TSTP Solution File: SEU349+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU349+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 : Fri May 19 11:58:26 EDT 2023
% Result : Theorem 79.04s 19.34s
% Output : Refutation 79.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 109
% Syntax : Number of formulae : 175 ( 27 unt; 45 typ; 0 def)
% Number of atoms : 509 ( 20 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1444 ( 87 ~; 2 |; 232 &; 978 @)
% ( 9 <=>; 136 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 45 usr; 2 con; 0-3 aty)
% Number of variables : 238 ( 0 ^; 206 !; 32 ?; 238 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_type,type,
empty_carrier: $i > $o ).
thf(lattice_type,type,
lattice: $i > $o ).
thf(latt_str_type,type,
latt_str: $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(the_carrier_type,type,
the_carrier: $i > $i ).
thf(latt_element_smaller_type,type,
latt_element_smaller: $i > $i > $i > $o ).
thf(relstr_set_smaller_type,type,
relstr_set_smaller: $i > $i > $i > $o ).
thf(poset_of_lattice_type,type,
poset_of_lattice: $i > $i ).
thf(cast_to_el_of_LattPOSet_type,type,
cast_to_el_of_LattPOSet: $i > $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(meet_semilatt_str_type,type,
meet_semilatt_str: $i > $o ).
thf(join_semilatt_str_type,type,
join_semilatt_str: $i > $o ).
thf(one_sorted_str_type,type,
one_sorted_str: $i > $o ).
thf(rel_str_type,type,
rel_str: $i > $o ).
thf(strict_rel_str_type,type,
strict_rel_str: $i > $o ).
thf(relation_of2_type,type,
relation_of2: $i > $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(relation_of2_as_subset_type,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(rel_str_of_type,type,
rel_str_of: $i > $i > $i ).
thf(reflexive_type,type,
reflexive: $i > $o ).
thf(antisymmetric_type,type,
antisymmetric: $i > $o ).
thf(transitive_type,type,
transitive: $i > $o ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(reflexive_relstr_type,type,
reflexive_relstr: $i > $o ).
thf(transitive_relstr_type,type,
transitive_relstr: $i > $o ).
thf(antisymmetric_relstr_type,type,
antisymmetric_relstr: $i > $o ).
thf(cartesian_product2_type,type,
cartesian_product2: $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(relation_type,type,
relation: $i > $o ).
thf(k2_lattice3_type,type,
k2_lattice3: $i > $i ).
thf(relation_of_lattice_type,type,
relation_of_lattice: $i > $i ).
thf(the_InternalRel_type,type,
the_InternalRel: $i > $i ).
thf(meet_commutative_type,type,
meet_commutative: $i > $o ).
thf(meet_absorbing_type,type,
meet_absorbing: $i > $o ).
thf(join_absorbing_type,type,
join_absorbing: $i > $o ).
thf(cast_to_el_of_lattice_type,type,
cast_to_el_of_lattice: $i > $i > $i ).
thf(below_type,type,
below: $i > $i > $i > $o ).
thf(related_type,type,
related: $i > $i > $i > $o ).
thf(join_commutative_type,type,
join_commutative: $i > $o ).
thf(join_associative_type,type,
join_associative: $i > $o ).
thf(meet_associative_type,type,
meet_associative: $i > $o ).
thf(42,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 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_orders_2) ).
thf(185,plain,
! [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 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(29,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(147,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(10,axiom,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(92,plain,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(43,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(188,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(24,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(129,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(30,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(149,plain,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( below_refl @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
thf(176,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( below_refl @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(28,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 ) )
=> ( ( 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 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lattice3) ).
thf(144,plain,
! [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 ) ) )
& ( ( related_reflexive @ ( poset_of_lattice @ A ) @ ( cast_to_el_of_LattPOSet @ A @ B ) @ ( cast_to_el_of_LattPOSet @ A @ C ) )
=> ( below_refl @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(37,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(167,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( below_refl @ A @ B @ C )
<=> ( below @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
thf(182,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( ( below_refl @ A @ B @ C )
=> ( below @ A @ B @ C ) )
& ( ( below @ A @ B @ C )
=> ( below_refl @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(32,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(154,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(25,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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(131,plain,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( rel_str @ ( rel_str_of @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(14,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(101,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(60,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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattice3) ).
thf(249,plain,
! [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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(8,axiom,
? [A: $i] : ( meet_semilatt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(88,plain,
? [A: $i] : ( meet_semilatt_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(38,axiom,
! [A: $i] :
( ( ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ( ( relation @ ( the_InternalRel @ A ) )
& ( reflexive @ ( the_InternalRel @ A ) )
& ( antisymmetric @ ( the_InternalRel @ A ) )
& ( transitive @ ( the_InternalRel @ A ) )
& ( v1_partfun1 @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_orders_2) ).
