TSTP Solution File: SEU346+1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU346+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.AUcU64zN6d true
% Computer : n003.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 : 300s
% DateTime : Thu Aug 31 19:12:17 EDT 2023
% Result : Theorem 28.91s 4.74s
% Output : Refutation 28.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 51
% Syntax : Number of formulae : 259 ( 114 unt; 33 typ; 0 def)
% Number of atoms : 549 ( 69 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 1923 ( 209 ~; 244 |; 44 &;1391 @)
% ( 6 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 33 usr; 4 con; 0-4 aty)
% Number of variables : 130 ( 0 ^; 130 !; 0 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
thf(reflexive_relstr_type,type,
reflexive_relstr: $i > $o ).
thf(rel_str_type,type,
rel_str: $i > $o ).
thf(transitive_type,type,
transitive: $i > $o ).
thf(reflexive_type,type,
reflexive: $i > $o ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(rel_str_of_type,type,
rel_str_of: $i > $i > $i ).
thf(cast_to_el_of_LattPOSet_type,type,
cast_to_el_of_LattPOSet: $i > $i > $i ).
thf(one_sorted_str_type,type,
one_sorted_str: $i > $o ).
thf(antisymmetric_type,type,
antisymmetric: $i > $o ).
thf(ordered_pair_as_product_element_type,type,
ordered_pair_as_product_element: $i > $i > $i > $i > $i ).
thf(below_refl_type,type,
below_refl: $i > $i > $i > $o ).
thf(related_reflexive_type,type,
related_reflexive: $i > $i > $i > $o ).
thf(poset_of_lattice_type,type,
poset_of_lattice: $i > $i ).
thf(k2_lattice3_type,type,
k2_lattice3: $i > $i ).
thf(sk__20_type,type,
sk__20: $i ).
thf(strict_rel_str_type,type,
strict_rel_str: $i > $o ).
thf(related_type,type,
related: $i > $i > $i > $o ).
thf(latt_str_type,type,
latt_str: $i > $o ).
thf(empty_carrier_type,type,
empty_carrier: $i > $o ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(relation_of2_as_subset_type,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(relation_of2_type,type,
relation_of2: $i > $i > $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(antisymmetric_relstr_type,type,
antisymmetric_relstr: $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(sk__19_type,type,
sk__19: $i ).
thf(sk__21_type,type,
sk__21: $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(the_InternalRel_type,type,
the_InternalRel: $i > $i ).
thf(lattice_type,type,
lattice: $i > $o ).
thf(transitive_relstr_type,type,
transitive_relstr: $i > $o ).
thf(the_carrier_type,type,
the_carrier: $i > $i ).
thf(relation_of_lattice_type,type,
relation_of_lattice: $i > $i ).
thf(t7_lattice3,conjecture,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( below_refl @ A @ B @ C )
<=> ( related_reflexive @ ( poset_of_lattice @ A ) @ ( cast_to_el_of_LattPOSet @ A @ B ) @ ( cast_to_el_of_LattPOSet @ A @ C ) ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( below_refl @ A @ B @ C )
<=> ( related_reflexive @ ( poset_of_lattice @ A ) @ ( cast_to_el_of_LattPOSet @ A @ B ) @ ( cast_to_el_of_LattPOSet @ A @ C ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[t7_lattice3]) ).
thf(zip_derived_cl174,plain,
~ ( empty_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl177,plain,
element @ sk__21 @ ( the_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl180,plain,
element @ sk__20 @ ( the_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(redefinition_k1_domain_1,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( element @ C @ A )
& ( element @ D @ B ) )
=> ( ( ordered_pair_as_product_element @ A @ B @ C @ D )
= ( ordered_pair @ C @ D ) ) ) ).
thf(zip_derived_cl153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( element @ X0 @ X1 )
| ( empty @ X2 )
| ( empty @ X1 )
| ~ ( element @ X3 @ X2 )
| ( ( ordered_pair_as_product_element @ X1 @ X2 @ X0 @ X3 )
= ( ordered_pair @ X0 @ X3 ) ) ),
inference(cnf,[status(esa)],[redefinition_k1_domain_1]) ).
thf(zip_derived_cl6268,plain,
! [X0: $i,X1: $i] :
( ( ( ordered_pair_as_product_element @ ( the_carrier @ sk__19 ) @ X1 @ sk__20 @ X0 )
= ( ordered_pair @ sk__20 @ X0 ) )
| ~ ( element @ X0 @ X1 )
| ( empty @ ( the_carrier @ sk__19 ) )
| ( empty @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl180,zip_derived_cl153]) ).
thf(zip_derived_cl25695,plain,
( ( empty @ ( the_carrier @ sk__19 ) )
| ( empty @ ( the_carrier @ sk__19 ) )
| ( ( ordered_pair_as_product_element @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ) @ sk__20 @ sk__21 )
= ( ordered_pair @ sk__20 @ sk__21 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl177,zip_derived_cl6268]) ).
thf(zip_derived_cl25740,plain,
( ( ( ordered_pair_as_product_element @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ) @ sk__20 @ sk__21 )
= ( ordered_pair @ sk__20 @ sk__21 ) )
| ( empty @ ( the_carrier @ sk__19 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl25695]) ).
thf(zip_derived_cl179,plain,
( ( related_reflexive @ ( poset_of_lattice @ sk__19 ) @ ( cast_to_el_of_LattPOSet @ sk__19 @ sk__20 ) @ ( cast_to_el_of_LattPOSet @ sk__19 @ sk__21 ) )
| ( below_refl @ sk__19 @ sk__20 @ sk__21 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl180_001,plain,
element @ sk__20 @ ( the_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(d3_lattice3,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( cast_to_el_of_LattPOSet @ A @ B )
= B ) ) ) ).
thf(zip_derived_cl15,plain,
! [X0: $i,X1: $i] :
( ~ ( element @ X0 @ ( the_carrier @ X1 ) )
| ( ( cast_to_el_of_LattPOSet @ X1 @ X0 )
= X0 )
| ~ ( latt_str @ X1 )
| ~ ( lattice @ X1 )
| ( empty_carrier @ X1 ) ),
inference(cnf,[status(esa)],[d3_lattice3]) ).
thf(zip_derived_cl725,plain,
( ( empty_carrier @ sk__19 )
| ~ ( lattice @ sk__19 )
| ~ ( latt_str @ sk__19 )
| ( ( cast_to_el_of_LattPOSet @ sk__19 @ sk__20 )
= sk__20 ) ),
inference('sup-',[status(thm)],[zip_derived_cl180,zip_derived_cl15]) ).
thf(zip_derived_cl174_002,plain,
~ ( empty_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl175,plain,
lattice @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl176,plain,
latt_str @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl729,plain,
( ( cast_to_el_of_LattPOSet @ sk__19 @ sk__20 )
= sk__20 ),
inference(demod,[status(thm)],[zip_derived_cl725,zip_derived_cl174,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl177_003,plain,
element @ sk__21 @ ( the_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl15_004,plain,
! [X0: $i,X1: $i] :
( ~ ( element @ X0 @ ( the_carrier @ X1 ) )
| ( ( cast_to_el_of_LattPOSet @ X1 @ X0 )
= X0 )
| ~ ( latt_str @ X1 )
| ~ ( lattice @ X1 )
| ( empty_carrier @ X1 ) ),
inference(cnf,[status(esa)],[d3_lattice3]) ).
