%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU305+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 : n006.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 1.18s 0.41s
% Output : CNFRefutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 27
% Syntax : Number of formulae : 342 ( 168 unt; 0 typ; 0 def)
% Number of atoms : 2791 ( 854 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 5527 (1310 ~; 826 |; 87 &;3222 @)
% ( 6 <=>; 76 =>; 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 : 35 ( 32 usr; 8 con; 0-6 aty)
% Number of variables : 714 ( 0 ^; 702 !; 12 ?; 714 :)
% 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_commut,type,
join_commut: $i > $i > $i > $i ).
thf(tp_join_commutative,type,
join_commutative: $i > $o ).
thf(tp_join_semilatt_str,type,
join_semilatt_str: $i > $o ).
thf(tp_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_SY46,type,
sK5_SY46: $i > $i ).
thf(tp_sK6_SY76,type,
sK6_SY76: $i ).
thf(tp_sK7_SY62,type,
sK7_SY62: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_the_L_join,type,
the_L_join: $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 )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( join_commut @ A @ B @ C )
= ( join @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_lattices) ).
thf(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] : ( join_semilatt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(24,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(25,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(27,axiom,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(28,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join_commut @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattices) ).
thf(30,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(32,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(33,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(34,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(35,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_binop_1) ).
thf(36,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(37,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( join @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_join @ A ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattices) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( join_commut @ A @ B @ C )
= ( join_commut @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_lattices) ).
thf(42,conjecture,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( below @ A @ B @ C )
& ( below @ A @ C @ B ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattices) ).
thf(43,negated_conjecture,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( below @ A @ B @ C )
& ( below @ A @ C @ B ) )
=> ( B = C ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[42]) ).
thf(44,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( below @ A @ B @ C )
& ( below @ A @ C @ B ) )
=> ( B = C ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[43]) ).
thf(45,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(46,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(47,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(48,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(50,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( join_commut @ A @ B @ C )
= ( join @ A @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(51,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(52,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(53,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(54,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(55,plain,
( ( ? [A: $i] : ( join_semilatt_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(56,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(57,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)],[24]) ).
thf(58,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(59,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(60,plain,
( ( ! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(61,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(62,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join_commut @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(63,plain,
$true = $true,
inference(unfold_def,[status(thm)],[30]) ).
thf(64,plain,
$true = $true,
inference(unfold_def,[status(thm)],[32]) ).
thf(65,plain,
$true = $true,
inference(unfold_def,[status(thm)],[33]) ).
thf(66,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)],[34]) ).
thf(67,plain,
$true = $true,
inference(unfold_def,[status(thm)],[35]) ).
thf(68,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)],[36]) ).
thf(69,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( join @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_join @ A ) @ B @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(70,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( join_commut @ A @ B @ C )
= ( join_commut @ A @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(71,plain,
( ( ( ~ ( empty_carrier @ sK1_A )
& ( join_commutative @ sK1_A )
& ( join_semilatt_str @ sK1_A ) )
=> ! [SY44: $i] :
( ( element @ SY44 @ ( the_carrier @ sK1_A ) )
=> ! [SY45: $i] :
( ( element @ SY45 @ ( the_carrier @ sK1_A ) )
=> ( ( ( below @ sK1_A @ SY44 @ SY45 )
& ( below @ sK1_A @ SY45 @ SY44 ) )
=> ( SY44 = SY45 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(72,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[71]) ).
thf(73,plain,
( ( join_commutative @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[71]) ).
thf(74,plain,
( ( join_semilatt_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[71]) ).
thf(75,plain,
( ( ! [SY44: $i] :
( ( element @ SY44 @ ( the_carrier @ sK1_A ) )
=> ! [SY45: $i] :
( ( element @ SY45 @ ( the_carrier @ sK1_A ) )
=> ( ( ( below @ sK1_A @ SY44 @ SY45 )
& ( below @ sK1_A @ SY45 @ SY44 ) )
=> ( SY44 = SY45 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[71]) ).
thf(76,plain,
( ( ~ ! [SY44: $i] :
( ( element @ SY44 @ ( the_carrier @ sK1_A ) )
=> ! [SY45: $i] :
( ( element @ SY45 @ ( the_carrier @ sK1_A ) )
=> ( ( ( below @ sK1_A @ SY44 @ SY45 )
& ( below @ sK1_A @ SY45 @ SY44 ) )
=> ( SY44 = SY45 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[75]) ).
thf(77,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( join_commut @ A @ B @ C )
= ( join_commut @ A @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
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 ) )
=> ( ( join @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_join @ A ) @ B @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(79,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)],[68]) ).
thf(80,plain,
$true = $true,
inference(copy,[status(thm)],[67]) ).
thf(81,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)],[66]) ).
thf(82,plain,
$true = $true,
inference(copy,[status(thm)],[65]) ).
thf(83,plain,
$true = $true,
inference(copy,[status(thm)],[64]) ).
thf(84,plain,
$true = $true,
inference(copy,[status(thm)],[63]) ).
thf(85,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join_commut @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(86,plain,
$true = $true,
inference(copy,[status(thm)],[61]) ).
thf(87,plain,
( ( ! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(88,plain,
$true = $true,
inference(copy,[status(thm)],[59]) ).
thf(89,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(90,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)],[57]) ).
thf(91,plain,
$true = $true,
inference(copy,[status(thm)],[56]) ).
thf(92,plain,
( ( ? [A: $i] : ( join_semilatt_str @ A ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(93,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(94,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(95,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(96,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)],[51]) ).
thf(97,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( join_commut @ A @ B @ C )
= ( join @ A @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(98,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(99,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(100,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(101,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(102,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(103,plain,
( ( join_semilatt_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(104,plain,
( ( join_commutative @ sK1_A )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(105,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(106,plain,
( ( ~ ! [SY44: $i] :
( ( element @ SY44 @ ( the_carrier @ sK1_A ) )
=> ! [SY45: $i] :
( ( element @ SY45 @ ( the_carrier @ sK1_A ) )
=> ( ( ( below @ sK1_A @ SY44 @ SY45 )
& ( below @ sK1_A @ SY45 @ SY44 ) )
=> ( SY44 = SY45 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(107,plain,
( ( ~ ! [SX0: $i] :
~ ( join_semilatt_str @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(108,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(109,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( join_commutative @ SX0 ) )
| ~ ( join_semilatt_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) ) )
| ( ( join_commut @ SX0 @ SX1 @ SX2 )
= ( join @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(112,plain,
( ( ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(113,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)],[90]) ).
thf(114,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(115,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)],[100]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( join_commutative @ SX0 ) )
| ~ ( join_semilatt_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) ) )
| ( element @ ( join_commut @ SX0 @ SX1 @ SX2 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(117,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 ) )
| ~ ( empty @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(118,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( join_commutative @ SX0 ) )
| ~ ( join_semilatt_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) ) )
| ( ( join_commut @ SX0 @ SX1 @ SX2 )
= ( join_commut @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(119,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)],[81]) ).
thf(120,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( join_semilatt_str @ SX0 ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ( ( join @ SX0 @ SX1 @ SX2 )
= ( apply_binary_as_element @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) @ ( the_L_join @ SX0 ) @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(121,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)],[96]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(123,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)],[79]) ).
