%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU401+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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:44:17 AM UTC 2026
% Result : Theorem 2.72s 0.69s
% Output : CNFRefutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 13
% Syntax : Number of formulae : 259 ( 103 unt; 0 typ; 0 def)
% Number of atoms : 2541 (1093 equ; 0 cnn)
% Maximal formula atoms : 22 ( 9 avg)
% Number of connectives : 8506 (2417 ~;1003 |; 141 &;4897 @)
% ( 21 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 52 usr; 9 con; 0-4 aty)
% Number of variables : 624 ( 0 ^; 585 !; 39 ?; 624 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_boundary_set,type,
boundary_set: $i > $i > $o ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_closed_subset,type,
closed_subset: $i > $i > $o ).
thf(tp_directed_relstr,type,
directed_relstr: $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_carrier,type,
empty_carrier: $i > $o ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_net_str,type,
net_str: $i > $i > $o ).
thf(tp_net_str_of,type,
net_str_of: $i > $i > $i > $i > $i ).
thf(tp_netstr_induced_subset,type,
netstr_induced_subset: $i > $i > $i > $o ).
thf(tp_netstr_restr_to_element,type,
netstr_restr_to_element: $i > $i > $i > $i ).
thf(tp_nowhere_dense,type,
nowhere_dense: $i > $i > $o ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_open_subset,type,
open_subset: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_quasi_total,type,
quasi_total: $i > $i > $i > $o ).
thf(tp_rel_str,type,
rel_str: $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_as_subset,type,
relation_rng_as_subset: $i > $i > $i > $i ).
thf(tp_sK10_SY93,type,
sK10_SY93: $i > $i ).
thf(tp_sK11_SY97,type,
sK11_SY97: $i > $i ).
thf(tp_sK12_SY98,type,
sK12_SY98: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY21,type,
sK2_SY21: $i ).
thf(tp_sK3_SY32,type,
sK3_SY32: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK6_SY55,type,
sK6_SY55: $i ).
thf(tp_sK7_SY68,type,
sK7_SY68: $i ).
thf(tp_sK8_SY67,type,
sK8_SY67: $i > $i > $i ).
thf(tp_sK9_SY89,type,
sK9_SY89: $i > $i ).
thf(tp_strict_net_str,type,
strict_net_str: $i > $i > $o ).
thf(tp_subnet,type,
subnet: $i > $i > $i > $o ).
thf(tp_subnetstr_of_element,type,
subnetstr_of_element: $i > $i > $i > $i ).
thf(tp_the_InternalRel,type,
the_InternalRel: $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_the_mapping,type,
the_mapping: $i > $i > $i ).
thf(tp_top_str,type,
top_str: $i > $o ).
thf(tp_topological_space,type,
topological_space: $i > $o ).
thf(tp_topstr_closure,type,
topstr_closure: $i > $i > $i ).
thf(tp_transitive_relstr,type,
transitive_relstr: $i > $o ).
thf(tp_v1_membered,type,
v1_membered: $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] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(3,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(7,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(21,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(30,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(51,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(69,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ! [G: $i] :
( ( in @ G @ E )
<=> ( ( in @ G @ ( the_carrier @ B ) )
& ? [H: $i] :
( ( netstr_induced_subset @ H @ A @ B )
& ? [I: $i] :
( ( element @ I @ ( the_carrier @ B ) )
& ( D
= ( topstr_closure @ A @ H ) )
& ( G = I )
& ( H
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ I ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ I ) ) ) ) ) ) ) )
& ! [G: $i] :
( ( in @ G @ F )
<=> ( ( in @ G @ ( the_carrier @ B ) )
& ? [J: $i] :
( ( netstr_induced_subset @ J @ A @ B )
& ? [K: $i] :
( ( element @ K @ ( the_carrier @ B ) )
& ( D
= ( topstr_closure @ A @ J ) )
& ( G = K )
& ( J
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ K ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ K ) ) ) ) ) ) ) ) )
=> ( E = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_xboole_0__e6_39_3__yellow19__1) ).
thf(70,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ! [G: $i] :
( ( in @ G @ E )
<=> ( ( in @ G @ ( the_carrier @ B ) )
& ? [H: $i] :
( ( netstr_induced_subset @ H @ A @ B )
& ? [I: $i] :
( ( element @ I @ ( the_carrier @ B ) )
& ( D
= ( topstr_closure @ A @ H ) )
& ( G = I )
& ( H
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ I ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ I ) ) ) ) ) ) ) )
& ! [G: $i] :
( ( in @ G @ F )
<=> ( ( in @ G @ ( the_carrier @ B ) )
& ? [J: $i] :
( ( netstr_induced_subset @ J @ A @ B )
& ? [K: $i] :
( ( element @ K @ ( the_carrier @ B ) )
& ( D
= ( topstr_closure @ A @ J ) )
& ( G = K )
& ( J
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ K ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ K ) ) ) ) ) ) ) ) )
=> ( E = F ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[69]) ).
thf(71,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ! [G: $i] :
( ( in @ G @ E )
<=> ( ( in @ G @ ( the_carrier @ B ) )
& ? [H: $i] :
( ( netstr_induced_subset @ H @ A @ B )
& ? [I: $i] :
( ( element @ I @ ( the_carrier @ B ) )
& ( D
= ( topstr_closure @ A @ H ) )
& ( G = I )
& ( H
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ I ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ I ) ) ) ) ) ) ) )
& ! [G: $i] :
( ( in @ G @ F )
<=> ( ( in @ G @ ( the_carrier @ B ) )
& ? [J: $i] :
( ( netstr_induced_subset @ J @ A @ B )
& ? [K: $i] :
( ( element @ K @ ( the_carrier @ B ) )
& ( D
= ( topstr_closure @ A @ J ) )
& ( G = K )
& ( J
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ K ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ K ) ) ) ) ) ) ) ) )
=> ( E = F ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[70]) ).
thf(72,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(73,plain,
$true = $true,
inference(unfold_def,[status(thm)],[3]) ).
thf(74,plain,
$true = $true,
inference(unfold_def,[status(thm)],[5]) ).
thf(75,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(76,plain,
( ( ! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(77,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(78,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(79,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(80,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(81,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(82,plain,
$true = $true,
inference(unfold_def,[status(thm)],[30]) ).
thf(83,plain,
$true = $true,
inference(unfold_def,[status(thm)],[51]) ).
thf(84,plain,
( ( ! [SY21: $i,SY22: $i] :
( ( ~ ( empty_carrier @ sK1_A )
& ( topological_space @ sK1_A )
& ( top_str @ sK1_A )
& ~ ( empty_carrier @ SY21 )
& ( transitive_relstr @ SY21 )
& ( directed_relstr @ SY21 )
& ( net_str @ SY21 @ sK1_A ) )
=> ! [SY23: $i,SY24: $i,SY25: $i] :
( ( ! [SY26: $i] :
( ( in @ SY26 @ SY24 )
<=> ( ( in @ SY26 @ ( the_carrier @ SY21 ) )
& ? [SY27: $i] :
( ( netstr_induced_subset @ SY27 @ sK1_A @ SY21 )
& ? [SY28: $i] :
( ( element @ SY28 @ ( the_carrier @ SY21 ) )
& ( SY23
= ( topstr_closure @ sK1_A @ SY27 ) )
& ( SY26 = SY28 )
& ( SY27
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ SY21 @ SY28 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ SY21 @ SY28 ) ) ) ) ) ) ) )
& ! [SY29: $i] :
( ( in @ SY29 @ SY25 )
<=> ( ( in @ SY29 @ ( the_carrier @ SY21 ) )
& ? [SY30: $i] :
( ( netstr_induced_subset @ SY30 @ sK1_A @ SY21 )
& ? [SY31: $i] :
( ( element @ SY31 @ ( the_carrier @ SY21 ) )
& ( SY23
= ( topstr_closure @ sK1_A @ SY30 ) )
& ( SY29 = SY31 )
& ( SY30
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ SY21 @ SY31 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ SY21 @ SY31 ) ) ) ) ) ) ) ) )
=> ( SY24 = SY25 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[71]) ).
