%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU348+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:44:04 AM UTC 2026
% Result : Theorem 7.97s 1.54s
% Output : CNFRefutation 7.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 40
% Syntax : Number of formulae : 296 ( 190 unt; 0 typ; 0 def)
% Number of atoms : 1909 ( 537 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 3338 ( 770 ~; 506 |; 58 &;1953 @)
% ( 11 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 165 ( 162 usr; 11 con; 0-6 aty)
% Number of variables : 314 ( 0 ^; 299 !; 15 ?; 314 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_1_0_filter_1,type,
a_1_0_filter_1: $i > $i ).
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_antisymmetric_relstr,type,
antisymmetric_relstr: $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_below_refl,type,
below_refl: $i > $i > $i > $o ).
thf(tp_boole_lattice,type,
boole_lattice: $i > $i ).
thf(tp_bottom_of_semilattstr,type,
bottom_of_semilattstr: $i > $i ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_cast_as_carrier_subset,type,
cast_as_carrier_subset: $i > $i ).
thf(tp_cast_to_el_of_LattPOSet,type,
cast_to_el_of_LattPOSet: $i > $i > $i ).
thf(tp_cast_to_el_of_lattice,type,
cast_to_el_of_lattice: $i > $i > $i ).
thf(tp_cast_to_subset,type,
cast_to_subset: $i > $i ).
thf(tp_centered,type,
centered: $i > $o ).
thf(tp_closed_subset,type,
closed_subset: $i > $i > $o ).
thf(tp_closed_subsets,type,
closed_subsets: $i > $i > $o ).
thf(tp_compact_top_space,type,
compact_top_space: $i > $o ).
thf(tp_complements_of_subsets,type,
complements_of_subsets: $i > $i > $i ).
thf(tp_connected,type,
connected: $i > $o ).
thf(tp_cup_closed,type,
cup_closed: $i > $o ).
thf(tp_diff_closed,type,
diff_closed: $i > $o ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_carrier,type,
empty_carrier: $i > $o ).
thf(tp_empty_carrier_subset,type,
empty_carrier_subset: $i > $i ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_equipotent,type,
equipotent: $i > $i > $o ).
thf(tp_fiber,type,
fiber: $i > $i > $i ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_function_inverse,type,
function_inverse: $i > $i ).
thf(tp_identity_relation,type,
identity_relation: $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_inclusion_relation,type,
inclusion_relation: $i > $i ).
thf(tp_interior,type,
interior: $i > $i > $i ).
thf(tp_is_a_cover_of_carrier,type,
is_a_cover_of_carrier: $i > $i > $o ).
thf(tp_is_antisymmetric_in,type,
is_antisymmetric_in: $i > $i > $o ).
thf(tp_is_connected_in,type,
is_connected_in: $i > $i > $o ).
thf(tp_is_reflexive_in,type,
is_reflexive_in: $i > $i > $o ).
thf(tp_is_transitive_in,type,
is_transitive_in: $i > $i > $o ).
thf(tp_is_well_founded_in,type,
is_well_founded_in: $i > $i > $o ).
thf(tp_join,type,
join: $i > $i > $i > $i ).
thf(tp_join_absorbing,type,
join_absorbing: $i > $o ).
thf(tp_join_associative,type,
join_associative: $i > $o ).
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_k10_filter_1,type,
k10_filter_1: $i > $i > $i > $i > $i ).
thf(tp_k2_lattice3,type,
k2_lattice3: $i > $i ).
thf(tp_k8_filter_1,type,
k8_filter_1: $i > $i > $i ).
thf(tp_latt_set_smaller,type,
latt_set_smaller: $i > $i > $i > $o ).
thf(tp_latt_str,type,
latt_str: $i > $o ).
thf(tp_latt_str_of,type,
latt_str_of: $i > $i > $i > $i ).
thf(tp_lattice,type,
lattice: $i > $o ).
thf(tp_lower_bounded_semilattstr,type,
lower_bounded_semilattstr: $i > $o ).
thf(tp_meet,type,
meet: $i > $i > $i > $i ).
thf(tp_meet_absorbing,type,
meet_absorbing: $i > $o ).
thf(tp_meet_associative,type,
meet_associative: $i > $o ).
thf(tp_meet_commut,type,
meet_commut: $i > $i > $i > $i ).
thf(tp_meet_commutative,type,
meet_commutative: $i > $o ).
thf(tp_meet_of_subsets,type,
meet_of_subsets: $i > $i > $i ).
thf(tp_meet_semilatt_str,type,
meet_semilatt_str: $i > $o ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_omega,type,
omega: $i ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_open_subset,type,
open_subset: $i > $i > $o ).
thf(tp_open_subsets,type,
open_subsets: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_ordered_pair_as_product_element,type,
ordered_pair_as_product_element: $i > $i > $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_point_neighbourhood,type,
point_neighbourhood: $i > $i > $i > $o ).
thf(tp_poset_of_lattice,type,
poset_of_lattice: $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_reflexive_relstr,type,
reflexive_relstr: $i > $o ).
thf(tp_rel_str,type,
rel_str: $i > $o ).
thf(tp_rel_str_of,type,
rel_str_of: $i > $i > $i ).
thf(tp_related,type,
related: $i > $i > $i > $o ).
thf(tp_related_reflexive,type,
related_reflexive: $i > $i > $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_of_lattice,type,
relation_of_lattice: $i > $i ).
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_relstr_element_smaller,type,
relstr_element_smaller: $i > $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY22,type,
sK2_SY22: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK6_SX0,type,
sK6_SX0: $i ).
thf(tp_sK7_SX0,type,
sK7_SX0: $i ).
thf(tp_sK8_SY29,type,
sK8_SY29: $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_strict_latt_str,type,
strict_latt_str: $i > $o ).
thf(tp_strict_rel_str,type,
strict_rel_str: $i > $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_subset_intersection2,type,
subset_intersection2: $i > $i > $i > $i ).
thf(tp_subset_union2,type,
subset_union2: $i > $i > $i > $i ).
thf(tp_succ,type,
succ: $i > $i ).
thf(tp_the_InternalRel,type,
the_InternalRel: $i > $i ).
thf(tp_the_L_join,type,
the_L_join: $i > $i ).
thf(tp_the_L_meet,type,
the_L_meet: $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_the_topology,type,
the_topology: $i > $i ).
thf(tp_top_str,type,
top_str: $i > $o ).
thf(tp_topological_space,type,
topological_space: $i > $o ).
thf(tp_topstr_closure,type,
topstr_closure: $i > $i > $i ).
thf(tp_transitive,type,
transitive: $i > $o ).
thf(tp_transitive_relstr,type,
transitive_relstr: $i > $o ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_union_of_subsets,type,
union_of_subsets: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(tp_unordered_triple,type,
unordered_triple: $i > $i > $i > $i ).
thf(tp_v1_binop_1,type,
v1_binop_1: $i > $i > $o ).
thf(tp_v1_int_1,type,
v1_int_1: $i > $o ).
