11_B @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(327,plain,
( ( ~ ( ~ ( empty @ sK13_A )
| ~ ( relation @ sK13_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(328,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_suprema_relstr @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_suprema_relstr @ SX0 )
| ( directed_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(329,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_infima_relstr @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_infima_relstr @ SX0 )
| ( filtered_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(330,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK20_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK20_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(331,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ( element @ ( sK10_B @ SX0 ) @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ~ ( empty @ ( sK10_B @ SX0 ) ) )
| ~ ( finite @ ( sK10_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(332,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ~ ( topological_space @ SX0 )
| ~ ( ~ ( closed_subset @ ( sK18_B @ SX0 ) @ SX0 )
| ~ ( element @ ( sK18_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(333,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( topological_space @ SX0 )
| ~ ( top_str @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK8_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ~ ( empty @ ( sK8_B @ SX0 ) ) )
| ~ ( open_subset @ ( sK8_B @ SX0 ) @ SX0 ) )
| ~ ( closed_subset @ ( sK8_B @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(334,plain,
! [SV1: $i] :
( ( ! [SY106: $i] :
( ~ ( in @ SV1 @ SY106 )
| ~ ( in @ SY106 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(335,plain,
! [SV2: $i] :
( ( ~ ( rel_str @ SV2 )
| ~ ( with_suprema_relstr @ SV2 )
| ~ ( empty_carrier @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(336,plain,
! [SV3: $i] :
( ( ~ ( finite @ SV3 )
| ! [SY107: $i] :
( ~ ( element @ SY107 @ ( powerset @ SV3 ) )
| ( finite @ SY107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(337,plain,
! [SV4: $i] :
( ( ~ ( rel_str @ SV4 )
| ~ ( with_infima_relstr @ SV4 )
| ~ ( empty_carrier @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(338,plain,
! [SV5: $i] :
( ( ( empty_carrier @ SV5 )
| ~ ( topological_space @ SV5 )
| ~ ( top_str @ SV5 )
| ! [SY108: $i] :
( ~ ( element @ SY108 @ ( the_carrier @ SV5 ) )
| ( ( neighborhood_system @ SV5 @ SY108 )
= ( a_2_0_yellow19 @ SV5 @ SY108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(339,plain,
! [SV6: $i] :
( ( ~ ( top_str @ SV6 )
| ( one_sorted_str @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(340,plain,
! [SV7: $i] :
( ( ! [SY109: $i] :
( ( empty_carrier @ SV7 )
| ~ ( topological_space @ SV7 )
| ~ ( top_str @ SV7 )
| ~ ( element @ SY109 @ ( the_carrier @ SV7 ) )
| ! [SY110: $i] :
( ~ ( point_neighbourhood @ SY110 @ SV7 @ SY109 )
| ( element @ SY110 @ ( powerset @ ( the_carrier @ SV7 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(341,plain,
! [SV8: $i] :
( ( ! [SY111: $i] :
( ( empty_carrier @ SV8 )
| ~ ( topological_space @ SV8 )
| ~ ( top_str @ SV8 )
| ~ ( element @ SY111 @ ( the_carrier @ SV8 ) )
| ( point_neighbourhood @ ( sK25_C @ SY111 @ SV8 ) @ SV8 @ SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(342,plain,
! [SV9: $i] :
( ( element @ ( sK24_B @ SV9 ) @ SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(343,plain,
! [SV10: $i] :
( ( ( empty_carrier @ SV10 )
| ~ ( one_sorted_str @ SV10 )
| ~ ( empty @ ( the_carrier @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(344,plain,
! [SV11: $i] :
( ( ~ ( top_str @ SV11 )
| ~ ( topological_space @ SV11 )
| ( closed_subset @ ( cast_as_carrier_subset @ SV11 ) @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(345,plain,
! [SV12: $i] :
( ( ~ ( top_str @ SV12 )
| ( dense @ ( cast_as_carrier_subset @ SV12 ) @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(346,plain,
! [SV13: $i] :
( ( ! [SY112: $i] :
( ~ ( in @ SV13 @ SY112 )
| ( element @ SV13 @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(347,plain,
! [SV14: $i] :
( ( ! [SY113: $i] :
( ~ ( element @ SV14 @ SY113 )
| ( empty @ SY113 )
| ( in @ SV14 @ SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(348,plain,
! [SV15: $i] :
( ( ! [SY114: $i,SY115: $i] :
( ~ ( element @ SY114 @ ( powerset @ SY115 ) )
| ~ ( in @ SV15 @ SY114 )
| ( element @ SV15 @ SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(349,plain,
! [SV16: $i] :
( ( ! [SY116: $i,SY117: $i] :
( ~ ( element @ SY116 @ ( powerset @ SY117 ) )
| ~ ( in @ SV16 @ SY116 )
| ~ ( empty @ SY117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(350,plain,
! [SV17: $i] :
( ( ! [SY118: $i] :
( ~ ( empty @ SY118 )
| ~ ( in @ SV17 @ SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(351,plain,
! [SV18: $i] :
( ( ~ ( empty @ SV18 )
| ( finite @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(352,plain,
! [SV19: $i] :
( ( ~ ( empty @ SV19 )
| ( relation @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(353,plain,
! [SV20: $i] :
( ( ~ ( top_str @ SV20 )
| ! [SY119: $i] :
( ~ ( element @ SY119 @ ( powerset @ ( the_carrier @ SV20 ) ) )
| ~ ( empty @ SY119 )
| ( boundary_set @ SY119 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(354,plain,
! [SV21: $i] :
( ( ~ ( top_str @ SV21 )
| ~ ( topological_space @ SV21 )
| ! [SY120: $i] :
( ~ ( element @ SY120 @ ( powerset @ ( the_carrier @ SV21 ) ) )
| ~ ( empty @ SY120 )
| ( nowhere_dense @ SY120 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(355,plain,
! [SV22: $i] :
( ( ! [SY121: $i] :
( ( empty_carrier @ SV22 )
| ~ ( topological_space @ SV22 )
| ~ ( top_str @ SV22 )
| ~ ( element @ SY121 @ ( the_carrier @ SV22 ) )
| ( element @ ( neighborhood_system @ SV22 @ SY121 ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV22 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(356,plain,
! [SV23: $i] :
( ( ~ ( one_sorted_str @ SV23 )
| ( element @ ( cast_as_carrier_subset @ SV23 ) @ ( powerset @ ( the_carrier @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(357,plain,
! [SV24: $i] :
( ( ~ ( rel_str @ SV24 )
| ( one_sorted_str @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(358,plain,
! [SV25: $i] :
( ( ! [SY122: $i] :
( ~ ( finite @ SV25 )
| ~ ( finite @ SY122 )
| ( finite @ ( cartesian_product2 @ SV25 @ SY122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(359,plain,
! [SV26: $i] :
( ( ~ ( empty @ ( powerset @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(360,plain,
! [SV27: $i] :
( ( ( empty_carrier @ SV27 )
| ~ ( one_sorted_str @ SV27 )
| ~ ( empty @ ( cast_as_carrier_subset @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(361,plain,
! [SV28: $i] :
( ( ( empty_carrier @ SV28 )
| ~ ( rel_str @ SV28 )
| ~ ( empty @ ( cast_as_carrier_subset @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(362,plain,
! [SV29: $i] :
( ( ! [SY123: $i] :
( ( empty @ SV29 )
| ( empty @ SY123 )
| ~ ( empty @ ( cartesian_product2 @ SV29 @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(363,plain,
! [SV30: $i] :
( ( subset @ SV30 @ SV30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(364,plain,
! [SV31: $i] :
( ( ~ ( empty @ SV31 )
| ( SV31 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(365,plain,
! [SV32: $i] :
( ( ! [SY124: $i] :
( ( SV32 = SY124 )
| ~ ( empty @ SV32 )
| ~ ( empty @ SY124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(366,plain,
( ( empty_carrier @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(367,plain,
( ( ~ ( one_sorted_str @ sK19_A )
| ~ ~ ( empty_carrier @ sK19_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(368,plain,
( ( ~ ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ~ ( topological_space @ SX0 )
| ( closed_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ~ ( topological_space @ SX0 )
| ( open_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(369,plain,
! [SV33: $i] :
( ( ( empty @ SV33 )
| ~ ( ~ ( element @ ( sK22_B @ SV33 ) @ ( powerset @ SV33 ) )
| ~ ~ ( empty @ ( sK22_B @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(370,plain,
! [SV34: $i] :
( ( ! [SY125: $i] :
( ~ ( ~ ( ~ ( in @ ( sK17_C @ SY125 @ SV34 ) @ SV34 )
| ~ ( in @ ( sK17_C @ SY125 @ SV34 ) @ SY125 ) )
| ~ ( ( in @ ( sK17_C @ SY125 @ SV34 ) @ SV34 )
| ( in @ ( sK17_C @ SY125 @ SV34 ) @ SY125 ) ) )
| ( SV34 = SY125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(371,plain,
! [SV35: $i] :
( ( ( empty_carrier @ SV35 )
| ~ ( one_sorted_str @ SV35 )
| ~ ( ~ ( element @ ( sK5_B @ SV35 ) @ ( powerset @ ( the_carrier @ SV35 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(372,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(373,plain,
! [SV36: $i] :
( ( ( empty @ SV36 )
| ~ ( ~ ~ ( ~ ( element @ ( sK6_B @ SV36 ) @ ( powerset @ SV36 ) )
| ~ ~ ( empty @ ( sK6_B @ SV36 ) ) )
| ~ ( finite @ ( sK6_B @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(374,plain,
! [SV37: $i] :
( ( ~ ( top_str @ SV37 )
| ~ ( topological_space @ SV37 )
| ~ ( ~ ( element @ ( sK21_B @ SV37 ) @ ( powerset @ ( the_carrier @ SV37 ) ) )
| ~ ( open_subset @ ( sK21_B @ SV37 ) @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(375,plain,
! [SV38: $i] :
( ( ~ ( one_sorted_str @ SV38 )
| ~ ( ~ ~ ( ~ ( element @ ( sK7_B @ SV38 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV38 ) ) ) )
| ~ ~ ( empty @ ( sK7_B @ SV38 ) ) )
| ~ ( finite @ ( sK7_B @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(376,plain,
! [SV39: $i] :
( ( ~ ( top_str @ SV39 )
| ~ ( topological_space @ SV39 )
| ~ ( ~ ! [SY126: $i] :
( ~ ( element @ SY126 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SY126 )
| ( closed_subset @ SY126 @ SV39 ) )
| ~ ! [SY127: $i] :
( ~ ( element @ SY127 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SY127 )
| ( open_subset @ SY127 @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(377,plain,
! [SV40: $i] :
( ( ~ ( ~ ! [SY128: $i,SY129: $i] :
( ( empty_carrier @ SY128 )
| ~ ( topological_space @ SY128 )
| ~ ( top_str @ SY128 )
| ~ ( element @ SY129 @ ( the_carrier @ SY128 ) )
| ! [SY130: $i] :
( ( SV40 != SY130 )
| ~ ( point_neighbourhood @ SY130 @ SY128 @ SY129 ) )
| ( in @ SV40 @ ( a_2_0_yellow19 @ SY128 @ SY129 ) ) )
| ~ ! [SY131: $i,SY132: $i] :
( ( empty_carrier @ SY131 )
| ~ ( topological_space @ SY131 )
| ~ ( top_str @ SY131 )
| ~ ( element @ SY132 @ ( the_carrier @ SY131 ) )
| ~ ( in @ SV40 @ ( a_2_0_yellow19 @ SY131 @ SY132 ) )
| ~ ( ( SV40
!= ( sK23_D @ SY132 @ SY131 @ SV40 ) )
| ~ ( point_neighbourhood @ ( sK23_D @ SY132 @ SY131 @ SV40 ) @ SY131 @ SY132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(378,plain,
! [SV41: $i] :
( ( ( empty @ SV41 )
| ~ ( ~ ~ ( ~ ( element @ ( sK9_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ~ ( empty @ ( sK9_B @ SV41 ) ) )
| ~ ( finite @ ( sK9_B @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(379,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_suprema_relstr @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_infima_relstr @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(380,plain,
! [SV42: $i] :
( ( ( empty_carrier @ SV42 )
| ~ ( topological_space @ SV42 )
| ~ ( top_str @ SV42 )
| ~ ( ~ ~ ( ~ ( element @ ( sK4_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) )
| ~ ~ ( empty @ ( sK4_B @ SV42 ) ) )
| ~ ( closed_subset @ ( sK4_B @ SV42 ) @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(381,plain,
( ( ~ ~ ( empty @ sK12_A )
| ~ ( relation @ sK12_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(382,plain,
( ( ~ ( element @ sK2_SY103 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( ~ ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ~ ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) )
| ~ ( ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(383,plain,
( ( ~ ~ ( empty @ sK14_A )
| ~ ( finite @ sK14_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(384,plain,
! [SV43: $i] :
( ( ~ ( top_str @ SV43 )
| ~ ( topological_space @ SV43 )
| ~ ( ~ ~ ( ~ ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
| ~ ( open_subset @ ( sK11_B @ SV43 ) @ SV43 ) )
| ~ ( closed_subset @ ( sK11_B @ SV43 ) @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(385,plain,
( ( ~ ( empty @ sK13_A )
| ~ ( relation @ sK13_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(386,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_suprema_relstr @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_suprema_relstr @ SX0 )
| ( directed_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(387,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_infima_relstr @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_infima_relstr @ SX0 )
| ( filtered_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(388,plain,
! [SV44: $i] :
( ( ~ ( ~ ( element @ ( sK20_B @ SV44 ) @ ( powerset @ SV44 ) )
| ~ ( empty @ ( sK20_B @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(389,plain,
! [SV45: $i] :
( ( ~ ( ~ ~ ( ~ ( element @ ( sK10_B @ SV45 ) @ ( powerset @ ( powerset @ SV45 ) ) )
| ~ ~ ( empty @ ( sK10_B @ SV45 ) ) )
| ~ ( finite @ ( sK10_B @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(390,plain,
! [SV46: $i] :
( ( ~ ( top_str @ SV46 )
| ~ ( topological_space @ SV46 )
| ~ ( ~ ( closed_subset @ ( sK18_B @ SV46 ) @ SV46 )
| ~ ( element @ ( sK18_B @ SV46 ) @ ( powerset @ ( the_carrier @ SV46 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(391,plain,
! [SV47: $i] :
( ( ( empty_carrier @ SV47 )
| ~ ( topological_space @ SV47 )
| ~ ( top_str @ SV47 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK8_B @ SV47 ) @ ( powerset @ ( the_carrier @ SV47 ) ) )
| ~ ~ ( empty @ ( sK8_B @ SV47 ) ) )
| ~ ( open_subset @ ( sK8_B @ SV47 ) @ SV47 ) )
| ~ ( closed_subset @ ( sK8_B @ SV47 ) @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(392,plain,
! [SV48: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV48 )
| ~ ( in @ SV48 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(393,plain,
! [SV2: $i] :
( ( ( ~ ( rel_str @ SV2 ) )
= $true )
| ( ( ~ ( with_suprema_relstr @ SV2 )
| ~ ( empty_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(394,plain,
! [SV3: $i] :
( ( ( ~ ( finite @ SV3 ) )
= $true )
| ( ( ! [SY107: $i] :
( ~ ( element @ SY107 @ ( powerset @ SV3 ) )
| ( finite @ SY107 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(395,plain,
! [SV4: $i] :
( ( ( ~ ( rel_str @ SV4 ) )
= $true )
| ( ( ~ ( with_infima_relstr @ SV4 )
| ~ ( empty_carrier @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(396,plain,
! [SV5: $i] :
( ( ( ( empty_carrier @ SV5 )
| ~ ( topological_space @ SV5 )
| ~ ( top_str @ SV5 ) )
= $true )
| ( ( ! [SY108: $i] :
( ~ ( element @ SY108 @ ( the_carrier @ SV5 ) )
| ( ( neighborhood_system @ SV5 @ SY108 )
= ( a_2_0_yellow19 @ SV5 @ SY108 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(397,plain,
! [SV6: $i] :
( ( ( ~ ( top_str @ SV6 ) )
= $true )
| ( ( one_sorted_str @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(398,plain,
! [SV49: $i,SV7: $i] :
( ( ( empty_carrier @ SV7 )
| ~ ( topological_space @ SV7 )
| ~ ( top_str @ SV7 )
| ~ ( element @ SV49 @ ( the_carrier @ SV7 ) )
| ! [SY133: $i] :
( ~ ( point_neighbourhood @ SY133 @ SV7 @ SV49 )
| ( element @ SY133 @ ( powerset @ ( the_carrier @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(399,plain,
! [SV50: $i,SV8: $i] :
( ( ( empty_carrier @ SV8 )
| ~ ( topological_space @ SV8 )
| ~ ( top_str @ SV8 )
| ~ ( element @ SV50 @ ( the_carrier @ SV8 ) )
| ( point_neighbourhood @ ( sK25_C @ SV50 @ SV8 ) @ SV8 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(400,plain,
! [SV10: $i] :
( ( ( ( empty_carrier @ SV10 )
| ~ ( one_sorted_str @ SV10 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(401,plain,
! [SV11: $i] :
( ( ( ~ ( top_str @ SV11 )
| ~ ( topological_space @ SV11 ) )
= $true )
| ( ( closed_subset @ ( cast_as_carrier_subset @ SV11 ) @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(402,plain,
! [SV12: $i] :
( ( ( ~ ( top_str @ SV12 ) )
= $true )
| ( ( dense @ ( cast_as_carrier_subset @ SV12 ) @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(403,plain,
! [SV51: $i,SV13: $i] :
( ( ~ ( in @ SV13 @ SV51 )
| ( element @ SV13 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(404,plain,
! [SV52: $i,SV14: $i] :
( ( ~ ( element @ SV14 @ SV52 )
| ( empty @ SV52 )
| ( in @ SV14 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(405,plain,
! [SV15: $i,SV53: $i] :
( ( ! [SY134: $i] :
( ~ ( element @ SV53 @ ( powerset @ SY134 ) )
| ~ ( in @ SV15 @ SV53 )
| ( element @ SV15 @ SY134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(406,plain,
! [SV16: $i,SV54: $i] :
( ( ! [SY135: $i] :
( ~ ( element @ SV54 @ ( powerset @ SY135 ) )
| ~ ( in @ SV16 @ SV54 )
| ~ ( empty @ SY135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(407,plain,
! [SV17: $i,SV55: $i] :
( ( ~ ( empty @ SV55 )
| ~ ( in @ SV17 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(408,plain,
! [SV18: $i] :
( ( ( ~ ( empty @ SV18 ) )
= $true )
| ( ( finite @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(409,plain,
! [SV19: $i] :
( ( ( ~ ( empty @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(410,plain,
! [SV20: $i] :
( ( ( ~ ( top_str @ SV20 ) )
= $true )
| ( ( ! [SY119: $i] :
( ~ ( element @ SY119 @ ( powerset @ ( the_carrier @ SV20 ) ) )
| ~ ( empty @ SY119 )
| ( boundary_set @ SY119 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(411,plain,
! [SV21: $i] :
( ( ( ~ ( top_str @ SV21 )
| ~ ( topological_space @ SV21 ) )
= $true )
| ( ( ! [SY120: $i] :
( ~ ( element @ SY120 @ ( powerset @ ( the_carrier @ SV21 ) ) )
| ~ ( empty @ SY120 )
| ( nowhere_dense @ SY120 @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(412,plain,
! [SV56: $i,SV22: $i] :
( ( ( empty_carrier @ SV22 )
| ~ ( topological_space @ SV22 )
| ~ ( top_str @ SV22 )
| ~ ( element @ SV56 @ ( the_carrier @ SV22 ) )
| ( element @ ( neighborhood_system @ SV22 @ SV56 ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV22 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(413,plain,
! [SV23: $i] :
( ( ( ~ ( one_sorted_str @ SV23 ) )
= $true )
| ( ( element @ ( cast_as_carrier_subset @ SV23 ) @ ( powerset @ ( the_carrier @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(414,plain,
! [SV24: $i] :
( ( ( ~ ( rel_str @ SV24 ) )
= $true )
| ( ( one_sorted_str @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(415,plain,
! [SV57: $i,SV25: $i] :
( ( ~ ( finite @ SV25 )
| ~ ( finite @ SV57 )
| ( finite @ ( cartesian_product2 @ SV25 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(416,plain,
! [SV26: $i] :
( ( empty @ ( powerset @ SV26 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(417,plain,
! [SV27: $i] :
( ( ( ( empty_carrier @ SV27 )
| ~ ( one_sorted_str @ SV27 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(418,plain,
! [SV28: $i] :
( ( ( ( empty_carrier @ SV28 )
| ~ ( rel_str @ SV28 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(419,plain,
! [SV58: $i,SV29: $i] :
( ( ( empty @ SV29 )
| ( empty @ SV58 )
| ~ ( empty @ ( cartesian_product2 @ SV29 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(420,plain,
! [SV31: $i] :
( ( ( ~ ( empty @ SV31 ) )
= $true )
| ( ( SV31 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(421,plain,
! [SV59: $i,SV32: $i] :
( ( ( SV32 = SV59 )
| ~ ( empty @ SV32 )
| ~ ( empty @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(422,plain,
( ( ~ ( one_sorted_str @ sK19_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[367]) ).
