%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU350+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 : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:44:04 AM UTC 2026
% Result : Theorem 1.07s 0.45s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 17
% Syntax : Number of formulae : 203 ( 99 unt; 0 typ; 0 def)
% Number of atoms : 1649 ( 467 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 3176 ( 692 ~; 488 |; 49 &;1896 @)
% ( 11 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 47 usr; 8 con; 0-3 aty)
% Number of variables : 304 ( 0 ^; 295 !; 9 ?; 304 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_antisymmetric_relstr,type,
antisymmetric_relstr: $i > $o ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_cast_to_el_of_LattPOSet,type,
cast_to_el_of_LattPOSet: $i > $i > $i ).
thf(tp_cast_to_el_of_lattice,type,
cast_to_el_of_lattice: $i > $i > $i ).
thf(tp_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_in,type,
in: $i > $i > $o ).
thf(tp_join_absorbing,type,
join_absorbing: $i > $o ).
thf(tp_join_associative,type,
join_associative: $i > $o ).
thf(tp_join_commutative,type,
join_commutative: $i > $o ).
thf(tp_join_semilatt_str,type,
join_semilatt_str: $i > $o ).
thf(tp_k2_lattice3,type,
k2_lattice3: $i > $i ).
thf(tp_latt_element_smaller,type,
latt_element_smaller: $i > $i > $i > $o ).
thf(tp_latt_str,type,
latt_str: $i > $o ).
thf(tp_lattice,type,
lattice: $i > $o ).
thf(tp_meet_absorbing,type,
meet_absorbing: $i > $o ).
thf(tp_meet_associative,type,
meet_associative: $i > $o ).
thf(tp_meet_commutative,type,
meet_commutative: $i > $o ).
thf(tp_meet_semilatt_str,type,
meet_semilatt_str: $i > $o ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_poset_of_lattice,type,
poset_of_lattice: $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_reflexive,type,
reflexive: $i > $o ).
thf(tp_reflexive_relstr,type,
reflexive_relstr: $i > $o ).
thf(tp_rel_str,type,
rel_str: $i > $o ).
thf(tp_rel_str_of,type,
rel_str_of: $i > $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_relation_of_lattice,type,
relation_of_lattice: $i > $i ).
thf(tp_relstr_set_smaller,type,
relstr_set_smaller: $i > $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY20,type,
sK2_SY20: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK6_SY30,type,
sK6_SY30: $i > $i ).
thf(tp_strict_rel_str,type,
strict_rel_str: $i > $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_the_InternalRel,type,
the_InternalRel: $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_transitive,type,
transitive: $i > $o ).
thf(tp_transitive_relstr,type,
transitive_relstr: $i > $o ).
thf(tp_v1_partfun1,type,
v1_partfun1: $i > $i > $i > $o ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( latt_element_smaller @ B @ C @ A )
<=> ( relstr_set_smaller @ ( poset_of_lattice @ B ) @ A @ ( cast_to_el_of_LattPOSet @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lattice3) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(14,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(31,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(33,axiom,
? [A: $i] : ( latt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(38,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(41,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(42,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(45,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) )
=> ( element @ ( cast_to_el_of_lattice @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattice3) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ( element @ ( cast_to_el_of_LattPOSet @ A @ B ) @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattice3) ).
thf(52,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(54,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(55,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(57,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) )
=> ( ( cast_to_el_of_lattice @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattice3) ).
thf(58,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( cast_to_el_of_LattPOSet @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice3) ).
thf(65,conjecture,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( poset_of_lattice @ B ) ) )
=> ( ( relstr_set_smaller @ ( poset_of_lattice @ B ) @ A @ C )
<=> ( latt_element_smaller @ B @ ( cast_to_el_of_lattice @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattice3) ).
thf(66,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( poset_of_lattice @ B ) ) )
=> ( ( relstr_set_smaller @ ( poset_of_lattice @ B ) @ A @ C )
<=> ( latt_element_smaller @ B @ ( cast_to_el_of_lattice @ B @ C ) @ A ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[65]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( poset_of_lattice @ B ) ) )
=> ( ( relstr_set_smaller @ ( poset_of_lattice @ B ) @ A @ C )
<=> ( latt_element_smaller @ B @ ( cast_to_el_of_lattice @ B @ C ) @ A ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[66]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( latt_element_smaller @ B @ C @ A )
<=> ( relstr_set_smaller @ ( poset_of_lattice @ B ) @ A @ ( cast_to_el_of_LattPOSet @ B @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(69,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(70,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(71,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(72,plain,
( ( ? [A: $i] : ( latt_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(73,plain,
$true = $true,
inference(unfold_def,[status(thm)],[38]) ).
thf(74,plain,
$true = $true,
inference(unfold_def,[status(thm)],[41]) ).
thf(75,plain,
$true = $true,
inference(unfold_def,[status(thm)],[42]) ).
thf(76,plain,
$true = $true,
inference(unfold_def,[status(thm)],[45]) ).
