%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU305+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 43.91s 7.60s
% Output : CNFRefutation 7.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 76
% Syntax : Number of formulae : 784 ( 388 unt; 0 typ; 0 def)
% Number of atoms : 5636 (1704 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 10906 (2497 ~;1572 |; 156 &;6497 @)
% ( 12 <=>; 172 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 109 ( 106 usr; 9 con; 0-6 aty)
% Number of variables : 1594 ( 0 ^;1573 !; 21 ?;1594 :)
% 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_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_SY138,type,
sK10_SY138: $i > $i ).
thf(tp_sK11_SY154,type,
sK11_SY154: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SY113,type,
sK5_SY113: $i > $i ).
thf(tp_sK6_SY146,type,
sK6_SY146: $i > $i ).
thf(tp_sK7_SY187,type,
sK7_SY187: $i ).
thf(tp_sK8_SY182,type,
sK8_SY182: $i > $i > $i ).
thf(tp_sK9_SY117,type,
sK9_SY117: $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_meet,type,
set_meet: $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_succ,type,
succ: $i > $i ).
thf(tp_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_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(6,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( join_commut @ A @ B @ C )
= ( join @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_lattices) ).
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/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(44,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(50,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(57,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(97,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(113,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(116,axiom,
? [A: $i] : ( join_semilatt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(120,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(123,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(124,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(125,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(126,axiom,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(127,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(129,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(133,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/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_1) ).
thf(139,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_ordinal2) ).
thf(140,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(141,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet_commut @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattices) ).
thf(145,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(146,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(147,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(148,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join_commut @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattices) ).
thf(150,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(151,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(153,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(154,axiom,
! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(155,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(156,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_mcart_1) ).
thf(157,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/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(160,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(161,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(163,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord1) ).
thf(164,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(165,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(166,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(167,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(168,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_mcart_1) ).
thf(169,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/sandbox2/benchmark/theBenchmark.p',dt_k1_lattices) ).
thf(170,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(171,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_enumset1) ).
thf(172,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_binop_1) ).
thf(173,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
thf(209,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( below @ A @ B @ C )
<=> ( ( join @ A @ B @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).
thf(214,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(230,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( join @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_join @ A ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattices) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( meet_commut @ A @ B @ C )
= ( meet_commut @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( join_commut @ A @ B @ C )
= ( join_commut @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_lattices) ).
thf(257,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(265,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_arytm_3) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(319,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(436,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
thf(443,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
thf(454,conjecture,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( below @ A @ B @ C )
& ( below @ A @ C @ B ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattices) ).
thf(455,negated_conjecture,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( below @ A @ B @ C )
& ( below @ A @ C @ B ) )
=> ( B = C ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[454]) ).
thf(456,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( below @ A @ B @ C )
& ( below @ A @ C @ B ) )
=> ( B = C ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[455]) ).
thf(457,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(458,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(459,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(460,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(461,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(462,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(463,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(464,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(465,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( join_commut @ A @ B @ C )
= ( join @ A @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(466,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(467,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(468,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(469,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(470,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(471,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)],[67]) ).
thf(472,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(473,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(474,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(475,plain,
( ( ? [A: $i] : ( join_semilatt_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(476,plain,
$true = $true,
inference(unfold_def,[status(thm)],[120]) ).
thf(477,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(478,plain,
$true = $true,
inference(unfold_def,[status(thm)],[123]) ).
thf(479,plain,
$true = $true,
inference(unfold_def,[status(thm)],[124]) ).
thf(480,plain,
( ( ! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(481,plain,
( ( ! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(482,plain,
$true = $true,
inference(unfold_def,[status(thm)],[127]) ).
thf(483,plain,
$true = $true,
inference(unfold_def,[status(thm)],[129]) ).
thf(484,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)],[131]) ).
thf(485,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)],[133]) ).
thf(486,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(487,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(488,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(489,plain,
$true = $true,
inference(unfold_def,[status(thm)],[139]) ).
thf(490,plain,
$true = $true,
inference(unfold_def,[status(thm)],[140]) ).
thf(491,plain,
$true = $true,
inference(unfold_def,[status(thm)],[141]) ).
thf(492,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(493,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet_commut @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(494,plain,
$true = $true,
inference(unfold_def,[status(thm)],[145]) ).
thf(495,plain,
$true = $true,
inference(unfold_def,[status(thm)],[146]) ).
thf(496,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(497,plain,
$true = $true,
inference(unfold_def,[status(thm)],[148]) ).
thf(498,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join_commut @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(499,plain,
$true = $true,
inference(unfold_def,[status(thm)],[150]) ).
thf(500,plain,
$true = $true,
inference(unfold_def,[status(thm)],[151]) ).
thf(501,plain,
$true = $true,
inference(unfold_def,[status(thm)],[153]) ).
thf(502,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(503,plain,
$true = $true,
inference(unfold_def,[status(thm)],[155]) ).
thf(504,plain,
$true = $true,
inference(unfold_def,[status(thm)],[156]) ).
thf(505,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)],[157]) ).
thf(506,plain,
$true = $true,
inference(unfold_def,[status(thm)],[160]) ).
thf(507,plain,
$true = $true,
inference(unfold_def,[status(thm)],[161]) ).
thf(508,plain,
$true = $true,
inference(unfold_def,[status(thm)],[163]) ).
thf(509,plain,
$true = $true,
inference(unfold_def,[status(thm)],[164]) ).
thf(510,plain,
$true = $true,
inference(unfold_def,[status(thm)],[165]) ).
thf(511,plain,
$true = $true,
inference(unfold_def,[status(thm)],[166]) ).
thf(512,plain,
$true = $true,
inference(unfold_def,[status(thm)],[167]) ).
thf(513,plain,
$true = $true,
inference(unfold_def,[status(thm)],[168]) ).
thf(514,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)],[169]) ).
thf(515,plain,
$true = $true,
inference(unfold_def,[status(thm)],[170]) ).
thf(516,plain,
$true = $true,
inference(unfold_def,[status(thm)],[171]) ).
thf(517,plain,
$true = $true,
inference(unfold_def,[status(thm)],[172]) ).
thf(518,plain,
$true = $true,
inference(unfold_def,[status(thm)],[173]) ).
thf(519,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(520,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( below @ A @ B @ C )
<=> ( ( join @ A @ B @ C )
= C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(521,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)],[214]) ).
thf(522,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( join @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_join @ A ) @ B @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(523,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( meet_commut @ A @ B @ C )
= ( meet_commut @ A @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(524,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( join_commut @ A @ B @ C )
= ( join_commut @ A @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(525,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(526,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(527,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(528,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(529,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(530,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(531,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(532,plain,
( ( ( ~ ( empty_carrier @ sK1_A )
& ( join_commutative @ sK1_A )
& ( join_semilatt_str @ sK1_A ) )
=> ! [SY111: $i] :
( ( element @ SY111 @ ( the_carrier @ sK1_A ) )
=> ! [SY112: $i] :
( ( element @ SY112 @ ( the_carrier @ sK1_A ) )
=> ( ( ( below @ sK1_A @ SY111 @ SY112 )
& ( below @ sK1_A @ SY112 @ SY111 ) )
=> ( SY111 = SY112 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[456]) ).
thf(533,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[532]) ).
thf(534,plain,
( ( join_commutative @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[532]) ).
thf(535,plain,
( ( join_semilatt_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[532]) ).
thf(536,plain,
( ( ! [SY111: $i] :
( ( element @ SY111 @ ( the_carrier @ sK1_A ) )
=> ! [SY112: $i] :
( ( element @ SY112 @ ( the_carrier @ sK1_A ) )
=> ( ( ( below @ sK1_A @ SY111 @ SY112 )
& ( below @ sK1_A @ SY112 @ SY111 ) )
=> ( SY111 = SY112 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[532]) ).
thf(537,plain,
( ( ~ ! [SY111: $i] :
( ( element @ SY111 @ ( the_carrier @ sK1_A ) )
=> ! [SY112: $i] :
( ( element @ SY112 @ ( the_carrier @ sK1_A ) )
=> ( ( ( below @ sK1_A @ SY111 @ SY112 )
& ( below @ sK1_A @ SY112 @ SY111 ) )
=> ( SY111 = SY112 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[536]) ).
thf(538,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(539,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(540,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(541,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(542,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(543,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(544,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[525]) ).
thf(545,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( join_commut @ A @ B @ C )
= ( join_commut @ A @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[524]) ).
thf(546,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( meet_commut @ A @ B @ C )
= ( meet_commut @ A @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(547,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( join @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_join @ A ) @ B @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[522]) ).
thf(548,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[521]) ).
thf(549,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( below @ A @ B @ C )
<=> ( ( join @ A @ B @ C )
= C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[520]) ).
thf(550,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(551,plain,
$true = $true,
inference(copy,[status(thm)],[518]) ).
thf(552,plain,
$true = $true,
inference(copy,[status(thm)],[517]) ).
thf(553,plain,
$true = $true,
inference(copy,[status(thm)],[516]) ).
thf(554,plain,
$true = $true,
inference(copy,[status(thm)],[515]) ).
thf(555,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)],[514]) ).
thf(556,plain,
$true = $true,
inference(copy,[status(thm)],[513]) ).
thf(557,plain,
$true = $true,
inference(copy,[status(thm)],[512]) ).
thf(558,plain,
$true = $true,
inference(copy,[status(thm)],[511]) ).
thf(559,plain,
$true = $true,
inference(copy,[status(thm)],[510]) ).
thf(560,plain,
$true = $true,
inference(copy,[status(thm)],[509]) ).
thf(561,plain,
$true = $true,
inference(copy,[status(thm)],[508]) ).
thf(562,plain,
$true = $true,
inference(copy,[status(thm)],[507]) ).
thf(563,plain,
$true = $true,
inference(copy,[status(thm)],[506]) ).
thf(564,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)],[505]) ).
thf(565,plain,
$true = $true,
inference(copy,[status(thm)],[504]) ).
thf(566,plain,
$true = $true,
inference(copy,[status(thm)],[503]) ).
thf(567,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(568,plain,
$true = $true,
inference(copy,[status(thm)],[501]) ).
thf(569,plain,
$true = $true,
inference(copy,[status(thm)],[500]) ).
thf(570,plain,
$true = $true,
inference(copy,[status(thm)],[499]) ).
thf(571,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join_commut @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(572,plain,
$true = $true,
inference(copy,[status(thm)],[497]) ).
thf(573,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[496]) ).
thf(574,plain,
$true = $true,
inference(copy,[status(thm)],[495]) ).
thf(575,plain,
$true = $true,
inference(copy,[status(thm)],[494]) ).
thf(576,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet_commut @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(577,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(578,plain,
$true = $true,
inference(copy,[status(thm)],[491]) ).
thf(579,plain,
$true = $true,
inference(copy,[status(thm)],[490]) ).
thf(580,plain,
$true = $true,
inference(copy,[status(thm)],[489]) ).
thf(581,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(582,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(583,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(584,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)],[485]) ).
thf(585,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(586,plain,
$true = $true,
inference(copy,[status(thm)],[483]) ).
thf(587,plain,
$true = $true,
inference(copy,[status(thm)],[482]) ).
thf(588,plain,
( ( ! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(589,plain,
( ( ! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(590,plain,
$true = $true,
inference(copy,[status(thm)],[479]) ).
thf(591,plain,
$true = $true,
inference(copy,[status(thm)],[478]) ).
thf(592,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(593,plain,
$true = $true,
inference(copy,[status(thm)],[476]) ).
thf(594,plain,
( ( ? [A: $i] : ( join_semilatt_str @ A ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(595,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(596,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(597,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(598,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)],[471]) ).
thf(599,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(600,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(601,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(602,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(603,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(604,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( join_commut @ A @ B @ C )
= ( join @ A @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(605,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(606,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(607,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(608,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(609,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(610,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(611,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(612,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(613,plain,
( ( join_semilatt_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(614,plain,
( ( join_commutative @ sK1_A )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(615,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(616,plain,
( ( ~ ! [SY111: $i] :
( ( element @ SY111 @ ( the_carrier @ sK1_A ) )
=> ! [SY112: $i] :
( ( element @ SY112 @ ( the_carrier @ sK1_A ) )
=> ( ( ( below @ sK1_A @ SY111 @ SY112 )
& ( below @ sK1_A @ SY112 @ SY111 ) )
=> ( SY111 = SY112 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(617,plain,
( ( ~ ! [SX0: $i] :
~ ( join_semilatt_str @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[594]) ).
thf(618,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[595]) ).
thf(619,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( join_semilatt_str @ SX0 ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( ~ ( ~ ( below @ SX0 @ SX1 @ SX2 )
| ( ( join @ SX0 @ SX1 @ SX2 )
= SX2 ) )
| ~ ( ( ( join @ SX0 @ SX1 @ SX2 )
!= SX2 )
| ( below @ SX0 @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(620,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( ( complements_of_subsets @ SX0 @ ( complements_of_subsets @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[598]) ).
thf(621,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) )
| ~ ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[601]) ).
thf(622,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(623,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ~ ( empty @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[612]) ).
thf(624,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( join_commutative @ SX0 ) )
| ~ ( join_semilatt_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) ) )
| ( element @ ( join_commut @ SX0 @ SX1 @ SX2 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(625,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( ( subset_difference @ SX0 @ SX1 @ SX2 )
= ( set_difference @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[607]) ).
thf(626,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( meet_commutative @ SX0 ) )
| ~ ( meet_semilatt_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) ) )
| ( ( meet_commut @ SX0 @ SX1 @ SX2 )
= ( meet_commut @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546]) ).
thf(627,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( ( meet_of_subsets @ SX0 @ SX1 )
= ( set_meet @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[606]) ).
thf(628,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SX1 )
| ~ ( epsilon_connected @ SX1 ) )
| ~ ( ordinal @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(629,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[602]) ).
thf(630,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ~ ( ~ ( in @ SX1 @ ( subset_complement @ SX0 @ SX2 ) )
| ~ ( in @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(631,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(632,plain,
( ( ! [SX0: $i] :
( ~ ( finite @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(633,plain,
( ( ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ~ ( ~ ( meet_semilatt_str @ SX0 )
| ~ ( join_semilatt_str @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(634,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(635,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( join_semilatt_str @ SX0 ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ( ( join @ SX0 @ SX1 @ SX2 )
= ( apply_binary_as_element @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) @ ( the_L_join @ SX0 ) @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[547]) ).
thf(636,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599]) ).
thf(637,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( element @ ( subset_complement @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(638,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( element @ ( relation_dom_as_subset @ SX0 @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[577]) ).
thf(639,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( meet_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583]) ).
thf(640,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1 != empty_set ) )
| ( ( complements_of_subsets @ SX0 @ SX1 )
!= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(641,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(642,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600]) ).
thf(643,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( join_semilatt_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) ) )
| ( element @ ( join @ SX0 @ SX1 @ SX2 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555]) ).
thf(644,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( element @ ( relation_rng_as_subset @ SX0 @ SX1 @ SX2 ) @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581]) ).
thf(645,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ~ ( empty @ SX0 )
| ~ ( ~ ( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( empty @ SX0 )
| ~ ( ~ ( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) )
| ~ ( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(646,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( join_commutative @ SX0 ) )
| ~ ( join_semilatt_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) ) )
| ( ( join_commut @ SX0 @ SX1 @ SX2 )
= ( join @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[604]) ).
thf(647,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(648,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( ( subset_complement @ SX0 @ ( subset_complement @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[597]) ).
thf(649,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( element @ ( subset_difference @ SX0 @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584]) ).
thf(650,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(651,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( union_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(652,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( below @ sK1_A @ SX0 @ SX1 )
| ~ ( below @ sK1_A @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616]) ).
thf(653,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( meet_commutative @ SX0 ) )
| ~ ( meet_semilatt_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) ) )
| ( element @ ( meet_commut @ SX0 @ SX1 @ SX2 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[576]) ).
thf(654,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( join_commutative @ SX0 ) )
| ~ ( join_semilatt_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) ) )
| ( ( join_commut @ SX0 @ SX1 @ SX2 )
= ( join_commut @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(655,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( element @ SX2 @ ( powerset @ ( cartesian_product2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[592]) ).
thf(656,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(657,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ( relation @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(658,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( ( union_of_subsets @ SX0 @ SX1 )
= ( union @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(659,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( meet_semilatt_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) ) )
| ( element @ ( meet @ SX0 @ SX1 @ SX2 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[564]) ).
thf(660,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 ) )
| ~ ( empty @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596]) ).
thf(661,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( ( subset_complement @ SX0 @ SX1 )
= ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(662,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( complements_of_subsets @ SX0 @ SX1 ) @ ( powerset @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[585]) ).
thf(663,plain,
( ( ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[588]) ).