thf(zip_derived_cl726,plain,
( ( empty_carrier @ sk__19 )
| ~ ( lattice @ sk__19 )
| ~ ( latt_str @ sk__19 )
| ( ( cast_to_el_of_LattPOSet @ sk__19 @ sk__21 )
= sk__21 ) ),
inference('sup-',[status(thm)],[zip_derived_cl177,zip_derived_cl15]) ).
thf(zip_derived_cl174_005,plain,
~ ( empty_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl175_006,plain,
lattice @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl176_007,plain,
latt_str @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl730,plain,
( ( cast_to_el_of_LattPOSet @ sk__19 @ sk__21 )
= sk__21 ),
inference(demod,[status(thm)],[zip_derived_cl726,zip_derived_cl174,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl7916,plain,
( ( related_reflexive @ ( poset_of_lattice @ sk__19 ) @ sk__20 @ sk__21 )
| ( below_refl @ sk__19 @ sk__20 @ sk__21 ) ),
inference(demod,[status(thm)],[zip_derived_cl179,zip_derived_cl729,zip_derived_cl730]) ).
thf(zip_derived_cl180_008,plain,
element @ sk__20 @ ( the_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(abstractness_v1_orders_2,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( strict_rel_str @ A )
=> ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) ) ).
thf(zip_derived_cl0,plain,
! [X0: $i] :
( ~ ( strict_rel_str @ X0 )
| ( X0
= ( rel_str_of @ ( the_carrier @ X0 ) @ ( the_InternalRel @ X0 ) ) )
| ~ ( rel_str @ X0 ) ),
inference(cnf,[status(esa)],[abstractness_v1_orders_2]) ).
thf(redefinition_k2_lattice3,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( k2_lattice3 @ A )
= ( relation_of_lattice @ A ) ) ) ).
thf(zip_derived_cl154,plain,
! [X0: $i] :
( ( ( k2_lattice3 @ X0 )
= ( relation_of_lattice @ X0 ) )
| ~ ( latt_str @ X0 )
| ~ ( lattice @ X0 )
| ( empty_carrier @ X0 ) ),
inference(cnf,[status(esa)],[redefinition_k2_lattice3]) ).
thf(zip_derived_cl174_009,plain,
~ ( empty_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl822,plain,
( ~ ( lattice @ sk__19 )
| ~ ( latt_str @ sk__19 )
| ( ( k2_lattice3 @ sk__19 )
= ( relation_of_lattice @ sk__19 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl154,zip_derived_cl174]) ).
thf(zip_derived_cl175_010,plain,
lattice @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl176_011,plain,
latt_str @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl825,plain,
( ( k2_lattice3 @ sk__19 )
= ( relation_of_lattice @ sk__19 ) ),
inference(demod,[status(thm)],[zip_derived_cl822,zip_derived_cl175,zip_derived_cl176]) ).
thf(d2_lattice3,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( poset_of_lattice @ A )
= ( rel_str_of @ ( the_carrier @ A ) @ ( k2_lattice3 @ A ) ) ) ) ).
thf(zip_derived_cl14,plain,
! [X0: $i] :
( ( ( poset_of_lattice @ X0 )
= ( rel_str_of @ ( the_carrier @ X0 ) @ ( k2_lattice3 @ X0 ) ) )
| ~ ( latt_str @ X0 )
| ~ ( lattice @ X0 )
| ( empty_carrier @ X0 ) ),
inference(cnf,[status(esa)],[d2_lattice3]) ).
thf(zip_derived_cl829,plain,
( ( ( poset_of_lattice @ sk__19 )
= ( rel_str_of @ ( the_carrier @ sk__19 ) @ ( relation_of_lattice @ sk__19 ) ) )
| ( empty_carrier @ sk__19 )
| ~ ( lattice @ sk__19 )
| ~ ( latt_str @ sk__19 ) ),
inference('sup+',[status(thm)],[zip_derived_cl825,zip_derived_cl14]) ).
thf(zip_derived_cl174_012,plain,
~ ( empty_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl175_013,plain,
lattice @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl176_014,plain,
latt_str @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl832,plain,
( ( poset_of_lattice @ sk__19 )
= ( rel_str_of @ ( the_carrier @ sk__19 ) @ ( relation_of_lattice @ sk__19 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl829,zip_derived_cl174,zip_derived_cl175,zip_derived_cl176]) ).
thf(free_g1_orders_2,axiom,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ! [C: $i,D: $i] :
( ( ( rel_str_of @ A @ B )
= ( rel_str_of @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ) ).
thf(zip_derived_cl114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( rel_str_of @ X2 @ X3 )
!= ( rel_str_of @ X0 @ X1 ) )
| ( X3 = X1 )
| ~ ( relation_of2 @ X3 @ X2 @ X2 ) ),
inference(cnf,[status(esa)],[free_g1_orders_2]) ).
thf(zip_derived_cl2300,plain,
! [X0: $i,X1: $i] :
( ( ( poset_of_lattice @ sk__19 )
!= ( rel_str_of @ X1 @ X0 ) )
| ~ ( relation_of2 @ ( relation_of_lattice @ sk__19 ) @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ) )
| ( ( relation_of_lattice @ sk__19 )
= X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl832,zip_derived_cl114]) ).
thf(zip_derived_cl825_015,plain,
( ( k2_lattice3 @ sk__19 )
= ( relation_of_lattice @ sk__19 ) ),
inference(demod,[status(thm)],[zip_derived_cl822,zip_derived_cl175,zip_derived_cl176]) ).
thf(dt_k2_lattice3,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( reflexive @ ( k2_lattice3 @ A ) )
& ( antisymmetric @ ( k2_lattice3 @ A ) )
& ( transitive @ ( k2_lattice3 @ A ) )
& ( v1_partfun1 @ ( k2_lattice3 @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( k2_lattice3 @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) ) ).
thf(zip_derived_cl32,plain,
! [X0: $i] :
( ( relation_of2_as_subset @ ( k2_lattice3 @ X0 ) @ ( the_carrier @ X0 ) @ ( the_carrier @ X0 ) )
| ~ ( latt_str @ X0 )
| ~ ( lattice @ X0 )
| ( empty_carrier @ X0 ) ),
inference(cnf,[status(esa)],[dt_k2_lattice3]) ).
thf(zip_derived_cl1320,plain,
( ( relation_of2_as_subset @ ( relation_of_lattice @ sk__19 ) @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ) )
| ( empty_carrier @ sk__19 )
| ~ ( lattice @ sk__19 )
| ~ ( latt_str @ sk__19 ) ),
inference('sup+',[status(thm)],[zip_derived_cl825,zip_derived_cl32]) ).
thf(zip_derived_cl174_016,plain,
~ ( empty_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl175_017,plain,
lattice @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl176_018,plain,
latt_str @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1322,plain,
relation_of2_as_subset @ ( relation_of_lattice @ sk__19 ) @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl1320,zip_derived_cl174,zip_derived_cl175,zip_derived_cl176]) ).
