TSTP Solution File: SEU400+1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : SEU400+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 08:10:09 EDT 2024
% Result : Theorem 7.59s 2.89s
% Output : Refutation 8.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 103
% Syntax : Number of formulae : 167 ( 3 unt; 41 typ; 0 def)
% Number of atoms : 791 ( 98 equ; 0 cnn)
% Maximal formula atoms : 84 ( 6 avg)
% Number of connectives : 2531 ( 114 ~; 0 |; 489 &;1752 @)
% ( 9 <=>; 167 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 41 usr; 1 con; 0-4 aty)
% Number of variables : 377 ( 0 ^ 262 !; 115 ?; 377 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_type,type,
empty_carrier: $i > $o ).
thf(topological_space_type,type,
topological_space: $i > $o ).
thf(top_str_type,type,
top_str: $i > $o ).
thf(transitive_relstr_type,type,
transitive_relstr: $i > $o ).
thf(directed_relstr_type,type,
directed_relstr: $i > $o ).
thf(net_str_type,type,
net_str: $i > $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(cartesian_product2_type,type,
cartesian_product2: $i > $i > $i ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(the_carrier_type,type,
the_carrier: $i > $i ).
thf(netstr_induced_subset_type,type,
netstr_induced_subset: $i > $i > $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(topstr_closure_type,type,
topstr_closure: $i > $i > $i ).
thf(relation_rng_as_subset_type,type,
relation_rng_as_subset: $i > $i > $i > $i ).
thf(subnetstr_of_element_type,type,
subnetstr_of_element: $i > $i > $i > $i ).
thf(the_mapping_type,type,
the_mapping: $i > $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(relation_type,type,
relation: $i > $o ).
thf(relation_rng_type,type,
relation_rng: $i > $i ).
thf(finite_type,type,
finite: $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(rel_str_type,type,
rel_str: $i > $o ).
thf(one_sorted_str_type,type,
one_sorted_str: $i > $o ).
thf(relation_of2_as_subset_type,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(relation_of2_type,type,
relation_of2: $i > $i > $i > $o ).
thf(closed_subset_type,type,
closed_subset: $i > $i > $o ).
thf(nowhere_dense_type,type,
nowhere_dense: $i > $i > $o ).
thf(boundary_set_type,type,
boundary_set: $i > $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(quasi_total_type,type,
quasi_total: $i > $i > $i > $o ).
thf(net_str_of_type,type,
net_str_of: $i > $i > $i > $i > $i ).
thf(netstr_restr_to_element_type,type,
netstr_restr_to_element: $i > $i > $i > $i ).
thf(open_subset_type,type,
open_subset: $i > $i > $o ).
thf(strict_net_str_type,type,
strict_net_str: $i > $i > $o ).
thf(the_InternalRel_type,type,
the_InternalRel: $i > $i ).
thf(subnet_type,type,
subnet: $i > $i > $i > $o ).
thf(v1_membered_type,type,
v1_membered: $i > $o ).
thf(v2_membered_type,type,
v2_membered: $i > $o ).
thf(v3_membered_type,type,
v3_membered: $i > $o ).
thf(v4_membered_type,type,
v4_membered: $i > $o ).
thf(v5_membered_type,type,
v5_membered: $i > $o ).
thf(40,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_tops_1) ).
thf(340,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(157,plain,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(348,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ~ ( empty_carrier @ ( netstr_restr_to_element @ A @ B @ C ) )
& ( strict_net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc22_waybel_9) ).
thf(324,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ~ ( empty_carrier @ ( netstr_restr_to_element @ A @ B @ C ) )
& ( strict_net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(57,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(403,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( strict_net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A )
& ( net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_waybel_9) ).
thf(363,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( strict_net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A )
& ( net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( ~ ( empty @ ( the_mapping @ A @ B ) )
& ( relation @ ( the_mapping @ A @ B ) )
& ( function @ ( the_mapping @ A @ B ) )
& ( quasi_total @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc15_yellow_6) ).
