%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU310+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 10:43:55 AM UTC 2026
% Result : Theorem 1.31s 0.42s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 17
% Syntax : Number of formulae : 395 ( 93 unt; 0 typ; 0 def)
% Number of atoms : 5589 (1985 equ; 0 cnn)
% Maximal formula atoms : 12 ( 14 avg)
% Number of connectives : 12764 (2824 ~;2036 |; 54 &;7798 @)
% ( 11 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 40 usr; 4 con; 0-3 aty)
% Number of variables : 1220 ( 0 ^;1197 !; 23 ?;1220 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cast_as_carrier_subset,type,
cast_as_carrier_subset: $i > $i ).
thf(tp_closed_subset,type,
closed_subset: $i > $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
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_SY50,type,
sK10_SY50: $i > $i > $i ).
thf(tp_sK11_SY50,type,
sK11_SY50: $i > $i > $i ).
thf(tp_sK12_SY50,type,
sK12_SY50: $i > $i > $i ).
thf(tp_sK13_SY61,type,
sK13_SY61: $i > $i > $i > $i ).
thf(tp_sK14_SY50,type,
sK14_SY50: $i > $i > $i ).
thf(tp_sK15_SY50,type,
sK15_SY50: $i > $i > $i ).
thf(tp_sK16_SY66,type,
sK16_SY66: $i > $i > $i > $i ).
thf(tp_sK17_SY71,type,
sK17_SY71: $i > $i > $i > $i ).
thf(tp_sK18_SY79,type,
sK18_SY79: $i > $i > $i > $i ).
thf(tp_sK19_SY81,type,
sK19_SY81: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY28,type,
sK2_SY28: $i ).
thf(tp_sK3_SY35,type,
sK3_SY35: $i > $i ).
thf(tp_sK4_SY54,type,
sK4_SY54: $i > $i ).
thf(tp_sK5_SY33,type,
sK5_SY33: $i > $i ).
thf(tp_sK6_SY34,type,
sK6_SY34: $i > $i ).
thf(tp_sK7_SY47,type,
sK7_SY47: $i > $i > $i ).
thf(tp_sK8_SY55,type,
sK8_SY55: $i > $i > $i ).
thf(tp_sK9_SY57,type,
sK9_SY57: $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_top_str,type,
top_str: $i > $o ).
thf(tp_topological_space,type,
topological_space: $i > $o ).
thf(tp_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(1,axiom,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B )
& ( C = E )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ E ) @ B ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e2_37_1_1__pre_topc__1) ).
thf(2,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(3,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_pre_topc) ).
thf(4,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(5,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(6,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(7,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(8,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(9,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(12,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(13,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(14,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( closed_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(15,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc37_membered) ).
thf(25,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_membered) ).
thf(36,conjecture,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( powerset @ ( the_carrier @ A ) ) )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).
thf(37,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( powerset @ ( the_carrier @ A ) ) )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[36]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( powerset @ ( the_carrier @ A ) ) )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[37]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B )
& ( C = E )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ E ) @ B ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(40,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(41,plain,
( ( ! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(42,plain,
$true = $true,
inference(unfold_def,[status(thm)],[4]) ).
thf(43,plain,
$true = $true,
inference(unfold_def,[status(thm)],[5]) ).
thf(44,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(45,plain,
$true = $true,
inference(unfold_def,[status(thm)],[7]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(47,plain,
$true = $true,
inference(unfold_def,[status(thm)],[9]) ).
thf(48,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(49,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(50,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(51,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)],[14]) ).
thf(52,plain,
$true = $true,
inference(unfold_def,[status(thm)],[15]) ).
thf(53,plain,
( ( ! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(54,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(55,plain,
( ( ! [SY28: $i] :
( ( ( topological_space @ sK1_A )
& ( top_str @ sK1_A )
& ( element @ SY28 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) ) )
=> ? [SY29: $i] :
! [SY30: $i] :
( ( in @ SY30 @ SY29 )
<=> ( ( in @ SY30 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ SY30 ) @ SY28 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(56,plain,
( ( ( ( topological_space @ sK1_A )
& ( top_str @ sK1_A )
& ( element @ sK2_SY28 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) ) )
=> ? [SY31: $i] :
! [SY32: $i] :
( ( in @ SY32 @ SY31 )
<=> ( ( in @ SY32 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ SY32 ) @ sK2_SY28 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[55]) ).
thf(57,plain,
( ( topological_space @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[56]) ).
thf(58,plain,
( ( top_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[56]) ).
thf(59,plain,
( ( element @ sK2_SY28 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[56]) ).
thf(60,plain,
( ( ? [SY31: $i] :
! [SY32: $i] :
( ( in @ SY32 @ SY31 )
<=> ( ( in @ SY32 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ SY32 ) @ sK2_SY28 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[56]) ).
thf(61,plain,
( ( ~ ? [SY31: $i] :
! [SY32: $i] :
( ( in @ SY32 @ SY31 )
<=> ( ( in @ SY32 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ SY32 ) @ sK2_SY28 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[60]) ).
thf(62,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(64,plain,
$true = $true,
inference(copy,[status(thm)],[52]) ).
thf(65,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)],[51]) ).
thf(66,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(67,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(69,plain,
$true = $true,
inference(copy,[status(thm)],[47]) ).
thf(70,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(71,plain,
$true = $true,
inference(copy,[status(thm)],[45]) ).
thf(72,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(73,plain,
$true = $true,
inference(copy,[status(thm)],[43]) ).
thf(74,plain,
$true = $true,
inference(copy,[status(thm)],[42]) ).
thf(75,plain,
( ( ! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(76,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(77,plain,
( ( ! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B )
& ( C = E )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ E ) @ B ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( powerset @ ( the_carrier @ A ) ) )
& ( E = D )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(78,plain,
( ( element @ sK2_SY28 @ ( powerset @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(79,plain,
( ( top_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(80,plain,
( ( topological_space @ sK1_A )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(81,plain,
( ( ~ ? [SY31: $i] :
! [SY32: $i] :
( ( in @ SY32 @ SY31 )
<=> ( ( in @ SY32 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ SY32 ) @ sK2_SY28 ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(82,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(83,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(84,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)],[65]) ).
