%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU394+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 10:44:16 AM UTC 2026
% Result : Theorem 12.02s 2.25s
% Output : CNFRefutation 12.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 84
% Syntax : Number of formulae : 1086 ( 592 unt; 0 typ; 0 def)
% Number of atoms : 8367 (2213 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 15019 (2679 ~;2696 |; 331 &;9181 @)
% ( 10 <=>; 122 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 86 ( 83 usr; 12 con; 0-4 aty)
% Number of variables : 1733 ( 0 ^;1687 !; 46 ?;1733 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_2_1_yellow19,type,
a_2_1_yellow19: $i > $i > $i ).
thf(tp_antisymmetric_relstr,type,
antisymmetric_relstr: $i > $o ).
thf(tp_boole_POSet,type,
boole_POSet: $i > $i ).
thf(tp_boolean_relstr,type,
boolean_relstr: $i > $o ).
thf(tp_bounded_relstr,type,
bounded_relstr: $i > $o ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_cast_as_carrier_subset,type,
cast_as_carrier_subset: $i > $i ).
thf(tp_complemented_relstr,type,
complemented_relstr: $i > $o ).
thf(tp_complete_relstr,type,
complete_relstr: $i > $o ).
thf(tp_connected_relstr,type,
connected_relstr: $i > $o ).
thf(tp_directed_relstr,type,
directed_relstr: $i > $o ).
thf(tp_directed_subset,type,
directed_subset: $i > $i > $o ).
thf(tp_distributive_relstr,type,
distributive_relstr: $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_carrier,type,
empty_carrier: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_filter_of_net_str,type,
filter_of_net_str: $i > $i > $i ).
thf(tp_filtered_subset,type,
filtered_subset: $i > $i > $o ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_heyting_relstr,type,
heyting_relstr: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_is_eventually_in,type,
is_eventually_in: $i > $i > $i > $o ).
thf(tp_join_complete_relstr,type,
join_complete_relstr: $i > $o ).
thf(tp_lower_bounded_relstr,type,
lower_bounded_relstr: $i > $o ).
thf(tp_lower_relstr_subset,type,
lower_relstr_subset: $i > $i > $o ).
thf(tp_net_of_bool_filter,type,
net_of_bool_filter: $i > $i > $i > $i ).
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_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_element,type,
proper_element: $i > $i > $o ).
thf(tp_quasi_total,type,
quasi_total: $i > $i > $i > $o ).
thf(tp_reflexive_relstr,type,
reflexive_relstr: $i > $o ).
thf(tp_rel_str,type,
rel_str: $i > $o ).
thf(tp_rel_str_of,type,
rel_str_of: $i > $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_sK10_B,type,
sK10_B: $i > $i ).
thf(tp_sK11_B,type,
sK11_B: $i > $i ).
thf(tp_sK12_B,type,
sK12_B: $i > $i ).
thf(tp_sK13_B,type,
sK13_B: $i > $i ).
thf(tp_sK14_B,type,
sK14_B: $i > $i ).
thf(tp_sK15_A,type,
sK15_A: $i ).
thf(tp_sK16_B,type,
sK16_B: $i > $i ).
thf(tp_sK17_B,type,
sK17_B: $i > $i ).
thf(tp_sK18_B,type,
sK18_B: $i > $i ).
thf(tp_sK19_A,type,
sK19_A: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_B,type,
sK20_B: $i > $i ).
thf(tp_sK21_B,type,
sK21_B: $i > $i ).
thf(tp_sK22_A,type,
sK22_A: $i ).
thf(tp_sK23_A,type,
sK23_A: $i ).
thf(tp_sK24_B,type,
sK24_B: $i > $i ).
thf(tp_sK25_B,type,
sK25_B: $i > $i ).
thf(tp_sK26_A,type,
sK26_A: $i ).
thf(tp_sK2_SY127,type,
sK2_SY127: $i ).
thf(tp_sK3_C,type,
sK3_C: $i > $i > $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_B,type,
sK5_B: $i > $i ).
thf(tp_sK6_D,type,
sK6_D: $i > $i > $i > $i ).
thf(tp_sK7_C,type,
sK7_C: $i > $i > $i ).
thf(tp_sK8_A,type,
sK8_A: $i ).
thf(tp_sK9_B,type,
sK9_B: $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_strict_net_str,type,
strict_net_str: $i > $i > $o ).
thf(tp_strict_rel_str,type,
strict_rel_str: $i > $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_the_InternalRel,type,
the_InternalRel: $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_the_mapping,type,
the_mapping: $i > $i > $i ).
thf(tp_transitive_relstr,type,
transitive_relstr: $i > $o ).
thf(tp_trivial_carrier,type,
trivial_carrier: $i > $o ).
thf(tp_up_complete_relstr,type,
up_complete_relstr: $i > $o ).
thf(tp_upper_bounded_relstr,type,
upper_bounded_relstr: $i > $o ).
thf(tp_upper_relstr_subset,type,
upper_relstr_subset: $i > $i > $o ).
thf(tp_v1_yellow_3,type,
v1_yellow_3: $i > $o ).
thf(tp_with_infima_relstr,type,
with_infima_relstr: $i > $o ).
thf(tp_with_suprema_relstr,type,
with_suprema_relstr: $i > $o ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(7,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(9,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(10,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ ( boole_POSet @ A ) )
& ( upper_relstr_subset @ B @ ( boole_POSet @ A ) )
& ( proper_element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ A ) ) ) )
& ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ A ) ) ) ) )
=> ! [C: $i] :
~ ( ( in @ C @ B )
& ( empty @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_yellow19) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(14,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( upper_relstr_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) )
=> ( ( set_difference @ B @ ( singleton @ empty_set ) )
= ( filter_of_net_str @ A @ ( net_of_bool_filter @ A @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_yellow19) ).
thf(15,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(18,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( lower_relstr_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc8_waybel_0) ).
thf(19,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( lower_relstr_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_waybel_0) ).
thf(21,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(24,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( net_str @ B @ A )
& ( strict_net_str @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_waybel_0) ).
thf(25,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(26,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_waybel_7) ).
thf(27,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(28,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(29,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(31,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_waybel_7) ).
thf(32,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B )
& ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_waybel_0) ).
thf(33,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(34,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(38,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_waybel_0) ).
thf(39,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(40,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(42,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ~ ( empty_carrier @ C )
& ( net_str @ C @ B ) )
=> ( ( in @ A @ ( a_2_1_yellow19 @ B @ C ) )
<=> ? [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ B ) ) )
& ( A = D )
& ( is_eventually_in @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_yellow19) ).
thf(55,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_waybel_0) ).
thf(57,axiom,
! [A: $i] :
( ( ( with_infima_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_waybel_0) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(59,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(61,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( upper_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_waybel_0) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(63,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_yellow_0) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( ~ ( empty @ ( filter_of_net_str @ A @ B ) )
& ( upper_relstr_subset @ ( filter_of_net_str @ A @ B ) @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_yellow19) ).
thf(66,axiom,
! [A: $i] :
( ( ( with_suprema_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_waybel_0) ).
thf(67,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(68,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pre_topc) ).
thf(71,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(72,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(73,axiom,
! [A: $i] :
( ~ ( empty @ ( singleton @ A ) )
& ( finite @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(75,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( lower_relstr_subset @ ( cast_as_carrier_subset @ A ) @ A )
& ( upper_relstr_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc15_waybel_0) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(77,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(79,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(80,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(82,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_waybel_0) ).
thf(83,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(84,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(86,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(87,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(89,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(90,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(91,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
thf(92,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(93,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(94,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(95,axiom,
! [A: $i] :
( ( strict_rel_str @ ( boole_POSet @ A ) )
& ( rel_str @ ( boole_POSet @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty @ B )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ C )
& ( filtered_subset @ C @ ( boole_POSet @ B ) )
& ( upper_relstr_subset @ C @ ( boole_POSet @ B ) )
& ( element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ B ) ) ) ) )
=> ( ~ ( empty_carrier @ ( net_of_bool_filter @ A @ B @ C ) )
& ( strict_net_str @ ( net_of_bool_filter @ A @ B @ C ) @ A )
& ( net_str @ ( net_of_bool_filter @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow19) ).
thf(97,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( element @ ( filter_of_net_str @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_yellow19) ).
thf(99,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(100,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(101,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(102,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(105,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( ( filter_of_net_str @ A @ B )
= ( a_2_1_yellow19 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_yellow19) ).
thf(112,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( with_infima_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(113,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(114,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow_0) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(116,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(117,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( with_suprema_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattice3) ).
thf(118,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(127,conjecture,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( upper_relstr_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( proper_element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) )
& ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) )
=> ( B
= ( filter_of_net_str @ A @ ( net_of_bool_filter @ A @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_yellow19) ).
thf(128,negated_conjecture,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( upper_relstr_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( proper_element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) )
& ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) )
=> ( B
= ( filter_of_net_str @ A @ ( net_of_bool_filter @ A @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[127]) ).
thf(129,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( upper_relstr_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( proper_element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) )
& ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) )
=> ( B
= ( filter_of_net_str @ A @ ( net_of_bool_filter @ A @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[128]) ).
thf(130,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(131,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(132,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(133,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(134,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( upper_relstr_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) )
=> ( ( set_difference @ B @ ( singleton @ empty_set ) )
= ( filter_of_net_str @ A @ ( net_of_bool_filter @ A @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(135,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(136,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(137,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(138,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B )
& ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(139,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ~ ( empty_carrier @ C )
& ( net_str @ C @ B ) )
=> ( ( in @ A @ ( a_2_1_yellow19 @ B @ C ) )
<=> ? [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ B ) ) )
& ( A = D )
& ( is_eventually_in @ B @ C @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(140,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( upper_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(141,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(142,plain,
( ( ! [A: $i] :
( ( ( with_suprema_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(143,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(144,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(145,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(146,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(147,plain,
( ( ? [A: $i] : ( rel_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(148,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(149,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(150,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(151,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(152,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(153,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(154,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(155,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(156,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(157,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ ( boole_POSet @ A ) )
& ( upper_relstr_subset @ B @ ( boole_POSet @ A ) )
& ( proper_element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ A ) ) ) )
& ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ A ) ) ) ) )
=> ! [C: $i] :
~ ( ( in @ C @ B )
& ( empty @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(158,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(159,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(160,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( lower_relstr_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(161,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( lower_relstr_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(162,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(163,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( net_str @ B @ A )
& ( strict_net_str @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(164,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(165,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(166,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(167,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(168,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(169,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(170,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(171,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(172,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(173,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(174,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(175,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(176,plain,
( ( ! [A: $i] :
( ( ( with_infima_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(177,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(178,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(179,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(180,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( ~ ( empty @ ( filter_of_net_str @ A @ B ) )
& ( upper_relstr_subset @ ( filter_of_net_str @ A @ B ) @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(181,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(182,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(183,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(184,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(185,plain,
( ( ! [A: $i] :
( ~ ( empty @ ( singleton @ A ) )
& ( finite @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(186,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( lower_relstr_subset @ ( cast_as_carrier_subset @ A ) @ A )
& ( upper_relstr_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(187,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(188,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(189,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(190,plain,
$true = $true,
inference(unfold_def,[status(thm)],[86]) ).
thf(191,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(192,plain,
$true = $true,
inference(unfold_def,[status(thm)],[89]) ).
thf(193,plain,
$true = $true,
inference(unfold_def,[status(thm)],[90]) ).
thf(194,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(195,plain,
$true = $true,
inference(unfold_def,[status(thm)],[92]) ).
thf(196,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(197,plain,
$true = $true,
inference(unfold_def,[status(thm)],[94]) ).
thf(198,plain,
( ( ! [A: $i] :
( ( strict_rel_str @ ( boole_POSet @ A ) )
& ( rel_str @ ( boole_POSet @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(199,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty @ B )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ C )
& ( filtered_subset @ C @ ( boole_POSet @ B ) )
& ( upper_relstr_subset @ C @ ( boole_POSet @ B ) )
& ( element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ B ) ) ) ) )
=> ( ~ ( empty_carrier @ ( net_of_bool_filter @ A @ B @ C ) )
& ( strict_net_str @ ( net_of_bool_filter @ A @ B @ C ) @ A )
& ( net_str @ ( net_of_bool_filter @ A @ B @ C ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(200,plain,
$true = $true,
inference(unfold_def,[status(thm)],[97]) ).
thf(201,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( element @ ( filter_of_net_str @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(202,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(203,plain,
$true = $true,
inference(unfold_def,[status(thm)],[100]) ).
thf(204,plain,
$true = $true,
inference(unfold_def,[status(thm)],[101]) ).
thf(205,plain,
$true = $true,
inference(unfold_def,[status(thm)],[102]) ).
thf(206,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( ( filter_of_net_str @ A @ B )
= ( a_2_1_yellow19 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(207,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( with_infima_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(208,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(209,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(210,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(211,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( with_suprema_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(212,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(213,plain,
( ( ( ~ ( empty_carrier @ sK1_A )
& ( one_sorted_str @ sK1_A ) )
=> ! [SY127: $i] :
( ( ~ ( empty @ SY127 )
& ( filtered_subset @ SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) )
& ( upper_relstr_subset @ SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) )
& ( proper_element @ SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) )
& ( element @ SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) )
=> ( SY127
= ( filter_of_net_str @ sK1_A @ ( net_of_bool_filter @ sK1_A @ ( cast_as_carrier_subset @ sK1_A ) @ SY127 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[129]) ).
thf(214,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[213]) ).
thf(215,plain,
( ( one_sorted_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[213]) ).
thf(216,plain,
( ( ! [SY127: $i] :
( ( ~ ( empty @ SY127 )
& ( filtered_subset @ SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) )
& ( upper_relstr_subset @ SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) )
& ( proper_element @ SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) )
& ( element @ SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) )
=> ( SY127
= ( filter_of_net_str @ sK1_A @ ( net_of_bool_filter @ sK1_A @ ( cast_as_carrier_subset @ sK1_A ) @ SY127 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[213]) ).
thf(217,plain,
( ( ~ ! [SY127: $i] :
( ( ~ ( empty @ SY127 )
& ( filtered_subset @ SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) )
& ( upper_relstr_subset @ SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) )
& ( proper_element @ SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) )
& ( element @ SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) )
=> ( SY127
= ( filter_of_net_str @ sK1_A @ ( net_of_bool_filter @ sK1_A @ ( cast_as_carrier_subset @ sK1_A ) @ SY127 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[216]) ).
thf(218,plain,
( ( ~ ( empty @ sK2_SY127 )
& ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) )
& ( upper_relstr_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) )
& ( proper_element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) )
& ( element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) )
& ( sK2_SY127
!= ( filter_of_net_str @ sK1_A @ ( net_of_bool_filter @ sK1_A @ ( cast_as_carrier_subset @ sK1_A ) @ sK2_SY127 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[217]) ).
thf(219,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[130]) ).
thf(220,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK3_C @ B @ A ) @ A )
| ~ ( in @ ( sK3_C @ B @ A ) @ B ) )
& ( ( in @ ( sK3_C @ B @ A ) @ A )
| ( in @ ( sK3_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[133]) ).
thf(221,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ! [B: $i] :
( ( empty @ B )
| ~ ( filtered_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
| ~ ( upper_relstr_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
| ~ ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) )
| ( ( set_difference @ B @ ( singleton @ empty_set ) )
= ( filter_of_net_str @ A @ ( net_of_bool_filter @ A @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[134]) ).
thf(222,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[135]) ).
thf(223,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[136]) ).
thf(224,plain,
( ( ( relation @ sK4_A )
& ( relation_empty_yielding @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[137]) ).
thf(225,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( reflexive_relstr @ A )
| ~ ( rel_str @ A )
| ( ( element @ ( sK5_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK5_B @ A ) )
& ( finite @ ( sK5_B @ A ) )
& ( directed_subset @ ( sK5_B @ A ) @ A )
& ( filtered_subset @ ( sK5_B @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[138]) ).
thf(226,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( empty_carrier @ B )
| ~ ( one_sorted_str @ B )
| ( empty_carrier @ C )
| ~ ( net_str @ C @ B )
| ! [D: $i] :
( ( A != D )
| ~ ( element @ D @ ( powerset @ ( the_carrier @ B ) ) )
| ~ ( is_eventually_in @ B @ C @ D ) )
| ( in @ A @ ( a_2_1_yellow19 @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ( empty_carrier @ B )
| ~ ( one_sorted_str @ B )
| ( empty_carrier @ C )
| ~ ( net_str @ C @ B )
| ~ ( in @ A @ ( a_2_1_yellow19 @ B @ C ) )
| ( ( A
= ( sK6_D @ C @ B @ A ) )
& ( element @ ( sK6_D @ C @ B @ A ) @ ( powerset @ ( the_carrier @ B ) ) )
& ( is_eventually_in @ B @ C @ ( sK6_D @ C @ B @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[139]) ).
thf(227,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( upper_bounded_relstr @ A )
| ~ ( rel_str @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) )
& ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( upper_bounded_relstr @ A )
| ~ ( rel_str @ A )
| ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[140]) ).
thf(228,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[141]) ).
thf(229,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_suprema_relstr @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_suprema_relstr @ A )
| ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[142]) ).
thf(230,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ A )
| ~ ( finite @ B )
| ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[143]) ).
thf(231,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] : ( finite @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[145]) ).
thf(232,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK7_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[146]) ).
thf(233,plain,
( ( rel_str @ sK8_A )
= $true ),
inference(extcnf_combined,[status(esa)],[147]) ).
thf(234,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[148]) ).
thf(235,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( complete_relstr @ A )
| ~ ( empty_carrier @ A ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( complete_relstr @ A )
| ( with_suprema_relstr @ A ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( complete_relstr @ A )
| ( with_infima_relstr @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(236,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[150]) ).
thf(237,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[151]) ).
thf(238,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[152]) ).
thf(239,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[153]) ).
thf(240,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[154]) ).
thf(241,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[155]) ).
thf(242,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[156]) ).
thf(243,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ( empty @ B )
| ~ ( filtered_subset @ B @ ( boole_POSet @ A ) )
| ~ ( upper_relstr_subset @ B @ ( boole_POSet @ A ) )
| ~ ( proper_element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ A ) ) ) )
| ~ ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ A ) ) ) )
| ! [C: $i] :
( ~ ( empty @ C )
| ~ ( in @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[157]) ).
thf(244,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[158]) ).
thf(245,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[159]) ).
thf(246,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( rel_str @ A )
| ( ( element @ ( sK9_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK9_B @ A ) )
& ( lower_relstr_subset @ ( sK9_B @ A ) @ A )
& ( upper_relstr_subset @ ( sK9_B @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[160]) ).
thf(247,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ( element @ ( sK10_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ( lower_relstr_subset @ ( sK10_B @ A ) @ A )
& ( upper_relstr_subset @ ( sK10_B @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[161]) ).
thf(248,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( ( element @ ( sK11_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK11_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[162]) ).
thf(249,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( net_str @ ( sK12_B @ A ) @ A )
& ( strict_net_str @ ( sK12_B @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[163]) ).
thf(250,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK13_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK13_B @ A ) )
& ( finite @ ( sK13_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[164]) ).
thf(251,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( element @ ( sK14_B @ A ) @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ~ ( empty @ ( sK14_B @ A ) )
& ( finite @ ( sK14_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[165]) ).
thf(252,plain,
( ( ( one_sorted_str @ sK15_A )
& ~ ( empty_carrier @ sK15_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[166]) ).
thf(253,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK16_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK16_B @ A ) )
& ( finite @ ( sK16_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[167]) ).
thf(254,plain,
( ( ! [A: $i] :
( ( element @ ( sK17_B @ A ) @ ( powerset @ ( powerset @ A ) ) )
& ~ ( empty @ ( sK17_B @ A ) )
& ( finite @ ( sK17_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[168]) ).
thf(255,plain,
( ( ! [A: $i] :
( ( element @ ( sK18_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK18_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[169]) ).
thf(256,plain,
( ( ~ ( empty @ sK19_A )
& ( relation @ sK19_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[170]) ).
thf(257,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ( directed_subset @ ( sK20_B @ A ) @ A )
& ( element @ ( sK20_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ( filtered_subset @ ( sK20_B @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[171]) ).
thf(258,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK21_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK21_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[172]) ).
thf(259,plain,
( ( ( empty @ sK22_A )
& ( relation @ sK22_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[173]) ).
thf(260,plain,
( ( ~ ( empty @ sK23_A )
& ( finite @ sK23_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[174]) ).
thf(261,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( lower_bounded_relstr @ A )
| ~ ( rel_str @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) )
& ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( lower_bounded_relstr @ A )
| ~ ( rel_str @ A )
| ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[175]) ).
thf(262,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_infima_relstr @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_infima_relstr @ A )
| ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[176]) ).
thf(263,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[177]) ).
thf(264,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( rel_str @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[179]) ).
thf(265,plain,
( ( ! [A: $i,B: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( empty_carrier @ B )
| ~ ( net_str @ B @ A )
| ~ ( empty @ ( filter_of_net_str @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( empty_carrier @ B )
| ~ ( net_str @ B @ A )
| ( upper_relstr_subset @ ( filter_of_net_str @ A @ B ) @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[180]) ).
thf(266,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[182]) ).
thf(267,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[184]) ).
thf(268,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) )
& ! [A: $i] : ( finite @ ( singleton @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[185]) ).
thf(269,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( rel_str @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) )
& ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( rel_str @ A )
| ( lower_relstr_subset @ ( cast_as_carrier_subset @ A ) @ A ) )
& ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( rel_str @ A )
| ( upper_relstr_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[186]) ).
thf(270,plain,
( ( ! [A: $i] : ( element @ ( sK24_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[187]) ).
thf(271,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( net_str @ ( sK25_B @ A ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[188]) ).
thf(272,plain,
( ( one_sorted_str @ sK26_A )
= $true ),
inference(extcnf_combined,[status(esa)],[189]) ).
thf(273,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[191]) ).
thf(274,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ! [B: $i] :
( ~ ( net_str @ B @ A )
| ( rel_str @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[194]) ).
thf(275,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[196]) ).
thf(276,plain,
( ( ! [A: $i] : ( rel_str @ ( boole_POSet @ A ) )
& ! [A: $i] : ( strict_rel_str @ ( boole_POSet @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[198]) ).
thf(277,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( empty @ B )
| ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ( empty @ C )
| ~ ( filtered_subset @ C @ ( boole_POSet @ B ) )
| ~ ( upper_relstr_subset @ C @ ( boole_POSet @ B ) )
| ~ ( element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ B ) ) ) )
| ~ ( empty_carrier @ ( net_of_bool_filter @ A @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( empty @ B )
| ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ( empty @ C )
| ~ ( filtered_subset @ C @ ( boole_POSet @ B ) )
| ~ ( upper_relstr_subset @ C @ ( boole_POSet @ B ) )
| ~ ( element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ B ) ) ) )
| ( strict_net_str @ ( net_of_bool_filter @ A @ B @ C ) @ A ) )
& ! [B: $i,C: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( empty @ B )
| ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ( empty @ C )
| ~ ( filtered_subset @ C @ ( boole_POSet @ B ) )
| ~ ( upper_relstr_subset @ C @ ( boole_POSet @ B ) )
| ~ ( element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ B ) ) ) )
| ( net_str @ ( net_of_bool_filter @ A @ B @ C ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[199]) ).
thf(278,plain,
( ( ! [A: $i,B: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( empty_carrier @ B )
| ~ ( net_str @ B @ A )
| ( element @ ( filter_of_net_str @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[201]) ).
thf(279,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[202]) ).
thf(280,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ! [B: $i] :
( ( empty_carrier @ B )
| ~ ( net_str @ B @ A )
| ( ( filter_of_net_str @ A @ B )
= ( a_2_1_yellow19 @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[206]) ).
thf(281,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_infima_relstr @ A )
| ~ ( empty_carrier @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[207]) ).
thf(282,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[208]) ).
thf(283,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[209]) ).
thf(284,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[210]) ).
thf(285,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_suprema_relstr @ A )
| ~ ( empty_carrier @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[211]) ).
thf(286,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[212]) ).
thf(287,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(288,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_suprema_relstr @ A )
| ~ ( empty_carrier @ A ) ) )
= $true ),
inference(copy,[status(thm)],[285]) ).
thf(289,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(290,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(291,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(292,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_infima_relstr @ A )
| ~ ( empty_carrier @ A ) ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(293,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ! [B: $i] :
( ( empty_carrier @ B )
| ~ ( net_str @ B @ A )
| ( ( filter_of_net_str @ A @ B )
= ( a_2_1_yellow19 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(294,plain,
$true = $true,
inference(copy,[status(thm)],[205]) ).
thf(295,plain,
$true = $true,
inference(copy,[status(thm)],[204]) ).
thf(296,plain,
$true = $true,
inference(copy,[status(thm)],[203]) ).
thf(297,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(298,plain,
( ( ! [A: $i,B: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( empty_carrier @ B )
| ~ ( net_str @ B @ A )
| ( element @ ( filter_of_net_str @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(299,plain,
$true = $true,
inference(copy,[status(thm)],[200]) ).
thf(300,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( empty @ B )
| ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ( empty @ C )
| ~ ( filtered_subset @ C @ ( boole_POSet @ B ) )
| ~ ( upper_relstr_subset @ C @ ( boole_POSet @ B ) )
| ~ ( element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ B ) ) ) )
| ~ ( empty_carrier @ ( net_of_bool_filter @ A @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( empty @ B )
| ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ( empty @ C )
| ~ ( filtered_subset @ C @ ( boole_POSet @ B ) )
| ~ ( upper_relstr_subset @ C @ ( boole_POSet @ B ) )
| ~ ( element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ B ) ) ) )
| ( strict_net_str @ ( net_of_bool_filter @ A @ B @ C ) @ A ) )
& ! [B: $i,C: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( empty @ B )
| ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ( empty @ C )
| ~ ( filtered_subset @ C @ ( boole_POSet @ B ) )
| ~ ( upper_relstr_subset @ C @ ( boole_POSet @ B ) )
| ~ ( element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ B ) ) ) )
| ( net_str @ ( net_of_bool_filter @ A @ B @ C ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(301,plain,
( ( ! [A: $i] : ( rel_str @ ( boole_POSet @ A ) )
& ! [A: $i] : ( strict_rel_str @ ( boole_POSet @ A ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(302,plain,
$true = $true,
inference(copy,[status(thm)],[197]) ).
thf(303,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(304,plain,
$true = $true,
inference(copy,[status(thm)],[195]) ).
thf(305,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ! [B: $i] :
( ~ ( net_str @ B @ A )
| ( rel_str @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(306,plain,
$true = $true,
inference(copy,[status(thm)],[193]) ).
thf(307,plain,
$true = $true,
inference(copy,[status(thm)],[192]) ).
thf(308,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(309,plain,
$true = $true,
inference(copy,[status(thm)],[190]) ).