thf(319,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( ~ ( empty @ ( the_mapping @ A @ B ) )
& ( relation @ ( the_mapping @ A @ B ) )
& ( function @ ( the_mapping @ A @ B ) )
& ( quasi_total @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(44,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(354,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ~ ( empty @ B )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ( ~ ( empty_carrier @ ( net_str_of @ A @ B @ C @ D ) )
& ( strict_net_str @ ( net_str_of @ A @ B @ C @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_waybel_0) ).
thf(308,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ~ ( empty @ B )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ( ~ ( empty_carrier @ ( net_str_of @ A @ B @ C @ D ) )
& ( strict_net_str @ ( net_str_of @ A @ B @ C @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(52,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
thf(379,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( net_str_of @ A @ B @ C @ D )
= ( net_str_of @ E @ F @ G @ H ) )
=> ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_waybel_0) ).
thf(174,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( net_str_of @ A @ B @ C @ D )
= ( net_str_of @ E @ F @ G @ H ) )
=> ( ( A = E )
& ( B = F )
& ( C = G )
& ( D = H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
thf(185,plain,
! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(61,axiom,
! [A: $i] :
( ( top_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( empty @ B )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( boundary_set @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_tops_1) ).
thf(417,plain,
! [A: $i] :
( ( top_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( empty @ B )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( boundary_set @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(11,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(147,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(55,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(396,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(53,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( empty @ B )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( boundary_set @ B @ A )
& ( nowhere_dense @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_tops_1) ).
thf(381,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( empty @ B )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( boundary_set @ B @ A )
& ( nowhere_dense @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(48,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tops_1) ).
thf(366,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(192,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(7,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(137,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( closed_subset @ B @ A )
& ( boundary_set @ B @ A ) )
=> ( ( boundary_set @ B @ A )
& ( nowhere_dense @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_tops_1) ).
thf(165,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( closed_subset @ B @ A )
& ( boundary_set @ B @ A ) )
=> ( ( boundary_set @ B @ A )
& ( nowhere_dense @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ( ( strict_net_str @ ( net_str_of @ A @ B @ C @ D ) @ A )
& ( net_str @ ( net_str_of @ A @ B @ C @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_waybel_0) ).
thf(393,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( one_sorted_str @ A )
& ( relation_of2 @ C @ B @ B )
& ( function @ D )
& ( quasi_total @ D @ B @ ( the_carrier @ A ) )
& ( relation_of2 @ D @ B @ ( the_carrier @ A ) ) )
=> ( ( strict_net_str @ ( net_str_of @ A @ B @ C @ D ) @ A )
& ( net_str @ ( net_str_of @ A @ B @ C @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(4,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(129,plain,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(134,plain,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(46,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(360,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(32,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( net_str @ B @ A )
& ( strict_net_str @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_waybel_0) ).
thf(311,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( net_str @ B @ A )
& ( strict_net_str @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( subnet @ C @ A @ B )
=> ( ~ ( empty_carrier @ C )
& ( transitive_relstr @ C )
& ( directed_relstr @ C )
& ( net_str @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_yellow_6) ).
