%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU306+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 : n009.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 10:43:53 AM UTC 2026
% Result : Theorem 4.39s 1.02s
% Output : CNFRefutation 4.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 85
% Syntax : Number of formulae : 617 ( 418 unt; 0 typ; 0 def)
% Number of atoms : 2938 ( 810 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 4285 ( 696 ~; 635 |; 84 &;2784 @)
% ( 6 <=>; 80 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 124 ( 121 usr; 14 con; 0-6 aty)
% Number of variables : 896 ( 0 ^; 868 !; 28 ?; 896 :)
% 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_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_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_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_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_A,type,
sK10_A: $i ).
thf(tp_sK11_B,type,
sK11_B: $i > $i ).
thf(tp_sK12_A,type,
sK12_A: $i ).
thf(tp_sK13_A,type,
sK13_A: $i ).
thf(tp_sK14_C,type,
sK14_C: $i > $i > $i ).
thf(tp_sK15_A,type,
sK15_A: $i ).
thf(tp_sK16_A,type,
sK16_A: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_B,type,
sK2_B: $i > $i ).
thf(tp_sK3_B,type,
sK3_B: $i > $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_B,type,
sK5_B: $i > $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_B,type,
sK8_B: $i > $i ).
thf(tp_sK9_A,type,
sK9_A: $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_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_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(2,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(5,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
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(9,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(42,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(44,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(48,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(49,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(50,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(51,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(56,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(57,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(58,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(65,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(68,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(70,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(81,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(86,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(91,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(96,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(97,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(98,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(99,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(102,axiom,
! [A: $i] :
~ ( empty @ ( succ @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal1) ).
thf(115,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(118,axiom,
? [A: $i] : ( join_semilatt_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(119,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(120,axiom,
? [A: $i] : ( meet_semilatt_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(122,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(125,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(126,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(127,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(128,axiom,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(129,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(130,axiom,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(131,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(133,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(135,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(136,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(138,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(141,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_ordinal2) ).
thf(142,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(143,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(147,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(148,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(149,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(150,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(152,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(153,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(155,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(156,axiom,
! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(157,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(158,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(159,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_mcart_1) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(163,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(164,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(166,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord1) ).
thf(167,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(168,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(169,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(170,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(171,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_mcart_1) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattices) ).
thf(173,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(174,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_enumset1) ).
thf(175,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_binop_1) ).
thf(176,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(211,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(264,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(268,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(271,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(273,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(278,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(289,axiom,
! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(456,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(463,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(474,conjecture,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_pre_topc) ).
thf(475,negated_conjecture,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[474]) ).
thf(476,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[475]) ).
thf(477,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(478,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(479,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(480,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(481,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(482,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(483,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(484,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(485,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(486,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(487,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(488,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(489,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(490,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(491,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(492,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(493,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(494,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)],[68]) ).
thf(495,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(496,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(497,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(498,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(499,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(500,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(501,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(502,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(503,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(504,plain,
( ( ! [A: $i] :
~ ( empty @ ( succ @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(505,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(506,plain,
( ( ? [A: $i] : ( join_semilatt_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(507,plain,
( ( ? [A: $i] : ( meet_semilatt_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(508,plain,
( ( ! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(509,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)],[133]) ).
thf(510,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)],[135]) ).
thf(511,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(512,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(513,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(514,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(515,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(516,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(517,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(518,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(519,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(520,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(521,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(522,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(523,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(524,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(525,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(526,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(527,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(528,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(529,plain,
$true = $true,
inference(unfold_def,[status(thm)],[122]) ).
thf(530,plain,
$true = $true,
inference(unfold_def,[status(thm)],[125]) ).
thf(531,plain,
$true = $true,
inference(unfold_def,[status(thm)],[126]) ).
thf(532,plain,
( ( ! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(533,plain,
$true = $true,
inference(unfold_def,[status(thm)],[129]) ).
thf(534,plain,
( ( ! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(535,plain,
$true = $true,
inference(unfold_def,[status(thm)],[131]) ).
thf(536,plain,
$true = $true,
inference(unfold_def,[status(thm)],[141]) ).
thf(537,plain,
$true = $true,
inference(unfold_def,[status(thm)],[142]) ).
thf(538,plain,
$true = $true,
inference(unfold_def,[status(thm)],[143]) ).
thf(539,plain,
$true = $true,
inference(unfold_def,[status(thm)],[147]) ).
thf(540,plain,
$true = $true,
inference(unfold_def,[status(thm)],[148]) ).
thf(541,plain,
$true = $true,
inference(unfold_def,[status(thm)],[150]) ).
thf(542,plain,
$true = $true,
inference(unfold_def,[status(thm)],[152]) ).
thf(543,plain,
$true = $true,
inference(unfold_def,[status(thm)],[153]) ).
thf(544,plain,
$true = $true,
inference(unfold_def,[status(thm)],[155]) ).
thf(545,plain,
$true = $true,
inference(unfold_def,[status(thm)],[157]) ).
thf(546,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(547,plain,
$true = $true,
inference(unfold_def,[status(thm)],[159]) ).
thf(548,plain,
$true = $true,
inference(unfold_def,[status(thm)],[163]) ).
thf(549,plain,
$true = $true,
inference(unfold_def,[status(thm)],[164]) ).
thf(550,plain,
$true = $true,
inference(unfold_def,[status(thm)],[166]) ).
thf(551,plain,
$true = $true,
inference(unfold_def,[status(thm)],[167]) ).
thf(552,plain,
$true = $true,
inference(unfold_def,[status(thm)],[168]) ).
thf(553,plain,
$true = $true,
inference(unfold_def,[status(thm)],[169]) ).
thf(554,plain,
$true = $true,
inference(unfold_def,[status(thm)],[170]) ).
thf(555,plain,
$true = $true,
inference(unfold_def,[status(thm)],[171]) ).
thf(556,plain,
$true = $true,
inference(unfold_def,[status(thm)],[173]) ).
thf(557,plain,
$true = $true,
inference(unfold_def,[status(thm)],[174]) ).
thf(558,plain,
$true = $true,
inference(unfold_def,[status(thm)],[175]) ).
thf(559,plain,
$true = $true,
inference(unfold_def,[status(thm)],[176]) ).
thf(560,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(561,plain,
( ( ( one_sorted_str @ sK1_A )
=> ( ( cast_as_carrier_subset @ sK1_A )
= ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[476]) ).
thf(562,plain,
( ( one_sorted_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[561]) ).
thf(563,plain,
( ( ( cast_as_carrier_subset @ sK1_A )
= ( the_carrier @ sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[561]) ).
thf(564,plain,
( ( ( cast_as_carrier_subset @ sK1_A )
!= ( the_carrier @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[563]) ).
thf(565,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[477]) ).
thf(566,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[478]) ).
thf(567,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[479]) ).
thf(568,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[480]) ).
thf(569,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[481]) ).
thf(570,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[482]) ).
thf(571,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[483]) ).
thf(572,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[484]) ).
thf(573,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( ( element @ ( sK2_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK2_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[485]) ).
thf(574,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK3_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK3_B @ A ) )
& ( finite @ ( sK3_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[486]) ).
thf(575,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[487]) ).
thf(576,plain,
( ( ! [A: $i] :
( ( element @ ( sK5_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK5_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[488]) ).
thf(577,plain,
( ( ~ ( empty @ sK6_A )
& ( relation @ sK6_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[489]) ).
thf(578,plain,
( ( empty @ sK7_A )
= $true ),
inference(extcnf_combined,[status(esa)],[490]) ).
thf(579,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK8_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK8_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[491]) ).
thf(580,plain,
( ( ( empty @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[492]) ).
thf(581,plain,
( ( ~ ( empty @ sK10_A )
& ( finite @ sK10_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[493]) ).
thf(582,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[494]) ).
thf(583,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[495]) ).
thf(584,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[496]) ).
thf(585,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[497]) ).
thf(586,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[499]) ).
thf(587,plain,
( ( ! [A: $i] : ( element @ ( sK11_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[505]) ).
thf(588,plain,
( ( join_semilatt_str @ sK12_A )
= $true ),
inference(extcnf_combined,[status(esa)],[506]) ).
thf(589,plain,
( ( meet_semilatt_str @ sK13_A )
= $true ),
inference(extcnf_combined,[status(esa)],[507]) ).
thf(590,plain,
( ( ! [A: $i] :
( ~ ( latt_str @ A )
| ( join_semilatt_str @ A ) )
& ! [A: $i] :
( ~ ( latt_str @ A )
| ( meet_semilatt_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[508]) ).
thf(591,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[509]) ).
thf(592,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(extcnf_combined,[status(esa)],[510]) ).
thf(593,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[511]) ).
thf(594,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[512]) ).
thf(595,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[513]) ).
thf(596,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( empty_carrier @ A )
| ~ ( meet_semilatt_str @ A )
| ~ ( element @ B @ ( the_carrier @ A ) )
| ~ ( element @ C @ ( the_carrier @ A ) )
| ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[515]) ).
thf(597,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( empty_carrier @ A )
| ~ ( join_semilatt_str @ A )
| ~ ( element @ B @ ( the_carrier @ A ) )
| ~ ( element @ C @ ( the_carrier @ A ) )
| ( element @ ( join @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[516]) ).
thf(598,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( in @ B @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( element @ B @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( empty @ B ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( empty @ B )
| ( element @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[517]) ).
