TSTP Solution File: SEU395+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU395+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 : Fri May 19 11:58:44 EDT 2023
% Result : Theorem 7.83s 2.81s
% Output : Refutation 8.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 198
% Syntax : Number of formulae : 329 ( 17 unt; 69 typ; 0 def)
% Number of atoms : 1466 ( 33 equ; 0 cnn)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 4136 ( 266 ~; 2 |; 918 &;2664 @)
% ( 7 <=>; 279 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 104 ( 104 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 69 usr; 2 con; 0-4 aty)
% Number of variables : 453 ( 0 ^; 362 !; 91 ?; 453 :)
% 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(empty_type,type,
empty: $i > $o ).
thf(filtered_subset_type,type,
filtered_subset: $i > $i > $o ).
thf(boole_POSet_type,type,
boole_POSet: $i > $i ).
thf(cast_as_carrier_subset_type,type,
cast_as_carrier_subset: $i > $i ).
thf(upper_relstr_subset_type,type,
upper_relstr_subset: $i > $i > $o ).
thf(proper_element_type,type,
proper_element: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(the_carrier_type,type,
the_carrier: $i > $i ).
thf(element_type,type,
element: $i > $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(lim_points_of_net_type,type,
lim_points_of_net: $i > $i > $i ).
thf(net_of_bool_filter_type,type,
net_of_bool_filter: $i > $i > $i > $i ).
thf(is_a_convergence_point_of_set_type,type,
is_a_convergence_point_of_set: $i > $i > $i > $o ).
thf(relation_type,type,
relation: $i > $o ).
thf(relation_empty_yielding_type,type,
relation_empty_yielding: $i > $o ).
thf(finite_type,type,
finite: $i > $o ).
thf(cartesian_product2_type,type,
cartesian_product2: $i > $i > $i ).
thf(relation_of2_type,type,
relation_of2: $i > $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(rel_str_type,type,
rel_str: $i > $o ).
thf(lower_bounded_relstr_type,type,
lower_bounded_relstr: $i > $o ).
thf(upper_bounded_relstr_type,type,
upper_bounded_relstr: $i > $o ).
thf(bounded_relstr_type,type,
bounded_relstr: $i > $o ).
thf(relation_of2_as_subset_type,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(rel_str_of_type,type,
rel_str_of: $i > $i > $i ).
thf(one_sorted_str_type,type,
one_sorted_str: $i > $o ).
thf(net_str_type,type,
net_str: $i > $i > $o ).
thf(strict_net_str_type,type,
strict_net_str: $i > $i > $o ).
thf(strict_rel_str_type,type,
strict_rel_str: $i > $o ).
thf(reflexive_relstr_type,type,
reflexive_relstr: $i > $o ).
thf(complete_relstr_type,type,
complete_relstr: $i > $o ).
thf(up_complete_relstr_type,type,
up_complete_relstr: $i > $o ).
thf(join_complete_relstr_type,type,
join_complete_relstr: $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(transitive_relstr_type,type,
transitive_relstr: $i > $o ).
thf(antisymmetric_relstr_type,type,
antisymmetric_relstr: $i > $o ).
thf(v1_yellow_3_type,type,
v1_yellow_3: $i > $o ).
thf(distributive_relstr_type,type,
distributive_relstr: $i > $o ).
thf(heyting_relstr_type,type,
heyting_relstr: $i > $o ).
thf(complemented_relstr_type,type,
complemented_relstr: $i > $o ).
thf(boolean_relstr_type,type,
boolean_relstr: $i > $o ).
thf(with_suprema_relstr_type,type,
with_suprema_relstr: $i > $o ).
thf(with_infima_relstr_type,type,
with_infima_relstr: $i > $o ).
thf(directed_subset_type,type,
directed_subset: $i > $i > $o ).
thf(trivial_carrier_type,type,
trivial_carrier: $i > $o ).
thf(closed_subset_type,type,
closed_subset: $i > $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(connected_relstr_type,type,
connected_relstr: $i > $o ).
