%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU386+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 : n015.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 08:38:39 AM UTC 2026
% Result : Theorem 6.68s 8.54s
% Output : Refutation 7.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 40
% Syntax : Number of formulae : 82 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 295 ( 7 equ; 0 cnn)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 772 ( 62 ~; 2 |; 108 &; 497 @)
% ( 4 <=>; 99 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 2 con; 0-3 aty)
% Number of variables : 153 ( 0 ^; 127 !; 26 ?; 153 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_decl,type,
empty_carrier: $i > $o ).
thf(topological_space_decl,type,
topological_space: $i > $o ).
thf(top_str_decl,type,
top_str: $i > $o ).
thf(transitive_relstr_decl,type,
transitive_relstr: $i > $o ).
thf(directed_relstr_decl,type,
directed_relstr: $i > $o ).
thf(net_str_decl,type,
net_str: $i > $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(lim_points_of_net_decl,type,
lim_points_of_net: $i > $i > $i ).
thf(is_a_cluster_point_of_netstr_decl,type,
is_a_cluster_point_of_netstr: $i > $i > $i > $o ).
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(empty_decl,type,
empty: $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(finite_decl,type,
finite: $i > $o ).
thf(rel_str_decl,type,
rel_str: $i > $o ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(point_neighbourhood_decl,type,
point_neighbourhood: $i > $i > $i > $o ).
thf(is_eventually_in_decl,type,
is_eventually_in: $i > $i > $i > $o ).
thf(is_often_in_decl,type,
is_often_in: $i > $i > $i > $o ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( B @ ( A @ lim_points_of_net ) @ ( C @ in ) )
=> ( C @ ( B @ ( A @ is_a_cluster_point_of_netstr ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_waybel_9) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( B @ ( A @ lim_points_of_net ) @ ( C @ in ) )
=> ( C @ ( B @ ( A @ is_a_cluster_point_of_netstr ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(42,plain,
~ ! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( B @ ( A @ lim_points_of_net ) @ ( C @ in ) )
=> ( C @ ( B @ ( A @ is_a_cluster_point_of_netstr ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(125,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(60,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ powerset @ preboolean )
& ( A @ powerset @ diff_closed )
& ( A @ powerset @ cup_closed )
& ~ ( A @ powerset @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finsub_1) ).
thf(70,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)],[9]) ).
thf(17,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(97,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(109,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(29,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ is_eventually_in ) ) )
=> ( C @ ( B @ ( A @ is_often_in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_yellow_6) ).
thf(129,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ is_eventually_in ) ) )
=> ( C @ ( B @ ( A @ is_often_in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(176,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,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(113,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ point_neighbourhood ) ) )
=> ( A @ the_carrier @ powerset @ ( C @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_connsp_2) ).
thf(127,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ point_neighbourhood ) ) )
=> ( A @ the_carrier @ powerset @ ( C @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(18,axiom,
? [A: $i] : ( A @ top_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(99,plain,
? [A: $i] : ( A @ top_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/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)],[25]) ).
thf(20,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(107,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(8,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(69,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(101,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(13,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(88,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ preboolean )
=> ( ( A @ diff_closed )
& ( A @ cup_closed ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finsub_1) ).
thf(56,plain,
! [A: $i] :
( ( A @ preboolean )
=> ( ( A @ diff_closed )
& ( A @ cup_closed ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(34,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(142,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(93,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(38,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( C
= ( B @ ( A @ lim_points_of_net ) ) )
<=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
<=> ! [E: $i] :
( ( D @ ( A @ ( E @ point_neighbourhood ) ) )
=> ( E @ ( B @ ( A @ is_eventually_in ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_yellow_6) ).
thf(152,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( A @ the_carrier @ powerset @ ( C @ element ) )
=> ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ! [E: $i] :
( ( D @ ( A @ ( E @ point_neighbourhood ) ) )
=> ( E @ ( B @ ( A @ is_eventually_in ) ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ! [E: $i] :
( ( D @ ( A @ ( E @ point_neighbourhood ) ) )
=> ( E @ ( B @ ( A @ is_eventually_in ) ) ) ) ) ) )
=> ( C
= ( B @ ( A @ lim_points_of_net ) ) ) )
& ( ( C
= ( B @ ( A @ lim_points_of_net ) ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( ! [E: $i] :
( ( D @ ( A @ ( E @ point_neighbourhood ) ) )
=> ( E @ ( B @ ( A @ is_eventually_in ) ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ! [E: $i] :
( ( D @ ( A @ ( E @ point_neighbourhood ) ) )
=> ( E @ ( B @ ( A @ is_eventually_in ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(26,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(121,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)],[26]) ).