thf(398,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( subnet @ C @ A @ B )
=> ( ~ ( empty_carrier @ C )
& ( transitive_relstr @ C )
& ( directed_relstr @ C )
& ( net_str @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(16,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(161,plain,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [D: $i] :
? [E: $i] :
! [F: $i] :
( ( in @ F @ E )
<=> ( ( in @ F @ ( cartesian_product2 @ C @ D ) )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= F )
& ( in @ G @ C )
& ? [I: $i] :
( ( H = I )
& ! [J: $i] :
( ( in @ J @ I )
<=> ( ( in @ J @ ( the_carrier @ B ) )
& ? [K: $i] :
( ( netstr_induced_subset @ K @ A @ B )
& ? [L: $i] :
( ( element @ L @ ( the_carrier @ B ) )
& ( G
= ( topstr_closure @ A @ K ) )
& ( J = L )
& ( K
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ L ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ L ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e6_39_3__yellow19__2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [D: $i] :
? [E: $i] :
! [F: $i] :
( ( in @ F @ E )
<=> ( ( in @ F @ ( cartesian_product2 @ C @ D ) )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= F )
& ( in @ G @ C )
& ? [I: $i] :
( ( H = I )
& ! [J: $i] :
( ( in @ J @ I )
<=> ( ( in @ J @ ( the_carrier @ B ) )
& ? [K: $i] :
( ( netstr_induced_subset @ K @ A @ B )
& ? [L: $i] :
( ( element @ L @ ( the_carrier @ B ) )
& ( G
= ( topstr_closure @ A @ K ) )
& ( J = L )
& ( K
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ L ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ L ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(64,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [D: $i] :
? [E: $i] :
! [F: $i] :
( ( ( in @ F @ E )
=> ( ( in @ F @ ( cartesian_product2 @ C @ D ) )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= F )
& ( in @ G @ C )
& ? [I: $i] :
( ( H = I )
& ! [J: $i] :
( ( ( in @ J @ I )
=> ( ( in @ J @ ( the_carrier @ B ) )
& ? [K: $i] :
( ( netstr_induced_subset @ K @ A @ B )
& ? [L: $i] :
( ( element @ L @ ( the_carrier @ B ) )
& ( G
= ( topstr_closure @ A @ K ) )
& ( J = L )
& ( K
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ L ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ L ) ) ) ) ) ) ) )
& ( ( ( in @ J @ ( the_carrier @ B ) )
& ? [K: $i] :
( ( netstr_induced_subset @ K @ A @ B )
& ? [L: $i] :
( ( element @ L @ ( the_carrier @ B ) )
& ( G
= ( topstr_closure @ A @ K ) )
& ( J = L )
& ( K
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ L ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ L ) ) ) ) ) ) )
=> ( in @ J @ I ) ) ) ) ) ) )
& ( ( ( in @ F @ ( cartesian_product2 @ C @ D ) )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= F )
& ( in @ G @ C )
& ? [I: $i] :
( ( H = I )
& ! [J: $i] :
( ( ( in @ J @ I )
=> ( ( in @ J @ ( the_carrier @ B ) )
& ? [K: $i] :
( ( netstr_induced_subset @ K @ A @ B )
& ? [L: $i] :
( ( element @ L @ ( the_carrier @ B ) )
& ( G
= ( topstr_closure @ A @ K ) )
& ( J = L )
& ( K
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ L ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ L ) ) ) ) ) ) ) )
& ( ( ( in @ J @ ( the_carrier @ B ) )
& ? [K: $i] :
( ( netstr_induced_subset @ K @ A @ B )
& ? [L: $i] :
( ( element @ L @ ( the_carrier @ B ) )
& ( G
= ( topstr_closure @ A @ K ) )
& ( J = L )
& ( K
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ L ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ L ) ) ) ) ) ) )
=> ( in @ J @ I ) ) ) ) ) )
=> ( in @ F @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(149,plain,
! [A: $i,B: $i,C: $i] :
( ( ( relation_of2_as_subset @ C @ A @ B )
=> ( relation_of2 @ C @ A @ B ) )
& ( ( relation_of2 @ C @ A @ B )
=> ( relation_of2_as_subset @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ( ( strict_net_str @ B @ A )
=> ( B
= ( net_str_of @ A @ ( the_carrier @ B ) @ ( the_InternalRel @ B ) @ ( the_mapping @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v6_waybel_0) ).
thf(335,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ( ( strict_net_str @ B @ A )
=> ( B
= ( net_str_of @ A @ ( the_carrier @ B ) @ ( the_InternalRel @ B ) @ ( the_mapping @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(43,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_waybel_7) ).
thf(350,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( netstr_induced_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( the_carrier @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_yellow19) ).
thf(159,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( netstr_induced_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( the_carrier @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( subnetstr_of_element @ A @ B @ C )
= ( netstr_restr_to_element @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_waybel_9) ).
thf(187,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( subnetstr_of_element @ A @ B @ C )
= ( netstr_restr_to_element @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(58,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(406,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(172,plain,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(51,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(377,plain,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(29,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( boundary_set @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_tops_1) ).
thf(303,plain,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( boundary_set @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( strict_net_str @ ( subnetstr_of_element @ A @ B @ C ) @ A )
& ( subnet @ ( subnetstr_of_element @ A @ B @ C ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_waybel_9) ).
