TSTP Solution File: SEU344+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU344+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:10:40 EDT 2022
% Result : Theorem 0.61s 1.07s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 133
% Syntax : Number of formulae : 873 ( 498 unt; 52 typ; 0 def)
% Number of atoms : 6452 (2020 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 13599 (1805 ~;2058 |; 180 &;9449 @)
% ( 13 <=>; 94 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 71 ( 71 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 52 usr; 15 con; 0-6 aty)
% Number of variables : 1997 ( 0 ^1967 !; 30 ?;1997 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_apply_binary,type,
apply_binary: $i > $i > $i > $i ).
thf(tp_apply_binary_as_element,type,
apply_binary_as_element: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_below,type,
below: $i > $i > $i > $o ).
thf(tp_boole_lattice,type,
boole_lattice: $i > $i ).
thf(tp_cartesian_product2,type,
cartesian_product2: $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_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_join,type,
join: $i > $i > $i > $i ).
thf(tp_join_semilatt_str,type,
join_semilatt_str: $i > $o ).
thf(tp_latt_str,type,
latt_str: $i > $o ).
thf(tp_latt_str_of,type,
latt_str_of: $i > $i > $i > $i ).
thf(tp_meet,type,
meet: $i > $i > $i > $i ).
thf(tp_meet_semilatt_str,type,
meet_semilatt_str: $i > $o ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_quasi_total,type,
quasi_total: $i > $i > $i > $o ).
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_sK10_A,type,
sK10_A: $i ).
thf(tp_sK11_B,type,
sK11_B: $i > $i ).
thf(tp_sK12_C,type,
sK12_C: $i > $i > $i ).
thf(tp_sK13_B,type,
sK13_B: $i > $i ).
thf(tp_sK14_C,type,
sK14_C: $i > $i > $i ).
thf(tp_sK15_A,type,
sK15_A: $i ).
thf(tp_sK16_A,type,
sK16_A: $i ).
thf(tp_sK17_A,type,
sK17_A: $i ).
thf(tp_sK18_A,type,
sK18_A: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY138,type,
sK2_SY138: $i ).
thf(tp_sK3_SY140,type,
sK3_SY140: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_B,type,
sK5_B: $i > $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_A,type,
sK8_A: $i ).
thf(tp_sK9_B,type,
sK9_B: $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_strict_latt_str,type,
strict_latt_str: $i > $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_the_L_join,type,
the_L_join: $i > $i ).
thf(tp_the_L_meet,type,
the_L_meet: $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(4,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(5,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(6,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(7,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(9,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(10,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] :
( ( element @ B @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ( ( ( join @ ( boole_lattice @ A ) @ B @ C )
= ( set_union2 @ B @ C ) )
& ( ( meet @ ( boole_lattice @ A ) @ B @ C )
= ( set_intersection2 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_lattice3) ).
thf(12,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(14,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( function @ D )
& ( quasi_total @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( relation_of2 @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( element @ E @ A )
& ( element @ F @ B ) )
=> ( ( apply_binary_as_element @ A @ B @ C @ D @ E @ F )
= ( apply_binary @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(17,axiom,
? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_lattices) ).
thf(18,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(19,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(20,axiom,
? [A: $i] :
( ( latt_str @ A )
& ( strict_latt_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_lattices) ).
thf(21,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(22,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(23,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(24,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( function @ B )
& ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( function @ C )
& ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( latt_str_of @ A @ B @ C )
= ( latt_str_of @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(30,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ( function @ B )
& ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( function @ C )
& ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A ) )
=> ( ~ ( empty_carrier @ ( latt_str_of @ A @ B @ C ) )
& ( strict_latt_str @ ( latt_str_of @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattices) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(33,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(34,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(35,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(36,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(37,axiom,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_lattice @ A ) )
& ( strict_latt_str @ ( boole_lattice @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice3) ).
thf(38,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(39,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(40,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(41,axiom,
? [A: $i] : ( latt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(42,axiom,
? [A: $i] : ( join_semilatt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(43,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(44,axiom,
? [A: $i] : ( meet_semilatt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(45,axiom,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( ( function @ ( the_L_join @ A ) )
& ( quasi_total @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(46,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(47,axiom,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( ( function @ ( the_L_meet @ A ) )
& ( quasi_total @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(48,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(49,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(50,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(51,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(52,axiom,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(53,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(54,axiom,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(55,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(56,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(57,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(58,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(59,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( function @ D )
& ( quasi_total @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( relation_of2 @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( element @ E @ A )
& ( element @ F @ B ) )
=> ( element @ ( apply_binary_as_element @ A @ B @ C @ D @ E @ F ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(62,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(63,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(64,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(65,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(66,axiom,
! [A: $i] :
( ( strict_latt_str @ ( boole_lattice @ A ) )
& ( latt_str @ ( boole_lattice @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice3) ).
thf(67,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(68,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_binop_1) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( function @ B )
& ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( function @ C )
& ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A ) )
=> ( ( strict_latt_str @ ( latt_str_of @ A @ B @ C ) )
& ( latt_str @ ( latt_str_of @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g3_lattices) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(71,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(72,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( meet @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_meet @ A ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattices) ).
thf(73,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(74,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( apply_binary @ A @ B @ C )
= ( apply @ A @ ( ordered_pair @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_binop_1) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(80,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( strict_latt_str @ A )
=> ( A
= ( latt_str_of @ ( the_carrier @ A ) @ ( the_L_join @ A ) @ ( the_L_meet @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
thf(81,conjecture,
! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ( ( below @ ( boole_lattice @ A ) @ B @ C )
<=> ( subset @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_lattice3) ).
thf(82,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ( ( below @ ( boole_lattice @ A ) @ B @ C )
<=> ( subset @ B @ C ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[81]) ).
thf(83,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ( ( below @ ( boole_lattice @ A ) @ B @ C )
<=> ( subset @ B @ C ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[82]) ).
thf(84,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(85,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(86,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(87,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(88,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(89,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(90,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(92,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ( ( ( join @ ( boole_lattice @ A ) @ B @ C )
= ( set_union2 @ B @ C ) )
& ( ( meet @ ( boole_lattice @ A ) @ B @ C )
= ( set_intersection2 @ B @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(95,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(98,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(99,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( function @ D )
& ( quasi_total @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( relation_of2 @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( element @ E @ A )
& ( element @ F @ B ) )
=> ( ( apply_binary_as_element @ A @ B @ C @ D @ E @ F )
= ( apply_binary @ D @ E @ F ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(100,plain,
( ( ? [A: $i] :
( ( latt_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_latt_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(101,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)],[18]) ).
thf(102,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(103,plain,
( ( ? [A: $i] :
( ( latt_str @ A )
& ( strict_latt_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(104,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(105,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(106,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(107,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(109,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(110,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( function @ B )
& ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( function @ C )
& ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( latt_str_of @ A @ B @ C )
= ( latt_str_of @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(111,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(113,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(114,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ( function @ B )
& ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( function @ C )
& ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A ) )
=> ( ~ ( empty_carrier @ ( latt_str_of @ A @ B @ C ) )
& ( strict_latt_str @ ( latt_str_of @ A @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(115,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(116,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(117,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(118,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(119,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(120,plain,
( ( ! [A: $i] :
( ~ ( empty_carrier @ ( boole_lattice @ A ) )
& ( strict_latt_str @ ( boole_lattice @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(121,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(122,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(123,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(124,plain,
( ( ? [A: $i] : ( latt_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(125,plain,
( ( ? [A: $i] : ( join_semilatt_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(126,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(127,plain,
( ( ? [A: $i] : ( meet_semilatt_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(128,plain,
( ( ! [A: $i] :
( ( join_semilatt_str @ A )
=> ( ( function @ ( the_L_join @ A ) )
& ( quasi_total @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(129,plain,
$true = $true,
inference(unfold_def,[status(thm)],[46]) ).
thf(130,plain,
( ( ! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( ( function @ ( the_L_meet @ A ) )
& ( quasi_total @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(131,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)],[48]) ).
thf(132,plain,
$true = $true,
inference(unfold_def,[status(thm)],[49]) ).
thf(133,plain,
$true = $true,
inference(unfold_def,[status(thm)],[50]) ).
thf(134,plain,
( ( ! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(135,plain,
( ( ! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(136,plain,
$true = $true,
inference(unfold_def,[status(thm)],[53]) ).
thf(137,plain,
( ( ! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(138,plain,
$true = $true,
inference(unfold_def,[status(thm)],[55]) ).
thf(139,plain,
$true = $true,
inference(unfold_def,[status(thm)],[56]) ).
thf(140,plain,
$true = $true,
inference(unfold_def,[status(thm)],[57]) ).
thf(141,plain,
$true = $true,
inference(unfold_def,[status(thm)],[58]) ).
thf(142,plain,
$true = $true,
inference(unfold_def,[status(thm)],[59]) ).
thf(143,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(144,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( function @ D )
& ( quasi_total @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( relation_of2 @ D @ ( cartesian_product2 @ A @ B ) @ C )
& ( element @ E @ A )
& ( element @ F @ B ) )
=> ( element @ ( apply_binary_as_element @ A @ B @ C @ D @ E @ F ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(145,plain,
$true = $true,
inference(unfold_def,[status(thm)],[62]) ).
thf(146,plain,
$true = $true,
inference(unfold_def,[status(thm)],[63]) ).
thf(147,plain,
$true = $true,
inference(unfold_def,[status(thm)],[64]) ).
thf(148,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)],[65]) ).
thf(149,plain,
( ( ! [A: $i] :
( ( strict_latt_str @ ( boole_lattice @ A ) )
& ( latt_str @ ( boole_lattice @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(150,plain,
$true = $true,
inference(unfold_def,[status(thm)],[67]) ).
thf(151,plain,
$true = $true,
inference(unfold_def,[status(thm)],[68]) ).
thf(152,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( function @ B )
& ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
& ( function @ C )
& ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
& ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A ) )
=> ( ( strict_latt_str @ ( latt_str_of @ A @ B @ C ) )
& ( latt_str @ ( latt_str_of @ A @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(153,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(154,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)],[71]) ).
thf(155,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( meet @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_meet @ A ) @ B @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(156,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)],[73]) ).
thf(157,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( apply_binary @ A @ B @ C )
= ( apply @ A @ ( ordered_pair @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(158,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(159,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(160,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(161,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(162,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(163,plain,
( ( ! [A: $i] :
( ( latt_str @ A )
=> ( ( strict_latt_str @ A )
=> ( A
= ( latt_str_of @ ( the_carrier @ A ) @ ( the_L_join @ A ) @ ( the_L_meet @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(164,plain,
( ( ! [SY138: $i] :
( ( element @ SY138 @ ( the_carrier @ ( boole_lattice @ sK1_A ) ) )
=> ! [SY139: $i] :
( ( element @ SY139 @ ( the_carrier @ ( boole_lattice @ sK1_A ) ) )
=> ( ( below @ ( boole_lattice @ sK1_A ) @ SY138 @ SY139 )
<=> ( subset @ SY138 @ SY139 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[83]) ).
thf(165,plain,
( ( ( element @ sK2_SY138 @ ( the_carrier @ ( boole_lattice @ sK1_A ) ) )
=> ! [SY140: $i] :
( ( element @ SY140 @ ( the_carrier @ ( boole_lattice @ sK1_A ) ) )
=> ( ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ SY140 )
<=> ( subset @ sK2_SY138 @ SY140 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[164]) ).
thf(166,plain,
( ( element @ sK2_SY138 @ ( the_carrier @ ( boole_lattice @ sK1_A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[165]) ).
thf(167,plain,
( ( ! [SY140: $i] :
( ( element @ SY140 @ ( the_carrier @ ( boole_lattice @ sK1_A ) ) )
=> ( ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ SY140 )
<=> ( subset @ sK2_SY138 @ SY140 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[165]) ).
thf(168,plain,
( ( ~ ! [SY140: $i] :
( ( element @ SY140 @ ( the_carrier @ ( boole_lattice @ sK1_A ) ) )
=> ( ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ SY140 )
<=> ( subset @ sK2_SY138 @ SY140 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[167]) ).
thf(169,plain,
( ( ( element @ sK3_SY140 @ ( the_carrier @ ( boole_lattice @ sK1_A ) ) )
& ( ~ ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ~ ( subset @ sK2_SY138 @ sK3_SY140 ) )
& ( ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ( subset @ sK2_SY138 @ sK3_SY140 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[168]) ).
thf(170,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(171,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(172,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(173,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(174,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(175,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[90]) ).
thf(176,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[91]) ).
thf(177,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(178,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( the_carrier @ ( boole_lattice @ A ) ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
| ( ( join @ ( boole_lattice @ A ) @ B @ C )
= ( set_union2 @ B @ C ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
| ( ( meet @ ( boole_lattice @ A ) @ B @ C )
= ( set_intersection2 @ B @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[94]) ).
thf(179,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[96]) ).
thf(180,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[97]) ).
thf(181,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[98]) ).
thf(182,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( function @ D )
| ~ ( quasi_total @ D @ ( cartesian_product2 @ A @ B ) @ C )
| ~ ( relation_of2 @ D @ ( cartesian_product2 @ A @ B ) @ C )
| ~ ( element @ E @ A )
| ~ ( element @ F @ B )
| ( ( apply_binary_as_element @ A @ B @ C @ D @ E @ F )
= ( apply_binary @ D @ E @ F ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[99]) ).
thf(183,plain,
( ( ( latt_str @ sK4_A )
& ~ ( empty_carrier @ sK4_A )
& ( strict_latt_str @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[100]) ).
thf(184,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( ( element @ ( sK5_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK5_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[101]) ).
thf(185,plain,
( ( ( one_sorted_str @ sK6_A )
& ~ ( empty_carrier @ sK6_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[102]) ).
thf(186,plain,
( ( ( latt_str @ sK7_A )
& ( strict_latt_str @ sK7_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[103]) ).
thf(187,plain,
( ( ~ ( empty @ sK8_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[104]) ).
thf(188,plain,
( ( ! [A: $i] :
( ( element @ ( sK9_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK9_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(189,plain,
( ( empty @ sK10_A )
= $true ),
inference(extcnf_combined,[status(esa)],[106]) ).
thf(190,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK11_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK11_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[107]) ).
thf(191,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[108]) ).
thf(192,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[109]) ).
thf(193,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ B )
| ~ ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( function @ C )
| ~ ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ! [D: $i] :
( ( ! [E: $i,F: $i] :
( ( latt_str_of @ A @ B @ C )
!= ( latt_str_of @ D @ E @ F ) )
| ( A = D ) )
& ! [E: $i] :
( ! [F: $i] :
( ( latt_str_of @ A @ B @ C )
!= ( latt_str_of @ D @ E @ F ) )
| ( B = E ) )
& ! [E: $i,F: $i] :
( ( ( latt_str_of @ A @ B @ C )
!= ( latt_str_of @ D @ E @ F ) )
| ( C = F ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(194,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(195,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[112]) ).
thf(196,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( empty @ A )
| ~ ( function @ B )
| ~ ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( function @ C )
| ~ ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( empty_carrier @ ( latt_str_of @ A @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ( empty @ A )
| ~ ( function @ B )
| ~ ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( function @ C )
| ~ ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ( strict_latt_str @ ( latt_str_of @ A @ B @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[114]) ).
thf(197,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[115]) ).
thf(198,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[119]) ).
thf(199,plain,
( ( ! [A: $i] :
~ ( empty_carrier @ ( boole_lattice @ A ) )
& ! [A: $i] : ( strict_latt_str @ ( boole_lattice @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[120]) ).
thf(200,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK12_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[121]) ).
thf(201,plain,
( ( ! [A: $i] : ( element @ ( sK13_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[122]) ).
thf(202,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK14_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[123]) ).
thf(203,plain,
( ( latt_str @ sK15_A )
= $true ),
inference(extcnf_combined,[status(esa)],[124]) ).
thf(204,plain,
( ( join_semilatt_str @ sK16_A )
= $true ),
inference(extcnf_combined,[status(esa)],[125]) ).
thf(205,plain,
( ( one_sorted_str @ sK17_A )
= $true ),
inference(extcnf_combined,[status(esa)],[126]) ).
thf(206,plain,
( ( meet_semilatt_str @ sK18_A )
= $true ),
inference(extcnf_combined,[status(esa)],[127]) ).
thf(207,plain,
( ( ! [A: $i] :
( ~ ( join_semilatt_str @ A )
| ( function @ ( the_L_join @ A ) ) )
& ! [A: $i] :
( ~ ( join_semilatt_str @ A )
| ( quasi_total @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) )
& ! [A: $i] :
( ~ ( join_semilatt_str @ A )
| ( relation_of2_as_subset @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[128]) ).
thf(208,plain,
( ( ! [A: $i] :
( ~ ( meet_semilatt_str @ A )
| ( function @ ( the_L_meet @ A ) ) )
& ! [A: $i] :
( ~ ( meet_semilatt_str @ A )
| ( quasi_total @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) )
& ! [A: $i] :
( ~ ( meet_semilatt_str @ A )
| ( relation_of2_as_subset @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[130]) ).
thf(209,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[131]) ).
thf(210,plain,
( ( ! [A: $i] :
( ~ ( latt_str @ A )
| ( join_semilatt_str @ A ) )
& ! [A: $i] :
( ~ ( latt_str @ A )
| ( meet_semilatt_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[134]) ).
thf(211,plain,
( ( ! [A: $i] :
( ~ ( join_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[135]) ).
thf(212,plain,
( ( ! [A: $i] :
( ~ ( meet_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[137]) ).
thf(213,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( empty_carrier @ A )
| ~ ( meet_semilatt_str @ A )
| ~ ( element @ B @ ( the_carrier @ A ) )
| ~ ( element @ C @ ( the_carrier @ A ) )
| ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[143]) ).
thf(214,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( function @ D )
| ~ ( quasi_total @ D @ ( cartesian_product2 @ A @ B ) @ C )
| ~ ( relation_of2 @ D @ ( cartesian_product2 @ A @ B ) @ C )
| ~ ( element @ E @ A )
| ~ ( element @ F @ B )
| ( element @ ( apply_binary_as_element @ A @ B @ C @ D @ E @ F ) @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[144]) ).
thf(215,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(extcnf_combined,[status(esa)],[148]) ).
thf(216,plain,
( ( ! [A: $i] : ( latt_str @ ( boole_lattice @ A ) )
& ! [A: $i] : ( strict_latt_str @ ( boole_lattice @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(217,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( function @ B )
| ~ ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( function @ C )
| ~ ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ( latt_str @ ( latt_str_of @ A @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( function @ B )
| ~ ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( function @ C )
| ~ ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ( strict_latt_str @ ( latt_str_of @ A @ B @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[152]) ).
thf(218,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 )
!= C )
| ( below @ A @ B @ C ) )
& ! [C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( below @ A @ B @ C )
| ( ( join @ A @ B @ C )
= C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[154]) ).
thf(219,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( meet_semilatt_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ! [C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ( ( meet @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_meet @ A ) @ B @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[155]) ).
thf(220,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(extcnf_combined,[status(esa)],[156]) ).
thf(221,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ! [B: $i,C: $i] :
( ( apply_binary @ A @ B @ C )
= ( apply @ A @ ( ordered_pair @ B @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[157]) ).
thf(222,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[161]) ).
thf(223,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[162]) ).
thf(224,plain,
( ( ! [A: $i] :
( ~ ( latt_str @ A )
| ~ ( strict_latt_str @ A )
| ( A
= ( latt_str_of @ ( the_carrier @ A ) @ ( the_L_join @ A ) @ ( the_L_meet @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[163]) ).
thf(225,plain,
( ( ! [A: $i] :
( ~ ( latt_str @ A )
| ~ ( strict_latt_str @ A )
| ( A
= ( latt_str_of @ ( the_carrier @ A ) @ ( the_L_join @ A ) @ ( the_L_meet @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(226,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(227,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(228,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(229,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(230,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(231,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ! [B: $i,C: $i] :
( ( apply_binary @ A @ B @ C )
= ( apply @ A @ ( ordered_pair @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(232,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)],[220]) ).
thf(233,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( meet_semilatt_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ! [C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ( ( meet @ A @ B @ C )
= ( apply_binary_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( the_L_meet @ A ) @ B @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(234,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 )
!= C )
| ( below @ A @ B @ C ) )
& ! [C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( below @ A @ B @ C )
| ( ( join @ A @ B @ C )
= C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(235,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(236,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( function @ B )
| ~ ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( function @ C )
| ~ ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ( latt_str @ ( latt_str_of @ A @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( function @ B )
| ~ ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( function @ C )
| ~ ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ( strict_latt_str @ ( latt_str_of @ A @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(237,plain,
$true = $true,
inference(copy,[status(thm)],[151]) ).
thf(238,plain,
$true = $true,
inference(copy,[status(thm)],[150]) ).
thf(239,plain,
( ( ! [A: $i] : ( latt_str @ ( boole_lattice @ A ) )
& ! [A: $i] : ( strict_latt_str @ ( boole_lattice @ A ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(240,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)],[215]) ).
thf(241,plain,
$true = $true,
inference(copy,[status(thm)],[147]) ).
thf(242,plain,
$true = $true,
inference(copy,[status(thm)],[146]) ).
thf(243,plain,
$true = $true,
inference(copy,[status(thm)],[145]) ).
thf(244,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( function @ D )
| ~ ( quasi_total @ D @ ( cartesian_product2 @ A @ B ) @ C )
| ~ ( relation_of2 @ D @ ( cartesian_product2 @ A @ B ) @ C )
| ~ ( element @ E @ A )
| ~ ( element @ F @ B )
| ( element @ ( apply_binary_as_element @ A @ B @ C @ D @ E @ F ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(245,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( empty_carrier @ A )
| ~ ( meet_semilatt_str @ A )
| ~ ( element @ B @ ( the_carrier @ A ) )
| ~ ( element @ C @ ( the_carrier @ A ) )
| ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(246,plain,
$true = $true,
inference(copy,[status(thm)],[142]) ).
thf(247,plain,
$true = $true,
inference(copy,[status(thm)],[141]) ).
