%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU326+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:59 AM UTC 2026
% Result : Theorem 4.33s 1.04s
% Output : CNFRefutation 4.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 64
% Syntax : Number of formulae : 690 ( 464 unt; 0 typ; 0 def)
% Number of atoms : 3201 (1167 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 5133 ( 908 ~; 592 |; 56 &;3468 @)
% ( 8 <=>; 101 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 130 ( 127 usr; 6 con; 0-6 aty)
% Number of variables : 1121 ( 0 ^;1109 !; 12 ?;1121 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_apply_binary,type,
apply_binary: $i > $i > $i > $i ).
thf(tp_apply_binary_as_element,type,
apply_binary_as_element: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_are_equipotent,type,
are_equipotent: $i > $i > $o ).
thf(tp_being_limit_ordinal,type,
being_limit_ordinal: $i > $o ).
thf(tp_below,type,
below: $i > $i > $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_cast_to_subset,type,
cast_to_subset: $i > $i ).
thf(tp_closed_subset,type,
closed_subset: $i > $i > $o ).
thf(tp_complements_of_subsets,type,
complements_of_subsets: $i > $i > $i ).
thf(tp_connected,type,
connected: $i > $o ).
thf(tp_cup_closed,type,
cup_closed: $i > $o ).
thf(tp_diff_closed,type,
diff_closed: $i > $o ).
thf(tp_disjoint,type,
disjoint: $i > $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_carrier_subset,type,
empty_carrier_subset: $i > $i ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_equipotent,type,
equipotent: $i > $i > $o ).
thf(tp_fiber,type,
fiber: $i > $i > $i ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_function_inverse,type,
function_inverse: $i > $i ).
thf(tp_identity_relation,type,
identity_relation: $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_inclusion_relation,type,
inclusion_relation: $i > $i ).
thf(tp_interior,type,
interior: $i > $i > $i ).
thf(tp_is_a_cover_of_carrier,type,
is_a_cover_of_carrier: $i > $i > $o ).
thf(tp_is_antisymmetric_in,type,
is_antisymmetric_in: $i > $i > $o ).
thf(tp_is_connected_in,type,
is_connected_in: $i > $i > $o ).
thf(tp_is_reflexive_in,type,
is_reflexive_in: $i > $i > $o ).
thf(tp_is_transitive_in,type,
is_transitive_in: $i > $i > $o ).
thf(tp_is_well_founded_in,type,
is_well_founded_in: $i > $i > $o ).
thf(tp_join,type,
join: $i > $i > $i > $i ).
thf(tp_join_commut,type,
join_commut: $i > $i > $i > $i ).
thf(tp_join_commutative,type,
join_commutative: $i > $o ).
thf(tp_join_semilatt_str,type,
join_semilatt_str: $i > $o ).
thf(tp_latt_str,type,
latt_str: $i > $o ).
thf(tp_meet,type,
meet: $i > $i > $i > $i ).
thf(tp_meet_absorbing,type,
meet_absorbing: $i > $o ).
thf(tp_meet_commut,type,
meet_commut: $i > $i > $i > $i ).
thf(tp_meet_commutative,type,
meet_commutative: $i > $o ).
thf(tp_meet_of_subsets,type,
meet_of_subsets: $i > $i > $i ).
thf(tp_meet_semilatt_str,type,
meet_semilatt_str: $i > $o ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_omega,type,
omega: $i ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_open_subset,type,
open_subset: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_ordinal_subset,type,
ordinal_subset: $i > $i > $o ).
thf(tp_pair_first,type,
pair_first: $i > $i ).
thf(tp_pair_second,type,
pair_second: $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_preboolean,type,
preboolean: $i > $o ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_quasi_total,type,
quasi_total: $i > $i > $i > $o ).
thf(tp_reflexive,type,
reflexive: $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_composition,type,
relation_composition: $i > $i > $i ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_dom_as_subset,type,
relation_dom_as_subset: $i > $i > $i > $i ).
thf(tp_relation_dom_restriction,type,
relation_dom_restriction: $i > $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_field,type,
relation_field: $i > $i ).
thf(tp_relation_image,type,
relation_image: $i > $i > $i ).
thf(tp_relation_inverse,type,
relation_inverse: $i > $i ).
thf(tp_relation_inverse_image,type,
relation_inverse_image: $i > $i > $i ).
thf(tp_relation_isomorphism,type,
relation_isomorphism: $i > $i > $i > $o ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_relation_restriction,type,
relation_restriction: $i > $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_as_subset,type,
relation_rng_as_subset: $i > $i > $i > $i ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_sK10_SY132,type,
sK10_SY132: $i > $i > $i ).
thf(tp_sK11_SY112,type,
sK11_SY112: $i > $i ).
thf(tp_sK12_SY119,type,
sK12_SY119: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY64,type,
sK2_SY64: $i ).
thf(tp_sK3_SY71,type,
sK3_SY71: $i > $i ).
thf(tp_sK4_SY87,type,
sK4_SY87: $i > $i ).
thf(tp_sK5_SY97,type,
sK5_SY97: $i > $i > $i ).
thf(tp_sK6_SY75,type,
sK6_SY75: $i > $i ).
thf(tp_sK7_SY80,type,
sK7_SY80: $i > $i ).
thf(tp_sK8_SY104,type,
sK8_SY104: $i > $i ).
thf(tp_sK9_SY129,type,
sK9_SY129: $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_meet,type,
set_meet: $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_subset_intersection2,type,
subset_intersection2: $i > $i > $i > $i ).
thf(tp_succ,type,
succ: $i > $i ).
thf(tp_the_L_join,type,
the_L_join: $i > $i ).
thf(tp_the_L_meet,type,
the_L_meet: $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_the_topology,type,
the_topology: $i > $i ).
thf(tp_top_str,type,
top_str: $i > $o ).
thf(tp_topological_space,type,
topological_space: $i > $o ).
thf(tp_topstr_closure,type,
topstr_closure: $i > $i > $i ).
thf(tp_transitive,type,
transitive: $i > $o ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_union_of_subsets,type,
union_of_subsets: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(tp_unordered_triple,type,
unordered_triple: $i > $i > $i > $i ).
thf(tp_v1_int_1,type,
v1_int_1: $i > $o ).
thf(tp_v1_membered,type,
v1_membered: $i > $o ).
thf(tp_v1_rat_1,type,
v1_rat_1: $i > $o ).
thf(tp_v1_xcmplx_0,type,
v1_xcmplx_0: $i > $o ).
thf(tp_v1_xreal_0,type,
v1_xreal_0: $i > $o ).
thf(tp_v2_membered,type,
v2_membered: $i > $o ).
thf(tp_v3_membered,type,
v3_membered: $i > $o ).
thf(tp_v4_membered,type,
v4_membered: $i > $o ).
thf(tp_v5_membered,type,
v5_membered: $i > $o ).
thf(tp_well_founded_relation,type,
well_founded_relation: $i > $o ).
thf(tp_well_ordering,type,
well_ordering: $i > $o ).
thf(tp_well_orders,type,
well_orders: $i > $i > $o ).
thf(5,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(8,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(10,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(13,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(15,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(55,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(63,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(125,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(126,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(144,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(152,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(156,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(157,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(160,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(163,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(175,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_ordinal2) ).
thf(176,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(177,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(181,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(182,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(184,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(186,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(187,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(189,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(190,axiom,
! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(191,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(193,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_mcart_1) ).
thf(197,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(198,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(200,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord1) ).
thf(202,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(203,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(204,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(206,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(207,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_mcart_1) ).
thf(209,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(210,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_enumset1) ).
thf(211,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_binop_1) ).
thf(212,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(264,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(309,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(323,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_membered) ).
thf(334,axiom,
! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(388,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(402,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(425,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(455,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(520,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
thf(528,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).
thf(537,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(539,conjecture,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ A @ B )
!= empty_set )
& ( B = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_tops_2) ).
thf(540,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ A @ B )
!= empty_set )
& ( B = empty_set ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[539]) ).
thf(541,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ A @ B )
!= empty_set )
& ( B = empty_set ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[540]) ).
thf(542,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(543,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(544,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(545,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(546,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(547,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(548,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(549,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(550,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(551,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(552,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(553,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(554,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(555,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(556,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(557,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(558,plain,
$true = $true,
inference(unfold_def,[status(thm)],[152]) ).
thf(559,plain,
$true = $true,
inference(unfold_def,[status(thm)],[156]) ).
thf(560,plain,
$true = $true,
inference(unfold_def,[status(thm)],[157]) ).
thf(561,plain,
$true = $true,
inference(unfold_def,[status(thm)],[160]) ).
thf(562,plain,
$true = $true,
inference(unfold_def,[status(thm)],[163]) ).
thf(563,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(564,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(565,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(566,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(567,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(568,plain,
$true = $true,
inference(unfold_def,[status(thm)],[175]) ).
thf(569,plain,
$true = $true,
inference(unfold_def,[status(thm)],[176]) ).
thf(570,plain,
$true = $true,
inference(unfold_def,[status(thm)],[177]) ).
thf(571,plain,
$true = $true,
inference(unfold_def,[status(thm)],[181]) ).
thf(572,plain,
$true = $true,
inference(unfold_def,[status(thm)],[182]) ).
thf(573,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(574,plain,
$true = $true,
inference(unfold_def,[status(thm)],[184]) ).
thf(575,plain,
$true = $true,
inference(unfold_def,[status(thm)],[186]) ).
thf(576,plain,
$true = $true,
inference(unfold_def,[status(thm)],[187]) ).
thf(577,plain,
$true = $true,
inference(unfold_def,[status(thm)],[189]) ).
thf(578,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(579,plain,
$true = $true,
inference(unfold_def,[status(thm)],[191]) ).
thf(580,plain,
$true = $true,
inference(unfold_def,[status(thm)],[193]) ).
thf(581,plain,
$true = $true,
inference(unfold_def,[status(thm)],[197]) ).
thf(582,plain,
$true = $true,
inference(unfold_def,[status(thm)],[198]) ).
thf(583,plain,
$true = $true,
inference(unfold_def,[status(thm)],[200]) ).
thf(584,plain,
$true = $true,
inference(unfold_def,[status(thm)],[202]) ).
thf(585,plain,
$true = $true,
inference(unfold_def,[status(thm)],[203]) ).
thf(586,plain,
$true = $true,
inference(unfold_def,[status(thm)],[204]) ).
thf(587,plain,
$true = $true,
inference(unfold_def,[status(thm)],[206]) ).
thf(588,plain,
$true = $true,
inference(unfold_def,[status(thm)],[207]) ).
thf(589,plain,
$true = $true,
inference(unfold_def,[status(thm)],[209]) ).
thf(590,plain,
$true = $true,
inference(unfold_def,[status(thm)],[210]) ).
thf(591,plain,
$true = $true,
inference(unfold_def,[status(thm)],[211]) ).
thf(592,plain,
$true = $true,
inference(unfold_def,[status(thm)],[212]) ).
thf(593,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(594,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(595,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(596,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(597,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(598,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(599,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(600,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(601,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(602,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(603,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(604,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(605,plain,
( ( ! [SY64: $i] :
( ( element @ SY64 @ ( powerset @ ( powerset @ sK1_A ) ) )
=> ( ~ ( ( SY64 != empty_set )
& ( ( complements_of_subsets @ sK1_A @ SY64 )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ sK1_A @ SY64 )
!= empty_set )
& ( SY64 = empty_set ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[541]) ).
thf(606,plain,
( ( ( element @ sK2_SY64 @ ( powerset @ ( powerset @ sK1_A ) ) )
=> ( ~ ( ( sK2_SY64 != empty_set )
& ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
!= empty_set )
& ( sK2_SY64 = empty_set ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[605]) ).
thf(607,plain,
( ( element @ sK2_SY64 @ ( powerset @ ( powerset @ sK1_A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[606]) ).
thf(608,plain,
( ( ~ ( ( sK2_SY64 != empty_set )
& ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
!= empty_set )
& ( sK2_SY64 = empty_set ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[606]) ).
thf(609,plain,
( ( ~ ( ( sK2_SY64 != empty_set )
& ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
= empty_set ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[608]) ).
thf(610,plain,
( ( ~ ( ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
!= empty_set )
& ( sK2_SY64 = empty_set ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[608]) ).
thf(611,plain,
( ( ( sK2_SY64 != empty_set )
& ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
= empty_set ) )
= $true ),
inference(polarity_switch,[status(thm)],[609]) ).
thf(612,plain,
( ( ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
!= empty_set )
& ( sK2_SY64 = empty_set ) )
= $true ),
inference(polarity_switch,[status(thm)],[610]) ).
thf(613,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[604]) ).
thf(614,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[603]) ).
thf(615,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[602]) ).
thf(616,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[601]) ).
thf(617,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[600]) ).
thf(618,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[599]) ).
thf(619,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[598]) ).
thf(620,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[597]) ).
thf(621,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[596]) ).
thf(622,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[595]) ).
thf(623,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[594]) ).
thf(624,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(625,plain,
$true = $true,
inference(copy,[status(thm)],[592]) ).
thf(626,plain,
$true = $true,
inference(copy,[status(thm)],[591]) ).
thf(627,plain,
$true = $true,
inference(copy,[status(thm)],[590]) ).
thf(628,plain,
$true = $true,
inference(copy,[status(thm)],[589]) ).
thf(629,plain,
$true = $true,
inference(copy,[status(thm)],[588]) ).
thf(630,plain,
$true = $true,
inference(copy,[status(thm)],[587]) ).
thf(631,plain,
$true = $true,
inference(copy,[status(thm)],[586]) ).
thf(632,plain,
$true = $true,
inference(copy,[status(thm)],[585]) ).
thf(633,plain,
$true = $true,
inference(copy,[status(thm)],[584]) ).
thf(634,plain,
$true = $true,
inference(copy,[status(thm)],[583]) ).
thf(635,plain,
$true = $true,
inference(copy,[status(thm)],[582]) ).
thf(636,plain,
$true = $true,
inference(copy,[status(thm)],[581]) ).
thf(637,plain,
$true = $true,
inference(copy,[status(thm)],[580]) ).