thf(423,plain,
( ( ~ ~ ( empty_carrier @ sK19_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[367]) ).
thf(424,plain,
( ( ~ ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ~ ( topological_space @ SX0 )
| ( closed_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(425,plain,
( ( ~ ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ~ ( topological_space @ SX0 )
| ( open_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(426,plain,
! [SV33: $i] :
( ( ( empty @ SV33 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK22_B @ SV33 ) @ ( powerset @ SV33 ) )
| ~ ~ ( empty @ ( sK22_B @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(427,plain,
! [SV34: $i,SV60: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV34 )
| ~ ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV60 ) )
| ~ ( ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV34 )
| ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV60 ) ) )
| ( SV34 = SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(428,plain,
! [SV35: $i] :
( ( ( ( empty_carrier @ SV35 )
| ~ ( one_sorted_str @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK5_B @ SV35 ) @ ( powerset @ ( the_carrier @ SV35 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV35 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(429,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(430,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(431,plain,
! [SV36: $i] :
( ( ( empty @ SV36 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK6_B @ SV36 ) @ ( powerset @ SV36 ) )
| ~ ~ ( empty @ ( sK6_B @ SV36 ) ) )
| ~ ( finite @ ( sK6_B @ SV36 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(432,plain,
! [SV37: $i] :
( ( ( ~ ( top_str @ SV37 )
| ~ ( topological_space @ SV37 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK21_B @ SV37 ) @ ( powerset @ ( the_carrier @ SV37 ) ) )
| ~ ( open_subset @ ( sK21_B @ SV37 ) @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(433,plain,
! [SV38: $i] :
( ( ( ~ ( one_sorted_str @ SV38 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK7_B @ SV38 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV38 ) ) ) )
| ~ ~ ( empty @ ( sK7_B @ SV38 ) ) )
| ~ ( finite @ ( sK7_B @ SV38 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(434,plain,
! [SV39: $i] :
( ( ( ~ ( top_str @ SV39 )
| ~ ( topological_space @ SV39 ) )
= $true )
| ( ( ~ ( ~ ! [SY126: $i] :
( ~ ( element @ SY126 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SY126 )
| ( closed_subset @ SY126 @ SV39 ) )
| ~ ! [SY127: $i] :
( ~ ( element @ SY127 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SY127 )
| ( open_subset @ SY127 @ SV39 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(435,plain,
! [SV40: $i] :
( ( ~ ! [SY128: $i,SY129: $i] :
( ( empty_carrier @ SY128 )
| ~ ( topological_space @ SY128 )
| ~ ( top_str @ SY128 )
| ~ ( element @ SY129 @ ( the_carrier @ SY128 ) )
| ! [SY130: $i] :
( ( SV40 != SY130 )
| ~ ( point_neighbourhood @ SY130 @ SY128 @ SY129 ) )
| ( in @ SV40 @ ( a_2_0_yellow19 @ SY128 @ SY129 ) ) )
| ~ ! [SY131: $i,SY132: $i] :
( ( empty_carrier @ SY131 )
| ~ ( topological_space @ SY131 )
| ~ ( top_str @ SY131 )
| ~ ( element @ SY132 @ ( the_carrier @ SY131 ) )
| ~ ( in @ SV40 @ ( a_2_0_yellow19 @ SY131 @ SY132 ) )
| ~ ( ( SV40
!= ( sK23_D @ SY132 @ SY131 @ SV40 ) )
| ~ ( point_neighbourhood @ ( sK23_D @ SY132 @ SY131 @ SV40 ) @ SY131 @ SY132 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(436,plain,
! [SV41: $i] :
( ( ( empty @ SV41 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK9_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ~ ( empty @ ( sK9_B @ SV41 ) ) )
| ~ ( finite @ ( sK9_B @ SV41 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(437,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_suprema_relstr @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(438,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_infima_relstr @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(439,plain,
! [SV42: $i] :
( ( ( ( empty_carrier @ SV42 )
| ~ ( topological_space @ SV42 )
| ~ ( top_str @ SV42 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK4_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) )
| ~ ~ ( empty @ ( sK4_B @ SV42 ) ) )
| ~ ( closed_subset @ ( sK4_B @ SV42 ) @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(440,plain,
( ( ~ ~ ( empty @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(441,plain,
( ( ~ ( relation @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(442,plain,
( ( ~ ( element @ sK2_SY103 @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[382]) ).
thf(443,plain,
( ( ~ ~ ( ~ ( ~ ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ~ ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) )
| ~ ( ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[382]) ).
thf(444,plain,
( ( ~ ~ ( empty @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[383]) ).
thf(445,plain,
( ( ~ ( finite @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[383]) ).
thf(446,plain,
! [SV43: $i] :
( ( ( ~ ( top_str @ SV43 )
| ~ ( topological_space @ SV43 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
| ~ ( open_subset @ ( sK11_B @ SV43 ) @ SV43 ) )
| ~ ( closed_subset @ ( sK11_B @ SV43 ) @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(447,plain,
( ( ~ ( empty @ sK13_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(448,plain,
( ( ~ ( relation @ sK13_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(449,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_suprema_relstr @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(450,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_suprema_relstr @ SX0 )
| ( directed_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(451,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_infima_relstr @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[387]) ).
thf(452,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_infima_relstr @ SX0 )
| ( filtered_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[387]) ).
thf(453,plain,
! [SV44: $i] :
( ( ~ ( element @ ( sK20_B @ SV44 ) @ ( powerset @ SV44 ) )
| ~ ( empty @ ( sK20_B @ SV44 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(454,plain,
! [SV45: $i] :
( ( ~ ~ ( ~ ( element @ ( sK10_B @ SV45 ) @ ( powerset @ ( powerset @ SV45 ) ) )
| ~ ~ ( empty @ ( sK10_B @ SV45 ) ) )
| ~ ( finite @ ( sK10_B @ SV45 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(455,plain,
! [SV46: $i] :
( ( ( ~ ( top_str @ SV46 )
| ~ ( topological_space @ SV46 ) )
= $true )
| ( ( ~ ( ~ ( closed_subset @ ( sK18_B @ SV46 ) @ SV46 )
| ~ ( element @ ( sK18_B @ SV46 ) @ ( powerset @ ( the_carrier @ SV46 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[390]) ).
thf(456,plain,
! [SV47: $i] :
( ( ( ( empty_carrier @ SV47 )
| ~ ( topological_space @ SV47 )
| ~ ( top_str @ SV47 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK8_B @ SV47 ) @ ( powerset @ ( the_carrier @ SV47 ) ) )
| ~ ~ ( empty @ ( sK8_B @ SV47 ) ) )
| ~ ( open_subset @ ( sK8_B @ SV47 ) @ SV47 ) )
| ~ ( closed_subset @ ( sK8_B @ SV47 ) @ SV47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(457,plain,
! [SV48: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV48 ) )
= $true )
| ( ( ~ ( in @ SV48 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(458,plain,
! [SV2: $i] :
( ( ( rel_str @ SV2 )
= $false )
| ( ( ~ ( with_suprema_relstr @ SV2 )
| ~ ( empty_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(459,plain,
! [SV3: $i] :
( ( ( finite @ SV3 )
= $false )
| ( ( ! [SY107: $i] :
( ~ ( element @ SY107 @ ( powerset @ SV3 ) )
| ( finite @ SY107 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(460,plain,
! [SV4: $i] :
( ( ( rel_str @ SV4 )
= $false )
| ( ( ~ ( with_infima_relstr @ SV4 )
| ~ ( empty_carrier @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(461,plain,
! [SV5: $i] :
( ( ( ( empty_carrier @ SV5 )
| ~ ( topological_space @ SV5 ) )
= $true )
| ( ( ~ ( top_str @ SV5 ) )
= $true )
| ( ( ! [SY108: $i] :
( ~ ( element @ SY108 @ ( the_carrier @ SV5 ) )
| ( ( neighborhood_system @ SV5 @ SY108 )
= ( a_2_0_yellow19 @ SV5 @ SY108 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(462,plain,
! [SV6: $i] :
( ( ( top_str @ SV6 )
= $false )
| ( ( one_sorted_str @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(463,plain,
! [SV49: $i,SV7: $i] :
( ( ( ( empty_carrier @ SV7 )
| ~ ( topological_space @ SV7 )
| ~ ( top_str @ SV7 )
| ~ ( element @ SV49 @ ( the_carrier @ SV7 ) ) )
= $true )
| ( ( ! [SY133: $i] :
( ~ ( point_neighbourhood @ SY133 @ SV7 @ SV49 )
| ( element @ SY133 @ ( powerset @ ( the_carrier @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(464,plain,
! [SV50: $i,SV8: $i] :
( ( ( ( empty_carrier @ SV8 )
| ~ ( topological_space @ SV8 )
| ~ ( top_str @ SV8 )
| ~ ( element @ SV50 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( point_neighbourhood @ ( sK25_C @ SV50 @ SV8 ) @ SV8 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(465,plain,
! [SV10: $i] :
( ( ( empty_carrier @ SV10 )
= $true )
| ( ( ~ ( one_sorted_str @ SV10 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(466,plain,
! [SV11: $i] :
( ( ( ~ ( top_str @ SV11 ) )
= $true )
| ( ( ~ ( topological_space @ SV11 ) )
= $true )
| ( ( closed_subset @ ( cast_as_carrier_subset @ SV11 ) @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(467,plain,
! [SV12: $i] :
( ( ( top_str @ SV12 )
= $false )
| ( ( dense @ ( cast_as_carrier_subset @ SV12 ) @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(468,plain,
! [SV51: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV51 ) )
= $true )
| ( ( element @ SV13 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(469,plain,
! [SV52: $i,SV14: $i] :
( ( ( ~ ( element @ SV14 @ SV52 ) )
= $true )
| ( ( ( empty @ SV52 )
| ( in @ SV14 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(470,plain,
! [SV15: $i,SV61: $i,SV53: $i] :
( ( ~ ( element @ SV53 @ ( powerset @ SV61 ) )
| ~ ( in @ SV15 @ SV53 )
| ( element @ SV15 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(471,plain,
! [SV16: $i,SV62: $i,SV54: $i] :
( ( ~ ( element @ SV54 @ ( powerset @ SV62 ) )
| ~ ( in @ SV16 @ SV54 )
| ~ ( empty @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(472,plain,
! [SV17: $i,SV55: $i] :
( ( ( ~ ( empty @ SV55 ) )
= $true )
| ( ( ~ ( in @ SV17 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(473,plain,
! [SV18: $i] :
( ( ( empty @ SV18 )
= $false )
| ( ( finite @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(474,plain,
! [SV19: $i] :
( ( ( empty @ SV19 )
= $false )
| ( ( relation @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(475,plain,
! [SV20: $i] :
( ( ( top_str @ SV20 )
= $false )
| ( ( ! [SY119: $i] :
( ~ ( element @ SY119 @ ( powerset @ ( the_carrier @ SV20 ) ) )
| ~ ( empty @ SY119 )
| ( boundary_set @ SY119 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(476,plain,
! [SV21: $i] :
( ( ( ~ ( top_str @ SV21 ) )
= $true )
| ( ( ~ ( topological_space @ SV21 ) )
= $true )
| ( ( ! [SY120: $i] :
( ~ ( element @ SY120 @ ( powerset @ ( the_carrier @ SV21 ) ) )
| ~ ( empty @ SY120 )
| ( nowhere_dense @ SY120 @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(477,plain,
! [SV56: $i,SV22: $i] :
( ( ( ( empty_carrier @ SV22 )
| ~ ( topological_space @ SV22 )
| ~ ( top_str @ SV22 )
| ~ ( element @ SV56 @ ( the_carrier @ SV22 ) ) )
= $true )
| ( ( element @ ( neighborhood_system @ SV22 @ SV56 ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(478,plain,
! [SV23: $i] :
( ( ( one_sorted_str @ SV23 )
= $false )
| ( ( element @ ( cast_as_carrier_subset @ SV23 ) @ ( powerset @ ( the_carrier @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(479,plain,
! [SV24: $i] :
( ( ( rel_str @ SV24 )
= $false )
| ( ( one_sorted_str @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(480,plain,
! [SV57: $i,SV25: $i] :
( ( ( ~ ( finite @ SV25 )
| ~ ( finite @ SV57 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV25 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(481,plain,
! [SV27: $i] :
( ( ( empty_carrier @ SV27 )
= $true )
| ( ( ~ ( one_sorted_str @ SV27 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(482,plain,
! [SV28: $i] :
( ( ( empty_carrier @ SV28 )
= $true )
| ( ( ~ ( rel_str @ SV28 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(483,plain,
! [SV58: $i,SV29: $i] :
( ( ( ( empty @ SV29 )
| ( empty @ SV58 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV29 @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(484,plain,
! [SV31: $i] :
( ( ( empty @ SV31 )
= $false )
| ( ( SV31 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(485,plain,
! [SV59: $i,SV32: $i] :
( ( ( ( SV32 = SV59 )
| ~ ( empty @ SV32 ) )
= $true )
| ( ( ~ ( empty @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(486,plain,
( ( one_sorted_str @ sK19_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(487,plain,
( ( ~ ( empty_carrier @ sK19_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(488,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ~ ( topological_space @ SX0 )
| ( closed_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[424]) ).