thf(77,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) )
=> ( element @ ( cast_to_el_of_lattice @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ( element @ ( cast_to_el_of_LattPOSet @ A @ B ) @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(79,plain,
$true = $true,
inference(unfold_def,[status(thm)],[52]) ).
thf(80,plain,
$true = $true,
inference(unfold_def,[status(thm)],[54]) ).
thf(81,plain,
$true = $true,
inference(unfold_def,[status(thm)],[55]) ).
thf(82,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) )
=> ( ( cast_to_el_of_lattice @ A @ B )
= B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(83,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( cast_to_el_of_LattPOSet @ A @ B )
= B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(84,plain,
( ( ! [SY20: $i] :
( ( ~ ( empty_carrier @ SY20 )
& ( lattice @ SY20 )
& ( latt_str @ SY20 ) )
=> ! [SY21: $i] :
( ( element @ SY21 @ ( the_carrier @ ( poset_of_lattice @ SY20 ) ) )
=> ( ( relstr_set_smaller @ ( poset_of_lattice @ SY20 ) @ sK1_A @ SY21 )
<=> ( latt_element_smaller @ SY20 @ ( cast_to_el_of_lattice @ SY20 @ SY21 ) @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[67]) ).
thf(85,plain,
( ( ( ~ ( empty_carrier @ sK2_SY20 )
& ( lattice @ sK2_SY20 )
& ( latt_str @ sK2_SY20 ) )
=> ! [SY22: $i] :
( ( element @ SY22 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY20 ) ) )
=> ( ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ SY22 )
<=> ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ SY22 ) @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[84]) ).
thf(86,plain,
( ( ~ ( empty_carrier @ sK2_SY20 ) )
= $true ),
inference(standard_cnf,[status(thm)],[85]) ).
thf(87,plain,
( ( lattice @ sK2_SY20 )
= $true ),
inference(standard_cnf,[status(thm)],[85]) ).
thf(88,plain,
( ( latt_str @ sK2_SY20 )
= $true ),
inference(standard_cnf,[status(thm)],[85]) ).
thf(89,plain,
( ( ! [SY22: $i] :
( ( element @ SY22 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY20 ) ) )
=> ( ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ SY22 )
<=> ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ SY22 ) @ sK1_A ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[85]) ).
thf(90,plain,
( ( ~ ! [SY22: $i] :
( ( element @ SY22 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY20 ) ) )
=> ( ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ SY22 )
<=> ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ SY22 ) @ sK1_A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[89]) ).
thf(91,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( cast_to_el_of_LattPOSet @ A @ B )
= B ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(92,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) )
=> ( ( cast_to_el_of_lattice @ A @ B )
= B ) ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(93,plain,
$true = $true,
inference(copy,[status(thm)],[81]) ).
thf(94,plain,
$true = $true,
inference(copy,[status(thm)],[80]) ).
thf(95,plain,
$true = $true,
inference(copy,[status(thm)],[79]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ( element @ ( cast_to_el_of_LattPOSet @ A @ B ) @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) )
=> ( element @ ( cast_to_el_of_lattice @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(98,plain,
$true = $true,
inference(copy,[status(thm)],[76]) ).
thf(99,plain,
$true = $true,
inference(copy,[status(thm)],[75]) ).
thf(100,plain,
$true = $true,
inference(copy,[status(thm)],[74]) ).
thf(101,plain,
$true = $true,
inference(copy,[status(thm)],[73]) ).
thf(102,plain,
( ( ? [A: $i] : ( latt_str @ A ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(103,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(104,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(105,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(106,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( latt_element_smaller @ B @ C @ A )
<=> ( relstr_set_smaller @ ( poset_of_lattice @ B ) @ A @ ( cast_to_el_of_LattPOSet @ B @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(107,plain,
( ( latt_str @ sK2_SY20 )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(108,plain,
( ( lattice @ sK2_SY20 )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(109,plain,
( ( ~ ( empty_carrier @ sK2_SY20 ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(110,plain,
( ( ~ ! [SY22: $i] :
( ( element @ SY22 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY20 ) ) )
=> ( ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ SY22 )
<=> ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ SY22 ) @ sK1_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(111,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( lattice @ SX0 ) )
| ~ ( latt_str @ SX0 ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ ( poset_of_lattice @ SX0 ) ) )
| ( ( cast_to_el_of_lattice @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( lattice @ SX0 ) )
| ~ ( latt_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ ( poset_of_lattice @ SX0 ) ) ) )
| ( element @ ( cast_to_el_of_lattice @ SX0 @ SX1 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(113,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( lattice @ SX0 ) )
| ~ ( latt_str @ SX0 ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ( ( cast_to_el_of_LattPOSet @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(114,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY20 ) ) )
| ~ ( ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ SX0 )
| ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ SX0 ) @ sK1_A ) )
| ~ ( ~ ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ SX0 ) @ sK1_A )
| ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(115,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( lattice @ SX0 ) )
| ~ ( latt_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ( element @ ( cast_to_el_of_LattPOSet @ SX0 @ SX1 ) @ ( the_carrier @ ( poset_of_lattice @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(117,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX1 )