thf(248,plain,
$true = $true,
inference(copy,[status(thm)],[140]) ).
thf(249,plain,
$true = $true,
inference(copy,[status(thm)],[139]) ).
thf(250,plain,
$true = $true,
inference(copy,[status(thm)],[138]) ).
thf(251,plain,
( ( ! [A: $i] :
( ~ ( meet_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(252,plain,
$true = $true,
inference(copy,[status(thm)],[136]) ).
thf(253,plain,
( ( ! [A: $i] :
( ~ ( join_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(254,plain,
( ( ! [A: $i] :
( ~ ( latt_str @ A )
| ( join_semilatt_str @ A ) )
& ! [A: $i] :
( ~ ( latt_str @ A )
| ( meet_semilatt_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(255,plain,
$true = $true,
inference(copy,[status(thm)],[133]) ).
thf(256,plain,
$true = $true,
inference(copy,[status(thm)],[132]) ).
thf(257,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)],[209]) ).
thf(258,plain,
( ( ! [A: $i] :
( ~ ( meet_semilatt_str @ A )
| ( function @ ( the_L_meet @ A ) ) )
& ! [A: $i] :
( ~ ( meet_semilatt_str @ A )
| ( quasi_total @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) )
& ! [A: $i] :
( ~ ( meet_semilatt_str @ A )
| ( relation_of2_as_subset @ ( the_L_meet @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(259,plain,
$true = $true,
inference(copy,[status(thm)],[129]) ).
thf(260,plain,
( ( ! [A: $i] :
( ~ ( join_semilatt_str @ A )
| ( function @ ( the_L_join @ A ) ) )
& ! [A: $i] :
( ~ ( join_semilatt_str @ A )
| ( quasi_total @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) )
& ! [A: $i] :
( ~ ( join_semilatt_str @ A )
| ( relation_of2_as_subset @ ( the_L_join @ A ) @ ( cartesian_product2 @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(261,plain,
( ( meet_semilatt_str @ sK18_A )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(262,plain,
( ( one_sorted_str @ sK17_A )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(263,plain,
( ( join_semilatt_str @ sK16_A )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(264,plain,
( ( latt_str @ sK15_A )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(265,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK14_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(266,plain,
( ( ! [A: $i] : ( element @ ( sK13_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(267,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK12_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(268,plain,
( ( ! [A: $i] :
~ ( empty_carrier @ ( boole_lattice @ A ) )
& ! [A: $i] : ( strict_latt_str @ ( boole_lattice @ A ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(269,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(270,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(271,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(272,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(273,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(274,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( empty @ A )
| ~ ( function @ B )
| ~ ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( function @ C )
| ~ ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( empty_carrier @ ( latt_str_of @ A @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ( empty @ A )
| ~ ( function @ B )
| ~ ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( function @ C )
| ~ ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ( strict_latt_str @ ( latt_str_of @ A @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(275,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(276,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(277,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(278,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ B )
| ~ ( quasi_total @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ B @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( function @ C )
| ~ ( quasi_total @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ~ ( relation_of2 @ C @ ( cartesian_product2 @ A @ A ) @ A )
| ! [D: $i] :
( ( ! [E: $i,F: $i] :
( ( latt_str_of @ A @ B @ C )
!= ( latt_str_of @ D @ E @ F ) )
| ( A = D ) )
& ! [E: $i] :
( ! [F: $i] :
( ( latt_str_of @ A @ B @ C )
!= ( latt_str_of @ D @ E @ F ) )
| ( B = E ) )
& ! [E: $i,F: $i] :
( ( ( latt_str_of @ A @ B @ C )
!= ( latt_str_of @ D @ E @ F ) )
| ( C = F ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(279,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(280,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(281,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK11_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK11_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(282,plain,
( ( empty @ sK10_A )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(283,plain,
( ( ! [A: $i] :
( ( element @ ( sK9_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK9_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(284,plain,
( ( ~ ( empty @ sK8_A ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(285,plain,
( ( ( latt_str @ sK7_A )
& ( strict_latt_str @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(286,plain,
( ( ( one_sorted_str @ sK6_A )
& ~ ( empty_carrier @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(287,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( ( element @ ( sK5_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK5_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(288,plain,
( ( ( latt_str @ sK4_A )
& ~ ( empty_carrier @ sK4_A )
& ( strict_latt_str @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(289,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( function @ D )
| ~ ( quasi_total @ D @ ( cartesian_product2 @ A @ B ) @ C )
| ~ ( relation_of2 @ D @ ( cartesian_product2 @ A @ B ) @ C )
| ~ ( element @ E @ A )
| ~ ( element @ F @ B )
| ( ( apply_binary_as_element @ A @ B @ C @ D @ E @ F )
= ( apply_binary @ D @ E @ F ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(290,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(291,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(292,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(293,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(294,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( the_carrier @ ( boole_lattice @ A ) ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
| ( ( join @ ( boole_lattice @ A ) @ B @ C )
= ( set_union2 @ B @ C ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
| ( ( meet @ ( boole_lattice @ A ) @ B @ C )
= ( set_intersection2 @ B @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(295,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(296,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(297,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(298,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(299,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(300,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(301,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(302,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(303,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(304,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(305,plain,
( ( element @ sK2_SY138 @ ( the_carrier @ ( boole_lattice @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(306,plain,
( ( ( element @ sK3_SY140 @ ( the_carrier @ ( boole_lattice @ sK1_A ) ) )
& ( ~ ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ~ ( subset @ sK2_SY138 @ sK3_SY140 ) )
& ( ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ( subset @ sK2_SY138 @ sK3_SY140 ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(307,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ~ ( ~ ( element @ ( sK5_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(308,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(309,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( function @ ( the_L_join @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( quasi_total @ ( the_L_join @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( relation_of2_as_subset @ ( the_L_join @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(310,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( function @ SX1 )
| ~ ( quasi_total @ SX1 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ~ ( relation_of2 @ SX1 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ~ ( function @ SX2 )
| ~ ( quasi_total @ SX2 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ~ ( relation_of2 @ SX2 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ! [SX3: $i] :
~ ( ~ ~ ( ~ ( ! [SX4: $i,SX5: $i] :
( ( latt_str_of @ SX0 @ SX1 @ SX2 )
!= ( latt_str_of @ SX3 @ SX4 @ SX5 ) )
| ( SX0 = SX3 ) )
| ~ ! [SX4: $i] :
( ! [SX5: $i] :
( ( latt_str_of @ SX0 @ SX1 @ SX2 )
!= ( latt_str_of @ SX3 @ SX4 @ SX5 ) )
| ( SX1 = SX4 ) ) )
| ~ ! [SX4: $i,SX5: $i] :
( ( ( latt_str_of @ SX0 @ SX1 @ SX2 )
!= ( latt_str_of @ SX3 @ SX4 @ SX5 ) )
| ( SX2 = SX5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(311,plain,
( ( ~ ( ~ ! [SX0: $i] :
~ ( empty_carrier @ ( boole_lattice @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_latt_str @ ( boole_lattice @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(312,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX1 )
| ~ ( quasi_total @ SX1 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ~ ( relation_of2 @ SX1 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ~ ( function @ SX2 )
| ~ ( quasi_total @ SX2 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ~ ( relation_of2 @ SX2 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ( latt_str @ ( latt_str_of @ SX0 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX1 )
| ~ ( quasi_total @ SX1 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ~ ( relation_of2 @ SX1 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ~ ( function @ SX2 )
| ~ ( quasi_total @ SX2 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ~ ( relation_of2 @ SX2 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ( strict_latt_str @ ( latt_str_of @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(313,plain,
( ( ~ ( ~ ~ ( ~ ( latt_str @ sK4_A )
| ~ ~ ( empty_carrier @ sK4_A ) )
| ~ ( strict_latt_str @ sK4_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(314,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( join_semilatt_str @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( meet_semilatt_str @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(315,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(316,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK11_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK11_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(317,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( empty @ SX0 )
| ~ ( function @ SX1 )
| ~ ( quasi_total @ SX1 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ~ ( relation_of2 @ SX1 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ~ ( function @ SX2 )
| ~ ( quasi_total @ SX2 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ~ ( relation_of2 @ SX2 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ~ ( empty_carrier @ ( latt_str_of @ SX0 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( empty @ SX0 )
| ~ ( function @ SX1 )
| ~ ( quasi_total @ SX1 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ~ ( relation_of2 @ SX1 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ~ ( function @ SX2 )
| ~ ( quasi_total @ SX2 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ~ ( relation_of2 @ SX2 @ ( cartesian_product2 @ SX0 @ SX0 ) @ SX0 )
| ( strict_latt_str @ ( latt_str_of @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(318,plain,
( ( ~ ( ~ ( element @ sK3_SY140 @ ( the_carrier @ ( boole_lattice @ sK1_A ) ) )
| ~ ~ ( ~ ( ~ ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ~ ( subset @ sK2_SY138 @ sK3_SY140 ) )
| ~ ( ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ( subset @ sK2_SY138 @ sK3_SY140 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(319,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( function @ ( the_L_meet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( quasi_total @ ( the_L_meet @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( relation_of2_as_subset @ ( the_L_meet @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(320,plain,
( ( ~ ( ~ ! [SX0: $i] : ( latt_str @ ( boole_lattice @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_latt_str @ ( boole_lattice @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(321,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK9_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK9_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(322,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 )
!= SX2 )
| ( below @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( below @ SX0 @ SX1 @ SX2 )
| ( ( join @ SX0 @ SX1 @ SX2 )
= SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(323,plain,
( ( ~ ( ~ ( latt_str @ sK7_A )
| ~ ( strict_latt_str @ sK7_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(324,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ ( boole_lattice @ SX0 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ ( boole_lattice @ SX0 ) ) )
| ( ( join @ ( boole_lattice @ SX0 ) @ SX1 @ SX2 )
= ( set_union2 @ SX1 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ ( boole_lattice @ SX0 ) ) )
| ( ( meet @ ( boole_lattice @ SX0 ) @ SX1 @ SX2 )
= ( set_intersection2 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(325,plain,
( ( ~ ( ~ ( one_sorted_str @ sK6_A )
| ~ ~ ( empty_carrier @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(326,plain,
! [SV1: $i] :
( ( ~ ( latt_str @ SV1 )
| ~ ( strict_latt_str @ SV1 )
| ( SV1
= ( latt_str_of @ ( the_carrier @ SV1 ) @ ( the_L_join @ SV1 ) @ ( the_L_meet @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(327,plain,
! [SV2: $i] :
( ( ! [SY141: $i] :
( ~ ( in @ SV2 @ SY141 )
| ~ ( in @ SY141 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(328,plain,
! [SV3: $i] :
( ( ! [SY142: $i,SY143: $i] :
( ~ ( element @ SY143 @ ( powerset @ ( cartesian_product2 @ SV3 @ SY142 ) ) )
| ( relation @ SY143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(329,plain,
! [SV4: $i] :
( ( ! [SY144: $i] :
( ( unordered_pair @ SV4 @ SY144 )
= ( unordered_pair @ SY144 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(330,plain,
! [SV5: $i] :
( ( ! [SY145: $i] :
( ( set_union2 @ SV5 @ SY145 )
= ( set_union2 @ SY145 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(331,plain,
! [SV6: $i] :
( ( ! [SY146: $i] :
( ( set_intersection2 @ SV6 @ SY146 )
= ( set_intersection2 @ SY146 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(332,plain,
! [SV7: $i] :
( ( ~ ( function @ SV7 )
| ~ ( relation @ SV7 )
| ! [SY147: $i,SY148: $i] :
( ( apply_binary @ SV7 @ SY147 @ SY148 )
= ( apply @ SV7 @ ( ordered_pair @ SY147 @ SY148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(333,plain,
! [SV8: $i] :
( ( ( empty_carrier @ SV8 )
| ~ ( join_semilatt_str @ SV8 )
| ! [SY149: $i] :
( ~ ( element @ SY149 @ ( the_carrier @ SV8 ) )
| ! [SY150: $i] :
( ~ ( element @ SY150 @ ( the_carrier @ SV8 ) )
| ( ( join @ SV8 @ SY149 @ SY150 )
= ( apply_binary_as_element @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_L_join @ SV8 ) @ SY149 @ SY150 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(334,plain,
! [SV9: $i] :
( ( ( empty_carrier @ SV9 )
| ~ ( meet_semilatt_str @ SV9 )
| ! [SY151: $i] :
( ~ ( element @ SY151 @ ( the_carrier @ SV9 ) )
| ! [SY152: $i] :
( ~ ( element @ SY152 @ ( the_carrier @ SV9 ) )
| ( ( meet @ SV9 @ SY151 @ SY152 )
= ( apply_binary_as_element @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_L_meet @ SV9 ) @ SY151 @ SY152 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(335,plain,
! [SV10: $i] :
( ( ! [SY153: $i] :
( ( ordered_pair @ SV10 @ SY153 )
= ( unordered_pair @ ( unordered_pair @ SV10 @ SY153 ) @ ( singleton @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(336,plain,
! [SV11: $i] :
( ( ! [SY154: $i,SY155: $i] :
( ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 )
| ~ ( element @ SY154 @ ( the_carrier @ SV11 ) )
| ~ ( element @ SY155 @ ( the_carrier @ SV11 ) )
| ( element @ ( join @ SV11 @ SY154 @ SY155 ) @ ( the_carrier @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(337,plain,
! [SV12: $i] :
( ( ! [SY156: $i,SY157: $i,SY158: $i,SY159: $i,SY160: $i] :
( ( empty @ SV12 )
| ( empty @ SY156 )
| ~ ( function @ SY158 )
| ~ ( quasi_total @ SY158 @ ( cartesian_product2 @ SV12 @ SY156 ) @ SY157 )
| ~ ( relation_of2 @ SY158 @ ( cartesian_product2 @ SV12 @ SY156 ) @ SY157 )
| ~ ( element @ SY159 @ SV12 )
| ~ ( element @ SY160 @ SY156 )
| ( element @ ( apply_binary_as_element @ SV12 @ SY156 @ SY157 @ SY158 @ SY159 @ SY160 ) @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(338,plain,
! [SV13: $i] :
( ( ! [SY161: $i,SY162: $i] :
( ( empty_carrier @ SV13 )
| ~ ( meet_semilatt_str @ SV13 )
| ~ ( element @ SY161 @ ( the_carrier @ SV13 ) )
| ~ ( element @ SY162 @ ( the_carrier @ SV13 ) )
| ( element @ ( meet @ SV13 @ SY161 @ SY162 ) @ ( the_carrier @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(339,plain,
! [SV14: $i] :
( ( ~ ( meet_semilatt_str @ SV14 )
| ( one_sorted_str @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(340,plain,
! [SV15: $i] :
( ( ~ ( join_semilatt_str @ SV15 )
| ( one_sorted_str @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(341,plain,
! [SV16: $i] :
( ( ! [SY163: $i,SY164: $i] :
( ~ ( relation_of2_as_subset @ SY164 @ SV16 @ SY163 )
| ( element @ SY164 @ ( powerset @ ( cartesian_product2 @ SV16 @ SY163 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(342,plain,
! [SV17: $i] :
( ( ! [SY165: $i] : ( relation_of2 @ ( sK14_C @ SY165 @ SV17 ) @ SV17 @ SY165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(343,plain,
! [SV18: $i] :
( ( element @ ( sK13_B @ SV18 ) @ SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(344,plain,
! [SV19: $i] :
( ( ! [SY166: $i] : ( relation_of2_as_subset @ ( sK12_C @ SY166 @ SV19 ) @ SV19 @ SY166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(345,plain,
! [SV20: $i] :
( ( ( empty_carrier @ SV20 )
| ~ ( one_sorted_str @ SV20 )
| ~ ( empty @ ( the_carrier @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(346,plain,
! [SV21: $i] :
( ( ~ ( empty @ ( powerset @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(347,plain,
! [SV22: $i] :
( ( ~ ( empty @ ( singleton @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(348,plain,
! [SV23: $i] :
( ( ( empty @ SV23 )
| ! [SY167: $i] :
~ ( empty @ ( set_union2 @ SV23 @ SY167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(349,plain,
! [SV24: $i] :
( ( ! [SY168: $i] :
~ ( empty @ ( unordered_pair @ SV24 @ SY168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(350,plain,
! [SV25: $i] :
( ( ( empty @ SV25 )
| ! [SY169: $i] :
~ ( empty @ ( set_union2 @ SY169 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(351,plain,
! [SV26: $i] :
( ( ! [SY170: $i] :
( ( empty @ SV26 )
| ( empty @ SY170 )
| ~ ( empty @ ( cartesian_product2 @ SV26 @ SY170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(352,plain,
! [SV27: $i] :
( ( ( set_union2 @ SV27 @ SV27 )
= SV27 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(353,plain,
! [SV28: $i] :
( ( ( set_intersection2 @ SV28 @ SV28 )
= SV28 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(354,plain,
( ( empty @ sK8_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(355,plain,
! [SV29: $i] :
( ( ! [SY171: $i,SY172: $i,SY173: $i,SY174: $i,SY175: $i] :
( ( empty @ SV29 )
| ( empty @ SY171 )
| ~ ( function @ SY173 )
| ~ ( quasi_total @ SY173 @ ( cartesian_product2 @ SV29 @ SY171 ) @ SY172 )
| ~ ( relation_of2 @ SY173 @ ( cartesian_product2 @ SV29 @ SY171 ) @ SY172 )
| ~ ( element @ SY174 @ SV29 )
| ~ ( element @ SY175 @ SY171 )
| ( ( apply_binary_as_element @ SV29 @ SY171 @ SY172 @ SY173 @ SY174 @ SY175 )
= ( apply_binary @ SY173 @ SY174 @ SY175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(356,plain,
! [SV30: $i] :
( ( subset @ SV30 @ SV30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(357,plain,
! [SV31: $i] :
( ( ! [SY176: $i] :
( ~ ( subset @ SV31 @ SY176 )
| ( ( set_union2 @ SV31 @ SY176 )
= SY176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(358,plain,
! [SV32: $i] :
( ( ( set_union2 @ SV32 @ empty_set )
= SV32 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(359,plain,
! [SV33: $i] :
( ( ! [SY177: $i] :
( ~ ( in @ SV33 @ SY177 )
| ( element @ SV33 @ SY177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(360,plain,
! [SV34: $i] :
( ( ( set_intersection2 @ SV34 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(361,plain,
! [SV35: $i] :
( ( ! [SY178: $i] :
( ~ ( element @ SV35 @ SY178 )
| ( empty @ SY178 )
| ( in @ SV35 @ SY178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(362,plain,
! [SV36: $i] :
( ( ! [SY179: $i,SY180: $i] :
( ~ ( element @ SY179 @ ( powerset @ SY180 ) )
| ~ ( in @ SV36 @ SY179 )
| ( element @ SV36 @ SY180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(363,plain,
! [SV37: $i] :
( ( ! [SY181: $i,SY182: $i] :
( ~ ( element @ SY181 @ ( powerset @ SY182 ) )
| ~ ( in @ SV37 @ SY181 )
| ~ ( empty @ SY182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(364,plain,
! [SV38: $i] :
( ( ~ ( empty @ SV38 )
| ( SV38 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(365,plain,
! [SV39: $i] :
( ( ! [SY183: $i] :
( ~ ( empty @ SY183 )
| ~ ( in @ SV39 @ SY183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(366,plain,
! [SV40: $i] :
( ( ! [SY184: $i] : ( subset @ SV40 @ ( set_union2 @ SV40 @ SY184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(367,plain,
! [SV41: $i] :
( ( ! [SY185: $i] :
( ( SV41 = SY185 )
| ~ ( empty @ SV41 )
| ~ ( empty @ SY185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(368,plain,
! [SV42: $i] :
( ( ( empty_carrier @ SV42 )
| ~ ( one_sorted_str @ SV42 )
| ~ ( ~ ( element @ ( sK5_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(369,plain,
! [SV43: $i] :
( ( ~ ( ~ ! [SY186: $i,SY187: $i] :
( ~ ( relation_of2 @ SY187 @ SV43 @ SY186 )
| ( relation_of2_as_subset @ SY187 @ SV43 @ SY186 ) )
| ~ ! [SY188: $i,SY189: $i] :
( ~ ( relation_of2_as_subset @ SY189 @ SV43 @ SY188 )
| ( relation_of2 @ SY189 @ SV43 @ SY188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(370,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( function @ ( the_L_join @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( quasi_total @ ( the_L_join @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( relation_of2_as_subset @ ( the_L_join @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(371,plain,
! [SV44: $i] :
( ( ! [SY190: $i,SY191: $i] :
( ~ ( function @ SY190 )
| ~ ( quasi_total @ SY190 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ~ ( relation_of2 @ SY190 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ~ ( function @ SY191 )
| ~ ( quasi_total @ SY191 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ~ ( relation_of2 @ SY191 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ! [SY192: $i] :
~ ( ~ ~ ( ~ ( ! [SY193: $i,SY194: $i] :
( ( latt_str_of @ SV44 @ SY190 @ SY191 )
!= ( latt_str_of @ SY192 @ SY193 @ SY194 ) )
| ( SV44 = SY192 ) )
| ~ ! [SY195: $i] :
( ! [SY196: $i] :
( ( latt_str_of @ SV44 @ SY190 @ SY191 )
!= ( latt_str_of @ SY192 @ SY195 @ SY196 ) )
| ( SY190 = SY195 ) ) )
| ~ ! [SY197: $i,SY198: $i] :
( ( ( latt_str_of @ SV44 @ SY190 @ SY191 )
!= ( latt_str_of @ SY192 @ SY197 @ SY198 ) )
| ( SY191 = SY198 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(372,plain,
( ( ~ ! [SX0: $i] :
~ ( empty_carrier @ ( boole_lattice @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_latt_str @ ( boole_lattice @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(373,plain,
! [SV45: $i] :
( ( ~ ( ~ ! [SY199: $i,SY200: $i] :
( ~ ( function @ SY199 )
| ~ ( quasi_total @ SY199 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY199 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SY200 )
| ~ ( quasi_total @ SY200 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY200 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ( latt_str @ ( latt_str_of @ SV45 @ SY199 @ SY200 ) ) )
| ~ ! [SY201: $i,SY202: $i] :
( ~ ( function @ SY201 )
| ~ ( quasi_total @ SY201 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY201 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SY202 )
| ~ ( quasi_total @ SY202 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY202 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ( strict_latt_str @ ( latt_str_of @ SV45 @ SY201 @ SY202 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(374,plain,
( ( ~ ~ ( ~ ( latt_str @ sK4_A )
| ~ ~ ( empty_carrier @ sK4_A ) )
| ~ ( strict_latt_str @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(375,plain,
( ( ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( join_semilatt_str @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( meet_semilatt_str @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(376,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(377,plain,
! [SV46: $i] :