thf(599,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[518]) ).
thf(600,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[519]) ).
thf(601,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[520]) ).
thf(602,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[521]) ).
thf(603,plain,
( ( ! [A: $i] :
( ~ ( v1_membered @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( v1_membered @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[522]) ).
thf(604,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK14_C @ B @ A ) @ A )
& ~ ( in @ ( sK14_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[524]) ).
thf(605,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[525]) ).
thf(606,plain,
( ( ( one_sorted_str @ sK15_A )
& ~ ( empty_carrier @ sK15_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[526]) ).
thf(607,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[527]) ).
thf(608,plain,
( ( one_sorted_str @ sK16_A )
= $true ),
inference(extcnf_combined,[status(esa)],[528]) ).
thf(609,plain,
( ( ! [A: $i] :
( ~ ( join_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[532]) ).
thf(610,plain,
( ( ! [A: $i] :
( ~ ( meet_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[534]) ).
thf(611,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[546]) ).
thf(612,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[560]) ).
thf(613,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[612]) ).
thf(614,plain,
$true = $true,
inference(copy,[status(thm)],[559]) ).
thf(615,plain,
$true = $true,
inference(copy,[status(thm)],[558]) ).
thf(616,plain,
$true = $true,
inference(copy,[status(thm)],[557]) ).
thf(617,plain,
$true = $true,
inference(copy,[status(thm)],[556]) ).
thf(618,plain,
$true = $true,
inference(copy,[status(thm)],[555]) ).
thf(619,plain,
$true = $true,
inference(copy,[status(thm)],[554]) ).
thf(620,plain,
$true = $true,
inference(copy,[status(thm)],[553]) ).
thf(621,plain,
$true = $true,
inference(copy,[status(thm)],[552]) ).
thf(622,plain,
$true = $true,
inference(copy,[status(thm)],[551]) ).
thf(623,plain,
$true = $true,
inference(copy,[status(thm)],[550]) ).
thf(624,plain,
$true = $true,
inference(copy,[status(thm)],[549]) ).
thf(625,plain,
$true = $true,
inference(copy,[status(thm)],[548]) ).
thf(626,plain,
$true = $true,
inference(copy,[status(thm)],[547]) ).
thf(627,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[611]) ).
thf(628,plain,
$true = $true,
inference(copy,[status(thm)],[545]) ).
thf(629,plain,
$true = $true,
inference(copy,[status(thm)],[544]) ).
thf(630,plain,
$true = $true,
inference(copy,[status(thm)],[543]) ).
thf(631,plain,
$true = $true,
inference(copy,[status(thm)],[542]) ).
thf(632,plain,
$true = $true,
inference(copy,[status(thm)],[541]) ).
thf(633,plain,
$true = $true,
inference(copy,[status(thm)],[540]) ).
thf(634,plain,
$true = $true,
inference(copy,[status(thm)],[539]) ).
thf(635,plain,
$true = $true,
inference(copy,[status(thm)],[538]) ).
thf(636,plain,
$true = $true,
inference(copy,[status(thm)],[537]) ).
thf(637,plain,
$true = $true,
inference(copy,[status(thm)],[536]) ).
thf(638,plain,
$true = $true,
inference(copy,[status(thm)],[535]) ).
thf(639,plain,
( ( ! [A: $i] :
( ~ ( meet_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[610]) ).
thf(640,plain,
$true = $true,
inference(copy,[status(thm)],[533]) ).
thf(641,plain,
( ( ! [A: $i] :
( ~ ( join_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[609]) ).
thf(642,plain,
$true = $true,
inference(copy,[status(thm)],[531]) ).
thf(643,plain,
$true = $true,
inference(copy,[status(thm)],[530]) ).
thf(644,plain,
$true = $true,
inference(copy,[status(thm)],[529]) ).
thf(645,plain,
( ( one_sorted_str @ sK16_A )
= $true ),
inference(copy,[status(thm)],[608]) ).
thf(646,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[607]) ).
thf(647,plain,
( ( ( one_sorted_str @ sK15_A )
& ~ ( empty_carrier @ sK15_A ) )
= $true ),
inference(copy,[status(thm)],[606]) ).
thf(648,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[605]) ).
thf(649,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK14_C @ B @ A ) @ A )
& ~ ( in @ ( sK14_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[604]) ).
thf(650,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(651,plain,
( ( ! [A: $i] :
( ~ ( v1_membered @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( v1_membered @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[603]) ).
thf(652,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[602]) ).
thf(653,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[601]) ).
thf(654,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[600]) ).
thf(655,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[599]) ).
thf(656,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( in @ B @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( element @ B @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( empty @ B ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( empty @ B )
| ( element @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[598]) ).
thf(657,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( empty_carrier @ A )
| ~ ( join_semilatt_str @ A )
| ~ ( element @ B @ ( the_carrier @ A ) )
| ~ ( element @ C @ ( the_carrier @ A ) )
| ( element @ ( join @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[597]) ).
thf(658,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( empty_carrier @ A )
| ~ ( meet_semilatt_str @ A )
| ~ ( element @ B @ ( the_carrier @ A ) )
| ~ ( element @ C @ ( the_carrier @ A ) )
| ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[596]) ).
thf(659,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(660,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[595]) ).
thf(661,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[594]) ).
thf(662,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(663,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)],[592]) ).
thf(664,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[591]) ).
thf(665,plain,
( ( ! [A: $i] :
( ~ ( latt_str @ A )
| ( join_semilatt_str @ A ) )
& ! [A: $i] :
( ~ ( latt_str @ A )
| ( meet_semilatt_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[590]) ).
thf(666,plain,
( ( meet_semilatt_str @ sK13_A )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(667,plain,
( ( join_semilatt_str @ sK12_A )
= $true ),
inference(copy,[status(thm)],[588]) ).
thf(668,plain,
( ( ! [A: $i] : ( element @ ( sK11_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[587]) ).
thf(669,plain,
( ( ! [A: $i] :
~ ( empty @ ( succ @ A ) ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(670,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[503]) ).
thf(671,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(672,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(673,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(674,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[586]) ).
thf(675,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(676,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[585]) ).
thf(677,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[584]) ).
thf(678,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[583]) ).
thf(679,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)],[582]) ).
thf(680,plain,
( ( ~ ( empty @ sK10_A )
& ( finite @ sK10_A ) )
= $true ),
inference(copy,[status(thm)],[581]) ).
thf(681,plain,
( ( ( empty @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(copy,[status(thm)],[580]) ).
thf(682,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK8_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK8_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(683,plain,
( ( empty @ sK7_A )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(684,plain,
( ( ~ ( empty @ sK6_A )
& ( relation @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(685,plain,
( ( ! [A: $i] :
( ( element @ ( sK5_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK5_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(686,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(687,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK3_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK3_B @ A ) )
& ( finite @ ( sK3_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[574]) ).
thf(688,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( ( element @ ( sK2_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK2_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(689,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(690,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[571]) ).
thf(691,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[570]) ).
thf(692,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(693,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[568]) ).
thf(694,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[567]) ).
thf(695,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[566]) ).
thf(696,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[565]) ).
thf(697,plain,
( ( one_sorted_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[562]) ).
thf(698,plain,
( ( ( cast_as_carrier_subset @ sK1_A )
!= ( the_carrier @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(699,plain,
( ( ~ ( ~ ~ ( empty @ sK6_A )
| ~ ( relation @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[684]) ).
thf(700,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[656]) ).
thf(701,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK8_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK8_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[682]) ).
thf(702,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( join_semilatt_str @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( meet_semilatt_str @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[665]) ).
thf(703,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK3_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK3_B @ SX0 ) ) )
| ~ ( finite @ ( sK3_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[687]) ).
thf(704,plain,
( ( ~ ( ~ ~ ( empty @ sK10_A )
| ~ ( finite @ sK10_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[680]) ).
thf(705,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ~ ( ~ ( element @ ( sK2_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ~ ( empty @ ( sK2_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[688]) ).
thf(706,plain,
( ( ~ ( ~ ( one_sorted_str @ sK15_A )
| ~ ~ ( empty_carrier @ sK15_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(707,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649]) ).
thf(708,plain,
( ( ~ ( ~ ( empty @ sK9_A )
| ~ ( relation @ sK9_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[681]) ).
thf(709,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK5_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK5_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[685]) ).
thf(710,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[691]) ).