thf(tp_v1_membered,type,
v1_membered: $i > $o ).
thf(tp_v1_partfun1,type,
v1_partfun1: $i > $i > $i > $o ).
thf(tp_v1_rat_1,type,
v1_rat_1: $i > $o ).
thf(tp_v1_xcmplx_0,type,
v1_xcmplx_0: $i > $o ).
thf(tp_v1_xreal_0,type,
v1_xreal_0: $i > $o ).
thf(tp_v2_binop_1,type,
v2_binop_1: $i > $i > $o ).
thf(tp_v2_membered,type,
v2_membered: $i > $o ).
thf(tp_v3_membered,type,
v3_membered: $i > $o ).
thf(tp_v4_membered,type,
v4_membered: $i > $o ).
thf(tp_v5_membered,type,
v5_membered: $i > $o ).
thf(tp_well_founded_relation,type,
well_founded_relation: $i > $o ).
thf(tp_well_ordering,type,
well_ordering: $i > $o ).
thf(tp_well_orders,type,
well_orders: $i > $i > $o ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(60,axiom,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_lattices) ).
thf(64,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(67,axiom,
? [A: $i] :
( ( latt_str @ A )
& ( strict_latt_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_lattices) ).
thf(178,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(181,axiom,
? [A: $i] : ( latt_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(188,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(193,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(194,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(198,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(202,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(216,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_ordinal2) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) )
=> ( element @ ( cast_to_el_of_lattice @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattice3) ).
thf(219,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(220,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ( element @ ( cast_to_el_of_LattPOSet @ A @ B ) @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattice3) ).
thf(226,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(227,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(229,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(232,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(233,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(235,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(237,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(239,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_mcart_1) ).
thf(244,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(245,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(247,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord1) ).
thf(249,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(250,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(251,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(253,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(254,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_mcart_1) ).
thf(257,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(258,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_enumset1) ).
thf(260,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_binop_1) ).
thf(261,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(302,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) )
=> ( ( cast_to_el_of_lattice @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lattice3) ).
thf(311,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( cast_to_el_of_LattPOSet @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
thf(510,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( latt_set_smaller @ B @ C @ A )
<=> ( relstr_element_smaller @ ( poset_of_lattice @ B ) @ A @ ( cast_to_el_of_LattPOSet @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_lattice3) ).
thf(636,conjecture,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( poset_of_lattice @ B ) ) )
=> ( ( relstr_element_smaller @ ( poset_of_lattice @ B ) @ A @ C )
<=> ( latt_set_smaller @ B @ ( cast_to_el_of_lattice @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_lattice3) ).
thf(637,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( poset_of_lattice @ B ) ) )
=> ( ( relstr_element_smaller @ ( poset_of_lattice @ B ) @ A @ C )
<=> ( latt_set_smaller @ B @ ( cast_to_el_of_lattice @ B @ C ) @ A ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[636]) ).
thf(638,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( poset_of_lattice @ B ) ) )
=> ( ( relstr_element_smaller @ ( poset_of_lattice @ B ) @ A @ C )
<=> ( latt_set_smaller @ B @ ( cast_to_el_of_lattice @ B @ C ) @ A ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[637]) ).
thf(639,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(640,plain,
( ( ? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(641,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(642,plain,
( ( ? [A: $i] :
( ( latt_str @ A )
& ( strict_latt_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(643,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(644,plain,
( ( ? [A: $i] : ( latt_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(645,plain,
$true = $true,
inference(unfold_def,[status(thm)],[188]) ).
thf(646,plain,
$true = $true,
inference(unfold_def,[status(thm)],[193]) ).
thf(647,plain,
$true = $true,
inference(unfold_def,[status(thm)],[194]) ).
thf(648,plain,
$true = $true,
inference(unfold_def,[status(thm)],[198]) ).
thf(649,plain,
$true = $true,
inference(unfold_def,[status(thm)],[202]) ).
thf(650,plain,
$true = $true,
inference(unfold_def,[status(thm)],[216]) ).
thf(651,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) )
=> ( element @ ( cast_to_el_of_lattice @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(652,plain,
$true = $true,
inference(unfold_def,[status(thm)],[219]) ).
thf(653,plain,
$true = $true,
inference(unfold_def,[status(thm)],[220]) ).
thf(654,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ( element @ ( cast_to_el_of_LattPOSet @ A @ B ) @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(655,plain,
$true = $true,
inference(unfold_def,[status(thm)],[226]) ).
thf(656,plain,
$true = $true,
inference(unfold_def,[status(thm)],[227]) ).
thf(657,plain,
$true = $true,
inference(unfold_def,[status(thm)],[229]) ).
thf(658,plain,
$true = $true,
inference(unfold_def,[status(thm)],[232]) ).
thf(659,plain,
$true = $true,
inference(unfold_def,[status(thm)],[233]) ).
thf(660,plain,
$true = $true,
inference(unfold_def,[status(thm)],[235]) ).
thf(661,plain,
$true = $true,
inference(unfold_def,[status(thm)],[237]) ).
thf(662,plain,
$true = $true,
inference(unfold_def,[status(thm)],[239]) ).
thf(663,plain,
$true = $true,
inference(unfold_def,[status(thm)],[244]) ).
thf(664,plain,
$true = $true,
inference(unfold_def,[status(thm)],[245]) ).
thf(665,plain,
$true = $true,
inference(unfold_def,[status(thm)],[247]) ).
thf(666,plain,
$true = $true,
inference(unfold_def,[status(thm)],[249]) ).
thf(667,plain,
$true = $true,
inference(unfold_def,[status(thm)],[250]) ).
thf(668,plain,
$true = $true,
inference(unfold_def,[status(thm)],[251]) ).
thf(669,plain,
$true = $true,
inference(unfold_def,[status(thm)],[253]) ).
thf(670,plain,
$true = $true,
inference(unfold_def,[status(thm)],[254]) ).
thf(671,plain,
$true = $true,
inference(unfold_def,[status(thm)],[257]) ).
thf(672,plain,
$true = $true,
inference(unfold_def,[status(thm)],[258]) ).
thf(673,plain,
$true = $true,
inference(unfold_def,[status(thm)],[260]) ).
thf(674,plain,
$true = $true,
inference(unfold_def,[status(thm)],[261]) ).
thf(675,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) )
=> ( ( cast_to_el_of_lattice @ A @ B )
= B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(676,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( cast_to_el_of_LattPOSet @ A @ B )
= B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(677,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( latt_set_smaller @ B @ C @ A )
<=> ( relstr_element_smaller @ ( poset_of_lattice @ B ) @ A @ ( cast_to_el_of_LattPOSet @ B @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(678,plain,
( ( ! [SY22: $i] :
( ( ~ ( empty_carrier @ SY22 )
& ( lattice @ SY22 )
& ( latt_str @ SY22 ) )
=> ! [SY23: $i] :
( ( element @ SY23 @ ( the_carrier @ ( poset_of_lattice @ SY22 ) ) )
=> ( ( relstr_element_smaller @ ( poset_of_lattice @ SY22 ) @ sK1_A @ SY23 )
<=> ( latt_set_smaller @ SY22 @ ( cast_to_el_of_lattice @ SY22 @ SY23 ) @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[638]) ).