( ( ( empty @ SV46 )
| ~ ( ~ ( element @ ( sK11_B @ SV46 ) @ ( powerset @ SV46 ) )
| ~ ~ ( empty @ ( sK11_B @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(378,plain,
! [SV47: $i] :
( ( ~ ( ~ ! [SY203: $i,SY204: $i] :
( ( empty @ SV47 )
| ~ ( function @ SY203 )
| ~ ( quasi_total @ SY203 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY203 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SY204 )
| ~ ( quasi_total @ SY204 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY204 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SY203 @ SY204 ) ) )
| ~ ! [SY205: $i,SY206: $i] :
( ( empty @ SV47 )
| ~ ( function @ SY205 )
| ~ ( quasi_total @ SY205 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY205 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SY206 )
| ~ ( quasi_total @ SY206 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY206 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ( strict_latt_str @ ( latt_str_of @ SV47 @ SY205 @ SY206 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(379,plain,
( ( ~ ( element @ sK3_SY140 @ ( the_carrier @ ( boole_lattice @ sK1_A ) ) )
| ~ ~ ( ~ ( ~ ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ~ ( subset @ sK2_SY138 @ sK3_SY140 ) )
| ~ ( ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ( subset @ sK2_SY138 @ sK3_SY140 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(380,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( function @ ( the_L_meet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( quasi_total @ ( the_L_meet @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( relation_of2_as_subset @ ( the_L_meet @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(381,plain,
( ( ~ ! [SX0: $i] : ( latt_str @ ( boole_lattice @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_latt_str @ ( boole_lattice @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(382,plain,
! [SV48: $i] :
( ( ~ ( ~ ( element @ ( sK9_B @ SV48 ) @ ( powerset @ SV48 ) )
| ~ ( empty @ ( sK9_B @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(383,plain,
! [SV49: $i] :
( ( ( empty_carrier @ SV49 )
| ~ ( join_semilatt_str @ SV49 )
| ! [SY207: $i] :
( ~ ( element @ SY207 @ ( the_carrier @ SV49 ) )
| ~ ( ~ ! [SY208: $i] :
( ~ ( element @ SY208 @ ( the_carrier @ SV49 ) )
| ( ( join @ SV49 @ SY207 @ SY208 )
!= SY208 )
| ( below @ SV49 @ SY207 @ SY208 ) )
| ~ ! [SY209: $i] :
( ~ ( element @ SY209 @ ( the_carrier @ SV49 ) )
| ~ ( below @ SV49 @ SY207 @ SY209 )
| ( ( join @ SV49 @ SY207 @ SY209 )
= SY209 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(384,plain,
( ( ~ ( latt_str @ sK7_A )
| ~ ( strict_latt_str @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(385,plain,
! [SV50: $i] :
( ( ! [SY210: $i] :
( ~ ( element @ SY210 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ~ ( ~ ! [SY211: $i] :
( ~ ( element @ SY211 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ( ( join @ ( boole_lattice @ SV50 ) @ SY210 @ SY211 )
= ( set_union2 @ SY210 @ SY211 ) ) )
| ~ ! [SY212: $i] :
( ~ ( element @ SY212 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ( ( meet @ ( boole_lattice @ SV50 ) @ SY210 @ SY212 )
= ( set_intersection2 @ SY210 @ SY212 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(386,plain,
( ( ~ ( one_sorted_str @ sK6_A )
| ~ ~ ( empty_carrier @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(387,plain,
! [SV1: $i] :
( ( ( ~ ( latt_str @ SV1 ) )
= $true )
| ( ( ~ ( strict_latt_str @ SV1 )
| ( SV1
= ( latt_str_of @ ( the_carrier @ SV1 ) @ ( the_L_join @ SV1 ) @ ( the_L_meet @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(388,plain,
! [SV51: $i,SV2: $i] :
( ( ~ ( in @ SV2 @ SV51 )
| ~ ( in @ SV51 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(389,plain,
! [SV52: $i,SV3: $i] :
( ( ! [SY213: $i] :
( ~ ( element @ SY213 @ ( powerset @ ( cartesian_product2 @ SV3 @ SV52 ) ) )
| ( relation @ SY213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(390,plain,
! [SV53: $i,SV4: $i] :
( ( ( unordered_pair @ SV4 @ SV53 )
= ( unordered_pair @ SV53 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(391,plain,
! [SV54: $i,SV5: $i] :
( ( ( set_union2 @ SV5 @ SV54 )
= ( set_union2 @ SV54 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(392,plain,
! [SV55: $i,SV6: $i] :
( ( ( set_intersection2 @ SV6 @ SV55 )
= ( set_intersection2 @ SV55 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(393,plain,
! [SV7: $i] :
( ( ( ~ ( function @ SV7 )
| ~ ( relation @ SV7 ) )
= $true )
| ( ( ! [SY147: $i,SY148: $i] :
( ( apply_binary @ SV7 @ SY147 @ SY148 )
= ( apply @ SV7 @ ( ordered_pair @ SY147 @ SY148 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(394,plain,
! [SV8: $i] :
( ( ( ( empty_carrier @ SV8 )
| ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ! [SY149: $i] :
( ~ ( element @ SY149 @ ( the_carrier @ SV8 ) )
| ! [SY150: $i] :
( ~ ( element @ SY150 @ ( the_carrier @ SV8 ) )
| ( ( join @ SV8 @ SY149 @ SY150 )
= ( apply_binary_as_element @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_L_join @ SV8 ) @ SY149 @ SY150 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(395,plain,
! [SV9: $i] :
( ( ( ( empty_carrier @ SV9 )
| ~ ( meet_semilatt_str @ SV9 ) )
= $true )
| ( ( ! [SY151: $i] :
( ~ ( element @ SY151 @ ( the_carrier @ SV9 ) )
| ! [SY152: $i] :
( ~ ( element @ SY152 @ ( the_carrier @ SV9 ) )
| ( ( meet @ SV9 @ SY151 @ SY152 )
= ( apply_binary_as_element @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_L_meet @ SV9 ) @ SY151 @ SY152 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(396,plain,
! [SV56: $i,SV10: $i] :
( ( ( ordered_pair @ SV10 @ SV56 )
= ( unordered_pair @ ( unordered_pair @ SV10 @ SV56 ) @ ( singleton @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(397,plain,
! [SV57: $i,SV11: $i] :
( ( ! [SY214: $i] :
( ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 )
| ~ ( element @ SV57 @ ( the_carrier @ SV11 ) )
| ~ ( element @ SY214 @ ( the_carrier @ SV11 ) )
| ( element @ ( join @ SV11 @ SV57 @ SY214 ) @ ( the_carrier @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(398,plain,
! [SV58: $i,SV12: $i] :
( ( ! [SY215: $i,SY216: $i,SY217: $i,SY218: $i] :
( ( empty @ SV12 )
| ( empty @ SV58 )
| ~ ( function @ SY216 )
| ~ ( quasi_total @ SY216 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SY215 )
| ~ ( relation_of2 @ SY216 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SY215 )
| ~ ( element @ SY217 @ SV12 )
| ~ ( element @ SY218 @ SV58 )
| ( element @ ( apply_binary_as_element @ SV12 @ SV58 @ SY215 @ SY216 @ SY217 @ SY218 ) @ SY215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(399,plain,
! [SV59: $i,SV13: $i] :
( ( ! [SY219: $i] :
( ( empty_carrier @ SV13 )
| ~ ( meet_semilatt_str @ SV13 )
| ~ ( element @ SV59 @ ( the_carrier @ SV13 ) )
| ~ ( element @ SY219 @ ( the_carrier @ SV13 ) )
| ( element @ ( meet @ SV13 @ SV59 @ SY219 ) @ ( the_carrier @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(400,plain,
! [SV14: $i] :
( ( ( ~ ( meet_semilatt_str @ SV14 ) )
= $true )
| ( ( one_sorted_str @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(401,plain,
! [SV15: $i] :
( ( ( ~ ( join_semilatt_str @ SV15 ) )
= $true )
| ( ( one_sorted_str @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(402,plain,
! [SV60: $i,SV16: $i] :
( ( ! [SY220: $i] :
( ~ ( relation_of2_as_subset @ SY220 @ SV16 @ SV60 )
| ( element @ SY220 @ ( powerset @ ( cartesian_product2 @ SV16 @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(403,plain,
! [SV17: $i,SV61: $i] :
( ( relation_of2 @ ( sK14_C @ SV61 @ SV17 ) @ SV17 @ SV61 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(404,plain,
! [SV19: $i,SV62: $i] :
( ( relation_of2_as_subset @ ( sK12_C @ SV62 @ SV19 ) @ SV19 @ SV62 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(405,plain,
! [SV20: $i] :
( ( ( ( empty_carrier @ SV20 )
| ~ ( one_sorted_str @ SV20 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(406,plain,
! [SV21: $i] :
( ( empty @ ( powerset @ SV21 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(407,plain,
! [SV22: $i] :
( ( empty @ ( singleton @ SV22 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(408,plain,
! [SV23: $i] :
( ( ( empty @ SV23 )
= $true )
| ( ( ! [SY167: $i] :
~ ( empty @ ( set_union2 @ SV23 @ SY167 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(409,plain,
! [SV63: $i,SV24: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV24 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(410,plain,
! [SV25: $i] :
( ( ( empty @ SV25 )
= $true )
| ( ( ! [SY169: $i] :
~ ( empty @ ( set_union2 @ SY169 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(411,plain,
! [SV64: $i,SV26: $i] :
( ( ( empty @ SV26 )
| ( empty @ SV64 )
| ~ ( empty @ ( cartesian_product2 @ SV26 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(412,plain,
! [SV65: $i,SV29: $i] :
( ( ! [SY221: $i,SY222: $i,SY223: $i,SY224: $i] :
( ( empty @ SV29 )
| ( empty @ SV65 )
| ~ ( function @ SY222 )
| ~ ( quasi_total @ SY222 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SY221 )
| ~ ( relation_of2 @ SY222 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SY221 )
| ~ ( element @ SY223 @ SV29 )
| ~ ( element @ SY224 @ SV65 )
| ( ( apply_binary_as_element @ SV29 @ SV65 @ SY221 @ SY222 @ SY223 @ SY224 )
= ( apply_binary @ SY222 @ SY223 @ SY224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(413,plain,
! [SV66: $i,SV31: $i] :
( ( ~ ( subset @ SV31 @ SV66 )
| ( ( set_union2 @ SV31 @ SV66 )
= SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(414,plain,
! [SV67: $i,SV33: $i] :
( ( ~ ( in @ SV33 @ SV67 )
| ( element @ SV33 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(415,plain,
! [SV68: $i,SV35: $i] :
( ( ~ ( element @ SV35 @ SV68 )
| ( empty @ SV68 )
| ( in @ SV35 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(416,plain,
! [SV36: $i,SV69: $i] :
( ( ! [SY225: $i] :
( ~ ( element @ SV69 @ ( powerset @ SY225 ) )
| ~ ( in @ SV36 @ SV69 )
| ( element @ SV36 @ SY225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(417,plain,
! [SV37: $i,SV70: $i] :
( ( ! [SY226: $i] :
( ~ ( element @ SV70 @ ( powerset @ SY226 ) )
| ~ ( in @ SV37 @ SV70 )
| ~ ( empty @ SY226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(418,plain,
! [SV38: $i] :
( ( ( ~ ( empty @ SV38 ) )
= $true )
| ( ( SV38 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(419,plain,
! [SV39: $i,SV71: $i] :
( ( ~ ( empty @ SV71 )
| ~ ( in @ SV39 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(420,plain,
! [SV72: $i,SV40: $i] :
( ( subset @ SV40 @ ( set_union2 @ SV40 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(421,plain,
! [SV73: $i,SV41: $i] :
( ( ( SV41 = SV73 )
| ~ ( empty @ SV41 )
| ~ ( empty @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(422,plain,
! [SV42: $i] :
( ( ( ( empty_carrier @ SV42 )
| ~ ( one_sorted_str @ SV42 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK5_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(423,plain,
! [SV43: $i] :
( ( ~ ! [SY186: $i,SY187: $i] :
( ~ ( relation_of2 @ SY187 @ SV43 @ SY186 )
| ( relation_of2_as_subset @ SY187 @ SV43 @ SY186 ) )
| ~ ! [SY188: $i,SY189: $i] :
( ~ ( relation_of2_as_subset @ SY189 @ SV43 @ SY188 )
| ( relation_of2 @ SY189 @ SV43 @ SY188 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(424,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( function @ ( the_L_join @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( quasi_total @ ( the_L_join @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(425,plain,
( ( ~ ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( relation_of2_as_subset @ ( the_L_join @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(426,plain,
! [SV44: $i,SV74: $i] :
( ( ! [SY227: $i] :
( ~ ( function @ SV74 )
| ~ ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ~ ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ~ ( function @ SY227 )
| ~ ( quasi_total @ SY227 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ~ ( relation_of2 @ SY227 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ! [SY228: $i] :
~ ( ~ ~ ( ~ ( ! [SY229: $i,SY230: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SY227 )
!= ( latt_str_of @ SY228 @ SY229 @ SY230 ) )
| ( SV44 = SY228 ) )
| ~ ! [SY231: $i] :
( ! [SY232: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SY227 )
!= ( latt_str_of @ SY228 @ SY231 @ SY232 ) )
| ( SV74 = SY231 ) ) )
| ~ ! [SY233: $i,SY234: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SY227 )
!= ( latt_str_of @ SY228 @ SY233 @ SY234 ) )
| ( SY227 = SY234 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(427,plain,
( ( ~ ! [SX0: $i] :
~ ( empty_carrier @ ( boole_lattice @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(428,plain,
( ( ~ ! [SX0: $i] : ( strict_latt_str @ ( boole_lattice @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(429,plain,
! [SV45: $i] :
( ( ~ ! [SY199: $i,SY200: $i] :
( ~ ( function @ SY199 )
| ~ ( quasi_total @ SY199 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY199 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SY200 )
| ~ ( quasi_total @ SY200 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY200 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ( latt_str @ ( latt_str_of @ SV45 @ SY199 @ SY200 ) ) )
| ~ ! [SY201: $i,SY202: $i] :
( ~ ( function @ SY201 )
| ~ ( quasi_total @ SY201 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY201 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SY202 )
| ~ ( quasi_total @ SY202 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY202 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ( strict_latt_str @ ( latt_str_of @ SV45 @ SY201 @ SY202 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(430,plain,
( ( ~ ~ ( ~ ( latt_str @ sK4_A )
| ~ ~ ( empty_carrier @ sK4_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[374]) ).
thf(431,plain,
( ( ~ ( strict_latt_str @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[374]) ).
thf(432,plain,
( ( ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( join_semilatt_str @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(433,plain,
( ( ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( meet_semilatt_str @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(434,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(435,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(436,plain,
! [SV46: $i] :
( ( ( empty @ SV46 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_B @ SV46 ) @ ( powerset @ SV46 ) )
| ~ ~ ( empty @ ( sK11_B @ SV46 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[377]) ).
thf(437,plain,
! [SV47: $i] :
( ( ~ ! [SY203: $i,SY204: $i] :
( ( empty @ SV47 )
| ~ ( function @ SY203 )
| ~ ( quasi_total @ SY203 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY203 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SY204 )
| ~ ( quasi_total @ SY204 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY204 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SY203 @ SY204 ) ) )
| ~ ! [SY205: $i,SY206: $i] :
( ( empty @ SV47 )
| ~ ( function @ SY205 )
| ~ ( quasi_total @ SY205 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY205 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SY206 )
| ~ ( quasi_total @ SY206 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY206 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ( strict_latt_str @ ( latt_str_of @ SV47 @ SY205 @ SY206 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(438,plain,
( ( ~ ( element @ sK3_SY140 @ ( the_carrier @ ( boole_lattice @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(439,plain,
( ( ~ ~ ( ~ ( ~ ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ~ ( subset @ sK2_SY138 @ sK3_SY140 ) )
| ~ ( ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ( subset @ sK2_SY138 @ sK3_SY140 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(440,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( function @ ( the_L_meet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( quasi_total @ ( the_L_meet @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(441,plain,
( ( ~ ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( relation_of2_as_subset @ ( the_L_meet @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(442,plain,
( ( ~ ! [SX0: $i] : ( latt_str @ ( boole_lattice @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(443,plain,
( ( ~ ! [SX0: $i] : ( strict_latt_str @ ( boole_lattice @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(444,plain,
! [SV48: $i] :
( ( ~ ( element @ ( sK9_B @ SV48 ) @ ( powerset @ SV48 ) )
| ~ ( empty @ ( sK9_B @ SV48 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(445,plain,
! [SV49: $i] :
( ( ( ( empty_carrier @ SV49 )
| ~ ( join_semilatt_str @ SV49 ) )
= $true )
| ( ( ! [SY207: $i] :
( ~ ( element @ SY207 @ ( the_carrier @ SV49 ) )
| ~ ( ~ ! [SY208: $i] :
( ~ ( element @ SY208 @ ( the_carrier @ SV49 ) )
| ( ( join @ SV49 @ SY207 @ SY208 )
!= SY208 )
| ( below @ SV49 @ SY207 @ SY208 ) )
| ~ ! [SY209: $i] :
( ~ ( element @ SY209 @ ( the_carrier @ SV49 ) )
| ~ ( below @ SV49 @ SY207 @ SY209 )
| ( ( join @ SV49 @ SY207 @ SY209 )
= SY209 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(446,plain,
( ( ~ ( latt_str @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(447,plain,
( ( ~ ( strict_latt_str @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(448,plain,
! [SV50: $i,SV75: $i] :
( ( ~ ( element @ SV75 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ~ ( ~ ! [SY235: $i] :
( ~ ( element @ SY235 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ( ( join @ ( boole_lattice @ SV50 ) @ SV75 @ SY235 )
= ( set_union2 @ SV75 @ SY235 ) ) )
| ~ ! [SY236: $i] :
( ~ ( element @ SY236 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ( ( meet @ ( boole_lattice @ SV50 ) @ SV75 @ SY236 )
= ( set_intersection2 @ SV75 @ SY236 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(449,plain,
( ( ~ ( one_sorted_str @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(450,plain,
( ( ~ ~ ( empty_carrier @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(451,plain,
! [SV1: $i] :
( ( ( latt_str @ SV1 )
= $false )
| ( ( ~ ( strict_latt_str @ SV1 )
| ( SV1
= ( latt_str_of @ ( the_carrier @ SV1 ) @ ( the_L_join @ SV1 ) @ ( the_L_meet @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(452,plain,
! [SV51: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV51 ) )
= $true )
| ( ( ~ ( in @ SV51 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(453,plain,
! [SV52: $i,SV3: $i,SV76: $i] :
( ( ~ ( element @ SV76 @ ( powerset @ ( cartesian_product2 @ SV3 @ SV52 ) ) )
| ( relation @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(454,plain,
! [SV7: $i] :
( ( ( ~ ( function @ SV7 ) )
= $true )
| ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( ! [SY147: $i,SY148: $i] :
( ( apply_binary @ SV7 @ SY147 @ SY148 )
= ( apply @ SV7 @ ( ordered_pair @ SY147 @ SY148 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(455,plain,
! [SV8: $i] :
( ( ( empty_carrier @ SV8 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV8 ) )
= $true )
| ( ( ! [SY149: $i] :
( ~ ( element @ SY149 @ ( the_carrier @ SV8 ) )
| ! [SY150: $i] :
( ~ ( element @ SY150 @ ( the_carrier @ SV8 ) )
| ( ( join @ SV8 @ SY149 @ SY150 )
= ( apply_binary_as_element @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_L_join @ SV8 ) @ SY149 @ SY150 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(456,plain,
! [SV9: $i] :
( ( ( empty_carrier @ SV9 )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV9 ) )
= $true )
| ( ( ! [SY151: $i] :
( ~ ( element @ SY151 @ ( the_carrier @ SV9 ) )
| ! [SY152: $i] :
( ~ ( element @ SY152 @ ( the_carrier @ SV9 ) )
| ( ( meet @ SV9 @ SY151 @ SY152 )
= ( apply_binary_as_element @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_L_meet @ SV9 ) @ SY151 @ SY152 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(457,plain,
! [SV77: $i,SV57: $i,SV11: $i] :
( ( ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 )
| ~ ( element @ SV57 @ ( the_carrier @ SV11 ) )
| ~ ( element @ SV77 @ ( the_carrier @ SV11 ) )
| ( element @ ( join @ SV11 @ SV57 @ SV77 ) @ ( the_carrier @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(458,plain,
! [SV78: $i,SV58: $i,SV12: $i] :
( ( ! [SY237: $i,SY238: $i,SY239: $i] :
( ( empty @ SV12 )
| ( empty @ SV58 )
| ~ ( function @ SY237 )
| ~ ( quasi_total @ SY237 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
| ~ ( relation_of2 @ SY237 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
| ~ ( element @ SY238 @ SV12 )
| ~ ( element @ SY239 @ SV58 )
| ( element @ ( apply_binary_as_element @ SV12 @ SV58 @ SV78 @ SY237 @ SY238 @ SY239 ) @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(459,plain,
! [SV79: $i,SV59: $i,SV13: $i] :
( ( ( empty_carrier @ SV13 )
| ~ ( meet_semilatt_str @ SV13 )
| ~ ( element @ SV59 @ ( the_carrier @ SV13 ) )
| ~ ( element @ SV79 @ ( the_carrier @ SV13 ) )
| ( element @ ( meet @ SV13 @ SV59 @ SV79 ) @ ( the_carrier @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(460,plain,
! [SV14: $i] :
( ( ( meet_semilatt_str @ SV14 )
= $false )
| ( ( one_sorted_str @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(461,plain,
! [SV15: $i] :
( ( ( join_semilatt_str @ SV15 )
= $false )
| ( ( one_sorted_str @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(462,plain,
! [SV60: $i,SV16: $i,SV80: $i] :
( ( ~ ( relation_of2_as_subset @ SV80 @ SV16 @ SV60 )
| ( element @ SV80 @ ( powerset @ ( cartesian_product2 @ SV16 @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(463,plain,
! [SV20: $i] :
( ( ( empty_carrier @ SV20 )
= $true )
| ( ( ~ ( one_sorted_str @ SV20 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(464,plain,
! [SV81: $i,SV23: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV23 @ SV81 ) ) )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(465,plain,
! [SV63: $i,SV24: $i] :
( ( empty @ ( unordered_pair @ SV24 @ SV63 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(466,plain,
! [SV25: $i,SV82: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV82 @ SV25 ) ) )
= $true )
| ( ( empty @ SV25 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(467,plain,
! [SV64: $i,SV26: $i] :
( ( ( ( empty @ SV26 )
| ( empty @ SV64 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV26 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(468,plain,
! [SV83: $i,SV65: $i,SV29: $i] :
( ( ! [SY240: $i,SY241: $i,SY242: $i] :
( ( empty @ SV29 )
| ( empty @ SV65 )
| ~ ( function @ SY240 )
| ~ ( quasi_total @ SY240 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
| ~ ( relation_of2 @ SY240 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
| ~ ( element @ SY241 @ SV29 )
| ~ ( element @ SY242 @ SV65 )
| ( ( apply_binary_as_element @ SV29 @ SV65 @ SV83 @ SY240 @ SY241 @ SY242 )
= ( apply_binary @ SY240 @ SY241 @ SY242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(469,plain,
! [SV66: $i,SV31: $i] :
( ( ( ~ ( subset @ SV31 @ SV66 ) )
= $true )
| ( ( ( set_union2 @ SV31 @ SV66 )
= SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(470,plain,
! [SV67: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV67 ) )
= $true )
| ( ( element @ SV33 @ SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(471,plain,
! [SV68: $i,SV35: $i] :
( ( ( ~ ( element @ SV35 @ SV68 ) )
= $true )
| ( ( ( empty @ SV68 )
| ( in @ SV35 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(472,plain,
! [SV36: $i,SV84: $i,SV69: $i] :
( ( ~ ( element @ SV69 @ ( powerset @ SV84 ) )
| ~ ( in @ SV36 @ SV69 )
| ( element @ SV36 @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(473,plain,
! [SV37: $i,SV85: $i,SV70: $i] :
( ( ~ ( element @ SV70 @ ( powerset @ SV85 ) )
| ~ ( in @ SV37 @ SV70 )
| ~ ( empty @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(474,plain,
! [SV38: $i] :
( ( ( empty @ SV38 )
= $false )
| ( ( SV38 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(475,plain,
! [SV39: $i,SV71: $i] :
( ( ( ~ ( empty @ SV71 ) )
= $true )
| ( ( ~ ( in @ SV39 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(476,plain,
! [SV73: $i,SV41: $i] :
( ( ( ( SV41 = SV73 )
| ~ ( empty @ SV41 ) )
= $true )
| ( ( ~ ( empty @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(477,plain,
! [SV42: $i] :
( ( ( empty_carrier @ SV42 )
= $true )
| ( ( ~ ( one_sorted_str @ SV42 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK5_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(478,plain,
! [SV43: $i] :
( ( ~ ! [SY186: $i,SY187: $i] :
( ~ ( relation_of2 @ SY187 @ SV43 @ SY186 )
| ( relation_of2_as_subset @ SY187 @ SV43 @ SY186 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(479,plain,
! [SV43: $i] :
( ( ~ ! [SY188: $i,SY189: $i] :
( ~ ( relation_of2_as_subset @ SY189 @ SV43 @ SY188 )
| ( relation_of2 @ SY189 @ SV43 @ SY188 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(480,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( function @ ( the_L_join @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( quasi_total @ ( the_L_join @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[424]) ).