thf(711,plain,
! [SV1: $i] :
( ( ~ ( one_sorted_str @ SV1 )
| ( ( cast_as_carrier_subset @ SV1 )
= ( the_carrier @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(712,plain,
! [SV2: $i] :
( ( ~ ( one_sorted_str @ SV2 )
| ( element @ ( cast_as_carrier_subset @ SV2 ) @ ( powerset @ ( the_carrier @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(713,plain,
! [SV3: $i] :
( ( ~ ( meet_semilatt_str @ SV3 )
| ( one_sorted_str @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(714,plain,
! [SV4: $i] :
( ( ~ ( join_semilatt_str @ SV4 )
| ( one_sorted_str @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(715,plain,
! [SV5: $i] :
( ( ( empty_carrier @ SV5 )
| ~ ( one_sorted_str @ SV5 )
| ~ ( empty @ ( the_carrier @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(716,plain,
! [SV6: $i] :
( ( ! [SY94: $i] :
( ~ ( element @ SY94 @ ( powerset @ SV6 ) )
| ! [SY95: $i] :
( ~ ( in @ SY95 @ SY94 )
| ( in @ SY95 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(717,plain,
! [SV7: $i] :
( ( ( union @ ( powerset @ SV7 ) )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(718,plain,
! [SV8: $i] :
( ( ~ ( v1_membered @ SV8 )
| ! [SY96: $i] :
( ~ ( element @ SY96 @ ( powerset @ SV8 ) )
| ( v1_membered @ SY96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(719,plain,
! [SV9: $i] :
( ( ~ ( empty @ SV9 )
| ( finite @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(720,plain,
! [SV10: $i] :
( ( ~ ( empty @ SV10 )
| ( function @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(721,plain,
! [SV11: $i] :
( ( ~ ( empty @ SV11 )
| ( relation @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(722,plain,
! [SV12: $i] :
( ( ~ ( finite @ SV12 )
| ! [SY97: $i] :
( ~ ( element @ SY97 @ ( powerset @ SV12 ) )
| ( finite @ SY97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(723,plain,
! [SV13: $i] :
( ( ! [SY98: $i,SY99: $i] :
( ( empty_carrier @ SV13 )
| ~ ( join_semilatt_str @ SV13 )
| ~ ( element @ SY98 @ ( the_carrier @ SV13 ) )
| ~ ( element @ SY99 @ ( the_carrier @ SV13 ) )
| ( element @ ( join @ SV13 @ SY98 @ SY99 ) @ ( the_carrier @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(724,plain,
! [SV14: $i] :
( ( ! [SY100: $i,SY101: $i] :
( ( empty_carrier @ SV14 )
| ~ ( meet_semilatt_str @ SV14 )
| ~ ( element @ SY100 @ ( the_carrier @ SV14 ) )
| ~ ( element @ SY101 @ ( the_carrier @ SV14 ) )
| ( element @ ( meet @ SV14 @ SY100 @ SY101 ) @ ( the_carrier @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(725,plain,
! [SV15: $i] :
( ( element @ ( cast_to_subset @ SV15 ) @ ( powerset @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(726,plain,
! [SV16: $i] :
( ( ! [SY102: $i] :
( ~ ( element @ SY102 @ ( powerset @ SV16 ) )
| ( element @ ( subset_complement @ SV16 @ SY102 ) @ ( powerset @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(727,plain,
! [SV17: $i] :
( ( ! [SY103: $i] :
( ~ ( element @ SY103 @ ( powerset @ ( powerset @ SV17 ) ) )
| ( element @ ( union_of_subsets @ SV17 @ SY103 ) @ ( powerset @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(728,plain,
! [SV18: $i] :
( ( ! [SY104: $i] :
( ~ ( element @ SY104 @ ( powerset @ ( powerset @ SV18 ) ) )
| ( element @ ( meet_of_subsets @ SV18 @ SY104 ) @ ( powerset @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(729,plain,
! [SV19: $i] :
( ( ! [SY105: $i,SY106: $i] :
( ~ ( element @ SY105 @ ( powerset @ SV19 ) )
| ~ ( element @ SY106 @ ( powerset @ SV19 ) )
| ( element @ ( subset_difference @ SV19 @ SY105 @ SY106 ) @ ( powerset @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(730,plain,
! [SV20: $i] :
( ( ! [SY107: $i] :
( ~ ( element @ SY107 @ ( powerset @ ( powerset @ SV20 ) ) )
| ( element @ ( complements_of_subsets @ SV20 @ SY107 ) @ ( powerset @ ( powerset @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(731,plain,
! [SV21: $i] :
( ( element @ ( sK11_B @ SV21 ) @ SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(732,plain,
! [SV22: $i] :
( ( ~ ( empty @ ( succ @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(733,plain,
! [SV23: $i] :
( ( ~ ( empty @ ( powerset @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(734,plain,
! [SV24: $i] :
( ( ! [SY108: $i] :
~ ( empty @ ( ordered_pair @ SV24 @ SY108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(735,plain,
! [SV25: $i] :
( ( ~ ( empty @ ( singleton @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(736,plain,
! [SV26: $i] :
( ( ( empty @ SV26 )
| ! [SY109: $i] :
~ ( empty @ ( set_union2 @ SV26 @ SY109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(737,plain,
! [SV27: $i] :
( ( ! [SY110: $i] :
~ ( empty @ ( unordered_pair @ SV27 @ SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(738,plain,
! [SV28: $i] :
( ( ( empty @ SV28 )
| ! [SY111: $i] :
~ ( empty @ ( set_union2 @ SY111 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(739,plain,
! [SV29: $i] :
( ( ! [SY112: $i] :
( ( empty @ SV29 )
| ( empty @ SY112 )
| ~ ( empty @ ( cartesian_product2 @ SV29 @ SY112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(740,plain,
! [SV30: $i] :
( ( ! [SY113: $i] :
( ~ ( element @ SY113 @ ( powerset @ SV30 ) )
| ( ( subset_complement @ SV30 @ ( subset_complement @ SV30 @ SY113 ) )
= SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(741,plain,
! [SV31: $i] :
( ( ! [SY114: $i] :
( ~ ( element @ SY114 @ ( powerset @ ( powerset @ SV31 ) ) )
| ( ( complements_of_subsets @ SV31 @ ( complements_of_subsets @ SV31 @ SY114 ) )
= SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(742,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(743,plain,
! [SV32: $i] :
( ( ! [SY115: $i] :
( ~ ( in @ SV32 @ SY115 )
| ( element @ SV32 @ SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(744,plain,
! [SV33: $i] :
( ( ! [SY116: $i] :
( ~ ( element @ SV33 @ SY116 )
| ( empty @ SY116 )
| ( in @ SV33 @ SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(745,plain,
! [SV34: $i] :
( ( ! [SY117: $i,SY118: $i] :
( ~ ( element @ SY117 @ ( powerset @ SY118 ) )
| ~ ( in @ SV34 @ SY117 )
| ( element @ SV34 @ SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(746,plain,
! [SV35: $i] :
( ( ! [SY119: $i,SY120: $i] :
( ~ ( element @ SY119 @ ( powerset @ SY120 ) )
| ~ ( in @ SV35 @ SY119 )
| ~ ( empty @ SY120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(747,plain,
! [SV36: $i] :
( ( ~ ( empty @ SV36 )
| ( SV36 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(748,plain,
! [SV37: $i] :
( ( ! [SY121: $i] :
( ~ ( empty @ SY121 )
| ~ ( in @ SV37 @ SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(749,plain,
! [SV38: $i] :
( ( ! [SY122: $i] :
( ( SV38 = SY122 )
| ~ ( empty @ SV38 )
| ~ ( empty @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(750,plain,
( ( ( cast_as_carrier_subset @ sK1_A )
= ( the_carrier @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(751,plain,
( ( ~ ~ ( empty @ sK6_A )
| ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(752,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(753,plain,
! [SV39: $i] :
( ( ( empty @ SV39 )
| ~ ( ~ ( element @ ( sK8_B @ SV39 ) @ ( powerset @ SV39 ) )
| ~ ~ ( empty @ ( sK8_B @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(754,plain,
( ( ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( join_semilatt_str @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( meet_semilatt_str @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(755,plain,
! [SV40: $i] :
( ( ( empty @ SV40 )
| ~ ( ~ ~ ( ~ ( element @ ( sK3_B @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( empty @ ( sK3_B @ SV40 ) ) )
| ~ ( finite @ ( sK3_B @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(756,plain,
( ( ~ ~ ( empty @ sK10_A )
| ~ ( finite @ sK10_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(757,plain,
! [SV41: $i] :
( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 )
| ~ ( ~ ( element @ ( sK2_B @ SV41 ) @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ~ ~ ( empty @ ( sK2_B @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(758,plain,
( ( ~ ( one_sorted_str @ sK15_A )
| ~ ~ ( empty_carrier @ sK15_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(759,plain,
! [SV42: $i] :
( ( ! [SY123: $i] :
( ~ ( ~ ( in @ ( sK14_C @ SY123 @ SV42 ) @ SV42 )
| ~ ~ ( in @ ( sK14_C @ SY123 @ SV42 ) @ SY123 ) )
| ( element @ SV42 @ ( powerset @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(760,plain,
( ( ~ ( empty @ sK9_A )
| ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(761,plain,
! [SV43: $i] :
( ( ~ ( ~ ( element @ ( sK5_B @ SV43 ) @ ( powerset @ SV43 ) )
| ~ ( empty @ ( sK5_B @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(762,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(763,plain,
! [SV1: $i] :
( ( ( ~ ( one_sorted_str @ SV1 ) )
= $true )
| ( ( ( cast_as_carrier_subset @ SV1 )
= ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[711]) ).
thf(764,plain,
! [SV2: $i] :
( ( ( ~ ( one_sorted_str @ SV2 ) )
= $true )
| ( ( element @ ( cast_as_carrier_subset @ SV2 ) @ ( powerset @ ( the_carrier @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[712]) ).