thf(310,plain,
( ( one_sorted_str @ sK26_A )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(311,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( net_str @ ( sK25_B @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(312,plain,
( ( ! [A: $i] : ( element @ ( sK24_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(313,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( rel_str @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) )
& ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( rel_str @ A )
| ( lower_relstr_subset @ ( cast_as_carrier_subset @ A ) @ A ) )
& ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( rel_str @ A )
| ( upper_relstr_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(314,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) )
& ! [A: $i] : ( finite @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(315,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(316,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(317,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(318,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(319,plain,
( ( ! [A: $i,B: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( empty_carrier @ B )
| ~ ( net_str @ B @ A )
| ~ ( empty @ ( filter_of_net_str @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( empty_carrier @ B )
| ~ ( net_str @ B @ A )
| ( upper_relstr_subset @ ( filter_of_net_str @ A @ B ) @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(320,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( rel_str @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(321,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(322,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(323,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_infima_relstr @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_infima_relstr @ A )
| ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(324,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( lower_bounded_relstr @ A )
| ~ ( rel_str @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) )
& ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( lower_bounded_relstr @ A )
| ~ ( rel_str @ A )
| ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(325,plain,
( ( ~ ( empty @ sK23_A )
& ( finite @ sK23_A ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(326,plain,
( ( ( empty @ sK22_A )
& ( relation @ sK22_A ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(327,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK21_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK21_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(328,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ( directed_subset @ ( sK20_B @ A ) @ A )
& ( element @ ( sK20_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ( filtered_subset @ ( sK20_B @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(329,plain,
( ( ~ ( empty @ sK19_A )
& ( relation @ sK19_A ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(330,plain,
( ( ! [A: $i] :
( ( element @ ( sK18_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK18_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(331,plain,
( ( ! [A: $i] :
( ( element @ ( sK17_B @ A ) @ ( powerset @ ( powerset @ A ) ) )
& ~ ( empty @ ( sK17_B @ A ) )
& ( finite @ ( sK17_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(332,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK16_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK16_B @ A ) )
& ( finite @ ( sK16_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(333,plain,
( ( ( one_sorted_str @ sK15_A )
& ~ ( empty_carrier @ sK15_A ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(334,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( element @ ( sK14_B @ A ) @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ~ ( empty @ ( sK14_B @ A ) )
& ( finite @ ( sK14_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(335,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK13_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK13_B @ A ) )
& ( finite @ ( sK13_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(336,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( net_str @ ( sK12_B @ A ) @ A )
& ( strict_net_str @ ( sK12_B @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(337,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( ( element @ ( sK11_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK11_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(338,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ( element @ ( sK10_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ( lower_relstr_subset @ ( sK10_B @ A ) @ A )
& ( upper_relstr_subset @ ( sK10_B @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(339,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( rel_str @ A )
| ( ( element @ ( sK9_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK9_B @ A ) )
& ( lower_relstr_subset @ ( sK9_B @ A ) @ A )
& ( upper_relstr_subset @ ( sK9_B @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(340,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(341,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(342,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ( empty @ B )
| ~ ( filtered_subset @ B @ ( boole_POSet @ A ) )
| ~ ( upper_relstr_subset @ B @ ( boole_POSet @ A ) )
| ~ ( proper_element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ A ) ) ) )
| ~ ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ A ) ) ) )
| ! [C: $i] :
( ~ ( empty @ C )
| ~ ( in @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(343,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(344,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(345,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(346,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(347,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(348,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(349,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(350,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( complete_relstr @ A )
| ~ ( empty_carrier @ A ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( complete_relstr @ A )
| ( with_suprema_relstr @ A ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( complete_relstr @ A )
| ( with_infima_relstr @ A ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(351,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(352,plain,
( ( rel_str @ sK8_A )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(353,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK7_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(354,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] : ( finite @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(355,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(356,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ A )
| ~ ( finite @ B )
| ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(357,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_suprema_relstr @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( with_suprema_relstr @ A )
| ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(358,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(359,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( upper_bounded_relstr @ A )
| ~ ( rel_str @ A )
| ~ ( empty @ ( cast_as_carrier_subset @ A ) ) )
& ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( upper_bounded_relstr @ A )
| ~ ( rel_str @ A )
| ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(360,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( empty_carrier @ B )
| ~ ( one_sorted_str @ B )
| ( empty_carrier @ C )
| ~ ( net_str @ C @ B )
| ! [D: $i] :
( ( A != D )
| ~ ( element @ D @ ( powerset @ ( the_carrier @ B ) ) )
| ~ ( is_eventually_in @ B @ C @ D ) )
| ( in @ A @ ( a_2_1_yellow19 @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ( empty_carrier @ B )
| ~ ( one_sorted_str @ B )
| ( empty_carrier @ C )
| ~ ( net_str @ C @ B )
| ~ ( in @ A @ ( a_2_1_yellow19 @ B @ C ) )
| ( ( A
= ( sK6_D @ C @ B @ A ) )
& ( element @ ( sK6_D @ C @ B @ A ) @ ( powerset @ ( the_carrier @ B ) ) )
& ( is_eventually_in @ B @ C @ ( sK6_D @ C @ B @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(361,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( reflexive_relstr @ A )
| ~ ( rel_str @ A )
| ( ( element @ ( sK5_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK5_B @ A ) )
& ( finite @ ( sK5_B @ A ) )
& ( directed_subset @ ( sK5_B @ A ) @ A )
& ( filtered_subset @ ( sK5_B @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(362,plain,
( ( ( relation @ sK4_A )
& ( relation_empty_yielding @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(363,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(364,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(365,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ! [B: $i] :
( ( empty @ B )
| ~ ( filtered_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
| ~ ( upper_relstr_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
| ~ ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) )
| ( ( set_difference @ B @ ( singleton @ empty_set ) )
= ( filter_of_net_str @ A @ ( net_of_bool_filter @ A @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(366,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK3_C @ B @ A ) @ A )
| ~ ( in @ ( sK3_C @ B @ A ) @ B ) )
& ( ( in @ ( sK3_C @ B @ A ) @ A )
| ( in @ ( sK3_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(367,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(368,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(369,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(370,plain,
( ( one_sorted_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(371,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(372,plain,
( ( ~ ( empty @ sK2_SY127 )
& ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) )
& ( upper_relstr_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) )
& ( proper_element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) )
& ( element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) )
& ( sK2_SY127
!= ( filter_of_net_str @ sK1_A @ ( net_of_bool_filter @ sK1_A @ ( cast_as_carrier_subset @ sK1_A ) @ sK2_SY127 ) ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(373,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ~ ( ~ ( net_str @ ( sK12_B @ SX0 ) @ SX0 )
| ~ ( strict_net_str @ ( sK12_B @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(374,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK21_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK21_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(375,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ( empty @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ( empty @ SX2 )
| ~ ( filtered_subset @ SX2 @ ( boole_POSet @ SX1 ) )
| ~ ( upper_relstr_subset @ SX2 @ ( boole_POSet @ SX1 ) )
| ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SX1 ) ) ) )
| ~ ( empty_carrier @ ( net_of_bool_filter @ SX0 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ( empty @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ( empty @ SX2 )
| ~ ( filtered_subset @ SX2 @ ( boole_POSet @ SX1 ) )
| ~ ( upper_relstr_subset @ SX2 @ ( boole_POSet @ SX1 ) )
| ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SX1 ) ) ) )
| ( strict_net_str @ ( net_of_bool_filter @ SX0 @ SX1 @ SX2 ) @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ( empty @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ( empty @ SX2 )
| ~ ( filtered_subset @ SX2 @ ( boole_POSet @ SX1 ) )
| ~ ( upper_relstr_subset @ SX2 @ ( boole_POSet @ SX1 ) )
| ~ ( element @ SX2 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SX1 ) ) ) )
| ( net_str @ ( net_of_bool_filter @ SX0 @ SX1 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(376,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( empty_carrier @ SX1 )
| ~ ( one_sorted_str @ SX1 )
| ( empty_carrier @ SX2 )
| ~ ( net_str @ SX2 @ SX1 )
| ! [SX3: $i] :
( ( SX0 != SX3 )
| ~ ( element @ SX3 @ ( powerset @ ( the_carrier @ SX1 ) ) )
| ~ ( is_eventually_in @ SX1 @ SX2 @ SX3 ) )
| ( in @ SX0 @ ( a_2_1_yellow19 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( empty_carrier @ SX1 )
| ~ ( one_sorted_str @ SX1 )
| ( empty_carrier @ SX2 )
| ~ ( net_str @ SX2 @ SX1 )
| ~ ( in @ SX0 @ ( a_2_1_yellow19 @ SX1 @ SX2 ) )
| ~ ( ~ ~ ( ( SX0
!= ( sK6_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( element @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ ( powerset @ ( the_carrier @ SX1 ) ) ) )
| ~ ( is_eventually_in @ SX1 @ SX2 @ ( sK6_D @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(377,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ~ ( ~ ( element @ ( sK11_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ~ ( empty @ ( sK11_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(378,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(379,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_suprema_relstr @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_infima_relstr @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(380,plain,
( ( ~ ( ~ ~ ( empty @ sK19_A )
| ~ ( relation @ sK19_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(381,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( reflexive_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SX0 ) ) )
| ~ ( finite @ ( sK5_B @ SX0 ) ) )
| ~ ( directed_subset @ ( sK5_B @ SX0 ) @ SX0 ) )
| ~ ( filtered_subset @ ( sK5_B @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(382,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK10_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ( lower_relstr_subset @ ( sK10_B @ SX0 ) @ SX0 ) )
| ~ ( upper_relstr_subset @ ( sK10_B @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(383,plain,
( ( ~ ( ~ ~ ( empty @ sK23_A )
| ~ ( finite @ sK23_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(384,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ( empty_carrier @ SX1 )
| ~ ( net_str @ SX1 @ SX0 )
| ~ ( empty @ ( filter_of_net_str @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ( empty_carrier @ SX1 )
| ~ ( net_str @ SX1 @ SX0 )
| ( upper_relstr_subset @ ( filter_of_net_str @ SX0 @ SX1 ) @ ( boole_POSet @ ( cast_as_carrier_subset @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(385,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_infima_relstr @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_infima_relstr @ SX0 )
| ( filtered_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(386,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(387,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK16_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK16_B @ SX0 ) ) )
| ~ ( finite @ ( sK16_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(388,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK13_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK13_B @ SX0 ) ) )
| ~ ( finite @ ( sK13_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(389,plain,
( ( ~ ( ~ ! [SX0: $i] : ( rel_str @ ( boole_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( boole_POSet @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(390,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(391,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( lower_bounded_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( lower_bounded_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( filtered_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(392,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SY127 )
| ~ ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( upper_relstr_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( proper_element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) )
| ~ ( element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) )
| ~ ( ( sK2_SY127
!= ( filter_of_net_str @ sK1_A @ ( net_of_bool_filter @ sK1_A @ ( cast_as_carrier_subset @ sK1_A ) @ sK2_SY127 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(393,plain,
( ( ~ ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(394,plain,
( ( ~ ( ~ ! [SX0: $i] :
~ ( empty @ ( singleton @ SX0 ) )
| ~ ! [SX0: $i] : ( finite @ ( singleton @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(395,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(396,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ~ ( empty @ ( sK9_B @ SX0 ) ) )
| ~ ( lower_relstr_subset @ ( sK9_B @ SX0 ) @ SX0 ) )
| ~ ( upper_relstr_subset @ ( sK9_B @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(397,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SX0 ) @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ~ ( empty @ ( sK17_B @ SX0 ) ) )
| ~ ( finite @ ( sK17_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(398,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(399,plain,
( ( ~ ( ~ ( one_sorted_str @ sK15_A )
| ~ ~ ( empty_carrier @ sK15_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(400,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(401,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( upper_bounded_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( upper_bounded_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( directed_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(402,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK18_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK18_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(403,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK14_B @ SX0 ) @ ( powerset @ ( powerset @ ( the_carrier @ SX0 ) ) ) )
| ~ ~ ( empty @ ( sK14_B @ SX0 ) ) )
| ~ ( finite @ ( sK14_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(404,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( ~ ~ ( ~ ( directed_subset @ ( sK20_B @ SX0 ) @ SX0 )
| ~ ( element @ ( sK20_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) )
| ~ ( filtered_subset @ ( sK20_B @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(405,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ( lower_relstr_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ( upper_relstr_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(406,plain,
( ( ~ ( ~ ( empty @ sK22_A )
| ~ ( relation @ sK22_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(407,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_suprema_relstr @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_suprema_relstr @ SX0 )
| ( directed_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(408,plain,
! [SV1: $i] :
( ( ~ ( empty @ SV1 )
| ( finite @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(409,plain,
! [SV2: $i] :
( ( ~ ( rel_str @ SV2 )
| ~ ( with_suprema_relstr @ SV2 )
| ~ ( empty_carrier @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(410,plain,
! [SV3: $i] :
( ( ~ ( empty @ SV3 )
| ( relation @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(411,plain,
! [SV4: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ~ ( element @ SY129 @ ( powerset @ ( cartesian_product2 @ SV4 @ SY128 ) ) )
| ( relation @ SY129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(412,plain,
! [SV5: $i] :
( ( ~ ( finite @ SV5 )
| ! [SY130: $i] :
( ~ ( element @ SY130 @ ( powerset @ SV5 ) )
| ( finite @ SY130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(413,plain,
! [SV6: $i] :
( ( ~ ( rel_str @ SV6 )
| ~ ( with_infima_relstr @ SV6 )
| ~ ( empty_carrier @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(414,plain,
! [SV7: $i] :
( ( ( empty_carrier @ SV7 )
| ~ ( one_sorted_str @ SV7 )
| ! [SY131: $i] :
( ( empty_carrier @ SY131 )
| ~ ( net_str @ SY131 @ SV7 )
| ( ( filter_of_net_str @ SV7 @ SY131 )
= ( a_2_1_yellow19 @ SV7 @ SY131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(415,plain,
! [SV8: $i] :
( ( ~ ( one_sorted_str @ SV8 )
| ( element @ ( cast_as_carrier_subset @ SV8 ) @ ( powerset @ ( the_carrier @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(416,plain,
! [SV9: $i] :
( ( ! [SY132: $i] :
( ( empty_carrier @ SV9 )
| ~ ( one_sorted_str @ SV9 )
| ( empty_carrier @ SY132 )
| ~ ( net_str @ SY132 @ SV9 )
| ( element @ ( filter_of_net_str @ SV9 @ SY132 ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV9 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(417,plain,
! [SV10: $i] :
( ( ~ ( rel_str @ SV10 )
| ( one_sorted_str @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(418,plain,
! [SV11: $i] :
( ( ~ ( one_sorted_str @ SV11 )
| ! [SY133: $i] :
( ~ ( net_str @ SY133 @ SV11 )
| ( rel_str @ SY133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(419,plain,
! [SV12: $i] :
( ( ! [SY134: $i,SY135: $i] :
( ~ ( relation_of2_as_subset @ SY135 @ SV12 @ SY134 )
| ( element @ SY135 @ ( powerset @ ( cartesian_product2 @ SV12 @ SY134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(420,plain,
! [SV13: $i] :
( ( ~ ( one_sorted_str @ SV13 )
| ( net_str @ ( sK25_B @ SV13 ) @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(421,plain,
! [SV14: $i] :
( ( element @ ( sK24_B @ SV14 ) @ SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(422,plain,
! [SV15: $i] :
( ( ( empty_carrier @ SV15 )
| ~ ( one_sorted_str @ SV15 )
| ~ ( empty @ ( the_carrier @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(423,plain,
! [SV16: $i] :
( ( ~ ( empty @ ( powerset @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(424,plain,
! [SV17: $i] :
( ( ( empty_carrier @ SV17 )
| ~ ( one_sorted_str @ SV17 )
| ~ ( empty @ ( cast_as_carrier_subset @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(425,plain,
! [SV18: $i] :
( ( ~ ( empty @ ( singleton @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(426,plain,
! [SV19: $i] :
( ( ( empty_carrier @ SV19 )
| ~ ( rel_str @ SV19 )
| ~ ( empty @ ( cast_as_carrier_subset @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(427,plain,
! [SV20: $i] :
( ( ! [SY136: $i] :
( ( empty @ SV20 )
| ( empty @ SY136 )
| ~ ( empty @ ( cartesian_product2 @ SV20 @ SY136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(428,plain,
! [SV21: $i] :
( ( ! [SY137: $i] :
( ~ ( in @ SV21 @ SY137 )
| ( element @ SV21 @ SY137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(429,plain,
! [SV22: $i] :
( ( ! [SY138: $i] :
( ~ ( element @ SV22 @ SY138 )
| ( empty @ SY138 )
| ( in @ SV22 @ SY138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(430,plain,
! [SV23: $i] :
( ( ( empty @ SV23 )
| ! [SY139: $i] :
( ( empty @ SY139 )
| ~ ( filtered_subset @ SY139 @ ( boole_POSet @ SV23 ) )
| ~ ( upper_relstr_subset @ SY139 @ ( boole_POSet @ SV23 ) )
| ~ ( proper_element @ SY139 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
| ~ ( element @ SY139 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
| ! [C: $i] :
( ~ ( empty @ C )
| ~ ( in @ C @ SY139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(431,plain,
! [SV24: $i] :
( ( ! [SY141: $i,SY142: $i] :
( ~ ( element @ SY141 @ ( powerset @ SY142 ) )
| ~ ( in @ SV24 @ SY141 )
| ( element @ SV24 @ SY142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(432,plain,
! [SV25: $i] :
( ( ! [SY143: $i,SY144: $i] :
( ~ ( element @ SY143 @ ( powerset @ SY144 ) )
| ~ ( in @ SV25 @ SY143 )
| ~ ( empty @ SY144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(433,plain,
! [SV26: $i] :
( ( ~ ( empty @ SV26 )
| ( SV26 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(434,plain,
! [SV27: $i] :
( ( ! [SY145: $i] :
( ~ ( empty @ SY145 )
| ~ ( in @ SV27 @ SY145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(435,plain,
! [SV28: $i] :
( ( ! [SY146: $i] :
( ( SV28 = SY146 )
| ~ ( empty @ SV28 )
| ~ ( empty @ SY146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(436,plain,
! [SV29: $i] :
( ( ! [SY147: $i] :
( ~ ( in @ SV29 @ SY147 )
| ~ ( in @ SY147 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(437,plain,
! [SV30: $i] :
( ( ~ ( rel_str @ SV30 )
| ( relation_of2_as_subset @ ( the_InternalRel @ SV30 ) @ ( the_carrier @ SV30 ) @ ( the_carrier @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(438,plain,
! [SV31: $i] :
( ( ! [SY148: $i] : ( relation_of2_as_subset @ ( sK7_C @ SY148 @ SV31 ) @ SV31 @ SY148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(439,plain,
! [SV32: $i] :
( ( ~ ( finite @ SV32 )
| ! [SY149: $i] : ( finite @ ( set_difference @ SV32 @ SY149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(440,plain,
! [SV33: $i] :
( ( ! [SY150: $i] :
( ~ ( finite @ SV33 )
| ~ ( finite @ SY150 )
| ( finite @ ( cartesian_product2 @ SV33 @ SY150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(441,plain,
! [SV34: $i] :
( ( ! [SY151: $i] :
( ~ ( relation @ SV34 )
| ~ ( relation @ SY151 )
| ( relation @ ( set_difference @ SV34 @ SY151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(442,plain,
! [SV35: $i] :
( ( subset @ SV35 @ SV35 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(443,plain,
! [SV36: $i] :
( ( ( empty_carrier @ SV36 )
| ~ ( one_sorted_str @ SV36 )
| ! [SY152: $i] :
( ( empty @ SY152 )
| ~ ( filtered_subset @ SY152 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
| ~ ( upper_relstr_subset @ SY152 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
| ~ ( element @ SY152 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) ) )
| ( ( set_difference @ SY152 @ ( singleton @ empty_set ) )
= ( filter_of_net_str @ SV36 @ ( net_of_bool_filter @ SV36 @ ( cast_as_carrier_subset @ SV36 ) @ SY152 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(444,plain,
! [SV37: $i] :
( ( ( set_difference @ SV37 @ empty_set )
= SV37 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(445,plain,
! [SV38: $i] :
( ( ( set_difference @ empty_set @ SV38 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(446,plain,
( ( empty_carrier @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(447,plain,
! [SV39: $i] :
( ( ~ ( one_sorted_str @ SV39 )
| ~ ( ~ ( net_str @ ( sK12_B @ SV39 ) @ SV39 )
| ~ ( strict_net_str @ ( sK12_B @ SV39 ) @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(448,plain,
! [SV40: $i] :
( ( ( empty @ SV40 )
| ~ ( ~ ( element @ ( sK21_B @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( empty @ ( sK21_B @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(449,plain,
! [SV41: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY153: $i,SY154: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY153 )
| ~ ( element @ SY153 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY154 )
| ~ ( filtered_subset @ SY154 @ ( boole_POSet @ SY153 ) )
| ~ ( upper_relstr_subset @ SY154 @ ( boole_POSet @ SY153 ) )
| ~ ( element @ SY154 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY153 ) ) ) )
| ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SY153 @ SY154 ) ) )
| ~ ! [SY155: $i,SY156: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY155 )
| ~ ( element @ SY155 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY156 )
| ~ ( filtered_subset @ SY156 @ ( boole_POSet @ SY155 ) )
| ~ ( upper_relstr_subset @ SY156 @ ( boole_POSet @ SY155 ) )
| ~ ( element @ SY156 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY155 ) ) ) )
| ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SY155 @ SY156 ) @ SV41 ) ) )
| ~ ! [SY157: $i,SY158: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY157 )
| ~ ( element @ SY157 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY158 )
| ~ ( filtered_subset @ SY158 @ ( boole_POSet @ SY157 ) )
| ~ ( upper_relstr_subset @ SY158 @ ( boole_POSet @ SY157 ) )
| ~ ( element @ SY158 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY157 ) ) ) )
| ( net_str @ ( net_of_bool_filter @ SV41 @ SY157 @ SY158 ) @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(450,plain,
! [SV42: $i] :
( ( ~ ( ~ ! [SY159: $i,SY160: $i] :
( ( empty_carrier @ SY159 )
| ~ ( one_sorted_str @ SY159 )
| ( empty_carrier @ SY160 )
| ~ ( net_str @ SY160 @ SY159 )
| ! [SY161: $i] :
( ( SV42 != SY161 )
| ~ ( element @ SY161 @ ( powerset @ ( the_carrier @ SY159 ) ) )
| ~ ( is_eventually_in @ SY159 @ SY160 @ SY161 ) )
| ( in @ SV42 @ ( a_2_1_yellow19 @ SY159 @ SY160 ) ) )
| ~ ! [SY162: $i,SY163: $i] :
( ( empty_carrier @ SY162 )
| ~ ( one_sorted_str @ SY162 )
| ( empty_carrier @ SY163 )
| ~ ( net_str @ SY163 @ SY162 )
| ~ ( in @ SV42 @ ( a_2_1_yellow19 @ SY162 @ SY163 ) )
| ~ ( ~ ~ ( ( SV42
!= ( sK6_D @ SY163 @ SY162 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SY163 @ SY162 @ SV42 ) @ ( powerset @ ( the_carrier @ SY162 ) ) ) )
| ~ ( is_eventually_in @ SY162 @ SY163 @ ( sK6_D @ SY163 @ SY162 @ SV42 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(451,plain,
! [SV43: $i] :
( ( ( empty_carrier @ SV43 )
| ~ ( one_sorted_str @ SV43 )
| ~ ( ~ ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
| ~ ~ ( empty @ ( sK11_B @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(452,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(453,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_suprema_relstr @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_infima_relstr @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(454,plain,
( ( ~ ~ ( empty @ sK19_A )
| ~ ( relation @ sK19_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(455,plain,
! [SV44: $i] :
( ( ( empty_carrier @ SV44 )
| ~ ( reflexive_relstr @ SV44 )
| ~ ( rel_str @ SV44 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV44 ) ) )
| ~ ( finite @ ( sK5_B @ SV44 ) ) )
| ~ ( directed_subset @ ( sK5_B @ SV44 ) @ SV44 ) )
| ~ ( filtered_subset @ ( sK5_B @ SV44 ) @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(456,plain,
! [SV45: $i] :
( ( ~ ( rel_str @ SV45 )
| ~ ( ~ ~ ( ~ ( element @ ( sK10_B @ SV45 ) @ ( powerset @ ( the_carrier @ SV45 ) ) )
| ~ ( lower_relstr_subset @ ( sK10_B @ SV45 ) @ SV45 ) )
| ~ ( upper_relstr_subset @ ( sK10_B @ SV45 ) @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(457,plain,
( ( ~ ~ ( empty @ sK23_A )
| ~ ( finite @ sK23_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(458,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ( empty_carrier @ SX1 )
| ~ ( net_str @ SX1 @ SX0 )
| ~ ( empty @ ( filter_of_net_str @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ( empty_carrier @ SX1 )
| ~ ( net_str @ SX1 @ SX0 )
| ( upper_relstr_subset @ ( filter_of_net_str @ SX0 @ SX1 ) @ ( boole_POSet @ ( cast_as_carrier_subset @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(459,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_infima_relstr @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_infima_relstr @ SX0 )
| ( filtered_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(460,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(461,plain,
! [SV46: $i] :
( ( ( empty @ SV46 )
| ~ ( ~ ~ ( ~ ( element @ ( sK16_B @ SV46 ) @ ( powerset @ SV46 ) )
| ~ ~ ( empty @ ( sK16_B @ SV46 ) ) )
| ~ ( finite @ ( sK16_B @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(462,plain,
! [SV47: $i] :
( ( ( empty @ SV47 )
| ~ ( ~ ~ ( ~ ( element @ ( sK13_B @ SV47 ) @ ( powerset @ SV47 ) )
| ~ ~ ( empty @ ( sK13_B @ SV47 ) ) )
| ~ ( finite @ ( sK13_B @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(463,plain,
( ( ~ ! [SX0: $i] : ( rel_str @ ( boole_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( boole_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(464,plain,
! [SV48: $i] :
( ( ~ ( ~ ! [SY164: $i,SY165: $i] :
( ~ ( relation_of2 @ SY165 @ SV48 @ SY164 )
| ( relation_of2_as_subset @ SY165 @ SV48 @ SY164 ) )
| ~ ! [SY166: $i,SY167: $i] :
( ~ ( relation_of2_as_subset @ SY167 @ SV48 @ SY166 )
| ( relation_of2 @ SY167 @ SV48 @ SY166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(465,plain,
( ( ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( lower_bounded_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( lower_bounded_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( filtered_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(466,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SY127 )
| ~ ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( upper_relstr_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( proper_element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) )
| ~ ( element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) )
| ~ ( ( sK2_SY127
!= ( filter_of_net_str @ sK1_A @ ( net_of_bool_filter @ sK1_A @ ( cast_as_carrier_subset @ sK1_A ) @ sK2_SY127 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(467,plain,
( ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(468,plain,
( ( ~ ! [SX0: $i] :
~ ( empty @ ( singleton @ SX0 ) )
| ~ ! [SX0: $i] : ( finite @ ( singleton @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(469,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(470,plain,
! [SV49: $i] :
( ( ( empty_carrier @ SV49 )