thf(679,plain,
( ( ( ~ ( empty_carrier @ sK2_SY22 )
& ( lattice @ sK2_SY22 )
& ( latt_str @ sK2_SY22 ) )
=> ! [SY24: $i] :
( ( element @ SY24 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY22 ) ) )
=> ( ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ SY24 )
<=> ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ SY24 ) @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[678]) ).
thf(680,plain,
( ( ~ ( empty_carrier @ sK2_SY22 ) )
= $true ),
inference(standard_cnf,[status(thm)],[679]) ).
thf(681,plain,
( ( lattice @ sK2_SY22 )
= $true ),
inference(standard_cnf,[status(thm)],[679]) ).
thf(682,plain,
( ( latt_str @ sK2_SY22 )
= $true ),
inference(standard_cnf,[status(thm)],[679]) ).
thf(683,plain,
( ( ! [SY24: $i] :
( ( element @ SY24 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY22 ) ) )
=> ( ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ SY24 )
<=> ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ SY24 ) @ sK1_A ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[679]) ).
thf(684,plain,
( ( ~ ! [SY24: $i] :
( ( element @ SY24 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY22 ) ) )
=> ( ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ SY24 )
<=> ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ SY24 ) @ sK1_A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[683]) ).
thf(685,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( latt_set_smaller @ B @ C @ A )
<=> ( relstr_element_smaller @ ( poset_of_lattice @ B ) @ A @ ( cast_to_el_of_LattPOSet @ B @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[677]) ).
thf(686,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( cast_to_el_of_LattPOSet @ A @ B )
= B ) ) ) )
= $true ),
inference(copy,[status(thm)],[676]) ).
thf(687,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) )
=> ( ( cast_to_el_of_lattice @ A @ B )
= B ) ) ) )
= $true ),
inference(copy,[status(thm)],[675]) ).
thf(688,plain,
$true = $true,
inference(copy,[status(thm)],[674]) ).
thf(689,plain,
$true = $true,
inference(copy,[status(thm)],[673]) ).
thf(690,plain,
$true = $true,
inference(copy,[status(thm)],[672]) ).
thf(691,plain,
$true = $true,
inference(copy,[status(thm)],[671]) ).
thf(692,plain,
$true = $true,
inference(copy,[status(thm)],[670]) ).
thf(693,plain,
$true = $true,
inference(copy,[status(thm)],[669]) ).
thf(694,plain,
$true = $true,
inference(copy,[status(thm)],[668]) ).
thf(695,plain,
$true = $true,
inference(copy,[status(thm)],[667]) ).
thf(696,plain,
$true = $true,
inference(copy,[status(thm)],[666]) ).
thf(697,plain,
$true = $true,
inference(copy,[status(thm)],[665]) ).
thf(698,plain,
$true = $true,
inference(copy,[status(thm)],[664]) ).
thf(699,plain,
$true = $true,
inference(copy,[status(thm)],[663]) ).
thf(700,plain,
$true = $true,
inference(copy,[status(thm)],[662]) ).
thf(701,plain,
$true = $true,
inference(copy,[status(thm)],[661]) ).
thf(702,plain,
$true = $true,
inference(copy,[status(thm)],[660]) ).
thf(703,plain,
$true = $true,
inference(copy,[status(thm)],[659]) ).
thf(704,plain,
$true = $true,
inference(copy,[status(thm)],[658]) ).
thf(705,plain,
$true = $true,
inference(copy,[status(thm)],[657]) ).
thf(706,plain,
$true = $true,
inference(copy,[status(thm)],[656]) ).
thf(707,plain,
$true = $true,
inference(copy,[status(thm)],[655]) ).
thf(708,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ( element @ ( cast_to_el_of_LattPOSet @ A @ B ) @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[654]) ).
thf(709,plain,
$true = $true,
inference(copy,[status(thm)],[653]) ).
thf(710,plain,
$true = $true,
inference(copy,[status(thm)],[652]) ).
thf(711,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) )
=> ( element @ ( cast_to_el_of_lattice @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[651]) ).
thf(712,plain,
$true = $true,
inference(copy,[status(thm)],[650]) ).
thf(713,plain,
$true = $true,
inference(copy,[status(thm)],[649]) ).
thf(714,plain,
$true = $true,
inference(copy,[status(thm)],[648]) ).
thf(715,plain,
$true = $true,
inference(copy,[status(thm)],[647]) ).
thf(716,plain,
$true = $true,
inference(copy,[status(thm)],[646]) ).
thf(717,plain,
$true = $true,
inference(copy,[status(thm)],[645]) ).
thf(718,plain,
( ( ? [A: $i] : ( latt_str @ A ) )
= $true ),
inference(copy,[status(thm)],[644]) ).
thf(719,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[643]) ).
thf(720,plain,
( ( ? [A: $i] :
( ( latt_str @ A )
& ( strict_latt_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[642]) ).
thf(721,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(copy,[status(thm)],[641]) ).
thf(722,plain,
( ( ? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[640]) ).
thf(723,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[639]) ).
thf(724,plain,
( ( latt_str @ sK2_SY22 )
= $true ),
inference(copy,[status(thm)],[682]) ).
thf(725,plain,
( ( lattice @ sK2_SY22 )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(726,plain,
( ( ~ ( empty_carrier @ sK2_SY22 ) )
= $true ),
inference(copy,[status(thm)],[680]) ).
thf(727,plain,
( ( ~ ! [SY24: $i] :
( ( element @ SY24 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY22 ) ) )
=> ( ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ SY24 )
<=> ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ SY24 ) @ sK1_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[684]) ).
thf(728,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( latt_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) )
| ~ ( strict_latt_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[722]) ).
thf(729,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( lattice @ SX0 ) )
| ~ ( latt_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ ( poset_of_lattice @ SX0 ) ) ) )
| ( element @ ( cast_to_el_of_lattice @ SX0 @ SX1 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[711]) ).
thf(730,plain,
( ( ~ ! [SX0: $i] :
~ ( latt_str @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[718]) ).
thf(731,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( lattice @ SX0 ) )
| ~ ( latt_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ( element @ ( cast_to_el_of_LattPOSet @ SX0 @ SX1 ) @ ( the_carrier @ ( poset_of_lattice @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[708]) ).
thf(732,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[723]) ).
thf(733,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[721]) ).
thf(734,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( latt_str @ SX0 )
| ~ ( strict_latt_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[720]) ).
thf(735,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( lattice @ SX0 ) )
| ~ ( latt_str @ SX0 ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ ( poset_of_lattice @ SX0 ) ) )
| ( ( cast_to_el_of_lattice @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[687]) ).
thf(736,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[719]) ).