| ~ ( lattice @ SX1 ) )
| ~ ( latt_str @ SX1 ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX1 ) )
| ~ ( ~ ( ~ ( latt_element_smaller @ SX1 @ SX2 @ SX0 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SX1 ) @ SX0 @ ( cast_to_el_of_LattPOSet @ SX1 @ SX2 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SX1 ) @ SX0 @ ( cast_to_el_of_LattPOSet @ SX1 @ SX2 ) )
| ( latt_element_smaller @ SX1 @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(118,plain,
( ( ~ ! [SX0: $i] :
~ ( latt_str @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(119,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(120,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(121,plain,
( ( empty_carrier @ sK2_SY20 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(122,plain,
! [SV1: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) )
| ~ ( latt_str @ SV1 ) )
| ! [SY23: $i] :
( ~ ( element @ SY23 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) )
| ( ( cast_to_el_of_lattice @ SV1 @ SY23 )
= SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(123,plain,
! [SV2: $i] :
( ( ! [SY24: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
| ~ ( latt_str @ SV2 ) )
| ~ ( element @ SY24 @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) )
| ( element @ ( cast_to_el_of_lattice @ SV2 @ SY24 ) @ ( the_carrier @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(124,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( lattice @ SV3 ) )
| ~ ( latt_str @ SV3 ) )
| ! [SY25: $i] :
( ~ ( element @ SY25 @ ( the_carrier @ SV3 ) )
| ( ( cast_to_el_of_LattPOSet @ SV3 @ SY25 )
= SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(125,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY20 ) ) )
| ~ ( ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ SX0 )
| ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ SX0 ) @ sK1_A ) )
| ~ ( ~ ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ SX0 ) @ sK1_A )
| ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(126,plain,
! [SV4: $i] :
( ( ! [SY26: $i] :
( ~ ( in @ SV4 @ SY26 )
| ( element @ SV4 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(127,plain,
! [SV5: $i] :
( ( ! [SY27: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( lattice @ SV5 ) )
| ~ ( latt_str @ SV5 ) )
| ~ ( element @ SY27 @ ( the_carrier @ SV5 ) ) )
| ( element @ ( cast_to_el_of_LattPOSet @ SV5 @ SY27 ) @ ( the_carrier @ ( poset_of_lattice @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(128,plain,
! [SV6: $i] :
( ( ! [SY28: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SY28 )
| ~ ( lattice @ SY28 ) )
| ~ ( latt_str @ SY28 ) )
| ! [SY29: $i] :
( ~ ( element @ SY29 @ ( the_carrier @ SY28 ) )
| ~ ( ~ ( ~ ( latt_element_smaller @ SY28 @ SY29 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SY28 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SY28 @ SY29 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SY28 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SY28 @ SY29 ) )
| ( latt_element_smaller @ SY28 @ SY29 @ SV6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(129,plain,
( ( ! [SX0: $i] :
~ ( latt_str @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(130,plain,
! [SV7: $i] :
( ( ~ ! [SY30: $i] :
~ ( element @ SY30 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(131,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ~ ( empty_carrier @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(132,plain,
! [SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) )
| ~ ( latt_str @ SV1 ) ) )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( element @ SY23 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) )
| ( ( cast_to_el_of_lattice @ SV1 @ SY23 )
= SY23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(133,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
| ~ ( latt_str @ SV2 ) )
| ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) )
| ( element @ ( cast_to_el_of_lattice @ SV2 @ SV8 ) @ ( the_carrier @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(134,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( lattice @ SV3 ) )
| ~ ( latt_str @ SV3 ) ) )
= $true )
| ( ( ! [SY25: $i] :
( ~ ( element @ SY25 @ ( the_carrier @ SV3 ) )
| ( ( cast_to_el_of_LattPOSet @ SV3 @ SY25 )
= SY25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(135,plain,
( ( ~ ( element @ sK3_SX0 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY20 ) ) )
| ~ ( ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 )
| ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A ) )
| ~ ( ~ ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A )
| ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[125]) ).
thf(136,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ SV9 )
| ( element @ SV4 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(137,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( lattice @ SV5 ) )
| ~ ( latt_str @ SV5 ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV5 ) ) )
| ( element @ ( cast_to_el_of_LattPOSet @ SV5 @ SV10 ) @ ( the_carrier @ ( poset_of_lattice @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(138,plain,
! [SV6: $i,SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( lattice @ SV11 ) )
| ~ ( latt_str @ SV11 ) )
| ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_element_smaller @ SV11 @ SY31 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) )
| ( latt_element_smaller @ SV11 @ SY31 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(139,plain,
( ( ~ ( latt_str @ sK4_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[129]) ).
thf(140,plain,
! [SV7: $i] :
( ( ! [SY30: $i] :
~ ( element @ SY30 @ SV7 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(141,plain,
( ( ~ ~ ( ~ ( one_sorted_str @ sK5_SX0 )
| ~ ~ ( empty_carrier @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[131]) ).