thf(765,plain,
! [SV3: $i] :
( ( ( ~ ( meet_semilatt_str @ SV3 ) )
= $true )
| ( ( one_sorted_str @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(766,plain,
! [SV4: $i] :
( ( ( ~ ( join_semilatt_str @ SV4 ) )
= $true )
| ( ( one_sorted_str @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(767,plain,
! [SV5: $i] :
( ( ( ( empty_carrier @ SV5 )
| ~ ( one_sorted_str @ SV5 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(768,plain,
! [SV6: $i,SV44: $i] :
( ( ~ ( element @ SV44 @ ( powerset @ SV6 ) )
| ! [SY124: $i] :
( ~ ( in @ SY124 @ SV44 )
| ( in @ SY124 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(769,plain,
! [SV8: $i] :
( ( ( ~ ( v1_membered @ SV8 ) )
= $true )
| ( ( ! [SY96: $i] :
( ~ ( element @ SY96 @ ( powerset @ SV8 ) )
| ( v1_membered @ SY96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(770,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ SV9 ) )
= $true )
| ( ( finite @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(771,plain,
! [SV10: $i] :
( ( ( ~ ( empty @ SV10 ) )
= $true )
| ( ( function @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(772,plain,
! [SV11: $i] :
( ( ( ~ ( empty @ SV11 ) )
= $true )
| ( ( relation @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(773,plain,
! [SV12: $i] :
( ( ( ~ ( finite @ SV12 ) )
= $true )
| ( ( ! [SY97: $i] :
( ~ ( element @ SY97 @ ( powerset @ SV12 ) )
| ( finite @ SY97 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(774,plain,
! [SV45: $i,SV13: $i] :
( ( ! [SY125: $i] :
( ( empty_carrier @ SV13 )
| ~ ( join_semilatt_str @ SV13 )
| ~ ( element @ SV45 @ ( the_carrier @ SV13 ) )
| ~ ( element @ SY125 @ ( the_carrier @ SV13 ) )
| ( element @ ( join @ SV13 @ SV45 @ SY125 ) @ ( the_carrier @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(775,plain,
! [SV46: $i,SV14: $i] :
( ( ! [SY126: $i] :
( ( empty_carrier @ SV14 )
| ~ ( meet_semilatt_str @ SV14 )
| ~ ( element @ SV46 @ ( the_carrier @ SV14 ) )
| ~ ( element @ SY126 @ ( the_carrier @ SV14 ) )
| ( element @ ( meet @ SV14 @ SV46 @ SY126 ) @ ( the_carrier @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(776,plain,
! [SV16: $i,SV47: $i] :
( ( ~ ( element @ SV47 @ ( powerset @ SV16 ) )
| ( element @ ( subset_complement @ SV16 @ SV47 ) @ ( powerset @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(777,plain,
! [SV17: $i,SV48: $i] :
( ( ~ ( element @ SV48 @ ( powerset @ ( powerset @ SV17 ) ) )
| ( element @ ( union_of_subsets @ SV17 @ SV48 ) @ ( powerset @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(778,plain,
! [SV18: $i,SV49: $i] :
( ( ~ ( element @ SV49 @ ( powerset @ ( powerset @ SV18 ) ) )
| ( element @ ( meet_of_subsets @ SV18 @ SV49 ) @ ( powerset @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(779,plain,
! [SV19: $i,SV50: $i] :
( ( ! [SY127: $i] :
( ~ ( element @ SV50 @ ( powerset @ SV19 ) )
| ~ ( element @ SY127 @ ( powerset @ SV19 ) )
| ( element @ ( subset_difference @ SV19 @ SV50 @ SY127 ) @ ( powerset @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(780,plain,
! [SV20: $i,SV51: $i] :
( ( ~ ( element @ SV51 @ ( powerset @ ( powerset @ SV20 ) ) )
| ( element @ ( complements_of_subsets @ SV20 @ SV51 ) @ ( powerset @ ( powerset @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(781,plain,
! [SV22: $i] :
( ( empty @ ( succ @ SV22 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(782,plain,
! [SV23: $i] :
( ( empty @ ( powerset @ SV23 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(783,plain,
! [SV52: $i,SV24: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV24 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(784,plain,
! [SV25: $i] :
( ( empty @ ( singleton @ SV25 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(785,plain,
! [SV26: $i] :
( ( ( empty @ SV26 )
= $true )
| ( ( ! [SY109: $i] :
~ ( empty @ ( set_union2 @ SV26 @ SY109 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(786,plain,
! [SV53: $i,SV27: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV27 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(787,plain,
! [SV28: $i] :
( ( ( empty @ SV28 )
= $true )
| ( ( ! [SY111: $i] :
~ ( empty @ ( set_union2 @ SY111 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[738]) ).
thf(788,plain,
! [SV54: $i,SV29: $i] :
( ( ( empty @ SV29 )
| ( empty @ SV54 )
| ~ ( empty @ ( cartesian_product2 @ SV29 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(789,plain,
! [SV30: $i,SV55: $i] :
( ( ~ ( element @ SV55 @ ( powerset @ SV30 ) )
| ( ( subset_complement @ SV30 @ ( subset_complement @ SV30 @ SV55 ) )
= SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(790,plain,
! [SV31: $i,SV56: $i] :
( ( ~ ( element @ SV56 @ ( powerset @ ( powerset @ SV31 ) ) )
| ( ( complements_of_subsets @ SV31 @ ( complements_of_subsets @ SV31 @ SV56 ) )
= SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(791,plain,
! [SV57: $i,SV32: $i] :
( ( ~ ( in @ SV32 @ SV57 )
| ( element @ SV32 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(792,plain,
! [SV58: $i,SV33: $i] :
( ( ~ ( element @ SV33 @ SV58 )
| ( empty @ SV58 )
| ( in @ SV33 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(793,plain,
! [SV34: $i,SV59: $i] :
( ( ! [SY128: $i] :
( ~ ( element @ SV59 @ ( powerset @ SY128 ) )
| ~ ( in @ SV34 @ SV59 )
| ( element @ SV34 @ SY128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(794,plain,
! [SV35: $i,SV60: $i] :
( ( ! [SY129: $i] :
( ~ ( element @ SV60 @ ( powerset @ SY129 ) )
| ~ ( in @ SV35 @ SV60 )
| ~ ( empty @ SY129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(795,plain,
! [SV36: $i] :
( ( ( ~ ( empty @ SV36 ) )
= $true )
| ( ( SV36 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[747]) ).
thf(796,plain,
! [SV37: $i,SV61: $i] :
( ( ~ ( empty @ SV61 )
| ~ ( in @ SV37 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(797,plain,
! [SV62: $i,SV38: $i] :
( ( ( SV38 = SV62 )
| ~ ( empty @ SV38 )
| ~ ( empty @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(798,plain,
( ( ~ ~ ( empty @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[751]) ).
thf(799,plain,
( ( ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[751]) ).
thf(800,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[752]) ).
thf(801,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[752]) ).
thf(802,plain,
! [SV39: $i] :
( ( ( empty @ SV39 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK8_B @ SV39 ) @ ( powerset @ SV39 ) )
| ~ ~ ( empty @ ( sK8_B @ SV39 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(803,plain,
( ( ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( join_semilatt_str @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(804,plain,
( ( ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( meet_semilatt_str @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(805,plain,
! [SV40: $i] :
( ( ( empty @ SV40 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK3_B @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( empty @ ( sK3_B @ SV40 ) ) )
| ~ ( finite @ ( sK3_B @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(806,plain,
( ( ~ ~ ( empty @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[756]) ).
thf(807,plain,
( ( ~ ( finite @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[756]) ).
thf(808,plain,
! [SV41: $i] :
( ( ( ( empty_carrier @ SV41 )
| ~ ( one_sorted_str @ SV41 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK2_B @ SV41 ) @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ~ ~ ( empty @ ( sK2_B @ SV41 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(809,plain,
( ( ~ ( one_sorted_str @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[758]) ).
thf(810,plain,
( ( ~ ~ ( empty_carrier @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[758]) ).
thf(811,plain,
! [SV42: $i,SV63: $i] :
( ( ~ ( ~ ( in @ ( sK14_C @ SV63 @ SV42 ) @ SV42 )
| ~ ~ ( in @ ( sK14_C @ SV63 @ SV42 ) @ SV63 ) )
| ( element @ SV42 @ ( powerset @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(812,plain,
( ( ~ ( empty @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[760]) ).
thf(813,plain,
( ( ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[760]) ).
thf(814,plain,
! [SV43: $i] :
( ( ~ ( element @ ( sK5_B @ SV43 ) @ ( powerset @ SV43 ) )
| ~ ( empty @ ( sK5_B @ SV43 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(815,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[762]) ).
thf(816,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[762]) ).
