%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU295+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 : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:50 AM UTC 2026
% Result : Theorem 2.62s 0.68s
% Output : CNFRefutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 48
% Syntax : Number of formulae : 369 ( 223 unt; 0 typ; 0 def)
% Number of atoms : 1980 ( 660 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 3692 ( 827 ~; 496 |; 30 &;2280 @)
% ( 9 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 82 ( 79 usr; 6 con; 0-3 aty)
% Number of variables : 687 ( 0 ^; 678 !; 9 ?; 687 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_apply,type,
apply: $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_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_cast_to_subset,type,
cast_to_subset: $i > $i ).
thf(tp_complements_of_subsets,type,
complements_of_subsets: $i > $i > $i ).
thf(tp_connected,type,
connected: $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_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_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_meet_of_subsets,type,
meet_of_subsets: $i > $i > $i ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $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_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_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY51,type,
sK2_SY51: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY75,type,
sK4_SY75: $i > $i ).
thf(tp_sK5_SY87,type,
sK5_SY87: $i > $i > $i > $i ).
thf(tp_sK6_SY82,type,
sK6_SY82: $i > $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_succ,type,
succ: $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_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(13,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(40,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(55,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( finite @ B )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(99,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(100,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(101,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(111,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(112,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(115,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(116,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(118,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(119,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(120,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(122,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(124,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(125,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_mcart_1) ).
thf(127,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(128,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(130,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord1) ).
thf(131,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(132,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(133,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(134,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(135,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_mcart_1) ).
thf(136,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(137,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_enumset1) ).
thf(138,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(149,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_wellord1) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(212,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(218,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(228,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom @ ( relation_dom_restriction @ B @ A ) )
= ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).
thf(265,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(268,axiom,
! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(307,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(335,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(348,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_image @ B @ A )
= ( relation_image @ B @ ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_relat_1) ).
thf(353,axiom,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
thf(358,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_rng_restriction @ A @ B ) )
= ( set_intersection2 @ ( relation_rng @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_relat_1) ).
thf(398,conjecture,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finset_1) ).
thf(399,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[398]) ).
thf(400,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[399]) ).
thf(401,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(402,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(403,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(404,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(405,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(406,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(407,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ B )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(408,plain,
$true = $true,
inference(unfold_def,[status(thm)],[99]) ).
thf(409,plain,
$true = $true,
inference(unfold_def,[status(thm)],[100]) ).
thf(410,plain,
$true = $true,
inference(unfold_def,[status(thm)],[101]) ).
thf(411,plain,
$true = $true,
inference(unfold_def,[status(thm)],[111]) ).
thf(412,plain,
$true = $true,
inference(unfold_def,[status(thm)],[112]) ).
thf(413,plain,
$true = $true,
inference(unfold_def,[status(thm)],[115]) ).
thf(414,plain,
$true = $true,
inference(unfold_def,[status(thm)],[116]) ).
thf(415,plain,
$true = $true,
inference(unfold_def,[status(thm)],[118]) ).
thf(416,plain,
$true = $true,
inference(unfold_def,[status(thm)],[119]) ).
thf(417,plain,
$true = $true,
inference(unfold_def,[status(thm)],[120]) ).
thf(418,plain,
$true = $true,
inference(unfold_def,[status(thm)],[122]) ).
thf(419,plain,
$true = $true,
inference(unfold_def,[status(thm)],[124]) ).
thf(420,plain,
$true = $true,
inference(unfold_def,[status(thm)],[125]) ).
thf(421,plain,
$true = $true,
inference(unfold_def,[status(thm)],[127]) ).
thf(422,plain,
$true = $true,
inference(unfold_def,[status(thm)],[128]) ).
thf(423,plain,
$true = $true,
inference(unfold_def,[status(thm)],[130]) ).
thf(424,plain,
$true = $true,
inference(unfold_def,[status(thm)],[131]) ).
thf(425,plain,
$true = $true,
inference(unfold_def,[status(thm)],[132]) ).
thf(426,plain,
$true = $true,
inference(unfold_def,[status(thm)],[133]) ).
thf(427,plain,
$true = $true,
inference(unfold_def,[status(thm)],[134]) ).
thf(428,plain,
$true = $true,
inference(unfold_def,[status(thm)],[135]) ).
thf(429,plain,
$true = $true,
inference(unfold_def,[status(thm)],[136]) ).
thf(430,plain,
$true = $true,
inference(unfold_def,[status(thm)],[137]) ).
thf(431,plain,
$true = $true,
inference(unfold_def,[status(thm)],[138]) ).
thf(432,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(433,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(434,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(435,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(436,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(437,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(438,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom @ ( relation_dom_restriction @ B @ A ) )
= ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(439,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(440,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(441,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(442,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(443,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(444,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(445,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_image @ B @ A )
= ( relation_image @ B @ ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(446,plain,
( ( ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(447,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_rng_restriction @ A @ B ) )
= ( set_intersection2 @ ( relation_rng @ B ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(448,plain,
( ( ! [SY51: $i] :
( ( finite @ sK1_A )
=> ( finite @ ( set_intersection2 @ sK1_A @ SY51 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[400]) ).
thf(449,plain,
( ( ( finite @ sK1_A )
=> ( finite @ ( set_intersection2 @ sK1_A @ sK2_SY51 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[448]) ).
thf(450,plain,
( ( finite @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[449]) ).
thf(451,plain,
( ( finite @ ( set_intersection2 @ sK1_A @ sK2_SY51 ) )
= $false ),
inference(standard_cnf,[status(thm)],[449]) ).
thf(452,plain,
( ( ~ ( finite @ ( set_intersection2 @ sK1_A @ sK2_SY51 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[451]) ).
thf(453,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_rng_restriction @ A @ B ) )
= ( set_intersection2 @ ( relation_rng @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(454,plain,
( ( ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(455,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_image @ B @ A )
= ( relation_image @ B @ ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(456,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(457,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(458,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(459,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(460,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(461,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(462,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom @ ( relation_dom_restriction @ B @ A ) )
= ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(463,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(464,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(465,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(466,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(467,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(468,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(469,plain,
$true = $true,
inference(copy,[status(thm)],[431]) ).
thf(470,plain,
$true = $true,
inference(copy,[status(thm)],[430]) ).
thf(471,plain,
$true = $true,
inference(copy,[status(thm)],[429]) ).
thf(472,plain,
$true = $true,
inference(copy,[status(thm)],[428]) ).
thf(473,plain,
$true = $true,
inference(copy,[status(thm)],[427]) ).
thf(474,plain,
$true = $true,
inference(copy,[status(thm)],[426]) ).
thf(475,plain,
$true = $true,
inference(copy,[status(thm)],[425]) ).
thf(476,plain,
$true = $true,
inference(copy,[status(thm)],[424]) ).