thf(142,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) )
| ~ ( latt_str @ SV1 ) ) )
= $false )
| ( ( ! [SY23: $i] :
( ~ ( element @ SY23 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) )
| ( ( cast_to_el_of_lattice @ SV1 @ SY23 )
= SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(143,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
| ~ ( latt_str @ SV2 ) )
| ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV2 @ SV8 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(144,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( lattice @ SV3 ) )
| ~ ( latt_str @ SV3 ) ) )
= $false )
| ( ( ! [SY25: $i] :
( ~ ( element @ SY25 @ ( the_carrier @ SV3 ) )
| ( ( cast_to_el_of_LattPOSet @ SV3 @ SY25 )
= SY25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(145,plain,
( ( ~ ( element @ sK3_SX0 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY20 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(146,plain,
( ( ~ ( ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 )
| ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A ) )
| ~ ( ~ ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A )
| ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(147,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV9 ) )
= $true )
| ( ( element @ SV4 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(148,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( lattice @ SV5 ) )
| ~ ( latt_str @ SV5 ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV5 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV5 @ SV10 ) @ ( the_carrier @ ( poset_of_lattice @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(149,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( lattice @ SV11 ) )
| ~ ( latt_str @ SV11 ) ) )
= $true )
| ( ( ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_element_smaller @ SV11 @ SY31 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) )
| ( latt_element_smaller @ SV11 @ SY31 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(150,plain,
( ( latt_str @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(151,plain,
! [SV7: $i] :
( ( ~ ( element @ ( sK6_SY30 @ SV7 ) @ SV7 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[140]) ).
thf(152,plain,
( ( ~ ( ~ ( one_sorted_str @ sK5_SX0 )
| ~ ~ ( empty_carrier @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(153,plain,
! [SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) )
| ~ ( latt_str @ SV1 ) )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( element @ SY23 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) )
| ( ( cast_to_el_of_lattice @ SV1 @ SY23 )
= SY23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(154,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
| ~ ( latt_str @ SV2 ) )
| ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) ) )
= $false )
| ( ( element @ ( cast_to_el_of_lattice @ SV2 @ SV8 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(155,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( lattice @ SV3 ) )
| ~ ( latt_str @ SV3 ) )
= $true )
| ( ( ! [SY25: $i] :
( ~ ( element @ SY25 @ ( the_carrier @ SV3 ) )
| ( ( cast_to_el_of_LattPOSet @ SV3 @ SY25 )
= SY25 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(156,plain,
( ( element @ sK3_SX0 @ ( the_carrier @ ( poset_of_lattice @ sK2_SY20 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(157,plain,
( ( ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 )
| ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A ) )
| ~ ( ~ ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A )
| ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(158,plain,
! [SV9: $i,SV4: $i] :
( ( ( in @ SV4 @ SV9 )
= $false )
| ( ( element @ SV4 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(159,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( lattice @ SV5 ) )
| ~ ( latt_str @ SV5 ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV5 ) ) ) )
= $false )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV5 @ SV10 ) @ ( the_carrier @ ( poset_of_lattice @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(160,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( lattice @ SV11 ) )
| ~ ( latt_str @ SV11 ) ) )
= $false )
| ( ( ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_element_smaller @ SV11 @ SY31 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) )
| ( latt_element_smaller @ SV11 @ SY31 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(161,plain,
! [SV7: $i] :
( ( element @ ( sK6_SY30 @ SV7 ) @ SV7 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(162,plain,
( ( ~ ( one_sorted_str @ sK5_SX0 )
| ~ ~ ( empty_carrier @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(163,plain,
! [SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) ) )
= $true )
| ( ( ~ ( latt_str @ SV1 ) )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( element @ SY23 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) )
| ( ( cast_to_el_of_lattice @ SV1 @ SY23 )
= SY23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(164,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
| ~ ( latt_str @ SV2 ) )
| ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV2 @ SV8 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(165,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( lattice @ SV3 ) ) )
= $true )
| ( ( ~ ( latt_str @ SV3 ) )
= $true )
| ( ( ! [SY25: $i] :
( ~ ( element @ SY25 @ ( the_carrier @ SV3 ) )
| ( ( cast_to_el_of_LattPOSet @ SV3 @ SY25 )
= SY25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(166,plain,
( ( ( ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 )
| ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A ) ) )
= $true )
| ( ( ~ ( ~ ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A )
| ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(167,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( lattice @ SV5 ) )