thf(737,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX1 )
| ~ ( lattice @ SX1 ) )
| ~ ( latt_str @ SX1 ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX1 ) )
| ~ ( ~ ( ~ ( latt_set_smaller @ SX1 @ SX2 @ SX0 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SX1 ) @ SX0 @ ( cast_to_el_of_LattPOSet @ SX1 @ SX2 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SX1 ) @ SX0 @ ( cast_to_el_of_LattPOSet @ SX1 @ SX2 ) )
| ( latt_set_smaller @ SX1 @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[685]) ).
thf(738,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY22 ) ) )
| ~ ( ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ SX0 )
| ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ SX0 ) @ sK1_A ) )
| ~ ( ~ ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ SX0 ) @ sK1_A )
| ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[727]) ).
thf(739,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( lattice @ SX0 ) )
| ~ ( latt_str @ SX0 ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ( ( cast_to_el_of_LattPOSet @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[686]) ).
thf(740,plain,
( ( empty_carrier @ sK2_SY22 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(741,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( latt_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) )
| ~ ( strict_latt_str @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(742,plain,
! [SV1: $i] :
( ( ! [SY25: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) )
| ~ ( latt_str @ SV1 ) )
| ~ ( element @ SY25 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) ) )
| ( element @ ( cast_to_el_of_lattice @ SV1 @ SY25 ) @ ( the_carrier @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(743,plain,
( ( ! [SX0: $i] :
~ ( latt_str @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(744,plain,
! [SV2: $i] :
( ( ! [SY26: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
| ~ ( latt_str @ SV2 ) )
| ~ ( element @ SY26 @ ( the_carrier @ SV2 ) ) )
| ( element @ ( cast_to_el_of_LattPOSet @ SV2 @ SY26 ) @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(745,plain,
! [SV3: $i] :
( ( ! [SY27: $i] :
( ~ ( in @ SV3 @ SY27 )
| ( element @ SV3 @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(746,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(747,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( latt_str @ SX0 )
| ~ ( strict_latt_str @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(748,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV4 )
| ~ ( lattice @ SV4 ) )
| ~ ( latt_str @ SV4 ) )
| ! [SY28: $i] :
( ~ ( element @ SY28 @ ( the_carrier @ ( poset_of_lattice @ SV4 ) ) )
| ( ( cast_to_el_of_lattice @ SV4 @ SY28 )
= SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(749,plain,
! [SV5: $i] :
( ( ~ ! [SY29: $i] :
~ ( element @ SY29 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(750,plain,
! [SV6: $i] :
( ( ! [SY30: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SY30 )
| ~ ( lattice @ SY30 ) )
| ~ ( latt_str @ SY30 ) )
| ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SY30 ) )
| ~ ( ~ ( ~ ( latt_set_smaller @ SY30 @ SY31 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SY30 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SY30 @ SY31 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SY30 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SY30 @ SY31 ) )
| ( latt_set_smaller @ SY30 @ SY31 @ SV6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(751,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY22 ) ) )
| ~ ( ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ SX0 )
| ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ SX0 ) @ sK1_A ) )
| ~ ( ~ ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ SX0 ) @ sK1_A )
| ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(752,plain,
! [SV7: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV7 )
| ~ ( lattice @ SV7 ) )
| ~ ( latt_str @ SV7 ) )
| ! [SY32: $i] :
( ~ ( element @ SY32 @ ( the_carrier @ SV7 ) )
| ( ( cast_to_el_of_LattPOSet @ SV7 @ SY32 )
= SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(753,plain,
( ( ~ ~ ( ~ ~ ( ~ ( latt_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) )
| ~ ( strict_latt_str @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[741]) ).
thf(754,plain,
! [SV8: $i,SV1: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) )
| ~ ( latt_str @ SV1 ) )
| ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) ) )
| ( element @ ( cast_to_el_of_lattice @ SV1 @ SV8 ) @ ( the_carrier @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(755,plain,
( ( ~ ( latt_str @ sK4_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[743]) ).
thf(756,plain,
! [SV9: $i,SV2: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
| ~ ( latt_str @ SV2 ) )
| ~ ( element @ SV9 @ ( the_carrier @ SV2 ) ) )
| ( element @ ( cast_to_el_of_LattPOSet @ SV2 @ SV9 ) @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(757,plain,
! [SV10: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ SV10 )
| ( element @ SV3 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(758,plain,
( ( ~ ~ ( ~ ( one_sorted_str @ sK5_SX0 )
| ~ ~ ( empty_carrier @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[746]) ).
thf(759,plain,
( ( ~ ~ ( ~ ( latt_str @ sK6_SX0 )
| ~ ( strict_latt_str @ sK6_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[747]) ).
thf(760,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV4 )
| ~ ( lattice @ SV4 ) )
| ~ ( latt_str @ SV4 ) ) )
= $true )
| ( ( ! [SY28: $i] :
( ~ ( element @ SY28 @ ( the_carrier @ ( poset_of_lattice @ SV4 ) ) )
| ( ( cast_to_el_of_lattice @ SV4 @ SY28 )
= SY28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(761,plain,
! [SV5: $i] :
( ( ! [SY29: $i] :
~ ( element @ SY29 @ SV5 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(762,plain,
! [SV6: $i,SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( lattice @ SV11 ) )
| ~ ( latt_str @ SV11 ) )
| ! [SY33: $i] :
( ~ ( element @ SY33 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_set_smaller @ SV11 @ SY33 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) )
| ( latt_set_smaller @ SV11 @ SY33 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(763,plain,
( ( ~ ( element @ sK7_SX0 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY22 ) ) )
| ~ ( ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 )
| ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A ) )
| ~ ( ~ ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A )
| ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[751]) ).
thf(764,plain,
! [SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV7 )
| ~ ( lattice @ SV7 ) )
| ~ ( latt_str @ SV7 ) ) )
= $true )
| ( ( ! [SY32: $i] :
( ~ ( element @ SY32 @ ( the_carrier @ SV7 ) )
| ( ( cast_to_el_of_LattPOSet @ SV7 @ SY32 )
= SY32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(765,plain,
( ( ~ ( ~ ~ ( ~ ( latt_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) )
| ~ ( strict_latt_str @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[753]) ).
thf(766,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) )
| ~ ( latt_str @ SV1 ) )
| ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV1 @ SV8 ) @ ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(767,plain,
( ( latt_str @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[755]) ).
thf(768,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
| ~ ( latt_str @ SV2 ) )
| ~ ( element @ SV9 @ ( the_carrier @ SV2 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV2 @ SV9 ) @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[756]) ).
thf(769,plain,
! [SV10: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV10 ) )
= $true )
| ( ( element @ SV3 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(770,plain,
( ( ~ ( ~ ( one_sorted_str @ sK5_SX0 )
| ~ ~ ( empty_carrier @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[758]) ).
thf(771,plain,
( ( ~ ( ~ ( latt_str @ sK6_SX0 )
| ~ ( strict_latt_str @ sK6_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[759]) ).