thf(85,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( topological_space @ SX0 )
| ~ ( top_str @ SX0 ) )
| ( closed_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(86,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(87,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( v1_membered @ SX0 )
| ( v1_membered @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(88,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(89,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( element @ ( cast_as_carrier_subset @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(90,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( topological_space @ SX0 )
| ~ ( top_str @ SX0 ) )
| ~ ( element @ SX1 @ ( powerset @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) )
| ~ ! [SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SX2 != SX3 )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SX0 ) @ SX3 ) @ SX1 ) )
| ( SX2 != SX4 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SX0 ) @ SX4 ) @ SX1 ) )
| ( SX3 = SX4 ) )
| ~ ! [SX2: $i] :
~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ( SX4 != SX3 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SX0 ) @ SX3 ) @ SX1 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ( SX4 != SX3 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SX0 ) @ SX3 ) @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(91,plain,
( ( ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( in @ SX1 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ SX1 ) @ sK2_SY28 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX1 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ SX1 ) @ sK2_SY28 ) )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(92,plain,
( ( ! [SX0: $i] :
( ~ ( v1_membered @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v1_membered @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(93,plain,
! [SV1: $i] :
( ( ~ ( empty @ ( powerset @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(94,plain,
! [SV2: $i] :
( ( ~ ~ ( empty @ SV2 )
| ~ ! [SY33: $i] :
~ ~ ( ~ ( element @ SY33 @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(95,plain,
! [SV3: $i] :
( ( ~ ( top_str @ SV3 )
| ( one_sorted_str @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(96,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ( topological_space @ SV4 )
| ~ ( top_str @ SV4 ) )
| ~ ! [SY34: $i] :
~ ~ ( ~ ( element @ SY34 @ ( powerset @ ( the_carrier @ SV4 ) ) )
| ~ ( closed_subset @ SY34 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(97,plain,
! [SV5: $i] :
( ( ~ ~ ( ~ ( topological_space @ SV5 )
| ~ ( top_str @ SV5 ) )
| ( closed_subset @ ( cast_as_carrier_subset @ SV5 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(98,plain,
! [SV6: $i] :
( ( ~ ! [SY35: $i] :
~ ~ ( ~ ( element @ SY35 @ ( powerset @ SV6 ) )
| ~ ( empty @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(99,plain,
! [SV7: $i] :
( ( ! [SY36: $i] :
( ~ ( v1_membered @ SV7 )
| ( v1_membered @ ( set_difference @ SV7 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(100,plain,
! [SV8: $i] :
( ( ! [SY37: $i] :
( ~ ( in @ SV8 @ SY37 )
| ~ ( in @ SY37 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(101,plain,
! [SV9: $i] :
( ( ~ ( one_sorted_str @ SV9 )
| ( element @ ( cast_as_carrier_subset @ SV9 ) @ ( powerset @ ( the_carrier @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(102,plain,
! [SV10: $i] :
( ( ! [SY38: $i] :
( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV10 )
| ~ ( top_str @ SV10 ) )
| ~ ( element @ SY38 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) ) )
| ~ ! [SY39: $i,SY40: $i,SY41: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY39 != SY40 )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY40 ) @ SY38 ) )
| ( SY39 != SY41 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY41 ) @ SY38 ) )
| ( SY40 = SY41 ) )
| ~ ! [SY42: $i] :
~ ! [SY43: $i] :
~ ( ~ ( ~ ( in @ SY43 @ SY42 )
| ~ ! [SY44: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY44 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY44 != SY43 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY43 ) @ SY38 ) ) )
| ~ ( ~ ~ ! [SY45: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY45 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY45 != SY43 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY43 ) @ SY38 ) )
| ( in @ SY43 @ SY42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(103,plain,
( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( in @ SX1 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ SX1 ) @ sK2_SY28 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX1 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ SX1 ) @ sK2_SY28 ) )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(104,plain,
! [SV11: $i] :
( ( ~ ( v1_membered @ SV11 )
| ! [SY46: $i] :
( ~ ( element @ SY46 @ ( powerset @ SV11 ) )
| ( v1_membered @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(105,plain,
! [SV1: $i] :
( ( empty @ ( powerset @ SV1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(106,plain,
! [SV2: $i] :
( ( ( ~ ~ ( empty @ SV2 ) )
= $true )
| ( ( ~ ! [SY33: $i] :
~ ~ ( ~ ( element @ SY33 @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ SY33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(107,plain,
! [SV3: $i] :
( ( ( ~ ( top_str @ SV3 ) )
= $true )
| ( ( one_sorted_str @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(108,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( topological_space @ SV4 )
| ~ ( top_str @ SV4 ) ) )
= $true )
| ( ( ~ ! [SY34: $i] :
~ ~ ( ~ ( element @ SY34 @ ( powerset @ ( the_carrier @ SV4 ) ) )
| ~ ( closed_subset @ SY34 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(109,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ( topological_space @ SV5 )
| ~ ( top_str @ SV5 ) ) )
= $true )
| ( ( closed_subset @ ( cast_as_carrier_subset @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(110,plain,
! [SV6: $i] :
( ( ! [SY35: $i] :
~ ~ ( ~ ( element @ SY35 @ ( powerset @ SV6 ) )
| ~ ( empty @ SY35 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(111,plain,
! [SV12: $i,SV7: $i] :
( ( ~ ( v1_membered @ SV7 )
| ( v1_membered @ ( set_difference @ SV7 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(112,plain,
! [SV13: $i,SV8: $i] :
( ( ~ ( in @ SV8 @ SV13 )
| ~ ( in @ SV13 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(113,plain,
! [SV9: $i] :
( ( ( ~ ( one_sorted_str @ SV9 ) )
= $true )
| ( ( element @ ( cast_as_carrier_subset @ SV9 ) @ ( powerset @ ( the_carrier @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(114,plain,
! [SV14: $i,SV10: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV10 )
| ~ ( top_str @ SV10 ) )
| ~ ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) ) )
| ~ ! [SY47: $i,SY48: $i,SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY47 != SY48 )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY48 ) @ SV14 ) )
| ( SY47 != SY49 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY49 ) @ SV14 ) )
| ( SY48 = SY49 ) )
| ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(115,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( in @ SX1 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ SX1 ) @ sK2_SY28 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX1 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ SX1 ) @ sK2_SY28 ) )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(116,plain,
! [SV11: $i] :
( ( ( ~ ( v1_membered @ SV11 ) )
= $true )
| ( ( ! [SY46: $i] :
( ~ ( element @ SY46 @ ( powerset @ SV11 ) )
| ( v1_membered @ SY46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(117,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $false )
| ( ( ~ ! [SY33: $i] :
~ ~ ( ~ ( element @ SY33 @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ SY33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(118,plain,
! [SV3: $i] :
( ( ( top_str @ SV3 )
= $false )
| ( ( one_sorted_str @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(119,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( topological_space @ SV4 )
| ~ ( top_str @ SV4 ) ) )
= $false )
| ( ( ~ ! [SY34: $i] :
~ ~ ( ~ ( element @ SY34 @ ( powerset @ ( the_carrier @ SV4 ) ) )
| ~ ( closed_subset @ SY34 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(120,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( topological_space @ SV5 )
| ~ ( top_str @ SV5 ) ) )
= $false )
| ( ( closed_subset @ ( cast_as_carrier_subset @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(121,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ( element @ ( sK3_SY35 @ SV6 ) @ ( powerset @ SV6 ) )
| ~ ( empty @ ( sK3_SY35 @ SV6 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[110]) ).
thf(122,plain,
! [SV12: $i,SV7: $i] :
( ( ( ~ ( v1_membered @ SV7 ) )
= $true )
| ( ( v1_membered @ ( set_difference @ SV7 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(123,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV13 ) )
= $true )
| ( ( ~ ( in @ SV13 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(124,plain,
! [SV9: $i] :
( ( ( one_sorted_str @ SV9 )
= $false )
| ( ( element @ ( cast_as_carrier_subset @ SV9 ) @ ( powerset @ ( the_carrier @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(125,plain,
! [SV14: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( topological_space @ SV10 )
| ~ ( top_str @ SV10 ) )
| ~ ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) ) ) )
= $true )
| ( ( ~ ! [SY47: $i,SY48: $i,SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY47 != SY48 )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY48 ) @ SV14 ) )
| ( SY47 != SY49 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY49 ) @ SV14 ) )
| ( SY48 = SY49 ) )
| ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(126,plain,
! [SV15: $i] :
( ( ~ ! [SY54: $i] :
~ ( ~ ( ~ ( in @ SY54 @ SV15 )