thf(nowhere_dense_type,type,
nowhere_dense: $i > $i > $o ).
thf(boundary_set_type,type,
boundary_set: $i > $i > $o ).
thf(directed_relstr_type,type,
directed_relstr: $i > $o ).
thf(filter_of_net_str_type,type,
filter_of_net_str: $i > $i > $i ).
thf(lower_relstr_subset_type,type,
lower_relstr_subset: $i > $i > $o ).
thf(open_subset_type,type,
open_subset: $i > $i > $o ).
thf(a_2_1_yellow19_type,type,
a_2_1_yellow19: $i > $i > $i ).
thf(is_eventually_in_type,type,
is_eventually_in: $i > $i > $i > $o ).
thf(the_mapping_type,type,
the_mapping: $i > $i > $i ).
thf(the_InternalRel_type,type,
the_InternalRel: $i > $i ).
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(dense_type,type,
dense: $i > $i > $o ).
thf(73,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_pre_topc) ).
thf(461,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(99,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(605,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)],[99]) ).
thf(115,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( transitive_relstr @ A )
& ( directed_relstr @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_yellow_6) ).
thf(711,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( transitive_relstr @ A )
& ( directed_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(52,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(346,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(128,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(760,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)],[128]) ).
thf(26,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( trivial_carrier @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( complete_relstr @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_yellow_0) ).
thf(249,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( trivial_carrier @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( complete_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty @ B )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ C )
& ( filtered_subset @ C @ ( boole_POSet @ B ) )
& ( upper_relstr_subset @ C @ ( boole_POSet @ B ) )
& ( element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ B ) ) ) ) )
=> ( ~ ( empty_carrier @ ( net_of_bool_filter @ A @ B @ C ) )
& ( strict_net_str @ ( net_of_bool_filter @ A @ B @ C ) @ A )
& ( net_str @ ( net_of_bool_filter @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow19) ).
thf(352,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty @ B )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ C )
& ( filtered_subset @ C @ ( boole_POSet @ B ) )
& ( upper_relstr_subset @ C @ ( boole_POSet @ B ) )
& ( element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ B ) ) ) ) )
=> ( ~ ( empty_carrier @ ( net_of_bool_filter @ A @ B @ C ) )
& ( strict_net_str @ ( net_of_bool_filter @ A @ B @ C ) @ A )
& ( net_str @ ( net_of_bool_filter @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(13,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(170,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(308,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(106,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_yellow_0) ).
thf(655,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(32,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(269,plain,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(120,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(730,plain,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(35,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_yellow_0) ).
thf(276,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(18,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(185,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(64,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(417,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)],[64]) ).
thf(36,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(288,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(44,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(320,plain,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(28,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(257,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)],[28]) ).
thf(125,axiom,
! [A: $i] :
( ( ( with_suprema_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_waybel_0) ).
thf(751,plain,
! [A: $i] :
( ( ( with_suprema_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(51,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(344,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
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 ) ) )
=> ( ( 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(196,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)],[21]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( element @ ( filter_of_net_str @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_yellow19) ).
thf(559,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( element @ ( filter_of_net_str @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(6,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(152,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(42,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(316,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)],[42]) ).
thf(127,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( lower_relstr_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_waybel_0) ).
thf(756,plain,
! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( lower_relstr_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(24,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B )
& ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_waybel_0) ).
thf(238,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B )
& ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(93,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(574,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(98,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_waybel_0) ).
thf(602,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(130,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 ) )
=> ( ~ ( empty @ ( filter_of_net_str @ A @ B ) )
& ( filtered_subset @ ( filter_of_net_str @ A @ B ) @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( upper_relstr_subset @ ( filter_of_net_str @ A @ B ) @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( proper_element @ ( filter_of_net_str @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_yellow19) ).
