%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU401+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 : n001.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 08:38:41 AM UTC 2026
% Result : Theorem 7.68s 3.11s
% Output : Refutation 8.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 62
% Syntax : Number of formulae : 126 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 669 ( 45 equ; 0 cnn)
% Maximal formula atoms : 36 ( 5 avg)
% Number of connectives : 2081 ( 110 ~; 0 |; 381 &;1428 @)
% ( 6 <=>; 156 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 1 con; 0-4 aty)
% Number of variables : 305 ( 0 ^; 249 !; 56 ?; 305 :)
% 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(in_decl,type,
in: $i > $i > $o ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(netstr_induced_subset_decl,type,
netstr_induced_subset: $i > $i > $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(topstr_closure_decl,type,
topstr_closure: $i > $i > $i ).
thf(relation_rng_as_subset_decl,type,
relation_rng_as_subset: $i > $i > $i > $i ).
thf(subnetstr_of_element_decl,type,
subnetstr_of_element: $i > $i > $i > $i ).
thf(the_mapping_decl,type,
the_mapping: $i > $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(relation_rng_decl,type,
relation_rng: $i > $i ).
thf(relation_decl,type,
relation: $i > $o ).
thf(finite_decl,type,
finite: $i > $o ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(rel_str_decl,type,
rel_str: $i > $o ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(closed_subset_decl,type,
closed_subset: $i > $i > $o ).
thf(nowhere_dense_decl,type,
nowhere_dense: $i > $i > $o ).
thf(boundary_set_decl,type,
boundary_set: $i > $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(quasi_total_decl,type,
quasi_total: $i > $i > $i > $o ).
thf(net_str_of_decl,type,
net_str_of: $i > $i > $i > $i > $i ).
thf(netstr_restr_to_element_decl,type,
netstr_restr_to_element: $i > $i > $i > $i ).
thf(open_subset_decl,type,
open_subset: $i > $i > $o ).
thf(strict_net_str_decl,type,
strict_net_str: $i > $i > $o ).
thf(the_InternalRel_decl,type,
the_InternalRel: $i > $i ).
thf(subnet_decl,type,
subnet: $i > $i > $i > $o ).
thf(v1_membered_decl,type,
v1_membered: $i > $o ).
thf(v2_membered_decl,type,
v2_membered: $i > $o ).
thf(v3_membered_decl,type,
v3_membered: $i > $o ).
thf(v4_membered_decl,type,
v4_membered: $i > $o ).
thf(v5_membered_decl,type,
v5_membered: $i > $o ).
thf(19,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ nowhere_dense ) )
=> ( A @ ( B @ boundary_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_tops_1) ).
thf(153,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ nowhere_dense ) )
=> ( A @ ( B @ boundary_set ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(63,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(356,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(60,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_tops_1) ).
thf(328,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(129,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(143,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [C: $i] :
( ( C @ directed_relstr )
& ( A @ ( C @ strict_net_str ) )
& ( C @ transitive_relstr )
& ~ ( C @ empty_carrier )
& ( B @ ( A @ ( C @ subnet ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_waybel_9) ).
thf(319,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [C: $i] :
( ( C @ directed_relstr )
& ( A @ ( C @ strict_net_str ) )
& ( C @ transitive_relstr )
& ~ ( C @ empty_carrier )
& ( B @ ( A @ ( C @ subnet ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(55,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(308,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)],[55]) ).
thf(47,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tops_1) ).
thf(269,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ~ ( B @ empty )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ strict_net_str ) )
& ~ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_waybel_0) ).
thf(202,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ~ ( B @ empty )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ strict_net_str ) )
& ~ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(23,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ empty )
=> ( A @ ( B @ nowhere_dense ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_tops_1) ).
thf(174,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ empty )
=> ( A @ ( B @ nowhere_dense ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(44,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(257,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ cartesian_product2 ) @ finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ cartesian_product2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(62,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ( A @ ( B @ nowhere_dense ) )
& ( A @ ( B @ open_subset ) ) )
=> ( ( A @ ( B @ nowhere_dense ) )
& ( A @ ( B @ boundary_set ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ( B @ empty ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_tops_1) ).