thf(124,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ~ ( empty @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(125,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( below @ sK1_A @ SX0 @ SX1 )
| ~ ( below @ sK1_A @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(126,plain,
( ( empty_carrier @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(127,plain,
( ( ! [SX0: $i] :
~ ( join_semilatt_str @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(128,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(129,plain,
! [SV1: $i] :
( ( ~ ! [SY46: $i] :
~ ( element @ SY46 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(130,plain,
! [SV2: $i] :
( ( ! [SY47: $i] :
( ~ ( element @ SV2 @ SY47 )
| ( empty @ SY47 )
| ( in @ SV2 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(131,plain,
! [SV3: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_commutative @ SV3 ) )
| ~ ( join_semilatt_str @ SV3 ) )
| ~ ( element @ SY48 @ ( the_carrier @ SV3 ) ) )
| ~ ( element @ SY49 @ ( the_carrier @ SV3 ) ) )
| ( ( join_commut @ SV3 @ SY48 @ SY49 )
= ( join @ SV3 @ SY48 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(132,plain,
! [SV4: $i] :
( ( ~ ( join_semilatt_str @ SV4 )
| ( one_sorted_str @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(133,plain,
! [SV5: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ~ ( relation_of2_as_subset @ SY51 @ SV5 @ SY50 )
| ( element @ SY51 @ ( powerset @ ( cartesian_product2 @ SV5 @ SY50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(134,plain,
! [SV6: $i] :
( ( ! [SY52: $i] :
( ~ ( in @ SV6 @ SY52 )
| ( element @ SV6 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(135,plain,
! [SV7: $i] :
( ( ! [SY53: $i] :
~ ( ~ ( ~ ( element @ SV7 @ ( powerset @ SY53 ) )
| ( subset @ SV7 @ SY53 ) )
| ~ ( ~ ( subset @ SV7 @ SY53 )
| ( element @ SV7 @ ( powerset @ SY53 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(136,plain,
! [SV8: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SY54 @ ( the_carrier @ SV8 ) ) )
| ~ ( element @ SY55 @ ( the_carrier @ SV8 ) ) )
| ( element @ ( join_commut @ SV8 @ SY54 @ SY55 ) @ ( the_carrier @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(137,plain,
! [SV9: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV9 )
| ~ ( one_sorted_str @ SV9 ) )
| ~ ( empty @ ( the_carrier @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(138,plain,
! [SV10: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( join_commutative @ SV10 ) )
| ~ ( join_semilatt_str @ SV10 ) )
| ~ ( element @ SY56 @ ( the_carrier @ SV10 ) ) )
| ~ ( element @ SY57 @ ( the_carrier @ SV10 ) ) )
| ( ( join_commut @ SV10 @ SY56 @ SY57 )
= ( join_commut @ SV10 @ SY57 @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(139,plain,
! [SV11: $i] :
( ( ! [SY58: $i,SY59: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 ) )
| ~ ( element @ SY58 @ ( the_carrier @ SV11 ) ) )
| ~ ( element @ SY59 @ ( the_carrier @ SV11 ) ) )
| ( element @ ( join @ SV11 @ SY58 @ SY59 ) @ ( the_carrier @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(140,plain,
! [SV12: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( join_semilatt_str @ SV12 ) )
| ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV12 ) )
| ! [SY61: $i] :
( ~ ( element @ SY61 @ ( the_carrier @ SV12 ) )
| ( ( join @ SV12 @ SY60 @ SY61 )
= ( apply_binary_as_element @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_L_join @ SV12 ) @ SY60 @ SY61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(141,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV13 )
| ~ ( one_sorted_str @ SV13 ) )
| ~ ! [SY62: $i] :
~ ~ ( ~ ( element @ SY62 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(142,plain,
! [SV14: $i] :
( ( ! [SY63: $i,SY64: $i] :
( ~ ~ ( ~ ( in @ SV14 @ SY63 )
| ~ ( element @ SY63 @ ( powerset @ SY64 ) ) )
| ( element @ SV14 @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(143,plain,
! [SV15: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV15 )
| ~ ( join_semilatt_str @ SV15 ) )
| ! [SY65: $i] :
( ~ ( element @ SY65 @ ( the_carrier @ SV15 ) )
| ! [SY66: $i] :
( ~ ( element @ SY66 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( below @ SV15 @ SY65 @ SY66 )
| ( ( join @ SV15 @ SY65 @ SY66 )
= SY66 ) )
| ~ ( ( ( join @ SV15 @ SY65 @ SY66 )
!= SY66 )
| ( below @ SV15 @ SY65 @ SY66 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(144,plain,
! [SV16: $i] :
( ( ! [SY67: $i,SY68: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV16 @ SY67 )
| ~ ( element @ SY67 @ ( powerset @ SY68 ) ) )
| ~ ( empty @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(145,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( below @ sK1_A @ SX0 @ SX1 )
| ~ ( below @ sK1_A @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(146,plain,
( ( ~ ( join_semilatt_str @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[127]) ).
thf(147,plain,
( ( ~ ~ ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[128]) ).
thf(148,plain,
! [SV1: $i] :
( ( ! [SY46: $i] :
~ ( element @ SY46 @ SV1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(149,plain,
! [SV17: $i,SV2: $i] :
( ( ~ ( element @ SV2 @ SV17 )
| ( empty @ SV17 )
| ( in @ SV2 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(150,plain,
! [SV18: $i,SV3: $i] :
( ( ! [SY69: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_commutative @ SV3 ) )
| ~ ( join_semilatt_str @ SV3 ) )
| ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) )
| ~ ( element @ SY69 @ ( the_carrier @ SV3 ) ) )
| ( ( join_commut @ SV3 @ SV18 @ SY69 )
= ( join @ SV3 @ SV18 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(151,plain,
! [SV4: $i] :
( ( ( ~ ( join_semilatt_str @ SV4 ) )
= $true )
| ( ( one_sorted_str @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(152,plain,
! [SV19: $i,SV5: $i] :
( ( ! [SY70: $i] :
( ~ ( relation_of2_as_subset @ SY70 @ SV5 @ SV19 )
| ( element @ SY70 @ ( powerset @ ( cartesian_product2 @ SV5 @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(153,plain,
! [SV20: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ SV20 )
| ( element @ SV6 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(154,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( element @ SV7 @ ( powerset @ SV21 ) )
| ( subset @ SV7 @ SV21 ) )
| ~ ( ~ ( subset @ SV7 @ SV21 )
| ( element @ SV7 @ ( powerset @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(155,plain,
! [SV22: $i,SV8: $i] :
( ( ! [SY71: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) )
| ~ ( element @ SY71 @ ( the_carrier @ SV8 ) ) )
| ( element @ ( join_commut @ SV8 @ SV22 @ SY71 ) @ ( the_carrier @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(156,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV9 )
| ~ ( one_sorted_str @ SV9 ) ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(157,plain,
! [SV23: $i,SV10: $i] :
( ( ! [SY72: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( join_commutative @ SV10 ) )
| ~ ( join_semilatt_str @ SV10 ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) )
| ~ ( element @ SY72 @ ( the_carrier @ SV10 ) ) )
| ( ( join_commut @ SV10 @ SV23 @ SY72 )
= ( join_commut @ SV10 @ SY72 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(158,plain,
! [SV24: $i,SV11: $i] :
( ( ! [SY73: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 ) )
| ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
| ~ ( element @ SY73 @ ( the_carrier @ SV11 ) ) )
| ( element @ ( join @ SV11 @ SV24 @ SY73 ) @ ( the_carrier @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(159,plain,
! [SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( join_semilatt_str @ SV12 ) ) )
= $true )
| ( ( ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV12 ) )
| ! [SY61: $i] :
( ~ ( element @ SY61 @ ( the_carrier @ SV12 ) )
| ( ( join @ SV12 @ SY60 @ SY61 )
= ( apply_binary_as_element @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_L_join @ SV12 ) @ SY60 @ SY61 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(160,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV13 )