thf(817,plain,
! [SV1: $i] :
( ( ( one_sorted_str @ SV1 )
= $false )
| ( ( ( cast_as_carrier_subset @ SV1 )
= ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(818,plain,
! [SV2: $i] :
( ( ( one_sorted_str @ SV2 )
= $false )
| ( ( element @ ( cast_as_carrier_subset @ SV2 ) @ ( powerset @ ( the_carrier @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(819,plain,
! [SV3: $i] :
( ( ( meet_semilatt_str @ SV3 )
= $false )
| ( ( one_sorted_str @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(820,plain,
! [SV4: $i] :
( ( ( join_semilatt_str @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(821,plain,
! [SV5: $i] :
( ( ( empty_carrier @ SV5 )
= $true )
| ( ( ~ ( one_sorted_str @ SV5 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(822,plain,
! [SV6: $i,SV44: $i] :
( ( ( ~ ( element @ SV44 @ ( powerset @ SV6 ) ) )
= $true )
| ( ( ! [SY124: $i] :
( ~ ( in @ SY124 @ SV44 )
| ( in @ SY124 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(823,plain,
! [SV8: $i] :
( ( ( v1_membered @ SV8 )
= $false )
| ( ( ! [SY96: $i] :
( ~ ( element @ SY96 @ ( powerset @ SV8 ) )
| ( v1_membered @ SY96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(824,plain,
! [SV9: $i] :
( ( ( empty @ SV9 )
= $false )
| ( ( finite @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(825,plain,
! [SV10: $i] :
( ( ( empty @ SV10 )
= $false )
| ( ( function @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(826,plain,
! [SV11: $i] :
( ( ( empty @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(827,plain,
! [SV12: $i] :
( ( ( finite @ SV12 )
= $false )
| ( ( ! [SY97: $i] :
( ~ ( element @ SY97 @ ( powerset @ SV12 ) )
| ( finite @ SY97 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(828,plain,
! [SV64: $i,SV45: $i,SV13: $i] :
( ( ( empty_carrier @ SV13 )
| ~ ( join_semilatt_str @ SV13 )
| ~ ( element @ SV45 @ ( the_carrier @ SV13 ) )
| ~ ( element @ SV64 @ ( the_carrier @ SV13 ) )
| ( element @ ( join @ SV13 @ SV45 @ SV64 ) @ ( the_carrier @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(829,plain,
! [SV65: $i,SV46: $i,SV14: $i] :
( ( ( empty_carrier @ SV14 )
| ~ ( meet_semilatt_str @ SV14 )
| ~ ( element @ SV46 @ ( the_carrier @ SV14 ) )
| ~ ( element @ SV65 @ ( the_carrier @ SV14 ) )
| ( element @ ( meet @ SV14 @ SV46 @ SV65 ) @ ( the_carrier @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(830,plain,
! [SV16: $i,SV47: $i] :
( ( ( ~ ( element @ SV47 @ ( powerset @ SV16 ) ) )
= $true )
| ( ( element @ ( subset_complement @ SV16 @ SV47 ) @ ( powerset @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(831,plain,
! [SV17: $i,SV48: $i] :
( ( ( ~ ( element @ SV48 @ ( powerset @ ( powerset @ SV17 ) ) ) )
= $true )
| ( ( element @ ( union_of_subsets @ SV17 @ SV48 ) @ ( powerset @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(832,plain,
! [SV18: $i,SV49: $i] :
( ( ( ~ ( element @ SV49 @ ( powerset @ ( powerset @ SV18 ) ) ) )
= $true )
| ( ( element @ ( meet_of_subsets @ SV18 @ SV49 ) @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(833,plain,
! [SV66: $i,SV19: $i,SV50: $i] :
( ( ~ ( element @ SV50 @ ( powerset @ SV19 ) )
| ~ ( element @ SV66 @ ( powerset @ SV19 ) )
| ( element @ ( subset_difference @ SV19 @ SV50 @ SV66 ) @ ( powerset @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(834,plain,
! [SV20: $i,SV51: $i] :
( ( ( ~ ( element @ SV51 @ ( powerset @ ( powerset @ SV20 ) ) ) )
= $true )
| ( ( element @ ( complements_of_subsets @ SV20 @ SV51 ) @ ( powerset @ ( powerset @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(835,plain,
! [SV52: $i,SV24: $i] :
( ( empty @ ( ordered_pair @ SV24 @ SV52 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(836,plain,
! [SV67: $i,SV26: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV26 @ SV67 ) ) )
= $true )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(837,plain,
! [SV53: $i,SV27: $i] :
( ( empty @ ( unordered_pair @ SV27 @ SV53 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(838,plain,
! [SV28: $i,SV68: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV68 @ SV28 ) ) )
= $true )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(839,plain,
! [SV54: $i,SV29: $i] :
( ( ( ( empty @ SV29 )
| ( empty @ SV54 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV29 @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(840,plain,
! [SV30: $i,SV55: $i] :
( ( ( ~ ( element @ SV55 @ ( powerset @ SV30 ) ) )
= $true )
| ( ( ( subset_complement @ SV30 @ ( subset_complement @ SV30 @ SV55 ) )
= SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(841,plain,
! [SV31: $i,SV56: $i] :
( ( ( ~ ( element @ SV56 @ ( powerset @ ( powerset @ SV31 ) ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV31 @ ( complements_of_subsets @ SV31 @ SV56 ) )
= SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[790]) ).
thf(842,plain,
! [SV57: $i,SV32: $i] :
( ( ( ~ ( in @ SV32 @ SV57 ) )
= $true )
| ( ( element @ SV32 @ SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[791]) ).
thf(843,plain,
! [SV58: $i,SV33: $i] :
( ( ( ~ ( element @ SV33 @ SV58 ) )
= $true )
| ( ( ( empty @ SV58 )
| ( in @ SV33 @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[792]) ).
thf(844,plain,
! [SV34: $i,SV69: $i,SV59: $i] :
( ( ~ ( element @ SV59 @ ( powerset @ SV69 ) )
| ~ ( in @ SV34 @ SV59 )
| ( element @ SV34 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(845,plain,
! [SV35: $i,SV70: $i,SV60: $i] :
( ( ~ ( element @ SV60 @ ( powerset @ SV70 ) )
| ~ ( in @ SV35 @ SV60 )
| ~ ( empty @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(846,plain,
! [SV36: $i] :
( ( ( empty @ SV36 )
= $false )
| ( ( SV36 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(847,plain,
! [SV37: $i,SV61: $i] :
( ( ( ~ ( empty @ SV61 ) )
= $true )
| ( ( ~ ( in @ SV37 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(848,plain,
! [SV62: $i,SV38: $i] :
( ( ( ( SV38 = SV62 )
| ~ ( empty @ SV38 ) )
= $true )
| ( ( ~ ( empty @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[797]) ).
thf(849,plain,
( ( ~ ( empty @ sK6_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(850,plain,
( ( relation @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(851,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(852,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(853,plain,
! [SV39: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV39 ) @ ( powerset @ SV39 ) )
| ~ ~ ( empty @ ( sK8_B @ SV39 ) ) )
= $false )
| ( ( empty @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(854,plain,
( ( ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( join_semilatt_str @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(855,plain,
( ( ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( meet_semilatt_str @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(856,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK3_B @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( empty @ ( sK3_B @ SV40 ) ) )
| ~ ( finite @ ( sK3_B @ SV40 ) ) )
= $false )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(857,plain,
( ( ~ ( empty @ sK10_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(858,plain,
( ( finite @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(859,plain,
! [SV41: $i] :
( ( ( empty_carrier @ SV41 )
= $true )
| ( ( ~ ( one_sorted_str @ SV41 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK2_B @ SV41 ) @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ~ ~ ( empty @ ( sK2_B @ SV41 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[808]) ).
thf(860,plain,
( ( one_sorted_str @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[809]) ).
thf(861,plain,
( ( ~ ( empty_carrier @ sK15_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(862,plain,
! [SV42: $i,SV63: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_C @ SV63 @ SV42 ) @ SV42 )
| ~ ~ ( in @ ( sK14_C @ SV63 @ SV42 ) @ SV63 ) ) )
= $true )
| ( ( element @ SV42 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[811]) ).
thf(863,plain,
( ( empty @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[812]) ).
thf(864,plain,
( ( relation @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[813]) ).
thf(865,plain,
! [SV43: $i] :
( ( ~ ( element @ ( sK5_B @ SV43 ) @ ( powerset @ SV43 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[814]) ).
thf(866,plain,
! [SV43: $i] :
( ( ~ ( empty @ ( sK5_B @ SV43 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[814]) ).
thf(867,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[815]) ).
thf(868,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[816]) ).
thf(869,plain,
! [SV5: $i] :
( ( ( one_sorted_str @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[821]) ).
thf(870,plain,
! [SV6: $i,SV44: $i] :
( ( ( element @ SV44 @ ( powerset @ SV6 ) )
= $false )
| ( ( ! [SY124: $i] :
( ~ ( in @ SY124 @ SV44 )
| ( in @ SY124 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[822]) ).
thf(871,plain,
! [SV8: $i,SV71: $i] :
( ( ( ~ ( element @ SV71 @ ( powerset @ SV8 ) )
| ( v1_membered @ SV71 ) )
= $true )
| ( ( v1_membered @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(872,plain,
! [SV12: $i,SV72: $i] :
( ( ( ~ ( element @ SV72 @ ( powerset @ SV12 ) )
| ( finite @ SV72 ) )
= $true )
| ( ( finite @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(873,plain,
! [SV64: $i,SV45: $i,SV13: $i] :
( ( ( ( empty_carrier @ SV13 )
| ~ ( join_semilatt_str @ SV13 )
| ~ ( element @ SV45 @ ( the_carrier @ SV13 ) )
| ~ ( element @ SV64 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( element @ ( join @ SV13 @ SV45 @ SV64 ) @ ( the_carrier @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[828]) ).