| ~ ( ~ ( in @ SY54 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ SY54 ) @ sK2_SY28 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY54 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ SY54 ) @ sK2_SY28 ) )
| ( in @ SY54 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(127,plain,
! [SV11: $i] :
( ( ( v1_membered @ SV11 )
= $false )
| ( ( ! [SY46: $i] :
( ~ ( element @ SY46 @ ( powerset @ SV11 ) )
| ( v1_membered @ SY46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(128,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $true )
| ( ( ~ ! [SY33: $i] :
~ ~ ( ~ ( element @ SY33 @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ SY33 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(129,plain,
! [SV4: $i] :
( ( ( ~ ( topological_space @ SV4 )
| ~ ( top_str @ SV4 ) )
= $true )
| ( ( ~ ! [SY34: $i] :
~ ~ ( ~ ( element @ SY34 @ ( powerset @ ( the_carrier @ SV4 ) ) )
| ~ ( closed_subset @ SY34 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(130,plain,
! [SV5: $i] :
( ( ( ~ ( topological_space @ SV5 )
| ~ ( top_str @ SV5 ) )
= $true )
| ( ( closed_subset @ ( cast_as_carrier_subset @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(131,plain,
! [SV6: $i] :
( ( ~ ( ~ ( element @ ( sK3_SY35 @ SV6 ) @ ( powerset @ SV6 ) )
| ~ ( empty @ ( sK3_SY35 @ SV6 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(132,plain,
! [SV12: $i,SV7: $i] :
( ( ( v1_membered @ SV7 )
= $false )
| ( ( v1_membered @ ( set_difference @ SV7 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(133,plain,
! [SV13: $i,SV8: $i] :
( ( ( in @ SV8 @ SV13 )
= $false )
| ( ( ~ ( in @ SV13 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(134,plain,
! [SV14: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ( topological_space @ SV10 )
| ~ ( top_str @ SV10 ) )
| ~ ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) ) ) )
= $false )
| ( ( ~ ! [SY47: $i,SY48: $i,SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY47 != SY48 )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY48 ) @ SV14 ) )
| ( SY47 != SY49 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY49 ) @ SV14 ) )
| ( SY48 = SY49 ) )
| ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(135,plain,
! [SV15: $i] :
( ( ! [SY54: $i] :
~ ( ~ ( ~ ( in @ SY54 @ SV15 )
| ~ ( ~ ( in @ SY54 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ SY54 ) @ sK2_SY28 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY54 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ SY54 ) @ sK2_SY28 ) )
| ( in @ SY54 @ SV15 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(136,plain,
! [SV11: $i,SV16: $i] :
( ( ( ~ ( element @ SV16 @ ( powerset @ SV11 ) )
| ( v1_membered @ SV16 ) )
= $true )
| ( ( v1_membered @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(137,plain,
! [SV2: $i] :
( ( ( ! [SY33: $i] :
~ ~ ( ~ ( element @ SY33 @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ SY33 ) ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(138,plain,
! [SV4: $i] :
( ( ( ~ ( topological_space @ SV4 ) )
= $true )
| ( ( ~ ( top_str @ SV4 ) )
= $true )
| ( ( ~ ! [SY34: $i] :
~ ~ ( ~ ( element @ SY34 @ ( powerset @ ( the_carrier @ SV4 ) ) )
| ~ ( closed_subset @ SY34 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(139,plain,
! [SV5: $i] :
( ( ( ~ ( topological_space @ SV5 ) )
= $true )
| ( ( ~ ( top_str @ SV5 ) )
= $true )
| ( ( closed_subset @ ( cast_as_carrier_subset @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(140,plain,
! [SV6: $i] :
( ( ~ ( element @ ( sK3_SY35 @ SV6 ) @ ( powerset @ SV6 ) )
| ~ ( empty @ ( sK3_SY35 @ SV6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(141,plain,
! [SV8: $i,SV13: $i] :
( ( ( in @ SV13 @ SV8 )
= $false )
| ( ( in @ SV8 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(142,plain,
! [SV14: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( topological_space @ SV10 )
| ~ ( top_str @ SV10 ) )
| ~ ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) ) )
= $true )
| ( ( ~ ! [SY47: $i,SY48: $i,SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY47 != SY48 )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY48 ) @ SV14 ) )
| ( SY47 != SY49 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY49 ) @ SV14 ) )
| ( SY48 = SY49 ) )
| ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(143,plain,
! [SV15: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ SV15 )
| ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
| ( in @ ( sK4_SY54 @ SV15 ) @ SV15 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[135]) ).
thf(144,plain,
! [SV11: $i,SV16: $i] :
( ( ( ~ ( element @ SV16 @ ( powerset @ SV11 ) ) )
= $true )
| ( ( v1_membered @ SV16 )
= $true )
| ( ( v1_membered @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(145,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK5_SY33 @ SV2 ) @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ ( sK5_SY33 @ SV2 ) ) ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[137]) ).
thf(146,plain,
! [SV4: $i] :
( ( ( topological_space @ SV4 )
= $false )
| ( ( ~ ( top_str @ SV4 ) )
= $true )
| ( ( ~ ! [SY34: $i] :
~ ~ ( ~ ( element @ SY34 @ ( powerset @ ( the_carrier @ SV4 ) ) )
| ~ ( closed_subset @ SY34 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(147,plain,
! [SV5: $i] :
( ( ( topological_space @ SV5 )
= $false )
| ( ( ~ ( top_str @ SV5 ) )
= $true )
| ( ( closed_subset @ ( cast_as_carrier_subset @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(148,plain,
! [SV6: $i] :
( ( ~ ( element @ ( sK3_SY35 @ SV6 ) @ ( powerset @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(149,plain,
! [SV6: $i] :
( ( ~ ( empty @ ( sK3_SY35 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(150,plain,
! [SV14: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( topological_space @ SV10 )
| ~ ( top_str @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) ) )
= $true )
| ( ( ~ ! [SY47: $i,SY48: $i,SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY47 != SY48 )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY48 ) @ SV14 ) )
| ( SY47 != SY49 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY49 ) @ SV14 ) )
| ( SY48 = SY49 ) )
| ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(151,plain,
! [SV15: $i] :
( ( ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ SV15 )
| ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
| ( in @ ( sK4_SY54 @ SV15 ) @ SV15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(152,plain,
! [SV11: $i,SV16: $i] :
( ( ( element @ SV16 @ ( powerset @ SV11 ) )
= $false )
| ( ( v1_membered @ SV16 )
= $true )
| ( ( v1_membered @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(153,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ( element @ ( sK5_SY33 @ SV2 ) @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ ( sK5_SY33 @ SV2 ) ) ) )
= $true )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(154,plain,
! [SV4: $i] :
( ( ( top_str @ SV4 )
= $false )
| ( ( topological_space @ SV4 )
= $false )
| ( ( ~ ! [SY34: $i] :
~ ~ ( ~ ( element @ SY34 @ ( powerset @ ( the_carrier @ SV4 ) ) )
| ~ ( closed_subset @ SY34 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(155,plain,
! [SV5: $i] :
( ( ( top_str @ SV5 )
= $false )
| ( ( topological_space @ SV5 )
= $false )
| ( ( closed_subset @ ( cast_as_carrier_subset @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(156,plain,
! [SV6: $i] :
( ( element @ ( sK3_SY35 @ SV6 ) @ ( powerset @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(157,plain,
! [SV6: $i] :
( ( empty @ ( sK3_SY35 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(158,plain,
! [SV14: $i,SV10: $i] :
( ( ( ~ ( ~ ( topological_space @ SV10 )
| ~ ( top_str @ SV10 ) ) )
= $false )
| ( ( ~ ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) ) )
= $true )
| ( ( ~ ! [SY47: $i,SY48: $i,SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY47 != SY48 )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY48 ) @ SV14 ) )
| ( SY47 != SY49 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY49 ) @ SV14 ) )
| ( SY48 = SY49 ) )
| ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(159,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ SV15 )
| ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
| ( in @ ( sK4_SY54 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(160,plain,
! [SV2: $i] :
( ( ( ~ ( element @ ( sK5_SY33 @ SV2 ) @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ ( sK5_SY33 @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(161,plain,
! [SV4: $i] :
( ( ( ! [SY34: $i] :
~ ~ ( ~ ( element @ SY34 @ ( powerset @ ( the_carrier @ SV4 ) ) )
| ~ ( closed_subset @ SY34 @ SV4 ) ) )
= $false )
| ( ( topological_space @ SV4 )
= $false )
| ( ( top_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(162,plain,
! [SV14: $i,SV10: $i] :
( ( ( ~ ( topological_space @ SV10 )
| ~ ( top_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) ) )
= $true )
| ( ( ~ ! [SY47: $i,SY48: $i,SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY47 != SY48 )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY48 ) @ SV14 ) )
| ( SY47 != SY49 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY49 ) @ SV14 ) )
| ( SY48 = SY49 ) )
| ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(163,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ SV15 )
| ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
| ( in @ ( sK4_SY54 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(164,plain,
! [SV2: $i] :
( ( ( ~ ( element @ ( sK5_SY33 @ SV2 ) @ ( powerset @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(165,plain,
! [SV2: $i] :
( ( ( ~ ~ ( empty @ ( sK5_SY33 @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(166,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK6_SY34 @ SV4 ) @ ( powerset @ ( the_carrier @ SV4 ) ) )
| ~ ( closed_subset @ ( sK6_SY34 @ SV4 ) @ SV4 ) ) )
= $false )
| ( ( topological_space @ SV4 )
= $false )
| ( ( top_str @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[161]) ).