thf(489,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ~ ( topological_space @ SX0 )
| ( open_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[425]) ).
thf(490,plain,
! [SV33: $i] :
( ( ( ~ ( element @ ( sK22_B @ SV33 ) @ ( powerset @ SV33 ) )
| ~ ~ ( empty @ ( sK22_B @ SV33 ) ) )
= $false )
| ( ( empty @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(491,plain,
! [SV34: $i,SV60: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV34 )
| ~ ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV60 ) )
| ~ ( ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV34 )
| ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV60 ) ) ) )
= $true )
| ( ( SV34 = SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(492,plain,
! [SV35: $i] :
( ( ( empty_carrier @ SV35 )
= $true )
| ( ( ~ ( one_sorted_str @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK5_B @ SV35 ) @ ( powerset @ ( the_carrier @ SV35 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV35 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(493,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[429]) ).
thf(494,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(495,plain,
! [SV36: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK6_B @ SV36 ) @ ( powerset @ SV36 ) )
| ~ ~ ( empty @ ( sK6_B @ SV36 ) ) )
| ~ ( finite @ ( sK6_B @ SV36 ) ) )
= $false )
| ( ( empty @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(496,plain,
! [SV37: $i] :
( ( ( ~ ( top_str @ SV37 ) )
= $true )
| ( ( ~ ( topological_space @ SV37 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK21_B @ SV37 ) @ ( powerset @ ( the_carrier @ SV37 ) ) )
| ~ ( open_subset @ ( sK21_B @ SV37 ) @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(497,plain,
! [SV38: $i] :
( ( ( one_sorted_str @ SV38 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK7_B @ SV38 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV38 ) ) ) )
| ~ ~ ( empty @ ( sK7_B @ SV38 ) ) )
| ~ ( finite @ ( sK7_B @ SV38 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(498,plain,
! [SV39: $i] :
( ( ( ~ ( top_str @ SV39 ) )
= $true )
| ( ( ~ ( topological_space @ SV39 ) )
= $true )
| ( ( ~ ( ~ ! [SY126: $i] :
( ~ ( element @ SY126 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SY126 )
| ( closed_subset @ SY126 @ SV39 ) )
| ~ ! [SY127: $i] :
( ~ ( element @ SY127 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SY127 )
| ( open_subset @ SY127 @ SV39 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(499,plain,
! [SV40: $i] :
( ( ~ ! [SY128: $i,SY129: $i] :
( ( empty_carrier @ SY128 )
| ~ ( topological_space @ SY128 )
| ~ ( top_str @ SY128 )
| ~ ( element @ SY129 @ ( the_carrier @ SY128 ) )
| ! [SY130: $i] :
( ( SV40 != SY130 )
| ~ ( point_neighbourhood @ SY130 @ SY128 @ SY129 ) )
| ( in @ SV40 @ ( a_2_0_yellow19 @ SY128 @ SY129 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(500,plain,
! [SV40: $i] :
( ( ~ ! [SY131: $i,SY132: $i] :
( ( empty_carrier @ SY131 )
| ~ ( topological_space @ SY131 )
| ~ ( top_str @ SY131 )
| ~ ( element @ SY132 @ ( the_carrier @ SY131 ) )
| ~ ( in @ SV40 @ ( a_2_0_yellow19 @ SY131 @ SY132 ) )
| ~ ( ( SV40
!= ( sK23_D @ SY132 @ SY131 @ SV40 ) )
| ~ ( point_neighbourhood @ ( sK23_D @ SY132 @ SY131 @ SV40 ) @ SY131 @ SY132 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(501,plain,
! [SV41: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ~ ( empty @ ( sK9_B @ SV41 ) ) )
| ~ ( finite @ ( sK9_B @ SV41 ) ) )
= $false )
| ( ( empty @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(502,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_suprema_relstr @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(503,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_infima_relstr @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(504,plain,
! [SV42: $i] :
( ( ( ( empty_carrier @ SV42 )
| ~ ( topological_space @ SV42 ) )
= $true )
| ( ( ~ ( top_str @ SV42 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK4_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) )
| ~ ~ ( empty @ ( sK4_B @ SV42 ) ) )
| ~ ( closed_subset @ ( sK4_B @ SV42 ) @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(505,plain,
( ( ~ ( empty @ sK12_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(506,plain,
( ( relation @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(507,plain,
( ( element @ sK2_SY103 @ ( the_carrier @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(508,plain,
( ( ~ ( ~ ( ~ ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ~ ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) )
| ~ ( ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(509,plain,
( ( ~ ( empty @ sK14_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(510,plain,
( ( finite @ sK14_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(511,plain,
! [SV43: $i] :
( ( ( ~ ( top_str @ SV43 ) )
= $true )
| ( ( ~ ( topological_space @ SV43 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
| ~ ( open_subset @ ( sK11_B @ SV43 ) @ SV43 ) )
| ~ ( closed_subset @ ( sK11_B @ SV43 ) @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(512,plain,
( ( empty @ sK13_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(513,plain,
( ( relation @ sK13_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(514,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_suprema_relstr @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(515,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_suprema_relstr @ SX0 )
| ( directed_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(516,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_infima_relstr @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(517,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_infima_relstr @ SX0 )
| ( filtered_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(518,plain,
! [SV44: $i] :
( ( ~ ( element @ ( sK20_B @ SV44 ) @ ( powerset @ SV44 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(519,plain,
! [SV44: $i] :
( ( ~ ( empty @ ( sK20_B @ SV44 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(520,plain,
! [SV45: $i] :
( ( ~ ~ ( ~ ( element @ ( sK10_B @ SV45 ) @ ( powerset @ ( powerset @ SV45 ) ) )
| ~ ~ ( empty @ ( sK10_B @ SV45 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(521,plain,
! [SV45: $i] :
( ( ~ ( finite @ ( sK10_B @ SV45 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(522,plain,
! [SV46: $i] :
( ( ( ~ ( top_str @ SV46 ) )
= $true )
| ( ( ~ ( topological_space @ SV46 ) )
= $true )
| ( ( ~ ( ~ ( closed_subset @ ( sK18_B @ SV46 ) @ SV46 )
| ~ ( element @ ( sK18_B @ SV46 ) @ ( powerset @ ( the_carrier @ SV46 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(523,plain,
! [SV47: $i] :
( ( ( ( empty_carrier @ SV47 )
| ~ ( topological_space @ SV47 ) )
= $true )
| ( ( ~ ( top_str @ SV47 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK8_B @ SV47 ) @ ( powerset @ ( the_carrier @ SV47 ) ) )
| ~ ~ ( empty @ ( sK8_B @ SV47 ) ) )
| ~ ( open_subset @ ( sK8_B @ SV47 ) @ SV47 ) )
| ~ ( closed_subset @ ( sK8_B @ SV47 ) @ SV47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(524,plain,
! [SV48: $i,SV1: $i] :
( ( ( in @ SV1 @ SV48 )
= $false )
| ( ( ~ ( in @ SV48 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(525,plain,
! [SV2: $i] :
( ( ( ~ ( with_suprema_relstr @ SV2 ) )
= $true )
| ( ( ~ ( empty_carrier @ SV2 ) )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(526,plain,
! [SV3: $i,SV63: $i] :
( ( ( ~ ( element @ SV63 @ ( powerset @ SV3 ) )
| ( finite @ SV63 ) )
= $true )
| ( ( finite @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(527,plain,
! [SV4: $i] :
( ( ( ~ ( with_infima_relstr @ SV4 ) )
= $true )
| ( ( ~ ( empty_carrier @ SV4 ) )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(528,plain,
! [SV5: $i] :
( ( ( empty_carrier @ SV5 )
= $true )
| ( ( ~ ( topological_space @ SV5 ) )
= $true )
| ( ( ~ ( top_str @ SV5 ) )
= $true )
| ( ( ! [SY108: $i] :
( ~ ( element @ SY108 @ ( the_carrier @ SV5 ) )
| ( ( neighborhood_system @ SV5 @ SY108 )
= ( a_2_0_yellow19 @ SV5 @ SY108 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(529,plain,
! [SV49: $i,SV7: $i] :
( ( ( ( empty_carrier @ SV7 )
| ~ ( topological_space @ SV7 )
| ~ ( top_str @ SV7 ) )
= $true )
| ( ( ~ ( element @ SV49 @ ( the_carrier @ SV7 ) ) )
= $true )
| ( ( ! [SY133: $i] :
( ~ ( point_neighbourhood @ SY133 @ SV7 @ SV49 )
| ( element @ SY133 @ ( powerset @ ( the_carrier @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(530,plain,
! [SV50: $i,SV8: $i] :
( ( ( ( empty_carrier @ SV8 )
| ~ ( topological_space @ SV8 )
| ~ ( top_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV50 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( point_neighbourhood @ ( sK25_C @ SV50 @ SV8 ) @ SV8 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(531,plain,
! [SV10: $i] :
( ( ( one_sorted_str @ SV10 )
= $false )
| ( ( empty_carrier @ SV10 )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(532,plain,
! [SV11: $i] :
( ( ( top_str @ SV11 )
= $false )
| ( ( ~ ( topological_space @ SV11 ) )
= $true )
| ( ( closed_subset @ ( cast_as_carrier_subset @ SV11 ) @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(533,plain,
! [SV51: $i,SV13: $i] :
( ( ( in @ SV13 @ SV51 )
= $false )
| ( ( element @ SV13 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(534,plain,
! [SV52: $i,SV14: $i] :
( ( ( element @ SV14 @ SV52 )
= $false )
| ( ( ( empty @ SV52 )
| ( in @ SV14 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(535,plain,
! [SV15: $i,SV61: $i,SV53: $i] :
( ( ( ~ ( element @ SV53 @ ( powerset @ SV61 ) )
| ~ ( in @ SV15 @ SV53 ) )
= $true )
| ( ( element @ SV15 @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(536,plain,
! [SV16: $i,SV62: $i,SV54: $i] :
( ( ( ~ ( element @ SV54 @ ( powerset @ SV62 ) )
| ~ ( in @ SV16 @ SV54 ) )
= $true )
| ( ( ~ ( empty @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(537,plain,
! [SV17: $i,SV55: $i] :
( ( ( empty @ SV55 )
= $false )
| ( ( ~ ( in @ SV17 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(538,plain,
! [SV20: $i,SV64: $i] :
( ( ( ~ ( element @ SV64 @ ( powerset @ ( the_carrier @ SV20 ) ) )
| ~ ( empty @ SV64 )
| ( boundary_set @ SV64 @ SV20 ) )
= $true )
| ( ( top_str @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(539,plain,
! [SV21: $i] :
( ( ( top_str @ SV21 )
= $false )
| ( ( ~ ( topological_space @ SV21 ) )
= $true )
| ( ( ! [SY120: $i] :
( ~ ( element @ SY120 @ ( powerset @ ( the_carrier @ SV21 ) ) )
| ~ ( empty @ SY120 )
| ( nowhere_dense @ SY120 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(540,plain,
! [SV56: $i,SV22: $i] :
( ( ( ( empty_carrier @ SV22 )
| ~ ( topological_space @ SV22 )
| ~ ( top_str @ SV22 ) )
= $true )
| ( ( ~ ( element @ SV56 @ ( the_carrier @ SV22 ) ) )
= $true )
| ( ( element @ ( neighborhood_system @ SV22 @ SV56 ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(541,plain,
! [SV57: $i,SV25: $i] :
( ( ( ~ ( finite @ SV25 ) )
= $true )
| ( ( ~ ( finite @ SV57 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV25 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(542,plain,
! [SV27: $i] :
( ( ( one_sorted_str @ SV27 )
= $false )
| ( ( empty_carrier @ SV27 )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(543,plain,
! [SV28: $i] :
( ( ( rel_str @ SV28 )
= $false )
| ( ( empty_carrier @ SV28 )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(544,plain,
! [SV58: $i,SV29: $i] :
( ( ( empty @ SV29 )
= $true )
| ( ( empty @ SV58 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV29 @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(545,plain,
! [SV59: $i,SV32: $i] :
( ( ( SV32 = SV59 )
= $true )
| ( ( ~ ( empty @ SV32 ) )
= $true )
| ( ( ~ ( empty @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(546,plain,
( ( empty_carrier @ sK19_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(547,plain,
! [SV65: $i] :
( ( ~ ( top_str @ SV65 )
| ~ ( topological_space @ SV65 )
| ( closed_subset @ ( cast_as_carrier_subset @ SV65 ) @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(548,plain,
! [SV66: $i] :
( ( ~ ( top_str @ SV66 )
| ~ ( topological_space @ SV66 )
| ( open_subset @ ( cast_as_carrier_subset @ SV66 ) @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(549,plain,
! [SV33: $i] :
( ( ( ~ ( element @ ( sK22_B @ SV33 ) @ ( powerset @ SV33 ) ) )
= $false )
| ( ( empty @ SV33 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(550,plain,
! [SV33: $i] :
( ( ( ~ ~ ( empty @ ( sK22_B @ SV33 ) ) )
= $false )
| ( ( empty @ SV33 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(551,plain,
! [SV34: $i,SV60: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV34 )
| ~ ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV60 ) )
| ~ ( ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV34 )
| ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV60 ) ) )
= $false )
| ( ( SV34 = SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(552,plain,
! [SV35: $i] :
( ( ( one_sorted_str @ SV35 )
= $false )
| ( ( empty_carrier @ SV35 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK5_B @ SV35 ) @ ( powerset @ ( the_carrier @ SV35 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV35 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(553,plain,
! [SV67: $i] :
( ( ! [SY136: $i] :
( ~ ( element @ SV67 @ ( powerset @ SY136 ) )
| ( subset @ SV67 @ SY136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(554,plain,
! [SV68: $i] :
( ( ! [SY137: $i] :
( ~ ( subset @ SV68 @ SY137 )
| ( element @ SV68 @ ( powerset @ SY137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(555,plain,
! [SV36: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK6_B @ SV36 ) @ ( powerset @ SV36 ) )
| ~ ~ ( empty @ ( sK6_B @ SV36 ) ) ) )
= $false )
| ( ( empty @ SV36 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(556,plain,
! [SV36: $i] :
( ( ( ~ ( finite @ ( sK6_B @ SV36 ) ) )
= $false )
| ( ( empty @ SV36 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(557,plain,
! [SV37: $i] :
( ( ( top_str @ SV37 )
= $false )
| ( ( ~ ( topological_space @ SV37 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK21_B @ SV37 ) @ ( powerset @ ( the_carrier @ SV37 ) ) )
| ~ ( open_subset @ ( sK21_B @ SV37 ) @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(558,plain,
! [SV38: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_B @ SV38 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV38 ) ) ) )
| ~ ~ ( empty @ ( sK7_B @ SV38 ) ) )
| ~ ( finite @ ( sK7_B @ SV38 ) ) )
= $false )
| ( ( one_sorted_str @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(559,plain,
! [SV39: $i] :
( ( ( top_str @ SV39 )
= $false )
| ( ( ~ ( topological_space @ SV39 ) )
= $true )
| ( ( ~ ( ~ ! [SY126: $i] :
( ~ ( element @ SY126 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SY126 )
| ( closed_subset @ SY126 @ SV39 ) )
| ~ ! [SY127: $i] :
( ~ ( element @ SY127 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SY127 )
| ( open_subset @ SY127 @ SV39 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(560,plain,
! [SV40: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ( empty_carrier @ SY128 )
| ~ ( topological_space @ SY128 )
| ~ ( top_str @ SY128 )
| ~ ( element @ SY129 @ ( the_carrier @ SY128 ) )
| ! [SY130: $i] :
( ( SV40 != SY130 )
| ~ ( point_neighbourhood @ SY130 @ SY128 @ SY129 ) )
| ( in @ SV40 @ ( a_2_0_yellow19 @ SY128 @ SY129 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(561,plain,
! [SV40: $i] :
( ( ! [SY131: $i,SY132: $i] :
( ( empty_carrier @ SY131 )
| ~ ( topological_space @ SY131 )
| ~ ( top_str @ SY131 )
| ~ ( element @ SY132 @ ( the_carrier @ SY131 ) )
| ~ ( in @ SV40 @ ( a_2_0_yellow19 @ SY131 @ SY132 ) )
| ~ ( ( SV40
!= ( sK23_D @ SY132 @ SY131 @ SV40 ) )
| ~ ( point_neighbourhood @ ( sK23_D @ SY132 @ SY131 @ SV40 ) @ SY131 @ SY132 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(562,plain,
! [SV41: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ~ ( empty @ ( sK9_B @ SV41 ) ) ) )
= $false )
| ( ( empty @ SV41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(563,plain,
! [SV41: $i] :
( ( ( ~ ( finite @ ( sK9_B @ SV41 ) ) )
= $false )
| ( ( empty @ SV41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(564,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_suprema_relstr @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(565,plain,
! [SV69: $i] :
( ( ~ ( rel_str @ SV69 )
| ( empty_carrier @ SV69 )
| ~ ( complete_relstr @ SV69 )
| ( with_infima_relstr @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(566,plain,
! [SV42: $i] :
( ( ( empty_carrier @ SV42 )
= $true )
| ( ( ~ ( topological_space @ SV42 ) )
= $true )
| ( ( ~ ( top_str @ SV42 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK4_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) )
| ~ ~ ( empty @ ( sK4_B @ SV42 ) ) )
| ~ ( closed_subset @ ( sK4_B @ SV42 ) @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(567,plain,
( ( empty @ sK12_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(568,plain,
( ( ~ ( ~ ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ~ ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) )
| ~ ( ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(569,plain,
( ( empty @ sK14_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(570,plain,
! [SV43: $i] :
( ( ( top_str @ SV43 )
= $false )
| ( ( ~ ( topological_space @ SV43 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
| ~ ( open_subset @ ( sK11_B @ SV43 ) @ SV43 ) )
| ~ ( closed_subset @ ( sK11_B @ SV43 ) @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(571,plain,
! [SV70: $i] :
( ( ~ ( rel_str @ SV70 )
| ~ ( with_suprema_relstr @ SV70 )
| ~ ( empty @ ( cast_as_carrier_subset @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(572,plain,
! [SV71: $i] :
( ( ~ ( rel_str @ SV71 )
| ~ ( with_suprema_relstr @ SV71 )
| ( directed_subset @ ( cast_as_carrier_subset @ SV71 ) @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(573,plain,
! [SV72: $i] :
( ( ~ ( rel_str @ SV72 )
| ~ ( with_infima_relstr @ SV72 )
| ~ ( empty @ ( cast_as_carrier_subset @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(574,plain,
! [SV73: $i] :
( ( ~ ( rel_str @ SV73 )
| ~ ( with_infima_relstr @ SV73 )
| ( filtered_subset @ ( cast_as_carrier_subset @ SV73 ) @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(575,plain,
! [SV44: $i] :
( ( element @ ( sK20_B @ SV44 ) @ ( powerset @ SV44 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(576,plain,
! [SV44: $i] :
( ( empty @ ( sK20_B @ SV44 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(577,plain,
! [SV45: $i] :
( ( ~ ( ~ ( element @ ( sK10_B @ SV45 ) @ ( powerset @ ( powerset @ SV45 ) ) )
| ~ ~ ( empty @ ( sK10_B @ SV45 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(578,plain,
! [SV45: $i] :
( ( finite @ ( sK10_B @ SV45 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(579,plain,
! [SV46: $i] :
( ( ( top_str @ SV46 )
= $false )
| ( ( ~ ( topological_space @ SV46 ) )
= $true )
| ( ( ~ ( ~ ( closed_subset @ ( sK18_B @ SV46 ) @ SV46 )
| ~ ( element @ ( sK18_B @ SV46 ) @ ( powerset @ ( the_carrier @ SV46 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(580,plain,
! [SV47: $i] :
( ( ( empty_carrier @ SV47 )
= $true )
| ( ( ~ ( topological_space @ SV47 ) )
= $true )
| ( ( ~ ( top_str @ SV47 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK8_B @ SV47 ) @ ( powerset @ ( the_carrier @ SV47 ) ) )
| ~ ~ ( empty @ ( sK8_B @ SV47 ) ) )
| ~ ( open_subset @ ( sK8_B @ SV47 ) @ SV47 ) )
| ~ ( closed_subset @ ( sK8_B @ SV47 ) @ SV47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(581,plain,
! [SV1: $i,SV48: $i] :
( ( ( in @ SV48 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(582,plain,
! [SV2: $i] :
( ( ( with_suprema_relstr @ SV2 )
= $false )
| ( ( ~ ( empty_carrier @ SV2 ) )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(583,plain,
! [SV3: $i,SV63: $i] :
( ( ( ~ ( element @ SV63 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( finite @ SV63 )
= $true )
| ( ( finite @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[526]) ).