| ~ ( one_sorted_str @ SV13 ) ) )
= $true )
| ( ( ~ ! [SY62: $i] :
~ ~ ( ~ ( element @ SY62 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(161,plain,
! [SV25: $i,SV14: $i] :
( ( ! [SY74: $i] :
( ~ ~ ( ~ ( in @ SV14 @ SV25 )
| ~ ( element @ SV25 @ ( powerset @ SY74 ) ) )
| ( element @ SV14 @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(162,plain,
! [SV15: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV15 )
| ~ ( join_semilatt_str @ SV15 ) ) )
= $true )
| ( ( ! [SY65: $i] :
( ~ ( element @ SY65 @ ( the_carrier @ SV15 ) )
| ! [SY66: $i] :
( ~ ( element @ SY66 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( below @ SV15 @ SY65 @ SY66 )
| ( ( join @ SV15 @ SY65 @ SY66 )
= SY66 ) )
| ~ ( ( ( join @ SV15 @ SY65 @ SY66 )
!= SY66 )
| ( below @ SV15 @ SY65 @ SY66 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(163,plain,
! [SV26: $i,SV16: $i] :
( ( ! [SY75: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV16 @ SV26 )
| ~ ( element @ SV26 @ ( powerset @ SY75 ) ) )
| ~ ( empty @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(164,plain,
( ( ~ ( element @ sK4_SX0 @ ( the_carrier @ sK1_A ) )
| ! [SY76: $i] :
( ~ ( element @ SY76 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( below @ sK1_A @ sK4_SX0 @ SY76 )
| ~ ( below @ sK1_A @ SY76 @ sK4_SX0 ) )
| ( sK4_SX0 = SY76 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[145]) ).
thf(165,plain,
( ( join_semilatt_str @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(166,plain,
( ( ~ ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(167,plain,
! [SV1: $i] :
( ( ~ ( element @ ( sK5_SY46 @ SV1 ) @ SV1 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[148]) ).
thf(168,plain,
! [SV17: $i,SV2: $i] :
( ( ( ~ ( element @ SV2 @ SV17 ) )
= $true )
| ( ( ( empty @ SV17 )
| ( in @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(169,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_commutative @ SV3 ) )
| ~ ( join_semilatt_str @ SV3 ) )
| ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) )
| ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) )
| ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(170,plain,
! [SV4: $i] :
( ( ( join_semilatt_str @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(171,plain,
! [SV19: $i,SV5: $i,SV28: $i] :
( ( ~ ( relation_of2_as_subset @ SV28 @ SV5 @ SV19 )
| ( element @ SV28 @ ( powerset @ ( cartesian_product2 @ SV5 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(172,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV20 ) )
= $true )
| ( ( element @ SV6 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(173,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ( ~ ( element @ SV7 @ ( powerset @ SV21 ) )
| ( subset @ SV7 @ SV21 ) )
| ~ ( ~ ( subset @ SV7 @ SV21 )
| ( element @ SV7 @ ( powerset @ SV21 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(174,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) )
| ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) )
| ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(175,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV9 )
| ~ ( one_sorted_str @ SV9 ) ) )
= $false )
| ( ( ~ ( empty @ ( the_carrier @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(176,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( join_commutative @ SV10 ) )
| ~ ( join_semilatt_str @ SV10 ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) )
| ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) )
| ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(177,plain,
! [SV31: $i,SV24: $i,SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 ) )
| ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
| ~ ( element @ SV31 @ ( the_carrier @ SV11 ) ) )
| ( element @ ( join @ SV11 @ SV24 @ SV31 ) @ ( the_carrier @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(178,plain,
! [SV12: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( join_semilatt_str @ SV12 ) ) )
= $false )
| ( ( ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV12 ) )
| ! [SY61: $i] :
( ~ ( element @ SY61 @ ( the_carrier @ SV12 ) )
| ( ( join @ SV12 @ SY60 @ SY61 )
= ( apply_binary_as_element @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_L_join @ SV12 ) @ SY60 @ SY61 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(179,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV13 )
| ~ ( one_sorted_str @ SV13 ) ) )
= $false )
| ( ( ~ ! [SY62: $i] :
~ ~ ( ~ ( element @ SY62 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(180,plain,
! [SV32: $i,SV25: $i,SV14: $i] :
( ( ~ ~ ( ~ ( in @ SV14 @ SV25 )
| ~ ( element @ SV25 @ ( powerset @ SV32 ) ) )
| ( element @ SV14 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(181,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV15 )
| ~ ( join_semilatt_str @ SV15 ) ) )
= $false )
| ( ( ! [SY65: $i] :
( ~ ( element @ SY65 @ ( the_carrier @ SV15 ) )
| ! [SY66: $i] :
( ~ ( element @ SY66 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( below @ SV15 @ SY65 @ SY66 )
| ( ( join @ SV15 @ SY65 @ SY66 )
= SY66 ) )
| ~ ( ( ( join @ SV15 @ SY65 @ SY66 )
!= SY66 )
| ( below @ SV15 @ SY65 @ SY66 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(182,plain,
! [SV33: $i,SV26: $i,SV16: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV16 @ SV26 )
| ~ ( element @ SV26 @ ( powerset @ SV33 ) ) )
| ~ ( empty @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(183,plain,
( ( ~ ( element @ sK4_SX0 @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(184,plain,
( ( ! [SY76: $i] :
( ~ ( element @ SY76 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( below @ sK1_A @ sK4_SX0 @ SY76 )
| ~ ( below @ sK1_A @ SY76 @ sK4_SX0 ) )
| ( sK4_SX0 = SY76 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(185,plain,
( ( ~ ( one_sorted_str @ sK3_SX0 )
| ~ ~ ( empty_carrier @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(186,plain,
! [SV1: $i] :
( ( element @ ( sK5_SY46 @ SV1 ) @ SV1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(187,plain,
! [SV17: $i,SV2: $i] :
( ( ( element @ SV2 @ SV17 )
= $false )
| ( ( ( empty @ SV17 )
| ( in @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(188,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_commutative @ SV3 ) )
| ~ ( join_semilatt_str @ SV3 ) )
| ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) )
| ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) ) )
= $true )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(189,plain,
! [SV19: $i,SV5: $i,SV28: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV28 @ SV5 @ SV19 ) )
= $true )
| ( ( element @ SV28 @ ( powerset @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(190,plain,
! [SV20: $i,SV6: $i] :
( ( ( in @ SV6 @ SV20 )
= $false )
| ( ( element @ SV6 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(191,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ( ~ ( element @ SV7 @ ( powerset @ SV21 ) )
| ( subset @ SV7 @ SV21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(192,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ( ~ ( subset @ SV7 @ SV21 )
| ( element @ SV7 @ ( powerset @ SV21 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(193,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) )
| ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(194,plain,
! [SV9: $i] :
( ( ( ~ ~ ( empty_carrier @ SV9 )
| ~ ( one_sorted_str @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(195,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( join_commutative @ SV10 ) )
| ~ ( join_semilatt_str @ SV10 ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) )
| ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) ) )
= $true )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(196,plain,
! [SV31: $i,SV24: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 ) )
| ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
| ~ ( element @ SV31 @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV24 @ SV31 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(197,plain,