thf(167,plain,
! [SV14: $i,SV10: $i] :
( ( ( ~ ( topological_space @ SV10 ) )
= $true )
| ( ( ~ ( top_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) ) )
= $true )
| ( ( ~ ! [SY47: $i,SY48: $i,SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY47 != SY48 )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY48 ) @ SV14 ) )
| ( SY47 != SY49 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY49 ) @ SV14 ) )
| ( SY48 = SY49 ) )
| ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(168,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ SV15 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
| ( in @ ( sK4_SY54 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(169,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
| ( in @ ( sK4_SY54 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(170,plain,
! [SV2: $i] :
( ( ( element @ ( sK5_SY33 @ SV2 ) @ ( powerset @ SV2 ) )
= $true )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(171,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ ( sK5_SY33 @ SV2 ) ) )
= $true )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(172,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( element @ ( sK6_SY34 @ SV4 ) @ ( powerset @ ( the_carrier @ SV4 ) ) )
| ~ ( closed_subset @ ( sK6_SY34 @ SV4 ) @ SV4 ) ) )
= $true )
| ( ( topological_space @ SV4 )
= $false )
| ( ( top_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(173,plain,
! [SV14: $i,SV10: $i] :
( ( ( topological_space @ SV10 )
= $false )
| ( ( ~ ( top_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) ) )
= $true )
| ( ( ~ ! [SY47: $i,SY48: $i,SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY47 != SY48 )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY48 ) @ SV14 ) )
| ( SY47 != SY49 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY49 ) @ SV14 ) )
| ( SY48 = SY49 ) )
| ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(174,plain,
! [SV15: $i] :
( ( ( in @ ( sK4_SY54 @ SV15 ) @ SV15 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
| ( in @ ( sK4_SY54 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(175,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
| ( in @ ( sK4_SY54 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(176,plain,
! [SV2: $i] :
( ( ( empty @ ( sK5_SY33 @ SV2 ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(177,plain,
! [SV4: $i] :
( ( ( ~ ( element @ ( sK6_SY34 @ SV4 ) @ ( powerset @ ( the_carrier @ SV4 ) ) )
| ~ ( closed_subset @ ( sK6_SY34 @ SV4 ) @ SV4 ) )
= $false )
| ( ( topological_space @ SV4 )
= $false )
| ( ( top_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(178,plain,
! [SV14: $i,SV10: $i] :
( ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( ~ ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) ) )
= $true )
| ( ( ~ ! [SY47: $i,SY48: $i,SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY47 != SY48 )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY48 ) @ SV14 ) )
| ( SY47 != SY49 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY49 ) @ SV14 ) )
| ( SY48 = SY49 ) )
| ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(179,plain,
! [SV15: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
| ( in @ ( sK4_SY54 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(180,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
| ( in @ ( sK4_SY54 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(181,plain,
! [SV4: $i] :
( ( ( ~ ( element @ ( sK6_SY34 @ SV4 ) @ ( powerset @ ( the_carrier @ SV4 ) ) ) )
= $false )
| ( ( topological_space @ SV4 )
= $false )
| ( ( top_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(182,plain,
! [SV4: $i] :
( ( ( ~ ( closed_subset @ ( sK6_SY34 @ SV4 ) @ SV4 ) )
= $false )
| ( ( topological_space @ SV4 )
= $false )
| ( ( top_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(183,plain,
! [SV10: $i,SV14: $i] :
( ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( ~ ! [SY47: $i,SY48: $i,SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY47 != SY48 )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY48 ) @ SV14 ) )
| ( SY47 != SY49 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY49 ) @ SV14 ) )
| ( SY48 = SY49 ) )
| ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(184,plain,
! [SV15: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) ) )
= $false )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(185,plain,
! [SV15: $i] :
( ( ( in @ ( sK4_SY54 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(186,plain,
! [SV15: $i] :
( ( ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
| ( in @ ( sK4_SY54 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(187,plain,
! [SV4: $i] :
( ( ( element @ ( sK6_SY34 @ SV4 ) @ ( powerset @ ( the_carrier @ SV4 ) ) )
= $true )
| ( ( topological_space @ SV4 )
= $false )
| ( ( top_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(188,plain,
! [SV4: $i] :
( ( ( closed_subset @ ( sK6_SY34 @ SV4 ) @ SV4 )
= $true )
| ( ( topological_space @ SV4 )
= $false )
| ( ( top_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(189,plain,
! [SV14: $i,SV10: $i] :
( ( ( ~ ! [SY47: $i,SY48: $i,SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY47 != SY48 )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY48 ) @ SV14 ) )
| ( SY47 != SY49 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY49 ) @ SV14 ) )
| ( SY48 = SY49 ) ) )
= $true )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(190,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) ) )
= $true )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(191,plain,
! [SV15: $i] :
( ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 )
= $false )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
| ( in @ ( sK4_SY54 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(192,plain,
! [SV14: $i,SV10: $i] :
( ( ( ! [SY47: $i,SY48: $i,SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY47 != SY48 )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY48 ) @ SV14 ) )
| ( SY47 != SY49 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY49 ) @ SV14 ) )
| ( SY48 = SY49 ) ) )
= $false )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(193,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
= $false )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(194,plain,
! [SV15: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
| ( in @ ( sK4_SY54 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(195,plain,
! [SV10: $i,SV14: $i] :
( ( ( ! [SY55: $i,SY56: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK7_SY47 @ SV14 @ SV10 )
!= SY55 )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY55 ) @ SV14 ) )
| ( ( sK7_SY47 @ SV14 @ SV10 )
!= SY56 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY56 ) @ SV14 ) )
| ( SY55 = SY56 ) ) )
= $false )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[192]) ).
thf(196,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(197,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
= $false )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(198,plain,
! [SV15: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) ) )
= $false )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(199,plain,
! [SV15: $i] :
( ( ( in @ ( sK4_SY54 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(200,plain,
! [SV10: $i,SV14: $i] :
( ( ( ! [SY57: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK8_SY55 @ SV10 @ SV14 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 ) )
| ( ( sK7_SY47 @ SV14 @ SV10 )
!= SY57 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY57 ) @ SV14 ) )
| ( ( sK8_SY55 @ SV10 @ SV14 )
= SY57 ) ) )
= $false )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[195]) ).
thf(201,plain,
! [SV15: $i] :
( ( ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $true )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(202,plain,
! [SV15: $i] :
( ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 )
= $true )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(203,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) ) )
= $true )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(204,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK8_SY55 @ SV10 @ SV14 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 ) )
| ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK9_SY57 @ SV10 @ SV14 ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 ) )
| ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) ) )
= $false )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[200]) ).
thf(205,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
= $false )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(206,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK8_SY55 @ SV10 @ SV14 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 ) )
| ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK9_SY57 @ SV10 @ SV14 ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 ) ) )
= $false )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(207,plain,
! [SV14: $i,SV10: $i] :
( ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(208,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(209,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 ) )
= $false )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(210,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK8_SY55 @ SV10 @ SV14 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 ) )
| ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK9_SY57 @ SV10 @ SV14 ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 ) ) )
= $true )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(211,plain,
! [SV14: $i,SV10: $i] :
( ( ( ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(212,plain,
! [SV15: $i] :
( ( ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $true )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(213,plain,
! [SV15: $i] :
( ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 )
= $true )
| ( ( in @ ( sK4_SY54 @ SV15 ) @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ sK1_A ) @ ( sK4_SY54 @ SV15 ) ) @ sK2_SY28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(214,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK8_SY55 @ SV10 @ SV14 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 ) )
| ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK9_SY57 @ SV10 @ SV14 ) ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 ) )
= $false )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(215,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ ( sK10_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY58 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY58 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY58 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY58 ) @ SV14 ) )
| ( in @ SY58 @ ( sK10_SY50 @ SV14 @ SV10 ) ) ) ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[211]) ).