thf(638,plain,
$true = $true,
inference(copy,[status(thm)],[579]) ).
thf(639,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(640,plain,
$true = $true,
inference(copy,[status(thm)],[577]) ).
thf(641,plain,
$true = $true,
inference(copy,[status(thm)],[576]) ).
thf(642,plain,
$true = $true,
inference(copy,[status(thm)],[575]) ).
thf(643,plain,
$true = $true,
inference(copy,[status(thm)],[574]) ).
thf(644,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(645,plain,
$true = $true,
inference(copy,[status(thm)],[572]) ).
thf(646,plain,
$true = $true,
inference(copy,[status(thm)],[571]) ).
thf(647,plain,
$true = $true,
inference(copy,[status(thm)],[570]) ).
thf(648,plain,
$true = $true,
inference(copy,[status(thm)],[569]) ).
thf(649,plain,
$true = $true,
inference(copy,[status(thm)],[568]) ).
thf(650,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[567]) ).
thf(651,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[566]) ).
thf(652,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[565]) ).
thf(653,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(654,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[563]) ).
thf(655,plain,
$true = $true,
inference(copy,[status(thm)],[562]) ).
thf(656,plain,
$true = $true,
inference(copy,[status(thm)],[561]) ).
thf(657,plain,
$true = $true,
inference(copy,[status(thm)],[560]) ).
thf(658,plain,
$true = $true,
inference(copy,[status(thm)],[559]) ).
thf(659,plain,
$true = $true,
inference(copy,[status(thm)],[558]) ).
thf(660,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(661,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(662,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[555]) ).
thf(663,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[554]) ).
thf(664,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(665,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(666,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[551]) ).
thf(667,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[550]) ).
thf(668,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[549]) ).
thf(669,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(670,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[547]) ).
thf(671,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[546]) ).
thf(672,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[545]) ).
thf(673,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[544]) ).
thf(674,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(675,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(676,plain,
( ( element @ sK2_SY64 @ ( powerset @ ( powerset @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[607]) ).
thf(677,plain,
( ( ( sK2_SY64 != empty_set )
& ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[611]) ).
thf(678,plain,
( ( ! [SX0: $i] :
( ~ ( v1_membered @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v1_membered @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[621]) ).
thf(679,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( meet_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[652]) ).
thf(680,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( ( subset_intersection2 @ SX0 @ SX1 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[663]) ).
thf(681,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[674]) ).
thf(682,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618]) ).
thf(683,plain,
( ( ~ ( ~ ( ( sK2_SY64 != empty_set ) )
| ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
!= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[677]) ).
thf(684,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(685,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[675]) ).
thf(686,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[669]) ).
thf(687,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[672]) ).
thf(688,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( ( complements_of_subsets @ SX0 @ ( complements_of_subsets @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[665]) ).
thf(689,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[666]) ).
thf(690,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[615]) ).
thf(691,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( union_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650]) ).
thf(692,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[624]) ).
thf(693,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( ( subset_complement @ SX0 @ ( subset_complement @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[664]) ).
thf(694,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( element @ ( subset_difference @ SX0 @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[653]) ).
thf(695,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[614]) ).
thf(696,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( element @ ( subset_complement @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[644]) ).
thf(697,plain,
( ( ! [SX0: $i] :
( ( singleton @ SX0 )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(698,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[667]) ).
thf(699,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( ( subset_intersection2 @ SX0 @ SX1 @ SX2 )
= ( subset_intersection2 @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623]) ).
thf(700,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( element @ ( subset_intersection2 @ SX0 @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[651]) ).
thf(701,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1 != empty_set ) )
| ( ( complements_of_subsets @ SX0 @ SX1 )
!= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619]) ).
thf(702,plain,
( ( ! [SX0: $i] :
( ~ ( finite @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[622]) ).
thf(703,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( complements_of_subsets @ SX0 @ SX1 ) @ ( powerset @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[654]) ).
thf(704,plain,
! [SV1: $i] :
( ( subset @ empty_set @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(705,plain,
! [SV2: $i] :
( ( ( union @ ( powerset @ SV2 ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(706,plain,
! [SV3: $i] :
( ( element @ ( cast_to_subset @ SV3 ) @ ( powerset @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(707,plain,
! [SV4: $i] :
( ( ~ ( empty @ ( powerset @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(708,plain,
! [SV5: $i] :
( ( ( set_union2 @ SV5 @ empty_set )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(709,plain,
! [SV6: $i] :
( ( ( set_intersection2 @ SV6 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(710,plain,
! [SV7: $i] :
( ( ( set_difference @ SV7 @ empty_set )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(711,plain,
! [SV8: $i] :
( ( ( set_difference @ empty_set @ SV8 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(712,plain,
! [SV9: $i] :
( ( ~ ( v1_membered @ SV9 )
| ! [SY65: $i] :
( ~ ( element @ SY65 @ ( powerset @ SV9 ) )
| ( v1_membered @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(713,plain,
! [SV10: $i] :
( ( ! [SY66: $i] :
( ~ ( element @ SY66 @ ( powerset @ ( powerset @ SV10 ) ) )
| ( element @ ( meet_of_subsets @ SV10 @ SY66 ) @ ( powerset @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(714,plain,
! [SV11: $i] :
( ( ! [SY67: $i,SY68: $i] :
( ~ ~ ( ~ ( element @ SY67 @ ( powerset @ SV11 ) )
| ~ ( element @ SY68 @ ( powerset @ SV11 ) ) )
| ( ( subset_intersection2 @ SV11 @ SY67 @ SY67 )
= SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(715,plain,
! [SV12: $i] :
( ( ! [SY69: $i,SY70: $i] :
( ~ ~ ( ~ ( in @ SV12 @ SY69 )
| ~ ( element @ SY69 @ ( powerset @ SY70 ) ) )
| ( element @ SV12 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(716,plain,
! [SV13: $i] :
( ( ~ ( subset @ SV13 @ empty_set )
| ( SV13 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(717,plain,
( ( ~ ( ( sK2_SY64 != empty_set ) )
| ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
!= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(718,plain,
! [SV14: $i] :
( ( ~ ! [SY71: $i] :
~ ( element @ SY71 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(719,plain,
! [SV15: $i] :
( ( ~ ( empty @ SV15 )
| ( SV15 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(720,plain,
! [SV16: $i] :
( ( ! [SY72: $i] :
( ~ ( in @ SV16 @ SY72 )
| ( element @ SV16 @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(721,plain,
! [SV17: $i] :
( ( ! [SY73: $i] :
~ ( ~ ( ~ ( element @ SV17 @ ( powerset @ SY73 ) )
| ( subset @ SV17 @ SY73 ) )
| ~ ( ~ ( subset @ SV17 @ SY73 )
| ( element @ SV17 @ ( powerset @ SY73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(722,plain,
! [SV18: $i] :
( ( ! [SY74: $i] :
( ~ ( element @ SY74 @ ( powerset @ ( powerset @ SV18 ) ) )
| ( ( complements_of_subsets @ SV18 @ ( complements_of_subsets @ SV18 @ SY74 ) )
= SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(723,plain,
! [SV19: $i] :
( ( ~ ~ ( empty @ SV19 )
| ~ ! [SY75: $i] :
~ ~ ( ~ ( element @ SY75 @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(724,plain,
! [SV20: $i] :
( ( ! [SY76: $i] :
( ~ ! [SY77: $i] :
( ~ ( in @ SY77 @ SV20 )
| ( in @ SY77 @ SY76 ) )
| ( element @ SV20 @ ( powerset @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(725,plain,
! [SV21: $i] :
( ( ! [SY78: $i] :
( ~ ( element @ SY78 @ ( powerset @ ( powerset @ SV21 ) ) )
| ( element @ ( union_of_subsets @ SV21 @ SY78 ) @ ( powerset @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(726,plain,
! [SV22: $i] :
( ( ~ ( ~ ( ( SV22 != empty_set )
| ! [SY79: $i] :
~ ( in @ SY79 @ SV22 ) )
| ~ ( ~ ! [SY80: $i] :
~ ( in @ SY80 @ SV22 )
| ( SV22 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(727,plain,
! [SV23: $i] :
( ( ! [SY81: $i] :
( ~ ( element @ SY81 @ ( powerset @ SV23 ) )
| ( ( subset_complement @ SV23 @ ( subset_complement @ SV23 @ SY81 ) )
= SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(728,plain,
! [SV24: $i] :
( ( ! [SY82: $i,SY83: $i] :
( ~ ~ ( ~ ( element @ SY82 @ ( powerset @ SV24 ) )
| ~ ( element @ SY83 @ ( powerset @ SV24 ) ) )
| ( element @ ( subset_difference @ SV24 @ SY82 @ SY83 ) @ ( powerset @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(729,plain,
! [SV25: $i] :
( ( ! [SY84: $i] :
( ~ ( element @ SY84 @ ( powerset @ SV25 ) )
| ! [SY85: $i] :
( ~ ( in @ SY85 @ SY84 )
| ( in @ SY85 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(730,plain,
! [SV26: $i] :
( ( ! [SY86: $i] :
( ~ ( element @ SY86 @ ( powerset @ SV26 ) )
| ( element @ ( subset_complement @ SV26 @ SY86 ) @ ( powerset @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(731,plain,
! [SV27: $i] :
( ( ( singleton @ SV27 )
!= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(732,plain,
! [SV28: $i] :
( ( ~ ! [SY87: $i] :
~ ~ ( ~ ( element @ SY87 @ ( powerset @ SV28 ) )
| ~ ( empty @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(733,plain,
! [SV29: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ~ ~ ( ~ ( element @ SY88 @ ( powerset @ SV29 ) )
| ~ ( element @ SY89 @ ( powerset @ SV29 ) ) )
| ( ( subset_intersection2 @ SV29 @ SY88 @ SY89 )
= ( subset_intersection2 @ SV29 @ SY89 @ SY88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(734,plain,
! [SV30: $i] :
( ( ! [SY90: $i,SY91: $i] :
( ~ ~ ( ~ ( element @ SY90 @ ( powerset @ SV30 ) )
| ~ ( element @ SY91 @ ( powerset @ SV30 ) ) )
| ( element @ ( subset_intersection2 @ SV30 @ SY90 @ SY91 ) @ ( powerset @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(735,plain,
! [SV31: $i] :
( ( ! [SY92: $i] :
( ~ ( element @ SY92 @ ( powerset @ ( powerset @ SV31 ) ) )
| ~ ~ ( ~ ( ( SY92 != empty_set ) )
| ( ( complements_of_subsets @ SV31 @ SY92 )
!= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(736,plain,
! [SV32: $i] :
( ( ~ ( finite @ SV32 )
| ! [SY93: $i] :
( ~ ( element @ SY93 @ ( powerset @ SV32 ) )
| ( finite @ SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(737,plain,
! [SV33: $i] :
( ( ! [SY94: $i] :
( ~ ( element @ SY94 @ ( powerset @ ( powerset @ SV33 ) ) )
| ( element @ ( complements_of_subsets @ SV33 @ SY94 ) @ ( powerset @ ( powerset @ SV33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(738,plain,
! [SV4: $i] :
( ( empty @ ( powerset @ SV4 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(739,plain,
! [SV9: $i] :
( ( ( ~ ( v1_membered @ SV9 ) )
= $true )
| ( ( ! [SY65: $i] :
( ~ ( element @ SY65 @ ( powerset @ SV9 ) )
| ( v1_membered @ SY65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[712]) ).
thf(740,plain,
! [SV10: $i,SV34: $i] :
( ( ~ ( element @ SV34 @ ( powerset @ ( powerset @ SV10 ) ) )
| ( element @ ( meet_of_subsets @ SV10 @ SV34 ) @ ( powerset @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(741,plain,
! [SV11: $i,SV35: $i] :
( ( ! [SY95: $i] :
( ~ ~ ( ~ ( element @ SV35 @ ( powerset @ SV11 ) )
| ~ ( element @ SY95 @ ( powerset @ SV11 ) ) )
| ( ( subset_intersection2 @ SV11 @ SV35 @ SV35 )
= SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(742,plain,
! [SV36: $i,SV12: $i] :
( ( ! [SY96: $i] :
( ~ ~ ( ~ ( in @ SV12 @ SV36 )
| ~ ( element @ SV36 @ ( powerset @ SY96 ) ) )
| ( element @ SV12 @ SY96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(743,plain,
! [SV13: $i] :
( ( ( ~ ( subset @ SV13 @ empty_set ) )
= $true )
| ( ( SV13 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[716]) ).
thf(744,plain,
( ( ~ ( ( sK2_SY64 != empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[717]) ).
thf(745,plain,
( ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
!= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[717]) ).
thf(746,plain,
! [SV14: $i] :
( ( ! [SY71: $i] :
~ ( element @ SY71 @ SV14 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(747,plain,
! [SV15: $i] :
( ( ( ~ ( empty @ SV15 ) )
= $true )
| ( ( SV15 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(748,plain,
! [SV37: $i,SV16: $i] :
( ( ~ ( in @ SV16 @ SV37 )
| ( element @ SV16 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(749,plain,
! [SV38: $i,SV17: $i] :
( ( ~ ( ~ ( ~ ( element @ SV17 @ ( powerset @ SV38 ) )
| ( subset @ SV17 @ SV38 ) )
| ~ ( ~ ( subset @ SV17 @ SV38 )
| ( element @ SV17 @ ( powerset @ SV38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(750,plain,
! [SV18: $i,SV39: $i] :
( ( ~ ( element @ SV39 @ ( powerset @ ( powerset @ SV18 ) ) )
| ( ( complements_of_subsets @ SV18 @ ( complements_of_subsets @ SV18 @ SV39 ) )
= SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(751,plain,
! [SV19: $i] :
( ( ( ~ ~ ( empty @ SV19 ) )
= $true )
| ( ( ~ ! [SY75: $i] :
~ ~ ( ~ ( element @ SY75 @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ SY75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[723]) ).