thf(11,axiom,
? [A: $i] : ( A @ rel_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(84,plain,
? [A: $i] : ( A @ rel_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] : ( A @ ( B @ net_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_waybel_0) ).
thf(133,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] : ( A @ ( B @ net_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(24,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(116,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ top_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(148,plain,
! [A: $i] :
( ( A @ top_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(6,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(64,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [A: $i] :
( ( ( A @ diff_closed )
& ( A @ cup_closed ) )
=> ( A @ preboolean ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(54,plain,
! [A: $i] :
( ( ( A @ diff_closed )
& ( A @ cup_closed ) )
=> ( A @ preboolean ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(86,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(33,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(140,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(7,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(66,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(32,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(135,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(10,axiom,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(80,plain,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ( B @ rel_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
thf(150,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ( B @ rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(95,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ powerset @ ( B @ ( A @ lim_points_of_net ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_yellow_6) ).
thf(146,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ powerset @ ( B @ ( A @ lim_points_of_net ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(41,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ is_a_cluster_point_of_netstr ) ) )
<=> ! [D: $i] :
( ( C @ ( A @ ( D @ point_neighbourhood ) ) )
=> ( D @ ( B @ ( A @ is_often_in ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_waybel_9) ).
thf(183,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ! [D: $i] :
( ( C @ ( A @ ( D @ point_neighbourhood ) ) )
=> ( D @ ( B @ ( A @ is_often_in ) ) ) )
=> ( C @ ( B @ ( A @ is_a_cluster_point_of_netstr ) ) ) )
& ( ( C @ ( B @ ( A @ is_a_cluster_point_of_netstr ) ) )
=> ! [D: $i] :
( ( C @ ( A @ ( D @ point_neighbourhood ) ) )
=> ( D @ ( B @ ( A @ is_often_in ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(131,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(40,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(178,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(90,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ point_neighbourhood ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_connsp_2) ).
thf(111,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ point_neighbourhood ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(200,plain,
$false,
inference(e,[status(thm)],[42,125,60,70,97,109,129,176,113,127,99,119,107,69,101,88,56,142,93,152,121,84,133,116,148,64,54,86,140,66,135,80,150,95,146,183,131,178,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU386+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.21/5.48 % Computer : n015.cluster.edu
% 0.21/5.48 % Model : x86_64 x86_64
% 0.21/5.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/5.48 % Memory : 8046.5625MB
% 0.21/5.48 % OS : Linux 6.8.0-71-generic
% 0.21/5.48 % CPULimit : 300
% 0.21/5.48 % WCLimit : 300
% 0.21/5.48 % DateTime : Sat Sep 26 09:27:19 UTC 2026
% 0.21/5.48 % CPUTime :
% 0.21/5.48 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
% 0.26/6.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.73/6.34 % [INFO] Parsing done (327ms).
% 1.73/6.36 % [INFO] Running in sequential loop mode.
% 2.81/6.99 % [INFO] eprover registered as external prover.
% 2.81/7.00 % [INFO] Scanning for conjecture ...
% 3.37/7.16 % [INFO] Found a conjecture (or negated_conjecture) and 44 axioms. Running axiom selection ...
% 3.47/7.30 % [INFO] Axiom selection finished. Selected 39 axioms (removed 5 axioms).
% 3.69/7.39 % [INFO] Problem is first-order (TPTP FOF).
% 3.92/7.41 % [INFO] Type checking passed.
% 3.92/7.42 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.68/8.54 % External prover 'e' found a proof!
% 6.68/8.54 % [INFO] Killing All external provers ...
% 6.68/8.54 % Time passed: 2930ms (effective reasoning time: 2163ms)
% 6.68/8.54 % 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)>
% 6.68/8.54 % Axioms used in derivation (39): cc2_finset_1, cc2_finsub_1, t5_subset, t4_subset, rc3_finset_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_finsub_1, rc4_finset_1, fc1_xboole_0, t1_subset, dt_l1_pre_topc, t6_boole, dt_l1_waybel_0, existence_l1_waybel_0, d9_waybel_9, t7_boole, existence_l1_orders_2, cc1_funct_1, rc3_struct_0, t3_subset, existence_m1_subset_1, t28_yellow_6, d18_yellow_6, existence_m1_connsp_2, dt_m1_connsp_2, dt_l1_orders_2, cc1_finsub_1, fc1_struct_0, existence_l1_pre_topc, reflexivity_r1_tarski, rc1_finset_1, cc1_finset_1, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, existence_l1_struct_0, dt_k11_yellow_6
% 6.68/8.54 % No. of inferences in proof: 82
% 6.68/8.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2930 ms resp. 2163 ms w/o parsing
% 7.11/8.65 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.11/8.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------