%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU304+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 : n026.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 08:38:23 AM UTC 2026
% Result : Theorem 8.52s 4.37s
% Output : Refutation 9.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 42
% Syntax : Number of formulae : 86 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 300 ( 20 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1017 ( 53 ~; 2 |; 121 &; 750 @)
% ( 4 <=>; 87 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 30 usr; 2 con; 0-6 aty)
% Number of variables : 190 ( 0 ^; 172 !; 18 ?; 190 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_decl,type,
empty_carrier: $i > $o ).
thf(meet_commutative_decl,type,
meet_commutative: $i > $o ).
thf(meet_absorbing_decl,type,
meet_absorbing: $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(below_decl,type,
below: $i > $i > $i > $o ).
thf(meet_commut_decl,type,
meet_commut: $i > $i > $i > $i ).
thf(cup_closed_decl,type,
cup_closed: $i > $o ).
thf(diff_closed_decl,type,
diff_closed: $i > $o ).
thf(preboolean_decl,type,
preboolean: $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(meet_semilatt_str_decl,type,
meet_semilatt_str: $i > $o ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(function_decl,type,
function: $i > $o ).
thf(the_L_meet_decl,type,
the_L_meet: $i > $i ).
thf(quasi_total_decl,type,
quasi_total: $i > $i > $i > $o ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(join_decl,type,
join: $i > $i > $i > $i ).
thf(meet_decl,type,
meet: $i > $i > $i > $i ).
thf(apply_binary_as_element_decl,type,
apply_binary_as_element: $i > $i > $i > $i > $i > $i > $i ).
thf(apply_binary_decl,type,
apply_binary: $i > $i > $i > $i ).
thf(the_L_join_decl,type,
the_L_join: $i > $i ).
thf(14,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(88,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(153,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ meet_commut ) ) )
= ( C @ ( B @ ( A @ meet ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
thf(174,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ meet_commut ) ) )
= ( C @ ( B @ ( A @ meet ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ join ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattices) ).
thf(157,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ join ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(27,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(137,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)],[27]) ).
thf(20,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(109,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(25,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(129,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)],[25]) ).
thf(11,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(81,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(39,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(167,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)],[39]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(119,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(38,axiom,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ join ) ) )
= ( C @ ( B @ ( A @ the_L_join @ ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_binary_as_element ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattices) ).
thf(164,plain,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ join ) ) )
= ( C @ ( B @ ( A @ the_L_join @ ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_binary_as_element ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(43,axiom,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ below ) ) )
<=> ( ( C @ ( B @ ( A @ join ) ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).
thf(179,plain,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( ( C @ ( B @ ( A @ join ) ) )
= C )
=> ( C @ ( B @ ( A @ below ) ) ) )
& ( ( C @ ( B @ ( A @ below ) ) )
=> ( ( C @ ( B @ ( A @ join ) ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(24,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ meet_absorbing )
<=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( C @ ( B @ ( A @ meet ) ) @ ( A @ join ) ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattices) ).
thf(121,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( C @ ( B @ ( A @ meet ) ) @ ( A @ join ) ) )
= C ) ) )
=> ( A @ meet_absorbing ) )
& ( ( A @ meet_absorbing )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( C @ ( B @ ( A @ meet ) ) @ ( A @ join ) ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(12,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(84,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ meet_commut ) ) )
= ( B @ ( C @ ( A @ meet_commut ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
thf(147,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ meet_commut ) ) )
= ( B @ ( C @ ( A @ meet_commut ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(61,plain,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(26,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(133,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ join_semilatt_str )
& ( A @ meet_semilatt_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(92,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(8,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(65,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(18,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(97,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)],[18]) ).
thf(3,axiom,
! [A: $i] :
( ( ( A @ diff_closed )
& ( A @ cup_closed ) )
=> ( A @ preboolean ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(53,plain,
! [A: $i] :
( ( ( A @ diff_closed )
& ( A @ cup_closed ) )
=> ( A @ preboolean ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ quasi_total ) ) )
& ( A @ the_L_join @ function ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(169,plain,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ quasi_total ) ) )
& ( A @ the_L_join @ function ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(29,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(141,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( B @ ( C @ ( B @ ( A @ meet_commut ) ) @ ( A @ below ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattices) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ latt_str )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( B @ ( C @ ( B @ ( A @ meet_commut ) ) @ ( A @ below ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(44,plain,
~ ! [A: $i] :
( ( ( A @ latt_str )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( B @ ( C @ ( B @ ( A @ meet_commut ) ) @ ( A @ below ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(59,plain,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ powerset @ preboolean )
& ( A @ powerset @ diff_closed )
& ( A @ powerset @ cup_closed )
& ~ ( A @ powerset @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finsub_1) ).
