%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU342+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n012.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 08:38:30 AM UTC 2026
% Result : Theorem 3.21s 1.78s
% Output : Refutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 36
% Syntax : Number of formulae : 74 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 253 ( 23 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 695 ( 57 ~; 2 |; 111 &; 459 @)
% ( 5 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 2 con; 0-4 aty)
% Number of variables : 135 ( 0 ^; 113 !; 22 ?; 135 :)
% 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(in_decl,type,
in: $i > $i > $o ).
thf(ordered_pair_as_product_element_decl,type,
ordered_pair_as_product_element: $i > $i > $i > $i > $i ).
thf(relation_of_lattice_decl,type,
relation_of_lattice: $i > $i ).
thf(below_refl_decl,type,
below_refl: $i > $i > $i > $o ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(join_semilatt_str_decl,type,
join_semilatt_str: $i > $o ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(meet_semilatt_str_decl,type,
meet_semilatt_str: $i > $o ).
thf(meet_commutative_decl,type,
meet_commutative: $i > $o ).
thf(meet_absorbing_decl,type,
meet_absorbing: $i > $o ).
thf(join_absorbing_decl,type,
join_absorbing: $i > $o ).
thf(below_decl,type,
below: $i > $i > $i > $o ).
thf(relation_decl,type,
relation: $i > $o ).
thf(a_1_0_filter_1_decl,type,
a_1_0_filter_1: $i > $i ).
thf(join_commutative_decl,type,
join_commutative: $i > $o ).
thf(join_associative_decl,type,
join_associative: $i > $o ).
thf(meet_associative_decl,type,
meet_associative: $i > $o ).
thf(16,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(88,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(52,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ element ) )
& ( A @ ( C @ element ) )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( ( D @ ( C @ ( B @ ( A @ ordered_pair_as_product_element ) ) ) )
= ( D @ ( C @ ordered_pair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
thf(129,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ element ) )
& ( A @ ( C @ element ) )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( ( D @ ( C @ ( B @ ( A @ ordered_pair_as_product_element ) ) ) )
= ( D @ ( C @ ordered_pair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(67,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(22,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(104,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(6,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(58,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(56,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(33,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ relation_of_lattice )
= ( A @ a_1_0_filter_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_1) ).
thf(142,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ relation_of_lattice )
= ( A @ a_1_0_filter_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(23,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(106,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(14,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(84,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
! [A: $i] :
~ ( A @ singleton @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(61,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ below_refl ) ) )
<=> ( C @ ( B @ ( A @ below ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
thf(132,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( ( C @ ( B @ ( A @ below ) ) )
=> ( C @ ( B @ ( A @ below_refl ) ) ) )
& ( ( C @ ( B @ ( A @ below_refl ) ) )
=> ( C @ ( B @ ( A @ below ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( A @ relation_of_lattice @ ( C @ ( B @ ( A @ the_carrier @ ( A @ the_carrier @ ordered_pair_as_product_element ) ) ) @ in ) )
<=> ( C @ ( B @ ( A @ below_refl ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_filter_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( A @ relation_of_lattice @ ( C @ ( B @ ( A @ the_carrier @ ( A @ the_carrier @ ordered_pair_as_product_element ) ) ) @ in ) )
<=> ( C @ ( B @ ( A @ below_refl ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(38,plain,
~ ! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( C @ ( B @ ( A @ below_refl ) ) )
=> ( A @ relation_of_lattice @ ( C @ ( B @ ( A @ the_carrier @ ( A @ the_carrier @ ordered_pair_as_product_element ) ) ) @ in ) ) )
& ( ( A @ relation_of_lattice @ ( C @ ( B @ ( A @ the_carrier @ ( A @ the_carrier @ ordered_pair_as_product_element ) ) ) @ in ) )
=> ( C @ ( B @ ( A @ below_refl ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(36,axiom,
? [A: $i] : ( A @ latt_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(160,plain,
? [A: $i] : ( A @ latt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(109,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(124,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(77,plain,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(96,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(64,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ( ( B @ a_1_0_filter_1 @ ( A @ in ) )
<=> ? [C: $i,D: $i] :
( ( D @ ( C @ ( B @ below_refl ) ) )
& ( A
= ( D @ ( C @ ( B @ the_carrier @ ( B @ the_carrier @ ordered_pair_as_product_element ) ) ) ) )
& ( B @ the_carrier @ ( D @ element ) )
& ( B @ the_carrier @ ( C @ element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_filter_1) ).