thf(216,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK8_SY55 @ SV10 @ SV14 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 ) )
| ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK9_SY57 @ SV10 @ SV14 ) ) ) )
= $false )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(217,plain,
! [SV14: $i,SV10: $i] :
( ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 ) )
= $false )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(218,plain,
! [SV10: $i,SV14: $i] :
( ( ( ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ ( sK10_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY58 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY58 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY58 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY58 ) @ SV14 ) )
| ( in @ SY58 @ ( sK10_SY50 @ SV14 @ SV10 ) ) ) ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(219,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK8_SY55 @ SV10 @ SV14 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 ) )
| ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK9_SY57 @ SV10 @ SV14 ) ) ) )
= $true )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(220,plain,
! [SV14: $i,SV10: $i] :
( ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(221,plain,
! [SV10: $i,SV14: $i,SV17: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY61 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY61 != SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY62 != SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) )
| ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) ) ) ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(222,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ~ ( ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK8_SY55 @ SV10 @ SV14 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 ) )
| ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK9_SY57 @ SV10 @ SV14 ) ) )
= $false )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(223,plain,
! [SV14: $i,SV10: $i] :
( ( ( ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(224,plain,
! [SV10: $i,SV14: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY61 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY61 != SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY62 != SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) )
| ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) ) ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(225,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ~ ( ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK8_SY55 @ SV10 @ SV14 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 ) ) )
= $false )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(226,plain,
! [SV10: $i,SV14: $i] :
( ( ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(227,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ! [SY63: $i] :
~ ( ~ ( ~ ( in @ SY63 @ ( sK11_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY63 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY63 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY63 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY63 ) @ SV14 ) )
| ( in @ SY63 @ ( sK11_SY50 @ SV14 @ SV10 ) ) ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[223]) ).
thf(228,plain,
! [SV10: $i,SV14: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY61 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY61 != SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) ) ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(229,plain,
! [SV14: $i,SV17: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY62 != SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) )
| ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) ) ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(230,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ( ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK8_SY55 @ SV10 @ SV14 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 ) ) )
= $true )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(231,plain,
! [SV10: $i,SV14: $i] :
( ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(232,plain,
! [SV10: $i,SV14: $i] :
( ( ( ! [SY63: $i] :
~ ( ~ ( ~ ( in @ SY63 @ ( sK11_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY63 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY63 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY63 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY63 ) @ SV14 ) )
| ( in @ SY63 @ ( sK11_SY50 @ SV14 @ SV10 ) ) ) ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(233,plain,
! [SV10: $i,SV14: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY61 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY61 != SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(234,plain,
! [SV14: $i,SV17: $i,SV10: $i] :
( ( ( ~ ~ ! [SY62: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY62 != SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) )
| ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(235,plain,
! [SV10: $i,SV14: $i] :
( ( ( ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK8_SY55 @ SV10 @ SV14 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 ) )
= $false )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(236,plain,
! [SV14: $i,SV10: $i] :
( ( ( ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(237,plain,
! [SV10: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY66 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY66 != SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY67: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY67 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY67 != SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) )
| ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) ) ) ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(238,plain,
! [SV10: $i,SV14: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY61 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY61 != SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(239,plain,
! [SV14: $i,SV17: $i,SV10: $i] :
( ( ( ~ ~ ! [SY62: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY62 != SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(240,plain,
! [SV10: $i,SV14: $i] :
( ( ( ( sK7_SY47 @ SV14 @ SV10 )
!= ( sK8_SY55 @ SV10 @ SV14 ) )
= $false )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(241,plain,
! [SV14: $i,SV10: $i] :
( ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 ) )
= $false )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(242,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ! [SY68: $i] :
~ ( ~ ( ~ ( in @ SY68 @ ( sK12_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY68 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY68 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY68 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY68 ) @ SV14 ) )
| ( in @ SY68 @ ( sK12_SY50 @ SV14 @ SV10 ) ) ) ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[236]) ).
thf(243,plain,
! [SV10: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY66 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY66 != SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY67: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY67 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY67 != SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) )
| ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(244,plain,
! [SV10: $i,SV14: $i,SV17: $i] :
( ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY61 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY61 != SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(245,plain,
! [SV14: $i,SV17: $i,SV10: $i] :
( ( ( ~ ! [SY62: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY62 != SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(246,plain,
! [SV10: $i,SV14: $i] :
( ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(247,plain,
! [SV14: $i,SV10: $i] :
( ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( ~ ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(248,plain,
! [SV10: $i,SV14: $i] :
( ( ( ! [SY68: $i] :
~ ( ~ ( ~ ( in @ SY68 @ ( sK12_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY68 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY68 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY68 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY68 ) @ SV14 ) )
| ( in @ SY68 @ ( sK12_SY50 @ SV14 @ SV10 ) ) ) ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(249,plain,
! [SV10: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY66 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY66 != SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(250,plain,
! [SV14: $i,SV18: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ! [SY67: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY67 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY67 != SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) )
| ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(251,plain,
! [SV14: $i,SV17: $i,SV10: $i] :
( ( ( ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY61 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY61 != SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(252,plain,
! [SV14: $i,SV17: $i,SV10: $i] :
( ( ( ! [SY62: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY62 != SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(253,plain,
! [SV14: $i,SV10: $i] :
( ( ( ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(254,plain,
! [SV14: $i,SV10: $i] :
( ( ( ! [SY50: $i] :
~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY50 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY51 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY51 ) @ SV14 ) )
| ( in @ SY51 @ SY50 ) ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(255,plain,
! [SV10: $i,SV14: $i,SV19: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY71 != SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY72 != SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) )
| ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) ) ) ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(256,plain,
! [SV10: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY66 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY66 != SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(257,plain,
! [SV14: $i,SV18: $i,SV10: $i] :
( ( ( ~ ~ ! [SY67: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY67 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY67 != SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) )
| ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(258,plain,
! [SV10: $i,SV17: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_SY61 @ SV14 @ SV17 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK13_SY61 @ SV14 @ SV17 @ SV10 )
!= SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[251]) ).
thf(259,plain,
! [SV14: $i,SV17: $i,SV10: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV20 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV20 != SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(260,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ! [SY73: $i] :
~ ( ~ ( ~ ( in @ SY73 @ ( sK14_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY73 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY73 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY73 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY73 ) @ SV14 ) )
| ( in @ SY73 @ ( sK14_SY50 @ SV14 @ SV10 ) ) ) ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[253]) ).
thf(261,plain,
! [SV10: $i,SV14: $i] :
( ( ( ~ ! [SY76: $i] :
~ ( ~ ( ~ ( in @ SY76 @ ( sK15_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY76 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY76 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY76 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY76 ) @ SV14 ) )
| ( in @ SY76 @ ( sK15_SY50 @ SV14 @ SV10 ) ) ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[254]) ).