thf(71,plain,
! [A: $i] :
( ( A @ powerset @ preboolean )
& ( A @ powerset @ diff_closed )
& ( A @ powerset @ cup_closed )
& ~ ( A @ powerset @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(86,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ element ) )
& ( A @ ( E @ element ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ relation_of2 ) ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ apply_binary_as_element ) ) ) ) ) )
= ( F @ ( E @ ( D @ apply_binary ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(159,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ element ) )
& ( A @ ( E @ element ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ relation_of2 ) ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ apply_binary_as_element ) ) ) ) ) )
= ( F @ ( E @ ( D @ apply_binary ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(103,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)],[19]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ meet_commut ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattices) ).
thf(155,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ meet_commut ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ meet ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(162,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ meet ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ element ) )
& ( A @ ( E @ element ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ relation_of2 ) ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ apply_binary_as_element ) ) ) ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(145,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ element ) )
& ( A @ ( E @ element ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ relation_of2 ) ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ apply_binary_as_element ) ) ) ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(7,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(63,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(32,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ meet ) ) )
= ( C @ ( B @ ( A @ the_L_meet @ ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_binary_as_element ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattices) ).
thf(150,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ meet ) ) )
= ( C @ ( B @ ( A @ the_L_meet @ ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_binary_as_element ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(17,axiom,
? [A: $i] : ( A @ join_semilatt_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(95,plain,
? [A: $i] : ( A @ join_semilatt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(67,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(42,axiom,
? [A: $i] : ( A @ latt_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(177,plain,
? [A: $i] : ( A @ latt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(28,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(139,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ preboolean )
=> ( ( A @ diff_closed )
& ( A @ cup_closed ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finsub_1) ).
thf(55,plain,
! [A: $i] :
( ( A @ preboolean )
=> ( ( A @ diff_closed )
& ( A @ cup_closed ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(114,plain,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(15,axiom,
? [A: $i] : ( A @ meet_semilatt_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(90,plain,
? [A: $i] : ( A @ meet_semilatt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(21,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(111,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(185,plain,
$false,
inference(e,[status(thm)],[88,153,174,157,137,109,129,81,167,119,164,179,121,84,147,61,133,92,65,97,53,169,141,44,59,71,86,159,103,155,162,145,63,150,95,67,177,139,55,114,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU304+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % 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
% 0.14/0.40 % Computer : n026.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 09:11:40 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 1.32/1.25 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.16/1.61 % [INFO] Parsing done (352ms).
% 2.16/1.63 % [INFO] Running in sequential loop mode.
% 3.16/2.27 % [INFO] eprover registered as external prover.
% 3.16/2.28 % [INFO] Scanning for conjecture ...
% 3.59/2.47 % [INFO] Found a conjecture (or negated_conjecture) and 49 axioms. Running axiom selection ...
% 3.99/2.63 % [INFO] Axiom selection finished. Selected 41 axioms (removed 8 axioms).
% 4.23/2.76 % [INFO] Problem is first-order (TPTP FOF).
% 4.23/2.78 % [INFO] Type checking passed.
% 4.23/2.79 % [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 ...
% 8.52/4.36 % External prover 'e' found a proof!
% 8.52/4.36 % [INFO] Killing All external provers ...
% 8.52/4.37 % Time passed: 3778ms (effective reasoning time: 2721ms)
% 8.52/4.37 % 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)>
% 8.52/4.37 % Axioms used in derivation (41): fc1_finsub_1, existence_l3_lattices, dt_m2_relset_1, dt_l1_lattices, t5_subset, dt_l2_lattices, existence_m2_relset_1, redefinition_k2_binop_1, d2_lattices, dt_k1_lattices, t8_boole, d8_lattices, d1_lattices, redefinition_m2_relset_1, existence_l1_lattices, t1_subset, dt_k2_binop_1, cc2_finsub_1, t6_boole, existence_l2_lattices, existence_m1_relset_1, dt_l3_lattices, d3_lattices, t4_subset, t7_boole, rc3_struct_0, commutativity_k4_lattices, t3_subset, dt_u1_lattices, existence_m1_subset_1, cc1_finsub_1, fc1_struct_0, dt_k4_lattices, reflexivity_r1_tarski, rc5_struct_0, t2_subset, existence_l1_struct_0, dt_k2_lattices, dt_u2_lattices, antisymmetry_r2_hidden, redefinition_k4_lattices
% 8.52/4.37 % No. of inferences in proof: 86
% 8.52/4.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3778 ms resp. 2721 ms w/o parsing
% 9.31/4.52 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.31/4.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------