thf(170,plain,
! [A: $i] :
( ( ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ( ( relation @ ( the_InternalRel @ A ) )
& ( reflexive @ ( the_InternalRel @ A ) )
& ( antisymmetric @ ( the_InternalRel @ A ) )
& ( transitive @ ( the_InternalRel @ A ) )
& ( v1_partfun1 @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(47,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(202,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation_of2 @ B @ A @ A ) )
=> ( ~ ( empty_carrier @ ( rel_str_of @ A @ B ) )
& ( strict_rel_str @ ( rel_str_of @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_orders_2) ).
thf(157,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation_of2 @ B @ A @ A ) )
=> ( ~ ( empty_carrier @ ( rel_str_of @ A @ B ) )
& ( strict_rel_str @ ( rel_str_of @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(40,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) )
=> ( ( cast_to_el_of_lattice @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattice3) ).
thf(179,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) )
=> ( ( cast_to_el_of_lattice @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(16,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(106,plain,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(84,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(117,plain,
? [A: $i] : ( one_sorted_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(65,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lattice3) ).
thf(270,plain,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( relstr_set_smaller @ A @ B @ C )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ D @ C ) ) )
=> ( relstr_set_smaller @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(7,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(85,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(63,axiom,
? [A: $i] : ( latt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(260,plain,
? [A: $i] : ( latt_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(160,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(45,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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_orders_2) ).
thf(192,plain,
! [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 ) )
& ( ( related @ A @ B @ C )
=> ( related_reflexive @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(165,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(22,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(124,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(12,axiom,
? [A: $i] :
( ( rel_str @ A )
& ( strict_rel_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_orders_2) ).
thf(96,plain,
? [A: $i] :
( ( rel_str @ A )
& ( strict_rel_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(26,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(134,plain,
! [A: $i,B: $i,C: $i] :
( ( ( relation_of2_as_subset @ C @ A @ B )
=> ( relation_of2 @ C @ A @ B ) )
& ( ( relation_of2 @ C @ A @ B )
=> ( relation_of2_as_subset @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(57,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(237,plain,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
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(205,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(5,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(81,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ( element @ ( cast_to_el_of_LattPOSet @ A @ B ) @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattice3) ).
thf(230,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) ) )
=> ( element @ ( cast_to_el_of_LattPOSet @ A @ B ) @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(15,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(103,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(50,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( relation @ ( relation_of_lattice @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_filter_1) ).
thf(213,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( relation @ ( relation_of_lattice @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( latt_element_smaller @ B @ C @ A )
<=> ( relstr_set_smaller @ ( poset_of_lattice @ B ) @ A @ ( cast_to_el_of_LattPOSet @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lattice3) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( latt_element_smaller @ B @ C @ A )
<=> ( relstr_set_smaller @ ( poset_of_lattice @ B ) @ A @ ( cast_to_el_of_LattPOSet @ B @ C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(66,plain,
~ ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( latt_str @ B ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ B ) )
=> ( ( ( latt_element_smaller @ B @ C @ A )
=> ( relstr_set_smaller @ ( poset_of_lattice @ B ) @ A @ ( cast_to_el_of_LattPOSet @ B @ C ) ) )
& ( ( relstr_set_smaller @ ( poset_of_lattice @ B ) @ A @ ( cast_to_el_of_LattPOSet @ B @ C ) )
=> ( latt_element_smaller @ B @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(58,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ 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 ) )
& ( rel_str @ ( poset_of_lattice @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice3) ).
thf(240,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ 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 ) )
& ( rel_str @ ( poset_of_lattice @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(17,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(108,plain,
? [A: $i] : ( rel_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(35,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(162,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(61,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( poset_of_lattice @ A )
= ( rel_str_of @ ( the_carrier @ A ) @ ( k2_lattice3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattice3) ).
thf(255,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( poset_of_lattice @ A )
= ( rel_str_of @ ( the_carrier @ A ) @ ( k2_lattice3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(19,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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(112,plain,
! [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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(13,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(99,plain,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(52,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( latt_element_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ C )
=> ( below @ A @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattice3) ).
thf(218,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( ( latt_element_smaller @ A @ B @ C )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ C )
=> ( below @ A @ D @ B ) ) ) )
& ( ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ C )
=> ( below @ A @ D @ B ) ) )
=> ( latt_element_smaller @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) )
=> ( element @ ( cast_to_el_of_lattice @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattice3) ).