thf(redefinition_m2_relset_1,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ) ).
thf(zip_derived_cl155,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_of2 @ X0 @ X1 @ X2 )
| ~ ( relation_of2_as_subset @ X0 @ X1 @ X2 ) ),
inference(cnf,[status(esa)],[redefinition_m2_relset_1]) ).
thf(zip_derived_cl1332,plain,
relation_of2 @ ( relation_of_lattice @ sk__19 ) @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ),
inference('sup-',[status(thm)],[zip_derived_cl1322,zip_derived_cl155]) ).
thf(zip_derived_cl2310,plain,
! [X0: $i,X1: $i] :
( ( ( poset_of_lattice @ sk__19 )
!= ( rel_str_of @ X1 @ X0 ) )
| ( ( relation_of_lattice @ sk__19 )
= X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2300,zip_derived_cl1332]) ).
thf(zip_derived_cl2319,plain,
! [X0: $i] :
( ( ( poset_of_lattice @ sk__19 )
!= X0 )
| ~ ( rel_str @ X0 )
| ~ ( strict_rel_str @ X0 )
| ( ( relation_of_lattice @ sk__19 )
= ( the_InternalRel @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl0,zip_derived_cl2310]) ).
thf(zip_derived_cl2334,plain,
( ( ( relation_of_lattice @ sk__19 )
= ( the_InternalRel @ ( poset_of_lattice @ sk__19 ) ) )
| ~ ( strict_rel_str @ ( poset_of_lattice @ sk__19 ) )
| ~ ( rel_str @ ( poset_of_lattice @ sk__19 ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl2319]) ).
thf(zip_derived_cl1332_019,plain,
relation_of2 @ ( relation_of_lattice @ sk__19 ) @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ),
inference('sup-',[status(thm)],[zip_derived_cl1322,zip_derived_cl155]) ).
thf(dt_g1_orders_2,axiom,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( rel_str @ ( rel_str_of @ A @ B ) ) ) ) ).
thf(zip_derived_cl19,plain,
! [X0: $i,X1: $i] :
( ( strict_rel_str @ ( rel_str_of @ X0 @ X1 ) )
| ~ ( relation_of2 @ X1 @ X0 @ X0 ) ),
inference(cnf,[status(esa)],[dt_g1_orders_2]) ).
thf(zip_derived_cl1346,plain,
strict_rel_str @ ( rel_str_of @ ( the_carrier @ sk__19 ) @ ( relation_of_lattice @ sk__19 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1332,zip_derived_cl19]) ).
thf(zip_derived_cl832_020,plain,
( ( poset_of_lattice @ sk__19 )
= ( rel_str_of @ ( the_carrier @ sk__19 ) @ ( relation_of_lattice @ sk__19 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl829,zip_derived_cl174,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl1361,plain,
strict_rel_str @ ( poset_of_lattice @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl1346,zip_derived_cl832]) ).
thf(zip_derived_cl1332_021,plain,
relation_of2 @ ( relation_of_lattice @ sk__19 ) @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ),
inference('sup-',[status(thm)],[zip_derived_cl1322,zip_derived_cl155]) ).
thf(zip_derived_cl20,plain,
! [X0: $i,X1: $i] :
( ( rel_str @ ( rel_str_of @ X0 @ X1 ) )
| ~ ( relation_of2 @ X1 @ X0 @ X0 ) ),
inference(cnf,[status(esa)],[dt_g1_orders_2]) ).
thf(zip_derived_cl1347,plain,
rel_str @ ( rel_str_of @ ( the_carrier @ sk__19 ) @ ( relation_of_lattice @ sk__19 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1332,zip_derived_cl20]) ).
thf(zip_derived_cl832_022,plain,
( ( poset_of_lattice @ sk__19 )
= ( rel_str_of @ ( the_carrier @ sk__19 ) @ ( relation_of_lattice @ sk__19 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl829,zip_derived_cl174,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl1362,plain,
rel_str @ ( poset_of_lattice @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl1347,zip_derived_cl832]) ).
thf(zip_derived_cl2335,plain,
( ( relation_of_lattice @ sk__19 )
= ( the_InternalRel @ ( poset_of_lattice @ sk__19 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2334,zip_derived_cl1361,zip_derived_cl1362]) ).
thf(zip_derived_cl0_023,plain,
! [X0: $i] :
( ~ ( strict_rel_str @ X0 )
| ( X0
= ( rel_str_of @ ( the_carrier @ X0 ) @ ( the_InternalRel @ X0 ) ) )
| ~ ( rel_str @ X0 ) ),
inference(cnf,[status(esa)],[abstractness_v1_orders_2]) ).
thf(zip_derived_cl2336,plain,
( ( ( poset_of_lattice @ sk__19 )
= ( rel_str_of @ ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) @ ( relation_of_lattice @ sk__19 ) ) )
| ~ ( rel_str @ ( poset_of_lattice @ sk__19 ) )
| ~ ( strict_rel_str @ ( poset_of_lattice @ sk__19 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2335,zip_derived_cl0]) ).
thf(zip_derived_cl1362_024,plain,
rel_str @ ( poset_of_lattice @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl1347,zip_derived_cl832]) ).
thf(zip_derived_cl1361_025,plain,
strict_rel_str @ ( poset_of_lattice @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl1346,zip_derived_cl832]) ).
thf(zip_derived_cl2348,plain,
( ( poset_of_lattice @ sk__19 )
= ( rel_str_of @ ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) @ ( relation_of_lattice @ sk__19 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2336,zip_derived_cl1362,zip_derived_cl1361]) ).
thf(zip_derived_cl832_026,plain,
( ( poset_of_lattice @ sk__19 )
= ( rel_str_of @ ( the_carrier @ sk__19 ) @ ( relation_of_lattice @ sk__19 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl829,zip_derived_cl174,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( rel_str_of @ X2 @ X3 )
!= ( rel_str_of @ X0 @ X1 ) )
| ( X2 = X0 )
| ~ ( relation_of2 @ X3 @ X2 @ X2 ) ),
inference(cnf,[status(esa)],[free_g1_orders_2]) ).
thf(zip_derived_cl5168,plain,
! [X0: $i,X1: $i] :
( ( ( poset_of_lattice @ sk__19 )
!= ( rel_str_of @ X1 @ X0 ) )
| ~ ( relation_of2 @ ( relation_of_lattice @ sk__19 ) @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ) )
| ( ( the_carrier @ sk__19 )
= X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl832,zip_derived_cl115]) ).
thf(zip_derived_cl1332_027,plain,
relation_of2 @ ( relation_of_lattice @ sk__19 ) @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ),
inference('sup-',[status(thm)],[zip_derived_cl1322,zip_derived_cl155]) ).
thf(zip_derived_cl5183,plain,
! [X0: $i,X1: $i] :
( ( ( poset_of_lattice @ sk__19 )
!= ( rel_str_of @ X1 @ X0 ) )
| ( ( the_carrier @ sk__19 )
= X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl5168,zip_derived_cl1332]) ).