| ~ ( latt_str @ SV5 ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV5 @ SV10 ) @ ( the_carrier @ ( poset_of_lattice @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(168,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( lattice @ SV11 ) )
| ~ ( latt_str @ SV11 ) )
= $true )
| ( ( ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_element_smaller @ SV11 @ SY31 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) )
| ( latt_element_smaller @ SV11 @ SY31 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(169,plain,
( ( ~ ( one_sorted_str @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(170,plain,
( ( ~ ~ ( empty_carrier @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(171,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) ) )
= $false )
| ( ( ~ ( latt_str @ SV1 ) )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( element @ SY23 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) )
| ( ( cast_to_el_of_lattice @ SV1 @ SY23 )
= SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(172,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
| ~ ( latt_str @ SV2 ) ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV2 @ SV8 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(173,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( lattice @ SV3 ) ) )
= $false )
| ( ( ~ ( latt_str @ SV3 ) )
= $true )
| ( ( ! [SY25: $i] :
( ~ ( element @ SY25 @ ( the_carrier @ SV3 ) )
| ( ( cast_to_el_of_LattPOSet @ SV3 @ SY25 )
= SY25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(174,plain,
( ( ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 )
| ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A ) )
= $false )
| ( ( ~ ( ~ ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A )
| ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(175,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( lattice @ SV5 ) )
| ~ ( latt_str @ SV5 ) ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV5 @ SV10 ) @ ( the_carrier @ ( poset_of_lattice @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(176,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( lattice @ SV11 ) ) )
= $true )
| ( ( ~ ( latt_str @ SV11 ) )
= $true )
| ( ( ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_element_smaller @ SV11 @ SY31 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) )
| ( latt_element_smaller @ SV11 @ SY31 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(177,plain,
( ( one_sorted_str @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(178,plain,
( ( ~ ( empty_carrier @ sK5_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(179,plain,
! [SV1: $i] :
( ( ( ~ ~ ( empty_carrier @ SV1 )
| ~ ( lattice @ SV1 ) )
= $true )
| ( ( ~ ( latt_str @ SV1 ) )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( element @ SY23 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) )
| ( ( cast_to_el_of_lattice @ SV1 @ SY23 )
= SY23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(180,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
| ~ ( latt_str @ SV2 ) ) )
= $false )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV2 @ SV8 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(181,plain,
! [SV3: $i] :
( ( ( ~ ~ ( empty_carrier @ SV3 )
| ~ ( lattice @ SV3 ) )
= $true )
| ( ( ~ ( latt_str @ SV3 ) )
= $true )
| ( ( ! [SY25: $i] :
( ~ ( element @ SY25 @ ( the_carrier @ SV3 ) )
| ( ( cast_to_el_of_LattPOSet @ SV3 @ SY25 )
= SY25 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(182,plain,
( ( ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 ) )
= $false )
| ( ( ~ ( ~ ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A )
| ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(183,plain,
( ( ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A )
= $false )
| ( ( ~ ( ~ ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A )
| ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(184,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( lattice @ SV5 ) )
| ~ ( latt_str @ SV5 ) ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV5 @ SV10 ) @ ( the_carrier @ ( poset_of_lattice @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(185,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( lattice @ SV11 ) ) )
= $false )
| ( ( ~ ( latt_str @ SV11 ) )
= $true )
| ( ( ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_element_smaller @ SV11 @ SY31 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) )
| ( latt_element_smaller @ SV11 @ SY31 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(186,plain,
( ( empty_carrier @ sK5_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(187,plain,
! [SV1: $i] :
( ( ( ~ ~ ( empty_carrier @ SV1 ) )
= $true )
| ( ( ~ ( lattice @ SV1 ) )
= $true )
| ( ( ~ ( latt_str @ SV1 ) )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( element @ SY23 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) )
| ( ( cast_to_el_of_lattice @ SV1 @ SY23 )
= SY23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(188,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
| ~ ( latt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV2 @ SV8 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(189,plain,
! [SV3: $i] :
( ( ( ~ ~ ( empty_carrier @ SV3 ) )
= $true )
| ( ( ~ ( lattice @ SV3 ) )
= $true )
| ( ( ~ ( latt_str @ SV3 ) )
= $true )
| ( ( ! [SY25: $i] :
( ~ ( element @ SY25 @ ( the_carrier @ SV3 ) )
| ( ( cast_to_el_of_LattPOSet @ SV3 @ SY25 )
= SY25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(190,plain,
( ( ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 )
= $true )
| ( ( ~ ( ~ ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A )
| ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(191,plain,
( ( ( ~ ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A )
| ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 ) )
= $false )
| ( ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(192,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( lattice @ SV5 ) )