thf(584,plain,
! [SV4: $i] :
( ( ( with_infima_relstr @ SV4 )
= $false )
| ( ( ~ ( empty_carrier @ SV4 ) )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(585,plain,
! [SV5: $i] :
( ( ( topological_space @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( ~ ( top_str @ SV5 ) )
= $true )
| ( ( ! [SY108: $i] :
( ~ ( element @ SY108 @ ( the_carrier @ SV5 ) )
| ( ( neighborhood_system @ SV5 @ SY108 )
= ( a_2_0_yellow19 @ SV5 @ SY108 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(586,plain,
! [SV49: $i,SV7: $i] :
( ( ( ( empty_carrier @ SV7 )
| ~ ( topological_space @ SV7 ) )
= $true )
| ( ( ~ ( top_str @ SV7 ) )
= $true )
| ( ( ~ ( element @ SV49 @ ( the_carrier @ SV7 ) ) )
= $true )
| ( ( ! [SY133: $i] :
( ~ ( point_neighbourhood @ SY133 @ SV7 @ SV49 )
| ( element @ SY133 @ ( powerset @ ( the_carrier @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(587,plain,
! [SV50: $i,SV8: $i] :
( ( ( ( empty_carrier @ SV8 )
| ~ ( topological_space @ SV8 ) )
= $true )
| ( ( ~ ( top_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV50 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( point_neighbourhood @ ( sK25_C @ SV50 @ SV8 ) @ SV8 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(588,plain,
! [SV10: $i] :
( ( ( empty @ ( the_carrier @ SV10 ) )
= $false )
| ( ( empty_carrier @ SV10 )
= $true )
| ( ( one_sorted_str @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(589,plain,
! [SV11: $i] :
( ( ( topological_space @ SV11 )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( closed_subset @ ( cast_as_carrier_subset @ SV11 ) @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(590,plain,
! [SV14: $i,SV52: $i] :
( ( ( empty @ SV52 )
= $true )
| ( ( in @ SV14 @ SV52 )
= $true )
| ( ( element @ SV14 @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(591,plain,
! [SV15: $i,SV61: $i,SV53: $i] :
( ( ( ~ ( element @ SV53 @ ( powerset @ SV61 ) ) )
= $true )
| ( ( ~ ( in @ SV15 @ SV53 ) )
= $true )
| ( ( element @ SV15 @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(592,plain,
! [SV16: $i,SV62: $i,SV54: $i] :
( ( ( ~ ( element @ SV54 @ ( powerset @ SV62 ) ) )
= $true )
| ( ( ~ ( in @ SV16 @ SV54 ) )
= $true )
| ( ( ~ ( empty @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(593,plain,
! [SV55: $i,SV17: $i] :
( ( ( in @ SV17 @ SV55 )
= $false )
| ( ( empty @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(594,plain,
! [SV20: $i,SV64: $i] :
( ( ( ~ ( element @ SV64 @ ( powerset @ ( the_carrier @ SV20 ) ) ) )
= $true )
| ( ( ~ ( empty @ SV64 )
| ( boundary_set @ SV64 @ SV20 ) )
= $true )
| ( ( top_str @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[538]) ).
thf(595,plain,
! [SV21: $i] :
( ( ( topological_space @ SV21 )
= $false )
| ( ( top_str @ SV21 )
= $false )
| ( ( ! [SY120: $i] :
( ~ ( element @ SY120 @ ( powerset @ ( the_carrier @ SV21 ) ) )
| ~ ( empty @ SY120 )
| ( nowhere_dense @ SY120 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(596,plain,
! [SV56: $i,SV22: $i] :
( ( ( ( empty_carrier @ SV22 )
| ~ ( topological_space @ SV22 ) )
= $true )
| ( ( ~ ( top_str @ SV22 ) )
= $true )
| ( ( ~ ( element @ SV56 @ ( the_carrier @ SV22 ) ) )
= $true )
| ( ( element @ ( neighborhood_system @ SV22 @ SV56 ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(597,plain,
! [SV57: $i,SV25: $i] :
( ( ( finite @ SV25 )
= $false )
| ( ( ~ ( finite @ SV57 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV25 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(598,plain,
! [SV27: $i] :
( ( ( empty @ ( cast_as_carrier_subset @ SV27 ) )
= $false )
| ( ( empty_carrier @ SV27 )
= $true )
| ( ( one_sorted_str @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(599,plain,
! [SV28: $i] :
( ( ( empty @ ( cast_as_carrier_subset @ SV28 ) )
= $false )
| ( ( empty_carrier @ SV28 )
= $true )
| ( ( rel_str @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(600,plain,
! [SV58: $i,SV29: $i] :
( ( ( empty @ ( cartesian_product2 @ SV29 @ SV58 ) )
= $false )
| ( ( empty @ SV58 )
= $true )
| ( ( empty @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(601,plain,
! [SV59: $i,SV32: $i] :
( ( ( empty @ SV32 )
= $false )
| ( ( SV32 = SV59 )
= $true )
| ( ( ~ ( empty @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(602,plain,
! [SV65: $i] :
( ( ( ~ ( top_str @ SV65 )
| ~ ( topological_space @ SV65 ) )
= $true )
| ( ( closed_subset @ ( cast_as_carrier_subset @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(603,plain,
! [SV66: $i] :
( ( ( ~ ( top_str @ SV66 )
| ~ ( topological_space @ SV66 ) )
= $true )
| ( ( open_subset @ ( cast_as_carrier_subset @ SV66 ) @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(604,plain,
! [SV33: $i] :
( ( ( element @ ( sK22_B @ SV33 ) @ ( powerset @ SV33 ) )
= $true )
| ( ( empty @ SV33 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(605,plain,
! [SV33: $i] :
( ( ( ~ ( empty @ ( sK22_B @ SV33 ) ) )
= $true )
| ( ( empty @ SV33 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(606,plain,
! [SV34: $i,SV60: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV34 )
| ~ ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV60 ) ) )
= $false )
| ( ( SV34 = SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[551]) ).
thf(607,plain,
! [SV34: $i,SV60: $i] :
( ( ( ~ ( ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV34 )
| ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV60 ) ) )
= $false )
| ( ( SV34 = SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[551]) ).
thf(608,plain,
! [SV35: $i] :
( ( ( ~ ( element @ ( sK5_B @ SV35 ) @ ( powerset @ ( the_carrier @ SV35 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV35 ) ) )
= $false )
| ( ( empty_carrier @ SV35 )
= $true )
| ( ( one_sorted_str @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(609,plain,
! [SV74: $i,SV67: $i] :
( ( ~ ( element @ SV67 @ ( powerset @ SV74 ) )
| ( subset @ SV67 @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(610,plain,
! [SV75: $i,SV68: $i] :
( ( ~ ( subset @ SV68 @ SV75 )
| ( element @ SV68 @ ( powerset @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(611,plain,
! [SV36: $i] :
( ( ( ~ ( ~ ( element @ ( sK6_B @ SV36 ) @ ( powerset @ SV36 ) )
| ~ ~ ( empty @ ( sK6_B @ SV36 ) ) ) )
= $true )
| ( ( empty @ SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(612,plain,
! [SV36: $i] :
( ( ( finite @ ( sK6_B @ SV36 ) )
= $true )
| ( ( empty @ SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[556]) ).
thf(613,plain,
! [SV37: $i] :
( ( ( topological_space @ SV37 )
= $false )
| ( ( top_str @ SV37 )
= $false )
| ( ( ~ ( ~ ( element @ ( sK21_B @ SV37 ) @ ( powerset @ ( the_carrier @ SV37 ) ) )
| ~ ( open_subset @ ( sK21_B @ SV37 ) @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(614,plain,
! [SV38: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_B @ SV38 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV38 ) ) ) )
| ~ ~ ( empty @ ( sK7_B @ SV38 ) ) ) )
= $false )
| ( ( one_sorted_str @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[558]) ).
thf(615,plain,
! [SV38: $i] :
( ( ( ~ ( finite @ ( sK7_B @ SV38 ) ) )
= $false )
| ( ( one_sorted_str @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[558]) ).
thf(616,plain,
! [SV39: $i] :
( ( ( topological_space @ SV39 )
= $false )
| ( ( top_str @ SV39 )
= $false )
| ( ( ~ ( ~ ! [SY126: $i] :
( ~ ( element @ SY126 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SY126 )
| ( closed_subset @ SY126 @ SV39 ) )
| ~ ! [SY127: $i] :
( ~ ( element @ SY127 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SY127 )
| ( open_subset @ SY127 @ SV39 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(617,plain,
! [SV40: $i,SV76: $i] :
( ( ! [SY138: $i] :
( ( empty_carrier @ SV76 )
| ~ ( topological_space @ SV76 )
| ~ ( top_str @ SV76 )
| ~ ( element @ SY138 @ ( the_carrier @ SV76 ) )
| ! [SY139: $i] :
( ( SV40 != SY139 )
| ~ ( point_neighbourhood @ SY139 @ SV76 @ SY138 ) )
| ( in @ SV40 @ ( a_2_0_yellow19 @ SV76 @ SY138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(618,plain,
! [SV40: $i,SV77: $i] :
( ( ! [SY140: $i] :
( ( empty_carrier @ SV77 )
| ~ ( topological_space @ SV77 )
| ~ ( top_str @ SV77 )
| ~ ( element @ SY140 @ ( the_carrier @ SV77 ) )
| ~ ( in @ SV40 @ ( a_2_0_yellow19 @ SV77 @ SY140 ) )
| ~ ( ( SV40
!= ( sK23_D @ SY140 @ SV77 @ SV40 ) )
| ~ ( point_neighbourhood @ ( sK23_D @ SY140 @ SV77 @ SV40 ) @ SV77 @ SY140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(619,plain,
! [SV41: $i] :
( ( ( ~ ( ~ ( element @ ( sK9_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ~ ( empty @ ( sK9_B @ SV41 ) ) ) )
= $true )
| ( ( empty @ SV41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(620,plain,
! [SV41: $i] :
( ( ( finite @ ( sK9_B @ SV41 ) )
= $true )
| ( ( empty @ SV41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(621,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[564]) ).
thf(622,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_suprema_relstr @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[564]) ).