thf(zip_derived_cl5375,plain,
( ( ( poset_of_lattice @ sk__19 )
!= ( poset_of_lattice @ sk__19 ) )
| ( ( the_carrier @ sk__19 )
= ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2348,zip_derived_cl5183]) ).
thf(zip_derived_cl5378,plain,
( ( the_carrier @ sk__19 )
= ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl5375]) ).
thf(redefinition_r3_orders_2,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( rel_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( related_reflexive @ A @ B @ C )
<=> ( related @ A @ B @ C ) ) ) ).
thf(zip_derived_cl160,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( element @ X0 @ ( the_carrier @ X1 ) )
| ~ ( rel_str @ X1 )
| ~ ( reflexive_relstr @ X1 )
| ( empty_carrier @ X1 )
| ~ ( element @ X2 @ ( the_carrier @ X1 ) )
| ( related @ X1 @ X0 @ X2 )
| ~ ( related_reflexive @ X1 @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[redefinition_r3_orders_2]) ).
thf(zip_derived_cl6801,plain,
! [X0: $i,X1: $i] :
( ~ ( element @ X0 @ ( the_carrier @ sk__19 ) )
| ~ ( related_reflexive @ ( poset_of_lattice @ sk__19 ) @ X0 @ X1 )
| ( related @ ( poset_of_lattice @ sk__19 ) @ X0 @ X1 )
| ~ ( element @ X1 @ ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) )
| ( empty_carrier @ ( poset_of_lattice @ sk__19 ) )
| ~ ( reflexive_relstr @ ( poset_of_lattice @ sk__19 ) )
| ~ ( rel_str @ ( poset_of_lattice @ sk__19 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl5378,zip_derived_cl160]) ).
thf(zip_derived_cl5378_028,plain,
( ( the_carrier @ sk__19 )
= ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl5375]) ).
thf(zip_derived_cl1332_029,plain,
relation_of2 @ ( relation_of_lattice @ sk__19 ) @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ),
inference('sup-',[status(thm)],[zip_derived_cl1322,zip_derived_cl155]) ).
thf(fc3_orders_2,axiom,
! [A: $i,B: $i] :
( ( ( reflexive @ B )
& ( antisymmetric @ B )
& ( transitive @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( relation_of2 @ B @ A @ A ) )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( reflexive_relstr @ ( rel_str_of @ A @ B ) )
& ( transitive_relstr @ ( rel_str_of @ A @ B ) )
& ( antisymmetric_relstr @ ( rel_str_of @ A @ B ) ) ) ) ).
thf(zip_derived_cl94,plain,
! [X0: $i,X1: $i] :
( ( reflexive_relstr @ ( rel_str_of @ X0 @ X1 ) )
| ~ ( relation_of2 @ X1 @ X0 @ X0 )
| ~ ( v1_partfun1 @ X1 @ X0 @ X0 )
| ~ ( transitive @ X1 )
| ~ ( antisymmetric @ X1 )
| ~ ( reflexive @ X1 ) ),
inference(cnf,[status(esa)],[fc3_orders_2]) ).
thf(zip_derived_cl4150,plain,
( ~ ( reflexive @ ( relation_of_lattice @ sk__19 ) )
| ~ ( antisymmetric @ ( relation_of_lattice @ sk__19 ) )
| ~ ( transitive @ ( relation_of_lattice @ sk__19 ) )
| ~ ( v1_partfun1 @ ( relation_of_lattice @ sk__19 ) @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ) )
| ( reflexive_relstr @ ( rel_str_of @ ( the_carrier @ sk__19 ) @ ( relation_of_lattice @ sk__19 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1332,zip_derived_cl94]) ).
thf(zip_derived_cl28,plain,
! [X0: $i] :
( ( reflexive @ ( k2_lattice3 @ X0 ) )
| ~ ( latt_str @ X0 )
| ~ ( lattice @ X0 )
| ( empty_carrier @ X0 ) ),
inference(cnf,[status(esa)],[dt_k2_lattice3]) ).
thf(zip_derived_cl174_030,plain,
~ ( empty_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl544,plain,
( ~ ( lattice @ sk__19 )
| ~ ( latt_str @ sk__19 )
| ( reflexive @ ( k2_lattice3 @ sk__19 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl28,zip_derived_cl174]) ).
thf(zip_derived_cl175_031,plain,
lattice @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl176_032,plain,
latt_str @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl547,plain,
reflexive @ ( k2_lattice3 @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl544,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl825_033,plain,
( ( k2_lattice3 @ sk__19 )
= ( relation_of_lattice @ sk__19 ) ),
inference(demod,[status(thm)],[zip_derived_cl822,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl826,plain,
reflexive @ ( relation_of_lattice @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl547,zip_derived_cl825]) ).
thf(zip_derived_cl29,plain,
! [X0: $i] :
( ( antisymmetric @ ( k2_lattice3 @ X0 ) )
| ~ ( latt_str @ X0 )
| ~ ( lattice @ X0 )
| ( empty_carrier @ X0 ) ),
inference(cnf,[status(esa)],[dt_k2_lattice3]) ).
thf(zip_derived_cl174_034,plain,
~ ( empty_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl578,plain,
( ~ ( lattice @ sk__19 )
| ~ ( latt_str @ sk__19 )
| ( antisymmetric @ ( k2_lattice3 @ sk__19 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl29,zip_derived_cl174]) ).
thf(zip_derived_cl175_035,plain,
lattice @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl176_036,plain,
latt_str @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl581,plain,
antisymmetric @ ( k2_lattice3 @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl578,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl825_037,plain,
( ( k2_lattice3 @ sk__19 )
= ( relation_of_lattice @ sk__19 ) ),
inference(demod,[status(thm)],[zip_derived_cl822,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl827,plain,
antisymmetric @ ( relation_of_lattice @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl581,zip_derived_cl825]) ).
thf(zip_derived_cl30,plain,
! [X0: $i] :
( ( transitive @ ( k2_lattice3 @ X0 ) )
| ~ ( latt_str @ X0 )
| ~ ( lattice @ X0 )
| ( empty_carrier @ X0 ) ),
inference(cnf,[status(esa)],[dt_k2_lattice3]) ).
thf(zip_derived_cl174_038,plain,
~ ( empty_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl591,plain,
( ~ ( lattice @ sk__19 )
| ~ ( latt_str @ sk__19 )
| ( transitive @ ( k2_lattice3 @ sk__19 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl174]) ).
thf(zip_derived_cl175_039,plain,
lattice @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl176_040,plain,
latt_str @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl594,plain,
transitive @ ( k2_lattice3 @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl591,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl825_041,plain,
( ( k2_lattice3 @ sk__19 )
= ( relation_of_lattice @ sk__19 ) ),
inference(demod,[status(thm)],[zip_derived_cl822,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl828,plain,
transitive @ ( relation_of_lattice @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl594,zip_derived_cl825]) ).