thf(344,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ( A @ ( B @ nowhere_dense ) )
& ( A @ ( B @ open_subset ) ) )
=> ( ( A @ ( B @ nowhere_dense ) )
& ( A @ ( B @ boundary_set ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ( B @ empty ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ empty )
=> ( A @ ( B @ boundary_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_tops_1) ).
thf(196,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ empty )
=> ( A @ ( B @ boundary_set ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( C @ ( B @ ( A @ relation_rng_as_subset ) ) )
= ( C @ relation_rng ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
thf(316,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( C @ ( B @ ( A @ relation_rng_as_subset ) ) )
= ( C @ relation_rng ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ the_carrier @ ( C @ element ) )
& ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ ( C @ ( B @ ( A @ netstr_restr_to_element ) ) @ net_str ) )
& ( A @ ( C @ ( B @ ( A @ netstr_restr_to_element ) ) @ strict_net_str ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_waybel_9) ).
thf(261,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ the_carrier @ ( C @ element ) )
& ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ ( C @ ( B @ ( A @ netstr_restr_to_element ) ) @ net_str ) )
& ( A @ ( C @ ( B @ ( A @ netstr_restr_to_element ) ) @ strict_net_str ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function )
& ( B @ ( A @ the_mapping ) @ relation )
& ~ ( B @ ( A @ the_mapping ) @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc15_yellow_6) ).
thf(216,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function )
& ( B @ ( A @ the_mapping ) @ relation )
& ~ ( B @ ( A @ the_mapping ) @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ( A @ one_sorted_str ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) )
= ( H @ ( G @ ( F @ ( E @ net_str_of ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_waybel_0) ).
thf(164,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ( A @ one_sorted_str ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) )
= ( H @ ( G @ ( F @ ( E @ net_str_of ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(106,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(147,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,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(133,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(46,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ open_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tops_1) ).
thf(265,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ open_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(56,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(312,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] :
( ( A @ ( B @ strict_net_str ) )
& ( A @ ( B @ net_str ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_waybel_0) ).
thf(206,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] :
( ( A @ ( B @ strict_net_str ) )
& ( A @ ( B @ net_str ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(116,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(243,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)],[40]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ top_str )
=> ? [B: $i] :
( ( A @ ( B @ boundary_set ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_tops_1) ).
thf(334,plain,
! [A: $i] :
( ( A @ top_str )
=> ? [B: $i] :
( ( A @ ( B @ boundary_set ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnet ) ) )
=> ( ( A @ ( C @ net_str ) )
& ( C @ directed_relstr )
& ( C @ transitive_relstr )
& ~ ( C @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_yellow_6) ).
thf(302,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ subnet ) ) )
=> ( ( A @ ( C @ net_str ) )
& ( C @ directed_relstr )
& ( C @ transitive_relstr )
& ~ ( C @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ powerset @ ( C @ ( B @ ( A @ relation_rng_as_subset ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_1) ).
thf(192,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ powerset @ ( C @ ( B @ ( A @ relation_rng_as_subset ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
<=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(137,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)],[14]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ net_str ) )
& ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ strict_net_str ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_waybel_0) ).
thf(296,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ net_str ) )
& ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ strict_net_str ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ netstr_induced_subset ) ) )
=> ( A @ the_carrier @ powerset @ ( C @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_yellow19) ).