thf(481,plain,
( ( ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( relation_of2_as_subset @ ( the_L_join @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[425]) ).
thf(482,plain,
! [SV86: $i,SV44: $i,SV74: $i] :
( ( ~ ( function @ SV74 )
| ~ ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ~ ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ~ ( function @ SV86 )
| ~ ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ~ ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ! [SY243: $i] :
~ ( ~ ~ ( ~ ( ! [SY244: $i,SY245: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY244 @ SY245 ) )
| ( SV44 = SY243 ) )
| ~ ! [SY246: $i] :
( ! [SY247: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY246 @ SY247 ) )
| ( SV74 = SY246 ) ) )
| ~ ! [SY248: $i,SY249: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY248 @ SY249 ) )
| ( SV86 = SY249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(483,plain,
( ( ! [SX0: $i] :
~ ( empty_carrier @ ( boole_lattice @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(484,plain,
( ( ! [SX0: $i] : ( strict_latt_str @ ( boole_lattice @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(485,plain,
! [SV45: $i] :
( ( ~ ! [SY199: $i,SY200: $i] :
( ~ ( function @ SY199 )
| ~ ( quasi_total @ SY199 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY199 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SY200 )
| ~ ( quasi_total @ SY200 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY200 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ( latt_str @ ( latt_str_of @ SV45 @ SY199 @ SY200 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(486,plain,
! [SV45: $i] :
( ( ~ ! [SY201: $i,SY202: $i] :
( ~ ( function @ SY201 )
| ~ ( quasi_total @ SY201 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY201 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SY202 )
| ~ ( quasi_total @ SY202 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY202 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ( strict_latt_str @ ( latt_str_of @ SV45 @ SY201 @ SY202 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(487,plain,
( ( ~ ( ~ ( latt_str @ sK4_A )
| ~ ~ ( empty_carrier @ sK4_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(488,plain,
( ( strict_latt_str @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(489,plain,
( ( ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( join_semilatt_str @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(490,plain,
( ( ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( meet_semilatt_str @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(491,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(492,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(493,plain,
! [SV46: $i] :
( ( ( ~ ( element @ ( sK11_B @ SV46 ) @ ( powerset @ SV46 ) )
| ~ ~ ( empty @ ( sK11_B @ SV46 ) ) )
= $false )
| ( ( empty @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(494,plain,
! [SV47: $i] :
( ( ~ ! [SY203: $i,SY204: $i] :
( ( empty @ SV47 )
| ~ ( function @ SY203 )
| ~ ( quasi_total @ SY203 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY203 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SY204 )
| ~ ( quasi_total @ SY204 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY204 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SY203 @ SY204 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(495,plain,
! [SV47: $i] :
( ( ~ ! [SY205: $i,SY206: $i] :
( ( empty @ SV47 )
| ~ ( function @ SY205 )
| ~ ( quasi_total @ SY205 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY205 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SY206 )
| ~ ( quasi_total @ SY206 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY206 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ( strict_latt_str @ ( latt_str_of @ SV47 @ SY205 @ SY206 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(496,plain,
( ( element @ sK3_SY140 @ ( the_carrier @ ( boole_lattice @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(497,plain,
( ( ~ ( ~ ( ~ ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ~ ( subset @ sK2_SY138 @ sK3_SY140 ) )
| ~ ( ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ( subset @ sK2_SY138 @ sK3_SY140 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(498,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( function @ ( the_L_meet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( quasi_total @ ( the_L_meet @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(499,plain,
( ( ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( relation_of2_as_subset @ ( the_L_meet @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(500,plain,
( ( ! [SX0: $i] : ( latt_str @ ( boole_lattice @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(501,plain,
( ( ! [SX0: $i] : ( strict_latt_str @ ( boole_lattice @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(502,plain,
! [SV48: $i] :
( ( ~ ( element @ ( sK9_B @ SV48 ) @ ( powerset @ SV48 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[444]) ).
thf(503,plain,
! [SV48: $i] :
( ( ~ ( empty @ ( sK9_B @ SV48 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[444]) ).
thf(504,plain,
! [SV49: $i] :
( ( ( empty_carrier @ SV49 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV49 ) )
= $true )
| ( ( ! [SY207: $i] :
( ~ ( element @ SY207 @ ( the_carrier @ SV49 ) )
| ~ ( ~ ! [SY208: $i] :
( ~ ( element @ SY208 @ ( the_carrier @ SV49 ) )
| ( ( join @ SV49 @ SY207 @ SY208 )
!= SY208 )
| ( below @ SV49 @ SY207 @ SY208 ) )
| ~ ! [SY209: $i] :
( ~ ( element @ SY209 @ ( the_carrier @ SV49 ) )
| ~ ( below @ SV49 @ SY207 @ SY209 )
| ( ( join @ SV49 @ SY207 @ SY209 )
= SY209 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(505,plain,
( ( latt_str @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(506,plain,
( ( strict_latt_str @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(507,plain,
! [SV50: $i,SV75: $i] :
( ( ( ~ ( element @ SV75 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY235: $i] :
( ~ ( element @ SY235 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ( ( join @ ( boole_lattice @ SV50 ) @ SV75 @ SY235 )
= ( set_union2 @ SV75 @ SY235 ) ) )
| ~ ! [SY236: $i] :
( ~ ( element @ SY236 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ( ( meet @ ( boole_lattice @ SV50 ) @ SV75 @ SY236 )
= ( set_intersection2 @ SV75 @ SY236 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(508,plain,
( ( one_sorted_str @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(509,plain,
( ( ~ ( empty_carrier @ sK6_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(510,plain,
! [SV1: $i] :
( ( ( ~ ( strict_latt_str @ SV1 ) )
= $true )
| ( ( SV1
= ( latt_str_of @ ( the_carrier @ SV1 ) @ ( the_L_join @ SV1 ) @ ( the_L_meet @ SV1 ) ) )
= $true )
| ( ( latt_str @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(511,plain,
! [SV51: $i,SV2: $i] :
( ( ( in @ SV2 @ SV51 )
= $false )
| ( ( ~ ( in @ SV51 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(512,plain,
! [SV52: $i,SV3: $i,SV76: $i] :
( ( ( ~ ( element @ SV76 @ ( powerset @ ( cartesian_product2 @ SV3 @ SV52 ) ) ) )
= $true )
| ( ( relation @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(513,plain,
! [SV7: $i] :
( ( ( function @ SV7 )
= $false )
| ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( ! [SY147: $i,SY148: $i] :
( ( apply_binary @ SV7 @ SY147 @ SY148 )
= ( apply @ SV7 @ ( ordered_pair @ SY147 @ SY148 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(514,plain,
! [SV8: $i] :
( ( ( join_semilatt_str @ SV8 )
= $false )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( ! [SY149: $i] :
( ~ ( element @ SY149 @ ( the_carrier @ SV8 ) )
| ! [SY150: $i] :
( ~ ( element @ SY150 @ ( the_carrier @ SV8 ) )
| ( ( join @ SV8 @ SY149 @ SY150 )
= ( apply_binary_as_element @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_L_join @ SV8 ) @ SY149 @ SY150 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(515,plain,
! [SV9: $i] :
( ( ( meet_semilatt_str @ SV9 )
= $false )
| ( ( empty_carrier @ SV9 )
= $true )
| ( ( ! [SY151: $i] :
( ~ ( element @ SY151 @ ( the_carrier @ SV9 ) )
| ! [SY152: $i] :
( ~ ( element @ SY152 @ ( the_carrier @ SV9 ) )
| ( ( meet @ SV9 @ SY151 @ SY152 )
= ( apply_binary_as_element @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_L_meet @ SV9 ) @ SY151 @ SY152 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(516,plain,
! [SV77: $i,SV57: $i,SV11: $i] :
( ( ( ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 )
| ~ ( element @ SV57 @ ( the_carrier @ SV11 ) )
| ~ ( element @ SV77 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV57 @ SV77 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(517,plain,
! [SV78: $i,SV87: $i,SV58: $i,SV12: $i] :
( ( ! [SY250: $i,SY251: $i] :
( ( empty @ SV12 )
| ( empty @ SV58 )
| ~ ( function @ SV87 )
| ~ ( quasi_total @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
| ~ ( relation_of2 @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
| ~ ( element @ SY250 @ SV12 )
| ~ ( element @ SY251 @ SV58 )
| ( element @ ( apply_binary_as_element @ SV12 @ SV58 @ SV78 @ SV87 @ SY250 @ SY251 ) @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(518,plain,
! [SV79: $i,SV59: $i,SV13: $i] :
( ( ( ( empty_carrier @ SV13 )
| ~ ( meet_semilatt_str @ SV13 )
| ~ ( element @ SV59 @ ( the_carrier @ SV13 ) )
| ~ ( element @ SV79 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( element @ ( meet @ SV13 @ SV59 @ SV79 ) @ ( the_carrier @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(519,plain,
! [SV60: $i,SV16: $i,SV80: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV80 @ SV16 @ SV60 ) )
= $true )
| ( ( element @ SV80 @ ( powerset @ ( cartesian_product2 @ SV16 @ SV60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(520,plain,
! [SV20: $i] :
( ( ( one_sorted_str @ SV20 )
= $false )
| ( ( empty_carrier @ SV20 )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(521,plain,
! [SV81: $i,SV23: $i] :
( ( ( empty @ ( set_union2 @ SV23 @ SV81 ) )
= $false )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(522,plain,
! [SV25: $i,SV82: $i] :
( ( ( empty @ ( set_union2 @ SV82 @ SV25 ) )
= $false )
| ( ( empty @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(523,plain,
! [SV64: $i,SV26: $i] :
( ( ( empty @ SV26 )
= $true )
| ( ( empty @ SV64 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV26 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(524,plain,
! [SV83: $i,SV88: $i,SV65: $i,SV29: $i] :
( ( ! [SY252: $i,SY253: $i] :
( ( empty @ SV29 )
| ( empty @ SV65 )
| ~ ( function @ SV88 )
| ~ ( quasi_total @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
| ~ ( relation_of2 @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
| ~ ( element @ SY252 @ SV29 )
| ~ ( element @ SY253 @ SV65 )
| ( ( apply_binary_as_element @ SV29 @ SV65 @ SV83 @ SV88 @ SY252 @ SY253 )
= ( apply_binary @ SV88 @ SY252 @ SY253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(525,plain,
! [SV66: $i,SV31: $i] :
( ( ( subset @ SV31 @ SV66 )
= $false )
| ( ( ( set_union2 @ SV31 @ SV66 )
= SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(526,plain,
! [SV67: $i,SV33: $i] :
( ( ( in @ SV33 @ SV67 )
= $false )
| ( ( element @ SV33 @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(527,plain,
! [SV68: $i,SV35: $i] :
( ( ( element @ SV35 @ SV68 )
= $false )
| ( ( ( empty @ SV68 )
| ( in @ SV35 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(528,plain,
! [SV36: $i,SV84: $i,SV69: $i] :
( ( ( ~ ( element @ SV69 @ ( powerset @ SV84 ) )
| ~ ( in @ SV36 @ SV69 ) )
= $true )
| ( ( element @ SV36 @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(529,plain,
! [SV37: $i,SV85: $i,SV70: $i] :
( ( ( ~ ( element @ SV70 @ ( powerset @ SV85 ) )
| ~ ( in @ SV37 @ SV70 ) )
= $true )
| ( ( ~ ( empty @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(530,plain,
! [SV39: $i,SV71: $i] :
( ( ( empty @ SV71 )
= $false )
| ( ( ~ ( in @ SV39 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(531,plain,
! [SV73: $i,SV41: $i] :
( ( ( SV41 = SV73 )
= $true )
| ( ( ~ ( empty @ SV41 ) )
= $true )
| ( ( ~ ( empty @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(532,plain,
! [SV42: $i] :
( ( ( one_sorted_str @ SV42 )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK5_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(533,plain,
! [SV43: $i] :
( ( ! [SY186: $i,SY187: $i] :
( ~ ( relation_of2 @ SY187 @ SV43 @ SY186 )
| ( relation_of2_as_subset @ SY187 @ SV43 @ SY186 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(534,plain,
! [SV43: $i] :
( ( ! [SY188: $i,SY189: $i] :
( ~ ( relation_of2_as_subset @ SY189 @ SV43 @ SY188 )
| ( relation_of2 @ SY189 @ SV43 @ SY188 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(535,plain,
( ( ~ ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( function @ ( the_L_join @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( quasi_total @ ( the_L_join @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(536,plain,
! [SV89: $i] :
( ( ~ ( join_semilatt_str @ SV89 )
| ( relation_of2_as_subset @ ( the_L_join @ SV89 ) @ ( cartesian_product2 @ ( the_carrier @ SV89 ) @ ( the_carrier @ SV89 ) ) @ ( the_carrier @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(537,plain,
! [SV86: $i,SV44: $i,SV74: $i] :
( ( ( ~ ( function @ SV74 )
| ~ ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ~ ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ~ ( function @ SV86 )
| ~ ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ~ ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ! [SY243: $i] :
~ ( ~ ~ ( ~ ( ! [SY244: $i,SY245: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY244 @ SY245 ) )
| ( SV44 = SY243 ) )
| ~ ! [SY246: $i] :
( ! [SY247: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY246 @ SY247 ) )
| ( SV74 = SY246 ) ) )
| ~ ! [SY248: $i,SY249: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY248 @ SY249 ) )
| ( SV86 = SY249 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(538,plain,
! [SV90: $i] :
( ( ~ ( empty_carrier @ ( boole_lattice @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(539,plain,
! [SV91: $i] :
( ( strict_latt_str @ ( boole_lattice @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(540,plain,
! [SV45: $i] :
( ( ! [SY199: $i,SY200: $i] :
( ~ ( function @ SY199 )
| ~ ( quasi_total @ SY199 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY199 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SY200 )
| ~ ( quasi_total @ SY200 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY200 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ( latt_str @ ( latt_str_of @ SV45 @ SY199 @ SY200 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[485]) ).
thf(541,plain,
! [SV45: $i] :
( ( ! [SY201: $i,SY202: $i] :
( ~ ( function @ SY201 )
| ~ ( quasi_total @ SY201 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY201 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SY202 )
| ~ ( quasi_total @ SY202 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY202 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ( strict_latt_str @ ( latt_str_of @ SV45 @ SY201 @ SY202 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(542,plain,
( ( ~ ( latt_str @ sK4_A )
| ~ ~ ( empty_carrier @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(543,plain,
! [SV92: $i] :
( ( ~ ( latt_str @ SV92 )
| ( join_semilatt_str @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(544,plain,
! [SV93: $i] :
( ( ~ ( latt_str @ SV93 )
| ( meet_semilatt_str @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(545,plain,
! [SV94: $i] :
( ( ! [SY254: $i] :
( ~ ( element @ SV94 @ ( powerset @ SY254 ) )
| ( subset @ SV94 @ SY254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(546,plain,
! [SV95: $i] :
( ( ! [SY255: $i] :
( ~ ( subset @ SV95 @ SY255 )
| ( element @ SV95 @ ( powerset @ SY255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(547,plain,
! [SV46: $i] :
( ( ( ~ ( element @ ( sK11_B @ SV46 ) @ ( powerset @ SV46 ) ) )
= $false )
| ( ( empty @ SV46 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(548,plain,
! [SV46: $i] :
( ( ( ~ ~ ( empty @ ( sK11_B @ SV46 ) ) )
= $false )
| ( ( empty @ SV46 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(549,plain,
! [SV47: $i] :
( ( ! [SY203: $i,SY204: $i] :
( ( empty @ SV47 )
| ~ ( function @ SY203 )
| ~ ( quasi_total @ SY203 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY203 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SY204 )
| ~ ( quasi_total @ SY204 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY204 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SY203 @ SY204 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(550,plain,
! [SV47: $i] :
( ( ! [SY205: $i,SY206: $i] :
( ( empty @ SV47 )
| ~ ( function @ SY205 )
| ~ ( quasi_total @ SY205 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY205 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SY206 )
| ~ ( quasi_total @ SY206 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY206 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ( strict_latt_str @ ( latt_str_of @ SV47 @ SY205 @ SY206 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(551,plain,
( ( ~ ( ~ ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ~ ( subset @ sK2_SY138 @ sK3_SY140 ) )
| ~ ( ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ( subset @ sK2_SY138 @ sK3_SY140 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(552,plain,
( ( ~ ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( function @ ( the_L_meet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( quasi_total @ ( the_L_meet @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(553,plain,
! [SV96: $i] :
( ( ~ ( meet_semilatt_str @ SV96 )
| ( relation_of2_as_subset @ ( the_L_meet @ SV96 ) @ ( cartesian_product2 @ ( the_carrier @ SV96 ) @ ( the_carrier @ SV96 ) ) @ ( the_carrier @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(554,plain,
! [SV97: $i] :
( ( latt_str @ ( boole_lattice @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(555,plain,
! [SV98: $i] :
( ( strict_latt_str @ ( boole_lattice @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(556,plain,
! [SV48: $i] :
( ( element @ ( sK9_B @ SV48 ) @ ( powerset @ SV48 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(557,plain,
! [SV48: $i] :
( ( empty @ ( sK9_B @ SV48 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[503]) ).