thf(664,plain,
! [SV1: $i] :
( ( element @ ( cast_to_subset @ SV1 ) @ ( powerset @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(665,plain,
( ( empty_carrier @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(666,plain,
( ( ! [SX0: $i] :
~ ( join_semilatt_str @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(667,plain,
! [SV2: $i] :
( ( ~ ! [SY113: $i] :
~ ( element @ SY113 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(668,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_semilatt_str @ SV3 ) )
| ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV3 ) )
| ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ SV3 ) )
| ~ ( ~ ( ~ ( below @ SV3 @ SY114 @ SY115 )
| ( ( join @ SV3 @ SY114 @ SY115 )
= SY115 ) )
| ~ ( ( ( join @ SV3 @ SY114 @ SY115 )
!= SY115 )
| ( below @ SV3 @ SY114 @ SY115 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(669,plain,
! [SV4: $i] :
( ( ! [SY116: $i] :
( ~ ( element @ SY116 @ ( powerset @ ( powerset @ SV4 ) ) )
| ( ( complements_of_subsets @ SV4 @ ( complements_of_subsets @ SV4 @ SY116 ) )
= SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(670,plain,
! [SV5: $i] :
( ( ~ ~ ( empty @ SV5 )
| ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY117 @ ( powerset @ SV5 ) )
| ~ ~ ( empty @ SY117 ) )
| ~ ( finite @ SY117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(671,plain,
! [SV6: $i] :
( ( ! [SY118: $i,SY119: $i] :
( ~ ~ ( ~ ( in @ SV6 @ SY118 )
| ~ ( element @ SY118 @ ( powerset @ SY119 ) ) )
| ( element @ SV6 @ SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(672,plain,
! [SV7: $i] :
( ( ! [SY120: $i,SY121: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV7 @ SY120 )
| ~ ( element @ SY120 @ ( powerset @ SY121 ) ) )
| ~ ( empty @ SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(673,plain,
! [SV8: $i] :
( ( ! [SY122: $i,SY123: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SY122 @ ( the_carrier @ SV8 ) ) )
| ~ ( element @ SY123 @ ( the_carrier @ SV8 ) ) )
| ( element @ ( join_commut @ SV8 @ SY122 @ SY123 ) @ ( the_carrier @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(674,plain,
! [SV9: $i] :
( ( ! [SY124: $i,SY125: $i] :
( ~ ~ ( ~ ( element @ SY124 @ ( powerset @ SV9 ) )
| ~ ( element @ SY125 @ ( powerset @ SV9 ) ) )
| ( ( subset_difference @ SV9 @ SY124 @ SY125 )
= ( set_difference @ SY124 @ SY125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(675,plain,
! [SV10: $i] :
( ( ! [SY126: $i,SY127: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( meet_commutative @ SV10 ) )
| ~ ( meet_semilatt_str @ SV10 ) )
| ~ ( element @ SY126 @ ( the_carrier @ SV10 ) ) )
| ~ ( element @ SY127 @ ( the_carrier @ SV10 ) ) )
| ( ( meet_commut @ SV10 @ SY126 @ SY127 )
= ( meet_commut @ SV10 @ SY127 @ SY126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(676,plain,
! [SV11: $i] :
( ( ! [SY128: $i] :
( ~ ( element @ SY128 @ ( powerset @ ( powerset @ SV11 ) ) )
| ( ( meet_of_subsets @ SV11 @ SY128 )
= ( set_meet @ SY128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(677,plain,
! [SV12: $i] :
( ( ~ ( ordinal @ SV12 )
| ! [SY129: $i] :
( ~ ( element @ SY129 @ SV12 )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SY129 )
| ~ ( epsilon_connected @ SY129 ) )
| ~ ( ordinal @ SY129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(678,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(679,plain,
! [SV13: $i] :
( ( ! [SY130: $i,SY131: $i] :
( ~ ( element @ SY131 @ ( powerset @ SV13 ) )
| ~ ~ ( ~ ( in @ SY130 @ ( subset_complement @ SV13 @ SY131 ) )
| ~ ( in @ SY130 @ SY131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(680,plain,
! [SV14: $i] :
( ( ! [SY132: $i] :
( ~ ( in @ SV14 @ SY132 )
| ( element @ SV14 @ SY132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(681,plain,
! [SV15: $i] :
( ( ~ ( finite @ SV15 )
| ! [SY133: $i] :
( ~ ( element @ SY133 @ ( powerset @ SV15 ) )
| ( finite @ SY133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(682,plain,
! [SV16: $i] :
( ( ~ ( latt_str @ SV16 )
| ~ ( ~ ( meet_semilatt_str @ SV16 )
| ~ ( join_semilatt_str @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(683,plain,
! [SV17: $i] :
( ( ! [SY134: $i] :
( ~ ( element @ SY134 @ ( powerset @ SV17 ) )
| ! [SY135: $i] :
( ~ ( in @ SY135 @ SY134 )
| ( in @ SY135 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(684,plain,
! [SV18: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV18 )
| ~ ( join_semilatt_str @ SV18 ) )
| ! [SY136: $i] :
( ~ ( element @ SY136 @ ( the_carrier @ SV18 ) )
| ! [SY137: $i] :
( ~ ( element @ SY137 @ ( the_carrier @ SV18 ) )
| ( ( join @ SV18 @ SY136 @ SY137 )
= ( apply_binary_as_element @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_L_join @ SV18 ) @ SY136 @ SY137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(685,plain,
! [SV19: $i] :
( ( ~ ~ ( empty @ SV19 )
| ~ ! [SY138: $i] :
~ ~ ( ~ ( element @ SY138 @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ SY138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(686,plain,
! [SV20: $i] :
( ( ! [SY139: $i] :
( ~ ( element @ SY139 @ ( powerset @ SV20 ) )
| ( element @ ( subset_complement @ SV20 @ SY139 ) @ ( powerset @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(687,plain,
! [SV21: $i] :
( ( ! [SY140: $i,SY141: $i] :
( ~ ( relation_of2 @ SY141 @ SV21 @ SY140 )
| ( element @ ( relation_dom_as_subset @ SV21 @ SY140 @ SY141 ) @ ( powerset @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(688,plain,
! [SV22: $i] :
( ( ! [SY142: $i] :
( ~ ( element @ SY142 @ ( powerset @ ( powerset @ SV22 ) ) )
| ( element @ ( meet_of_subsets @ SV22 @ SY142 ) @ ( powerset @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(689,plain,
! [SV23: $i] :
( ( ! [SY143: $i] :
( ~ ( element @ SY143 @ ( powerset @ ( powerset @ SV23 ) ) )
| ~ ~ ( ~ ( ( SY143 != empty_set ) )
| ( ( complements_of_subsets @ SV23 @ SY143 )
!= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(690,plain,
! [SV24: $i] :
( ( ! [SY144: $i] :
( ~ ! [SY145: $i] :
( ~ ( in @ SY145 @ SV24 )
| ( in @ SY145 @ SY144 ) )
| ( element @ SV24 @ ( powerset @ SY144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(691,plain,
! [SV25: $i] :
( ( ~ ! [SY146: $i] :
~ ~ ( ~ ( element @ SY146 @ ( powerset @ SV25 ) )
| ~ ( empty @ SY146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(692,plain,
! [SV26: $i] :
( ( ! [SY147: $i,SY148: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV26 )
| ~ ( join_semilatt_str @ SV26 ) )
| ~ ( element @ SY147 @ ( the_carrier @ SV26 ) ) )
| ~ ( element @ SY148 @ ( the_carrier @ SV26 ) ) )
| ( element @ ( join @ SV26 @ SY147 @ SY148 ) @ ( the_carrier @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(693,plain,
! [SV27: $i] :
( ( ! [SY149: $i,SY150: $i] :
( ~ ( relation_of2 @ SY150 @ SV27 @ SY149 )
| ( element @ ( relation_rng_as_subset @ SV27 @ SY149 @ SY150 ) @ ( powerset @ SY149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(694,plain,
! [SV28: $i] :
( ( ! [SY151: $i] :
~ ( ~ ( ~ ~ ( empty @ SV28 )
| ~ ( ~ ( ~ ( element @ SY151 @ SV28 )
| ( in @ SY151 @ SV28 ) )
| ~ ( ~ ( in @ SY151 @ SV28 )
| ( element @ SY151 @ SV28 ) ) ) )
| ~ ( ~ ( empty @ SV28 )
| ~ ( ~ ( ~ ( element @ SY151 @ SV28 )
| ( empty @ SY151 ) )
| ~ ( ~ ( empty @ SY151 )
| ( element @ SY151 @ SV28 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(695,plain,
! [SV29: $i] :
( ( ! [SY152: $i,SY153: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV29 )
| ~ ( join_commutative @ SV29 ) )
| ~ ( join_semilatt_str @ SV29 ) )
| ~ ( element @ SY152 @ ( the_carrier @ SV29 ) ) )
| ~ ( element @ SY153 @ ( the_carrier @ SV29 ) ) )
| ( ( join_commut @ SV29 @ SY152 @ SY153 )
= ( join @ SV29 @ SY152 @ SY153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(696,plain,
! [SV30: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV30 )
| ~ ( one_sorted_str @ SV30 ) )
| ~ ! [SY154: $i] :
~ ~ ( ~ ( element @ SY154 @ ( powerset @ ( the_carrier @ SV30 ) ) )
| ~ ~ ( empty @ SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(697,plain,
! [SV31: $i] :
( ( ! [SY155: $i] :
( ~ ( element @ SY155 @ ( powerset @ SV31 ) )
| ( ( subset_complement @ SV31 @ ( subset_complement @ SV31 @ SY155 ) )
= SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(698,plain,
! [SV32: $i] :
( ( ! [SY156: $i,SY157: $i] :
( ~ ~ ( ~ ( element @ SY156 @ ( powerset @ SV32 ) )
| ~ ( element @ SY157 @ ( powerset @ SV32 ) ) )
| ( element @ ( subset_difference @ SV32 @ SY156 @ SY157 ) @ ( powerset @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(699,plain,
! [SV33: $i] :
( ( ! [SY158: $i] :
( ~ ( element @ SV33 @ SY158 )
| ( empty @ SY158 )
| ( in @ SV33 @ SY158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(700,plain,
! [SV34: $i] :
( ( ! [SY159: $i] :
( ~ ( element @ SY159 @ ( powerset @ ( powerset @ SV34 ) ) )
| ( element @ ( union_of_subsets @ SV34 @ SY159 ) @ ( powerset @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(701,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( below @ sK1_A @ SX0 @ SX1 )
| ~ ( below @ sK1_A @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(702,plain,
! [SV35: $i] :
( ( ! [SY160: $i,SY161: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV35 )
| ~ ( meet_commutative @ SV35 ) )
| ~ ( meet_semilatt_str @ SV35 ) )
| ~ ( element @ SY160 @ ( the_carrier @ SV35 ) ) )
| ~ ( element @ SY161 @ ( the_carrier @ SV35 ) ) )
| ( element @ ( meet_commut @ SV35 @ SY160 @ SY161 ) @ ( the_carrier @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(703,plain,
! [SV36: $i] :
( ( ! [SY162: $i,SY163: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV36 )
| ~ ( join_commutative @ SV36 ) )
| ~ ( join_semilatt_str @ SV36 ) )
| ~ ( element @ SY162 @ ( the_carrier @ SV36 ) ) )
| ~ ( element @ SY163 @ ( the_carrier @ SV36 ) ) )
| ( ( join_commut @ SV36 @ SY162 @ SY163 )
= ( join_commut @ SV36 @ SY163 @ SY162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(704,plain,
! [SV37: $i] :
( ( ! [SY164: $i,SY165: $i] :
( ~ ( relation_of2_as_subset @ SY165 @ SV37 @ SY164 )
| ( element @ SY165 @ ( powerset @ ( cartesian_product2 @ SV37 @ SY164 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(705,plain,
! [SV38: $i] :
( ( ! [SY166: $i] :
~ ( ~ ( ~ ( element @ SV38 @ ( powerset @ SY166 ) )
| ( subset @ SV38 @ SY166 ) )
| ~ ( ~ ( subset @ SV38 @ SY166 )
| ( element @ SV38 @ ( powerset @ SY166 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(706,plain,
! [SV39: $i] :
( ( ! [SY167: $i,SY168: $i] :
( ~ ( element @ SY168 @ ( powerset @ ( cartesian_product2 @ SV39 @ SY167 ) ) )
| ( relation @ SY168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(707,plain,
! [SV40: $i] :
( ( ! [SY169: $i] :
( ~ ( element @ SY169 @ ( powerset @ ( powerset @ SV40 ) ) )
| ( ( union_of_subsets @ SV40 @ SY169 )
= ( union @ SY169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(708,plain,
! [SV41: $i] :
( ( ! [SY170: $i,SY171: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV41 )
| ~ ( meet_semilatt_str @ SV41 ) )
| ~ ( element @ SY170 @ ( the_carrier @ SV41 ) ) )
| ~ ( element @ SY171 @ ( the_carrier @ SV41 ) ) )
| ( element @ ( meet @ SV41 @ SY170 @ SY171 ) @ ( the_carrier @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(709,plain,
! [SV42: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV42 )
| ~ ( one_sorted_str @ SV42 ) )
| ~ ( empty @ ( the_carrier @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(710,plain,
! [SV43: $i] :
( ( ! [SY172: $i] :
( ~ ( element @ SY172 @ ( powerset @ SV43 ) )
| ( ( subset_complement @ SV43 @ SY172 )
= ( set_difference @ SV43 @ SY172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(711,plain,
! [SV44: $i] :
( ( ! [SY173: $i] :
( ~ ( element @ SY173 @ ( powerset @ ( powerset @ SV44 ) ) )
| ( element @ ( complements_of_subsets @ SV44 @ SY173 ) @ ( powerset @ ( powerset @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(712,plain,
! [SV45: $i] :
( ( ~ ( join_semilatt_str @ SV45 )
| ( one_sorted_str @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(713,plain,
( ( ~ ( join_semilatt_str @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[666]) ).
thf(714,plain,
! [SV2: $i] :
( ( ! [SY113: $i] :
~ ( element @ SY113 @ SV2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(715,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_semilatt_str @ SV3 ) ) )
= $true )
| ( ( ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV3 ) )
| ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ SV3 ) )
| ~ ( ~ ( ~ ( below @ SV3 @ SY114 @ SY115 )
| ( ( join @ SV3 @ SY114 @ SY115 )
= SY115 ) )
| ~ ( ( ( join @ SV3 @ SY114 @ SY115 )
!= SY115 )
| ( below @ SV3 @ SY114 @ SY115 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(716,plain,
! [SV4: $i,SV46: $i] :
( ( ~ ( element @ SV46 @ ( powerset @ ( powerset @ SV4 ) ) )
| ( ( complements_of_subsets @ SV4 @ ( complements_of_subsets @ SV4 @ SV46 ) )
= SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(717,plain,
! [SV5: $i] :
( ( ( ~ ~ ( empty @ SV5 ) )
= $true )
| ( ( ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY117 @ ( powerset @ SV5 ) )
| ~ ~ ( empty @ SY117 ) )
| ~ ( finite @ SY117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(718,plain,
! [SV47: $i,SV6: $i] :
( ( ! [SY174: $i] :
( ~ ~ ( ~ ( in @ SV6 @ SV47 )
| ~ ( element @ SV47 @ ( powerset @ SY174 ) ) )
| ( element @ SV6 @ SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(719,plain,
! [SV48: $i,SV7: $i] :
( ( ! [SY175: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV7 @ SV48 )
| ~ ( element @ SV48 @ ( powerset @ SY175 ) ) )
| ~ ( empty @ SY175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(720,plain,
! [SV49: $i,SV8: $i] :
( ( ! [SY176: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) )
| ~ ( element @ SY176 @ ( the_carrier @ SV8 ) ) )
| ( element @ ( join_commut @ SV8 @ SV49 @ SY176 ) @ ( the_carrier @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(721,plain,
! [SV9: $i,SV50: $i] :
( ( ! [SY177: $i] :
( ~ ~ ( ~ ( element @ SV50 @ ( powerset @ SV9 ) )
| ~ ( element @ SY177 @ ( powerset @ SV9 ) ) )
| ( ( subset_difference @ SV9 @ SV50 @ SY177 )
= ( set_difference @ SV50 @ SY177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(722,plain,
! [SV51: $i,SV10: $i] :
( ( ! [SY178: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( meet_commutative @ SV10 ) )
| ~ ( meet_semilatt_str @ SV10 ) )
| ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) )
| ~ ( element @ SY178 @ ( the_carrier @ SV10 ) ) )
| ( ( meet_commut @ SV10 @ SV51 @ SY178 )
= ( meet_commut @ SV10 @ SY178 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(723,plain,
! [SV11: $i,SV52: $i] :
( ( ~ ( element @ SV52 @ ( powerset @ ( powerset @ SV11 ) ) )
| ( ( meet_of_subsets @ SV11 @ SV52 )
= ( set_meet @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(724,plain,
! [SV12: $i] :
( ( ( ~ ( ordinal @ SV12 ) )
= $true )
| ( ( ! [SY129: $i] :
( ~ ( element @ SY129 @ SV12 )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SY129 )
| ~ ( epsilon_connected @ SY129 ) )
| ~ ( ordinal @ SY129 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(725,plain,
( ( ~ ~ ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[678]) ).
thf(726,plain,
! [SV53: $i,SV13: $i] :
( ( ! [SY179: $i] :
( ~ ( element @ SY179 @ ( powerset @ SV13 ) )
| ~ ~ ( ~ ( in @ SV53 @ ( subset_complement @ SV13 @ SY179 ) )
| ~ ( in @ SV53 @ SY179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(727,plain,
! [SV54: $i,SV14: $i] :
( ( ~ ( in @ SV14 @ SV54 )
| ( element @ SV14 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(728,plain,
! [SV15: $i] :
( ( ( ~ ( finite @ SV15 ) )
= $true )
| ( ( ! [SY133: $i] :
( ~ ( element @ SY133 @ ( powerset @ SV15 ) )
| ( finite @ SY133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(729,plain,
! [SV16: $i] :
( ( ( ~ ( latt_str @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( meet_semilatt_str @ SV16 )
| ~ ( join_semilatt_str @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(730,plain,
! [SV17: $i,SV55: $i] :
( ( ~ ( element @ SV55 @ ( powerset @ SV17 ) )
| ! [SY180: $i] :
( ~ ( in @ SY180 @ SV55 )
| ( in @ SY180 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(731,plain,
! [SV18: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV18 )
| ~ ( join_semilatt_str @ SV18 ) ) )
= $true )
| ( ( ! [SY136: $i] :
( ~ ( element @ SY136 @ ( the_carrier @ SV18 ) )
| ! [SY137: $i] :
( ~ ( element @ SY137 @ ( the_carrier @ SV18 ) )
| ( ( join @ SV18 @ SY136 @ SY137 )
= ( apply_binary_as_element @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_L_join @ SV18 ) @ SY136 @ SY137 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[684]) ).
thf(732,plain,
! [SV19: $i] :
( ( ( ~ ~ ( empty @ SV19 ) )
= $true )
| ( ( ~ ! [SY138: $i] :
~ ~ ( ~ ( element @ SY138 @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ SY138 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[685]) ).
