%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU304+1 : 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 : n014.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 1.66s 0.55s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 28
% Syntax : Number of formulae : 380 ( 168 unt; 0 typ; 0 def)
% Number of atoms : 3308 ( 999 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 6497 (1526 ~;1025 |; 96 &;3769 @)
% ( 9 <=>; 72 =>; 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 : 42 ( 39 usr; 8 con; 0-6 aty)
% Number of variables : 842 ( 0 ^; 830 !; 12 ?; 842 :)
% Comments :
%------------------------------------------------------------------------------
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_below,type,
below: $i > $i > $i > $o ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_cup_closed,type,
cup_closed: $i > $o ).
thf(tp_diff_closed,type,
diff_closed: $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_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_join,type,
join: $i > $i > $i > $i ).
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_semilatt_str,type,
meet_semilatt_str: $i > $o ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_preboolean,type,
preboolean: $i > $o ).
thf(tp_quasi_total,type,
quasi_total: $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_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_SY73,type,
sK5_SY73: $i > $i ).
thf(tp_sK6_SY81,type,
sK6_SY81: $i ).
thf(tp_sK7_SY60,type,
sK7_SY60: $i > $i ).
thf(tp_sK8_SY70,type,
sK8_SY70: $i > $i ).
thf(tp_sK9_SY87,type,
sK9_SY87: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
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(4,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(5,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(6,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(11,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 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
thf(13,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(14,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(15,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(18,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(20,axiom,
? [A: $i] : ( latt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(27,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(28,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(30,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(32,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(34,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(35,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(36,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(38,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(39,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(40,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(41,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_binop_1) ).
thf(42,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( ( meet_absorbing @ A )
<=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( join @ A @ ( meet @ A @ B @ C ) @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattices) ).
thf(43,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(46,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(50,conjecture,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_absorbing @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( below @ A @ ( meet_commut @ A @ B @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattices) ).
thf(51,negated_conjecture,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_absorbing @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( below @ A @ ( meet_commut @ A @ B @ C ) @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[50]) ).
thf(52,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_absorbing @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( below @ A @ ( meet_commut @ A @ B @ C ) @ B ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[51]) ).
thf(53,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(54,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(56,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(57,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(58,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 @ A @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(59,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)],[13]) ).
thf(60,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(61,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(62,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(63,plain,
( ( ? [A: $i] : ( latt_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(64,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(65,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)],[27]) ).
thf(66,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(67,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(68,plain,
( ( ! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(69,plain,
$true = $true,
inference(unfold_def,[status(thm)],[32]) ).
thf(70,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)],[34]) ).
thf(71,plain,
$true = $true,
inference(unfold_def,[status(thm)],[35]) ).
thf(72,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)],[36]) ).
thf(73,plain,
$true = $true,
inference(unfold_def,[status(thm)],[38]) ).
thf(74,plain,
$true = $true,
inference(unfold_def,[status(thm)],[39]) ).
thf(75,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)],[40]) ).
thf(76,plain,
$true = $true,
inference(unfold_def,[status(thm)],[41]) ).
thf(77,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( ( meet_absorbing @ A )
<=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( join @ A @ ( meet @ A @ B @ C ) @ C )
= C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(78,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)],[43]) ).
thf(79,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)],[46]) ).
thf(80,plain,
( ( ( ~ ( empty_carrier @ sK1_A )
& ( meet_commutative @ sK1_A )
& ( meet_absorbing @ sK1_A )
& ( latt_str @ sK1_A ) )
=> ! [SY47: $i] :
( ( element @ SY47 @ ( the_carrier @ sK1_A ) )
=> ! [SY48: $i] :
( ( element @ SY48 @ ( the_carrier @ sK1_A ) )
=> ( below @ sK1_A @ ( meet_commut @ sK1_A @ SY47 @ SY48 ) @ SY47 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[52]) ).
thf(81,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(82,plain,
( ( meet_commutative @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(83,plain,
( ( meet_absorbing @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(84,plain,
( ( latt_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(85,plain,
( ( ! [SY47: $i] :
( ( element @ SY47 @ ( the_carrier @ sK1_A ) )
=> ! [SY48: $i] :
( ( element @ SY48 @ ( the_carrier @ sK1_A ) )
=> ( below @ sK1_A @ ( meet_commut @ sK1_A @ SY47 @ SY48 ) @ SY47 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(86,plain,
( ( ~ ! [SY47: $i] :
( ( element @ SY47 @ ( the_carrier @ sK1_A ) )
=> ! [SY48: $i] :
( ( element @ SY48 @ ( the_carrier @ sK1_A ) )
=> ( below @ sK1_A @ ( meet_commut @ sK1_A @ SY47 @ SY48 ) @ SY47 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[85]) ).
thf(87,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)],[79]) ).
thf(88,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)],[78]) ).
thf(89,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( ( meet_absorbing @ A )
<=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( join @ A @ ( meet @ A @ B @ C ) @ C )
= C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(90,plain,
$true = $true,
inference(copy,[status(thm)],[76]) ).
thf(91,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)],[75]) ).
thf(92,plain,
$true = $true,
inference(copy,[status(thm)],[74]) ).
thf(93,plain,
$true = $true,
inference(copy,[status(thm)],[73]) ).
thf(94,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)],[72]) ).
thf(95,plain,
$true = $true,
inference(copy,[status(thm)],[71]) ).
thf(96,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)],[70]) ).
thf(97,plain,
$true = $true,
inference(copy,[status(thm)],[69]) ).
thf(98,plain,
( ( ! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(99,plain,
$true = $true,
inference(copy,[status(thm)],[67]) ).
thf(100,plain,
$true = $true,
inference(copy,[status(thm)],[66]) ).
thf(101,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)],[65]) ).
thf(102,plain,
$true = $true,
inference(copy,[status(thm)],[64]) ).
thf(103,plain,
( ( ? [A: $i] : ( latt_str @ A ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(104,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(105,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(106,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(107,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)],[59]) ).
thf(108,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 @ A @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(109,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(110,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(111,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(112,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(113,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(114,plain,
( ( latt_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(115,plain,
( ( meet_absorbing @ sK1_A )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(116,plain,
( ( meet_commutative @ sK1_A )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(117,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(118,plain,
( ( ~ ! [SY47: $i] :
( ( element @ SY47 @ ( the_carrier @ sK1_A ) )
=> ! [SY48: $i] :
( ( element @ SY48 @ ( the_carrier @ sK1_A ) )
=> ( below @ sK1_A @ ( meet_commut @ sK1_A @ SY47 @ SY48 ) @ SY47 ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(119,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)],[88]) ).
thf(120,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)],[91]) ).
thf(121,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ~ ( empty @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(123,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)],[87]) ).
thf(124,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(125,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)],[107]) ).
thf(126,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 ) )
| ~ ( empty @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(127,plain,
( ( ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ~ ( ~ ( meet_semilatt_str @ SX0 )
| ~ ( join_semilatt_str @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(128,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(129,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)],[94]) ).
thf(130,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ sK1_A ) )
| ( below @ sK1_A @ ( meet_commut @ sK1_A @ SX0 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(131,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)],[96]) ).
thf(132,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)],[101]) ).
thf(133,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( latt_str @ SX0 ) )
| ~ ( ~ ( ~ ( meet_absorbing @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ( ( join @ SX0 @ ( meet @ SX0 @ SX1 @ SX2 ) @ SX2 )
= SX2 ) ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ( ( join @ SX0 @ ( meet @ SX0 @ SX1 @ SX2 ) @ SX2 )
= SX2 ) ) )
| ( meet_absorbing @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(134,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)],[111]) ).