thf(623,plain,
! [SV69: $i] :
( ( ( ~ ( rel_str @ SV69 ) )
= $true )
| ( ( ( empty_carrier @ SV69 )
| ~ ( complete_relstr @ SV69 )
| ( with_infima_relstr @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(624,plain,
! [SV42: $i] :
( ( ( topological_space @ SV42 )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( ~ ( top_str @ SV42 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK4_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) )
| ~ ~ ( empty @ ( sK4_B @ SV42 ) ) )
| ~ ( closed_subset @ ( sK4_B @ SV42 ) @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(625,plain,
( ( ~ ( ~ ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ~ ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(626,plain,
( ( ~ ( ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(627,plain,
! [SV43: $i] :
( ( ( topological_space @ SV43 )
= $false )
| ( ( top_str @ SV43 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
| ~ ( open_subset @ ( sK11_B @ SV43 ) @ SV43 ) )
| ~ ( closed_subset @ ( sK11_B @ SV43 ) @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(628,plain,
! [SV70: $i] :
( ( ( ~ ( rel_str @ SV70 )
| ~ ( with_suprema_relstr @ SV70 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(629,plain,
! [SV71: $i] :
( ( ( ~ ( rel_str @ SV71 )
| ~ ( with_suprema_relstr @ SV71 ) )
= $true )
| ( ( directed_subset @ ( cast_as_carrier_subset @ SV71 ) @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(630,plain,
! [SV72: $i] :
( ( ( ~ ( rel_str @ SV72 )
| ~ ( with_infima_relstr @ SV72 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(631,plain,
! [SV73: $i] :
( ( ( ~ ( rel_str @ SV73 )
| ~ ( with_infima_relstr @ SV73 ) )
= $true )
| ( ( filtered_subset @ ( cast_as_carrier_subset @ SV73 ) @ SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(632,plain,
! [SV45: $i] :
( ( ~ ( element @ ( sK10_B @ SV45 ) @ ( powerset @ ( powerset @ SV45 ) ) )
| ~ ~ ( empty @ ( sK10_B @ SV45 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(633,plain,
! [SV46: $i] :
( ( ( topological_space @ SV46 )
= $false )
| ( ( top_str @ SV46 )
= $false )
| ( ( ~ ( ~ ( closed_subset @ ( sK18_B @ SV46 ) @ SV46 )
| ~ ( element @ ( sK18_B @ SV46 ) @ ( powerset @ ( the_carrier @ SV46 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(634,plain,
! [SV47: $i] :
( ( ( topological_space @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( ~ ( top_str @ SV47 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK8_B @ SV47 ) @ ( powerset @ ( the_carrier @ SV47 ) ) )
| ~ ~ ( empty @ ( sK8_B @ SV47 ) ) )
| ~ ( open_subset @ ( sK8_B @ SV47 ) @ SV47 ) )
| ~ ( closed_subset @ ( sK8_B @ SV47 ) @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(635,plain,
! [SV2: $i] :
( ( ( empty_carrier @ SV2 )
= $false )
| ( ( with_suprema_relstr @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(636,plain,
! [SV3: $i,SV63: $i] :
( ( ( element @ SV63 @ ( powerset @ SV3 ) )
= $false )
| ( ( finite @ SV63 )
= $true )
| ( ( finite @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(637,plain,
! [SV4: $i] :
( ( ( empty_carrier @ SV4 )
= $false )
| ( ( with_infima_relstr @ SV4 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(638,plain,
! [SV5: $i] :
( ( ( top_str @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( topological_space @ SV5 )
= $false )
| ( ( ! [SY108: $i] :
( ~ ( element @ SY108 @ ( the_carrier @ SV5 ) )
| ( ( neighborhood_system @ SV5 @ SY108 )
= ( a_2_0_yellow19 @ SV5 @ SY108 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(639,plain,
! [SV49: $i,SV7: $i] :
( ( ( empty_carrier @ SV7 )
= $true )
| ( ( ~ ( topological_space @ SV7 ) )
= $true )
| ( ( ~ ( top_str @ SV7 ) )
= $true )
| ( ( ~ ( element @ SV49 @ ( the_carrier @ SV7 ) ) )
= $true )
| ( ( ! [SY133: $i] :
( ~ ( point_neighbourhood @ SY133 @ SV7 @ SV49 )
| ( element @ SY133 @ ( powerset @ ( the_carrier @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(640,plain,
! [SV50: $i,SV8: $i] :
( ( ( empty_carrier @ SV8 )
= $true )
| ( ( ~ ( topological_space @ SV8 ) )
= $true )
| ( ( ~ ( top_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV50 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( point_neighbourhood @ ( sK25_C @ SV50 @ SV8 ) @ SV8 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(641,plain,
! [SV15: $i,SV61: $i,SV53: $i] :
( ( ( element @ SV53 @ ( powerset @ SV61 ) )
= $false )
| ( ( ~ ( in @ SV15 @ SV53 ) )
= $true )
| ( ( element @ SV15 @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(642,plain,
! [SV16: $i,SV62: $i,SV54: $i] :
( ( ( element @ SV54 @ ( powerset @ SV62 ) )
= $false )
| ( ( ~ ( in @ SV16 @ SV54 ) )
= $true )
| ( ( ~ ( empty @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(643,plain,
! [SV20: $i,SV64: $i] :
( ( ( element @ SV64 @ ( powerset @ ( the_carrier @ SV20 ) ) )
= $false )
| ( ( ~ ( empty @ SV64 )
| ( boundary_set @ SV64 @ SV20 ) )
= $true )
| ( ( top_str @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(644,plain,
! [SV21: $i,SV78: $i] :
( ( ( ~ ( element @ SV78 @ ( powerset @ ( the_carrier @ SV21 ) ) )
| ~ ( empty @ SV78 )
| ( nowhere_dense @ SV78 @ SV21 ) )
= $true )
| ( ( top_str @ SV21 )
= $false )
| ( ( topological_space @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(645,plain,
! [SV56: $i,SV22: $i] :
( ( ( empty_carrier @ SV22 )
= $true )
| ( ( ~ ( topological_space @ SV22 ) )
= $true )
| ( ( ~ ( top_str @ SV22 ) )
= $true )
| ( ( ~ ( element @ SV56 @ ( the_carrier @ SV22 ) ) )
= $true )
| ( ( element @ ( neighborhood_system @ SV22 @ SV56 ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(646,plain,
! [SV25: $i,SV57: $i] :
( ( ( finite @ SV57 )
= $false )
| ( ( finite @ SV25 )
= $false )
| ( ( finite @ ( cartesian_product2 @ SV25 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(647,plain,
! [SV32: $i,SV59: $i] :
( ( ( empty @ SV59 )
= $false )
| ( ( SV32 = SV59 )
= $true )
| ( ( empty @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(648,plain,
! [SV65: $i] :
( ( ( ~ ( top_str @ SV65 ) )
= $true )
| ( ( ~ ( topological_space @ SV65 ) )
= $true )
| ( ( closed_subset @ ( cast_as_carrier_subset @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[602]) ).
thf(649,plain,
! [SV66: $i] :
( ( ( ~ ( top_str @ SV66 ) )
= $true )
| ( ( ~ ( topological_space @ SV66 ) )
= $true )
| ( ( open_subset @ ( cast_as_carrier_subset @ SV66 ) @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(650,plain,
! [SV33: $i] :
( ( ( empty @ ( sK22_B @ SV33 ) )
= $false )
| ( ( empty @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(651,plain,
! [SV34: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV34 )
| ~ ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV60 ) )
= $true )
| ( ( SV34 = SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(652,plain,
! [SV34: $i,SV60: $i] :
( ( ( ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV34 )
| ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV60 ) )
= $true )
| ( ( SV34 = SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(653,plain,
! [SV35: $i] :
( ( ( ~ ( element @ ( sK5_B @ SV35 ) @ ( powerset @ ( the_carrier @ SV35 ) ) ) )
= $false )
| ( ( empty_carrier @ SV35 )
= $true )
| ( ( one_sorted_str @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[608]) ).
thf(654,plain,
! [SV35: $i] :
( ( ( ~ ~ ( empty @ ( sK5_B @ SV35 ) ) )
= $false )
| ( ( empty_carrier @ SV35 )
= $true )
| ( ( one_sorted_str @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[608]) ).
thf(655,plain,
! [SV74: $i,SV67: $i] :
( ( ( ~ ( element @ SV67 @ ( powerset @ SV74 ) ) )
= $true )
| ( ( subset @ SV67 @ SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(656,plain,
! [SV75: $i,SV68: $i] :
( ( ( ~ ( subset @ SV68 @ SV75 ) )
= $true )
| ( ( element @ SV68 @ ( powerset @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[610]) ).
thf(657,plain,
! [SV36: $i] :
( ( ( ~ ( element @ ( sK6_B @ SV36 ) @ ( powerset @ SV36 ) )
| ~ ~ ( empty @ ( sK6_B @ SV36 ) ) )
= $false )
| ( ( empty @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(658,plain,
! [SV37: $i] :
( ( ( ~ ( element @ ( sK21_B @ SV37 ) @ ( powerset @ ( the_carrier @ SV37 ) ) )
| ~ ( open_subset @ ( sK21_B @ SV37 ) @ SV37 ) )
= $false )
| ( ( top_str @ SV37 )
= $false )
| ( ( topological_space @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(659,plain,
! [SV38: $i] :
( ( ( ~ ( ~ ( element @ ( sK7_B @ SV38 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV38 ) ) ) )
| ~ ~ ( empty @ ( sK7_B @ SV38 ) ) ) )
= $true )
| ( ( one_sorted_str @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[614]) ).
thf(660,plain,
! [SV38: $i] :
( ( ( finite @ ( sK7_B @ SV38 ) )
= $true )
| ( ( one_sorted_str @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[615]) ).
thf(661,plain,
! [SV39: $i] :
( ( ( ~ ! [SY126: $i] :
( ~ ( element @ SY126 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SY126 )
| ( closed_subset @ SY126 @ SV39 ) )
| ~ ! [SY127: $i] :
( ~ ( element @ SY127 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SY127 )
| ( open_subset @ SY127 @ SV39 ) ) )
= $false )
| ( ( top_str @ SV39 )
= $false )
| ( ( topological_space @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(662,plain,
! [SV40: $i,SV79: $i,SV76: $i] :
( ( ( empty_carrier @ SV76 )
| ~ ( topological_space @ SV76 )
| ~ ( top_str @ SV76 )
| ~ ( element @ SV79 @ ( the_carrier @ SV76 ) )
| ! [SY141: $i] :
( ( SV40 != SY141 )
| ~ ( point_neighbourhood @ SY141 @ SV76 @ SV79 ) )
| ( in @ SV40 @ ( a_2_0_yellow19 @ SV76 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(663,plain,
! [SV40: $i,SV80: $i,SV77: $i] :
( ( ( empty_carrier @ SV77 )
| ~ ( topological_space @ SV77 )
| ~ ( top_str @ SV77 )
| ~ ( element @ SV80 @ ( the_carrier @ SV77 ) )
| ~ ( in @ SV40 @ ( a_2_0_yellow19 @ SV77 @ SV80 ) )
| ~ ( ( SV40
!= ( sK23_D @ SV80 @ SV77 @ SV40 ) )
| ~ ( point_neighbourhood @ ( sK23_D @ SV80 @ SV77 @ SV40 ) @ SV77 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(664,plain,
! [SV41: $i] :
( ( ( ~ ( element @ ( sK9_B @ SV41 ) @ ( powerset @ SV41 ) )
| ~ ~ ( empty @ ( sK9_B @ SV41 ) ) )
= $false )
| ( ( empty @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(665,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[621]) ).
thf(666,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_suprema_relstr @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(667,plain,
! [SV69: $i] :
( ( ( rel_str @ SV69 )
= $false )
| ( ( ( empty_carrier @ SV69 )
| ~ ( complete_relstr @ SV69 )
| ( with_infima_relstr @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(668,plain,
! [SV42: $i] :
( ( ( top_str @ SV42 )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( topological_space @ SV42 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK4_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) )
| ~ ~ ( empty @ ( sK4_B @ SV42 ) ) )
| ~ ( closed_subset @ ( sK4_B @ SV42 ) @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(669,plain,
( ( ~ ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ~ ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[625]) ).
thf(670,plain,
( ( ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
| ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(671,plain,
! [SV43: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
| ~ ( open_subset @ ( sK11_B @ SV43 ) @ SV43 ) )
| ~ ( closed_subset @ ( sK11_B @ SV43 ) @ SV43 ) )
= $false )
| ( ( top_str @ SV43 )
= $false )
| ( ( topological_space @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(672,plain,
! [SV70: $i] :
( ( ( ~ ( rel_str @ SV70 ) )
= $true )
| ( ( ~ ( with_suprema_relstr @ SV70 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(673,plain,
! [SV71: $i] :
( ( ( ~ ( rel_str @ SV71 ) )
= $true )
| ( ( ~ ( with_suprema_relstr @ SV71 ) )
= $true )
| ( ( directed_subset @ ( cast_as_carrier_subset @ SV71 ) @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(674,plain,
! [SV72: $i] :
( ( ( ~ ( rel_str @ SV72 ) )
= $true )
| ( ( ~ ( with_infima_relstr @ SV72 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[630]) ).
thf(675,plain,
! [SV73: $i] :
( ( ( ~ ( rel_str @ SV73 ) )
= $true )
| ( ( ~ ( with_infima_relstr @ SV73 ) )
= $true )
| ( ( filtered_subset @ ( cast_as_carrier_subset @ SV73 ) @ SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[631]) ).
thf(676,plain,
! [SV45: $i] :
( ( ~ ( element @ ( sK10_B @ SV45 ) @ ( powerset @ ( powerset @ SV45 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[632]) ).
thf(677,plain,
! [SV45: $i] :
( ( ~ ~ ( empty @ ( sK10_B @ SV45 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[632]) ).
thf(678,plain,
! [SV46: $i] :
( ( ( ~ ( closed_subset @ ( sK18_B @ SV46 ) @ SV46 )
| ~ ( element @ ( sK18_B @ SV46 ) @ ( powerset @ ( the_carrier @ SV46 ) ) ) )
= $false )
| ( ( top_str @ SV46 )
= $false )
| ( ( topological_space @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(679,plain,
! [SV47: $i] :
( ( ( top_str @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( topological_space @ SV47 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK8_B @ SV47 ) @ ( powerset @ ( the_carrier @ SV47 ) ) )
| ~ ~ ( empty @ ( sK8_B @ SV47 ) ) )
| ~ ( open_subset @ ( sK8_B @ SV47 ) @ SV47 ) )
| ~ ( closed_subset @ ( sK8_B @ SV47 ) @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(680,plain,
! [SV5: $i,SV81: $i] :
( ( ( ~ ( element @ SV81 @ ( the_carrier @ SV5 ) )
| ( ( neighborhood_system @ SV5 @ SV81 )
= ( a_2_0_yellow19 @ SV5 @ SV81 ) ) )
= $true )
| ( ( topological_space @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( top_str @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(681,plain,
! [SV49: $i,SV7: $i] :
( ( ( topological_space @ SV7 )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( ~ ( top_str @ SV7 ) )
= $true )
| ( ( ~ ( element @ SV49 @ ( the_carrier @ SV7 ) ) )
= $true )
| ( ( ! [SY133: $i] :
( ~ ( point_neighbourhood @ SY133 @ SV7 @ SV49 )
| ( element @ SY133 @ ( powerset @ ( the_carrier @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(682,plain,
! [SV50: $i,SV8: $i] :
( ( ( topological_space @ SV8 )
= $false )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( ~ ( top_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV50 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( point_neighbourhood @ ( sK25_C @ SV50 @ SV8 ) @ SV8 @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(683,plain,
! [SV61: $i,SV53: $i,SV15: $i] :
( ( ( in @ SV15 @ SV53 )
= $false )
| ( ( element @ SV53 @ ( powerset @ SV61 ) )
= $false )
| ( ( element @ SV15 @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(684,plain,
! [SV62: $i,SV54: $i,SV16: $i] :
( ( ( in @ SV16 @ SV54 )
= $false )
| ( ( element @ SV54 @ ( powerset @ SV62 ) )
= $false )
| ( ( ~ ( empty @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[642]) ).
thf(685,plain,
! [SV20: $i,SV64: $i] :
( ( ( ~ ( empty @ SV64 ) )
= $true )
| ( ( boundary_set @ SV64 @ SV20 )
= $true )
| ( ( element @ SV64 @ ( powerset @ ( the_carrier @ SV20 ) ) )
= $false )
| ( ( top_str @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(686,plain,
! [SV21: $i,SV78: $i] :
( ( ( ~ ( element @ SV78 @ ( powerset @ ( the_carrier @ SV21 ) ) ) )
= $true )
| ( ( ~ ( empty @ SV78 )
| ( nowhere_dense @ SV78 @ SV21 ) )
= $true )
| ( ( top_str @ SV21 )
= $false )
| ( ( topological_space @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(687,plain,
! [SV56: $i,SV22: $i] :
( ( ( topological_space @ SV22 )
= $false )
| ( ( empty_carrier @ SV22 )
= $true )
| ( ( ~ ( top_str @ SV22 ) )
= $true )
| ( ( ~ ( element @ SV56 @ ( the_carrier @ SV22 ) ) )
= $true )
| ( ( element @ ( neighborhood_system @ SV22 @ SV56 ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(688,plain,
! [SV65: $i] :
( ( ( top_str @ SV65 )
= $false )
| ( ( ~ ( topological_space @ SV65 ) )
= $true )
| ( ( closed_subset @ ( cast_as_carrier_subset @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(689,plain,
! [SV66: $i] :
( ( ( top_str @ SV66 )
= $false )
| ( ( ~ ( topological_space @ SV66 ) )
= $true )
| ( ( open_subset @ ( cast_as_carrier_subset @ SV66 ) @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(690,plain,
! [SV34: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV34 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV60 ) )
= $true )
| ( ( SV34 = SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(691,plain,
! [SV34: $i,SV60: $i] :
( ( ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV34 )
= $true )
| ( ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV60 )
= $true )
| ( ( SV34 = SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(692,plain,
! [SV35: $i] :
( ( ( element @ ( sK5_B @ SV35 ) @ ( powerset @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( empty_carrier @ SV35 )
= $true )
| ( ( one_sorted_str @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[653]) ).
thf(693,plain,
! [SV35: $i] :
( ( ( ~ ( empty @ ( sK5_B @ SV35 ) ) )
= $true )
| ( ( empty_carrier @ SV35 )
= $true )
| ( ( one_sorted_str @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[654]) ).
thf(694,plain,
! [SV74: $i,SV67: $i] :
( ( ( element @ SV67 @ ( powerset @ SV74 ) )
= $false )
| ( ( subset @ SV67 @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(695,plain,
! [SV75: $i,SV68: $i] :
( ( ( subset @ SV68 @ SV75 )
= $false )
| ( ( element @ SV68 @ ( powerset @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(696,plain,
! [SV36: $i] :
( ( ( ~ ( element @ ( sK6_B @ SV36 ) @ ( powerset @ SV36 ) ) )
= $false )
| ( ( empty @ SV36 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[657]) ).