thf(733,plain,
! [SV20: $i,SV56: $i] :
( ( ~ ( element @ SV56 @ ( powerset @ SV20 ) )
| ( element @ ( subset_complement @ SV20 @ SV56 ) @ ( powerset @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(734,plain,
! [SV57: $i,SV21: $i] :
( ( ! [SY181: $i] :
( ~ ( relation_of2 @ SY181 @ SV21 @ SV57 )
| ( element @ ( relation_dom_as_subset @ SV21 @ SV57 @ SY181 ) @ ( powerset @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(735,plain,
! [SV22: $i,SV58: $i] :
( ( ~ ( element @ SV58 @ ( powerset @ ( powerset @ SV22 ) ) )
| ( element @ ( meet_of_subsets @ SV22 @ SV58 ) @ ( powerset @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(736,plain,
! [SV23: $i,SV59: $i] :
( ( ~ ( element @ SV59 @ ( powerset @ ( powerset @ SV23 ) ) )
| ~ ~ ( ~ ( ( SV59 != empty_set ) )
| ( ( complements_of_subsets @ SV23 @ SV59 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(737,plain,
! [SV60: $i,SV24: $i] :
( ( ~ ! [SY182: $i] :
( ~ ( in @ SY182 @ SV24 )
| ( in @ SY182 @ SV60 ) )
| ( element @ SV24 @ ( powerset @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(738,plain,
! [SV25: $i] :
( ( ! [SY146: $i] :
~ ~ ( ~ ( element @ SY146 @ ( powerset @ SV25 ) )
| ~ ( empty @ SY146 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(739,plain,
! [SV61: $i,SV26: $i] :
( ( ! [SY183: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV26 )
| ~ ( join_semilatt_str @ SV26 ) )
| ~ ( element @ SV61 @ ( the_carrier @ SV26 ) ) )
| ~ ( element @ SY183 @ ( the_carrier @ SV26 ) ) )
| ( element @ ( join @ SV26 @ SV61 @ SY183 ) @ ( the_carrier @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(740,plain,
! [SV62: $i,SV27: $i] :
( ( ! [SY184: $i] :
( ~ ( relation_of2 @ SY184 @ SV27 @ SV62 )
| ( element @ ( relation_rng_as_subset @ SV27 @ SV62 @ SY184 ) @ ( powerset @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(741,plain,
! [SV63: $i,SV28: $i] :
( ( ~ ( ~ ( ~ ~ ( empty @ SV28 )
| ~ ( ~ ( ~ ( element @ SV63 @ SV28 )
| ( in @ SV63 @ SV28 ) )
| ~ ( ~ ( in @ SV63 @ SV28 )
| ( element @ SV63 @ SV28 ) ) ) )
| ~ ( ~ ( empty @ SV28 )
| ~ ( ~ ( ~ ( element @ SV63 @ SV28 )
| ( empty @ SV63 ) )
| ~ ( ~ ( empty @ SV63 )
| ( element @ SV63 @ SV28 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(742,plain,
! [SV64: $i,SV29: $i] :
( ( ! [SY185: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV29 )
| ~ ( join_commutative @ SV29 ) )
| ~ ( join_semilatt_str @ SV29 ) )
| ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) )
| ~ ( element @ SY185 @ ( the_carrier @ SV29 ) ) )
| ( ( join_commut @ SV29 @ SV64 @ SY185 )
= ( join @ SV29 @ SV64 @ SY185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(743,plain,
! [SV30: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV30 )
| ~ ( one_sorted_str @ SV30 ) ) )
= $true )
| ( ( ~ ! [SY154: $i] :
~ ~ ( ~ ( element @ SY154 @ ( powerset @ ( the_carrier @ SV30 ) ) )
| ~ ~ ( empty @ SY154 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(744,plain,
! [SV31: $i,SV65: $i] :
( ( ~ ( element @ SV65 @ ( powerset @ SV31 ) )
| ( ( subset_complement @ SV31 @ ( subset_complement @ SV31 @ SV65 ) )
= SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(745,plain,
! [SV32: $i,SV66: $i] :
( ( ! [SY186: $i] :
( ~ ~ ( ~ ( element @ SV66 @ ( powerset @ SV32 ) )
| ~ ( element @ SY186 @ ( powerset @ SV32 ) ) )
| ( element @ ( subset_difference @ SV32 @ SV66 @ SY186 ) @ ( powerset @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(746,plain,
! [SV67: $i,SV33: $i] :
( ( ~ ( element @ SV33 @ SV67 )
| ( empty @ SV67 )
| ( in @ SV33 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(747,plain,
! [SV34: $i,SV68: $i] :
( ( ~ ( element @ SV68 @ ( powerset @ ( powerset @ SV34 ) ) )
| ( element @ ( union_of_subsets @ SV34 @ SV68 ) @ ( powerset @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(748,plain,
( ( ~ ( element @ sK4_SX0 @ ( the_carrier @ sK1_A ) )
| ! [SY187: $i] :
( ~ ( element @ SY187 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( below @ sK1_A @ sK4_SX0 @ SY187 )
| ~ ( below @ sK1_A @ SY187 @ sK4_SX0 ) )
| ( sK4_SX0 = SY187 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[701]) ).
thf(749,plain,
! [SV69: $i,SV35: $i] :
( ( ! [SY188: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV35 )
| ~ ( meet_commutative @ SV35 ) )
| ~ ( meet_semilatt_str @ SV35 ) )
| ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) )
| ~ ( element @ SY188 @ ( the_carrier @ SV35 ) ) )
| ( element @ ( meet_commut @ SV35 @ SV69 @ SY188 ) @ ( the_carrier @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(750,plain,
! [SV70: $i,SV36: $i] :
( ( ! [SY189: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV36 )
| ~ ( join_commutative @ SV36 ) )
| ~ ( join_semilatt_str @ SV36 ) )
| ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) )
| ~ ( element @ SY189 @ ( the_carrier @ SV36 ) ) )
| ( ( join_commut @ SV36 @ SV70 @ SY189 )
= ( join_commut @ SV36 @ SY189 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(751,plain,
! [SV71: $i,SV37: $i] :
( ( ! [SY190: $i] :
( ~ ( relation_of2_as_subset @ SY190 @ SV37 @ SV71 )
| ( element @ SY190 @ ( powerset @ ( cartesian_product2 @ SV37 @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(752,plain,
! [SV72: $i,SV38: $i] :
( ( ~ ( ~ ( ~ ( element @ SV38 @ ( powerset @ SV72 ) )
| ( subset @ SV38 @ SV72 ) )
| ~ ( ~ ( subset @ SV38 @ SV72 )
| ( element @ SV38 @ ( powerset @ SV72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(753,plain,
! [SV73: $i,SV39: $i] :
( ( ! [SY191: $i] :
( ~ ( element @ SY191 @ ( powerset @ ( cartesian_product2 @ SV39 @ SV73 ) ) )
| ( relation @ SY191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(754,plain,
! [SV40: $i,SV74: $i] :
( ( ~ ( element @ SV74 @ ( powerset @ ( powerset @ SV40 ) ) )
| ( ( union_of_subsets @ SV40 @ SV74 )
= ( union @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(755,plain,
! [SV75: $i,SV41: $i] :
( ( ! [SY192: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV41 )
| ~ ( meet_semilatt_str @ SV41 ) )
| ~ ( element @ SV75 @ ( the_carrier @ SV41 ) ) )
| ~ ( element @ SY192 @ ( the_carrier @ SV41 ) ) )
| ( element @ ( meet @ SV41 @ SV75 @ SY192 ) @ ( the_carrier @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(756,plain,
! [SV42: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV42 )
| ~ ( one_sorted_str @ SV42 ) ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(757,plain,
! [SV43: $i,SV76: $i] :
( ( ~ ( element @ SV76 @ ( powerset @ SV43 ) )
| ( ( subset_complement @ SV43 @ SV76 )
= ( set_difference @ SV43 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(758,plain,
! [SV44: $i,SV77: $i] :
( ( ~ ( element @ SV77 @ ( powerset @ ( powerset @ SV44 ) ) )
| ( element @ ( complements_of_subsets @ SV44 @ SV77 ) @ ( powerset @ ( powerset @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(759,plain,
! [SV45: $i] :
( ( ( ~ ( join_semilatt_str @ SV45 ) )
= $true )
| ( ( one_sorted_str @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[712]) ).
thf(760,plain,
( ( join_semilatt_str @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[713]) ).
thf(761,plain,
! [SV2: $i] :
( ( ~ ( element @ ( sK5_SY113 @ SV2 ) @ SV2 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[714]) ).
thf(762,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_semilatt_str @ SV3 ) ) )
= $false )
| ( ( ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV3 ) )
| ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ SV3 ) )
| ~ ( ~ ( ~ ( below @ SV3 @ SY114 @ SY115 )
| ( ( join @ SV3 @ SY114 @ SY115 )
= SY115 ) )
| ~ ( ( ( join @ SV3 @ SY114 @ SY115 )
!= SY115 )
| ( below @ SV3 @ SY114 @ SY115 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(763,plain,
! [SV4: $i,SV46: $i] :
( ( ( ~ ( element @ SV46 @ ( powerset @ ( powerset @ SV4 ) ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV4 @ ( complements_of_subsets @ SV4 @ SV46 ) )
= SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[716]) ).
thf(764,plain,
! [SV5: $i] :
( ( ( ~ ( empty @ SV5 ) )
= $false )
| ( ( ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY117 @ ( powerset @ SV5 ) )
| ~ ~ ( empty @ SY117 ) )
| ~ ( finite @ SY117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(765,plain,
! [SV78: $i,SV47: $i,SV6: $i] :
( ( ~ ~ ( ~ ( in @ SV6 @ SV47 )
| ~ ( element @ SV47 @ ( powerset @ SV78 ) ) )
| ( element @ SV6 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(766,plain,
! [SV79: $i,SV48: $i,SV7: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV7 @ SV48 )
| ~ ( element @ SV48 @ ( powerset @ SV79 ) ) )
| ~ ( empty @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(767,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) )
| ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) )
| ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(768,plain,
! [SV81: $i,SV9: $i,SV50: $i] :
( ( ~ ~ ( ~ ( element @ SV50 @ ( powerset @ SV9 ) )
| ~ ( element @ SV81 @ ( powerset @ SV9 ) ) )
| ( ( subset_difference @ SV9 @ SV50 @ SV81 )
= ( set_difference @ SV50 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(769,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( meet_commutative @ SV10 ) )
| ~ ( meet_semilatt_str @ SV10 ) )
| ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) )
| ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) )
| ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(770,plain,
! [SV11: $i,SV52: $i] :
( ( ( ~ ( element @ SV52 @ ( powerset @ ( powerset @ SV11 ) ) ) )
= $true )
| ( ( ( meet_of_subsets @ SV11 @ SV52 )
= ( set_meet @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[723]) ).
thf(771,plain,
! [SV12: $i] :
( ( ( ordinal @ SV12 )
= $false )
| ( ( ! [SY129: $i] :
( ~ ( element @ SY129 @ SV12 )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SY129 )
| ~ ( epsilon_connected @ SY129 ) )
| ~ ( ordinal @ SY129 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(772,plain,
( ( ~ ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[725]) ).
thf(773,plain,
! [SV53: $i,SV13: $i,SV83: $i] :
( ( ~ ( element @ SV83 @ ( powerset @ SV13 ) )
| ~ ~ ( ~ ( in @ SV53 @ ( subset_complement @ SV13 @ SV83 ) )
| ~ ( in @ SV53 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(774,plain,
! [SV54: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV54 ) )
= $true )
| ( ( element @ SV14 @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(775,plain,
! [SV15: $i] :
( ( ( finite @ SV15 )
= $false )
| ( ( ! [SY133: $i] :
( ~ ( element @ SY133 @ ( powerset @ SV15 ) )
| ( finite @ SY133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(776,plain,
! [SV16: $i] :
( ( ( latt_str @ SV16 )
= $false )
| ( ( ~ ( ~ ( meet_semilatt_str @ SV16 )
| ~ ( join_semilatt_str @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(777,plain,
! [SV17: $i,SV55: $i] :
( ( ( ~ ( element @ SV55 @ ( powerset @ SV17 ) ) )
= $true )
| ( ( ! [SY180: $i] :
( ~ ( in @ SY180 @ SV55 )
| ( in @ SY180 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(778,plain,
! [SV18: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV18 )
| ~ ( join_semilatt_str @ SV18 ) ) )
= $false )
| ( ( ! [SY136: $i] :
( ~ ( element @ SY136 @ ( the_carrier @ SV18 ) )
| ! [SY137: $i] :
( ~ ( element @ SY137 @ ( the_carrier @ SV18 ) )
| ( ( join @ SV18 @ SY136 @ SY137 )
= ( apply_binary_as_element @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_L_join @ SV18 ) @ SY136 @ SY137 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(779,plain,
! [SV19: $i] :
( ( ( ~ ( empty @ SV19 ) )
= $false )
| ( ( ~ ! [SY138: $i] :
~ ~ ( ~ ( element @ SY138 @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ SY138 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(780,plain,
! [SV20: $i,SV56: $i] :
( ( ( ~ ( element @ SV56 @ ( powerset @ SV20 ) ) )
= $true )
| ( ( element @ ( subset_complement @ SV20 @ SV56 ) @ ( powerset @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(781,plain,
! [SV57: $i,SV21: $i,SV84: $i] :
( ( ~ ( relation_of2 @ SV84 @ SV21 @ SV57 )
| ( element @ ( relation_dom_as_subset @ SV21 @ SV57 @ SV84 ) @ ( powerset @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(782,plain,
! [SV22: $i,SV58: $i] :
( ( ( ~ ( element @ SV58 @ ( powerset @ ( powerset @ SV22 ) ) ) )
= $true )
| ( ( element @ ( meet_of_subsets @ SV22 @ SV58 ) @ ( powerset @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(783,plain,
! [SV23: $i,SV59: $i] :
( ( ( ~ ( element @ SV59 @ ( powerset @ ( powerset @ SV23 ) ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV59 != empty_set ) )
| ( ( complements_of_subsets @ SV23 @ SV59 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(784,plain,
! [SV60: $i,SV24: $i] :
( ( ( ~ ! [SY182: $i] :
( ~ ( in @ SY182 @ SV24 )
| ( in @ SY182 @ SV60 ) ) )
= $true )
| ( ( element @ SV24 @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(785,plain,
! [SV25: $i] :
( ( ~ ~ ( ~ ( element @ ( sK6_SY146 @ SV25 ) @ ( powerset @ SV25 ) )
| ~ ( empty @ ( sK6_SY146 @ SV25 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[738]) ).
thf(786,plain,
! [SV85: $i,SV61: $i,SV26: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV26 )
| ~ ( join_semilatt_str @ SV26 ) )
| ~ ( element @ SV61 @ ( the_carrier @ SV26 ) ) )
| ~ ( element @ SV85 @ ( the_carrier @ SV26 ) ) )
| ( element @ ( join @ SV26 @ SV61 @ SV85 ) @ ( the_carrier @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(787,plain,
! [SV62: $i,SV27: $i,SV86: $i] :
( ( ~ ( relation_of2 @ SV86 @ SV27 @ SV62 )
| ( element @ ( relation_rng_as_subset @ SV27 @ SV62 @ SV86 ) @ ( powerset @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(788,plain,
! [SV63: $i,SV28: $i] :
( ( ~ ( ~ ~ ( empty @ SV28 )
| ~ ( ~ ( ~ ( element @ SV63 @ SV28 )
| ( in @ SV63 @ SV28 ) )
| ~ ( ~ ( in @ SV63 @ SV28 )
| ( element @ SV63 @ SV28 ) ) ) )
| ~ ( ~ ( empty @ SV28 )
| ~ ( ~ ( ~ ( element @ SV63 @ SV28 )
| ( empty @ SV63 ) )
| ~ ( ~ ( empty @ SV63 )
| ( element @ SV63 @ SV28 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(789,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV29 )
| ~ ( join_commutative @ SV29 ) )
| ~ ( join_semilatt_str @ SV29 ) )
| ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) )
| ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) )
| ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(790,plain,
! [SV30: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV30 )
| ~ ( one_sorted_str @ SV30 ) ) )
= $false )
| ( ( ~ ! [SY154: $i] :
~ ~ ( ~ ( element @ SY154 @ ( powerset @ ( the_carrier @ SV30 ) ) )
| ~ ~ ( empty @ SY154 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(791,plain,
! [SV31: $i,SV65: $i] :
( ( ( ~ ( element @ SV65 @ ( powerset @ SV31 ) ) )
= $true )
| ( ( ( subset_complement @ SV31 @ ( subset_complement @ SV31 @ SV65 ) )
= SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(792,plain,
! [SV88: $i,SV32: $i,SV66: $i] :
( ( ~ ~ ( ~ ( element @ SV66 @ ( powerset @ SV32 ) )
| ~ ( element @ SV88 @ ( powerset @ SV32 ) ) )
| ( element @ ( subset_difference @ SV32 @ SV66 @ SV88 ) @ ( powerset @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(793,plain,
! [SV67: $i,SV33: $i] :
( ( ( ~ ( element @ SV33 @ SV67 ) )
= $true )
| ( ( ( empty @ SV67 )
| ( in @ SV33 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(794,plain,
! [SV34: $i,SV68: $i] :
( ( ( ~ ( element @ SV68 @ ( powerset @ ( powerset @ SV34 ) ) ) )
= $true )
| ( ( element @ ( union_of_subsets @ SV34 @ SV68 ) @ ( powerset @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[747]) ).
thf(795,plain,
( ( ~ ( element @ sK4_SX0 @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[748]) ).
thf(796,plain,
( ( ! [SY187: $i] :
( ~ ( element @ SY187 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( below @ sK1_A @ sK4_SX0 @ SY187 )
| ~ ( below @ sK1_A @ SY187 @ sK4_SX0 ) )
| ( sK4_SX0 = SY187 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[748]) ).
thf(797,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV35 )
| ~ ( meet_commutative @ SV35 ) )
| ~ ( meet_semilatt_str @ SV35 ) )
| ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) )
| ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) )
| ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(798,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV36 )
| ~ ( join_commutative @ SV36 ) )
| ~ ( join_semilatt_str @ SV36 ) )
| ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) )
| ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) )
| ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(799,plain,
! [SV71: $i,SV37: $i,SV91: $i] :
( ( ~ ( relation_of2_as_subset @ SV91 @ SV37 @ SV71 )
| ( element @ SV91 @ ( powerset @ ( cartesian_product2 @ SV37 @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(800,plain,
! [SV72: $i,SV38: $i] :
( ( ~ ( ~ ( element @ SV38 @ ( powerset @ SV72 ) )
| ( subset @ SV38 @ SV72 ) )
| ~ ( ~ ( subset @ SV38 @ SV72 )
| ( element @ SV38 @ ( powerset @ SV72 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(801,plain,
! [SV73: $i,SV39: $i,SV92: $i] :
( ( ~ ( element @ SV92 @ ( powerset @ ( cartesian_product2 @ SV39 @ SV73 ) ) )
| ( relation @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(802,plain,
! [SV40: $i,SV74: $i] :
( ( ( ~ ( element @ SV74 @ ( powerset @ ( powerset @ SV40 ) ) ) )
= $true )
| ( ( ( union_of_subsets @ SV40 @ SV74 )
= ( union @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(803,plain,
! [SV93: $i,SV75: $i,SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV41 )
| ~ ( meet_semilatt_str @ SV41 ) )
| ~ ( element @ SV75 @ ( the_carrier @ SV41 ) ) )
| ~ ( element @ SV93 @ ( the_carrier @ SV41 ) ) )
| ( element @ ( meet @ SV41 @ SV75 @ SV93 ) @ ( the_carrier @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(804,plain,
! [SV42: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV42 )
| ~ ( one_sorted_str @ SV42 ) ) )
= $false )
| ( ( ~ ( empty @ ( the_carrier @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(805,plain,
! [SV43: $i,SV76: $i] :
( ( ( ~ ( element @ SV76 @ ( powerset @ SV43 ) ) )
= $true )
| ( ( ( subset_complement @ SV43 @ SV76 )
= ( set_difference @ SV43 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(806,plain,
! [SV44: $i,SV77: $i] :
( ( ( ~ ( element @ SV77 @ ( powerset @ ( powerset @ SV44 ) ) ) )
= $true )
| ( ( element @ ( complements_of_subsets @ SV44 @ SV77 ) @ ( powerset @ ( powerset @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[758]) ).