thf(zip_derived_cl825_042,plain,
( ( k2_lattice3 @ sk__19 )
= ( relation_of_lattice @ sk__19 ) ),
inference(demod,[status(thm)],[zip_derived_cl822,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl31,plain,
! [X0: $i] :
( ( v1_partfun1 @ ( k2_lattice3 @ X0 ) @ ( the_carrier @ X0 ) @ ( the_carrier @ X0 ) )
| ~ ( latt_str @ X0 )
| ~ ( lattice @ X0 )
| ( empty_carrier @ X0 ) ),
inference(cnf,[status(esa)],[dt_k2_lattice3]) ).
thf(zip_derived_cl1251,plain,
( ( v1_partfun1 @ ( relation_of_lattice @ sk__19 ) @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ) )
| ( empty_carrier @ sk__19 )
| ~ ( lattice @ sk__19 )
| ~ ( latt_str @ sk__19 ) ),
inference('sup+',[status(thm)],[zip_derived_cl825,zip_derived_cl31]) ).
thf(zip_derived_cl174_043,plain,
~ ( empty_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl175_044,plain,
lattice @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl176_045,plain,
latt_str @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1253,plain,
v1_partfun1 @ ( relation_of_lattice @ sk__19 ) @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl1251,zip_derived_cl174,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl832_046,plain,
( ( poset_of_lattice @ sk__19 )
= ( rel_str_of @ ( the_carrier @ sk__19 ) @ ( relation_of_lattice @ sk__19 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl829,zip_derived_cl174,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl4155,plain,
reflexive_relstr @ ( poset_of_lattice @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl4150,zip_derived_cl826,zip_derived_cl827,zip_derived_cl828,zip_derived_cl1253,zip_derived_cl832]) ).
thf(zip_derived_cl1362_047,plain,
rel_str @ ( poset_of_lattice @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl1347,zip_derived_cl832]) ).
thf(zip_derived_cl6808,plain,
! [X0: $i,X1: $i] :
( ~ ( element @ X0 @ ( the_carrier @ sk__19 ) )
| ~ ( related_reflexive @ ( poset_of_lattice @ sk__19 ) @ X0 @ X1 )
| ( related @ ( poset_of_lattice @ sk__19 ) @ X0 @ X1 )
| ~ ( element @ X1 @ ( the_carrier @ sk__19 ) )
| ( empty_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl6801,zip_derived_cl5378,zip_derived_cl4155,zip_derived_cl1362]) ).
thf(zip_derived_cl21483,plain,
! [X0: $i] :
( ( empty_carrier @ ( poset_of_lattice @ sk__19 ) )
| ~ ( element @ X0 @ ( the_carrier @ sk__19 ) )
| ( related @ ( poset_of_lattice @ sk__19 ) @ sk__20 @ X0 )
| ~ ( related_reflexive @ ( poset_of_lattice @ sk__19 ) @ sk__20 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl180,zip_derived_cl6808]) ).
thf(zip_derived_cl21505,plain,
( ( below_refl @ sk__19 @ sk__20 @ sk__21 )
| ( related @ ( poset_of_lattice @ sk__19 ) @ sk__20 @ sk__21 )
| ~ ( element @ sk__21 @ ( the_carrier @ sk__19 ) )
| ( empty_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl7916,zip_derived_cl21483]) ).
thf(zip_derived_cl177_048,plain,
element @ sk__21 @ ( the_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl21516,plain,
( ( below_refl @ sk__19 @ sk__20 @ sk__21 )
| ( related @ ( poset_of_lattice @ sk__19 ) @ sk__20 @ sk__21 )
| ( empty_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl21505,zip_derived_cl177]) ).
thf(zip_derived_cl180_049,plain,
element @ sk__20 @ ( the_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(dt_k4_lattice3,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ( element @ ( cast_to_el_of_LattPOSet @ A @ B ) @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) ) ).
thf(zip_derived_cl40,plain,
! [X0: $i,X1: $i] :
( ~ ( latt_str @ X0 )
| ~ ( lattice @ X0 )
| ( empty_carrier @ X0 )
| ~ ( element @ X1 @ ( the_carrier @ X0 ) )
| ( element @ ( cast_to_el_of_LattPOSet @ X0 @ X1 ) @ ( the_carrier @ ( poset_of_lattice @ X0 ) ) ) ),
inference(cnf,[status(esa)],[dt_k4_lattice3]) ).
thf(zip_derived_cl1413,plain,
( ( element @ ( cast_to_el_of_LattPOSet @ sk__19 @ sk__20 ) @ ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) )
| ( empty_carrier @ sk__19 )
| ~ ( lattice @ sk__19 )
| ~ ( latt_str @ sk__19 ) ),
inference('sup-',[status(thm)],[zip_derived_cl180,zip_derived_cl40]) ).
thf(zip_derived_cl729_050,plain,
( ( cast_to_el_of_LattPOSet @ sk__19 @ sk__20 )
= sk__20 ),
inference(demod,[status(thm)],[zip_derived_cl725,zip_derived_cl174,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl174_051,plain,
~ ( empty_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl175_052,plain,
lattice @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl176_053,plain,
latt_str @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1417,plain,
element @ sk__20 @ ( the_carrier @ ( poset_of_lattice @ sk__19 ) ),
inference(demod,[status(thm)],[zip_derived_cl1413,zip_derived_cl729,zip_derived_cl174,zip_derived_cl175,zip_derived_cl176]) ).
thf(d9_orders_2,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( related @ A @ B @ C )
<=> ( in @ ( ordered_pair @ B @ C ) @ ( the_InternalRel @ A ) ) ) ) ) ) ).
thf(zip_derived_cl17,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( element @ X0 @ ( the_carrier @ X1 ) )
| ~ ( related @ X1 @ X0 @ X2 )
| ( in @ ( ordered_pair @ X0 @ X2 ) @ ( the_InternalRel @ X1 ) )
| ~ ( element @ X2 @ ( the_carrier @ X1 ) )
| ~ ( rel_str @ X1 ) ),
inference(cnf,[status(esa)],[d9_orders_2]) ).
thf(zip_derived_cl1477,plain,
! [X0: $i] :
( ~ ( rel_str @ ( poset_of_lattice @ sk__19 ) )
| ~ ( element @ X0 @ ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) )
| ( in @ ( ordered_pair @ sk__20 @ X0 ) @ ( the_InternalRel @ ( poset_of_lattice @ sk__19 ) ) )
| ~ ( related @ ( poset_of_lattice @ sk__19 ) @ sk__20 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1417,zip_derived_cl17]) ).
thf(zip_derived_cl1362_054,plain,
rel_str @ ( poset_of_lattice @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl1347,zip_derived_cl832]) ).
thf(zip_derived_cl1488,plain,
! [X0: $i] :
( ~ ( element @ X0 @ ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) )
| ( in @ ( ordered_pair @ sk__20 @ X0 ) @ ( the_InternalRel @ ( poset_of_lattice @ sk__19 ) ) )
| ~ ( related @ ( poset_of_lattice @ sk__19 ) @ sk__20 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1477,zip_derived_cl1362]) ).
thf(zip_derived_cl5378_055,plain,
( ( the_carrier @ sk__19 )
= ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl5375]) ).