| ~ ( rel_str @ SV49 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_B @ SV49 ) @ ( powerset @ ( the_carrier @ SV49 ) ) )
| ~ ~ ( empty @ ( sK9_B @ SV49 ) ) )
| ~ ( lower_relstr_subset @ ( sK9_B @ SV49 ) @ SV49 ) )
| ~ ( upper_relstr_subset @ ( sK9_B @ SV49 ) @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(471,plain,
! [SV50: $i] :
( ( ~ ( ~ ~ ( ~ ( element @ ( sK17_B @ SV50 ) @ ( powerset @ ( powerset @ SV50 ) ) )
| ~ ~ ( empty @ ( sK17_B @ SV50 ) ) )
| ~ ( finite @ ( sK17_B @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(472,plain,
! [SV51: $i] :
( ( ! [SY168: $i] :
( ~ ( ~ ( ~ ( in @ ( sK3_C @ SY168 @ SV51 ) @ SV51 )
| ~ ( in @ ( sK3_C @ SY168 @ SV51 ) @ SY168 ) )
| ~ ( ( in @ ( sK3_C @ SY168 @ SV51 ) @ SV51 )
| ( in @ ( sK3_C @ SY168 @ SV51 ) @ SY168 ) ) )
| ( SV51 = SY168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(473,plain,
( ( ~ ( one_sorted_str @ sK15_A )
| ~ ~ ( empty_carrier @ sK15_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(474,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(475,plain,
( ( ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( upper_bounded_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( upper_bounded_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( directed_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(476,plain,
! [SV52: $i] :
( ( ~ ( ~ ( element @ ( sK18_B @ SV52 ) @ ( powerset @ SV52 ) )
| ~ ( empty @ ( sK18_B @ SV52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(477,plain,
! [SV53: $i] :
( ( ~ ( one_sorted_str @ SV53 )
| ~ ( ~ ~ ( ~ ( element @ ( sK14_B @ SV53 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV53 ) ) ) )
| ~ ~ ( empty @ ( sK14_B @ SV53 ) ) )
| ~ ( finite @ ( sK14_B @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(478,plain,
! [SV54: $i] :
( ( ~ ( rel_str @ SV54 )
| ~ ( ~ ~ ( ~ ( directed_subset @ ( sK20_B @ SV54 ) @ SV54 )
| ~ ( element @ ( sK20_B @ SV54 ) @ ( powerset @ ( the_carrier @ SV54 ) ) ) )
| ~ ( filtered_subset @ ( sK20_B @ SV54 ) @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(479,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ( lower_relstr_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ( upper_relstr_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(480,plain,
( ( ~ ( empty @ sK22_A )
| ~ ( relation @ sK22_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(481,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_suprema_relstr @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_suprema_relstr @ SX0 )
| ( directed_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(482,plain,
! [SV1: $i] :
( ( ( ~ ( empty @ SV1 ) )
= $true )
| ( ( finite @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(483,plain,
! [SV2: $i] :
( ( ( ~ ( rel_str @ SV2 ) )
= $true )
| ( ( ~ ( with_suprema_relstr @ SV2 )
| ~ ( empty_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(484,plain,
! [SV3: $i] :
( ( ( ~ ( empty @ SV3 ) )
= $true )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(485,plain,
! [SV55: $i,SV4: $i] :
( ( ! [SY169: $i] :
( ~ ( element @ SY169 @ ( powerset @ ( cartesian_product2 @ SV4 @ SV55 ) ) )
| ( relation @ SY169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(486,plain,
! [SV5: $i] :
( ( ( ~ ( finite @ SV5 ) )
= $true )
| ( ( ! [SY130: $i] :
( ~ ( element @ SY130 @ ( powerset @ SV5 ) )
| ( finite @ SY130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(487,plain,
! [SV6: $i] :
( ( ( ~ ( rel_str @ SV6 ) )
= $true )
| ( ( ~ ( with_infima_relstr @ SV6 )
| ~ ( empty_carrier @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(488,plain,
! [SV7: $i] :
( ( ( ( empty_carrier @ SV7 )
| ~ ( one_sorted_str @ SV7 ) )
= $true )
| ( ( ! [SY131: $i] :
( ( empty_carrier @ SY131 )
| ~ ( net_str @ SY131 @ SV7 )
| ( ( filter_of_net_str @ SV7 @ SY131 )
= ( a_2_1_yellow19 @ SV7 @ SY131 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(489,plain,
! [SV8: $i] :
( ( ( ~ ( one_sorted_str @ SV8 ) )
= $true )
| ( ( element @ ( cast_as_carrier_subset @ SV8 ) @ ( powerset @ ( the_carrier @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(490,plain,
! [SV56: $i,SV9: $i] :
( ( ( empty_carrier @ SV9 )
| ~ ( one_sorted_str @ SV9 )
| ( empty_carrier @ SV56 )
| ~ ( net_str @ SV56 @ SV9 )
| ( element @ ( filter_of_net_str @ SV9 @ SV56 ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV9 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(491,plain,
! [SV10: $i] :
( ( ( ~ ( rel_str @ SV10 ) )
= $true )
| ( ( one_sorted_str @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(492,plain,
! [SV11: $i] :
( ( ( ~ ( one_sorted_str @ SV11 ) )
= $true )
| ( ( ! [SY133: $i] :
( ~ ( net_str @ SY133 @ SV11 )
| ( rel_str @ SY133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(493,plain,
! [SV57: $i,SV12: $i] :
( ( ! [SY170: $i] :
( ~ ( relation_of2_as_subset @ SY170 @ SV12 @ SV57 )
| ( element @ SY170 @ ( powerset @ ( cartesian_product2 @ SV12 @ SV57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(494,plain,
! [SV13: $i] :
( ( ( ~ ( one_sorted_str @ SV13 ) )
= $true )
| ( ( net_str @ ( sK25_B @ SV13 ) @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(495,plain,
! [SV15: $i] :
( ( ( ( empty_carrier @ SV15 )
| ~ ( one_sorted_str @ SV15 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(496,plain,
! [SV16: $i] :
( ( empty @ ( powerset @ SV16 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(497,plain,
! [SV17: $i] :
( ( ( ( empty_carrier @ SV17 )
| ~ ( one_sorted_str @ SV17 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(498,plain,
! [SV18: $i] :
( ( empty @ ( singleton @ SV18 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(499,plain,
! [SV19: $i] :
( ( ( ( empty_carrier @ SV19 )
| ~ ( rel_str @ SV19 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(500,plain,
! [SV58: $i,SV20: $i] :
( ( ( empty @ SV20 )
| ( empty @ SV58 )
| ~ ( empty @ ( cartesian_product2 @ SV20 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(501,plain,
! [SV59: $i,SV21: $i] :
( ( ~ ( in @ SV21 @ SV59 )
| ( element @ SV21 @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(502,plain,
! [SV60: $i,SV22: $i] :
( ( ~ ( element @ SV22 @ SV60 )
| ( empty @ SV60 )
| ( in @ SV22 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(503,plain,
! [SV23: $i] :
( ( ( empty @ SV23 )
= $true )
| ( ( ! [SY139: $i] :
( ( empty @ SY139 )
| ~ ( filtered_subset @ SY139 @ ( boole_POSet @ SV23 ) )
| ~ ( upper_relstr_subset @ SY139 @ ( boole_POSet @ SV23 ) )
| ~ ( proper_element @ SY139 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
| ~ ( element @ SY139 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
| ! [C: $i] :
( ~ ( empty @ C )
| ~ ( in @ C @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(504,plain,
! [SV24: $i,SV61: $i] :
( ( ! [SY171: $i] :
( ~ ( element @ SV61 @ ( powerset @ SY171 ) )
| ~ ( in @ SV24 @ SV61 )
| ( element @ SV24 @ SY171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(505,plain,
! [SV25: $i,SV62: $i] :
( ( ! [SY172: $i] :
( ~ ( element @ SV62 @ ( powerset @ SY172 ) )
| ~ ( in @ SV25 @ SV62 )
| ~ ( empty @ SY172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(506,plain,
! [SV26: $i] :
( ( ( ~ ( empty @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(507,plain,
! [SV27: $i,SV63: $i] :
( ( ~ ( empty @ SV63 )
| ~ ( in @ SV27 @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(508,plain,
! [SV64: $i,SV28: $i] :
( ( ( SV28 = SV64 )
| ~ ( empty @ SV28 )
| ~ ( empty @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(509,plain,
! [SV65: $i,SV29: $i] :
( ( ~ ( in @ SV29 @ SV65 )
| ~ ( in @ SV65 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(510,plain,
! [SV30: $i] :
( ( ( ~ ( rel_str @ SV30 ) )
= $true )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV30 ) @ ( the_carrier @ SV30 ) @ ( the_carrier @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(511,plain,
! [SV31: $i,SV66: $i] :
( ( relation_of2_as_subset @ ( sK7_C @ SV66 @ SV31 ) @ SV31 @ SV66 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(512,plain,
! [SV32: $i] :
( ( ( ~ ( finite @ SV32 ) )
= $true )
| ( ( ! [SY149: $i] : ( finite @ ( set_difference @ SV32 @ SY149 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(513,plain,
! [SV67: $i,SV33: $i] :
( ( ~ ( finite @ SV33 )
| ~ ( finite @ SV67 )
| ( finite @ ( cartesian_product2 @ SV33 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(514,plain,
! [SV68: $i,SV34: $i] :
( ( ~ ( relation @ SV34 )
| ~ ( relation @ SV68 )
| ( relation @ ( set_difference @ SV34 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(515,plain,
! [SV36: $i] :
( ( ( ( empty_carrier @ SV36 )
| ~ ( one_sorted_str @ SV36 ) )
= $true )
| ( ( ! [SY152: $i] :
( ( empty @ SY152 )
| ~ ( filtered_subset @ SY152 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
| ~ ( upper_relstr_subset @ SY152 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
| ~ ( element @ SY152 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) ) )
| ( ( set_difference @ SY152 @ ( singleton @ empty_set ) )
= ( filter_of_net_str @ SV36 @ ( net_of_bool_filter @ SV36 @ ( cast_as_carrier_subset @ SV36 ) @ SY152 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(516,plain,
! [SV39: $i] :
( ( ( ~ ( one_sorted_str @ SV39 ) )
= $true )
| ( ( ~ ( ~ ( net_str @ ( sK12_B @ SV39 ) @ SV39 )
| ~ ( strict_net_str @ ( sK12_B @ SV39 ) @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(517,plain,
! [SV40: $i] :
( ( ( empty @ SV40 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK21_B @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( empty @ ( sK21_B @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(518,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ! [SY153: $i,SY154: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY153 )
| ~ ( element @ SY153 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY154 )
| ~ ( filtered_subset @ SY154 @ ( boole_POSet @ SY153 ) )
| ~ ( upper_relstr_subset @ SY154 @ ( boole_POSet @ SY153 ) )
| ~ ( element @ SY154 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY153 ) ) ) )
| ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SY153 @ SY154 ) ) )
| ~ ! [SY155: $i,SY156: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY155 )
| ~ ( element @ SY155 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY156 )
| ~ ( filtered_subset @ SY156 @ ( boole_POSet @ SY155 ) )
| ~ ( upper_relstr_subset @ SY156 @ ( boole_POSet @ SY155 ) )
| ~ ( element @ SY156 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY155 ) ) ) )
| ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SY155 @ SY156 ) @ SV41 ) ) )
| ~ ! [SY157: $i,SY158: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY157 )
| ~ ( element @ SY157 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY158 )
| ~ ( filtered_subset @ SY158 @ ( boole_POSet @ SY157 ) )
| ~ ( upper_relstr_subset @ SY158 @ ( boole_POSet @ SY157 ) )
| ~ ( element @ SY158 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY157 ) ) ) )
| ( net_str @ ( net_of_bool_filter @ SV41 @ SY157 @ SY158 ) @ SV41 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(519,plain,
! [SV42: $i] :
( ( ~ ! [SY159: $i,SY160: $i] :
( ( empty_carrier @ SY159 )
| ~ ( one_sorted_str @ SY159 )
| ( empty_carrier @ SY160 )
| ~ ( net_str @ SY160 @ SY159 )
| ! [SY161: $i] :
( ( SV42 != SY161 )
| ~ ( element @ SY161 @ ( powerset @ ( the_carrier @ SY159 ) ) )
| ~ ( is_eventually_in @ SY159 @ SY160 @ SY161 ) )
| ( in @ SV42 @ ( a_2_1_yellow19 @ SY159 @ SY160 ) ) )
| ~ ! [SY162: $i,SY163: $i] :
( ( empty_carrier @ SY162 )
| ~ ( one_sorted_str @ SY162 )
| ( empty_carrier @ SY163 )
| ~ ( net_str @ SY163 @ SY162 )
| ~ ( in @ SV42 @ ( a_2_1_yellow19 @ SY162 @ SY163 ) )
| ~ ( ~ ~ ( ( SV42
!= ( sK6_D @ SY163 @ SY162 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SY163 @ SY162 @ SV42 ) @ ( powerset @ ( the_carrier @ SY162 ) ) ) )
| ~ ( is_eventually_in @ SY162 @ SY163 @ ( sK6_D @ SY163 @ SY162 @ SV42 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(520,plain,
! [SV43: $i] :
( ( ( ( empty_carrier @ SV43 )
| ~ ( one_sorted_str @ SV43 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
| ~ ~ ( empty @ ( sK11_B @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(521,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(522,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(523,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_suprema_relstr @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(524,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_infima_relstr @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(525,plain,
( ( ~ ~ ( empty @ sK19_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(526,plain,
( ( ~ ( relation @ sK19_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(527,plain,
! [SV44: $i] :
( ( ( ( empty_carrier @ SV44 )
| ~ ( reflexive_relstr @ SV44 )
| ~ ( rel_str @ SV44 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV44 ) ) )
| ~ ( finite @ ( sK5_B @ SV44 ) ) )
| ~ ( directed_subset @ ( sK5_B @ SV44 ) @ SV44 ) )
| ~ ( filtered_subset @ ( sK5_B @ SV44 ) @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(528,plain,
! [SV45: $i] :
( ( ( ~ ( rel_str @ SV45 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK10_B @ SV45 ) @ ( powerset @ ( the_carrier @ SV45 ) ) )
| ~ ( lower_relstr_subset @ ( sK10_B @ SV45 ) @ SV45 ) )
| ~ ( upper_relstr_subset @ ( sK10_B @ SV45 ) @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(529,plain,
( ( ~ ~ ( empty @ sK23_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[457]) ).
thf(530,plain,
( ( ~ ( finite @ sK23_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[457]) ).
thf(531,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ( empty_carrier @ SX1 )
| ~ ( net_str @ SX1 @ SX0 )
| ~ ( empty @ ( filter_of_net_str @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(532,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ( empty_carrier @ SX1 )
| ~ ( net_str @ SX1 @ SX0 )
| ( upper_relstr_subset @ ( filter_of_net_str @ SX0 @ SX1 ) @ ( boole_POSet @ ( cast_as_carrier_subset @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(533,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_infima_relstr @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(534,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_infima_relstr @ SX0 )
| ( filtered_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(535,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(536,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(537,plain,
! [SV46: $i] :
( ( ( empty @ SV46 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK16_B @ SV46 ) @ ( powerset @ SV46 ) )
| ~ ~ ( empty @ ( sK16_B @ SV46 ) ) )
| ~ ( finite @ ( sK16_B @ SV46 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(538,plain,
! [SV47: $i] :
( ( ( empty @ SV47 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK13_B @ SV47 ) @ ( powerset @ SV47 ) )
| ~ ~ ( empty @ ( sK13_B @ SV47 ) ) )
| ~ ( finite @ ( sK13_B @ SV47 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(539,plain,
( ( ~ ! [SX0: $i] : ( rel_str @ ( boole_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(540,plain,
( ( ~ ! [SX0: $i] : ( strict_rel_str @ ( boole_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(541,plain,
! [SV48: $i] :
( ( ~ ! [SY164: $i,SY165: $i] :
( ~ ( relation_of2 @ SY165 @ SV48 @ SY164 )
| ( relation_of2_as_subset @ SY165 @ SV48 @ SY164 ) )
| ~ ! [SY166: $i,SY167: $i] :
( ~ ( relation_of2_as_subset @ SY167 @ SV48 @ SY166 )
| ( relation_of2 @ SY167 @ SV48 @ SY166 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(542,plain,
( ( ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( lower_bounded_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(543,plain,
( ( ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( lower_bounded_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( filtered_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(544,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SY127 )
| ~ ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( upper_relstr_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( proper_element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) )
| ~ ( element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[466]) ).
thf(545,plain,
( ( ~ ( ( sK2_SY127
!= ( filter_of_net_str @ sK1_A @ ( net_of_bool_filter @ sK1_A @ ( cast_as_carrier_subset @ sK1_A ) @ sK2_SY127 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[466]) ).
thf(546,plain,
( ( ~ ( relation @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(547,plain,
( ( ~ ( relation_empty_yielding @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(548,plain,
( ( ~ ! [SX0: $i] :
~ ( empty @ ( singleton @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(549,plain,
( ( ~ ! [SX0: $i] : ( finite @ ( singleton @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(550,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(551,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(552,plain,
! [SV49: $i] :
( ( ( ( empty_carrier @ SV49 )
| ~ ( rel_str @ SV49 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_B @ SV49 ) @ ( powerset @ ( the_carrier @ SV49 ) ) )
| ~ ~ ( empty @ ( sK9_B @ SV49 ) ) )
| ~ ( lower_relstr_subset @ ( sK9_B @ SV49 ) @ SV49 ) )
| ~ ( upper_relstr_subset @ ( sK9_B @ SV49 ) @ SV49 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(553,plain,
! [SV50: $i] :
( ( ~ ~ ( ~ ( element @ ( sK17_B @ SV50 ) @ ( powerset @ ( powerset @ SV50 ) ) )
| ~ ~ ( empty @ ( sK17_B @ SV50 ) ) )
| ~ ( finite @ ( sK17_B @ SV50 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(554,plain,
! [SV51: $i,SV69: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV51 )
| ~ ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV69 ) )
| ~ ( ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV51 )
| ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV69 ) ) )
| ( SV51 = SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(555,plain,
( ( ~ ( one_sorted_str @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[473]) ).
thf(556,plain,
( ( ~ ~ ( empty_carrier @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[473]) ).
thf(557,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(558,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(559,plain,
( ( ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( upper_bounded_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(560,plain,
( ( ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( upper_bounded_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( directed_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(561,plain,
! [SV52: $i] :
( ( ~ ( element @ ( sK18_B @ SV52 ) @ ( powerset @ SV52 ) )
| ~ ( empty @ ( sK18_B @ SV52 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(562,plain,
! [SV53: $i] :
( ( ( ~ ( one_sorted_str @ SV53 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK14_B @ SV53 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV53 ) ) ) )
| ~ ~ ( empty @ ( sK14_B @ SV53 ) ) )
| ~ ( finite @ ( sK14_B @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(563,plain,
! [SV54: $i] :
( ( ( ~ ( rel_str @ SV54 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( directed_subset @ ( sK20_B @ SV54 ) @ SV54 )
| ~ ( element @ ( sK20_B @ SV54 ) @ ( powerset @ ( the_carrier @ SV54 ) ) ) )
| ~ ( filtered_subset @ ( sK20_B @ SV54 ) @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(564,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ( lower_relstr_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[479]) ).
thf(565,plain,
( ( ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ( upper_relstr_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[479]) ).
thf(566,plain,
( ( ~ ( empty @ sK22_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(567,plain,
( ( ~ ( relation @ sK22_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(568,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_suprema_relstr @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(569,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_suprema_relstr @ SX0 )
| ( directed_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(570,plain,
! [SV1: $i] :
( ( ( empty @ SV1 )
= $false )
| ( ( finite @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(571,plain,
! [SV2: $i] :
( ( ( rel_str @ SV2 )
= $false )
| ( ( ~ ( with_suprema_relstr @ SV2 )
| ~ ( empty_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(572,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(573,plain,
! [SV55: $i,SV4: $i,SV70: $i] :
( ( ~ ( element @ SV70 @ ( powerset @ ( cartesian_product2 @ SV4 @ SV55 ) ) )
| ( relation @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(574,plain,
! [SV5: $i] :
( ( ( finite @ SV5 )
= $false )
| ( ( ! [SY130: $i] :
( ~ ( element @ SY130 @ ( powerset @ SV5 ) )
| ( finite @ SY130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(575,plain,
! [SV6: $i] :
( ( ( rel_str @ SV6 )
= $false )
| ( ( ~ ( with_infima_relstr @ SV6 )
| ~ ( empty_carrier @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(576,plain,
! [SV7: $i] :
( ( ( empty_carrier @ SV7 )
= $true )
| ( ( ~ ( one_sorted_str @ SV7 ) )
= $true )
| ( ( ! [SY131: $i] :
( ( empty_carrier @ SY131 )
| ~ ( net_str @ SY131 @ SV7 )
| ( ( filter_of_net_str @ SV7 @ SY131 )
= ( a_2_1_yellow19 @ SV7 @ SY131 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(577,plain,
! [SV8: $i] :
( ( ( one_sorted_str @ SV8 )
= $false )
| ( ( element @ ( cast_as_carrier_subset @ SV8 ) @ ( powerset @ ( the_carrier @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(578,plain,
! [SV56: $i,SV9: $i] :
( ( ( ( empty_carrier @ SV9 )
| ~ ( one_sorted_str @ SV9 )
| ( empty_carrier @ SV56 )
| ~ ( net_str @ SV56 @ SV9 ) )
= $true )
| ( ( element @ ( filter_of_net_str @ SV9 @ SV56 ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(579,plain,
! [SV10: $i] :
( ( ( rel_str @ SV10 )
= $false )
| ( ( one_sorted_str @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(580,plain,
! [SV11: $i] :
( ( ( one_sorted_str @ SV11 )
= $false )
| ( ( ! [SY133: $i] :
( ~ ( net_str @ SY133 @ SV11 )
| ( rel_str @ SY133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(581,plain,
! [SV57: $i,SV12: $i,SV71: $i] :
( ( ~ ( relation_of2_as_subset @ SV71 @ SV12 @ SV57 )
| ( element @ SV71 @ ( powerset @ ( cartesian_product2 @ SV12 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(582,plain,
! [SV13: $i] :
( ( ( one_sorted_str @ SV13 )
= $false )
| ( ( net_str @ ( sK25_B @ SV13 ) @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(583,plain,
! [SV15: $i] :
( ( ( empty_carrier @ SV15 )
= $true )
| ( ( ~ ( one_sorted_str @ SV15 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(584,plain,
! [SV17: $i] :
( ( ( empty_carrier @ SV17 )
= $true )
| ( ( ~ ( one_sorted_str @ SV17 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(585,plain,
! [SV19: $i] :
( ( ( empty_carrier @ SV19 )
= $true )
| ( ( ~ ( rel_str @ SV19 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(586,plain,
! [SV58: $i,SV20: $i] :
( ( ( ( empty @ SV20 )
| ( empty @ SV58 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV20 @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(587,plain,
! [SV59: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV59 ) )
= $true )
| ( ( element @ SV21 @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(588,plain,
! [SV60: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ SV60 ) )
= $true )
| ( ( ( empty @ SV60 )
| ( in @ SV22 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(589,plain,
! [SV23: $i,SV72: $i] :
( ( ( ( empty @ SV72 )
| ~ ( filtered_subset @ SV72 @ ( boole_POSet @ SV23 ) )
| ~ ( upper_relstr_subset @ SV72 @ ( boole_POSet @ SV23 ) )
| ~ ( proper_element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
| ~ ( element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
| ! [SY173: $i] :
( ~ ( empty @ SY173 )
| ~ ( in @ SY173 @ SV72 ) ) )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(590,plain,
! [SV24: $i,SV73: $i,SV61: $i] :
( ( ~ ( element @ SV61 @ ( powerset @ SV73 ) )
| ~ ( in @ SV24 @ SV61 )
| ( element @ SV24 @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(591,plain,
! [SV25: $i,SV74: $i,SV62: $i] :
( ( ~ ( element @ SV62 @ ( powerset @ SV74 ) )
| ~ ( in @ SV25 @ SV62 )
| ~ ( empty @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(592,plain,
! [SV26: $i] :
( ( ( empty @ SV26 )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(593,plain,
! [SV27: $i,SV63: $i] :
( ( ( ~ ( empty @ SV63 ) )
= $true )
| ( ( ~ ( in @ SV27 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[507]) ).
thf(594,plain,
! [SV64: $i,SV28: $i] :
( ( ( ( SV28 = SV64 )
| ~ ( empty @ SV28 ) )
= $true )
| ( ( ~ ( empty @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(595,plain,
! [SV65: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV65 ) )
= $true )
| ( ( ~ ( in @ SV65 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(596,plain,
! [SV30: $i] :
( ( ( rel_str @ SV30 )
= $false )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV30 ) @ ( the_carrier @ SV30 ) @ ( the_carrier @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(597,plain,
! [SV32: $i] :
( ( ( finite @ SV32 )
= $false )
| ( ( ! [SY149: $i] : ( finite @ ( set_difference @ SV32 @ SY149 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(598,plain,
! [SV67: $i,SV33: $i] :
( ( ( ~ ( finite @ SV33 )
| ~ ( finite @ SV67 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV33 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(599,plain,
! [SV68: $i,SV34: $i] :
( ( ( ~ ( relation @ SV34 )
| ~ ( relation @ SV68 ) )
= $true )
| ( ( relation @ ( set_difference @ SV34 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(600,plain,
! [SV36: $i] :
( ( ( empty_carrier @ SV36 )
= $true )
| ( ( ~ ( one_sorted_str @ SV36 ) )
= $true )
| ( ( ! [SY152: $i] :
( ( empty @ SY152 )
| ~ ( filtered_subset @ SY152 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
| ~ ( upper_relstr_subset @ SY152 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
| ~ ( element @ SY152 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) ) )
| ( ( set_difference @ SY152 @ ( singleton @ empty_set ) )
= ( filter_of_net_str @ SV36 @ ( net_of_bool_filter @ SV36 @ ( cast_as_carrier_subset @ SV36 ) @ SY152 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(601,plain,
! [SV39: $i] :
( ( ( one_sorted_str @ SV39 )
= $false )
| ( ( ~ ( ~ ( net_str @ ( sK12_B @ SV39 ) @ SV39 )
| ~ ( strict_net_str @ ( sK12_B @ SV39 ) @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(602,plain,
! [SV40: $i] :
( ( ( ~ ( element @ ( sK21_B @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( empty @ ( sK21_B @ SV40 ) ) )
= $false )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(603,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ! [SY153: $i,SY154: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY153 )
| ~ ( element @ SY153 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY154 )
| ~ ( filtered_subset @ SY154 @ ( boole_POSet @ SY153 ) )
| ~ ( upper_relstr_subset @ SY154 @ ( boole_POSet @ SY153 ) )
| ~ ( element @ SY154 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY153 ) ) ) )
| ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SY153 @ SY154 ) ) )
| ~ ! [SY155: $i,SY156: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY155 )
| ~ ( element @ SY155 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY156 )
| ~ ( filtered_subset @ SY156 @ ( boole_POSet @ SY155 ) )
| ~ ( upper_relstr_subset @ SY156 @ ( boole_POSet @ SY155 ) )
| ~ ( element @ SY156 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY155 ) ) ) )
| ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SY155 @ SY156 ) @ SV41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[518]) ).
thf(604,plain,
! [SV41: $i] :
( ( ~ ! [SY157: $i,SY158: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY157 )
| ~ ( element @ SY157 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY158 )
| ~ ( filtered_subset @ SY158 @ ( boole_POSet @ SY157 ) )
| ~ ( upper_relstr_subset @ SY158 @ ( boole_POSet @ SY157 ) )
| ~ ( element @ SY158 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY157 ) ) ) )
| ( net_str @ ( net_of_bool_filter @ SV41 @ SY157 @ SY158 ) @ SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[518]) ).
thf(605,plain,
! [SV42: $i] :
( ( ~ ! [SY159: $i,SY160: $i] :
( ( empty_carrier @ SY159 )
| ~ ( one_sorted_str @ SY159 )
| ( empty_carrier @ SY160 )
| ~ ( net_str @ SY160 @ SY159 )
| ! [SY161: $i] :
( ( SV42 != SY161 )
| ~ ( element @ SY161 @ ( powerset @ ( the_carrier @ SY159 ) ) )
| ~ ( is_eventually_in @ SY159 @ SY160 @ SY161 ) )
| ( in @ SV42 @ ( a_2_1_yellow19 @ SY159 @ SY160 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[519]) ).
thf(606,plain,
! [SV42: $i] :
( ( ~ ! [SY162: $i,SY163: $i] :
( ( empty_carrier @ SY162 )
| ~ ( one_sorted_str @ SY162 )
| ( empty_carrier @ SY163 )
| ~ ( net_str @ SY163 @ SY162 )
| ~ ( in @ SV42 @ ( a_2_1_yellow19 @ SY162 @ SY163 ) )
| ~ ( ~ ~ ( ( SV42
!= ( sK6_D @ SY163 @ SY162 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SY163 @ SY162 @ SV42 ) @ ( powerset @ ( the_carrier @ SY162 ) ) ) )
| ~ ( is_eventually_in @ SY162 @ SY163 @ ( sK6_D @ SY163 @ SY162 @ SV42 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[519]) ).
thf(607,plain,
! [SV43: $i] :
( ( ( empty_carrier @ SV43 )
= $true )
| ( ( ~ ( one_sorted_str @ SV43 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
| ~ ~ ( empty @ ( sK11_B @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(608,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(609,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(610,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_suprema_relstr @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(611,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_infima_relstr @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(612,plain,
( ( ~ ( empty @ sK19_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(613,plain,
( ( relation @ sK19_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(614,plain,
! [SV44: $i] :
( ( ( ( empty_carrier @ SV44 )
| ~ ( reflexive_relstr @ SV44 ) )
= $true )
| ( ( ~ ( rel_str @ SV44 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV44 ) ) )
| ~ ( finite @ ( sK5_B @ SV44 ) ) )
| ~ ( directed_subset @ ( sK5_B @ SV44 ) @ SV44 ) )
| ~ ( filtered_subset @ ( sK5_B @ SV44 ) @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(615,plain,
! [SV45: $i] :
( ( ( rel_str @ SV45 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK10_B @ SV45 ) @ ( powerset @ ( the_carrier @ SV45 ) ) )
| ~ ( lower_relstr_subset @ ( sK10_B @ SV45 ) @ SV45 ) )
| ~ ( upper_relstr_subset @ ( sK10_B @ SV45 ) @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(616,plain,
( ( ~ ( empty @ sK23_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(617,plain,
( ( finite @ sK23_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(618,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ( empty_carrier @ SX1 )
| ~ ( net_str @ SX1 @ SX0 )
| ~ ( empty @ ( filter_of_net_str @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(619,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ( empty_carrier @ SX1 )
| ~ ( net_str @ SX1 @ SX0 )
| ( upper_relstr_subset @ ( filter_of_net_str @ SX0 @ SX1 ) @ ( boole_POSet @ ( cast_as_carrier_subset @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(620,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_infima_relstr @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[533]) ).
thf(621,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_infima_relstr @ SX0 )
| ( filtered_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(622,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[535]) ).
thf(623,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(624,plain,
! [SV46: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK16_B @ SV46 ) @ ( powerset @ SV46 ) )
| ~ ~ ( empty @ ( sK16_B @ SV46 ) ) )
| ~ ( finite @ ( sK16_B @ SV46 ) ) )
= $false )
| ( ( empty @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(625,plain,
! [SV47: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK13_B @ SV47 ) @ ( powerset @ SV47 ) )
| ~ ~ ( empty @ ( sK13_B @ SV47 ) ) )
| ~ ( finite @ ( sK13_B @ SV47 ) ) )
= $false )
| ( ( empty @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(626,plain,
( ( ! [SX0: $i] : ( rel_str @ ( boole_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(627,plain,
( ( ! [SX0: $i] : ( strict_rel_str @ ( boole_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(628,plain,
! [SV48: $i] :
( ( ~ ! [SY164: $i,SY165: $i] :
( ~ ( relation_of2 @ SY165 @ SV48 @ SY164 )
| ( relation_of2_as_subset @ SY165 @ SV48 @ SY164 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[541]) ).
