%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU351+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 : n010.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 55.85s 12.11s
% Output : Refutation 47.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 33
% Syntax : Number of formulae : 68 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 307 ( 21 equ; 0 cnn)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 831 ( 51 ~; 2 |; 126 &; 541 @)
% ( 9 <=>; 102 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 2 con; 0-3 aty)
% Number of variables : 140 ( 0 ^; 118 !; 22 ?; 140 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_decl,type,
empty_carrier: $i > $o ).
thf(lattice_decl,type,
lattice: $i > $o ).
thf(complete_latt_str_decl,type,
complete_latt_str: $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(meet_of_latt_set_decl,type,
meet_of_latt_set: $i > $i > $i ).
thf(latt_set_smaller_decl,type,
latt_set_smaller: $i > $i > $i > $o ).
thf(below_refl_decl,type,
below_refl: $i > $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(empty_set_decl,type,
empty_set: $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(in_decl,type,
in: $i > $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(join_of_latt_set_decl,type,
join_of_latt_set: $i > $i > $i ).
thf(latt_element_smaller_decl,type,
latt_element_smaller: $i > $i > $i > $o ).
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(a_2_2_lattice3_decl,type,
a_2_2_lattice3: $i > $i > $i ).
thf(a_2_3_lattice3_decl,type,
a_2_3_lattice3: $i > $i > $i ).
thf(10,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
<=> ( B @ ( C @ in ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(69,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)],[10]) ).
thf(4,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(56,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
? [A: $i] : ( A @ meet_semilatt_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(84,plain,
? [A: $i] : ( A @ meet_semilatt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( B @ ( A @ meet_of_latt_set ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k16_lattice3) ).
thf(165,plain,
! [A: $i,B: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( B @ ( A @ meet_of_latt_set ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(21,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(129,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)],[21]) ).
thf(18,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(112,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ join_semilatt_str )
& ( A @ meet_semilatt_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(17,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C
= ( B @ ( A @ join_of_latt_set ) ) )
<=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ ( A @ latt_element_smaller ) ) )
=> ( D @ ( C @ ( A @ below ) ) ) ) )
& ( B @ ( C @ ( A @ latt_element_smaller ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d21_lattice3) ).
thf(95,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ ( A @ latt_element_smaller ) ) )
=> ( D @ ( C @ ( A @ below ) ) ) ) )
& ( B @ ( C @ ( A @ latt_element_smaller ) ) ) )
=> ( C
= ( B @ ( A @ join_of_latt_set ) ) ) )
& ( ( C
= ( B @ ( A @ join_of_latt_set ) ) )
=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ ( A @ latt_element_smaller ) ) )
=> ( D @ ( C @ ( A @ below ) ) ) ) )
& ( B @ ( C @ ( A @ latt_element_smaller ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/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)],[3]) ).
thf(33,axiom,
? [A: $i] : ( A @ latt_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(184,plain,
? [A: $i] : ( A @ latt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(6,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(61,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( B @ ( A @ join_of_latt_set ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_lattice3) ).
thf(116,plain,
! [A: $i,B: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( B @ ( A @ join_of_latt_set ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(15,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)],[15]) ).
thf(22,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(133,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(161,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(64,plain,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(25,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(149,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(32,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( B @ ( A @ meet_of_latt_set ) )
= ( B @ ( A @ a_2_2_lattice3 ) @ ( A @ join_of_latt_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d22_lattice3) ).
thf(181,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( B @ ( A @ meet_of_latt_set ) )
= ( B @ ( A @ a_2_2_lattice3 ) @ ( A @ join_of_latt_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(86,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
thf(91,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)],[16]) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(66,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(23,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(135,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( B
= ( C @ ( A @ meet_of_latt_set ) ) )
<=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ ( A @ latt_set_smaller ) ) )
=> ( B @ ( D @ ( A @ below_refl ) ) ) ) )
& ( C @ ( B @ ( A @ latt_set_smaller ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattice3) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( B
= ( C @ ( A @ meet_of_latt_set ) ) )
<=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ ( A @ latt_set_smaller ) ) )
=> ( B @ ( D @ ( A @ below_refl ) ) ) ) )
& ( C @ ( B @ ( A @ latt_set_smaller ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ ! [A: $i] :
( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ ( A @ latt_set_smaller ) ) )
=> ( B @ ( D @ ( A @ below_refl ) ) ) ) )
& ( C @ ( B @ ( A @ latt_set_smaller ) ) ) )
=> ( B
= ( C @ ( A @ meet_of_latt_set ) ) ) )
& ( ( B
= ( C @ ( A @ meet_of_latt_set ) ) )
=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ ( A @ latt_set_smaller ) ) )
=> ( B @ ( D @ ( A @ below_refl ) ) ) ) )
& ( C @ ( B @ ( A @ latt_set_smaller ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(34,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(186,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)],[34]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ latt_str )
& ( B @ complete_latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ( ( C @ ( B @ a_2_3_lattice3 ) @ ( A @ in ) )
<=> ? [D: $i] :
( ( C @ ( D @ ( B @ latt_set_smaller ) ) )
& ( A = D )
& ( B @ the_carrier @ ( D @ element ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_3_lattice3) ).