! [SV12: $i] :
( ( ( ~ ~ ( empty_carrier @ SV12 )
| ~ ( join_semilatt_str @ SV12 ) )
= $true )
| ( ( ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV12 ) )
| ! [SY61: $i] :
( ~ ( element @ SY61 @ ( the_carrier @ SV12 ) )
| ( ( join @ SV12 @ SY60 @ SY61 )
= ( apply_binary_as_element @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_L_join @ SV12 ) @ SY60 @ SY61 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(198,plain,
! [SV13: $i] :
( ( ( ~ ~ ( empty_carrier @ SV13 )
| ~ ( one_sorted_str @ SV13 ) )
= $true )
| ( ( ~ ! [SY62: $i] :
~ ~ ( ~ ( element @ SY62 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY62 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(199,plain,
! [SV32: $i,SV25: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ SV14 @ SV25 )
| ~ ( element @ SV25 @ ( powerset @ SV32 ) ) ) )
= $true )
| ( ( element @ SV14 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(200,plain,
! [SV15: $i] :
( ( ( ~ ~ ( empty_carrier @ SV15 )
| ~ ( join_semilatt_str @ SV15 ) )
= $true )
| ( ( ! [SY65: $i] :
( ~ ( element @ SY65 @ ( the_carrier @ SV15 ) )
| ! [SY66: $i] :
( ~ ( element @ SY66 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( below @ SV15 @ SY65 @ SY66 )
| ( ( join @ SV15 @ SY65 @ SY66 )
= SY66 ) )
| ~ ( ( ( join @ SV15 @ SY65 @ SY66 )
!= SY66 )
| ( below @ SV15 @ SY65 @ SY66 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(201,plain,
! [SV33: $i,SV26: $i,SV16: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV16 @ SV26 )
| ~ ( element @ SV26 @ ( powerset @ SV33 ) ) )
| ~ ( empty @ SV33 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(202,plain,
( ( element @ sK4_SX0 @ ( the_carrier @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(203,plain,
( ( ~ ( element @ sK6_SY76 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( below @ sK1_A @ sK4_SX0 @ sK6_SY76 )
| ~ ( below @ sK1_A @ sK6_SY76 @ sK4_SX0 ) )
| ( sK4_SX0 = sK6_SY76 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[184]) ).
thf(204,plain,
( ( ~ ( one_sorted_str @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(205,plain,
( ( ~ ~ ( empty_carrier @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(206,plain,
! [SV2: $i,SV17: $i] :
( ( ( empty @ SV17 )
= $true )
| ( ( in @ SV2 @ SV17 )
= $true )
| ( ( element @ SV2 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(207,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_commutative @ SV3 ) )
| ~ ( join_semilatt_str @ SV3 ) )
| ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) )
| ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) ) )
= $false )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(208,plain,
! [SV19: $i,SV5: $i,SV28: $i] :
( ( ( relation_of2_as_subset @ SV28 @ SV5 @ SV19 )
= $false )
| ( ( element @ SV28 @ ( powerset @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(209,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ( element @ SV7 @ ( powerset @ SV21 ) )
| ( subset @ SV7 @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(210,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ( subset @ SV7 @ SV21 )
| ( element @ SV7 @ ( powerset @ SV21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(211,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) )
| ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) ) )
= $false )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(212,plain,
! [SV9: $i] :
( ( ( ~ ~ ( empty_carrier @ SV9 ) )
= $true )
| ( ( ~ ( one_sorted_str @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(213,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( join_commutative @ SV10 ) )
| ~ ( join_semilatt_str @ SV10 ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) )
| ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) ) )
= $false )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(214,plain,
! [SV31: $i,SV24: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 ) )
| ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
| ~ ( element @ SV31 @ ( the_carrier @ SV11 ) ) ) )
= $false )
| ( ( element @ ( join @ SV11 @ SV24 @ SV31 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(215,plain,
! [SV12: $i] :
( ( ( ~ ~ ( empty_carrier @ SV12 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV12 ) )
= $true )
| ( ( ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV12 ) )
| ! [SY61: $i] :
( ~ ( element @ SY61 @ ( the_carrier @ SV12 ) )
| ( ( join @ SV12 @ SY60 @ SY61 )
= ( apply_binary_as_element @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_L_join @ SV12 ) @ SY60 @ SY61 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(216,plain,
! [SV13: $i] :
( ( ( ~ ~ ( empty_carrier @ SV13 ) )
= $true )
| ( ( ~ ( one_sorted_str @ SV13 ) )
= $true )
| ( ( ~ ! [SY62: $i] :
~ ~ ( ~ ( element @ SY62 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(217,plain,
! [SV32: $i,SV25: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ SV14 @ SV25 )
| ~ ( element @ SV25 @ ( powerset @ SV32 ) ) ) )
= $false )
| ( ( element @ SV14 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(218,plain,
! [SV15: $i] :
( ( ( ~ ~ ( empty_carrier @ SV15 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV15 ) )
= $true )
| ( ( ! [SY65: $i] :
( ~ ( element @ SY65 @ ( the_carrier @ SV15 ) )
| ! [SY66: $i] :
( ~ ( element @ SY66 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( below @ SV15 @ SY65 @ SY66 )
| ( ( join @ SV15 @ SY65 @ SY66 )
= SY66 ) )
| ~ ( ( ( join @ SV15 @ SY65 @ SY66 )
!= SY66 )
| ( below @ SV15 @ SY65 @ SY66 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(219,plain,
! [SV33: $i,SV26: $i,SV16: $i] :
( ( ~ ~ ( ~ ( in @ SV16 @ SV26 )
| ~ ( element @ SV26 @ ( powerset @ SV33 ) ) )
| ~ ( empty @ SV33 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(220,plain,
( ( ~ ( element @ sK6_SY76 @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(221,plain,
( ( ~ ~ ( ~ ( below @ sK1_A @ sK4_SX0 @ sK6_SY76 )
| ~ ( below @ sK1_A @ sK6_SY76 @ sK4_SX0 ) )
| ( sK4_SX0 = sK6_SY76 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(222,plain,
( ( one_sorted_str @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(223,plain,
( ( ~ ( empty_carrier @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(224,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_commutative @ SV3 ) )
| ~ ( join_semilatt_str @ SV3 ) )
| ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) )
| ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(225,plain,
! [SV21: $i,SV7: $i] :
( ( ( ~ ( element @ SV7 @ ( powerset @ SV21 ) ) )
= $true )
| ( ( subset @ SV7 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(226,plain,
! [SV21: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV21 ) )
= $true )
| ( ( element @ SV7 @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(227,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) )
| ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(228,plain,
! [SV9: $i] :
( ( ( ~ ( empty_carrier @ SV9 ) )
= $false )
| ( ( ~ ( one_sorted_str @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(229,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( join_commutative @ SV10 ) )
| ~ ( join_semilatt_str @ SV10 ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) )
| ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(230,plain,
! [SV31: $i,SV24: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 ) )
| ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
| ~ ( element @ SV31 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV24 @ SV31 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(231,plain,
! [SV12: $i] :
( ( ( ~ ( empty_carrier @ SV12 ) )
= $false )
| ( ( ~ ( join_semilatt_str @ SV12 ) )
= $true )
| ( ( ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV12 ) )
| ! [SY61: $i] :
( ~ ( element @ SY61 @ ( the_carrier @ SV12 ) )
| ( ( join @ SV12 @ SY60 @ SY61 )
= ( apply_binary_as_element @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_L_join @ SV12 ) @ SY60 @ SY61 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(232,plain,