thf(477,plain,
$true = $true,
inference(copy,[status(thm)],[423]) ).
thf(478,plain,
$true = $true,
inference(copy,[status(thm)],[422]) ).
thf(479,plain,
$true = $true,
inference(copy,[status(thm)],[421]) ).
thf(480,plain,
$true = $true,
inference(copy,[status(thm)],[420]) ).
thf(481,plain,
$true = $true,
inference(copy,[status(thm)],[419]) ).
thf(482,plain,
$true = $true,
inference(copy,[status(thm)],[418]) ).
thf(483,plain,
$true = $true,
inference(copy,[status(thm)],[417]) ).
thf(484,plain,
$true = $true,
inference(copy,[status(thm)],[416]) ).
thf(485,plain,
$true = $true,
inference(copy,[status(thm)],[415]) ).
thf(486,plain,
$true = $true,
inference(copy,[status(thm)],[414]) ).
thf(487,plain,
$true = $true,
inference(copy,[status(thm)],[413]) ).
thf(488,plain,
$true = $true,
inference(copy,[status(thm)],[412]) ).
thf(489,plain,
$true = $true,
inference(copy,[status(thm)],[411]) ).
thf(490,plain,
$true = $true,
inference(copy,[status(thm)],[410]) ).
thf(491,plain,
$true = $true,
inference(copy,[status(thm)],[409]) ).
thf(492,plain,
$true = $true,
inference(copy,[status(thm)],[408]) ).
thf(493,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ B )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(494,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(495,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(496,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(497,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(498,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(499,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(500,plain,
( ( finite @ sK1_A )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(501,plain,
( ( ~ ( finite @ ( set_intersection2 @ sK1_A @ sK2_SY51 ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(502,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( ( relation_image @ SX1 @ SX0 )
= ( relation_image @ SX1 @ ( set_intersection2 @ ( relation_dom @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(503,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( ( relation_dom @ ( relation_dom_restriction @ SX1 @ SX0 ) )
= ( set_intersection2 @ ( relation_dom @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(504,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( finite @ SX0 )
| ( finite @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(505,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(506,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( relation_restriction @ SX0 @ SX1 )
= ( set_intersection2 @ SX0 @ ( cartesian_product2 @ SX1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(507,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(508,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( finite @ SX1 )
| ( finite @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(509,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(510,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( finite @ SX1 ) )
| ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(511,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(512,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( ( relation_rng @ ( relation_rng_restriction @ SX0 @ SX1 ) )
= ( set_intersection2 @ ( relation_rng @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(513,plain,
( ( ! [SX0: $i] :
( ~ ( finite @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(514,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ~ ~ ( ~ ~ ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(515,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(516,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX0 @ SX2 ) )
| ( subset @ SX0 @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(517,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) )
| ~ ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(518,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_intersection2 @ SX0 @ SX2 ) @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(519,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(520,plain,
! [SV1: $i] :
( ( ! [SY52: $i] : ( subset @ ( set_intersection2 @ SV1 @ SY52 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(521,plain,
! [SV2: $i] :
( ( ! [SY53: $i] :
( ( set_difference @ SV2 @ ( set_difference @ SV2 @ SY53 ) )
= ( set_intersection2 @ SV2 @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(522,plain,
! [SV3: $i] :
( ( ! [SY54: $i] :
( ( set_intersection2 @ SV3 @ SY54 )
= ( set_intersection2 @ SY54 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(523,plain,
! [SV4: $i] :
( ( ! [SY55: $i] :
( ( set_intersection2 @ SV4 @ SV4 )
= SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(524,plain,
! [SV5: $i] :
( ( ( set_intersection2 @ SV5 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(525,plain,
( ( finite @ ( set_intersection2 @ sK1_A @ sK2_SY51 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(526,plain,
! [SV6: $i] :
( ( ! [SY56: $i] :
( ~ ( relation @ SY56 )
| ( ( relation_image @ SY56 @ SV6 )
= ( relation_image @ SY56 @ ( set_intersection2 @ ( relation_dom @ SY56 ) @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(527,plain,
! [SV7: $i] :
( ( ! [SY57: $i] :
( ~ ( relation @ SY57 )
| ( ( relation_dom @ ( relation_dom_restriction @ SY57 @ SV7 ) )
= ( set_intersection2 @ ( relation_dom @ SY57 ) @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(528,plain,
! [SV8: $i] :
( ( ! [SY58: $i] :
( ~ ( finite @ SV8 )
| ( finite @ ( set_intersection2 @ SV8 @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(529,plain,
! [SV9: $i] :
( ( ! [SY59: $i] :
~ ( ~ ( ~ ( disjoint @ SV9 @ SY59 )
| ( ( set_intersection2 @ SV9 @ SY59 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV9 @ SY59 )
!= empty_set )
| ( disjoint @ SV9 @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(530,plain,
! [SV10: $i] :
( ( ~ ( relation @ SV10 )
| ! [SY60: $i] :
( ( relation_restriction @ SV10 @ SY60 )
= ( set_intersection2 @ SV10 @ ( cartesian_product2 @ SY60 @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(531,plain,
! [SV11: $i] :
( ( ! [SY61: $i,SY62: $i] :
~ ( ~ ( ( SY62
!= ( set_intersection2 @ SV11 @ SY61 ) )
| ! [SY63: $i] :
~ ( ~ ( ~ ( in @ SY63 @ SY62 )
| ~ ( ~ ( in @ SY63 @ SV11 )
| ~ ( in @ SY63 @ SY61 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY63 @ SV11 )
| ~ ( in @ SY63 @ SY61 ) )
| ( in @ SY63 @ SY62 ) ) ) )
| ~ ( ~ ! [SY64: $i] :
~ ( ~ ( ~ ( in @ SY64 @ SY62 )
| ~ ( ~ ( in @ SY64 @ SV11 )
| ~ ( in @ SY64 @ SY61 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY64 @ SV11 )
| ~ ( in @ SY64 @ SY61 ) )
| ( in @ SY64 @ SY62 ) ) )
| ( SY62
= ( set_intersection2 @ SV11 @ SY61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(532,plain,