thf(874,plain,
! [SV65: $i,SV46: $i,SV14: $i] :
( ( ( ( empty_carrier @ SV14 )
| ~ ( meet_semilatt_str @ SV14 )
| ~ ( element @ SV46 @ ( the_carrier @ SV14 ) )
| ~ ( element @ SV65 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( element @ ( meet @ SV14 @ SV46 @ SV65 ) @ ( the_carrier @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(875,plain,
! [SV16: $i,SV47: $i] :
( ( ( element @ SV47 @ ( powerset @ SV16 ) )
= $false )
| ( ( element @ ( subset_complement @ SV16 @ SV47 ) @ ( powerset @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(876,plain,
! [SV17: $i,SV48: $i] :
( ( ( element @ SV48 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false )
| ( ( element @ ( union_of_subsets @ SV17 @ SV48 ) @ ( powerset @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(877,plain,
! [SV18: $i,SV49: $i] :
( ( ( element @ SV49 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false )
| ( ( element @ ( meet_of_subsets @ SV18 @ SV49 ) @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(878,plain,
! [SV66: $i,SV19: $i,SV50: $i] :
( ( ( ~ ( element @ SV50 @ ( powerset @ SV19 ) )
| ~ ( element @ SV66 @ ( powerset @ SV19 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV19 @ SV50 @ SV66 ) @ ( powerset @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[833]) ).
thf(879,plain,
! [SV20: $i,SV51: $i] :
( ( ( element @ SV51 @ ( powerset @ ( powerset @ SV20 ) ) )
= $false )
| ( ( element @ ( complements_of_subsets @ SV20 @ SV51 ) @ ( powerset @ ( powerset @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(880,plain,
! [SV67: $i,SV26: $i] :
( ( ( empty @ ( set_union2 @ SV26 @ SV67 ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(881,plain,
! [SV28: $i,SV68: $i] :
( ( ( empty @ ( set_union2 @ SV68 @ SV28 ) )
= $false )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(882,plain,
! [SV54: $i,SV29: $i] :
( ( ( empty @ SV29 )
= $true )
| ( ( empty @ SV54 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV29 @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(883,plain,
! [SV30: $i,SV55: $i] :
( ( ( element @ SV55 @ ( powerset @ SV30 ) )
= $false )
| ( ( ( subset_complement @ SV30 @ ( subset_complement @ SV30 @ SV55 ) )
= SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[840]) ).
thf(884,plain,
! [SV31: $i,SV56: $i] :
( ( ( element @ SV56 @ ( powerset @ ( powerset @ SV31 ) ) )
= $false )
| ( ( ( complements_of_subsets @ SV31 @ ( complements_of_subsets @ SV31 @ SV56 ) )
= SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(885,plain,
! [SV57: $i,SV32: $i] :
( ( ( in @ SV32 @ SV57 )
= $false )
| ( ( element @ SV32 @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(886,plain,
! [SV58: $i,SV33: $i] :
( ( ( element @ SV33 @ SV58 )
= $false )
| ( ( ( empty @ SV58 )
| ( in @ SV33 @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(887,plain,
! [SV34: $i,SV69: $i,SV59: $i] :
( ( ( ~ ( element @ SV59 @ ( powerset @ SV69 ) )
| ~ ( in @ SV34 @ SV59 ) )
= $true )
| ( ( element @ SV34 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(888,plain,
! [SV35: $i,SV70: $i,SV60: $i] :
( ( ( ~ ( element @ SV60 @ ( powerset @ SV70 ) )
| ~ ( in @ SV35 @ SV60 ) )
= $true )
| ( ( ~ ( empty @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[845]) ).
thf(889,plain,
! [SV37: $i,SV61: $i] :
( ( ( empty @ SV61 )
= $false )
| ( ( ~ ( in @ SV37 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(890,plain,
! [SV62: $i,SV38: $i] :
( ( ( SV38 = SV62 )
= $true )
| ( ( ~ ( empty @ SV38 ) )
= $true )
| ( ( ~ ( empty @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(891,plain,
( ( empty @ sK6_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(892,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(893,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(894,plain,
! [SV39: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV39 ) @ ( powerset @ SV39 ) ) )
= $false )
| ( ( empty @ SV39 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(895,plain,
! [SV39: $i] :
( ( ( ~ ~ ( empty @ ( sK8_B @ SV39 ) ) )
= $false )
| ( ( empty @ SV39 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(896,plain,
! [SV73: $i] :
( ( ~ ( latt_str @ SV73 )
| ( join_semilatt_str @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(897,plain,
! [SV74: $i] :
( ( ~ ( latt_str @ SV74 )
| ( meet_semilatt_str @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(898,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK3_B @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( empty @ ( sK3_B @ SV40 ) ) ) )
= $false )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(899,plain,
! [SV40: $i] :
( ( ( ~ ( finite @ ( sK3_B @ SV40 ) ) )
= $false )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(900,plain,
( ( empty @ sK10_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(901,plain,
! [SV41: $i] :
( ( ( one_sorted_str @ SV41 )
= $false )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK2_B @ SV41 ) @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ~ ~ ( empty @ ( sK2_B @ SV41 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(902,plain,
( ( empty_carrier @ sK15_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(903,plain,
! [SV42: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK14_C @ SV63 @ SV42 ) @ SV42 )
| ~ ~ ( in @ ( sK14_C @ SV63 @ SV42 ) @ SV63 ) )
= $false )
| ( ( element @ SV42 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(904,plain,
! [SV43: $i] :
( ( element @ ( sK5_B @ SV43 ) @ ( powerset @ SV43 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[865]) ).
thf(905,plain,
! [SV43: $i] :
( ( empty @ ( sK5_B @ SV43 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[866]) ).
thf(906,plain,
! [SV75: $i] :
( ( ! [SY130: $i] :
( ~ ( element @ SV75 @ ( powerset @ SY130 ) )
| ( subset @ SV75 @ SY130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(907,plain,
! [SV76: $i] :
( ( ! [SY131: $i] :
( ~ ( subset @ SV76 @ SY131 )
| ( element @ SV76 @ ( powerset @ SY131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(908,plain,
! [SV5: $i] :
( ( ( empty @ ( the_carrier @ SV5 ) )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( one_sorted_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(909,plain,
! [SV6: $i,SV44: $i,SV77: $i] :
( ( ( ~ ( in @ SV77 @ SV44 )
| ( in @ SV77 @ SV6 ) )
= $true )
| ( ( element @ SV44 @ ( powerset @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(910,plain,
! [SV8: $i,SV71: $i] :
( ( ( ~ ( element @ SV71 @ ( powerset @ SV8 ) ) )
= $true )
| ( ( v1_membered @ SV71 )
= $true )
| ( ( v1_membered @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(911,plain,
! [SV12: $i,SV72: $i] :
( ( ( ~ ( element @ SV72 @ ( powerset @ SV12 ) ) )
= $true )
| ( ( finite @ SV72 )
= $true )
| ( ( finite @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(912,plain,
! [SV64: $i,SV45: $i,SV13: $i] :
( ( ( ( empty_carrier @ SV13 )
| ~ ( join_semilatt_str @ SV13 )
| ~ ( element @ SV45 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( ~ ( element @ SV64 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( element @ ( join @ SV13 @ SV45 @ SV64 ) @ ( the_carrier @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(913,plain,
! [SV65: $i,SV46: $i,SV14: $i] :
( ( ( ( empty_carrier @ SV14 )
| ~ ( meet_semilatt_str @ SV14 )
| ~ ( element @ SV46 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( element @ SV65 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( element @ ( meet @ SV14 @ SV46 @ SV65 ) @ ( the_carrier @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(914,plain,
! [SV66: $i,SV19: $i,SV50: $i] :
( ( ( ~ ( element @ SV50 @ ( powerset @ SV19 ) ) )
= $true )
| ( ( ~ ( element @ SV66 @ ( powerset @ SV19 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV19 @ SV50 @ SV66 ) @ ( powerset @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(915,plain,
! [SV54: $i,SV29: $i] :
( ( ( empty @ ( cartesian_product2 @ SV29 @ SV54 ) )
= $false )
| ( ( empty @ SV54 )
= $true )
| ( ( empty @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(916,plain,
! [SV33: $i,SV58: $i] :
( ( ( empty @ SV58 )
= $true )
| ( ( in @ SV33 @ SV58 )
= $true )
| ( ( element @ SV33 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(917,plain,
! [SV34: $i,SV69: $i,SV59: $i] :
( ( ( ~ ( element @ SV59 @ ( powerset @ SV69 ) ) )
= $true )
| ( ( ~ ( in @ SV34 @ SV59 ) )
= $true )
| ( ( element @ SV34 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(918,plain,
! [SV35: $i,SV70: $i,SV60: $i] :
( ( ( ~ ( element @ SV60 @ ( powerset @ SV70 ) ) )
= $true )
| ( ( ~ ( in @ SV35 @ SV60 ) )
= $true )
| ( ( ~ ( empty @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(919,plain,
! [SV61: $i,SV37: $i] :
( ( ( in @ SV37 @ SV61 )
= $false )
| ( ( empty @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(920,plain,
! [SV62: $i,SV38: $i] :
( ( ( empty @ SV38 )
= $false )
| ( ( SV38 = SV62 )
= $true )
| ( ( ~ ( empty @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(921,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(922,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(923,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[893]) ).
thf(924,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[893]) ).
thf(925,plain,
! [SV39: $i] :
( ( ( element @ ( sK8_B @ SV39 ) @ ( powerset @ SV39 ) )
= $true )
| ( ( empty @ SV39 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[894]) ).
thf(926,plain,
! [SV39: $i] :
( ( ( ~ ( empty @ ( sK8_B @ SV39 ) ) )
= $true )
| ( ( empty @ SV39 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[895]) ).