thf(85,plain,
( ( ! [SY32: $i] :
( ( ~ ( empty_carrier @ sK1_A )
& ( topological_space @ sK1_A )
& ( top_str @ sK1_A )
& ~ ( empty_carrier @ sK2_SY21 )
& ( transitive_relstr @ sK2_SY21 )
& ( directed_relstr @ sK2_SY21 )
& ( net_str @ sK2_SY21 @ sK1_A ) )
=> ! [SY33: $i,SY34: $i,SY35: $i] :
( ( ! [SY36: $i] :
( ( in @ SY36 @ SY34 )
<=> ( ( in @ SY36 @ ( the_carrier @ sK2_SY21 ) )
& ? [SY37: $i] :
( ( netstr_induced_subset @ SY37 @ sK1_A @ sK2_SY21 )
& ? [SY38: $i] :
( ( element @ SY38 @ ( the_carrier @ sK2_SY21 ) )
& ( SY33
= ( topstr_closure @ sK1_A @ SY37 ) )
& ( SY36 = SY38 )
& ( SY37
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY38 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY38 ) ) ) ) ) ) ) )
& ! [SY39: $i] :
( ( in @ SY39 @ SY35 )
<=> ( ( in @ SY39 @ ( the_carrier @ sK2_SY21 ) )
& ? [SY40: $i] :
( ( netstr_induced_subset @ SY40 @ sK1_A @ sK2_SY21 )
& ? [SY41: $i] :
( ( element @ SY41 @ ( the_carrier @ sK2_SY21 ) )
& ( SY33
= ( topstr_closure @ sK1_A @ SY40 ) )
& ( SY39 = SY41 )
& ( SY40
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY41 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY41 ) ) ) ) ) ) ) ) )
=> ( SY34 = SY35 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[84]) ).
thf(86,plain,
( ( ( ~ ( empty_carrier @ sK1_A )
& ( topological_space @ sK1_A )
& ( top_str @ sK1_A )
& ~ ( empty_carrier @ sK2_SY21 )
& ( transitive_relstr @ sK2_SY21 )
& ( directed_relstr @ sK2_SY21 )
& ( net_str @ sK2_SY21 @ sK1_A ) )
=> ! [SY33: $i,SY34: $i,SY35: $i] :
( ( ! [SY36: $i] :
( ( in @ SY36 @ SY34 )
<=> ( ( in @ SY36 @ ( the_carrier @ sK2_SY21 ) )
& ? [SY37: $i] :
( ( netstr_induced_subset @ SY37 @ sK1_A @ sK2_SY21 )
& ? [SY38: $i] :
( ( element @ SY38 @ ( the_carrier @ sK2_SY21 ) )
& ( SY33
= ( topstr_closure @ sK1_A @ SY37 ) )
& ( SY36 = SY38 )
& ( SY37
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY38 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY38 ) ) ) ) ) ) ) )
& ! [SY39: $i] :
( ( in @ SY39 @ SY35 )
<=> ( ( in @ SY39 @ ( the_carrier @ sK2_SY21 ) )
& ? [SY40: $i] :
( ( netstr_induced_subset @ SY40 @ sK1_A @ sK2_SY21 )
& ? [SY41: $i] :
( ( element @ SY41 @ ( the_carrier @ sK2_SY21 ) )
& ( SY33
= ( topstr_closure @ sK1_A @ SY40 ) )
& ( SY39 = SY41 )
& ( SY40
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY41 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY41 ) ) ) ) ) ) ) ) )
=> ( SY34 = SY35 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[85]) ).
thf(87,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[86]) ).
thf(88,plain,
( ( topological_space @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[86]) ).
thf(89,plain,
( ( top_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[86]) ).
thf(90,plain,
( ( ~ ( empty_carrier @ sK2_SY21 ) )
= $true ),
inference(standard_cnf,[status(thm)],[86]) ).
thf(91,plain,
( ( transitive_relstr @ sK2_SY21 )
= $true ),
inference(standard_cnf,[status(thm)],[86]) ).
thf(92,plain,
( ( directed_relstr @ sK2_SY21 )
= $true ),
inference(standard_cnf,[status(thm)],[86]) ).
thf(93,plain,
( ( net_str @ sK2_SY21 @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[86]) ).
thf(94,plain,
( ( ! [SY33: $i,SY34: $i,SY35: $i] :
( ( ! [SY36: $i] :
( ( in @ SY36 @ SY34 )
<=> ( ( in @ SY36 @ ( the_carrier @ sK2_SY21 ) )
& ? [SY37: $i] :
( ( netstr_induced_subset @ SY37 @ sK1_A @ sK2_SY21 )
& ? [SY38: $i] :
( ( element @ SY38 @ ( the_carrier @ sK2_SY21 ) )
& ( SY33
= ( topstr_closure @ sK1_A @ SY37 ) )
& ( SY36 = SY38 )
& ( SY37
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY38 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY38 ) ) ) ) ) ) ) )
& ! [SY39: $i] :
( ( in @ SY39 @ SY35 )
<=> ( ( in @ SY39 @ ( the_carrier @ sK2_SY21 ) )
& ? [SY40: $i] :
( ( netstr_induced_subset @ SY40 @ sK1_A @ sK2_SY21 )
& ? [SY41: $i] :
( ( element @ SY41 @ ( the_carrier @ sK2_SY21 ) )
& ( SY33
= ( topstr_closure @ sK1_A @ SY40 ) )
& ( SY39 = SY41 )
& ( SY40
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY41 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY41 ) ) ) ) ) ) ) ) )
=> ( SY34 = SY35 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[86]) ).
thf(95,plain,
( ( ~ ! [SY33: $i,SY34: $i,SY35: $i] :
( ( ! [SY36: $i] :
( ( in @ SY36 @ SY34 )
<=> ( ( in @ SY36 @ ( the_carrier @ sK2_SY21 ) )
& ? [SY37: $i] :
( ( netstr_induced_subset @ SY37 @ sK1_A @ sK2_SY21 )
& ? [SY38: $i] :
( ( element @ SY38 @ ( the_carrier @ sK2_SY21 ) )
& ( SY33
= ( topstr_closure @ sK1_A @ SY37 ) )
& ( SY36 = SY38 )
& ( SY37
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY38 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY38 ) ) ) ) ) ) ) )
& ! [SY39: $i] :
( ( in @ SY39 @ SY35 )
<=> ( ( in @ SY39 @ ( the_carrier @ sK2_SY21 ) )
& ? [SY40: $i] :
( ( netstr_induced_subset @ SY40 @ sK1_A @ sK2_SY21 )
& ? [SY41: $i] :
( ( element @ SY41 @ ( the_carrier @ sK2_SY21 ) )
& ( SY33
= ( topstr_closure @ sK1_A @ SY40 ) )
& ( SY39 = SY41 )
& ( SY40
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY41 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY41 ) ) ) ) ) ) ) ) )
=> ( SY34 = SY35 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[94]) ).
thf(96,plain,
$true = $true,
inference(copy,[status(thm)],[83]) ).
thf(97,plain,
$true = $true,
inference(copy,[status(thm)],[82]) ).
thf(98,plain,
$true = $true,
inference(copy,[status(thm)],[81]) ).
thf(99,plain,
$true = $true,
inference(copy,[status(thm)],[80]) ).
thf(100,plain,
$true = $true,
inference(copy,[status(thm)],[79]) ).
thf(101,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(102,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(103,plain,
( ( ! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(104,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(105,plain,
$true = $true,
inference(copy,[status(thm)],[74]) ).
thf(106,plain,
$true = $true,
inference(copy,[status(thm)],[73]) ).
