%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU315+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:56 AM UTC 2026
% Result : Theorem 248.44s 41.61s
% Output : CNFRefutation 248.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 19
% Syntax : Number of formulae : 330 ( 114 unt; 0 typ; 0 def)
% Number of atoms : 3616 (1102 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 8352 (2363 ~;1347 |; 78 &;4501 @)
% ( 17 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 5 con; 0-3 aty)
% Number of variables : 781 ( 0 ^; 747 !; 34 ?; 781 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_closed_subset,type,
closed_subset: $i > $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_sK10_SY65,type,
sK10_SY65: $i > $i ).
thf(tp_sK11_SY69,type,
sK11_SY69: $i > $i > $i > $i ).
thf(tp_sK12_SY65,type,
sK12_SY65: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY33,type,
sK2_SY33: $i ).
thf(tp_sK3_SY46,type,
sK3_SY46: $i > $i ).
thf(tp_sK4_SY54,type,
sK4_SY54: $i > $i ).
thf(tp_sK5_SY56,type,
sK5_SY56: $i > $i > $i ).
thf(tp_sK6_SY48,type,
sK6_SY48: $i > $i ).
thf(tp_sK7_SY61,type,
sK7_SY61: $i > $i ).
thf(tp_sK8_SY47,type,
sK8_SY47: $i > $i ).
thf(tp_sK9_SY57,type,
sK9_SY57: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
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_v1_int_1,type,
v1_int_1: $i > $o ).
thf(tp_v1_membered,type,
v1_membered: $i > $o ).
thf(tp_v1_rat_1,type,
v1_rat_1: $i > $o ).
thf(tp_v1_xcmplx_0,type,
v1_xcmplx_0: $i > $o ).
thf(tp_v1_xreal_0,type,
v1_xreal_0: $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(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
thf(8,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(9,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( powerset @ ( the_carrier @ A ) ) )
& ? [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( closed_subset @ E @ A )
& ( subset @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e1_40__pre_topc__1) ).
thf(12,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(13,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(14,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(15,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(16,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(17,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(19,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(21,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(22,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(28,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_membered) ).
thf(39,conjecture,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ? [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( in @ D @ C )
<=> ? [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( closed_subset @ E @ A )
& ( subset @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_subset_1__e1_40__pre_topc) ).
thf(40,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ? [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( in @ D @ C )
<=> ? [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( closed_subset @ E @ A )
& ( subset @ B @ D ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[39]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ? [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( in @ D @ C )
<=> ? [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( closed_subset @ E @ A )
& ( subset @ B @ D ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[40]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(44,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(45,plain,
$true = $true,
inference(unfold_def,[status(thm)],[9]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( powerset @ ( the_carrier @ A ) ) )
& ? [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( closed_subset @ E @ A )
& ( subset @ B @ D ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(48,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(49,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)],[13]) ).
thf(50,plain,
$true = $true,
inference(unfold_def,[status(thm)],[14]) ).
thf(51,plain,
$true = $true,
inference(unfold_def,[status(thm)],[15]) ).
thf(52,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(53,plain,
$true = $true,
inference(unfold_def,[status(thm)],[17]) ).
thf(54,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(56,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(57,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(58,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(59,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(60,plain,
( ( ! [SY33: $i] :
( ( ( topological_space @ sK1_A )
& ( top_str @ sK1_A )
& ( element @ SY33 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
=> ? [SY34: $i] :
( ( element @ SY34 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
& ! [SY35: $i] :
( ( element @ SY35 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( ( in @ SY35 @ SY34 )
<=> ? [SY36: $i] :
( ( element @ SY36 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( SY36 = SY35 )
& ( closed_subset @ SY36 @ sK1_A )
& ( subset @ SY33 @ SY35 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(61,plain,
( ( ( ( topological_space @ sK1_A )
& ( top_str @ sK1_A )
& ( element @ sK2_SY33 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
=> ? [SY37: $i] :
( ( element @ SY37 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
& ! [SY38: $i] :
( ( element @ SY38 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( ( in @ SY38 @ SY37 )
<=> ? [SY39: $i] :
( ( element @ SY39 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( SY39 = SY38 )
& ( closed_subset @ SY39 @ sK1_A )
& ( subset @ sK2_SY33 @ SY38 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[60]) ).
thf(62,plain,
( ( topological_space @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[61]) ).
thf(63,plain,
( ( top_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[61]) ).
thf(64,plain,
( ( element @ sK2_SY33 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[61]) ).
thf(65,plain,
( ( ? [SY37: $i] :
( ( element @ SY37 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
& ! [SY38: $i] :
( ( element @ SY38 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( ( in @ SY38 @ SY37 )
<=> ? [SY39: $i] :
( ( element @ SY39 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( SY39 = SY38 )
& ( closed_subset @ SY39 @ sK1_A )
& ( subset @ sK2_SY33 @ SY38 ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[61]) ).
thf(66,plain,
( ( ~ ? [SY37: $i] :
( ( element @ SY37 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
& ! [SY38: $i] :
( ( element @ SY38 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( ( in @ SY38 @ SY37 )
<=> ? [SY39: $i] :
( ( element @ SY39 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( SY39 = SY38 )
& ( closed_subset @ SY39 @ sK1_A )
& ( subset @ sK2_SY33 @ SY38 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[65]) ).
thf(67,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(68,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(69,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(70,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(72,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(73,plain,
$true = $true,
inference(copy,[status(thm)],[53]) ).
thf(74,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(75,plain,
$true = $true,
inference(copy,[status(thm)],[51]) ).
thf(76,plain,
$true = $true,
inference(copy,[status(thm)],[50]) ).
thf(77,plain,
( ( ! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( closed_subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(78,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( powerset @ ( the_carrier @ A ) ) )
& ? [E: $i] :
( ( element @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( closed_subset @ E @ A )
& ( subset @ B @ D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(81,plain,
$true = $true,
inference(copy,[status(thm)],[45]) ).