thf(zip_derived_cl2335_056,plain,
( ( relation_of_lattice @ sk__19 )
= ( the_InternalRel @ ( poset_of_lattice @ sk__19 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2334,zip_derived_cl1361,zip_derived_cl1362]) ).
thf(zip_derived_cl15421,plain,
! [X0: $i] :
( ~ ( element @ X0 @ ( the_carrier @ sk__19 ) )
| ( in @ ( ordered_pair @ sk__20 @ X0 ) @ ( relation_of_lattice @ sk__19 ) )
| ~ ( related @ ( poset_of_lattice @ sk__19 ) @ sk__20 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1488,zip_derived_cl5378,zip_derived_cl2335]) ).
thf(zip_derived_cl21517,plain,
( ( empty_carrier @ ( poset_of_lattice @ sk__19 ) )
| ( below_refl @ sk__19 @ sk__20 @ sk__21 )
| ( in @ ( ordered_pair @ sk__20 @ sk__21 ) @ ( relation_of_lattice @ sk__19 ) )
| ~ ( element @ sk__21 @ ( the_carrier @ sk__19 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl21516,zip_derived_cl15421]) ).
thf(zip_derived_cl177_057,plain,
element @ sk__21 @ ( the_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl21529,plain,
( ( empty_carrier @ ( poset_of_lattice @ sk__19 ) )
| ( below_refl @ sk__19 @ sk__20 @ sk__21 )
| ( in @ ( ordered_pair @ sk__20 @ sk__21 ) @ ( relation_of_lattice @ sk__19 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl21517,zip_derived_cl177]) ).
thf(zip_derived_cl25740_058,plain,
( ( ( ordered_pair_as_product_element @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ) @ sk__20 @ sk__21 )
= ( ordered_pair @ sk__20 @ sk__21 ) )
| ( empty @ ( the_carrier @ sk__19 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl25695]) ).
thf(t32_filter_1,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( in @ ( ordered_pair_as_product_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ B @ C ) @ ( relation_of_lattice @ A ) )
<=> ( below_refl @ A @ B @ C ) ) ) ) ) ).
thf(zip_derived_cl166,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( element @ X0 @ ( the_carrier @ X1 ) )
| ~ ( in @ ( ordered_pair_as_product_element @ ( the_carrier @ X1 ) @ ( the_carrier @ X1 ) @ X0 @ X2 ) @ ( relation_of_lattice @ X1 ) )
| ( below_refl @ X1 @ X0 @ X2 )
| ~ ( element @ X2 @ ( the_carrier @ X1 ) )
| ~ ( latt_str @ X1 )
| ~ ( lattice @ X1 )
| ( empty_carrier @ X1 ) ),
inference(cnf,[status(esa)],[t32_filter_1]) ).
thf(zip_derived_cl26070,plain,
( ~ ( in @ ( ordered_pair @ sk__20 @ sk__21 ) @ ( relation_of_lattice @ sk__19 ) )
| ( empty @ ( the_carrier @ sk__19 ) )
| ( empty_carrier @ sk__19 )
| ~ ( lattice @ sk__19 )
| ~ ( latt_str @ sk__19 )
| ~ ( element @ sk__21 @ ( the_carrier @ sk__19 ) )
| ( below_refl @ sk__19 @ sk__20 @ sk__21 )
| ~ ( element @ sk__20 @ ( the_carrier @ sk__19 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl25740,zip_derived_cl166]) ).
thf(zip_derived_cl174_059,plain,
~ ( empty_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl175_060,plain,
lattice @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl176_061,plain,
latt_str @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl177_062,plain,
element @ sk__21 @ ( the_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl180_063,plain,
element @ sk__20 @ ( the_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl26107,plain,
( ~ ( in @ ( ordered_pair @ sk__20 @ sk__21 ) @ ( relation_of_lattice @ sk__19 ) )
| ( empty @ ( the_carrier @ sk__19 ) )
| ( below_refl @ sk__19 @ sk__20 @ sk__21 ) ),
inference(demod,[status(thm)],[zip_derived_cl26070,zip_derived_cl174,zip_derived_cl175,zip_derived_cl176,zip_derived_cl177,zip_derived_cl180]) ).
thf(zip_derived_cl26269,plain,
( ( below_refl @ sk__19 @ sk__20 @ sk__21 )
| ( empty_carrier @ ( poset_of_lattice @ sk__19 ) )
| ( below_refl @ sk__19 @ sk__20 @ sk__21 )
| ( empty @ ( the_carrier @ sk__19 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl21529,zip_derived_cl26107]) ).
thf(zip_derived_cl26283,plain,
( ( empty @ ( the_carrier @ sk__19 ) )
| ( empty_carrier @ ( poset_of_lattice @ sk__19 ) )
| ( below_refl @ sk__19 @ sk__20 @ sk__21 ) ),
inference(simplify,[status(thm)],[zip_derived_cl26269]) ).
thf(zip_derived_cl5378_064,plain,
( ( the_carrier @ sk__19 )
= ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl5375]) ).
thf(fc1_struct_0,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) ).
thf(zip_derived_cl72,plain,
! [X0: $i] :
( ~ ( empty @ ( the_carrier @ X0 ) )
| ~ ( one_sorted_str @ X0 )
| ( empty_carrier @ X0 ) ),
inference(cnf,[status(esa)],[fc1_struct_0]) ).
thf(zip_derived_cl5430,plain,
( ~ ( empty @ ( the_carrier @ sk__19 ) )
| ( empty_carrier @ ( poset_of_lattice @ sk__19 ) )
| ~ ( one_sorted_str @ ( poset_of_lattice @ sk__19 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl5378,zip_derived_cl72]) ).
thf(zip_derived_cl1362_065,plain,
rel_str @ ( poset_of_lattice @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl1347,zip_derived_cl832]) ).
thf(dt_l1_orders_2,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) ).
thf(zip_derived_cl46,plain,
! [X0: $i] :
( ( one_sorted_str @ X0 )
| ~ ( rel_str @ X0 ) ),
inference(cnf,[status(esa)],[dt_l1_orders_2]) ).
thf(zip_derived_cl1367,plain,
one_sorted_str @ ( poset_of_lattice @ sk__19 ),
inference('sup-',[status(thm)],[zip_derived_cl1362,zip_derived_cl46]) ).
thf(zip_derived_cl5489,plain,
( ~ ( empty @ ( the_carrier @ sk__19 ) )
| ( empty_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl5430,zip_derived_cl1367]) ).
thf(zip_derived_cl26291,plain,
( ( below_refl @ sk__19 @ sk__20 @ sk__21 )
| ( empty_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl26283,zip_derived_cl5489]) ).
thf(zip_derived_cl177_066,plain,
element @ sk__21 @ ( the_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl180_067,plain,
element @ sk__20 @ ( the_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl167,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( element @ X0 @ ( the_carrier @ X1 ) )
| ~ ( below_refl @ X1 @ X0 @ X2 )
| ( in @ ( ordered_pair_as_product_element @ ( the_carrier @ X1 ) @ ( the_carrier @ X1 ) @ X0 @ X2 ) @ ( relation_of_lattice @ X1 ) )
| ~ ( element @ X2 @ ( the_carrier @ X1 ) )
| ~ ( latt_str @ X1 )
| ~ ( lattice @ X1 )
| ( empty_carrier @ X1 ) ),
inference(cnf,[status(esa)],[t32_filter_1]) ).