thf(807,plain,
! [SV45: $i] :
( ( ( join_semilatt_str @ SV45 )
= $false )
| ( ( one_sorted_str @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(808,plain,
! [SV2: $i] :
( ( element @ ( sK5_SY113 @ SV2 ) @ SV2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[761]) ).
thf(809,plain,
! [SV3: $i] :
( ( ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_semilatt_str @ SV3 ) )
= $true )
| ( ( ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV3 ) )
| ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ SV3 ) )
| ~ ( ~ ( ~ ( below @ SV3 @ SY114 @ SY115 )
| ( ( join @ SV3 @ SY114 @ SY115 )
= SY115 ) )
| ~ ( ( ( join @ SV3 @ SY114 @ SY115 )
!= SY115 )
| ( below @ SV3 @ SY114 @ SY115 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[762]) ).
thf(810,plain,
! [SV4: $i,SV46: $i] :
( ( ( element @ SV46 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( ( complements_of_subsets @ SV4 @ ( complements_of_subsets @ SV4 @ SV46 ) )
= SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(811,plain,
! [SV5: $i] :
( ( ( empty @ SV5 )
= $true )
| ( ( ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY117 @ ( powerset @ SV5 ) )
| ~ ~ ( empty @ SY117 ) )
| ~ ( finite @ SY117 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[764]) ).
thf(812,plain,
! [SV78: $i,SV47: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( in @ SV6 @ SV47 )
| ~ ( element @ SV47 @ ( powerset @ SV78 ) ) ) )
= $true )
| ( ( element @ SV6 @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(813,plain,
! [SV79: $i,SV48: $i,SV7: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV7 @ SV48 )
| ~ ( element @ SV48 @ ( powerset @ SV79 ) ) )
| ~ ( empty @ SV79 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(814,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) )
| ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(815,plain,
! [SV81: $i,SV9: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( element @ SV50 @ ( powerset @ SV9 ) )
| ~ ( element @ SV81 @ ( powerset @ SV9 ) ) ) )
= $true )
| ( ( ( subset_difference @ SV9 @ SV50 @ SV81 )
= ( set_difference @ SV50 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(816,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( meet_commutative @ SV10 ) )
| ~ ( meet_semilatt_str @ SV10 ) )
| ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) )
| ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) ) )
= $true )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(817,plain,
! [SV11: $i,SV52: $i] :
( ( ( element @ SV52 @ ( powerset @ ( powerset @ SV11 ) ) )
= $false )
| ( ( ( meet_of_subsets @ SV11 @ SV52 )
= ( set_meet @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(818,plain,
! [SV12: $i,SV94: $i] :
( ( ( ~ ( element @ SV94 @ SV12 )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV94 )
| ~ ( epsilon_connected @ SV94 ) )
| ~ ( ordinal @ SV94 ) ) )
= $true )
| ( ( ordinal @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(819,plain,
( ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(820,plain,
! [SV53: $i,SV13: $i,SV83: $i] :
( ( ( ~ ( element @ SV83 @ ( powerset @ SV13 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( in @ SV53 @ ( subset_complement @ SV13 @ SV83 ) )
| ~ ( in @ SV53 @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[773]) ).
thf(821,plain,
! [SV54: $i,SV14: $i] :
( ( ( in @ SV14 @ SV54 )
= $false )
| ( ( element @ SV14 @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(822,plain,
! [SV15: $i,SV95: $i] :
( ( ( ~ ( element @ SV95 @ ( powerset @ SV15 ) )
| ( finite @ SV95 ) )
= $true )
| ( ( finite @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(823,plain,
! [SV16: $i] :
( ( ( ~ ( meet_semilatt_str @ SV16 )
| ~ ( join_semilatt_str @ SV16 ) )
= $false )
| ( ( latt_str @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(824,plain,
! [SV17: $i,SV55: $i] :
( ( ( element @ SV55 @ ( powerset @ SV17 ) )
= $false )
| ( ( ! [SY180: $i] :
( ~ ( in @ SY180 @ SV55 )
| ( in @ SY180 @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(825,plain,
! [SV18: $i] :
( ( ( ~ ~ ( empty_carrier @ SV18 )
| ~ ( join_semilatt_str @ SV18 ) )
= $true )
| ( ( ! [SY136: $i] :
( ~ ( element @ SY136 @ ( the_carrier @ SV18 ) )
| ! [SY137: $i] :
( ~ ( element @ SY137 @ ( the_carrier @ SV18 ) )
| ( ( join @ SV18 @ SY136 @ SY137 )
= ( apply_binary_as_element @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_L_join @ SV18 ) @ SY136 @ SY137 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[778]) ).
thf(826,plain,
! [SV19: $i] :
( ( ( empty @ SV19 )
= $true )
| ( ( ~ ! [SY138: $i] :
~ ~ ( ~ ( element @ SY138 @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ SY138 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[779]) ).
thf(827,plain,
! [SV20: $i,SV56: $i] :
( ( ( element @ SV56 @ ( powerset @ SV20 ) )
= $false )
| ( ( element @ ( subset_complement @ SV20 @ SV56 ) @ ( powerset @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(828,plain,
! [SV57: $i,SV21: $i,SV84: $i] :
( ( ( ~ ( relation_of2 @ SV84 @ SV21 @ SV57 ) )
= $true )
| ( ( element @ ( relation_dom_as_subset @ SV21 @ SV57 @ SV84 ) @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[781]) ).
thf(829,plain,
! [SV22: $i,SV58: $i] :
( ( ( element @ SV58 @ ( powerset @ ( powerset @ SV22 ) ) )
= $false )
| ( ( element @ ( meet_of_subsets @ SV22 @ SV58 ) @ ( powerset @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(830,plain,
! [SV23: $i,SV59: $i] :
( ( ( element @ SV59 @ ( powerset @ ( powerset @ SV23 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ( SV59 != empty_set ) )
| ( ( complements_of_subsets @ SV23 @ SV59 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(831,plain,
! [SV60: $i,SV24: $i] :
( ( ( ! [SY182: $i] :
( ~ ( in @ SY182 @ SV24 )
| ( in @ SY182 @ SV60 ) ) )
= $false )
| ( ( element @ SV24 @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[784]) ).
thf(832,plain,
! [SV25: $i] :
( ( ~ ( ~ ( element @ ( sK6_SY146 @ SV25 ) @ ( powerset @ SV25 ) )
| ~ ( empty @ ( sK6_SY146 @ SV25 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(833,plain,
! [SV85: $i,SV61: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV26 )
| ~ ( join_semilatt_str @ SV26 ) )
| ~ ( element @ SV61 @ ( the_carrier @ SV26 ) ) )
| ~ ( element @ SV85 @ ( the_carrier @ SV26 ) ) ) )
= $true )
| ( ( element @ ( join @ SV26 @ SV61 @ SV85 ) @ ( the_carrier @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[786]) ).
thf(834,plain,
! [SV62: $i,SV27: $i,SV86: $i] :
( ( ( ~ ( relation_of2 @ SV86 @ SV27 @ SV62 ) )
= $true )
| ( ( element @ ( relation_rng_as_subset @ SV27 @ SV62 @ SV86 ) @ ( powerset @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[787]) ).
thf(835,plain,
! [SV63: $i,SV28: $i] :
( ( ~ ( ~ ~ ( empty @ SV28 )
| ~ ( ~ ( ~ ( element @ SV63 @ SV28 )
| ( in @ SV63 @ SV28 ) )
| ~ ( ~ ( in @ SV63 @ SV28 )
| ( element @ SV63 @ SV28 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[788]) ).
thf(836,plain,
! [SV63: $i,SV28: $i] :
( ( ~ ( ~ ( empty @ SV28 )
| ~ ( ~ ( ~ ( element @ SV63 @ SV28 )
| ( empty @ SV63 ) )
| ~ ( ~ ( empty @ SV63 )
| ( element @ SV63 @ SV28 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[788]) ).
thf(837,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV29 )
| ~ ( join_commutative @ SV29 ) )
| ~ ( join_semilatt_str @ SV29 ) )
| ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) )
| ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) ) )
= $true )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(838,plain,
! [SV30: $i] :
( ( ( ~ ~ ( empty_carrier @ SV30 )
| ~ ( one_sorted_str @ SV30 ) )
= $true )
| ( ( ~ ! [SY154: $i] :
~ ~ ( ~ ( element @ SY154 @ ( powerset @ ( the_carrier @ SV30 ) ) )
| ~ ~ ( empty @ SY154 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(839,plain,
! [SV31: $i,SV65: $i] :
( ( ( element @ SV65 @ ( powerset @ SV31 ) )
= $false )
| ( ( ( subset_complement @ SV31 @ ( subset_complement @ SV31 @ SV65 ) )
= SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(840,plain,
! [SV88: $i,SV32: $i,SV66: $i] :
( ( ( ~ ~ ( ~ ( element @ SV66 @ ( powerset @ SV32 ) )
| ~ ( element @ SV88 @ ( powerset @ SV32 ) ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV32 @ SV66 @ SV88 ) @ ( powerset @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[792]) ).
thf(841,plain,
! [SV67: $i,SV33: $i] :
( ( ( element @ SV33 @ SV67 )
= $false )
| ( ( ( empty @ SV67 )
| ( in @ SV33 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(842,plain,
! [SV34: $i,SV68: $i] :
( ( ( element @ SV68 @ ( powerset @ ( powerset @ SV34 ) ) )
= $false )
| ( ( element @ ( union_of_subsets @ SV34 @ SV68 ) @ ( powerset @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(843,plain,
( ( element @ sK4_SX0 @ ( the_carrier @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(844,plain,
( ( ~ ( element @ sK7_SY187 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( below @ sK1_A @ sK4_SX0 @ sK7_SY187 )
| ~ ( below @ sK1_A @ sK7_SY187 @ sK4_SX0 ) )
| ( sK4_SX0 = sK7_SY187 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[796]) ).
thf(845,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV35 )
| ~ ( meet_commutative @ SV35 ) )
| ~ ( meet_semilatt_str @ SV35 ) )
| ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) )
| ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[797]) ).
thf(846,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV36 )
| ~ ( join_commutative @ SV36 ) )
| ~ ( join_semilatt_str @ SV36 ) )
| ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) )
| ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) ) )
= $true )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(847,plain,
! [SV71: $i,SV37: $i,SV91: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV91 @ SV37 @ SV71 ) )
= $true )
| ( ( element @ SV91 @ ( powerset @ ( cartesian_product2 @ SV37 @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(848,plain,
! [SV72: $i,SV38: $i] :
( ( ~ ( ~ ( element @ SV38 @ ( powerset @ SV72 ) )
| ( subset @ SV38 @ SV72 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[800]) ).
thf(849,plain,
! [SV72: $i,SV38: $i] :
( ( ~ ( ~ ( subset @ SV38 @ SV72 )
| ( element @ SV38 @ ( powerset @ SV72 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[800]) ).
thf(850,plain,
! [SV73: $i,SV39: $i,SV92: $i] :
( ( ( ~ ( element @ SV92 @ ( powerset @ ( cartesian_product2 @ SV39 @ SV73 ) ) ) )
= $true )
| ( ( relation @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(851,plain,
! [SV40: $i,SV74: $i] :
( ( ( element @ SV74 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( ( union_of_subsets @ SV40 @ SV74 )
= ( union @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(852,plain,
! [SV93: $i,SV75: $i,SV41: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV41 )
| ~ ( meet_semilatt_str @ SV41 ) )
| ~ ( element @ SV75 @ ( the_carrier @ SV41 ) ) )
| ~ ( element @ SV93 @ ( the_carrier @ SV41 ) ) ) )
= $true )
| ( ( element @ ( meet @ SV41 @ SV75 @ SV93 ) @ ( the_carrier @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[803]) ).
thf(853,plain,
! [SV42: $i] :
( ( ( ~ ~ ( empty_carrier @ SV42 )
| ~ ( one_sorted_str @ SV42 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(854,plain,
! [SV43: $i,SV76: $i] :
( ( ( element @ SV76 @ ( powerset @ SV43 ) )
= $false )
| ( ( ( subset_complement @ SV43 @ SV76 )
= ( set_difference @ SV43 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(855,plain,
! [SV44: $i,SV77: $i] :
( ( ( element @ SV77 @ ( powerset @ ( powerset @ SV44 ) ) )
= $false )
| ( ( element @ ( complements_of_subsets @ SV44 @ SV77 ) @ ( powerset @ ( powerset @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(856,plain,
! [SV3: $i] :
( ( ( ~ ~ ( empty_carrier @ SV3 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV3 ) )
= $true )
| ( ( ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV3 ) )
| ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ SV3 ) )
| ~ ( ~ ( ~ ( below @ SV3 @ SY114 @ SY115 )
| ( ( join @ SV3 @ SY114 @ SY115 )
= SY115 ) )
| ~ ( ( ( join @ SV3 @ SY114 @ SY115 )
!= SY115 )
| ( below @ SV3 @ SY114 @ SY115 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[809]) ).
thf(857,plain,
! [SV5: $i] :
( ( ( ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY117 @ ( powerset @ SV5 ) )
| ~ ~ ( empty @ SY117 ) )
| ~ ( finite @ SY117 ) ) )
= $false )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(858,plain,
! [SV78: $i,SV47: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ SV6 @ SV47 )
| ~ ( element @ SV47 @ ( powerset @ SV78 ) ) ) )
= $false )
| ( ( element @ SV6 @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(859,plain,
! [SV79: $i,SV48: $i,SV7: $i] :
( ( ~ ~ ( ~ ( in @ SV7 @ SV48 )
| ~ ( element @ SV48 @ ( powerset @ SV79 ) ) )
| ~ ( empty @ SV79 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[813]) ).
thf(860,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) )
| ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) ) )
= $false )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(861,plain,
! [SV81: $i,SV9: $i,SV50: $i] :
( ( ( ~ ( ~ ( element @ SV50 @ ( powerset @ SV9 ) )
| ~ ( element @ SV81 @ ( powerset @ SV9 ) ) ) )
= $false )
| ( ( ( subset_difference @ SV9 @ SV50 @ SV81 )
= ( set_difference @ SV50 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(862,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( meet_commutative @ SV10 ) )
| ~ ( meet_semilatt_str @ SV10 ) )
| ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) )
| ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) ) )
= $false )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(863,plain,
! [SV12: $i,SV94: $i] :
( ( ( ~ ( element @ SV94 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV94 )
| ~ ( epsilon_connected @ SV94 ) )
| ~ ( ordinal @ SV94 ) ) )
= $true )
| ( ( ordinal @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[818]) ).
thf(864,plain,
( ( ~ ( one_sorted_str @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(865,plain,
( ( ~ ~ ( empty_carrier @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(866,plain,
! [SV53: $i,SV13: $i,SV83: $i] :
( ( ( element @ SV83 @ ( powerset @ SV13 ) )
= $false )
| ( ( ~ ~ ( ~ ( in @ SV53 @ ( subset_complement @ SV13 @ SV83 ) )
| ~ ( in @ SV53 @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(867,plain,
! [SV15: $i,SV95: $i] :
( ( ( ~ ( element @ SV95 @ ( powerset @ SV15 ) ) )
= $true )
| ( ( finite @ SV95 )
= $true )
| ( ( finite @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[822]) ).
thf(868,plain,
! [SV16: $i] :
( ( ( ~ ( meet_semilatt_str @ SV16 ) )
= $false )
| ( ( latt_str @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[823]) ).
thf(869,plain,
! [SV16: $i] :
( ( ( ~ ( join_semilatt_str @ SV16 ) )
= $false )
| ( ( latt_str @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[823]) ).
thf(870,plain,
! [SV17: $i,SV55: $i,SV96: $i] :
( ( ( ~ ( in @ SV96 @ SV55 )
| ( in @ SV96 @ SV17 ) )
= $true )
| ( ( element @ SV55 @ ( powerset @ SV17 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(871,plain,
! [SV18: $i] :
( ( ( ~ ~ ( empty_carrier @ SV18 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV18 ) )
= $true )
| ( ( ! [SY136: $i] :
( ~ ( element @ SY136 @ ( the_carrier @ SV18 ) )
| ! [SY137: $i] :
( ~ ( element @ SY137 @ ( the_carrier @ SV18 ) )
| ( ( join @ SV18 @ SY136 @ SY137 )
= ( apply_binary_as_element @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_L_join @ SV18 ) @ SY136 @ SY137 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[825]) ).
thf(872,plain,
! [SV19: $i] :
( ( ( ! [SY138: $i] :
~ ~ ( ~ ( element @ SY138 @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ SY138 ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(873,plain,
! [SV57: $i,SV21: $i,SV84: $i] :
( ( ( relation_of2 @ SV84 @ SV21 @ SV57 )
= $false )
| ( ( element @ ( relation_dom_as_subset @ SV21 @ SV57 @ SV84 ) @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(874,plain,
! [SV23: $i,SV59: $i] :
( ( ( ~ ( ~ ( ( SV59 != empty_set ) )
| ( ( complements_of_subsets @ SV23 @ SV59 )
!= empty_set ) ) )
= $false )
| ( ( element @ SV59 @ ( powerset @ ( powerset @ SV23 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(875,plain,
! [SV24: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK8_SY182 @ SV60 @ SV24 ) @ SV24 )
| ( in @ ( sK8_SY182 @ SV60 @ SV24 ) @ SV60 ) )
= $false )
| ( ( element @ SV24 @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[831]) ).