thf(82,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(83,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(84,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(85,plain,
( ( element @ sK2_SY33 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(86,plain,
( ( top_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(87,plain,
( ( topological_space @ sK1_A )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(88,plain,
( ( ~ ? [SY37: $i] :
( ( element @ SY37 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
& ! [SY38: $i] :
( ( element @ SY38 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( ( in @ SY38 @ SY37 )
<=> ? [SY39: $i] :
( ( element @ SY39 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( SY39 = SY38 )
& ( closed_subset @ SY39 @ sK1_A )
& ( subset @ sK2_SY33 @ SY38 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(89,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( element @ SX0 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SX1 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SX1 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SX1 ) )
| ( in @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(90,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(91,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(92,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(93,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(94,plain,
( ( ! [SX0: $i] :
( ~ ( v1_membered @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v1_membered @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(95,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(96,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( topological_space @ SX0 )
| ~ ( top_str @ SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ( closed_subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(97,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(98,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( topological_space @ SX0 )
| ~ ( top_str @ SX0 ) )
| ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) ) )
| ~ ! [SX2: $i] :
~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX4 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ( SX4 != SX3 ) )
| ~ ( closed_subset @ SX4 @ SX0 ) )
| ~ ( subset @ SX1 @ SX3 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX4 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ( SX4 != SX3 ) )
| ~ ( closed_subset @ SX4 @ SX0 ) )
| ~ ( subset @ SX1 @ SX3 ) ) )
| ( in @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(99,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(100,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ~ ( empty @ SX0 )
| ~ ( ~ ( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( empty @ SX0 )
| ~ ( ~ ( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) )
| ~ ( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(101,plain,
! [SV1: $i] :
( ( ! [SY40: $i] : ( subset @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(102,plain,
! [SV2: $i] :
( ( ~ ( empty @ ( powerset @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(103,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( element @ SX0 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SX1 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SX1 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SX1 ) )
| ( in @ SX1 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(104,plain,
! [SV3: $i] :
( ( ! [SY41: $i] :
( ~ ! [SY42: $i] :
( ~ ( in @ SY42 @ SV3 )
| ( in @ SY42 @ SY41 ) )
| ( element @ SV3 @ ( powerset @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(105,plain,
! [SV4: $i] :
( ( ! [SY43: $i] :
( ~ ( in @ SV4 @ SY43 )
| ~ ( in @ SY43 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(106,plain,
! [SV5: $i] :
( ( ~ ( top_str @ SV5 )
| ( one_sorted_str @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(107,plain,
! [SV6: $i] :
( ( ! [SY44: $i] :
~ ~ ( ~ ( in @ SV6 @ SY44 )
| ~ ( empty @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(108,plain,
! [SV7: $i] :
( ( ~ ( v1_membered @ SV7 )
| ! [SY45: $i] :
( ~ ( element @ SY45 @ ( powerset @ SV7 ) )
| ( v1_membered @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(109,plain,
! [SV8: $i] :
( ( ~ ! [SY46: $i] :
~ ~ ( ~ ( element @ SY46 @ ( powerset @ SV8 ) )
| ~ ( empty @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(110,plain,
! [SV9: $i] :
( ( ~ ~ ( ~ ( topological_space @ SV9 )
| ~ ( top_str @ SV9 ) )
| ~ ! [SY47: $i] :
~ ~ ( ~ ( element @ SY47 @ ( powerset @ ( the_carrier @ SV9 ) ) )
| ~ ( closed_subset @ SY47 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(111,plain,
! [SV10: $i] :
( ( ~ ~ ( empty @ SV10 )
| ~ ! [SY48: $i] :
~ ~ ( ~ ( element @ SY48 @ ( powerset @ SV10 ) )
| ~ ~ ( empty @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(112,plain,
! [SV11: $i] :
( ( ! [SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV11 )
| ~ ( top_str @ SV11 ) )
| ~ ( element @ SY49 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
| ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ( ~ ( in @ SY51 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY52 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY52 != SY51 ) )
| ~ ( closed_subset @ SY52 @ SV11 ) )
| ~ ( subset @ SY49 @ SY51 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY51 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY53 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY53 != SY51 ) )
| ~ ( closed_subset @ SY53 @ SV11 ) )
| ~ ( subset @ SY49 @ SY51 ) ) )
| ( in @ SY51 @ SY50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(113,plain,
! [SV12: $i] :
( ( ~ ! [SY54: $i] :
~ ( element @ SY54 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(114,plain,
! [SV13: $i] :
( ( ! [SY55: $i] :
~ ( ~ ( ~ ~ ( empty @ SV13 )
| ~ ( ~ ( ~ ( element @ SY55 @ SV13 )
| ( in @ SY55 @ SV13 ) )
| ~ ( ~ ( in @ SY55 @ SV13 )
| ( element @ SY55 @ SV13 ) ) ) )
| ~ ( ~ ( empty @ SV13 )
| ~ ( ~ ( ~ ( element @ SY55 @ SV13 )
| ( empty @ SY55 ) )
| ~ ( ~ ( empty @ SY55 )
| ( element @ SY55 @ SV13 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(115,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(116,plain,
! [SV2: $i] :
( ( empty @ ( powerset @ SV2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(117,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( element @ SX0 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SX1 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SX1 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SX1 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SX1 ) )
| ( in @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(118,plain,
! [SV15: $i,SV3: $i] :
( ( ~ ! [SY56: $i] :
( ~ ( in @ SY56 @ SV3 )
| ( in @ SY56 @ SV15 ) )
| ( element @ SV3 @ ( powerset @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(119,plain,
! [SV16: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ SV16 )
| ~ ( in @ SV16 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(120,plain,
! [SV5: $i] :
( ( ( ~ ( top_str @ SV5 ) )
= $true )
| ( ( one_sorted_str @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(121,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ~ ( ~ ( in @ SV6 @ SV17 )
| ~ ( empty @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(122,plain,
! [SV7: $i] :
( ( ( ~ ( v1_membered @ SV7 ) )
= $true )
| ( ( ! [SY45: $i] :
( ~ ( element @ SY45 @ ( powerset @ SV7 ) )
| ( v1_membered @ SY45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(123,plain,
! [SV8: $i] :
( ( ! [SY46: $i] :
~ ~ ( ~ ( element @ SY46 @ ( powerset @ SV8 ) )
| ~ ( empty @ SY46 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(124,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ( topological_space @ SV9 )
| ~ ( top_str @ SV9 ) ) )
= $true )
| ( ( ~ ! [SY47: $i] :
~ ~ ( ~ ( element @ SY47 @ ( powerset @ ( the_carrier @ SV9 ) ) )
| ~ ( closed_subset @ SY47 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(125,plain,
! [SV10: $i] :
( ( ( ~ ~ ( empty @ SV10 ) )
= $true )
| ( ( ~ ! [SY48: $i] :
~ ~ ( ~ ( element @ SY48 @ ( powerset @ SV10 ) )
| ~ ~ ( empty @ SY48 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(126,plain,
! [SV18: $i,SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV11 )
| ~ ( top_str @ SV11 ) )
| ~ ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
| ~ ! [SY57: $i] :
~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SY57 )
| ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY59 != SY58 ) )
| ~ ( closed_subset @ SY59 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY60 != SY58 ) )
| ~ ( closed_subset @ SY60 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) )
| ( in @ SY58 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(127,plain,
! [SV12: $i] :
( ( ! [SY54: $i] :
~ ( element @ SY54 @ SV12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(128,plain,
! [SV19: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ~ ( empty @ SV13 )
| ~ ( ~ ( ~ ( element @ SV19 @ SV13 )
| ( in @ SV19 @ SV13 ) )
| ~ ( ~ ( in @ SV19 @ SV13 )
| ( element @ SV19 @ SV13 ) ) ) )
| ~ ( ~ ( empty @ SV13 )
| ~ ( ~ ( ~ ( element @ SV19 @ SV13 )
| ( empty @ SV19 ) )
| ~ ( ~ ( empty @ SV19 )
| ( element @ SV19 @ SV13 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(129,plain,
! [SV20: $i] :
( ( ~ ~ ( ~ ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
| ~ ! [SY61: $i] :
( ~ ( element @ SY61 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( ~ ( ~ ( in @ SY61 @ SV20 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SY61 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SY61 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SY61 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SY61 ) )
| ( in @ SY61 @ SV20 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV15: $i,SV3: $i] :
( ( ( ~ ! [SY56: $i] :
( ~ ( in @ SY56 @ SV3 )
| ( in @ SY56 @ SV15 ) ) )
= $true )
| ( ( element @ SV3 @ ( powerset @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(131,plain,
! [SV16: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV16 ) )
= $true )
| ( ( ~ ( in @ SV16 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(132,plain,
! [SV5: $i] :
( ( ( top_str @ SV5 )
= $false )
| ( ( one_sorted_str @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(133,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ( ~ ( in @ SV6 @ SV17 )
| ~ ( empty @ SV17 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(134,plain,
! [SV7: $i] :
( ( ( v1_membered @ SV7 )
= $false )
| ( ( ! [SY45: $i] :
( ~ ( element @ SY45 @ ( powerset @ SV7 ) )
| ( v1_membered @ SY45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(135,plain,
! [SV8: $i] :
( ( ~ ~ ( ~ ( element @ ( sK3_SY46 @ SV8 ) @ ( powerset @ SV8 ) )
| ~ ( empty @ ( sK3_SY46 @ SV8 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[123]) ).
