%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU350+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:38:32 AM UTC 2026
% Result : Theorem 8.79s 4.49s
% Output : Refutation 9.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 58
% Syntax : Number of formulae : 118 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 409 ( 20 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1125 ( 77 ~; 2 |; 186 &; 757 @)
% ( 5 <=>; 98 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 41 usr; 2 con; 0-3 aty)
% Number of variables : 196 ( 0 ^; 164 !; 32 ?; 196 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_decl,type,
empty_carrier: $i > $o ).
thf(lattice_decl,type,
lattice: $i > $o ).
thf(latt_str_decl,type,
latt_str: $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(poset_of_lattice_decl,type,
poset_of_lattice: $i > $i ).
thf(relstr_set_smaller_decl,type,
relstr_set_smaller: $i > $i > $i > $o ).
thf(latt_element_smaller_decl,type,
latt_element_smaller: $i > $i > $i > $o ).
thf(cast_to_el_of_lattice_decl,type,
cast_to_el_of_lattice: $i > $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(meet_semilatt_str_decl,type,
meet_semilatt_str: $i > $o ).
thf(join_semilatt_str_decl,type,
join_semilatt_str: $i > $o ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(rel_str_decl,type,
rel_str: $i > $o ).
thf(strict_rel_str_decl,type,
strict_rel_str: $i > $o ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(rel_str_of_decl,type,
rel_str_of: $i > $i > $i ).
thf(reflexive_decl,type,
reflexive: $i > $o ).
thf(antisymmetric_decl,type,
antisymmetric: $i > $o ).
thf(transitive_decl,type,
transitive: $i > $o ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(reflexive_relstr_decl,type,
reflexive_relstr: $i > $o ).
thf(transitive_relstr_decl,type,
transitive_relstr: $i > $o ).
thf(antisymmetric_relstr_decl,type,
antisymmetric_relstr: $i > $o ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(relation_decl,type,
relation: $i > $o ).
thf(k2_lattice3_decl,type,
k2_lattice3: $i > $i ).
thf(relation_of_lattice_decl,type,
relation_of_lattice: $i > $i ).
thf(cast_to_el_of_LattPOSet_decl,type,
cast_to_el_of_LattPOSet: $i > $i > $i ).
thf(the_InternalRel_decl,type,
the_InternalRel: $i > $i ).
thf(join_commutative_decl,type,
join_commutative: $i > $o ).
thf(join_associative_decl,type,
join_associative: $i > $o ).
thf(meet_commutative_decl,type,
meet_commutative: $i > $o ).
thf(meet_associative_decl,type,
meet_associative: $i > $o ).
thf(meet_absorbing_decl,type,
meet_absorbing: $i > $o ).
thf(join_absorbing_decl,type,
join_absorbing: $i > $o ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ the_carrier @ ( C @ element ) )
=> ( ( A @ ( C @ ( B @ latt_element_smaller ) ) )
<=> ( C @ ( B @ cast_to_el_of_LattPOSet ) @ ( A @ ( B @ poset_of_lattice @ relstr_set_smaller ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lattice3) ).
thf(174,plain,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ the_carrier @ ( C @ element ) )
=> ( ( ( C @ ( B @ cast_to_el_of_LattPOSet ) @ ( A @ ( B @ poset_of_lattice @ relstr_set_smaller ) ) )
=> ( A @ ( C @ ( B @ latt_element_smaller ) ) ) )
& ( ( A @ ( C @ ( B @ latt_element_smaller ) ) )
=> ( C @ ( B @ cast_to_el_of_LattPOSet ) @ ( A @ ( B @ poset_of_lattice @ relstr_set_smaller ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(152,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(43,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_lattice3) ).
thf(188,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ( ( B @ ( A @ rel_str_of ) @ rel_str )
& ( B @ ( A @ rel_str_of ) @ strict_rel_str ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(129,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ( ( B @ ( A @ rel_str_of ) @ rel_str )
& ( B @ ( A @ rel_str_of ) @ strict_rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(159,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(13,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(95,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ strict_rel_str )
=> ( A
= ( A @ the_InternalRel @ ( A @ the_carrier @ rel_str_of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(207,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ strict_rel_str )
=> ( A
= ( A @ the_InternalRel @ ( A @ the_carrier @ rel_str_of ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ relation_of2_as_subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(178,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ relation_of2_as_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(51,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ rel_str )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice3) ).