thf(876,plain,
! [SV25: $i] :
( ( ~ ( element @ ( sK6_SY146 @ SV25 ) @ ( powerset @ SV25 ) )
| ~ ( empty @ ( sK6_SY146 @ SV25 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(877,plain,
! [SV85: $i,SV61: $i,SV26: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV26 )
| ~ ( join_semilatt_str @ SV26 ) )
| ~ ( element @ SV61 @ ( the_carrier @ SV26 ) ) )
| ~ ( element @ SV85 @ ( the_carrier @ SV26 ) ) ) )
= $false )
| ( ( element @ ( join @ SV26 @ SV61 @ SV85 ) @ ( the_carrier @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(878,plain,
! [SV62: $i,SV27: $i,SV86: $i] :
( ( ( relation_of2 @ SV86 @ SV27 @ SV62 )
= $false )
| ( ( element @ ( relation_rng_as_subset @ SV27 @ SV62 @ SV86 ) @ ( powerset @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(879,plain,
! [SV63: $i,SV28: $i] :
( ( ~ ~ ( empty @ SV28 )
| ~ ( ~ ( ~ ( element @ SV63 @ SV28 )
| ( in @ SV63 @ SV28 ) )
| ~ ( ~ ( in @ SV63 @ SV28 )
| ( element @ SV63 @ SV28 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[835]) ).
thf(880,plain,
! [SV63: $i,SV28: $i] :
( ( ~ ( empty @ SV28 )
| ~ ( ~ ( ~ ( element @ SV63 @ SV28 )
| ( empty @ SV63 ) )
| ~ ( ~ ( empty @ SV63 )
| ( element @ SV63 @ SV28 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[836]) ).
thf(881,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV29 )
| ~ ( join_commutative @ SV29 ) )
| ~ ( join_semilatt_str @ SV29 ) )
| ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) )
| ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) ) )
= $false )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(882,plain,
! [SV30: $i] :
( ( ( ~ ~ ( empty_carrier @ SV30 ) )
= $true )
| ( ( ~ ( one_sorted_str @ SV30 ) )
= $true )
| ( ( ~ ! [SY154: $i] :
~ ~ ( ~ ( element @ SY154 @ ( powerset @ ( the_carrier @ SV30 ) ) )
| ~ ~ ( empty @ SY154 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(883,plain,
! [SV88: $i,SV32: $i,SV66: $i] :
( ( ( ~ ( ~ ( element @ SV66 @ ( powerset @ SV32 ) )
| ~ ( element @ SV88 @ ( powerset @ SV32 ) ) ) )
= $false )
| ( ( element @ ( subset_difference @ SV32 @ SV66 @ SV88 ) @ ( powerset @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[840]) ).
thf(884,plain,
! [SV33: $i,SV67: $i] :
( ( ( empty @ SV67 )
= $true )
| ( ( in @ SV33 @ SV67 )
= $true )
| ( ( element @ SV33 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[841]) ).
thf(885,plain,
( ( ~ ( element @ sK7_SY187 @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[844]) ).
thf(886,plain,
( ( ~ ~ ( ~ ( below @ sK1_A @ sK4_SX0 @ sK7_SY187 )
| ~ ( below @ sK1_A @ sK7_SY187 @ sK4_SX0 ) )
| ( sK4_SX0 = sK7_SY187 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[844]) ).
thf(887,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV35 )
| ~ ( meet_commutative @ SV35 ) )
| ~ ( meet_semilatt_str @ SV35 ) )
| ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) )
| ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) ) )
= $false )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(888,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV36 )
| ~ ( join_commutative @ SV36 ) )
| ~ ( join_semilatt_str @ SV36 ) )
| ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) )
| ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) ) )
= $false )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(889,plain,
! [SV71: $i,SV37: $i,SV91: $i] :
( ( ( relation_of2_as_subset @ SV91 @ SV37 @ SV71 )
= $false )
| ( ( element @ SV91 @ ( powerset @ ( cartesian_product2 @ SV37 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(890,plain,
! [SV72: $i,SV38: $i] :
( ( ~ ( element @ SV38 @ ( powerset @ SV72 ) )
| ( subset @ SV38 @ SV72 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[848]) ).
thf(891,plain,
! [SV72: $i,SV38: $i] :
( ( ~ ( subset @ SV38 @ SV72 )
| ( element @ SV38 @ ( powerset @ SV72 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[849]) ).
thf(892,plain,
! [SV73: $i,SV39: $i,SV92: $i] :
( ( ( element @ SV92 @ ( powerset @ ( cartesian_product2 @ SV39 @ SV73 ) ) )
= $false )
| ( ( relation @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(893,plain,
! [SV93: $i,SV75: $i,SV41: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV41 )
| ~ ( meet_semilatt_str @ SV41 ) )
| ~ ( element @ SV75 @ ( the_carrier @ SV41 ) ) )
| ~ ( element @ SV93 @ ( the_carrier @ SV41 ) ) ) )
= $false )
| ( ( element @ ( meet @ SV41 @ SV75 @ SV93 ) @ ( the_carrier @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(894,plain,
! [SV42: $i] :
( ( ( ~ ~ ( empty_carrier @ SV42 ) )
= $true )
| ( ( ~ ( one_sorted_str @ SV42 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(895,plain,
! [SV3: $i] :
( ( ( ~ ( empty_carrier @ SV3 ) )
= $false )
| ( ( ~ ( join_semilatt_str @ SV3 ) )
= $true )
| ( ( ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV3 ) )
| ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ SV3 ) )
| ~ ( ~ ( ~ ( below @ SV3 @ SY114 @ SY115 )
| ( ( join @ SV3 @ SY114 @ SY115 )
= SY115 ) )
| ~ ( ( ( join @ SV3 @ SY114 @ SY115 )
!= SY115 )
| ( below @ SV3 @ SY114 @ SY115 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(896,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_SY117 @ SV5 ) @ ( powerset @ SV5 ) )
| ~ ~ ( empty @ ( sK9_SY117 @ SV5 ) ) )
| ~ ( finite @ ( sK9_SY117 @ SV5 ) ) ) )
= $false )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[857]) ).
thf(897,plain,
! [SV78: $i,SV47: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV47 )
| ~ ( element @ SV47 @ ( powerset @ SV78 ) ) )
= $true )
| ( ( element @ SV6 @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[858]) ).
thf(898,plain,
! [SV79: $i,SV48: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ SV7 @ SV48 )
| ~ ( element @ SV48 @ ( powerset @ SV79 ) ) ) )
= $true )
| ( ( ~ ( empty @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(899,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) )
| ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[860]) ).
thf(900,plain,
! [SV81: $i,SV9: $i,SV50: $i] :
( ( ( ~ ( element @ SV50 @ ( powerset @ SV9 ) )
| ~ ( element @ SV81 @ ( powerset @ SV9 ) ) )
= $true )
| ( ( ( subset_difference @ SV9 @ SV50 @ SV81 )
= ( set_difference @ SV50 @ SV81 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[861]) ).
thf(901,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( meet_commutative @ SV10 ) )
| ~ ( meet_semilatt_str @ SV10 ) )
| ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) )
| ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[862]) ).
thf(902,plain,
! [SV12: $i,SV94: $i] :
( ( ( element @ SV94 @ SV12 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV94 )
| ~ ( epsilon_connected @ SV94 ) )
| ~ ( ordinal @ SV94 ) ) )
= $true )
| ( ( ordinal @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(903,plain,
( ( one_sorted_str @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[864]) ).
thf(904,plain,
( ( ~ ( empty_carrier @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[865]) ).
thf(905,plain,
! [SV83: $i,SV13: $i,SV53: $i] :
( ( ( ~ ( ~ ( in @ SV53 @ ( subset_complement @ SV13 @ SV83 ) )
| ~ ( in @ SV53 @ SV83 ) ) )
= $false )
| ( ( element @ SV83 @ ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(906,plain,
! [SV15: $i,SV95: $i] :
( ( ( element @ SV95 @ ( powerset @ SV15 ) )
= $false )
| ( ( finite @ SV95 )
= $true )
| ( ( finite @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(907,plain,
! [SV16: $i] :
( ( ( meet_semilatt_str @ SV16 )
= $true )
| ( ( latt_str @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(908,plain,
! [SV16: $i] :
( ( ( join_semilatt_str @ SV16 )
= $true )
| ( ( latt_str @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[869]) ).
thf(909,plain,
! [SV17: $i,SV55: $i,SV96: $i] :
( ( ( ~ ( in @ SV96 @ SV55 ) )
= $true )
| ( ( in @ SV96 @ SV17 )
= $true )
| ( ( element @ SV55 @ ( powerset @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(910,plain,
! [SV18: $i] :
( ( ( ~ ( empty_carrier @ SV18 ) )
= $false )
| ( ( ~ ( join_semilatt_str @ SV18 ) )
= $true )
| ( ( ! [SY136: $i] :
( ~ ( element @ SY136 @ ( the_carrier @ SV18 ) )
| ! [SY137: $i] :
( ~ ( element @ SY137 @ ( the_carrier @ SV18 ) )
| ( ( join @ SV18 @ SY136 @ SY137 )
= ( apply_binary_as_element @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_L_join @ SV18 ) @ SY136 @ SY137 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(911,plain,
! [SV19: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK10_SY138 @ SV19 ) @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ ( sK10_SY138 @ SV19 ) ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[872]) ).
thf(912,plain,
! [SV23: $i,SV59: $i] :
( ( ( ~ ( ( SV59 != empty_set ) )
| ( ( complements_of_subsets @ SV23 @ SV59 )
!= empty_set ) )
= $true )
| ( ( element @ SV59 @ ( powerset @ ( powerset @ SV23 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[874]) ).
thf(913,plain,
! [SV24: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK8_SY182 @ SV60 @ SV24 ) @ SV24 ) )
= $false )
| ( ( element @ SV24 @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[875]) ).
thf(914,plain,
! [SV24: $i,SV60: $i] :
( ( ( in @ ( sK8_SY182 @ SV60 @ SV24 ) @ SV60 )
= $false )
| ( ( element @ SV24 @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[875]) ).
thf(915,plain,
! [SV25: $i] :
( ( ~ ( element @ ( sK6_SY146 @ SV25 ) @ ( powerset @ SV25 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[876]) ).
thf(916,plain,
! [SV25: $i] :
( ( ~ ( empty @ ( sK6_SY146 @ SV25 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[876]) ).
thf(917,plain,
! [SV85: $i,SV61: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV26 )
| ~ ( join_semilatt_str @ SV26 ) )
| ~ ( element @ SV61 @ ( the_carrier @ SV26 ) ) )
| ~ ( element @ SV85 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( element @ ( join @ SV26 @ SV61 @ SV85 ) @ ( the_carrier @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[877]) ).
thf(918,plain,
! [SV63: $i,SV28: $i] :
( ( ( ~ ~ ( empty @ SV28 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV63 @ SV28 )
| ( in @ SV63 @ SV28 ) )
| ~ ( ~ ( in @ SV63 @ SV28 )
| ( element @ SV63 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(919,plain,
! [SV63: $i,SV28: $i] :
( ( ( ~ ( empty @ SV28 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV63 @ SV28 )
| ( empty @ SV63 ) )
| ~ ( ~ ( empty @ SV63 )
| ( element @ SV63 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(920,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV29 )
| ~ ( join_commutative @ SV29 ) )
| ~ ( join_semilatt_str @ SV29 ) )
| ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) )
| ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[881]) ).
thf(921,plain,
! [SV30: $i] :
( ( ( ~ ( empty_carrier @ SV30 ) )
= $false )
| ( ( ~ ( one_sorted_str @ SV30 ) )
= $true )
| ( ( ~ ! [SY154: $i] :
~ ~ ( ~ ( element @ SY154 @ ( powerset @ ( the_carrier @ SV30 ) ) )
| ~ ~ ( empty @ SY154 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(922,plain,
! [SV88: $i,SV32: $i,SV66: $i] :
( ( ( ~ ( element @ SV66 @ ( powerset @ SV32 ) )
| ~ ( element @ SV88 @ ( powerset @ SV32 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV32 @ SV66 @ SV88 ) @ ( powerset @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[883]) ).
thf(923,plain,
( ( element @ sK7_SY187 @ ( the_carrier @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[885]) ).
thf(924,plain,
( ( ~ ~ ( ~ ( below @ sK1_A @ sK4_SX0 @ sK7_SY187 )
| ~ ( below @ sK1_A @ sK7_SY187 @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[886]) ).
thf(925,plain,
( ( sK4_SX0 = sK7_SY187 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[886]) ).
thf(926,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV35 )
| ~ ( meet_commutative @ SV35 ) )
| ~ ( meet_semilatt_str @ SV35 ) )
| ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) )
| ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[887]) ).
thf(927,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV36 )
| ~ ( join_commutative @ SV36 ) )
| ~ ( join_semilatt_str @ SV36 ) )
| ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) )
| ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[888]) ).
thf(928,plain,
! [SV72: $i,SV38: $i] :
( ( ( ~ ( element @ SV38 @ ( powerset @ SV72 ) ) )
= $true )
| ( ( subset @ SV38 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(929,plain,
! [SV72: $i,SV38: $i] :
( ( ( ~ ( subset @ SV38 @ SV72 ) )
= $true )
| ( ( element @ SV38 @ ( powerset @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(930,plain,
! [SV93: $i,SV75: $i,SV41: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV41 )
| ~ ( meet_semilatt_str @ SV41 ) )
| ~ ( element @ SV75 @ ( the_carrier @ SV41 ) ) )
| ~ ( element @ SV93 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( element @ ( meet @ SV41 @ SV75 @ SV93 ) @ ( the_carrier @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[893]) ).
thf(931,plain,
! [SV42: $i] :
( ( ( ~ ( empty_carrier @ SV42 ) )
= $false )
| ( ( ~ ( one_sorted_str @ SV42 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(932,plain,
! [SV3: $i] :
( ( ( empty_carrier @ SV3 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV3 ) )
= $true )
| ( ( ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV3 ) )
| ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ SV3 ) )
| ~ ( ~ ( ~ ( below @ SV3 @ SY114 @ SY115 )
| ( ( join @ SV3 @ SY114 @ SY115 )
= SY115 ) )
| ~ ( ( ( join @ SV3 @ SY114 @ SY115 )
!= SY115 )
| ( below @ SV3 @ SY114 @ SY115 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[895]) ).
thf(933,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK9_SY117 @ SV5 ) @ ( powerset @ SV5 ) )
| ~ ~ ( empty @ ( sK9_SY117 @ SV5 ) ) )
| ~ ( finite @ ( sK9_SY117 @ SV5 ) ) ) )
= $true )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[896]) ).
thf(934,plain,
! [SV78: $i,SV47: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV47 ) )
= $true )
| ( ( ~ ( element @ SV47 @ ( powerset @ SV78 ) ) )
= $true )
| ( ( element @ SV6 @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(935,plain,
! [SV79: $i,SV48: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ SV7 @ SV48 )
| ~ ( element @ SV48 @ ( powerset @ SV79 ) ) ) )
= $false )
| ( ( ~ ( empty @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(936,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) ) )
= $true )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(937,plain,
! [SV81: $i,SV9: $i,SV50: $i] :
( ( ( ~ ( element @ SV50 @ ( powerset @ SV9 ) ) )
= $true )
| ( ( ~ ( element @ SV81 @ ( powerset @ SV9 ) ) )
= $true )
| ( ( ( subset_difference @ SV9 @ SV50 @ SV81 )
= ( set_difference @ SV50 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(938,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( meet_commutative @ SV10 ) )
| ~ ( meet_semilatt_str @ SV10 ) )
| ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) ) )
= $true )
| ( ( ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(939,plain,
! [SV12: $i,SV94: $i] :
( ( ( ~ ~ ( ~ ( epsilon_transitive @ SV94 )
| ~ ( epsilon_connected @ SV94 ) )
| ~ ( ordinal @ SV94 ) )
= $false )
| ( ( element @ SV94 @ SV12 )
= $false )
| ( ( ordinal @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(940,plain,
( ( empty_carrier @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(941,plain,
! [SV83: $i,SV13: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ ( subset_complement @ SV13 @ SV83 ) )
| ~ ( in @ SV53 @ SV83 ) )
= $true )
| ( ( element @ SV83 @ ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[905]) ).
thf(942,plain,
! [SV17: $i,SV55: $i,SV96: $i] :
( ( ( in @ SV96 @ SV55 )
= $false )
| ( ( in @ SV96 @ SV17 )
= $true )
| ( ( element @ SV55 @ ( powerset @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(943,plain,
! [SV18: $i] :
( ( ( empty_carrier @ SV18 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV18 ) )
= $true )
| ( ( ! [SY136: $i] :
( ~ ( element @ SY136 @ ( the_carrier @ SV18 ) )
| ! [SY137: $i] :
( ~ ( element @ SY137 @ ( the_carrier @ SV18 ) )
| ( ( join @ SV18 @ SY136 @ SY137 )
= ( apply_binary_as_element @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_L_join @ SV18 ) @ SY136 @ SY137 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[910]) ).
thf(944,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ( element @ ( sK10_SY138 @ SV19 ) @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ ( sK10_SY138 @ SV19 ) ) ) )
= $true )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[911]) ).
thf(945,plain,
! [SV23: $i,SV59: $i] :
( ( ( ~ ( ( SV59 != empty_set ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV23 @ SV59 )
!= empty_set )
= $true )
| ( ( element @ SV59 @ ( powerset @ ( powerset @ SV23 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(946,plain,
! [SV24: $i,SV60: $i] :
( ( ( in @ ( sK8_SY182 @ SV60 @ SV24 ) @ SV24 )
= $true )
| ( ( element @ SV24 @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[913]) ).
thf(947,plain,
! [SV25: $i] :
( ( element @ ( sK6_SY146 @ SV25 ) @ ( powerset @ SV25 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[915]) ).
thf(948,plain,
! [SV25: $i] :
( ( empty @ ( sK6_SY146 @ SV25 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[916]) ).