thf(558,plain,
! [SV49: $i] :
( ( ( join_semilatt_str @ SV49 )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( ! [SY207: $i] :
( ~ ( element @ SY207 @ ( the_carrier @ SV49 ) )
| ~ ( ~ ! [SY208: $i] :
( ~ ( element @ SY208 @ ( the_carrier @ SV49 ) )
| ( ( join @ SV49 @ SY207 @ SY208 )
!= SY208 )
| ( below @ SV49 @ SY207 @ SY208 ) )
| ~ ! [SY209: $i] :
( ~ ( element @ SY209 @ ( the_carrier @ SV49 ) )
| ~ ( below @ SV49 @ SY207 @ SY209 )
| ( ( join @ SV49 @ SY207 @ SY209 )
= SY209 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(559,plain,
! [SV50: $i,SV75: $i] :
( ( ( element @ SV75 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY235: $i] :
( ~ ( element @ SY235 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ( ( join @ ( boole_lattice @ SV50 ) @ SV75 @ SY235 )
= ( set_union2 @ SV75 @ SY235 ) ) )
| ~ ! [SY236: $i] :
( ~ ( element @ SY236 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ( ( meet @ ( boole_lattice @ SV50 ) @ SV75 @ SY236 )
= ( set_intersection2 @ SV75 @ SY236 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(560,plain,
( ( empty_carrier @ sK6_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(561,plain,
! [SV1: $i] :
( ( ( strict_latt_str @ SV1 )
= $false )
| ( ( SV1
= ( latt_str_of @ ( the_carrier @ SV1 ) @ ( the_L_join @ SV1 ) @ ( the_L_meet @ SV1 ) ) )
= $true )
| ( ( latt_str @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(562,plain,
! [SV2: $i,SV51: $i] :
( ( ( in @ SV51 @ SV2 )
= $false )
| ( ( in @ SV2 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(563,plain,
! [SV52: $i,SV3: $i,SV76: $i] :
( ( ( element @ SV76 @ ( powerset @ ( cartesian_product2 @ SV3 @ SV52 ) ) )
= $false )
| ( ( relation @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(564,plain,
! [SV7: $i] :
( ( ( relation @ SV7 )
= $false )
| ( ( function @ SV7 )
= $false )
| ( ( ! [SY147: $i,SY148: $i] :
( ( apply_binary @ SV7 @ SY147 @ SY148 )
= ( apply @ SV7 @ ( ordered_pair @ SY147 @ SY148 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(565,plain,
! [SV8: $i,SV99: $i] :
( ( ( ~ ( element @ SV99 @ ( the_carrier @ SV8 ) )
| ! [SY256: $i] :
( ~ ( element @ SY256 @ ( the_carrier @ SV8 ) )
| ( ( join @ SV8 @ SV99 @ SY256 )
= ( apply_binary_as_element @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_L_join @ SV8 ) @ SV99 @ SY256 ) ) ) )
= $true )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( join_semilatt_str @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(566,plain,
! [SV9: $i,SV100: $i] :
( ( ( ~ ( element @ SV100 @ ( the_carrier @ SV9 ) )
| ! [SY257: $i] :
( ~ ( element @ SY257 @ ( the_carrier @ SV9 ) )
| ( ( meet @ SV9 @ SV100 @ SY257 )
= ( apply_binary_as_element @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_L_meet @ SV9 ) @ SV100 @ SY257 ) ) ) )
= $true )
| ( ( empty_carrier @ SV9 )
= $true )
| ( ( meet_semilatt_str @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(567,plain,
! [SV77: $i,SV57: $i,SV11: $i] :
( ( ( ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 )
| ~ ( element @ SV57 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV77 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV57 @ SV77 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(568,plain,
! [SV101: $i,SV78: $i,SV87: $i,SV58: $i,SV12: $i] :
( ( ! [SY258: $i] :
( ( empty @ SV12 )
| ( empty @ SV58 )
| ~ ( function @ SV87 )
| ~ ( quasi_total @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
| ~ ( relation_of2 @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
| ~ ( element @ SV101 @ SV12 )
| ~ ( element @ SY258 @ SV58 )
| ( element @ ( apply_binary_as_element @ SV12 @ SV58 @ SV78 @ SV87 @ SV101 @ SY258 ) @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(569,plain,
! [SV79: $i,SV59: $i,SV13: $i] :
( ( ( ( empty_carrier @ SV13 )
| ~ ( meet_semilatt_str @ SV13 )
| ~ ( element @ SV59 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( ~ ( element @ SV79 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( element @ ( meet @ SV13 @ SV59 @ SV79 ) @ ( the_carrier @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[518]) ).
thf(570,plain,
! [SV60: $i,SV16: $i,SV80: $i] :
( ( ( relation_of2_as_subset @ SV80 @ SV16 @ SV60 )
= $false )
| ( ( element @ SV80 @ ( powerset @ ( cartesian_product2 @ SV16 @ SV60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(571,plain,
! [SV20: $i] :
( ( ( empty @ ( the_carrier @ SV20 ) )
= $false )
| ( ( empty_carrier @ SV20 )
= $true )
| ( ( one_sorted_str @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(572,plain,
! [SV64: $i,SV26: $i] :
( ( ( empty @ ( cartesian_product2 @ SV26 @ SV64 ) )
= $false )
| ( ( empty @ SV64 )
= $true )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(573,plain,
! [SV102: $i,SV83: $i,SV88: $i,SV65: $i,SV29: $i] :
( ( ! [SY259: $i] :
( ( empty @ SV29 )
| ( empty @ SV65 )
| ~ ( function @ SV88 )
| ~ ( quasi_total @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
| ~ ( relation_of2 @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
| ~ ( element @ SV102 @ SV29 )
| ~ ( element @ SY259 @ SV65 )
| ( ( apply_binary_as_element @ SV29 @ SV65 @ SV83 @ SV88 @ SV102 @ SY259 )
= ( apply_binary @ SV88 @ SV102 @ SY259 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(574,plain,
! [SV35: $i,SV68: $i] :
( ( ( empty @ SV68 )
= $true )
| ( ( in @ SV35 @ SV68 )
= $true )
| ( ( element @ SV35 @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(575,plain,
! [SV36: $i,SV84: $i,SV69: $i] :
( ( ( ~ ( element @ SV69 @ ( powerset @ SV84 ) ) )
= $true )
| ( ( ~ ( in @ SV36 @ SV69 ) )
= $true )
| ( ( element @ SV36 @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[528]) ).
thf(576,plain,
! [SV37: $i,SV85: $i,SV70: $i] :
( ( ( ~ ( element @ SV70 @ ( powerset @ SV85 ) ) )
= $true )
| ( ( ~ ( in @ SV37 @ SV70 ) )
= $true )
| ( ( ~ ( empty @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(577,plain,
! [SV71: $i,SV39: $i] :
( ( ( in @ SV39 @ SV71 )
= $false )
| ( ( empty @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(578,plain,
! [SV73: $i,SV41: $i] :
( ( ( empty @ SV41 )
= $false )
| ( ( SV41 = SV73 )
= $true )
| ( ( ~ ( empty @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(579,plain,
! [SV42: $i] :
( ( ( ~ ( element @ ( sK5_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) )
| ~ ~ ( empty @ ( sK5_B @ SV42 ) ) )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( one_sorted_str @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(580,plain,
! [SV103: $i,SV43: $i] :
( ( ! [SY260: $i] :
( ~ ( relation_of2 @ SY260 @ SV43 @ SV103 )
| ( relation_of2_as_subset @ SY260 @ SV43 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(581,plain,
! [SV104: $i,SV43: $i] :
( ( ! [SY261: $i] :
( ~ ( relation_of2_as_subset @ SY261 @ SV43 @ SV104 )
| ( relation_of2 @ SY261 @ SV43 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(582,plain,
( ( ~ ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( function @ ( the_L_join @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(583,plain,
( ( ~ ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( quasi_total @ ( the_L_join @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(584,plain,
! [SV89: $i] :
( ( ( ~ ( join_semilatt_str @ SV89 ) )
= $true )
| ( ( relation_of2_as_subset @ ( the_L_join @ SV89 ) @ ( cartesian_product2 @ ( the_carrier @ SV89 ) @ ( the_carrier @ SV89 ) ) @ ( the_carrier @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(585,plain,
! [SV86: $i,SV44: $i,SV74: $i] :
( ( ( ~ ( function @ SV74 )
| ~ ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ~ ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ~ ( function @ SV86 )
| ~ ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ! [SY243: $i] :
~ ( ~ ~ ( ~ ( ! [SY244: $i,SY245: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY244 @ SY245 ) )
| ( SV44 = SY243 ) )
| ~ ! [SY246: $i] :
( ! [SY247: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY246 @ SY247 ) )
| ( SV74 = SY246 ) ) )
| ~ ! [SY248: $i,SY249: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY248 @ SY249 ) )
| ( SV86 = SY249 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[537]) ).
thf(586,plain,
! [SV90: $i] :
( ( empty_carrier @ ( boole_lattice @ SV90 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(587,plain,
! [SV45: $i,SV105: $i] :
( ( ! [SY262: $i] :
( ~ ( function @ SV105 )
| ~ ( quasi_total @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SY262 )
| ~ ( quasi_total @ SY262 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY262 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ( latt_str @ ( latt_str_of @ SV45 @ SV105 @ SY262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(588,plain,
! [SV45: $i,SV106: $i] :
( ( ! [SY263: $i] :
( ~ ( function @ SV106 )
| ~ ( quasi_total @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SY263 )
| ~ ( quasi_total @ SY263 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SY263 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ( strict_latt_str @ ( latt_str_of @ SV45 @ SV106 @ SY263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(589,plain,
( ( ~ ( latt_str @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(590,plain,
( ( ~ ~ ( empty_carrier @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(591,plain,
! [SV92: $i] :
( ( ( ~ ( latt_str @ SV92 ) )
= $true )
| ( ( join_semilatt_str @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(592,plain,
! [SV93: $i] :
( ( ( ~ ( latt_str @ SV93 ) )
= $true )
| ( ( meet_semilatt_str @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(593,plain,
! [SV107: $i,SV94: $i] :
( ( ~ ( element @ SV94 @ ( powerset @ SV107 ) )
| ( subset @ SV94 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(594,plain,
! [SV108: $i,SV95: $i] :
( ( ~ ( subset @ SV95 @ SV108 )
| ( element @ SV95 @ ( powerset @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(595,plain,
! [SV46: $i] :
( ( ( element @ ( sK11_B @ SV46 ) @ ( powerset @ SV46 ) )
= $true )
| ( ( empty @ SV46 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(596,plain,
! [SV46: $i] :
( ( ( ~ ( empty @ ( sK11_B @ SV46 ) ) )
= $true )
| ( ( empty @ SV46 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(597,plain,
! [SV109: $i,SV47: $i] :
( ( ! [SY264: $i] :
( ( empty @ SV47 )
| ~ ( function @ SV109 )
| ~ ( quasi_total @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SY264 )
| ~ ( quasi_total @ SY264 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY264 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SV109 @ SY264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(598,plain,
! [SV110: $i,SV47: $i] :
( ( ! [SY265: $i] :
( ( empty @ SV47 )
| ~ ( function @ SV110 )
| ~ ( quasi_total @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SY265 )
| ~ ( quasi_total @ SY265 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SY265 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ( strict_latt_str @ ( latt_str_of @ SV47 @ SV110 @ SY265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(599,plain,
( ( ~ ( ~ ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ~ ( subset @ sK2_SY138 @ sK3_SY140 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[551]) ).
thf(600,plain,
( ( ~ ( ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ( subset @ sK2_SY138 @ sK3_SY140 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[551]) ).
thf(601,plain,
( ( ~ ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( function @ ( the_L_meet @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(602,plain,
( ( ~ ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( quasi_total @ ( the_L_meet @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(603,plain,
! [SV96: $i] :
( ( ( ~ ( meet_semilatt_str @ SV96 ) )
= $true )
| ( ( relation_of2_as_subset @ ( the_L_meet @ SV96 ) @ ( cartesian_product2 @ ( the_carrier @ SV96 ) @ ( the_carrier @ SV96 ) ) @ ( the_carrier @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(604,plain,
! [SV49: $i,SV111: $i] :
( ( ( ~ ( element @ SV111 @ ( the_carrier @ SV49 ) )
| ~ ( ~ ! [SY266: $i] :
( ~ ( element @ SY266 @ ( the_carrier @ SV49 ) )
| ( ( join @ SV49 @ SV111 @ SY266 )
!= SY266 )
| ( below @ SV49 @ SV111 @ SY266 ) )
| ~ ! [SY267: $i] :
( ~ ( element @ SY267 @ ( the_carrier @ SV49 ) )
| ~ ( below @ SV49 @ SV111 @ SY267 )
| ( ( join @ SV49 @ SV111 @ SY267 )
= SY267 ) ) ) )
= $true )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(605,plain,
! [SV75: $i,SV50: $i] :
( ( ( ~ ! [SY235: $i] :
( ~ ( element @ SY235 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ( ( join @ ( boole_lattice @ SV50 ) @ SV75 @ SY235 )
= ( set_union2 @ SV75 @ SY235 ) ) )
| ~ ! [SY236: $i] :
( ~ ( element @ SY236 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ( ( meet @ ( boole_lattice @ SV50 ) @ SV75 @ SY236 )
= ( set_intersection2 @ SV75 @ SY236 ) ) ) )
= $false )
| ( ( element @ SV75 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(606,plain,
! [SV112: $i,SV7: $i] :
( ( ( ! [SY268: $i] :
( ( apply_binary @ SV7 @ SV112 @ SY268 )
= ( apply @ SV7 @ ( ordered_pair @ SV112 @ SY268 ) ) ) )
= $true )
| ( ( function @ SV7 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(607,plain,
! [SV8: $i,SV99: $i] :
( ( ( ~ ( element @ SV99 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ! [SY256: $i] :
( ~ ( element @ SY256 @ ( the_carrier @ SV8 ) )
| ( ( join @ SV8 @ SV99 @ SY256 )
= ( apply_binary_as_element @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_L_join @ SV8 ) @ SV99 @ SY256 ) ) ) )
= $true )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( join_semilatt_str @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(608,plain,
! [SV9: $i,SV100: $i] :
( ( ( ~ ( element @ SV100 @ ( the_carrier @ SV9 ) ) )
= $true )
| ( ( ! [SY257: $i] :
( ~ ( element @ SY257 @ ( the_carrier @ SV9 ) )
| ( ( meet @ SV9 @ SV100 @ SY257 )
= ( apply_binary_as_element @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_L_meet @ SV9 ) @ SV100 @ SY257 ) ) ) )
= $true )
| ( ( empty_carrier @ SV9 )
= $true )
| ( ( meet_semilatt_str @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(609,plain,
! [SV77: $i,SV57: $i,SV11: $i] :
( ( ( ( empty_carrier @ SV11 )
| ~ ( join_semilatt_str @ SV11 ) )
= $true )
| ( ( ~ ( element @ SV57 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV77 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV57 @ SV77 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[567]) ).
thf(610,plain,
! [SV113: $i,SV101: $i,SV78: $i,SV87: $i,SV58: $i,SV12: $i] :
( ( ( empty @ SV12 )
| ( empty @ SV58 )
| ~ ( function @ SV87 )
| ~ ( quasi_total @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
| ~ ( relation_of2 @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
| ~ ( element @ SV101 @ SV12 )
| ~ ( element @ SV113 @ SV58 )
| ( element @ ( apply_binary_as_element @ SV12 @ SV58 @ SV78 @ SV87 @ SV101 @ SV113 ) @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(611,plain,
! [SV79: $i,SV59: $i,SV13: $i] :
( ( ( ( empty_carrier @ SV13 )
| ~ ( meet_semilatt_str @ SV13 ) )
= $true )
| ( ( ~ ( element @ SV59 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( ~ ( element @ SV79 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( element @ ( meet @ SV13 @ SV59 @ SV79 ) @ ( the_carrier @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(612,plain,
! [SV114: $i,SV102: $i,SV83: $i,SV88: $i,SV65: $i,SV29: $i] :
( ( ( empty @ SV29 )
| ( empty @ SV65 )
| ~ ( function @ SV88 )
| ~ ( quasi_total @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
| ~ ( relation_of2 @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
| ~ ( element @ SV102 @ SV29 )
| ~ ( element @ SV114 @ SV65 )
| ( ( apply_binary_as_element @ SV29 @ SV65 @ SV83 @ SV88 @ SV102 @ SV114 )
= ( apply_binary @ SV88 @ SV102 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(613,plain,
! [SV36: $i,SV84: $i,SV69: $i] :
( ( ( element @ SV69 @ ( powerset @ SV84 ) )
= $false )
| ( ( ~ ( in @ SV36 @ SV69 ) )
= $true )
| ( ( element @ SV36 @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(614,plain,
! [SV37: $i,SV85: $i,SV70: $i] :
( ( ( element @ SV70 @ ( powerset @ SV85 ) )
= $false )
| ( ( ~ ( in @ SV37 @ SV70 ) )
= $true )
| ( ( ~ ( empty @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(615,plain,
! [SV41: $i,SV73: $i] :
( ( ( empty @ SV73 )
= $false )
| ( ( SV41 = SV73 )
= $true )
| ( ( empty @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(616,plain,
! [SV42: $i] :
( ( ( ~ ( element @ ( sK5_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) ) )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( one_sorted_str @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[579]) ).
thf(617,plain,
! [SV42: $i] :
( ( ( ~ ~ ( empty @ ( sK5_B @ SV42 ) ) )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( one_sorted_str @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[579]) ).
thf(618,plain,
! [SV103: $i,SV43: $i,SV115: $i] :
( ( ~ ( relation_of2 @ SV115 @ SV43 @ SV103 )
| ( relation_of2_as_subset @ SV115 @ SV43 @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(619,plain,
! [SV104: $i,SV43: $i,SV116: $i] :
( ( ~ ( relation_of2_as_subset @ SV116 @ SV43 @ SV104 )
| ( relation_of2 @ SV116 @ SV43 @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(620,plain,
( ( ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( function @ ( the_L_join @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(621,plain,
( ( ! [SX0: $i] :
( ~ ( join_semilatt_str @ SX0 )
| ( quasi_total @ ( the_L_join @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[583]) ).
thf(622,plain,
! [SV89: $i] :
( ( ( join_semilatt_str @ SV89 )
= $false )
| ( ( relation_of2_as_subset @ ( the_L_join @ SV89 ) @ ( cartesian_product2 @ ( the_carrier @ SV89 ) @ ( the_carrier @ SV89 ) ) @ ( the_carrier @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(623,plain,
! [SV86: $i,SV44: $i,SV74: $i] :
( ( ( ~ ( function @ SV74 )
| ~ ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ~ ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ~ ( function @ SV86 ) )
= $true )
| ( ( ~ ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ! [SY243: $i] :
~ ( ~ ~ ( ~ ( ! [SY244: $i,SY245: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY244 @ SY245 ) )
| ( SV44 = SY243 ) )
| ~ ! [SY246: $i] :
( ! [SY247: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY246 @ SY247 ) )
| ( SV74 = SY246 ) ) )
| ~ ! [SY248: $i,SY249: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY248 @ SY249 ) )
| ( SV86 = SY249 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(624,plain,
! [SV117: $i,SV45: $i,SV105: $i] :
( ( ~ ( function @ SV105 )
| ~ ( quasi_total @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SV117 )
| ~ ( quasi_total @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ( latt_str @ ( latt_str_of @ SV45 @ SV105 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(625,plain,
! [SV118: $i,SV45: $i,SV106: $i] :
( ( ~ ( function @ SV106 )
| ~ ( quasi_total @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SV118 )
| ~ ( quasi_total @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ( strict_latt_str @ ( latt_str_of @ SV45 @ SV106 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(626,plain,
( ( latt_str @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[589]) ).
thf(627,plain,
( ( ~ ( empty_carrier @ sK4_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[590]) ).
thf(628,plain,
! [SV92: $i] :
( ( ( latt_str @ SV92 )
= $false )
| ( ( join_semilatt_str @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(629,plain,
! [SV93: $i] :
( ( ( latt_str @ SV93 )
= $false )
| ( ( meet_semilatt_str @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(630,plain,
! [SV107: $i,SV94: $i] :
( ( ( ~ ( element @ SV94 @ ( powerset @ SV107 ) ) )
= $true )
| ( ( subset @ SV94 @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(631,plain,
! [SV108: $i,SV95: $i] :
( ( ( ~ ( subset @ SV95 @ SV108 ) )
= $true )
| ( ( element @ SV95 @ ( powerset @ SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(632,plain,
! [SV46: $i] :
( ( ( empty @ ( sK11_B @ SV46 ) )
= $false )
| ( ( empty @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(633,plain,
! [SV119: $i,SV109: $i,SV47: $i] :
( ( ( empty @ SV47 )
| ~ ( function @ SV109 )
| ~ ( quasi_total @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SV119 )
| ~ ( quasi_total @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SV109 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(634,plain,
! [SV120: $i,SV110: $i,SV47: $i] :
( ( ( empty @ SV47 )
| ~ ( function @ SV110 )
| ~ ( quasi_total @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SV120 )
| ~ ( quasi_total @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ( strict_latt_str @ ( latt_str_of @ SV47 @ SV110 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(635,plain,
( ( ~ ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ~ ( subset @ sK2_SY138 @ sK3_SY140 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[599]) ).
thf(636,plain,
( ( ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
| ( subset @ sK2_SY138 @ sK3_SY140 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[600]) ).
thf(637,plain,
( ( ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( function @ ( the_L_meet @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[601]) ).
thf(638,plain,
( ( ! [SX0: $i] :
( ~ ( meet_semilatt_str @ SX0 )
| ( quasi_total @ ( the_L_meet @ SX0 ) @ ( cartesian_product2 @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[602]) ).
thf(639,plain,
! [SV96: $i] :
( ( ( meet_semilatt_str @ SV96 )
= $false )
| ( ( relation_of2_as_subset @ ( the_L_meet @ SV96 ) @ ( cartesian_product2 @ ( the_carrier @ SV96 ) @ ( the_carrier @ SV96 ) ) @ ( the_carrier @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(640,plain,
! [SV49: $i,SV111: $i] :
( ( ( ~ ( element @ SV111 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY266: $i] :
( ~ ( element @ SY266 @ ( the_carrier @ SV49 ) )
| ( ( join @ SV49 @ SV111 @ SY266 )
!= SY266 )
| ( below @ SV49 @ SV111 @ SY266 ) )
| ~ ! [SY267: $i] :
( ~ ( element @ SY267 @ ( the_carrier @ SV49 ) )
| ~ ( below @ SV49 @ SV111 @ SY267 )
| ( ( join @ SV49 @ SV111 @ SY267 )
= SY267 ) ) ) )
= $true )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(641,plain,
! [SV75: $i,SV50: $i] :
( ( ( ~ ! [SY235: $i] :
( ~ ( element @ SY235 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ( ( join @ ( boole_lattice @ SV50 ) @ SV75 @ SY235 )
= ( set_union2 @ SV75 @ SY235 ) ) ) )
= $false )
| ( ( element @ SV75 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[605]) ).