thf(345,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ( strict_net_str @ ( subnetstr_of_element @ A @ B @ C ) @ A )
& ( subnet @ ( subnetstr_of_element @ A @ B @ C ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(8,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(140,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(62,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( open_subset @ B @ A )
& ( nowhere_dense @ B @ A ) )
=> ( ( empty @ B )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( boundary_set @ B @ A )
& ( nowhere_dense @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_tops_1) ).
thf(426,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( open_subset @ B @ A )
& ( nowhere_dense @ B @ A ) )
=> ( ( empty @ B )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A )
& ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B )
& ( boundary_set @ B @ A )
& ( nowhere_dense @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [D: $i] :
( ! [E: $i,F: $i,G: $i] :
( ( ( E = F )
& ? [H: $i,I: $i] :
( ( ( ordered_pair @ H @ I )
= F )
& ( in @ H @ C )
& ? [J: $i] :
( ( I = J )
& ! [K: $i] :
( ( in @ K @ J )
<=> ( ( in @ K @ ( the_carrier @ B ) )
& ? [L: $i] :
( ( netstr_induced_subset @ L @ A @ B )
& ? [M: $i] :
( ( element @ M @ ( the_carrier @ B ) )
& ( H
= ( topstr_closure @ A @ L ) )
& ( K = M )
& ( L
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ M ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ M ) ) ) ) ) ) ) ) ) )
& ( E = G )
& ? [H: $i,I: $i] :
( ( ( ordered_pair @ H @ I )
= G )
& ( in @ H @ C )
& ? [J: $i] :
( ( I = J )
& ! [K: $i] :
( ( in @ K @ J )
<=> ( ( in @ K @ ( the_carrier @ B ) )
& ? [L: $i] :
( ( netstr_induced_subset @ L @ A @ B )
& ? [M: $i] :
( ( element @ M @ ( the_carrier @ B ) )
& ( H
= ( topstr_closure @ A @ L ) )
& ( K = M )
& ( L
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ M ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ M ) ) ) ) ) ) ) ) ) ) )
=> ( F = G ) )
=> ? [E: $i] :
! [F: $i] :
( ( in @ F @ E )
<=> ? [G: $i] :
( ( in @ G @ ( cartesian_product2 @ C @ D ) )
& ( G = F )
& ? [H: $i,I: $i] :
( ( ( ordered_pair @ H @ I )
= F )
& ( in @ H @ C )
& ? [J: $i] :
( ( I = J )
& ! [K: $i] :
( ( in @ K @ J )
<=> ( ( in @ K @ ( the_carrier @ B ) )
& ? [L: $i] :
( ( netstr_induced_subset @ L @ A @ B )
& ? [M: $i] :
( ( element @ M @ ( the_carrier @ B ) )
& ( H
= ( topstr_closure @ A @ L ) )
& ( K = M )
& ( L
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ M ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ M ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e6_39_3__yellow19__3) ).