thf(752,plain,
! [SV40: $i,SV20: $i] :
( ( ~ ! [SY97: $i] :
( ~ ( in @ SY97 @ SV20 )
| ( in @ SY97 @ SV40 ) )
| ( element @ SV20 @ ( powerset @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(753,plain,
! [SV21: $i,SV41: $i] :
( ( ~ ( element @ SV41 @ ( powerset @ ( powerset @ SV21 ) ) )
| ( element @ ( union_of_subsets @ SV21 @ SV41 ) @ ( powerset @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(754,plain,
! [SV22: $i] :
( ( ~ ( ( SV22 != empty_set )
| ! [SY79: $i] :
~ ( in @ SY79 @ SV22 ) )
| ~ ( ~ ! [SY80: $i] :
~ ( in @ SY80 @ SV22 )
| ( SV22 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(755,plain,
! [SV23: $i,SV42: $i] :
( ( ~ ( element @ SV42 @ ( powerset @ SV23 ) )
| ( ( subset_complement @ SV23 @ ( subset_complement @ SV23 @ SV42 ) )
= SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(756,plain,
! [SV24: $i,SV43: $i] :
( ( ! [SY98: $i] :
( ~ ~ ( ~ ( element @ SV43 @ ( powerset @ SV24 ) )
| ~ ( element @ SY98 @ ( powerset @ SV24 ) ) )
| ( element @ ( subset_difference @ SV24 @ SV43 @ SY98 ) @ ( powerset @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(757,plain,
! [SV25: $i,SV44: $i] :
( ( ~ ( element @ SV44 @ ( powerset @ SV25 ) )
| ! [SY99: $i] :
( ~ ( in @ SY99 @ SV44 )
| ( in @ SY99 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(758,plain,
! [SV26: $i,SV45: $i] :
( ( ~ ( element @ SV45 @ ( powerset @ SV26 ) )
| ( element @ ( subset_complement @ SV26 @ SV45 ) @ ( powerset @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(759,plain,
! [SV27: $i] :
( ( ( singleton @ SV27 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(760,plain,
! [SV28: $i] :
( ( ! [SY87: $i] :
~ ~ ( ~ ( element @ SY87 @ ( powerset @ SV28 ) )
| ~ ( empty @ SY87 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(761,plain,
! [SV29: $i,SV46: $i] :
( ( ! [SY100: $i] :
( ~ ~ ( ~ ( element @ SV46 @ ( powerset @ SV29 ) )
| ~ ( element @ SY100 @ ( powerset @ SV29 ) ) )
| ( ( subset_intersection2 @ SV29 @ SV46 @ SY100 )
= ( subset_intersection2 @ SV29 @ SY100 @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(762,plain,
! [SV30: $i,SV47: $i] :
( ( ! [SY101: $i] :
( ~ ~ ( ~ ( element @ SV47 @ ( powerset @ SV30 ) )
| ~ ( element @ SY101 @ ( powerset @ SV30 ) ) )
| ( element @ ( subset_intersection2 @ SV30 @ SV47 @ SY101 ) @ ( powerset @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(763,plain,
! [SV31: $i,SV48: $i] :
( ( ~ ( element @ SV48 @ ( powerset @ ( powerset @ SV31 ) ) )
| ~ ~ ( ~ ( ( SV48 != empty_set ) )
| ( ( complements_of_subsets @ SV31 @ SV48 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(764,plain,
! [SV32: $i] :
( ( ( ~ ( finite @ SV32 ) )
= $true )
| ( ( ! [SY93: $i] :
( ~ ( element @ SY93 @ ( powerset @ SV32 ) )
| ( finite @ SY93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(765,plain,
! [SV33: $i,SV49: $i] :
( ( ~ ( element @ SV49 @ ( powerset @ ( powerset @ SV33 ) ) )
| ( element @ ( complements_of_subsets @ SV33 @ SV49 ) @ ( powerset @ ( powerset @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(766,plain,
! [SV9: $i] :
( ( ( v1_membered @ SV9 )
= $false )
| ( ( ! [SY65: $i] :
( ~ ( element @ SY65 @ ( powerset @ SV9 ) )
| ( v1_membered @ SY65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(767,plain,
! [SV10: $i,SV34: $i] :
( ( ( ~ ( element @ SV34 @ ( powerset @ ( powerset @ SV10 ) ) ) )
= $true )
| ( ( element @ ( meet_of_subsets @ SV10 @ SV34 ) @ ( powerset @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[740]) ).
thf(768,plain,
! [SV50: $i,SV11: $i,SV35: $i] :
( ( ~ ~ ( ~ ( element @ SV35 @ ( powerset @ SV11 ) )
| ~ ( element @ SV50 @ ( powerset @ SV11 ) ) )
| ( ( subset_intersection2 @ SV11 @ SV35 @ SV35 )
= SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(769,plain,
! [SV51: $i,SV36: $i,SV12: $i] :
( ( ~ ~ ( ~ ( in @ SV12 @ SV36 )
| ~ ( element @ SV36 @ ( powerset @ SV51 ) ) )
| ( element @ SV12 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(770,plain,
! [SV13: $i] :
( ( ( subset @ SV13 @ empty_set )
= $false )
| ( ( SV13 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(771,plain,
( ( sK2_SY64 != empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[744]) ).
thf(772,plain,
( ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[745]) ).
thf(773,plain,
! [SV14: $i] :
( ( ~ ( element @ ( sK3_SY71 @ SV14 ) @ SV14 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[746]) ).
thf(774,plain,
! [SV15: $i] :
( ( ( empty @ SV15 )
= $false )
| ( ( SV15 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(775,plain,
! [SV37: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV37 ) )
= $true )
| ( ( element @ SV16 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(776,plain,
! [SV38: $i,SV17: $i] :
( ( ~ ( ~ ( element @ SV17 @ ( powerset @ SV38 ) )
| ( subset @ SV17 @ SV38 ) )
| ~ ( ~ ( subset @ SV17 @ SV38 )
| ( element @ SV17 @ ( powerset @ SV38 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(777,plain,
! [SV18: $i,SV39: $i] :
( ( ( ~ ( element @ SV39 @ ( powerset @ ( powerset @ SV18 ) ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV18 @ ( complements_of_subsets @ SV18 @ SV39 ) )
= SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(778,plain,
! [SV19: $i] :
( ( ( ~ ( empty @ SV19 ) )
= $false )
| ( ( ~ ! [SY75: $i] :
~ ~ ( ~ ( element @ SY75 @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ SY75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(779,plain,
! [SV40: $i,SV20: $i] :
( ( ( ~ ! [SY97: $i] :
( ~ ( in @ SY97 @ SV20 )
| ( in @ SY97 @ SV40 ) ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(780,plain,
! [SV21: $i,SV41: $i] :
( ( ( ~ ( element @ SV41 @ ( powerset @ ( powerset @ SV21 ) ) ) )
= $true )
| ( ( element @ ( union_of_subsets @ SV21 @ SV41 ) @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(781,plain,
! [SV22: $i] :
( ( ~ ( ( SV22 != empty_set )
| ! [SY79: $i] :
~ ( in @ SY79 @ SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(782,plain,
! [SV22: $i] :
( ( ~ ( ~ ! [SY80: $i] :
~ ( in @ SY80 @ SV22 )
| ( SV22 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(783,plain,
! [SV23: $i,SV42: $i] :
( ( ( ~ ( element @ SV42 @ ( powerset @ SV23 ) ) )
= $true )
| ( ( ( subset_complement @ SV23 @ ( subset_complement @ SV23 @ SV42 ) )
= SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(784,plain,
! [SV52: $i,SV24: $i,SV43: $i] :
( ( ~ ~ ( ~ ( element @ SV43 @ ( powerset @ SV24 ) )
| ~ ( element @ SV52 @ ( powerset @ SV24 ) ) )
| ( element @ ( subset_difference @ SV24 @ SV43 @ SV52 ) @ ( powerset @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(785,plain,
! [SV25: $i,SV44: $i] :
( ( ( ~ ( element @ SV44 @ ( powerset @ SV25 ) ) )
= $true )
| ( ( ! [SY99: $i] :
( ~ ( in @ SY99 @ SV44 )
| ( in @ SY99 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(786,plain,
! [SV26: $i,SV45: $i] :
( ( ( ~ ( element @ SV45 @ ( powerset @ SV26 ) ) )
= $true )
| ( ( element @ ( subset_complement @ SV26 @ SV45 ) @ ( powerset @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[758]) ).
thf(787,plain,
! [SV28: $i] :
( ( ~ ~ ( ~ ( element @ ( sK4_SY87 @ SV28 ) @ ( powerset @ SV28 ) )
| ~ ( empty @ ( sK4_SY87 @ SV28 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[760]) ).
thf(788,plain,
! [SV53: $i,SV29: $i,SV46: $i] :
( ( ~ ~ ( ~ ( element @ SV46 @ ( powerset @ SV29 ) )
| ~ ( element @ SV53 @ ( powerset @ SV29 ) ) )
| ( ( subset_intersection2 @ SV29 @ SV46 @ SV53 )
= ( subset_intersection2 @ SV29 @ SV53 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(789,plain,
! [SV54: $i,SV30: $i,SV47: $i] :
( ( ~ ~ ( ~ ( element @ SV47 @ ( powerset @ SV30 ) )
| ~ ( element @ SV54 @ ( powerset @ SV30 ) ) )
| ( element @ ( subset_intersection2 @ SV30 @ SV47 @ SV54 ) @ ( powerset @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(790,plain,
! [SV31: $i,SV48: $i] :
( ( ( ~ ( element @ SV48 @ ( powerset @ ( powerset @ SV31 ) ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV48 != empty_set ) )
| ( ( complements_of_subsets @ SV31 @ SV48 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(791,plain,
! [SV32: $i] :
( ( ( finite @ SV32 )
= $false )
| ( ( ! [SY93: $i] :
( ~ ( element @ SY93 @ ( powerset @ SV32 ) )
| ( finite @ SY93 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(792,plain,
! [SV33: $i,SV49: $i] :
( ( ( ~ ( element @ SV49 @ ( powerset @ ( powerset @ SV33 ) ) ) )
= $true )
| ( ( element @ ( complements_of_subsets @ SV33 @ SV49 ) @ ( powerset @ ( powerset @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(793,plain,
! [SV9: $i,SV55: $i] :
( ( ( ~ ( element @ SV55 @ ( powerset @ SV9 ) )
| ( v1_membered @ SV55 ) )
= $true )
| ( ( v1_membered @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(794,plain,
! [SV10: $i,SV34: $i] :
( ( ( element @ SV34 @ ( powerset @ ( powerset @ SV10 ) ) )
= $false )
| ( ( element @ ( meet_of_subsets @ SV10 @ SV34 ) @ ( powerset @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(795,plain,
! [SV50: $i,SV11: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( element @ SV35 @ ( powerset @ SV11 ) )
| ~ ( element @ SV50 @ ( powerset @ SV11 ) ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV11 @ SV35 @ SV35 )
= SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(796,plain,
! [SV51: $i,SV36: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( in @ SV12 @ SV36 )
| ~ ( element @ SV36 @ ( powerset @ SV51 ) ) ) )
= $true )
| ( ( element @ SV12 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(797,plain,
( ( sK2_SY64 = empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(798,plain,
! [SV14: $i] :
( ( element @ ( sK3_SY71 @ SV14 ) @ SV14 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[773]) ).
thf(799,plain,
! [SV37: $i,SV16: $i] :
( ( ( in @ SV16 @ SV37 )
= $false )
| ( ( element @ SV16 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(800,plain,
! [SV38: $i,SV17: $i] :
( ( ~ ( ~ ( element @ SV17 @ ( powerset @ SV38 ) )
| ( subset @ SV17 @ SV38 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[776]) ).
thf(801,plain,
! [SV38: $i,SV17: $i] :
( ( ~ ( ~ ( subset @ SV17 @ SV38 )
| ( element @ SV17 @ ( powerset @ SV38 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[776]) ).
thf(802,plain,
! [SV18: $i,SV39: $i] :
( ( ( element @ SV39 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false )
| ( ( ( complements_of_subsets @ SV18 @ ( complements_of_subsets @ SV18 @ SV39 ) )
= SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(803,plain,
! [SV19: $i] :
( ( ( empty @ SV19 )
= $true )
| ( ( ~ ! [SY75: $i] :
~ ~ ( ~ ( element @ SY75 @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ SY75 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[778]) ).
thf(804,plain,
! [SV40: $i,SV20: $i] :
( ( ( ! [SY97: $i] :
( ~ ( in @ SY97 @ SV20 )
| ( in @ SY97 @ SV40 ) ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(805,plain,
! [SV21: $i,SV41: $i] :
( ( ( element @ SV41 @ ( powerset @ ( powerset @ SV21 ) ) )
= $false )
| ( ( element @ ( union_of_subsets @ SV21 @ SV41 ) @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(806,plain,
! [SV22: $i] :
( ( ( SV22 != empty_set )
| ! [SY79: $i] :
~ ( in @ SY79 @ SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[781]) ).
thf(807,plain,
! [SV22: $i] :
( ( ~ ! [SY80: $i] :
~ ( in @ SY80 @ SV22 )
| ( SV22 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[782]) ).
thf(808,plain,
! [SV23: $i,SV42: $i] :
( ( ( element @ SV42 @ ( powerset @ SV23 ) )
= $false )
| ( ( ( subset_complement @ SV23 @ ( subset_complement @ SV23 @ SV42 ) )
= SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(809,plain,
! [SV52: $i,SV24: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( element @ SV43 @ ( powerset @ SV24 ) )
| ~ ( element @ SV52 @ ( powerset @ SV24 ) ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV24 @ SV43 @ SV52 ) @ ( powerset @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[784]) ).
thf(810,plain,
! [SV25: $i,SV44: $i] :
( ( ( element @ SV44 @ ( powerset @ SV25 ) )
= $false )
| ( ( ! [SY99: $i] :
( ~ ( in @ SY99 @ SV44 )
| ( in @ SY99 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(811,plain,
! [SV26: $i,SV45: $i] :
( ( ( element @ SV45 @ ( powerset @ SV26 ) )
= $false )
| ( ( element @ ( subset_complement @ SV26 @ SV45 ) @ ( powerset @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(812,plain,
! [SV28: $i] :
( ( ~ ( ~ ( element @ ( sK4_SY87 @ SV28 ) @ ( powerset @ SV28 ) )
| ~ ( empty @ ( sK4_SY87 @ SV28 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[787]) ).