! [SV12: $i] :
( ( ! [SY65: $i] :
( ~ ( finite @ SY65 )
| ( finite @ ( set_intersection2 @ SV12 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(533,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(534,plain,
! [SV13: $i] :
( ( ! [SY66: $i] :
( ~ ~ ( ~ ( subset @ SV13 @ SY66 )
| ~ ( finite @ SY66 ) )
| ( finite @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(535,plain,
! [SV14: $i] :
( ( ~ ( empty @ SV14 )
| ( finite @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(536,plain,
! [SV15: $i] :
( ( ! [SY67: $i] :
( ~ ( relation @ SY67 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV15 @ SY67 ) )
= ( set_intersection2 @ ( relation_rng @ SY67 ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(537,plain,
! [SV16: $i] :
( ( ~ ( finite @ SV16 )
| ! [SY68: $i] :
( ~ ( element @ SY68 @ ( powerset @ SV16 ) )
| ( finite @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(538,plain,
! [SV17: $i] :
( ( ! [SY69: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV17 @ SY69 )
| ~ ! [SY70: $i] :
~ ( in @ SY70 @ ( set_intersection2 @ SV17 @ SY69 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY71: $i] :
~ ( in @ SY71 @ ( set_intersection2 @ SV17 @ SY69 ) )
| ~ ( disjoint @ SV17 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(539,plain,
! [SV18: $i] :
( ( ! [SY72: $i] :
( ~ ~ ( ~ ( relation @ SV18 )
| ~ ( relation @ SY72 ) )
| ( relation @ ( set_intersection2 @ SV18 @ SY72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(540,plain,
! [SV19: $i] :
( ( ! [SY73: $i,SY74: $i] :
( ~ ~ ( ~ ( subset @ SV19 @ SY73 )
| ~ ( subset @ SV19 @ SY74 ) )
| ( subset @ SV19 @ ( set_intersection2 @ SY73 @ SY74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(541,plain,
! [SV20: $i] :
( ( ~ ~ ( empty @ SV20 )
| ~ ! [SY75: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY75 @ ( powerset @ SV20 ) )
| ~ ~ ( empty @ SY75 ) )
| ~ ( finite @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(542,plain,
! [SV21: $i] :
( ( ! [SY76: $i,SY77: $i] :
( ~ ( subset @ SV21 @ SY76 )
| ( subset @ ( set_intersection2 @ SV21 @ SY77 ) @ ( set_intersection2 @ SY76 @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(543,plain,
! [SV22: $i] :
( ( ! [SY78: $i] :
( ~ ( subset @ SV22 @ SY78 )
| ( ( set_intersection2 @ SV22 @ SY78 )
= SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(544,plain,
! [SV23: $i,SV1: $i] :
( ( subset @ ( set_intersection2 @ SV1 @ SV23 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(545,plain,
! [SV24: $i,SV2: $i] :
( ( ( set_difference @ SV2 @ ( set_difference @ SV2 @ SV24 ) )
= ( set_intersection2 @ SV2 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(546,plain,
! [SV25: $i,SV3: $i] :
( ( ( set_intersection2 @ SV3 @ SV25 )
= ( set_intersection2 @ SV25 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(547,plain,
! [SV4: $i] :
( ( ( set_intersection2 @ SV4 @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(548,plain,
! [SV6: $i,SV27: $i] :
( ( ~ ( relation @ SV27 )
| ( ( relation_image @ SV27 @ SV6 )
= ( relation_image @ SV27 @ ( set_intersection2 @ ( relation_dom @ SV27 ) @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(549,plain,
! [SV7: $i,SV28: $i] :
( ( ~ ( relation @ SV28 )
| ( ( relation_dom @ ( relation_dom_restriction @ SV28 @ SV7 ) )
= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(550,plain,
! [SV29: $i,SV8: $i] :
( ( ~ ( finite @ SV8 )
| ( finite @ ( set_intersection2 @ SV8 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(551,plain,
! [SV30: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( disjoint @ SV9 @ SV30 )
| ( ( set_intersection2 @ SV9 @ SV30 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV9 @ SV30 )
!= empty_set )
| ( disjoint @ SV9 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(552,plain,
! [SV10: $i] :
( ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( ! [SY60: $i] :
( ( relation_restriction @ SV10 @ SY60 )
= ( set_intersection2 @ SV10 @ ( cartesian_product2 @ SY60 @ SY60 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(553,plain,
! [SV31: $i,SV11: $i] :
( ( ! [SY79: $i] :
~ ( ~ ( ( SY79
!= ( set_intersection2 @ SV11 @ SV31 ) )
| ! [SY80: $i] :
~ ( ~ ( ~ ( in @ SY80 @ SY79 )
| ~ ( ~ ( in @ SY80 @ SV11 )
| ~ ( in @ SY80 @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY80 @ SV11 )
| ~ ( in @ SY80 @ SV31 ) )
| ( in @ SY80 @ SY79 ) ) ) )
| ~ ( ~ ! [SY81: $i] :
~ ( ~ ( ~ ( in @ SY81 @ SY79 )
| ~ ( ~ ( in @ SY81 @ SV11 )
| ~ ( in @ SY81 @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY81 @ SV11 )
| ~ ( in @ SY81 @ SV31 ) )
| ( in @ SY81 @ SY79 ) ) )
| ( SY79
= ( set_intersection2 @ SV11 @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(554,plain,
! [SV12: $i,SV32: $i] :
( ( ~ ( finite @ SV32 )
| ( finite @ ( set_intersection2 @ SV12 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(555,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[533]) ).
thf(556,plain,
! [SV33: $i,SV13: $i] :
( ( ~ ~ ( ~ ( subset @ SV13 @ SV33 )
| ~ ( finite @ SV33 ) )
| ( finite @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(557,plain,
! [SV14: $i] :
( ( ( ~ ( empty @ SV14 ) )
= $true )
| ( ( finite @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(558,plain,
! [SV15: $i,SV34: $i] :
( ( ~ ( relation @ SV34 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV15 @ SV34 ) )
= ( set_intersection2 @ ( relation_rng @ SV34 ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(559,plain,
! [SV16: $i] :
( ( ( ~ ( finite @ SV16 ) )
= $true )
| ( ( ! [SY68: $i] :
( ~ ( element @ SY68 @ ( powerset @ SV16 ) )
| ( finite @ SY68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[537]) ).
thf(560,plain,
! [SV35: $i,SV17: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV17 @ SV35 )
| ~ ! [SY82: $i] :
~ ( in @ SY82 @ ( set_intersection2 @ SV17 @ SV35 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY83: $i] :
~ ( in @ SY83 @ ( set_intersection2 @ SV17 @ SV35 ) )
| ~ ( disjoint @ SV17 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(561,plain,
! [SV36: $i,SV18: $i] :
( ( ~ ~ ( ~ ( relation @ SV18 )
| ~ ( relation @ SV36 ) )
| ( relation @ ( set_intersection2 @ SV18 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(562,plain,
! [SV37: $i,SV19: $i] :
( ( ! [SY84: $i] :
( ~ ~ ( ~ ( subset @ SV19 @ SV37 )
| ~ ( subset @ SV19 @ SY84 ) )
| ( subset @ SV19 @ ( set_intersection2 @ SV37 @ SY84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(563,plain,
! [SV20: $i] :
( ( ( ~ ~ ( empty @ SV20 ) )
= $true )
| ( ( ~ ! [SY75: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY75 @ ( powerset @ SV20 ) )
| ~ ~ ( empty @ SY75 ) )
| ~ ( finite @ SY75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[541]) ).