thf(194,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [D: $i] :
( ! [E: $i,F: $i,G: $i] :
( ( ( E = F )
& ? [H: $i,I: $i] :
( ( ( ordered_pair @ H @ I )
= F )
& ( in @ H @ C )
& ? [J: $i] :
( ( I = J )
& ! [K: $i] :
( ( ( in @ K @ J )
=> ( ( in @ K @ ( the_carrier @ B ) )
& ? [L: $i] :
( ( netstr_induced_subset @ L @ A @ B )
& ? [M: $i] :
( ( element @ M @ ( the_carrier @ B ) )
& ( H
= ( topstr_closure @ A @ L ) )
& ( K = M )
& ( L
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ M ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ M ) ) ) ) ) ) ) )
& ( ( ( in @ K @ ( the_carrier @ B ) )
& ? [L: $i] :
( ( netstr_induced_subset @ L @ A @ B )
& ? [M: $i] :
( ( element @ M @ ( the_carrier @ B ) )
& ( H
= ( topstr_closure @ A @ L ) )
& ( K = M )
& ( L
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ M ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ M ) ) ) ) ) ) )
=> ( in @ K @ J ) ) ) ) )
& ( E = G )
& ? [H: $i,I: $i] :
( ( ( ordered_pair @ H @ I )
= G )
& ( in @ H @ C )
& ? [J: $i] :
( ( I = J )
& ! [K: $i] :
( ( ( in @ K @ J )
=> ( ( in @ K @ ( the_carrier @ B ) )
& ? [L: $i] :
( ( netstr_induced_subset @ L @ A @ B )
& ? [M: $i] :
( ( element @ M @ ( the_carrier @ B ) )
& ( H
= ( topstr_closure @ A @ L ) )
& ( K = M )
& ( L
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ M ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ M ) ) ) ) ) ) ) )
& ( ( ( in @ K @ ( the_carrier @ B ) )
& ? [L: $i] :
( ( netstr_induced_subset @ L @ A @ B )
& ? [M: $i] :
( ( element @ M @ ( the_carrier @ B ) )
& ( H
= ( topstr_closure @ A @ L ) )
& ( K = M )
& ( L
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ M ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ M ) ) ) ) ) ) )
=> ( in @ K @ J ) ) ) ) ) )
=> ( F = G ) )
=> ? [E: $i] :
! [F: $i] :
( ( ( in @ F @ E )
=> ? [G: $i] :
( ( in @ G @ ( cartesian_product2 @ C @ D ) )
& ( G = F )
& ? [H: $i,I: $i] :
( ( ( ordered_pair @ H @ I )
= F )
& ( in @ H @ C )
& ? [J: $i] :
( ( I = J )
& ! [K: $i] :
( ( ( in @ K @ J )
=> ( ( in @ K @ ( the_carrier @ B ) )
& ? [L: $i] :
( ( netstr_induced_subset @ L @ A @ B )
& ? [M: $i] :
( ( element @ M @ ( the_carrier @ B ) )
& ( H
= ( topstr_closure @ A @ L ) )
& ( K = M )
& ( L
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ M ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ M ) ) ) ) ) ) ) )
& ( ( ( in @ K @ ( the_carrier @ B ) )
& ? [L: $i] :
( ( netstr_induced_subset @ L @ A @ B )
& ? [M: $i] :
( ( element @ M @ ( the_carrier @ B ) )
& ( H
= ( topstr_closure @ A @ L ) )
& ( K = M )
& ( L
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ M ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ M ) ) ) ) ) ) )
=> ( in @ K @ J ) ) ) ) ) ) )
& ( ? [G: $i] :
( ( in @ G @ ( cartesian_product2 @ C @ D ) )
& ( G = F )
& ? [H: $i,I: $i] :
( ( ( ordered_pair @ H @ I )
= F )
& ( in @ H @ C )
& ? [J: $i] :
( ( I = J )
& ! [K: $i] :
( ( ( in @ K @ J )
=> ( ( in @ K @ ( the_carrier @ B ) )
& ? [L: $i] :
( ( netstr_induced_subset @ L @ A @ B )
& ? [M: $i] :
( ( element @ M @ ( the_carrier @ B ) )
& ( H
= ( topstr_closure @ A @ L ) )
& ( K = M )
& ( L
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ M ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ M ) ) ) ) ) ) ) )
& ( ( ( in @ K @ ( the_carrier @ B ) )
& ? [L: $i] :
( ( netstr_induced_subset @ L @ A @ B )
& ? [M: $i] :
( ( element @ M @ ( the_carrier @ B ) )
& ( H
= ( topstr_closure @ A @ L ) )
& ( K = M )
& ( L
= ( relation_rng_as_subset @ ( the_carrier @ ( subnetstr_of_element @ A @ B @ M ) ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ ( subnetstr_of_element @ A @ B @ M ) ) ) ) ) ) )
=> ( in @ K @ J ) ) ) ) ) )
=> ( in @ F @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(10,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(145,plain,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(36,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( closed_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_pre_topc) ).
thf(327,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( closed_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ? [C: $i] :
( ( subnet @ C @ A @ B )
& ~ ( empty_carrier @ C )
& ( transitive_relstr @ C )
& ( strict_net_str @ C @ A )
& ( directed_relstr @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_waybel_9) ).