thf(697,plain,
! [SV36: $i] :
( ( ( ~ ~ ( empty @ ( sK6_B @ SV36 ) ) )
= $false )
| ( ( empty @ SV36 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[657]) ).
thf(698,plain,
! [SV37: $i] :
( ( ( ~ ( element @ ( sK21_B @ SV37 ) @ ( powerset @ ( the_carrier @ SV37 ) ) ) )
= $false )
| ( ( top_str @ SV37 )
= $false )
| ( ( topological_space @ SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[658]) ).
thf(699,plain,
! [SV37: $i] :
( ( ( ~ ( open_subset @ ( sK21_B @ SV37 ) @ SV37 ) )
= $false )
| ( ( top_str @ SV37 )
= $false )
| ( ( topological_space @ SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[658]) ).
thf(700,plain,
! [SV38: $i] :
( ( ( ~ ( element @ ( sK7_B @ SV38 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV38 ) ) ) )
| ~ ~ ( empty @ ( sK7_B @ SV38 ) ) )
= $false )
| ( ( one_sorted_str @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(701,plain,
! [SV39: $i] :
( ( ( ~ ! [SY126: $i] :
( ~ ( element @ SY126 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SY126 )
| ( closed_subset @ SY126 @ SV39 ) ) )
= $false )
| ( ( top_str @ SV39 )
= $false )
| ( ( topological_space @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[661]) ).
thf(702,plain,
! [SV39: $i] :
( ( ( ~ ! [SY127: $i] :
( ~ ( element @ SY127 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SY127 )
| ( open_subset @ SY127 @ SV39 ) ) )
= $false )
| ( ( top_str @ SV39 )
= $false )
| ( ( topological_space @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[661]) ).
thf(703,plain,
! [SV40: $i,SV79: $i,SV76: $i] :
( ( ( ( empty_carrier @ SV76 )
| ~ ( topological_space @ SV76 )
| ~ ( top_str @ SV76 )
| ~ ( element @ SV79 @ ( the_carrier @ SV76 ) ) )
= $true )
| ( ( ! [SY141: $i] :
( ( SV40 != SY141 )
| ~ ( point_neighbourhood @ SY141 @ SV76 @ SV79 ) )
| ( in @ SV40 @ ( a_2_0_yellow19 @ SV76 @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(704,plain,
! [SV40: $i,SV80: $i,SV77: $i] :
( ( ( ( empty_carrier @ SV77 )
| ~ ( topological_space @ SV77 )
| ~ ( top_str @ SV77 )
| ~ ( element @ SV80 @ ( the_carrier @ SV77 ) ) )
= $true )
| ( ( ~ ( in @ SV40 @ ( a_2_0_yellow19 @ SV77 @ SV80 ) )
| ~ ( ( SV40
!= ( sK23_D @ SV80 @ SV77 @ SV40 ) )
| ~ ( point_neighbourhood @ ( sK23_D @ SV80 @ SV77 @ SV40 ) @ SV77 @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[663]) ).
thf(705,plain,
! [SV41: $i] :
( ( ( ~ ( element @ ( sK9_B @ SV41 ) @ ( powerset @ SV41 ) ) )
= $false )
| ( ( empty @ SV41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[664]) ).
thf(706,plain,
! [SV41: $i] :
( ( ( ~ ~ ( empty @ ( sK9_B @ SV41 ) ) )
= $false )
| ( ( empty @ SV41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[664]) ).
thf(707,plain,
! [SV82: $i] :
( ( ~ ( rel_str @ SV82 )
| ( empty_carrier @ SV82 )
| ~ ( complete_relstr @ SV82 )
| ~ ( empty_carrier @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(708,plain,
! [SV83: $i] :
( ( ~ ( rel_str @ SV83 )
| ( empty_carrier @ SV83 )
| ~ ( complete_relstr @ SV83 )
| ( with_suprema_relstr @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(709,plain,
! [SV69: $i] :
( ( ( ( empty_carrier @ SV69 )
| ~ ( complete_relstr @ SV69 ) )
= $true )
| ( ( with_infima_relstr @ SV69 )
= $true )
| ( ( rel_str @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[667]) ).
thf(710,plain,
! [SV42: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK4_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) )
| ~ ~ ( empty @ ( sK4_B @ SV42 ) ) )
| ~ ( closed_subset @ ( sK4_B @ SV42 ) @ SV42 ) )
= $false )
| ( ( topological_space @ SV42 )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( top_str @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(711,plain,
( ( ( ~ ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) ) )
= $true )
| ( ( ~ ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(712,plain,
( ( ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
= $true )
| ( ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(713,plain,
! [SV43: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
| ~ ( open_subset @ ( sK11_B @ SV43 ) @ SV43 ) ) )
= $false )
| ( ( top_str @ SV43 )
= $false )
| ( ( topological_space @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[671]) ).
thf(714,plain,
! [SV43: $i] :
( ( ( ~ ( closed_subset @ ( sK11_B @ SV43 ) @ SV43 ) )
= $false )
| ( ( top_str @ SV43 )
= $false )
| ( ( topological_space @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[671]) ).
thf(715,plain,
! [SV70: $i] :
( ( ( rel_str @ SV70 )
= $false )
| ( ( ~ ( with_suprema_relstr @ SV70 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(716,plain,
! [SV71: $i] :
( ( ( rel_str @ SV71 )
= $false )
| ( ( ~ ( with_suprema_relstr @ SV71 ) )
= $true )
| ( ( directed_subset @ ( cast_as_carrier_subset @ SV71 ) @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(717,plain,
! [SV72: $i] :
( ( ( rel_str @ SV72 )
= $false )
| ( ( ~ ( with_infima_relstr @ SV72 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV72 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(718,plain,
! [SV73: $i] :
( ( ( rel_str @ SV73 )
= $false )
| ( ( ~ ( with_infima_relstr @ SV73 ) )
= $true )
| ( ( filtered_subset @ ( cast_as_carrier_subset @ SV73 ) @ SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(719,plain,
! [SV45: $i] :
( ( element @ ( sK10_B @ SV45 ) @ ( powerset @ ( powerset @ SV45 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[676]) ).
thf(720,plain,
! [SV45: $i] :
( ( ~ ( empty @ ( sK10_B @ SV45 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[677]) ).
thf(721,plain,
! [SV46: $i] :
( ( ( ~ ( closed_subset @ ( sK18_B @ SV46 ) @ SV46 ) )
= $false )
| ( ( top_str @ SV46 )
= $false )
| ( ( topological_space @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[678]) ).
thf(722,plain,
! [SV46: $i] :
( ( ( ~ ( element @ ( sK18_B @ SV46 ) @ ( powerset @ ( the_carrier @ SV46 ) ) ) )
= $false )
| ( ( top_str @ SV46 )
= $false )
| ( ( topological_space @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[678]) ).
thf(723,plain,
! [SV47: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK8_B @ SV47 ) @ ( powerset @ ( the_carrier @ SV47 ) ) )
| ~ ~ ( empty @ ( sK8_B @ SV47 ) ) )
| ~ ( open_subset @ ( sK8_B @ SV47 ) @ SV47 ) )
| ~ ( closed_subset @ ( sK8_B @ SV47 ) @ SV47 ) )
= $false )
| ( ( topological_space @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( top_str @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(724,plain,
! [SV5: $i,SV81: $i] :
( ( ( ~ ( element @ SV81 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ( neighborhood_system @ SV5 @ SV81 )
= ( a_2_0_yellow19 @ SV5 @ SV81 ) )
= $true )
| ( ( topological_space @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( top_str @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(725,plain,
! [SV49: $i,SV7: $i] :
( ( ( top_str @ SV7 )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( topological_space @ SV7 )
= $false )
| ( ( ~ ( element @ SV49 @ ( the_carrier @ SV7 ) ) )
= $true )
| ( ( ! [SY133: $i] :
( ~ ( point_neighbourhood @ SY133 @ SV7 @ SV49 )
| ( element @ SY133 @ ( powerset @ ( the_carrier @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(726,plain,
! [SV50: $i,SV8: $i] :
( ( ( top_str @ SV8 )
= $false )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( topological_space @ SV8 )
= $false )
| ( ( ~ ( element @ SV50 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( point_neighbourhood @ ( sK25_C @ SV50 @ SV8 ) @ SV8 @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(727,plain,
! [SV16: $i,SV54: $i,SV62: $i] :
( ( ( empty @ SV62 )
= $false )
| ( ( element @ SV54 @ ( powerset @ SV62 ) )
= $false )
| ( ( in @ SV16 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(728,plain,
! [SV20: $i,SV64: $i] :
( ( ( empty @ SV64 )
= $false )
| ( ( boundary_set @ SV64 @ SV20 )
= $true )
| ( ( element @ SV64 @ ( powerset @ ( the_carrier @ SV20 ) ) )
= $false )
| ( ( top_str @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(729,plain,
! [SV21: $i,SV78: $i] :
( ( ( element @ SV78 @ ( powerset @ ( the_carrier @ SV21 ) ) )
= $false )
| ( ( ~ ( empty @ SV78 )
| ( nowhere_dense @ SV78 @ SV21 ) )
= $true )
| ( ( top_str @ SV21 )
= $false )
| ( ( topological_space @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(730,plain,
! [SV56: $i,SV22: $i] :
( ( ( top_str @ SV22 )
= $false )
| ( ( empty_carrier @ SV22 )
= $true )
| ( ( topological_space @ SV22 )
= $false )
| ( ( ~ ( element @ SV56 @ ( the_carrier @ SV22 ) ) )
= $true )
| ( ( element @ ( neighborhood_system @ SV22 @ SV56 ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(731,plain,
! [SV65: $i] :
( ( ( topological_space @ SV65 )
= $false )
| ( ( top_str @ SV65 )
= $false )
| ( ( closed_subset @ ( cast_as_carrier_subset @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(732,plain,
! [SV66: $i] :
( ( ( topological_space @ SV66 )
= $false )
| ( ( top_str @ SV66 )
= $false )
| ( ( open_subset @ ( cast_as_carrier_subset @ SV66 ) @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(733,plain,
! [SV34: $i,SV60: $i] :
( ( ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV34 )
= $false )
| ( ( ~ ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV60 ) )
= $true )
| ( ( SV34 = SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(734,plain,
! [SV35: $i] :
( ( ( empty @ ( sK5_B @ SV35 ) )
= $false )
| ( ( empty_carrier @ SV35 )
= $true )
| ( ( one_sorted_str @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(735,plain,
! [SV36: $i] :
( ( ( element @ ( sK6_B @ SV36 ) @ ( powerset @ SV36 ) )
= $true )
| ( ( empty @ SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[696]) ).
thf(736,plain,
! [SV36: $i] :
( ( ( ~ ( empty @ ( sK6_B @ SV36 ) ) )
= $true )
| ( ( empty @ SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[697]) ).
thf(737,plain,
! [SV37: $i] :
( ( ( element @ ( sK21_B @ SV37 ) @ ( powerset @ ( the_carrier @ SV37 ) ) )
= $true )
| ( ( top_str @ SV37 )
= $false )
| ( ( topological_space @ SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[698]) ).
thf(738,plain,
! [SV37: $i] :
( ( ( open_subset @ ( sK21_B @ SV37 ) @ SV37 )
= $true )
| ( ( top_str @ SV37 )
= $false )
| ( ( topological_space @ SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[699]) ).
thf(739,plain,
! [SV38: $i] :
( ( ( ~ ( element @ ( sK7_B @ SV38 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV38 ) ) ) ) )
= $false )
| ( ( one_sorted_str @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(740,plain,
! [SV38: $i] :
( ( ( ~ ~ ( empty @ ( sK7_B @ SV38 ) ) )
= $false )
| ( ( one_sorted_str @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(741,plain,
! [SV39: $i] :
( ( ( ! [SY126: $i] :
( ~ ( element @ SY126 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SY126 )
| ( closed_subset @ SY126 @ SV39 ) ) )
= $true )
| ( ( top_str @ SV39 )
= $false )
| ( ( topological_space @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[701]) ).
thf(742,plain,
! [SV39: $i] :
( ( ( ! [SY127: $i] :
( ~ ( element @ SY127 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SY127 )
| ( open_subset @ SY127 @ SV39 ) ) )
= $true )
| ( ( top_str @ SV39 )
= $false )
| ( ( topological_space @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[702]) ).
thf(743,plain,
! [SV40: $i,SV79: $i,SV76: $i] :
( ( ( ( empty_carrier @ SV76 )
| ~ ( topological_space @ SV76 )
| ~ ( top_str @ SV76 ) )
= $true )
| ( ( ~ ( element @ SV79 @ ( the_carrier @ SV76 ) ) )
= $true )
| ( ( ! [SY141: $i] :
( ( SV40 != SY141 )
| ~ ( point_neighbourhood @ SY141 @ SV76 @ SV79 ) )
| ( in @ SV40 @ ( a_2_0_yellow19 @ SV76 @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(744,plain,
! [SV40: $i,SV80: $i,SV77: $i] :
( ( ( ( empty_carrier @ SV77 )
| ~ ( topological_space @ SV77 )
| ~ ( top_str @ SV77 ) )
= $true )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV77 ) ) )
= $true )
| ( ( ~ ( in @ SV40 @ ( a_2_0_yellow19 @ SV77 @ SV80 ) )
| ~ ( ( SV40
!= ( sK23_D @ SV80 @ SV77 @ SV40 ) )
| ~ ( point_neighbourhood @ ( sK23_D @ SV80 @ SV77 @ SV40 ) @ SV77 @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[704]) ).
thf(745,plain,
! [SV41: $i] :
( ( ( element @ ( sK9_B @ SV41 ) @ ( powerset @ SV41 ) )
= $true )
| ( ( empty @ SV41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[705]) ).
thf(746,plain,
! [SV41: $i] :
( ( ( ~ ( empty @ ( sK9_B @ SV41 ) ) )
= $true )
| ( ( empty @ SV41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[706]) ).
thf(747,plain,
! [SV82: $i] :
( ( ( ~ ( rel_str @ SV82 ) )
= $true )
| ( ( ( empty_carrier @ SV82 )
| ~ ( complete_relstr @ SV82 )
| ~ ( empty_carrier @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[707]) ).
thf(748,plain,
! [SV83: $i] :
( ( ( ~ ( rel_str @ SV83 ) )
= $true )
| ( ( ( empty_carrier @ SV83 )
| ~ ( complete_relstr @ SV83 )
| ( with_suprema_relstr @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[708]) ).
thf(749,plain,
! [SV69: $i] :
( ( ( empty_carrier @ SV69 )
= $true )
| ( ( ~ ( complete_relstr @ SV69 ) )
= $true )
| ( ( with_infima_relstr @ SV69 )
= $true )
| ( ( rel_str @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(750,plain,
! [SV42: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK4_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) )
| ~ ~ ( empty @ ( sK4_B @ SV42 ) ) ) )
= $false )
| ( ( topological_space @ SV42 )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( top_str @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[710]) ).
thf(751,plain,
! [SV42: $i] :
( ( ( ~ ( closed_subset @ ( sK4_B @ SV42 ) @ SV42 ) )
= $false )
| ( ( topological_space @ SV42 )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( top_str @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[710]) ).
thf(752,plain,
( ( ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
= $false )
| ( ( ~ ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(753,plain,
! [SV43: $i] :
( ( ( ~ ( ~ ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
| ~ ( open_subset @ ( sK11_B @ SV43 ) @ SV43 ) ) )
= $true )
| ( ( top_str @ SV43 )
= $false )
| ( ( topological_space @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[713]) ).
thf(754,plain,
! [SV43: $i] :
( ( ( closed_subset @ ( sK11_B @ SV43 ) @ SV43 )
= $true )
| ( ( top_str @ SV43 )
= $false )
| ( ( topological_space @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[714]) ).
thf(755,plain,
! [SV70: $i] :
( ( ( with_suprema_relstr @ SV70 )
= $false )
| ( ( rel_str @ SV70 )
= $false )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(756,plain,
! [SV71: $i] :
( ( ( with_suprema_relstr @ SV71 )
= $false )
| ( ( rel_str @ SV71 )
= $false )
| ( ( directed_subset @ ( cast_as_carrier_subset @ SV71 ) @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(757,plain,
! [SV72: $i] :
( ( ( with_infima_relstr @ SV72 )
= $false )
| ( ( rel_str @ SV72 )
= $false )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV72 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(758,plain,
! [SV73: $i] :
( ( ( with_infima_relstr @ SV73 )
= $false )
| ( ( rel_str @ SV73 )
= $false )
| ( ( filtered_subset @ ( cast_as_carrier_subset @ SV73 ) @ SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(759,plain,
! [SV45: $i] :
( ( empty @ ( sK10_B @ SV45 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(760,plain,
! [SV46: $i] :
( ( ( closed_subset @ ( sK18_B @ SV46 ) @ SV46 )
= $true )
| ( ( top_str @ SV46 )
= $false )
| ( ( topological_space @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[721]) ).