thf(564,plain,
! [SV38: $i,SV21: $i] :
( ( ! [SY85: $i] :
( ~ ( subset @ SV21 @ SV38 )
| ( subset @ ( set_intersection2 @ SV21 @ SY85 ) @ ( set_intersection2 @ SV38 @ SY85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(565,plain,
! [SV39: $i,SV22: $i] :
( ( ~ ( subset @ SV22 @ SV39 )
| ( ( set_intersection2 @ SV22 @ SV39 )
= SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(566,plain,
! [SV6: $i,SV27: $i] :
( ( ( ~ ( relation @ SV27 ) )
= $true )
| ( ( ( relation_image @ SV27 @ SV6 )
= ( relation_image @ SV27 @ ( set_intersection2 @ ( relation_dom @ SV27 ) @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(567,plain,
! [SV7: $i,SV28: $i] :
( ( ( ~ ( relation @ SV28 ) )
= $true )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV28 @ SV7 ) )
= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(568,plain,
! [SV29: $i,SV8: $i] :
( ( ( ~ ( finite @ SV8 ) )
= $true )
| ( ( finite @ ( set_intersection2 @ SV8 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(569,plain,
! [SV30: $i,SV9: $i] :
( ( ~ ( ~ ( disjoint @ SV9 @ SV30 )
| ( ( set_intersection2 @ SV9 @ SV30 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV9 @ SV30 )
!= empty_set )
| ( disjoint @ SV9 @ SV30 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(570,plain,
! [SV10: $i] :
( ( ( relation @ SV10 )
= $false )
| ( ( ! [SY60: $i] :
( ( relation_restriction @ SV10 @ SY60 )
= ( set_intersection2 @ SV10 @ ( cartesian_product2 @ SY60 @ SY60 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(571,plain,
! [SV31: $i,SV11: $i,SV40: $i] :
( ( ~ ( ~ ( ( SV40
!= ( set_intersection2 @ SV11 @ SV31 ) )
| ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SV40 )
| ~ ( ~ ( in @ SY86 @ SV11 )
| ~ ( in @ SY86 @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY86 @ SV11 )
| ~ ( in @ SY86 @ SV31 ) )
| ( in @ SY86 @ SV40 ) ) ) )
| ~ ( ~ ! [SY87: $i] :
~ ( ~ ( ~ ( in @ SY87 @ SV40 )
| ~ ( ~ ( in @ SY87 @ SV11 )
| ~ ( in @ SY87 @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY87 @ SV11 )
| ~ ( in @ SY87 @ SV31 ) )
| ( in @ SY87 @ SV40 ) ) )
| ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(572,plain,
! [SV12: $i,SV32: $i] :
( ( ( ~ ( finite @ SV32 ) )
= $true )
| ( ( finite @ ( set_intersection2 @ SV12 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(573,plain,
( ( ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(574,plain,
! [SV33: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV13 @ SV33 )
| ~ ( finite @ SV33 ) ) )
= $true )
| ( ( finite @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(575,plain,
! [SV14: $i] :
( ( ( empty @ SV14 )
= $false )
| ( ( finite @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(576,plain,
! [SV15: $i,SV34: $i] :
( ( ( ~ ( relation @ SV34 ) )
= $true )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV15 @ SV34 ) )
= ( set_intersection2 @ ( relation_rng @ SV34 ) @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(577,plain,
! [SV16: $i] :
( ( ( finite @ SV16 )
= $false )
| ( ( ! [SY68: $i] :
( ~ ( element @ SY68 @ ( powerset @ SV16 ) )
| ( finite @ SY68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(578,plain,
! [SV35: $i,SV17: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV17 @ SV35 )
| ~ ! [SY82: $i] :
~ ( in @ SY82 @ ( set_intersection2 @ SV17 @ SV35 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY83: $i] :
~ ( in @ SY83 @ ( set_intersection2 @ SV17 @ SV35 ) )
| ~ ( disjoint @ SV17 @ SV35 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(579,plain,
! [SV36: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV18 )
| ~ ( relation @ SV36 ) ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV18 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(580,plain,
! [SV41: $i,SV37: $i,SV19: $i] :
( ( ~ ~ ( ~ ( subset @ SV19 @ SV37 )
| ~ ( subset @ SV19 @ SV41 ) )
| ( subset @ SV19 @ ( set_intersection2 @ SV37 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(581,plain,
! [SV20: $i] :
( ( ( ~ ( empty @ SV20 ) )
= $false )
| ( ( ~ ! [SY75: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY75 @ ( powerset @ SV20 ) )
| ~ ~ ( empty @ SY75 ) )
| ~ ( finite @ SY75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(582,plain,
! [SV42: $i,SV38: $i,SV21: $i] :
( ( ~ ( subset @ SV21 @ SV38 )
| ( subset @ ( set_intersection2 @ SV21 @ SV42 ) @ ( set_intersection2 @ SV38 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(583,plain,
! [SV39: $i,SV22: $i] :
( ( ( ~ ( subset @ SV22 @ SV39 ) )
= $true )
| ( ( ( set_intersection2 @ SV22 @ SV39 )
= SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(584,plain,
! [SV6: $i,SV27: $i] :
( ( ( relation @ SV27 )
= $false )
| ( ( ( relation_image @ SV27 @ SV6 )
= ( relation_image @ SV27 @ ( set_intersection2 @ ( relation_dom @ SV27 ) @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(585,plain,
! [SV7: $i,SV28: $i] :
( ( ( relation @ SV28 )
= $false )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV28 @ SV7 ) )
= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(586,plain,
! [SV29: $i,SV8: $i] :
( ( ( finite @ SV8 )
= $false )
| ( ( finite @ ( set_intersection2 @ SV8 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(587,plain,
! [SV30: $i,SV9: $i] :
( ( ~ ( ~ ( disjoint @ SV9 @ SV30 )
| ( ( set_intersection2 @ SV9 @ SV30 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(588,plain,
! [SV30: $i,SV9: $i] :
( ( ~ ( ( ( set_intersection2 @ SV9 @ SV30 )
!= empty_set )
| ( disjoint @ SV9 @ SV30 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(589,plain,
! [SV43: $i,SV10: $i] :
( ( ( ( relation_restriction @ SV10 @ SV43 )
= ( set_intersection2 @ SV10 @ ( cartesian_product2 @ SV43 @ SV43 ) ) )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(590,plain,
! [SV31: $i,SV11: $i,SV40: $i] :
( ( ~ ( ( SV40
!= ( set_intersection2 @ SV11 @ SV31 ) )
| ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SV40 )
| ~ ( ~ ( in @ SY86 @ SV11 )
| ~ ( in @ SY86 @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY86 @ SV11 )
| ~ ( in @ SY86 @ SV31 ) )
| ( in @ SY86 @ SV40 ) ) ) )
| ~ ( ~ ! [SY87: $i] :
~ ( ~ ( ~ ( in @ SY87 @ SV40 )
| ~ ( ~ ( in @ SY87 @ SV11 )
| ~ ( in @ SY87 @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY87 @ SV11 )
| ~ ( in @ SY87 @ SV31 ) )
| ( in @ SY87 @ SV40 ) ) )
| ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(591,plain,
! [SV12: $i,SV32: $i] :
( ( ( finite @ SV32 )
= $false )
| ( ( finite @ ( set_intersection2 @ SV12 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(592,plain,
( ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(593,plain,
! [SV33: $i,SV13: $i] :
( ( ( ~ ( ~ ( subset @ SV13 @ SV33 )
| ~ ( finite @ SV33 ) ) )
= $false )
| ( ( finite @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(594,plain,
! [SV15: $i,SV34: $i] :
( ( ( relation @ SV34 )
= $false )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV15 @ SV34 ) )
= ( set_intersection2 @ ( relation_rng @ SV34 ) @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(595,plain,
! [SV16: $i,SV44: $i] :
( ( ( ~ ( element @ SV44 @ ( powerset @ SV16 ) )
| ( finite @ SV44 ) )
= $true )
| ( ( finite @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(596,plain,
! [SV35: $i,SV17: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV17 @ SV35 )
| ~ ! [SY82: $i] :
~ ( in @ SY82 @ ( set_intersection2 @ SV17 @ SV35 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[578]) ).