thf(107,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(108,plain,
( ( net_str @ sK2_SY21 @ sK1_A )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(109,plain,
( ( directed_relstr @ sK2_SY21 )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(110,plain,
( ( transitive_relstr @ sK2_SY21 )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(111,plain,
( ( ~ ( empty_carrier @ sK2_SY21 ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(112,plain,
( ( top_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(113,plain,
( ( topological_space @ sK1_A )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(114,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(115,plain,
( ( ~ ! [SY33: $i,SY34: $i,SY35: $i] :
( ( ! [SY36: $i] :
( ( in @ SY36 @ SY34 )
<=> ( ( in @ SY36 @ ( the_carrier @ sK2_SY21 ) )
& ? [SY37: $i] :
( ( netstr_induced_subset @ SY37 @ sK1_A @ sK2_SY21 )
& ? [SY38: $i] :
( ( element @ SY38 @ ( the_carrier @ sK2_SY21 ) )
& ( SY33
= ( topstr_closure @ sK1_A @ SY37 ) )
& ( SY36 = SY38 )
& ( SY37
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY38 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY38 ) ) ) ) ) ) ) )
& ! [SY39: $i] :
( ( in @ SY39 @ SY35 )
<=> ( ( in @ SY39 @ ( the_carrier @ sK2_SY21 ) )
& ? [SY40: $i] :
( ( netstr_induced_subset @ SY40 @ sK1_A @ sK2_SY21 )
& ? [SY41: $i] :
( ( element @ SY41 @ ( the_carrier @ sK2_SY21 ) )
& ( SY33
= ( topstr_closure @ sK1_A @ SY40 ) )
& ( SY39 = SY41 )
& ( SY40
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY41 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY41 ) ) ) ) ) ) ) ) )
=> ( SY34 = SY35 ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(116,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ( ~ ( in @ SX3 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SX4 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX5 @ ( the_carrier @ sK2_SY21 ) )
| ( SX0
!= ( topstr_closure @ sK1_A @ SX4 ) ) )
| ( SX3 != SX5 ) )
| ( SX4
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SX5 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SX5 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SX4 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX5 @ ( the_carrier @ sK2_SY21 ) )
| ( SX0
!= ( topstr_closure @ sK1_A @ SX4 ) ) )
| ( SX3 != SX5 ) )
| ( SX4
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SX5 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SX5 ) ) ) ) ) ) )
| ( in @ SX3 @ SX1 ) ) )
| ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SX4 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX5 @ ( the_carrier @ sK2_SY21 ) )
| ( SX0
!= ( topstr_closure @ sK1_A @ SX4 ) ) )
| ( SX3 != SX5 ) )
| ( SX4
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SX5 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SX5 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SX4 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX5 @ ( the_carrier @ sK2_SY21 ) )
| ( SX0
!= ( topstr_closure @ sK1_A @ SX4 ) ) )
| ( SX3 != SX5 ) )
| ( SX4
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SX5 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SX5 ) ) ) ) ) ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(117,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(118,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(119,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(120,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( top_str @ SX0 )
| ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) ) )
| ( element @ ( topstr_closure @ SX0 @ SX1 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(121,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(122,plain,
( ( empty_carrier @ sK2_SY21 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(123,plain,
( ( empty_carrier @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(124,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ( ~ ( in @ SX3 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SX4 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX5 @ ( the_carrier @ sK2_SY21 ) )
| ( SX0
!= ( topstr_closure @ sK1_A @ SX4 ) ) )
| ( SX3 != SX5 ) )
| ( SX4
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SX5 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SX5 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SX4 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX5 @ ( the_carrier @ sK2_SY21 ) )
| ( SX0
!= ( topstr_closure @ sK1_A @ SX4 ) ) )
| ( SX3 != SX5 ) )
| ( SX4
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SX5 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SX5 ) ) ) ) ) ) )
| ( in @ SX3 @ SX1 ) ) )
| ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SX4 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX5 @ ( the_carrier @ sK2_SY21 ) )
| ( SX0
!= ( topstr_closure @ sK1_A @ SX4 ) ) )
| ( SX3 != SX5 ) )
| ( SX4
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SX5 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SX5 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SX4 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX5 @ ( the_carrier @ sK2_SY21 ) )
| ( SX0
!= ( topstr_closure @ sK1_A @ SX4 ) ) )
| ( SX3 != SX5 ) )
| ( SX4
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SX5 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SX5 ) ) ) ) ) ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ( SX1 = SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(125,plain,
! [SV1: $i] :
( ( ! [SY51: $i] :
( ~ ! [SY52: $i] :
~ ( ~ ( ~ ( in @ SY52 @ SV1 )
| ( in @ SY52 @ SY51 ) )
| ~ ( ~ ( in @ SY52 @ SY51 )
| ( in @ SY52 @ SV1 ) ) )
| ( SV1 = SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(126,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(127,plain,
! [SV2: $i] :
( ( ! [SY53: $i] :
( ~ ( in @ SV2 @ SY53 )
| ~ ( in @ SY53 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(128,plain,
! [SV3: $i] :
( ( ! [SY54: $i] :
( ~ ~ ( ~ ( top_str @ SV3 )
| ~ ( element @ SY54 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
| ( element @ ( topstr_closure @ SV3 @ SY54 ) @ ( powerset @ ( the_carrier @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(129,plain,
! [SV4: $i] :
( ( ~ ( top_str @ SV4 )
| ( one_sorted_str @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(130,plain,
( ( ! [SY55: $i,SY56: $i] :
( ~ ~ ( ~ ! [SY57: $i] :
~ ( ~ ( ~ ( in @ SY57 @ SY55 )
| ~ ( ~ ( in @ SY57 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY58: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY58 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY58 ) ) )
| ( SY57 != SY59 ) )
| ( SY58
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY59 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY59 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY57 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY60 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY61 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY60 ) ) )
| ( SY57 != SY61 ) )
| ( SY60
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY61 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY61 ) ) ) ) ) ) )
| ( in @ SY57 @ SY55 ) ) )
| ~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY56 )
| ~ ( ~ ( in @ SY62 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY63 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY63 ) ) )
| ( SY62 != SY64 ) )
| ( SY63
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY64 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY64 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY62 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY65: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY65 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY66 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY65 ) ) )
| ( SY62 != SY66 ) )
| ( SY65
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY66 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY66 ) ) ) ) ) ) )
| ( in @ SY62 @ SY56 ) ) ) )
| ( SY55 = SY56 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[124]) ).
thf(131,plain,
! [SV5: $i,SV1: $i] :
( ( ~ ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV1 )
| ( in @ SY67 @ SV5 ) )
| ~ ( ~ ( in @ SY67 @ SV5 )
| ( in @ SY67 @ SV1 ) ) )
| ( SV1 = SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(132,plain,
( ( ~ ~ ( ~ ( one_sorted_str @ sK5_SX0 )
| ~ ~ ( empty_carrier @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[126]) ).
thf(133,plain,
! [SV6: $i,SV2: $i] :
( ( ~ ( in @ SV2 @ SV6 )
| ~ ( in @ SV6 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(134,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ~ ( ~ ( top_str @ SV3 )
| ~ ( element @ SV7 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
| ( element @ ( topstr_closure @ SV3 @ SV7 ) @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(135,plain,
! [SV4: $i] :
( ( ( ~ ( top_str @ SV4 ) )
= $true )
| ( ( one_sorted_str @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(136,plain,
( ( ! [SY68: $i] :
( ~ ~ ( ~ ! [SY69: $i] :
~ ( ~ ( ~ ( in @ SY69 @ sK6_SY55 )
| ~ ( ~ ( in @ SY69 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY58: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY58 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY58 ) ) )
| ( SY69 != SY59 ) )
| ( SY58
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY59 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY59 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY69 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY60 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY61 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY60 ) ) )
| ( SY69 != SY61 ) )
| ( SY60
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY61 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY61 ) ) ) ) ) ) )
| ( in @ SY69 @ sK6_SY55 ) ) )
| ~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY68 )
| ~ ( ~ ( in @ SY62 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY63 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY63 ) ) )
| ( SY62 != SY64 ) )
| ( SY63
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY64 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY64 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY62 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY65: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY65 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY66 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY65 ) ) )
| ( SY62 != SY66 ) )
| ( SY65
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY66 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY66 ) ) ) ) ) ) )
| ( in @ SY62 @ SY68 ) ) ) )
| ( sK6_SY55 = SY68 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[130]) ).