thf(171,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ latt_str )
& ( B @ complete_latt_str )
& ( B @ lattice )
& ~ ( B @ empty_carrier ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ ( B @ latt_set_smaller ) ) )
& ( A = D )
& ( B @ the_carrier @ ( D @ element ) ) )
=> ( C @ ( B @ a_2_3_lattice3 ) @ ( A @ in ) ) )
& ( ( C @ ( B @ a_2_3_lattice3 ) @ ( A @ in ) )
=> ? [D: $i] :
( ( C @ ( D @ ( B @ latt_set_smaller ) ) )
& ( A = D )
& ( B @ the_carrier @ ( D @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ latt_str )
& ~ ( B @ empty_carrier ) )
=> ( ( C @ ( B @ a_2_2_lattice3 ) @ ( A @ in ) )
<=> ? [D: $i] :
( ( C @ ( D @ ( B @ latt_set_smaller ) ) )
& ( A = D )
& ( B @ the_carrier @ ( D @ element ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_lattice3) ).
thf(139,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ latt_str )
& ~ ( B @ empty_carrier ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ ( B @ latt_set_smaller ) ) )
& ( A = D )
& ( B @ the_carrier @ ( D @ element ) ) )
=> ( C @ ( B @ a_2_2_lattice3 ) @ ( A @ in ) ) )
& ( ( C @ ( B @ a_2_2_lattice3 ) @ ( A @ in ) )
=> ? [D: $i] :
( ( C @ ( D @ ( B @ latt_set_smaller ) ) )
& ( A = D )
& ( B @ the_carrier @ ( D @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(12,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(82,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ latt_element_smaller ) ) )
<=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
=> ( B @ ( D @ ( A @ below ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattice3) ).
thf(119,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
=> ( B @ ( D @ ( A @ below ) ) ) ) )
=> ( C @ ( B @ ( A @ latt_element_smaller ) ) ) )
& ( ( C @ ( B @ ( A @ latt_element_smaller ) ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
=> ( B @ ( D @ ( A @ below ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(58,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(26,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ latt_set_smaller ) ) )
<=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
=> ( D @ ( B @ ( A @ below ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattice3) ).
thf(151,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
=> ( D @ ( B @ ( A @ below ) ) ) ) )
=> ( C @ ( B @ ( A @ latt_set_smaller ) ) ) )
& ( ( C @ ( B @ ( A @ latt_set_smaller ) ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
=> ( D @ ( B @ ( A @ below ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
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 ) )
=> ( B @ ( B @ ( A @ below_refl ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
thf(168,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)],[30]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(163,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(62,plain,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24083,plain,
$false,
inference(e,[status(thm)],[69,56,84,165,129,112,95,52,184,61,116,89,133,161,64,149,181,86,91,66,135,80,35,186,171,139,82,119,58,151,168,163,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU351+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % 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
% 0.13/0.39 % Computer : n010.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 09:18:22 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.84/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/1.18 % [INFO] Parsing done (204ms).
% 1.20/1.19 % [INFO] Running in sequential loop mode.
% 1.86/1.59 % [INFO] eprover registered as external prover.
% 1.86/1.60 % [INFO] Scanning for conjecture ...
% 2.23/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 36 axioms. Running axiom selection ...
% 2.23/1.80 % [INFO] Axiom selection finished. Selected 32 axioms (removed 4 axioms).
% 2.43/1.86 % [INFO] Problem is first-order (TPTP FOF).
% 2.43/1.87 % [INFO] Type checking passed.
% 2.43/1.88 % [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 ...
% 55.85/12.10 % External prover 'e' found a proof!
% 55.85/12.10 % [INFO] Killing All external provers ...
% 55.85/12.10 % Time passed: 11572ms (effective reasoning time: 10904ms)
% 55.85/12.11 % 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)>
% 55.85/12.11 % Axioms used in derivation (32): d16_lattice3, existence_l3_lattices, d22_lattice3, d21_lattice3, cc1_lattices, redefinition_r3_lattices, fraenkel_a_2_2_lattice3, fc1_struct_0, t2_subset, existence_l1_struct_0, rc2_xboole_0, fc1_xboole_0, existence_l1_lattices, t1_subset, reflexivity_r3_lattices, dt_l1_lattices, t6_boole, existence_l2_lattices, fraenkel_a_2_3_lattice3, dt_l3_lattices, dt_l2_lattices, t2_tarski, t7_boole, d17_lattice3, rc3_struct_0, existence_m1_subset_1, dt_k16_lattice3, dt_k15_lattice3, t8_boole, rc1_xboole_0, antisymmetry_r2_hidden, cc2_lattices
% 55.85/12.11 % No. of inferences in proof: 68
% 55.85/12.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11572 ms resp. 10904 ms w/o parsing
% 47.88/12.16 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 47.88/12.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------