| ~ ( latt_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV5 @ SV10 ) @ ( the_carrier @ ( poset_of_lattice @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(193,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ~ ( empty_carrier @ SV11 )
| ~ ( lattice @ SV11 ) )
= $true )
| ( ( ~ ( latt_str @ SV11 ) )
= $true )
| ( ( ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_element_smaller @ SV11 @ SY31 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) )
| ( latt_element_smaller @ SV11 @ SY31 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(194,plain,
! [SV1: $i] :
( ( ( ~ ( empty_carrier @ SV1 ) )
= $false )
| ( ( ~ ( lattice @ SV1 ) )
= $true )
| ( ( ~ ( latt_str @ SV1 ) )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( element @ SY23 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) )
| ( ( cast_to_el_of_lattice @ SV1 @ SY23 )
= SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(195,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) ) )
= $true )
| ( ( ~ ( latt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV2 @ SV8 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(196,plain,
! [SV3: $i] :
( ( ( ~ ( empty_carrier @ SV3 ) )
= $false )
| ( ( ~ ( lattice @ SV3 ) )
= $true )
| ( ( ~ ( latt_str @ SV3 ) )
= $true )
| ( ( ! [SY25: $i] :
( ~ ( element @ SY25 @ ( the_carrier @ SV3 ) )
| ( ( cast_to_el_of_LattPOSet @ SV3 @ SY25 )
= SY25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(197,plain,
( ( ( ~ ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A )
| ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 ) )
= $false )
| ( ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(198,plain,
( ( ( ~ ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A ) )
= $false )
| ( ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(199,plain,
( ( ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 )
= $false )
| ( ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(200,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( lattice @ SV5 ) ) )
= $true )
| ( ( ~ ( latt_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV5 @ SV10 ) @ ( the_carrier @ ( poset_of_lattice @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(201,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ~ ( empty_carrier @ SV11 ) )
= $true )
| ( ( ~ ( lattice @ SV11 ) )
= $true )
| ( ( ~ ( latt_str @ SV11 ) )
= $true )
| ( ( ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_element_smaller @ SV11 @ SY31 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) )
| ( latt_element_smaller @ SV11 @ SY31 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(202,plain,
! [SV1: $i] :
( ( ( empty_carrier @ SV1 )
= $true )
| ( ( ~ ( lattice @ SV1 ) )
= $true )
| ( ( ~ ( latt_str @ SV1 ) )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( element @ SY23 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) )
| ( ( cast_to_el_of_lattice @ SV1 @ SY23 )
= SY23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(203,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) ) )
= $false )
| ( ( ~ ( latt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV2 @ SV8 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(204,plain,
! [SV3: $i] :
( ( ( empty_carrier @ SV3 )
= $true )
| ( ( ~ ( lattice @ SV3 ) )
= $true )
| ( ( ~ ( latt_str @ SV3 ) )
= $true )
| ( ( ! [SY25: $i] :
( ~ ( element @ SY25 @ ( the_carrier @ SV3 ) )
| ( ( cast_to_el_of_LattPOSet @ SV3 @ SY25 )
= SY25 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(205,plain,
( ( ( ~ ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A ) )
= $false )
| ( ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(206,plain,
( ( ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 )
= $false )
| ( ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(207,plain,
( ( ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A )
= $true )
| ( ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(208,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( lattice @ SV5 ) ) )
= $false )
| ( ( ~ ( latt_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV5 @ SV10 ) @ ( the_carrier @ ( poset_of_lattice @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(209,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( empty_carrier @ SV11 ) )
= $false )
| ( ( ~ ( lattice @ SV11 ) )
= $true )
| ( ( ~ ( latt_str @ SV11 ) )
= $true )
| ( ( ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_element_smaller @ SV11 @ SY31 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) )
| ( latt_element_smaller @ SV11 @ SY31 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(210,plain,
! [SV1: $i] :
( ( ( lattice @ SV1 )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( ~ ( latt_str @ SV1 ) )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( element @ SY23 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) )
| ( ( cast_to_el_of_lattice @ SV1 @ SY23 )
= SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(211,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ~ ( empty_carrier @ SV2 )
| ~ ( lattice @ SV2 ) )
= $true )
| ( ( ~ ( latt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV2 @ SV8 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(212,plain,
! [SV3: $i] :
( ( ( lattice @ SV3 )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( ~ ( latt_str @ SV3 ) )
= $true )
| ( ( ! [SY25: $i] :
( ~ ( element @ SY25 @ ( the_carrier @ SV3 ) )
| ( ( cast_to_el_of_LattPOSet @ SV3 @ SY25 )
= SY25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(213,plain,
( ( ( latt_element_smaller @ sK2_SY20 @ ( cast_to_el_of_lattice @ sK2_SY20 @ sK3_SX0 ) @ sK1_A )
= $true )
| ( ( relstr_set_smaller @ ( poset_of_lattice @ sK2_SY20 ) @ sK1_A @ sK3_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(214,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ~ ( empty_carrier @ SV5 )
| ~ ( lattice @ SV5 ) )
= $true )