thf(135,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(136,plain,
( ( ~ ! [SX0: $i] :
~ ( latt_str @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(137,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(138,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 @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(139,plain,
( ( empty_carrier @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(140,plain,
! [SV1: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( join_semilatt_str @ SV1 ) )
| ! [SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV1 ) )
| ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV1 ) )
| ~ ( ~ ( ~ ( below @ SV1 @ SY49 @ SY50 )
| ( ( join @ SV1 @ SY49 @ SY50 )
= SY50 ) )
| ~ ( ( ( join @ SV1 @ SY49 @ SY50 )
!= SY50 )
| ( below @ SV1 @ SY49 @ SY50 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(141,plain,
! [SV2: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( join_semilatt_str @ SV2 ) )
| ~ ( element @ SY51 @ ( the_carrier @ SV2 ) ) )
| ~ ( element @ SY52 @ ( the_carrier @ SV2 ) ) )
| ( element @ ( join @ SV2 @ SY51 @ SY52 ) @ ( the_carrier @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(142,plain,
! [SV3: $i] :
( ( ! [SY53: $i,SY54: $i] :
( ~ ~ ( ~ ( in @ SV3 @ SY53 )
| ~ ( element @ SY53 @ ( powerset @ SY54 ) ) )
| ( element @ SV3 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(143,plain,
! [SV4: $i] :
( ( ! [SY55: $i,SY56: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV4 @ SY55 )
| ~ ( element @ SY55 @ ( powerset @ SY56 ) ) )
| ~ ( empty @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(144,plain,
! [SV5: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( meet_commutative @ SV5 ) )
| ~ ( meet_semilatt_str @ SV5 ) )
| ~ ( element @ SY57 @ ( the_carrier @ SV5 ) ) )
| ~ ( element @ SY58 @ ( the_carrier @ SV5 ) ) )
| ( ( meet_commut @ SV5 @ SY57 @ SY58 )
= ( meet_commut @ SV5 @ SY58 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(145,plain,
! [SV6: $i] :
( ( ! [SY59: $i] :
( ~ ( element @ SV6 @ SY59 )
| ( empty @ SY59 )
| ( in @ SV6 @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(146,plain,
! [SV7: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV7 )
| ~ ( one_sorted_str @ SV7 ) )
| ~ ! [SY60: $i] :
~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV7 ) ) )
| ~ ~ ( empty @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(147,plain,
! [SV8: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( one_sorted_str @ SV8 ) )
| ~ ( empty @ ( the_carrier @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(148,plain,
! [SV9: $i] :
( ( ~ ( latt_str @ SV9 )
| ~ ( ~ ( meet_semilatt_str @ SV9 )
| ~ ( join_semilatt_str @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(149,plain,
! [SV10: $i] :
( ( ! [SY61: $i] :
( ~ ( in @ SV10 @ SY61 )
| ( element @ SV10 @ SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(150,plain,
! [SV11: $i] :
( ( ! [SY62: $i,SY63: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( meet_semilatt_str @ SV11 ) )
| ~ ( element @ SY62 @ ( the_carrier @ SV11 ) ) )
| ~ ( element @ SY63 @ ( the_carrier @ SV11 ) ) )
| ( element @ ( meet @ SV11 @ SY62 @ SY63 ) @ ( the_carrier @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(151,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ sK1_A ) )
| ( below @ sK1_A @ ( meet_commut @ sK1_A @ SX0 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(152,plain,
! [SV12: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( meet_commutative @ SV12 ) )
| ~ ( meet_semilatt_str @ SV12 ) )
| ~ ( element @ SY64 @ ( the_carrier @ SV12 ) ) )
| ~ ( element @ SY65 @ ( the_carrier @ SV12 ) ) )
| ( element @ ( meet_commut @ SV12 @ SY64 @ SY65 ) @ ( the_carrier @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(153,plain,
! [SV13: $i] :
( ( ! [SY66: $i,SY67: $i] :
( ~ ( relation_of2_as_subset @ SY67 @ SV13 @ SY66 )
| ( element @ SY67 @ ( powerset @ ( cartesian_product2 @ SV13 @ SY66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(154,plain,
! [SV14: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV14 )
| ~ ( latt_str @ SV14 ) )
| ~ ( ~ ( ~ ( meet_absorbing @ SV14 )
| ! [SY68: $i] :
( ~ ( element @ SY68 @ ( the_carrier @ SV14 ) )
| ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY68 @ SY69 ) @ SY69 )
= SY69 ) ) ) )
| ~ ( ~ ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV14 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY70 @ SY71 ) @ SY71 )
= SY71 ) ) )
| ( meet_absorbing @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(155,plain,
! [SV15: $i] :
( ( ! [SY72: $i] :
~ ( ~ ( ~ ( element @ SV15 @ ( powerset @ SY72 ) )
| ( subset @ SV15 @ SY72 ) )
| ~ ( ~ ( subset @ SV15 @ SY72 )
| ( element @ SV15 @ ( powerset @ SY72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(156,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(157,plain,
( ( ! [SX0: $i] :
~ ( latt_str @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(158,plain,
! [SV16: $i] :
( ( ~ ! [SY73: $i] :
~ ( element @ SY73 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(159,plain,
! [SV17: $i] :
( ( ! [SY74: $i,SY75: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV17 )
| ~ ( meet_commutative @ SV17 ) )
| ~ ( meet_semilatt_str @ SV17 ) )
| ~ ( element @ SY74 @ ( the_carrier @ SV17 ) ) )
| ~ ( element @ SY75 @ ( the_carrier @ SV17 ) ) )
| ( ( meet_commut @ SV17 @ SY74 @ SY75 )
= ( meet @ SV17 @ SY74 @ SY75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(160,plain,
! [SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( join_semilatt_str @ SV1 ) ) )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV1 ) )
| ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV1 ) )
| ~ ( ~ ( ~ ( below @ SV1 @ SY49 @ SY50 )
| ( ( join @ SV1 @ SY49 @ SY50 )
= SY50 ) )
| ~ ( ( ( join @ SV1 @ SY49 @ SY50 )
!= SY50 )
| ( below @ SV1 @ SY49 @ SY50 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(161,plain,
! [SV18: $i,SV2: $i] :
( ( ! [SY76: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( join_semilatt_str @ SV2 ) )
| ~ ( element @ SV18 @ ( the_carrier @ SV2 ) ) )
| ~ ( element @ SY76 @ ( the_carrier @ SV2 ) ) )
| ( element @ ( join @ SV2 @ SV18 @ SY76 ) @ ( the_carrier @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(162,plain,
! [SV19: $i,SV3: $i] :
( ( ! [SY77: $i] :
( ~ ~ ( ~ ( in @ SV3 @ SV19 )
| ~ ( element @ SV19 @ ( powerset @ SY77 ) ) )
| ( element @ SV3 @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(163,plain,
! [SV20: $i,SV4: $i] :
( ( ! [SY78: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV4 @ SV20 )
| ~ ( element @ SV20 @ ( powerset @ SY78 ) ) )
| ~ ( empty @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(164,plain,
! [SV21: $i,SV5: $i] :
( ( ! [SY79: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( meet_commutative @ SV5 ) )
| ~ ( meet_semilatt_str @ SV5 ) )
| ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) )
| ~ ( element @ SY79 @ ( the_carrier @ SV5 ) ) )
| ( ( meet_commut @ SV5 @ SV21 @ SY79 )
= ( meet_commut @ SV5 @ SY79 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(165,plain,
! [SV22: $i,SV6: $i] :
( ( ~ ( element @ SV6 @ SV22 )
| ( empty @ SV22 )
| ( in @ SV6 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(166,plain,
! [SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV7 )
| ~ ( one_sorted_str @ SV7 ) ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV7 ) ) )
| ~ ~ ( empty @ SY60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(167,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( one_sorted_str @ SV8 ) ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(168,plain,
! [SV9: $i] :
( ( ( ~ ( latt_str @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( meet_semilatt_str @ SV9 )
| ~ ( join_semilatt_str @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(169,plain,
! [SV23: $i,SV10: $i] :
( ( ~ ( in @ SV10 @ SV23 )
| ( element @ SV10 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(170,plain,
! [SV24: $i,SV11: $i] :
( ( ! [SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( meet_semilatt_str @ SV11 ) )
| ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
| ~ ( element @ SY80 @ ( the_carrier @ SV11 ) ) )
| ( element @ ( meet @ SV11 @ SV24 @ SY80 ) @ ( the_carrier @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(171,plain,
( ( ~ ( element @ sK2_SX0 @ ( the_carrier @ sK1_A ) )
| ! [SY81: $i] :
( ~ ( element @ SY81 @ ( the_carrier @ sK1_A ) )
| ( below @ sK1_A @ ( meet_commut @ sK1_A @ sK2_SX0 @ SY81 ) @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[151]) ).
thf(172,plain,
! [SV25: $i,SV12: $i] :
( ( ! [SY82: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( meet_commutative @ SV12 ) )
| ~ ( meet_semilatt_str @ SV12 ) )
| ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) )
| ~ ( element @ SY82 @ ( the_carrier @ SV12 ) ) )
| ( element @ ( meet_commut @ SV12 @ SV25 @ SY82 ) @ ( the_carrier @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(173,plain,
! [SV26: $i,SV13: $i] :
( ( ! [SY83: $i] :
( ~ ( relation_of2_as_subset @ SY83 @ SV13 @ SV26 )
| ( element @ SY83 @ ( powerset @ ( cartesian_product2 @ SV13 @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(174,plain,
! [SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV14 )
| ~ ( latt_str @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( meet_absorbing @ SV14 )
| ! [SY68: $i] :
( ~ ( element @ SY68 @ ( the_carrier @ SV14 ) )
| ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY68 @ SY69 ) @ SY69 )
= SY69 ) ) ) )
| ~ ( ~ ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV14 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY70 @ SY71 ) @ SY71 )
= SY71 ) ) )
| ( meet_absorbing @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(175,plain,
! [SV27: $i,SV15: $i] :
( ( ~ ( ~ ( ~ ( element @ SV15 @ ( powerset @ SV27 ) )
| ( subset @ SV15 @ SV27 ) )
| ~ ( ~ ( subset @ SV15 @ SV27 )
| ( element @ SV15 @ ( powerset @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(176,plain,
( ( ~ ~ ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[156]) ).