thf(149,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ netstr_induced_subset ) ) )
=> ( A @ the_carrier @ powerset @ ( C @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ top_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(279,plain,
! [A: $i] :
( ( A @ top_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ! [G: $i] :
( ( F @ ( G @ in ) )
<=> ( ? [H: $i] :
( ? [I: $i] :
( ( H
= ( I @ ( B @ ( A @ subnetstr_of_element ) ) @ ( A @ the_mapping ) @ ( A @ the_carrier @ ( I @ ( B @ ( A @ subnetstr_of_element ) ) @ the_carrier @ relation_rng_as_subset ) ) ) )
& ( G = I )
& ( D
= ( H @ ( A @ topstr_closure ) ) )
& ( B @ the_carrier @ ( I @ element ) ) )
& ( B @ ( A @ ( H @ netstr_induced_subset ) ) ) )
& ( B @ the_carrier @ ( G @ in ) ) ) )
& ! [G: $i] :
( ( E @ ( G @ in ) )
<=> ( ? [H: $i] :
( ? [I: $i] :
( ( H
= ( I @ ( B @ ( A @ subnetstr_of_element ) ) @ ( A @ the_mapping ) @ ( A @ the_carrier @ ( I @ ( B @ ( A @ subnetstr_of_element ) ) @ the_carrier @ relation_rng_as_subset ) ) ) )
& ( G = I )
& ( D
= ( H @ ( A @ topstr_closure ) ) )
& ( B @ the_carrier @ ( I @ element ) ) )
& ( B @ ( A @ ( H @ netstr_induced_subset ) ) ) )
& ( B @ the_carrier @ ( G @ in ) ) ) ) )
=> ( E = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_xboole_0__e6_39_3__yellow19__1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ! [G: $i] :
( ( F @ ( G @ in ) )
<=> ( ? [H: $i] :
( ? [I: $i] :
( ( H
= ( I @ ( B @ ( A @ subnetstr_of_element ) ) @ ( A @ the_mapping ) @ ( A @ the_carrier @ ( I @ ( B @ ( A @ subnetstr_of_element ) ) @ the_carrier @ relation_rng_as_subset ) ) ) )
& ( G = I )
& ( D
= ( H @ ( A @ topstr_closure ) ) )
& ( B @ the_carrier @ ( I @ element ) ) )
& ( B @ ( A @ ( H @ netstr_induced_subset ) ) ) )
& ( B @ the_carrier @ ( G @ in ) ) ) )
& ! [G: $i] :
( ( E @ ( G @ in ) )
<=> ( ? [H: $i] :
( ? [I: $i] :
( ( H
= ( I @ ( B @ ( A @ subnetstr_of_element ) ) @ ( A @ the_mapping ) @ ( A @ the_carrier @ ( I @ ( B @ ( A @ subnetstr_of_element ) ) @ the_carrier @ relation_rng_as_subset ) ) ) )
& ( G = I )
& ( D
= ( H @ ( A @ topstr_closure ) ) )
& ( B @ the_carrier @ ( I @ element ) ) )
& ( B @ ( A @ ( H @ netstr_induced_subset ) ) ) )
& ( B @ the_carrier @ ( G @ in ) ) ) ) )
=> ( E = F ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(64,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 ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( ( ? [G: $i] :
( ? [H: $i] :
( ( G
= ( H @ ( B @ ( A @ subnetstr_of_element ) ) @ ( A @ the_mapping ) @ ( A @ the_carrier @ ( H @ ( B @ ( A @ subnetstr_of_element ) ) @ the_carrier @ relation_rng_as_subset ) ) ) )
& ( F = H )
& ( C
= ( G @ ( A @ topstr_closure ) ) )
& ( B @ the_carrier @ ( H @ element ) ) )
& ( B @ ( A @ ( G @ netstr_induced_subset ) ) ) )
& ( B @ the_carrier @ ( F @ in ) ) )
=> ( E @ ( F @ in ) ) )
& ( ( E @ ( F @ in ) )
=> ( ? [G: $i] :
( ? [H: $i] :
( ( G
= ( H @ ( B @ ( A @ subnetstr_of_element ) ) @ ( A @ the_mapping ) @ ( A @ the_carrier @ ( H @ ( B @ ( A @ subnetstr_of_element ) ) @ the_carrier @ relation_rng_as_subset ) ) ) )
& ( F = H )
& ( C
= ( G @ ( A @ topstr_closure ) ) )
& ( B @ the_carrier @ ( H @ element ) ) )
& ( B @ ( A @ ( G @ netstr_induced_subset ) ) ) )
& ( B @ the_carrier @ ( F @ in ) ) ) ) )
& ! [F: $i] :
( ( ( ? [G: $i] :
( ? [H: $i] :
( ( G
= ( H @ ( B @ ( A @ subnetstr_of_element ) ) @ ( A @ the_mapping ) @ ( A @ the_carrier @ ( H @ ( B @ ( A @ subnetstr_of_element ) ) @ the_carrier @ relation_rng_as_subset ) ) ) )
& ( F = H )
& ( C
= ( G @ ( A @ topstr_closure ) ) )
& ( B @ the_carrier @ ( H @ element ) ) )
& ( B @ ( A @ ( G @ netstr_induced_subset ) ) ) )
& ( B @ the_carrier @ ( F @ in ) ) )
=> ( D @ ( F @ in ) ) )
& ( ( D @ ( F @ in ) )
=> ( ? [G: $i] :
( ? [H: $i] :
( ( G
= ( H @ ( B @ ( A @ subnetstr_of_element ) ) @ ( A @ the_mapping ) @ ( A @ the_carrier @ ( H @ ( B @ ( A @ subnetstr_of_element ) ) @ the_carrier @ relation_rng_as_subset ) ) ) )
& ( F = H )
& ( C
= ( G @ ( A @ topstr_closure ) ) )
& ( B @ the_carrier @ ( H @ element ) ) )
& ( B @ ( A @ ( G @ netstr_induced_subset ) ) ) )
& ( B @ the_carrier @ ( F @ in ) ) ) ) ) )
=> ( D = E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str ) )
=> ( A @ the_carrier @ powerset @ ( B @ ( A @ topstr_closure ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
thf(176,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str ) )
=> ( A @ the_carrier @ powerset @ ( B @ ( A @ topstr_closure ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(7,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(118,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(50,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(281,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ( B @ rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( B @ strict_net_str ) )