thf(zip_derived_cl7848,plain,
! [X0: $i] :
( ( empty_carrier @ sk__19 )
| ~ ( lattice @ sk__19 )
| ~ ( latt_str @ sk__19 )
| ~ ( element @ X0 @ ( the_carrier @ sk__19 ) )
| ( in @ ( ordered_pair_as_product_element @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ) @ sk__20 @ X0 ) @ ( relation_of_lattice @ sk__19 ) )
| ~ ( below_refl @ sk__19 @ sk__20 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl180,zip_derived_cl167]) ).
thf(zip_derived_cl174_068,plain,
~ ( empty_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl175_069,plain,
lattice @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl176_070,plain,
latt_str @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl7860,plain,
! [X0: $i] :
( ~ ( element @ X0 @ ( the_carrier @ sk__19 ) )
| ( in @ ( ordered_pair_as_product_element @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ) @ sk__20 @ X0 ) @ ( relation_of_lattice @ sk__19 ) )
| ~ ( below_refl @ sk__19 @ sk__20 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl7848,zip_derived_cl174,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl20362,plain,
( ~ ( below_refl @ sk__19 @ sk__20 @ sk__21 )
| ( in @ ( ordered_pair_as_product_element @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ) @ sk__20 @ sk__21 ) @ ( relation_of_lattice @ sk__19 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl177,zip_derived_cl7860]) ).
thf(zip_derived_cl26293,plain,
( ( empty_carrier @ ( poset_of_lattice @ sk__19 ) )
| ( in @ ( ordered_pair_as_product_element @ ( the_carrier @ sk__19 ) @ ( the_carrier @ sk__19 ) @ sk__20 @ sk__21 ) @ ( relation_of_lattice @ sk__19 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl26291,zip_derived_cl20362]) ).
thf(zip_derived_cl26646,plain,
( ( in @ ( ordered_pair @ sk__20 @ sk__21 ) @ ( relation_of_lattice @ sk__19 ) )
| ( empty @ ( the_carrier @ sk__19 ) )
| ( empty_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl25740,zip_derived_cl26293]) ).
thf(zip_derived_cl5489_071,plain,
( ~ ( empty @ ( the_carrier @ sk__19 ) )
| ( empty_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl5430,zip_derived_cl1367]) ).
thf(zip_derived_cl26688,plain,
( ( empty_carrier @ ( poset_of_lattice @ sk__19 ) )
| ( in @ ( ordered_pair @ sk__20 @ sk__21 ) @ ( relation_of_lattice @ sk__19 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl26646,zip_derived_cl5489]) ).
thf(zip_derived_cl2335_072,plain,
( ( relation_of_lattice @ sk__19 )
= ( the_InternalRel @ ( poset_of_lattice @ sk__19 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2334,zip_derived_cl1361,zip_derived_cl1362]) ).
thf(zip_derived_cl18,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( element @ X0 @ ( the_carrier @ X1 ) )
| ~ ( in @ ( ordered_pair @ X0 @ X2 ) @ ( the_InternalRel @ X1 ) )
| ( related @ X1 @ X0 @ X2 )
| ~ ( element @ X2 @ ( the_carrier @ X1 ) )
| ~ ( rel_str @ X1 ) ),
inference(cnf,[status(esa)],[d9_orders_2]) ).
thf(zip_derived_cl2342,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( ordered_pair @ X1 @ X0 ) @ ( relation_of_lattice @ sk__19 ) )
| ~ ( rel_str @ ( poset_of_lattice @ sk__19 ) )
| ~ ( element @ X0 @ ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) )
| ( related @ ( poset_of_lattice @ sk__19 ) @ X1 @ X0 )
| ~ ( element @ X1 @ ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2335,zip_derived_cl18]) ).
thf(zip_derived_cl1362_073,plain,
rel_str @ ( poset_of_lattice @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl1347,zip_derived_cl832]) ).
thf(zip_derived_cl2354,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( ordered_pair @ X1 @ X0 ) @ ( relation_of_lattice @ sk__19 ) )
| ~ ( element @ X0 @ ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) )
| ( related @ ( poset_of_lattice @ sk__19 ) @ X1 @ X0 )
| ~ ( element @ X1 @ ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2342,zip_derived_cl1362]) ).
thf(zip_derived_cl5378_074,plain,
( ( the_carrier @ sk__19 )
= ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl5375]) ).
thf(zip_derived_cl5378_075,plain,
( ( the_carrier @ sk__19 )
= ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl5375]) ).
thf(zip_derived_cl23447,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( ordered_pair @ X1 @ X0 ) @ ( relation_of_lattice @ sk__19 ) )
| ~ ( element @ X0 @ ( the_carrier @ sk__19 ) )
| ( related @ ( poset_of_lattice @ sk__19 ) @ X1 @ X0 )
| ~ ( element @ X1 @ ( the_carrier @ sk__19 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2354,zip_derived_cl5378,zip_derived_cl5378]) ).
thf(zip_derived_cl26693,plain,
( ( empty_carrier @ ( poset_of_lattice @ sk__19 ) )
| ~ ( element @ sk__20 @ ( the_carrier @ sk__19 ) )
| ( related @ ( poset_of_lattice @ sk__19 ) @ sk__20 @ sk__21 )
| ~ ( element @ sk__21 @ ( the_carrier @ sk__19 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl26688,zip_derived_cl23447]) ).
thf(zip_derived_cl180_076,plain,
element @ sk__20 @ ( the_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl177_077,plain,
element @ sk__21 @ ( the_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl26716,plain,
( ( empty_carrier @ ( poset_of_lattice @ sk__19 ) )
| ( related @ ( poset_of_lattice @ sk__19 ) @ sk__20 @ sk__21 ) ),
inference(demod,[status(thm)],[zip_derived_cl26693,zip_derived_cl180,zip_derived_cl177]) ).
thf(zip_derived_cl180_078,plain,
element @ sk__20 @ ( the_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl5378_079,plain,
( ( the_carrier @ sk__19 )
= ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl5375]) ).
thf(zip_derived_cl159,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( element @ X0 @ ( the_carrier @ X1 ) )
| ~ ( rel_str @ X1 )
| ~ ( reflexive_relstr @ X1 )
| ( empty_carrier @ X1 )
| ~ ( element @ X2 @ ( the_carrier @ X1 ) )
| ( related_reflexive @ X1 @ X0 @ X2 )
| ~ ( related @ X1 @ X0 @ X2 ) ),
inference(cnf,[status(esa)],[redefinition_r3_orders_2]) ).