thf(136,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ( topological_space @ SV9 )
| ~ ( top_str @ SV9 ) ) )
= $false )
| ( ( ~ ! [SY47: $i] :
~ ~ ( ~ ( element @ SY47 @ ( powerset @ ( the_carrier @ SV9 ) ) )
| ~ ( closed_subset @ SY47 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV10: $i] :
( ( ( ~ ( empty @ SV10 ) )
= $false )
| ( ( ~ ! [SY48: $i] :
~ ~ ( ~ ( element @ SY48 @ ( powerset @ SV10 ) )
| ~ ~ ( empty @ SY48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV18: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV11 )
| ~ ( top_str @ SV11 ) )
| ~ ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) ) ) )
= $true )
| ( ( ~ ! [SY57: $i] :
~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SY57 )
| ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY59 != SY58 ) )
| ~ ( closed_subset @ SY59 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY60 != SY58 ) )
| ~ ( closed_subset @ SY60 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) )
| ( in @ SY58 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(139,plain,
! [SV12: $i] :
( ( ~ ( element @ ( sK4_SY54 @ SV12 ) @ SV12 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[127]) ).
thf(140,plain,
! [SV19: $i,SV13: $i] :
( ( ~ ( ~ ~ ( empty @ SV13 )
| ~ ( ~ ( ~ ( element @ SV19 @ SV13 )
| ( in @ SV19 @ SV13 ) )
| ~ ( ~ ( in @ SV19 @ SV13 )
| ( element @ SV19 @ SV13 ) ) ) )
| ~ ( ~ ( empty @ SV13 )
| ~ ( ~ ( ~ ( element @ SV19 @ SV13 )
| ( empty @ SV19 ) )
| ~ ( ~ ( empty @ SV19 )
| ( element @ SV19 @ SV13 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(141,plain,
! [SV20: $i] :
( ( ~ ( ~ ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
| ~ ! [SY61: $i] :
( ~ ( element @ SY61 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( ~ ( ~ ( in @ SY61 @ SV20 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SY61 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SY61 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SY61 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SY61 ) )
| ( in @ SY61 @ SV20 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(142,plain,
! [SV15: $i,SV3: $i] :
( ( ( ! [SY56: $i] :
( ~ ( in @ SY56 @ SV3 )
| ( in @ SY56 @ SV15 ) ) )
= $false )
| ( ( element @ SV3 @ ( powerset @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(143,plain,
! [SV16: $i,SV4: $i] :
( ( ( in @ SV4 @ SV16 )
= $false )
| ( ( ~ ( in @ SV16 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ SV17 )
| ~ ( empty @ SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(145,plain,
! [SV7: $i,SV21: $i] :
( ( ( ~ ( element @ SV21 @ ( powerset @ SV7 ) )
| ( v1_membered @ SV21 ) )
= $true )
| ( ( v1_membered @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(146,plain,
! [SV8: $i] :
( ( ~ ( ~ ( element @ ( sK3_SY46 @ SV8 ) @ ( powerset @ SV8 ) )
| ~ ( empty @ ( sK3_SY46 @ SV8 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(147,plain,
! [SV9: $i] :
( ( ( ~ ( topological_space @ SV9 )
| ~ ( top_str @ SV9 ) )
= $true )
| ( ( ~ ! [SY47: $i] :
~ ~ ( ~ ( element @ SY47 @ ( powerset @ ( the_carrier @ SV9 ) ) )
| ~ ( closed_subset @ SY47 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(148,plain,
! [SV10: $i] :
( ( ( empty @ SV10 )
= $true )
| ( ( ~ ! [SY48: $i] :
~ ~ ( ~ ( element @ SY48 @ ( powerset @ SV10 ) )
| ~ ~ ( empty @ SY48 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(149,plain,
! [SV18: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ( topological_space @ SV11 )
| ~ ( top_str @ SV11 ) )
| ~ ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) ) ) )
= $false )
| ( ( ~ ! [SY57: $i] :
~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SY57 )
| ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY59 != SY58 ) )
| ~ ( closed_subset @ SY59 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY60 != SY58 ) )
| ~ ( closed_subset @ SY60 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) )
| ( in @ SY58 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(150,plain,
! [SV12: $i] :
( ( element @ ( sK4_SY54 @ SV12 ) @ SV12 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(151,plain,
! [SV19: $i,SV13: $i] :
( ( ~ ( ~ ~ ( empty @ SV13 )
| ~ ( ~ ( ~ ( element @ SV19 @ SV13 )
| ( in @ SV19 @ SV13 ) )
| ~ ( ~ ( in @ SV19 @ SV13 )
| ( element @ SV19 @ SV13 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(152,plain,
! [SV19: $i,SV13: $i] :
( ( ~ ( ~ ( empty @ SV13 )
| ~ ( ~ ( ~ ( element @ SV19 @ SV13 )
| ( empty @ SV19 ) )
| ~ ( ~ ( empty @ SV19 )
| ( element @ SV19 @ SV13 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(153,plain,
! [SV20: $i] :
( ( ~ ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
| ~ ! [SY61: $i] :
( ~ ( element @ SY61 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( ~ ( ~ ( in @ SY61 @ SV20 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SY61 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SY61 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SY61 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SY61 ) )
| ( in @ SY61 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(154,plain,
! [SV3: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK5_SY56 @ SV15 @ SV3 ) @ SV3 )
| ( in @ ( sK5_SY56 @ SV15 @ SV3 ) @ SV15 ) )
= $false )
| ( ( element @ SV3 @ ( powerset @ SV15 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[142]) ).