thf(772,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV4 )
| ~ ( lattice @ SV4 ) )
| ~ ( latt_str @ SV4 ) ) )
= $false )
| ( ( ! [SY28: $i] :
( ~ ( element @ SY28 @ ( the_carrier @ ( poset_of_lattice @ SV4 ) ) )
| ( ( cast_to_el_of_lattice @ SV4 @ SY28 )
= SY28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(773,plain,
! [SV5: $i] :
( ( ~ ( element @ ( sK8_SY29 @ SV5 ) @ SV5 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[761]) ).
thf(774,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( lattice @ SV11 ) )
| ~ ( latt_str @ SV11 ) ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( element @ SY33 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_set_smaller @ SV11 @ SY33 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) )
| ( latt_set_smaller @ SV11 @ SY33 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(775,plain,
( ( ~ ( element @ sK7_SX0 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY22 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[763]) ).
thf(776,plain,
( ( ~ ( ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 )
| ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A ) )
| ~ ( ~ ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A )
| ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[763]) ).
thf(777,plain,
! [SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV7 )
| ~ ( lattice @ SV7 ) )
| ~ ( latt_str @ SV7 ) ) )
= $false )
| ( ( ! [SY32: $i] :
( ~ ( element @ SY32 @ ( the_carrier @ SV7 ) )
| ( ( cast_to_el_of_LattPOSet @ SV7 @ SY32 )
= SY32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(778,plain,
( ( ~ ~ ( ~ ( latt_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) )
| ~ ( strict_latt_str @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(779,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) )
| ~ ( latt_str @ SV1 ) )
| ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) ) ) )
= $false )
| ( ( element @ ( cast_to_el_of_lattice @ SV1 @ SV8 ) @ ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(780,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
| ~ ( latt_str @ SV2 ) )
| ~ ( element @ SV9 @ ( the_carrier @ SV2 ) ) ) )
= $false )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV2 @ SV9 ) @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(781,plain,
! [SV10: $i,SV3: $i] :
( ( ( in @ SV3 @ SV10 )
= $false )
| ( ( element @ SV3 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(782,plain,
( ( ~ ( one_sorted_str @ sK5_SX0 )
| ~ ~ ( empty_carrier @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(783,plain,
( ( ~ ( latt_str @ sK6_SX0 )
| ~ ( strict_latt_str @ sK6_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(784,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV4 )
| ~ ( lattice @ SV4 ) )
| ~ ( latt_str @ SV4 ) )
= $true )
| ( ( ! [SY28: $i] :
( ~ ( element @ SY28 @ ( the_carrier @ ( poset_of_lattice @ SV4 ) ) )
| ( ( cast_to_el_of_lattice @ SV4 @ SY28 )
= SY28 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[772]) ).
thf(785,plain,
! [SV5: $i] :
( ( element @ ( sK8_SY29 @ SV5 ) @ SV5 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[773]) ).
thf(786,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( lattice @ SV11 ) )
| ~ ( latt_str @ SV11 ) ) )
= $false )
| ( ( ! [SY33: $i] :
( ~ ( element @ SY33 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_set_smaller @ SV11 @ SY33 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) )
| ( latt_set_smaller @ SV11 @ SY33 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(787,plain,
( ( element @ sK7_SX0 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY22 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[775]) ).
thf(788,plain,
( ( ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 )
| ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A ) )
| ~ ( ~ ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A )
| ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[776]) ).
thf(789,plain,
! [SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV7 )
| ~ ( lattice @ SV7 ) )
| ~ ( latt_str @ SV7 ) )
= $true )
| ( ( ! [SY32: $i] :
( ~ ( element @ SY32 @ ( the_carrier @ SV7 ) )
| ( ( cast_to_el_of_LattPOSet @ SV7 @ SY32 )
= SY32 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[777]) ).
thf(790,plain,
( ( ~ ~ ( ~ ( latt_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[778]) ).
thf(791,plain,
( ( ~ ( strict_latt_str @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[778]) ).
thf(792,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) )
| ~ ( latt_str @ SV1 ) )
| ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV1 @ SV8 ) @ ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[779]) ).
thf(793,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
| ~ ( latt_str @ SV2 ) )
| ~ ( element @ SV9 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV2 @ SV9 ) @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[780]) ).
thf(794,plain,
( ( ~ ( one_sorted_str @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[782]) ).
thf(795,plain,
( ( ~ ~ ( empty_carrier @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[782]) ).
thf(796,plain,
( ( ~ ( latt_str @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[783]) ).
thf(797,plain,
( ( ~ ( strict_latt_str @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[783]) ).
thf(798,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV4 )
| ~ ( lattice @ SV4 ) ) )
= $true )
| ( ( ~ ( latt_str @ SV4 ) )
= $true )
| ( ( ! [SY28: $i] :
( ~ ( element @ SY28 @ ( the_carrier @ ( poset_of_lattice @ SV4 ) ) )
| ( ( cast_to_el_of_lattice @ SV4 @ SY28 )
= SY28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[784]) ).
thf(799,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( lattice @ SV11 ) )
| ~ ( latt_str @ SV11 ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( element @ SY33 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_set_smaller @ SV11 @ SY33 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) )
| ( latt_set_smaller @ SV11 @ SY33 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[786]) ).
thf(800,plain,
( ( ( ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 )
| ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A ) ) )
= $true )
| ( ( ~ ( ~ ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A )
| ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(801,plain,
! [SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV7 )
| ~ ( lattice @ SV7 ) ) )
= $true )
| ( ( ~ ( latt_str @ SV7 ) )
= $true )
| ( ( ! [SY32: $i] :
( ~ ( element @ SY32 @ ( the_carrier @ SV7 ) )
| ( ( cast_to_el_of_LattPOSet @ SV7 @ SY32 )
= SY32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(802,plain,
( ( ~ ( ~ ( latt_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(803,plain,
( ( strict_latt_str @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[791]) ).
thf(804,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) )
| ~ ( latt_str @ SV1 ) ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV1 @ SV8 ) @ ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[792]) ).
thf(805,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
| ~ ( latt_str @ SV2 ) ) )
= $true )
| ( ( ~ ( element @ SV9 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV2 @ SV9 ) @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[793]) ).
thf(806,plain,
( ( one_sorted_str @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(807,plain,
( ( ~ ( empty_carrier @ sK5_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(808,plain,
( ( latt_str @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[796]) ).
thf(809,plain,
( ( strict_latt_str @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[797]) ).