thf(774,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 ) )
=> ( ~ ( empty @ ( filter_of_net_str @ A @ B ) )
& ( filtered_subset @ ( filter_of_net_str @ A @ B ) @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( upper_relstr_subset @ ( filter_of_net_str @ A @ B ) @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( proper_element @ ( filter_of_net_str @ A @ B ) @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(60,axiom,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_yellow_1) ).
thf(396,plain,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(37,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_waybel_0) ).
thf(292,plain,
! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(70,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(452,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(380,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( in @ C @ A )
=> ( in @ C @ B ) )
& ( ( in @ C @ B )
=> ( in @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(83,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ~ ( trivial_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ~ ( v1_yellow_3 @ A )
& ( distributive_relstr @ A )
& ( heyting_relstr @ A )
& ( complemented_relstr @ A )
& ( boolean_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_waybel_7) ).
thf(529,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ~ ( trivial_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ~ ( v1_yellow_3 @ A )
& ( distributive_relstr @ A )
& ( heyting_relstr @ A )
& ( complemented_relstr @ A )
& ( boolean_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(108,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( upper_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_waybel_0) ).
thf(661,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( upper_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( directed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ! [C: $i,D: $i] :
( ( ( rel_str_of @ A @ B )
= ( rel_str_of @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(160,plain,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ! [C: $i,D: $i] :
( ( ( rel_str_of @ A @ B )
= ( rel_str_of @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(89,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(561,plain,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(11,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(165,plain,
? [A: $i] : ( one_sorted_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(29,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(260,plain,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(53,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(349,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(20,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(192,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(61,axiom,
! [A: $i] :
( ( strict_rel_str @ ( boole_POSet @ A ) )
& ( rel_str @ ( boole_POSet @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
thf(407,plain,
! [A: $i] :
( ( strict_rel_str @ ( boole_POSet @ A ) )
& ( rel_str @ ( boole_POSet @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(55,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( join_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( upper_bounded_relstr @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc14_waybel_0) ).
thf(356,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( join_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( upper_bounded_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(8,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(156,plain,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(102,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ~ ( trivial_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( up_complete_relstr @ ( boole_POSet @ A ) )
& ( join_complete_relstr @ ( boole_POSet @ A ) )
& ~ ( v1_yellow_3 @ ( boole_POSet @ A ) )
& ( distributive_relstr @ ( boole_POSet @ A ) )
& ( heyting_relstr @ ( boole_POSet @ A ) )
& ( complemented_relstr @ ( boole_POSet @ A ) )
& ( boolean_relstr @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_waybel_7) ).
thf(615,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ~ ( trivial_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( up_complete_relstr @ ( boole_POSet @ A ) )
& ( join_complete_relstr @ ( boole_POSet @ A ) )
& ~ ( v1_yellow_3 @ ( boole_POSet @ A ) )
& ( distributive_relstr @ ( boole_POSet @ A ) )
& ( heyting_relstr @ ( boole_POSet @ A ) )
& ( complemented_relstr @ ( boole_POSet @ A ) )
& ( boolean_relstr @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(49,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ( ( open_subset @ ( cast_as_carrier_subset @ A ) @ A )
& ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_tops_1) ).
thf(339,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ( ( open_subset @ ( cast_as_carrier_subset @ A ) @ A )
& ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(86,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(554,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(104,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(637,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(79,axiom,
! [A: $i] :
( ( ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A )
& ( lower_relstr_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc11_waybel_0) ).
thf(489,plain,
! [A: $i] :
( ( ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( directed_subset @ B @ A )
& ( filtered_subset @ B @ A )
& ( lower_relstr_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(84,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( lower_relstr_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc8_waybel_0) ).
thf(547,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( lower_relstr_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(244,plain,
! [A: $i,B: $i] :
( ( ( element @ A @ ( powerset @ B ) )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( element @ A @ ( powerset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty @ B )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ C )
& ( filtered_subset @ C @ ( boole_POSet @ B ) )
& ( upper_relstr_subset @ C @ ( boole_POSet @ B ) )
& ( element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ B ) ) ) ) )
=> ( ~ ( empty_carrier @ ( net_of_bool_filter @ A @ B @ C ) )
& ( reflexive_relstr @ ( net_of_bool_filter @ A @ B @ C ) )
& ( transitive_relstr @ ( net_of_bool_filter @ A @ B @ C ) )
& ( strict_net_str @ ( net_of_bool_filter @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_yellow19) ).