thf(597,plain,
! [SV35: $i,SV17: $i] :
( ( ~ ~ ~ ( ~ ~ ! [SY83: $i] :
~ ( in @ SY83 @ ( set_intersection2 @ SV17 @ SV35 ) )
| ~ ( disjoint @ SV17 @ SV35 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[578]) ).
thf(598,plain,
! [SV36: $i,SV18: $i] :
( ( ( ~ ( ~ ( relation @ SV18 )
| ~ ( relation @ SV36 ) ) )
= $false )
| ( ( relation @ ( set_intersection2 @ SV18 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(599,plain,
! [SV41: $i,SV37: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV19 @ SV37 )
| ~ ( subset @ SV19 @ SV41 ) ) )
= $true )
| ( ( subset @ SV19 @ ( set_intersection2 @ SV37 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(600,plain,
! [SV20: $i] :
( ( ( empty @ SV20 )
= $true )
| ( ( ~ ! [SY75: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY75 @ ( powerset @ SV20 ) )
| ~ ~ ( empty @ SY75 ) )
| ~ ( finite @ SY75 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(601,plain,
! [SV42: $i,SV38: $i,SV21: $i] :
( ( ( ~ ( subset @ SV21 @ SV38 ) )
= $true )
| ( ( subset @ ( set_intersection2 @ SV21 @ SV42 ) @ ( set_intersection2 @ SV38 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(602,plain,
! [SV39: $i,SV22: $i] :
( ( ( subset @ SV22 @ SV39 )
= $false )
| ( ( ( set_intersection2 @ SV22 @ SV39 )
= SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(603,plain,
! [SV30: $i,SV9: $i] :
( ( ~ ( disjoint @ SV9 @ SV30 )
| ( ( set_intersection2 @ SV9 @ SV30 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(604,plain,
! [SV30: $i,SV9: $i] :
( ( ( ( set_intersection2 @ SV9 @ SV30 )
!= empty_set )
| ( disjoint @ SV9 @ SV30 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(605,plain,
! [SV31: $i,SV11: $i,SV40: $i] :
( ( ~ ( ( SV40
!= ( set_intersection2 @ SV11 @ SV31 ) )
| ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SV40 )
| ~ ( ~ ( in @ SY86 @ SV11 )
| ~ ( in @ SY86 @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY86 @ SV11 )
| ~ ( in @ SY86 @ SV31 ) )
| ( in @ SY86 @ SV40 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[590]) ).
thf(606,plain,
! [SV31: $i,SV11: $i,SV40: $i] :
( ( ~ ( ~ ! [SY87: $i] :
~ ( ~ ( ~ ( in @ SY87 @ SV40 )
| ~ ( ~ ( in @ SY87 @ SV11 )
| ~ ( in @ SY87 @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY87 @ SV11 )
| ~ ( in @ SY87 @ SV31 ) )
| ( in @ SY87 @ SV40 ) ) )
| ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[590]) ).
thf(607,plain,
( ( ~ ~ ( empty @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[592]) ).
thf(608,plain,
( ( ~ ( finite @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[592]) ).
thf(609,plain,
! [SV33: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV33 )
| ~ ( finite @ SV33 ) )
= $true )
| ( ( finite @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[593]) ).
thf(610,plain,
! [SV16: $i,SV44: $i] :
( ( ( ~ ( element @ SV44 @ ( powerset @ SV16 ) ) )
= $true )
| ( ( finite @ SV44 )
= $true )
| ( ( finite @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(611,plain,
! [SV35: $i,SV17: $i] :
( ( ~ ~ ( ~ ~ ( disjoint @ SV17 @ SV35 )
| ~ ! [SY82: $i] :
~ ( in @ SY82 @ ( set_intersection2 @ SV17 @ SV35 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[596]) ).
thf(612,plain,
! [SV35: $i,SV17: $i] :
( ( ~ ~ ( ~ ~ ! [SY83: $i] :
~ ( in @ SY83 @ ( set_intersection2 @ SV17 @ SV35 ) )
| ~ ( disjoint @ SV17 @ SV35 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[597]) ).
thf(613,plain,
! [SV36: $i,SV18: $i] :
( ( ( ~ ( relation @ SV18 )
| ~ ( relation @ SV36 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV18 @ SV36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[598]) ).
thf(614,plain,
! [SV41: $i,SV37: $i,SV19: $i] :
( ( ( ~ ( ~ ( subset @ SV19 @ SV37 )
| ~ ( subset @ SV19 @ SV41 ) ) )
= $false )
| ( ( subset @ SV19 @ ( set_intersection2 @ SV37 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(615,plain,
! [SV20: $i] :
( ( ( ! [SY75: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY75 @ ( powerset @ SV20 ) )
| ~ ~ ( empty @ SY75 ) )
| ~ ( finite @ SY75 ) ) )
= $false )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(616,plain,
! [SV42: $i,SV38: $i,SV21: $i] :
( ( ( subset @ SV21 @ SV38 )
= $false )
| ( ( subset @ ( set_intersection2 @ SV21 @ SV42 ) @ ( set_intersection2 @ SV38 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(617,plain,
! [SV30: $i,SV9: $i] :
( ( ( ~ ( disjoint @ SV9 @ SV30 ) )
= $true )
| ( ( ( set_intersection2 @ SV9 @ SV30 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(618,plain,
! [SV30: $i,SV9: $i] :
( ( ( ( set_intersection2 @ SV9 @ SV30 )
!= empty_set )
= $true )
| ( ( disjoint @ SV9 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(619,plain,
! [SV31: $i,SV11: $i,SV40: $i] :
( ( ( SV40
!= ( set_intersection2 @ SV11 @ SV31 ) )
| ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SV40 )
| ~ ( ~ ( in @ SY86 @ SV11 )
| ~ ( in @ SY86 @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY86 @ SV11 )
| ~ ( in @ SY86 @ SV31 ) )
| ( in @ SY86 @ SV40 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[605]) ).