thf(642,plain,
! [SV75: $i,SV50: $i] :
( ( ( ~ ! [SY236: $i] :
( ~ ( element @ SY236 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ( ( meet @ ( boole_lattice @ SV50 ) @ SV75 @ SY236 )
= ( set_intersection2 @ SV75 @ SY236 ) ) ) )
= $false )
| ( ( element @ SV75 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[605]) ).
thf(643,plain,
! [SV121: $i,SV112: $i,SV7: $i] :
( ( ( ( apply_binary @ SV7 @ SV112 @ SV121 )
= ( apply @ SV7 @ ( ordered_pair @ SV112 @ SV121 ) ) )
= $true )
| ( ( function @ SV7 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(644,plain,
! [SV8: $i,SV99: $i] :
( ( ( element @ SV99 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( ! [SY256: $i] :
( ~ ( element @ SY256 @ ( the_carrier @ SV8 ) )
| ( ( join @ SV8 @ SV99 @ SY256 )
= ( apply_binary_as_element @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_L_join @ SV8 ) @ SV99 @ SY256 ) ) ) )
= $true )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( join_semilatt_str @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(645,plain,
! [SV9: $i,SV100: $i] :
( ( ( element @ SV100 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( ! [SY257: $i] :
( ~ ( element @ SY257 @ ( the_carrier @ SV9 ) )
| ( ( meet @ SV9 @ SV100 @ SY257 )
= ( apply_binary_as_element @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_L_meet @ SV9 ) @ SV100 @ SY257 ) ) ) )
= $true )
| ( ( empty_carrier @ SV9 )
= $true )
| ( ( meet_semilatt_str @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(646,plain,
! [SV77: $i,SV57: $i,SV11: $i] :
( ( ( empty_carrier @ SV11 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV11 ) )
= $true )
| ( ( ~ ( element @ SV57 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV77 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV57 @ SV77 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(647,plain,
! [SV113: $i,SV101: $i,SV78: $i,SV87: $i,SV58: $i,SV12: $i] :
( ( ( ( empty @ SV12 )
| ( empty @ SV58 )
| ~ ( function @ SV87 )
| ~ ( quasi_total @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
| ~ ( relation_of2 @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
| ~ ( element @ SV101 @ SV12 )
| ~ ( element @ SV113 @ SV58 ) )
= $true )
| ( ( element @ ( apply_binary_as_element @ SV12 @ SV58 @ SV78 @ SV87 @ SV101 @ SV113 ) @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[610]) ).
thf(648,plain,
! [SV79: $i,SV59: $i,SV13: $i] :
( ( ( empty_carrier @ SV13 )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV13 ) )
= $true )
| ( ( ~ ( element @ SV59 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( ~ ( element @ SV79 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( element @ ( meet @ SV13 @ SV59 @ SV79 ) @ ( the_carrier @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(649,plain,
! [SV114: $i,SV102: $i,SV83: $i,SV88: $i,SV65: $i,SV29: $i] :
( ( ( ( empty @ SV29 )
| ( empty @ SV65 )
| ~ ( function @ SV88 )
| ~ ( quasi_total @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
| ~ ( relation_of2 @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
| ~ ( element @ SV102 @ SV29 )
| ~ ( element @ SV114 @ SV65 ) )
= $true )
| ( ( ( apply_binary_as_element @ SV29 @ SV65 @ SV83 @ SV88 @ SV102 @ SV114 )
= ( apply_binary @ SV88 @ SV102 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(650,plain,
! [SV84: $i,SV69: $i,SV36: $i] :
( ( ( in @ SV36 @ SV69 )
= $false )
| ( ( element @ SV69 @ ( powerset @ SV84 ) )
= $false )
| ( ( element @ SV36 @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(651,plain,
! [SV85: $i,SV70: $i,SV37: $i] :
( ( ( in @ SV37 @ SV70 )
= $false )
| ( ( element @ SV70 @ ( powerset @ SV85 ) )
= $false )
| ( ( ~ ( empty @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(652,plain,
! [SV42: $i] :
( ( ( element @ ( sK5_B @ SV42 ) @ ( powerset @ ( the_carrier @ SV42 ) ) )
= $true )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( one_sorted_str @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[616]) ).
thf(653,plain,
! [SV42: $i] :
( ( ( ~ ( empty @ ( sK5_B @ SV42 ) ) )
= $true )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( one_sorted_str @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[617]) ).
thf(654,plain,
! [SV103: $i,SV43: $i,SV115: $i] :
( ( ( ~ ( relation_of2 @ SV115 @ SV43 @ SV103 ) )
= $true )
| ( ( relation_of2_as_subset @ SV115 @ SV43 @ SV103 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(655,plain,
! [SV104: $i,SV43: $i,SV116: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV116 @ SV43 @ SV104 ) )
= $true )
| ( ( relation_of2 @ SV116 @ SV43 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(656,plain,
! [SV122: $i] :
( ( ~ ( join_semilatt_str @ SV122 )
| ( function @ ( the_L_join @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(657,plain,
! [SV123: $i] :
( ( ~ ( join_semilatt_str @ SV123 )
| ( quasi_total @ ( the_L_join @ SV123 ) @ ( cartesian_product2 @ ( the_carrier @ SV123 ) @ ( the_carrier @ SV123 ) ) @ ( the_carrier @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(658,plain,
! [SV86: $i,SV44: $i,SV74: $i] :
( ( ( ~ ( function @ SV74 )
| ~ ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
| ~ ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ~ ( function @ SV86 ) )
= $true )
| ( ( ~ ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ! [SY243: $i] :
~ ( ~ ~ ( ~ ( ! [SY244: $i,SY245: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY244 @ SY245 ) )
| ( SV44 = SY243 ) )
| ~ ! [SY246: $i] :
( ! [SY247: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY246 @ SY247 ) )
| ( SV74 = SY246 ) ) )
| ~ ! [SY248: $i,SY249: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY248 @ SY249 ) )
| ( SV86 = SY249 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[623]) ).
thf(659,plain,
! [SV117: $i,SV45: $i,SV105: $i] :
( ( ( ~ ( function @ SV105 )
| ~ ( quasi_total @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SV117 )
| ~ ( quasi_total @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( latt_str @ ( latt_str_of @ SV45 @ SV105 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(660,plain,
! [SV118: $i,SV45: $i,SV106: $i] :
( ( ( ~ ( function @ SV106 )
| ~ ( quasi_total @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SV118 )
| ~ ( quasi_total @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV45 @ SV106 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(661,plain,
( ( empty_carrier @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(662,plain,
! [SV107: $i,SV94: $i] :
( ( ( element @ SV94 @ ( powerset @ SV107 ) )
= $false )
| ( ( subset @ SV94 @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(663,plain,
! [SV108: $i,SV95: $i] :
( ( ( subset @ SV95 @ SV108 )
= $false )
| ( ( element @ SV95 @ ( powerset @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(664,plain,
! [SV119: $i,SV109: $i,SV47: $i] :
( ( ( ( empty @ SV47 )
| ~ ( function @ SV109 )
| ~ ( quasi_total @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SV119 )
| ~ ( quasi_total @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SV109 @ SV119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(665,plain,
! [SV120: $i,SV110: $i,SV47: $i] :
( ( ( ( empty @ SV47 )
| ~ ( function @ SV110 )
| ~ ( quasi_total @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SV120 )
| ~ ( quasi_total @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV47 @ SV110 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(666,plain,
( ( ( ~ ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 ) )
= $true )
| ( ( ~ ( subset @ sK2_SY138 @ sK3_SY140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(667,plain,
( ( ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
= $true )
| ( ( subset @ sK2_SY138 @ sK3_SY140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(668,plain,
! [SV124: $i] :
( ( ~ ( meet_semilatt_str @ SV124 )
| ( function @ ( the_L_meet @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(669,plain,
! [SV125: $i] :
( ( ~ ( meet_semilatt_str @ SV125 )
| ( quasi_total @ ( the_L_meet @ SV125 ) @ ( cartesian_product2 @ ( the_carrier @ SV125 ) @ ( the_carrier @ SV125 ) ) @ ( the_carrier @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(670,plain,
! [SV49: $i,SV111: $i] :
( ( ( element @ SV111 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( ~ ( ~ ! [SY266: $i] :
( ~ ( element @ SY266 @ ( the_carrier @ SV49 ) )
| ( ( join @ SV49 @ SV111 @ SY266 )
!= SY266 )
| ( below @ SV49 @ SV111 @ SY266 ) )
| ~ ! [SY267: $i] :
( ~ ( element @ SY267 @ ( the_carrier @ SV49 ) )
| ~ ( below @ SV49 @ SV111 @ SY267 )
| ( ( join @ SV49 @ SV111 @ SY267 )
= SY267 ) ) ) )
= $true )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(671,plain,
! [SV75: $i,SV50: $i] :
( ( ( ! [SY235: $i] :
( ~ ( element @ SY235 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ( ( join @ ( boole_lattice @ SV50 ) @ SV75 @ SY235 )
= ( set_union2 @ SV75 @ SY235 ) ) ) )
= $true )
| ( ( element @ SV75 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[641]) ).
thf(672,plain,
! [SV75: $i,SV50: $i] :
( ( ( ! [SY236: $i] :
( ~ ( element @ SY236 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ( ( meet @ ( boole_lattice @ SV50 ) @ SV75 @ SY236 )
= ( set_intersection2 @ SV75 @ SY236 ) ) ) )
= $true )
| ( ( element @ SV75 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[642]) ).
thf(673,plain,
! [SV99: $i,SV8: $i,SV126: $i] :
( ( ( ~ ( element @ SV126 @ ( the_carrier @ SV8 ) )
| ( ( join @ SV8 @ SV99 @ SV126 )
= ( apply_binary_as_element @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_L_join @ SV8 ) @ SV99 @ SV126 ) ) )
= $true )
| ( ( element @ SV99 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( join_semilatt_str @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(674,plain,
! [SV100: $i,SV9: $i,SV127: $i] :
( ( ( ~ ( element @ SV127 @ ( the_carrier @ SV9 ) )
| ( ( meet @ SV9 @ SV100 @ SV127 )
= ( apply_binary_as_element @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_L_meet @ SV9 ) @ SV100 @ SV127 ) ) )
= $true )
| ( ( element @ SV100 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( empty_carrier @ SV9 )
= $true )
| ( ( meet_semilatt_str @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(675,plain,
! [SV77: $i,SV57: $i,SV11: $i] :
( ( ( join_semilatt_str @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( ~ ( element @ SV57 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( element @ SV77 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV57 @ SV77 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(676,plain,
! [SV113: $i,SV101: $i,SV78: $i,SV87: $i,SV58: $i,SV12: $i] :
( ( ( ( empty @ SV12 )
| ( empty @ SV58 )
| ~ ( function @ SV87 )
| ~ ( quasi_total @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
| ~ ( relation_of2 @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
| ~ ( element @ SV101 @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV113 @ SV58 ) )
= $true )
| ( ( element @ ( apply_binary_as_element @ SV12 @ SV58 @ SV78 @ SV87 @ SV101 @ SV113 ) @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(677,plain,
! [SV79: $i,SV59: $i,SV13: $i] :
( ( ( meet_semilatt_str @ SV13 )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( ~ ( element @ SV59 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( ~ ( element @ SV79 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( element @ ( meet @ SV13 @ SV59 @ SV79 ) @ ( the_carrier @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(678,plain,
! [SV114: $i,SV102: $i,SV83: $i,SV88: $i,SV65: $i,SV29: $i] :
( ( ( ( empty @ SV29 )
| ( empty @ SV65 )
| ~ ( function @ SV88 )
| ~ ( quasi_total @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
| ~ ( relation_of2 @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
| ~ ( element @ SV102 @ SV29 ) )
= $true )
| ( ( ~ ( element @ SV114 @ SV65 ) )
= $true )
| ( ( ( apply_binary_as_element @ SV29 @ SV65 @ SV83 @ SV88 @ SV102 @ SV114 )
= ( apply_binary @ SV88 @ SV102 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(679,plain,
! [SV37: $i,SV70: $i,SV85: $i] :
( ( ( empty @ SV85 )
= $false )
| ( ( element @ SV70 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV37 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(680,plain,
! [SV42: $i] :
( ( ( empty @ ( sK5_B @ SV42 ) )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( one_sorted_str @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(681,plain,
! [SV103: $i,SV43: $i,SV115: $i] :
( ( ( relation_of2 @ SV115 @ SV43 @ SV103 )
= $false )
| ( ( relation_of2_as_subset @ SV115 @ SV43 @ SV103 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(682,plain,
! [SV104: $i,SV43: $i,SV116: $i] :
( ( ( relation_of2_as_subset @ SV116 @ SV43 @ SV104 )
= $false )
| ( ( relation_of2 @ SV116 @ SV43 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(683,plain,
! [SV122: $i] :
( ( ( ~ ( join_semilatt_str @ SV122 ) )
= $true )
| ( ( function @ ( the_L_join @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(684,plain,
! [SV123: $i] :
( ( ( ~ ( join_semilatt_str @ SV123 ) )
= $true )
| ( ( quasi_total @ ( the_L_join @ SV123 ) @ ( cartesian_product2 @ ( the_carrier @ SV123 ) @ ( the_carrier @ SV123 ) ) @ ( the_carrier @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[657]) ).
thf(685,plain,
! [SV86: $i,SV44: $i,SV74: $i] :
( ( ( ~ ( function @ SV74 )
| ~ ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ~ ( function @ SV86 ) )
= $true )
| ( ( ~ ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ! [SY243: $i] :
~ ( ~ ~ ( ~ ( ! [SY244: $i,SY245: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY244 @ SY245 ) )
| ( SV44 = SY243 ) )
| ~ ! [SY246: $i] :
( ! [SY247: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY246 @ SY247 ) )
| ( SV74 = SY246 ) ) )
| ~ ! [SY248: $i,SY249: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY248 @ SY249 ) )
| ( SV86 = SY249 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(686,plain,
! [SV117: $i,SV45: $i,SV105: $i] :
( ( ( ~ ( function @ SV105 )
| ~ ( quasi_total @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SV117 )
| ~ ( quasi_total @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( latt_str @ ( latt_str_of @ SV45 @ SV105 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(687,plain,
! [SV118: $i,SV45: $i,SV106: $i] :
( ( ( ~ ( function @ SV106 )
| ~ ( quasi_total @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SV118 )
| ~ ( quasi_total @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV45 @ SV106 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(688,plain,
! [SV119: $i,SV109: $i,SV47: $i] :
( ( ( ( empty @ SV47 )
| ~ ( function @ SV109 )
| ~ ( quasi_total @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SV119 )
| ~ ( quasi_total @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SV109 @ SV119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[664]) ).
thf(689,plain,
! [SV120: $i,SV110: $i,SV47: $i] :
( ( ( ( empty @ SV47 )
| ~ ( function @ SV110 )
| ~ ( quasi_total @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SV120 )
| ~ ( quasi_total @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV47 @ SV110 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[665]) ).
thf(690,plain,
( ( ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
= $false )
| ( ( ~ ( subset @ sK2_SY138 @ sK3_SY140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(691,plain,
! [SV124: $i] :
( ( ( ~ ( meet_semilatt_str @ SV124 ) )
= $true )
| ( ( function @ ( the_L_meet @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(692,plain,
! [SV125: $i] :
( ( ( ~ ( meet_semilatt_str @ SV125 ) )
= $true )
| ( ( quasi_total @ ( the_L_meet @ SV125 ) @ ( cartesian_product2 @ ( the_carrier @ SV125 ) @ ( the_carrier @ SV125 ) ) @ ( the_carrier @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(693,plain,
! [SV111: $i,SV49: $i] :
( ( ( ~ ! [SY266: $i] :
( ~ ( element @ SY266 @ ( the_carrier @ SV49 ) )
| ( ( join @ SV49 @ SV111 @ SY266 )
!= SY266 )
| ( below @ SV49 @ SV111 @ SY266 ) )
| ~ ! [SY267: $i] :
( ~ ( element @ SY267 @ ( the_carrier @ SV49 ) )
| ~ ( below @ SV49 @ SV111 @ SY267 )
| ( ( join @ SV49 @ SV111 @ SY267 )
= SY267 ) ) )
= $false )
| ( ( element @ SV111 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(694,plain,
! [SV75: $i,SV50: $i,SV128: $i] :
( ( ( ~ ( element @ SV128 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ( ( join @ ( boole_lattice @ SV50 ) @ SV75 @ SV128 )
= ( set_union2 @ SV75 @ SV128 ) ) )
= $true )
| ( ( element @ SV75 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(695,plain,
! [SV75: $i,SV50: $i,SV129: $i] :
( ( ( ~ ( element @ SV129 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
| ( ( meet @ ( boole_lattice @ SV50 ) @ SV75 @ SV129 )
= ( set_intersection2 @ SV75 @ SV129 ) ) )
= $true )
| ( ( element @ SV75 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(696,plain,
! [SV99: $i,SV8: $i,SV126: $i] :
( ( ( ~ ( element @ SV126 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ( join @ SV8 @ SV99 @ SV126 )
= ( apply_binary_as_element @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_L_join @ SV8 ) @ SV99 @ SV126 ) )
= $true )
| ( ( element @ SV99 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( join_semilatt_str @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(697,plain,
! [SV100: $i,SV9: $i,SV127: $i] :
( ( ( ~ ( element @ SV127 @ ( the_carrier @ SV9 ) ) )
= $true )
| ( ( ( meet @ SV9 @ SV100 @ SV127 )
= ( apply_binary_as_element @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_L_meet @ SV9 ) @ SV100 @ SV127 ) )
= $true )
| ( ( element @ SV100 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( empty_carrier @ SV9 )
= $true )
| ( ( meet_semilatt_str @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(698,plain,
! [SV77: $i,SV11: $i,SV57: $i] :
( ( ( element @ SV57 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( join_semilatt_str @ SV11 )
= $false )
| ( ( ~ ( element @ SV77 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( element @ ( join @ SV11 @ SV57 @ SV77 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(699,plain,
! [SV113: $i,SV101: $i,SV78: $i,SV87: $i,SV58: $i,SV12: $i] :
( ( ( ( empty @ SV12 )
| ( empty @ SV58 )
| ~ ( function @ SV87 )
| ~ ( quasi_total @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
| ~ ( relation_of2 @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 ) )
= $true )
| ( ( ~ ( element @ SV101 @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV113 @ SV58 ) )
= $true )
| ( ( element @ ( apply_binary_as_element @ SV12 @ SV58 @ SV78 @ SV87 @ SV101 @ SV113 ) @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(700,plain,
! [SV79: $i,SV13: $i,SV59: $i] :
( ( ( element @ SV59 @ ( the_carrier @ SV13 ) )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( meet_semilatt_str @ SV13 )
= $false )
| ( ( ~ ( element @ SV79 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( element @ ( meet @ SV13 @ SV59 @ SV79 ) @ ( the_carrier @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(701,plain,
! [SV114: $i,SV102: $i,SV83: $i,SV88: $i,SV65: $i,SV29: $i] :
( ( ( ( empty @ SV29 )
| ( empty @ SV65 )
| ~ ( function @ SV88 )
| ~ ( quasi_total @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
| ~ ( relation_of2 @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 ) )
= $true )
| ( ( ~ ( element @ SV102 @ SV29 ) )
= $true )
| ( ( ~ ( element @ SV114 @ SV65 ) )
= $true )
| ( ( ( apply_binary_as_element @ SV29 @ SV65 @ SV83 @ SV88 @ SV102 @ SV114 )
= ( apply_binary @ SV88 @ SV102 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(702,plain,
! [SV122: $i] :
( ( ( join_semilatt_str @ SV122 )
= $false )
| ( ( function @ ( the_L_join @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(703,plain,
! [SV123: $i] :
( ( ( join_semilatt_str @ SV123 )
= $false )
| ( ( quasi_total @ ( the_L_join @ SV123 ) @ ( cartesian_product2 @ ( the_carrier @ SV123 ) @ ( the_carrier @ SV123 ) ) @ ( the_carrier @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(704,plain,
! [SV86: $i,SV44: $i,SV74: $i] :
( ( ( ~ ( function @ SV74 ) )
= $true )
| ( ( ~ ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ~ ( function @ SV86 ) )
= $true )
| ( ( ~ ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ! [SY243: $i] :
~ ( ~ ~ ( ~ ( ! [SY244: $i,SY245: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY244 @ SY245 ) )
| ( SV44 = SY243 ) )
| ~ ! [SY246: $i] :
( ! [SY247: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY246 @ SY247 ) )
| ( SV74 = SY246 ) ) )
| ~ ! [SY248: $i,SY249: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY248 @ SY249 ) )
| ( SV86 = SY249 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[685]) ).
thf(705,plain,
! [SV117: $i,SV45: $i,SV105: $i] :
( ( ( ~ ( function @ SV105 )
| ~ ( quasi_total @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SV117 ) )
= $true )
| ( ( ~ ( quasi_total @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( latt_str @ ( latt_str_of @ SV45 @ SV105 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[686]) ).
thf(706,plain,
! [SV118: $i,SV45: $i,SV106: $i] :
( ( ( ~ ( function @ SV106 )
| ~ ( quasi_total @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( function @ SV118 ) )
= $true )
| ( ( ~ ( quasi_total @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV45 @ SV106 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(707,plain,
! [SV119: $i,SV109: $i,SV47: $i] :
( ( ( ( empty @ SV47 )
| ~ ( function @ SV109 )
| ~ ( quasi_total @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SV119 ) )
= $true )
| ( ( ~ ( quasi_total @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SV109 @ SV119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[688]) ).