thf(813,plain,
! [SV53: $i,SV29: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ( element @ SV46 @ ( powerset @ SV29 ) )
| ~ ( element @ SV53 @ ( powerset @ SV29 ) ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV29 @ SV46 @ SV53 )
= ( subset_intersection2 @ SV29 @ SV53 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(814,plain,
! [SV54: $i,SV30: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ( element @ SV47 @ ( powerset @ SV30 ) )
| ~ ( element @ SV54 @ ( powerset @ SV30 ) ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV30 @ SV47 @ SV54 ) @ ( powerset @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(815,plain,
! [SV31: $i,SV48: $i] :
( ( ( element @ SV48 @ ( powerset @ ( powerset @ SV31 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ( SV48 != empty_set ) )
| ( ( complements_of_subsets @ SV31 @ SV48 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(816,plain,
! [SV32: $i,SV56: $i] :
( ( ( ~ ( element @ SV56 @ ( powerset @ SV32 ) )
| ( finite @ SV56 ) )
= $true )
| ( ( finite @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(817,plain,
! [SV33: $i,SV49: $i] :
( ( ( element @ SV49 @ ( powerset @ ( powerset @ SV33 ) ) )
= $false )
| ( ( element @ ( complements_of_subsets @ SV33 @ SV49 ) @ ( powerset @ ( powerset @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(818,plain,
! [SV9: $i,SV55: $i] :
( ( ( ~ ( element @ SV55 @ ( powerset @ SV9 ) ) )
= $true )
| ( ( v1_membered @ SV55 )
= $true )
| ( ( v1_membered @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[793]) ).
thf(819,plain,
! [SV50: $i,SV11: $i,SV35: $i] :
( ( ( ~ ( ~ ( element @ SV35 @ ( powerset @ SV11 ) )
| ~ ( element @ SV50 @ ( powerset @ SV11 ) ) ) )
= $false )
| ( ( ( subset_intersection2 @ SV11 @ SV35 @ SV35 )
= SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(820,plain,
! [SV51: $i,SV36: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ SV12 @ SV36 )
| ~ ( element @ SV36 @ ( powerset @ SV51 ) ) ) )
= $false )
| ( ( element @ SV12 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(821,plain,
! [SV38: $i,SV17: $i] :
( ( ~ ( element @ SV17 @ ( powerset @ SV38 ) )
| ( subset @ SV17 @ SV38 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(822,plain,
! [SV38: $i,SV17: $i] :
( ( ~ ( subset @ SV17 @ SV38 )
| ( element @ SV17 @ ( powerset @ SV38 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(823,plain,
! [SV19: $i] :
( ( ( ! [SY75: $i] :
~ ~ ( ~ ( element @ SY75 @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ SY75 ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(824,plain,
! [SV20: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK5_SY97 @ SV40 @ SV20 ) @ SV20 )
| ( in @ ( sK5_SY97 @ SV40 @ SV20 ) @ SV40 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[804]) ).
thf(825,plain,
! [SV22: $i] :
( ( ( SV22 != empty_set )
= $true )
| ( ( ! [SY79: $i] :
~ ( in @ SY79 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[806]) ).
thf(826,plain,
! [SV22: $i] :
( ( ( ~ ! [SY80: $i] :
~ ( in @ SY80 @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[807]) ).
thf(827,plain,
! [SV52: $i,SV24: $i,SV43: $i] :
( ( ( ~ ( ~ ( element @ SV43 @ ( powerset @ SV24 ) )
| ~ ( element @ SV52 @ ( powerset @ SV24 ) ) ) )
= $false )
| ( ( element @ ( subset_difference @ SV24 @ SV43 @ SV52 ) @ ( powerset @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(828,plain,
! [SV25: $i,SV44: $i,SV57: $i] :
( ( ( ~ ( in @ SV57 @ SV44 )
| ( in @ SV57 @ SV25 ) )
= $true )
| ( ( element @ SV44 @ ( powerset @ SV25 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(829,plain,
! [SV28: $i] :
( ( ~ ( element @ ( sK4_SY87 @ SV28 ) @ ( powerset @ SV28 ) )
| ~ ( empty @ ( sK4_SY87 @ SV28 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(830,plain,
! [SV53: $i,SV29: $i,SV46: $i] :
( ( ( ~ ( ~ ( element @ SV46 @ ( powerset @ SV29 ) )
| ~ ( element @ SV53 @ ( powerset @ SV29 ) ) ) )
= $false )
| ( ( ( subset_intersection2 @ SV29 @ SV46 @ SV53 )
= ( subset_intersection2 @ SV29 @ SV53 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(831,plain,
! [SV54: $i,SV30: $i,SV47: $i] :
( ( ( ~ ( ~ ( element @ SV47 @ ( powerset @ SV30 ) )
| ~ ( element @ SV54 @ ( powerset @ SV30 ) ) ) )
= $false )
| ( ( element @ ( subset_intersection2 @ SV30 @ SV47 @ SV54 ) @ ( powerset @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(832,plain,
! [SV31: $i,SV48: $i] :
( ( ( ~ ( ~ ( ( SV48 != empty_set ) )
| ( ( complements_of_subsets @ SV31 @ SV48 )
!= empty_set ) ) )
= $false )
| ( ( element @ SV48 @ ( powerset @ ( powerset @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(833,plain,
! [SV32: $i,SV56: $i] :
( ( ( ~ ( element @ SV56 @ ( powerset @ SV32 ) ) )
= $true )
| ( ( finite @ SV56 )
= $true )
| ( ( finite @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(834,plain,
! [SV9: $i,SV55: $i] :
( ( ( element @ SV55 @ ( powerset @ SV9 ) )
= $false )
| ( ( v1_membered @ SV55 )
= $true )
| ( ( v1_membered @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[818]) ).
thf(835,plain,
! [SV50: $i,SV11: $i,SV35: $i] :
( ( ( ~ ( element @ SV35 @ ( powerset @ SV11 ) )
| ~ ( element @ SV50 @ ( powerset @ SV11 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV11 @ SV35 @ SV35 )
= SV35 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[819]) ).
thf(836,plain,
! [SV51: $i,SV36: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV36 )
| ~ ( element @ SV36 @ ( powerset @ SV51 ) ) )
= $true )
| ( ( element @ SV12 @ SV51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(837,plain,
! [SV38: $i,SV17: $i] :
( ( ( ~ ( element @ SV17 @ ( powerset @ SV38 ) ) )
= $true )
| ( ( subset @ SV17 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(838,plain,
! [SV38: $i,SV17: $i] :
( ( ( ~ ( subset @ SV17 @ SV38 ) )
= $true )
| ( ( element @ SV17 @ ( powerset @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[822]) ).
thf(839,plain,
! [SV19: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK6_SY75 @ SV19 ) @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ ( sK6_SY75 @ SV19 ) ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[823]) ).
thf(840,plain,
! [SV20: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK5_SY97 @ SV40 @ SV20 ) @ SV20 ) )
= $false )
| ( ( element @ SV20 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[824]) ).
thf(841,plain,
! [SV20: $i,SV40: $i] :
( ( ( in @ ( sK5_SY97 @ SV40 @ SV20 ) @ SV40 )
= $false )
| ( ( element @ SV20 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[824]) ).
thf(842,plain,
! [SV22: $i] :
( ( ( SV22 = empty_set )
= $false )
| ( ( ! [SY79: $i] :
~ ( in @ SY79 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(843,plain,
! [SV22: $i] :
( ( ( ! [SY80: $i] :
~ ( in @ SY80 @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(844,plain,
! [SV52: $i,SV24: $i,SV43: $i] :
( ( ( ~ ( element @ SV43 @ ( powerset @ SV24 ) )
| ~ ( element @ SV52 @ ( powerset @ SV24 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV24 @ SV43 @ SV52 ) @ ( powerset @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[827]) ).
thf(845,plain,
! [SV25: $i,SV44: $i,SV57: $i] :
( ( ( ~ ( in @ SV57 @ SV44 ) )
= $true )
| ( ( in @ SV57 @ SV25 )
= $true )
| ( ( element @ SV44 @ ( powerset @ SV25 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[828]) ).
thf(846,plain,
! [SV28: $i] :
( ( ~ ( element @ ( sK4_SY87 @ SV28 ) @ ( powerset @ SV28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[829]) ).
thf(847,plain,
! [SV28: $i] :
( ( ~ ( empty @ ( sK4_SY87 @ SV28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[829]) ).
thf(848,plain,
! [SV53: $i,SV29: $i,SV46: $i] :
( ( ( ~ ( element @ SV46 @ ( powerset @ SV29 ) )
| ~ ( element @ SV53 @ ( powerset @ SV29 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV29 @ SV46 @ SV53 )
= ( subset_intersection2 @ SV29 @ SV53 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(849,plain,
! [SV54: $i,SV30: $i,SV47: $i] :
( ( ( ~ ( element @ SV47 @ ( powerset @ SV30 ) )
| ~ ( element @ SV54 @ ( powerset @ SV30 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV30 @ SV47 @ SV54 ) @ ( powerset @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(850,plain,
! [SV31: $i,SV48: $i] :
( ( ( ~ ( ( SV48 != empty_set ) )
| ( ( complements_of_subsets @ SV31 @ SV48 )
!= empty_set ) )
= $true )
| ( ( element @ SV48 @ ( powerset @ ( powerset @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[832]) ).
thf(851,plain,
! [SV32: $i,SV56: $i] :
( ( ( element @ SV56 @ ( powerset @ SV32 ) )
= $false )
| ( ( finite @ SV56 )
= $true )
| ( ( finite @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(852,plain,
! [SV50: $i,SV11: $i,SV35: $i] :
( ( ( ~ ( element @ SV35 @ ( powerset @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV50 @ ( powerset @ SV11 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV11 @ SV35 @ SV35 )
= SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(853,plain,
! [SV51: $i,SV36: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV36 ) )
= $true )
| ( ( ~ ( element @ SV36 @ ( powerset @ SV51 ) ) )
= $true )
| ( ( element @ SV12 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(854,plain,
! [SV38: $i,SV17: $i] :
( ( ( element @ SV17 @ ( powerset @ SV38 ) )
= $false )
| ( ( subset @ SV17 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(855,plain,
! [SV38: $i,SV17: $i] :
( ( ( subset @ SV17 @ SV38 )
= $false )
| ( ( element @ SV17 @ ( powerset @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(856,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ( element @ ( sK6_SY75 @ SV19 ) @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ ( sK6_SY75 @ SV19 ) ) ) )
= $true )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[839]) ).
thf(857,plain,
! [SV20: $i,SV40: $i] :
( ( ( in @ ( sK5_SY97 @ SV40 @ SV20 ) @ SV20 )
= $true )
| ( ( element @ SV20 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[840]) ).
thf(858,plain,
! [SV22: $i,SV58: $i] :
( ( ( ~ ( in @ SV58 @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(859,plain,
! [SV22: $i] :
( ( ( ~ ( in @ ( sK7_SY80 @ SV22 ) @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[843]) ).
thf(860,plain,
! [SV52: $i,SV24: $i,SV43: $i] :
( ( ( ~ ( element @ SV43 @ ( powerset @ SV24 ) ) )
= $true )
| ( ( ~ ( element @ SV52 @ ( powerset @ SV24 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV24 @ SV43 @ SV52 ) @ ( powerset @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(861,plain,
! [SV25: $i,SV44: $i,SV57: $i] :
( ( ( in @ SV57 @ SV44 )
= $false )
| ( ( in @ SV57 @ SV25 )
= $true )
| ( ( element @ SV44 @ ( powerset @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(862,plain,
! [SV28: $i] :
( ( element @ ( sK4_SY87 @ SV28 ) @ ( powerset @ SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[846]) ).
thf(863,plain,
! [SV28: $i] :
( ( empty @ ( sK4_SY87 @ SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[847]) ).
thf(864,plain,
! [SV53: $i,SV29: $i,SV46: $i] :
( ( ( ~ ( element @ SV46 @ ( powerset @ SV29 ) ) )
= $true )
| ( ( ~ ( element @ SV53 @ ( powerset @ SV29 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV29 @ SV46 @ SV53 )
= ( subset_intersection2 @ SV29 @ SV53 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(865,plain,
! [SV54: $i,SV30: $i,SV47: $i] :
( ( ( ~ ( element @ SV47 @ ( powerset @ SV30 ) ) )
= $true )
| ( ( ~ ( element @ SV54 @ ( powerset @ SV30 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV30 @ SV47 @ SV54 ) @ ( powerset @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(866,plain,
! [SV31: $i,SV48: $i] :
( ( ( ~ ( ( SV48 != empty_set ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV31 @ SV48 )
!= empty_set )
= $true )
| ( ( element @ SV48 @ ( powerset @ ( powerset @ SV31 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(867,plain,
! [SV50: $i,SV11: $i,SV35: $i] :
( ( ( element @ SV35 @ ( powerset @ SV11 ) )
= $false )
| ( ( ~ ( element @ SV50 @ ( powerset @ SV11 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV11 @ SV35 @ SV35 )
= SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(868,plain,
! [SV51: $i,SV36: $i,SV12: $i] :
( ( ( in @ SV12 @ SV36 )
= $false )
| ( ( ~ ( element @ SV36 @ ( powerset @ SV51 ) ) )
= $true )
| ( ( element @ SV12 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(869,plain,
! [SV19: $i] :
( ( ( ~ ( element @ ( sK6_SY75 @ SV19 ) @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ ( sK6_SY75 @ SV19 ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(870,plain,
! [SV22: $i,SV58: $i] :
( ( ( in @ SV58 @ SV22 )
= $false )
| ( ( SV22 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(871,plain,
! [SV22: $i] :
( ( ( in @ ( sK7_SY80 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[859]) ).