thf(629,plain,
! [SV48: $i] :
( ( ~ ! [SY166: $i,SY167: $i] :
( ~ ( relation_of2_as_subset @ SY167 @ SV48 @ SY166 )
| ( relation_of2 @ SY167 @ SV48 @ SY166 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[541]) ).
thf(630,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( lower_bounded_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[542]) ).
thf(631,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( lower_bounded_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( filtered_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[543]) ).
thf(632,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SY127 )
| ~ ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( upper_relstr_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( proper_element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) )
| ~ ( element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[544]) ).
thf(633,plain,
( ( sK2_SY127
!= ( filter_of_net_str @ sK1_A @ ( net_of_bool_filter @ sK1_A @ ( cast_as_carrier_subset @ sK1_A ) @ sK2_SY127 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[545]) ).
thf(634,plain,
( ( relation @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[546]) ).
thf(635,plain,
( ( relation_empty_yielding @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(636,plain,
( ( ! [SX0: $i] :
~ ( empty @ ( singleton @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(637,plain,
( ( ! [SX0: $i] : ( finite @ ( singleton @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(638,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(639,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(640,plain,
! [SV49: $i] :
( ( ( empty_carrier @ SV49 )
= $true )
| ( ( ~ ( rel_str @ SV49 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_B @ SV49 ) @ ( powerset @ ( the_carrier @ SV49 ) ) )
| ~ ~ ( empty @ ( sK9_B @ SV49 ) ) )
| ~ ( lower_relstr_subset @ ( sK9_B @ SV49 ) @ SV49 ) )
| ~ ( upper_relstr_subset @ ( sK9_B @ SV49 ) @ SV49 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(641,plain,
! [SV50: $i] :
( ( ~ ~ ( ~ ( element @ ( sK17_B @ SV50 ) @ ( powerset @ ( powerset @ SV50 ) ) )
| ~ ~ ( empty @ ( sK17_B @ SV50 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[553]) ).
thf(642,plain,
! [SV50: $i] :
( ( ~ ( finite @ ( sK17_B @ SV50 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[553]) ).
thf(643,plain,
! [SV51: $i,SV69: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV51 )
| ~ ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV69 ) )
| ~ ( ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV51 )
| ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV69 ) ) ) )
= $true )
| ( ( SV51 = SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(644,plain,
( ( one_sorted_str @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(645,plain,
( ( ~ ( empty_carrier @ sK15_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[556]) ).
thf(646,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(647,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(648,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( upper_bounded_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(649,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( upper_bounded_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( directed_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(650,plain,
! [SV52: $i] :
( ( ~ ( element @ ( sK18_B @ SV52 ) @ ( powerset @ SV52 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[561]) ).
thf(651,plain,
! [SV52: $i] :
( ( ~ ( empty @ ( sK18_B @ SV52 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[561]) ).
thf(652,plain,
! [SV53: $i] :
( ( ( one_sorted_str @ SV53 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK14_B @ SV53 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV53 ) ) ) )
| ~ ~ ( empty @ ( sK14_B @ SV53 ) ) )
| ~ ( finite @ ( sK14_B @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(653,plain,
! [SV54: $i] :
( ( ( rel_str @ SV54 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( directed_subset @ ( sK20_B @ SV54 ) @ SV54 )
| ~ ( element @ ( sK20_B @ SV54 ) @ ( powerset @ ( the_carrier @ SV54 ) ) ) )
| ~ ( filtered_subset @ ( sK20_B @ SV54 ) @ SV54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(654,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ( lower_relstr_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(655,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ( upper_relstr_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(656,plain,
( ( empty @ sK22_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(657,plain,
( ( relation @ sK22_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(658,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_suprema_relstr @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[568]) ).
thf(659,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( with_suprema_relstr @ SX0 )
| ( directed_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(660,plain,
! [SV2: $i] :
( ( ( ~ ( with_suprema_relstr @ SV2 ) )
= $true )
| ( ( ~ ( empty_carrier @ SV2 ) )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(661,plain,
! [SV55: $i,SV4: $i,SV70: $i] :
( ( ( ~ ( element @ SV70 @ ( powerset @ ( cartesian_product2 @ SV4 @ SV55 ) ) ) )
= $true )
| ( ( relation @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(662,plain,
! [SV5: $i,SV75: $i] :
( ( ( ~ ( element @ SV75 @ ( powerset @ SV5 ) )
| ( finite @ SV75 ) )
= $true )
| ( ( finite @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(663,plain,
! [SV6: $i] :
( ( ( ~ ( with_infima_relstr @ SV6 ) )
= $true )
| ( ( ~ ( empty_carrier @ SV6 ) )
= $true )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[575]) ).
thf(664,plain,
! [SV7: $i] :
( ( ( one_sorted_str @ SV7 )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( ! [SY131: $i] :
( ( empty_carrier @ SY131 )
| ~ ( net_str @ SY131 @ SV7 )
| ( ( filter_of_net_str @ SV7 @ SY131 )
= ( a_2_1_yellow19 @ SV7 @ SY131 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(665,plain,
! [SV56: $i,SV9: $i] :
( ( ( ( empty_carrier @ SV9 )
| ~ ( one_sorted_str @ SV9 )
| ( empty_carrier @ SV56 ) )
= $true )
| ( ( ~ ( net_str @ SV56 @ SV9 ) )
= $true )
| ( ( element @ ( filter_of_net_str @ SV9 @ SV56 ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(666,plain,
! [SV11: $i,SV76: $i] :
( ( ( ~ ( net_str @ SV76 @ SV11 )
| ( rel_str @ SV76 ) )
= $true )
| ( ( one_sorted_str @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(667,plain,
! [SV57: $i,SV12: $i,SV71: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV71 @ SV12 @ SV57 ) )
= $true )
| ( ( element @ SV71 @ ( powerset @ ( cartesian_product2 @ SV12 @ SV57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[581]) ).
thf(668,plain,
! [SV15: $i] :
( ( ( one_sorted_str @ SV15 )
= $false )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(669,plain,
! [SV17: $i] :
( ( ( one_sorted_str @ SV17 )
= $false )
| ( ( empty_carrier @ SV17 )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(670,plain,
! [SV19: $i] :
( ( ( rel_str @ SV19 )
= $false )
| ( ( empty_carrier @ SV19 )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(671,plain,
! [SV58: $i,SV20: $i] :
( ( ( empty @ SV20 )
= $true )
| ( ( empty @ SV58 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV20 @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(672,plain,
! [SV59: $i,SV21: $i] :
( ( ( in @ SV21 @ SV59 )
= $false )
| ( ( element @ SV21 @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(673,plain,
! [SV60: $i,SV22: $i] :
( ( ( element @ SV22 @ SV60 )
= $false )
| ( ( ( empty @ SV60 )
| ( in @ SV22 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(674,plain,
! [SV23: $i,SV72: $i] :
( ( ( ( empty @ SV72 )
| ~ ( filtered_subset @ SV72 @ ( boole_POSet @ SV23 ) )
| ~ ( upper_relstr_subset @ SV72 @ ( boole_POSet @ SV23 ) )
| ~ ( proper_element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
| ~ ( element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) ) )
= $true )
| ( ( ! [SY173: $i] :
( ~ ( empty @ SY173 )
| ~ ( in @ SY173 @ SV72 ) ) )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(675,plain,
! [SV24: $i,SV73: $i,SV61: $i] :
( ( ( ~ ( element @ SV61 @ ( powerset @ SV73 ) )
| ~ ( in @ SV24 @ SV61 ) )
= $true )
| ( ( element @ SV24 @ SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(676,plain,
! [SV25: $i,SV74: $i,SV62: $i] :
( ( ( ~ ( element @ SV62 @ ( powerset @ SV74 ) )
| ~ ( in @ SV25 @ SV62 ) )
= $true )
| ( ( ~ ( empty @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(677,plain,
! [SV27: $i,SV63: $i] :
( ( ( empty @ SV63 )
= $false )
| ( ( ~ ( in @ SV27 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(678,plain,
! [SV64: $i,SV28: $i] :
( ( ( SV28 = SV64 )
= $true )
| ( ( ~ ( empty @ SV28 ) )
= $true )
| ( ( ~ ( empty @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(679,plain,
! [SV65: $i,SV29: $i] :
( ( ( in @ SV29 @ SV65 )
= $false )
| ( ( ~ ( in @ SV65 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(680,plain,
! [SV77: $i,SV32: $i] :
( ( ( finite @ ( set_difference @ SV32 @ SV77 ) )
= $true )
| ( ( finite @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(681,plain,
! [SV67: $i,SV33: $i] :
( ( ( ~ ( finite @ SV33 ) )
= $true )
| ( ( ~ ( finite @ SV67 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV33 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(682,plain,
! [SV68: $i,SV34: $i] :
( ( ( ~ ( relation @ SV34 ) )
= $true )
| ( ( ~ ( relation @ SV68 ) )
= $true )
| ( ( relation @ ( set_difference @ SV34 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(683,plain,
! [SV36: $i] :
( ( ( one_sorted_str @ SV36 )
= $false )
| ( ( empty_carrier @ SV36 )
= $true )
| ( ( ! [SY152: $i] :
( ( empty @ SY152 )
| ~ ( filtered_subset @ SY152 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
| ~ ( upper_relstr_subset @ SY152 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
| ~ ( element @ SY152 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) ) )
| ( ( set_difference @ SY152 @ ( singleton @ empty_set ) )
= ( filter_of_net_str @ SV36 @ ( net_of_bool_filter @ SV36 @ ( cast_as_carrier_subset @ SV36 ) @ SY152 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(684,plain,
! [SV39: $i] :
( ( ( ~ ( net_str @ ( sK12_B @ SV39 ) @ SV39 )
| ~ ( strict_net_str @ ( sK12_B @ SV39 ) @ SV39 ) )
= $false )
| ( ( one_sorted_str @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(685,plain,
! [SV40: $i] :
( ( ( ~ ( element @ ( sK21_B @ SV40 ) @ ( powerset @ SV40 ) ) )
= $false )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[602]) ).
thf(686,plain,
! [SV40: $i] :
( ( ( ~ ~ ( empty @ ( sK21_B @ SV40 ) ) )
= $false )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[602]) ).
thf(687,plain,
! [SV41: $i] :
( ( ~ ( ~ ! [SY153: $i,SY154: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY153 )
| ~ ( element @ SY153 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY154 )
| ~ ( filtered_subset @ SY154 @ ( boole_POSet @ SY153 ) )
| ~ ( upper_relstr_subset @ SY154 @ ( boole_POSet @ SY153 ) )
| ~ ( element @ SY154 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY153 ) ) ) )
| ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SY153 @ SY154 ) ) )
| ~ ! [SY155: $i,SY156: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY155 )
| ~ ( element @ SY155 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY156 )
| ~ ( filtered_subset @ SY156 @ ( boole_POSet @ SY155 ) )
| ~ ( upper_relstr_subset @ SY156 @ ( boole_POSet @ SY155 ) )
| ~ ( element @ SY156 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY155 ) ) ) )
| ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SY155 @ SY156 ) @ SV41 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[603]) ).
thf(688,plain,
! [SV41: $i] :
( ( ! [SY157: $i,SY158: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY157 )
| ~ ( element @ SY157 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY158 )
| ~ ( filtered_subset @ SY158 @ ( boole_POSet @ SY157 ) )
| ~ ( upper_relstr_subset @ SY158 @ ( boole_POSet @ SY157 ) )
| ~ ( element @ SY158 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY157 ) ) ) )
| ( net_str @ ( net_of_bool_filter @ SV41 @ SY157 @ SY158 ) @ SV41 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[604]) ).
thf(689,plain,
! [SV42: $i] :
( ( ! [SY159: $i,SY160: $i] :
( ( empty_carrier @ SY159 )
| ~ ( one_sorted_str @ SY159 )
| ( empty_carrier @ SY160 )
| ~ ( net_str @ SY160 @ SY159 )
| ! [SY161: $i] :
( ( SV42 != SY161 )
| ~ ( element @ SY161 @ ( powerset @ ( the_carrier @ SY159 ) ) )
| ~ ( is_eventually_in @ SY159 @ SY160 @ SY161 ) )
| ( in @ SV42 @ ( a_2_1_yellow19 @ SY159 @ SY160 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[605]) ).
thf(690,plain,
! [SV42: $i] :
( ( ! [SY162: $i,SY163: $i] :
( ( empty_carrier @ SY162 )
| ~ ( one_sorted_str @ SY162 )
| ( empty_carrier @ SY163 )
| ~ ( net_str @ SY163 @ SY162 )
| ~ ( in @ SV42 @ ( a_2_1_yellow19 @ SY162 @ SY163 ) )
| ~ ( ~ ~ ( ( SV42
!= ( sK6_D @ SY163 @ SY162 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SY163 @ SY162 @ SV42 ) @ ( powerset @ ( the_carrier @ SY162 ) ) ) )
| ~ ( is_eventually_in @ SY162 @ SY163 @ ( sK6_D @ SY163 @ SY162 @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(691,plain,
! [SV43: $i] :
( ( ( one_sorted_str @ SV43 )
= $false )
| ( ( empty_carrier @ SV43 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
| ~ ~ ( empty @ ( sK11_B @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(692,plain,
! [SV78: $i] :
( ( ! [SY174: $i] :
( ( ( set_difference @ SV78 @ ( singleton @ SY174 ) )
!= SV78 )
| ~ ( in @ SY174 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(693,plain,
! [SV79: $i] :
( ( ! [SY175: $i] :
( ( in @ SY175 @ SV79 )
| ( ( set_difference @ SV79 @ ( singleton @ SY175 ) )
= SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(694,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_suprema_relstr @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(695,plain,
! [SV80: $i] :
( ( ~ ( rel_str @ SV80 )
| ( empty_carrier @ SV80 )
| ~ ( complete_relstr @ SV80 )
| ( with_infima_relstr @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(696,plain,
( ( empty @ sK19_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(697,plain,
! [SV44: $i] :
( ( ( empty_carrier @ SV44 )
= $true )
| ( ( ~ ( reflexive_relstr @ SV44 ) )
= $true )
| ( ( ~ ( rel_str @ SV44 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV44 ) ) )
| ~ ( finite @ ( sK5_B @ SV44 ) ) )
| ~ ( directed_subset @ ( sK5_B @ SV44 ) @ SV44 ) )
| ~ ( filtered_subset @ ( sK5_B @ SV44 ) @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(698,plain,
! [SV45: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK10_B @ SV45 ) @ ( powerset @ ( the_carrier @ SV45 ) ) )
| ~ ( lower_relstr_subset @ ( sK10_B @ SV45 ) @ SV45 ) )
| ~ ( upper_relstr_subset @ ( sK10_B @ SV45 ) @ SV45 ) )
= $false )
| ( ( rel_str @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(699,plain,
( ( empty @ sK23_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(700,plain,
! [SV81: $i] :
( ( ! [SY176: $i] :
( ( empty_carrier @ SV81 )
| ~ ( one_sorted_str @ SV81 )
| ( empty_carrier @ SY176 )
| ~ ( net_str @ SY176 @ SV81 )
| ~ ( empty @ ( filter_of_net_str @ SV81 @ SY176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(701,plain,
! [SV82: $i] :
( ( ! [SY177: $i] :
( ( empty_carrier @ SV82 )
| ~ ( one_sorted_str @ SV82 )
| ( empty_carrier @ SY177 )
| ~ ( net_str @ SY177 @ SV82 )
| ( upper_relstr_subset @ ( filter_of_net_str @ SV82 @ SY177 ) @ ( boole_POSet @ ( cast_as_carrier_subset @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(702,plain,
! [SV83: $i] :
( ( ~ ( rel_str @ SV83 )
| ~ ( with_infima_relstr @ SV83 )
| ~ ( empty @ ( cast_as_carrier_subset @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(703,plain,
! [SV84: $i] :
( ( ~ ( rel_str @ SV84 )
| ~ ( with_infima_relstr @ SV84 )
| ( filtered_subset @ ( cast_as_carrier_subset @ SV84 ) @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(704,plain,
! [SV85: $i] :
( ( ! [SY178: $i] :
( ~ ( element @ SV85 @ ( powerset @ SY178 ) )
| ( subset @ SV85 @ SY178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(705,plain,
! [SV86: $i] :
( ( ! [SY179: $i] :
( ~ ( subset @ SV86 @ SY179 )
| ( element @ SV86 @ ( powerset @ SY179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(706,plain,
! [SV46: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK16_B @ SV46 ) @ ( powerset @ SV46 ) )
| ~ ~ ( empty @ ( sK16_B @ SV46 ) ) ) )
= $false )
| ( ( empty @ SV46 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[624]) ).
thf(707,plain,
! [SV46: $i] :
( ( ( ~ ( finite @ ( sK16_B @ SV46 ) ) )
= $false )
| ( ( empty @ SV46 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[624]) ).
thf(708,plain,
! [SV47: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK13_B @ SV47 ) @ ( powerset @ SV47 ) )
| ~ ~ ( empty @ ( sK13_B @ SV47 ) ) ) )
= $false )
| ( ( empty @ SV47 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[625]) ).
thf(709,plain,
! [SV47: $i] :
( ( ( ~ ( finite @ ( sK13_B @ SV47 ) ) )
= $false )
| ( ( empty @ SV47 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[625]) ).
thf(710,plain,
! [SV87: $i] :
( ( rel_str @ ( boole_POSet @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(711,plain,
! [SV88: $i] :
( ( strict_rel_str @ ( boole_POSet @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(712,plain,
! [SV48: $i] :
( ( ! [SY164: $i,SY165: $i] :
( ~ ( relation_of2 @ SY165 @ SV48 @ SY164 )
| ( relation_of2_as_subset @ SY165 @ SV48 @ SY164 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[628]) ).
thf(713,plain,
! [SV48: $i] :
( ( ! [SY166: $i,SY167: $i] :
( ~ ( relation_of2_as_subset @ SY167 @ SV48 @ SY166 )
| ( relation_of2 @ SY167 @ SV48 @ SY166 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[629]) ).
thf(714,plain,
! [SV89: $i] :
( ( ( empty_carrier @ SV89 )
| ~ ( lower_bounded_relstr @ SV89 )
| ~ ( rel_str @ SV89 )
| ~ ( empty @ ( cast_as_carrier_subset @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(715,plain,
! [SV90: $i] :
( ( ( empty_carrier @ SV90 )
| ~ ( lower_bounded_relstr @ SV90 )
| ~ ( rel_str @ SV90 )
| ( filtered_subset @ ( cast_as_carrier_subset @ SV90 ) @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(716,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SY127 )
| ~ ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( upper_relstr_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( proper_element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) )
| ~ ( element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(717,plain,
( ( sK2_SY127
= ( filter_of_net_str @ sK1_A @ ( net_of_bool_filter @ sK1_A @ ( cast_as_carrier_subset @ sK1_A ) @ sK2_SY127 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(718,plain,
! [SV91: $i] :
( ( ~ ( empty @ ( singleton @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(719,plain,
! [SV92: $i] :
( ( finite @ ( singleton @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(720,plain,
! [SV49: $i] :
( ( ( rel_str @ SV49 )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_B @ SV49 ) @ ( powerset @ ( the_carrier @ SV49 ) ) )
| ~ ~ ( empty @ ( sK9_B @ SV49 ) ) )
| ~ ( lower_relstr_subset @ ( sK9_B @ SV49 ) @ SV49 ) )
| ~ ( upper_relstr_subset @ ( sK9_B @ SV49 ) @ SV49 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(721,plain,
! [SV50: $i] :
( ( ~ ( ~ ( element @ ( sK17_B @ SV50 ) @ ( powerset @ ( powerset @ SV50 ) ) )
| ~ ~ ( empty @ ( sK17_B @ SV50 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[641]) ).
thf(722,plain,
! [SV50: $i] :
( ( finite @ ( sK17_B @ SV50 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[642]) ).
thf(723,plain,
! [SV51: $i,SV69: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV51 )
| ~ ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV69 ) )
| ~ ( ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV51 )
| ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV69 ) ) )
= $false )
| ( ( SV51 = SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(724,plain,
( ( empty_carrier @ sK15_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(725,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(726,plain,
! [SV93: $i] :
( ( ( empty_carrier @ SV93 )
| ~ ( upper_bounded_relstr @ SV93 )
| ~ ( rel_str @ SV93 )
| ~ ( empty @ ( cast_as_carrier_subset @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(727,plain,
! [SV94: $i] :
( ( ( empty_carrier @ SV94 )
| ~ ( upper_bounded_relstr @ SV94 )
| ~ ( rel_str @ SV94 )
| ( directed_subset @ ( cast_as_carrier_subset @ SV94 ) @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(728,plain,
! [SV52: $i] :
( ( element @ ( sK18_B @ SV52 ) @ ( powerset @ SV52 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(729,plain,
! [SV52: $i] :
( ( empty @ ( sK18_B @ SV52 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[651]) ).
thf(730,plain,
! [SV53: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK14_B @ SV53 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV53 ) ) ) )
| ~ ~ ( empty @ ( sK14_B @ SV53 ) ) )
| ~ ( finite @ ( sK14_B @ SV53 ) ) )
= $false )
| ( ( one_sorted_str @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(731,plain,
! [SV54: $i] :
( ( ( ~ ~ ( ~ ( directed_subset @ ( sK20_B @ SV54 ) @ SV54 )
| ~ ( element @ ( sK20_B @ SV54 ) @ ( powerset @ ( the_carrier @ SV54 ) ) ) )
| ~ ( filtered_subset @ ( sK20_B @ SV54 ) @ SV54 ) )
= $false )
| ( ( rel_str @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(732,plain,
( ( ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ( lower_relstr_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(733,plain,
! [SV95: $i] :
( ( ( empty_carrier @ SV95 )
| ~ ( rel_str @ SV95 )
| ( upper_relstr_subset @ ( cast_as_carrier_subset @ SV95 ) @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(734,plain,
! [SV96: $i] :
( ( ~ ( rel_str @ SV96 )
| ~ ( with_suprema_relstr @ SV96 )
| ~ ( empty @ ( cast_as_carrier_subset @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(735,plain,
! [SV97: $i] :
( ( ~ ( rel_str @ SV97 )
| ~ ( with_suprema_relstr @ SV97 )
| ( directed_subset @ ( cast_as_carrier_subset @ SV97 ) @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(736,plain,
! [SV2: $i] :
( ( ( with_suprema_relstr @ SV2 )
= $false )
| ( ( ~ ( empty_carrier @ SV2 ) )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(737,plain,
! [SV55: $i,SV4: $i,SV70: $i] :
( ( ( element @ SV70 @ ( powerset @ ( cartesian_product2 @ SV4 @ SV55 ) ) )
= $false )
| ( ( relation @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(738,plain,
! [SV5: $i,SV75: $i] :
( ( ( ~ ( element @ SV75 @ ( powerset @ SV5 ) ) )
= $true )
| ( ( finite @ SV75 )
= $true )
| ( ( finite @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(739,plain,
! [SV6: $i] :
( ( ( with_infima_relstr @ SV6 )
= $false )
| ( ( ~ ( empty_carrier @ SV6 ) )
= $true )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(740,plain,
! [SV7: $i,SV98: $i] :
( ( ( ( empty_carrier @ SV98 )
| ~ ( net_str @ SV98 @ SV7 )
| ( ( filter_of_net_str @ SV7 @ SV98 )
= ( a_2_1_yellow19 @ SV7 @ SV98 ) ) )
= $true )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(741,plain,
! [SV56: $i,SV9: $i] :
( ( ( ( empty_carrier @ SV9 )
| ~ ( one_sorted_str @ SV9 ) )
= $true )
| ( ( empty_carrier @ SV56 )
= $true )
| ( ( ~ ( net_str @ SV56 @ SV9 ) )
= $true )
| ( ( element @ ( filter_of_net_str @ SV9 @ SV56 ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[665]) ).
thf(742,plain,
! [SV11: $i,SV76: $i] :
( ( ( ~ ( net_str @ SV76 @ SV11 ) )
= $true )
| ( ( rel_str @ SV76 )
= $true )
| ( ( one_sorted_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(743,plain,
! [SV57: $i,SV12: $i,SV71: $i] :
( ( ( relation_of2_as_subset @ SV71 @ SV12 @ SV57 )
= $false )
| ( ( element @ SV71 @ ( powerset @ ( cartesian_product2 @ SV12 @ SV57 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(744,plain,
! [SV15: $i] :
( ( ( empty @ ( the_carrier @ SV15 ) )
= $false )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( one_sorted_str @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(745,plain,
! [SV17: $i] :
( ( ( empty @ ( cast_as_carrier_subset @ SV17 ) )
= $false )
| ( ( empty_carrier @ SV17 )
= $true )
| ( ( one_sorted_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(746,plain,
! [SV19: $i] :
( ( ( empty @ ( cast_as_carrier_subset @ SV19 ) )
= $false )
| ( ( empty_carrier @ SV19 )
= $true )
| ( ( rel_str @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(747,plain,
! [SV58: $i,SV20: $i] :
( ( ( empty @ ( cartesian_product2 @ SV20 @ SV58 ) )
= $false )
| ( ( empty @ SV58 )
= $true )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(748,plain,
! [SV22: $i,SV60: $i] :
( ( ( empty @ SV60 )
= $true )
| ( ( in @ SV22 @ SV60 )
= $true )
| ( ( element @ SV22 @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(749,plain,
! [SV23: $i,SV72: $i] :
( ( ( ( empty @ SV72 )
| ~ ( filtered_subset @ SV72 @ ( boole_POSet @ SV23 ) )
| ~ ( upper_relstr_subset @ SV72 @ ( boole_POSet @ SV23 ) )
| ~ ( proper_element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) ) )
= $true )
| ( ( ~ ( element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) ) )
= $true )
| ( ( ! [SY173: $i] :
( ~ ( empty @ SY173 )
| ~ ( in @ SY173 @ SV72 ) ) )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(750,plain,
! [SV24: $i,SV73: $i,SV61: $i] :
( ( ( ~ ( element @ SV61 @ ( powerset @ SV73 ) ) )
= $true )
| ( ( ~ ( in @ SV24 @ SV61 ) )
= $true )
| ( ( element @ SV24 @ SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(751,plain,
! [SV25: $i,SV74: $i,SV62: $i] :
( ( ( ~ ( element @ SV62 @ ( powerset @ SV74 ) ) )
= $true )
| ( ( ~ ( in @ SV25 @ SV62 ) )
= $true )
| ( ( ~ ( empty @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(752,plain,
! [SV63: $i,SV27: $i] :
( ( ( in @ SV27 @ SV63 )
= $false )
| ( ( empty @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(753,plain,
! [SV64: $i,SV28: $i] :
( ( ( empty @ SV28 )
= $false )
| ( ( SV28 = SV64 )
= $true )
| ( ( ~ ( empty @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(754,plain,
! [SV29: $i,SV65: $i] :
( ( ( in @ SV65 @ SV29 )
= $false )
| ( ( in @ SV29 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(755,plain,
! [SV67: $i,SV33: $i] :
( ( ( finite @ SV33 )
= $false )
| ( ( ~ ( finite @ SV67 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV33 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(756,plain,
! [SV68: $i,SV34: $i] :
( ( ( relation @ SV34 )
= $false )
| ( ( ~ ( relation @ SV68 ) )
= $true )
| ( ( relation @ ( set_difference @ SV34 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(757,plain,
! [SV36: $i,SV99: $i] :
( ( ( ( empty @ SV99 )
| ~ ( filtered_subset @ SV99 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
| ~ ( upper_relstr_subset @ SV99 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
| ~ ( element @ SV99 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) ) )
| ( ( set_difference @ SV99 @ ( singleton @ empty_set ) )
= ( filter_of_net_str @ SV36 @ ( net_of_bool_filter @ SV36 @ ( cast_as_carrier_subset @ SV36 ) @ SV99 ) ) ) )
= $true )
| ( ( empty_carrier @ SV36 )
= $true )
| ( ( one_sorted_str @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(758,plain,
! [SV39: $i] :
( ( ( ~ ( net_str @ ( sK12_B @ SV39 ) @ SV39 ) )
= $false )
| ( ( one_sorted_str @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(759,plain,
! [SV39: $i] :
( ( ( ~ ( strict_net_str @ ( sK12_B @ SV39 ) @ SV39 ) )
= $false )
| ( ( one_sorted_str @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(760,plain,
! [SV40: $i] :
( ( ( element @ ( sK21_B @ SV40 ) @ ( powerset @ SV40 ) )
= $true )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[685]) ).
thf(761,plain,
! [SV40: $i] :
( ( ( ~ ( empty @ ( sK21_B @ SV40 ) ) )
= $true )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[686]) ).