! [SV13: $i] :
( ( ( ~ ( empty_carrier @ SV13 ) )
= $false )
| ( ( ~ ( one_sorted_str @ SV13 ) )
= $true )
| ( ( ~ ! [SY62: $i] :
~ ~ ( ~ ( element @ SY62 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(233,plain,
! [SV32: $i,SV25: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV25 )
| ~ ( element @ SV25 @ ( powerset @ SV32 ) ) )
= $true )
| ( ( element @ SV14 @ SV32 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(234,plain,
! [SV15: $i] :
( ( ( ~ ( empty_carrier @ SV15 ) )
= $false )
| ( ( ~ ( join_semilatt_str @ SV15 ) )
= $true )
| ( ( ! [SY65: $i] :
( ~ ( element @ SY65 @ ( the_carrier @ SV15 ) )
| ! [SY66: $i] :
( ~ ( element @ SY66 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( below @ SV15 @ SY65 @ SY66 )
| ( ( join @ SV15 @ SY65 @ SY66 )
= SY66 ) )
| ~ ( ( ( join @ SV15 @ SY65 @ SY66 )
!= SY66 )
| ( below @ SV15 @ SY65 @ SY66 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(235,plain,
! [SV33: $i,SV26: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( in @ SV16 @ SV26 )
| ~ ( element @ SV26 @ ( powerset @ SV33 ) ) ) )
= $true )
| ( ( ~ ( empty @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(236,plain,
( ( element @ sK6_SY76 @ ( the_carrier @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(237,plain,
( ( ~ ~ ( ~ ( below @ sK1_A @ sK4_SX0 @ sK6_SY76 )
| ~ ( below @ sK1_A @ sK6_SY76 @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(238,plain,
( ( sK4_SX0 = sK6_SY76 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(239,plain,
( ( empty_carrier @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(240,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_commutative @ SV3 ) )
| ~ ( join_semilatt_str @ SV3 ) )
| ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) ) )
= $true )
| ( ( ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(241,plain,
! [SV21: $i,SV7: $i] :
( ( ( element @ SV7 @ ( powerset @ SV21 ) )
= $false )
| ( ( subset @ SV7 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(242,plain,
! [SV21: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV21 )
= $false )
| ( ( element @ SV7 @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(243,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(244,plain,
! [SV9: $i] :
( ( ( empty_carrier @ SV9 )
= $true )
| ( ( ~ ( one_sorted_str @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(245,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( join_commutative @ SV10 ) )
| ~ ( join_semilatt_str @ SV10 ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) ) )
= $true )
| ( ( ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(246,plain,
! [SV31: $i,SV24: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 ) )
| ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) ) )
= $true )
| ( ( ~ ( element @ SV31 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV24 @ SV31 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(247,plain,
! [SV12: $i] :
( ( ( empty_carrier @ SV12 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV12 ) )
= $true )
| ( ( ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV12 ) )
| ! [SY61: $i] :
( ~ ( element @ SY61 @ ( the_carrier @ SV12 ) )
| ( ( join @ SV12 @ SY60 @ SY61 )
= ( apply_binary_as_element @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_L_join @ SV12 ) @ SY60 @ SY61 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(248,plain,
! [SV13: $i] :
( ( ( empty_carrier @ SV13 )
= $true )
| ( ( ~ ( one_sorted_str @ SV13 ) )
= $true )
| ( ( ~ ! [SY62: $i] :
~ ~ ( ~ ( element @ SY62 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY62 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(249,plain,
! [SV32: $i,SV25: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV25 ) )
= $true )
| ( ( ~ ( element @ SV25 @ ( powerset @ SV32 ) ) )
= $true )
| ( ( element @ SV14 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(250,plain,
! [SV15: $i] :
( ( ( empty_carrier @ SV15 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV15 ) )
= $true )
| ( ( ! [SY65: $i] :
( ~ ( element @ SY65 @ ( the_carrier @ SV15 ) )
| ! [SY66: $i] :
( ~ ( element @ SY66 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( below @ SV15 @ SY65 @ SY66 )
| ( ( join @ SV15 @ SY65 @ SY66 )
= SY66 ) )
| ~ ( ( ( join @ SV15 @ SY65 @ SY66 )
!= SY66 )
| ( below @ SV15 @ SY65 @ SY66 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(251,plain,
! [SV33: $i,SV26: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ SV16 @ SV26 )
| ~ ( element @ SV26 @ ( powerset @ SV33 ) ) ) )
= $false )
| ( ( ~ ( empty @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(252,plain,
( ( ~ ( ~ ( below @ sK1_A @ sK4_SX0 @ sK6_SY76 )
| ~ ( below @ sK1_A @ sK6_SY76 @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(253,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_commutative @ SV3 ) )
| ~ ( join_semilatt_str @ SV3 ) )
| ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) ) )
= $false )
| ( ( ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(254,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) ) )
= $false )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(255,plain,
! [SV9: $i] :
( ( ( one_sorted_str @ SV9 )
= $false )
| ( ( empty_carrier @ SV9 )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(256,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( join_commutative @ SV10 ) )
| ~ ( join_semilatt_str @ SV10 ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) ) )
= $false )
| ( ( ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(257,plain,
! [SV31: $i,SV24: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 ) )
| ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) ) )
= $false )
| ( ( ~ ( element @ SV31 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV24 @ SV31 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(258,plain,
! [SV12: $i] :
( ( ( join_semilatt_str @ SV12 )
= $false )
| ( ( empty_carrier @ SV12 )
= $true )
| ( ( ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV12 ) )
| ! [SY61: $i] :
( ~ ( element @ SY61 @ ( the_carrier @ SV12 ) )
| ( ( join @ SV12 @ SY60 @ SY61 )
= ( apply_binary_as_element @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_L_join @ SV12 ) @ SY60 @ SY61 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(259,plain,
! [SV13: $i] :
( ( ( one_sorted_str @ SV13 )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( ~ ! [SY62: $i] :
~ ~ ( ~ ( element @ SY62 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(260,plain,
! [SV32: $i,SV25: $i,SV14: $i] :
( ( ( in @ SV14 @ SV25 )
= $false )
| ( ( ~ ( element @ SV25 @ ( powerset @ SV32 ) ) )
= $true )
| ( ( element @ SV14 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(261,plain,
! [SV15: $i] :
( ( ( join_semilatt_str @ SV15 )
= $false )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( ! [SY65: $i] :
( ~ ( element @ SY65 @ ( the_carrier @ SV15 ) )
| ! [SY66: $i] :
( ~ ( element @ SY66 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( below @ SV15 @ SY65 @ SY66 )
| ( ( join @ SV15 @ SY65 @ SY66 )
= SY66 ) )
| ~ ( ( ( join @ SV15 @ SY65 @ SY66 )
!= SY66 )
| ( below @ SV15 @ SY65 @ SY66 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(262,plain,
! [SV33: $i,SV26: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV26 )
| ~ ( element @ SV26 @ ( powerset @ SV33 ) ) )
= $true )
| ( ( ~ ( empty @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(263,plain,
( ( ~ ( below @ sK1_A @ sK4_SX0 @ sK6_SY76 )
| ~ ( below @ sK1_A @ sK6_SY76 @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(264,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_commutative @ SV3 ) )
| ~ ( join_semilatt_str @ SV3 ) )
| ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(265,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
| ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(266,plain,
! [SV9: $i] :
( ( ( empty @ ( the_carrier @ SV9 ) )
= $false )
| ( ( empty_carrier @ SV9 )
= $true )