thf(137,plain,
! [SV5: $i,SV1: $i] :
( ( ( ~ ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV1 )
| ( in @ SY67 @ SV5 ) )
| ~ ( ~ ( in @ SY67 @ SV5 )
| ( in @ SY67 @ SV1 ) ) ) )
= $true )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(138,plain,
( ( ~ ( ~ ( one_sorted_str @ sK5_SX0 )
| ~ ~ ( empty_carrier @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(139,plain,
! [SV6: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV6 ) )
= $true )
| ( ( ~ ( in @ SV6 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(140,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( top_str @ SV3 )
| ~ ( element @ SV7 @ ( powerset @ ( the_carrier @ SV3 ) ) ) ) )
= $true )
| ( ( element @ ( topstr_closure @ SV3 @ SV7 ) @ ( powerset @ ( the_carrier @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(141,plain,
! [SV4: $i] :
( ( ( top_str @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(142,plain,
( ( ~ ~ ( ~ ! [SY69: $i] :
~ ( ~ ( ~ ( in @ SY69 @ sK6_SY55 )
| ~ ( ~ ( in @ SY69 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY58: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY58 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY58 ) ) )
| ( SY69 != SY59 ) )
| ( SY58
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY59 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY59 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY69 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY60 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY61 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY60 ) ) )
| ( SY69 != SY61 ) )
| ( SY60
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY61 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY61 ) ) ) ) ) ) )
| ( in @ SY69 @ sK6_SY55 ) ) )
| ~ ! [SY84: $i] :
~ ( ~ ( ~ ( in @ SY84 @ sK7_SY68 )
| ~ ( ~ ( in @ SY84 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY63 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY63 ) ) )
| ( SY84 != SY64 ) )
| ( SY63
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY64 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY64 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY84 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY65: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY65 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY66 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY65 ) ) )
| ( SY84 != SY66 ) )
| ( SY65
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY66 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY66 ) ) ) ) ) ) )
| ( in @ SY84 @ sK7_SY68 ) ) ) )
| ( sK6_SY55 = sK7_SY68 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[136]) ).
thf(143,plain,
! [SV5: $i,SV1: $i] :
( ( ( ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV1 )
| ( in @ SY67 @ SV5 ) )
| ~ ( ~ ( in @ SY67 @ SV5 )
| ( in @ SY67 @ SV1 ) ) ) )
= $false )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(144,plain,
( ( ~ ( one_sorted_str @ sK5_SX0 )
| ~ ~ ( empty_carrier @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(145,plain,
! [SV6: $i,SV2: $i] :
( ( ( in @ SV2 @ SV6 )
= $false )
| ( ( ~ ( in @ SV6 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(146,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( ~ ( top_str @ SV3 )
| ~ ( element @ SV7 @ ( powerset @ ( the_carrier @ SV3 ) ) ) ) )
= $false )
| ( ( element @ ( topstr_closure @ SV3 @ SV7 ) @ ( powerset @ ( the_carrier @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(147,plain,
( ( ~ ~ ( ~ ! [SY69: $i] :
~ ( ~ ( ~ ( in @ SY69 @ sK6_SY55 )
| ~ ( ~ ( in @ SY69 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY58: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY58 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY58 ) ) )
| ( SY69 != SY59 ) )
| ( SY58
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY59 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY59 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY69 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY60 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY61 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY60 ) ) )
| ( SY69 != SY61 ) )
| ( SY60
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY61 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY61 ) ) ) ) ) ) )
| ( in @ SY69 @ sK6_SY55 ) ) )
| ~ ! [SY84: $i] :
~ ( ~ ( ~ ( in @ SY84 @ sK7_SY68 )
| ~ ( ~ ( in @ SY84 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY63 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY63 ) ) )
| ( SY84 != SY64 ) )
| ( SY63
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY64 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY64 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY84 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY65: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY65 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY66 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY65 ) ) )
| ( SY84 != SY66 ) )
| ( SY65
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY66 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY66 ) ) ) ) ) ) )
| ( in @ SY84 @ sK7_SY68 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(148,plain,
( ( sK6_SY55 = sK7_SY68 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(149,plain,
! [SV1: $i,SV5: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 )
| ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 ) )
| ~ ( ~ ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 )
| ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 ) ) ) )
= $false )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[143]) ).
thf(150,plain,
( ( ~ ( one_sorted_str @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(151,plain,
( ( ~ ~ ( empty_carrier @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(152,plain,
! [SV2: $i,SV6: $i] :
( ( ( in @ SV6 @ SV2 )
= $false )
| ( ( in @ SV2 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(153,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( top_str @ SV3 )
| ~ ( element @ SV7 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
= $true )
| ( ( element @ ( topstr_closure @ SV3 @ SV7 ) @ ( powerset @ ( the_carrier @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(154,plain,
( ( ~ ( ~ ! [SY69: $i] :
~ ( ~ ( ~ ( in @ SY69 @ sK6_SY55 )
| ~ ( ~ ( in @ SY69 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY58: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY58 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY58 ) ) )
| ( SY69 != SY59 ) )
| ( SY58
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY59 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY59 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY69 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY60 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY61 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY60 ) ) )
| ( SY69 != SY61 ) )
| ( SY60
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY61 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY61 ) ) ) ) ) ) )
| ( in @ SY69 @ sK6_SY55 ) ) )
| ~ ! [SY84: $i] :
~ ( ~ ( ~ ( in @ SY84 @ sK7_SY68 )
| ~ ( ~ ( in @ SY84 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY63 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY63 ) ) )
| ( SY84 != SY64 ) )
| ( SY63
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY64 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY64 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY84 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY65: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY65 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY66 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY65 ) ) )
| ( SY84 != SY66 ) )
| ( SY65
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY66 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY66 ) ) ) ) ) ) )
| ( in @ SY84 @ sK7_SY68 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(155,plain,
! [SV1: $i,SV5: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 )
| ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 ) )
| ~ ( ~ ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 )
| ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 ) ) )
= $true )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(156,plain,
( ( one_sorted_str @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(157,plain,
( ( ~ ( empty_carrier @ sK5_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(158,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( top_str @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV7 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
= $true )
| ( ( element @ ( topstr_closure @ SV3 @ SV7 ) @ ( powerset @ ( the_carrier @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(159,plain,
( ( ~ ! [SY69: $i] :
~ ( ~ ( ~ ( in @ SY69 @ sK6_SY55 )
| ~ ( ~ ( in @ SY69 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY58: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY58 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY58 ) ) )
| ( SY69 != SY59 ) )
| ( SY58
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY59 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY59 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY69 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY60 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY61 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY60 ) ) )
| ( SY69 != SY61 ) )
| ( SY60
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY61 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY61 ) ) ) ) ) ) )
| ( in @ SY69 @ sK6_SY55 ) ) )
| ~ ! [SY84: $i] :
~ ( ~ ( ~ ( in @ SY84 @ sK7_SY68 )
| ~ ( ~ ( in @ SY84 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY63 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY63 ) ) )
| ( SY84 != SY64 ) )
| ( SY63
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY64 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY64 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY84 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY65: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY65 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY66 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY65 ) ) )
| ( SY84 != SY66 ) )
| ( SY65
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY66 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY66 ) ) ) ) ) ) )
| ( in @ SY84 @ sK7_SY68 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(160,plain,
! [SV1: $i,SV5: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 )
| ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 )
| ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 ) ) )
= $true )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(161,plain,
( ( empty_carrier @ sK5_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(162,plain,
! [SV7: $i,SV3: $i] :
( ( ( top_str @ SV3 )
= $false )
| ( ( ~ ( element @ SV7 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
= $true )
| ( ( element @ ( topstr_closure @ SV3 @ SV7 ) @ ( powerset @ ( the_carrier @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(163,plain,
( ( ~ ! [SY69: $i] :
~ ( ~ ( ~ ( in @ SY69 @ sK6_SY55 )
| ~ ( ~ ( in @ SY69 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY58: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY58 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY58 ) ) )
| ( SY69 != SY59 ) )
| ( SY58
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY59 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY59 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY69 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY60 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY61 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY60 ) ) )
| ( SY69 != SY61 ) )
| ( SY60
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY61 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY61 ) ) ) ) ) ) )
| ( in @ SY69 @ sK6_SY55 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(164,plain,
( ( ~ ! [SY84: $i] :
~ ( ~ ( ~ ( in @ SY84 @ sK7_SY68 )
| ~ ( ~ ( in @ SY84 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY63 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY63 ) ) )
| ( SY84 != SY64 ) )
| ( SY63
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY64 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY64 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY84 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY65: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY65 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY66 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY65 ) ) )
| ( SY84 != SY66 ) )
| ( SY65
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY66 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY66 ) ) ) ) ) ) )
| ( in @ SY84 @ sK7_SY68 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(165,plain,
! [SV1: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 )
| ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 )
| ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 ) ) )
= $true )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(166,plain,
! [SV3: $i,SV7: $i] :
( ( ( element @ SV7 @ ( powerset @ ( the_carrier @ SV3 ) ) )
= $false )
| ( ( top_str @ SV3 )
= $false )
| ( ( element @ ( topstr_closure @ SV3 @ SV7 ) @ ( powerset @ ( the_carrier @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(167,plain,
( ( ! [SY69: $i] :
~ ( ~ ( ~ ( in @ SY69 @ sK6_SY55 )
| ~ ( ~ ( in @ SY69 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY58: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY58 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY58 ) ) )
| ( SY69 != SY59 ) )
| ( SY58
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY59 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY59 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY69 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY60 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY61 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY60 ) ) )
| ( SY69 != SY61 ) )
| ( SY60
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY61 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY61 ) ) ) ) ) ) )
| ( in @ SY69 @ sK6_SY55 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(168,plain,
( ( ! [SY84: $i] :
~ ( ~ ( ~ ( in @ SY84 @ sK7_SY68 )
| ~ ( ~ ( in @ SY84 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY63 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY63 ) ) )
| ( SY84 != SY64 ) )
| ( SY63