thf(927,plain,
! [SV73: $i] :
( ( ( ~ ( latt_str @ SV73 ) )
= $true )
| ( ( join_semilatt_str @ SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[896]) ).
thf(928,plain,
! [SV74: $i] :
( ( ( ~ ( latt_str @ SV74 ) )
= $true )
| ( ( meet_semilatt_str @ SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(929,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ( element @ ( sK3_B @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( empty @ ( sK3_B @ SV40 ) ) ) )
= $true )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[898]) ).
thf(930,plain,
! [SV40: $i] :
( ( ( finite @ ( sK3_B @ SV40 ) )
= $true )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[899]) ).
thf(931,plain,
! [SV41: $i] :
( ( ( ~ ( element @ ( sK2_B @ SV41 ) @ ( powerset @ ( the_carrier @ SV41 ) ) )
| ~ ~ ( empty @ ( sK2_B @ SV41 ) ) )
= $false )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(932,plain,
! [SV42: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK14_C @ SV63 @ SV42 ) @ SV42 ) )
= $false )
| ( ( element @ SV42 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[903]) ).
thf(933,plain,
! [SV42: $i,SV63: $i] :
( ( ( ~ ~ ( in @ ( sK14_C @ SV63 @ SV42 ) @ SV63 ) )
= $false )
| ( ( element @ SV42 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[903]) ).
thf(934,plain,
! [SV78: $i,SV75: $i] :
( ( ~ ( element @ SV75 @ ( powerset @ SV78 ) )
| ( subset @ SV75 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(935,plain,
! [SV79: $i,SV76: $i] :
( ( ~ ( subset @ SV76 @ SV79 )
| ( element @ SV76 @ ( powerset @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(936,plain,
! [SV6: $i,SV44: $i,SV77: $i] :
( ( ( ~ ( in @ SV77 @ SV44 ) )
= $true )
| ( ( in @ SV77 @ SV6 )
= $true )
| ( ( element @ SV44 @ ( powerset @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[909]) ).
thf(937,plain,
! [SV8: $i,SV71: $i] :
( ( ( element @ SV71 @ ( powerset @ SV8 ) )
= $false )
| ( ( v1_membered @ SV71 )
= $true )
| ( ( v1_membered @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(938,plain,
! [SV12: $i,SV72: $i] :
( ( ( element @ SV72 @ ( powerset @ SV12 ) )
= $false )
| ( ( finite @ SV72 )
= $true )
| ( ( finite @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(939,plain,
! [SV64: $i,SV45: $i,SV13: $i] :
( ( ( ( empty_carrier @ SV13 )
| ~ ( join_semilatt_str @ SV13 ) )
= $true )
| ( ( ~ ( element @ SV45 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( ~ ( element @ SV64 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( element @ ( join @ SV13 @ SV45 @ SV64 ) @ ( the_carrier @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(940,plain,
! [SV65: $i,SV46: $i,SV14: $i] :
( ( ( ( empty_carrier @ SV14 )
| ~ ( meet_semilatt_str @ SV14 ) )
= $true )
| ( ( ~ ( element @ SV46 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( element @ SV65 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( element @ ( meet @ SV14 @ SV46 @ SV65 ) @ ( the_carrier @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(941,plain,
! [SV66: $i,SV19: $i,SV50: $i] :
( ( ( element @ SV50 @ ( powerset @ SV19 ) )
= $false )
| ( ( ~ ( element @ SV66 @ ( powerset @ SV19 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV19 @ SV50 @ SV66 ) @ ( powerset @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(942,plain,
! [SV34: $i,SV69: $i,SV59: $i] :
( ( ( element @ SV59 @ ( powerset @ SV69 ) )
= $false )
| ( ( ~ ( in @ SV34 @ SV59 ) )
= $true )
| ( ( element @ SV34 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(943,plain,
! [SV35: $i,SV70: $i,SV60: $i] :
( ( ( element @ SV60 @ ( powerset @ SV70 ) )
= $false )
| ( ( ~ ( in @ SV35 @ SV60 ) )
= $true )
| ( ( ~ ( empty @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(944,plain,
! [SV38: $i,SV62: $i] :
( ( ( empty @ SV62 )
= $false )
| ( ( SV38 = SV62 )
= $true )
| ( ( empty @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(945,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[921]) ).
thf(946,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[922]) ).
thf(947,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[923]) ).
thf(948,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[924]) ).
thf(949,plain,
! [SV39: $i] :
( ( ( empty @ ( sK8_B @ SV39 ) )
= $false )
| ( ( empty @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(950,plain,
! [SV73: $i] :
( ( ( latt_str @ SV73 )
= $false )
| ( ( join_semilatt_str @ SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(951,plain,
! [SV74: $i] :
( ( ( latt_str @ SV74 )
= $false )
| ( ( meet_semilatt_str @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(952,plain,
! [SV40: $i] :
( ( ( ~ ( element @ ( sK3_B @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( empty @ ( sK3_B @ SV40 ) ) )
= $false )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(953,plain,
! [SV41: $i] :
( ( ( ~ ( element @ ( sK2_B @ SV41 ) @ ( powerset @ ( the_carrier @ SV41 ) ) ) )
= $false )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[931]) ).
thf(954,plain,
! [SV41: $i] :
( ( ( ~ ~ ( empty @ ( sK2_B @ SV41 ) ) )
= $false )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[931]) ).
thf(955,plain,
! [SV42: $i,SV63: $i] :
( ( ( in @ ( sK14_C @ SV63 @ SV42 ) @ SV42 )
= $true )
| ( ( element @ SV42 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[932]) ).
thf(956,plain,
! [SV42: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK14_C @ SV63 @ SV42 ) @ SV63 ) )
= $true )
| ( ( element @ SV42 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[933]) ).
thf(957,plain,
! [SV78: $i,SV75: $i] :
( ( ( ~ ( element @ SV75 @ ( powerset @ SV78 ) ) )
= $true )
| ( ( subset @ SV75 @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[934]) ).
thf(958,plain,
! [SV79: $i,SV76: $i] :
( ( ( ~ ( subset @ SV76 @ SV79 ) )
= $true )
| ( ( element @ SV76 @ ( powerset @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[935]) ).
thf(959,plain,
! [SV6: $i,SV44: $i,SV77: $i] :
( ( ( in @ SV77 @ SV44 )
= $false )
| ( ( in @ SV77 @ SV6 )
= $true )
| ( ( element @ SV44 @ ( powerset @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(960,plain,
! [SV64: $i,SV45: $i,SV13: $i] :
( ( ( empty_carrier @ SV13 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV13 ) )
= $true )
| ( ( ~ ( element @ SV45 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( ~ ( element @ SV64 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( element @ ( join @ SV13 @ SV45 @ SV64 ) @ ( the_carrier @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(961,plain,
! [SV65: $i,SV46: $i,SV14: $i] :
( ( ( empty_carrier @ SV14 )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV14 ) )
= $true )
| ( ( ~ ( element @ SV46 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( element @ SV65 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( element @ ( meet @ SV14 @ SV46 @ SV65 ) @ ( the_carrier @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(962,plain,
! [SV50: $i,SV19: $i,SV66: $i] :
( ( ( element @ SV66 @ ( powerset @ SV19 ) )
= $false )
| ( ( element @ SV50 @ ( powerset @ SV19 ) )
= $false )
| ( ( element @ ( subset_difference @ SV19 @ SV50 @ SV66 ) @ ( powerset @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(963,plain,
! [SV69: $i,SV59: $i,SV34: $i] :
( ( ( in @ SV34 @ SV59 )
= $false )
| ( ( element @ SV59 @ ( powerset @ SV69 ) )
= $false )
| ( ( element @ SV34 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[942]) ).
thf(964,plain,
! [SV70: $i,SV60: $i,SV35: $i] :
( ( ( in @ SV35 @ SV60 )
= $false )
| ( ( element @ SV60 @ ( powerset @ SV70 ) )
= $false )
| ( ( ~ ( empty @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(965,plain,
! [SV80: $i] :
( ( ( empty @ SV80 )
| ! [SY132: $i] :
( ~ ( element @ SY132 @ SV80 )
| ( in @ SY132 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(966,plain,
! [SV81: $i] :
( ( ( empty @ SV81 )
| ! [SY133: $i] :
( ~ ( in @ SY133 @ SV81 )
| ( element @ SY133 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(967,plain,
! [SV82: $i] :
( ( ~ ( empty @ SV82 )
| ! [SY134: $i] :
( ~ ( element @ SY134 @ SV82 )
| ( empty @ SY134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(968,plain,
! [SV83: $i] :
( ( ~ ( empty @ SV83 )
| ! [SY135: $i] :
( ~ ( empty @ SY135 )
| ( element @ SY135 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(969,plain,
! [SV40: $i] :
( ( ( ~ ( element @ ( sK3_B @ SV40 ) @ ( powerset @ SV40 ) ) )
= $false )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[952]) ).
thf(970,plain,
! [SV40: $i] :
( ( ( ~ ~ ( empty @ ( sK3_B @ SV40 ) ) )
= $false )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[952]) ).
thf(971,plain,
! [SV41: $i] :
( ( ( element @ ( sK2_B @ SV41 ) @ ( powerset @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[953]) ).