thf(620,plain,
! [SV31: $i,SV11: $i,SV40: $i] :
( ( ~ ! [SY87: $i] :
~ ( ~ ( ~ ( in @ SY87 @ SV40 )
| ~ ( ~ ( in @ SY87 @ SV11 )
| ~ ( in @ SY87 @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY87 @ SV11 )
| ~ ( in @ SY87 @ SV31 ) )
| ( in @ SY87 @ SV40 ) ) )
| ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(621,plain,
( ( ~ ( empty @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(622,plain,
( ( finite @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[608]) ).
thf(623,plain,
! [SV33: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV33 ) )
= $true )
| ( ( ~ ( finite @ SV33 ) )
= $true )
| ( ( finite @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(624,plain,
! [SV16: $i,SV44: $i] :
( ( ( element @ SV44 @ ( powerset @ SV16 ) )
= $false )
| ( ( finite @ SV44 )
= $true )
| ( ( finite @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(625,plain,
! [SV35: $i,SV17: $i] :
( ( ~ ( ~ ~ ( disjoint @ SV17 @ SV35 )
| ~ ! [SY82: $i] :
~ ( in @ SY82 @ ( set_intersection2 @ SV17 @ SV35 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(626,plain,
! [SV35: $i,SV17: $i] :
( ( ~ ( ~ ~ ! [SY83: $i] :
~ ( in @ SY83 @ ( set_intersection2 @ SV17 @ SV35 ) )
| ~ ( disjoint @ SV17 @ SV35 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(627,plain,
! [SV36: $i,SV18: $i] :
( ( ( ~ ( relation @ SV18 ) )
= $true )
| ( ( ~ ( relation @ SV36 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV18 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(628,plain,
! [SV41: $i,SV37: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV37 )
| ~ ( subset @ SV19 @ SV41 ) )
= $true )
| ( ( subset @ SV19 @ ( set_intersection2 @ SV37 @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[614]) ).
thf(629,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK4_SY75 @ SV20 ) @ ( powerset @ SV20 ) )
| ~ ~ ( empty @ ( sK4_SY75 @ SV20 ) ) )
| ~ ( finite @ ( sK4_SY75 @ SV20 ) ) ) )
= $false )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[615]) ).
thf(630,plain,
! [SV30: $i,SV9: $i] :
( ( ( disjoint @ SV9 @ SV30 )
= $false )
| ( ( ( set_intersection2 @ SV9 @ SV30 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(631,plain,
! [SV30: $i,SV9: $i] :
( ( ( ( set_intersection2 @ SV9 @ SV30 )
= empty_set )
= $false )
| ( ( disjoint @ SV9 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(632,plain,
! [SV31: $i,SV11: $i,SV40: $i] :
( ( ( SV40
!= ( set_intersection2 @ SV11 @ SV31 ) )
= $true )
| ( ( ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SV40 )
| ~ ( ~ ( in @ SY86 @ SV11 )
| ~ ( in @ SY86 @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY86 @ SV11 )
| ~ ( in @ SY86 @ SV31 ) )
| ( in @ SY86 @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(633,plain,
! [SV31: $i,SV11: $i,SV40: $i] :
( ( ( ~ ! [SY87: $i] :
~ ( ~ ( ~ ( in @ SY87 @ SV40 )
| ~ ( ~ ( in @ SY87 @ SV11 )
| ~ ( in @ SY87 @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY87 @ SV11 )
| ~ ( in @ SY87 @ SV31 ) )
| ( in @ SY87 @ SV40 ) ) ) )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(634,plain,
( ( empty @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(635,plain,
! [SV33: $i,SV13: $i] :
( ( ( subset @ SV13 @ SV33 )
= $false )
| ( ( ~ ( finite @ SV33 ) )
= $true )
| ( ( finite @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(636,plain,
! [SV35: $i,SV17: $i] :
( ( ~ ~ ( disjoint @ SV17 @ SV35 )
| ~ ! [SY82: $i] :
~ ( in @ SY82 @ ( set_intersection2 @ SV17 @ SV35 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[625]) ).
thf(637,plain,
! [SV35: $i,SV17: $i] :
( ( ~ ~ ! [SY83: $i] :
~ ( in @ SY83 @ ( set_intersection2 @ SV17 @ SV35 ) )
| ~ ( disjoint @ SV17 @ SV35 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(638,plain,
! [SV36: $i,SV18: $i] :
( ( ( relation @ SV18 )
= $false )
| ( ( ~ ( relation @ SV36 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV18 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(639,plain,
! [SV41: $i,SV37: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV37 ) )
= $true )
| ( ( ~ ( subset @ SV19 @ SV41 ) )
= $true )
| ( ( subset @ SV19 @ ( set_intersection2 @ SV37 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(640,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK4_SY75 @ SV20 ) @ ( powerset @ SV20 ) )
| ~ ~ ( empty @ ( sK4_SY75 @ SV20 ) ) )
| ~ ( finite @ ( sK4_SY75 @ SV20 ) ) ) )
= $true )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[629]) ).