thf(311,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty @ B )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ C )
& ( filtered_subset @ C @ ( boole_POSet @ B ) )
& ( upper_relstr_subset @ C @ ( boole_POSet @ B ) )
& ( element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ B ) ) ) ) )
=> ( ~ ( empty_carrier @ ( net_of_bool_filter @ A @ B @ C ) )
& ( reflexive_relstr @ ( net_of_bool_filter @ A @ B @ C ) )
& ( transitive_relstr @ ( net_of_bool_filter @ A @ B @ C ) )
& ( strict_net_str @ ( net_of_bool_filter @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(107,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( join_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( lower_bounded_relstr @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc11_waybel_0) ).
thf(657,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( join_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( lower_bounded_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(112,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(674,plain,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(96,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(586,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)],[96]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( ~ ( empty @ ( filter_of_net_str @ A @ B ) )
& ( upper_relstr_subset @ ( filter_of_net_str @ A @ B ) @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_yellow19) ).
thf(412,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( ~ ( empty @ ( filter_of_net_str @ A @ B ) )
& ( upper_relstr_subset @ ( filter_of_net_str @ A @ B ) @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(4,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(148,plain,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(69,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( net_str @ B @ A )
& ~ ( empty_carrier @ B )
& ( reflexive_relstr @ B )
& ( transitive_relstr @ B )
& ( antisymmetric_relstr @ B )
& ( strict_net_str @ B @ A )
& ( directed_relstr @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_waybel_0) ).
thf(444,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] :
( ( net_str @ B @ A )
& ~ ( empty_carrier @ B )
& ( reflexive_relstr @ B )
& ( transitive_relstr @ B )
& ( antisymmetric_relstr @ B )
& ( strict_net_str @ B @ A )
& ( directed_relstr @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ( element @ ( lim_points_of_net @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_yellow_6) ).
thf(733,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A )
& ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ( element @ ( lim_points_of_net @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(17,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(180,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)],[17]) ).
thf(38,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(296,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(101,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(611,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(48,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( lower_relstr_subset @ ( cast_as_carrier_subset @ A ) @ A )
& ( upper_relstr_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc15_waybel_0) ).
thf(335,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( lower_relstr_subset @ ( cast_as_carrier_subset @ A ) @ A )
& ( upper_relstr_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(23,axiom,
? [A: $i] : ( top_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(236,plain,
? [A: $i] : ( top_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(19,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc10_waybel_0) ).
thf(187,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(14,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( bounded_relstr @ A )
=> ( ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_yellow_0) ).
thf(172,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( bounded_relstr @ A )
=> ( ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ~ ( empty_carrier @ C )
& ( net_str @ C @ B ) )
=> ( ( in @ A @ ( a_2_1_yellow19 @ B @ C ) )
<=> ? [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ B ) ) )
& ( A = D )
& ( is_eventually_in @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_yellow19) ).
thf(419,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( one_sorted_str @ B )
& ~ ( empty_carrier @ C )
& ( net_str @ C @ B ) )
=> ( ( ( in @ A @ ( a_2_1_yellow19 @ B @ C ) )
=> ? [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ B ) ) )
& ( A = D )
& ( is_eventually_in @ B @ C @ D ) ) )
& ( ? [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ B ) ) )
& ( A = D )
& ( is_eventually_in @ B @ C @ D ) )
=> ( in @ A @ ( a_2_1_yellow19 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(33,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(271,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)],[33]) ).
thf(56,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( complete_relstr @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_lattice3) ).
thf(362,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( complete_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(91,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(567,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(123,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(737,plain,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(318,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(76,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( directed_subset @ B @ A )
& ( lower_relstr_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc9_waybel_0) ).