thf(216,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ rel_str )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(58,axiom,
? [A: $i] : ( A @ latt_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(253,plain,
? [A: $i] : ( A @ latt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(106,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(147,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(4,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(74,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
? [A: $i] : ( A @ join_semilatt_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(89,plain,
? [A: $i] : ( A @ join_semilatt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
<=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(133,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ) )
& ( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ transitive )
& ( B @ antisymmetric )
& ( B @ reflexive ) )
=> ( ( B @ ( A @ rel_str_of ) @ antisymmetric_relstr )
& ( B @ ( A @ rel_str_of ) @ transitive_relstr )
& ( B @ ( A @ rel_str_of ) @ reflexive_relstr )
& ( B @ ( A @ rel_str_of ) @ strict_rel_str ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_orders_2) ).
thf(116,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ transitive )
& ( B @ antisymmetric )
& ( B @ reflexive ) )
=> ( ( B @ ( A @ rel_str_of ) @ antisymmetric_relstr )
& ( B @ ( A @ rel_str_of ) @ transitive_relstr )
& ( B @ ( A @ rel_str_of ) @ reflexive_relstr )
& ( B @ ( A @ rel_str_of ) @ strict_rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(56,axiom,
? [A: $i] :
( ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_orders_2) ).
thf(243,plain,
? [A: $i] :
( ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ poset_of_lattice @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( A @ ( B @ poset_of_lattice @ relstr_set_smaller ) ) )
<=> ( A @ ( C @ ( B @ cast_to_el_of_lattice ) @ ( B @ latt_element_smaller ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattice3) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ poset_of_lattice @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( A @ ( B @ poset_of_lattice @ relstr_set_smaller ) ) )
<=> ( A @ ( C @ ( B @ cast_to_el_of_lattice ) @ ( B @ latt_element_smaller ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(60,plain,
~ ! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ poset_of_lattice @ the_carrier @ ( C @ element ) )
=> ( ( ( A @ ( C @ ( B @ cast_to_el_of_lattice ) @ ( B @ latt_element_smaller ) ) )
=> ( C @ ( A @ ( B @ poset_of_lattice @ relstr_set_smaller ) ) ) )
& ( ( C @ ( A @ ( B @ poset_of_lattice @ relstr_set_smaller ) ) )
=> ( A @ ( C @ ( B @ cast_to_el_of_lattice ) @ ( B @ latt_element_smaller ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(102,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(85,plain,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lattice )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattices) ).
thf(201,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lattice )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(70,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(165,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(45,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(197,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(14,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(97,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(124,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(50,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(212,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(54,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice )
= ( A @ k2_lattice3 @ ( A @ the_carrier @ rel_str_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattice3) ).
thf(237,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice )
= ( A @ k2_lattice3 @ ( A @ the_carrier @ rel_str_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ poset_of_lattice @ the_carrier @ ( B @ ( A @ cast_to_el_of_LattPOSet ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattice3) ).
thf(205,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ poset_of_lattice @ the_carrier @ ( B @ ( A @ cast_to_el_of_LattPOSet ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(34,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(161,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(180,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(30,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ k2_lattice3 )
= ( A @ relation_of_lattice ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_lattice3) ).
thf(149,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ k2_lattice3 )
= ( A @ relation_of_lattice ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(53,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ k2_lattice3 @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ k2_lattice3 @ v1_partfun1 ) ) )
& ( A @ k2_lattice3 @ transitive )
& ( A @ k2_lattice3 @ antisymmetric )
& ( A @ k2_lattice3 @ reflexive ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattice3) ).
thf(230,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ k2_lattice3 @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ k2_lattice3 @ v1_partfun1 ) ) )
& ( A @ k2_lattice3 @ transitive )
& ( A @ k2_lattice3 @ antisymmetric )
& ( A @ k2_lattice3 @ reflexive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(5,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(76,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
? [A: $i] :
( ( A @ strict_rel_str )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_orders_2) ).
thf(91,plain,
? [A: $i] :
( ( A @ strict_rel_str )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ relation_of2 ) ) )
& ~ ( A @ empty ) )
=> ( ( B @ ( A @ rel_str_of ) @ strict_rel_str )
& ~ ( B @ ( A @ rel_str_of ) @ empty_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_orders_2) ).
thf(155,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ relation_of2 ) ) )
& ~ ( A @ empty ) )
=> ( ( B @ ( A @ rel_str_of ) @ strict_rel_str )
& ~ ( B @ ( A @ rel_str_of ) @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ rel_str_of ) )
= ( D @ ( C @ rel_str_of ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(108,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ rel_str_of ) )
= ( D @ ( C @ rel_str_of ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(55,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ poset_of_lattice @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ cast_to_el_of_lattice ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattice3) ).