thf(708,plain,
! [SV120: $i,SV110: $i,SV47: $i] :
( ( ( ( empty @ SV47 )
| ~ ( function @ SV110 )
| ~ ( quasi_total @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( function @ SV120 ) )
= $true )
| ( ( ~ ( quasi_total @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV47 @ SV110 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(709,plain,
( ( ( subset @ sK2_SY138 @ sK3_SY140 )
= $false )
| ( ( below @ ( boole_lattice @ sK1_A ) @ sK2_SY138 @ sK3_SY140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(710,plain,
! [SV124: $i] :
( ( ( meet_semilatt_str @ SV124 )
= $false )
| ( ( function @ ( the_L_meet @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(711,plain,
! [SV125: $i] :
( ( ( meet_semilatt_str @ SV125 )
= $false )
| ( ( quasi_total @ ( the_L_meet @ SV125 ) @ ( cartesian_product2 @ ( the_carrier @ SV125 ) @ ( the_carrier @ SV125 ) ) @ ( the_carrier @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(712,plain,
! [SV111: $i,SV49: $i] :
( ( ( ~ ! [SY266: $i] :
( ~ ( element @ SY266 @ ( the_carrier @ SV49 ) )
| ( ( join @ SV49 @ SV111 @ SY266 )
!= SY266 )
| ( below @ SV49 @ SV111 @ SY266 ) ) )
= $false )
| ( ( element @ SV111 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[693]) ).
thf(713,plain,
! [SV111: $i,SV49: $i] :
( ( ( ~ ! [SY267: $i] :
( ~ ( element @ SY267 @ ( the_carrier @ SV49 ) )
| ~ ( below @ SV49 @ SV111 @ SY267 )
| ( ( join @ SV49 @ SV111 @ SY267 )
= SY267 ) ) )
= $false )
| ( ( element @ SV111 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[693]) ).
thf(714,plain,
! [SV75: $i,SV50: $i,SV128: $i] :
( ( ( ~ ( element @ SV128 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) ) )
= $true )
| ( ( ( join @ ( boole_lattice @ SV50 ) @ SV75 @ SV128 )
= ( set_union2 @ SV75 @ SV128 ) )
= $true )
| ( ( element @ SV75 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(715,plain,
! [SV75: $i,SV50: $i,SV129: $i] :
( ( ( ~ ( element @ SV129 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) ) )
= $true )
| ( ( ( meet @ ( boole_lattice @ SV50 ) @ SV75 @ SV129 )
= ( set_intersection2 @ SV75 @ SV129 ) )
= $true )
| ( ( element @ SV75 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(716,plain,
! [SV99: $i,SV8: $i,SV126: $i] :
( ( ( element @ SV126 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( ( join @ SV8 @ SV99 @ SV126 )
= ( apply_binary_as_element @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_L_join @ SV8 ) @ SV99 @ SV126 ) )
= $true )
| ( ( element @ SV99 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( empty_carrier @ SV8 )
= $true )
| ( ( join_semilatt_str @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[696]) ).
thf(717,plain,
! [SV100: $i,SV9: $i,SV127: $i] :
( ( ( element @ SV127 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( ( meet @ SV9 @ SV100 @ SV127 )
= ( apply_binary_as_element @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_carrier @ SV9 ) @ ( the_L_meet @ SV9 ) @ SV100 @ SV127 ) )
= $true )
| ( ( element @ SV100 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( empty_carrier @ SV9 )
= $true )
| ( ( meet_semilatt_str @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(718,plain,
! [SV57: $i,SV11: $i,SV77: $i] :
( ( ( element @ SV77 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( join_semilatt_str @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( element @ SV57 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ ( join @ SV11 @ SV57 @ SV77 ) @ ( the_carrier @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(719,plain,
! [SV113: $i,SV101: $i,SV78: $i,SV87: $i,SV58: $i,SV12: $i] :
( ( ( ( empty @ SV12 )
| ( empty @ SV58 )
| ~ ( function @ SV87 )
| ~ ( quasi_total @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 ) )
= $true )
| ( ( ~ ( element @ SV101 @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV113 @ SV58 ) )
= $true )
| ( ( element @ ( apply_binary_as_element @ SV12 @ SV58 @ SV78 @ SV87 @ SV101 @ SV113 ) @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[699]) ).
thf(720,plain,
! [SV59: $i,SV13: $i,SV79: $i] :
( ( ( element @ SV79 @ ( the_carrier @ SV13 ) )
= $false )
| ( ( meet_semilatt_str @ SV13 )
= $false )
| ( ( empty_carrier @ SV13 )
= $true )
| ( ( element @ SV59 @ ( the_carrier @ SV13 ) )
= $false )
| ( ( element @ ( meet @ SV13 @ SV59 @ SV79 ) @ ( the_carrier @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(721,plain,
! [SV114: $i,SV102: $i,SV83: $i,SV88: $i,SV65: $i,SV29: $i] :
( ( ( ( empty @ SV29 )
| ( empty @ SV65 )
| ~ ( function @ SV88 )
| ~ ( quasi_total @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 ) )
= $true )
| ( ( ~ ( element @ SV102 @ SV29 ) )
= $true )
| ( ( ~ ( element @ SV114 @ SV65 ) )
= $true )
| ( ( ( apply_binary_as_element @ SV29 @ SV65 @ SV83 @ SV88 @ SV102 @ SV114 )
= ( apply_binary @ SV88 @ SV102 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[701]) ).
thf(722,plain,
! [SV86: $i,SV44: $i,SV74: $i] :
( ( ( function @ SV74 )
= $false )
| ( ( ~ ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ~ ( function @ SV86 ) )
= $true )
| ( ( ~ ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ! [SY243: $i] :
~ ( ~ ~ ( ~ ( ! [SY244: $i,SY245: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY244 @ SY245 ) )
| ( SV44 = SY243 ) )
| ~ ! [SY246: $i] :
( ! [SY247: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY246 @ SY247 ) )
| ( SV74 = SY246 ) ) )
| ~ ! [SY248: $i,SY249: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY248 @ SY249 ) )
| ( SV86 = SY249 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(723,plain,
! [SV117: $i,SV45: $i,SV105: $i] :
( ( ( ~ ( function @ SV105 )
| ~ ( quasi_total @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( function @ SV117 ) )
= $true )
| ( ( ~ ( quasi_total @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( latt_str @ ( latt_str_of @ SV45 @ SV105 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(724,plain,
! [SV118: $i,SV45: $i,SV106: $i] :
( ( ( ~ ( function @ SV106 )
| ~ ( quasi_total @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
| ~ ( relation_of2 @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( function @ SV118 ) )
= $true )
| ( ( ~ ( quasi_total @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV45 @ SV106 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[706]) ).
thf(725,plain,
! [SV119: $i,SV109: $i,SV47: $i] :
( ( ( ( empty @ SV47 )
| ~ ( function @ SV109 )
| ~ ( quasi_total @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( function @ SV119 ) )
= $true )
| ( ( ~ ( quasi_total @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SV109 @ SV119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[707]) ).
thf(726,plain,
! [SV120: $i,SV110: $i,SV47: $i] :
( ( ( ( empty @ SV47 )
| ~ ( function @ SV110 )
| ~ ( quasi_total @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
| ~ ( relation_of2 @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( function @ SV120 ) )
= $true )
| ( ( ~ ( quasi_total @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV47 @ SV110 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[708]) ).
thf(727,plain,
! [SV111: $i,SV49: $i] :
( ( ( ! [SY266: $i] :
( ~ ( element @ SY266 @ ( the_carrier @ SV49 ) )
| ( ( join @ SV49 @ SV111 @ SY266 )
!= SY266 )
| ( below @ SV49 @ SV111 @ SY266 ) ) )
= $true )
| ( ( element @ SV111 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[712]) ).
thf(728,plain,
! [SV111: $i,SV49: $i] :
( ( ( ! [SY267: $i] :
( ~ ( element @ SY267 @ ( the_carrier @ SV49 ) )
| ~ ( below @ SV49 @ SV111 @ SY267 )
| ( ( join @ SV49 @ SV111 @ SY267 )
= SY267 ) ) )
= $true )
| ( ( element @ SV111 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[713]) ).
thf(729,plain,
! [SV75: $i,SV50: $i,SV128: $i] :
( ( ( element @ SV128 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
= $false )
| ( ( ( join @ ( boole_lattice @ SV50 ) @ SV75 @ SV128 )
= ( set_union2 @ SV75 @ SV128 ) )
= $true )
| ( ( element @ SV75 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(730,plain,
! [SV75: $i,SV50: $i,SV129: $i] :
( ( ( element @ SV129 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
= $false )
| ( ( ( meet @ ( boole_lattice @ SV50 ) @ SV75 @ SV129 )
= ( set_intersection2 @ SV75 @ SV129 ) )
= $true )
| ( ( element @ SV75 @ ( the_carrier @ ( boole_lattice @ SV50 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(731,plain,
! [SV113: $i,SV101: $i,SV78: $i,SV87: $i,SV58: $i,SV12: $i] :
( ( ( ( empty @ SV12 )
| ( empty @ SV58 )
| ~ ( function @ SV87 ) )
= $true )
| ( ( ~ ( quasi_total @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 ) )
= $true )
| ( ( ~ ( element @ SV101 @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV113 @ SV58 ) )
= $true )
| ( ( element @ ( apply_binary_as_element @ SV12 @ SV58 @ SV78 @ SV87 @ SV101 @ SV113 ) @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(732,plain,
! [SV114: $i,SV102: $i,SV83: $i,SV88: $i,SV65: $i,SV29: $i] :
( ( ( ( empty @ SV29 )
| ( empty @ SV65 )
| ~ ( function @ SV88 ) )
= $true )
| ( ( ~ ( quasi_total @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 ) )
= $true )
| ( ( ~ ( element @ SV102 @ SV29 ) )
= $true )
| ( ( ~ ( element @ SV114 @ SV65 ) )
= $true )
| ( ( ( apply_binary_as_element @ SV29 @ SV65 @ SV83 @ SV88 @ SV102 @ SV114 )
= ( apply_binary @ SV88 @ SV102 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(733,plain,
! [SV86: $i,SV44: $i,SV74: $i] :
( ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( ~ ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ~ ( function @ SV86 ) )
= $true )
| ( ( ~ ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ! [SY243: $i] :
~ ( ~ ~ ( ~ ( ! [SY244: $i,SY245: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY244 @ SY245 ) )
| ( SV44 = SY243 ) )
| ~ ! [SY246: $i] :
( ! [SY247: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY246 @ SY247 ) )
| ( SV74 = SY246 ) ) )
| ~ ! [SY248: $i,SY249: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY248 @ SY249 ) )
| ( SV86 = SY249 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(734,plain,
! [SV117: $i,SV45: $i,SV105: $i] :
( ( ( ~ ( function @ SV105 )
| ~ ( quasi_total @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( function @ SV117 ) )
= $true )
| ( ( ~ ( quasi_total @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( latt_str @ ( latt_str_of @ SV45 @ SV105 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[723]) ).
thf(735,plain,
! [SV118: $i,SV45: $i,SV106: $i] :
( ( ( ~ ( function @ SV106 )
| ~ ( quasi_total @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( function @ SV118 ) )
= $true )
| ( ( ~ ( quasi_total @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV45 @ SV106 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[724]) ).
thf(736,plain,
! [SV119: $i,SV109: $i,SV47: $i] :
( ( ( ( empty @ SV47 )
| ~ ( function @ SV109 )
| ~ ( quasi_total @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( function @ SV119 ) )
= $true )
| ( ( ~ ( quasi_total @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SV109 @ SV119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[725]) ).
thf(737,plain,
! [SV120: $i,SV110: $i,SV47: $i] :
( ( ( ( empty @ SV47 )
| ~ ( function @ SV110 )
| ~ ( quasi_total @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( function @ SV120 ) )
= $true )
| ( ( ~ ( quasi_total @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV47 @ SV110 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[726]) ).
thf(738,plain,
! [SV111: $i,SV49: $i,SV130: $i] :
( ( ( ~ ( element @ SV130 @ ( the_carrier @ SV49 ) )
| ( ( join @ SV49 @ SV111 @ SV130 )
!= SV130 )
| ( below @ SV49 @ SV111 @ SV130 ) )
= $true )
| ( ( element @ SV111 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(739,plain,
! [SV111: $i,SV49: $i,SV131: $i] :
( ( ( ~ ( element @ SV131 @ ( the_carrier @ SV49 ) )
| ~ ( below @ SV49 @ SV111 @ SV131 )
| ( ( join @ SV49 @ SV111 @ SV131 )
= SV131 ) )
= $true )
| ( ( element @ SV111 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(740,plain,
! [SV113: $i,SV101: $i,SV78: $i,SV87: $i,SV58: $i,SV12: $i] :
( ( ( ( empty @ SV12 )
| ( empty @ SV58 ) )
= $true )
| ( ( ~ ( function @ SV87 ) )
= $true )
| ( ( ~ ( quasi_total @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 ) )
= $true )
| ( ( ~ ( element @ SV101 @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV113 @ SV58 ) )
= $true )
| ( ( element @ ( apply_binary_as_element @ SV12 @ SV58 @ SV78 @ SV87 @ SV101 @ SV113 ) @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(741,plain,
! [SV114: $i,SV102: $i,SV83: $i,SV88: $i,SV65: $i,SV29: $i] :
( ( ( ( empty @ SV29 )
| ( empty @ SV65 ) )
= $true )
| ( ( ~ ( function @ SV88 ) )
= $true )
| ( ( ~ ( quasi_total @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 ) )
= $true )
| ( ( ~ ( element @ SV102 @ SV29 ) )
= $true )
| ( ( ~ ( element @ SV114 @ SV65 ) )
= $true )
| ( ( ( apply_binary_as_element @ SV29 @ SV65 @ SV83 @ SV88 @ SV102 @ SV114 )
= ( apply_binary @ SV88 @ SV102 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(742,plain,
! [SV86: $i,SV44: $i,SV74: $i] :
( ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( ~ ( function @ SV86 ) )
= $true )
| ( ( ~ ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ! [SY243: $i] :
~ ( ~ ~ ( ~ ( ! [SY244: $i,SY245: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY244 @ SY245 ) )
| ( SV44 = SY243 ) )
| ~ ! [SY246: $i] :
( ! [SY247: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY246 @ SY247 ) )
| ( SV74 = SY246 ) ) )
| ~ ! [SY248: $i,SY249: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY248 @ SY249 ) )
| ( SV86 = SY249 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(743,plain,
! [SV117: $i,SV45: $i,SV105: $i] :
( ( ( ~ ( function @ SV105 ) )
= $true )
| ( ( ~ ( quasi_total @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( function @ SV117 ) )
= $true )
| ( ( ~ ( quasi_total @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( latt_str @ ( latt_str_of @ SV45 @ SV105 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(744,plain,
! [SV118: $i,SV45: $i,SV106: $i] :
( ( ( ~ ( function @ SV106 ) )
= $true )
| ( ( ~ ( quasi_total @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( function @ SV118 ) )
= $true )
| ( ( ~ ( quasi_total @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV45 @ SV106 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(745,plain,
! [SV119: $i,SV109: $i,SV47: $i] :
( ( ( ( empty @ SV47 )
| ~ ( function @ SV109 ) )
= $true )
| ( ( ~ ( quasi_total @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( function @ SV119 ) )
= $true )
| ( ( ~ ( quasi_total @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SV109 @ SV119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(746,plain,
! [SV120: $i,SV110: $i,SV47: $i] :
( ( ( ( empty @ SV47 )
| ~ ( function @ SV110 ) )
= $true )
| ( ( ~ ( quasi_total @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( function @ SV120 ) )
= $true )
| ( ( ~ ( quasi_total @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV47 @ SV110 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(747,plain,
! [SV111: $i,SV49: $i,SV130: $i] :
( ( ( ~ ( element @ SV130 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( ( ( join @ SV49 @ SV111 @ SV130 )
!= SV130 )
| ( below @ SV49 @ SV111 @ SV130 ) )
= $true )
| ( ( element @ SV111 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[738]) ).
thf(748,plain,
! [SV111: $i,SV49: $i,SV131: $i] :
( ( ( ~ ( element @ SV131 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( ~ ( below @ SV49 @ SV111 @ SV131 )
| ( ( join @ SV49 @ SV111 @ SV131 )
= SV131 ) )
= $true )
| ( ( element @ SV111 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[739]) ).
thf(749,plain,
! [SV113: $i,SV101: $i,SV78: $i,SV87: $i,SV58: $i,SV12: $i] :
( ( ( empty @ SV12 )
= $true )
| ( ( empty @ SV58 )
= $true )
| ( ( ~ ( function @ SV87 ) )
= $true )
| ( ( ~ ( quasi_total @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 ) )
= $true )
| ( ( ~ ( element @ SV101 @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV113 @ SV58 ) )
= $true )
| ( ( element @ ( apply_binary_as_element @ SV12 @ SV58 @ SV78 @ SV87 @ SV101 @ SV113 ) @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[740]) ).
thf(750,plain,
! [SV114: $i,SV102: $i,SV83: $i,SV88: $i,SV65: $i,SV29: $i] :
( ( ( empty @ SV29 )
= $true )
| ( ( empty @ SV65 )
= $true )
| ( ( ~ ( function @ SV88 ) )
= $true )
| ( ( ~ ( quasi_total @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 ) )
= $true )
| ( ( ~ ( element @ SV102 @ SV29 ) )
= $true )
| ( ( ~ ( element @ SV114 @ SV65 ) )
= $true )
| ( ( ( apply_binary_as_element @ SV29 @ SV65 @ SV83 @ SV88 @ SV102 @ SV114 )
= ( apply_binary @ SV88 @ SV102 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[741]) ).
thf(751,plain,
! [SV44: $i,SV74: $i,SV86: $i] :
( ( ( function @ SV86 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( ~ ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ! [SY243: $i] :
~ ( ~ ~ ( ~ ( ! [SY244: $i,SY245: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY244 @ SY245 ) )
| ( SV44 = SY243 ) )
| ~ ! [SY246: $i] :
( ! [SY247: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY246 @ SY247 ) )
| ( SV74 = SY246 ) ) )
| ~ ! [SY248: $i,SY249: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY248 @ SY249 ) )
| ( SV86 = SY249 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(752,plain,
! [SV117: $i,SV45: $i,SV105: $i] :
( ( ( function @ SV105 )
= $false )
| ( ( ~ ( quasi_total @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( function @ SV117 ) )
= $true )
| ( ( ~ ( quasi_total @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( latt_str @ ( latt_str_of @ SV45 @ SV105 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(753,plain,
! [SV118: $i,SV45: $i,SV106: $i] :
( ( ( function @ SV106 )
= $false )
| ( ( ~ ( quasi_total @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( function @ SV118 ) )
= $true )
| ( ( ~ ( quasi_total @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV45 @ SV106 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(754,plain,
! [SV119: $i,SV109: $i,SV47: $i] :
( ( ( empty @ SV47 )
= $true )
| ( ( ~ ( function @ SV109 ) )
= $true )
| ( ( ~ ( quasi_total @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( function @ SV119 ) )
= $true )
| ( ( ~ ( quasi_total @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SV109 @ SV119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(755,plain,
! [SV120: $i,SV110: $i,SV47: $i] :
( ( ( empty @ SV47 )
= $true )
| ( ( ~ ( function @ SV110 ) )
= $true )
| ( ( ~ ( quasi_total @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( function @ SV120 ) )
= $true )
| ( ( ~ ( quasi_total @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV47 @ SV110 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(756,plain,
! [SV111: $i,SV49: $i,SV130: $i] :
( ( ( element @ SV130 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( ( ( join @ SV49 @ SV111 @ SV130 )
!= SV130 )
| ( below @ SV49 @ SV111 @ SV130 ) )
= $true )
| ( ( element @ SV111 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(757,plain,
! [SV111: $i,SV49: $i,SV131: $i] :
( ( ( element @ SV131 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( ~ ( below @ SV49 @ SV111 @ SV131 )
| ( ( join @ SV49 @ SV111 @ SV131 )
= SV131 ) )
= $true )
| ( ( element @ SV111 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(758,plain,
! [SV113: $i,SV101: $i,SV78: $i,SV12: $i,SV58: $i,SV87: $i] :
( ( ( function @ SV87 )
= $false )
| ( ( empty @ SV58 )
= $true )
| ( ( empty @ SV12 )
= $true )
| ( ( ~ ( quasi_total @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 ) )
= $true )
| ( ( ~ ( element @ SV101 @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV113 @ SV58 ) )
= $true )
| ( ( element @ ( apply_binary_as_element @ SV12 @ SV58 @ SV78 @ SV87 @ SV101 @ SV113 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(759,plain,
! [SV114: $i,SV102: $i,SV83: $i,SV29: $i,SV65: $i,SV88: $i] :
( ( ( function @ SV88 )
= $false )
| ( ( empty @ SV65 )
= $true )
| ( ( empty @ SV29 )
= $true )
| ( ( ~ ( quasi_total @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 ) )
= $true )
| ( ( ~ ( element @ SV102 @ SV29 ) )
= $true )
| ( ( ~ ( element @ SV114 @ SV65 ) )
= $true )
| ( ( ( apply_binary_as_element @ SV29 @ SV65 @ SV83 @ SV88 @ SV102 @ SV114 )
= ( apply_binary @ SV88 @ SV102 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(760,plain,
! [SV74: $i,SV44: $i,SV86: $i] :
( ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( ~ ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 ) )
= $true )
| ( ( ! [SY243: $i] :
~ ( ~ ~ ( ~ ( ! [SY244: $i,SY245: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY244 @ SY245 ) )
| ( SV44 = SY243 ) )
| ~ ! [SY246: $i] :
( ! [SY247: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY246 @ SY247 ) )
| ( SV74 = SY246 ) ) )
| ~ ! [SY248: $i,SY249: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY248 @ SY249 ) )
| ( SV86 = SY249 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(761,plain,
! [SV117: $i,SV45: $i,SV105: $i] :
( ( ( quasi_total @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( ~ ( relation_of2 @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( function @ SV117 ) )
= $true )
| ( ( ~ ( quasi_total @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( latt_str @ ( latt_str_of @ SV45 @ SV105 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(762,plain,
! [SV118: $i,SV45: $i,SV106: $i] :
( ( ( quasi_total @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( function @ SV106 )
= $false )
| ( ( ~ ( relation_of2 @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( function @ SV118 ) )
= $true )
| ( ( ~ ( quasi_total @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV45 @ SV106 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(763,plain,
! [SV119: $i,SV47: $i,SV109: $i] :
( ( ( function @ SV109 )
= $false )
| ( ( empty @ SV47 )
= $true )
| ( ( ~ ( quasi_total @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( function @ SV119 ) )
= $true )
| ( ( ~ ( quasi_total @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SV109 @ SV119 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(764,plain,
! [SV120: $i,SV47: $i,SV110: $i] :
( ( ( function @ SV110 )
= $false )
| ( ( empty @ SV47 )
= $true )
| ( ( ~ ( quasi_total @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( function @ SV120 ) )
= $true )
| ( ( ~ ( quasi_total @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV47 @ SV110 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(765,plain,
! [SV130: $i,SV111: $i,SV49: $i] :
( ( ( ( ( join @ SV49 @ SV111 @ SV130 )
!= SV130 ) )
= $true )
| ( ( below @ SV49 @ SV111 @ SV130 )
= $true )
| ( ( element @ SV130 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( element @ SV111 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[756]) ).