| ( ( one_sorted_str @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(267,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( join_commutative @ SV10 ) )
| ~ ( join_semilatt_str @ SV10 ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(268,plain,
! [SV31: $i,SV24: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 ) )
| ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV31 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV24 @ SV31 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(269,plain,
! [SV12: $i,SV34: $i] :
( ( ( ~ ( element @ SV34 @ ( the_carrier @ SV12 ) )
| ! [SY77: $i] :
( ~ ( element @ SY77 @ ( the_carrier @ SV12 ) )
| ( ( join @ SV12 @ SV34 @ SY77 )
= ( apply_binary_as_element @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_L_join @ SV12 ) @ SV34 @ SY77 ) ) ) )
= $true )
| ( ( empty_carrier @ SV12 )
= $true )
| ( ( join_semilatt_str @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(270,plain,
! [SV13: $i] :
( ( ( ! [SY62: $i] :
~ ~ ( ~ ( element @ SY62 @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ SY62 ) ) )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(271,plain,
! [SV14: $i,SV32: $i,SV25: $i] :
( ( ( element @ SV25 @ ( powerset @ SV32 ) )
= $false )
| ( ( in @ SV14 @ SV25 )
= $false )
| ( ( element @ SV14 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(272,plain,
! [SV15: $i,SV35: $i] :
( ( ( ~ ( element @ SV35 @ ( the_carrier @ SV15 ) )
| ! [SY78: $i] :
( ~ ( element @ SY78 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( below @ SV15 @ SV35 @ SY78 )
| ( ( join @ SV15 @ SV35 @ SY78 )
= SY78 ) )
| ~ ( ( ( join @ SV15 @ SV35 @ SY78 )
!= SY78 )
| ( below @ SV15 @ SV35 @ SY78 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( join_semilatt_str @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(273,plain,
! [SV33: $i,SV26: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( element @ SV26 @ ( powerset @ SV33 ) ) )
= $true )
| ( ( ~ ( empty @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(274,plain,
( ( ~ ( below @ sK1_A @ sK4_SX0 @ sK6_SY76 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(275,plain,
( ( ~ ( below @ sK1_A @ sK6_SY76 @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(276,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_commutative @ SV3 ) )
| ~ ( join_semilatt_str @ SV3 ) ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(277,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(278,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( join_commutative @ SV10 ) )
| ~ ( join_semilatt_str @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(279,plain,
! [SV31: $i,SV24: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV31 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV24 @ SV31 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(280,plain,
! [SV12: $i,SV34: $i] :
( ( ( ~ ( element @ SV34 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( ! [SY77: $i] :
( ~ ( element @ SY77 @ ( the_carrier @ SV12 ) )
| ( ( join @ SV12 @ SV34 @ SY77 )
= ( apply_binary_as_element @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_L_join @ SV12 ) @ SV34 @ SY77 ) ) ) )
= $true )
| ( ( empty_carrier @ SV12 )
= $true )
| ( ( join_semilatt_str @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(281,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_SY62 @ SV13 ) @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ ( sK7_SY62 @ SV13 ) ) ) )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[270]) ).
thf(282,plain,
! [SV15: $i,SV35: $i] :
( ( ( ~ ( element @ SV35 @ ( the_carrier @ SV15 ) ) )
= $true )
| ( ( ! [SY78: $i] :
( ~ ( element @ SY78 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( below @ SV15 @ SV35 @ SY78 )
| ( ( join @ SV15 @ SV35 @ SY78 )
= SY78 ) )
| ~ ( ( ( join @ SV15 @ SV35 @ SY78 )
!= SY78 )
| ( below @ SV15 @ SV35 @ SY78 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( join_semilatt_str @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(283,plain,
! [SV33: $i,SV26: $i,SV16: $i] :
( ( ( in @ SV16 @ SV26 )
= $false )
| ( ( ~ ( element @ SV26 @ ( powerset @ SV33 ) ) )
= $true )
| ( ( ~ ( empty @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(284,plain,
( ( below @ sK1_A @ sK4_SX0 @ sK6_SY76 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(285,plain,
( ( below @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(286,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_commutative @ SV3 ) )
| ~ ( join_semilatt_str @ SV3 ) ) )
= $false )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(287,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) ) )
= $false )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(288,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( join_commutative @ SV10 ) )
| ~ ( join_semilatt_str @ SV10 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(289,plain,
! [SV31: $i,SV24: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 ) ) )
= $false )
| ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV31 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV24 @ SV31 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(290,plain,
! [SV12: $i,SV34: $i] :
( ( ( element @ SV34 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( ! [SY77: $i] :
( ~ ( element @ SY77 @ ( the_carrier @ SV12 ) )
| ( ( join @ SV12 @ SV34 @ SY77 )
= ( apply_binary_as_element @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_L_join @ SV12 ) @ SV34 @ SY77 ) ) ) )
= $true )
| ( ( empty_carrier @ SV12 )
= $true )
| ( ( join_semilatt_str @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(291,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ( element @ ( sK7_SY62 @ SV13 ) @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ ( sK7_SY62 @ SV13 ) ) ) )
= $true )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(292,plain,
! [SV15: $i,SV35: $i] :
( ( ( element @ SV35 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( ! [SY78: $i] :
( ~ ( element @ SY78 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( below @ SV15 @ SV35 @ SY78 )
| ( ( join @ SV15 @ SV35 @ SY78 )
= SY78 ) )
| ~ ( ( ( join @ SV15 @ SV35 @ SY78 )
!= SY78 )
| ( below @ SV15 @ SV35 @ SY78 ) ) ) ) )
= $true )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( join_semilatt_str @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(293,plain,
! [SV16: $i,SV33: $i,SV26: $i] :
( ( ( element @ SV26 @ ( powerset @ SV33 ) )
= $false )
| ( ( in @ SV16 @ SV26 )
= $false )
| ( ( ~ ( empty @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(294,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_commutative @ SV3 ) )
| ~ ( join_semilatt_str @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(295,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
| ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(296,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( join_commutative @ SV10 ) )
| ~ ( join_semilatt_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(297,plain,
! [SV31: $i,SV24: $i,SV11: $i] :
( ( ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 ) )
= $true )
| ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV31 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV24 @ SV31 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(298,plain,
! [SV34: $i,SV12: $i,SV36: $i] :
( ( ( ~ ( element @ SV36 @ ( the_carrier @ SV12 ) )
| ( ( join @ SV12 @ SV34 @ SV36 )
= ( apply_binary_as_element @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_L_join @ SV12 ) @ SV34 @ SV36 ) ) )
= $true )
| ( ( element @ SV34 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( empty_carrier @ SV12 )
= $true )
| ( ( join_semilatt_str @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(299,plain,
! [SV13: $i] :
( ( ( ~ ( element @ ( sK7_SY62 @ SV13 ) @ ( powerset @ ( the_carrier @ SV13 ) ) )
| ~ ~ ( empty @ ( sK7_SY62 @ SV13 ) ) )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(300,plain,
! [SV35: $i,SV15: $i,SV37: $i] :