thf(409,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ? [C: $i] :
( ( subnet @ C @ A @ B )
& ~ ( empty_carrier @ C )
& ( transitive_relstr @ C )
& ( strict_net_str @ C @ A )
& ( directed_relstr @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(37,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(331,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(338,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(13,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( closed_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(154,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( closed_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ~ ( empty_carrier @ ( netstr_restr_to_element @ A @ B @ C ) )
& ( transitive_relstr @ ( netstr_restr_to_element @ A @ B @ C ) )
& ( strict_net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A )
& ( directed_relstr @ ( netstr_restr_to_element @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc26_waybel_9) ).
thf(314,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A )
& ( element @ C @ ( the_carrier @ B ) ) )
=> ( ~ ( empty_carrier @ ( netstr_restr_to_element @ A @ B @ C ) )
& ( transitive_relstr @ ( netstr_restr_to_element @ A @ B @ C ) )
& ( strict_net_str @ ( netstr_restr_to_element @ A @ B @ C ) @ A )
& ( directed_relstr @ ( netstr_restr_to_element @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(9,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(143,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_rng_as_subset @ A @ B @ C )
= ( relation_rng @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
thf(300,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_rng_as_subset @ A @ B @ C )
= ( relation_rng @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(19,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_waybel_7) ).
thf(168,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_1) ).
thf(190,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(22,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( nowhere_dense @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_tops_1) ).
thf(183,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( nowhere_dense @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ( ( function @ ( the_mapping @ A @ B ) )
& ( quasi_total @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_waybel_0) ).
thf(373,plain,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ( ( function @ ( the_mapping @ A @ B ) )
& ( quasi_total @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( the_mapping @ A @ B ) @ ( the_carrier @ B ) @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(30,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_tops_1) ).
thf(305,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( empty @ B )
=> ( ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(3,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(126,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( closed_subset @ ( topstr_closure @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_tops_1) ).
thf(358,plain,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( closed_subset @ ( topstr_closure @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(63,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(437,plain,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(60,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(415,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(5,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(131,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( nowhere_dense @ B @ A )
=> ( boundary_set @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_tops_1) ).
thf(163,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( nowhere_dense @ B @ A )
=> ( boundary_set @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(49,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tops_1) ).
thf(369,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( open_subset @ B @ A )
& ( closed_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(443,plain,
$false,
inference(cvc4,[status(thm)],[340,157,348,324,403,363,319,354,308,379,174,185,417,147,396,381,366,192,137,165,393,129,134,360,311,398,161,64,149,335,350,159,187,406,172,377,303,345,140,426,194,145,327,409,331,338,154,314,143,300,168,190,183,373,305,126,358,437,415,131,163,369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU400+1 : TPTP v8.1.2. Released v3.3.0.
% 0.15/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n023.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 10:33:24 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.99/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.53/1.10 % [INFO] Parsing done (177ms).
% 1.53/1.11 % [INFO] Running in sequential loop mode.
% 2.06/1.32 % [INFO] eprover registered as external prover.
% 2.06/1.32 % [INFO] cvc4 registered as external prover.
% 2.06/1.32 % [INFO] Scanning for conjecture ...
% 2.21/1.42 % [INFO] Found a conjecture and 69 axioms. Running axiom selection ...
% 2.65/1.50 % [INFO] Axiom selection finished. Selected 61 axioms (removed 8 axioms).
% 2.82/1.58 % [INFO] Problem is first-order (TPTP FOF).
% 2.82/1.59 % [INFO] Type checking passed.
% 2.82/1.59 % [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 ...
% 7.59/2.89 % External prover 'cvc4' found a proof!
% 7.59/2.89 % [INFO] Killing All external provers ...
% 7.59/2.89 % Time passed: 2344ms (effective reasoning time: 1773ms)
% 7.59/2.89 % 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)>
% 7.59/2.89 % 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, s1_tarski__e6_39_3__yellow19__3, 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, 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
% 7.59/2.89 % No. of inferences in proof: 126
% 7.59/2.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2344 ms resp. 1773 ms w/o parsing
% 8.09/2.96 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.09/2.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------