thf(972,plain,
! [SV41: $i] :
( ( ( ~ ( empty @ ( sK2_B @ SV41 ) ) )
= $true )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[954]) ).
thf(973,plain,
! [SV42: $i,SV63: $i] :
( ( ( in @ ( sK14_C @ SV63 @ SV42 ) @ SV63 )
= $false )
| ( ( element @ SV42 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(974,plain,
! [SV78: $i,SV75: $i] :
( ( ( element @ SV75 @ ( powerset @ SV78 ) )
= $false )
| ( ( subset @ SV75 @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(975,plain,
! [SV79: $i,SV76: $i] :
( ( ( subset @ SV76 @ SV79 )
= $false )
| ( ( element @ SV76 @ ( powerset @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(976,plain,
! [SV64: $i,SV45: $i,SV13: $i] :
( ( ( join_semilatt_str @ SV13 )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( ~ ( element @ SV45 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( ~ ( element @ SV64 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( element @ ( join @ SV13 @ SV45 @ SV64 ) @ ( the_carrier @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(977,plain,
! [SV65: $i,SV46: $i,SV14: $i] :
( ( ( meet_semilatt_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( ~ ( element @ SV46 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( element @ SV65 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( element @ ( meet @ SV14 @ SV46 @ SV65 ) @ ( the_carrier @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(978,plain,
! [SV35: $i,SV60: $i,SV70: $i] :
( ( ( empty @ SV70 )
= $false )
| ( ( element @ SV60 @ ( powerset @ SV70 ) )
= $false )
| ( ( in @ SV35 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(979,plain,
! [SV80: $i] :
( ( ( empty @ SV80 )
= $true )
| ( ( ! [SY132: $i] :
( ~ ( element @ SY132 @ SV80 )
| ( in @ SY132 @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(980,plain,
! [SV81: $i] :
( ( ( empty @ SV81 )
= $true )
| ( ( ! [SY133: $i] :
( ~ ( in @ SY133 @ SV81 )
| ( element @ SY133 @ SV81 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(981,plain,
! [SV82: $i] :
( ( ( ~ ( empty @ SV82 ) )
= $true )
| ( ( ! [SY134: $i] :
( ~ ( element @ SY134 @ SV82 )
| ( empty @ SY134 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(982,plain,
! [SV83: $i] :
( ( ( ~ ( empty @ SV83 ) )
= $true )
| ( ( ! [SY135: $i] :
( ~ ( empty @ SY135 )
| ( element @ SY135 @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[968]) ).
thf(983,plain,
! [SV40: $i] :
( ( ( element @ ( sK3_B @ SV40 ) @ ( powerset @ SV40 ) )
= $true )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[969]) ).
thf(984,plain,
! [SV40: $i] :
( ( ( ~ ( empty @ ( sK3_B @ SV40 ) ) )
= $true )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[970]) ).
thf(985,plain,
! [SV41: $i] :
( ( ( empty @ ( sK2_B @ SV41 ) )
= $false )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( one_sorted_str @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(986,plain,
! [SV64: $i,SV13: $i,SV45: $i] :
( ( ( element @ SV45 @ ( the_carrier @ SV13 ) )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( join_semilatt_str @ SV13 )
= $false )
| ( ( ~ ( element @ SV64 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( element @ ( join @ SV13 @ SV45 @ SV64 ) @ ( the_carrier @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(987,plain,
! [SV65: $i,SV14: $i,SV46: $i] :
( ( ( element @ SV46 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( meet_semilatt_str @ SV14 )
= $false )
| ( ( ~ ( element @ SV65 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( element @ ( meet @ SV14 @ SV46 @ SV65 ) @ ( the_carrier @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(988,plain,
! [SV80: $i,SV84: $i] :
( ( ( ~ ( element @ SV84 @ SV80 )
| ( in @ SV84 @ SV80 ) )
= $true )
| ( ( empty @ SV80 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(989,plain,
! [SV81: $i,SV85: $i] :
( ( ( ~ ( in @ SV85 @ SV81 )
| ( element @ SV85 @ SV81 ) )
= $true )
| ( ( empty @ SV81 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(990,plain,
! [SV82: $i] :
( ( ( empty @ SV82 )
= $false )
| ( ( ! [SY134: $i] :
( ~ ( element @ SY134 @ SV82 )
| ( empty @ SY134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(991,plain,
! [SV83: $i] :
( ( ( empty @ SV83 )
= $false )
| ( ( ! [SY135: $i] :
( ~ ( empty @ SY135 )
| ( element @ SY135 @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(992,plain,
! [SV40: $i] :
( ( ( empty @ ( sK3_B @ SV40 ) )
= $false )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(993,plain,
! [SV45: $i,SV13: $i,SV64: $i] :
( ( ( element @ SV64 @ ( the_carrier @ SV13 ) )
= $false )
| ( ( join_semilatt_str @ SV13 )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( element @ SV45 @ ( the_carrier @ SV13 ) )
= $false )
| ( ( element @ ( join @ SV13 @ SV45 @ SV64 ) @ ( the_carrier @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(994,plain,
! [SV46: $i,SV14: $i,SV65: $i] :
( ( ( element @ SV65 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( meet_semilatt_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( element @ SV46 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( element @ ( meet @ SV14 @ SV46 @ SV65 ) @ ( the_carrier @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(995,plain,
! [SV80: $i,SV84: $i] :
( ( ( ~ ( element @ SV84 @ SV80 ) )
= $true )
| ( ( in @ SV84 @ SV80 )
= $true )
| ( ( empty @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[988]) ).
thf(996,plain,
! [SV81: $i,SV85: $i] :
( ( ( ~ ( in @ SV85 @ SV81 ) )
= $true )
| ( ( element @ SV85 @ SV81 )
= $true )
| ( ( empty @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[989]) ).
thf(997,plain,
! [SV82: $i,SV86: $i] :
( ( ( ~ ( element @ SV86 @ SV82 )
| ( empty @ SV86 ) )
= $true )
| ( ( empty @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(998,plain,
! [SV83: $i,SV87: $i] :
( ( ( ~ ( empty @ SV87 )
| ( element @ SV87 @ SV83 ) )
= $true )
| ( ( empty @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(999,plain,
! [SV80: $i,SV84: $i] :
( ( ( element @ SV84 @ SV80 )
= $false )
| ( ( in @ SV84 @ SV80 )
= $true )
| ( ( empty @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1000,plain,
! [SV81: $i,SV85: $i] :
( ( ( in @ SV85 @ SV81 )
= $false )
| ( ( element @ SV85 @ SV81 )
= $true )
| ( ( empty @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1001,plain,
! [SV82: $i,SV86: $i] :
( ( ( ~ ( element @ SV86 @ SV82 ) )
= $true )
| ( ( empty @ SV86 )
= $true )
| ( ( empty @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1002,plain,
! [SV83: $i,SV87: $i] :
( ( ( ~ ( empty @ SV87 ) )
= $true )
| ( ( element @ SV87 @ SV83 )
= $true )
| ( ( empty @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1003,plain,
! [SV82: $i,SV86: $i] :
( ( ( element @ SV86 @ SV82 )
= $false )
| ( ( empty @ SV86 )
= $true )
| ( ( empty @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1004,plain,
! [SV83: $i,SV87: $i] :
( ( ( empty @ SV87 )
= $false )
| ( ( element @ SV87 @ SV83 )
= $true )
| ( ( empty @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1005,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[614,1004,1003,1000,999,994,993,992,985,983,978,975,974,973,971,963,962,959,955,951,950,949,944,938,937,930,925,919,916,915,908,905,904,902,900,891,885,884,883,881,880,879,877,876,875,864,863,860,858,850,846,837,835,826,825,824,820,819,818,817,784,782,781,750,742,731,725,717,697,683,671,667,666,645,644,643,642,640,638,637,636,635,634,633,632,631,630,629,628,626,625,624,623,622,621,620,619,618,617,616,615]) ).
thf(1006,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1005]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU306+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
% 0.14/0.17 % Computer : n009.cluster.edu
% 0.14/0.17 % Model : x86_64 x86_64
% 0.14/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.17 % Memory : 8046.5625MB
% 0.14/0.17 % OS : Linux 6.8.0-71-generic
% 0.14/0.17 % CPULimit : 300
% 0.14/0.17 % WCLimit : 300
% 0.14/0.17 % DateTime : Tue Oct 6 15:13:05 UTC 2026
% 0.14/0.17 % CPUTime :
% 0.14/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.39/1.02 ....
% 4.39/1.02
% 4.39/1.02 No.of.Axioms: 473
% 4.39/1.02
% 4.39/1.02 Length.of.Defs: 0
% 4.39/1.02
% 4.39/1.02 Contains.Choice.Funs: false
% 4.39/1.02 ...................
% 4.39/1.02
% 4.39/1.02 ********************************
% 4.39/1.02 * All subproblems solved! *
% 4.39/1.02 ********************************
% 4.39/1.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:85,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1005,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 4.39/1.02
% 4.39/1.02 %**** Beginning of derivation protocol ****
% 4.39/1.02 % SZS output start CNFRefutation
% See solution above
% 4.39/1.02
% 4.39/1.02 %**** End of derivation protocol ****
% 4.39/1.02 %**** no. of clauses in derivation: 617 ****
% 4.39/1.02 %**** clause counter: 1005 ****
% 4.39/1.02
% 4.39/1.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:85,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1005,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------