=> ( B
= ( B @ ( A @ the_mapping ) @ ( B @ the_InternalRel @ ( B @ the_carrier @ ( A @ net_str_of ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v6_waybel_0) ).
thf(236,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( B @ strict_net_str ) )
=> ( B
= ( B @ ( A @ the_mapping ) @ ( B @ the_InternalRel @ ( B @ the_carrier @ ( A @ net_str_of ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
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(181,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(21,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_waybel_7) ).
thf(159,plain,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_waybel_0) ).
thf(274,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_waybel_7) ).
thf(245,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(20,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ( A @ ( B @ boundary_set ) )
& ( A @ ( B @ closed_subset ) ) )
=> ( ( A @ ( B @ nowhere_dense ) )
& ( A @ ( B @ boundary_set ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_tops_1) ).
thf(155,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ( A @ ( B @ boundary_set ) )
& ( A @ ( B @ closed_subset ) ) )
=> ( ( A @ ( B @ nowhere_dense ) )
& ( A @ ( B @ boundary_set ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(30,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ empty )
=> ( ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_tops_1) ).
thf(198,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ empty )
=> ( ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(13,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(135,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(36,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_pre_topc) ).
thf(226,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( B @ ( A @ topstr_closure ) @ closed_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_tops_1) ).
thf(255,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( B @ ( A @ topstr_closure ) @ closed_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(5,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(112,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(194,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(42,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(250,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(37,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(231,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(151,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(53,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(300,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ the_carrier @ ( C @ element ) )
& ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ netstr_restr_to_element ) ) @ directed_relstr )
& ( A @ ( C @ ( B @ ( A @ netstr_restr_to_element ) ) @ strict_net_str ) )
& ( C @ ( B @ ( A @ netstr_restr_to_element ) ) @ transitive_relstr )
& ~ ( C @ ( B @ ( A @ netstr_restr_to_element ) ) @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc26_waybel_9) ).
thf(210,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ the_carrier @ ( C @ element ) )
& ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ netstr_restr_to_element ) ) @ directed_relstr )
& ( A @ ( C @ ( B @ ( A @ netstr_restr_to_element ) ) @ strict_net_str ) )
& ( C @ ( B @ ( A @ netstr_restr_to_element ) ) @ transitive_relstr )
& ~ ( C @ ( B @ ( A @ netstr_restr_to_element ) ) @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ relation_of2_as_subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(326,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ relation_of2_as_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ the_carrier @ ( C @ element ) )
& ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( B @ ( A @ ( C @ ( B @ ( A @ subnetstr_of_element ) ) @ subnet ) ) )
& ( A @ ( C @ ( B @ ( A @ subnetstr_of_element ) ) @ strict_net_str ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_waybel_9) ).
thf(239,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ the_carrier @ ( C @ element ) )
& ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( B @ ( A @ ( C @ ( B @ ( A @ subnetstr_of_element ) ) @ subnet ) ) )
& ( A @ ( C @ ( B @ ( A @ subnetstr_of_element ) ) @ strict_net_str ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(9,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(126,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(51,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ nowhere_dense ) )
& ( A @ ( B @ boundary_set ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_tops_1) ).