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY64 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY64 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY84 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY65: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY65 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY66 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY65 ) ) )
| ( SY84 != SY66 ) )
| ( SY65
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY66 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY66 ) ) ) ) ) ) )
| ( in @ SY84 @ sK7_SY68 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(169,plain,
! [SV1: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 )
| ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 ) ) )
= $true )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(170,plain,
! [SV1: $i,SV5: $i] :
( ( ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 )
| ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 ) ) )
= $true )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(171,plain,
! [SV8: $i] :
( ( ~ ( ~ ( ~ ( in @ SV8 @ sK6_SY55 )
| ~ ( ~ ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY89 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY90 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY89 ) ) )
| ( SV8 != SY90 ) )
| ( SY89
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY91: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY91 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY92 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY91 ) ) )
| ( SV8 != SY92 ) )
| ( SY91
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) ) ) ) ) )
| ( in @ SV8 @ sK6_SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(172,plain,
! [SV9: $i] :
( ( ~ ( ~ ( ~ ( in @ SV9 @ sK7_SY68 )
| ~ ( ~ ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY93: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY93 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY94 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY93 ) ) )
| ( SV9 != SY94 ) )
| ( SY93
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY95 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY96: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY96 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY95 ) ) )
| ( SV9 != SY96 ) )
| ( SY95
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) ) ) ) ) )
| ( in @ SV9 @ sK7_SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(173,plain,
! [SV1: $i,SV5: $i] :
( ( ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 )
| ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 ) ) )
= $true )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(174,plain,
! [SV1: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 )
| ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 ) )
= $false )
| ( ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 )
= $false )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(175,plain,
! [SV8: $i] :
( ( ~ ( ~ ( in @ SV8 @ sK6_SY55 )
| ~ ( ~ ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY89 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY90 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY89 ) ) )
| ( SV8 != SY90 ) )
| ( SY89
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY91: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY91 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY92 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY91 ) ) )
| ( SV8 != SY92 ) )
| ( SY91
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) ) ) ) ) )
| ( in @ SV8 @ sK6_SY55 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(176,plain,
! [SV9: $i] :
( ( ~ ( ~ ( in @ SV9 @ sK7_SY68 )
| ~ ( ~ ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY93: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY93 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY94 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY93 ) ) )
| ( SV9 != SY94 ) )
| ( SY93
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY95 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY96: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY96 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY95 ) ) )
| ( SV9 != SY96 ) )
| ( SY95
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) ) ) ) ) )
| ( in @ SV9 @ sK7_SY68 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(177,plain,
! [SV1: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 )
| ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 ) )
= $false )
| ( ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 )
= $true )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(178,plain,
! [SV1: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 ) )
= $false )
| ( ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 )
= $false )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(179,plain,
! [SV1: $i,SV5: $i] :
( ( ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 )
= $false )
| ( ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 )
= $false )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(180,plain,
! [SV8: $i] :
( ( ~ ( ~ ( in @ SV8 @ sK6_SY55 )
| ~ ( ~ ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY89 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY90 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY89 ) ) )
| ( SV8 != SY90 ) )
| ( SY89
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(181,plain,
! [SV8: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY91: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY91 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY92 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY91 ) ) )
| ( SV8 != SY92 ) )
| ( SY91
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) ) ) ) ) )
| ( in @ SV8 @ sK6_SY55 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(182,plain,
! [SV9: $i] :
( ( ~ ( ~ ( in @ SV9 @ sK7_SY68 )
| ~ ( ~ ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY93: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY93 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY94 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY93 ) ) )
| ( SV9 != SY94 ) )
| ( SY93
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(183,plain,
! [SV9: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY95 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY96: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY96 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY95 ) ) )
| ( SV9 != SY96 ) )
| ( SY95
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) ) ) ) ) )
| ( in @ SV9 @ sK7_SY68 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(184,plain,
! [SV1: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 ) )
= $false )
| ( ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 )
= $true )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(185,plain,
! [SV1: $i,SV5: $i] :
( ( ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 )
= $false )
| ( ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 )
= $true )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(186,plain,
! [SV1: $i,SV5: $i] :
( ( ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 )
= $true )
| ( ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 )
= $false )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(187,plain,
! [SV8: $i] :
( ( ~ ( in @ SV8 @ sK6_SY55 )
| ~ ( ~ ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY89 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY90 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY89 ) ) )
| ( SV8 != SY90 ) )
| ( SY89
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(188,plain,
! [SV8: $i] :
( ( ~ ~ ( ~ ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY91: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY91 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY92 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY91 ) ) )
| ( SV8 != SY92 ) )
| ( SY91
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) ) ) ) ) )
| ( in @ SV8 @ sK6_SY55 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(189,plain,
! [SV9: $i] :
( ( ~ ( in @ SV9 @ sK7_SY68 )
| ~ ( ~ ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY93: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY93 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY94 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY93 ) ) )
| ( SV9 != SY94 ) )
| ( SY93
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(190,plain,
! [SV9: $i] :
( ( ~ ~ ( ~ ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY95 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY96: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY96 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY95 ) ) )
| ( SV9 != SY96 ) )
| ( SY95
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) ) ) ) ) )
| ( in @ SV9 @ sK7_SY68 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(191,plain,
! [SV1: $i,SV5: $i] :
( ( ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV5 )
= $true )
| ( ( in @ ( sK8_SY67 @ SV5 @ SV1 ) @ SV1 )
= $true )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(192,plain,
! [SV8: $i] :
( ( ( ~ ( in @ SV8 @ sK6_SY55 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY89 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY90 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY89 ) ) )
| ( SV8 != SY90 ) )
| ( SY89
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(193,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY91: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY91 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY92 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY91 ) ) )
| ( SV8 != SY92 ) )
| ( SY91
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) ) ) ) ) ) )
= $true )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(194,plain,
! [SV9: $i] :
( ( ( ~ ( in @ SV9 @ sK7_SY68 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY93: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY93 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY94 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY93 ) ) )
| ( SV9 != SY94 ) )
| ( SY93
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(195,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY95 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY96: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY96 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY95 ) ) )
| ( SV9 != SY96 ) )
| ( SY95
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) ) ) ) ) ) )
= $true )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(196,plain,
! [SV8: $i] :
( ( ( in @ SV8 @ sK6_SY55 )
= $false )
| ( ( ~ ( ~ ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY89 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY90 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY89 ) ) )
| ( SV8 != SY90 ) )
| ( SY89
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(197,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY91: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY91 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY92 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY91 ) ) )
| ( SV8 != SY92 ) )
| ( SY91
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) ) ) ) ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(198,plain,
! [SV9: $i] :
( ( ( in @ SV9 @ sK7_SY68 )
= $false )
| ( ( ~ ( ~ ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY93: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY93 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY94 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY93 ) ) )
| ( SV9 != SY94 ) )
| ( SY93
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(199,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY95 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY96: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY96 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY95 ) ) )
| ( SV9 != SY96 ) )
| ( SY95
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) ) ) ) ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(200,plain,
! [SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY89 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY90 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY89 ) ) )
| ( SV8 != SY90 ) )
| ( SY89
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) ) ) ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(201,plain,
! [SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY91: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY91 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY92 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY91 ) ) )
| ( SV8 != SY92 ) )
| ( SY91
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(202,plain,
! [SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY93: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY93 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY94 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY93 ) ) )
| ( SV9 != SY94 ) )
| ( SY93
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) ) ) ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(203,plain,
! [SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY95 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY96: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY96 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY95 ) ) )
| ( SV9 != SY96 ) )
| ( SY95
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(204,plain,
! [SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(205,plain,
! [SV8: $i] :
( ( ( ~ ~ ! [SY89: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY89 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY90 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY89 ) ) )
| ( SV8 != SY90 ) )
| ( SY89
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) ) ) ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(206,plain,
! [SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) ) )
= $true )
| ( ( ~ ~ ! [SY91: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY91 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY92 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY91 ) ) )
| ( SV8 != SY92 ) )
| ( SY91
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(207,plain,
! [SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(208,plain,
! [SV9: $i] :
( ( ( ~ ~ ! [SY93: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY93 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY94 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY93 ) ) )
| ( SV9 != SY94 ) )
| ( SY93
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) ) ) ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(209,plain,