thf(149,plain,
! [A: $i,B: $i] :
( ( ( B @ latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ( ( ? [C: $i,D: $i] :
( ( D @ ( C @ ( B @ below_refl ) ) )
& ( A
= ( D @ ( C @ ( B @ the_carrier @ ( B @ the_carrier @ ordered_pair_as_product_element ) ) ) ) )
& ( B @ the_carrier @ ( D @ element ) )
& ( B @ the_carrier @ ( C @ element ) ) )
=> ( B @ a_1_0_filter_1 @ ( A @ in ) ) )
& ( ( B @ a_1_0_filter_1 @ ( A @ in ) )
=> ? [C: $i,D: $i] :
( ( D @ ( C @ ( B @ below_refl ) ) )
& ( A
= ( D @ ( C @ ( B @ the_carrier @ ( B @ the_carrier @ ordered_pair_as_product_element ) ) ) ) )
& ( B @ the_carrier @ ( D @ element ) )
& ( B @ the_carrier @ ( C @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(49,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
? [A: $i] : ( A @ meet_semilatt_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(86,plain,
? [A: $i] : ( A @ meet_semilatt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
<=> ( B @ ( C @ in ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(113,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) )
& ( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(81,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ element ) )
& ( A @ ( C @ element ) )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( B @ ( A @ cartesian_product2 ) @ ( D @ ( C @ ( B @ ( A @ ordered_pair_as_product_element ) ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_domain_1) ).
thf(98,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ element ) )
& ( A @ ( C @ element ) )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( B @ ( A @ cartesian_product2 ) @ ( D @ ( C @ ( B @ ( A @ ordered_pair_as_product_element ) ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(32,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ relation_of_lattice @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_filter_1) ).
thf(140,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ relation_of_lattice @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(91,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(37,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/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
thf(162,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)],[37]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',cc2_lattices) ).
thf(145,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)],[34]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(79,plain,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(18,axiom,
? [A: $i] : ( A @ join_semilatt_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(94,plain,
? [A: $i] : ( A @ join_semilatt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( B @ ( B @ ( A @ below_refl ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
thf(126,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( B @ ( B @ ( A @ below_refl ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ join_semilatt_str )
& ( A @ meet_semilatt_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(136,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ join_semilatt_str )
& ( A @ meet_semilatt_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(111,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(21,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(100,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(199,plain,
$false,
inference(e,[status(thm)],[88,52,65,129,67,104,58,56,142,106,84,61,132,38,160,109,124,77,96,64,149,49,86,113,81,98,140,91,162,145,79,94,126,136,111,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU342+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.08/0.32 % Computer : n012.cluster.edu
% 0.08/0.32 % Model : x86_64 x86_64
% 0.08/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.32 % Memory : 8046.5625MB
% 0.08/0.32 % OS : Linux 6.8.0-71-generic
% 0.08/0.32 % CPULimit : 300
% 0.08/0.32 % WCLimit : 300
% 0.08/0.32 % DateTime : Sat Sep 26 09:15:35 UTC 2026
% 0.08/0.33 % CPUTime :
% 0.08/0.33 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.52/0.63 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.74 % [INFO] Parsing done (111ms).
% 0.66/0.75 % [INFO] Running in sequential loop mode.
% 1.06/0.95 % [INFO] eprover registered as external prover.
% 1.06/0.96 % [INFO] Scanning for conjecture ...
% 1.06/1.01 % [INFO] Found a conjecture (or negated_conjecture) and 43 axioms. Running axiom selection ...
% 1.33/1.07 % [INFO] Axiom selection finished. Selected 35 axioms (removed 8 axioms).
% 1.33/1.10 % [INFO] Problem is first-order (TPTP FOF).
% 1.33/1.11 % [INFO] Type checking passed.
% 1.33/1.11 % [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 ...
% 3.21/1.78 % External prover 'e' found a proof!
% 3.21/1.78 % [INFO] Killing All external provers ...
% 3.21/1.78 % Time passed: 1373ms (effective reasoning time: 1021ms)
% 3.21/1.78 % 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)>
% 3.21/1.78 % Axioms used in derivation (35): fraenkel_a_1_0_filter_1, fc3_subset_1, dt_k9_filter_1, dt_k1_domain_1, redefinition_r3_lattices, t2_subset, existence_l1_struct_0, rc2_xboole_0, fc1_xboole_0, existence_l1_lattices, d5_tarski, t1_subset, fc4_subset_1, existence_l3_lattices, reflexivity_r3_lattices, dt_l1_lattices, t6_boole, existence_l2_lattices, dt_l3_lattices, fc2_subset_1, dt_l2_lattices, t2_tarski, t7_boole, rc3_struct_0, t33_zfmisc_1, redefinition_k1_domain_1, cc1_lattices, existence_m1_subset_1, commutativity_k2_tarski, fc1_struct_0, d8_filter_1, t8_boole, rc1_xboole_0, antisymmetry_r2_hidden, cc2_lattices
% 3.21/1.78 % No. of inferences in proof: 74
% 3.21/1.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1373 ms resp. 1021 ms w/o parsing
% 3.76/1.82 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.76/1.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------