thf(872,plain,
! [SV52: $i,SV24: $i,SV43: $i] :
( ( ( element @ SV43 @ ( powerset @ SV24 ) )
= $false )
| ( ( ~ ( element @ SV52 @ ( powerset @ SV24 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV24 @ SV43 @ SV52 ) @ ( powerset @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(873,plain,
! [SV53: $i,SV29: $i,SV46: $i] :
( ( ( element @ SV46 @ ( powerset @ SV29 ) )
= $false )
| ( ( ~ ( element @ SV53 @ ( powerset @ SV29 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV29 @ SV46 @ SV53 )
= ( subset_intersection2 @ SV29 @ SV53 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(874,plain,
! [SV54: $i,SV30: $i,SV47: $i] :
( ( ( element @ SV47 @ ( powerset @ SV30 ) )
= $false )
| ( ( ~ ( element @ SV54 @ ( powerset @ SV30 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV30 @ SV47 @ SV54 ) @ ( powerset @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(875,plain,
! [SV31: $i,SV48: $i] :
( ( ( SV48 != empty_set )
= $false )
| ( ( ( complements_of_subsets @ SV31 @ SV48 )
!= empty_set )
= $true )
| ( ( element @ SV48 @ ( powerset @ ( powerset @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(876,plain,
! [SV35: $i,SV11: $i,SV50: $i] :
( ( ( element @ SV50 @ ( powerset @ SV11 ) )
= $false )
| ( ( element @ SV35 @ ( powerset @ SV11 ) )
= $false )
| ( ( ( subset_intersection2 @ SV11 @ SV35 @ SV35 )
= SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(877,plain,
! [SV12: $i,SV51: $i,SV36: $i] :
( ( ( element @ SV36 @ ( powerset @ SV51 ) )
= $false )
| ( ( in @ SV12 @ SV36 )
= $false )
| ( ( element @ SV12 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(878,plain,
! [SV19: $i] :
( ( ( ~ ( element @ ( sK6_SY75 @ SV19 ) @ ( powerset @ SV19 ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[869]) ).
thf(879,plain,
! [SV19: $i] :
( ( ( ~ ~ ( empty @ ( sK6_SY75 @ SV19 ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[869]) ).
thf(880,plain,
! [SV43: $i,SV24: $i,SV52: $i] :
( ( ( element @ SV52 @ ( powerset @ SV24 ) )
= $false )
| ( ( element @ SV43 @ ( powerset @ SV24 ) )
= $false )
| ( ( element @ ( subset_difference @ SV24 @ SV43 @ SV52 ) @ ( powerset @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(881,plain,
! [SV46: $i,SV29: $i,SV53: $i] :
( ( ( element @ SV53 @ ( powerset @ SV29 ) )
= $false )
| ( ( element @ SV46 @ ( powerset @ SV29 ) )
= $false )
| ( ( ( subset_intersection2 @ SV29 @ SV46 @ SV53 )
= ( subset_intersection2 @ SV29 @ SV53 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(882,plain,
! [SV47: $i,SV30: $i,SV54: $i] :
( ( ( element @ SV54 @ ( powerset @ SV30 ) )
= $false )
| ( ( element @ SV47 @ ( powerset @ SV30 ) )
= $false )
| ( ( element @ ( subset_intersection2 @ SV30 @ SV47 @ SV54 ) @ ( powerset @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(883,plain,
! [SV31: $i,SV48: $i] :
( ( ( SV48 = empty_set )
= $true )
| ( ( ( complements_of_subsets @ SV31 @ SV48 )
!= empty_set )
= $true )
| ( ( element @ SV48 @ ( powerset @ ( powerset @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[875]) ).
thf(884,plain,
! [SV19: $i] :
( ( ( element @ ( sK6_SY75 @ SV19 ) @ ( powerset @ SV19 ) )
= $true )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[878]) ).
thf(885,plain,
! [SV19: $i] :
( ( ( ~ ( empty @ ( sK6_SY75 @ SV19 ) ) )
= $true )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[879]) ).
thf(886,plain,
! [SV48: $i,SV31: $i] :
( ( ( ( complements_of_subsets @ SV31 @ SV48 )
= empty_set )
= $false )
| ( ( SV48 = empty_set )
= $true )
| ( ( element @ SV48 @ ( powerset @ ( powerset @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(887,plain,
! [SV19: $i] :
( ( ( empty @ ( sK6_SY75 @ SV19 ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(888,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[616,887,886,884,882,881,880,877,876,871,870,863,862,861,857,855,854,851,841,834,817,811,808,805,802,799,798,797,794,774,772,770,759,738,711,710,709,708,706,705,704,676,662,659,658,657,656,655,649,648,647,646,645,643,642,641,640,638,637,636,635,634,633,632,631,630,629,628,627,626,625]) ).
thf(889,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[604]) ).
thf(890,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[603]) ).
thf(891,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[602]) ).
thf(892,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[601]) ).
thf(893,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[600]) ).
thf(894,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[599]) ).
thf(895,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[598]) ).
thf(896,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[597]) ).
thf(897,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[596]) ).
thf(898,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[595]) ).
thf(899,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[594]) ).
thf(900,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(901,plain,
$true = $true,
inference(copy,[status(thm)],[592]) ).
thf(902,plain,
$true = $true,
inference(copy,[status(thm)],[591]) ).
thf(903,plain,
$true = $true,
inference(copy,[status(thm)],[590]) ).
thf(904,plain,
$true = $true,
inference(copy,[status(thm)],[589]) ).
thf(905,plain,
$true = $true,
inference(copy,[status(thm)],[588]) ).
thf(906,plain,
$true = $true,
inference(copy,[status(thm)],[587]) ).
thf(907,plain,
$true = $true,
inference(copy,[status(thm)],[586]) ).
thf(908,plain,
$true = $true,
inference(copy,[status(thm)],[585]) ).
thf(909,plain,
$true = $true,
inference(copy,[status(thm)],[584]) ).
thf(910,plain,
$true = $true,
inference(copy,[status(thm)],[583]) ).
thf(911,plain,
$true = $true,
inference(copy,[status(thm)],[582]) ).
thf(912,plain,
$true = $true,
inference(copy,[status(thm)],[581]) ).
thf(913,plain,
$true = $true,
inference(copy,[status(thm)],[580]) ).
thf(914,plain,
$true = $true,
inference(copy,[status(thm)],[579]) ).
thf(915,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(916,plain,
$true = $true,
inference(copy,[status(thm)],[577]) ).
thf(917,plain,
$true = $true,
inference(copy,[status(thm)],[576]) ).
thf(918,plain,
$true = $true,
inference(copy,[status(thm)],[575]) ).
thf(919,plain,
$true = $true,
inference(copy,[status(thm)],[574]) ).
thf(920,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(921,plain,
$true = $true,
inference(copy,[status(thm)],[572]) ).
thf(922,plain,
$true = $true,
inference(copy,[status(thm)],[571]) ).
thf(923,plain,
$true = $true,
inference(copy,[status(thm)],[570]) ).
thf(924,plain,
$true = $true,
inference(copy,[status(thm)],[569]) ).
thf(925,plain,
$true = $true,
inference(copy,[status(thm)],[568]) ).
thf(926,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[567]) ).
thf(927,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[566]) ).
thf(928,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[565]) ).
thf(929,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(930,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[563]) ).
thf(931,plain,
$true = $true,
inference(copy,[status(thm)],[562]) ).
thf(932,plain,
$true = $true,
inference(copy,[status(thm)],[561]) ).
thf(933,plain,
$true = $true,
inference(copy,[status(thm)],[560]) ).
thf(934,plain,
$true = $true,
inference(copy,[status(thm)],[559]) ).
thf(935,plain,
$true = $true,
inference(copy,[status(thm)],[558]) ).
thf(936,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(937,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(938,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[555]) ).
thf(939,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[554]) ).
thf(940,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(941,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(942,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[551]) ).
thf(943,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[550]) ).
thf(944,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[549]) ).
thf(945,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(946,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[547]) ).
thf(947,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[546]) ).
thf(948,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[545]) ).
thf(949,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[544]) ).
thf(950,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(951,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(952,plain,
( ( element @ sK2_SY64 @ ( powerset @ ( powerset @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[607]) ).
thf(953,plain,
( ( ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
!= empty_set )
& ( sK2_SY64 = empty_set ) )
= $true ),
inference(copy,[status(thm)],[612]) ).
thf(954,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[891]) ).
thf(955,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[936]) ).
thf(956,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( element @ ( subset_intersection2 @ SX0 @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[927]) ).
thf(957,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1 != empty_set ) )
| ( ( complements_of_subsets @ SX0 @ SX1 )
!= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[895]) ).
thf(958,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[951]) ).
thf(959,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[890]) ).
thf(960,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( element @ ( subset_difference @ SX0 @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[929]) ).
thf(961,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[942]) ).
thf(962,plain,
( ( ! [SX0: $i] :
( ~ ( v1_membered @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v1_membered @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[897]) ).
thf(963,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( ( complements_of_subsets @ SX0 @ ( complements_of_subsets @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[941]) ).
thf(964,plain,
( ( ! [SX0: $i] :
( ~ ( finite @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[898]) ).
thf(965,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( ( subset_intersection2 @ SX0 @ SX1 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[939]) ).
thf(966,plain,
( ( ~ ( ~ ( ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
!= empty_set ) )
| ( sK2_SY64 != empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[953]) ).
thf(967,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[900]) ).
thf(968,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( meet_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[928]) ).
thf(969,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( ( subset_complement @ SX0 @ ( subset_complement @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[940]) ).
thf(970,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[945]) ).
thf(971,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( ( subset_intersection2 @ SX0 @ SX1 @ SX2 )
= ( subset_intersection2 @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[899]) ).
thf(972,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( element @ ( subset_complement @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[920]) ).
thf(973,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[950]) ).
thf(974,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[894]) ).
thf(975,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[948]) ).
thf(976,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[943]) ).
thf(977,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( union_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[926]) ).
thf(978,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( complements_of_subsets @ SX0 @ SX1 ) @ ( powerset @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[930]) ).
thf(979,plain,
( ( ! [SX0: $i] :
( ( singleton @ SX0 )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[889]) ).
thf(980,plain,
! [SV59: $i] :
( ( subset @ empty_set @ SV59 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(981,plain,
! [SV60: $i] :
( ( ( union @ ( powerset @ SV60 ) )
= SV60 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(982,plain,
! [SV61: $i] :
( ( element @ ( cast_to_subset @ SV61 ) @ ( powerset @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(983,plain,
! [SV62: $i] :
( ( ~ ( empty @ ( powerset @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(984,plain,
! [SV63: $i] :
( ( ( set_union2 @ SV63 @ empty_set )
= SV63 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(985,plain,
! [SV64: $i] :
( ( ( set_intersection2 @ SV64 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(986,plain,
! [SV65: $i] :
( ( ( set_difference @ SV65 @ empty_set )
= SV65 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(987,plain,
! [SV66: $i] :
( ( ( set_difference @ empty_set @ SV66 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(988,plain,
! [SV67: $i] :
( ( ! [SY102: $i] :
( ~ ! [SY103: $i] :
( ~ ( in @ SY103 @ SV67 )
| ( in @ SY103 @ SY102 ) )
| ( element @ SV67 @ ( powerset @ SY102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(989,plain,
! [SV68: $i] :
( ( ~ ! [SY104: $i] :
~ ( element @ SY104 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(990,plain,
! [SV69: $i] :
( ( ! [SY105: $i,SY106: $i] :
( ~ ~ ( ~ ( element @ SY105 @ ( powerset @ SV69 ) )
| ~ ( element @ SY106 @ ( powerset @ SV69 ) ) )