thf(177,plain,
( ( ~ ( latt_str @ sK4_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[157]) ).
thf(178,plain,
! [SV16: $i] :
( ( ! [SY73: $i] :
~ ( element @ SY73 @ SV16 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(179,plain,
! [SV28: $i,SV17: $i] :
( ( ! [SY84: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV17 )
| ~ ( meet_commutative @ SV17 ) )
| ~ ( meet_semilatt_str @ SV17 ) )
| ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) )
| ~ ( element @ SY84 @ ( the_carrier @ SV17 ) ) )
| ( ( meet_commut @ SV17 @ SV28 @ SY84 )
= ( meet @ SV17 @ SV28 @ SY84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(180,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( join_semilatt_str @ SV1 ) ) )
= $false )
| ( ( ! [SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV1 ) )
| ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV1 ) )
| ~ ( ~ ( ~ ( below @ SV1 @ SY49 @ SY50 )
| ( ( join @ SV1 @ SY49 @ SY50 )
= SY50 ) )
| ~ ( ( ( join @ SV1 @ SY49 @ SY50 )
!= SY50 )
| ( below @ SV1 @ SY49 @ SY50 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(181,plain,
! [SV29: $i,SV18: $i,SV2: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( join_semilatt_str @ SV2 ) )
| ~ ( element @ SV18 @ ( the_carrier @ SV2 ) ) )
| ~ ( element @ SV29 @ ( the_carrier @ SV2 ) ) )
| ( element @ ( join @ SV2 @ SV18 @ SV29 ) @ ( the_carrier @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(182,plain,
! [SV30: $i,SV19: $i,SV3: $i] :
( ( ~ ~ ( ~ ( in @ SV3 @ SV19 )
| ~ ( element @ SV19 @ ( powerset @ SV30 ) ) )
| ( element @ SV3 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(183,plain,
! [SV31: $i,SV20: $i,SV4: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV4 @ SV20 )
| ~ ( element @ SV20 @ ( powerset @ SV31 ) ) )
| ~ ( empty @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(184,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( meet_commutative @ SV5 ) )
| ~ ( meet_semilatt_str @ SV5 ) )
| ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) )
| ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) )
| ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(185,plain,
! [SV22: $i,SV6: $i] :
( ( ( ~ ( element @ SV6 @ SV22 ) )
= $true )
| ( ( ( empty @ SV22 )
| ( in @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(186,plain,
! [SV7: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV7 )
| ~ ( one_sorted_str @ SV7 ) ) )
= $false )
| ( ( ~ ! [SY60: $i] :
~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV7 ) ) )
| ~ ~ ( empty @ SY60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(187,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( one_sorted_str @ SV8 ) ) )
= $false )
| ( ( ~ ( empty @ ( the_carrier @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(188,plain,
! [SV9: $i] :
( ( ( latt_str @ SV9 )
= $false )
| ( ( ~ ( ~ ( meet_semilatt_str @ SV9 )
| ~ ( join_semilatt_str @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(189,plain,
! [SV23: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV23 ) )
= $true )
| ( ( element @ SV10 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(190,plain,
! [SV33: $i,SV24: $i,SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( meet_semilatt_str @ SV11 ) )
| ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
| ~ ( element @ SV33 @ ( the_carrier @ SV11 ) ) )
| ( element @ ( meet @ SV11 @ SV24 @ SV33 ) @ ( the_carrier @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(191,plain,
( ( ~ ( element @ sK2_SX0 @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(192,plain,
( ( ! [SY81: $i] :
( ~ ( element @ SY81 @ ( the_carrier @ sK1_A ) )
| ( below @ sK1_A @ ( meet_commut @ sK1_A @ sK2_SX0 @ SY81 ) @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(193,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( meet_commutative @ SV12 ) )
| ~ ( meet_semilatt_str @ SV12 ) )
| ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) )
| ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
| ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(194,plain,
! [SV26: $i,SV13: $i,SV35: $i] :
( ( ~ ( relation_of2_as_subset @ SV35 @ SV13 @ SV26 )
| ( element @ SV35 @ ( powerset @ ( cartesian_product2 @ SV13 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(195,plain,
! [SV14: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV14 )
| ~ ( latt_str @ SV14 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( meet_absorbing @ SV14 )
| ! [SY68: $i] :
( ~ ( element @ SY68 @ ( the_carrier @ SV14 ) )
| ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY68 @ SY69 ) @ SY69 )
= SY69 ) ) ) )
| ~ ( ~ ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV14 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY70 @ SY71 ) @ SY71 )
= SY71 ) ) )
| ( meet_absorbing @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(196,plain,
! [SV27: $i,SV15: $i] :
( ( ~ ( ~ ( element @ SV15 @ ( powerset @ SV27 ) )
| ( subset @ SV15 @ SV27 ) )
| ~ ( ~ ( subset @ SV15 @ SV27 )
| ( element @ SV15 @ ( powerset @ SV27 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(197,plain,
( ( ~ ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(198,plain,
( ( latt_str @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(199,plain,
! [SV16: $i] :
( ( ~ ( element @ ( sK5_SY73 @ SV16 ) @ SV16 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[178]) ).
thf(200,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV17 )
| ~ ( meet_commutative @ SV17 ) )
| ~ ( meet_semilatt_str @ SV17 ) )
| ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) )
| ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) )
| ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(201,plain,
! [SV1: $i] :
( ( ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( join_semilatt_str @ SV1 ) )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV1 ) )
| ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV1 ) )
| ~ ( ~ ( ~ ( below @ SV1 @ SY49 @ SY50 )
| ( ( join @ SV1 @ SY49 @ SY50 )
= SY50 ) )
| ~ ( ( ( join @ SV1 @ SY49 @ SY50 )
!= SY50 )
| ( below @ SV1 @ SY49 @ SY50 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(202,plain,
! [SV29: $i,SV18: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( join_semilatt_str @ SV2 ) )
| ~ ( element @ SV18 @ ( the_carrier @ SV2 ) ) )
| ~ ( element @ SV29 @ ( the_carrier @ SV2 ) ) ) )
= $true )
| ( ( element @ ( join @ SV2 @ SV18 @ SV29 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(203,plain,
! [SV30: $i,SV19: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( in @ SV3 @ SV19 )
| ~ ( element @ SV19 @ ( powerset @ SV30 ) ) ) )
= $true )
| ( ( element @ SV3 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(204,plain,
! [SV31: $i,SV20: $i,SV4: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV4 @ SV20 )
| ~ ( element @ SV20 @ ( powerset @ SV31 ) ) )
| ~ ( empty @ SV31 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(205,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( meet_commutative @ SV5 ) )
| ~ ( meet_semilatt_str @ SV5 ) )
| ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) )
| ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) ) )
= $true )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(206,plain,
! [SV22: $i,SV6: $i] :
( ( ( element @ SV6 @ SV22 )
= $false )
| ( ( ( empty @ SV22 )
| ( in @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(207,plain,
! [SV7: $i] :
( ( ( ~ ~ ( empty_carrier @ SV7 )
| ~ ( one_sorted_str @ SV7 ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV7 ) ) )
| ~ ~ ( empty @ SY60 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(208,plain,
! [SV8: $i] :
( ( ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( one_sorted_str @ SV8 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(209,plain,
! [SV9: $i] :
( ( ( ~ ( meet_semilatt_str @ SV9 )
| ~ ( join_semilatt_str @ SV9 ) )
= $false )
| ( ( latt_str @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(210,plain,
! [SV23: $i,SV10: $i] :
( ( ( in @ SV10 @ SV23 )
= $false )
| ( ( element @ SV10 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(211,plain,
! [SV33: $i,SV24: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( meet_semilatt_str @ SV11 ) )
| ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
| ~ ( element @ SV33 @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( element @ ( meet @ SV11 @ SV24 @ SV33 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(212,plain,
( ( element @ sK2_SX0 @ ( the_carrier @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(213,plain,
( ( ~ ( element @ sK6_SY81 @ ( the_carrier @ sK1_A ) )
| ( below @ sK1_A @ ( meet_commut @ sK1_A @ sK2_SX0 @ sK6_SY81 ) @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[192]) ).