thf(477,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( directed_subset @ B @ A )
& ( lower_relstr_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(85,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(552,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)],[85]) ).
thf(45,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( in @ C @ ( lim_points_of_net @ A @ B ) )
<=> ( is_a_convergence_point_of_set @ A @ ( filter_of_net_str @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_yellow19) ).
thf(323,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( transitive_relstr @ B )
& ( directed_relstr @ B )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( in @ C @ ( lim_points_of_net @ A @ B ) )
=> ( is_a_convergence_point_of_set @ A @ ( filter_of_net_str @ A @ B ) @ C ) )
& ( ( is_a_convergence_point_of_set @ A @ ( filter_of_net_str @ A @ B ) @ C )
=> ( in @ C @ ( lim_points_of_net @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(119,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_yellow_0) ).
thf(726,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(110,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(668,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(71,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(455,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)],[71]) ).
thf(90,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(563,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)],[90]) ).
thf(39,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(299,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)],[39]) ).
thf(31,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(267,plain,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(67,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(438,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)],[67]) ).
thf(12,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(167,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)],[12]) ).
thf(118,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(722,plain,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(27,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(255,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(78,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pre_topc) ).
thf(487,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( cast_as_carrier_subset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(342,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(126,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( with_suprema_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattice3) ).
thf(754,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( with_suprema_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(72,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( upper_relstr_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( proper_element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) )
& ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) )
=> ( B
= ( filter_of_net_str @ A @ ( net_of_bool_filter @ A @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_yellow19) ).
thf(458,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( upper_relstr_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( proper_element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) )
& ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) )
=> ( B
= ( filter_of_net_str @ A @ ( net_of_bool_filter @ A @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(3,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(145,plain,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(557,plain,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(105,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc13_waybel_0) ).
thf(640,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A )
& ( up_complete_relstr @ A )
& ( join_complete_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(124,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(739,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)],[124]) ).
thf(30,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( trivial_carrier @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( connected_relstr @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_waybel_0) ).
thf(263,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( trivial_carrier @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( connected_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(5,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(150,plain,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(114,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(707,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)],[114]) ).
thf(22,axiom,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( up_complete_relstr @ ( boole_POSet @ A ) )
& ( join_complete_relstr @ ( boole_POSet @ A ) )
& ~ ( v1_yellow_3 @ ( boole_POSet @ A ) )
& ( distributive_relstr @ ( boole_POSet @ A ) )
& ( heyting_relstr @ ( boole_POSet @ A ) )
& ( complemented_relstr @ ( boole_POSet @ A ) )
& ( boolean_relstr @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_waybel_7) ).
thf(199,plain,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( up_complete_relstr @ ( boole_POSet @ A ) )
& ( join_complete_relstr @ ( boole_POSet @ A ) )
& ~ ( v1_yellow_3 @ ( boole_POSet @ A ) )
& ( distributive_relstr @ ( boole_POSet @ A ) )
& ( heyting_relstr @ ( boole_POSet @ A ) )
& ( complemented_relstr @ ( boole_POSet @ A ) )
& ( boolean_relstr @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( rel_str @ ( rel_str_of @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(177,plain,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( rel_str @ ( rel_str_of @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(68,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( bounded_relstr @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_yellow_0) ).
thf(441,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( bounded_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(57,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_lattice3) ).
thf(370,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(116,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( strict_rel_str @ A )
=> ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(717,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( strict_rel_str @ A )
=> ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(74,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( trivial_carrier @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_yellow_0) ).
thf(463,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( trivial_carrier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(94,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc10_waybel_0) ).
thf(576,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(7,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A ) )
=> ( bounded_relstr @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_yellow_0) ).
thf(154,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A ) )
=> ( bounded_relstr @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_waybel_0) ).
thf(175,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(92,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(571,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)],[92]) ).
thf(97,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( connected_relstr @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc12_waybel_0) ).