| ( ( ~ ( latt_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV5 @ SV10 ) @ ( the_carrier @ ( poset_of_lattice @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(215,plain,
! [SV6: $i,SV11: $i] :
( ( ( empty_carrier @ SV11 )
= $true )
| ( ( ~ ( lattice @ SV11 ) )
= $true )
| ( ( ~ ( latt_str @ SV11 ) )
= $true )
| ( ( ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_element_smaller @ SV11 @ SY31 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) )
| ( latt_element_smaller @ SV11 @ SY31 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(216,plain,
! [SV1: $i] :
( ( ( latt_str @ SV1 )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( lattice @ SV1 )
= $false )
| ( ( ! [SY23: $i] :
( ~ ( element @ SY23 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) )
| ( ( cast_to_el_of_lattice @ SV1 @ SY23 )
= SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(217,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ~ ( empty_carrier @ SV2 ) )
= $true )
| ( ( ~ ( lattice @ SV2 ) )
= $true )
| ( ( ~ ( latt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV2 @ SV8 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(218,plain,
! [SV3: $i] :
( ( ( latt_str @ SV3 )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( lattice @ SV3 )
= $false )
| ( ( ! [SY25: $i] :
( ~ ( element @ SY25 @ ( the_carrier @ SV3 ) )
| ( ( cast_to_el_of_LattPOSet @ SV3 @ SY25 )
= SY25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(219,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ~ ( empty_carrier @ SV5 ) )
= $true )
| ( ( ~ ( lattice @ SV5 ) )
= $true )
| ( ( ~ ( latt_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV5 @ SV10 ) @ ( the_carrier @ ( poset_of_lattice @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(220,plain,
! [SV6: $i,SV11: $i] :
( ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( ~ ( latt_str @ SV11 ) )
= $true )
| ( ( ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_element_smaller @ SV11 @ SY31 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) )
| ( latt_element_smaller @ SV11 @ SY31 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(221,plain,
! [SV1: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) )
| ( ( cast_to_el_of_lattice @ SV1 @ SV12 )
= SV12 ) )
= $true )
| ( ( lattice @ SV1 )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( latt_str @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(222,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ( empty_carrier @ SV2 ) )
= $false )
| ( ( ~ ( lattice @ SV2 ) )
= $true )
| ( ( ~ ( latt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV2 @ SV8 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(223,plain,
! [SV3: $i,SV13: $i] :
( ( ( ~ ( element @ SV13 @ ( the_carrier @ SV3 ) )
| ( ( cast_to_el_of_LattPOSet @ SV3 @ SV13 )
= SV13 ) )
= $true )
| ( ( lattice @ SV3 )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( latt_str @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(224,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( empty_carrier @ SV5 ) )
= $false )
| ( ( ~ ( lattice @ SV5 ) )
= $true )
| ( ( ~ ( latt_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV5 @ SV10 ) @ ( the_carrier @ ( poset_of_lattice @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(225,plain,
! [SV6: $i,SV11: $i] :
( ( ( latt_str @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( lattice @ SV11 )
= $false )
| ( ( ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_element_smaller @ SV11 @ SY31 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SY31 ) )
| ( latt_element_smaller @ SV11 @ SY31 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(226,plain,
! [SV1: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) ) )
= $true )
| ( ( ( cast_to_el_of_lattice @ SV1 @ SV12 )
= SV12 )
= $true )
| ( ( lattice @ SV1 )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( latt_str @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(227,plain,
! [SV8: $i,SV2: $i] :
( ( ( empty_carrier @ SV2 )
= $true )
| ( ( ~ ( lattice @ SV2 ) )
= $true )
| ( ( ~ ( latt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV2 @ SV8 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(228,plain,
! [SV3: $i,SV13: $i] :
( ( ( ~ ( element @ SV13 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ( cast_to_el_of_LattPOSet @ SV3 @ SV13 )
= SV13 )
= $true )
| ( ( lattice @ SV3 )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( latt_str @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(229,plain,
! [SV10: $i,SV5: $i] :
( ( ( empty_carrier @ SV5 )
= $true )
| ( ( ~ ( lattice @ SV5 ) )
= $true )
| ( ( ~ ( latt_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV5 @ SV10 ) @ ( the_carrier @ ( poset_of_lattice @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(230,plain,
! [SV6: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( element @ SV14 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( ~ ( latt_element_smaller @ SV11 @ SV14 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
| ( latt_element_smaller @ SV11 @ SV14 @ SV6 ) ) ) )
= $true )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(231,plain,
! [SV1: $i,SV12: $i] :
( ( ( element @ SV12 @ ( the_carrier @ ( poset_of_lattice @ SV1 ) ) )
= $false )
| ( ( ( cast_to_el_of_lattice @ SV1 @ SV12 )
= SV12 )
= $true )
| ( ( lattice @ SV1 )
= $false )
| ( ( empty_carrier @ SV1 )
= $true )
| ( ( latt_str @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(232,plain,
! [SV8: $i,SV2: $i] :
( ( ( lattice @ SV2 )
= $false )
| ( ( empty_carrier @ SV2 )
= $true )
| ( ( ~ ( latt_str @ SV2 ) )
= $true )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV2 @ SV8 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(233,plain,
! [SV3: $i,SV13: $i] :
( ( ( element @ SV13 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( ( cast_to_el_of_LattPOSet @ SV3 @ SV13 )
= SV13 )
= $true )
| ( ( lattice @ SV3 )
= $false )
| ( ( empty_carrier @ SV3 )
= $true )
| ( ( latt_str @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(234,plain,