thf(214,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( meet_commutative @ SV12 ) )
| ~ ( meet_semilatt_str @ SV12 ) )
| ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) )
| ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(215,plain,
! [SV26: $i,SV13: $i,SV35: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV35 @ SV13 @ SV26 ) )
= $true )
| ( ( element @ SV35 @ ( powerset @ ( cartesian_product2 @ SV13 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(216,plain,
! [SV14: $i] :
( ( ( ~ ~ ( empty_carrier @ SV14 )
| ~ ( latt_str @ SV14 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( meet_absorbing @ SV14 )
| ! [SY68: $i] :
( ~ ( element @ SY68 @ ( the_carrier @ SV14 ) )
| ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY68 @ SY69 ) @ SY69 )
= SY69 ) ) ) )
| ~ ( ~ ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV14 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY70 @ SY71 ) @ SY71 )
= SY71 ) ) )
| ( meet_absorbing @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(217,plain,
! [SV27: $i,SV15: $i] :
( ( ~ ( ~ ( element @ SV15 @ ( powerset @ SV27 ) )
| ( subset @ SV15 @ SV27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(218,plain,
! [SV27: $i,SV15: $i] :
( ( ~ ( ~ ( subset @ SV15 @ SV27 )
| ( element @ SV15 @ ( powerset @ SV27 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(219,plain,
( ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(220,plain,
! [SV16: $i] :
( ( element @ ( sK5_SY73 @ SV16 ) @ SV16 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(221,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV17 )
| ~ ( meet_commutative @ SV17 ) )
| ~ ( meet_semilatt_str @ SV17 ) )
| ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) )
| ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) ) )
= $true )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(222,plain,
! [SV1: $i] :
( ( ( ~ ~ ( empty_carrier @ SV1 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV1 ) )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV1 ) )
| ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV1 ) )
| ~ ( ~ ( ~ ( below @ SV1 @ SY49 @ SY50 )
| ( ( join @ SV1 @ SY49 @ SY50 )
= SY50 ) )
| ~ ( ( ( join @ SV1 @ SY49 @ SY50 )
!= SY50 )
| ( below @ SV1 @ SY49 @ SY50 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(223,plain,
! [SV29: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( join_semilatt_str @ SV2 ) )
| ~ ( element @ SV18 @ ( the_carrier @ SV2 ) ) )
| ~ ( element @ SV29 @ ( the_carrier @ SV2 ) ) ) )
= $false )
| ( ( element @ ( join @ SV2 @ SV18 @ SV29 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(224,plain,
! [SV30: $i,SV19: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ SV3 @ SV19 )
| ~ ( element @ SV19 @ ( powerset @ SV30 ) ) ) )
= $false )
| ( ( element @ SV3 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(225,plain,
! [SV31: $i,SV20: $i,SV4: $i] :
( ( ~ ~ ( ~ ( in @ SV4 @ SV20 )
| ~ ( element @ SV20 @ ( powerset @ SV31 ) ) )
| ~ ( empty @ SV31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(226,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( meet_commutative @ SV5 ) )
| ~ ( meet_semilatt_str @ SV5 ) )
| ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) )
| ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) ) )
= $false )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(227,plain,
! [SV6: $i,SV22: $i] :
( ( ( empty @ SV22 )
= $true )
| ( ( in @ SV6 @ SV22 )
= $true )
| ( ( element @ SV6 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(228,plain,
! [SV7: $i] :
( ( ( ~ ~ ( empty_carrier @ SV7 ) )
= $true )
| ( ( ~ ( one_sorted_str @ SV7 ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV7 ) ) )
| ~ ~ ( empty @ SY60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(229,plain,
! [SV8: $i] :
( ( ( ~ ~ ( empty_carrier @ SV8 ) )
= $true )
| ( ( ~ ( one_sorted_str @ SV8 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(230,plain,
! [SV9: $i] :
( ( ( ~ ( meet_semilatt_str @ SV9 ) )
= $false )
| ( ( latt_str @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(231,plain,
! [SV9: $i] :
( ( ( ~ ( join_semilatt_str @ SV9 ) )
= $false )
| ( ( latt_str @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(232,plain,
! [SV33: $i,SV24: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( meet_semilatt_str @ SV11 ) )
| ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
| ~ ( element @ SV33 @ ( the_carrier @ SV11 ) ) ) )
= $false )
| ( ( element @ ( meet @ SV11 @ SV24 @ SV33 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(233,plain,
( ( ~ ( element @ sK6_SY81 @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(234,plain,
( ( below @ sK1_A @ ( meet_commut @ sK1_A @ sK2_SX0 @ sK6_SY81 ) @ sK2_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(235,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( meet_commutative @ SV12 ) )
| ~ ( meet_semilatt_str @ SV12 ) )
| ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) )
| ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) ) )
= $false )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(236,plain,
! [SV26: $i,SV13: $i,SV35: $i] :
( ( ( relation_of2_as_subset @ SV35 @ SV13 @ SV26 )
= $false )
| ( ( element @ SV35 @ ( powerset @ ( cartesian_product2 @ SV13 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(237,plain,
! [SV14: $i] :
( ( ( ~ ~ ( empty_carrier @ SV14 ) )
= $true )
| ( ( ~ ( latt_str @ SV14 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( meet_absorbing @ SV14 )
| ! [SY68: $i] :
( ~ ( element @ SY68 @ ( the_carrier @ SV14 ) )
| ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY68 @ SY69 ) @ SY69 )
= SY69 ) ) ) )
| ~ ( ~ ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV14 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY70 @ SY71 ) @ SY71 )
= SY71 ) ) )
| ( meet_absorbing @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(238,plain,
! [SV27: $i,SV15: $i] :
( ( ~ ( element @ SV15 @ ( powerset @ SV27 ) )
| ( subset @ SV15 @ SV27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(239,plain,
! [SV27: $i,SV15: $i] :
( ( ~ ( subset @ SV15 @ SV27 )
| ( element @ SV15 @ ( powerset @ SV27 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(240,plain,
( ( ~ ( one_sorted_str @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(241,plain,
( ( ~ ~ ( empty_carrier @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(242,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV17 )
| ~ ( meet_commutative @ SV17 ) )
| ~ ( meet_semilatt_str @ SV17 ) )
| ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) )
| ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) ) )
= $false )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(243,plain,
! [SV1: $i] :
( ( ( ~ ( empty_carrier @ SV1 ) )
= $false )
| ( ( ~ ( join_semilatt_str @ SV1 ) )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV1 ) )
| ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV1 ) )
| ~ ( ~ ( ~ ( below @ SV1 @ SY49 @ SY50 )
| ( ( join @ SV1 @ SY49 @ SY50 )
= SY50 ) )
| ~ ( ( ( join @ SV1 @ SY49 @ SY50 )
!= SY50 )
| ( below @ SV1 @ SY49 @ SY50 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(244,plain,
! [SV29: $i,SV18: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( join_semilatt_str @ SV2 ) )
| ~ ( element @ SV18 @ ( the_carrier @ SV2 ) ) )
| ~ ( element @ SV29 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( join @ SV2 @ SV18 @ SV29 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(245,plain,
! [SV30: $i,SV19: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV19 )
| ~ ( element @ SV19 @ ( powerset @ SV30 ) ) )
= $true )
| ( ( element @ SV3 @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(246,plain,
! [SV31: $i,SV20: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ SV4 @ SV20 )
| ~ ( element @ SV20 @ ( powerset @ SV31 ) ) ) )
= $true )
| ( ( ~ ( empty @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(247,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( meet_commutative @ SV5 ) )
| ~ ( meet_semilatt_str @ SV5 ) )
| ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) )
| ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(248,plain,
! [SV7: $i] :
( ( ( ~ ( empty_carrier @ SV7 ) )
= $false )
| ( ( ~ ( one_sorted_str @ SV7 ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV7 ) ) )
| ~ ~ ( empty @ SY60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(249,plain,
! [SV8: $i] :
( ( ( ~ ( empty_carrier @ SV8 ) )
= $false )
| ( ( ~ ( one_sorted_str @ SV8 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(250,plain,
! [SV9: $i] :
( ( ( meet_semilatt_str @ SV9 )
= $true )
| ( ( latt_str @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(251,plain,
! [SV9: $i] :
( ( ( join_semilatt_str @ SV9 )
= $true )
| ( ( latt_str @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(252,plain,
! [SV33: $i,SV24: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( meet_semilatt_str @ SV11 ) )
| ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
| ~ ( element @ SV33 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( meet @ SV11 @ SV24 @ SV33 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(253,plain,
( ( element @ sK6_SY81 @ ( the_carrier @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(254,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( meet_commutative @ SV12 ) )
| ~ ( meet_semilatt_str @ SV12 ) )
| ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) )
| ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(255,plain,
! [SV14: $i] :
( ( ( ~ ( empty_carrier @ SV14 ) )
= $false )
| ( ( ~ ( latt_str @ SV14 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( meet_absorbing @ SV14 )
| ! [SY68: $i] :
( ~ ( element @ SY68 @ ( the_carrier @ SV14 ) )
| ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY68 @ SY69 ) @ SY69 )
= SY69 ) ) ) )
| ~ ( ~ ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV14 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY70 @ SY71 ) @ SY71 )
= SY71 ) ) )
| ( meet_absorbing @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(256,plain,
! [SV27: $i,SV15: $i] :
( ( ( ~ ( element @ SV15 @ ( powerset @ SV27 ) ) )
= $true )
| ( ( subset @ SV15 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(257,plain,
! [SV27: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV27 ) )
= $true )
| ( ( element @ SV15 @ ( powerset @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(258,plain,
( ( one_sorted_str @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(259,plain,
( ( ~ ( empty_carrier @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(260,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV17 )
| ~ ( meet_commutative @ SV17 ) )
| ~ ( meet_semilatt_str @ SV17 ) )
| ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) )
| ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(261,plain,
! [SV1: $i] :
( ( ( empty_carrier @ SV1 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV1 ) )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV1 ) )
| ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV1 ) )
| ~ ( ~ ( ~ ( below @ SV1 @ SY49 @ SY50 )
| ( ( join @ SV1 @ SY49 @ SY50 )
= SY50 ) )
| ~ ( ( ( join @ SV1 @ SY49 @ SY50 )
!= SY50 )
| ( below @ SV1 @ SY49 @ SY50 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(262,plain,
! [SV29: $i,SV18: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( join_semilatt_str @ SV2 ) )
| ~ ( element @ SV18 @ ( the_carrier @ SV2 ) ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( join @ SV2 @ SV18 @ SV29 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(263,plain,
! [SV30: $i,SV19: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV19 ) )
= $true )
| ( ( ~ ( element @ SV19 @ ( powerset @ SV30 ) ) )
= $true )
| ( ( element @ SV3 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(264,plain,
! [SV31: $i,SV20: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ SV4 @ SV20 )
| ~ ( element @ SV20 @ ( powerset @ SV31 ) ) ) )
= $false )
| ( ( ~ ( empty @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(265,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( meet_commutative @ SV5 ) )
| ~ ( meet_semilatt_str @ SV5 ) )
| ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) ) )
= $true )
| ( ( ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(266,plain,
! [SV7: $i] :
( ( ( empty_carrier @ SV7 )
= $true )
| ( ( ~ ( one_sorted_str @ SV7 ) )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV7 ) ) )
| ~ ~ ( empty @ SY60 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(267,plain,
! [SV8: $i] :
( ( ( empty_carrier @ SV8 )
= $true )
| ( ( ~ ( one_sorted_str @ SV8 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(268,plain,
! [SV33: $i,SV24: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( meet_semilatt_str @ SV11 ) )
| ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( meet @ SV11 @ SV24 @ SV33 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(269,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( meet_commutative @ SV12 ) )
| ~ ( meet_semilatt_str @ SV12 ) )
| ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(270,plain,
! [SV14: $i] :
( ( ( empty_carrier @ SV14 )
= $true )
| ( ( ~ ( latt_str @ SV14 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( meet_absorbing @ SV14 )
| ! [SY68: $i] :
( ~ ( element @ SY68 @ ( the_carrier @ SV14 ) )
| ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY68 @ SY69 ) @ SY69 )
= SY69 ) ) ) )
| ~ ( ~ ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV14 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY70 @ SY71 ) @ SY71 )
= SY71 ) ) )
| ( meet_absorbing @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(271,plain,
! [SV27: $i,SV15: $i] :
( ( ( element @ SV15 @ ( powerset @ SV27 ) )
= $false )
| ( ( subset @ SV15 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(272,plain,
! [SV27: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV27 )
= $false )
| ( ( element @ SV15 @ ( powerset @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(273,plain,
( ( empty_carrier @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(274,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV17 )
| ~ ( meet_commutative @ SV17 ) )
| ~ ( meet_semilatt_str @ SV17 ) )
| ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) ) )
= $true )
| ( ( ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(275,plain,
! [SV1: $i] :
( ( ( join_semilatt_str @ SV1 )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV1 ) )
| ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV1 ) )
| ~ ( ~ ( ~ ( below @ SV1 @ SY49 @ SY50 )
| ( ( join @ SV1 @ SY49 @ SY50 )
= SY50 ) )
| ~ ( ( ( join @ SV1 @ SY49 @ SY50 )
!= SY50 )
| ( below @ SV1 @ SY49 @ SY50 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(276,plain,
! [SV29: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( join_semilatt_str @ SV2 ) )
| ~ ( element @ SV18 @ ( the_carrier @ SV2 ) ) ) )
= $false )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( join @ SV2 @ SV18 @ SV29 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(277,plain,
! [SV30: $i,SV19: $i,SV3: $i] :
( ( ( in @ SV3 @ SV19 )
= $false )
| ( ( ~ ( element @ SV19 @ ( powerset @ SV30 ) ) )
= $true )
| ( ( element @ SV3 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(278,plain,
! [SV31: $i,SV20: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV20 )
| ~ ( element @ SV20 @ ( powerset @ SV31 ) ) )
= $true )
| ( ( ~ ( empty @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(279,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( meet_commutative @ SV5 ) )
| ~ ( meet_semilatt_str @ SV5 ) )
| ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) ) )
= $false )
| ( ( ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(280,plain,
! [SV7: $i] :
( ( ( one_sorted_str @ SV7 )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( ~ ! [SY60: $i] :
~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV7 ) ) )
| ~ ~ ( empty @ SY60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(281,plain,
! [SV8: $i] :
( ( ( one_sorted_str @ SV8 )
= $false )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(282,plain,
! [SV33: $i,SV24: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( meet_semilatt_str @ SV11 ) )
| ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) ) )
= $false )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( meet @ SV11 @ SV24 @ SV33 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(283,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( meet_commutative @ SV12 ) )
| ~ ( meet_semilatt_str @ SV12 ) )
| ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) ) )
= $false )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(284,plain,
! [SV14: $i] :
( ( ( latt_str @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( ~ ( ~ ( ~ ( meet_absorbing @ SV14 )
| ! [SY68: $i] :
( ~ ( element @ SY68 @ ( the_carrier @ SV14 ) )
| ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY68 @ SY69 ) @ SY69 )
= SY69 ) ) ) )
| ~ ( ~ ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV14 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY70 @ SY71 ) @ SY71 )
= SY71 ) ) )
| ( meet_absorbing @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(285,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV17 )
| ~ ( meet_commutative @ SV17 ) )
| ~ ( meet_semilatt_str @ SV17 ) )
| ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) ) )
= $false )
| ( ( ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(286,plain,
! [SV1: $i,SV37: $i] :
( ( ( ~ ( element @ SV37 @ ( the_carrier @ SV1 ) )
| ! [SY85: $i] :
( ~ ( element @ SY85 @ ( the_carrier @ SV1 ) )
| ~ ( ~ ( ~ ( below @ SV1 @ SV37 @ SY85 )
| ( ( join @ SV1 @ SV37 @ SY85 )
= SY85 ) )
| ~ ( ( ( join @ SV1 @ SV37 @ SY85 )
!= SY85 )
| ( below @ SV1 @ SV37 @ SY85 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( join_semilatt_str @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(287,plain,
! [SV29: $i,SV18: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( join_semilatt_str @ SV2 ) )
| ~ ( element @ SV18 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( join @ SV2 @ SV18 @ SV29 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(288,plain,
! [SV3: $i,SV30: $i,SV19: $i] :
( ( ( element @ SV19 @ ( powerset @ SV30 ) )
= $false )
| ( ( in @ SV3 @ SV19 )
= $false )
| ( ( element @ SV3 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(289,plain,
! [SV31: $i,SV20: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV20 ) )
= $true )
| ( ( ~ ( element @ SV20 @ ( powerset @ SV31 ) ) )
= $true )
| ( ( ~ ( empty @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(290,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( meet_commutative @ SV5 ) )
| ~ ( meet_semilatt_str @ SV5 ) )
| ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(291,plain,
! [SV7: $i] :
( ( ( ! [SY60: $i] :
~ ~ ( ~ ( element @ SY60 @ ( powerset @ ( the_carrier @ SV7 ) ) )
| ~ ~ ( empty @ SY60 ) ) )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(292,plain,
! [SV8: $i] :
( ( ( empty @ ( the_carrier @ SV8 ) )
= $false )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( one_sorted_str @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(293,plain,
! [SV33: $i,SV24: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( meet_semilatt_str @ SV11 ) )
| ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( meet @ SV11 @ SV24 @ SV33 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(294,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( meet_commutative @ SV12 ) )
| ~ ( meet_semilatt_str @ SV12 ) )
| ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(295,plain,
! [SV14: $i] :
( ( ( ~ ( ~ ( meet_absorbing @ SV14 )
| ! [SY68: $i] :
( ~ ( element @ SY68 @ ( the_carrier @ SV14 ) )
| ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY68 @ SY69 ) @ SY69 )
= SY69 ) ) ) )
| ~ ( ~ ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV14 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY70 @ SY71 ) @ SY71 )
= SY71 ) ) )
| ( meet_absorbing @ SV14 ) ) )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(296,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV17 )
| ~ ( meet_commutative @ SV17 ) )
| ~ ( meet_semilatt_str @ SV17 ) )
| ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(297,plain,
! [SV1: $i,SV37: $i] :
( ( ( ~ ( element @ SV37 @ ( the_carrier @ SV1 ) ) )
= $true )
| ( ( ! [SY85: $i] :
( ~ ( element @ SY85 @ ( the_carrier @ SV1 ) )
| ~ ( ~ ( ~ ( below @ SV1 @ SV37 @ SY85 )
| ( ( join @ SV1 @ SV37 @ SY85 )
= SY85 ) )
| ~ ( ( ( join @ SV1 @ SV37 @ SY85 )
!= SY85 )
| ( below @ SV1 @ SV37 @ SY85 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( join_semilatt_str @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(298,plain,
! [SV29: $i,SV18: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( join_semilatt_str @ SV2 ) ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( join @ SV2 @ SV18 @ SV29 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(299,plain,
! [SV31: $i,SV20: $i,SV4: $i] :
( ( ( in @ SV4 @ SV20 )
= $false )
| ( ( ~ ( element @ SV20 @ ( powerset @ SV31 ) ) )
= $true )
| ( ( ~ ( empty @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(300,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( meet_commutative @ SV5 ) )
| ~ ( meet_semilatt_str @ SV5 ) ) )
= $true )
| ( ( ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(301,plain,
! [SV7: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_SY60 @ SV7 ) @ ( powerset @ ( the_carrier @ SV7 ) ) )
| ~ ~ ( empty @ ( sK7_SY60 @ SV7 ) ) ) )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[291]) ).