thf(949,plain,
! [SV85: $i,SV61: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV26 )
| ~ ( join_semilatt_str @ SV26 ) )
| ~ ( element @ SV61 @ ( the_carrier @ SV26 ) ) ) )
= $true )
| ( ( ~ ( element @ SV85 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( element @ ( join @ SV26 @ SV61 @ SV85 ) @ ( the_carrier @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(950,plain,
! [SV63: $i,SV28: $i] :
( ( ( ~ ( empty @ SV28 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( element @ SV63 @ SV28 )
| ( in @ SV63 @ SV28 ) )
| ~ ( ~ ( in @ SV63 @ SV28 )
| ( element @ SV63 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(951,plain,
! [SV63: $i,SV28: $i] :
( ( ( empty @ SV28 )
= $false )
| ( ( ~ ( ~ ( ~ ( element @ SV63 @ SV28 )
| ( empty @ SV63 ) )
| ~ ( ~ ( empty @ SV63 )
| ( element @ SV63 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(952,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV29 )
| ~ ( join_commutative @ SV29 ) )
| ~ ( join_semilatt_str @ SV29 ) )
| ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) ) )
= $true )
| ( ( ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(953,plain,
! [SV30: $i] :
( ( ( empty_carrier @ SV30 )
= $true )
| ( ( ~ ( one_sorted_str @ SV30 ) )
= $true )
| ( ( ~ ! [SY154: $i] :
~ ~ ( ~ ( element @ SY154 @ ( powerset @ ( the_carrier @ SV30 ) ) )
| ~ ~ ( empty @ SY154 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[921]) ).
thf(954,plain,
! [SV88: $i,SV32: $i,SV66: $i] :
( ( ( ~ ( element @ SV66 @ ( powerset @ SV32 ) ) )
= $true )
| ( ( ~ ( element @ SV88 @ ( powerset @ SV32 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV32 @ SV66 @ SV88 ) @ ( powerset @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(955,plain,
( ( ~ ( ~ ( below @ sK1_A @ sK4_SX0 @ sK7_SY187 )
| ~ ( below @ sK1_A @ sK7_SY187 @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[924]) ).
thf(956,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV35 )
| ~ ( meet_commutative @ SV35 ) )
| ~ ( meet_semilatt_str @ SV35 ) )
| ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) ) )
= $true )
| ( ( ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(957,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV36 )
| ~ ( join_commutative @ SV36 ) )
| ~ ( join_semilatt_str @ SV36 ) )
| ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) ) )
= $true )
| ( ( ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(958,plain,
! [SV72: $i,SV38: $i] :
( ( ( element @ SV38 @ ( powerset @ SV72 ) )
= $false )
| ( ( subset @ SV38 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(959,plain,
! [SV72: $i,SV38: $i] :
( ( ( subset @ SV38 @ SV72 )
= $false )
| ( ( element @ SV38 @ ( powerset @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(960,plain,
! [SV93: $i,SV75: $i,SV41: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV41 )
| ~ ( meet_semilatt_str @ SV41 ) )
| ~ ( element @ SV75 @ ( the_carrier @ SV41 ) ) ) )
= $true )
| ( ( ~ ( element @ SV93 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( element @ ( meet @ SV41 @ SV75 @ SV93 ) @ ( the_carrier @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(961,plain,
! [SV42: $i] :
( ( ( empty_carrier @ SV42 )
= $true )
| ( ( ~ ( one_sorted_str @ SV42 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[931]) ).
thf(962,plain,
! [SV3: $i] :
( ( ( join_semilatt_str @ SV3 )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV3 ) )
| ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ SV3 ) )
| ~ ( ~ ( ~ ( below @ SV3 @ SY114 @ SY115 )
| ( ( join @ SV3 @ SY114 @ SY115 )
= SY115 ) )
| ~ ( ( ( join @ SV3 @ SY114 @ SY115 )
!= SY115 )
| ( below @ SV3 @ SY114 @ SY115 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(963,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_SY117 @ SV5 ) @ ( powerset @ SV5 ) )
| ~ ~ ( empty @ ( sK9_SY117 @ SV5 ) ) )
| ~ ( finite @ ( sK9_SY117 @ SV5 ) ) )
= $false )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(964,plain,
! [SV78: $i,SV47: $i,SV6: $i] :
( ( ( in @ SV6 @ SV47 )
= $false )
| ( ( ~ ( element @ SV47 @ ( powerset @ SV78 ) ) )
= $true )
| ( ( element @ SV6 @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(965,plain,
! [SV79: $i,SV48: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV48 )
| ~ ( element @ SV48 @ ( powerset @ SV79 ) ) )
= $true )
| ( ( ~ ( empty @ SV79 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[935]) ).
thf(966,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) ) )
= $false )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(967,plain,
! [SV81: $i,SV9: $i,SV50: $i] :
( ( ( element @ SV50 @ ( powerset @ SV9 ) )
= $false )
| ( ( ~ ( element @ SV81 @ ( powerset @ SV9 ) ) )
= $true )
| ( ( ( subset_difference @ SV9 @ SV50 @ SV81 )
= ( set_difference @ SV50 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(968,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( meet_commutative @ SV10 ) )
| ~ ( meet_semilatt_str @ SV10 ) )
| ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) ) )
= $false )
| ( ( ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(969,plain,
! [SV12: $i,SV94: $i] :
( ( ( ~ ~ ( ~ ( epsilon_transitive @ SV94 )
| ~ ( epsilon_connected @ SV94 ) ) )
= $false )
| ( ( element @ SV94 @ SV12 )
= $false )
| ( ( ordinal @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[939]) ).
thf(970,plain,
! [SV12: $i,SV94: $i] :
( ( ( ~ ( ordinal @ SV94 ) )
= $false )
| ( ( element @ SV94 @ SV12 )
= $false )
| ( ( ordinal @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[939]) ).
thf(971,plain,
! [SV83: $i,SV13: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ ( subset_complement @ SV13 @ SV83 ) ) )
= $true )
| ( ( ~ ( in @ SV53 @ SV83 ) )
= $true )
| ( ( element @ SV83 @ ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(972,plain,
! [SV18: $i] :
( ( ( join_semilatt_str @ SV18 )
= $false )
| ( ( empty_carrier @ SV18 )
= $true )
| ( ( ! [SY136: $i] :
( ~ ( element @ SY136 @ ( the_carrier @ SV18 ) )
| ! [SY137: $i] :
( ~ ( element @ SY137 @ ( the_carrier @ SV18 ) )
| ( ( join @ SV18 @ SY136 @ SY137 )
= ( apply_binary_as_element @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_L_join @ SV18 ) @ SY136 @ SY137 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(973,plain,
! [SV19: $i] :
( ( ( ~ ( element @ ( sK10_SY138 @ SV19 ) @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ ( sK10_SY138 @ SV19 ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(974,plain,
! [SV23: $i,SV59: $i] :
( ( ( SV59 != empty_set )
= $false )
| ( ( ( complements_of_subsets @ SV23 @ SV59 )
!= empty_set )
= $true )
| ( ( element @ SV59 @ ( powerset @ ( powerset @ SV23 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(975,plain,
! [SV85: $i,SV61: $i,SV26: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV26 )
| ~ ( join_semilatt_str @ SV26 ) )
| ~ ( element @ SV61 @ ( the_carrier @ SV26 ) ) ) )
= $false )
| ( ( ~ ( element @ SV85 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( element @ ( join @ SV26 @ SV61 @ SV85 ) @ ( the_carrier @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(976,plain,
! [SV63: $i,SV28: $i] :
( ( ( empty @ SV28 )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV63 @ SV28 )
| ( in @ SV63 @ SV28 ) )
| ~ ( ~ ( in @ SV63 @ SV28 )
| ( element @ SV63 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(977,plain,
! [SV28: $i,SV63: $i] :
( ( ( ~ ( ~ ( element @ SV63 @ SV28 )
| ( empty @ SV63 ) )
| ~ ( ~ ( empty @ SV63 )
| ( element @ SV63 @ SV28 ) ) )
= $false )
| ( ( empty @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(978,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV29 )
| ~ ( join_commutative @ SV29 ) )
| ~ ( join_semilatt_str @ SV29 ) )
| ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) ) )
= $false )
| ( ( ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(979,plain,
! [SV30: $i] :
( ( ( one_sorted_str @ SV30 )
= $false )
| ( ( empty_carrier @ SV30 )
= $true )
| ( ( ~ ! [SY154: $i] :
~ ~ ( ~ ( element @ SY154 @ ( powerset @ ( the_carrier @ SV30 ) ) )
| ~ ~ ( empty @ SY154 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(980,plain,
! [SV88: $i,SV32: $i,SV66: $i] :
( ( ( element @ SV66 @ ( powerset @ SV32 ) )
= $false )
| ( ( ~ ( element @ SV88 @ ( powerset @ SV32 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV32 @ SV66 @ SV88 ) @ ( powerset @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(981,plain,
( ( ~ ( below @ sK1_A @ sK4_SX0 @ sK7_SY187 )
| ~ ( below @ sK1_A @ sK7_SY187 @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(982,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV35 )
| ~ ( meet_commutative @ SV35 ) )
| ~ ( meet_semilatt_str @ SV35 ) )
| ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) ) )
= $false )
| ( ( ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(983,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV36 )
| ~ ( join_commutative @ SV36 ) )
| ~ ( join_semilatt_str @ SV36 ) )
| ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) ) )
= $false )
| ( ( ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(984,plain,
! [SV93: $i,SV75: $i,SV41: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV41 )
| ~ ( meet_semilatt_str @ SV41 ) )
| ~ ( element @ SV75 @ ( the_carrier @ SV41 ) ) ) )
= $false )
| ( ( ~ ( element @ SV93 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( element @ ( meet @ SV41 @ SV75 @ SV93 ) @ ( the_carrier @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(985,plain,
! [SV42: $i] :
( ( ( one_sorted_str @ SV42 )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(986,plain,
! [SV3: $i,SV97: $i] :
( ( ( ~ ( element @ SV97 @ ( the_carrier @ SV3 ) )
| ! [SY193: $i] :
( ~ ( element @ SY193 @ ( the_carrier @ SV3 ) )
| ~ ( ~ ( ~ ( below @ SV3 @ SV97 @ SY193 )
| ( ( join @ SV3 @ SV97 @ SY193 )
= SY193 ) )
| ~ ( ( ( join @ SV3 @ SV97 @ SY193 )
!= SY193 )
| ( below @ SV3 @ SV97 @ SY193 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_semilatt_str @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(987,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_SY117 @ SV5 ) @ ( powerset @ SV5 ) )
| ~ ~ ( empty @ ( sK9_SY117 @ SV5 ) ) ) )
= $false )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[963]) ).
thf(988,plain,
! [SV5: $i] :
( ( ( ~ ( finite @ ( sK9_SY117 @ SV5 ) ) )
= $false )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[963]) ).
thf(989,plain,
! [SV6: $i,SV78: $i,SV47: $i] :
( ( ( element @ SV47 @ ( powerset @ SV78 ) )
= $false )
| ( ( in @ SV6 @ SV47 )
= $false )
| ( ( element @ SV6 @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(990,plain,
! [SV79: $i,SV48: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV48 ) )
= $true )
| ( ( ~ ( element @ SV48 @ ( powerset @ SV79 ) ) )
= $true )
| ( ( ~ ( empty @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(991,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(992,plain,
! [SV50: $i,SV9: $i,SV81: $i] :
( ( ( element @ SV81 @ ( powerset @ SV9 ) )
= $false )
| ( ( element @ SV50 @ ( powerset @ SV9 ) )
= $false )
| ( ( ( subset_difference @ SV9 @ SV50 @ SV81 )
= ( set_difference @ SV50 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(993,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( meet_commutative @ SV10 ) )
| ~ ( meet_semilatt_str @ SV10 ) )
| ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[968]) ).
thf(994,plain,
! [SV12: $i,SV94: $i] :
( ( ( ~ ( ~ ( epsilon_transitive @ SV94 )
| ~ ( epsilon_connected @ SV94 ) ) )
= $true )
| ( ( element @ SV94 @ SV12 )
= $false )
| ( ( ordinal @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[969]) ).
thf(995,plain,
! [SV12: $i,SV94: $i] :
( ( ( ordinal @ SV94 )
= $true )
| ( ( element @ SV94 @ SV12 )
= $false )
| ( ( ordinal @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[970]) ).
thf(996,plain,
! [SV83: $i,SV13: $i,SV53: $i] :
( ( ( in @ SV53 @ ( subset_complement @ SV13 @ SV83 ) )
= $false )
| ( ( ~ ( in @ SV53 @ SV83 ) )
= $true )
| ( ( element @ SV83 @ ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(997,plain,
! [SV18: $i,SV98: $i] :
( ( ( ~ ( element @ SV98 @ ( the_carrier @ SV18 ) )
| ! [SY194: $i] :
( ~ ( element @ SY194 @ ( the_carrier @ SV18 ) )
| ( ( join @ SV18 @ SV98 @ SY194 )
= ( apply_binary_as_element @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_L_join @ SV18 ) @ SV98 @ SY194 ) ) ) )
= $true )
| ( ( empty_carrier @ SV18 )
= $true )
| ( ( join_semilatt_str @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(998,plain,
! [SV19: $i] :
( ( ( ~ ( element @ ( sK10_SY138 @ SV19 ) @ ( powerset @ SV19 ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(999,plain,
! [SV19: $i] :
( ( ( ~ ~ ( empty @ ( sK10_SY138 @ SV19 ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(1000,plain,
! [SV23: $i,SV59: $i] :
( ( ( SV59 = empty_set )
= $true )
| ( ( ( complements_of_subsets @ SV23 @ SV59 )
!= empty_set )
= $true )
| ( ( element @ SV59 @ ( powerset @ ( powerset @ SV23 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[974]) ).
thf(1001,plain,
! [SV85: $i,SV61: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV26 )
| ~ ( join_semilatt_str @ SV26 ) )
| ~ ( element @ SV61 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( ~ ( element @ SV85 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( element @ ( join @ SV26 @ SV61 @ SV85 ) @ ( the_carrier @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[975]) ).
thf(1002,plain,
! [SV28: $i,SV63: $i] :
( ( ( ~ ( ~ ( element @ SV63 @ SV28 )
| ( in @ SV63 @ SV28 ) )
| ~ ( ~ ( in @ SV63 @ SV28 )
| ( element @ SV63 @ SV28 ) ) )
= $false )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1003,plain,
! [SV28: $i,SV63: $i] :
( ( ( ~ ( ~ ( element @ SV63 @ SV28 )
| ( empty @ SV63 ) ) )
= $false )
| ( ( empty @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1004,plain,
! [SV28: $i,SV63: $i] :
( ( ( ~ ( ~ ( empty @ SV63 )
| ( element @ SV63 @ SV28 ) ) )
= $false )
| ( ( empty @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1005,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV29 )
| ~ ( join_commutative @ SV29 ) )
| ~ ( join_semilatt_str @ SV29 ) )
| ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[978]) ).
thf(1006,plain,
! [SV30: $i] :
( ( ( ! [SY154: $i] :
~ ~ ( ~ ( element @ SY154 @ ( powerset @ ( the_carrier @ SV30 ) ) )
| ~ ~ ( empty @ SY154 ) ) )
= $false )
| ( ( empty_carrier @ SV30 )
= $true )
| ( ( one_sorted_str @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(1007,plain,
! [SV66: $i,SV32: $i,SV88: $i] :
( ( ( element @ SV88 @ ( powerset @ SV32 ) )
= $false )
| ( ( element @ SV66 @ ( powerset @ SV32 ) )
= $false )
| ( ( element @ ( subset_difference @ SV32 @ SV66 @ SV88 ) @ ( powerset @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1008,plain,
( ( ~ ( below @ sK1_A @ sK4_SX0 @ sK7_SY187 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[981]) ).
thf(1009,plain,
( ( ~ ( below @ sK1_A @ sK7_SY187 @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[981]) ).
thf(1010,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV35 )
| ~ ( meet_commutative @ SV35 ) )
| ~ ( meet_semilatt_str @ SV35 ) )
| ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[982]) ).
thf(1011,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV36 )
| ~ ( join_commutative @ SV36 ) )
| ~ ( join_semilatt_str @ SV36 ) )
| ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(1012,plain,
! [SV93: $i,SV75: $i,SV41: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV41 )
| ~ ( meet_semilatt_str @ SV41 ) )
| ~ ( element @ SV75 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( ~ ( element @ SV93 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( element @ ( meet @ SV41 @ SV75 @ SV93 ) @ ( the_carrier @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(1013,plain,
! [SV42: $i] :
( ( ( empty @ ( the_carrier @ SV42 ) )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( one_sorted_str @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1014,plain,
! [SV3: $i,SV97: $i] :
( ( ( ~ ( element @ SV97 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ! [SY193: $i] :
( ~ ( element @ SY193 @ ( the_carrier @ SV3 ) )
| ~ ( ~ ( ~ ( below @ SV3 @ SV97 @ SY193 )
| ( ( join @ SV3 @ SV97 @ SY193 )
= SY193 ) )
| ~ ( ( ( join @ SV3 @ SV97 @ SY193 )
!= SY193 )
| ( below @ SV3 @ SV97 @ SY193 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_semilatt_str @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[986]) ).
thf(1015,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( element @ ( sK9_SY117 @ SV5 ) @ ( powerset @ SV5 ) )
| ~ ~ ( empty @ ( sK9_SY117 @ SV5 ) ) ) )
= $true )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[987]) ).
thf(1016,plain,
! [SV5: $i] :
( ( ( finite @ ( sK9_SY117 @ SV5 ) )
= $true )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[988]) ).
thf(1017,plain,
! [SV79: $i,SV48: $i,SV7: $i] :
( ( ( in @ SV7 @ SV48 )
= $false )
| ( ( ~ ( element @ SV48 @ ( powerset @ SV79 ) ) )
= $true )
| ( ( ~ ( empty @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1018,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[991]) ).
thf(1019,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( meet_commutative @ SV10 ) )
| ~ ( meet_semilatt_str @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1020,plain,
! [SV12: $i,SV94: $i] :
( ( ( ~ ( epsilon_transitive @ SV94 )
| ~ ( epsilon_connected @ SV94 ) )
= $false )
| ( ( element @ SV94 @ SV12 )
= $false )
| ( ( ordinal @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1021,plain,
! [SV13: $i,SV83: $i,SV53: $i] :
( ( ( in @ SV53 @ SV83 )
= $false )
| ( ( in @ SV53 @ ( subset_complement @ SV13 @ SV83 ) )
= $false )
| ( ( element @ SV83 @ ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1022,plain,
! [SV18: $i,SV98: $i] :
( ( ( ~ ( element @ SV98 @ ( the_carrier @ SV18 ) ) )
= $true )
| ( ( ! [SY194: $i] :
( ~ ( element @ SY194 @ ( the_carrier @ SV18 ) )
| ( ( join @ SV18 @ SV98 @ SY194 )
= ( apply_binary_as_element @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_L_join @ SV18 ) @ SV98 @ SY194 ) ) ) )
= $true )
| ( ( empty_carrier @ SV18 )
= $true )
| ( ( join_semilatt_str @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1023,plain,
! [SV19: $i] :
( ( ( element @ ( sK10_SY138 @ SV19 ) @ ( powerset @ SV19 ) )
= $true )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[998]) ).