thf(155,plain,
! [SV4: $i,SV16: $i] :
( ( ( in @ SV16 @ SV4 )
= $false )
| ( ( in @ SV4 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(156,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV17 ) )
= $true )
| ( ( ~ ( empty @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(157,plain,
! [SV7: $i,SV21: $i] :
( ( ( ~ ( element @ SV21 @ ( powerset @ SV7 ) ) )
= $true )
| ( ( v1_membered @ SV21 )
= $true )
| ( ( v1_membered @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(158,plain,
! [SV8: $i] :
( ( ~ ( element @ ( sK3_SY46 @ SV8 ) @ ( powerset @ SV8 ) )
| ~ ( empty @ ( sK3_SY46 @ SV8 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(159,plain,
! [SV9: $i] :
( ( ( ~ ( topological_space @ SV9 ) )
= $true )
| ( ( ~ ( top_str @ SV9 ) )
= $true )
| ( ( ~ ! [SY47: $i] :
~ ~ ( ~ ( element @ SY47 @ ( powerset @ ( the_carrier @ SV9 ) ) )
| ~ ( closed_subset @ SY47 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(160,plain,
! [SV10: $i] :
( ( ( ! [SY48: $i] :
~ ~ ( ~ ( element @ SY48 @ ( powerset @ SV10 ) )
| ~ ~ ( empty @ SY48 ) ) )
= $false )
| ( ( empty @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(161,plain,
! [SV18: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( topological_space @ SV11 )
| ~ ( top_str @ SV11 ) )
| ~ ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( ~ ! [SY57: $i] :
~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SY57 )
| ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY59 != SY58 ) )
| ~ ( closed_subset @ SY59 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY60 != SY58 ) )
| ~ ( closed_subset @ SY60 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) )
| ( in @ SY58 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(162,plain,
! [SV19: $i,SV13: $i] :
( ( ~ ~ ( empty @ SV13 )
| ~ ( ~ ( ~ ( element @ SV19 @ SV13 )
| ( in @ SV19 @ SV13 ) )
| ~ ( ~ ( in @ SV19 @ SV13 )
| ( element @ SV19 @ SV13 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(163,plain,
! [SV19: $i,SV13: $i] :
( ( ~ ( empty @ SV13 )
| ~ ( ~ ( ~ ( element @ SV19 @ SV13 )
| ( empty @ SV19 ) )
| ~ ( ~ ( empty @ SV19 )
| ( element @ SV19 @ SV13 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(164,plain,
! [SV20: $i] :
( ( ( ~ ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) ) )
= $true )
| ( ( ~ ! [SY61: $i] :
( ~ ( element @ SY61 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( ~ ( ~ ( in @ SY61 @ SV20 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SY61 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SY61 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SY61 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SY61 ) )
| ( in @ SY61 @ SV20 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(165,plain,
! [SV3: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK5_SY56 @ SV15 @ SV3 ) @ SV3 ) )
= $false )
| ( ( element @ SV3 @ ( powerset @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(166,plain,
! [SV3: $i,SV15: $i] :
( ( ( in @ ( sK5_SY56 @ SV15 @ SV3 ) @ SV15 )
= $false )
| ( ( element @ SV3 @ ( powerset @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(167,plain,
! [SV17: $i,SV6: $i] :
( ( ( in @ SV6 @ SV17 )
= $false )
| ( ( ~ ( empty @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(168,plain,
! [SV7: $i,SV21: $i] :
( ( ( element @ SV21 @ ( powerset @ SV7 ) )
= $false )
| ( ( v1_membered @ SV21 )
= $true )
| ( ( v1_membered @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(169,plain,
! [SV8: $i] :
( ( ~ ( element @ ( sK3_SY46 @ SV8 ) @ ( powerset @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(170,plain,
! [SV8: $i] :
( ( ~ ( empty @ ( sK3_SY46 @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(171,plain,
! [SV9: $i] :
( ( ( topological_space @ SV9 )
= $false )
| ( ( ~ ( top_str @ SV9 ) )
= $true )
| ( ( ~ ! [SY47: $i] :
~ ~ ( ~ ( element @ SY47 @ ( powerset @ ( the_carrier @ SV9 ) ) )
| ~ ( closed_subset @ SY47 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(172,plain,
! [SV10: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK6_SY48 @ SV10 ) @ ( powerset @ SV10 ) )
| ~ ~ ( empty @ ( sK6_SY48 @ SV10 ) ) ) )
= $false )
| ( ( empty @ SV10 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[160]) ).
thf(173,plain,
! [SV18: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( topological_space @ SV11 )
| ~ ( top_str @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( ~ ! [SY57: $i] :
~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SY57 )
| ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY59 != SY58 ) )
| ~ ( closed_subset @ SY59 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY60 != SY58 ) )
| ~ ( closed_subset @ SY60 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) )
| ( in @ SY58 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(174,plain,
! [SV19: $i,SV13: $i] :
( ( ( ~ ~ ( empty @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV19 @ SV13 )
| ( in @ SV19 @ SV13 ) )
| ~ ( ~ ( in @ SV19 @ SV13 )
| ( element @ SV19 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(175,plain,
! [SV19: $i,SV13: $i] :
( ( ( ~ ( empty @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV19 @ SV13 )
| ( empty @ SV19 ) )
| ~ ( ~ ( empty @ SV19 )
| ( element @ SV19 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(176,plain,
! [SV20: $i] :
( ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false )
| ( ( ~ ! [SY61: $i] :
( ~ ( element @ SY61 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( ~ ( ~ ( in @ SY61 @ SV20 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SY61 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SY61 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SY61 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SY61 ) )
| ( in @ SY61 @ SV20 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(177,plain,
! [SV3: $i,SV15: $i] :
( ( ( in @ ( sK5_SY56 @ SV15 @ SV3 ) @ SV3 )
= $true )
| ( ( element @ SV3 @ ( powerset @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(178,plain,
! [SV6: $i,SV17: $i] :
( ( ( empty @ SV17 )
= $false )
| ( ( in @ SV6 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(179,plain,
! [SV8: $i] :
( ( element @ ( sK3_SY46 @ SV8 ) @ ( powerset @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(180,plain,
! [SV8: $i] :
( ( empty @ ( sK3_SY46 @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(181,plain,
! [SV9: $i] :
( ( ( top_str @ SV9 )
= $false )
| ( ( topological_space @ SV9 )
= $false )
| ( ( ~ ! [SY47: $i] :
~ ~ ( ~ ( element @ SY47 @ ( powerset @ ( the_carrier @ SV9 ) ) )
| ~ ( closed_subset @ SY47 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(182,plain,
! [SV10: $i] :
( ( ( ~ ( ~ ( element @ ( sK6_SY48 @ SV10 ) @ ( powerset @ SV10 ) )
| ~ ~ ( empty @ ( sK6_SY48 @ SV10 ) ) ) )
= $true )
| ( ( empty @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(183,plain,
! [SV18: $i,SV11: $i] :
( ( ( ~ ( ~ ( topological_space @ SV11 )
| ~ ( top_str @ SV11 ) ) )
= $false )
| ( ( ~ ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( ~ ! [SY57: $i] :
~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SY57 )
| ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY59 != SY58 ) )
| ~ ( closed_subset @ SY59 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY60 != SY58 ) )
| ~ ( closed_subset @ SY60 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) )
| ( in @ SY58 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(184,plain,
! [SV19: $i,SV13: $i] :
( ( ( ~ ( empty @ SV13 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( element @ SV19 @ SV13 )
| ( in @ SV19 @ SV13 ) )
| ~ ( ~ ( in @ SV19 @ SV13 )
| ( element @ SV19 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(185,plain,
! [SV19: $i,SV13: $i] :
( ( ( empty @ SV13 )
= $false )
| ( ( ~ ( ~ ( ~ ( element @ SV19 @ SV13 )
| ( empty @ SV19 ) )
| ~ ( ~ ( empty @ SV19 )
| ( element @ SV19 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(186,plain,
! [SV20: $i] :
( ( ( ! [SY61: $i] :
( ~ ( element @ SY61 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( ~ ( ~ ( in @ SY61 @ SV20 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SY61 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SY61 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SX2 != SY61 ) )
| ~ ( closed_subset @ SX2 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ SY61 ) )
| ( in @ SY61 @ SV20 ) ) ) ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(187,plain,
! [SV9: $i] :
( ( ( ! [SY47: $i] :
~ ~ ( ~ ( element @ SY47 @ ( powerset @ ( the_carrier @ SV9 ) ) )
| ~ ( closed_subset @ SY47 @ SV9 ) ) )
= $false )
| ( ( topological_space @ SV9 )
= $false )
| ( ( top_str @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(188,plain,
! [SV10: $i] :
( ( ( ~ ( element @ ( sK6_SY48 @ SV10 ) @ ( powerset @ SV10 ) )
| ~ ~ ( empty @ ( sK6_SY48 @ SV10 ) ) )
= $false )
| ( ( empty @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(189,plain,
! [SV18: $i,SV11: $i] :
( ( ( ~ ( topological_space @ SV11 )
| ~ ( top_str @ SV11 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( ~ ! [SY57: $i] :
~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SY57 )
| ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY59 != SY58 ) )
| ~ ( closed_subset @ SY59 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY60 != SY58 ) )
| ~ ( closed_subset @ SY60 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) )
| ( in @ SY58 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(190,plain,
! [SV19: $i,SV13: $i] :
( ( ( empty @ SV13 )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV19 @ SV13 )
| ( in @ SV19 @ SV13 ) )
| ~ ( ~ ( in @ SV19 @ SV13 )
| ( element @ SV19 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(191,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( ~ ( element @ SV19 @ SV13 )
| ( empty @ SV19 ) )
| ~ ( ~ ( empty @ SV19 )
| ( element @ SV19 @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(192,plain,
! [SV20: $i] :
( ( ( ~ ( element @ ( sK7_SY61 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( ~ ( ~ ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
| ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY64
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY64 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[186]) ).