thf(762,plain,
! [SV41: $i] :
( ( ~ ! [SY153: $i,SY154: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY153 )
| ~ ( element @ SY153 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY154 )
| ~ ( filtered_subset @ SY154 @ ( boole_POSet @ SY153 ) )
| ~ ( upper_relstr_subset @ SY154 @ ( boole_POSet @ SY153 ) )
| ~ ( element @ SY154 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY153 ) ) ) )
| ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SY153 @ SY154 ) ) )
| ~ ! [SY155: $i,SY156: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY155 )
| ~ ( element @ SY155 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY156 )
| ~ ( filtered_subset @ SY156 @ ( boole_POSet @ SY155 ) )
| ~ ( upper_relstr_subset @ SY156 @ ( boole_POSet @ SY155 ) )
| ~ ( element @ SY156 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY155 ) ) ) )
| ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SY155 @ SY156 ) @ SV41 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(763,plain,
! [SV100: $i,SV41: $i] :
( ( ! [SY180: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV100 )
| ~ ( element @ SV100 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY180 )
| ~ ( filtered_subset @ SY180 @ ( boole_POSet @ SV100 ) )
| ~ ( upper_relstr_subset @ SY180 @ ( boole_POSet @ SV100 ) )
| ~ ( element @ SY180 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV100 ) ) ) )
| ( net_str @ ( net_of_bool_filter @ SV41 @ SV100 @ SY180 ) @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(764,plain,
! [SV42: $i,SV101: $i] :
( ( ! [SY181: $i] :
( ( empty_carrier @ SV101 )
| ~ ( one_sorted_str @ SV101 )
| ( empty_carrier @ SY181 )
| ~ ( net_str @ SY181 @ SV101 )
| ! [SY182: $i] :
( ( SV42 != SY182 )
| ~ ( element @ SY182 @ ( powerset @ ( the_carrier @ SV101 ) ) )
| ~ ( is_eventually_in @ SV101 @ SY181 @ SY182 ) )
| ( in @ SV42 @ ( a_2_1_yellow19 @ SV101 @ SY181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(765,plain,
! [SV42: $i,SV102: $i] :
( ( ! [SY183: $i] :
( ( empty_carrier @ SV102 )
| ~ ( one_sorted_str @ SV102 )
| ( empty_carrier @ SY183 )
| ~ ( net_str @ SY183 @ SV102 )
| ~ ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SY183 ) )
| ~ ( ~ ~ ( ( SV42
!= ( sK6_D @ SY183 @ SV102 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SY183 @ SV102 @ SV42 ) @ ( powerset @ ( the_carrier @ SV102 ) ) ) )
| ~ ( is_eventually_in @ SV102 @ SY183 @ ( sK6_D @ SY183 @ SV102 @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(766,plain,
! [SV43: $i] :
( ( ( ~ ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
| ~ ~ ( empty @ ( sK11_B @ SV43 ) ) )
= $false )
| ( ( empty_carrier @ SV43 )
= $true )
| ( ( one_sorted_str @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(767,plain,
! [SV103: $i,SV78: $i] :
( ( ( ( set_difference @ SV78 @ ( singleton @ SV103 ) )
!= SV78 )
| ~ ( in @ SV103 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(768,plain,
! [SV79: $i,SV104: $i] :
( ( ( in @ SV104 @ SV79 )
| ( ( set_difference @ SV79 @ ( singleton @ SV104 ) )
= SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(769,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(770,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_suprema_relstr @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(771,plain,
! [SV80: $i] :
( ( ( ~ ( rel_str @ SV80 ) )
= $true )
| ( ( ( empty_carrier @ SV80 )
| ~ ( complete_relstr @ SV80 )
| ( with_infima_relstr @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(772,plain,
! [SV44: $i] :
( ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( ~ ( rel_str @ SV44 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV44 ) ) )
| ~ ( finite @ ( sK5_B @ SV44 ) ) )
| ~ ( directed_subset @ ( sK5_B @ SV44 ) @ SV44 ) )
| ~ ( filtered_subset @ ( sK5_B @ SV44 ) @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(773,plain,
! [SV45: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK10_B @ SV45 ) @ ( powerset @ ( the_carrier @ SV45 ) ) )
| ~ ( lower_relstr_subset @ ( sK10_B @ SV45 ) @ SV45 ) ) )
= $false )
| ( ( rel_str @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[698]) ).
thf(774,plain,
! [SV45: $i] :
( ( ( ~ ( upper_relstr_subset @ ( sK10_B @ SV45 ) @ SV45 ) )
= $false )
| ( ( rel_str @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[698]) ).
thf(775,plain,
! [SV105: $i,SV81: $i] :
( ( ( empty_carrier @ SV81 )
| ~ ( one_sorted_str @ SV81 )
| ( empty_carrier @ SV105 )
| ~ ( net_str @ SV105 @ SV81 )
| ~ ( empty @ ( filter_of_net_str @ SV81 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(776,plain,
! [SV106: $i,SV82: $i] :
( ( ( empty_carrier @ SV82 )
| ~ ( one_sorted_str @ SV82 )
| ( empty_carrier @ SV106 )
| ~ ( net_str @ SV106 @ SV82 )
| ( upper_relstr_subset @ ( filter_of_net_str @ SV82 @ SV106 ) @ ( boole_POSet @ ( cast_as_carrier_subset @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(777,plain,
! [SV83: $i] :
( ( ( ~ ( rel_str @ SV83 )
| ~ ( with_infima_relstr @ SV83 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[702]) ).
thf(778,plain,
! [SV84: $i] :
( ( ( ~ ( rel_str @ SV84 )
| ~ ( with_infima_relstr @ SV84 ) )
= $true )
| ( ( filtered_subset @ ( cast_as_carrier_subset @ SV84 ) @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(779,plain,
! [SV107: $i,SV85: $i] :
( ( ~ ( element @ SV85 @ ( powerset @ SV107 ) )
| ( subset @ SV85 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(780,plain,
! [SV108: $i,SV86: $i] :
( ( ~ ( subset @ SV86 @ SV108 )
| ( element @ SV86 @ ( powerset @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(781,plain,
! [SV46: $i] :
( ( ( ~ ( ~ ( element @ ( sK16_B @ SV46 ) @ ( powerset @ SV46 ) )
| ~ ~ ( empty @ ( sK16_B @ SV46 ) ) ) )
= $true )
| ( ( empty @ SV46 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[706]) ).
thf(782,plain,
! [SV46: $i] :
( ( ( finite @ ( sK16_B @ SV46 ) )
= $true )
| ( ( empty @ SV46 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[707]) ).
thf(783,plain,
! [SV47: $i] :
( ( ( ~ ( ~ ( element @ ( sK13_B @ SV47 ) @ ( powerset @ SV47 ) )
| ~ ~ ( empty @ ( sK13_B @ SV47 ) ) ) )
= $true )
| ( ( empty @ SV47 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[708]) ).
thf(784,plain,
! [SV47: $i] :
( ( ( finite @ ( sK13_B @ SV47 ) )
= $true )
| ( ( empty @ SV47 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(785,plain,
! [SV109: $i,SV48: $i] :
( ( ! [SY184: $i] :
( ~ ( relation_of2 @ SY184 @ SV48 @ SV109 )
| ( relation_of2_as_subset @ SY184 @ SV48 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(786,plain,
! [SV110: $i,SV48: $i] :
( ( ! [SY185: $i] :
( ~ ( relation_of2_as_subset @ SY185 @ SV48 @ SV110 )
| ( relation_of2 @ SY185 @ SV48 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(787,plain,
! [SV89: $i] :
( ( ( ( empty_carrier @ SV89 )
| ~ ( lower_bounded_relstr @ SV89 )
| ~ ( rel_str @ SV89 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(788,plain,
! [SV90: $i] :
( ( ( ( empty_carrier @ SV90 )
| ~ ( lower_bounded_relstr @ SV90 )
| ~ ( rel_str @ SV90 ) )
= $true )
| ( ( filtered_subset @ ( cast_as_carrier_subset @ SV90 ) @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(789,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SY127 )
| ~ ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( upper_relstr_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( proper_element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[716]) ).
thf(790,plain,
( ( ~ ( element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[716]) ).
thf(791,plain,
! [SV91: $i] :
( ( empty @ ( singleton @ SV91 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(792,plain,
! [SV49: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_B @ SV49 ) @ ( powerset @ ( the_carrier @ SV49 ) ) )
| ~ ~ ( empty @ ( sK9_B @ SV49 ) ) )
| ~ ( lower_relstr_subset @ ( sK9_B @ SV49 ) @ SV49 ) )
| ~ ( upper_relstr_subset @ ( sK9_B @ SV49 ) @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(793,plain,
! [SV50: $i] :
( ( ~ ( element @ ( sK17_B @ SV50 ) @ ( powerset @ ( powerset @ SV50 ) ) )
| ~ ~ ( empty @ ( sK17_B @ SV50 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(794,plain,
! [SV51: $i,SV69: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV51 )
| ~ ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV69 ) ) )
= $false )
| ( ( SV51 = SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[723]) ).
thf(795,plain,
! [SV51: $i,SV69: $i] :
( ( ( ~ ( ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV51 )
| ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV69 ) ) )
= $false )
| ( ( SV51 = SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[723]) ).
thf(796,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[725]) ).
thf(797,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[725]) ).
thf(798,plain,
! [SV93: $i] :
( ( ( ( empty_carrier @ SV93 )
| ~ ( upper_bounded_relstr @ SV93 )
| ~ ( rel_str @ SV93 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[726]) ).
thf(799,plain,
! [SV94: $i] :
( ( ( ( empty_carrier @ SV94 )
| ~ ( upper_bounded_relstr @ SV94 )
| ~ ( rel_str @ SV94 ) )
= $true )
| ( ( directed_subset @ ( cast_as_carrier_subset @ SV94 ) @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(800,plain,
! [SV53: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK14_B @ SV53 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV53 ) ) ) )
| ~ ~ ( empty @ ( sK14_B @ SV53 ) ) ) )
= $false )
| ( ( one_sorted_str @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[730]) ).
thf(801,plain,
! [SV53: $i] :
( ( ( ~ ( finite @ ( sK14_B @ SV53 ) ) )
= $false )
| ( ( one_sorted_str @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[730]) ).
thf(802,plain,
! [SV54: $i] :
( ( ( ~ ~ ( ~ ( directed_subset @ ( sK20_B @ SV54 ) @ SV54 )
| ~ ( element @ ( sK20_B @ SV54 ) @ ( powerset @ ( the_carrier @ SV54 ) ) ) ) )
= $false )
| ( ( rel_str @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(803,plain,
! [SV54: $i] :
( ( ( ~ ( filtered_subset @ ( sK20_B @ SV54 ) @ SV54 ) )
= $false )
| ( ( rel_str @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(804,plain,
( ( ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(805,plain,
( ( ~ ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ( lower_relstr_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(806,plain,
! [SV95: $i] :
( ( ( ( empty_carrier @ SV95 )
| ~ ( rel_str @ SV95 ) )
= $true )
| ( ( upper_relstr_subset @ ( cast_as_carrier_subset @ SV95 ) @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(807,plain,
! [SV96: $i] :
( ( ( ~ ( rel_str @ SV96 )
| ~ ( with_suprema_relstr @ SV96 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(808,plain,
! [SV97: $i] :
( ( ( ~ ( rel_str @ SV97 )
| ~ ( with_suprema_relstr @ SV97 ) )
= $true )
| ( ( directed_subset @ ( cast_as_carrier_subset @ SV97 ) @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(809,plain,
! [SV2: $i] :
( ( ( empty_carrier @ SV2 )
= $false )
| ( ( with_suprema_relstr @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(810,plain,
! [SV5: $i,SV75: $i] :
( ( ( element @ SV75 @ ( powerset @ SV5 ) )
= $false )
| ( ( finite @ SV75 )
= $true )
| ( ( finite @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(811,plain,
! [SV6: $i] :
( ( ( empty_carrier @ SV6 )
= $false )
| ( ( with_infima_relstr @ SV6 )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(812,plain,
! [SV7: $i,SV98: $i] :
( ( ( ( empty_carrier @ SV98 )
| ~ ( net_str @ SV98 @ SV7 ) )
= $true )
| ( ( ( filter_of_net_str @ SV7 @ SV98 )
= ( a_2_1_yellow19 @ SV7 @ SV98 ) )
= $true )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[740]) ).
thf(813,plain,
! [SV56: $i,SV9: $i] :
( ( ( empty_carrier @ SV9 )
= $true )
| ( ( ~ ( one_sorted_str @ SV9 ) )
= $true )
| ( ( empty_carrier @ SV56 )
= $true )
| ( ( ~ ( net_str @ SV56 @ SV9 ) )
= $true )
| ( ( element @ ( filter_of_net_str @ SV9 @ SV56 ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[741]) ).
thf(814,plain,
! [SV11: $i,SV76: $i] :
( ( ( net_str @ SV76 @ SV11 )
= $false )
| ( ( rel_str @ SV76 )
= $true )
| ( ( one_sorted_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(815,plain,
! [SV23: $i,SV72: $i] :
( ( ( ( empty @ SV72 )
| ~ ( filtered_subset @ SV72 @ ( boole_POSet @ SV23 ) )
| ~ ( upper_relstr_subset @ SV72 @ ( boole_POSet @ SV23 ) ) )
= $true )
| ( ( ~ ( proper_element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) ) )
= $true )
| ( ( ~ ( element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) ) )
= $true )
| ( ( ! [SY173: $i] :
( ~ ( empty @ SY173 )
| ~ ( in @ SY173 @ SV72 ) ) )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(816,plain,
! [SV24: $i,SV73: $i,SV61: $i] :
( ( ( element @ SV61 @ ( powerset @ SV73 ) )
= $false )
| ( ( ~ ( in @ SV24 @ SV61 ) )
= $true )
| ( ( element @ SV24 @ SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(817,plain,
! [SV25: $i,SV74: $i,SV62: $i] :
( ( ( element @ SV62 @ ( powerset @ SV74 ) )
= $false )
| ( ( ~ ( in @ SV25 @ SV62 ) )
= $true )
| ( ( ~ ( empty @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(818,plain,
! [SV28: $i,SV64: $i] :
( ( ( empty @ SV64 )
= $false )
| ( ( SV28 = SV64 )
= $true )
| ( ( empty @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(819,plain,
! [SV33: $i,SV67: $i] :
( ( ( finite @ SV67 )
= $false )
| ( ( finite @ SV33 )
= $false )
| ( ( finite @ ( cartesian_product2 @ SV33 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(820,plain,
! [SV34: $i,SV68: $i] :
( ( ( relation @ SV68 )
= $false )
| ( ( relation @ SV34 )
= $false )
| ( ( relation @ ( set_difference @ SV34 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(821,plain,
! [SV36: $i,SV99: $i] :
( ( ( ( empty @ SV99 )
| ~ ( filtered_subset @ SV99 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
| ~ ( upper_relstr_subset @ SV99 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
| ~ ( element @ SV99 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) ) ) )
= $true )
| ( ( ( set_difference @ SV99 @ ( singleton @ empty_set ) )
= ( filter_of_net_str @ SV36 @ ( net_of_bool_filter @ SV36 @ ( cast_as_carrier_subset @ SV36 ) @ SV99 ) ) )
= $true )
| ( ( empty_carrier @ SV36 )
= $true )
| ( ( one_sorted_str @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(822,plain,
! [SV39: $i] :
( ( ( net_str @ ( sK12_B @ SV39 ) @ SV39 )
= $true )
| ( ( one_sorted_str @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[758]) ).
thf(823,plain,
! [SV39: $i] :
( ( ( strict_net_str @ ( sK12_B @ SV39 ) @ SV39 )
= $true )
| ( ( one_sorted_str @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[759]) ).
thf(824,plain,
! [SV40: $i] :
( ( ( empty @ ( sK21_B @ SV40 ) )
= $false )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(825,plain,
! [SV41: $i] :
( ( ~ ! [SY153: $i,SY154: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY153 )
| ~ ( element @ SY153 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY154 )
| ~ ( filtered_subset @ SY154 @ ( boole_POSet @ SY153 ) )
| ~ ( upper_relstr_subset @ SY154 @ ( boole_POSet @ SY153 ) )
| ~ ( element @ SY154 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY153 ) ) ) )
| ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SY153 @ SY154 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[762]) ).
thf(826,plain,
! [SV41: $i] :
( ( ~ ! [SY155: $i,SY156: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY155 )
| ~ ( element @ SY155 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY156 )
| ~ ( filtered_subset @ SY156 @ ( boole_POSet @ SY155 ) )
| ~ ( upper_relstr_subset @ SY156 @ ( boole_POSet @ SY155 ) )
| ~ ( element @ SY156 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY155 ) ) ) )
| ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SY155 @ SY156 ) @ SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[762]) ).
thf(827,plain,
! [SV111: $i,SV100: $i,SV41: $i] :
( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV100 )
| ~ ( element @ SV100 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SV111 )
| ~ ( filtered_subset @ SV111 @ ( boole_POSet @ SV100 ) )
| ~ ( upper_relstr_subset @ SV111 @ ( boole_POSet @ SV100 ) )
| ~ ( element @ SV111 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV100 ) ) ) )
| ( net_str @ ( net_of_bool_filter @ SV41 @ SV100 @ SV111 ) @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(828,plain,
! [SV42: $i,SV112: $i,SV101: $i] :
( ( ( empty_carrier @ SV101 )
| ~ ( one_sorted_str @ SV101 )
| ( empty_carrier @ SV112 )
| ~ ( net_str @ SV112 @ SV101 )
| ! [SY186: $i] :
( ( SV42 != SY186 )
| ~ ( element @ SY186 @ ( powerset @ ( the_carrier @ SV101 ) ) )
| ~ ( is_eventually_in @ SV101 @ SV112 @ SY186 ) )
| ( in @ SV42 @ ( a_2_1_yellow19 @ SV101 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(829,plain,
! [SV42: $i,SV113: $i,SV102: $i] :
( ( ( empty_carrier @ SV102 )
| ~ ( one_sorted_str @ SV102 )
| ( empty_carrier @ SV113 )
| ~ ( net_str @ SV113 @ SV102 )
| ~ ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
| ~ ( ~ ~ ( ( SV42
!= ( sK6_D @ SV113 @ SV102 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SV113 @ SV102 @ SV42 ) @ ( powerset @ ( the_carrier @ SV102 ) ) ) )
| ~ ( is_eventually_in @ SV102 @ SV113 @ ( sK6_D @ SV113 @ SV102 @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(830,plain,
! [SV43: $i] :
( ( ( ~ ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) ) )
= $false )
| ( ( empty_carrier @ SV43 )
= $true )
| ( ( one_sorted_str @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[766]) ).
thf(831,plain,
! [SV43: $i] :
( ( ( ~ ~ ( empty @ ( sK11_B @ SV43 ) ) )
= $false )
| ( ( empty_carrier @ SV43 )
= $true )
| ( ( one_sorted_str @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[766]) ).
thf(832,plain,
! [SV103: $i,SV78: $i] :
( ( ( ( set_difference @ SV78 @ ( singleton @ SV103 ) )
!= SV78 )
= $true )
| ( ( ~ ( in @ SV103 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(833,plain,
! [SV79: $i,SV104: $i] :
( ( ( in @ SV104 @ SV79 )
= $true )
| ( ( ( set_difference @ SV79 @ ( singleton @ SV104 ) )
= SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(834,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[769]) ).
thf(835,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( complete_relstr @ SX0 )
| ( with_suprema_relstr @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[770]) ).
thf(836,plain,
! [SV80: $i] :
( ( ( rel_str @ SV80 )
= $false )
| ( ( ( empty_carrier @ SV80 )
| ~ ( complete_relstr @ SV80 )
| ( with_infima_relstr @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(837,plain,
! [SV44: $i] :
( ( ( rel_str @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV44 ) ) )
| ~ ( finite @ ( sK5_B @ SV44 ) ) )
| ~ ( directed_subset @ ( sK5_B @ SV44 ) @ SV44 ) )
| ~ ( filtered_subset @ ( sK5_B @ SV44 ) @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(838,plain,
! [SV45: $i] :
( ( ( ~ ( ~ ( element @ ( sK10_B @ SV45 ) @ ( powerset @ ( the_carrier @ SV45 ) ) )
| ~ ( lower_relstr_subset @ ( sK10_B @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( rel_str @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[773]) ).
thf(839,plain,
! [SV45: $i] :
( ( ( upper_relstr_subset @ ( sK10_B @ SV45 ) @ SV45 )
= $true )
| ( ( rel_str @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[774]) ).
thf(840,plain,
! [SV105: $i,SV81: $i] :
( ( ( ( empty_carrier @ SV81 )
| ~ ( one_sorted_str @ SV81 )
| ( empty_carrier @ SV105 )
| ~ ( net_str @ SV105 @ SV81 ) )
= $true )
| ( ( ~ ( empty @ ( filter_of_net_str @ SV81 @ SV105 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(841,plain,
! [SV106: $i,SV82: $i] :
( ( ( ( empty_carrier @ SV82 )
| ~ ( one_sorted_str @ SV82 )
| ( empty_carrier @ SV106 )
| ~ ( net_str @ SV106 @ SV82 ) )
= $true )
| ( ( upper_relstr_subset @ ( filter_of_net_str @ SV82 @ SV106 ) @ ( boole_POSet @ ( cast_as_carrier_subset @ SV82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(842,plain,
! [SV83: $i] :
( ( ( ~ ( rel_str @ SV83 ) )
= $true )
| ( ( ~ ( with_infima_relstr @ SV83 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(843,plain,
! [SV84: $i] :
( ( ( ~ ( rel_str @ SV84 ) )
= $true )
| ( ( ~ ( with_infima_relstr @ SV84 ) )
= $true )
| ( ( filtered_subset @ ( cast_as_carrier_subset @ SV84 ) @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(844,plain,
! [SV107: $i,SV85: $i] :
( ( ( ~ ( element @ SV85 @ ( powerset @ SV107 ) ) )
= $true )
| ( ( subset @ SV85 @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[779]) ).
thf(845,plain,
! [SV108: $i,SV86: $i] :
( ( ( ~ ( subset @ SV86 @ SV108 ) )
= $true )
| ( ( element @ SV86 @ ( powerset @ SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(846,plain,
! [SV46: $i] :
( ( ( ~ ( element @ ( sK16_B @ SV46 ) @ ( powerset @ SV46 ) )
| ~ ~ ( empty @ ( sK16_B @ SV46 ) ) )
= $false )
| ( ( empty @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(847,plain,
! [SV47: $i] :
( ( ( ~ ( element @ ( sK13_B @ SV47 ) @ ( powerset @ SV47 ) )
| ~ ~ ( empty @ ( sK13_B @ SV47 ) ) )
= $false )
| ( ( empty @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(848,plain,
! [SV109: $i,SV48: $i,SV114: $i] :
( ( ~ ( relation_of2 @ SV114 @ SV48 @ SV109 )
| ( relation_of2_as_subset @ SV114 @ SV48 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(849,plain,
! [SV110: $i,SV48: $i,SV115: $i] :
( ( ~ ( relation_of2_as_subset @ SV115 @ SV48 @ SV110 )
| ( relation_of2 @ SV115 @ SV48 @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(850,plain,
! [SV89: $i] :
( ( ( ( empty_carrier @ SV89 )
| ~ ( lower_bounded_relstr @ SV89 ) )
= $true )
| ( ( ~ ( rel_str @ SV89 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[787]) ).
thf(851,plain,
! [SV90: $i] :
( ( ( ( empty_carrier @ SV90 )
| ~ ( lower_bounded_relstr @ SV90 ) )
= $true )
| ( ( ~ ( rel_str @ SV90 ) )
= $true )
| ( ( filtered_subset @ ( cast_as_carrier_subset @ SV90 ) @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(852,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SY127 )
| ~ ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( upper_relstr_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( proper_element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(853,plain,
( ( element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(854,plain,
! [SV49: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_B @ SV49 ) @ ( powerset @ ( the_carrier @ SV49 ) ) )
| ~ ~ ( empty @ ( sK9_B @ SV49 ) ) )
| ~ ( lower_relstr_subset @ ( sK9_B @ SV49 ) @ SV49 ) ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[792]) ).
thf(855,plain,
! [SV49: $i] :
( ( ( ~ ( upper_relstr_subset @ ( sK9_B @ SV49 ) @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[792]) ).
thf(856,plain,
! [SV50: $i] :
( ( ~ ( element @ ( sK17_B @ SV50 ) @ ( powerset @ ( powerset @ SV50 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(857,plain,
! [SV50: $i] :
( ( ~ ~ ( empty @ ( sK17_B @ SV50 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(858,plain,
! [SV51: $i,SV69: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV51 )
| ~ ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV69 ) )
= $true )
| ( ( SV51 = SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(859,plain,
! [SV51: $i,SV69: $i] :
( ( ( ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV51 )
| ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV69 ) )
= $true )
| ( ( SV51 = SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(860,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[796]) ).
thf(861,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[797]) ).
thf(862,plain,
! [SV93: $i] :
( ( ( ( empty_carrier @ SV93 )
| ~ ( upper_bounded_relstr @ SV93 ) )
= $true )
| ( ( ~ ( rel_str @ SV93 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(863,plain,
! [SV94: $i] :
( ( ( ( empty_carrier @ SV94 )
| ~ ( upper_bounded_relstr @ SV94 ) )
= $true )
| ( ( ~ ( rel_str @ SV94 ) )
= $true )
| ( ( directed_subset @ ( cast_as_carrier_subset @ SV94 ) @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(864,plain,
! [SV53: $i] :
( ( ( ~ ( ~ ( element @ ( sK14_B @ SV53 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV53 ) ) ) )
| ~ ~ ( empty @ ( sK14_B @ SV53 ) ) ) )
= $true )
| ( ( one_sorted_str @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(865,plain,
! [SV53: $i] :
( ( ( finite @ ( sK14_B @ SV53 ) )
= $true )
| ( ( one_sorted_str @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(866,plain,
! [SV54: $i] :
( ( ( ~ ( ~ ( directed_subset @ ( sK20_B @ SV54 ) @ SV54 )
| ~ ( element @ ( sK20_B @ SV54 ) @ ( powerset @ ( the_carrier @ SV54 ) ) ) ) )
= $true )
| ( ( rel_str @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[802]) ).
thf(867,plain,
! [SV54: $i] :
( ( ( filtered_subset @ ( sK20_B @ SV54 ) @ SV54 )
= $true )
| ( ( rel_str @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(868,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( empty @ ( cast_as_carrier_subset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(869,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( rel_str @ SX0 )
| ( lower_relstr_subset @ ( cast_as_carrier_subset @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[805]) ).
thf(870,plain,
! [SV95: $i] :
( ( ( empty_carrier @ SV95 )
= $true )
| ( ( ~ ( rel_str @ SV95 ) )
= $true )
| ( ( upper_relstr_subset @ ( cast_as_carrier_subset @ SV95 ) @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[806]) ).
thf(871,plain,
! [SV96: $i] :
( ( ( ~ ( rel_str @ SV96 ) )
= $true )
| ( ( ~ ( with_suprema_relstr @ SV96 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[807]) ).
thf(872,plain,
! [SV97: $i] :
( ( ( ~ ( rel_str @ SV97 ) )
= $true )
| ( ( ~ ( with_suprema_relstr @ SV97 ) )
= $true )
| ( ( directed_subset @ ( cast_as_carrier_subset @ SV97 ) @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[808]) ).
thf(873,plain,
! [SV7: $i,SV98: $i] :
( ( ( empty_carrier @ SV98 )
= $true )
| ( ( ~ ( net_str @ SV98 @ SV7 ) )
= $true )
| ( ( ( filter_of_net_str @ SV7 @ SV98 )
= ( a_2_1_yellow19 @ SV7 @ SV98 ) )
= $true )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[812]) ).
thf(874,plain,
! [SV56: $i,SV9: $i] :
( ( ( one_sorted_str @ SV9 )
= $false )
| ( ( empty_carrier @ SV9 )
= $true )
| ( ( empty_carrier @ SV56 )
= $true )
| ( ( ~ ( net_str @ SV56 @ SV9 ) )
= $true )
| ( ( element @ ( filter_of_net_str @ SV9 @ SV56 ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(875,plain,
! [SV23: $i,SV72: $i] :
( ( ( ( empty @ SV72 )
| ~ ( filtered_subset @ SV72 @ ( boole_POSet @ SV23 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV72 @ ( boole_POSet @ SV23 ) ) )
= $true )
| ( ( ~ ( proper_element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) ) )
= $true )
| ( ( ~ ( element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) ) )
= $true )
| ( ( ! [SY173: $i] :
( ~ ( empty @ SY173 )
| ~ ( in @ SY173 @ SV72 ) ) )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(876,plain,
! [SV73: $i,SV61: $i,SV24: $i] :
( ( ( in @ SV24 @ SV61 )
= $false )
| ( ( element @ SV61 @ ( powerset @ SV73 ) )
= $false )
| ( ( element @ SV24 @ SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(877,plain,
! [SV74: $i,SV62: $i,SV25: $i] :
( ( ( in @ SV25 @ SV62 )
= $false )
| ( ( element @ SV62 @ ( powerset @ SV74 ) )
= $false )
| ( ( ~ ( empty @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[817]) ).