thf(302,plain,
! [SV33: $i,SV24: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( meet_semilatt_str @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( meet @ SV11 @ SV24 @ SV33 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(303,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( meet_commutative @ SV12 ) )
| ~ ( meet_semilatt_str @ SV12 ) ) )
= $true )
| ( ( ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(304,plain,
! [SV14: $i] :
( ( ( ~ ( ~ ( meet_absorbing @ SV14 )
| ! [SY68: $i] :
( ~ ( element @ SY68 @ ( the_carrier @ SV14 ) )
| ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY68 @ SY69 ) @ SY69 )
= SY69 ) ) ) ) )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(305,plain,
! [SV14: $i] :
( ( ( ~ ( ~ ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV14 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY70 @ SY71 ) @ SY71 )
= SY71 ) ) )
| ( meet_absorbing @ SV14 ) ) )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(306,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV17 )
| ~ ( meet_commutative @ SV17 ) )
| ~ ( meet_semilatt_str @ SV17 ) ) )
= $true )
| ( ( ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(307,plain,
! [SV1: $i,SV37: $i] :
( ( ( element @ SV37 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( ! [SY85: $i] :
( ~ ( element @ SY85 @ ( the_carrier @ SV1 ) )
| ~ ( ~ ( ~ ( below @ SV1 @ SV37 @ SY85 )
| ( ( join @ SV1 @ SV37 @ SY85 )
= SY85 ) )
| ~ ( ( ( join @ SV1 @ SV37 @ SY85 )
!= SY85 )
| ( below @ SV1 @ SV37 @ SY85 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( join_semilatt_str @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(308,plain,
! [SV29: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( join_semilatt_str @ SV2 ) ) )
= $false )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( join @ SV2 @ SV18 @ SV29 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(309,plain,
! [SV4: $i,SV31: $i,SV20: $i] :
( ( ( element @ SV20 @ ( powerset @ SV31 ) )
= $false )
| ( ( in @ SV4 @ SV20 )
= $false )
| ( ( ~ ( empty @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(310,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( meet_commutative @ SV5 ) )
| ~ ( meet_semilatt_str @ SV5 ) ) )
= $false )
| ( ( ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(311,plain,
! [SV7: $i] :
( ( ( ~ ( ~ ( element @ ( sK7_SY60 @ SV7 ) @ ( powerset @ ( the_carrier @ SV7 ) ) )
| ~ ~ ( empty @ ( sK7_SY60 @ SV7 ) ) ) )
= $true )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(312,plain,
! [SV33: $i,SV24: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( meet_semilatt_str @ SV11 ) ) )
= $false )
| ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( meet @ SV11 @ SV24 @ SV33 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(313,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( meet_commutative @ SV12 ) )
| ~ ( meet_semilatt_str @ SV12 ) ) )
= $false )
| ( ( ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(314,plain,
! [SV14: $i] :
( ( ( ~ ( meet_absorbing @ SV14 )
| ! [SY68: $i] :
( ~ ( element @ SY68 @ ( the_carrier @ SV14 ) )
| ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY68 @ SY69 ) @ SY69 )
= SY69 ) ) ) )
= $true )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(315,plain,
! [SV14: $i] :
( ( ( ~ ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV14 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY70 @ SY71 ) @ SY71 )
= SY71 ) ) )
| ( meet_absorbing @ SV14 ) )
= $true )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(316,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV17 )
| ~ ( meet_commutative @ SV17 ) )
| ~ ( meet_semilatt_str @ SV17 ) ) )
= $false )
| ( ( ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(317,plain,
! [SV37: $i,SV1: $i,SV38: $i] :
( ( ( ~ ( element @ SV38 @ ( the_carrier @ SV1 ) )
| ~ ( ~ ( ~ ( below @ SV1 @ SV37 @ SV38 )
| ( ( join @ SV1 @ SV37 @ SV38 )
= SV38 ) )
| ~ ( ( ( join @ SV1 @ SV37 @ SV38 )
!= SV38 )
| ( below @ SV1 @ SV37 @ SV38 ) ) ) )
= $true )
| ( ( element @ SV37 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( join_semilatt_str @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(318,plain,
! [SV29: $i,SV18: $i,SV2: $i] :
( ( ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( join_semilatt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( join @ SV2 @ SV18 @ SV29 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(319,plain,
! [SV20: $i,SV4: $i,SV31: $i] :
( ( ( empty @ SV31 )
= $false )
| ( ( in @ SV4 @ SV20 )
= $false )
| ( ( element @ SV20 @ ( powerset @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(320,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( meet_commutative @ SV5 ) )
| ~ ( meet_semilatt_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(321,plain,
! [SV7: $i] :
( ( ( ~ ( element @ ( sK7_SY60 @ SV7 ) @ ( powerset @ ( the_carrier @ SV7 ) ) )
| ~ ~ ( empty @ ( sK7_SY60 @ SV7 ) ) )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(322,plain,
! [SV33: $i,SV24: $i,SV11: $i] :
( ( ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( meet_semilatt_str @ SV11 ) )
= $true )
| ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( meet @ SV11 @ SV24 @ SV33 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(323,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( meet_commutative @ SV12 ) )
| ~ ( meet_semilatt_str @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(324,plain,
! [SV14: $i] :
( ( ( ~ ( meet_absorbing @ SV14 ) )
= $true )
| ( ( ! [SY68: $i] :
( ~ ( element @ SY68 @ ( the_carrier @ SV14 ) )
| ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY68 @ SY69 ) @ SY69 )
= SY69 ) ) ) )
= $true )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(325,plain,
! [SV14: $i] :
( ( ( ~ ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV14 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY70 @ SY71 ) @ SY71 )
= SY71 ) ) ) )
= $true )
| ( ( meet_absorbing @ SV14 )
= $true )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(326,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV17 )
| ~ ( meet_commutative @ SV17 ) )
| ~ ( meet_semilatt_str @ SV17 ) )
= $true )
| ( ( ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(327,plain,
! [SV37: $i,SV1: $i,SV38: $i] :
( ( ( ~ ( element @ SV38 @ ( the_carrier @ SV1 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( below @ SV1 @ SV37 @ SV38 )
| ( ( join @ SV1 @ SV37 @ SV38 )
= SV38 ) )
| ~ ( ( ( join @ SV1 @ SV37 @ SV38 )
!= SV38 )
| ( below @ SV1 @ SV37 @ SV38 ) ) ) )
= $true )
| ( ( element @ SV37 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( join_semilatt_str @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(328,plain,
! [SV29: $i,SV18: $i,SV2: $i] :
( ( ( ~ ~ ( empty_carrier @ SV2 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( join @ SV2 @ SV18 @ SV29 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(329,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( meet_commutative @ SV5 ) ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(330,plain,
! [SV7: $i] :
( ( ( ~ ( element @ ( sK7_SY60 @ SV7 ) @ ( powerset @ ( the_carrier @ SV7 ) ) ) )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(331,plain,
! [SV7: $i] :
( ( ( ~ ~ ( empty @ ( sK7_SY60 @ SV7 ) ) )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(332,plain,
! [SV33: $i,SV24: $i,SV11: $i] :
( ( ( ~ ~ ( empty_carrier @ SV11 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV11 ) )
= $true )
| ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( meet @ SV11 @ SV24 @ SV33 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(333,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( meet_commutative @ SV12 ) ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(334,plain,
! [SV14: $i] :