thf(193,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK8_SY47 @ SV9 ) @ ( powerset @ ( the_carrier @ SV9 ) ) )
| ~ ( closed_subset @ ( sK8_SY47 @ SV9 ) @ SV9 ) ) )
= $false )
| ( ( topological_space @ SV9 )
= $false )
| ( ( top_str @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[187]) ).
thf(194,plain,
! [SV10: $i] :
( ( ( ~ ( element @ ( sK6_SY48 @ SV10 ) @ ( powerset @ SV10 ) ) )
= $false )
| ( ( empty @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(195,plain,
! [SV10: $i] :
( ( ( ~ ~ ( empty @ ( sK6_SY48 @ SV10 ) ) )
= $false )
| ( ( empty @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(196,plain,
! [SV18: $i,SV11: $i] :
( ( ( ~ ( topological_space @ SV11 ) )
= $true )
| ( ( ~ ( top_str @ SV11 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( ~ ! [SY57: $i] :
~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SY57 )
| ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY59 != SY58 ) )
| ~ ( closed_subset @ SY59 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY60 != SY58 ) )
| ~ ( closed_subset @ SY60 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) )
| ( in @ SY58 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(197,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( ~ ( element @ SV19 @ SV13 )
| ( in @ SV19 @ SV13 ) )
| ~ ( ~ ( in @ SV19 @ SV13 )
| ( element @ SV19 @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(198,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( ~ ( element @ SV19 @ SV13 )
| ( empty @ SV19 ) ) )
= $false )
| ( ( empty @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(199,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( ~ ( empty @ SV19 )
| ( element @ SV19 @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(200,plain,
! [SV20: $i] :
( ( ( ~ ( element @ ( sK7_SY61 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(201,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
| ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY64
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY64 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(202,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ( element @ ( sK8_SY47 @ SV9 ) @ ( powerset @ ( the_carrier @ SV9 ) ) )
| ~ ( closed_subset @ ( sK8_SY47 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( topological_space @ SV9 )
= $false )
| ( ( top_str @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(203,plain,
! [SV10: $i] :
( ( ( element @ ( sK6_SY48 @ SV10 ) @ ( powerset @ SV10 ) )
= $true )
| ( ( empty @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(204,plain,
! [SV10: $i] :
( ( ( ~ ( empty @ ( sK6_SY48 @ SV10 ) ) )
= $true )
| ( ( empty @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(205,plain,
! [SV18: $i,SV11: $i] :
( ( ( topological_space @ SV11 )
= $false )
| ( ( ~ ( top_str @ SV11 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( ~ ! [SY57: $i] :
~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SY57 )
| ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY59 != SY58 ) )
| ~ ( closed_subset @ SY59 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY60 != SY58 ) )
| ~ ( closed_subset @ SY60 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) )
| ( in @ SY58 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(206,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( ~ ( element @ SV19 @ SV13 )
| ( in @ SV19 @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(207,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ SV19 @ SV13 )
| ( element @ SV19 @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(208,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( element @ SV19 @ SV13 )
| ( empty @ SV19 ) )
= $true )
| ( ( empty @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(209,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( empty @ SV19 )
| ( element @ SV19 @ SV13 ) )
= $true )
| ( ( empty @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(210,plain,
! [SV20: $i] :
( ( ( element @ ( sK7_SY61 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(211,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
| ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY64
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY64 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(212,plain,
! [SV9: $i] :
( ( ( ~ ( element @ ( sK8_SY47 @ SV9 ) @ ( powerset @ ( the_carrier @ SV9 ) ) )
| ~ ( closed_subset @ ( sK8_SY47 @ SV9 ) @ SV9 ) )
= $false )
| ( ( topological_space @ SV9 )
= $false )
| ( ( top_str @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(213,plain,
! [SV10: $i] :
( ( ( empty @ ( sK6_SY48 @ SV10 ) )
= $false )
| ( ( empty @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(214,plain,
! [SV18: $i,SV11: $i] :
( ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( ~ ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( ~ ! [SY57: $i] :
~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SY57 )
| ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY59 != SY58 ) )
| ~ ( closed_subset @ SY59 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY60 != SY58 ) )
| ~ ( closed_subset @ SY60 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) )
| ( in @ SY58 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(215,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( element @ SV19 @ SV13 )
| ( in @ SV19 @ SV13 ) )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(216,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV13 )
| ( element @ SV19 @ SV13 ) )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(217,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( element @ SV19 @ SV13 ) )
= $true )
| ( ( empty @ SV19 )
= $true )
| ( ( empty @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(218,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( empty @ SV19 ) )
= $true )
| ( ( element @ SV19 @ SV13 )
= $true )
| ( ( empty @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(219,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
| ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY64
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY64 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(220,plain,
! [SV9: $i] :
( ( ( ~ ( element @ ( sK8_SY47 @ SV9 ) @ ( powerset @ ( the_carrier @ SV9 ) ) ) )
= $false )
| ( ( topological_space @ SV9 )
= $false )
| ( ( top_str @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(221,plain,
! [SV9: $i] :
( ( ( ~ ( closed_subset @ ( sK8_SY47 @ SV9 ) @ SV9 ) )
= $false )
| ( ( topological_space @ SV9 )
= $false )
| ( ( top_str @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(222,plain,
! [SV11: $i,SV18: $i] :
( ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( ~ ! [SY57: $i] :
~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SY57 )
| ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY59 != SY58 ) )
| ~ ( closed_subset @ SY59 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY60 != SY58 ) )
| ~ ( closed_subset @ SY60 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) )
| ( in @ SY58 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(223,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( element @ SV19 @ SV13 ) )
= $true )
| ( ( in @ SV19 @ SV13 )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(224,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV13 ) )
= $true )
| ( ( element @ SV19 @ SV13 )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(225,plain,
! [SV13: $i,SV19: $i] :
( ( ( element @ SV19 @ SV13 )
= $false )
| ( ( empty @ SV19 )
= $true )
| ( ( empty @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(226,plain,
! [SV13: $i,SV19: $i] :
( ( ( empty @ SV19 )
= $false )
| ( ( element @ SV19 @ SV13 )
= $true )
| ( ( empty @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(227,plain,
! [SV20: $i] :
( ( ( ~ ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
| ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY64
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY64 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(228,plain,
! [SV9: $i] :
( ( ( element @ ( sK8_SY47 @ SV9 ) @ ( powerset @ ( the_carrier @ SV9 ) ) )
= $true )
| ( ( topological_space @ SV9 )
= $false )
| ( ( top_str @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(229,plain,
! [SV9: $i] :
( ( ( closed_subset @ ( sK8_SY47 @ SV9 ) @ SV9 )
= $true )
| ( ( topological_space @ SV9 )
= $false )
| ( ( top_str @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(230,plain,
! [SV18: $i,SV11: $i] :
( ( ( ! [SY57: $i] :
~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SY57 )
| ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY59 != SY58 ) )
| ~ ( closed_subset @ SY59 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY58 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY60 != SY58 ) )
| ~ ( closed_subset @ SY60 @ SV11 ) )
| ~ ( subset @ SV18 @ SY58 ) ) )
| ( in @ SY58 @ SY57 ) ) ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(231,plain,
! [SV13: $i,SV19: $i] :
( ( ( element @ SV19 @ SV13 )
= $false )
| ( ( in @ SV19 @ SV13 )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(232,plain,
! [SV13: $i,SV19: $i] :
( ( ( in @ SV19 @ SV13 )
= $false )
| ( ( element @ SV19 @ SV13 )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(233,plain,
! [SV20: $i] :
( ( ( ~ ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(234,plain,
! [SV20: $i] :
( ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY64
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY64 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(235,plain,
! [SV11: $i,SV18: $i] :
( ( ( ~ ! [SY66: $i] :
~ ( ~ ( ~ ( in @ SY66 @ ( sK9_SY57 @ SV18 @ SV11 ) )
| ~ ( ~ ( in @ SY66 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY59 != SY66 ) )
| ~ ( closed_subset @ SY59 @ SV11 ) )
| ~ ( subset @ SV18 @ SY66 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY66 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY60 != SY66 ) )
| ~ ( closed_subset @ SY60 @ SV11 ) )
| ~ ( subset @ SV18 @ SY66 ) ) )
| ( in @ SY66 @ ( sK9_SY57 @ SV18 @ SV11 ) ) ) ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[230]) ).