thf(641,plain,
! [SV31: $i,SV11: $i,SV40: $i] :
( ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false )
| ( ( ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SV40 )
| ~ ( ~ ( in @ SY86 @ SV11 )
| ~ ( in @ SY86 @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY86 @ SV11 )
| ~ ( in @ SY86 @ SV31 ) )
| ( in @ SY86 @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(642,plain,
! [SV31: $i,SV11: $i,SV40: $i] :
( ( ( ! [SY87: $i] :
~ ( ~ ( ~ ( in @ SY87 @ SV40 )
| ~ ( ~ ( in @ SY87 @ SV11 )
| ~ ( in @ SY87 @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY87 @ SV11 )
| ~ ( in @ SY87 @ SV31 ) )
| ( in @ SY87 @ SV40 ) ) ) )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(643,plain,
! [SV13: $i,SV33: $i] :
( ( ( finite @ SV33 )
= $false )
| ( ( subset @ SV13 @ SV33 )
= $false )
| ( ( finite @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(644,plain,
! [SV35: $i,SV17: $i] :
( ( ( ~ ~ ( disjoint @ SV17 @ SV35 ) )
= $true )
| ( ( ~ ! [SY82: $i] :
~ ( in @ SY82 @ ( set_intersection2 @ SV17 @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(645,plain,
! [SV35: $i,SV17: $i] :
( ( ( ~ ~ ! [SY83: $i] :
~ ( in @ SY83 @ ( set_intersection2 @ SV17 @ SV35 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV17 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(646,plain,
! [SV18: $i,SV36: $i] :
( ( ( relation @ SV36 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV18 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(647,plain,
! [SV41: $i,SV37: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV37 )
= $false )
| ( ( ~ ( subset @ SV19 @ SV41 ) )
= $true )
| ( ( subset @ SV19 @ ( set_intersection2 @ SV37 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(648,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK4_SY75 @ SV20 ) @ ( powerset @ SV20 ) )
| ~ ~ ( empty @ ( sK4_SY75 @ SV20 ) ) )
| ~ ( finite @ ( sK4_SY75 @ SV20 ) ) )
= $false )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(649,plain,
! [SV31: $i,SV11: $i,SV40: $i,SV45: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV45 @ SV40 )
| ~ ( ~ ( in @ SV45 @ SV11 )
| ~ ( in @ SV45 @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV45 @ SV11 )
| ~ ( in @ SV45 @ SV31 ) )
| ( in @ SV45 @ SV40 ) ) ) )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(650,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 )
| ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
| ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 ) ) ) )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[642]) ).
thf(651,plain,
! [SV35: $i,SV17: $i] :
( ( ( ~ ( disjoint @ SV17 @ SV35 ) )
= $false )
| ( ( ~ ! [SY82: $i] :
~ ( in @ SY82 @ ( set_intersection2 @ SV17 @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(652,plain,
! [SV35: $i,SV17: $i] :
( ( ( ~ ! [SY83: $i] :
~ ( in @ SY83 @ ( set_intersection2 @ SV17 @ SV35 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV17 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(653,plain,
! [SV37: $i,SV41: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV41 )
= $false )
| ( ( subset @ SV19 @ SV37 )
= $false )
| ( ( subset @ SV19 @ ( set_intersection2 @ SV37 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(654,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK4_SY75 @ SV20 ) @ ( powerset @ SV20 ) )
| ~ ~ ( empty @ ( sK4_SY75 @ SV20 ) ) ) )
= $false )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[648]) ).
thf(655,plain,
! [SV20: $i] :
( ( ( ~ ( finite @ ( sK4_SY75 @ SV20 ) ) )
= $false )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[648]) ).
thf(656,plain,
! [SV31: $i,SV11: $i,SV40: $i,SV45: $i] :
( ( ( ~ ( ~ ( in @ SV45 @ SV40 )
| ~ ( ~ ( in @ SV45 @ SV11 )
| ~ ( in @ SV45 @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV45 @ SV11 )
| ~ ( in @ SV45 @ SV31 ) )
| ( in @ SV45 @ SV40 ) ) )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(657,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 )
| ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
| ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 ) ) )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(658,plain,
! [SV35: $i,SV17: $i] :
( ( ( disjoint @ SV17 @ SV35 )
= $true )
| ( ( ~ ! [SY82: $i] :
~ ( in @ SY82 @ ( set_intersection2 @ SV17 @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[651]) ).
thf(659,plain,
! [SV35: $i,SV17: $i] :
( ( ( ! [SY83: $i] :
~ ( in @ SY83 @ ( set_intersection2 @ SV17 @ SV35 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV17 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[652]) ).
thf(660,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ( element @ ( sK4_SY75 @ SV20 ) @ ( powerset @ SV20 ) )
| ~ ~ ( empty @ ( sK4_SY75 @ SV20 ) ) ) )
= $true )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[654]) ).
thf(661,plain,
! [SV20: $i] :
( ( ( finite @ ( sK4_SY75 @ SV20 ) )
= $true )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[655]) ).
thf(662,plain,
! [SV31: $i,SV11: $i,SV40: $i,SV45: $i] :
( ( ( ~ ( ~ ( in @ SV45 @ SV40 )
| ~ ( ~ ( in @ SV45 @ SV11 )
| ~ ( in @ SV45 @ SV31 ) ) ) )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[656]) ).
thf(663,plain,
! [SV40: $i,SV31: $i,SV11: $i,SV45: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV45 @ SV11 )
| ~ ( in @ SV45 @ SV31 ) )
| ( in @ SV45 @ SV40 ) ) )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[656]) ).
thf(664,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 )
| ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
| ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 ) ) )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[657]) ).
thf(665,plain,
! [SV35: $i,SV17: $i] :
( ( ( ! [SY82: $i] :
~ ( in @ SY82 @ ( set_intersection2 @ SV17 @ SV35 ) ) )
= $false )
| ( ( disjoint @ SV17 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(666,plain,
! [SV35: $i,SV17: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ ( set_intersection2 @ SV17 @ SV35 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV17 @ SV35 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(667,plain,
! [SV20: $i] :
( ( ( ~ ( element @ ( sK4_SY75 @ SV20 ) @ ( powerset @ SV20 ) )
| ~ ~ ( empty @ ( sK4_SY75 @ SV20 ) ) )
= $false )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(668,plain,
! [SV31: $i,SV11: $i,SV40: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV40 )
| ~ ( ~ ( in @ SV45 @ SV11 )
| ~ ( in @ SV45 @ SV31 ) ) )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[662]) ).
thf(669,plain,
! [SV40: $i,SV31: $i,SV11: $i,SV45: $i] :
( ( ( ~ ~ ( ~ ( in @ SV45 @ SV11 )
| ~ ( in @ SV45 @ SV31 ) )
| ( in @ SV45 @ SV40 ) )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[663]) ).
thf(670,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 )
| ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
| ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 ) ) )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(671,plain,
! [SV17: $i,SV35: $i] :
( ( ( ~ ( in @ ( sK6_SY82 @ SV35 @ SV17 ) @ ( set_intersection2 @ SV17 @ SV35 ) ) )
= $false )
| ( ( disjoint @ SV17 @ SV35 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[665]) ).