( ( ( meet_absorbing @ SV14 )
= $false )
| ( ( ! [SY68: $i] :
( ~ ( element @ SY68 @ ( the_carrier @ SV14 ) )
| ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY68 @ SY69 ) @ SY69 )
= SY69 ) ) ) )
= $true )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(335,plain,
! [SV14: $i] :
( ( ( ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV14 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SY70 @ SY71 ) @ SY71 )
= SY71 ) ) ) )
= $false )
| ( ( meet_absorbing @ SV14 )
= $true )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(336,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV17 )
| ~ ( meet_commutative @ SV17 ) ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV17 ) )
= $true )
| ( ( ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(337,plain,
! [SV37: $i,SV1: $i,SV38: $i] :
( ( ( element @ SV38 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( below @ SV1 @ SV37 @ SV38 )
| ( ( join @ SV1 @ SV37 @ SV38 )
= SV38 ) )
| ~ ( ( ( join @ SV1 @ SV37 @ SV38 )
!= SV38 )
| ( below @ SV1 @ SV37 @ SV38 ) ) ) )
= $true )
| ( ( element @ SV37 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( join_semilatt_str @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(338,plain,
! [SV29: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( empty_carrier @ SV2 ) )
= $false )
| ( ( ~ ( join_semilatt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( join @ SV2 @ SV18 @ SV29 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(339,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( meet_commutative @ SV5 ) ) )
= $false )
| ( ( ~ ( meet_semilatt_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(340,plain,
! [SV7: $i] :
( ( ( element @ ( sK7_SY60 @ SV7 ) @ ( powerset @ ( the_carrier @ SV7 ) ) )
= $true )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(341,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ ( sK7_SY60 @ SV7 ) ) )
= $true )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(342,plain,
! [SV33: $i,SV24: $i,SV11: $i] :
( ( ( ~ ( empty_carrier @ SV11 ) )
= $false )
| ( ( ~ ( meet_semilatt_str @ SV11 ) )
= $true )
| ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( meet @ SV11 @ SV24 @ SV33 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(343,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( meet_commutative @ SV12 ) ) )
= $false )
| ( ( ~ ( meet_semilatt_str @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(344,plain,
! [SV14: $i,SV39: $i] :
( ( ( ~ ( element @ SV39 @ ( the_carrier @ SV14 ) )
| ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SV39 @ SY86 ) @ SY86 )
= SY86 ) ) )
= $true )
| ( ( meet_absorbing @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(345,plain,
! [SV14: $i] :
( ( ( ~ ( element @ ( sK8_SY70 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ! [SY87: $i] :
( ~ ( element @ SY87 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ ( sK8_SY70 @ SV14 ) @ SY87 ) @ SY87 )
= SY87 ) ) )
= $false )
| ( ( meet_absorbing @ SV14 )
= $true )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[335]) ).
thf(346,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV17 )
| ~ ( meet_commutative @ SV17 ) ) )
= $false )
| ( ( ~ ( meet_semilatt_str @ SV17 ) )
= $true )
| ( ( ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(347,plain,
! [SV38: $i,SV37: $i,SV1: $i] :
( ( ( ~ ( ~ ( below @ SV1 @ SV37 @ SV38 )
| ( ( join @ SV1 @ SV37 @ SV38 )
= SV38 ) )
| ~ ( ( ( join @ SV1 @ SV37 @ SV38 )
!= SV38 )
| ( below @ SV1 @ SV37 @ SV38 ) ) )
= $false )
| ( ( element @ SV38 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( join_semilatt_str @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(348,plain,
! [SV29: $i,SV18: $i,SV2: $i] :
( ( ( empty_carrier @ SV2 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( join @ SV2 @ SV18 @ SV29 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(349,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( meet_commutative @ SV5 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(350,plain,
! [SV7: $i] :
( ( ( empty @ ( sK7_SY60 @ SV7 ) )
= $false )
| ( ( empty_carrier @ SV7 )
= $true )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(351,plain,
! [SV33: $i,SV24: $i,SV11: $i] :
( ( ( empty_carrier @ SV11 )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV11 ) )
= $true )
| ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( meet @ SV11 @ SV24 @ SV33 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(352,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( meet_commutative @ SV12 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(353,plain,
! [SV14: $i,SV39: $i] :
( ( ( ~ ( element @ SV39 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SV39 @ SY86 ) @ SY86 )
= SY86 ) ) )
= $true )
| ( ( meet_absorbing @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(354,plain,
! [SV14: $i] :
( ( ( ~ ( element @ ( sK8_SY70 @ SV14 ) @ ( the_carrier @ SV14 ) ) )
= $false )
| ( ( meet_absorbing @ SV14 )
= $true )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[345]) ).
thf(355,plain,
! [SV14: $i] :
( ( ( ! [SY87: $i] :
( ~ ( element @ SY87 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ ( sK8_SY70 @ SV14 ) @ SY87 ) @ SY87 )
= SY87 ) ) )
= $false )
| ( ( meet_absorbing @ SV14 )
= $true )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[345]) ).
thf(356,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ( ~ ~ ( empty_carrier @ SV17 )
| ~ ( meet_commutative @ SV17 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV17 ) )
= $true )
| ( ( ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(357,plain,
! [SV38: $i,SV37: $i,SV1: $i] :
( ( ( ~ ( ~ ( below @ SV1 @ SV37 @ SV38 )
| ( ( join @ SV1 @ SV37 @ SV38 )
= SV38 ) ) )
= $false )
| ( ( element @ SV38 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( join_semilatt_str @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(358,plain,
! [SV38: $i,SV37: $i,SV1: $i] :
( ( ( ~ ( ( ( join @ SV1 @ SV37 @ SV38 )
!= SV38 )
| ( below @ SV1 @ SV37 @ SV38 ) ) )
= $false )
| ( ( element @ SV38 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( join_semilatt_str @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(359,plain,
! [SV29: $i,SV18: $i,SV2: $i] :
( ( ( join_semilatt_str @ SV2 )
= $false )
| ( ( empty_carrier @ SV2 )
= $true )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( join @ SV2 @ SV18 @ SV29 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(360,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ( ~ ~ ( empty_carrier @ SV5 ) )
= $true )
| ( ( ~ ( meet_commutative @ SV5 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(361,plain,
! [SV33: $i,SV24: $i,SV11: $i] :
( ( ( meet_semilatt_str @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( meet @ SV11 @ SV24 @ SV33 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(362,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( ~ ~ ( empty_carrier @ SV12 ) )
= $true )
| ( ( ~ ( meet_commutative @ SV12 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(363,plain,
! [SV14: $i,SV39: $i] :
( ( ( element @ SV39 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SV39 @ SY86 ) @ SY86 )
= SY86 ) ) )
= $true )
| ( ( meet_absorbing @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(364,plain,
! [SV14: $i] :
( ( ( element @ ( sK8_SY70 @ SV14 ) @ ( the_carrier @ SV14 ) )
= $true )
| ( ( meet_absorbing @ SV14 )
= $true )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(365,plain,
! [SV14: $i] :
( ( ( ~ ( element @ ( sK9_SY87 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ ( sK8_SY70 @ SV14 ) @ ( sK9_SY87 @ SV14 ) ) @ ( sK9_SY87 @ SV14 ) )
= ( sK9_SY87 @ SV14 ) ) )
= $false )
| ( ( meet_absorbing @ SV14 )
= $true )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[355]) ).