thf(236,plain,
! [SV20: $i] :
( ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(237,plain,
! [SV20: $i] :
( ( ( ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY64
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY64 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(238,plain,
! [SV11: $i,SV18: $i] :
( ( ( ! [SY66: $i] :
~ ( ~ ( ~ ( in @ SY66 @ ( sK9_SY57 @ SV18 @ SV11 ) )
| ~ ( ~ ( in @ SY66 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY59 != SY66 ) )
| ~ ( closed_subset @ SY59 @ SV11 ) )
| ~ ( subset @ SV18 @ SY66 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY66 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY60 != SY66 ) )
| ~ ( closed_subset @ SY60 @ SV11 ) )
| ~ ( subset @ SV18 @ SY66 ) ) )
| ( in @ SY66 @ ( sK9_SY57 @ SV18 @ SV11 ) ) ) ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(239,plain,
! [SV20: $i] :
( ( ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) )
= $false )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(240,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SV22
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SV22 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(241,plain,
! [SV11: $i,SV18: $i,SV23: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
| ~ ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY69: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY69 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY69 != SV23 ) )
| ~ ( closed_subset @ SY69 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY70 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY70 != SV23 ) )
| ~ ( closed_subset @ SY70 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) )
| ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) ) ) ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(242,plain,
! [SV20: $i] :
( ( ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
= $false )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(243,plain,
! [SV20: $i] :
( ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $false )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(244,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SV22
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SV22 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(245,plain,
! [SV11: $i,SV18: $i,SV23: $i] :
( ( ( ~ ( ~ ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
| ~ ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY69: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY69 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY69 != SV23 ) )
| ~ ( closed_subset @ SY69 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY70 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY70 != SV23 ) )
| ~ ( closed_subset @ SY70 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) )
| ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) ) ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(246,plain,
! [SV20: $i] :
( ( ( ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
= $true )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(247,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SV22
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SV22 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(248,plain,
! [SV11: $i,SV18: $i,SV23: $i] :
( ( ( ~ ( ~ ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
| ~ ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY69: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY69 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY69 != SV23 ) )
| ~ ( closed_subset @ SY69 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) ) ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(249,plain,
! [SV18: $i,SV11: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY70 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY70 != SV23 ) )
| ~ ( closed_subset @ SY70 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) )
| ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) ) ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(250,plain,
! [SV20: $i] :
( ( ( ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
= $false )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(251,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SV22
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SV22 @ sK1_A ) ) )
= $true )
| ( ( ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(252,plain,
! [SV11: $i,SV18: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
| ~ ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY69: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY69 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY69 != SV23 ) )
| ~ ( closed_subset @ SY69 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(253,plain,
! [SV18: $i,SV11: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY70 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY70 != SV23 ) )
| ~ ( closed_subset @ SY70 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) )
| ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(254,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK10_SY65 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK10_SY65 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ ( sK10_SY65 @ SV20 ) @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
= $false )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[250]) ).
thf(255,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SV22
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SV22 @ sK1_A ) ) )
= $false )
| ( ( ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(256,plain,
! [SV11: $i,SV18: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY69: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY69 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY69 != SV23 ) )
| ~ ( closed_subset @ SY69 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(257,plain,
! [SV18: $i,SV11: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY70 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY70 != SV23 ) )
| ~ ( closed_subset @ SY70 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) ) )
= $true )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(258,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK10_SY65 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK10_SY65 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ ( sK10_SY65 @ SV20 ) @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
= $true )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(259,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SV22
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SV22 @ sK1_A ) )
= $true )
| ( ( ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(260,plain,
! [SV11: $i,SV18: $i,SV23: $i] :
( ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY69: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY69 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY69 != SV23 ) )
| ~ ( closed_subset @ SY69 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(261,plain,
! [SV18: $i,SV11: $i,SV23: $i] :
( ( ( ~ ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY70 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY70 != SV23 ) )
| ~ ( closed_subset @ SY70 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(262,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK10_SY65 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK10_SY65 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ ( sK10_SY65 @ SV20 ) @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
= $false )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(263,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SV22
!= ( sK7_SY61 @ SV20 ) ) ) )
= $true )
| ( ( ~ ( closed_subset @ SV22 @ sK1_A ) )
= $true )
| ( ( ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(264,plain,
! [SV18: $i,SV11: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY69: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY69 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY69 != SV23 ) )
| ~ ( closed_subset @ SY69 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(265,plain,
! [SV18: $i,SV11: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY70 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY70 != SV23 ) )
| ~ ( closed_subset @ SY70 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) )
= $true )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(266,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK10_SY65 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK10_SY65 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ ( sK10_SY65 @ SV20 ) @ sK1_A ) ) )
= $false )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(267,plain,
! [SV20: $i] :
( ( ( ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
= $false )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(268,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ( ~ ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SV22
!= ( sK7_SY61 @ SV20 ) ) ) )
= $false )
| ( ( ~ ( closed_subset @ SV22 @ sK1_A ) )
= $true )
| ( ( ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(269,plain,
! [SV18: $i,SV11: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(270,plain,
! [SV18: $i,SV23: $i,SV11: $i] :
( ( ( ~ ~ ! [SY69: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY69 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY69 != SV23 ) )
| ~ ( closed_subset @ SY69 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(271,plain,
! [SV18: $i,SV11: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY70 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY70 != SV23 ) )
| ~ ( closed_subset @ SY70 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) )
= $true )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(272,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK10_SY65 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK10_SY65 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ ( sK10_SY65 @ SV20 ) @ sK1_A ) ) )
= $true )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(273,plain,
! [SV20: $i] :
( ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $true )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(274,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SV22
!= ( sK7_SY61 @ SV20 ) ) )
= $true )
| ( ( ~ ( closed_subset @ SV22 @ sK1_A ) )
= $true )
| ( ( ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(275,plain,
! [SV18: $i,SV11: $i,SV23: $i] :
( ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(276,plain,
! [SV18: $i,SV23: $i,SV11: $i] :
( ( ( ~ ! [SY69: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY69 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY69 != SV23 ) )
| ~ ( closed_subset @ SY69 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) )
= $true )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(277,plain,
! [SV18: $i,SV11: $i,SV23: $i] :
( ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY70 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY70 != SV23 ) )
| ~ ( closed_subset @ SY70 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) )
= $true )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(278,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK10_SY65 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK10_SY65 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ ( sK10_SY65 @ SV20 ) @ sK1_A ) )
= $false )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(279,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $true )
| ( ( SV22
!= ( sK7_SY61 @ SV20 ) )
= $true )
| ( ( ~ ( closed_subset @ SV22 @ sK1_A ) )
= $true )
| ( ( ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(280,plain,
! [SV18: $i,SV23: $i,SV11: $i] :
( ( ( ! [SY69: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY69 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY69 != SV23 ) )
| ~ ( closed_subset @ SY69 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(281,plain,
! [SV18: $i,SV23: $i,SV11: $i] :
( ( ( ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY70 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY70 != SV23 ) )
| ~ ( closed_subset @ SY70 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) )
= $false )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(282,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK10_SY65 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK10_SY65 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) ) )
= $false )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(283,plain,
! [SV20: $i] :
( ( ( ~ ( closed_subset @ ( sK10_SY65 @ SV20 ) @ sK1_A ) )
= $false )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(284,plain,
! [SV20: $i,SV22: $i] :
( ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
!= ( sK7_SY61 @ SV20 ) )
= $true )
| ( ( ~ ( closed_subset @ SV22 @ sK1_A ) )
= $true )
| ( ( ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(285,plain,
! [SV11: $i,SV23: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( ( sK11_SY69 @ SV18 @ SV23 @ SV11 )
!= SV23 ) )
| ~ ( closed_subset @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[280]) ).