thf(766,plain,
! [SV131: $i,SV111: $i,SV49: $i] :
( ( ( ~ ( below @ SV49 @ SV111 @ SV131 ) )
= $true )
| ( ( ( join @ SV49 @ SV111 @ SV131 )
= SV131 )
= $true )
| ( ( element @ SV131 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( element @ SV111 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(767,plain,
! [SV113: $i,SV101: $i,SV78: $i,SV58: $i,SV12: $i,SV87: $i] :
( ( ( quasi_total @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
= $false )
| ( ( empty @ SV12 )
= $true )
| ( ( empty @ SV58 )
= $true )
| ( ( function @ SV87 )
= $false )
| ( ( ~ ( relation_of2 @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 ) )
= $true )
| ( ( ~ ( element @ SV101 @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV113 @ SV58 ) )
= $true )
| ( ( element @ ( apply_binary_as_element @ SV12 @ SV58 @ SV78 @ SV87 @ SV101 @ SV113 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(768,plain,
! [SV114: $i,SV102: $i,SV83: $i,SV65: $i,SV29: $i,SV88: $i] :
( ( ( quasi_total @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
= $false )
| ( ( empty @ SV29 )
= $true )
| ( ( empty @ SV65 )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( ~ ( relation_of2 @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 ) )
= $true )
| ( ( ~ ( element @ SV102 @ SV29 ) )
= $true )
| ( ( ~ ( element @ SV114 @ SV65 ) )
= $true )
| ( ( ( apply_binary_as_element @ SV29 @ SV65 @ SV83 @ SV88 @ SV102 @ SV114 )
= ( apply_binary @ SV88 @ SV102 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(769,plain,
! [SV74: $i,SV44: $i,SV86: $i] :
( ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( ! [SY243: $i] :
~ ( ~ ~ ( ~ ( ! [SY244: $i,SY245: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY244 @ SY245 ) )
| ( SV44 = SY243 ) )
| ~ ! [SY246: $i] :
( ! [SY247: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY246 @ SY247 ) )
| ( SV74 = SY246 ) ) )
| ~ ! [SY248: $i,SY249: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SY243 @ SY248 @ SY249 ) )
| ( SV86 = SY249 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(770,plain,
! [SV117: $i,SV45: $i,SV105: $i] :
( ( ( relation_of2 @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( quasi_total @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( ~ ( function @ SV117 ) )
= $true )
| ( ( ~ ( quasi_total @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( latt_str @ ( latt_str_of @ SV45 @ SV105 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(771,plain,
! [SV118: $i,SV45: $i,SV106: $i] :
( ( ( relation_of2 @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( function @ SV106 )
= $false )
| ( ( quasi_total @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( ~ ( function @ SV118 ) )
= $true )
| ( ( ~ ( quasi_total @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV45 @ SV106 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(772,plain,
! [SV119: $i,SV47: $i,SV109: $i] :
( ( ( quasi_total @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( empty @ SV47 )
= $true )
| ( ( function @ SV109 )
= $false )
| ( ( ~ ( relation_of2 @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( function @ SV119 ) )
= $true )
| ( ( ~ ( quasi_total @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SV109 @ SV119 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(773,plain,
! [SV120: $i,SV47: $i,SV110: $i] :
( ( ( quasi_total @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( empty @ SV47 )
= $true )
| ( ( function @ SV110 )
= $false )
| ( ( ~ ( relation_of2 @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( function @ SV120 ) )
= $true )
| ( ( ~ ( quasi_total @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV47 @ SV110 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(774,plain,
! [SV130: $i,SV111: $i,SV49: $i] :
( ( ( ( join @ SV49 @ SV111 @ SV130 )
= SV130 )
= $false )
| ( ( below @ SV49 @ SV111 @ SV130 )
= $true )
| ( ( element @ SV130 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( element @ SV111 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(775,plain,
! [SV131: $i,SV111: $i,SV49: $i] :
( ( ( below @ SV49 @ SV111 @ SV131 )
= $false )
| ( ( ( join @ SV49 @ SV111 @ SV131 )
= SV131 )
= $true )
| ( ( element @ SV131 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( element @ SV111 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(776,plain,
! [SV113: $i,SV101: $i,SV78: $i,SV58: $i,SV12: $i,SV87: $i] :
( ( ( relation_of2 @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
= $false )
| ( ( function @ SV87 )
= $false )
| ( ( empty @ SV58 )
= $true )
| ( ( empty @ SV12 )
= $true )
| ( ( quasi_total @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
= $false )
| ( ( ~ ( element @ SV101 @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV113 @ SV58 ) )
= $true )
| ( ( element @ ( apply_binary_as_element @ SV12 @ SV58 @ SV78 @ SV87 @ SV101 @ SV113 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(777,plain,
! [SV114: $i,SV102: $i,SV83: $i,SV65: $i,SV29: $i,SV88: $i] :
( ( ( relation_of2 @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( empty @ SV65 )
= $true )
| ( ( empty @ SV29 )
= $true )
| ( ( quasi_total @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
= $false )
| ( ( ~ ( element @ SV102 @ SV29 ) )
= $true )
| ( ( ~ ( element @ SV114 @ SV65 ) )
= $true )
| ( ( ( apply_binary_as_element @ SV29 @ SV65 @ SV83 @ SV88 @ SV102 @ SV114 )
= ( apply_binary @ SV88 @ SV102 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(778,plain,
! [SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ! [SY269: $i,SY270: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY269 @ SY270 ) )
| ( SV44 = SV132 ) )
| ~ ! [SY271: $i] :
( ! [SY272: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY271 @ SY272 ) )
| ( SV74 = SY271 ) ) )
| ~ ! [SY273: $i,SY274: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY273 @ SY274 ) )
| ( SV86 = SY274 ) ) ) )
= $true )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(779,plain,
! [SV45: $i,SV105: $i,SV117: $i] :
( ( ( function @ SV117 )
= $false )
| ( ( quasi_total @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation_of2 @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( ~ ( quasi_total @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( latt_str @ ( latt_str_of @ SV45 @ SV105 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(780,plain,
! [SV45: $i,SV106: $i,SV118: $i] :
( ( ( function @ SV118 )
= $false )
| ( ( quasi_total @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( function @ SV106 )
= $false )
| ( ( relation_of2 @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( ~ ( quasi_total @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV45 @ SV106 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(781,plain,
! [SV119: $i,SV47: $i,SV109: $i] :
( ( ( relation_of2 @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( function @ SV109 )
= $false )
| ( ( empty @ SV47 )
= $true )
| ( ( quasi_total @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( ~ ( function @ SV119 ) )
= $true )
| ( ( ~ ( quasi_total @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SV109 @ SV119 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(782,plain,
! [SV120: $i,SV47: $i,SV110: $i] :
( ( ( relation_of2 @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( empty @ SV47 )
= $true )
| ( ( quasi_total @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( ~ ( function @ SV120 ) )
= $true )
| ( ( ~ ( quasi_total @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV47 @ SV110 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(783,plain,
! [SV113: $i,SV78: $i,SV58: $i,SV87: $i,SV12: $i,SV101: $i] :
( ( ( element @ SV101 @ SV12 )
= $false )
| ( ( quasi_total @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
= $false )
| ( ( empty @ SV12 )
= $true )
| ( ( empty @ SV58 )
= $true )
| ( ( function @ SV87 )
= $false )
| ( ( relation_of2 @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
= $false )
| ( ( ~ ( element @ SV113 @ SV58 ) )
= $true )
| ( ( element @ ( apply_binary_as_element @ SV12 @ SV58 @ SV78 @ SV87 @ SV101 @ SV113 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(784,plain,
! [SV114: $i,SV83: $i,SV65: $i,SV88: $i,SV29: $i,SV102: $i] :
( ( ( element @ SV102 @ SV29 )
= $false )
| ( ( quasi_total @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
= $false )
| ( ( empty @ SV29 )
= $true )
| ( ( empty @ SV65 )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation_of2 @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
= $false )
| ( ( ~ ( element @ SV114 @ SV65 ) )
= $true )
| ( ( ( apply_binary_as_element @ SV29 @ SV65 @ SV83 @ SV88 @ SV102 @ SV114 )
= ( apply_binary @ SV88 @ SV102 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(785,plain,
! [SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ~ ~ ( ~ ( ! [SY269: $i,SY270: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY269 @ SY270 ) )
| ( SV44 = SV132 ) )
| ~ ! [SY271: $i] :
( ! [SY272: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY271 @ SY272 ) )
| ( SV74 = SY271 ) ) )
| ~ ! [SY273: $i,SY274: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY273 @ SY274 ) )
| ( SV86 = SY274 ) ) )
= $false )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[778]) ).
thf(786,plain,
! [SV105: $i,SV45: $i,SV117: $i] :
( ( ( quasi_total @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( relation_of2 @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( quasi_total @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( function @ SV117 )
= $false )
| ( ( ~ ( relation_of2 @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( latt_str @ ( latt_str_of @ SV45 @ SV105 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(787,plain,
! [SV106: $i,SV45: $i,SV118: $i] :
( ( ( quasi_total @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( relation_of2 @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( function @ SV106 )
= $false )
| ( ( quasi_total @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( function @ SV118 )
= $false )
| ( ( ~ ( relation_of2 @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV45 @ SV106 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(788,plain,
! [SV47: $i,SV109: $i,SV119: $i] :
( ( ( function @ SV119 )
= $false )
| ( ( quasi_total @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( empty @ SV47 )
= $true )
| ( ( function @ SV109 )
= $false )
| ( ( relation_of2 @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( ~ ( quasi_total @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SV109 @ SV119 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(789,plain,
! [SV47: $i,SV110: $i,SV120: $i] :
( ( ( function @ SV120 )
= $false )
| ( ( quasi_total @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( empty @ SV47 )
= $true )
| ( ( function @ SV110 )
= $false )
| ( ( relation_of2 @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( ~ ( quasi_total @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV47 @ SV110 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(790,plain,
! [SV101: $i,SV78: $i,SV12: $i,SV87: $i,SV58: $i,SV113: $i] :
( ( ( element @ SV113 @ SV58 )
= $false )
| ( ( relation_of2 @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
= $false )
| ( ( function @ SV87 )
= $false )
| ( ( empty @ SV58 )
= $true )
| ( ( empty @ SV12 )
= $true )
| ( ( quasi_total @ SV87 @ ( cartesian_product2 @ SV12 @ SV58 ) @ SV78 )
= $false )
| ( ( element @ SV101 @ SV12 )
= $false )
| ( ( element @ ( apply_binary_as_element @ SV12 @ SV58 @ SV78 @ SV87 @ SV101 @ SV113 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(791,plain,
! [SV102: $i,SV83: $i,SV29: $i,SV88: $i,SV65: $i,SV114: $i] :
( ( ( element @ SV114 @ SV65 )
= $false )
| ( ( relation_of2 @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( empty @ SV65 )
= $true )
| ( ( empty @ SV29 )
= $true )
| ( ( quasi_total @ SV88 @ ( cartesian_product2 @ SV29 @ SV65 ) @ SV83 )
= $false )
| ( ( element @ SV102 @ SV29 )
= $false )
| ( ( ( apply_binary_as_element @ SV29 @ SV65 @ SV83 @ SV88 @ SV102 @ SV114 )
= ( apply_binary @ SV88 @ SV102 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[784]) ).
thf(792,plain,
! [SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ~ ~ ( ~ ( ! [SY269: $i,SY270: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY269 @ SY270 ) )
| ( SV44 = SV132 ) )
| ~ ! [SY271: $i] :
( ! [SY272: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY271 @ SY272 ) )
| ( SV74 = SY271 ) ) ) )
= $false )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[785]) ).
thf(793,plain,
! [SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ~ ! [SY273: $i,SY274: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY273 @ SY274 ) )
| ( SV86 = SY274 ) ) )
= $false )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[785]) ).
thf(794,plain,
! [SV105: $i,SV45: $i,SV117: $i] :
( ( ( relation_of2 @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( function @ SV117 )
= $false )
| ( ( quasi_total @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation_of2 @ SV105 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( quasi_total @ SV117 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( latt_str @ ( latt_str_of @ SV45 @ SV105 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(795,plain,
! [SV106: $i,SV45: $i,SV118: $i] :
( ( ( relation_of2 @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( function @ SV118 )
= $false )
| ( ( quasi_total @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( function @ SV106 )
= $false )
| ( ( relation_of2 @ SV106 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( quasi_total @ SV118 @ ( cartesian_product2 @ SV45 @ SV45 ) @ SV45 )
= $false )
| ( ( strict_latt_str @ ( latt_str_of @ SV45 @ SV106 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(796,plain,
! [SV109: $i,SV47: $i,SV119: $i] :
( ( ( quasi_total @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( relation_of2 @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( function @ SV109 )
= $false )
| ( ( empty @ SV47 )
= $true )
| ( ( quasi_total @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( function @ SV119 )
= $false )
| ( ( ~ ( relation_of2 @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SV109 @ SV119 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(797,plain,
! [SV110: $i,SV47: $i,SV120: $i] :
( ( ( quasi_total @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( relation_of2 @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( empty @ SV47 )
= $true )
| ( ( quasi_total @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( function @ SV120 )
= $false )
| ( ( ~ ( relation_of2 @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 ) )
= $true )
| ( ( strict_latt_str @ ( latt_str_of @ SV47 @ SV110 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(798,plain,
! [SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ~ ( ~ ( ! [SY269: $i,SY270: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY269 @ SY270 ) )
| ( SV44 = SV132 ) )
| ~ ! [SY271: $i] :
( ! [SY272: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY271 @ SY272 ) )
| ( SV74 = SY271 ) ) ) )
= $true )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(799,plain,
! [SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ! [SY273: $i,SY274: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY273 @ SY274 ) )
| ( SV86 = SY274 ) ) )
= $true )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[793]) ).
thf(800,plain,
! [SV109: $i,SV47: $i,SV119: $i] :
( ( ( relation_of2 @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( function @ SV119 )
= $false )
| ( ( quasi_total @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( empty @ SV47 )
= $true )
| ( ( function @ SV109 )
= $false )
| ( ( relation_of2 @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( quasi_total @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( ~ ( empty_carrier @ ( latt_str_of @ SV47 @ SV109 @ SV119 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(801,plain,
! [SV110: $i,SV47: $i,SV120: $i] :
( ( ( relation_of2 @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( function @ SV120 )
= $false )
| ( ( quasi_total @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( empty @ SV47 )
= $true )
| ( ( function @ SV110 )
= $false )
| ( ( relation_of2 @ SV110 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( quasi_total @ SV120 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( strict_latt_str @ ( latt_str_of @ SV47 @ SV110 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(802,plain,
! [SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ~ ( ! [SY269: $i,SY270: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY269 @ SY270 ) )
| ( SV44 = SV132 ) )
| ~ ! [SY271: $i] :
( ! [SY272: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY271 @ SY272 ) )
| ( SV74 = SY271 ) ) )
= $false )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(803,plain,
! [SV133: $i,SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ! [SY275: $i] :
( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SV133 @ SY275 ) )
| ( SV86 = SY275 ) ) )
= $true )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(804,plain,
! [SV119: $i,SV109: $i,SV47: $i] :
( ( ( empty_carrier @ ( latt_str_of @ SV47 @ SV109 @ SV119 ) )
= $false )
| ( ( quasi_total @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( relation_of2 @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( function @ SV109 )
= $false )
| ( ( empty @ SV47 )
= $true )
| ( ( quasi_total @ SV109 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false )
| ( ( function @ SV119 )
= $false )
| ( ( relation_of2 @ SV119 @ ( cartesian_product2 @ SV47 @ SV47 ) @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(805,plain,
! [SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ~ ( ! [SY269: $i,SY270: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY269 @ SY270 ) )
| ( SV44 = SV132 ) ) )
= $false )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[802]) ).
thf(806,plain,
! [SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ~ ! [SY271: $i] :
( ! [SY272: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY271 @ SY272 ) )
| ( SV74 = SY271 ) ) )
= $false )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[802]) ).
thf(807,plain,
! [SV134: $i,SV133: $i,SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SV133 @ SV134 ) )
| ( SV86 = SV134 ) )
= $true )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(808,plain,
! [SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ! [SY269: $i,SY270: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY269 @ SY270 ) )
| ( SV44 = SV132 ) )
= $true )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[805]) ).
thf(809,plain,
! [SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ! [SY271: $i] :
( ! [SY272: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY271 @ SY272 ) )
| ( SV74 = SY271 ) ) )
= $true )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(810,plain,
! [SV134: $i,SV133: $i,SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SV133 @ SV134 ) ) )
= $true )
| ( ( SV86 = SV134 )
= $true )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[807]) ).
thf(811,plain,
! [SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ! [SY269: $i,SY270: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SY269 @ SY270 ) ) )
= $true )
| ( ( SV44 = SV132 )
= $true )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[808]) ).
thf(812,plain,
! [SV135: $i,SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ! [SY276: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SV135 @ SY276 ) )
| ( SV74 = SV135 ) )
= $true )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(813,plain,
! [SV134: $i,SV133: $i,SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
= ( latt_str_of @ SV132 @ SV133 @ SV134 ) )
= $false )
| ( ( SV86 = SV134 )
= $true )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(814,plain,
! [SV136: $i,SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ! [SY277: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SV136 @ SY277 ) ) )
= $true )
| ( ( SV44 = SV132 )
= $true )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(815,plain,
! [SV135: $i,SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ! [SY276: $i] :
( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SV135 @ SY276 ) ) )
= $true )
| ( ( SV74 = SV135 )
= $true )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[812]) ).
thf(816,plain,
! [SV137: $i,SV136: $i,SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SV136 @ SV137 ) ) )
= $true )
| ( ( SV44 = SV132 )
= $true )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(817,plain,
! [SV138: $i,SV135: $i,SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
!= ( latt_str_of @ SV132 @ SV135 @ SV138 ) ) )
= $true )
| ( ( SV74 = SV135 )
= $true )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(818,plain,
! [SV137: $i,SV136: $i,SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
= ( latt_str_of @ SV132 @ SV136 @ SV137 ) )
= $false )
| ( ( SV44 = SV132 )
= $true )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(819,plain,
! [SV138: $i,SV135: $i,SV132: $i,SV86: $i,SV74: $i,SV44: $i] :
( ( ( ( latt_str_of @ SV44 @ SV74 @ SV86 )
= ( latt_str_of @ SV132 @ SV135 @ SV138 ) )
= $false )
| ( ( SV74 = SV135 )
= $true )
| ( ( quasi_total @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( relation_of2 @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( quasi_total @ SV74 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation_of2 @ SV86 @ ( cartesian_product2 @ SV44 @ SV44 ) @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[817]) ).
thf(820,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[237,819,818,813,804,801,795,794,791,790,775,774,730,729,720,718,717,716,711,710,709,703,702,682,681,680,679,667,663,662,661,652,650,643,639,632,629,628,626,622,615,595,586,577,574,572,571,570,563,562,561,560,557,556,555,554,539,526,525,522,521,508,506,505,496,488,474,465,461,460,420,407,406,404,403,396,392,391,390,360,358,356,354,353,352,343,305,282,271,264,263,262,261,259,256,255,252,250,249,248,247,246,243,242,241,238]) ).
thf(821,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[820]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU344+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 11:24:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.37 .
% 0.18/0.41
% 0.18/0.41 No.of.Axioms: 80
% 0.18/0.41
% 0.18/0.41 Length.of.Defs: 0
% 0.18/0.41
% 0.18/0.41 Contains.Choice.Funs: false
% 0.18/0.43 ..
% 0.18/0.46 (rf:0,axioms:80,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:82,loop_count:0,foatp_calls:0,translation:fof_full).................................................
% 0.61/1.07
% 0.61/1.07 ********************************
% 0.61/1.07 * All subproblems solved! *
% 0.61/1.07 ********************************
% 0.61/1.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:81,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:820,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.12/1.35
% 1.12/1.35 %**** Beginning of derivation protocol ****
% 1.12/1.35 % SZS output start CNFRefutation
% See solution above
% 1.12/1.35
% 1.12/1.35 %**** End of derivation protocol ****
% 1.12/1.35 %**** no. of clauses in derivation: 821 ****
% 1.12/1.35 %**** clause counter: 820 ****
% 1.12/1.35
% 1.12/1.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:81,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:820,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------