thf(595,plain,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( connected_relstr @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(77,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(482,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)],[77]) ).
thf(111,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( ( filter_of_net_str @ A @ B )
= ( a_2_1_yellow19 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_yellow19) ).
thf(671,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty_carrier @ B )
& ( net_str @ B @ A ) )
=> ( ( filter_of_net_str @ A @ B )
= ( a_2_1_yellow19 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(95,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(581,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)],[95]) ).
thf(129,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(771,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)],[129]) ).
thf(9,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(158,plain,
? [A: $i] : ( rel_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(59,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ~ ( trivial_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( proper_element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_waybel_7) ).
thf(390,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ~ ( trivial_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( proper_element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(34,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(273,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)],[34]) ).
thf(122,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( dense @ ( cast_as_carrier_subset @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_tops_1) ).
thf(735,plain,
! [A: $i] :
( ( top_str @ A )
=> ( dense @ ( cast_as_carrier_subset @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty @ B )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ C )
& ( filtered_subset @ C @ ( boole_POSet @ B ) )
& ( upper_relstr_subset @ C @ ( boole_POSet @ B ) )
& ( proper_element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ B ) ) ) )
& ( element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ B ) ) ) ) )
=> ( ~ ( empty_carrier @ ( net_of_bool_filter @ A @ B @ C ) )
& ( reflexive_relstr @ ( net_of_bool_filter @ A @ B @ C ) )
& ( transitive_relstr @ ( net_of_bool_filter @ A @ B @ C ) )
& ( strict_net_str @ ( net_of_bool_filter @ A @ B @ C ) @ A )
& ( directed_relstr @ ( net_of_bool_filter @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_yellow19) ).
thf(326,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A )
& ~ ( empty @ B )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ C )
& ( filtered_subset @ C @ ( boole_POSet @ B ) )
& ( upper_relstr_subset @ C @ ( boole_POSet @ B ) )
& ( proper_element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ B ) ) ) )
& ( element @ C @ ( powerset @ ( the_carrier @ ( boole_POSet @ B ) ) ) ) )
=> ( ~ ( empty_carrier @ ( net_of_bool_filter @ A @ B @ C ) )
& ( reflexive_relstr @ ( net_of_bool_filter @ A @ B @ C ) )
& ( transitive_relstr @ ( net_of_bool_filter @ A @ B @ C ) )
& ( strict_net_str @ ( net_of_bool_filter @ A @ B @ C ) @ A )
& ( directed_relstr @ ( net_of_bool_filter @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(82,axiom,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_yellow_1) ).
thf(506,plain,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(75,axiom,
! [A: $i] :
( ( ( with_infima_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_waybel_0) ).
thf(474,plain,
! [A: $i] :
( ( ( with_infima_relstr @ A )
& ( rel_str @ A ) )
=> ( ~ ( empty @ ( cast_as_carrier_subset @ A ) )
& ( filtered_subset @ ( cast_as_carrier_subset @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(109,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(664,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)],[109]) ).
thf(103,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( with_infima_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(635,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( with_infima_relstr @ A )
=> ~ ( empty_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(117,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(720,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(415,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(47,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(332,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)],[47]) ).
thf(66,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( up_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc12_waybel_0) ).