thf(1024,plain,
! [SV19: $i] :
( ( ( ~ ( empty @ ( sK10_SY138 @ SV19 ) ) )
= $true )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[999]) ).
thf(1025,plain,
! [SV59: $i,SV23: $i] :
( ( ( ( complements_of_subsets @ SV23 @ SV59 )
= empty_set )
= $false )
| ( ( SV59 = empty_set )
= $true )
| ( ( element @ SV59 @ ( powerset @ ( powerset @ SV23 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1026,plain,
! [SV85: $i,SV61: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV26 )
| ~ ( join_semilatt_str @ SV26 ) ) )
= $true )
| ( ( ~ ( element @ SV61 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( ~ ( element @ SV85 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( element @ ( join @ SV26 @ SV61 @ SV85 ) @ ( the_carrier @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1027,plain,
! [SV28: $i,SV63: $i] :
( ( ( ~ ( ~ ( element @ SV63 @ SV28 )
| ( in @ SV63 @ SV28 ) ) )
= $false )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1028,plain,
! [SV28: $i,SV63: $i] :
( ( ( ~ ( ~ ( in @ SV63 @ SV28 )
| ( element @ SV63 @ SV28 ) ) )
= $false )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1029,plain,
! [SV28: $i,SV63: $i] :
( ( ( ~ ( element @ SV63 @ SV28 )
| ( empty @ SV63 ) )
= $true )
| ( ( empty @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1003]) ).
thf(1030,plain,
! [SV28: $i,SV63: $i] :
( ( ( ~ ( empty @ SV63 )
| ( element @ SV63 @ SV28 ) )
= $true )
| ( ( empty @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1004]) ).
thf(1031,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV29 )
| ~ ( join_commutative @ SV29 ) )
| ~ ( join_semilatt_str @ SV29 ) ) )
= $true )
| ( ( ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1032,plain,
! [SV30: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK11_SY154 @ SV30 ) @ ( powerset @ ( the_carrier @ SV30 ) ) )
| ~ ~ ( empty @ ( sK11_SY154 @ SV30 ) ) ) )
= $false )
| ( ( empty_carrier @ SV30 )
= $true )
| ( ( one_sorted_str @ SV30 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1006]) ).
thf(1033,plain,
( ( below @ sK1_A @ sK4_SX0 @ sK7_SY187 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1008]) ).
thf(1034,plain,
( ( below @ sK1_A @ sK7_SY187 @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1009]) ).
thf(1035,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV35 )
| ~ ( meet_commutative @ SV35 ) )
| ~ ( meet_semilatt_str @ SV35 ) ) )
= $true )
| ( ( ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1010]) ).
thf(1036,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV36 )
| ~ ( join_commutative @ SV36 ) )
| ~ ( join_semilatt_str @ SV36 ) ) )
= $true )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1037,plain,
! [SV93: $i,SV75: $i,SV41: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV41 )
| ~ ( meet_semilatt_str @ SV41 ) ) )
= $true )
| ( ( ~ ( element @ SV75 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( ~ ( element @ SV93 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( element @ ( meet @ SV41 @ SV75 @ SV93 ) @ ( the_carrier @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1038,plain,
! [SV3: $i,SV97: $i] :
( ( ( element @ SV97 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( ! [SY193: $i] :
( ~ ( element @ SY193 @ ( the_carrier @ SV3 ) )
| ~ ( ~ ( ~ ( below @ SV3 @ SV97 @ SY193 )
| ( ( join @ SV3 @ SV97 @ SY193 )
= SY193 ) )
| ~ ( ( ( join @ SV3 @ SV97 @ SY193 )
!= SY193 )
| ( below @ SV3 @ SV97 @ SY193 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_semilatt_str @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1039,plain,
! [SV5: $i] :
( ( ( ~ ( element @ ( sK9_SY117 @ SV5 ) @ ( powerset @ SV5 ) )
| ~ ~ ( empty @ ( sK9_SY117 @ SV5 ) ) )
= $false )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1040,plain,
! [SV7: $i,SV79: $i,SV48: $i] :
( ( ( element @ SV48 @ ( powerset @ SV79 ) )
= $false )
| ( ( in @ SV7 @ SV48 )
= $false )
| ( ( ~ ( empty @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1041,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) ) )
= $false )
| ( ( ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1042,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( meet_commutative @ SV10 ) )
| ~ ( meet_semilatt_str @ SV10 ) ) )
= $false )
| ( ( ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1043,plain,
! [SV12: $i,SV94: $i] :
( ( ( ~ ( epsilon_transitive @ SV94 ) )
= $false )
| ( ( element @ SV94 @ SV12 )
= $false )
| ( ( ordinal @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1044,plain,
! [SV12: $i,SV94: $i] :
( ( ( ~ ( epsilon_connected @ SV94 ) )
= $false )
| ( ( element @ SV94 @ SV12 )
= $false )
| ( ( ordinal @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1045,plain,
! [SV18: $i,SV98: $i] :
( ( ( element @ SV98 @ ( the_carrier @ SV18 ) )
= $false )
| ( ( ! [SY194: $i] :
( ~ ( element @ SY194 @ ( the_carrier @ SV18 ) )
| ( ( join @ SV18 @ SV98 @ SY194 )
= ( apply_binary_as_element @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_L_join @ SV18 ) @ SV98 @ SY194 ) ) ) )
= $true )
| ( ( empty_carrier @ SV18 )
= $true )
| ( ( join_semilatt_str @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1046,plain,
! [SV19: $i] :
( ( ( empty @ ( sK10_SY138 @ SV19 ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1047,plain,
! [SV85: $i,SV61: $i,SV26: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV26 )
| ~ ( join_semilatt_str @ SV26 ) ) )
= $false )
| ( ( ~ ( element @ SV61 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( ~ ( element @ SV85 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( element @ ( join @ SV26 @ SV61 @ SV85 ) @ ( the_carrier @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1048,plain,
! [SV28: $i,SV63: $i] :
( ( ( ~ ( element @ SV63 @ SV28 )
| ( in @ SV63 @ SV28 ) )
= $true )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1049,plain,
! [SV28: $i,SV63: $i] :
( ( ( ~ ( in @ SV63 @ SV28 )
| ( element @ SV63 @ SV28 ) )
= $true )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1028]) ).
thf(1050,plain,
! [SV28: $i,SV63: $i] :
( ( ( ~ ( element @ SV63 @ SV28 ) )
= $true )
| ( ( empty @ SV63 )
= $true )
| ( ( empty @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1029]) ).
thf(1051,plain,
! [SV28: $i,SV63: $i] :
( ( ( ~ ( empty @ SV63 ) )
= $true )
| ( ( element @ SV63 @ SV28 )
= $true )
| ( ( empty @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1052,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV29 )
| ~ ( join_commutative @ SV29 ) )
| ~ ( join_semilatt_str @ SV29 ) ) )
= $false )
| ( ( ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1053,plain,
! [SV30: $i] :
( ( ( ~ ( ~ ( element @ ( sK11_SY154 @ SV30 ) @ ( powerset @ ( the_carrier @ SV30 ) ) )
| ~ ~ ( empty @ ( sK11_SY154 @ SV30 ) ) ) )
= $true )
| ( ( empty_carrier @ SV30 )
= $true )
| ( ( one_sorted_str @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1032]) ).
thf(1054,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV35 )
| ~ ( meet_commutative @ SV35 ) )
| ~ ( meet_semilatt_str @ SV35 ) ) )
= $false )
| ( ( ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1055,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV36 )
| ~ ( join_commutative @ SV36 ) )
| ~ ( join_semilatt_str @ SV36 ) ) )
= $false )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1056,plain,
! [SV93: $i,SV75: $i,SV41: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV41 )
| ~ ( meet_semilatt_str @ SV41 ) ) )
= $false )
| ( ( ~ ( element @ SV75 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( ~ ( element @ SV93 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( element @ ( meet @ SV41 @ SV75 @ SV93 ) @ ( the_carrier @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1057,plain,
! [SV97: $i,SV3: $i,SV99: $i] :
( ( ( ~ ( element @ SV99 @ ( the_carrier @ SV3 ) )
| ~ ( ~ ( ~ ( below @ SV3 @ SV97 @ SV99 )
| ( ( join @ SV3 @ SV97 @ SV99 )
= SV99 ) )
| ~ ( ( ( join @ SV3 @ SV97 @ SV99 )
!= SV99 )
| ( below @ SV3 @ SV97 @ SV99 ) ) ) )
= $true )
| ( ( element @ SV97 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_semilatt_str @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1058,plain,
! [SV5: $i] :
( ( ( ~ ( element @ ( sK9_SY117 @ SV5 ) @ ( powerset @ SV5 ) ) )
= $false )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1039]) ).
thf(1059,plain,
! [SV5: $i] :
( ( ( ~ ~ ( empty @ ( sK9_SY117 @ SV5 ) ) )
= $false )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1039]) ).
thf(1060,plain,
! [SV48: $i,SV7: $i,SV79: $i] :
( ( ( empty @ SV79 )
= $false )
| ( ( in @ SV7 @ SV48 )
= $false )
| ( ( element @ SV48 @ ( powerset @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1040]) ).
thf(1061,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1062,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( meet_commutative @ SV10 ) )
| ~ ( meet_semilatt_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1063,plain,
! [SV12: $i,SV94: $i] :
( ( ( epsilon_transitive @ SV94 )
= $true )
| ( ( element @ SV94 @ SV12 )
= $false )
| ( ( ordinal @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1043]) ).
thf(1064,plain,
! [SV12: $i,SV94: $i] :
( ( ( epsilon_connected @ SV94 )
= $true )
| ( ( element @ SV94 @ SV12 )
= $false )
| ( ( ordinal @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1044]) ).
thf(1065,plain,
! [SV98: $i,SV18: $i,SV100: $i] :
( ( ( ~ ( element @ SV100 @ ( the_carrier @ SV18 ) )
| ( ( join @ SV18 @ SV98 @ SV100 )
= ( apply_binary_as_element @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_L_join @ SV18 ) @ SV98 @ SV100 ) ) )
= $true )
| ( ( element @ SV98 @ ( the_carrier @ SV18 ) )
= $false )
| ( ( empty_carrier @ SV18 )
= $true )
| ( ( join_semilatt_str @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1066,plain,
! [SV85: $i,SV61: $i,SV26: $i] :
( ( ( ~ ~ ( empty_carrier @ SV26 )
| ~ ( join_semilatt_str @ SV26 ) )
= $true )
| ( ( ~ ( element @ SV61 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( ~ ( element @ SV85 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( element @ ( join @ SV26 @ SV61 @ SV85 ) @ ( the_carrier @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1047]) ).
thf(1067,plain,
! [SV28: $i,SV63: $i] :
( ( ( ~ ( element @ SV63 @ SV28 ) )
= $true )
| ( ( in @ SV63 @ SV28 )
= $true )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1068,plain,
! [SV28: $i,SV63: $i] :
( ( ( ~ ( in @ SV63 @ SV28 ) )
= $true )
| ( ( element @ SV63 @ SV28 )
= $true )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1069,plain,
! [SV28: $i,SV63: $i] :
( ( ( element @ SV63 @ SV28 )
= $false )
| ( ( empty @ SV63 )
= $true )
| ( ( empty @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1070,plain,
! [SV28: $i,SV63: $i] :
( ( ( empty @ SV63 )
= $false )
| ( ( element @ SV63 @ SV28 )
= $true )
| ( ( empty @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1071,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV29 )
| ~ ( join_commutative @ SV29 ) )
| ~ ( join_semilatt_str @ SV29 ) )
= $true )
| ( ( ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1052]) ).
thf(1072,plain,
! [SV30: $i] :
( ( ( ~ ( element @ ( sK11_SY154 @ SV30 ) @ ( powerset @ ( the_carrier @ SV30 ) ) )
| ~ ~ ( empty @ ( sK11_SY154 @ SV30 ) ) )
= $false )
| ( ( empty_carrier @ SV30 )
= $true )
| ( ( one_sorted_str @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1073,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV35 )
| ~ ( meet_commutative @ SV35 ) )
| ~ ( meet_semilatt_str @ SV35 ) )
= $true )
| ( ( ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1054]) ).
thf(1074,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV36 )
| ~ ( join_commutative @ SV36 ) )
| ~ ( join_semilatt_str @ SV36 ) )
= $true )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1055]) ).
thf(1075,plain,
! [SV93: $i,SV75: $i,SV41: $i] :
( ( ( ~ ~ ( empty_carrier @ SV41 )
| ~ ( meet_semilatt_str @ SV41 ) )
= $true )
| ( ( ~ ( element @ SV75 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( ~ ( element @ SV93 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( element @ ( meet @ SV41 @ SV75 @ SV93 ) @ ( the_carrier @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1056]) ).
thf(1076,plain,
! [SV97: $i,SV3: $i,SV99: $i] :
( ( ( ~ ( element @ SV99 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( below @ SV3 @ SV97 @ SV99 )
| ( ( join @ SV3 @ SV97 @ SV99 )
= SV99 ) )
| ~ ( ( ( join @ SV3 @ SV97 @ SV99 )
!= SV99 )
| ( below @ SV3 @ SV97 @ SV99 ) ) ) )
= $true )
| ( ( element @ SV97 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_semilatt_str @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1077,plain,
! [SV5: $i] :
( ( ( element @ ( sK9_SY117 @ SV5 ) @ ( powerset @ SV5 ) )
= $true )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1058]) ).
thf(1078,plain,
! [SV5: $i] :
( ( ( ~ ( empty @ ( sK9_SY117 @ SV5 ) ) )
= $true )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1059]) ).
thf(1079,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1080,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( meet_commutative @ SV10 ) ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1081,plain,
! [SV98: $i,SV18: $i,SV100: $i] :
( ( ( ~ ( element @ SV100 @ ( the_carrier @ SV18 ) ) )
= $true )
| ( ( ( join @ SV18 @ SV98 @ SV100 )
= ( apply_binary_as_element @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_L_join @ SV18 ) @ SV98 @ SV100 ) )
= $true )
| ( ( element @ SV98 @ ( the_carrier @ SV18 ) )
= $false )
| ( ( empty_carrier @ SV18 )
= $true )
| ( ( join_semilatt_str @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1082,plain,
! [SV85: $i,SV61: $i,SV26: $i] :
( ( ( ~ ~ ( empty_carrier @ SV26 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV26 ) )
= $true )
| ( ( ~ ( element @ SV61 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( ~ ( element @ SV85 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( element @ ( join @ SV26 @ SV61 @ SV85 ) @ ( the_carrier @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1083,plain,
! [SV28: $i,SV63: $i] :
( ( ( element @ SV63 @ SV28 )
= $false )
| ( ( in @ SV63 @ SV28 )
= $true )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1084,plain,
! [SV28: $i,SV63: $i] :
( ( ( in @ SV63 @ SV28 )
= $false )
| ( ( element @ SV63 @ SV28 )
= $true )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1085,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV29 )
| ~ ( join_commutative @ SV29 ) ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV29 ) )
= $true )
| ( ( ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1071]) ).
thf(1086,plain,
! [SV30: $i] :
( ( ( ~ ( element @ ( sK11_SY154 @ SV30 ) @ ( powerset @ ( the_carrier @ SV30 ) ) ) )
= $false )
| ( ( empty_carrier @ SV30 )
= $true )
| ( ( one_sorted_str @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1072]) ).
thf(1087,plain,
! [SV30: $i] :
( ( ( ~ ~ ( empty @ ( sK11_SY154 @ SV30 ) ) )
= $false )
| ( ( empty_carrier @ SV30 )
= $true )
| ( ( one_sorted_str @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1072]) ).
thf(1088,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV35 )
| ~ ( meet_commutative @ SV35 ) ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV35 ) )
= $true )
| ( ( ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1073]) ).
thf(1089,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV36 )
| ~ ( join_commutative @ SV36 ) ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV36 ) )
= $true )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1074]) ).
thf(1090,plain,
! [SV93: $i,SV75: $i,SV41: $i] :
( ( ( ~ ~ ( empty_carrier @ SV41 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV41 ) )
= $true )
| ( ( ~ ( element @ SV75 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( ~ ( element @ SV93 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( element @ ( meet @ SV41 @ SV75 @ SV93 ) @ ( the_carrier @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1091,plain,
! [SV97: $i,SV3: $i,SV99: $i] :
( ( ( element @ SV99 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( below @ SV3 @ SV97 @ SV99 )
| ( ( join @ SV3 @ SV97 @ SV99 )
= SV99 ) )
| ~ ( ( ( join @ SV3 @ SV97 @ SV99 )
!= SV99 )
| ( below @ SV3 @ SV97 @ SV99 ) ) ) )
= $true )
| ( ( element @ SV97 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_semilatt_str @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1092,plain,
! [SV5: $i] :
( ( ( empty @ ( sK9_SY117 @ SV5 ) )
= $false )
| ( ( empty @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1093,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) ) )
= $false )
| ( ( ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1094,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( meet_commutative @ SV10 ) ) )
= $false )
| ( ( ~ ( meet_semilatt_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1095,plain,
! [SV98: $i,SV18: $i,SV100: $i] :
( ( ( element @ SV100 @ ( the_carrier @ SV18 ) )
= $false )
| ( ( ( join @ SV18 @ SV98 @ SV100 )
= ( apply_binary_as_element @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_carrier @ SV18 ) @ ( the_L_join @ SV18 ) @ SV98 @ SV100 ) )
= $true )
| ( ( element @ SV98 @ ( the_carrier @ SV18 ) )
= $false )
| ( ( empty_carrier @ SV18 )
= $true )
| ( ( join_semilatt_str @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1096,plain,
! [SV85: $i,SV61: $i,SV26: $i] :
( ( ( ~ ( empty_carrier @ SV26 ) )
= $false )
| ( ( ~ ( join_semilatt_str @ SV26 ) )
= $true )
| ( ( ~ ( element @ SV61 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( ~ ( element @ SV85 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( element @ ( join @ SV26 @ SV61 @ SV85 ) @ ( the_carrier @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1097,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV29 )
| ~ ( join_commutative @ SV29 ) ) )
= $false )
| ( ( ~ ( join_semilatt_str @ SV29 ) )
= $true )
| ( ( ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1098,plain,
! [SV30: $i] :
( ( ( element @ ( sK11_SY154 @ SV30 ) @ ( powerset @ ( the_carrier @ SV30 ) ) )
= $true )
| ( ( empty_carrier @ SV30 )
= $true )
| ( ( one_sorted_str @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1086]) ).