! [SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) ) )
= $true )
| ( ( ~ ~ ! [SY95: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY95 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY96: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY96 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY95 ) ) )
| ( SV9 != SY96 ) )
| ( SY95
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(210,plain,
! [SV8: $i] :
( ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $true )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(211,plain,
! [SV8: $i] :
( ( ( ~ ! [SY89: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY89 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY90 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY89 ) ) )
| ( SV8 != SY90 ) )
| ( SY89
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(212,plain,
! [SV8: $i] :
( ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( ~ ~ ! [SY91: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY91 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY92 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY91 ) ) )
| ( SV8 != SY92 ) )
| ( SY91
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(213,plain,
! [SV9: $i] :
( ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $true )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(214,plain,
! [SV9: $i] :
( ( ( ~ ! [SY93: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY93 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY94 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY93 ) ) )
| ( SV9 != SY94 ) )
| ( SY93
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(215,plain,
! [SV9: $i] :
( ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( ~ ~ ! [SY95: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY95 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY96: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY96 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY95 ) ) )
| ( SV9 != SY96 ) )
| ( SY95
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(216,plain,
! [SV8: $i] :
( ( ( ! [SY89: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY89 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY90 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY89 ) ) )
| ( SV8 != SY90 ) )
| ( SY89
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY90 ) ) ) ) ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(217,plain,
! [SV8: $i] :
( ( ( ~ ! [SY91: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY91 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY92 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY91 ) ) )
| ( SV8 != SY92 ) )
| ( SY91
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) ) ) ) ) )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(218,plain,
! [SV9: $i] :
( ( ( ! [SY93: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY93 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY94 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY93 ) ) )
| ( SV9 != SY94 ) )
| ( SY93
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY94 ) ) ) ) ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(219,plain,
! [SV9: $i] :
( ( ( ~ ! [SY95: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY95 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY96: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY96 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY95 ) ) )
| ( SV9 != SY96 ) )
| ( SY95
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) ) ) ) ) )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(220,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( netstr_induced_subset @ ( sK9_SY89 @ SV8 ) @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY97 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK9_SY89 @ SV8 ) ) ) )
| ( SV8 != SY97 ) )
| ( ( sK9_SY89 @ SV8 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY97 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY97 ) ) ) ) ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[216]) ).
thf(221,plain,
! [SV8: $i] :
( ( ( ! [SY91: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY91 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY92 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY91 ) ) )
| ( SV8 != SY92 ) )
| ( SY91
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY92 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(222,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ( netstr_induced_subset @ ( sK10_SY93 @ SV9 ) @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY98: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY98 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK10_SY93 @ SV9 ) ) ) )
| ( SV9 != SY98 ) )
| ( ( sK10_SY93 @ SV9 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY98 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY98 ) ) ) ) ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[218]) ).
thf(223,plain,
! [SV9: $i] :
( ( ( ! [SY95: $i] :
~ ~ ( ~ ( netstr_induced_subset @ SY95 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY96: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY96 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SY95 ) ) )
| ( SV9 != SY96 ) )
| ( SY95
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY96 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(224,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( netstr_induced_subset @ ( sK9_SY89 @ SV8 ) @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY97 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK9_SY89 @ SV8 ) ) ) )
| ( SV8 != SY97 ) )
| ( ( sK9_SY89 @ SV8 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY97 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY97 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(225,plain,
! [SV8: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY99 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) ) )
| ( SV8 != SY99 ) )
| ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY99 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY99 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(226,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ( netstr_induced_subset @ ( sK10_SY93 @ SV9 ) @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY98: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY98 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK10_SY93 @ SV9 ) ) ) )
| ( SV9 != SY98 ) )
| ( ( sK10_SY93 @ SV9 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY98 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY98 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(227,plain,
! [SV9: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY100: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY100 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) ) )
| ( SV9 != SY100 ) )
| ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY100 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY100 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(228,plain,
! [SV8: $i] :
( ( ( ~ ( netstr_induced_subset @ ( sK9_SY89 @ SV8 ) @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY97 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK9_SY89 @ SV8 ) ) ) )
| ( SV8 != SY97 ) )
| ( ( sK9_SY89 @ SV8 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY97 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY97 ) ) ) ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(229,plain,
! [SV8: $i,SV10: $i] :
( ( ( ~ ( ~ ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY99 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) ) )
| ( SV8 != SY99 ) )
| ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY99 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY99 ) ) ) ) ) ) )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(230,plain,
! [SV9: $i] :
( ( ( ~ ( netstr_induced_subset @ ( sK10_SY93 @ SV9 ) @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY98: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY98 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK10_SY93 @ SV9 ) ) ) )
| ( SV9 != SY98 ) )
| ( ( sK10_SY93 @ SV9 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY98 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY98 ) ) ) ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(231,plain,
! [SV9: $i,SV11: $i] :
( ( ( ~ ( ~ ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY100: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY100 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) ) )
| ( SV9 != SY100 ) )
| ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY100 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY100 ) ) ) ) ) ) )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(232,plain,
! [SV8: $i] :
( ( ( ~ ( netstr_induced_subset @ ( sK9_SY89 @ SV8 ) @ sK1_A @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(233,plain,
! [SV8: $i] :
( ( ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY97 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK9_SY89 @ SV8 ) ) ) )
| ( SV8 != SY97 ) )
| ( ( sK9_SY89 @ SV8 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY97 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY97 ) ) ) ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(234,plain,
! [SV8: $i,SV10: $i] :
( ( ( ~ ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY99 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) ) )
| ( SV8 != SY99 ) )
| ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY99 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY99 ) ) ) ) ) )
= $true )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(235,plain,
! [SV9: $i] :
( ( ( ~ ( netstr_induced_subset @ ( sK10_SY93 @ SV9 ) @ sK1_A @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(236,plain,
! [SV9: $i] :
( ( ( ~ ~ ! [SY98: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY98 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK10_SY93 @ SV9 ) ) ) )
| ( SV9 != SY98 ) )
| ( ( sK10_SY93 @ SV9 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY98 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY98 ) ) ) ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(237,plain,
! [SV9: $i,SV11: $i] :
( ( ( ~ ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
| ~ ~ ! [SY100: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY100 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) ) )
| ( SV9 != SY100 ) )
| ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY100 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY100 ) ) ) ) ) )
= $true )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(238,plain,
! [SV8: $i] :
( ( ( netstr_induced_subset @ ( sK9_SY89 @ SV8 ) @ sK1_A @ sK2_SY21 )
= $true )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(239,plain,
! [SV8: $i] :
( ( ( ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY97 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK9_SY89 @ SV8 ) ) ) )
| ( SV8 != SY97 ) )
| ( ( sK9_SY89 @ SV8 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY97 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY97 ) ) ) ) ) )
= $true )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(240,plain,
! [SV8: $i,SV10: $i] :
( ( ( ~ ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 ) )
= $true )
| ( ( ~ ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY99 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) ) )
| ( SV8 != SY99 ) )
| ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY99 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY99 ) ) ) ) ) )
= $true )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(241,plain,
! [SV9: $i] :
( ( ( netstr_induced_subset @ ( sK10_SY93 @ SV9 ) @ sK1_A @ sK2_SY21 )
= $true )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(242,plain,
! [SV9: $i] :
( ( ( ~ ! [SY98: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY98 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK10_SY93 @ SV9 ) ) ) )
| ( SV9 != SY98 ) )
| ( ( sK10_SY93 @ SV9 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY98 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY98 ) ) ) ) ) )
= $true )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(243,plain,
! [SV9: $i,SV11: $i] :
( ( ( ~ ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 ) )
= $true )
| ( ( ~ ~ ! [SY100: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY100 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) ) )
| ( SV9 != SY100 ) )
| ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY100 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY100 ) ) ) ) ) )
= $true )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(244,plain,
! [SV8: $i] :
( ( ( ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY97 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK9_SY89 @ SV8 ) ) ) )
| ( SV8 != SY97 ) )
| ( ( sK9_SY89 @ SV8 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY97 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY97 ) ) ) ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(245,plain,
! [SV8: $i,SV10: $i] :
( ( ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( ~ ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY99 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) ) )
| ( SV8 != SY99 ) )
| ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY99 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY99 ) ) ) ) ) )
= $true )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(246,plain,
! [SV9: $i] :
( ( ( ! [SY98: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY98 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK10_SY93 @ SV9 ) ) ) )
| ( SV9 != SY98 ) )
| ( ( sK10_SY93 @ SV9 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY98 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY98 ) ) ) ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(247,plain,
! [SV9: $i,SV11: $i] :
( ( ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( ~ ~ ! [SY100: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY100 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) ) )
| ( SV9 != SY100 ) )
| ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY100 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY100 ) ) ) ) ) )
= $true )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(248,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK11_SY97 @ SV8 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK9_SY89 @ SV8 ) ) ) )
| ( SV8
!= ( sK11_SY97 @ SV8 ) ) )
| ( ( sK9_SY89 @ SV8 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK11_SY97 @ SV8 ) ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK11_SY97 @ SV8 ) ) ) ) ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[244]) ).