| ( element @ ( subset_intersection2 @ SV69 @ SY105 @ SY106 ) @ ( powerset @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(991,plain,
! [SV70: $i] :
( ( ! [SY107: $i] :
( ~ ( element @ SY107 @ ( powerset @ ( powerset @ SV70 ) ) )
| ~ ~ ( ~ ( ( SY107 != empty_set ) )
| ( ( complements_of_subsets @ SV70 @ SY107 )
!= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(992,plain,
! [SV71: $i] :
( ( ~ ( empty @ SV71 )
| ( SV71 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(993,plain,
! [SV72: $i] :
( ( ! [SY108: $i] :
( ~ ( element @ SY108 @ ( powerset @ SV72 ) )
| ! [SY109: $i] :
( ~ ( in @ SY109 @ SY108 )
| ( in @ SY109 @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(994,plain,
! [SV73: $i] :
( ( ! [SY110: $i,SY111: $i] :
( ~ ~ ( ~ ( element @ SY110 @ ( powerset @ SV73 ) )
| ~ ( element @ SY111 @ ( powerset @ SV73 ) ) )
| ( element @ ( subset_difference @ SV73 @ SY110 @ SY111 ) @ ( powerset @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(995,plain,
! [SV74: $i] :
( ( ~ ~ ( empty @ SV74 )
| ~ ! [SY112: $i] :
~ ~ ( ~ ( element @ SY112 @ ( powerset @ SV74 ) )
| ~ ~ ( empty @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(996,plain,
! [SV75: $i] :
( ( ~ ( v1_membered @ SV75 )
| ! [SY113: $i] :
( ~ ( element @ SY113 @ ( powerset @ SV75 ) )
| ( v1_membered @ SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(997,plain,
! [SV76: $i] :
( ( ! [SY114: $i] :
( ~ ( element @ SY114 @ ( powerset @ ( powerset @ SV76 ) ) )
| ( ( complements_of_subsets @ SV76 @ ( complements_of_subsets @ SV76 @ SY114 ) )
= SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(998,plain,
! [SV77: $i] :
( ( ~ ( finite @ SV77 )
| ! [SY115: $i] :
( ~ ( element @ SY115 @ ( powerset @ SV77 ) )
| ( finite @ SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(999,plain,
! [SV78: $i] :
( ( ! [SY116: $i,SY117: $i] :
( ~ ~ ( ~ ( element @ SY116 @ ( powerset @ SV78 ) )
| ~ ( element @ SY117 @ ( powerset @ SV78 ) ) )
| ( ( subset_intersection2 @ SV78 @ SY116 @ SY116 )
= SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1000,plain,
( ( ~ ( ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
!= empty_set ) )
| ( sK2_SY64 != empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1001,plain,
! [SV79: $i] :
( ( ~ ( ~ ( ( SV79 != empty_set )
| ! [SY118: $i] :
~ ( in @ SY118 @ SV79 ) )
| ~ ( ~ ! [SY119: $i] :
~ ( in @ SY119 @ SV79 )
| ( SV79 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1002,plain,
! [SV80: $i] :
( ( ! [SY120: $i] :
( ~ ( element @ SY120 @ ( powerset @ ( powerset @ SV80 ) ) )
| ( element @ ( meet_of_subsets @ SV80 @ SY120 ) @ ( powerset @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1003,plain,
! [SV81: $i] :
( ( ! [SY121: $i] :
( ~ ( element @ SY121 @ ( powerset @ SV81 ) )
| ( ( subset_complement @ SV81 @ ( subset_complement @ SV81 @ SY121 ) )
= SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1004,plain,
! [SV82: $i] :
( ( ! [SY122: $i] :
( ~ ( in @ SV82 @ SY122 )
| ( element @ SV82 @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1005,plain,
! [SV83: $i] :
( ( ! [SY123: $i,SY124: $i] :
( ~ ~ ( ~ ( element @ SY123 @ ( powerset @ SV83 ) )
| ~ ( element @ SY124 @ ( powerset @ SV83 ) ) )
| ( ( subset_intersection2 @ SV83 @ SY123 @ SY124 )
= ( subset_intersection2 @ SV83 @ SY124 @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1006,plain,
! [SV84: $i] :
( ( ! [SY125: $i] :
( ~ ( element @ SY125 @ ( powerset @ SV84 ) )
| ( element @ ( subset_complement @ SV84 @ SY125 ) @ ( powerset @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1007,plain,
! [SV85: $i] :
( ( ! [SY126: $i,SY127: $i] :
( ~ ~ ( ~ ( in @ SV85 @ SY126 )
| ~ ( element @ SY126 @ ( powerset @ SY127 ) ) )
| ( element @ SV85 @ SY127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1008,plain,
! [SV86: $i] :
( ( ~ ( subset @ SV86 @ empty_set )
| ( SV86 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1009,plain,
! [SV87: $i] :
( ( ! [SY128: $i] :
~ ( ~ ( ~ ( element @ SV87 @ ( powerset @ SY128 ) )
| ( subset @ SV87 @ SY128 ) )
| ~ ( ~ ( subset @ SV87 @ SY128 )
| ( element @ SV87 @ ( powerset @ SY128 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1010,plain,
! [SV88: $i] :
( ( ~ ! [SY129: $i] :
~ ~ ( ~ ( element @ SY129 @ ( powerset @ SV88 ) )
| ~ ( empty @ SY129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1011,plain,
! [SV89: $i] :
( ( ! [SY130: $i] :
( ~ ( element @ SY130 @ ( powerset @ ( powerset @ SV89 ) ) )
| ( element @ ( union_of_subsets @ SV89 @ SY130 ) @ ( powerset @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1012,plain,
! [SV90: $i] :
( ( ! [SY131: $i] :
( ~ ( element @ SY131 @ ( powerset @ ( powerset @ SV90 ) ) )
| ( element @ ( complements_of_subsets @ SV90 @ SY131 ) @ ( powerset @ ( powerset @ SV90 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1013,plain,
! [SV91: $i] :
( ( ( singleton @ SV91 )
!= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1014,plain,
! [SV62: $i] :
( ( empty @ ( powerset @ SV62 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1015,plain,
! [SV92: $i,SV67: $i] :
( ( ~ ! [SY132: $i] :
( ~ ( in @ SY132 @ SV67 )
| ( in @ SY132 @ SV92 ) )
| ( element @ SV67 @ ( powerset @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1016,plain,
! [SV68: $i] :
( ( ! [SY104: $i] :
~ ( element @ SY104 @ SV68 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1017,plain,
! [SV69: $i,SV93: $i] :
( ( ! [SY133: $i] :
( ~ ~ ( ~ ( element @ SV93 @ ( powerset @ SV69 ) )
| ~ ( element @ SY133 @ ( powerset @ SV69 ) ) )
| ( element @ ( subset_intersection2 @ SV69 @ SV93 @ SY133 ) @ ( powerset @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1018,plain,
! [SV70: $i,SV94: $i] :
( ( ~ ( element @ SV94 @ ( powerset @ ( powerset @ SV70 ) ) )
| ~ ~ ( ~ ( ( SV94 != empty_set ) )
| ( ( complements_of_subsets @ SV70 @ SV94 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1019,plain,
! [SV71: $i] :
( ( ( ~ ( empty @ SV71 ) )
= $true )
| ( ( SV71 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[992]) ).
thf(1020,plain,
! [SV72: $i,SV95: $i] :
( ( ~ ( element @ SV95 @ ( powerset @ SV72 ) )
| ! [SY134: $i] :
( ~ ( in @ SY134 @ SV95 )
| ( in @ SY134 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1021,plain,
! [SV73: $i,SV96: $i] :
( ( ! [SY135: $i] :
( ~ ~ ( ~ ( element @ SV96 @ ( powerset @ SV73 ) )
| ~ ( element @ SY135 @ ( powerset @ SV73 ) ) )
| ( element @ ( subset_difference @ SV73 @ SV96 @ SY135 ) @ ( powerset @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1022,plain,
! [SV74: $i] :
( ( ( ~ ~ ( empty @ SV74 ) )
= $true )
| ( ( ~ ! [SY112: $i] :
~ ~ ( ~ ( element @ SY112 @ ( powerset @ SV74 ) )
| ~ ~ ( empty @ SY112 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[995]) ).
thf(1023,plain,
! [SV75: $i] :
( ( ( ~ ( v1_membered @ SV75 ) )
= $true )
| ( ( ! [SY113: $i] :
( ~ ( element @ SY113 @ ( powerset @ SV75 ) )
| ( v1_membered @ SY113 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[996]) ).
thf(1024,plain,
! [SV76: $i,SV97: $i] :
( ( ~ ( element @ SV97 @ ( powerset @ ( powerset @ SV76 ) ) )
| ( ( complements_of_subsets @ SV76 @ ( complements_of_subsets @ SV76 @ SV97 ) )
= SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1025,plain,
! [SV77: $i] :
( ( ( ~ ( finite @ SV77 ) )
= $true )
| ( ( ! [SY115: $i] :
( ~ ( element @ SY115 @ ( powerset @ SV77 ) )
| ( finite @ SY115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1026,plain,
! [SV78: $i,SV98: $i] :
( ( ! [SY136: $i] :
( ~ ~ ( ~ ( element @ SV98 @ ( powerset @ SV78 ) )
| ~ ( element @ SY136 @ ( powerset @ SV78 ) ) )
| ( ( subset_intersection2 @ SV78 @ SV98 @ SV98 )
= SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1027,plain,
( ( ~ ( ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
!= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1000]) ).
thf(1028,plain,
( ( sK2_SY64 != empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1000]) ).
thf(1029,plain,
! [SV79: $i] :
( ( ~ ( ( SV79 != empty_set )
| ! [SY118: $i] :
~ ( in @ SY118 @ SV79 ) )
| ~ ( ~ ! [SY119: $i] :
~ ( in @ SY119 @ SV79 )
| ( SV79 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1030,plain,
! [SV80: $i,SV99: $i] :
( ( ~ ( element @ SV99 @ ( powerset @ ( powerset @ SV80 ) ) )
| ( element @ ( meet_of_subsets @ SV80 @ SV99 ) @ ( powerset @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1031,plain,
! [SV81: $i,SV100: $i] :
( ( ~ ( element @ SV100 @ ( powerset @ SV81 ) )
| ( ( subset_complement @ SV81 @ ( subset_complement @ SV81 @ SV100 ) )
= SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1032,plain,
! [SV101: $i,SV82: $i] :
( ( ~ ( in @ SV82 @ SV101 )
| ( element @ SV82 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1033,plain,
! [SV83: $i,SV102: $i] :
( ( ! [SY137: $i] :
( ~ ~ ( ~ ( element @ SV102 @ ( powerset @ SV83 ) )
| ~ ( element @ SY137 @ ( powerset @ SV83 ) ) )
| ( ( subset_intersection2 @ SV83 @ SV102 @ SY137 )
= ( subset_intersection2 @ SV83 @ SY137 @ SV102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1034,plain,
! [SV84: $i,SV103: $i] :
( ( ~ ( element @ SV103 @ ( powerset @ SV84 ) )
| ( element @ ( subset_complement @ SV84 @ SV103 ) @ ( powerset @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1035,plain,
! [SV104: $i,SV85: $i] :
( ( ! [SY138: $i] :
( ~ ~ ( ~ ( in @ SV85 @ SV104 )
| ~ ( element @ SV104 @ ( powerset @ SY138 ) ) )
| ( element @ SV85 @ SY138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1036,plain,
! [SV86: $i] :
( ( ( ~ ( subset @ SV86 @ empty_set ) )
= $true )
| ( ( SV86 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1037,plain,
! [SV105: $i,SV87: $i] :
( ( ~ ( ~ ( ~ ( element @ SV87 @ ( powerset @ SV105 ) )
| ( subset @ SV87 @ SV105 ) )
| ~ ( ~ ( subset @ SV87 @ SV105 )
| ( element @ SV87 @ ( powerset @ SV105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1038,plain,
! [SV88: $i] :
( ( ! [SY129: $i] :
~ ~ ( ~ ( element @ SY129 @ ( powerset @ SV88 ) )
| ~ ( empty @ SY129 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1039,plain,
! [SV89: $i,SV106: $i] :
( ( ~ ( element @ SV106 @ ( powerset @ ( powerset @ SV89 ) ) )
| ( element @ ( union_of_subsets @ SV89 @ SV106 ) @ ( powerset @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1040,plain,
! [SV90: $i,SV107: $i] :
( ( ~ ( element @ SV107 @ ( powerset @ ( powerset @ SV90 ) ) )
| ( element @ ( complements_of_subsets @ SV90 @ SV107 ) @ ( powerset @ ( powerset @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1041,plain,
! [SV91: $i] :
( ( ( singleton @ SV91 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1042,plain,
! [SV92: $i,SV67: $i] :
( ( ( ~ ! [SY132: $i] :
( ~ ( in @ SY132 @ SV67 )
| ( in @ SY132 @ SV92 ) ) )
= $true )
| ( ( element @ SV67 @ ( powerset @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1043,plain,
! [SV68: $i] :
( ( ~ ( element @ ( sK8_SY104 @ SV68 ) @ SV68 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1016]) ).
thf(1044,plain,
! [SV108: $i,SV69: $i,SV93: $i] :
( ( ~ ~ ( ~ ( element @ SV93 @ ( powerset @ SV69 ) )
| ~ ( element @ SV108 @ ( powerset @ SV69 ) ) )
| ( element @ ( subset_intersection2 @ SV69 @ SV93 @ SV108 ) @ ( powerset @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1045,plain,
! [SV70: $i,SV94: $i] :
( ( ( ~ ( element @ SV94 @ ( powerset @ ( powerset @ SV70 ) ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV94 != empty_set ) )
| ( ( complements_of_subsets @ SV70 @ SV94 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1018]) ).
thf(1046,plain,
! [SV71: $i] :
( ( ( empty @ SV71 )
= $false )
| ( ( SV71 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1047,plain,
! [SV72: $i,SV95: $i] :
( ( ( ~ ( element @ SV95 @ ( powerset @ SV72 ) ) )
= $true )
| ( ( ! [SY134: $i] :
( ~ ( in @ SY134 @ SV95 )
| ( in @ SY134 @ SV72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1020]) ).
thf(1048,plain,
! [SV109: $i,SV73: $i,SV96: $i] :
( ( ~ ~ ( ~ ( element @ SV96 @ ( powerset @ SV73 ) )
| ~ ( element @ SV109 @ ( powerset @ SV73 ) ) )
| ( element @ ( subset_difference @ SV73 @ SV96 @ SV109 ) @ ( powerset @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1049,plain,
! [SV74: $i] :
( ( ( ~ ( empty @ SV74 ) )
= $false )
| ( ( ~ ! [SY112: $i] :
~ ~ ( ~ ( element @ SY112 @ ( powerset @ SV74 ) )
| ~ ~ ( empty @ SY112 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1050,plain,
! [SV75: $i] :
( ( ( v1_membered @ SV75 )
= $false )
| ( ( ! [SY113: $i] :
( ~ ( element @ SY113 @ ( powerset @ SV75 ) )
| ( v1_membered @ SY113 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1051,plain,
! [SV76: $i,SV97: $i] :
( ( ( ~ ( element @ SV97 @ ( powerset @ ( powerset @ SV76 ) ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV76 @ ( complements_of_subsets @ SV76 @ SV97 ) )
= SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1052,plain,
! [SV77: $i] :
( ( ( finite @ SV77 )
= $false )
| ( ( ! [SY115: $i] :
( ~ ( element @ SY115 @ ( powerset @ SV77 ) )
| ( finite @ SY115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1053,plain,
! [SV110: $i,SV78: $i,SV98: $i] :
( ( ~ ~ ( ~ ( element @ SV98 @ ( powerset @ SV78 ) )
| ~ ( element @ SV110 @ ( powerset @ SV78 ) ) )
| ( ( subset_intersection2 @ SV78 @ SV98 @ SV98 )
= SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1054,plain,
( ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
!= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1055,plain,
( ( sK2_SY64 = empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1028]) ).