! [SV10: $i,SV5: $i] :
( ( ( lattice @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( ~ ( latt_str @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV5 @ SV10 ) @ ( the_carrier @ ( poset_of_lattice @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(235,plain,
! [SV6: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( element @ SV14 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( latt_element_smaller @ SV11 @ SV14 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
| ( latt_element_smaller @ SV11 @ SV14 @ SV6 ) ) ) )
= $true )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(236,plain,
! [SV8: $i,SV2: $i] :
( ( ( latt_str @ SV2 )
= $false )
| ( ( empty_carrier @ SV2 )
= $true )
| ( ( lattice @ SV2 )
= $false )
| ( ( ~ ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_lattice @ SV2 @ SV8 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(237,plain,
! [SV10: $i,SV5: $i] :
( ( ( latt_str @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( lattice @ SV5 )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV5 @ SV10 ) @ ( the_carrier @ ( poset_of_lattice @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(238,plain,
! [SV6: $i,SV11: $i,SV14: $i] :
( ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( latt_element_smaller @ SV11 @ SV14 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
| ( latt_element_smaller @ SV11 @ SV14 @ SV6 ) ) ) )
= $true )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(239,plain,
! [SV2: $i,SV8: $i] :
( ( ( element @ SV8 @ ( the_carrier @ ( poset_of_lattice @ SV2 ) ) )
= $false )
| ( ( lattice @ SV2 )
= $false )
| ( ( empty_carrier @ SV2 )
= $true )
| ( ( latt_str @ SV2 )
= $false )
| ( ( element @ ( cast_to_el_of_lattice @ SV2 @ SV8 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(240,plain,
! [SV5: $i,SV10: $i] :
( ( ( element @ SV10 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( lattice @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( latt_str @ SV5 )
= $false )
| ( ( element @ ( cast_to_el_of_LattPOSet @ SV5 @ SV10 ) @ ( the_carrier @ ( poset_of_lattice @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(241,plain,
! [SV6: $i,SV14: $i,SV11: $i] :
( ( ( ~ ( ~ ( latt_element_smaller @ SV11 @ SV14 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) ) )
| ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
| ( latt_element_smaller @ SV11 @ SV14 @ SV6 ) ) )
= $false )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(242,plain,
! [SV6: $i,SV14: $i,SV11: $i] :
( ( ( ~ ( ~ ( latt_element_smaller @ SV11 @ SV14 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) ) ) )
= $false )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(243,plain,
! [SV14: $i,SV6: $i,SV11: $i] :
( ( ( ~ ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
| ( latt_element_smaller @ SV11 @ SV14 @ SV6 ) ) )
= $false )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(244,plain,
! [SV6: $i,SV14: $i,SV11: $i] :
( ( ( ~ ( latt_element_smaller @ SV11 @ SV14 @ SV6 )
| ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) ) )
= $true )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(245,plain,
! [SV14: $i,SV6: $i,SV11: $i] :
( ( ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
| ( latt_element_smaller @ SV11 @ SV14 @ SV6 ) )
= $true )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(246,plain,
! [SV6: $i,SV14: $i,SV11: $i] :
( ( ( ~ ( latt_element_smaller @ SV11 @ SV14 @ SV6 ) )
= $true )
| ( ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
= $true )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(247,plain,
! [SV14: $i,SV6: $i,SV11: $i] :
( ( ( ~ ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) ) )
= $true )
| ( ( latt_element_smaller @ SV11 @ SV14 @ SV6 )
= $true )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(248,plain,
! [SV6: $i,SV14: $i,SV11: $i] :
( ( ( latt_element_smaller @ SV11 @ SV14 @ SV6 )
= $false )
| ( ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
= $true )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(249,plain,
! [SV14: $i,SV6: $i,SV11: $i] :
( ( ( relstr_set_smaller @ ( poset_of_lattice @ SV11 ) @ SV6 @ ( cast_to_el_of_LattPOSet @ SV11 @ SV14 ) )
= $false )
| ( ( latt_element_smaller @ SV11 @ SV14 @ SV6 )
= $true )
| ( ( element @ SV14 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( lattice @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( latt_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(250,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[93,249,248,240,239,233,231,213,207,206,199,186,177,161,158,156,150,121,108,107,101,100,99,98,95,94]) ).
thf(251,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU350+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.20 % Computer : n007.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.21 % CPULimit : 300
% 0.07/0.21 % WCLimit : 300
% 0.07/0.21 % DateTime : Tue Oct 6 15:13:30 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.07/0.45
% 1.07/0.45 No.of.Axioms: 16
% 1.07/0.45
% 1.07/0.45 Length.of.Defs: 0
% 1.07/0.45
% 1.07/0.45 Contains.Choice.Funs: false
% 1.07/0.45 .....
% 1.07/0.45
% 1.07/0.45 ********************************
% 1.07/0.45 * All subproblems solved! *
% 1.07/0.45 ********************************
% 1.07/0.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:19,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:250,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.07/0.45
% 1.07/0.45 %**** Beginning of derivation protocol ****
% 1.07/0.45 % SZS output start CNFRefutation
% See solution above
% 1.07/0.45
% 1.07/0.45 %**** End of derivation protocol ****
% 1.07/0.45 %**** no. of clauses in derivation: 203 ****
% 1.07/0.45 %**** clause counter: 250 ****
% 1.07/0.45
% 1.07/0.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:19,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:250,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------