thf(249,plain,
! [SV8: $i,SV10: $i] :
( ( ( ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY99 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) ) )
| ( SV8 != SY99 ) )
| ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY99 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY99 ) ) ) ) ) )
= $false )
| ( ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(250,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK12_SY98 @ SV9 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK10_SY93 @ SV9 ) ) ) )
| ( SV9
!= ( sK12_SY98 @ SV9 ) ) )
| ( ( sK10_SY93 @ SV9 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK12_SY98 @ SV9 ) ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK12_SY98 @ SV9 ) ) ) ) ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[246]) ).
thf(251,plain,
! [SV9: $i,SV11: $i] :
( ( ( ~ ! [SY100: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY100 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) ) )
| ( SV9 != SY100 ) )
| ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY100 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY100 ) ) ) ) ) )
= $false )
| ( ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(252,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK11_SY97 @ SV8 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK9_SY89 @ SV8 ) ) ) )
| ( SV8
!= ( sK11_SY97 @ SV8 ) ) )
| ( ( sK9_SY89 @ SV8 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK11_SY97 @ SV8 ) ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK11_SY97 @ SV8 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(253,plain,
! [SV8: $i,SV10: $i] :
( ( ( ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY99 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) ) )
| ( SV8 != SY99 ) )
| ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY99 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY99 ) ) ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(254,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK12_SY98 @ SV9 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK10_SY93 @ SV9 ) ) ) )
| ( SV9
!= ( sK12_SY98 @ SV9 ) ) )
| ( ( sK10_SY93 @ SV9 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK12_SY98 @ SV9 ) ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK12_SY98 @ SV9 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(255,plain,
! [SV9: $i,SV11: $i] :
( ( ( ! [SY100: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY100 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) ) )
| ( SV9 != SY100 ) )
| ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY100 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SY100 ) ) ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(256,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK11_SY97 @ SV8 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK9_SY89 @ SV8 ) ) ) )
| ( SV8
!= ( sK11_SY97 @ SV8 ) ) )
| ( ( sK9_SY89 @ SV8 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK11_SY97 @ SV8 ) ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK11_SY97 @ SV8 ) ) ) ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(257,plain,
! [SV8: $i,SV10: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SV12 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) ) )
| ( SV8 != SV12 ) )
| ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(258,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK12_SY98 @ SV9 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK10_SY93 @ SV9 ) ) ) )
| ( SV9
!= ( sK12_SY98 @ SV9 ) ) )
| ( ( sK10_SY93 @ SV9 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK12_SY98 @ SV9 ) ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK12_SY98 @ SV9 ) ) ) ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(259,plain,
! [SV9: $i,SV11: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SV13 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) ) )
| ( SV9 != SV13 ) )
| ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(260,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK11_SY97 @ SV8 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK9_SY89 @ SV8 ) ) ) )
| ( SV8
!= ( sK11_SY97 @ SV8 ) ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(261,plain,
! [SV8: $i] :
( ( ( ( sK9_SY89 @ SV8 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK11_SY97 @ SV8 ) ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK11_SY97 @ SV8 ) ) ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(262,plain,
! [SV8: $i,SV10: $i,SV12: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SV12 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) ) )
| ( SV8 != SV12 ) )
| ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) ) ) ) )
= $false )
| ( ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(263,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK12_SY98 @ SV9 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK10_SY93 @ SV9 ) ) ) )
| ( SV9
!= ( sK12_SY98 @ SV9 ) ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(264,plain,
! [SV9: $i] :
( ( ( ( sK10_SY93 @ SV9 )
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK12_SY98 @ SV9 ) ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK12_SY98 @ SV9 ) ) ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(265,plain,
! [SV9: $i,SV11: $i,SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SV13 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) ) )
| ( SV9 != SV13 ) )
| ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) ) ) ) )
= $false )
| ( ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(266,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK11_SY97 @ SV8 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK9_SY89 @ SV8 ) ) ) )
| ( SV8
!= ( sK11_SY97 @ SV8 ) ) ) )
= $true )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(267,plain,
! [SV8: $i] :
( ( ( ( sK9_SY89 @ SV8 )
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK11_SY97 @ SV8 ) ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK11_SY97 @ SV8 ) ) ) ) )
= $true )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(268,plain,
! [SV8: $i,SV10: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ SV12 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) ) )
| ( SV8 != SV12 ) )
| ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(269,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK12_SY98 @ SV9 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK10_SY93 @ SV9 ) ) ) )
| ( SV9
!= ( sK12_SY98 @ SV9 ) ) ) )
= $true )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(270,plain,
! [SV9: $i] :
( ( ( ( sK10_SY93 @ SV9 )
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK12_SY98 @ SV9 ) ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ ( sK12_SY98 @ SV9 ) ) ) ) )
= $true )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(271,plain,
! [SV9: $i,SV11: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ SV13 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) ) )
| ( SV9 != SV13 ) )
| ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(272,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK11_SY97 @ SV8 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK9_SY89 @ SV8 ) ) ) )
| ( SV8
!= ( sK11_SY97 @ SV8 ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(273,plain,
! [SV8: $i,SV10: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ SV12 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) ) )
| ( SV8 != SV12 ) ) )
= $true )
| ( ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(274,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK12_SY98 @ SV9 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK10_SY93 @ SV9 ) ) ) )
| ( SV9
!= ( sK12_SY98 @ SV9 ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(275,plain,
! [SV9: $i,SV11: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ SV13 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) ) )
| ( SV9 != SV13 ) ) )
= $true )
| ( ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(276,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK11_SY97 @ SV8 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK9_SY89 @ SV8 ) ) ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(277,plain,
! [SV8: $i] :
( ( ( SV8
!= ( sK11_SY97 @ SV8 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(278,plain,
! [SV8: $i,SV10: $i,SV12: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ SV12 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) ) )
| ( SV8 != SV12 ) ) )
= $false )
| ( ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(279,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK12_SY98 @ SV9 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK10_SY93 @ SV9 ) ) ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(280,plain,
! [SV9: $i] :
( ( ( SV9
!= ( sK12_SY98 @ SV9 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(281,plain,
! [SV9: $i,SV11: $i,SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ SV13 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) ) )
| ( SV9 != SV13 ) ) )
= $false )
| ( ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(282,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( element @ ( sK11_SY97 @ SV8 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK9_SY89 @ SV8 ) ) ) ) )
= $true )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(283,plain,
! [SV8: $i] :
( ( ( SV8
= ( sK11_SY97 @ SV8 ) )
= $true )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(284,plain,
! [SV8: $i,SV10: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( element @ SV12 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) ) )
| ( SV8 != SV12 ) )
= $true )
| ( ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(285,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ( element @ ( sK12_SY98 @ SV9 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK10_SY93 @ SV9 ) ) ) ) )
= $true )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(286,plain,
! [SV9: $i] :
( ( ( SV9
= ( sK12_SY98 @ SV9 ) )
= $true )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(287,plain,
! [SV9: $i,SV11: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( element @ SV13 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) ) )
| ( SV9 != SV13 ) )
= $true )
| ( ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(288,plain,
! [SV8: $i] :
( ( ( ~ ( element @ ( sK11_SY97 @ SV8 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK9_SY89 @ SV8 ) ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(289,plain,
! [SV8: $i,SV10: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( element @ SV12 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) ) ) )
= $true )
| ( ( SV8 != SV12 )
= $true )
| ( ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(290,plain,
! [SV9: $i] :
( ( ( ~ ( element @ ( sK12_SY98 @ SV9 ) @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK10_SY93 @ SV9 ) ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(291,plain,
! [SV9: $i,SV11: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( element @ SV13 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) ) ) )
= $true )
| ( ( SV9 != SV13 )
= $true )
| ( ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(292,plain,
! [SV8: $i] :
( ( ( ~ ( element @ ( sK11_SY97 @ SV8 ) @ ( the_carrier @ sK2_SY21 ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(293,plain,
! [SV8: $i] :
( ( ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK9_SY89 @ SV8 ) ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(294,plain,
! [SV8: $i,SV10: $i,SV12: $i] :
( ( ( ~ ( ~ ( element @ SV12 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) ) ) )
= $false )
| ( ( SV8 != SV12 )
= $true )
| ( ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(295,plain,
! [SV9: $i] :
( ( ( ~ ( element @ ( sK12_SY98 @ SV9 ) @ ( the_carrier @ sK2_SY21 ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(296,plain,
! [SV9: $i] :
( ( ( sK4_SX0
!= ( topstr_closure @ sK1_A @ ( sK10_SY93 @ SV9 ) ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(297,plain,
! [SV9: $i,SV11: $i,SV13: $i] :
( ( ( ~ ( ~ ( element @ SV13 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) ) ) )
= $false )
| ( ( SV9 != SV13 )
= $true )
| ( ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(298,plain,
! [SV8: $i] :
( ( ( element @ ( sK11_SY97 @ SV8 ) @ ( the_carrier @ sK2_SY21 ) )
= $true )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(299,plain,
! [SV8: $i] :
( ( ( sK4_SX0
= ( topstr_closure @ sK1_A @ ( sK9_SY89 @ SV8 ) ) )
= $true )
| ( ( in @ SV8 @ sK6_SY55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(300,plain,
! [SV8: $i,SV10: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) ) )
= $true )
| ( ( SV8 != SV12 )
= $true )
| ( ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(301,plain,
! [SV9: $i] :
( ( ( element @ ( sK12_SY98 @ SV9 ) @ ( the_carrier @ sK2_SY21 ) )
= $true )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(302,plain,
! [SV9: $i] :
( ( ( sK4_SX0
= ( topstr_closure @ sK1_A @ ( sK10_SY93 @ SV9 ) ) )
= $true )
| ( ( in @ SV9 @ sK7_SY68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(303,plain,
! [SV9: $i,SV11: $i,SV13: $i] :
( ( ( ~ ( element @ SV13 @ ( the_carrier @ sK2_SY21 ) )
| ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) ) )
= $true )
| ( ( SV9 != SV13 )
= $true )
| ( ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(304,plain,
! [SV8: $i,SV10: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ ( the_carrier @ sK2_SY21 ) ) )
= $true )
| ( ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) )
= $true )
| ( ( SV8 != SV12 )
= $true )
| ( ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(305,plain,
! [SV9: $i,SV11: $i,SV13: $i] :
( ( ( ~ ( element @ SV13 @ ( the_carrier @ sK2_SY21 ) ) )
= $true )
| ( ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) )
= $true )
| ( ( SV9 != SV13 )
= $true )
| ( ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(306,plain,
! [SV8: $i,SV10: $i,SV12: $i] :
( ( ( element @ SV12 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV10 ) )
= $true )
| ( ( SV8 != SV12 )
= $true )
| ( ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(307,plain,
! [SV9: $i,SV11: $i,SV13: $i] :
( ( ( element @ SV13 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( sK4_SX0
!= ( topstr_closure @ sK1_A @ SV11 ) )
= $true )
| ( ( SV9 != SV13 )
= $true )
| ( ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(308,plain,
! [SV8: $i,SV12: $i,SV10: $i] :
( ( ( sK4_SX0
= ( topstr_closure @ sK1_A @ SV10 ) )
= $false )
| ( ( element @ SV12 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( SV8 != SV12 )
= $true )
| ( ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(309,plain,
! [SV9: $i,SV13: $i,SV11: $i] :
( ( ( sK4_SX0
= ( topstr_closure @ sK1_A @ SV11 ) )
= $false )
| ( ( element @ SV13 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( SV9 != SV13 )
= $true )
| ( ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(310,plain,
! [SV10: $i,SV12: $i,SV8: $i] :
( ( ( SV8 = SV12 )
= $false )
| ( ( element @ SV12 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( sK4_SX0
= ( topstr_closure @ sK1_A @ SV10 ) )
= $false )
| ( ( SV10
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(311,plain,
! [SV11: $i,SV13: $i,SV9: $i] :
( ( ( SV9 = SV13 )
= $false )
| ( ( element @ SV13 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( sK4_SX0
= ( topstr_closure @ sK1_A @ SV11 ) )
= $false )
| ( ( SV11
!= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) ) )
= $true )
| ( ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(312,plain,
! [SV8: $i,SV12: $i,SV10: $i] :
( ( ( SV10
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV12 ) ) ) )
= $false )
| ( ( sK4_SX0
= ( topstr_closure @ sK1_A @ SV10 ) )
= $false )
| ( ( element @ SV12 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( SV8 = SV12 )
= $false )
| ( ( netstr_induced_subset @ SV10 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV8 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV8 @ sK6_SY55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(313,plain,
! [SV9: $i,SV13: $i,SV11: $i] :
( ( ( SV11
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) @ ( the_carrier @ sK1_A ) @ ( the_mapping @ sK1_A @ ( subnetstr_of_element @ sK1_A @ sK2_SY21 @ SV13 ) ) ) )
= $false )
| ( ( sK4_SX0
= ( topstr_closure @ sK1_A @ SV11 ) )
= $false )
| ( ( element @ SV13 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( SV9 = SV13 )
= $false )
| ( ( netstr_induced_subset @ SV11 @ sK1_A @ sK2_SY21 )
= $false )
| ( ( in @ SV9 @ ( the_carrier @ sK2_SY21 ) )
= $false )
| ( ( in @ SV9 @ sK7_SY68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(314,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[96,313,312,302,301,299,298,286,283,270,267,241,238,213,210,191,186,185,179,166,161,156,152,148,141,123,122,113,112,110,109,108,106,105,100,99,98,97]) ).
thf(315,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[314]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU401+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n008.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:19:24 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.72/0.69
% 2.72/0.69 No.of.Axioms: 12
% 2.72/0.69
% 2.72/0.69 Length.of.Defs: 0
% 2.72/0.69
% 2.72/0.69 Contains.Choice.Funs: false
% 2.72/0.69 .............
% 2.72/0.69
% 2.72/0.69 ********************************
% 2.72/0.69 * All subproblems solved! *
% 2.72/0.69 ********************************
% 2.72/0.69 % 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:314,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.72/0.69
% 2.72/0.69 %**** Beginning of derivation protocol ****
% 2.72/0.69 % SZS output start CNFRefutation
% See solution above
% 2.72/0.70
% 2.72/0.70 %**** End of derivation protocol ****
% 2.72/0.70 %**** no. of clauses in derivation: 259 ****
% 2.72/0.70 %**** clause counter: 314 ****
% 2.72/0.70
% 2.72/0.70 % 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:314,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------