thf(810,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV4 )
| ~ ( lattice @ SV4 ) ) )
= $false )
| ( ( ~ ( latt_str @ SV4 ) )
= $true )
| ( ( ! [SY28: $i] :
( ~ ( element @ SY28 @ ( the_carrier @ ( poset_of_lattice @ SV4 ) ) )
| ( ( cast_to_el_of_lattice @ SV4 @ SY28 )
= SY28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(811,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( lattice @ SV11 ) ) )
= $true )
| ( ( ~ ( latt_str @ SV11 ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( element @ SY33 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_set_smaller @ SV11 @ SY33 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) )
| ( latt_set_smaller @ SV11 @ SY33 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(812,plain,
( ( ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 )
| ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A ) )
= $false )
| ( ( ~ ( ~ ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A )
| ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(813,plain,
! [SV7: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV7 )
| ~ ( lattice @ SV7 ) ) )
= $false )
| ( ( ~ ( latt_str @ SV7 ) )
= $true )
| ( ( ! [SY32: $i] :
( ~ ( element @ SY32 @ ( the_carrier @ SV7 ) )
| ( ( cast_to_el_of_LattPOSet @ SV7 @ SY32 )
= SY32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(814,plain,
( ( ~ ( latt_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(815,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) )
| ~ ( latt_str @ SV1 ) ) )
= $false )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV1 @ SV8 ) @ ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(816,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
| ~ ( latt_str @ SV2 ) ) )
= $false )
| ( ( ~ ( element @ SV9 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV2 @ SV9 ) @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(817,plain,
( ( empty_carrier @ sK5_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(818,plain,
! [SV4: $i] :
( ( ( ~ ~ ( empty_carrier @ SV4 )
| ~ ( lattice @ SV4 ) )
= $true )
| ( ( ~ ( latt_str @ SV4 ) )
= $true )
| ( ( ! [SY28: $i] :
( ~ ( element @ SY28 @ ( the_carrier @ ( poset_of_lattice @ SV4 ) ) )
| ( ( cast_to_el_of_lattice @ SV4 @ SY28 )
= SY28 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(819,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( lattice @ SV11 ) ) )
= $false )
| ( ( ~ ( latt_str @ SV11 ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( element @ SY33 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_set_smaller @ SV11 @ SY33 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) )
| ( latt_set_smaller @ SV11 @ SY33 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(820,plain,
( ( ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 ) )
= $false )
| ( ( ~ ( ~ ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A )
| ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[812]) ).
thf(821,plain,
( ( ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A )
= $false )
| ( ( ~ ( ~ ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A )
| ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[812]) ).
thf(822,plain,
! [SV7: $i] :
( ( ( ~ ~ ( empty_carrier @ SV7 )
| ~ ( lattice @ SV7 ) )
= $true )
| ( ( ~ ( latt_str @ SV7 ) )
= $true )
| ( ( ! [SY32: $i] :
( ~ ( element @ SY32 @ ( the_carrier @ SV7 ) )
| ( ( cast_to_el_of_LattPOSet @ SV7 @ SY32 )
= SY32 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[813]) ).
thf(823,plain,
( ( ~ ( latt_str @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[814]) ).
thf(824,plain,
( ( ~ ~ ( empty_carrier @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[814]) ).
thf(825,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) )
| ~ ( latt_str @ SV1 ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV1 @ SV8 ) @ ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[815]) ).
thf(826,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
| ~ ( latt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV9 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV2 @ SV9 ) @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[816]) ).
thf(827,plain,
! [SV4: $i] :
( ( ( ~ ~ ( empty_carrier @ SV4 ) )
= $true )
| ( ( ~ ( lattice @ SV4 ) )
= $true )
| ( ( ~ ( latt_str @ SV4 ) )
= $true )
| ( ( ! [SY28: $i] :
( ~ ( element @ SY28 @ ( the_carrier @ ( poset_of_lattice @ SV4 ) ) )
| ( ( cast_to_el_of_lattice @ SV4 @ SY28 )
= SY28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[818]) ).
thf(828,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( lattice @ SV11 ) )
= $true )
| ( ( ~ ( latt_str @ SV11 ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( element @ SY33 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_set_smaller @ SV11 @ SY33 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) )
| ( latt_set_smaller @ SV11 @ SY33 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[819]) ).
thf(829,plain,
( ( ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 )
= $true )
| ( ( ~ ( ~ ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A )
| ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(830,plain,
( ( ( ~ ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A )
| ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 ) )
= $false )
| ( ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[821]) ).
thf(831,plain,
! [SV7: $i] :
( ( ( ~ ~ ( empty_carrier @ SV7 ) )
= $true )
| ( ( ~ ( lattice @ SV7 ) )
= $true )
| ( ( ~ ( latt_str @ SV7 ) )
= $true )
| ( ( ! [SY32: $i] :
( ~ ( element @ SY32 @ ( the_carrier @ SV7 ) )
| ( ( cast_to_el_of_LattPOSet @ SV7 @ SY32 )
= SY32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[822]) ).
thf(832,plain,
( ( latt_str @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(833,plain,
( ( ~ ( empty_carrier @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(834,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) ) )
= $true )
| ( ( ~ ( latt_str @ SV1 ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV1 @ SV8 ) @ ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[825]) ).
thf(835,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) ) )
= $true )
| ( ( ~ ( latt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV9 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV2 @ SV9 ) @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(836,plain,
! [SV4: $i] :
( ( ( ~ ( empty_carrier @ SV4 ) )
= $false )
| ( ( ~ ( lattice @ SV4 ) )
= $true )
| ( ( ~ ( latt_str @ SV4 ) )
= $true )
| ( ( ! [SY28: $i] :
( ~ ( element @ SY28 @ ( the_carrier @ ( poset_of_lattice @ SV4 ) ) )
| ( ( cast_to_el_of_lattice @ SV4 @ SY28 )
= SY28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(837,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ~ ( empty_carrier @ SV11 ) )
= $true )
| ( ( ~ ( lattice @ SV11 ) )
= $true )
| ( ( ~ ( latt_str @ SV11 ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( element @ SY33 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_set_smaller @ SV11 @ SY33 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) )
| ( latt_set_smaller @ SV11 @ SY33 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[828]) ).
thf(838,plain,
( ( ( ~ ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A )
| ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 ) )
= $false )
| ( ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[829]) ).
thf(839,plain,
( ( ( ~ ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A ) )
= $false )
| ( ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[830]) ).
thf(840,plain,
( ( ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 )
= $false )
| ( ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[830]) ).
thf(841,plain,
! [SV7: $i] :
( ( ( ~ ( empty_carrier @ SV7 ) )
= $false )
| ( ( ~ ( lattice @ SV7 ) )
= $true )
| ( ( ~ ( latt_str @ SV7 ) )
= $true )
| ( ( ! [SY32: $i] :
( ~ ( element @ SY32 @ ( the_carrier @ SV7 ) )
| ( ( cast_to_el_of_LattPOSet @ SV7 @ SY32 )
= SY32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(842,plain,
( ( empty_carrier @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(843,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) ) )
= $false )
| ( ( ~ ( latt_str @ SV1 ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV1 @ SV8 ) @ ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(844,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) ) )
= $false )
| ( ( ~ ( latt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV9 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV2 @ SV9 ) @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[835]) ).