thf(240,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ poset_of_lattice @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ cast_to_el_of_lattice ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( ( A @ poset_of_lattice @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( B @ ( A @ cast_to_el_of_lattice ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattice3) ).
thf(251,plain,
! [A: $i,B: $i] :
( ( ( A @ poset_of_lattice @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( B @ ( A @ cast_to_el_of_lattice ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(52,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ v1_partfun1 ) ) )
& ( A @ the_InternalRel @ transitive )
& ( A @ the_InternalRel @ antisymmetric )
& ( A @ the_InternalRel @ reflexive )
& ( A @ the_InternalRel @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_orders_2) ).
thf(223,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ v1_partfun1 ) ) )
& ( A @ the_InternalRel @ transitive )
& ( A @ the_InternalRel @ antisymmetric )
& ( A @ the_InternalRel @ reflexive )
& ( A @ the_InternalRel @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(7,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(80,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(36,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(167,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
thf(255,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(28,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(145,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ join_semilatt_str )
& ( A @ meet_semilatt_str ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(182,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ join_semilatt_str )
& ( A @ meet_semilatt_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(127,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(15,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(99,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(87,plain,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(17,axiom,
? [A: $i] : ( A @ rel_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(104,plain,
? [A: $i] : ( A @ rel_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(186,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(20,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(114,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(37,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ cast_to_el_of_LattPOSet ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice3) ).
thf(171,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ cast_to_el_of_LattPOSet ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(139,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( B @ powerset @ ( A @ element ) ) )
& ( ( B @ powerset @ ( A @ element ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(49,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(210,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(6,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(79,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(44,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ relation_of_lattice @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_filter_1) ).
thf(195,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ relation_of_lattice @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(122,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(8,axiom,
? [A: $i] : ( A @ meet_semilatt_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(83,plain,
? [A: $i] : ( A @ meet_semilatt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(267,plain,
$false,
inference(e,[status(thm)],[174,152,188,129,159,95,207,178,216,253,106,147,74,89,133,116,243,60,102,85,201,70,165,197,97,124,212,237,205,161,180,149,230,76,91,155,108,240,251,223,80,167,255,145,182,127,99,87,104,186,114,171,139,210,79,195,122,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU350+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.24/0.49 % Computer : n014.cluster.edu
% 0.24/0.49 % Model : x86_64 x86_64
% 0.24/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.49 % Memory : 8046.5625MB
% 0.24/0.49 % OS : Linux 6.8.0-71-generic
% 0.24/0.49 % CPULimit : 300
% 0.24/0.49 % WCLimit : 300
% 0.24/0.49 % DateTime : Sat Sep 26 09:17:01 UTC 2026
% 0.24/0.49 % CPUTime :
% 0.24/0.49 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.41/1.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.92/1.69 % [INFO] Parsing done (351ms).
% 2.33/1.71 % [INFO] Running in sequential loop mode.
% 3.39/2.32 % [INFO] eprover registered as external prover.
% 3.39/2.34 % [INFO] Scanning for conjecture ...
% 3.79/2.52 % [INFO] Found a conjecture (or negated_conjecture) and 64 axioms. Running axiom selection ...
% 4.01/2.68 % [INFO] Axiom selection finished. Selected 57 axioms (removed 7 axioms).
% 4.55/2.82 % [INFO] Problem is first-order (TPTP FOF).
% 4.55/2.84 % [INFO] Type checking passed.
% 4.55/2.84 % [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 ...
% 8.79/4.49 % External prover 'e' found a proof!
% 8.79/4.49 % [INFO] Killing All external provers ...
% 8.79/4.49 % Time passed: 3789ms (effective reasoning time: 2765ms)
% 8.79/4.49 % 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)>
% 8.79/4.49 % Axioms used in derivation (57): redefinition_m2_relset_1, dt_m2_relset_1, abstractness_v1_orders_2, dt_k2_lattice3, existence_l1_struct_0, rc2_xboole_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, dt_k5_lattice3, dt_l1_lattices, t6_boole, rc2_subset_1, existence_l2_lattices, t5_subset, t30_lattice3, 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, rc1_orders_2, rc3_struct_0, fc1_subset_1, dt_g1_orders_2, rc1_subset_1, cc1_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, redefinition_k2_lattice3, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, antisymmetry_r2_hidden, cc2_lattices
% 8.79/4.49 % No. of inferences in proof: 118
% 8.79/4.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3789 ms resp. 2765 ms w/o parsing
% 9.61/4.67 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.61/4.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------