thf(878,plain,
! [SV36: $i,SV99: $i] :
( ( ( ( empty @ SV99 )
| ~ ( filtered_subset @ SV99 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
| ~ ( upper_relstr_subset @ SV99 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) )
= $true )
| ( ( ~ ( element @ SV99 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) ) ) )
= $true )
| ( ( ( set_difference @ SV99 @ ( singleton @ empty_set ) )
= ( filter_of_net_str @ SV36 @ ( net_of_bool_filter @ SV36 @ ( cast_as_carrier_subset @ SV36 ) @ SV99 ) ) )
= $true )
| ( ( empty_carrier @ SV36 )
= $true )
| ( ( one_sorted_str @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(879,plain,
! [SV41: $i] :
( ( ! [SY153: $i,SY154: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY153 )
| ~ ( element @ SY153 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY154 )
| ~ ( filtered_subset @ SY154 @ ( boole_POSet @ SY153 ) )
| ~ ( upper_relstr_subset @ SY154 @ ( boole_POSet @ SY153 ) )
| ~ ( element @ SY154 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY153 ) ) ) )
| ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SY153 @ SY154 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(880,plain,
! [SV41: $i] :
( ( ! [SY155: $i,SY156: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SY155 )
| ~ ( element @ SY155 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY156 )
| ~ ( filtered_subset @ SY156 @ ( boole_POSet @ SY155 ) )
| ~ ( upper_relstr_subset @ SY156 @ ( boole_POSet @ SY155 ) )
| ~ ( element @ SY156 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SY155 ) ) ) )
| ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SY155 @ SY156 ) @ SV41 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[826]) ).
thf(881,plain,
! [SV111: $i,SV100: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV100 )
| ~ ( element @ SV100 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SV111 )
| ~ ( filtered_subset @ SV111 @ ( boole_POSet @ SV100 ) )
| ~ ( upper_relstr_subset @ SV111 @ ( boole_POSet @ SV100 ) )
| ~ ( element @ SV111 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV100 ) ) ) ) )
= $true )
| ( ( net_str @ ( net_of_bool_filter @ SV41 @ SV100 @ SV111 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[827]) ).
thf(882,plain,
! [SV42: $i,SV112: $i,SV101: $i] :
( ( ( ( empty_carrier @ SV101 )
| ~ ( one_sorted_str @ SV101 )
| ( empty_carrier @ SV112 )
| ~ ( net_str @ SV112 @ SV101 ) )
= $true )
| ( ( ! [SY186: $i] :
( ( SV42 != SY186 )
| ~ ( element @ SY186 @ ( powerset @ ( the_carrier @ SV101 ) ) )
| ~ ( is_eventually_in @ SV101 @ SV112 @ SY186 ) )
| ( in @ SV42 @ ( a_2_1_yellow19 @ SV101 @ SV112 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[828]) ).
thf(883,plain,
! [SV42: $i,SV113: $i,SV102: $i] :
( ( ( ( empty_carrier @ SV102 )
| ~ ( one_sorted_str @ SV102 )
| ( empty_carrier @ SV113 )
| ~ ( net_str @ SV113 @ SV102 ) )
= $true )
| ( ( ~ ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
| ~ ( ~ ~ ( ( SV42
!= ( sK6_D @ SV113 @ SV102 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SV113 @ SV102 @ SV42 ) @ ( powerset @ ( the_carrier @ SV102 ) ) ) )
| ~ ( is_eventually_in @ SV102 @ SV113 @ ( sK6_D @ SV113 @ SV102 @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(884,plain,
! [SV43: $i] :
( ( ( element @ ( sK11_B @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
= $true )
| ( ( empty_carrier @ SV43 )
= $true )
| ( ( one_sorted_str @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(885,plain,
! [SV43: $i] :
( ( ( ~ ( empty @ ( sK11_B @ SV43 ) ) )
= $true )
| ( ( empty_carrier @ SV43 )
= $true )
| ( ( one_sorted_str @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(886,plain,
! [SV103: $i,SV78: $i] :
( ( ( ( set_difference @ SV78 @ ( singleton @ SV103 ) )
= SV78 )
= $false )
| ( ( ~ ( in @ SV103 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(887,plain,
! [SV116: $i] :
( ( ~ ( rel_str @ SV116 )
| ( empty_carrier @ SV116 )
| ~ ( complete_relstr @ SV116 )
| ~ ( empty_carrier @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(888,plain,
! [SV117: $i] :
( ( ~ ( rel_str @ SV117 )
| ( empty_carrier @ SV117 )
| ~ ( complete_relstr @ SV117 )
| ( with_suprema_relstr @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(889,plain,
! [SV80: $i] :
( ( ( ( empty_carrier @ SV80 )
| ~ ( complete_relstr @ SV80 ) )
= $true )
| ( ( with_infima_relstr @ SV80 )
= $true )
| ( ( rel_str @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(890,plain,
! [SV44: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV44 ) ) )
| ~ ( finite @ ( sK5_B @ SV44 ) ) )
| ~ ( directed_subset @ ( sK5_B @ SV44 ) @ SV44 ) )
| ~ ( filtered_subset @ ( sK5_B @ SV44 ) @ SV44 ) )
= $false )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(891,plain,
! [SV45: $i] :
( ( ( ~ ( element @ ( sK10_B @ SV45 ) @ ( powerset @ ( the_carrier @ SV45 ) ) )
| ~ ( lower_relstr_subset @ ( sK10_B @ SV45 ) @ SV45 ) )
= $false )
| ( ( rel_str @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(892,plain,
! [SV105: $i,SV81: $i] :
( ( ( ( empty_carrier @ SV81 )
| ~ ( one_sorted_str @ SV81 )
| ( empty_carrier @ SV105 ) )
= $true )
| ( ( ~ ( net_str @ SV105 @ SV81 ) )
= $true )
| ( ( ~ ( empty @ ( filter_of_net_str @ SV81 @ SV105 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(893,plain,
! [SV106: $i,SV82: $i] :
( ( ( ( empty_carrier @ SV82 )
| ~ ( one_sorted_str @ SV82 )
| ( empty_carrier @ SV106 ) )
= $true )
| ( ( ~ ( net_str @ SV106 @ SV82 ) )
= $true )
| ( ( upper_relstr_subset @ ( filter_of_net_str @ SV82 @ SV106 ) @ ( boole_POSet @ ( cast_as_carrier_subset @ SV82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[841]) ).
thf(894,plain,
! [SV83: $i] :
( ( ( rel_str @ SV83 )
= $false )
| ( ( ~ ( with_infima_relstr @ SV83 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(895,plain,
! [SV84: $i] :
( ( ( rel_str @ SV84 )
= $false )
| ( ( ~ ( with_infima_relstr @ SV84 ) )
= $true )
| ( ( filtered_subset @ ( cast_as_carrier_subset @ SV84 ) @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(896,plain,
! [SV107: $i,SV85: $i] :
( ( ( element @ SV85 @ ( powerset @ SV107 ) )
= $false )
| ( ( subset @ SV85 @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(897,plain,
! [SV108: $i,SV86: $i] :
( ( ( subset @ SV86 @ SV108 )
= $false )
| ( ( element @ SV86 @ ( powerset @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(898,plain,
! [SV46: $i] :
( ( ( ~ ( element @ ( sK16_B @ SV46 ) @ ( powerset @ SV46 ) ) )
= $false )
| ( ( empty @ SV46 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[846]) ).
thf(899,plain,
! [SV46: $i] :
( ( ( ~ ~ ( empty @ ( sK16_B @ SV46 ) ) )
= $false )
| ( ( empty @ SV46 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[846]) ).
thf(900,plain,
! [SV47: $i] :
( ( ( ~ ( element @ ( sK13_B @ SV47 ) @ ( powerset @ SV47 ) ) )
= $false )
| ( ( empty @ SV47 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[847]) ).
thf(901,plain,
! [SV47: $i] :
( ( ( ~ ~ ( empty @ ( sK13_B @ SV47 ) ) )
= $false )
| ( ( empty @ SV47 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[847]) ).
thf(902,plain,
! [SV109: $i,SV48: $i,SV114: $i] :
( ( ( ~ ( relation_of2 @ SV114 @ SV48 @ SV109 ) )
= $true )
| ( ( relation_of2_as_subset @ SV114 @ SV48 @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(903,plain,
! [SV110: $i,SV48: $i,SV115: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV115 @ SV48 @ SV110 ) )
= $true )
| ( ( relation_of2 @ SV115 @ SV48 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(904,plain,
! [SV89: $i] :
( ( ( empty_carrier @ SV89 )
= $true )
| ( ( ~ ( lower_bounded_relstr @ SV89 ) )
= $true )
| ( ( ~ ( rel_str @ SV89 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(905,plain,
! [SV90: $i] :
( ( ( empty_carrier @ SV90 )
= $true )
| ( ( ~ ( lower_bounded_relstr @ SV90 ) )
= $true )
| ( ( ~ ( rel_str @ SV90 ) )
= $true )
| ( ( filtered_subset @ ( cast_as_carrier_subset @ SV90 ) @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(906,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SY127 )
| ~ ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( upper_relstr_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( proper_element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(907,plain,
! [SV49: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK9_B @ SV49 ) @ ( powerset @ ( the_carrier @ SV49 ) ) )
| ~ ~ ( empty @ ( sK9_B @ SV49 ) ) )
| ~ ( lower_relstr_subset @ ( sK9_B @ SV49 ) @ SV49 ) ) )
= $true )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[854]) ).
thf(908,plain,
! [SV49: $i] :
( ( ( upper_relstr_subset @ ( sK9_B @ SV49 ) @ SV49 )
= $true )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[855]) ).
thf(909,plain,
! [SV50: $i] :
( ( element @ ( sK17_B @ SV50 ) @ ( powerset @ ( powerset @ SV50 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[856]) ).
thf(910,plain,
! [SV50: $i] :
( ( ~ ( empty @ ( sK17_B @ SV50 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[857]) ).
thf(911,plain,
! [SV51: $i,SV69: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV51 ) )
= $true )
| ( ( ~ ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV69 ) )
= $true )
| ( ( SV51 = SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[858]) ).
thf(912,plain,
! [SV51: $i,SV69: $i] :
( ( ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV51 )
= $true )
| ( ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV69 )
= $true )
| ( ( SV51 = SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(913,plain,
! [SV93: $i] :
( ( ( empty_carrier @ SV93 )
= $true )
| ( ( ~ ( upper_bounded_relstr @ SV93 ) )
= $true )
| ( ( ~ ( rel_str @ SV93 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(914,plain,
! [SV94: $i] :
( ( ( empty_carrier @ SV94 )
= $true )
| ( ( ~ ( upper_bounded_relstr @ SV94 ) )
= $true )
| ( ( ~ ( rel_str @ SV94 ) )
= $true )
| ( ( directed_subset @ ( cast_as_carrier_subset @ SV94 ) @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(915,plain,
! [SV53: $i] :
( ( ( ~ ( element @ ( sK14_B @ SV53 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV53 ) ) ) )
| ~ ~ ( empty @ ( sK14_B @ SV53 ) ) )
= $false )
| ( ( one_sorted_str @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(916,plain,
! [SV54: $i] :
( ( ( ~ ( directed_subset @ ( sK20_B @ SV54 ) @ SV54 )
| ~ ( element @ ( sK20_B @ SV54 ) @ ( powerset @ ( the_carrier @ SV54 ) ) ) )
= $false )
| ( ( rel_str @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(917,plain,
! [SV118: $i] :
( ( ( empty_carrier @ SV118 )
| ~ ( rel_str @ SV118 )
| ~ ( empty @ ( cast_as_carrier_subset @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(918,plain,
! [SV119: $i] :
( ( ( empty_carrier @ SV119 )
| ~ ( rel_str @ SV119 )
| ( lower_relstr_subset @ ( cast_as_carrier_subset @ SV119 ) @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(919,plain,
! [SV95: $i] :
( ( ( rel_str @ SV95 )
= $false )
| ( ( empty_carrier @ SV95 )
= $true )
| ( ( upper_relstr_subset @ ( cast_as_carrier_subset @ SV95 ) @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(920,plain,
! [SV96: $i] :
( ( ( rel_str @ SV96 )
= $false )
| ( ( ~ ( with_suprema_relstr @ SV96 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(921,plain,
! [SV97: $i] :
( ( ( rel_str @ SV97 )
= $false )
| ( ( ~ ( with_suprema_relstr @ SV97 ) )
= $true )
| ( ( directed_subset @ ( cast_as_carrier_subset @ SV97 ) @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(922,plain,
! [SV7: $i,SV98: $i] :
( ( ( net_str @ SV98 @ SV7 )
= $false )
| ( ( empty_carrier @ SV98 )
= $true )
| ( ( ( filter_of_net_str @ SV7 @ SV98 )
= ( a_2_1_yellow19 @ SV7 @ SV98 ) )
= $true )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(923,plain,
! [SV9: $i,SV56: $i] :
( ( ( net_str @ SV56 @ SV9 )
= $false )
| ( ( empty_carrier @ SV56 )
= $true )
| ( ( empty_carrier @ SV9 )
= $true )
| ( ( one_sorted_str @ SV9 )
= $false )
| ( ( element @ ( filter_of_net_str @ SV9 @ SV56 ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(924,plain,
! [SV23: $i,SV72: $i] :
( ( ( empty @ SV72 )
= $true )
| ( ( ~ ( filtered_subset @ SV72 @ ( boole_POSet @ SV23 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV72 @ ( boole_POSet @ SV23 ) ) )
= $true )
| ( ( ~ ( proper_element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) ) )
= $true )
| ( ( ~ ( element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) ) )
= $true )
| ( ( ! [SY173: $i] :
( ~ ( empty @ SY173 )
| ~ ( in @ SY173 @ SV72 ) ) )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(925,plain,
! [SV25: $i,SV62: $i,SV74: $i] :
( ( ( empty @ SV74 )
= $false )
| ( ( element @ SV62 @ ( powerset @ SV74 ) )
= $false )
| ( ( in @ SV25 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(926,plain,
! [SV36: $i,SV99: $i] :
( ( ( ( empty @ SV99 )
| ~ ( filtered_subset @ SV99 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV99 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) )
= $true )
| ( ( ~ ( element @ SV99 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) ) ) )
= $true )
| ( ( ( set_difference @ SV99 @ ( singleton @ empty_set ) )
= ( filter_of_net_str @ SV36 @ ( net_of_bool_filter @ SV36 @ ( cast_as_carrier_subset @ SV36 ) @ SV99 ) ) )
= $true )
| ( ( empty_carrier @ SV36 )
= $true )
| ( ( one_sorted_str @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(927,plain,
! [SV120: $i,SV41: $i] :
( ( ! [SY187: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV120 )
| ~ ( element @ SV120 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY187 )
| ~ ( filtered_subset @ SY187 @ ( boole_POSet @ SV120 ) )
| ~ ( upper_relstr_subset @ SY187 @ ( boole_POSet @ SV120 ) )
| ~ ( element @ SY187 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV120 ) ) ) )
| ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SV120 @ SY187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(928,plain,
! [SV121: $i,SV41: $i] :
( ( ! [SY188: $i] :
( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV121 )
| ~ ( element @ SV121 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SY188 )
| ~ ( filtered_subset @ SY188 @ ( boole_POSet @ SV121 ) )
| ~ ( upper_relstr_subset @ SY188 @ ( boole_POSet @ SV121 ) )
| ~ ( element @ SY188 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV121 ) ) ) )
| ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SV121 @ SY188 ) @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(929,plain,
! [SV111: $i,SV100: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV100 )
| ~ ( element @ SV100 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SV111 )
| ~ ( filtered_subset @ SV111 @ ( boole_POSet @ SV100 ) )
| ~ ( upper_relstr_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( element @ SV111 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV100 ) ) ) ) )
= $true )
| ( ( net_str @ ( net_of_bool_filter @ SV41 @ SV100 @ SV111 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(930,plain,
! [SV42: $i,SV112: $i,SV101: $i] :
( ( ( ( empty_carrier @ SV101 )
| ~ ( one_sorted_str @ SV101 )
| ( empty_carrier @ SV112 ) )
= $true )
| ( ( ~ ( net_str @ SV112 @ SV101 ) )
= $true )
| ( ( ! [SY186: $i] :
( ( SV42 != SY186 )
| ~ ( element @ SY186 @ ( powerset @ ( the_carrier @ SV101 ) ) )
| ~ ( is_eventually_in @ SV101 @ SV112 @ SY186 ) )
| ( in @ SV42 @ ( a_2_1_yellow19 @ SV101 @ SV112 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(931,plain,
! [SV42: $i,SV113: $i,SV102: $i] :
( ( ( ( empty_carrier @ SV102 )
| ~ ( one_sorted_str @ SV102 )
| ( empty_carrier @ SV113 ) )
= $true )
| ( ( ~ ( net_str @ SV113 @ SV102 ) )
= $true )
| ( ( ~ ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
| ~ ( ~ ~ ( ( SV42
!= ( sK6_D @ SV113 @ SV102 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SV113 @ SV102 @ SV42 ) @ ( powerset @ ( the_carrier @ SV102 ) ) ) )
| ~ ( is_eventually_in @ SV102 @ SV113 @ ( sK6_D @ SV113 @ SV102 @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[883]) ).
thf(932,plain,
! [SV43: $i] :
( ( ( empty @ ( sK11_B @ SV43 ) )
= $false )
| ( ( empty_carrier @ SV43 )
= $true )
| ( ( one_sorted_str @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(933,plain,
! [SV78: $i,SV103: $i] :
( ( ( in @ SV103 @ SV78 )
= $false )
| ( ( ( set_difference @ SV78 @ ( singleton @ SV103 ) )
= SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(934,plain,
! [SV116: $i] :
( ( ( ~ ( rel_str @ SV116 ) )
= $true )
| ( ( ( empty_carrier @ SV116 )
| ~ ( complete_relstr @ SV116 )
| ~ ( empty_carrier @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(935,plain,
! [SV117: $i] :
( ( ( ~ ( rel_str @ SV117 ) )
= $true )
| ( ( ( empty_carrier @ SV117 )
| ~ ( complete_relstr @ SV117 )
| ( with_suprema_relstr @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(936,plain,
! [SV80: $i] :
( ( ( empty_carrier @ SV80 )
= $true )
| ( ( ~ ( complete_relstr @ SV80 ) )
= $true )
| ( ( with_infima_relstr @ SV80 )
= $true )
| ( ( rel_str @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(937,plain,
! [SV44: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV44 ) ) )
| ~ ( finite @ ( sK5_B @ SV44 ) ) )
| ~ ( directed_subset @ ( sK5_B @ SV44 ) @ SV44 ) ) )
= $false )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[890]) ).
thf(938,plain,
! [SV44: $i] :
( ( ( ~ ( filtered_subset @ ( sK5_B @ SV44 ) @ SV44 ) )
= $false )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[890]) ).
thf(939,plain,
! [SV45: $i] :
( ( ( ~ ( element @ ( sK10_B @ SV45 ) @ ( powerset @ ( the_carrier @ SV45 ) ) ) )
= $false )
| ( ( rel_str @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[891]) ).
thf(940,plain,
! [SV45: $i] :
( ( ( ~ ( lower_relstr_subset @ ( sK10_B @ SV45 ) @ SV45 ) )
= $false )
| ( ( rel_str @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[891]) ).
thf(941,plain,
! [SV105: $i,SV81: $i] :
( ( ( ( empty_carrier @ SV81 )
| ~ ( one_sorted_str @ SV81 ) )
= $true )
| ( ( empty_carrier @ SV105 )
= $true )
| ( ( ~ ( net_str @ SV105 @ SV81 ) )
= $true )
| ( ( ~ ( empty @ ( filter_of_net_str @ SV81 @ SV105 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(942,plain,
! [SV106: $i,SV82: $i] :
( ( ( ( empty_carrier @ SV82 )
| ~ ( one_sorted_str @ SV82 ) )
= $true )
| ( ( empty_carrier @ SV106 )
= $true )
| ( ( ~ ( net_str @ SV106 @ SV82 ) )
= $true )
| ( ( upper_relstr_subset @ ( filter_of_net_str @ SV82 @ SV106 ) @ ( boole_POSet @ ( cast_as_carrier_subset @ SV82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(943,plain,
! [SV83: $i] :
( ( ( with_infima_relstr @ SV83 )
= $false )
| ( ( rel_str @ SV83 )
= $false )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(944,plain,
! [SV84: $i] :
( ( ( with_infima_relstr @ SV84 )
= $false )
| ( ( rel_str @ SV84 )
= $false )
| ( ( filtered_subset @ ( cast_as_carrier_subset @ SV84 ) @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(945,plain,
! [SV46: $i] :
( ( ( element @ ( sK16_B @ SV46 ) @ ( powerset @ SV46 ) )
= $true )
| ( ( empty @ SV46 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[898]) ).
thf(946,plain,
! [SV46: $i] :
( ( ( ~ ( empty @ ( sK16_B @ SV46 ) ) )
= $true )
| ( ( empty @ SV46 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[899]) ).
thf(947,plain,
! [SV47: $i] :
( ( ( element @ ( sK13_B @ SV47 ) @ ( powerset @ SV47 ) )
= $true )
| ( ( empty @ SV47 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[900]) ).
thf(948,plain,
! [SV47: $i] :
( ( ( ~ ( empty @ ( sK13_B @ SV47 ) ) )
= $true )
| ( ( empty @ SV47 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[901]) ).
thf(949,plain,
! [SV109: $i,SV48: $i,SV114: $i] :
( ( ( relation_of2 @ SV114 @ SV48 @ SV109 )
= $false )
| ( ( relation_of2_as_subset @ SV114 @ SV48 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(950,plain,
! [SV110: $i,SV48: $i,SV115: $i] :
( ( ( relation_of2_as_subset @ SV115 @ SV48 @ SV110 )
= $false )
| ( ( relation_of2 @ SV115 @ SV48 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(951,plain,
! [SV89: $i] :
( ( ( lower_bounded_relstr @ SV89 )
= $false )
| ( ( empty_carrier @ SV89 )
= $true )
| ( ( ~ ( rel_str @ SV89 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(952,plain,
! [SV90: $i] :
( ( ( lower_bounded_relstr @ SV90 )
= $false )
| ( ( empty_carrier @ SV90 )
= $true )
| ( ( ~ ( rel_str @ SV90 ) )
= $true )
| ( ( filtered_subset @ ( cast_as_carrier_subset @ SV90 ) @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(953,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SY127 )
| ~ ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( upper_relstr_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(954,plain,
( ( ~ ( proper_element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(955,plain,
! [SV49: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_B @ SV49 ) @ ( powerset @ ( the_carrier @ SV49 ) ) )
| ~ ~ ( empty @ ( sK9_B @ SV49 ) ) )
| ~ ( lower_relstr_subset @ ( sK9_B @ SV49 ) @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(956,plain,
! [SV50: $i] :
( ( empty @ ( sK17_B @ SV50 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(957,plain,
! [SV51: $i,SV69: $i] :
( ( ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV51 )
= $false )
| ( ( ~ ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV69 ) )
= $true )
| ( ( SV51 = SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(958,plain,
! [SV93: $i] :
( ( ( upper_bounded_relstr @ SV93 )
= $false )
| ( ( empty_carrier @ SV93 )
= $true )
| ( ( ~ ( rel_str @ SV93 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV93 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(959,plain,
! [SV94: $i] :
( ( ( upper_bounded_relstr @ SV94 )
= $false )
| ( ( empty_carrier @ SV94 )
= $true )
| ( ( ~ ( rel_str @ SV94 ) )
= $true )
| ( ( directed_subset @ ( cast_as_carrier_subset @ SV94 ) @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(960,plain,
! [SV53: $i] :
( ( ( ~ ( element @ ( sK14_B @ SV53 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV53 ) ) ) ) )
= $false )
| ( ( one_sorted_str @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(961,plain,
! [SV53: $i] :
( ( ( ~ ~ ( empty @ ( sK14_B @ SV53 ) ) )
= $false )
| ( ( one_sorted_str @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(962,plain,
! [SV54: $i] :
( ( ( ~ ( directed_subset @ ( sK20_B @ SV54 ) @ SV54 ) )
= $false )
| ( ( rel_str @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[916]) ).
thf(963,plain,
! [SV54: $i] :
( ( ( ~ ( element @ ( sK20_B @ SV54 ) @ ( powerset @ ( the_carrier @ SV54 ) ) ) )
= $false )
| ( ( rel_str @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[916]) ).
thf(964,plain,
! [SV118: $i] :
( ( ( ( empty_carrier @ SV118 )
| ~ ( rel_str @ SV118 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV118 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(965,plain,
! [SV119: $i] :
( ( ( ( empty_carrier @ SV119 )
| ~ ( rel_str @ SV119 ) )
= $true )
| ( ( lower_relstr_subset @ ( cast_as_carrier_subset @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(966,plain,
! [SV96: $i] :
( ( ( with_suprema_relstr @ SV96 )
= $false )
| ( ( rel_str @ SV96 )
= $false )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(967,plain,
! [SV97: $i] :
( ( ( with_suprema_relstr @ SV97 )
= $false )
| ( ( rel_str @ SV97 )
= $false )
| ( ( directed_subset @ ( cast_as_carrier_subset @ SV97 ) @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(968,plain,
! [SV23: $i,SV72: $i] :
( ( ( filtered_subset @ SV72 @ ( boole_POSet @ SV23 ) )
= $false )
| ( ( empty @ SV72 )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV72 @ ( boole_POSet @ SV23 ) ) )
= $true )
| ( ( ~ ( proper_element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) ) )
= $true )
| ( ( ~ ( element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) ) )
= $true )
| ( ( ! [SY173: $i] :
( ~ ( empty @ SY173 )
| ~ ( in @ SY173 @ SV72 ) ) )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(969,plain,
! [SV36: $i,SV99: $i] :
( ( ( empty @ SV99 )
= $true )
| ( ( ~ ( filtered_subset @ SV99 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV99 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) )
= $true )
| ( ( ~ ( element @ SV99 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) ) ) )
= $true )
| ( ( ( set_difference @ SV99 @ ( singleton @ empty_set ) )
= ( filter_of_net_str @ SV36 @ ( net_of_bool_filter @ SV36 @ ( cast_as_carrier_subset @ SV36 ) @ SV99 ) ) )
= $true )
| ( ( empty_carrier @ SV36 )
= $true )
| ( ( one_sorted_str @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(970,plain,
! [SV122: $i,SV120: $i,SV41: $i] :
( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV120 )
| ~ ( element @ SV120 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SV122 )
| ~ ( filtered_subset @ SV122 @ ( boole_POSet @ SV120 ) )
| ~ ( upper_relstr_subset @ SV122 @ ( boole_POSet @ SV120 ) )
| ~ ( element @ SV122 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV120 ) ) ) )
| ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SV120 @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(971,plain,
! [SV123: $i,SV121: $i,SV41: $i] :
( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV121 )
| ~ ( element @ SV121 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SV123 )
| ~ ( filtered_subset @ SV123 @ ( boole_POSet @ SV121 ) )
| ~ ( upper_relstr_subset @ SV123 @ ( boole_POSet @ SV121 ) )
| ~ ( element @ SV123 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV121 ) ) ) )
| ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SV121 @ SV123 ) @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(972,plain,
! [SV111: $i,SV100: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV100 )
| ~ ( element @ SV100 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SV111 )
| ~ ( filtered_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( element @ SV111 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV100 ) ) ) ) )
= $true )
| ( ( net_str @ ( net_of_bool_filter @ SV41 @ SV100 @ SV111 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(973,plain,
! [SV42: $i,SV112: $i,SV101: $i] :
( ( ( ( empty_carrier @ SV101 )
| ~ ( one_sorted_str @ SV101 ) )
= $true )
| ( ( empty_carrier @ SV112 )
= $true )
| ( ( ~ ( net_str @ SV112 @ SV101 ) )
= $true )
| ( ( ! [SY186: $i] :
( ( SV42 != SY186 )
| ~ ( element @ SY186 @ ( powerset @ ( the_carrier @ SV101 ) ) )
| ~ ( is_eventually_in @ SV101 @ SV112 @ SY186 ) )
| ( in @ SV42 @ ( a_2_1_yellow19 @ SV101 @ SV112 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(974,plain,
! [SV42: $i,SV113: $i,SV102: $i] :
( ( ( ( empty_carrier @ SV102 )
| ~ ( one_sorted_str @ SV102 ) )
= $true )
| ( ( empty_carrier @ SV113 )
= $true )
| ( ( ~ ( net_str @ SV113 @ SV102 ) )
= $true )
| ( ( ~ ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
| ~ ( ~ ~ ( ( SV42
!= ( sK6_D @ SV113 @ SV102 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SV113 @ SV102 @ SV42 ) @ ( powerset @ ( the_carrier @ SV102 ) ) ) )
| ~ ( is_eventually_in @ SV102 @ SV113 @ ( sK6_D @ SV113 @ SV102 @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(975,plain,
! [SV116: $i] :
( ( ( rel_str @ SV116 )
= $false )
| ( ( ( empty_carrier @ SV116 )
| ~ ( complete_relstr @ SV116 )
| ~ ( empty_carrier @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(976,plain,
! [SV117: $i] :
( ( ( rel_str @ SV117 )
= $false )
| ( ( ( empty_carrier @ SV117 )
| ~ ( complete_relstr @ SV117 )
| ( with_suprema_relstr @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(977,plain,
! [SV80: $i] :
( ( ( complete_relstr @ SV80 )
= $false )
| ( ( empty_carrier @ SV80 )
= $true )
| ( ( with_infima_relstr @ SV80 )
= $true )
| ( ( rel_str @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(978,plain,
! [SV44: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV44 ) ) )
| ~ ( finite @ ( sK5_B @ SV44 ) ) )
| ~ ( directed_subset @ ( sK5_B @ SV44 ) @ SV44 ) ) )
= $true )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[937]) ).