( ( ( ~ ( element @ SV37 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( below @ SV15 @ SV35 @ SV37 )
| ( ( join @ SV15 @ SV35 @ SV37 )
= SV37 ) )
| ~ ( ( ( join @ SV15 @ SV35 @ SV37 )
!= SV37 )
| ( below @ SV15 @ SV35 @ SV37 ) ) ) )
= $true )
| ( ( element @ SV35 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( join_semilatt_str @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(301,plain,
! [SV26: $i,SV16: $i,SV33: $i] :
( ( ( empty @ SV33 )
= $false )
| ( ( in @ SV16 @ SV26 )
= $false )
| ( ( element @ SV26 @ ( powerset @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(302,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_commutative @ SV3 ) ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(303,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(304,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( join_commutative @ SV10 ) ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(305,plain,
! [SV31: $i,SV24: $i,SV11: $i] :
( ( ( ~ ~ ( empty_carrier @ SV11 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV11 ) )
= $true )
| ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV31 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV24 @ SV31 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(306,plain,
! [SV34: $i,SV12: $i,SV36: $i] :
( ( ( ~ ( element @ SV36 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( ( join @ SV12 @ SV34 @ SV36 )
= ( apply_binary_as_element @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_L_join @ SV12 ) @ SV34 @ SV36 ) )
= $true )
| ( ( element @ SV34 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( empty_carrier @ SV12 )
= $true )
| ( ( join_semilatt_str @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(307,plain,
! [SV13: $i] :
( ( ( ~ ( element @ ( sK7_SY62 @ SV13 ) @ ( powerset @ ( the_carrier @ SV13 ) ) ) )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(308,plain,
! [SV13: $i] :
( ( ( ~ ~ ( empty @ ( sK7_SY62 @ SV13 ) ) )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(309,plain,
! [SV35: $i,SV15: $i,SV37: $i] :
( ( ( ~ ( element @ SV37 @ ( the_carrier @ SV15 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( below @ SV15 @ SV35 @ SV37 )
| ( ( join @ SV15 @ SV35 @ SV37 )
= SV37 ) )
| ~ ( ( ( join @ SV15 @ SV35 @ SV37 )
!= SV37 )
| ( below @ SV15 @ SV35 @ SV37 ) ) ) )
= $true )
| ( ( element @ SV35 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( join_semilatt_str @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(310,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_commutative @ SV3 ) ) )
= $false )
| ( ( ~ ( join_semilatt_str @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(311,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) ) )
= $false )
| ( ( ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(312,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( join_commutative @ SV10 ) ) )
= $false )
| ( ( ~ ( join_semilatt_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(313,plain,
! [SV31: $i,SV24: $i,SV11: $i] :
( ( ( ~ ( empty_carrier @ SV11 ) )
= $false )
| ( ( ~ ( join_semilatt_str @ SV11 ) )
= $true )
| ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV31 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV24 @ SV31 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(314,plain,
! [SV34: $i,SV12: $i,SV36: $i] :
( ( ( element @ SV36 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( ( join @ SV12 @ SV34 @ SV36 )
= ( apply_binary_as_element @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_carrier @ SV12 ) @ ( the_L_join @ SV12 ) @ SV34 @ SV36 ) )
= $true )
| ( ( element @ SV34 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( empty_carrier @ SV12 )
= $true )
| ( ( join_semilatt_str @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(315,plain,
! [SV13: $i] :
( ( ( element @ ( sK7_SY62 @ SV13 ) @ ( powerset @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(316,plain,
! [SV13: $i] :
( ( ( ~ ( empty @ ( sK7_SY62 @ SV13 ) ) )
= $true )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(317,plain,
! [SV35: $i,SV15: $i,SV37: $i] :
( ( ( element @ SV37 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( below @ SV15 @ SV35 @ SV37 )
| ( ( join @ SV15 @ SV35 @ SV37 )
= SV37 ) )
| ~ ( ( ( join @ SV15 @ SV35 @ SV37 )
!= SV37 )
| ( below @ SV15 @ SV35 @ SV37 ) ) ) )
= $true )
| ( ( element @ SV35 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( join_semilatt_str @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(318,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( join_commutative @ SV3 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(319,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( empty_carrier @ SV8 )
| ~ ( join_commutative @ SV8 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(320,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ( ~ ~ ( empty_carrier @ SV10 )
| ~ ( join_commutative @ SV10 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(321,plain,
! [SV31: $i,SV24: $i,SV11: $i] :
( ( ( empty_carrier @ SV11 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV11 ) )
= $true )
| ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV31 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV24 @ SV31 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(322,plain,
! [SV13: $i] :
( ( ( empty @ ( sK7_SY62 @ SV13 ) )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( one_sorted_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(323,plain,
! [SV37: $i,SV35: $i,SV15: $i] :
( ( ( ~ ( ~ ( below @ SV15 @ SV35 @ SV37 )
| ( ( join @ SV15 @ SV35 @ SV37 )
= SV37 ) )
| ~ ( ( ( join @ SV15 @ SV35 @ SV37 )
!= SV37 )
| ( below @ SV15 @ SV35 @ SV37 ) ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV35 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( join_semilatt_str @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(324,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ( ~ ~ ( empty_carrier @ SV3 ) )
= $true )
| ( ( ~ ( join_commutative @ SV3 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(325,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ( ~ ~ ( empty_carrier @ SV8 ) )
= $true )
| ( ( ~ ( join_commutative @ SV8 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(326,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ( ~ ~ ( empty_carrier @ SV10 ) )
= $true )
| ( ( ~ ( join_commutative @ SV10 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(327,plain,
! [SV31: $i,SV24: $i,SV11: $i] :
( ( ( join_semilatt_str @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV31 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV24 @ SV31 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(328,plain,
! [SV37: $i,SV35: $i,SV15: $i] :
( ( ( ~ ( ~ ( below @ SV15 @ SV35 @ SV37 )
| ( ( join @ SV15 @ SV35 @ SV37 )
= SV37 ) ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV35 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( join_semilatt_str @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(329,plain,
! [SV37: $i,SV35: $i,SV15: $i] :
( ( ( ~ ( ( ( join @ SV15 @ SV35 @ SV37 )
!= SV37 )
| ( below @ SV15 @ SV35 @ SV37 ) ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV35 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( join_semilatt_str @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(330,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ( ~ ( empty_carrier @ SV3 ) )
= $false )
| ( ( ~ ( join_commutative @ SV3 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(331,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ( ~ ( empty_carrier @ SV8 ) )
= $false )
| ( ( ~ ( join_commutative @ SV8 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(332,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ( ~ ( empty_carrier @ SV10 ) )
= $false )
| ( ( ~ ( join_commutative @ SV10 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(333,plain,
! [SV31: $i,SV11: $i,SV24: $i] :
( ( ( element @ SV24 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( join_semilatt_str @ SV11 )
= $false )