thf(262,plain,
! [SV10: $i,SV14: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY71 != SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY72 != SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) )
| ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) ) ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(263,plain,
! [SV10: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY66 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY66 != SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(264,plain,
! [SV14: $i,SV18: $i,SV10: $i] :
( ( ( ~ ~ ! [SY67: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY67 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY67 != SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(265,plain,
! [SV10: $i,SV17: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK13_SY61 @ SV14 @ SV17 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK13_SY61 @ SV14 @ SV17 @ SV10 )
!= SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(266,plain,
! [SV14: $i,SV17: $i,SV10: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV20 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV20 != SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(267,plain,
! [SV10: $i,SV14: $i] :
( ( ( ! [SY73: $i] :
~ ( ~ ( ~ ( in @ SY73 @ ( sK14_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY73 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY73 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY73 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY73 ) @ SV14 ) )
| ( in @ SY73 @ ( sK14_SY50 @ SV14 @ SV10 ) ) ) ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(268,plain,
! [SV10: $i,SV14: $i] :
( ( ( ! [SY76: $i] :
~ ( ~ ( ~ ( in @ SY76 @ ( sK15_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY52 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY52 != SY76 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY76 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY53 != SY76 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SY76 ) @ SV14 ) )
| ( in @ SY76 @ ( sK15_SY50 @ SV14 @ SV10 ) ) ) ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(269,plain,
! [SV10: $i,SV14: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY71 != SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) ) ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(270,plain,
! [SV14: $i,SV19: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY72 != SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) )
| ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) ) ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(271,plain,
! [SV10: $i,SV14: $i,SV18: $i] :
( ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ~ ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY66 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY66 != SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(272,plain,
! [SV14: $i,SV18: $i,SV10: $i] :
( ( ( ~ ! [SY67: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY67 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY67 != SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(273,plain,
! [SV10: $i,SV17: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY61 @ SV14 @ SV17 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK13_SY61 @ SV14 @ SV17 @ SV10 )
!= SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) )
= $false )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(274,plain,
! [SV14: $i,SV17: $i,SV10: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( in @ SV20 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV20 != SV17 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) )
= $true )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(275,plain,
! [SV10: $i,SV14: $i,SV21: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY79 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY79 != SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY80: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY80 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY80 != SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) )
| ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) ) ) ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(276,plain,
! [SV10: $i,SV14: $i,SV22: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY81 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY81 != SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY82 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY82 != SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) )
| ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) ) ) ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(277,plain,
! [SV10: $i,SV14: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY71 != SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(278,plain,
! [SV14: $i,SV19: $i,SV10: $i] :
( ( ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY72 != SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) )
| ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(279,plain,
! [SV14: $i,SV18: $i,SV10: $i] :
( ( ( ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY66 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY66 != SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(280,plain,
! [SV14: $i,SV18: $i,SV10: $i] :
( ( ( ! [SY67: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY67 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY67 != SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(281,plain,
! [SV10: $i,SV17: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY61 @ SV14 @ SV17 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK13_SY61 @ SV14 @ SV17 @ SV10 )
!= SV17 ) ) )
= $false )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(282,plain,
! [SV14: $i,SV17: $i,SV10: $i] :
( ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) )
= $false )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(283,plain,
! [SV14: $i,SV17: $i,SV10: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( in @ SV20 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV20 != SV17 ) ) )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) )
= $true )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(284,plain,
! [SV10: $i,SV14: $i,SV21: $i] :
( ( ( ~ ( ~ ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY79 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY79 != SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY80: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY80 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY80 != SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) )
| ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) ) ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(285,plain,
! [SV10: $i,SV14: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY81 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY81 != SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) ) )
| ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY82 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY82 != SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) )
| ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(286,plain,
! [SV10: $i,SV14: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY71 != SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(287,plain,
! [SV14: $i,SV19: $i,SV10: $i] :
( ( ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY72 != SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(288,plain,
! [SV10: $i,SV18: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY66 @ SV14 @ SV18 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK16_SY66 @ SV14 @ SV18 @ SV10 )
!= SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[279]) ).
thf(289,plain,
! [SV14: $i,SV18: $i,SV10: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV23 != SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(290,plain,
! [SV10: $i,SV17: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY61 @ SV14 @ SV17 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK13_SY61 @ SV14 @ SV17 @ SV10 )
!= SV17 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(291,plain,
! [SV14: $i,SV17: $i,SV10: $i] :
( ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 )
= $true )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(292,plain,
! [SV14: $i,SV17: $i,SV10: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ SV20 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV20 != SV17 ) ) )
= $false )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) )
= $true )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(293,plain,
! [SV10: $i,SV14: $i,SV21: $i] :
( ( ( ~ ( ~ ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY79 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY79 != SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) ) ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(294,plain,
! [SV14: $i,SV21: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ! [SY80: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY80 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY80 != SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) )
| ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) ) ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(295,plain,
! [SV10: $i,SV14: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY81 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY81 != SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(296,plain,
! [SV14: $i,SV22: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY82 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY82 != SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) )
| ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) ) ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(297,plain,
! [SV10: $i,SV14: $i,SV19: $i] :
( ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY71 != SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(298,plain,
! [SV14: $i,SV19: $i,SV10: $i] :
( ( ( ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY72 != SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(299,plain,
! [SV10: $i,SV18: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK16_SY66 @ SV14 @ SV18 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK16_SY66 @ SV14 @ SV18 @ SV10 )
!= SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(300,plain,
! [SV14: $i,SV18: $i,SV10: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV23 != SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(301,plain,
! [SV10: $i,SV17: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK13_SY61 @ SV14 @ SV17 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK13_SY61 @ SV14 @ SV17 @ SV10 )
!= SV17 ) )
= $false )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(302,plain,
! [SV14: $i,SV17: $i,SV10: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV20 != SV17 ) )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) )
= $true )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(303,plain,
! [SV10: $i,SV14: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY79 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY79 != SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(304,plain,
! [SV14: $i,SV21: $i,SV10: $i] :
( ( ( ~ ~ ! [SY80: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY80 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY80 != SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) )
| ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(305,plain,
! [SV10: $i,SV14: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
| ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY81 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY81 != SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(306,plain,
! [SV14: $i,SV22: $i,SV10: $i] :
( ( ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY82 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY82 != SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) )
| ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(307,plain,
! [SV14: $i,SV19: $i,SV10: $i] :
( ( ( ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY71 != SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(308,plain,
! [SV14: $i,SV19: $i,SV10: $i] :
( ( ( ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY72 != SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(309,plain,
! [SV10: $i,SV18: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK16_SY66 @ SV14 @ SV18 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK16_SY66 @ SV14 @ SV18 @ SV10 )
!= SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) )
= $false )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(310,plain,
! [SV14: $i,SV18: $i,SV10: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV23 != SV18 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) )
= $true )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(311,plain,
! [SV10: $i,SV17: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK13_SY61 @ SV14 @ SV17 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(312,plain,
! [SV10: $i,SV17: $i,SV14: $i] :
( ( ( ( sK13_SY61 @ SV14 @ SV17 @ SV10 )
!= SV17 )
= $false )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(313,plain,
! [SV14: $i,SV17: $i,SV10: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $true )
| ( ( SV20 != SV17 )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) )
= $true )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(314,plain,
! [SV10: $i,SV14: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY79 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY79 != SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(315,plain,
! [SV14: $i,SV21: $i,SV10: $i] :
( ( ( ~ ~ ! [SY80: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY80 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY80 != SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(316,plain,
! [SV10: $i,SV14: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) ) )
= $true )
| ( ( ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY81 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY81 != SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(317,plain,
! [SV14: $i,SV22: $i,SV10: $i] :
( ( ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY82 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY82 != SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(318,plain,
! [SV10: $i,SV19: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY71 @ SV14 @ SV19 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK17_SY71 @ SV14 @ SV19 @ SV10 )
!= SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[307]) ).