thf(1099,plain,
! [SV30: $i] :
( ( ( ~ ( empty @ ( sK11_SY154 @ SV30 ) ) )
= $true )
| ( ( empty_carrier @ SV30 )
= $true )
| ( ( one_sorted_str @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1087]) ).
thf(1100,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV35 )
| ~ ( meet_commutative @ SV35 ) ) )
= $false )
| ( ( ~ ( meet_semilatt_str @ SV35 ) )
= $true )
| ( ( ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1101,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV36 )
| ~ ( join_commutative @ SV36 ) ) )
= $false )
| ( ( ~ ( join_semilatt_str @ SV36 ) )
= $true )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1102,plain,
! [SV93: $i,SV75: $i,SV41: $i] :
( ( ( ~ ( empty_carrier @ SV41 ) )
= $false )
| ( ( ~ ( meet_semilatt_str @ SV41 ) )
= $true )
| ( ( ~ ( element @ SV75 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( ~ ( element @ SV93 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( element @ ( meet @ SV41 @ SV75 @ SV93 ) @ ( the_carrier @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1103,plain,
! [SV99: $i,SV97: $i,SV3: $i] :
( ( ( ~ ( ~ ( below @ SV3 @ SV97 @ SV99 )
| ( ( join @ SV3 @ SV97 @ SV99 )
= SV99 ) )
| ~ ( ( ( join @ SV3 @ SV97 @ SV99 )
!= SV99 )
| ( below @ SV3 @ SV97 @ SV99 ) ) )
= $false )
| ( ( element @ SV99 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( element @ SV97 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_semilatt_str @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1104,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1093]) ).
thf(1105,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( meet_commutative @ SV10 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1106,plain,
! [SV85: $i,SV61: $i,SV26: $i] :
( ( ( empty_carrier @ SV26 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV26 ) )
= $true )
| ( ( ~ ( element @ SV61 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( ~ ( element @ SV85 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( element @ ( join @ SV26 @ SV61 @ SV85 ) @ ( the_carrier @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1096]) ).
thf(1107,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ( ~ ~ ( empty_carrier @ SV29 )
| ~ ( join_commutative @ SV29 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV29 ) )
= $true )
| ( ( ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1097]) ).
thf(1108,plain,
! [SV30: $i] :
( ( ( empty @ ( sK11_SY154 @ SV30 ) )
= $false )
| ( ( empty_carrier @ SV30 )
= $true )
| ( ( one_sorted_str @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1109,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ( ~ ~ ( empty_carrier @ SV35 )
| ~ ( meet_commutative @ SV35 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV35 ) )
= $true )
| ( ( ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1100]) ).
thf(1110,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ( ~ ~ ( empty_carrier @ SV36 )
| ~ ( join_commutative @ SV36 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV36 ) )
= $true )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1101]) ).
thf(1111,plain,
! [SV93: $i,SV75: $i,SV41: $i] :
( ( ( empty_carrier @ SV41 )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV41 ) )
= $true )
| ( ( ~ ( element @ SV75 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( ~ ( element @ SV93 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( element @ ( meet @ SV41 @ SV75 @ SV93 ) @ ( the_carrier @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1102]) ).
thf(1112,plain,
! [SV99: $i,SV97: $i,SV3: $i] :
( ( ( ~ ( ~ ( below @ SV3 @ SV97 @ SV99 )
| ( ( join @ SV3 @ SV97 @ SV99 )
= SV99 ) ) )
= $false )
| ( ( element @ SV99 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( element @ SV97 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_semilatt_str @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1113,plain,
! [SV99: $i,SV97: $i,SV3: $i] :
( ( ( ~ ( ( ( join @ SV3 @ SV97 @ SV99 )
!= SV99 )
| ( below @ SV3 @ SV97 @ SV99 ) ) )
= $false )
| ( ( element @ SV99 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( element @ SV97 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_semilatt_str @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1114,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ( ~ ~ ( empty_carrier @ SV8 ) )
= $true )
| ( ( ~ ( join_commutative @ SV8 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1104]) ).
thf(1115,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ( ~ ~ ( empty_carrier @ SV10 ) )
= $true )
| ( ( ~ ( meet_commutative @ SV10 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1116,plain,
! [SV85: $i,SV61: $i,SV26: $i] :
( ( ( join_semilatt_str @ SV26 )
= $false )
| ( ( empty_carrier @ SV26 )
= $true )
| ( ( ~ ( element @ SV61 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( ~ ( element @ SV85 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( element @ ( join @ SV26 @ SV61 @ SV85 ) @ ( the_carrier @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1117,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ( ~ ~ ( empty_carrier @ SV29 ) )
= $true )
| ( ( ~ ( join_commutative @ SV29 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV29 ) )
= $true )
| ( ( ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1118,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ( ~ ~ ( empty_carrier @ SV35 ) )
= $true )
| ( ( ~ ( meet_commutative @ SV35 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV35 ) )
= $true )
| ( ( ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1119,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ( ~ ~ ( empty_carrier @ SV36 ) )
= $true )
| ( ( ~ ( join_commutative @ SV36 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV36 ) )
= $true )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1110]) ).
thf(1120,plain,
! [SV93: $i,SV75: $i,SV41: $i] :
( ( ( meet_semilatt_str @ SV41 )
= $false )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( ~ ( element @ SV75 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( ~ ( element @ SV93 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( element @ ( meet @ SV41 @ SV75 @ SV93 ) @ ( the_carrier @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1121,plain,
! [SV99: $i,SV97: $i,SV3: $i] :
( ( ( ~ ( below @ SV3 @ SV97 @ SV99 )
| ( ( join @ SV3 @ SV97 @ SV99 )
= SV99 ) )
= $true )
| ( ( element @ SV99 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( element @ SV97 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_semilatt_str @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1112]) ).
thf(1122,plain,
! [SV99: $i,SV97: $i,SV3: $i] :
( ( ( ( ( join @ SV3 @ SV97 @ SV99 )
!= SV99 )
| ( below @ SV3 @ SV97 @ SV99 ) )
= $true )
| ( ( element @ SV99 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( element @ SV97 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_semilatt_str @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1113]) ).
thf(1123,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ( ~ ( empty_carrier @ SV8 ) )
= $false )
| ( ( ~ ( join_commutative @ SV8 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1124,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ( ~ ( empty_carrier @ SV10 ) )
= $false )
| ( ( ~ ( meet_commutative @ SV10 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1125,plain,
! [SV85: $i,SV26: $i,SV61: $i] :
( ( ( element @ SV61 @ ( the_carrier @ SV26 ) )
= $false )
| ( ( empty_carrier @ SV26 )
= $true )
| ( ( join_semilatt_str @ SV26 )
= $false )
| ( ( ~ ( element @ SV85 @ ( the_carrier @ SV26 ) ) )
= $true )
| ( ( element @ ( join @ SV26 @ SV61 @ SV85 ) @ ( the_carrier @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1126,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ( ~ ( empty_carrier @ SV29 ) )
= $false )
| ( ( ~ ( join_commutative @ SV29 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV29 ) )
= $true )
| ( ( ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1127,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ( ~ ( empty_carrier @ SV35 ) )
= $false )
| ( ( ~ ( meet_commutative @ SV35 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV35 ) )
= $true )
| ( ( ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1128,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ( ~ ( empty_carrier @ SV36 ) )
= $false )
| ( ( ~ ( join_commutative @ SV36 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV36 ) )
= $true )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1129,plain,
! [SV93: $i,SV41: $i,SV75: $i] :
( ( ( element @ SV75 @ ( the_carrier @ SV41 ) )
= $false )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( meet_semilatt_str @ SV41 )
= $false )
| ( ( ~ ( element @ SV93 @ ( the_carrier @ SV41 ) ) )
= $true )
| ( ( element @ ( meet @ SV41 @ SV75 @ SV93 ) @ ( the_carrier @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1130,plain,
! [SV99: $i,SV97: $i,SV3: $i] :
( ( ( ~ ( below @ SV3 @ SV97 @ SV99 ) )
= $true )
| ( ( ( join @ SV3 @ SV97 @ SV99 )
= SV99 )
= $true )
| ( ( element @ SV99 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( element @ SV97 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_semilatt_str @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1131,plain,
! [SV99: $i,SV97: $i,SV3: $i] :
( ( ( ( join @ SV3 @ SV97 @ SV99 )
!= SV99 )
= $true )
| ( ( below @ SV3 @ SV97 @ SV99 )
= $true )
| ( ( element @ SV99 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( element @ SV97 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_semilatt_str @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1122]) ).
thf(1132,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ( empty_carrier @ SV8 )
= $true )
| ( ( ~ ( join_commutative @ SV8 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1123]) ).
thf(1133,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ( empty_carrier @ SV10 )
= $true )
| ( ( ~ ( meet_commutative @ SV10 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1134,plain,
! [SV61: $i,SV26: $i,SV85: $i] :
( ( ( element @ SV85 @ ( the_carrier @ SV26 ) )
= $false )
| ( ( join_semilatt_str @ SV26 )
= $false )
| ( ( empty_carrier @ SV26 )
= $true )
| ( ( element @ SV61 @ ( the_carrier @ SV26 ) )
= $false )
| ( ( element @ ( join @ SV26 @ SV61 @ SV85 ) @ ( the_carrier @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1135,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ( empty_carrier @ SV29 )
= $true )
| ( ( ~ ( join_commutative @ SV29 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV29 ) )
= $true )
| ( ( ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1126]) ).
thf(1136,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ( empty_carrier @ SV35 )
= $true )
| ( ( ~ ( meet_commutative @ SV35 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV35 ) )
= $true )
| ( ( ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1127]) ).
thf(1137,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ( empty_carrier @ SV36 )
= $true )
| ( ( ~ ( join_commutative @ SV36 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV36 ) )
= $true )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1138,plain,
! [SV75: $i,SV41: $i,SV93: $i] :
( ( ( element @ SV93 @ ( the_carrier @ SV41 ) )
= $false )
| ( ( meet_semilatt_str @ SV41 )
= $false )
| ( ( empty_carrier @ SV41 )
= $true )
| ( ( element @ SV75 @ ( the_carrier @ SV41 ) )
= $false )
| ( ( element @ ( meet @ SV41 @ SV75 @ SV93 ) @ ( the_carrier @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1139,plain,
! [SV99: $i,SV97: $i,SV3: $i] :
( ( ( below @ SV3 @ SV97 @ SV99 )
= $false )
| ( ( ( join @ SV3 @ SV97 @ SV99 )
= SV99 )
= $true )
| ( ( element @ SV99 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( element @ SV97 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_semilatt_str @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1140,plain,
! [SV99: $i,SV97: $i,SV3: $i] :
( ( ( ( join @ SV3 @ SV97 @ SV99 )
= SV99 )
= $false )
| ( ( below @ SV3 @ SV97 @ SV99 )
= $true )
| ( ( element @ SV99 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( element @ SV97 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_semilatt_str @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1141,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ( join_commutative @ SV8 )
= $false )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1142,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ( meet_commutative @ SV10 )
= $false )
| ( ( empty_carrier @ SV10 )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1143,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ( join_commutative @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV29 ) )
= $true )
| ( ( ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1144,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ( meet_commutative @ SV35 )
= $false )
| ( ( empty_carrier @ SV35 )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV35 ) )
= $true )
| ( ( ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1145,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ( join_commutative @ SV36 )
= $false )
| ( ( empty_carrier @ SV36 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV36 ) )
= $true )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1146,plain,
! [SV80: $i,SV49: $i,SV8: $i] :
( ( ( join_semilatt_str @ SV8 )
= $false )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( join_commutative @ SV8 )
= $false )
| ( ( ~ ( element @ SV49 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1147,plain,
! [SV82: $i,SV51: $i,SV10: $i] :
( ( ( meet_semilatt_str @ SV10 )
= $false )
| ( ( empty_carrier @ SV10 )
= $true )
| ( ( meet_commutative @ SV10 )
= $false )
| ( ( ~ ( element @ SV51 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1148,plain,
! [SV87: $i,SV64: $i,SV29: $i] :
( ( ( join_semilatt_str @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( join_commutative @ SV29 )
= $false )
| ( ( ~ ( element @ SV64 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1149,plain,
! [SV89: $i,SV69: $i,SV35: $i] :
( ( ( meet_semilatt_str @ SV35 )
= $false )
| ( ( empty_carrier @ SV35 )
= $true )
| ( ( meet_commutative @ SV35 )
= $false )
| ( ( ~ ( element @ SV69 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1150,plain,
! [SV90: $i,SV70: $i,SV36: $i] :
( ( ( join_semilatt_str @ SV36 )
= $false )
| ( ( empty_carrier @ SV36 )
= $true )
| ( ( join_commutative @ SV36 )
= $false )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1151,plain,
! [SV80: $i,SV8: $i,SV49: $i] :
( ( ( element @ SV49 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( join_commutative @ SV8 )
= $false )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( join_semilatt_str @ SV8 )
= $false )
| ( ( ~ ( element @ SV80 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1152,plain,
! [SV82: $i,SV10: $i,SV51: $i] :
( ( ( element @ SV51 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( meet_commutative @ SV10 )
= $false )
| ( ( empty_carrier @ SV10 )
= $true )
| ( ( meet_semilatt_str @ SV10 )
= $false )
| ( ( ~ ( element @ SV82 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1153,plain,
! [SV87: $i,SV29: $i,SV64: $i] :
( ( ( element @ SV64 @ ( the_carrier @ SV29 ) )
= $false )
| ( ( join_commutative @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( join_semilatt_str @ SV29 )
= $false )
| ( ( ~ ( element @ SV87 @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1154,plain,
! [SV89: $i,SV35: $i,SV69: $i] :
( ( ( element @ SV69 @ ( the_carrier @ SV35 ) )
= $false )
| ( ( meet_commutative @ SV35 )
= $false )
| ( ( empty_carrier @ SV35 )
= $true )
| ( ( meet_semilatt_str @ SV35 )
= $false )
| ( ( ~ ( element @ SV89 @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1155,plain,
! [SV90: $i,SV36: $i,SV70: $i] :
( ( ( element @ SV70 @ ( the_carrier @ SV36 ) )
= $false )
| ( ( join_commutative @ SV36 )
= $false )
| ( ( empty_carrier @ SV36 )
= $true )
| ( ( join_semilatt_str @ SV36 )
= $false )
| ( ( ~ ( element @ SV90 @ ( the_carrier @ SV36 ) ) )
= $true )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1156,plain,
! [SV49: $i,SV8: $i,SV80: $i] :
( ( ( element @ SV80 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( join_semilatt_str @ SV8 )
= $false )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( join_commutative @ SV8 )
= $false )
| ( ( element @ SV49 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( element @ ( join_commut @ SV8 @ SV49 @ SV80 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1157,plain,
! [SV51: $i,SV10: $i,SV82: $i] :
( ( ( element @ SV82 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( meet_semilatt_str @ SV10 )
= $false )
| ( ( empty_carrier @ SV10 )
= $true )
| ( ( meet_commutative @ SV10 )
= $false )
| ( ( element @ SV51 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( ( meet_commut @ SV10 @ SV51 @ SV82 )
= ( meet_commut @ SV10 @ SV82 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1158,plain,
! [SV64: $i,SV29: $i,SV87: $i] :
( ( ( element @ SV87 @ ( the_carrier @ SV29 ) )
= $false )
| ( ( join_semilatt_str @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( join_commutative @ SV29 )
= $false )
| ( ( element @ SV64 @ ( the_carrier @ SV29 ) )
= $false )
| ( ( ( join_commut @ SV29 @ SV64 @ SV87 )
= ( join @ SV29 @ SV64 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1159,plain,
! [SV69: $i,SV35: $i,SV89: $i] :
( ( ( element @ SV89 @ ( the_carrier @ SV35 ) )
= $false )
| ( ( meet_semilatt_str @ SV35 )
= $false )
| ( ( empty_carrier @ SV35 )
= $true )
| ( ( meet_commutative @ SV35 )
= $false )
| ( ( element @ SV69 @ ( the_carrier @ SV35 ) )
= $false )
| ( ( element @ ( meet_commut @ SV35 @ SV69 @ SV89 ) @ ( the_carrier @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1160,plain,
! [SV70: $i,SV36: $i,SV90: $i] :
( ( ( element @ SV90 @ ( the_carrier @ SV36 ) )
= $false )
| ( ( join_semilatt_str @ SV36 )
= $false )
| ( ( empty_carrier @ SV36 )
= $true )
| ( ( join_commutative @ SV36 )
= $false )
| ( ( element @ SV70 @ ( the_carrier @ SV36 ) )
= $false )
| ( ( ( join_commut @ SV36 @ SV70 @ SV90 )
= ( join_commut @ SV36 @ SV90 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1161,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[551,1160,1159,1158,1157,1156,1140,1139,1138,1134,1108,1098,1095,1092,1084,1083,1077,1070,1069,1064,1063,1060,1046,1034,1033,1025,1023,1021,1016,1013,1007,995,992,989,959,958,948,947,946,942,940,925,923,914,908,907,906,903,892,889,884,878,873,855,854,851,843,842,839,829,827,821,817,810,808,807,760,665,664,614,613,593,591,590,587,586,580,579,578,575,574,572,570,569,568,566,565,563,562,561,560,559,558,557,556,554,553,552]) ).
thf(1162,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU305+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n019.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 15:13:03 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 43.91/7.60 ....
% 43.91/7.60
% 43.91/7.60 No.of.Axioms: 75
% 43.91/7.60
% 43.91/7.60 Length.of.Defs: 0
% 43.91/7.60
% 43.91/7.60 Contains.Choice.Funs: false
% 43.91/7.60 .........................
% 43.91/7.60
% 43.91/7.60 ********************************
% 43.91/7.60 * All subproblems solved! *
% 43.91/7.60 ********************************
% 43.91/7.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:78,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1161,loop_count:0,foatp_calls:1,translation:fof_full)
% 43.91/7.60
% 43.91/7.60 %**** Beginning of derivation protocol ****
% 43.91/7.60 % SZS output start CNFRefutation
% See solution above
% 7.54/7.61
% 7.54/7.61 %**** End of derivation protocol ****
% 7.54/7.61 %**** no. of clauses in derivation: 784 ****
% 7.54/7.61 %**** clause counter: 1161 ****
% 7.54/7.61
% 7.54/7.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:78,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1161,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------