thf(979,plain,
! [SV44: $i] :
( ( ( filtered_subset @ ( sK5_B @ SV44 ) @ SV44 )
= $true )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[938]) ).
thf(980,plain,
! [SV45: $i] :
( ( ( element @ ( sK10_B @ SV45 ) @ ( powerset @ ( the_carrier @ SV45 ) ) )
= $true )
| ( ( rel_str @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[939]) ).
thf(981,plain,
! [SV45: $i] :
( ( ( lower_relstr_subset @ ( sK10_B @ SV45 ) @ SV45 )
= $true )
| ( ( rel_str @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[940]) ).
thf(982,plain,
! [SV105: $i,SV81: $i] :
( ( ( empty_carrier @ SV81 )
= $true )
| ( ( ~ ( one_sorted_str @ SV81 ) )
= $true )
| ( ( empty_carrier @ SV105 )
= $true )
| ( ( ~ ( net_str @ SV105 @ SV81 ) )
= $true )
| ( ( ~ ( empty @ ( filter_of_net_str @ SV81 @ SV105 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(983,plain,
! [SV106: $i,SV82: $i] :
( ( ( empty_carrier @ SV82 )
= $true )
| ( ( ~ ( one_sorted_str @ SV82 ) )
= $true )
| ( ( empty_carrier @ SV106 )
= $true )
| ( ( ~ ( net_str @ SV106 @ SV82 ) )
= $true )
| ( ( upper_relstr_subset @ ( filter_of_net_str @ SV82 @ SV106 ) @ ( boole_POSet @ ( cast_as_carrier_subset @ SV82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(984,plain,
! [SV83: $i] :
( ( ( empty @ ( cast_as_carrier_subset @ SV83 ) )
= $false )
| ( ( rel_str @ SV83 )
= $false )
| ( ( with_infima_relstr @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(985,plain,
! [SV46: $i] :
( ( ( empty @ ( sK16_B @ SV46 ) )
= $false )
| ( ( empty @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(986,plain,
! [SV47: $i] :
( ( ( empty @ ( sK13_B @ SV47 ) )
= $false )
| ( ( empty @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[948]) ).
thf(987,plain,
! [SV89: $i] :
( ( ( rel_str @ SV89 )
= $false )
| ( ( empty_carrier @ SV89 )
= $true )
| ( ( lower_bounded_relstr @ SV89 )
= $false )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(988,plain,
! [SV90: $i] :
( ( ( rel_str @ SV90 )
= $false )
| ( ( empty_carrier @ SV90 )
= $true )
| ( ( lower_bounded_relstr @ SV90 )
= $false )
| ( ( filtered_subset @ ( cast_as_carrier_subset @ SV90 ) @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(989,plain,
( ( ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SY127 )
| ~ ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( upper_relstr_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[953]) ).
thf(990,plain,
( ( proper_element @ sK2_SY127 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[954]) ).
thf(991,plain,
! [SV49: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_B @ SV49 ) @ ( powerset @ ( the_carrier @ SV49 ) ) )
| ~ ~ ( empty @ ( sK9_B @ SV49 ) ) ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[955]) ).
thf(992,plain,
! [SV49: $i] :
( ( ( ~ ( lower_relstr_subset @ ( sK9_B @ SV49 ) @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[955]) ).
thf(993,plain,
! [SV51: $i,SV69: $i] :
( ( ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV69 )
= $false )
| ( ( in @ ( sK3_C @ SV69 @ SV51 ) @ SV51 )
= $false )
| ( ( SV51 = SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(994,plain,
! [SV93: $i] :
( ( ( rel_str @ SV93 )
= $false )
| ( ( empty_carrier @ SV93 )
= $true )
| ( ( upper_bounded_relstr @ SV93 )
= $false )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV93 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(995,plain,
! [SV94: $i] :
( ( ( rel_str @ SV94 )
= $false )
| ( ( empty_carrier @ SV94 )
= $true )
| ( ( upper_bounded_relstr @ SV94 )
= $false )
| ( ( directed_subset @ ( cast_as_carrier_subset @ SV94 ) @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(996,plain,
! [SV53: $i] :
( ( ( element @ ( sK14_B @ SV53 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV53 ) ) ) )
= $true )
| ( ( one_sorted_str @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[960]) ).
thf(997,plain,
! [SV53: $i] :
( ( ( ~ ( empty @ ( sK14_B @ SV53 ) ) )
= $true )
| ( ( one_sorted_str @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[961]) ).
thf(998,plain,
! [SV54: $i] :
( ( ( directed_subset @ ( sK20_B @ SV54 ) @ SV54 )
= $true )
| ( ( rel_str @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[962]) ).
thf(999,plain,
! [SV54: $i] :
( ( ( element @ ( sK20_B @ SV54 ) @ ( powerset @ ( the_carrier @ SV54 ) ) )
= $true )
| ( ( rel_str @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[963]) ).
thf(1000,plain,
! [SV118: $i] :
( ( ( empty_carrier @ SV118 )
= $true )
| ( ( ~ ( rel_str @ SV118 ) )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV118 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1001,plain,
! [SV119: $i] :
( ( ( empty_carrier @ SV119 )
= $true )
| ( ( ~ ( rel_str @ SV119 ) )
= $true )
| ( ( lower_relstr_subset @ ( cast_as_carrier_subset @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1002,plain,
! [SV96: $i] :
( ( ( empty @ ( cast_as_carrier_subset @ SV96 ) )
= $false )
| ( ( rel_str @ SV96 )
= $false )
| ( ( with_suprema_relstr @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1003,plain,
! [SV23: $i,SV72: $i] :
( ( ( upper_relstr_subset @ SV72 @ ( boole_POSet @ SV23 ) )
= $false )
| ( ( empty @ SV72 )
= $true )
| ( ( filtered_subset @ SV72 @ ( boole_POSet @ SV23 ) )
= $false )
| ( ( ~ ( proper_element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) ) )
= $true )
| ( ( ~ ( element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) ) )
= $true )
| ( ( ! [SY173: $i] :
( ~ ( empty @ SY173 )
| ~ ( in @ SY173 @ SV72 ) ) )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1004,plain,
! [SV36: $i,SV99: $i] :
( ( ( filtered_subset @ SV99 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
= $false )
| ( ( empty @ SV99 )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV99 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) )
= $true )
| ( ( ~ ( element @ SV99 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) ) ) )
= $true )
| ( ( ( set_difference @ SV99 @ ( singleton @ empty_set ) )
= ( filter_of_net_str @ SV36 @ ( net_of_bool_filter @ SV36 @ ( cast_as_carrier_subset @ SV36 ) @ SV99 ) ) )
= $true )
| ( ( empty_carrier @ SV36 )
= $true )
| ( ( one_sorted_str @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[969]) ).
thf(1005,plain,
! [SV122: $i,SV120: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV120 )
| ~ ( element @ SV120 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SV122 )
| ~ ( filtered_subset @ SV122 @ ( boole_POSet @ SV120 ) )
| ~ ( upper_relstr_subset @ SV122 @ ( boole_POSet @ SV120 ) )
| ~ ( element @ SV122 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV120 ) ) ) ) )
= $true )
| ( ( ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SV120 @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1006,plain,
! [SV123: $i,SV121: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV121 )
| ~ ( element @ SV121 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SV123 )
| ~ ( filtered_subset @ SV123 @ ( boole_POSet @ SV121 ) )
| ~ ( upper_relstr_subset @ SV123 @ ( boole_POSet @ SV121 ) )
| ~ ( element @ SV123 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV121 ) ) ) ) )
= $true )
| ( ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SV121 @ SV123 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1007,plain,
! [SV111: $i,SV100: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV100 )
| ~ ( element @ SV100 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SV111 ) )
= $true )
| ( ( ~ ( filtered_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( element @ SV111 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV100 ) ) ) ) )
= $true )
| ( ( net_str @ ( net_of_bool_filter @ SV41 @ SV100 @ SV111 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[972]) ).
thf(1008,plain,
! [SV42: $i,SV112: $i,SV101: $i] :
( ( ( empty_carrier @ SV101 )
= $true )
| ( ( ~ ( one_sorted_str @ SV101 ) )
= $true )
| ( ( empty_carrier @ SV112 )
= $true )
| ( ( ~ ( net_str @ SV112 @ SV101 ) )
= $true )
| ( ( ! [SY186: $i] :
( ( SV42 != SY186 )
| ~ ( element @ SY186 @ ( powerset @ ( the_carrier @ SV101 ) ) )
| ~ ( is_eventually_in @ SV101 @ SV112 @ SY186 ) )
| ( in @ SV42 @ ( a_2_1_yellow19 @ SV101 @ SV112 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[973]) ).
thf(1009,plain,
! [SV42: $i,SV113: $i,SV102: $i] :
( ( ( empty_carrier @ SV102 )
= $true )
| ( ( ~ ( one_sorted_str @ SV102 ) )
= $true )
| ( ( empty_carrier @ SV113 )
= $true )
| ( ( ~ ( net_str @ SV113 @ SV102 ) )
= $true )
| ( ( ~ ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
| ~ ( ~ ~ ( ( SV42
!= ( sK6_D @ SV113 @ SV102 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SV113 @ SV102 @ SV42 ) @ ( powerset @ ( the_carrier @ SV102 ) ) ) )
| ~ ( is_eventually_in @ SV102 @ SV113 @ ( sK6_D @ SV113 @ SV102 @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[974]) ).
thf(1010,plain,
! [SV116: $i] :
( ( ( ( empty_carrier @ SV116 )
| ~ ( complete_relstr @ SV116 ) )
= $true )
| ( ( ~ ( empty_carrier @ SV116 ) )
= $true )
| ( ( rel_str @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[975]) ).
thf(1011,plain,
! [SV117: $i] :
( ( ( ( empty_carrier @ SV117 )
| ~ ( complete_relstr @ SV117 ) )
= $true )
| ( ( with_suprema_relstr @ SV117 )
= $true )
| ( ( rel_str @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(1012,plain,
! [SV44: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV44 ) ) )
| ~ ( finite @ ( sK5_B @ SV44 ) ) )
| ~ ( directed_subset @ ( sK5_B @ SV44 ) @ SV44 ) )
= $false )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1013,plain,
! [SV105: $i,SV81: $i] :
( ( ( one_sorted_str @ SV81 )
= $false )
| ( ( empty_carrier @ SV81 )
= $true )
| ( ( empty_carrier @ SV105 )
= $true )
| ( ( ~ ( net_str @ SV105 @ SV81 ) )
= $true )
| ( ( ~ ( empty @ ( filter_of_net_str @ SV81 @ SV105 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1014,plain,
! [SV106: $i,SV82: $i] :
( ( ( one_sorted_str @ SV82 )
= $false )
| ( ( empty_carrier @ SV82 )
= $true )
| ( ( empty_carrier @ SV106 )
= $true )
| ( ( ~ ( net_str @ SV106 @ SV82 ) )
= $true )
| ( ( upper_relstr_subset @ ( filter_of_net_str @ SV82 @ SV106 ) @ ( boole_POSet @ ( cast_as_carrier_subset @ SV82 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1015,plain,
! [SV89: $i] :
( ( ( empty @ ( cast_as_carrier_subset @ SV89 ) )
= $false )
| ( ( lower_bounded_relstr @ SV89 )
= $false )
| ( ( empty_carrier @ SV89 )
= $true )
| ( ( rel_str @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1016,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK2_SY127 )
| ~ ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
| ~ ( upper_relstr_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1017,plain,
! [SV49: $i] :
( ( ( ~ ( ~ ( element @ ( sK9_B @ SV49 ) @ ( powerset @ ( the_carrier @ SV49 ) ) )
| ~ ~ ( empty @ ( sK9_B @ SV49 ) ) ) )
= $true )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[991]) ).
thf(1018,plain,
! [SV49: $i] :
( ( ( lower_relstr_subset @ ( sK9_B @ SV49 ) @ SV49 )
= $true )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1019,plain,
! [SV93: $i] :
( ( ( empty @ ( cast_as_carrier_subset @ SV93 ) )
= $false )
| ( ( upper_bounded_relstr @ SV93 )
= $false )
| ( ( empty_carrier @ SV93 )
= $true )
| ( ( rel_str @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1020,plain,
! [SV53: $i] :
( ( ( empty @ ( sK14_B @ SV53 ) )
= $false )
| ( ( one_sorted_str @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1021,plain,
! [SV118: $i] :
( ( ( rel_str @ SV118 )
= $false )
| ( ( empty_carrier @ SV118 )
= $true )
| ( ( ~ ( empty @ ( cast_as_carrier_subset @ SV118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1022,plain,
! [SV119: $i] :
( ( ( rel_str @ SV119 )
= $false )
| ( ( empty_carrier @ SV119 )
= $true )
| ( ( lower_relstr_subset @ ( cast_as_carrier_subset @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1023,plain,
! [SV23: $i,SV72: $i] :
( ( ( proper_element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
= $false )
| ( ( filtered_subset @ SV72 @ ( boole_POSet @ SV23 ) )
= $false )
| ( ( empty @ SV72 )
= $true )
| ( ( upper_relstr_subset @ SV72 @ ( boole_POSet @ SV23 ) )
= $false )
| ( ( ~ ( element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) ) )
= $true )
| ( ( ! [SY173: $i] :
( ~ ( empty @ SY173 )
| ~ ( in @ SY173 @ SV72 ) ) )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1024,plain,
! [SV36: $i,SV99: $i] :
( ( ( upper_relstr_subset @ SV99 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
= $false )
| ( ( empty @ SV99 )
= $true )
| ( ( filtered_subset @ SV99 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
= $false )
| ( ( ~ ( element @ SV99 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) ) ) )
= $true )
| ( ( ( set_difference @ SV99 @ ( singleton @ empty_set ) )
= ( filter_of_net_str @ SV36 @ ( net_of_bool_filter @ SV36 @ ( cast_as_carrier_subset @ SV36 ) @ SV99 ) ) )
= $true )
| ( ( empty_carrier @ SV36 )
= $true )
| ( ( one_sorted_str @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1025,plain,
! [SV122: $i,SV120: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV120 )
| ~ ( element @ SV120 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SV122 )
| ~ ( filtered_subset @ SV122 @ ( boole_POSet @ SV120 ) )
| ~ ( upper_relstr_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( element @ SV122 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV120 ) ) ) ) )
= $true )
| ( ( ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SV120 @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1026,plain,
! [SV123: $i,SV121: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV121 )
| ~ ( element @ SV121 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SV123 )
| ~ ( filtered_subset @ SV123 @ ( boole_POSet @ SV121 ) )
| ~ ( upper_relstr_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV121 ) ) ) ) )
= $true )
| ( ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SV121 @ SV123 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1027,plain,
! [SV111: $i,SV100: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV100 )
| ~ ( element @ SV100 @ ( powerset @ ( the_carrier @ SV41 ) ) ) )
= $true )
| ( ( empty @ SV111 )
= $true )
| ( ( ~ ( filtered_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( element @ SV111 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV100 ) ) ) ) )
= $true )
| ( ( net_str @ ( net_of_bool_filter @ SV41 @ SV100 @ SV111 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1007]) ).
thf(1028,plain,
! [SV42: $i,SV112: $i,SV101: $i] :
( ( ( one_sorted_str @ SV101 )
= $false )
| ( ( empty_carrier @ SV101 )
= $true )
| ( ( empty_carrier @ SV112 )
= $true )
| ( ( ~ ( net_str @ SV112 @ SV101 ) )
= $true )
| ( ( ! [SY186: $i] :
( ( SV42 != SY186 )
| ~ ( element @ SY186 @ ( powerset @ ( the_carrier @ SV101 ) ) )
| ~ ( is_eventually_in @ SV101 @ SV112 @ SY186 ) )
| ( in @ SV42 @ ( a_2_1_yellow19 @ SV101 @ SV112 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1029,plain,
! [SV42: $i,SV113: $i,SV102: $i] :
( ( ( one_sorted_str @ SV102 )
= $false )
| ( ( empty_carrier @ SV102 )
= $true )
| ( ( empty_carrier @ SV113 )
= $true )
| ( ( ~ ( net_str @ SV113 @ SV102 ) )
= $true )
| ( ( ~ ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
| ~ ( ~ ~ ( ( SV42
!= ( sK6_D @ SV113 @ SV102 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SV113 @ SV102 @ SV42 ) @ ( powerset @ ( the_carrier @ SV102 ) ) ) )
| ~ ( is_eventually_in @ SV102 @ SV113 @ ( sK6_D @ SV113 @ SV102 @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1030,plain,
! [SV116: $i] :
( ( ( empty_carrier @ SV116 )
= $true )
| ( ( ~ ( complete_relstr @ SV116 ) )
= $true )
| ( ( ~ ( empty_carrier @ SV116 ) )
= $true )
| ( ( rel_str @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1010]) ).
thf(1031,plain,
! [SV117: $i] :
( ( ( empty_carrier @ SV117 )
= $true )
| ( ( ~ ( complete_relstr @ SV117 ) )
= $true )
| ( ( with_suprema_relstr @ SV117 )
= $true )
| ( ( rel_str @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1032,plain,
! [SV44: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV44 ) ) )
| ~ ( finite @ ( sK5_B @ SV44 ) ) ) )
= $false )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1012]) ).
thf(1033,plain,
! [SV44: $i] :
( ( ( ~ ( directed_subset @ ( sK5_B @ SV44 ) @ SV44 ) )
= $false )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1012]) ).
thf(1034,plain,
! [SV81: $i,SV105: $i] :
( ( ( net_str @ SV105 @ SV81 )
= $false )
| ( ( empty_carrier @ SV105 )
= $true )
| ( ( empty_carrier @ SV81 )
= $true )
| ( ( one_sorted_str @ SV81 )
= $false )
| ( ( ~ ( empty @ ( filter_of_net_str @ SV81 @ SV105 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1035,plain,
! [SV82: $i,SV106: $i] :
( ( ( net_str @ SV106 @ SV82 )
= $false )
| ( ( empty_carrier @ SV106 )
= $true )
| ( ( empty_carrier @ SV82 )
= $true )
| ( ( one_sorted_str @ SV82 )
= $false )
| ( ( upper_relstr_subset @ ( filter_of_net_str @ SV82 @ SV106 ) @ ( boole_POSet @ ( cast_as_carrier_subset @ SV82 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1036,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK2_SY127 )
| ~ ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1037,plain,
( ( ~ ( upper_relstr_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1038,plain,
! [SV49: $i] :
( ( ( ~ ( element @ ( sK9_B @ SV49 ) @ ( powerset @ ( the_carrier @ SV49 ) ) )
| ~ ~ ( empty @ ( sK9_B @ SV49 ) ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1039,plain,
! [SV118: $i] :
( ( ( empty @ ( cast_as_carrier_subset @ SV118 ) )
= $false )
| ( ( empty_carrier @ SV118 )
= $true )
| ( ( rel_str @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1040,plain,
! [SV23: $i,SV72: $i] :
( ( ( element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
= $false )
| ( ( upper_relstr_subset @ SV72 @ ( boole_POSet @ SV23 ) )
= $false )
| ( ( empty @ SV72 )
= $true )
| ( ( filtered_subset @ SV72 @ ( boole_POSet @ SV23 ) )
= $false )
| ( ( proper_element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
= $false )
| ( ( ! [SY173: $i] :
( ~ ( empty @ SY173 )
| ~ ( in @ SY173 @ SV72 ) ) )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1041,plain,
! [SV36: $i,SV99: $i] :
( ( ( element @ SV99 @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) ) ) )
= $false )
| ( ( filtered_subset @ SV99 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
= $false )
| ( ( empty @ SV99 )
= $true )
| ( ( upper_relstr_subset @ SV99 @ ( boole_POSet @ ( cast_as_carrier_subset @ SV36 ) ) )
= $false )
| ( ( ( set_difference @ SV99 @ ( singleton @ empty_set ) )
= ( filter_of_net_str @ SV36 @ ( net_of_bool_filter @ SV36 @ ( cast_as_carrier_subset @ SV36 ) @ SV99 ) ) )
= $true )
| ( ( empty_carrier @ SV36 )
= $true )
| ( ( one_sorted_str @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1042,plain,
! [SV122: $i,SV120: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV120 )
| ~ ( element @ SV120 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SV122 )
| ~ ( filtered_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( element @ SV122 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV120 ) ) ) ) )
= $true )
| ( ( ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SV120 @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1043,plain,
! [SV123: $i,SV121: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV121 )
| ~ ( element @ SV121 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SV123 )
| ~ ( filtered_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV121 ) ) ) ) )
= $true )
| ( ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SV121 @ SV123 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1044,plain,
! [SV111: $i,SV100: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV100 ) )
= $true )
| ( ( ~ ( element @ SV100 @ ( powerset @ ( the_carrier @ SV41 ) ) ) )
= $true )
| ( ( empty @ SV111 )
= $true )
| ( ( ~ ( filtered_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( element @ SV111 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV100 ) ) ) ) )
= $true )
| ( ( net_str @ ( net_of_bool_filter @ SV41 @ SV100 @ SV111 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1045,plain,
! [SV42: $i,SV101: $i,SV112: $i] :
( ( ( net_str @ SV112 @ SV101 )
= $false )
| ( ( empty_carrier @ SV112 )
= $true )
| ( ( empty_carrier @ SV101 )
= $true )
| ( ( one_sorted_str @ SV101 )
= $false )
| ( ( ! [SY186: $i] :
( ( SV42 != SY186 )
| ~ ( element @ SY186 @ ( powerset @ ( the_carrier @ SV101 ) ) )
| ~ ( is_eventually_in @ SV101 @ SV112 @ SY186 ) )
| ( in @ SV42 @ ( a_2_1_yellow19 @ SV101 @ SV112 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1046,plain,
! [SV42: $i,SV102: $i,SV113: $i] :
( ( ( net_str @ SV113 @ SV102 )
= $false )
| ( ( empty_carrier @ SV113 )
= $true )
| ( ( empty_carrier @ SV102 )
= $true )
| ( ( one_sorted_str @ SV102 )
= $false )
| ( ( ~ ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
| ~ ( ~ ~ ( ( SV42
!= ( sK6_D @ SV113 @ SV102 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SV113 @ SV102 @ SV42 ) @ ( powerset @ ( the_carrier @ SV102 ) ) ) )
| ~ ( is_eventually_in @ SV102 @ SV113 @ ( sK6_D @ SV113 @ SV102 @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1047,plain,
! [SV116: $i] :
( ( ( complete_relstr @ SV116 )
= $false )
| ( ( empty_carrier @ SV116 )
= $true )
| ( ( ~ ( empty_carrier @ SV116 ) )
= $true )
| ( ( rel_str @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1048,plain,
! [SV117: $i] :
( ( ( complete_relstr @ SV117 )
= $false )
| ( ( empty_carrier @ SV117 )
= $true )
| ( ( with_suprema_relstr @ SV117 )
= $true )
| ( ( rel_str @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1049,plain,
! [SV44: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV44 ) ) )
| ~ ( finite @ ( sK5_B @ SV44 ) ) ) )
= $true )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1032]) ).
thf(1050,plain,
! [SV44: $i] :
( ( ( directed_subset @ ( sK5_B @ SV44 ) @ SV44 )
= $true )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1051,plain,
! [SV105: $i,SV81: $i] :
( ( ( empty @ ( filter_of_net_str @ SV81 @ SV105 ) )
= $false )
| ( ( one_sorted_str @ SV81 )
= $false )
| ( ( empty_carrier @ SV81 )
= $true )
| ( ( empty_carrier @ SV105 )
= $true )
| ( ( net_str @ SV105 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1052,plain,
( ( ~ ( ~ ~ ( empty @ sK2_SY127 )
| ~ ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1036]) ).
thf(1053,plain,
( ( upper_relstr_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1037]) ).
thf(1054,plain,
! [SV49: $i] :
( ( ( ~ ( element @ ( sK9_B @ SV49 ) @ ( powerset @ ( the_carrier @ SV49 ) ) ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1038]) ).
thf(1055,plain,
! [SV49: $i] :
( ( ( ~ ~ ( empty @ ( sK9_B @ SV49 ) ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1038]) ).
thf(1056,plain,
! [SV23: $i,SV72: $i,SV124: $i] :
( ( ( ~ ( empty @ SV124 )
| ~ ( in @ SV124 @ SV72 ) )
= $true )
| ( ( proper_element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
= $false )
| ( ( filtered_subset @ SV72 @ ( boole_POSet @ SV23 ) )
= $false )
| ( ( empty @ SV72 )
= $true )
| ( ( upper_relstr_subset @ SV72 @ ( boole_POSet @ SV23 ) )
= $false )
| ( ( element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
= $false )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1057,plain,
! [SV122: $i,SV120: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV120 )
| ~ ( element @ SV120 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SV122 ) )
= $true )
| ( ( ~ ( filtered_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( element @ SV122 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV120 ) ) ) ) )
= $true )
| ( ( ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SV120 @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1058,plain,
! [SV123: $i,SV121: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV121 )
| ~ ( element @ SV121 @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ( empty @ SV123 ) )
= $true )
| ( ( ~ ( filtered_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV121 ) ) ) ) )
= $true )
| ( ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SV121 @ SV123 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1043]) ).
thf(1059,plain,
! [SV111: $i,SV100: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 ) )
= $true )
| ( ( empty @ SV100 )
= $true )
| ( ( ~ ( element @ SV100 @ ( powerset @ ( the_carrier @ SV41 ) ) ) )
= $true )
| ( ( empty @ SV111 )
= $true )
| ( ( ~ ( filtered_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( element @ SV111 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV100 ) ) ) ) )
= $true )
| ( ( net_str @ ( net_of_bool_filter @ SV41 @ SV100 @ SV111 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1060,plain,
! [SV112: $i,SV101: $i,SV42: $i] :
( ( ( ! [SY186: $i] :
( ( SV42 != SY186 )
| ~ ( element @ SY186 @ ( powerset @ ( the_carrier @ SV101 ) ) )
| ~ ( is_eventually_in @ SV101 @ SV112 @ SY186 ) ) )
= $true )
| ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV101 @ SV112 ) )
= $true )
| ( ( one_sorted_str @ SV101 )
= $false )
| ( ( empty_carrier @ SV101 )
= $true )
| ( ( empty_carrier @ SV112 )
= $true )
| ( ( net_str @ SV112 @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1061,plain,
! [SV113: $i,SV102: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV42
!= ( sK6_D @ SV113 @ SV102 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SV113 @ SV102 @ SV42 ) @ ( powerset @ ( the_carrier @ SV102 ) ) ) )
| ~ ( is_eventually_in @ SV102 @ SV113 @ ( sK6_D @ SV113 @ SV102 @ SV42 ) ) ) )
= $true )
| ( ( one_sorted_str @ SV102 )
= $false )
| ( ( empty_carrier @ SV102 )
= $true )
| ( ( empty_carrier @ SV113 )
= $true )
| ( ( net_str @ SV113 @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1062,plain,
! [SV116: $i] :
( ( ( empty_carrier @ SV116 )
= $false )
| ( ( empty_carrier @ SV116 )
= $true )
| ( ( complete_relstr @ SV116 )
= $false )
| ( ( rel_str @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1063,plain,
! [SV44: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV44 ) ) )
| ~ ( finite @ ( sK5_B @ SV44 ) ) )
= $false )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1064,plain,
( ( ~ ~ ( empty @ sK2_SY127 )
| ~ ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1065,plain,
! [SV49: $i] :
( ( ( element @ ( sK9_B @ SV49 ) @ ( powerset @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1054]) ).