thf(427,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( up_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_suprema_relstr @ A )
& ( with_infima_relstr @ A )
& ( complete_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( upper_bounded_relstr @ A )
& ( bounded_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( upper_relstr_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( proper_element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) )
& ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( in @ C @ ( lim_points_of_net @ A @ ( net_of_bool_filter @ A @ ( cast_as_carrier_subset @ A ) @ B ) ) )
<=> ( is_a_convergence_point_of_set @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_yellow19) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( upper_relstr_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( proper_element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) )
& ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( in @ C @ ( lim_points_of_net @ A @ ( net_of_bool_filter @ A @ ( cast_as_carrier_subset @ A ) @ B ) ) )
<=> ( is_a_convergence_point_of_set @ A @ B @ C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(131,plain,
~ ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( topological_space @ A )
& ( top_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( upper_relstr_subset @ B @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) )
& ( proper_element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) )
& ( element @ B @ ( powerset @ ( the_carrier @ ( boole_POSet @ ( cast_as_carrier_subset @ A ) ) ) ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( in @ C @ ( lim_points_of_net @ A @ ( net_of_bool_filter @ A @ ( cast_as_carrier_subset @ A ) @ B ) ) )
=> ( is_a_convergence_point_of_set @ A @ B @ C ) )
& ( ( is_a_convergence_point_of_set @ A @ B @ C )
=> ( in @ C @ ( lim_points_of_net @ A @ ( net_of_bool_filter @ A @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(81,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ( reflexive_relstr @ A )
& ( with_suprema_relstr @ A )
& ( up_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( with_suprema_relstr @ A )
& ( upper_bounded_relstr @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc9_waybel_0) ).
thf(501,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ( reflexive_relstr @ A )
& ( with_suprema_relstr @ A )
& ( up_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( with_suprema_relstr @ A )
& ( upper_bounded_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(100,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(607,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)],[100]) ).
thf(113,axiom,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( directed_relstr @ ( boole_POSet @ A ) )
& ( up_complete_relstr @ ( boole_POSet @ A ) )
& ( join_complete_relstr @ ( boole_POSet @ A ) )
& ~ ( v1_yellow_3 @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_yellow_6) ).
thf(676,plain,
! [A: $i] :
( ~ ( empty_carrier @ ( boole_POSet @ A ) )
& ( strict_rel_str @ ( boole_POSet @ A ) )
& ( reflexive_relstr @ ( boole_POSet @ A ) )
& ( transitive_relstr @ ( boole_POSet @ A ) )
& ( antisymmetric_relstr @ ( boole_POSet @ A ) )
& ( lower_bounded_relstr @ ( boole_POSet @ A ) )
& ( upper_bounded_relstr @ ( boole_POSet @ A ) )
& ( bounded_relstr @ ( boole_POSet @ A ) )
& ( directed_relstr @ ( boole_POSet @ A ) )
& ( up_complete_relstr @ ( boole_POSet @ A ) )
& ( join_complete_relstr @ ( boole_POSet @ A ) )
& ~ ( v1_yellow_3 @ ( boole_POSet @ A ) )
& ( with_suprema_relstr @ ( boole_POSet @ A ) )
& ( with_infima_relstr @ ( boole_POSet @ A ) )
& ( complete_relstr @ ( boole_POSet @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(80,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( join_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_infima_relstr @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc13_waybel_0) ).
thf(496,plain,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( join_complete_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( with_infima_relstr @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(785,plain,
$false,
inference(cvc4,[status(thm)],[461,605,711,346,760,249,352,170,308,655,269,730,276,185,417,288,320,257,751,344,196,559,152,316,756,238,574,602,774,396,292,452,380,529,661,160,561,165,260,349,192,407,356,156,615,339,554,637,489,547,244,311,657,674,586,412,148,444,733,180,296,611,335,236,187,172,419,271,362,567,737,318,477,552,323,726,668,455,563,299,267,438,167,722,255,487,342,754,458,145,557,640,739,263,150,707,199,177,441,370,717,463,576,154,175,571,595,482,671,581,771,158,390,273,735,326,506,474,664,635,720,415,332,427,131,501,607,676,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU395+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n018.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 : Thu May 18 13:37:28 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.64/1.07 % [INFO] Parsing done (201ms).
% 1.64/1.08 % [INFO] Running in sequential loop mode.
% 2.00/1.28 % [INFO] eprover registered as external prover.
% 2.00/1.29 % [INFO] cvc4 registered as external prover.
% 2.00/1.29 % [INFO] Scanning for conjecture ...
% 2.36/1.39 % [INFO] Found a conjecture and 135 axioms. Running axiom selection ...