thf(286,plain,
! [SV18: $i,SV23: $i,SV11: $i] :
( ( ( ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY70 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SY70 != SV23 ) )
| ~ ( closed_subset @ SY70 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) )
= $true )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(287,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ( element @ ( sK10_SY65 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK10_SY65 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) ) )
= $true )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(288,plain,
! [SV20: $i] :
( ( ( closed_subset @ ( sK10_SY65 @ SV20 ) @ sK1_A )
= $true )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(289,plain,
! [SV20: $i,SV22: $i] :
( ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( ~ ( closed_subset @ SV22 @ sK1_A ) )
= $true )
| ( ( ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(290,plain,
! [SV11: $i,SV23: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( ( sK11_SY69 @ SV18 @ SV23 @ SV11 )
!= SV23 ) )
| ~ ( closed_subset @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) )
= $true )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(291,plain,
! [SV18: $i,SV23: $i,SV11: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SV24 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SV24 != SV23 ) )
| ~ ( closed_subset @ SV24 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) )
= $true )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(292,plain,
! [SV20: $i] :
( ( ( ~ ( element @ ( sK10_SY65 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK10_SY65 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) )
= $false )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(293,plain,
! [SV20: $i,SV22: $i] :
( ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(294,plain,
! [SV11: $i,SV23: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( ( sK11_SY69 @ SV18 @ SV23 @ SV11 )
!= SV23 ) )
| ~ ( closed_subset @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(295,plain,
! [SV18: $i,SV23: $i,SV11: $i,SV24: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SV24 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SV24 != SV23 ) )
| ~ ( closed_subset @ SV24 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) ) )
= $false )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(296,plain,
! [SV20: $i] :
( ( ( ~ ( element @ ( sK10_SY65 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(297,plain,
! [SV20: $i] :
( ( ( ( sK10_SY65 @ SV20 )
!= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(298,plain,
! [SV22: $i,SV20: $i] :
( ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(299,plain,
! [SV11: $i,SV23: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( ( sK11_SY69 @ SV18 @ SV23 @ SV11 )
!= SV23 ) )
| ~ ( closed_subset @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ SV11 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(300,plain,
! [SV11: $i,SV23: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV23 ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(301,plain,
! [SV18: $i,SV23: $i,SV11: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ SV24 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SV24 != SV23 ) )
| ~ ( closed_subset @ SV24 @ SV11 ) )
| ~ ( subset @ SV18 @ SV23 ) )
= $true )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(302,plain,
! [SV20: $i] :
( ( ( element @ ( sK10_SY65 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $true )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(303,plain,
! [SV20: $i] :
( ( ( ( sK10_SY65 @ SV20 )
= ( sK7_SY61 @ SV20 ) )
= $true )
| ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(304,plain,
! [SV22: $i,SV20: $i] :
( ( ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
| ( in @ ( sK7_SY61 @ SV20 ) @ SV20 ) )
= $false )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(305,plain,
! [SV11: $i,SV23: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( ( sK11_SY69 @ SV18 @ SV23 @ SV11 )
!= SV23 ) )
| ~ ( closed_subset @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(306,plain,
! [SV11: $i,SV23: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV23 )
= $true )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(307,plain,
! [SV18: $i,SV23: $i,SV11: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ SV24 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SV24 != SV23 ) )
| ~ ( closed_subset @ SV24 @ SV11 ) ) )
= $true )
| ( ( ~ ( subset @ SV18 @ SV23 ) )
= $true )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(308,plain,
! [SV22: $i,SV20: $i] :
( ( ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
= $false )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[304]) ).
thf(309,plain,
! [SV22: $i,SV20: $i] :
( ( ( in @ ( sK7_SY61 @ SV20 ) @ SV20 )
= $false )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[304]) ).
thf(310,plain,
! [SV11: $i,SV23: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( ( sK11_SY69 @ SV18 @ SV23 @ SV11 )
!= SV23 ) )
| ~ ( closed_subset @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(311,plain,
! [SV18: $i,SV23: $i,SV11: $i,SV24: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ SV24 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SV24 != SV23 ) )
| ~ ( closed_subset @ SV24 @ SV11 ) ) )
= $false )
| ( ( ~ ( subset @ SV18 @ SV23 ) )
= $true )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(312,plain,
! [SV22: $i,SV20: $i] :
( ( ( ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
= $true )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(313,plain,
! [SV11: $i,SV23: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( ( sK11_SY69 @ SV18 @ SV23 @ SV11 )
!= SV23 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(314,plain,
! [SV11: $i,SV23: $i,SV18: $i] :
( ( ( ~ ( closed_subset @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(315,plain,
! [SV18: $i,SV23: $i,SV11: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( element @ SV24 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SV24 != SV23 ) )
| ~ ( closed_subset @ SV24 @ SV11 ) )
= $true )
| ( ( ~ ( subset @ SV18 @ SV23 ) )
= $true )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(316,plain,
! [SV22: $i,SV20: $i] :
( ( ( ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY65 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( SY65
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ SY65 @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
= $false )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(317,plain,
! [SV11: $i,SV23: $i,SV18: $i] :
( ( ( ~ ( ~ ( element @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( ( sK11_SY69 @ SV18 @ SV23 @ SV11 )
!= SV23 ) ) )
= $true )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(318,plain,
! [SV11: $i,SV23: $i,SV18: $i] :
( ( ( closed_subset @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ SV11 )
= $true )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(319,plain,
! [SV18: $i,SV23: $i,SV11: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( element @ SV24 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SV24 != SV23 ) ) )
= $true )
| ( ( ~ ( closed_subset @ SV24 @ SV11 ) )
= $true )
| ( ( ~ ( subset @ SV18 @ SV23 ) )
= $true )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(320,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK12_SY65 @ SV22 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK12_SY65 @ SV22 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ ( sK12_SY65 @ SV22 @ SV20 ) @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
= $false )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[316]) ).