thf(1066,plain,
! [SV49: $i] :
( ( ( ~ ( empty @ ( sK9_B @ SV49 ) ) )
= $true )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1055]) ).
thf(1067,plain,
! [SV23: $i,SV72: $i,SV124: $i] :
( ( ( ~ ( empty @ SV124 ) )
= $true )
| ( ( ~ ( in @ SV124 @ SV72 ) )
= $true )
| ( ( proper_element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
= $false )
| ( ( filtered_subset @ SV72 @ ( boole_POSet @ SV23 ) )
= $false )
| ( ( empty @ SV72 )
= $true )
| ( ( upper_relstr_subset @ SV72 @ ( boole_POSet @ SV23 ) )
= $false )
| ( ( element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
= $false )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1068,plain,
! [SV122: $i,SV120: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV120 )
| ~ ( element @ SV120 @ ( powerset @ ( the_carrier @ SV41 ) ) ) )
= $true )
| ( ( empty @ SV122 )
= $true )
| ( ( ~ ( filtered_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( element @ SV122 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV120 ) ) ) ) )
= $true )
| ( ( ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SV120 @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1069,plain,
! [SV123: $i,SV121: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV121 )
| ~ ( element @ SV121 @ ( powerset @ ( the_carrier @ SV41 ) ) ) )
= $true )
| ( ( empty @ SV123 )
= $true )
| ( ( ~ ( filtered_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV121 ) ) ) ) )
= $true )
| ( ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SV121 @ SV123 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1070,plain,
! [SV111: $i,SV100: $i,SV41: $i] :
( ( ( empty_carrier @ SV41 )
= $true )
| ( ( ~ ( one_sorted_str @ SV41 ) )
= $true )
| ( ( empty @ SV100 )
= $true )
| ( ( ~ ( element @ SV100 @ ( powerset @ ( the_carrier @ SV41 ) ) ) )
= $true )
| ( ( empty @ SV111 )
= $true )
| ( ( ~ ( filtered_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( element @ SV111 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV100 ) ) ) ) )
= $true )
| ( ( net_str @ ( net_of_bool_filter @ SV41 @ SV100 @ SV111 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1071,plain,
! [SV112: $i,SV101: $i,SV125: $i,SV42: $i] :
( ( ( ( SV42 != SV125 )
| ~ ( element @ SV125 @ ( powerset @ ( the_carrier @ SV101 ) ) )
| ~ ( is_eventually_in @ SV101 @ SV112 @ SV125 ) )
= $true )
| ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV101 @ SV112 ) )
= $true )
| ( ( one_sorted_str @ SV101 )
= $false )
| ( ( empty_carrier @ SV101 )
= $true )
| ( ( empty_carrier @ SV112 )
= $true )
| ( ( net_str @ SV112 @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1072,plain,
! [SV113: $i,SV102: $i,SV42: $i] :
( ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV42
!= ( sK6_D @ SV113 @ SV102 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SV113 @ SV102 @ SV42 ) @ ( powerset @ ( the_carrier @ SV102 ) ) ) )
| ~ ( is_eventually_in @ SV102 @ SV113 @ ( sK6_D @ SV113 @ SV102 @ SV42 ) ) ) )
= $true )
| ( ( one_sorted_str @ SV102 )
= $false )
| ( ( empty_carrier @ SV102 )
= $true )
| ( ( empty_carrier @ SV113 )
= $true )
| ( ( net_str @ SV113 @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1073,plain,
! [SV44: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV44 ) ) ) )
= $false )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1063]) ).
thf(1074,plain,
! [SV44: $i] :
( ( ( ~ ( finite @ ( sK5_B @ SV44 ) ) )
= $false )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1063]) ).
thf(1075,plain,
( ( ~ ~ ( empty @ sK2_SY127 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1064]) ).
thf(1076,plain,
( ( ~ ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1064]) ).
thf(1077,plain,
! [SV49: $i] :
( ( ( empty @ ( sK9_B @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1078,plain,
! [SV23: $i,SV72: $i,SV124: $i] :
( ( ( empty @ SV124 )
= $false )
| ( ( ~ ( in @ SV124 @ SV72 ) )
= $true )
| ( ( proper_element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
= $false )
| ( ( filtered_subset @ SV72 @ ( boole_POSet @ SV23 ) )
= $false )
| ( ( empty @ SV72 )
= $true )
| ( ( upper_relstr_subset @ SV72 @ ( boole_POSet @ SV23 ) )
= $false )
| ( ( element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
= $false )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1079,plain,
! [SV122: $i,SV120: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV120 ) )
= $true )
| ( ( ~ ( element @ SV120 @ ( powerset @ ( the_carrier @ SV41 ) ) ) )
= $true )
| ( ( empty @ SV122 )
= $true )
| ( ( ~ ( filtered_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( element @ SV122 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV120 ) ) ) ) )
= $true )
| ( ( ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SV120 @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1080,plain,
! [SV123: $i,SV121: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ( empty @ SV121 ) )
= $true )
| ( ( ~ ( element @ SV121 @ ( powerset @ ( the_carrier @ SV41 ) ) ) )
= $true )
| ( ( empty @ SV123 )
= $true )
| ( ( ~ ( filtered_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV121 ) ) ) ) )
= $true )
| ( ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SV121 @ SV123 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1081,plain,
! [SV111: $i,SV100: $i,SV41: $i] :
( ( ( one_sorted_str @ SV41 )
= $false )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( empty @ SV100 )
= $true )
| ( ( ~ ( element @ SV100 @ ( powerset @ ( the_carrier @ SV41 ) ) ) )
= $true )
| ( ( empty @ SV111 )
= $true )
| ( ( ~ ( filtered_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( element @ SV111 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV100 ) ) ) ) )
= $true )
| ( ( net_str @ ( net_of_bool_filter @ SV41 @ SV100 @ SV111 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1070]) ).
thf(1082,plain,
! [SV112: $i,SV101: $i,SV125: $i,SV42: $i] :
( ( ( ( SV42 != SV125 )
| ~ ( element @ SV125 @ ( powerset @ ( the_carrier @ SV101 ) ) ) )
= $true )
| ( ( ~ ( is_eventually_in @ SV101 @ SV112 @ SV125 ) )
= $true )
| ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV101 @ SV112 ) )
= $true )
| ( ( one_sorted_str @ SV101 )
= $false )
| ( ( empty_carrier @ SV101 )
= $true )
| ( ( empty_carrier @ SV112 )
= $true )
| ( ( net_str @ SV112 @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1071]) ).
thf(1083,plain,
! [SV102: $i,SV113: $i,SV42: $i] :
( ( ( ~ ~ ( ( SV42
!= ( sK6_D @ SV113 @ SV102 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SV113 @ SV102 @ SV42 ) @ ( powerset @ ( the_carrier @ SV102 ) ) ) )
| ~ ( is_eventually_in @ SV102 @ SV113 @ ( sK6_D @ SV113 @ SV102 @ SV42 ) ) )
= $false )
| ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
= $false )
| ( ( one_sorted_str @ SV102 )
= $false )
| ( ( empty_carrier @ SV102 )
= $true )
| ( ( empty_carrier @ SV113 )
= $true )
| ( ( net_str @ SV113 @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1084,plain,
! [SV44: $i] :
( ( ( ~ ( ~ ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV44 ) ) ) )
= $true )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1085,plain,
! [SV44: $i] :
( ( ( finite @ ( sK5_B @ SV44 ) )
= $true )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1086,plain,
( ( ~ ( empty @ sK2_SY127 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1075]) ).
thf(1087,plain,
( ( filtered_subset @ sK2_SY127 @ ( boole_POSet @ ( cast_as_carrier_subset @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1076]) ).
thf(1088,plain,
! [SV23: $i,SV72: $i,SV124: $i] :
( ( ( in @ SV124 @ SV72 )
= $false )
| ( ( empty @ SV124 )
= $false )
| ( ( proper_element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
= $false )
| ( ( filtered_subset @ SV72 @ ( boole_POSet @ SV23 ) )
= $false )
| ( ( empty @ SV72 )
= $true )
| ( ( upper_relstr_subset @ SV72 @ ( boole_POSet @ SV23 ) )
= $false )
| ( ( element @ SV72 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV23 ) ) ) )
= $false )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1089,plain,
! [SV122: $i,SV120: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 ) )
= $true )
| ( ( empty @ SV120 )
= $true )
| ( ( ~ ( element @ SV120 @ ( powerset @ ( the_carrier @ SV41 ) ) ) )
= $true )
| ( ( empty @ SV122 )
= $true )
| ( ( ~ ( filtered_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( element @ SV122 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV120 ) ) ) ) )
= $true )
| ( ( ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SV120 @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1090,plain,
! [SV123: $i,SV121: $i,SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 ) )
= $true )
| ( ( empty @ SV121 )
= $true )
| ( ( ~ ( element @ SV121 @ ( powerset @ ( the_carrier @ SV41 ) ) ) )
= $true )
| ( ( empty @ SV123 )
= $true )
| ( ( ~ ( filtered_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV121 ) ) ) ) )
= $true )
| ( ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SV121 @ SV123 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1080]) ).
thf(1091,plain,
! [SV111: $i,SV41: $i,SV100: $i] :
( ( ( element @ SV100 @ ( powerset @ ( the_carrier @ SV41 ) ) )
= $false )
| ( ( empty @ SV100 )
= $true )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false )
| ( ( empty @ SV111 )
= $true )
| ( ( ~ ( filtered_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( element @ SV111 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV100 ) ) ) ) )
= $true )
| ( ( net_str @ ( net_of_bool_filter @ SV41 @ SV100 @ SV111 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1092,plain,
! [SV112: $i,SV101: $i,SV125: $i,SV42: $i] :
( ( ( SV42 != SV125 )
= $true )
| ( ( ~ ( element @ SV125 @ ( powerset @ ( the_carrier @ SV101 ) ) ) )
= $true )
| ( ( ~ ( is_eventually_in @ SV101 @ SV112 @ SV125 ) )
= $true )
| ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV101 @ SV112 ) )
= $true )
| ( ( one_sorted_str @ SV101 )
= $false )
| ( ( empty_carrier @ SV101 )
= $true )
| ( ( empty_carrier @ SV112 )
= $true )
| ( ( net_str @ SV112 @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1093,plain,
! [SV102: $i,SV113: $i,SV42: $i] :
( ( ( ~ ~ ( ( SV42
!= ( sK6_D @ SV113 @ SV102 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SV113 @ SV102 @ SV42 ) @ ( powerset @ ( the_carrier @ SV102 ) ) ) ) )
= $false )
| ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
= $false )
| ( ( one_sorted_str @ SV102 )
= $false )
| ( ( empty_carrier @ SV102 )
= $true )
| ( ( empty_carrier @ SV113 )
= $true )
| ( ( net_str @ SV113 @ SV102 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1094,plain,
! [SV42: $i,SV113: $i,SV102: $i] :
( ( ( ~ ( is_eventually_in @ SV102 @ SV113 @ ( sK6_D @ SV113 @ SV102 @ SV42 ) ) )
= $false )
| ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
= $false )
| ( ( one_sorted_str @ SV102 )
= $false )
| ( ( empty_carrier @ SV102 )
= $true )
| ( ( empty_carrier @ SV113 )
= $true )
| ( ( net_str @ SV113 @ SV102 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1095,plain,
! [SV44: $i] :
( ( ( ~ ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV44 ) ) )
= $false )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1096,plain,
( ( empty @ sK2_SY127 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1097,plain,
! [SV122: $i,SV120: $i,SV41: $i] :
( ( ( empty_carrier @ SV41 )
= $true )
| ( ( ~ ( one_sorted_str @ SV41 ) )
= $true )
| ( ( empty @ SV120 )
= $true )
| ( ( ~ ( element @ SV120 @ ( powerset @ ( the_carrier @ SV41 ) ) ) )
= $true )
| ( ( empty @ SV122 )
= $true )
| ( ( ~ ( filtered_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( element @ SV122 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV120 ) ) ) ) )
= $true )
| ( ( ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SV120 @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1098,plain,
! [SV123: $i,SV121: $i,SV41: $i] :
( ( ( empty_carrier @ SV41 )
= $true )
| ( ( ~ ( one_sorted_str @ SV41 ) )
= $true )
| ( ( empty @ SV121 )
= $true )
| ( ( ~ ( element @ SV121 @ ( powerset @ ( the_carrier @ SV41 ) ) ) )
= $true )
| ( ( empty @ SV123 )
= $true )
| ( ( ~ ( filtered_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV121 ) ) ) ) )
= $true )
| ( ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SV121 @ SV123 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1099,plain,
! [SV41: $i,SV100: $i,SV111: $i] :
( ( ( filtered_subset @ SV111 @ ( boole_POSet @ SV100 ) )
= $false )
| ( ( empty @ SV111 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( empty @ SV100 )
= $true )
| ( ( element @ SV100 @ ( powerset @ ( the_carrier @ SV41 ) ) )
= $false )
| ( ( ~ ( upper_relstr_subset @ SV111 @ ( boole_POSet @ SV100 ) ) )
= $true )
| ( ( ~ ( element @ SV111 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV100 ) ) ) ) )
= $true )
| ( ( net_str @ ( net_of_bool_filter @ SV41 @ SV100 @ SV111 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1100,plain,
! [SV112: $i,SV101: $i,SV125: $i,SV42: $i] :
( ( ( SV42 = SV125 )
= $false )
| ( ( ~ ( element @ SV125 @ ( powerset @ ( the_carrier @ SV101 ) ) ) )
= $true )
| ( ( ~ ( is_eventually_in @ SV101 @ SV112 @ SV125 ) )
= $true )
| ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV101 @ SV112 ) )
= $true )
| ( ( one_sorted_str @ SV101 )
= $false )
| ( ( empty_carrier @ SV101 )
= $true )
| ( ( empty_carrier @ SV112 )
= $true )
| ( ( net_str @ SV112 @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1101,plain,
! [SV102: $i,SV113: $i,SV42: $i] :
( ( ( ~ ( ( SV42
!= ( sK6_D @ SV113 @ SV102 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SV113 @ SV102 @ SV42 ) @ ( powerset @ ( the_carrier @ SV102 ) ) ) ) )
= $true )
| ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
= $false )
| ( ( one_sorted_str @ SV102 )
= $false )
| ( ( empty_carrier @ SV102 )
= $true )
| ( ( empty_carrier @ SV113 )
= $true )
| ( ( net_str @ SV113 @ SV102 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1093]) ).
thf(1102,plain,
! [SV42: $i,SV113: $i,SV102: $i] :
( ( ( is_eventually_in @ SV102 @ SV113 @ ( sK6_D @ SV113 @ SV102 @ SV42 ) )
= $true )
| ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
= $false )
| ( ( one_sorted_str @ SV102 )
= $false )
| ( ( empty_carrier @ SV102 )
= $true )
| ( ( empty_carrier @ SV113 )
= $true )
| ( ( net_str @ SV113 @ SV102 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1103,plain,
! [SV44: $i] :
( ( ( ~ ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) ) )
= $false )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1095]) ).
thf(1104,plain,
! [SV44: $i] :
( ( ( ~ ~ ( empty @ ( sK5_B @ SV44 ) ) )
= $false )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1095]) ).
thf(1105,plain,
! [SV122: $i,SV120: $i,SV41: $i] :
( ( ( one_sorted_str @ SV41 )
= $false )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( empty @ SV120 )
= $true )
| ( ( ~ ( element @ SV120 @ ( powerset @ ( the_carrier @ SV41 ) ) ) )
= $true )
| ( ( empty @ SV122 )
= $true )
| ( ( ~ ( filtered_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( element @ SV122 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV120 ) ) ) ) )
= $true )
| ( ( ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SV120 @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1106,plain,
! [SV123: $i,SV121: $i,SV41: $i] :
( ( ( one_sorted_str @ SV41 )
= $false )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( empty @ SV121 )
= $true )
| ( ( ~ ( element @ SV121 @ ( powerset @ ( the_carrier @ SV41 ) ) ) )
= $true )
| ( ( empty @ SV123 )
= $true )
| ( ( ~ ( filtered_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV121 ) ) ) ) )
= $true )
| ( ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SV121 @ SV123 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1107,plain,
! [SV41: $i,SV100: $i,SV111: $i] :
( ( ( upper_relstr_subset @ SV111 @ ( boole_POSet @ SV100 ) )
= $false )
| ( ( element @ SV100 @ ( powerset @ ( the_carrier @ SV41 ) ) )
= $false )
| ( ( empty @ SV100 )
= $true )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false )
| ( ( empty @ SV111 )
= $true )
| ( ( filtered_subset @ SV111 @ ( boole_POSet @ SV100 ) )
= $false )
| ( ( ~ ( element @ SV111 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV100 ) ) ) ) )
= $true )
| ( ( net_str @ ( net_of_bool_filter @ SV41 @ SV100 @ SV111 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1108,plain,
! [SV112: $i,SV42: $i,SV101: $i,SV125: $i] :
( ( ( element @ SV125 @ ( powerset @ ( the_carrier @ SV101 ) ) )
= $false )
| ( ( SV42 = SV125 )
= $false )
| ( ( ~ ( is_eventually_in @ SV101 @ SV112 @ SV125 ) )
= $true )
| ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV101 @ SV112 ) )
= $true )
| ( ( one_sorted_str @ SV101 )
= $false )
| ( ( empty_carrier @ SV101 )
= $true )
| ( ( empty_carrier @ SV112 )
= $true )
| ( ( net_str @ SV112 @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1109,plain,
! [SV102: $i,SV113: $i,SV42: $i] :
( ( ( ( SV42
!= ( sK6_D @ SV113 @ SV102 @ SV42 ) )
| ~ ( element @ ( sK6_D @ SV113 @ SV102 @ SV42 ) @ ( powerset @ ( the_carrier @ SV102 ) ) ) )
= $false )
| ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
= $false )
| ( ( one_sorted_str @ SV102 )
= $false )
| ( ( empty_carrier @ SV102 )
= $true )
| ( ( empty_carrier @ SV113 )
= $true )
| ( ( net_str @ SV113 @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1110,plain,
! [SV44: $i] :
( ( ( element @ ( sK5_B @ SV44 ) @ ( powerset @ ( the_carrier @ SV44 ) ) )
= $true )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1111,plain,
! [SV44: $i] :
( ( ( ~ ( empty @ ( sK5_B @ SV44 ) ) )
= $true )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1104]) ).
thf(1112,plain,
! [SV122: $i,SV41: $i,SV120: $i] :
( ( ( element @ SV120 @ ( powerset @ ( the_carrier @ SV41 ) ) )
= $false )
| ( ( empty @ SV120 )
= $true )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false )
| ( ( empty @ SV122 )
= $true )
| ( ( ~ ( filtered_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( element @ SV122 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV120 ) ) ) ) )
= $true )
| ( ( ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SV120 @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1113,plain,
! [SV123: $i,SV41: $i,SV121: $i] :
( ( ( element @ SV121 @ ( powerset @ ( the_carrier @ SV41 ) ) )
= $false )
| ( ( empty @ SV121 )
= $true )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false )
| ( ( empty @ SV123 )
= $true )
| ( ( ~ ( filtered_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV121 ) ) ) ) )
= $true )
| ( ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SV121 @ SV123 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1114,plain,
! [SV41: $i,SV100: $i,SV111: $i] :
( ( ( element @ SV111 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV100 ) ) ) )
= $false )
| ( ( filtered_subset @ SV111 @ ( boole_POSet @ SV100 ) )
= $false )
| ( ( empty @ SV111 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( empty @ SV100 )
= $true )
| ( ( element @ SV100 @ ( powerset @ ( the_carrier @ SV41 ) ) )
= $false )
| ( ( upper_relstr_subset @ SV111 @ ( boole_POSet @ SV100 ) )
= $false )
| ( ( net_str @ ( net_of_bool_filter @ SV41 @ SV100 @ SV111 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1115,plain,
! [SV42: $i,SV125: $i,SV112: $i,SV101: $i] :
( ( ( is_eventually_in @ SV101 @ SV112 @ SV125 )
= $false )
| ( ( SV42 = SV125 )
= $false )
| ( ( element @ SV125 @ ( powerset @ ( the_carrier @ SV101 ) ) )
= $false )
| ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV101 @ SV112 ) )
= $true )
| ( ( one_sorted_str @ SV101 )
= $false )
| ( ( empty_carrier @ SV101 )
= $true )
| ( ( empty_carrier @ SV112 )
= $true )
| ( ( net_str @ SV112 @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1116,plain,
! [SV102: $i,SV113: $i,SV42: $i] :
( ( ( SV42
!= ( sK6_D @ SV113 @ SV102 @ SV42 ) )
= $false )
| ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
= $false )
| ( ( one_sorted_str @ SV102 )
= $false )
| ( ( empty_carrier @ SV102 )
= $true )
| ( ( empty_carrier @ SV113 )
= $true )
| ( ( net_str @ SV113 @ SV102 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1109]) ).
thf(1117,plain,
! [SV42: $i,SV102: $i,SV113: $i] :
( ( ( ~ ( element @ ( sK6_D @ SV113 @ SV102 @ SV42 ) @ ( powerset @ ( the_carrier @ SV102 ) ) ) )
= $false )
| ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
= $false )
| ( ( one_sorted_str @ SV102 )
= $false )
| ( ( empty_carrier @ SV102 )
= $true )
| ( ( empty_carrier @ SV113 )
= $true )
| ( ( net_str @ SV113 @ SV102 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1109]) ).
thf(1118,plain,
! [SV44: $i] :
( ( ( empty @ ( sK5_B @ SV44 ) )
= $false )
| ( ( reflexive_relstr @ SV44 )
= $false )
| ( ( empty_carrier @ SV44 )
= $true )
| ( ( rel_str @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1119,plain,
! [SV41: $i,SV120: $i,SV122: $i] :
( ( ( filtered_subset @ SV122 @ ( boole_POSet @ SV120 ) )
= $false )
| ( ( empty @ SV122 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( empty @ SV120 )
= $true )
| ( ( element @ SV120 @ ( powerset @ ( the_carrier @ SV41 ) ) )
= $false )
| ( ( ~ ( upper_relstr_subset @ SV122 @ ( boole_POSet @ SV120 ) ) )
= $true )
| ( ( ~ ( element @ SV122 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV120 ) ) ) ) )
= $true )
| ( ( ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SV120 @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1120,plain,
! [SV41: $i,SV121: $i,SV123: $i] :
( ( ( filtered_subset @ SV123 @ ( boole_POSet @ SV121 ) )
= $false )
| ( ( empty @ SV123 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( empty @ SV121 )
= $true )
| ( ( element @ SV121 @ ( powerset @ ( the_carrier @ SV41 ) ) )
= $false )
| ( ( ~ ( upper_relstr_subset @ SV123 @ ( boole_POSet @ SV121 ) ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV121 ) ) ) ) )
= $true )
| ( ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SV121 @ SV123 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1121,plain,
! [SV102: $i,SV113: $i,SV42: $i] :
( ( ( SV42
= ( sK6_D @ SV113 @ SV102 @ SV42 ) )
= $true )
| ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
= $false )
| ( ( one_sorted_str @ SV102 )
= $false )
| ( ( empty_carrier @ SV102 )
= $true )
| ( ( empty_carrier @ SV113 )
= $true )
| ( ( net_str @ SV113 @ SV102 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1116]) ).
thf(1122,plain,
! [SV42: $i,SV102: $i,SV113: $i] :
( ( ( element @ ( sK6_D @ SV113 @ SV102 @ SV42 ) @ ( powerset @ ( the_carrier @ SV102 ) ) )
= $true )
| ( ( in @ SV42 @ ( a_2_1_yellow19 @ SV102 @ SV113 ) )
= $false )
| ( ( one_sorted_str @ SV102 )
= $false )
| ( ( empty_carrier @ SV102 )
= $true )
| ( ( empty_carrier @ SV113 )
= $true )
| ( ( net_str @ SV113 @ SV102 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1117]) ).
thf(1123,plain,
! [SV41: $i,SV120: $i,SV122: $i] :
( ( ( upper_relstr_subset @ SV122 @ ( boole_POSet @ SV120 ) )
= $false )
| ( ( element @ SV120 @ ( powerset @ ( the_carrier @ SV41 ) ) )
= $false )
| ( ( empty @ SV120 )
= $true )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false )
| ( ( empty @ SV122 )
= $true )
| ( ( filtered_subset @ SV122 @ ( boole_POSet @ SV120 ) )
= $false )
| ( ( ~ ( element @ SV122 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV120 ) ) ) ) )
= $true )
| ( ( ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SV120 @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1124,plain,
! [SV41: $i,SV121: $i,SV123: $i] :
( ( ( upper_relstr_subset @ SV123 @ ( boole_POSet @ SV121 ) )
= $false )
| ( ( element @ SV121 @ ( powerset @ ( the_carrier @ SV41 ) ) )
= $false )
| ( ( empty @ SV121 )
= $true )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false )
| ( ( empty @ SV123 )
= $true )
| ( ( filtered_subset @ SV123 @ ( boole_POSet @ SV121 ) )
= $false )
| ( ( ~ ( element @ SV123 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV121 ) ) ) ) )
= $true )
| ( ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SV121 @ SV123 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1125,plain,
! [SV41: $i,SV120: $i,SV122: $i] :
( ( ( element @ SV122 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV120 ) ) ) )
= $false )
| ( ( filtered_subset @ SV122 @ ( boole_POSet @ SV120 ) )
= $false )
| ( ( empty @ SV122 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( empty @ SV120 )
= $true )
| ( ( element @ SV120 @ ( powerset @ ( the_carrier @ SV41 ) ) )
= $false )
| ( ( upper_relstr_subset @ SV122 @ ( boole_POSet @ SV120 ) )
= $false )
| ( ( ~ ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SV120 @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1126,plain,
! [SV41: $i,SV121: $i,SV123: $i] :
( ( ( element @ SV123 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV121 ) ) ) )
= $false )
| ( ( filtered_subset @ SV123 @ ( boole_POSet @ SV121 ) )
= $false )
| ( ( empty @ SV123 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( empty @ SV121 )
= $true )
| ( ( element @ SV121 @ ( powerset @ ( the_carrier @ SV41 ) ) )
= $false )
| ( ( upper_relstr_subset @ SV123 @ ( boole_POSet @ SV121 ) )
= $false )
| ( ( strict_net_str @ ( net_of_bool_filter @ SV41 @ SV121 @ SV123 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1127,plain,
! [SV122: $i,SV120: $i,SV41: $i] :
( ( ( empty_carrier @ ( net_of_bool_filter @ SV41 @ SV120 @ SV122 ) )
= $false )
| ( ( upper_relstr_subset @ SV122 @ ( boole_POSet @ SV120 ) )
= $false )
| ( ( element @ SV120 @ ( powerset @ ( the_carrier @ SV41 ) ) )
= $false )
| ( ( empty @ SV120 )
= $true )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false )
| ( ( empty @ SV122 )
= $true )
| ( ( filtered_subset @ SV122 @ ( boole_POSet @ SV120 ) )
= $false )
| ( ( element @ SV122 @ ( powerset @ ( the_carrier @ ( boole_POSet @ SV120 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1128,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[294,1127,1126,1122,1121,1118,1115,1114,1110,1102,1096,1088,1087,1085,1077,1065,1062,1053,1051,1050,1048,1041,1039,1035,1022,1020,1019,1018,1015,1002,999,998,996,995,993,990,988,986,985,984,981,980,979,977,967,956,950,949,947,945,944,933,932,925,923,922,919,912,909,908,897,896,884,876,867,865,861,860,853,839,833,824,823,822,820,819,818,814,811,810,809,791,784,782,760,754,752,748,747,746,745,744,743,737,729,728,724,722,719,717,711,710,699,696,680,672,657,656,647,644,639,638,635,634,617,613,596,592,582,579,577,572,570,511,498,496,446,445,444,442,421,370,352,310,309,307,306,304,302,299,296,295]) ).
thf(1129,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU394+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n020.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 15:19:36 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.02/2.25
% 12.02/2.25 No.of.Axioms: 126
% 12.02/2.25
% 12.02/2.25 Length.of.Defs: 0
% 12.02/2.25
% 12.02/2.25 Contains.Choice.Funs: false
% 12.02/2.25 ..................................
% 12.02/2.25
% 12.02/2.25 ********************************
% 12.02/2.25 * All subproblems solved! *
% 12.02/2.25 ********************************
% 12.02/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:85,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1128,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 12.02/2.25
% 12.02/2.25 %**** Beginning of derivation protocol ****
% 12.02/2.25 % SZS output start CNFRefutation
% See solution above
% 12.02/2.26
% 12.02/2.26 %**** End of derivation protocol ****
% 12.02/2.26 %**** no. of clauses in derivation: 1086 ****
% 12.02/2.26 %**** clause counter: 1128 ****
% 12.02/2.26
% 12.02/2.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:85,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1128,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------