thf(761,plain,
! [SV46: $i] :
( ( ( element @ ( sK18_B @ SV46 ) @ ( powerset @ ( the_carrier @ SV46 ) ) )
= $true )
| ( ( top_str @ SV46 )
= $false )
| ( ( topological_space @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[722]) ).
thf(762,plain,
! [SV47: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK8_B @ SV47 ) @ ( powerset @ ( the_carrier @ SV47 ) ) )
| ~ ~ ( empty @ ( sK8_B @ SV47 ) ) )
| ~ ( open_subset @ ( sK8_B @ SV47 ) @ SV47 ) ) )
= $false )
| ( ( topological_space @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( top_str @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[723]) ).
thf(763,plain,
! [SV47: $i] :
( ( ( ~ ( closed_subset @ ( sK8_B @ SV47 ) @ SV47 ) )
= $false )
| ( ( topological_space @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( top_str @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[723]) ).
thf(764,plain,
! [SV5: $i,SV81: $i] :
( ( ( element @ SV81 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( ( neighborhood_system @ SV5 @ SV81 )
= ( a_2_0_yellow19 @ SV5 @ SV81 ) )
= $true )
| ( ( topological_space @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( top_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(765,plain,
! [SV7: $i,SV49: $i] :
( ( ( element @ SV49 @ ( the_carrier @ SV7 ) )
= $false )
| ( ( topological_space @ SV7 )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( top_str @ SV7 )
= $false )
| ( ( ! [SY133: $i] :
( ~ ( point_neighbourhood @ SY133 @ SV7 @ SV49 )
| ( element @ SY133 @ ( powerset @ ( the_carrier @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(766,plain,
! [SV8: $i,SV50: $i] :
( ( ( element @ SV50 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( topological_space @ SV8 )
= $false )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( top_str @ SV8 )
= $false )
| ( ( point_neighbourhood @ ( sK25_C @ SV50 @ SV8 ) @ SV8 @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(767,plain,
! [SV21: $i,SV78: $i] :
( ( ( ~ ( empty @ SV78 ) )
= $true )
| ( ( nowhere_dense @ SV78 @ SV21 )
= $true )
| ( ( element @ SV78 @ ( powerset @ ( the_carrier @ SV21 ) ) )
= $false )
| ( ( top_str @ SV21 )
= $false )
| ( ( topological_space @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[729]) ).
thf(768,plain,
! [SV22: $i,SV56: $i] :
( ( ( element @ SV56 @ ( the_carrier @ SV22 ) )
= $false )
| ( ( topological_space @ SV22 )
= $false )
| ( ( empty_carrier @ SV22 )
= $true )
| ( ( top_str @ SV22 )
= $false )
| ( ( element @ ( neighborhood_system @ SV22 @ SV56 ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(769,plain,
! [SV34: $i,SV60: $i] :
( ( ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV60 )
= $false )
| ( ( in @ ( sK17_C @ SV60 @ SV34 ) @ SV34 )
= $false )
| ( ( SV34 = SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(770,plain,
! [SV36: $i] :
( ( ( empty @ ( sK6_B @ SV36 ) )
= $false )
| ( ( empty @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(771,plain,
! [SV38: $i] :
( ( ( element @ ( sK7_B @ SV38 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV38 ) ) ) )
= $true )
| ( ( one_sorted_str @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(772,plain,
! [SV38: $i] :
( ( ( ~ ( empty @ ( sK7_B @ SV38 ) ) )
= $true )
| ( ( one_sorted_str @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[740]) ).
thf(773,plain,
! [SV39: $i,SV84: $i] :
( ( ( ~ ( element @ SV84 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SV84 )
| ( closed_subset @ SV84 @ SV39 ) )
= $true )
| ( ( top_str @ SV39 )
= $false )
| ( ( topological_space @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(774,plain,
! [SV39: $i,SV85: $i] :
( ( ( ~ ( element @ SV85 @ ( powerset @ ( the_carrier @ SV39 ) ) )
| ~ ( empty @ SV85 )
| ( open_subset @ SV85 @ SV39 ) )
= $true )
| ( ( top_str @ SV39 )
= $false )
| ( ( topological_space @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(775,plain,
! [SV40: $i,SV79: $i,SV76: $i] :
( ( ( ( empty_carrier @ SV76 )
| ~ ( topological_space @ SV76 ) )
= $true )
| ( ( ~ ( top_str @ SV76 ) )
= $true )
| ( ( ~ ( element @ SV79 @ ( the_carrier @ SV76 ) ) )
= $true )
| ( ( ! [SY141: $i] :
( ( SV40 != SY141 )
| ~ ( point_neighbourhood @ SY141 @ SV76 @ SV79 ) )
| ( in @ SV40 @ ( a_2_0_yellow19 @ SV76 @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(776,plain,
! [SV40: $i,SV80: $i,SV77: $i] :
( ( ( ( empty_carrier @ SV77 )
| ~ ( topological_space @ SV77 ) )
= $true )
| ( ( ~ ( top_str @ SV77 ) )
= $true )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV77 ) ) )
= $true )
| ( ( ~ ( in @ SV40 @ ( a_2_0_yellow19 @ SV77 @ SV80 ) )
| ~ ( ( SV40
!= ( sK23_D @ SV80 @ SV77 @ SV40 ) )
| ~ ( point_neighbourhood @ ( sK23_D @ SV80 @ SV77 @ SV40 ) @ SV77 @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(777,plain,
! [SV41: $i] :
( ( ( empty @ ( sK9_B @ SV41 ) )
= $false )
| ( ( empty @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(778,plain,
! [SV82: $i] :
( ( ( rel_str @ SV82 )
= $false )
| ( ( ( empty_carrier @ SV82 )
| ~ ( complete_relstr @ SV82 )
| ~ ( empty_carrier @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(779,plain,
! [SV83: $i] :
( ( ( rel_str @ SV83 )
= $false )
| ( ( ( empty_carrier @ SV83 )
| ~ ( complete_relstr @ SV83 )
| ( with_suprema_relstr @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(780,plain,
! [SV69: $i] :
( ( ( complete_relstr @ SV69 )
= $false )
| ( ( empty_carrier @ SV69 )
= $true )
| ( ( with_infima_relstr @ SV69 )
= $true )
| ( ( rel_str @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(781,plain,
! [SV42: $i] :
( ( ( ~ ( ~ ( element @ ( sK4_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) )
| ~ ~ ( empty @ ( sK4_B @ SV42 ) ) ) )
= $true )
| ( ( topological_space @ SV42 )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( top_str @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[750]) ).
thf(782,plain,
! [SV42: $i] :
( ( ( closed_subset @ ( sK4_B @ SV42 ) @ SV42 )
= $true )
| ( ( topological_space @ SV42 )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( top_str @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[751]) ).
thf(783,plain,
( ( ( point_neighbourhood @ sK3_SY105 @ sK1_A @ sK2_SY103 )
= $false )
| ( ( in @ sK3_SY105 @ ( neighborhood_system @ sK1_A @ sK2_SY103 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(784,plain,
! [SV43: $i] :
( ( ( ~ ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
| ~ ( open_subset @ ( sK11_B @ SV43 ) @ SV43 ) )
= $false )
| ( ( top_str @ SV43 )
= $false )
| ( ( topological_space @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(785,plain,
! [SV70: $i] :
( ( ( empty @ ( cast_as_carrier_subset @ SV70 ) )
= $false )
| ( ( rel_str @ SV70 )
= $false )
| ( ( with_suprema_relstr @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(786,plain,
! [SV72: $i] :
( ( ( empty @ ( cast_as_carrier_subset @ SV72 ) )
= $false )
| ( ( rel_str @ SV72 )
= $false )
| ( ( with_infima_relstr @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(787,plain,
! [SV47: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK8_B @ SV47 ) @ ( powerset @ ( the_carrier @ SV47 ) ) )
| ~ ~ ( empty @ ( sK8_B @ SV47 ) ) )
| ~ ( open_subset @ ( sK8_B @ SV47 ) @ SV47 ) ) )
= $true )
| ( ( topological_space @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( top_str @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[762]) ).
thf(788,plain,
! [SV47: $i] :
( ( ( closed_subset @ ( sK8_B @ SV47 ) @ SV47 )
= $true )
| ( ( topological_space @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( top_str @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[763]) ).
thf(789,plain,
! [SV49: $i,SV7: $i,SV86: $i] :
( ( ( ~ ( point_neighbourhood @ SV86 @ SV7 @ SV49 )
| ( element @ SV86 @ ( powerset @ ( the_carrier @ SV7 ) ) ) )
= $true )
| ( ( top_str @ SV7 )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( topological_space @ SV7 )
= $false )
| ( ( element @ SV49 @ ( the_carrier @ SV7 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(790,plain,
! [SV21: $i,SV78: $i] :
( ( ( empty @ SV78 )
= $false )
| ( ( nowhere_dense @ SV78 @ SV21 )
= $true )
| ( ( element @ SV78 @ ( powerset @ ( the_carrier @ SV21 ) ) )
= $false )
| ( ( top_str @ SV21 )
= $false )
| ( ( topological_space @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(791,plain,
! [SV38: $i] :
( ( ( empty @ ( sK7_B @ SV38 ) )
= $false )
| ( ( one_sorted_str @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(792,plain,
! [SV39: $i,SV84: $i] :
( ( ( ~ ( element @ SV84 @ ( powerset @ ( the_carrier @ SV39 ) ) ) )
= $true )
| ( ( ~ ( empty @ SV84 )
| ( closed_subset @ SV84 @ SV39 ) )
= $true )
| ( ( top_str @ SV39 )
= $false )
| ( ( topological_space @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[773]) ).
thf(793,plain,
! [SV39: $i,SV85: $i] :
( ( ( ~ ( element @ SV85 @ ( powerset @ ( the_carrier @ SV39 ) ) ) )
= $true )
| ( ( ~ ( empty @ SV85 )
| ( open_subset @ SV85 @ SV39 ) )
= $true )
| ( ( top_str @ SV39 )
= $false )
| ( ( topological_space @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(794,plain,
! [SV40: $i,SV79: $i,SV76: $i] :
( ( ( empty_carrier @ SV76 )
= $true )
| ( ( ~ ( topological_space @ SV76 ) )
= $true )
| ( ( ~ ( top_str @ SV76 ) )
= $true )
| ( ( ~ ( element @ SV79 @ ( the_carrier @ SV76 ) ) )
= $true )
| ( ( ! [SY141: $i] :
( ( SV40 != SY141 )
| ~ ( point_neighbourhood @ SY141 @ SV76 @ SV79 ) )
| ( in @ SV40 @ ( a_2_0_yellow19 @ SV76 @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(795,plain,
! [SV40: $i,SV80: $i,SV77: $i] :
( ( ( empty_carrier @ SV77 )
= $true )
| ( ( ~ ( topological_space @ SV77 ) )
= $true )
| ( ( ~ ( top_str @ SV77 ) )
= $true )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV77 ) ) )
= $true )
| ( ( ~ ( in @ SV40 @ ( a_2_0_yellow19 @ SV77 @ SV80 ) )
| ~ ( ( SV40
!= ( sK23_D @ SV80 @ SV77 @ SV40 ) )
| ~ ( point_neighbourhood @ ( sK23_D @ SV80 @ SV77 @ SV40 ) @ SV77 @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(796,plain,
! [SV82: $i] :
( ( ( ( empty_carrier @ SV82 )
| ~ ( complete_relstr @ SV82 ) )
= $true )
| ( ( ~ ( empty_carrier @ SV82 ) )
= $true )
| ( ( rel_str @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(797,plain,
! [SV83: $i] :
( ( ( ( empty_carrier @ SV83 )
| ~ ( complete_relstr @ SV83 ) )
= $true )
| ( ( with_suprema_relstr @ SV83 )
= $true )
| ( ( rel_str @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[779]) ).
thf(798,plain,
! [SV42: $i] :
( ( ( ~ ( element @ ( sK4_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) )
| ~ ~ ( empty @ ( sK4_B @ SV42 ) ) )
= $false )
| ( ( topological_space @ SV42 )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( top_str @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(799,plain,
! [SV43: $i] :
( ( ( ~ ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) ) )
= $false )
| ( ( top_str @ SV43 )
= $false )
| ( ( topological_space @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(800,plain,
! [SV43: $i] :
( ( ( ~ ( open_subset @ ( sK11_B @ SV43 ) @ SV43 ) )
= $false )
| ( ( top_str @ SV43 )
= $false )
| ( ( topological_space @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(801,plain,
! [SV47: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK8_B @ SV47 ) @ ( powerset @ ( the_carrier @ SV47 ) ) )
| ~ ~ ( empty @ ( sK8_B @ SV47 ) ) )
| ~ ( open_subset @ ( sK8_B @ SV47 ) @ SV47 ) )
= $false )
| ( ( topological_space @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( top_str @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(802,plain,
! [SV49: $i,SV7: $i,SV86: $i] :
( ( ( ~ ( point_neighbourhood @ SV86 @ SV7 @ SV49 ) )
= $true )
| ( ( element @ SV86 @ ( powerset @ ( the_carrier @ SV7 ) ) )
= $true )
| ( ( top_str @ SV7 )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( topological_space @ SV7 )
= $false )
| ( ( element @ SV49 @ ( the_carrier @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(803,plain,
! [SV39: $i,SV84: $i] :
( ( ( element @ SV84 @ ( powerset @ ( the_carrier @ SV39 ) ) )
= $false )
| ( ( ~ ( empty @ SV84 )
| ( closed_subset @ SV84 @ SV39 ) )
= $true )
| ( ( top_str @ SV39 )
= $false )
| ( ( topological_space @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(804,plain,
! [SV39: $i,SV85: $i] :
( ( ( element @ SV85 @ ( powerset @ ( the_carrier @ SV39 ) ) )
= $false )
| ( ( ~ ( empty @ SV85 )
| ( open_subset @ SV85 @ SV39 ) )
= $true )
| ( ( top_str @ SV39 )
= $false )
| ( ( topological_space @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(805,plain,
! [SV40: $i,SV79: $i,SV76: $i] :
( ( ( topological_space @ SV76 )
= $false )
| ( ( empty_carrier @ SV76 )
= $true )
| ( ( ~ ( top_str @ SV76 ) )
= $true )
| ( ( ~ ( element @ SV79 @ ( the_carrier @ SV76 ) ) )
= $true )
| ( ( ! [SY141: $i] :
( ( SV40 != SY141 )
| ~ ( point_neighbourhood @ SY141 @ SV76 @ SV79 ) )
| ( in @ SV40 @ ( a_2_0_yellow19 @ SV76 @ SV79 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(806,plain,
! [SV40: $i,SV80: $i,SV77: $i] :
( ( ( topological_space @ SV77 )
= $false )
| ( ( empty_carrier @ SV77 )
= $true )
| ( ( ~ ( top_str @ SV77 ) )
= $true )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV77 ) ) )
= $true )
| ( ( ~ ( in @ SV40 @ ( a_2_0_yellow19 @ SV77 @ SV80 ) )
| ~ ( ( SV40
!= ( sK23_D @ SV80 @ SV77 @ SV40 ) )
| ~ ( point_neighbourhood @ ( sK23_D @ SV80 @ SV77 @ SV40 ) @ SV77 @ SV80 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(807,plain,
! [SV82: $i] :
( ( ( empty_carrier @ SV82 )
= $true )
| ( ( ~ ( complete_relstr @ SV82 ) )
= $true )
| ( ( ~ ( empty_carrier @ SV82 ) )
= $true )
| ( ( rel_str @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(808,plain,
! [SV83: $i] :
( ( ( empty_carrier @ SV83 )
= $true )
| ( ( ~ ( complete_relstr @ SV83 ) )
= $true )
| ( ( with_suprema_relstr @ SV83 )
= $true )
| ( ( rel_str @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[797]) ).
thf(809,plain,
! [SV42: $i] :
( ( ( ~ ( element @ ( sK4_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) ) )
= $false )
| ( ( topological_space @ SV42 )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( top_str @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(810,plain,
! [SV42: $i] :
( ( ( ~ ~ ( empty @ ( sK4_B @ SV42 ) ) )
= $false )
| ( ( topological_space @ SV42 )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( top_str @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(811,plain,
! [SV43: $i] :
( ( ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
= $true )
| ( ( top_str @ SV43 )
= $false )
| ( ( topological_space @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(812,plain,
! [SV43: $i] :
( ( ( open_subset @ ( sK11_B @ SV43 ) @ SV43 )
= $true )
| ( ( top_str @ SV43 )
= $false )
| ( ( topological_space @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(813,plain,
! [SV47: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK8_B @ SV47 ) @ ( powerset @ ( the_carrier @ SV47 ) ) )
| ~ ~ ( empty @ ( sK8_B @ SV47 ) ) ) )
= $false )
| ( ( topological_space @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( top_str @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[801]) ).