thf(366,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ( ~ ~ ( empty_carrier @ SV17 ) )
= $true )
| ( ( ~ ( meet_commutative @ SV17 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV17 ) )
= $true )
| ( ( ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(367,plain,
! [SV38: $i,SV37: $i,SV1: $i] :
( ( ( ~ ( below @ SV1 @ SV37 @ SV38 )
| ( ( join @ SV1 @ SV37 @ SV38 )
= SV38 ) )
= $true )
| ( ( element @ SV38 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( join_semilatt_str @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(368,plain,
! [SV38: $i,SV37: $i,SV1: $i] :
( ( ( ( ( join @ SV1 @ SV37 @ SV38 )
!= SV38 )
| ( below @ SV1 @ SV37 @ SV38 ) )
= $true )
| ( ( element @ SV38 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( join_semilatt_str @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(369,plain,
! [SV29: $i,SV2: $i,SV18: $i] :
( ( ( element @ SV18 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( empty_carrier @ SV2 )
= $true )
| ( ( join_semilatt_str @ SV2 )
= $false )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( element @ ( join @ SV2 @ SV18 @ SV29 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(370,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ( ~ ( empty_carrier @ SV5 ) )
= $false )
| ( ( ~ ( meet_commutative @ SV5 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(371,plain,
! [SV33: $i,SV11: $i,SV24: $i] :
( ( ( element @ SV24 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( meet_semilatt_str @ SV11 )
= $false )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( meet @ SV11 @ SV24 @ SV33 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(372,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( empty_carrier @ SV12 ) )
= $false )
| ( ( ~ ( meet_commutative @ SV12 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(373,plain,
! [SV39: $i,SV14: $i,SV40: $i] :
( ( ( ~ ( element @ SV40 @ ( the_carrier @ SV14 ) )
| ( ( join @ SV14 @ ( meet @ SV14 @ SV39 @ SV40 ) @ SV40 )
= SV40 ) )
= $true )
| ( ( element @ SV39 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( meet_absorbing @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(374,plain,
! [SV14: $i] :
( ( ( ~ ( element @ ( sK9_SY87 @ SV14 ) @ ( the_carrier @ SV14 ) ) )
= $false )
| ( ( meet_absorbing @ SV14 )
= $true )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(375,plain,
! [SV14: $i] :
( ( ( ( join @ SV14 @ ( meet @ SV14 @ ( sK8_SY70 @ SV14 ) @ ( sK9_SY87 @ SV14 ) ) @ ( sK9_SY87 @ SV14 ) )
= ( sK9_SY87 @ SV14 ) )
= $false )
| ( ( meet_absorbing @ SV14 )
= $true )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(376,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ( ~ ( empty_carrier @ SV17 ) )
= $false )
| ( ( ~ ( meet_commutative @ SV17 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV17 ) )
= $true )
| ( ( ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(377,plain,
! [SV38: $i,SV37: $i,SV1: $i] :
( ( ( ~ ( below @ SV1 @ SV37 @ SV38 ) )
= $true )
| ( ( ( join @ SV1 @ SV37 @ SV38 )
= SV38 )
= $true )
| ( ( element @ SV38 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( join_semilatt_str @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(378,plain,
! [SV38: $i,SV37: $i,SV1: $i] :
( ( ( ( join @ SV1 @ SV37 @ SV38 )
!= SV38 )
= $true )
| ( ( below @ SV1 @ SV37 @ SV38 )
= $true )
| ( ( element @ SV38 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( join_semilatt_str @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(379,plain,
! [SV18: $i,SV2: $i,SV29: $i] :
( ( ( element @ SV29 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( join_semilatt_str @ SV2 )
= $false )
| ( ( empty_carrier @ SV2 )
= $true )
| ( ( element @ SV18 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( join @ SV2 @ SV18 @ SV29 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(380,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ( empty_carrier @ SV5 )
= $true )
| ( ( ~ ( meet_commutative @ SV5 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(381,plain,
! [SV24: $i,SV11: $i,SV33: $i] :
( ( ( element @ SV33 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( meet_semilatt_str @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ ( meet @ SV11 @ SV24 @ SV33 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(382,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( empty_carrier @ SV12 )
= $true )
| ( ( ~ ( meet_commutative @ SV12 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(383,plain,
! [SV39: $i,SV14: $i,SV40: $i] :
( ( ( ~ ( element @ SV40 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ( join @ SV14 @ ( meet @ SV14 @ SV39 @ SV40 ) @ SV40 )
= SV40 )
= $true )
| ( ( element @ SV39 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( meet_absorbing @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(384,plain,
! [SV14: $i] :
( ( ( element @ ( sK9_SY87 @ SV14 ) @ ( the_carrier @ SV14 ) )
= $true )
| ( ( meet_absorbing @ SV14 )
= $true )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(385,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ( empty_carrier @ SV17 )
= $true )
| ( ( ~ ( meet_commutative @ SV17 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV17 ) )
= $true )
| ( ( ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(386,plain,
! [SV38: $i,SV37: $i,SV1: $i] :
( ( ( below @ SV1 @ SV37 @ SV38 )
= $false )
| ( ( ( join @ SV1 @ SV37 @ SV38 )
= SV38 )
= $true )
| ( ( element @ SV38 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( join_semilatt_str @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(387,plain,
! [SV38: $i,SV37: $i,SV1: $i] :
( ( ( ( join @ SV1 @ SV37 @ SV38 )
= SV38 )
= $false )
| ( ( below @ SV1 @ SV37 @ SV38 )
= $true )
| ( ( element @ SV38 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV1 ) )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( join_semilatt_str @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(388,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ( meet_commutative @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(389,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( meet_commutative @ SV12 )
= $false )
| ( ( empty_carrier @ SV12 )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(390,plain,
! [SV39: $i,SV14: $i,SV40: $i] :
( ( ( element @ SV40 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( ( join @ SV14 @ ( meet @ SV14 @ SV39 @ SV40 ) @ SV40 )
= SV40 )
= $true )
| ( ( element @ SV39 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( meet_absorbing @ SV14 )
= $false )
| ( ( empty_carrier @ SV14 )
= $true )
| ( ( latt_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(391,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ( meet_commutative @ SV17 )
= $false )
| ( ( empty_carrier @ SV17 )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV17 ) )
= $true )
| ( ( ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(392,plain,
! [SV32: $i,SV21: $i,SV5: $i] :
( ( ( meet_semilatt_str @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( meet_commutative @ SV5 )
= $false )
| ( ( ~ ( element @ SV21 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(393,plain,
! [SV34: $i,SV25: $i,SV12: $i] :
( ( ( meet_semilatt_str @ SV12 )
= $false )
| ( ( empty_carrier @ SV12 )
= $true )
| ( ( meet_commutative @ SV12 )
= $false )
| ( ( ~ ( element @ SV25 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(394,plain,
! [SV36: $i,SV28: $i,SV17: $i] :
( ( ( meet_semilatt_str @ SV17 )
= $false )
| ( ( empty_carrier @ SV17 )
= $true )
| ( ( meet_commutative @ SV17 )
= $false )
| ( ( ~ ( element @ SV28 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(395,plain,
! [SV32: $i,SV5: $i,SV21: $i] :
( ( ( element @ SV21 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( meet_commutative @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( meet_semilatt_str @ SV5 )
= $false )
| ( ( ~ ( element @ SV32 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(396,plain,
! [SV34: $i,SV12: $i,SV25: $i] :
( ( ( element @ SV25 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( meet_commutative @ SV12 )
= $false )
| ( ( empty_carrier @ SV12 )
= $true )
| ( ( meet_semilatt_str @ SV12 )
= $false )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(397,plain,
! [SV36: $i,SV17: $i,SV28: $i] :
( ( ( element @ SV28 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( meet_commutative @ SV17 )
= $false )
| ( ( empty_carrier @ SV17 )
= $true )
| ( ( meet_semilatt_str @ SV17 )
= $false )
| ( ( ~ ( element @ SV36 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(398,plain,
! [SV21: $i,SV5: $i,SV32: $i] :
( ( ( element @ SV32 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( meet_semilatt_str @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( meet_commutative @ SV5 )
= $false )
| ( ( element @ SV21 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( ( meet_commut @ SV5 @ SV21 @ SV32 )
= ( meet_commut @ SV5 @ SV32 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(399,plain,
! [SV25: $i,SV12: $i,SV34: $i] :
( ( ( element @ SV34 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( meet_semilatt_str @ SV12 )
= $false )
| ( ( empty_carrier @ SV12 )
= $true )
| ( ( meet_commutative @ SV12 )
= $false )
| ( ( element @ SV25 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( element @ ( meet_commut @ SV12 @ SV25 @ SV34 ) @ ( the_carrier @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(400,plain,
! [SV28: $i,SV17: $i,SV36: $i] :
( ( ( element @ SV36 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( meet_semilatt_str @ SV17 )
= $false )
| ( ( empty_carrier @ SV17 )
= $true )
| ( ( meet_commutative @ SV17 )
= $false )
| ( ( element @ SV28 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ( meet_commut @ SV17 @ SV28 @ SV36 )
= ( meet @ SV17 @ SV28 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(401,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[90,400,399,398,390,387,386,384,381,379,375,364,350,340,319,292,288,273,272,271,258,253,251,250,236,234,227,220,212,210,198,139,116,115,114,102,100,99,97,95,93,92]) ).
thf(402,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[401]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU304+1 : 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
% 0.06/0.17 % Computer : n014.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Oct 6 15:12:41 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.66/0.55
% 1.66/0.55 No.of.Axioms: 27
% 1.66/0.55
% 1.66/0.55 Length.of.Defs: 0
% 1.66/0.55
% 1.66/0.55 Contains.Choice.Funs: false
% 1.66/0.55 ...........
% 1.66/0.55
% 1.66/0.55 ********************************
% 1.66/0.55 * All subproblems solved! *
% 1.66/0.55 ********************************
% 1.66/0.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:31,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:401,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.66/0.55
% 1.66/0.55 %**** Beginning of derivation protocol ****
% 1.66/0.55 % SZS output start CNFRefutation
% See solution above
% 1.66/0.55
% 1.66/0.55 %**** End of derivation protocol ****
% 1.66/0.55 %**** no. of clauses in derivation: 380 ****
% 1.66/0.55 %**** clause counter: 401 ****
% 1.66/0.55
% 1.66/0.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:31,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:401,loop_count:0,foatp_calls:1,translation:fof_full)
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