thf(845,plain,
! [SV4: $i] :
( ( ( empty_carrier @ SV4 )
= $true )
| ( ( ~ ( lattice @ SV4 ) )
= $true )
| ( ( ~ ( latt_str @ SV4 ) )
= $true )
| ( ( ! [SY28: $i] :
( ~ ( element @ SY28 @ ( the_carrier @ ( poset_of_lattice @ SV4 ) ) )
| ( ( cast_to_el_of_lattice @ SV4 @ SY28 )
= SY28 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[836]) ).
thf(846,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( empty_carrier @ SV11 ) )
= $false )
| ( ( ~ ( lattice @ SV11 ) )
= $true )
| ( ( ~ ( latt_str @ SV11 ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( element @ SY33 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_set_smaller @ SV11 @ SY33 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) )
| ( latt_set_smaller @ SV11 @ SY33 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(847,plain,
( ( ( ~ ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A ) )
= $false )
| ( ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[838]) ).
thf(848,plain,
( ( ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 )
= $false )
| ( ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[838]) ).
thf(849,plain,
( ( ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A )
= $true )
| ( ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[839]) ).
thf(850,plain,
! [SV7: $i] :
( ( ( empty_carrier @ SV7 )
= $true )
| ( ( ~ ( lattice @ SV7 ) )
= $true )
| ( ( ~ ( latt_str @ SV7 ) )
= $true )
| ( ( ! [SY32: $i] :
( ~ ( element @ SY32 @ ( the_carrier @ SV7 ) )
| ( ( cast_to_el_of_LattPOSet @ SV7 @ SY32 )
= SY32 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[841]) ).
thf(851,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) )
= $true )
| ( ( ~ ( latt_str @ SV1 ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV1 @ SV8 ) @ ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[843]) ).
thf(852,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
= $true )
| ( ( ~ ( latt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV9 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV2 @ SV9 ) @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[844]) ).
thf(853,plain,
! [SV4: $i] :
( ( ( lattice @ SV4 )
= $false )
| ( ( empty_carrier @ SV4 )
= $true )
| ( ( ~ ( latt_str @ SV4 ) )
= $true )
| ( ( ! [SY28: $i] :
( ~ ( element @ SY28 @ ( the_carrier @ ( poset_of_lattice @ SV4 ) ) )
| ( ( cast_to_el_of_lattice @ SV4 @ SY28 )
= SY28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(854,plain,
! [SV6: $i,SV11: $i] :
( ( ( empty_carrier @ SV11 )
= $true )
| ( ( ~ ( lattice @ SV11 ) )
= $true )
| ( ( ~ ( latt_str @ SV11 ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( element @ SY33 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_set_smaller @ SV11 @ SY33 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) )
| ( latt_set_smaller @ SV11 @ SY33 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[846]) ).
thf(855,plain,
( ( ( latt_set_smaller @ sK2_SY22 @ ( cast_to_el_of_lattice @ sK2_SY22 @ sK7_SX0 ) @ sK1_A )
= $true )
| ( ( relstr_element_smaller @ ( poset_of_lattice @ sK2_SY22 ) @ sK1_A @ sK7_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[847]) ).
thf(856,plain,
! [SV7: $i] :
( ( ( lattice @ SV7 )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( ~ ( latt_str @ SV7 ) )
= $true )
| ( ( ! [SY32: $i] :
( ~ ( element @ SY32 @ ( the_carrier @ SV7 ) )
| ( ( cast_to_el_of_LattPOSet @ SV7 @ SY32 )
= SY32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(857,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ~ ( empty_carrier @ SV1 ) )
= $true )
| ( ( ~ ( lattice @ SV1 ) )
= $true )
| ( ( ~ ( latt_str @ SV1 ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV1 @ SV8 ) @ ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(858,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ~ ( empty_carrier @ SV2 ) )
= $true )
| ( ( ~ ( lattice @ SV2 ) )
= $true )
| ( ( ~ ( latt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV9 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV2 @ SV9 ) @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(859,plain,
! [SV4: $i] :
( ( ( latt_str @ SV4 )
= $false )
| ( ( empty_carrier @ SV4 )
= $true )
| ( ( lattice @ SV4 )
= $false )
| ( ( ! [SY28: $i] :
( ~ ( element @ SY28 @ ( the_carrier @ ( poset_of_lattice @ SV4 ) ) )
| ( ( cast_to_el_of_lattice @ SV4 @ SY28 )
= SY28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(860,plain,
! [SV6: $i,SV11: $i] :
( ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( ~ ( latt_str @ SV11 ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( element @ SY33 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_set_smaller @ SV11 @ SY33 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) )
| ( latt_set_smaller @ SV11 @ SY33 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(861,plain,
! [SV7: $i] :
( ( ( latt_str @ SV7 )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( lattice @ SV7 )
= $false )
| ( ( ! [SY32: $i] :
( ~ ( element @ SY32 @ ( the_carrier @ SV7 ) )
| ( ( cast_to_el_of_LattPOSet @ SV7 @ SY32 )
= SY32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(862,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ( empty_carrier @ SV1 ) )
= $false )
| ( ( ~ ( lattice @ SV1 ) )
= $true )
| ( ( ~ ( latt_str @ SV1 ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV1 @ SV8 ) @ ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(863,plain,
! [SV9: $i,SV2: $i] :
( ( ( ~ ( empty_carrier @ SV2 ) )
= $false )
| ( ( ~ ( lattice @ SV2 ) )
= $true )
| ( ( ~ ( latt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV9 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV2 @ SV9 ) @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(864,plain,
! [SV4: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ ( the_carrier @ ( poset_of_lattice @ SV4 ) ) )
| ( ( cast_to_el_of_lattice @ SV4 @ SV12 )
= SV12 ) )
= $true )
| ( ( lattice @ SV4 )
= $false )
| ( ( empty_carrier @ SV4 )
= $true )
| ( ( latt_str @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(865,plain,
! [SV6: $i,SV11: $i] :
( ( ( latt_str @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( lattice @ SV11 )
= $false )
| ( ( ! [SY33: $i] :
( ~ ( element @ SY33 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_set_smaller @ SV11 @ SY33 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY33 ) )
| ( latt_set_smaller @ SV11 @ SY33 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(866,plain,
! [SV7: $i,SV13: $i] :
( ( ( ~ ( element @ SV13 @ ( the_carrier @ SV7 ) )
| ( ( cast_to_el_of_LattPOSet @ SV7 @ SV13 )
= SV13 ) )
= $true )
| ( ( lattice @ SV7 )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( latt_str @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(867,plain,
! [SV8: $i,SV1: $i] :
( ( ( empty_carrier @ SV1 )
= $true )
| ( ( ~ ( lattice @ SV1 ) )
= $true )
| ( ( ~ ( latt_str @ SV1 ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV1 @ SV8 ) @ ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[862]) ).
thf(868,plain,
! [SV9: $i,SV2: $i] :
( ( ( empty_carrier @ SV2 )
= $true )
| ( ( ~ ( lattice @ SV2 ) )
= $true )
| ( ( ~ ( latt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV9 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV2 @ SV9 ) @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[863]) ).