| ( ( ~ ( element @ SV31 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV24 @ SV31 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(334,plain,
! [SV37: $i,SV35: $i,SV15: $i] :
( ( ( ~ ( below @ SV15 @ SV35 @ SV37 )
| ( ( join @ SV15 @ SV35 @ SV37 )
= SV37 ) )
= $true )
| ( ( element @ SV37 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV35 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( join_semilatt_str @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(335,plain,
! [SV37: $i,SV35: $i,SV15: $i] :
( ( ( ( ( join @ SV15 @ SV35 @ SV37 )
!= SV37 )
| ( below @ SV15 @ SV35 @ SV37 ) )
= $true )
| ( ( element @ SV37 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV35 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( join_semilatt_str @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(336,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ( empty_carrier @ SV3 )
= $true )
| ( ( ~ ( join_commutative @ SV3 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(337,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ( empty_carrier @ SV8 )
= $true )
| ( ( ~ ( join_commutative @ SV8 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(338,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ( empty_carrier @ SV10 )
= $true )
| ( ( ~ ( join_commutative @ SV10 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(339,plain,
! [SV24: $i,SV11: $i,SV31: $i] :
( ( ( element @ SV31 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( join_semilatt_str @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ ( join @ SV11 @ SV24 @ SV31 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(340,plain,
! [SV37: $i,SV35: $i,SV15: $i] :
( ( ( ~ ( below @ SV15 @ SV35 @ SV37 ) )
= $true )
| ( ( ( join @ SV15 @ SV35 @ SV37 )
= SV37 )
= $true )
| ( ( element @ SV37 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV35 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( join_semilatt_str @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(341,plain,
! [SV37: $i,SV35: $i,SV15: $i] :
( ( ( ( join @ SV15 @ SV35 @ SV37 )
!= SV37 )
= $true )
| ( ( below @ SV15 @ SV35 @ SV37 )
= $true )
| ( ( element @ SV37 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV35 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( join_semilatt_str @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(342,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ( join_commutative @ SV3 )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV3 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(343,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ( join_commutative @ SV8 )
= $false )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(344,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ( join_commutative @ SV10 )
= $false )
| ( ( empty_carrier @ SV10 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(345,plain,
! [SV37: $i,SV35: $i,SV15: $i] :
( ( ( below @ SV15 @ SV35 @ SV37 )
= $false )
| ( ( ( join @ SV15 @ SV35 @ SV37 )
= SV37 )
= $true )
| ( ( element @ SV37 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV35 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( join_semilatt_str @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(346,plain,
! [SV37: $i,SV35: $i,SV15: $i] :
( ( ( ( join @ SV15 @ SV35 @ SV37 )
= SV37 )
= $false )
| ( ( below @ SV15 @ SV35 @ SV37 )
= $true )
| ( ( element @ SV37 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV35 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( empty_carrier @ SV15 )
= $true )
| ( ( join_semilatt_str @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(347,plain,
! [SV27: $i,SV18: $i,SV3: $i] :
( ( ( join_semilatt_str @ SV3 )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_commutative @ SV3 )
= $false )
| ( ( ~ ( element @ SV18 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(348,plain,
! [SV29: $i,SV22: $i,SV8: $i] :
( ( ( join_semilatt_str @ SV8 )
= $false )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( join_commutative @ SV8 )
= $false )
| ( ( ~ ( element @ SV22 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(349,plain,
! [SV30: $i,SV23: $i,SV10: $i] :
( ( ( join_semilatt_str @ SV10 )
= $false )
| ( ( empty_carrier @ SV10 )
= $true )
| ( ( join_commutative @ SV10 )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(350,plain,
! [SV27: $i,SV3: $i,SV18: $i] :
( ( ( element @ SV18 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( join_commutative @ SV3 )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_semilatt_str @ SV3 )
= $false )
| ( ( ~ ( element @ SV27 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(351,plain,
! [SV29: $i,SV8: $i,SV22: $i] :
( ( ( element @ SV22 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( join_commutative @ SV8 )
= $false )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( join_semilatt_str @ SV8 )
= $false )
| ( ( ~ ( element @ SV29 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(352,plain,
! [SV30: $i,SV10: $i,SV23: $i] :
( ( ( element @ SV23 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( join_commutative @ SV10 )
= $false )
| ( ( empty_carrier @ SV10 )
= $true )
| ( ( join_semilatt_str @ SV10 )
= $false )
| ( ( ~ ( element @ SV30 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(353,plain,
! [SV18: $i,SV3: $i,SV27: $i] :
( ( ( element @ SV27 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( join_semilatt_str @ SV3 )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( join_commutative @ SV3 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( ( join_commut @ SV3 @ SV18 @ SV27 )
= ( join @ SV3 @ SV18 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(354,plain,
! [SV22: $i,SV8: $i,SV29: $i] :
( ( ( element @ SV29 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( join_semilatt_str @ SV8 )
= $false )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( join_commutative @ SV8 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( element @ ( join_commut @ SV8 @ SV22 @ SV29 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(355,plain,
! [SV23: $i,SV10: $i,SV30: $i] :
( ( ( element @ SV30 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( join_semilatt_str @ SV10 )
= $false )
| ( ( empty_carrier @ SV10 )
= $true )
| ( ( join_commutative @ SV10 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( ( join_commut @ SV10 @ SV23 @ SV30 )
= ( join_commut @ SV10 @ SV30 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(356,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[80,355,354,353,346,345,339,322,315,314,301,285,284,271,266,242,241,239,238,236,222,208,206,202,190,186,170,165,126,104,103,91,89,88,86,84,83,82]) ).
thf(357,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[356]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU305+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
% 0.10/0.17 % Computer : n006.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 15:12:40 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.18/0.41
% 1.18/0.41 No.of.Axioms: 26
% 1.18/0.41
% 1.18/0.41 Length.of.Defs: 0
% 1.18/0.41
% 1.18/0.41 Contains.Choice.Funs: false
% 1.18/0.41 ..........
% 1.18/0.41
% 1.18/0.41 ********************************
% 1.18/0.41 * All subproblems solved! *
% 1.18/0.41 ********************************
% 1.18/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:29,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:356,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.18/0.41
% 1.18/0.41 %**** Beginning of derivation protocol ****
% 1.18/0.41 % SZS output start CNFRefutation
% See solution above
% 1.18/0.41
% 1.18/0.41 %**** End of derivation protocol ****
% 1.18/0.41 %**** no. of clauses in derivation: 342 ****
% 1.18/0.41 %**** clause counter: 356 ****
% 1.18/0.41
% 1.18/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:29,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:356,loop_count:0,foatp_calls:1,translation:fof_full)
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