thf(672,plain,
! [SV35: $i,SV17: $i,SV46: $i] :
( ( ( in @ SV46 @ ( set_intersection2 @ SV17 @ SV35 ) )
= $false )
| ( ( ~ ( disjoint @ SV17 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(673,plain,
! [SV20: $i] :
( ( ( ~ ( element @ ( sK4_SY75 @ SV20 ) @ ( powerset @ SV20 ) ) )
= $false )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(674,plain,
! [SV20: $i] :
( ( ( ~ ~ ( empty @ ( sK4_SY75 @ SV20 ) ) )
= $false )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(675,plain,
! [SV31: $i,SV11: $i,SV40: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV40 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV45 @ SV11 )
| ~ ( in @ SV45 @ SV31 ) ) )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(676,plain,
! [SV40: $i,SV31: $i,SV11: $i,SV45: $i] :
( ( ( ~ ~ ( ~ ( in @ SV45 @ SV11 )
| ~ ( in @ SV45 @ SV31 ) ) )
= $true )
| ( ( in @ SV45 @ SV40 )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(677,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
| ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 ) ) )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[670]) ).
thf(678,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
| ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 ) ) )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[670]) ).
thf(679,plain,
! [SV17: $i,SV35: $i] :
( ( ( in @ ( sK6_SY82 @ SV35 @ SV17 ) @ ( set_intersection2 @ SV17 @ SV35 ) )
= $true )
| ( ( disjoint @ SV17 @ SV35 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[671]) ).
thf(680,plain,
! [SV46: $i,SV35: $i,SV17: $i] :
( ( ( disjoint @ SV17 @ SV35 )
= $false )
| ( ( in @ SV46 @ ( set_intersection2 @ SV17 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(681,plain,
! [SV20: $i] :
( ( ( element @ ( sK4_SY75 @ SV20 ) @ ( powerset @ SV20 ) )
= $true )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[673]) ).
thf(682,plain,
! [SV20: $i] :
( ( ( ~ ( empty @ ( sK4_SY75 @ SV20 ) ) )
= $true )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[674]) ).
thf(683,plain,
! [SV31: $i,SV11: $i,SV40: $i,SV45: $i] :
( ( ( in @ SV45 @ SV40 )
= $false )
| ( ( ~ ( ~ ( in @ SV45 @ SV11 )
| ~ ( in @ SV45 @ SV31 ) ) )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(684,plain,
! [SV40: $i,SV31: $i,SV11: $i,SV45: $i] :
( ( ( ~ ( ~ ( in @ SV45 @ SV11 )
| ~ ( in @ SV45 @ SV31 ) ) )
= $false )
| ( ( in @ SV45 @ SV40 )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(685,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
| ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 ) ) )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[677]) ).
thf(686,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
| ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 ) ) )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[678]) ).
thf(687,plain,
! [SV20: $i] :
( ( ( empty @ ( sK4_SY75 @ SV20 ) )
= $false )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(688,plain,
! [SV40: $i,SV31: $i,SV11: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV11 )
| ~ ( in @ SV45 @ SV31 ) )
= $false )
| ( ( in @ SV45 @ SV40 )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(689,plain,
! [SV40: $i,SV31: $i,SV11: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV11 )
| ~ ( in @ SV45 @ SV31 ) )
= $true )
| ( ( in @ SV45 @ SV40 )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[684]) ).
thf(690,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
| ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 ) )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(691,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 ) )
= $true )
| ( ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
| ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 ) ) )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[686]) ).
thf(692,plain,
! [SV31: $i,SV40: $i,SV11: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV11 ) )
= $false )
| ( ( in @ SV45 @ SV40 )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(693,plain,
! [SV11: $i,SV40: $i,SV31: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV31 ) )
= $false )
| ( ( in @ SV45 @ SV40 )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(694,plain,
! [SV40: $i,SV31: $i,SV11: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV11 ) )
= $true )
| ( ( ~ ( in @ SV45 @ SV31 ) )
= $true )
| ( ( in @ SV45 @ SV40 )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(695,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) ) )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(696,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(697,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
= $false )
| ( ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
| ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 ) ) )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(698,plain,
! [SV31: $i,SV40: $i,SV11: $i,SV45: $i] :
( ( ( in @ SV45 @ SV11 )
= $true )
| ( ( in @ SV45 @ SV40 )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[692]) ).
thf(699,plain,
! [SV11: $i,SV40: $i,SV31: $i,SV45: $i] :
( ( ( in @ SV45 @ SV31 )
= $true )
| ( ( in @ SV45 @ SV40 )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[693]) ).
thf(700,plain,
! [SV40: $i,SV31: $i,SV11: $i,SV45: $i] :
( ( ( in @ SV45 @ SV11 )
= $false )
| ( ( ~ ( in @ SV45 @ SV31 ) )
= $true )
| ( ( in @ SV45 @ SV40 )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(701,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) ) )
= $true )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[695]) ).
thf(702,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
| ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 ) ) )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(703,plain,
! [SV40: $i,SV11: $i,SV31: $i,SV45: $i] :
( ( ( in @ SV45 @ SV31 )
= $false )
| ( ( in @ SV45 @ SV11 )
= $false )
| ( ( in @ SV45 @ SV40 )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(704,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(705,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
| ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 ) )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(706,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 ) )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(707,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(708,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) ) )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(709,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(710,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
= $true )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[706]) ).
thf(711,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 )
= $true )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV40 )
= $true )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[707]) ).
thf(712,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) ) )
= $true )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[708]) ).
thf(713,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
| ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(714,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 ) )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[713]) ).
thf(715,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 ) )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[713]) ).
thf(716,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
= $true )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[714]) ).
thf(717,plain,
! [SV40: $i,SV11: $i,SV31: $i] :
( ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 )
= $true )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY87 @ SV31 @ SV11 @ SV40 ) @ SV31 )
= $false )
| ( ( SV40
= ( set_intersection2 @ SV11 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[715]) ).
thf(718,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[469,717,716,711,710,709,703,699,698,696,687,681,680,679,661,653,646,643,634,631,630,624,622,616,602,594,591,589,586,585,584,575,547,546,545,544,525,524,500,492,491,490,489,488,487,486,485,484,483,482,481,480,479,478,477,476,475,474,473,472,471,470]) ).
thf(719,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[718]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU295+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
% 0.08/0.19 % Computer : n011.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 15:12:21 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
% 2.62/0.68 ...
% 2.62/0.68
% 2.62/0.68 No.of.Axioms: 47
% 2.62/0.68
% 2.62/0.68 Length.of.Defs: 0
% 2.62/0.68
% 2.62/0.68 Contains.Choice.Funs: false
% 2.62/0.68 .............
% 2.62/0.68
% 2.62/0.68 ********************************
% 2.62/0.68 * All subproblems solved! *
% 2.62/0.68 ********************************
% 2.62/0.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:48,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:718,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.62/0.68
% 2.62/0.68 %**** Beginning of derivation protocol ****
% 2.62/0.68 % SZS output start CNFRefutation
% See solution above
% 2.62/0.68
% 2.62/0.68 %**** End of derivation protocol ****
% 2.62/0.68 %**** no. of clauses in derivation: 369 ****
% 2.62/0.68 %**** clause counter: 718 ****
% 2.62/0.68
% 2.62/0.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:48,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:718,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------