thf(319,plain,
! [SV14: $i,SV19: $i,SV10: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV24 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV24 != SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(320,plain,
! [SV10: $i,SV18: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK16_SY66 @ SV14 @ SV18 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK16_SY66 @ SV14 @ SV18 @ SV10 )
!= SV18 ) ) )
= $false )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(321,plain,
! [SV14: $i,SV18: $i,SV10: $i] :
( ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) )
= $false )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(322,plain,
! [SV14: $i,SV18: $i,SV10: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV23 != SV18 ) ) )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) )
= $true )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(323,plain,
! [SV10: $i,SV17: $i,SV14: $i] :
( ( ( in @ ( sK13_SY61 @ SV14 @ SV17 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(324,plain,
! [SV10: $i,SV17: $i,SV14: $i] :
( ( ( ( sK13_SY61 @ SV14 @ SV17 @ SV10 )
= SV17 )
= $true )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(325,plain,
! [SV14: $i,SV17: $i,SV10: $i,SV20: $i] :
( ( ( in @ SV20 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( SV20 != SV17 )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) )
= $true )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(326,plain,
! [SV10: $i,SV14: $i,SV21: $i] :
( ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY79 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY79 != SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(327,plain,
! [SV14: $i,SV21: $i,SV10: $i] :
( ( ( ~ ! [SY80: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY80 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY80 != SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(328,plain,
! [SV10: $i,SV14: $i,SV22: $i] :
( ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY81 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY81 != SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(329,plain,
! [SV14: $i,SV22: $i,SV10: $i] :
( ( ( ~ ! [SY82: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY82 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY82 != SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(330,plain,
! [SV10: $i,SV19: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY71 @ SV14 @ SV19 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK17_SY71 @ SV14 @ SV19 @ SV10 )
!= SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(331,plain,
! [SV14: $i,SV19: $i,SV10: $i,SV24: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV24 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV24 != SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(332,plain,
! [SV10: $i,SV18: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY66 @ SV14 @ SV18 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK16_SY66 @ SV14 @ SV18 @ SV10 )
!= SV18 ) ) )
= $true )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(333,plain,
! [SV14: $i,SV18: $i,SV10: $i] :
( ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 )
= $true )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(334,plain,
! [SV14: $i,SV18: $i,SV10: $i,SV23: $i] :
( ( ( ~ ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV23 != SV18 ) ) )
= $false )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) )
= $true )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(335,plain,
! [SV14: $i,SV10: $i,SV17: $i,SV20: $i] :
( ( ( SV20 = SV17 )
= $false )
| ( ( in @ SV20 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 ) )
= $true )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(336,plain,
! [SV14: $i,SV21: $i,SV10: $i] :
( ( ( ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY79 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY79 != SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(337,plain,
! [SV14: $i,SV21: $i,SV10: $i] :
( ( ( ! [SY80: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY80 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY80 != SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(338,plain,
! [SV14: $i,SV22: $i,SV10: $i] :
( ( ( ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY81 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY81 != SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(339,plain,
! [SV14: $i,SV22: $i,SV10: $i] :
( ( ( ! [SY82: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY82 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SY82 != SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(340,plain,
! [SV10: $i,SV19: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_SY71 @ SV14 @ SV19 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK17_SY71 @ SV14 @ SV19 @ SV10 )
!= SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) )
= $false )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(341,plain,
! [SV14: $i,SV19: $i,SV10: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( in @ SV24 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV24 != SV19 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) )
= $true )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(342,plain,
! [SV10: $i,SV18: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK16_SY66 @ SV14 @ SV18 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK16_SY66 @ SV14 @ SV18 @ SV10 )
!= SV18 ) )
= $false )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(343,plain,
! [SV14: $i,SV18: $i,SV10: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV23 != SV18 ) )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) )
= $true )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(344,plain,
! [SV20: $i,SV14: $i,SV17: $i,SV10: $i] :
( ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV17 ) @ SV14 )
= $false )
| ( ( in @ SV20 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( SV20 = SV17 )
= $false )
| ( ( in @ SV17 @ ( sK10_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK8_SY55 @ SV10 @ SV14 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $false )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(345,plain,
! [SV10: $i,SV21: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY79 @ SV14 @ SV21 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK18_SY79 @ SV14 @ SV21 @ SV10 )
!= SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[336]) ).
thf(346,plain,
! [SV14: $i,SV21: $i,SV10: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV25 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV25 != SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(347,plain,
! [SV10: $i,SV22: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_SY81 @ SV14 @ SV22 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK19_SY81 @ SV14 @ SV22 @ SV10 )
!= SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[338]) ).
thf(348,plain,
! [SV14: $i,SV22: $i,SV10: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV26 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV26 != SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(349,plain,
! [SV10: $i,SV19: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_SY71 @ SV14 @ SV19 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK17_SY71 @ SV14 @ SV19 @ SV10 )
!= SV19 ) ) )
= $false )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(350,plain,
! [SV14: $i,SV19: $i,SV10: $i] :
( ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) )
= $false )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(351,plain,
! [SV14: $i,SV19: $i,SV10: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( in @ SV24 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV24 != SV19 ) ) )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) )
= $true )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(352,plain,
! [SV10: $i,SV18: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK16_SY66 @ SV14 @ SV18 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(353,plain,
! [SV10: $i,SV18: $i,SV14: $i] :
( ( ( ( sK16_SY66 @ SV14 @ SV18 @ SV10 )
!= SV18 )
= $false )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(354,plain,
! [SV14: $i,SV18: $i,SV10: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $true )
| ( ( SV23 != SV18 )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) )
= $true )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(355,plain,
! [SV10: $i,SV21: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY79 @ SV14 @ SV21 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK18_SY79 @ SV14 @ SV21 @ SV10 )
!= SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(356,plain,
! [SV14: $i,SV21: $i,SV10: $i,SV25: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV25 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV25 != SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(357,plain,
! [SV10: $i,SV22: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_SY81 @ SV14 @ SV22 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK19_SY81 @ SV14 @ SV22 @ SV10 )
!= SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(358,plain,
! [SV14: $i,SV22: $i,SV10: $i,SV26: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV26 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV26 != SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(359,plain,
! [SV10: $i,SV19: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY71 @ SV14 @ SV19 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK17_SY71 @ SV14 @ SV19 @ SV10 )
!= SV19 ) ) )
= $true )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(360,plain,
! [SV14: $i,SV19: $i,SV10: $i] :
( ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 )
= $true )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[350]) ).
thf(361,plain,
! [SV14: $i,SV19: $i,SV10: $i,SV24: $i] :
( ( ( ~ ( ~ ( in @ SV24 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV24 != SV19 ) ) )
= $false )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) )
= $true )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(362,plain,
! [SV10: $i,SV18: $i,SV14: $i] :
( ( ( in @ ( sK16_SY66 @ SV14 @ SV18 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(363,plain,
! [SV10: $i,SV18: $i,SV14: $i] :
( ( ( ( sK16_SY66 @ SV14 @ SV18 @ SV10 )
= SV18 )
= $true )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(364,plain,
! [SV14: $i,SV18: $i,SV10: $i,SV23: $i] :
( ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( SV23 != SV18 )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) )
= $true )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(365,plain,
! [SV10: $i,SV21: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY79 @ SV14 @ SV21 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK18_SY79 @ SV14 @ SV21 @ SV10 )
!= SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) )
= $false )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(366,plain,
! [SV14: $i,SV21: $i,SV10: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( in @ SV25 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV25 != SV21 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) )
= $true )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[356]) ).
thf(367,plain,
! [SV10: $i,SV22: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY81 @ SV14 @ SV22 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK19_SY81 @ SV14 @ SV22 @ SV10 )
!= SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) )
= $false )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(368,plain,
! [SV14: $i,SV22: $i,SV10: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( in @ SV26 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV26 != SV22 ) )
| ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) )
= $true )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(369,plain,
! [SV10: $i,SV19: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK17_SY71 @ SV14 @ SV19 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK17_SY71 @ SV14 @ SV19 @ SV10 )
!= SV19 ) )
= $false )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(370,plain,
! [SV14: $i,SV19: $i,SV10: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV24 != SV19 ) )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) )
= $true )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(371,plain,
! [SV14: $i,SV10: $i,SV18: $i,SV23: $i] :
( ( ( SV23 = SV18 )
= $false )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 ) )
= $true )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(372,plain,
! [SV10: $i,SV21: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY79 @ SV14 @ SV21 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK18_SY79 @ SV14 @ SV21 @ SV10 )
!= SV21 ) ) )
= $false )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(373,plain,
! [SV14: $i,SV21: $i,SV10: $i] :
( ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) )
= $false )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(374,plain,
! [SV14: $i,SV21: $i,SV10: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( in @ SV25 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV25 != SV21 ) ) )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) )
= $true )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(375,plain,
! [SV10: $i,SV22: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY81 @ SV14 @ SV22 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK19_SY81 @ SV14 @ SV22 @ SV10 )
!= SV22 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[367]) ).
thf(376,plain,
! [SV14: $i,SV22: $i,SV10: $i] :
( ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) )
= $false )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[367]) ).