thf(321,plain,
! [SV11: $i,SV23: $i,SV18: $i] :
( ( ( ~ ( element @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( ( sK11_SY69 @ SV18 @ SV23 @ SV11 )
!= SV23 ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(322,plain,
! [SV18: $i,SV23: $i,SV11: $i,SV24: $i] :
( ( ( ~ ( ~ ( element @ SV24 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SV24 != SV23 ) ) )
= $false )
| ( ( ~ ( closed_subset @ SV24 @ SV11 ) )
= $true )
| ( ( ~ ( subset @ SV18 @ SV23 ) )
= $true )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(323,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK12_SY65 @ SV22 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK12_SY65 @ SV22 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ ( sK12_SY65 @ SV22 @ SV20 ) @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) ) )
= $true )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(324,plain,
! [SV11: $i,SV23: $i,SV18: $i] :
( ( ( ~ ( element @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(325,plain,
! [SV11: $i,SV23: $i,SV18: $i] :
( ( ( ( sK11_SY69 @ SV18 @ SV23 @ SV11 )
!= SV23 )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(326,plain,
! [SV18: $i,SV23: $i,SV11: $i,SV24: $i] :
( ( ( ~ ( element @ SV24 @ ( powerset @ ( the_carrier @ SV11 ) ) )
| ( SV24 != SV23 ) )
= $true )
| ( ( ~ ( closed_subset @ SV24 @ SV11 ) )
= $true )
| ( ( ~ ( subset @ SV18 @ SV23 ) )
= $true )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(327,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK12_SY65 @ SV22 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK12_SY65 @ SV22 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ ( sK12_SY65 @ SV22 @ SV20 ) @ sK1_A ) )
| ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
= $false )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(328,plain,
! [SV11: $i,SV23: $i,SV18: $i] :
( ( ( element @ ( sK11_SY69 @ SV18 @ SV23 @ SV11 ) @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(329,plain,
! [SV11: $i,SV23: $i,SV18: $i] :
( ( ( ( sK11_SY69 @ SV18 @ SV23 @ SV11 )
= SV23 )
= $true )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $false )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(330,plain,
! [SV18: $i,SV23: $i,SV11: $i,SV24: $i] :
( ( ( ~ ( element @ SV24 @ ( powerset @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( SV24 != SV23 )
= $true )
| ( ( ~ ( closed_subset @ SV24 @ SV11 ) )
= $true )
| ( ( ~ ( subset @ SV18 @ SV23 ) )
= $true )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(331,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK12_SY65 @ SV22 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK12_SY65 @ SV22 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ ( sK12_SY65 @ SV22 @ SV20 ) @ sK1_A ) ) )
= $false )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[327]) ).
thf(332,plain,
! [SV22: $i,SV20: $i] :
( ( ( ~ ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) ) )
= $false )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[327]) ).
thf(333,plain,
! [SV18: $i,SV23: $i,SV11: $i,SV24: $i] :
( ( ( element @ SV24 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( SV24 != SV23 )
= $true )
| ( ( ~ ( closed_subset @ SV24 @ SV11 ) )
= $true )
| ( ( ~ ( subset @ SV18 @ SV23 ) )
= $true )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(334,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK12_SY65 @ SV22 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK12_SY65 @ SV22 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ ( sK12_SY65 @ SV22 @ SV20 ) @ sK1_A ) ) )
= $true )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(335,plain,
! [SV22: $i,SV20: $i] :
( ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $true )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(336,plain,
! [SV18: $i,SV11: $i,SV23: $i,SV24: $i] :
( ( ( SV24 = SV23 )
= $false )
| ( ( element @ SV24 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( ~ ( closed_subset @ SV24 @ SV11 ) )
= $true )
| ( ( ~ ( subset @ SV18 @ SV23 ) )
= $true )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(337,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK12_SY65 @ SV22 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK12_SY65 @ SV22 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) )
| ~ ( closed_subset @ ( sK12_SY65 @ SV22 @ SV20 ) @ sK1_A ) )
= $false )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(338,plain,
! [SV18: $i,SV23: $i,SV11: $i,SV24: $i] :
( ( ( closed_subset @ SV24 @ SV11 )
= $false )
| ( ( element @ SV24 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( SV24 = SV23 )
= $false )
| ( ( ~ ( subset @ SV18 @ SV23 ) )
= $true )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(339,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK12_SY65 @ SV22 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK12_SY65 @ SV22 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) ) )
= $false )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(340,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ( closed_subset @ ( sK12_SY65 @ SV22 @ SV20 ) @ sK1_A ) )
= $false )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(341,plain,
! [SV11: $i,SV24: $i,SV23: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV23 )
= $false )
| ( ( SV24 = SV23 )
= $false )
| ( ( element @ SV24 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( closed_subset @ SV24 @ SV11 )
= $false )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK9_SY57 @ SV18 @ SV11 ) )
= $true )
| ( ( top_str @ SV11 )
= $false )
| ( ( topological_space @ SV11 )
= $false )
| ( ( element @ SV18 @ ( powerset @ ( the_carrier @ SV11 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(342,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ( ~ ( element @ ( sK12_SY65 @ SV22 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK12_SY65 @ SV22 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) ) )
= $true )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(343,plain,
! [SV20: $i,SV22: $i] :
( ( ( closed_subset @ ( sK12_SY65 @ SV22 @ SV20 ) @ sK1_A )
= $true )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(344,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ( element @ ( sK12_SY65 @ SV22 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( ( sK12_SY65 @ SV22 @ SV20 )
!= ( sK7_SY61 @ SV20 ) ) )
= $false )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(345,plain,
! [SV20: $i,SV22: $i] :
( ( ( ~ ( element @ ( sK12_SY65 @ SV22 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(346,plain,
! [SV20: $i,SV22: $i] :
( ( ( ( sK12_SY65 @ SV22 @ SV20 )
!= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(347,plain,
! [SV20: $i,SV22: $i] :
( ( ( element @ ( sK12_SY65 @ SV22 @ SV20 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $true )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(348,plain,
! [SV20: $i,SV22: $i] :
( ( ( ( sK12_SY65 @ SV22 @ SV20 )
= ( sK7_SY61 @ SV20 ) )
= $true )
| ( ( closed_subset @ SV22 @ sK1_A )
= $false )
| ( ( element @ SV22 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( SV22
= ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( subset @ sK2_SY33 @ ( sK7_SY61 @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(349,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[68,348,347,343,341,335,329,328,318,309,306,303,302,288,275,273,243,232,231,229,228,226,225,213,210,203,180,179,178,177,168,166,155,150,132,116,115,87,86,85,81,76,75,73]) ).
thf(350,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[349]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU315+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.18 % Computer : n011.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Oct 6 15:13:21 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 248.44/41.61
% 248.44/41.61 No.of.Axioms: 18
% 248.44/41.61
% 248.44/41.61 Length.of.Defs: 0
% 248.44/41.61
% 248.44/41.61 Contains.Choice.Funs: false
% 248.44/41.61 ..........
% 248.44/41.61
% 248.44/41.61 ********************************
% 248.44/41.61 * All subproblems solved! *
% 248.44/41.61 ********************************
% 248.44/41.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:21,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:349,loop_count:0,foatp_calls:1,translation:fof_full)
% 248.44/41.61
% 248.44/41.61 %**** Beginning of derivation protocol ****
% 248.44/41.61 % SZS output start CNFRefutation
% See solution above
% 248.44/41.61
% 248.44/41.61 %**** End of derivation protocol ****
% 248.44/41.61 %**** no. of clauses in derivation: 330 ****
% 248.44/41.61 %**** clause counter: 349 ****
% 248.44/41.61
% 248.44/41.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:21,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:349,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------