thf(1056,plain,
! [SV79: $i] :
( ( ~ ( ( SV79 != empty_set )
| ! [SY118: $i] :
~ ( in @ SY118 @ SV79 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1057,plain,
! [SV79: $i] :
( ( ~ ( ~ ! [SY119: $i] :
~ ( in @ SY119 @ SV79 )
| ( SV79 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1058,plain,
! [SV80: $i,SV99: $i] :
( ( ( ~ ( element @ SV99 @ ( powerset @ ( powerset @ SV80 ) ) ) )
= $true )
| ( ( element @ ( meet_of_subsets @ SV80 @ SV99 ) @ ( powerset @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1059,plain,
! [SV81: $i,SV100: $i] :
( ( ( ~ ( element @ SV100 @ ( powerset @ SV81 ) ) )
= $true )
| ( ( ( subset_complement @ SV81 @ ( subset_complement @ SV81 @ SV100 ) )
= SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1060,plain,
! [SV101: $i,SV82: $i] :
( ( ( ~ ( in @ SV82 @ SV101 ) )
= $true )
| ( ( element @ SV82 @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1061,plain,
! [SV111: $i,SV83: $i,SV102: $i] :
( ( ~ ~ ( ~ ( element @ SV102 @ ( powerset @ SV83 ) )
| ~ ( element @ SV111 @ ( powerset @ SV83 ) ) )
| ( ( subset_intersection2 @ SV83 @ SV102 @ SV111 )
= ( subset_intersection2 @ SV83 @ SV111 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1062,plain,
! [SV84: $i,SV103: $i] :
( ( ( ~ ( element @ SV103 @ ( powerset @ SV84 ) ) )
= $true )
| ( ( element @ ( subset_complement @ SV84 @ SV103 ) @ ( powerset @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1063,plain,
! [SV112: $i,SV104: $i,SV85: $i] :
( ( ~ ~ ( ~ ( in @ SV85 @ SV104 )
| ~ ( element @ SV104 @ ( powerset @ SV112 ) ) )
| ( element @ SV85 @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1064,plain,
! [SV86: $i] :
( ( ( subset @ SV86 @ empty_set )
= $false )
| ( ( SV86 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1065,plain,
! [SV105: $i,SV87: $i] :
( ( ~ ( ~ ( element @ SV87 @ ( powerset @ SV105 ) )
| ( subset @ SV87 @ SV105 ) )
| ~ ( ~ ( subset @ SV87 @ SV105 )
| ( element @ SV87 @ ( powerset @ SV105 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1066,plain,
! [SV88: $i] :
( ( ~ ~ ( ~ ( element @ ( sK9_SY129 @ SV88 ) @ ( powerset @ SV88 ) )
| ~ ( empty @ ( sK9_SY129 @ SV88 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1038]) ).
thf(1067,plain,
! [SV89: $i,SV106: $i] :
( ( ( ~ ( element @ SV106 @ ( powerset @ ( powerset @ SV89 ) ) ) )
= $true )
| ( ( element @ ( union_of_subsets @ SV89 @ SV106 ) @ ( powerset @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1068,plain,
! [SV90: $i,SV107: $i] :
( ( ( ~ ( element @ SV107 @ ( powerset @ ( powerset @ SV90 ) ) ) )
= $true )
| ( ( element @ ( complements_of_subsets @ SV90 @ SV107 ) @ ( powerset @ ( powerset @ SV90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1040]) ).
thf(1069,plain,
! [SV92: $i,SV67: $i] :
( ( ( ! [SY132: $i] :
( ~ ( in @ SY132 @ SV67 )
| ( in @ SY132 @ SV92 ) ) )
= $false )
| ( ( element @ SV67 @ ( powerset @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1070,plain,
! [SV68: $i] :
( ( element @ ( sK8_SY104 @ SV68 ) @ SV68 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1043]) ).
thf(1071,plain,
! [SV108: $i,SV69: $i,SV93: $i] :
( ( ( ~ ~ ( ~ ( element @ SV93 @ ( powerset @ SV69 ) )
| ~ ( element @ SV108 @ ( powerset @ SV69 ) ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV69 @ SV93 @ SV108 ) @ ( powerset @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1072,plain,
! [SV70: $i,SV94: $i] :
( ( ( element @ SV94 @ ( powerset @ ( powerset @ SV70 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ( SV94 != empty_set ) )
| ( ( complements_of_subsets @ SV70 @ SV94 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1073,plain,
! [SV72: $i,SV95: $i] :
( ( ( element @ SV95 @ ( powerset @ SV72 ) )
= $false )
| ( ( ! [SY134: $i] :
( ~ ( in @ SY134 @ SV95 )
| ( in @ SY134 @ SV72 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1074,plain,
! [SV109: $i,SV73: $i,SV96: $i] :
( ( ( ~ ~ ( ~ ( element @ SV96 @ ( powerset @ SV73 ) )
| ~ ( element @ SV109 @ ( powerset @ SV73 ) ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV73 @ SV96 @ SV109 ) @ ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1075,plain,
! [SV74: $i] :
( ( ( empty @ SV74 )
= $true )
| ( ( ~ ! [SY112: $i] :
~ ~ ( ~ ( element @ SY112 @ ( powerset @ SV74 ) )
| ~ ~ ( empty @ SY112 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1049]) ).
thf(1076,plain,
! [SV75: $i,SV113: $i] :
( ( ( ~ ( element @ SV113 @ ( powerset @ SV75 ) )
| ( v1_membered @ SV113 ) )
= $true )
| ( ( v1_membered @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1077,plain,
! [SV76: $i,SV97: $i] :
( ( ( element @ SV97 @ ( powerset @ ( powerset @ SV76 ) ) )
= $false )
| ( ( ( complements_of_subsets @ SV76 @ ( complements_of_subsets @ SV76 @ SV97 ) )
= SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1078,plain,
! [SV77: $i,SV114: $i] :
( ( ( ~ ( element @ SV114 @ ( powerset @ SV77 ) )
| ( finite @ SV114 ) )
= $true )
| ( ( finite @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1079,plain,
! [SV110: $i,SV78: $i,SV98: $i] :
( ( ( ~ ~ ( ~ ( element @ SV98 @ ( powerset @ SV78 ) )
| ~ ( element @ SV110 @ ( powerset @ SV78 ) ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV78 @ SV98 @ SV98 )
= SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1080,plain,
( ( ( complements_of_subsets @ sK1_A @ sK2_SY64 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1081,plain,
! [SV79: $i] :
( ( ( SV79 != empty_set )
| ! [SY118: $i] :
~ ( in @ SY118 @ SV79 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1056]) ).
thf(1082,plain,
! [SV79: $i] :
( ( ~ ! [SY119: $i] :
~ ( in @ SY119 @ SV79 )
| ( SV79 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1057]) ).
thf(1083,plain,
! [SV80: $i,SV99: $i] :
( ( ( element @ SV99 @ ( powerset @ ( powerset @ SV80 ) ) )
= $false )
| ( ( element @ ( meet_of_subsets @ SV80 @ SV99 ) @ ( powerset @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1084,plain,
! [SV81: $i,SV100: $i] :
( ( ( element @ SV100 @ ( powerset @ SV81 ) )
= $false )
| ( ( ( subset_complement @ SV81 @ ( subset_complement @ SV81 @ SV100 ) )
= SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1085,plain,
! [SV101: $i,SV82: $i] :
( ( ( in @ SV82 @ SV101 )
= $false )
| ( ( element @ SV82 @ SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1086,plain,
! [SV111: $i,SV83: $i,SV102: $i] :
( ( ( ~ ~ ( ~ ( element @ SV102 @ ( powerset @ SV83 ) )
| ~ ( element @ SV111 @ ( powerset @ SV83 ) ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV83 @ SV102 @ SV111 )
= ( subset_intersection2 @ SV83 @ SV111 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1087,plain,
! [SV84: $i,SV103: $i] :
( ( ( element @ SV103 @ ( powerset @ SV84 ) )
= $false )
| ( ( element @ ( subset_complement @ SV84 @ SV103 ) @ ( powerset @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1088,plain,
! [SV112: $i,SV104: $i,SV85: $i] :
( ( ( ~ ~ ( ~ ( in @ SV85 @ SV104 )
| ~ ( element @ SV104 @ ( powerset @ SV112 ) ) ) )
= $true )
| ( ( element @ SV85 @ SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1089,plain,
! [SV105: $i,SV87: $i] :
( ( ~ ( ~ ( element @ SV87 @ ( powerset @ SV105 ) )
| ( subset @ SV87 @ SV105 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1090,plain,
! [SV105: $i,SV87: $i] :
( ( ~ ( ~ ( subset @ SV87 @ SV105 )
| ( element @ SV87 @ ( powerset @ SV105 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1091,plain,
! [SV88: $i] :
( ( ~ ( ~ ( element @ ( sK9_SY129 @ SV88 ) @ ( powerset @ SV88 ) )
| ~ ( empty @ ( sK9_SY129 @ SV88 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1066]) ).
thf(1092,plain,
! [SV89: $i,SV106: $i] :
( ( ( element @ SV106 @ ( powerset @ ( powerset @ SV89 ) ) )
= $false )
| ( ( element @ ( union_of_subsets @ SV89 @ SV106 ) @ ( powerset @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1093,plain,
! [SV90: $i,SV107: $i] :
( ( ( element @ SV107 @ ( powerset @ ( powerset @ SV90 ) ) )
= $false )
| ( ( element @ ( complements_of_subsets @ SV90 @ SV107 ) @ ( powerset @ ( powerset @ SV90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1094,plain,
! [SV67: $i,SV92: $i] :
( ( ( ~ ( in @ ( sK10_SY132 @ SV92 @ SV67 ) @ SV67 )
| ( in @ ( sK10_SY132 @ SV92 @ SV67 ) @ SV92 ) )
= $false )
| ( ( element @ SV67 @ ( powerset @ SV92 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1069]) ).
thf(1095,plain,
! [SV108: $i,SV69: $i,SV93: $i] :
( ( ( ~ ( ~ ( element @ SV93 @ ( powerset @ SV69 ) )
| ~ ( element @ SV108 @ ( powerset @ SV69 ) ) ) )
= $false )
| ( ( element @ ( subset_intersection2 @ SV69 @ SV93 @ SV108 ) @ ( powerset @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1096,plain,
! [SV70: $i,SV94: $i] :
( ( ( ~ ( ~ ( ( SV94 != empty_set ) )
| ( ( complements_of_subsets @ SV70 @ SV94 )
!= empty_set ) ) )
= $false )
| ( ( element @ SV94 @ ( powerset @ ( powerset @ SV70 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1097,plain,
! [SV72: $i,SV95: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV95 )
| ( in @ SV115 @ SV72 ) )
= $true )
| ( ( element @ SV95 @ ( powerset @ SV72 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1098,plain,
! [SV109: $i,SV73: $i,SV96: $i] :
( ( ( ~ ( ~ ( element @ SV96 @ ( powerset @ SV73 ) )
| ~ ( element @ SV109 @ ( powerset @ SV73 ) ) ) )
= $false )
| ( ( element @ ( subset_difference @ SV73 @ SV96 @ SV109 ) @ ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1099,plain,
! [SV74: $i] :
( ( ( ! [SY112: $i] :
~ ~ ( ~ ( element @ SY112 @ ( powerset @ SV74 ) )
| ~ ~ ( empty @ SY112 ) ) )
= $false )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1100,plain,
! [SV75: $i,SV113: $i] :
( ( ( ~ ( element @ SV113 @ ( powerset @ SV75 ) ) )
= $true )
| ( ( v1_membered @ SV113 )
= $true )
| ( ( v1_membered @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1101,plain,
! [SV77: $i,SV114: $i] :
( ( ( ~ ( element @ SV114 @ ( powerset @ SV77 ) ) )
= $true )
| ( ( finite @ SV114 )
= $true )
| ( ( finite @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1102,plain,
! [SV110: $i,SV78: $i,SV98: $i] :
( ( ( ~ ( ~ ( element @ SV98 @ ( powerset @ SV78 ) )
| ~ ( element @ SV110 @ ( powerset @ SV78 ) ) ) )
= $false )
| ( ( ( subset_intersection2 @ SV78 @ SV98 @ SV98 )
= SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1103,plain,
! [SV79: $i] :
( ( ( SV79 != empty_set )
= $true )
| ( ( ! [SY118: $i] :
~ ( in @ SY118 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1104,plain,
! [SV79: $i] :
( ( ( ~ ! [SY119: $i] :
~ ( in @ SY119 @ SV79 ) )
= $true )
| ( ( SV79 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1105,plain,
! [SV111: $i,SV83: $i,SV102: $i] :
( ( ( ~ ( ~ ( element @ SV102 @ ( powerset @ SV83 ) )
| ~ ( element @ SV111 @ ( powerset @ SV83 ) ) ) )
= $false )
| ( ( ( subset_intersection2 @ SV83 @ SV102 @ SV111 )
= ( subset_intersection2 @ SV83 @ SV111 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1106,plain,
! [SV112: $i,SV104: $i,SV85: $i] :
( ( ( ~ ( ~ ( in @ SV85 @ SV104 )
| ~ ( element @ SV104 @ ( powerset @ SV112 ) ) ) )
= $false )
| ( ( element @ SV85 @ SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1107,plain,
! [SV105: $i,SV87: $i] :
( ( ~ ( element @ SV87 @ ( powerset @ SV105 ) )
| ( subset @ SV87 @ SV105 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1089]) ).
thf(1108,plain,
! [SV105: $i,SV87: $i] :
( ( ~ ( subset @ SV87 @ SV105 )
| ( element @ SV87 @ ( powerset @ SV105 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1090]) ).
thf(1109,plain,
! [SV88: $i] :
( ( ~ ( element @ ( sK9_SY129 @ SV88 ) @ ( powerset @ SV88 ) )
| ~ ( empty @ ( sK9_SY129 @ SV88 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1110,plain,
! [SV67: $i,SV92: $i] :
( ( ( ~ ( in @ ( sK10_SY132 @ SV92 @ SV67 ) @ SV67 ) )
= $false )
| ( ( element @ SV67 @ ( powerset @ SV92 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1094]) ).
thf(1111,plain,
! [SV67: $i,SV92: $i] :
( ( ( in @ ( sK10_SY132 @ SV92 @ SV67 ) @ SV92 )
= $false )
| ( ( element @ SV67 @ ( powerset @ SV92 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1094]) ).
thf(1112,plain,
! [SV108: $i,SV69: $i,SV93: $i] :
( ( ( ~ ( element @ SV93 @ ( powerset @ SV69 ) )
| ~ ( element @ SV108 @ ( powerset @ SV69 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV69 @ SV93 @ SV108 ) @ ( powerset @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1095]) ).
thf(1113,plain,
! [SV70: $i,SV94: $i] :
( ( ( ~ ( ( SV94 != empty_set ) )
| ( ( complements_of_subsets @ SV70 @ SV94 )
!= empty_set ) )
= $true )
| ( ( element @ SV94 @ ( powerset @ ( powerset @ SV70 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1096]) ).