thf(377,plain,
! [SV14: $i,SV22: $i,SV10: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( in @ SV26 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV26 != SV22 ) ) )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) )
= $true )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(378,plain,
! [SV10: $i,SV19: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK17_SY71 @ SV14 @ SV19 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(379,plain,
! [SV10: $i,SV19: $i,SV14: $i] :
( ( ( ( sK17_SY71 @ SV14 @ SV19 @ SV10 )
!= SV19 )
= $false )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(380,plain,
! [SV14: $i,SV19: $i,SV10: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $true )
| ( ( SV24 != SV19 )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) )
= $true )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(381,plain,
! [SV23: $i,SV14: $i,SV18: $i,SV10: $i] :
( ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV18 ) @ SV14 )
= $false )
| ( ( in @ SV23 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( SV23 = SV18 )
= $false )
| ( ( in @ SV18 @ ( sK11_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK9_SY57 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(382,plain,
! [SV10: $i,SV21: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY79 @ SV14 @ SV21 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK18_SY79 @ SV14 @ SV21 @ SV10 )
!= SV21 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(383,plain,
! [SV14: $i,SV21: $i,SV10: $i] :
( ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 )
= $true )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(384,plain,
! [SV14: $i,SV21: $i,SV10: $i,SV25: $i] :
( ( ( ~ ( ~ ( in @ SV25 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV25 != SV21 ) ) )
= $false )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) )
= $true )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(385,plain,
! [SV10: $i,SV22: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY81 @ SV14 @ SV22 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK19_SY81 @ SV14 @ SV22 @ SV10 )
!= SV22 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(386,plain,
! [SV14: $i,SV22: $i,SV10: $i] :
( ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 )
= $true )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(387,plain,
! [SV14: $i,SV22: $i,SV10: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ SV26 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV26 != SV22 ) ) )
= $false )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) )
= $true )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(388,plain,
! [SV10: $i,SV19: $i,SV14: $i] :
( ( ( in @ ( sK17_SY71 @ SV14 @ SV19 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[378]) ).
thf(389,plain,
! [SV10: $i,SV19: $i,SV14: $i] :
( ( ( ( sK17_SY71 @ SV14 @ SV19 @ SV10 )
= SV19 )
= $true )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[379]) ).
thf(390,plain,
! [SV14: $i,SV19: $i,SV10: $i,SV24: $i] :
( ( ( in @ SV24 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( SV24 != SV19 )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) )
= $true )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(391,plain,
! [SV10: $i,SV21: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK18_SY79 @ SV14 @ SV21 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK18_SY79 @ SV14 @ SV21 @ SV10 )
!= SV21 ) )
= $false )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(392,plain,
! [SV14: $i,SV21: $i,SV10: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV25 != SV21 ) )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) )
= $true )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(393,plain,
! [SV10: $i,SV22: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK19_SY81 @ SV14 @ SV22 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( ( sK19_SY81 @ SV14 @ SV22 @ SV10 )
!= SV22 ) )
= $false )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(394,plain,
! [SV14: $i,SV22: $i,SV10: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ ( powerset @ ( the_carrier @ SV10 ) ) )
| ( SV26 != SV22 ) )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) )
= $true )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(395,plain,
! [SV14: $i,SV10: $i,SV19: $i,SV24: $i] :
( ( ( SV24 = SV19 )
= $false )
| ( ( in @ SV24 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 ) )
= $true )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(396,plain,
! [SV10: $i,SV21: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK18_SY79 @ SV14 @ SV21 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[391]) ).
thf(397,plain,
! [SV10: $i,SV21: $i,SV14: $i] :
( ( ( ( sK18_SY79 @ SV14 @ SV21 @ SV10 )
!= SV21 )
= $false )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[391]) ).
thf(398,plain,
! [SV14: $i,SV21: $i,SV10: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $true )
| ( ( SV25 != SV21 )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) )
= $true )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(399,plain,
! [SV10: $i,SV22: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK19_SY81 @ SV14 @ SV22 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[393]) ).
thf(400,plain,
! [SV10: $i,SV22: $i,SV14: $i] :
( ( ( ( sK19_SY81 @ SV14 @ SV22 @ SV10 )
!= SV22 )
= $false )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[393]) ).
thf(401,plain,
! [SV14: $i,SV22: $i,SV10: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $true )
| ( ( SV26 != SV22 )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) )
= $true )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(402,plain,
! [SV24: $i,SV14: $i,SV19: $i,SV10: $i] :
( ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV19 ) @ SV14 )
= $false )
| ( ( in @ SV24 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( SV24 = SV19 )
= $false )
| ( ( in @ SV19 @ ( sK12_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK9_SY57 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(403,plain,
! [SV10: $i,SV21: $i,SV14: $i] :
( ( ( in @ ( sK18_SY79 @ SV14 @ SV21 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(404,plain,
! [SV10: $i,SV21: $i,SV14: $i] :
( ( ( ( sK18_SY79 @ SV14 @ SV21 @ SV10 )
= SV21 )
= $true )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[397]) ).
thf(405,plain,
! [SV14: $i,SV21: $i,SV10: $i,SV25: $i] :
( ( ( in @ SV25 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( SV25 != SV21 )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) )
= $true )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(406,plain,
! [SV10: $i,SV22: $i,SV14: $i] :
( ( ( in @ ( sK19_SY81 @ SV14 @ SV22 @ SV10 ) @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(407,plain,
! [SV10: $i,SV22: $i,SV14: $i] :
( ( ( ( sK19_SY81 @ SV14 @ SV22 @ SV10 )
= SV22 )
= $true )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $false )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(408,plain,
! [SV14: $i,SV22: $i,SV10: $i,SV26: $i] :
( ( ( in @ SV26 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( SV26 != SV22 )
= $true )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) )
= $true )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(409,plain,
! [SV14: $i,SV10: $i,SV21: $i,SV25: $i] :
( ( ( SV25 = SV21 )
= $false )
| ( ( in @ SV25 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 ) )
= $true )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(410,plain,
! [SV14: $i,SV10: $i,SV22: $i,SV26: $i] :
( ( ( SV26 = SV22 )
= $false )
| ( ( in @ SV26 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( ~ ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 ) )
= $true )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(411,plain,
! [SV25: $i,SV14: $i,SV21: $i,SV10: $i] :
( ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV21 ) @ SV14 )
= $false )
| ( ( in @ SV25 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( SV25 = SV21 )
= $false )
| ( ( in @ SV21 @ ( sK14_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( ( sK7_SY47 @ SV14 @ SV10 )
= ( sK8_SY55 @ SV10 @ SV14 ) )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(412,plain,
! [SV26: $i,SV14: $i,SV22: $i,SV10: $i] :
( ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ SV22 ) @ SV14 )
= $false )
| ( ( in @ SV26 @ ( powerset @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( SV26 = SV22 )
= $false )
| ( ( in @ SV22 @ ( sK15_SY50 @ SV14 @ SV10 ) )
= $true )
| ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ SV10 ) @ ( sK8_SY55 @ SV10 @ SV14 ) ) @ SV14 )
= $true )
| ( ( top_str @ SV10 )
= $false )
| ( ( topological_space @ SV10 )
= $false )
| ( ( element @ SV14 @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(413,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[64,412,411,407,406,404,403,402,389,388,386,383,381,363,362,360,344,333,324,323,291,213,212,202,201,199,188,187,185,176,170,157,156,155,152,141,132,124,118,105,80,79,78,74,73,71,69]) ).
thf(414,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[413]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU310+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 15:12:33 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.31/0.42
% 1.31/0.42 No.of.Axioms: 16
% 1.31/0.42
% 1.31/0.42 Length.of.Defs: 0
% 1.31/0.42
% 1.31/0.42 Contains.Choice.Funs: false
% 1.31/0.42 ............
% 1.31/0.42
% 1.31/0.42 ********************************
% 1.31/0.42 * All subproblems solved! *
% 1.31/0.42 ********************************
% 1.31/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:19,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:413,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.31/0.42
% 1.31/0.42 %**** Beginning of derivation protocol ****
% 1.31/0.42 % SZS output start CNFRefutation
% See solution above
% 1.31/0.42
% 1.31/0.42 %**** End of derivation protocol ****
% 1.31/0.42 %**** no. of clauses in derivation: 395 ****
% 1.31/0.42 %**** clause counter: 413 ****
% 1.31/0.42
% 1.31/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:19,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:413,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------