thf(869,plain,
! [SV4: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ ( the_carrier @ ( poset_of_lattice @ SV4 ) ) ) )
= $true )
| ( ( ( cast_to_el_of_lattice @ SV4 @ SV12 )
= SV12 )
= $true )
| ( ( lattice @ SV4 )
= $false )
| ( ( empty_carrier @ SV4 )
= $true )
| ( ( latt_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(870,plain,
! [SV6: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( element @ SV14 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_set_smaller @ SV11 @ SV14 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
| ( latt_set_smaller @ SV11 @ SV14 @ SV6 ) ) ) )
= $true )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(871,plain,
! [SV7: $i,SV13: $i] :
( ( ( ~ ( element @ SV13 @ ( the_carrier @ SV7 ) ) )
= $true )
| ( ( ( cast_to_el_of_LattPOSet @ SV7 @ SV13 )
= SV13 )
= $true )
| ( ( lattice @ SV7 )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( latt_str @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(872,plain,
! [SV8: $i,SV1: $i] :
( ( ( lattice @ SV1 )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( ~ ( latt_str @ SV1 ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV1 @ SV8 ) @ ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(873,plain,
! [SV9: $i,SV2: $i] :
( ( ( lattice @ SV2 )
= $false )
| ( ( empty_carrier @ SV2 )
= $true )
| ( ( ~ ( latt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV9 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV2 @ SV9 ) @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(874,plain,
! [SV4: $i,SV12: $i] :
( ( ( element @ SV12 @ ( the_carrier @ ( poset_of_lattice @ SV4 ) ) )
= $false )
| ( ( ( cast_to_el_of_lattice @ SV4 @ SV12 )
= SV12 )
= $true )
| ( ( lattice @ SV4 )
= $false )
| ( ( empty_carrier @ SV4 )
= $true )
| ( ( latt_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(875,plain,
! [SV6: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( element @ SV14 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( latt_set_smaller @ SV11 @ SV14 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
| ( latt_set_smaller @ SV11 @ SV14 @ SV6 ) ) ) )
= $true )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(876,plain,
! [SV7: $i,SV13: $i] :
( ( ( element @ SV13 @ ( the_carrier @ SV7 ) )
= $false )
| ( ( ( cast_to_el_of_LattPOSet @ SV7 @ SV13 )
= SV13 )
= $true )
| ( ( lattice @ SV7 )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( latt_str @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(877,plain,
! [SV8: $i,SV1: $i] :
( ( ( latt_str @ SV1 )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( lattice @ SV1 )
= $false )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV1 @ SV8 ) @ ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(878,plain,
! [SV9: $i,SV2: $i] :
( ( ( latt_str @ SV2 )
= $false )
| ( ( empty_carrier @ SV2 )
= $true )
| ( ( lattice @ SV2 )
= $false )
| ( ( ~ ( element @ SV9 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV2 @ SV9 ) @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(879,plain,
! [SV6: $i,SV11: $i,SV14: $i] :
( ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( latt_set_smaller @ SV11 @ SV14 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
| ( latt_set_smaller @ SV11 @ SV14 @ SV6 ) ) ) )
= $true )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[875]) ).
thf(880,plain,
! [SV1: $i,SV8: $i] :
( ( ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) )
= $false )
| ( ( lattice @ SV1 )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( latt_str @ SV1 )
= $false )
| ( ( element @ ( cast_to_el_of_lattice @ SV1 @ SV8 ) @ ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(881,plain,
! [SV2: $i,SV9: $i] :
( ( ( element @ SV9 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( lattice @ SV2 )
= $false )
| ( ( empty_carrier @ SV2 )
= $true )
| ( ( latt_str @ SV2 )
= $false )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV2 @ SV9 ) @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(882,plain,
! [SV6: $i,SV14: $i,SV11: $i] :
( ( ( ~ ( ~ ( latt_set_smaller @ SV11 @ SV14 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) ) )
| ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
| ( latt_set_smaller @ SV11 @ SV14 @ SV6 ) ) )
= $false )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(883,plain,
! [SV6: $i,SV14: $i,SV11: $i] :
( ( ( ~ ( ~ ( latt_set_smaller @ SV11 @ SV14 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) ) ) )
= $false )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[882]) ).
thf(884,plain,
! [SV14: $i,SV6: $i,SV11: $i] :
( ( ( ~ ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
| ( latt_set_smaller @ SV11 @ SV14 @ SV6 ) ) )
= $false )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[882]) ).
thf(885,plain,
! [SV6: $i,SV14: $i,SV11: $i] :
( ( ( ~ ( latt_set_smaller @ SV11 @ SV14 @ SV6 )
| ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) ) )
= $true )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[883]) ).
thf(886,plain,
! [SV14: $i,SV6: $i,SV11: $i] :
( ( ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
| ( latt_set_smaller @ SV11 @ SV14 @ SV6 ) )
= $true )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[884]) ).
thf(887,plain,
! [SV6: $i,SV14: $i,SV11: $i] :
( ( ( ~ ( latt_set_smaller @ SV11 @ SV14 @ SV6 ) )
= $true )
| ( ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
= $true )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(888,plain,
! [SV14: $i,SV6: $i,SV11: $i] :
( ( ( ~ ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) ) )
= $true )
| ( ( latt_set_smaller @ SV11 @ SV14 @ SV6 )
= $true )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(889,plain,
! [SV6: $i,SV14: $i,SV11: $i] :
( ( ( latt_set_smaller @ SV11 @ SV14 @ SV6 )
= $false )
| ( ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
= $true )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(890,plain,
! [SV14: $i,SV6: $i,SV11: $i] :
( ( ( relstr_element_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
= $false )
| ( ( latt_set_smaller @ SV11 @ SV14 @ SV6 )
= $true )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(891,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[688,890,889,881,880,876,874,855,849,848,842,840,832,817,809,808,806,803,787,785,781,767,740,725,724,717,716,715,714,713,712,710,709,707,706,705,704,703,702,701,700,699,698,697,696,695,694,693,692,691,690,689]) ).
thf(892,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[891]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU348+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n004.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 15:15:09 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.97/1.54 .....
% 7.97/1.54
% 7.97/1.54 No.of.Axioms: 39
% 7.97/1.54
% 7.97/1.54 Length.of.Defs: 0
% 7.97/1.54
% 7.97/1.54 Contains.Choice.Funs: false
% 7.97/1.54 .............
% 7.97/1.54
% 7.97/1.54 ********************************
% 7.97/1.54 * All subproblems solved! *
% 7.97/1.54 ********************************
% 7.97/1.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:42,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:891,loop_count:0,foatp_calls:1,translation:fof_full)
% 7.97/1.54
% 7.97/1.54 %**** Beginning of derivation protocol ****
% 7.97/1.54 % SZS output start CNFRefutation
% See solution above
% 7.97/1.54
% 7.97/1.54 %**** End of derivation protocol ****
% 7.97/1.54 %**** no. of clauses in derivation: 296 ****
% 7.97/1.54 %**** clause counter: 891 ****
% 7.97/1.54
% 7.97/1.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:42,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:891,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------