thf(258,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ ( poset_of_lattice @ A ) ) ) )
=> ( element @ ( cast_to_el_of_lattice @ A @ B ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(139,plain,
! [A: $i,B: $i] :
( ( ( element @ A @ ( powerset @ B ) )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( element @ A @ ( powerset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(75,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_orders_2) ).
thf(119,plain,
! [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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(49,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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_lattice3) ).
thf(207,plain,
! [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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(56,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(235,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(59,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( cast_to_el_of_LattPOSet @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice3) ).
thf(246,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( cast_to_el_of_LattPOSet @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(31,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( k2_lattice3 @ A )
= ( relation_of_lattice @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_lattice3) ).
thf(151,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( latt_str @ A ) )
=> ( ( k2_lattice3 @ A )
= ( relation_of_lattice @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(64,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( lattice @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
thf(262,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( lattice @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(44,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(190,plain,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(23,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(126,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(4,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(79,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(46,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_orders_2) ).
thf(195,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(11,axiom,
? [A: $i] : ( join_semilatt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(94,plain,
? [A: $i] : ( join_semilatt_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(90,plain,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(53,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( lattice @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattices) ).
thf(227,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( lattice @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(51,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(215,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(55,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( strict_rel_str @ A )
=> ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(232,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( strict_rel_str @ A )
=> ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(30487,plain,
$false,
inference(cvc4,[status(thm)],[185,147,92,188,129,149,176,144,167,182,154,131,101,249,88,170,202,110,157,179,106,84,117,270,85,260,160,192,165,124,96,134,237,205,81,230,103,213,66,240,108,162,255,112,99,218,258,139,75,119,207,235,246,151,262,190,126,79,195,94,90,227,215,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU349+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n009.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 13:30:34 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.92/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.40/0.99 % [INFO] Parsing done (154ms).
% 1.40/1.00 % [INFO] Running in sequential loop mode.
% 1.80/1.20 % [INFO] eprover registered as external prover.
% 1.80/1.20 % [INFO] cvc4 registered as external prover.
% 1.80/1.20 % [INFO] Scanning for conjecture ...
% 2.03/1.28 % [INFO] Found a conjecture and 70 axioms. Running axiom selection ...
% 2.26/1.34 % [INFO] Axiom selection finished. Selected 63 axioms (removed 7 axioms).
% 2.39/1.41 % [INFO] Problem is first-order (TPTP FOF).
% 2.39/1.42 % [INFO] Type checking passed.
% 2.39/1.42 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 79.04/19.33 % External prover 'cvc4' found a proof!
% 79.04/19.33 % [INFO] Killing All external provers ...
% 79.04/19.34 % Time passed: 18822ms (effective reasoning time: 18334ms)
% 79.04/19.34 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 79.04/19.34 % Axioms used in derivation (63): redefinition_m2_relset_1, dt_m2_relset_1, existence_l1_struct_0, fc1_xboole_0, existence_l1_lattices, t1_subset, fc4_lattice3, fc4_subset_1, existence_l3_lattices, d2_lattice3, rc2_orders_2, dt_k4_lattice3, dt_u1_orders_2, reflexivity_r3_lattices, dt_k5_lattice3, dt_l1_lattices, t6_boole, rc2_subset_1, existence_l2_lattices, redefinition_r3_orders_2, t5_subset, existence_m1_relset_1, dt_l3_lattices, dt_l2_lattices, d4_lattice3, dt_k3_lattice3, dt_k9_filter_1, t4_subset, d3_lattice3, fc2_orders_2, t7_boole, existence_l1_orders_2, d17_lattice3, rc1_orders_2, rc3_struct_0, fc1_subset_1, reflexivity_r3_orders_2, dt_g1_orders_2, rc1_subset_1, cc1_lattices, abstractness_v1_orders_2, redefinition_r3_lattices, t3_subset, cc1_relset_1, existence_m1_subset_1, fc3_orders_2, existence_m2_relset_1, dt_l1_orders_2, fc1_orders_2, free_g1_orders_2, fc1_struct_0, reflexivity_r1_tarski, dt_k2_lattice3, t7_lattice3, redefinition_k2_lattice3, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, d9_lattice3, rc2_xboole_0, antisymmetry_r2_hidden, cc2_lattices
% 79.04/19.34 % No. of inferences in proof: 130
% 79.04/19.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18822 ms resp. 18334 ms w/o parsing
% 79.04/19.38 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 79.04/19.38 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------