thf(zip_derived_cl6714,plain,
! [X0: $i,X1: $i] :
( ~ ( element @ X0 @ ( the_carrier @ sk__19 ) )
| ~ ( related @ ( poset_of_lattice @ sk__19 ) @ X0 @ X1 )
| ( related_reflexive @ ( poset_of_lattice @ sk__19 ) @ X0 @ X1 )
| ~ ( element @ X1 @ ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) )
| ( empty_carrier @ ( poset_of_lattice @ sk__19 ) )
| ~ ( reflexive_relstr @ ( poset_of_lattice @ sk__19 ) )
| ~ ( rel_str @ ( poset_of_lattice @ sk__19 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl5378,zip_derived_cl159]) ).
thf(zip_derived_cl5378_080,plain,
( ( the_carrier @ sk__19 )
= ( the_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl5375]) ).
thf(zip_derived_cl4155_081,plain,
reflexive_relstr @ ( poset_of_lattice @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl4150,zip_derived_cl826,zip_derived_cl827,zip_derived_cl828,zip_derived_cl1253,zip_derived_cl832]) ).
thf(zip_derived_cl1362_082,plain,
rel_str @ ( poset_of_lattice @ sk__19 ),
inference(demod,[status(thm)],[zip_derived_cl1347,zip_derived_cl832]) ).
thf(zip_derived_cl6721,plain,
! [X0: $i,X1: $i] :
( ~ ( element @ X0 @ ( the_carrier @ sk__19 ) )
| ~ ( related @ ( poset_of_lattice @ sk__19 ) @ X0 @ X1 )
| ( related_reflexive @ ( poset_of_lattice @ sk__19 ) @ X0 @ X1 )
| ~ ( element @ X1 @ ( the_carrier @ sk__19 ) )
| ( empty_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl6714,zip_derived_cl5378,zip_derived_cl4155,zip_derived_cl1362]) ).
thf(zip_derived_cl19970,plain,
! [X0: $i] :
( ( empty_carrier @ ( poset_of_lattice @ sk__19 ) )
| ~ ( element @ X0 @ ( the_carrier @ sk__19 ) )
| ( related_reflexive @ ( poset_of_lattice @ sk__19 ) @ sk__20 @ X0 )
| ~ ( related @ ( poset_of_lattice @ sk__19 ) @ sk__20 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl180,zip_derived_cl6721]) ).
thf(zip_derived_cl26718,plain,
( ( empty_carrier @ ( poset_of_lattice @ sk__19 ) )
| ( related_reflexive @ ( poset_of_lattice @ sk__19 ) @ sk__20 @ sk__21 )
| ~ ( element @ sk__21 @ ( the_carrier @ sk__19 ) )
| ( empty_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl26716,zip_derived_cl19970]) ).
thf(zip_derived_cl177_083,plain,
element @ sk__21 @ ( the_carrier @ sk__19 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl26730,plain,
( ( empty_carrier @ ( poset_of_lattice @ sk__19 ) )
| ( related_reflexive @ ( poset_of_lattice @ sk__19 ) @ sk__20 @ sk__21 )
| ( empty_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl26718,zip_derived_cl177]) ).
thf(zip_derived_cl26731,plain,
( ( related_reflexive @ ( poset_of_lattice @ sk__19 ) @ sk__20 @ sk__21 )
| ( empty_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl26730]) ).
thf(zip_derived_cl178,plain,
( ~ ( related_reflexive @ ( poset_of_lattice @ sk__19 ) @ ( cast_to_el_of_LattPOSet @ sk__19 @ sk__20 ) @ ( cast_to_el_of_LattPOSet @ sk__19 @ sk__21 ) )
| ~ ( below_refl @ sk__19 @ sk__20 @ sk__21 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl729_084,plain,
( ( cast_to_el_of_LattPOSet @ sk__19 @ sk__20 )
= sk__20 ),
inference(demod,[status(thm)],[zip_derived_cl725,zip_derived_cl174,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl730_085,plain,
( ( cast_to_el_of_LattPOSet @ sk__19 @ sk__21 )
= sk__21 ),
inference(demod,[status(thm)],[zip_derived_cl726,zip_derived_cl174,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl1006,plain,
( ~ ( related_reflexive @ ( poset_of_lattice @ sk__19 ) @ sk__20 @ sk__21 )
| ~ ( below_refl @ sk__19 @ sk__20 @ sk__21 ) ),
inference(demod,[status(thm)],[zip_derived_cl178,zip_derived_cl729,zip_derived_cl730]) ).
thf(zip_derived_cl26815,plain,
( ( empty_carrier @ ( poset_of_lattice @ sk__19 ) )
| ~ ( below_refl @ sk__19 @ sk__20 @ sk__21 ) ),
inference('sup-',[status(thm)],[zip_derived_cl26731,zip_derived_cl1006]) ).
thf(zip_derived_cl26291_086,plain,
( ( below_refl @ sk__19 @ sk__20 @ sk__21 )
| ( empty_carrier @ ( poset_of_lattice @ sk__19 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl26283,zip_derived_cl5489]) ).
thf(zip_derived_cl26828,plain,
empty_carrier @ ( poset_of_lattice @ sk__19 ),
inference(clc,[status(thm)],[zip_derived_cl26815,zip_derived_cl26291]) ).
thf(fc4_lattice3,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ~ ( empty_carrier @ ( poset_of_lattice @ A ) )
& ( strict_rel_str @ ( poset_of_lattice @ A ) )
& ( reflexive_relstr @ ( poset_of_lattice @ A ) )
& ( transitive_relstr @ ( poset_of_lattice @ A ) )
& ( antisymmetric_relstr @ ( poset_of_lattice @ A ) ) ) ) ).
thf(zip_derived_cl103,plain,
! [X0: $i] :
( ~ ( empty_carrier @ ( poset_of_lattice @ X0 ) )
| ~ ( latt_str @ X0 )
| ~ ( lattice @ X0 )
| ( empty_carrier @ X0 ) ),
inference(cnf,[status(esa)],[fc4_lattice3]) ).
thf(zip_derived_cl26865,plain,
( ( empty_carrier @ sk__19 )
| ~ ( lattice @ sk__19 )
| ~ ( latt_str @ sk__19 ) ),
inference('sup-',[status(thm)],[zip_derived_cl26828,zip_derived_cl103]) ).
thf(zip_derived_cl175_087,plain,
lattice @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl176_088,plain,
latt_str @ sk__19,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl26872,plain,
empty_carrier @ sk__19,
inference(demod,[status(thm)],[zip_derived_cl26865,zip_derived_cl175,zip_derived_cl176]) ).
thf(zip_derived_cl26873,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl174,zip_derived_cl26872]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU346+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.AUcU64zN6d true
% 0.15/0.35 % Computer : n003.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Aug 23 17:54:22 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.36 % Python version: Python 3.6.8
% 0.15/0.36 % Running in FO mode
% 0.22/0.65 % Total configuration time : 435
% 0.22/0.65 % Estimated wc time : 1092
% 0.22/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 1.82/0.84 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 28.91/4.74 % Solved by fo/fo5.sh.
% 28.91/4.74 % done 2937 iterations in 3.946s
% 28.91/4.74 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 28.91/4.74 % SZS output start Refutation
% See solution above
% 28.91/4.75
% 28.91/4.75
% 28.91/4.75 % Terminating...
% 29.33/4.88 % Runner terminated.
% 29.33/4.88 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------