thf(814,plain,
! [SV47: $i] :
( ( ( ~ ( open_subset @ ( sK8_B @ SV47 ) @ SV47 ) )
= $false )
| ( ( topological_space @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( top_str @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[801]) ).
thf(815,plain,
! [SV49: $i,SV7: $i,SV86: $i] :
( ( ( point_neighbourhood @ SV86 @ SV7 @ SV49 )
= $false )
| ( ( element @ SV86 @ ( powerset @ ( the_carrier @ SV7 ) ) )
= $true )
| ( ( top_str @ SV7 )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( topological_space @ SV7 )
= $false )
| ( ( element @ SV49 @ ( the_carrier @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(816,plain,
! [SV39: $i,SV84: $i] :
( ( ( ~ ( empty @ SV84 ) )
= $true )
| ( ( closed_subset @ SV84 @ SV39 )
= $true )
| ( ( element @ SV84 @ ( powerset @ ( the_carrier @ SV39 ) ) )
= $false )
| ( ( top_str @ SV39 )
= $false )
| ( ( topological_space @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[803]) ).
thf(817,plain,
! [SV39: $i,SV85: $i] :
( ( ( ~ ( empty @ SV85 ) )
= $true )
| ( ( open_subset @ SV85 @ SV39 )
= $true )
| ( ( element @ SV85 @ ( powerset @ ( the_carrier @ SV39 ) ) )
= $false )
| ( ( top_str @ SV39 )
= $false )
| ( ( topological_space @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[804]) ).
thf(818,plain,
! [SV40: $i,SV79: $i,SV76: $i] :
( ( ( top_str @ SV76 )
= $false )
| ( ( empty_carrier @ SV76 )
= $true )
| ( ( topological_space @ SV76 )
= $false )
| ( ( ~ ( element @ SV79 @ ( the_carrier @ SV76 ) ) )
= $true )
| ( ( ! [SY141: $i] :
( ( SV40 != SY141 )
| ~ ( point_neighbourhood @ SY141 @ SV76 @ SV79 ) )
| ( in @ SV40 @ ( a_2_0_yellow19 @ SV76 @ SV79 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(819,plain,
! [SV40: $i,SV80: $i,SV77: $i] :
( ( ( top_str @ SV77 )
= $false )
| ( ( empty_carrier @ SV77 )
= $true )
| ( ( topological_space @ SV77 )
= $false )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV77 ) ) )
= $true )
| ( ( ~ ( in @ SV40 @ ( a_2_0_yellow19 @ SV77 @ SV80 ) )
| ~ ( ( SV40
!= ( sK23_D @ SV80 @ SV77 @ SV40 ) )
| ~ ( point_neighbourhood @ ( sK23_D @ SV80 @ SV77 @ SV40 ) @ SV77 @ SV80 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(820,plain,
! [SV82: $i] :
( ( ( complete_relstr @ SV82 )
= $false )
| ( ( empty_carrier @ SV82 )
= $true )
| ( ( ~ ( empty_carrier @ SV82 ) )
= $true )
| ( ( rel_str @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(821,plain,
! [SV83: $i] :
( ( ( complete_relstr @ SV83 )
= $false )
| ( ( empty_carrier @ SV83 )
= $true )
| ( ( with_suprema_relstr @ SV83 )
= $true )
| ( ( rel_str @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(822,plain,
! [SV42: $i] :
( ( ( element @ ( sK4_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) )
= $true )
| ( ( topological_space @ SV42 )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( top_str @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[809]) ).
thf(823,plain,
! [SV42: $i] :
( ( ( ~ ( empty @ ( sK4_B @ SV42 ) ) )
= $true )
| ( ( topological_space @ SV42 )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( top_str @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(824,plain,
! [SV47: $i] :
( ( ( ~ ( ~ ( element @ ( sK8_B @ SV47 ) @ ( powerset @ ( the_carrier @ SV47 ) ) )
| ~ ~ ( empty @ ( sK8_B @ SV47 ) ) ) )
= $true )
| ( ( topological_space @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( top_str @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[813]) ).
thf(825,plain,
! [SV47: $i] :
( ( ( open_subset @ ( sK8_B @ SV47 ) @ SV47 )
= $true )
| ( ( topological_space @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( top_str @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[814]) ).
thf(826,plain,
! [SV39: $i,SV84: $i] :
( ( ( empty @ SV84 )
= $false )
| ( ( closed_subset @ SV84 @ SV39 )
= $true )
| ( ( element @ SV84 @ ( powerset @ ( the_carrier @ SV39 ) ) )
= $false )
| ( ( top_str @ SV39 )
= $false )
| ( ( topological_space @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(827,plain,
! [SV39: $i,SV85: $i] :
( ( ( empty @ SV85 )
= $false )
| ( ( open_subset @ SV85 @ SV39 )
= $true )
| ( ( element @ SV85 @ ( powerset @ ( the_carrier @ SV39 ) ) )
= $false )
| ( ( top_str @ SV39 )
= $false )
| ( ( topological_space @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[817]) ).
thf(828,plain,
! [SV40: $i,SV76: $i,SV79: $i] :
( ( ( element @ SV79 @ ( the_carrier @ SV76 ) )
= $false )
| ( ( topological_space @ SV76 )
= $false )
| ( ( empty_carrier @ SV76 )
= $true )
| ( ( top_str @ SV76 )
= $false )
| ( ( ! [SY141: $i] :
( ( SV40 != SY141 )
| ~ ( point_neighbourhood @ SY141 @ SV76 @ SV79 ) )
| ( in @ SV40 @ ( a_2_0_yellow19 @ SV76 @ SV79 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[818]) ).
thf(829,plain,
! [SV40: $i,SV77: $i,SV80: $i] :
( ( ( element @ SV80 @ ( the_carrier @ SV77 ) )
= $false )
| ( ( topological_space @ SV77 )
= $false )
| ( ( empty_carrier @ SV77 )
= $true )
| ( ( top_str @ SV77 )
= $false )
| ( ( ~ ( in @ SV40 @ ( a_2_0_yellow19 @ SV77 @ SV80 ) )
| ~ ( ( SV40
!= ( sK23_D @ SV80 @ SV77 @ SV40 ) )
| ~ ( point_neighbourhood @ ( sK23_D @ SV80 @ SV77 @ SV40 ) @ SV77 @ SV80 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[819]) ).
thf(830,plain,
! [SV82: $i] :
( ( ( empty_carrier @ SV82 )
= $false )
| ( ( empty_carrier @ SV82 )
= $true )
| ( ( complete_relstr @ SV82 )
= $false )
| ( ( rel_str @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(831,plain,
! [SV42: $i] :
( ( ( empty @ ( sK4_B @ SV42 ) )
= $false )
| ( ( topological_space @ SV42 )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( top_str @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(832,plain,
! [SV47: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV47 ) @ ( powerset @ ( the_carrier @ SV47 ) ) )
| ~ ~ ( empty @ ( sK8_B @ SV47 ) ) )
= $false )
| ( ( topological_space @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( top_str @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[824]) ).
thf(833,plain,
! [SV79: $i,SV76: $i,SV40: $i] :
( ( ( ! [SY141: $i] :
( ( SV40 != SY141 )
| ~ ( point_neighbourhood @ SY141 @ SV76 @ SV79 ) ) )
= $true )
| ( ( in @ SV40 @ ( a_2_0_yellow19 @ SV76 @ SV79 ) )
= $true )
| ( ( top_str @ SV76 )
= $false )
| ( ( empty_carrier @ SV76 )
= $true )
| ( ( topological_space @ SV76 )
= $false )
| ( ( element @ SV79 @ ( the_carrier @ SV76 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[828]) ).
thf(834,plain,
! [SV80: $i,SV77: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ ( a_2_0_yellow19 @ SV77 @ SV80 ) ) )
= $true )
| ( ( ~ ( ( SV40
!= ( sK23_D @ SV80 @ SV77 @ SV40 ) )
| ~ ( point_neighbourhood @ ( sK23_D @ SV80 @ SV77 @ SV40 ) @ SV77 @ SV80 ) ) )
= $true )
| ( ( top_str @ SV77 )
= $false )
| ( ( empty_carrier @ SV77 )
= $true )
| ( ( topological_space @ SV77 )
= $false )
| ( ( element @ SV80 @ ( the_carrier @ SV77 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(835,plain,
! [SV47: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV47 ) @ ( powerset @ ( the_carrier @ SV47 ) ) ) )
= $false )
| ( ( topological_space @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( top_str @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[832]) ).
thf(836,plain,
! [SV47: $i] :
( ( ( ~ ~ ( empty @ ( sK8_B @ SV47 ) ) )
= $false )
| ( ( topological_space @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( top_str @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[832]) ).
thf(837,plain,
! [SV79: $i,SV76: $i,SV87: $i,SV40: $i] :
( ( ( ( SV40 != SV87 )
| ~ ( point_neighbourhood @ SV87 @ SV76 @ SV79 ) )
= $true )
| ( ( in @ SV40 @ ( a_2_0_yellow19 @ SV76 @ SV79 ) )
= $true )
| ( ( top_str @ SV76 )
= $false )
| ( ( empty_carrier @ SV76 )
= $true )
| ( ( topological_space @ SV76 )
= $false )
| ( ( element @ SV79 @ ( the_carrier @ SV76 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(838,plain,
! [SV80: $i,SV77: $i,SV40: $i] :
( ( ( in @ SV40 @ ( a_2_0_yellow19 @ SV77 @ SV80 ) )
= $false )
| ( ( ~ ( ( SV40
!= ( sK23_D @ SV80 @ SV77 @ SV40 ) )
| ~ ( point_neighbourhood @ ( sK23_D @ SV80 @ SV77 @ SV40 ) @ SV77 @ SV80 ) ) )
= $true )
| ( ( top_str @ SV77 )
= $false )
| ( ( empty_carrier @ SV77 )
= $true )
| ( ( topological_space @ SV77 )
= $false )
| ( ( element @ SV80 @ ( the_carrier @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(839,plain,
! [SV47: $i] :
( ( ( element @ ( sK8_B @ SV47 ) @ ( powerset @ ( the_carrier @ SV47 ) ) )
= $true )
| ( ( topological_space @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( top_str @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[835]) ).
thf(840,plain,
! [SV47: $i] :
( ( ( ~ ( empty @ ( sK8_B @ SV47 ) ) )
= $true )
| ( ( topological_space @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( top_str @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[836]) ).
thf(841,plain,
! [SV79: $i,SV76: $i,SV87: $i,SV40: $i] :
( ( ( ( SV40 != SV87 ) )
= $true )
| ( ( ~ ( point_neighbourhood @ SV87 @ SV76 @ SV79 ) )
= $true )
| ( ( in @ SV40 @ ( a_2_0_yellow19 @ SV76 @ SV79 ) )
= $true )
| ( ( top_str @ SV76 )
= $false )
| ( ( empty_carrier @ SV76 )
= $true )
| ( ( topological_space @ SV76 )
= $false )
| ( ( element @ SV79 @ ( the_carrier @ SV76 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(842,plain,
! [SV77: $i,SV80: $i,SV40: $i] :
( ( ( ( SV40
!= ( sK23_D @ SV80 @ SV77 @ SV40 ) )
| ~ ( point_neighbourhood @ ( sK23_D @ SV80 @ SV77 @ SV40 ) @ SV77 @ SV80 ) )
= $false )
| ( ( in @ SV40 @ ( a_2_0_yellow19 @ SV77 @ SV80 ) )
= $false )
| ( ( top_str @ SV77 )
= $false )
| ( ( empty_carrier @ SV77 )
= $true )
| ( ( topological_space @ SV77 )
= $false )
| ( ( element @ SV80 @ ( the_carrier @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(843,plain,
! [SV47: $i] :
( ( ( empty @ ( sK8_B @ SV47 ) )
= $false )
| ( ( topological_space @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( top_str @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[840]) ).
thf(844,plain,
! [SV79: $i,SV76: $i,SV87: $i,SV40: $i] :
( ( ( SV40 = SV87 )
= $false )
| ( ( ~ ( point_neighbourhood @ SV87 @ SV76 @ SV79 ) )
= $true )
| ( ( in @ SV40 @ ( a_2_0_yellow19 @ SV76 @ SV79 ) )
= $true )
| ( ( top_str @ SV76 )
= $false )
| ( ( empty_carrier @ SV76 )
= $true )
| ( ( topological_space @ SV76 )
= $false )
| ( ( element @ SV79 @ ( the_carrier @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(845,plain,
! [SV77: $i,SV80: $i,SV40: $i] :
( ( ( ( SV40
!= ( sK23_D @ SV80 @ SV77 @ SV40 ) ) )
= $false )
| ( ( in @ SV40 @ ( a_2_0_yellow19 @ SV77 @ SV80 ) )
= $false )
| ( ( top_str @ SV77 )
= $false )
| ( ( empty_carrier @ SV77 )
= $true )
| ( ( topological_space @ SV77 )
= $false )
| ( ( element @ SV80 @ ( the_carrier @ SV77 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[842]) ).
thf(846,plain,
! [SV40: $i,SV77: $i,SV80: $i] :
( ( ( ~ ( point_neighbourhood @ ( sK23_D @ SV80 @ SV77 @ SV40 ) @ SV77 @ SV80 ) )
= $false )
| ( ( in @ SV40 @ ( a_2_0_yellow19 @ SV77 @ SV80 ) )
= $false )
| ( ( top_str @ SV77 )
= $false )
| ( ( empty_carrier @ SV77 )
= $true )
| ( ( topological_space @ SV77 )
= $false )
| ( ( element @ SV80 @ ( the_carrier @ SV77 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[842]) ).
thf(847,plain,
! [SV40: $i,SV79: $i,SV76: $i,SV87: $i] :
( ( ( point_neighbourhood @ SV87 @ SV76 @ SV79 )
= $false )
| ( ( SV40 = SV87 )
= $false )
| ( ( in @ SV40 @ ( a_2_0_yellow19 @ SV76 @ SV79 ) )
= $true )
| ( ( top_str @ SV76 )
= $false )
| ( ( empty_carrier @ SV76 )
= $true )
| ( ( topological_space @ SV76 )
= $false )
| ( ( element @ SV79 @ ( the_carrier @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(848,plain,
! [SV77: $i,SV80: $i,SV40: $i] :
( ( ( SV40
= ( sK23_D @ SV80 @ SV77 @ SV40 ) )
= $true )
| ( ( in @ SV40 @ ( a_2_0_yellow19 @ SV77 @ SV80 ) )
= $false )
| ( ( top_str @ SV77 )
= $false )
| ( ( empty_carrier @ SV77 )
= $true )
| ( ( topological_space @ SV77 )
= $false )
| ( ( element @ SV80 @ ( the_carrier @ SV77 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[845]) ).
thf(849,plain,
! [SV40: $i,SV77: $i,SV80: $i] :
( ( ( point_neighbourhood @ ( sK23_D @ SV80 @ SV77 @ SV40 ) @ SV77 @ SV80 )
= $true )
| ( ( in @ SV40 @ ( a_2_0_yellow19 @ SV77 @ SV80 ) )
= $false )
| ( ( top_str @ SV77 )
= $false )
| ( ( empty_carrier @ SV77 )
= $true )
| ( ( topological_space @ SV77 )
= $false )
| ( ( element @ SV80 @ ( the_carrier @ SV77 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[846]) ).
thf(850,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[253,849,848,847,843,839,831,830,827,826,825,822,821,815,812,811,791,790,788,786,785,783,782,780,777,771,770,769,768,766,764,761,760,759,758,756,754,745,738,737,735,734,732,731,728,727,719,712,695,694,692,691,683,660,650,647,646,637,636,635,620,612,604,600,599,598,593,590,589,588,581,578,576,575,569,567,546,533,513,512,510,507,506,486,484,479,478,474,473,467,462,416,366,363,342,306,305,282,281]) ).
thf(851,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[850]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU388+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 20 10:44:31 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.41 ..
% 0.20/0.50
% 0.20/0.50 No.of.Axioms: 118
% 0.20/0.50
% 0.20/0.50 Length.of.Defs: 0
% 0.20/0.50
% 0.20/0.50 Contains.Choice.Funs: false
% 0.20/0.53 .......
% 0.39/0.56 (rf:2,axioms:59,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:120,loop_count:0,foatp_calls:0,translation:fof_full)................................
% 16.63/16.86
% 16.63/16.86 ********************************
% 16.63/16.86 * All subproblems solved! *
% 16.63/16.86 ********************************
% 16.63/16.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:62,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:850,loop_count:0,foatp_calls:1,translation:fof_full)
% 16.88/17.11
% 16.88/17.11 %**** Beginning of derivation protocol ****
% 16.88/17.11 % SZS output start CNFRefutation
% See solution above
% 16.88/17.12
% 16.88/17.12 %**** End of derivation protocol ****
% 16.88/17.12 %**** no. of clauses in derivation: 792 ****
% 16.88/17.12 %**** clause counter: 850 ****
% 16.88/17.12
% 16.88/17.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:62,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:850,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------