% 2.68/1.46 % [INFO] Axiom selection finished. Selected 128 axioms (removed 7 axioms).
% 2.99/1.57 % [INFO] Problem is first-order (TPTP FOF).
% 2.99/1.58 % [INFO] Type checking passed.
% 2.99/1.58 % [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 ...
% 7.83/2.80 % External prover 'cvc4' found a proof!
% 7.83/2.80 % [INFO] Killing All external provers ...
% 7.83/2.81 % Time passed: 2271ms (effective reasoning time: 1723ms)
% 7.83/2.81 % 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)>
% 7.83/2.81 % Axioms used in derivation (128): t15_yellow19, dt_l1_orders_2, redefinition_m2_relset_1, cc1_tops_1, fc8_tops_1, fc15_waybel_0, cc2_finset_1, rc2_waybel_0, rc4_finset_1, fc2_pre_topc, fraenkel_a_2_1_yellow19, t1_subset, rc3_tops_1, fc4_relat_1, fc4_subset_1, fc8_yellow_6, fc2_waybel_0, fc3_yellow19, rc2_yellow_0, cc5_tops_1, cc12_waybel_0, rc4_yellow_6, fc2_waybel_7, cc3_tops_1, cc1_lattice3, dt_m2_relset_1, cc1_relat_1, cc14_waybel_0, cc11_waybel_0, rc13_waybel_0, fc5_pre_topc, dt_k2_yellow19, dt_u1_orders_2, rc6_pre_topc, dt_u1_waybel_0, rc11_waybel_0, dt_g1_waybel_0, rc5_waybel_0, rc1_lattice3, rc1_tops_1, dt_l1_pre_topc, dt_k3_yellow_1, rc2_lattice3, rc3_relat_1, t6_boole, rc2_subset_1, cc5_waybel_0, rc2_waybel_7, rc5_tops_1, fc5_waybel_0, rc1_waybel_7, t5_subset, fc1_waybel_7, cc9_waybel_0, existence_m1_relset_1, cc2_yellow_0, rc3_waybel_7, dt_l1_waybel_0, abstractness_v6_waybel_0, t2_tarski, fc8_yellow_1, rc4_tops_1, existence_l1_waybel_0, t4_subset, dt_k3_yellow19, fc2_yellow_0, cc6_tops_1, rc8_waybel_0, t7_boole, existence_l1_orders_2, fc9_tops_1, rc3_struct_0, fc1_subset_1, rc4_waybel_7, cc13_waybel_0, dt_g1_orders_2, rc9_waybel_0, rc1_subset_1, abstractness_v1_orders_2, cc4_yellow_0, fc15_yellow_6, rc4_waybel_0, t3_subset, cc1_relset_1, existence_m1_subset_1, cc2_tops_1, fc6_waybel_0, rc2_relat_1, existence_m2_relset_1, fc4_yellow19, free_g1_orders_2, fc1_struct_0, existence_l1_pre_topc, rc1_relat_1, reflexivity_r1_tarski, rc10_waybel_0, free_g1_waybel_0, cc10_waybel_0, rc7_pre_topc, cc5_yellow_0, rc3_finset_1, rc1_finset_1, rc2_tops_1, cc1_finset_1, t13_yellow19, cc1_yellow_0, t8_boole, t2_subset, fc5_yellow19, fc12_relat_1, rc5_struct_0, cc4_tops_1, d3_yellow19, rc1_yellow_0, cc2_lattice3, existence_l1_struct_0, rc7_waybel_0, fc7_yellow_1, rc1_waybel_0, rc12_waybel_0, dt_k11_yellow_6, fc3_waybel_0, fc14_finset_1, fc2_yellow19, cc3_yellow_0, antisymmetry_r2_hidden, fc4_waybel_0, dt_k2_pre_topc
% 7.83/2.81 % No. of inferences in proof: 260
% 7.83/2.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2271 ms resp. 1723 ms w/o parsing
% 8.67/2.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.67/2.90 % [INFO] Killing All external provers ...
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