thf(283,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ nowhere_dense ) )
& ( A @ ( B @ boundary_set ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(131,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ the_carrier @ ( C @ element ) )
& ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ subnetstr_of_element ) ) )
= ( C @ ( B @ ( A @ netstr_restr_to_element ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_waybel_9) ).
thf(178,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ the_carrier @ ( C @ element ) )
& ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ subnetstr_of_element ) ) )
= ( C @ ( B @ ( A @ netstr_restr_to_element ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(8,axiom,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(122,plain,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ the_carrier @ ( C @ element ) )
& ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ ( C @ ( B @ ( A @ netstr_restr_to_element ) ) @ strict_net_str ) )
& ~ ( C @ ( B @ ( A @ netstr_restr_to_element ) ) @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc22_waybel_9) ).
thf(222,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ the_carrier @ ( C @ element ) )
& ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ ( C @ ( B @ ( A @ netstr_restr_to_element ) ) @ strict_net_str ) )
& ~ ( C @ ( B @ ( A @ netstr_restr_to_element ) ) @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(415,plain,
$false,
inference(e,[status(thm)],[153,356,328,129,143,319,308,269,202,174,257,110,344,196,316,261,216,164,106,147,133,265,312,206,116,243,334,302,192,137,296,149,279,64,176,118,281,236,181,159,274,245,155,198,135,226,255,112,194,250,231,151,300,210,326,239,126,283,131,178,122,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU401+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % 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
% 0.12/0.38 % Computer : n001.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 09:33:12 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 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
% 0.95/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.94/1.31 % [INFO] Parsing done (295ms).
% 1.94/1.32 % [INFO] Running in sequential loop mode.
% 2.68/1.62 % [INFO] eprover registered as external prover.
% 2.68/1.63 % [INFO] Scanning for conjecture ...
% 3.02/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 68 axioms. Running axiom selection ...
% 3.02/1.79 % [INFO] Axiom selection finished. Selected 61 axioms (removed 7 axioms).
% 3.29/1.86 % [INFO] Problem is first-order (TPTP FOF).
% 3.29/1.87 % [INFO] Type checking passed.
% 3.29/1.87 % [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 ...
% 7.68/3.11 % External prover 'e' found a proof!
% 7.68/3.11 % [INFO] Killing All external provers ...
% 7.68/3.11 % Time passed: 2542ms (effective reasoning time: 1780ms)
% 7.68/3.11 % 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)>
% 7.68/3.11 % Axioms used in derivation (61): cc2_finset_1, rc3_tops_1, fc4_subset_1, cc5_tops_1, fc2_tops_1, cc6_tops_1, rc1_subset_1, dt_l1_orders_2, antisymmetry_r2_hidden, dt_k5_waybel_9, redefinition_m2_relset_1, cc1_tops_1, dt_k5_relset_1, rc4_finset_1, cc3_tops_1, dt_m2_relset_1, cc1_relat_1, dt_u1_waybel_0, dt_u1_orders_2, rc6_pre_topc, dt_g1_waybel_0, rc1_tops_1, dt_l1_pre_topc, rc2_subset_1, rc2_waybel_7, rc5_tops_1, rc3_waybel_7, dt_l1_waybel_0, abstractness_v6_waybel_0, t2_tarski, rc4_tops_1, fc26_waybel_9, dt_m1_yellow19, rc3_struct_0, fc1_subset_1, redefinition_k6_waybel_9, fc15_yellow_6, rc4_waybel_0, cc1_relset_1, cc2_tops_1, fc6_waybel_0, rc2_relat_1, fc1_struct_0, rc1_relat_1, fc6_relat_1, free_g1_waybel_0, rc7_pre_topc, rc3_finset_1, rc1_finset_1, rc2_tops_1, cc1_finset_1, rc1_waybel_9, dt_m2_yellow_6, fc8_relat_1, rc5_struct_0, cc4_tops_1, dt_k6_waybel_9, redefinition_k5_relset_1, fc22_waybel_9, fc14_finset_1, dt_k6_pre_topc
% 7.68/3.11 % No. of inferences in proof: 126
% 7.68/3.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2542 ms resp. 1780 ms w/o parsing
% 8.28/3.18 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.28/3.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------