thf(1114,plain,
! [SV72: $i,SV95: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV95 ) )
= $true )
| ( ( in @ SV115 @ SV72 )
= $true )
| ( ( element @ SV95 @ ( powerset @ SV72 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1115,plain,
! [SV109: $i,SV73: $i,SV96: $i] :
( ( ( ~ ( element @ SV96 @ ( powerset @ SV73 ) )
| ~ ( element @ SV109 @ ( powerset @ SV73 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV73 @ SV96 @ SV109 ) @ ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1116,plain,
! [SV74: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK11_SY112 @ SV74 ) @ ( powerset @ SV74 ) )
| ~ ~ ( empty @ ( sK11_SY112 @ SV74 ) ) ) )
= $false )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1099]) ).
thf(1117,plain,
! [SV75: $i,SV113: $i] :
( ( ( element @ SV113 @ ( powerset @ SV75 ) )
= $false )
| ( ( v1_membered @ SV113 )
= $true )
| ( ( v1_membered @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1118,plain,
! [SV77: $i,SV114: $i] :
( ( ( element @ SV114 @ ( powerset @ SV77 ) )
= $false )
| ( ( finite @ SV114 )
= $true )
| ( ( finite @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1119,plain,
! [SV110: $i,SV78: $i,SV98: $i] :
( ( ( ~ ( element @ SV98 @ ( powerset @ SV78 ) )
| ~ ( element @ SV110 @ ( powerset @ SV78 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV78 @ SV98 @ SV98 )
= SV98 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1102]) ).
thf(1120,plain,
! [SV79: $i] :
( ( ( SV79 = empty_set )
= $false )
| ( ( ! [SY118: $i] :
~ ( in @ SY118 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1103]) ).
thf(1121,plain,
! [SV79: $i] :
( ( ( ! [SY119: $i] :
~ ( in @ SY119 @ SV79 ) )
= $false )
| ( ( SV79 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1122,plain,
! [SV111: $i,SV83: $i,SV102: $i] :
( ( ( ~ ( element @ SV102 @ ( powerset @ SV83 ) )
| ~ ( element @ SV111 @ ( powerset @ SV83 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV83 @ SV102 @ SV111 )
= ( subset_intersection2 @ SV83 @ SV111 @ SV102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1105]) ).
thf(1123,plain,
! [SV112: $i,SV104: $i,SV85: $i] :
( ( ( ~ ( in @ SV85 @ SV104 )
| ~ ( element @ SV104 @ ( powerset @ SV112 ) ) )
= $true )
| ( ( element @ SV85 @ SV112 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1124,plain,
! [SV105: $i,SV87: $i] :
( ( ( ~ ( element @ SV87 @ ( powerset @ SV105 ) ) )
= $true )
| ( ( subset @ SV87 @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1125,plain,
! [SV105: $i,SV87: $i] :
( ( ( ~ ( subset @ SV87 @ SV105 ) )
= $true )
| ( ( element @ SV87 @ ( powerset @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1126,plain,
! [SV88: $i] :
( ( ~ ( element @ ( sK9_SY129 @ SV88 ) @ ( powerset @ SV88 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1109]) ).
thf(1127,plain,
! [SV88: $i] :
( ( ~ ( empty @ ( sK9_SY129 @ SV88 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1109]) ).
thf(1128,plain,
! [SV67: $i,SV92: $i] :
( ( ( in @ ( sK10_SY132 @ SV92 @ SV67 ) @ SV67 )
= $true )
| ( ( element @ SV67 @ ( powerset @ SV92 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1110]) ).
thf(1129,plain,
! [SV108: $i,SV69: $i,SV93: $i] :
( ( ( ~ ( element @ SV93 @ ( powerset @ SV69 ) ) )
= $true )
| ( ( ~ ( element @ SV108 @ ( powerset @ SV69 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV69 @ SV93 @ SV108 ) @ ( powerset @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1112]) ).
thf(1130,plain,
! [SV70: $i,SV94: $i] :
( ( ( ~ ( ( SV94 != empty_set ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV70 @ SV94 )
!= empty_set )
= $true )
| ( ( element @ SV94 @ ( powerset @ ( powerset @ SV70 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1113]) ).
thf(1131,plain,
! [SV72: $i,SV95: $i,SV115: $i] :
( ( ( in @ SV115 @ SV95 )
= $false )
| ( ( in @ SV115 @ SV72 )
= $true )
| ( ( element @ SV95 @ ( powerset @ SV72 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1132,plain,
! [SV109: $i,SV73: $i,SV96: $i] :
( ( ( ~ ( element @ SV96 @ ( powerset @ SV73 ) ) )
= $true )
| ( ( ~ ( element @ SV109 @ ( powerset @ SV73 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV73 @ SV96 @ SV109 ) @ ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1115]) ).
thf(1133,plain,
! [SV74: $i] :
( ( ( ~ ( ~ ( element @ ( sK11_SY112 @ SV74 ) @ ( powerset @ SV74 ) )
| ~ ~ ( empty @ ( sK11_SY112 @ SV74 ) ) ) )
= $true )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1116]) ).
thf(1134,plain,
! [SV110: $i,SV78: $i,SV98: $i] :
( ( ( ~ ( element @ SV98 @ ( powerset @ SV78 ) ) )
= $true )
| ( ( ~ ( element @ SV110 @ ( powerset @ SV78 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV78 @ SV98 @ SV98 )
= SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1135,plain,
! [SV79: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV79 ) )
= $true )
| ( ( SV79 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1136,plain,
! [SV79: $i] :
( ( ( ~ ( in @ ( sK12_SY119 @ SV79 ) @ SV79 ) )
= $false )
| ( ( SV79 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1121]) ).
thf(1137,plain,
! [SV111: $i,SV83: $i,SV102: $i] :
( ( ( ~ ( element @ SV102 @ ( powerset @ SV83 ) ) )
= $true )
| ( ( ~ ( element @ SV111 @ ( powerset @ SV83 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV83 @ SV102 @ SV111 )
= ( subset_intersection2 @ SV83 @ SV111 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1122]) ).
thf(1138,plain,
! [SV112: $i,SV104: $i,SV85: $i] :
( ( ( ~ ( in @ SV85 @ SV104 ) )
= $true )
| ( ( ~ ( element @ SV104 @ ( powerset @ SV112 ) ) )
= $true )
| ( ( element @ SV85 @ SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1139,plain,
! [SV105: $i,SV87: $i] :
( ( ( element @ SV87 @ ( powerset @ SV105 ) )
= $false )
| ( ( subset @ SV87 @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1140,plain,
! [SV105: $i,SV87: $i] :
( ( ( subset @ SV87 @ SV105 )
= $false )
| ( ( element @ SV87 @ ( powerset @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1141,plain,
! [SV88: $i] :
( ( element @ ( sK9_SY129 @ SV88 ) @ ( powerset @ SV88 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1126]) ).
thf(1142,plain,
! [SV88: $i] :
( ( empty @ ( sK9_SY129 @ SV88 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1127]) ).
thf(1143,plain,
! [SV108: $i,SV69: $i,SV93: $i] :
( ( ( element @ SV93 @ ( powerset @ SV69 ) )
= $false )
| ( ( ~ ( element @ SV108 @ ( powerset @ SV69 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV69 @ SV93 @ SV108 ) @ ( powerset @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1144,plain,
! [SV70: $i,SV94: $i] :
( ( ( SV94 != empty_set )
= $false )
| ( ( ( complements_of_subsets @ SV70 @ SV94 )
!= empty_set )
= $true )
| ( ( element @ SV94 @ ( powerset @ ( powerset @ SV70 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1145,plain,
! [SV109: $i,SV73: $i,SV96: $i] :
( ( ( element @ SV96 @ ( powerset @ SV73 ) )
= $false )
| ( ( ~ ( element @ SV109 @ ( powerset @ SV73 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV73 @ SV96 @ SV109 ) @ ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1146,plain,
! [SV74: $i] :
( ( ( ~ ( element @ ( sK11_SY112 @ SV74 ) @ ( powerset @ SV74 ) )
| ~ ~ ( empty @ ( sK11_SY112 @ SV74 ) ) )
= $false )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1147,plain,
! [SV110: $i,SV78: $i,SV98: $i] :
( ( ( element @ SV98 @ ( powerset @ SV78 ) )
= $false )
| ( ( ~ ( element @ SV110 @ ( powerset @ SV78 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV78 @ SV98 @ SV98 )
= SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1148,plain,
! [SV79: $i,SV116: $i] :
( ( ( in @ SV116 @ SV79 )
= $false )
| ( ( SV79 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1149,plain,
! [SV79: $i] :
( ( ( in @ ( sK12_SY119 @ SV79 ) @ SV79 )
= $true )
| ( ( SV79 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1136]) ).
thf(1150,plain,
! [SV111: $i,SV83: $i,SV102: $i] :
( ( ( element @ SV102 @ ( powerset @ SV83 ) )
= $false )
| ( ( ~ ( element @ SV111 @ ( powerset @ SV83 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV83 @ SV102 @ SV111 )
= ( subset_intersection2 @ SV83 @ SV111 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1151,plain,
! [SV112: $i,SV104: $i,SV85: $i] :
( ( ( in @ SV85 @ SV104 )
= $false )
| ( ( ~ ( element @ SV104 @ ( powerset @ SV112 ) ) )
= $true )
| ( ( element @ SV85 @ SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1152,plain,
! [SV93: $i,SV69: $i,SV108: $i] :
( ( ( element @ SV108 @ ( powerset @ SV69 ) )
= $false )
| ( ( element @ SV93 @ ( powerset @ SV69 ) )
= $false )
| ( ( element @ ( subset_intersection2 @ SV69 @ SV93 @ SV108 ) @ ( powerset @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1153,plain,
! [SV70: $i,SV94: $i] :
( ( ( SV94 = empty_set )
= $true )
| ( ( ( complements_of_subsets @ SV70 @ SV94 )
!= empty_set )
= $true )
| ( ( element @ SV94 @ ( powerset @ ( powerset @ SV70 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1144]) ).
thf(1154,plain,
! [SV96: $i,SV73: $i,SV109: $i] :
( ( ( element @ SV109 @ ( powerset @ SV73 ) )
= $false )
| ( ( element @ SV96 @ ( powerset @ SV73 ) )
= $false )
| ( ( element @ ( subset_difference @ SV73 @ SV96 @ SV109 ) @ ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1155,plain,
! [SV74: $i] :
( ( ( ~ ( element @ ( sK11_SY112 @ SV74 ) @ ( powerset @ SV74 ) ) )
= $false )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1146]) ).
thf(1156,plain,
! [SV74: $i] :
( ( ( ~ ~ ( empty @ ( sK11_SY112 @ SV74 ) ) )
= $false )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1146]) ).
thf(1157,plain,
! [SV98: $i,SV78: $i,SV110: $i] :
( ( ( element @ SV110 @ ( powerset @ SV78 ) )
= $false )
| ( ( element @ SV98 @ ( powerset @ SV78 ) )
= $false )
| ( ( ( subset_intersection2 @ SV78 @ SV98 @ SV98 )
= SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1158,plain,
! [SV102: $i,SV83: $i,SV111: $i] :
( ( ( element @ SV111 @ ( powerset @ SV83 ) )
= $false )
| ( ( element @ SV102 @ ( powerset @ SV83 ) )
= $false )
| ( ( ( subset_intersection2 @ SV83 @ SV102 @ SV111 )
= ( subset_intersection2 @ SV83 @ SV111 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1159,plain,
! [SV85: $i,SV112: $i,SV104: $i] :
( ( ( element @ SV104 @ ( powerset @ SV112 ) )
= $false )
| ( ( in @ SV85 @ SV104 )
= $false )
| ( ( element @ SV85 @ SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1160,plain,
! [SV94: $i,SV70: $i] :
( ( ( ( complements_of_subsets @ SV70 @ SV94 )
= empty_set )
= $false )
| ( ( SV94 = empty_set )
= $true )
| ( ( element @ SV94 @ ( powerset @ ( powerset @ SV70 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1161,plain,
! [SV74: $i] :
( ( ( element @ ( sK11_SY112 @ SV74 ) @ ( powerset @ SV74 ) )
= $true )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1155]) ).
thf(1162,plain,
! [SV74: $i] :
( ( ( ~ ( empty @ ( sK11_SY112 @ SV74 ) ) )
= $true )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1156]) ).
thf(1163,plain,
! [SV74: $i] :
( ( ( empty @ ( sK11_SY112 @ SV74 ) )
= $false )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1164,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[892,1163,1161,1160,1159,1158,1157,1154,1152,1149,1148,1142,1141,1140,1139,1131,1128,1118,1117,1111,1093,1092,1087,1085,1084,1083,1080,1077,1070,1064,1055,1046,1041,1014,987,986,985,984,982,981,980,952,938,935,934,933,932,931,925,924,923,922,921,919,918,917,916,914,913,912,911,910,909,908,907,906,905,904,903,902,901]) ).
thf(1165,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1164,888]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU326+2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:13:36 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.33/1.04 ....
% 4.33/1.04
% 4.33/1.04 No.of.Axioms: 63
% 4.33/1.04
% 4.33/1.04 Length.of.Defs: 0
% 4.33/1.04
% 4.33/1.04 Contains.Choice.Funs: false
% 4.33/1.04 ......................
% 4.33/1.04
% 4.33/1.04 ********************************
% 4.33/1.04 * All subproblems solved! *
% 4.33/1.04 ********************************
% 4.33/1.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:64,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1164,loop_count:0,foatp_calls:1,translation:fof_full)
% 4.33/1.04
% 4.33/1.04 %**** Beginning of derivation protocol ****
% 4.33/1.04 % SZS output start CNFRefutation
% See solution above
% 4.33/1.05
% 4.33/1.05 %**** End of derivation protocol ****
% 4.33/1.05 %**** no. of clauses in derivation: 690 ****
% 4.33/1.05 %**** clause counter: 1164 ****
% 4.33/1.05
% 4.33/1.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:64,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1164,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------