%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU388+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:38:39 AM UTC 2026
% Result : Theorem 10.42s 3.94s
% Output : Refutation 11.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 112
% Syntax : Number of formulae : 226 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 1170 ( 19 equ; 0 cnn)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 2977 ( 195 ~; 2 |; 706 &;1838 @)
% ( 6 <=>; 230 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 59 usr; 2 con; 0-3 aty)
% Number of variables : 361 ( 0 ^; 276 !; 85 ?; 361 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_decl,type,
empty_carrier: $i > $o ).
thf(topological_space_decl,type,
topological_space: $i > $o ).
thf(top_str_decl,type,
top_str: $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(neighborhood_system_decl,type,
neighborhood_system: $i > $i > $i ).
thf(point_neighbourhood_decl,type,
point_neighbourhood: $i > $i > $i > $o ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(relation_decl,type,
relation: $i > $o ).
thf(relation_empty_yielding_decl,type,
relation_empty_yielding: $i > $o ).
thf(finite_decl,type,
finite: $i > $o ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(rel_str_decl,type,
rel_str: $i > $o ).
thf(bounded_relstr_decl,type,
bounded_relstr: $i > $o ).
thf(lower_bounded_relstr_decl,type,
lower_bounded_relstr: $i > $o ).
thf(upper_bounded_relstr_decl,type,
upper_bounded_relstr: $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(with_suprema_relstr_decl,type,
with_suprema_relstr: $i > $o ).
thf(cast_as_carrier_subset_decl,type,
cast_as_carrier_subset: $i > $i ).
thf(directed_subset_decl,type,
directed_subset: $i > $i > $o ).
thf(strict_rel_str_decl,type,
strict_rel_str: $i > $o ).
thf(boole_POSet_decl,type,
boole_POSet: $i > $i ).
thf(rel_str_of_decl,type,
rel_str_of: $i > $i > $i ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(with_infima_relstr_decl,type,
with_infima_relstr: $i > $o ).
thf(filtered_subset_decl,type,
filtered_subset: $i > $i > $o ).
thf(reflexive_relstr_decl,type,
reflexive_relstr: $i > $o ).
thf(complete_relstr_decl,type,
complete_relstr: $i > $o ).
thf(up_complete_relstr_decl,type,
up_complete_relstr: $i > $o ).
thf(join_complete_relstr_decl,type,
join_complete_relstr: $i > $o ).
thf(transitive_relstr_decl,type,
transitive_relstr: $i > $o ).
thf(antisymmetric_relstr_decl,type,
antisymmetric_relstr: $i > $o ).
thf(v1_yellow_3_decl,type,
v1_yellow_3: $i > $o ).
thf(distributive_relstr_decl,type,
distributive_relstr: $i > $o ).
thf(heyting_relstr_decl,type,
heyting_relstr: $i > $o ).
thf(complemented_relstr_decl,type,
complemented_relstr: $i > $o ).
thf(boolean_relstr_decl,type,
boolean_relstr: $i > $o ).
thf(trivial_carrier_decl,type,
trivial_carrier: $i > $o ).
thf(closed_subset_decl,type,
closed_subset: $i > $i > $o ).
thf(connected_relstr_decl,type,
connected_relstr: $i > $o ).
thf(nowhere_dense_decl,type,
nowhere_dense: $i > $i > $o ).
thf(boundary_set_decl,type,
boundary_set: $i > $i > $o ).
thf(lower_relstr_subset_decl,type,
lower_relstr_subset: $i > $i > $o ).
thf(upper_relstr_subset_decl,type,
upper_relstr_subset: $i > $i > $o ).
thf(open_subset_decl,type,
open_subset: $i > $i > $o ).
thf(a_2_0_yellow19_decl,type,
a_2_0_yellow19: $i > $i > $i ).
thf(the_InternalRel_decl,type,
the_InternalRel: $i > $i ).
thf(v1_membered_decl,type,
v1_membered: $i > $o ).
thf(v2_membered_decl,type,
v2_membered: $i > $o ).
thf(v3_membered_decl,type,
v3_membered: $i > $o ).
thf(v4_membered_decl,type,
v4_membered: $i > $o ).
thf(v5_membered_decl,type,
v5_membered: $i > $o ).
thf(directed_relstr_decl,type,
directed_relstr: $i > $o ).
thf(dense_decl,type,
dense: $i > $i > $o ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(328,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(95,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_infima_relstr )
=> ~ ( A @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(622,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_infima_relstr )
=> ~ ( A @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(53,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ( ( A @ ( A @ cast_as_carrier_subset @ closed_subset ) )
& ( A @ ( A @ cast_as_carrier_subset @ open_subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_tops_1) ).
thf(347,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ( ( A @ ( A @ cast_as_carrier_subset @ closed_subset ) )
& ( A @ ( A @ cast_as_carrier_subset @ open_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(97,axiom,
? [A: $i] :
( ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc13_waybel_0) ).
thf(628,plain,
? [A: $i] :
( ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(86,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ upper_relstr_subset ) )
& ( A @ ( B @ filtered_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc10_waybel_0) ).
thf(555,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ upper_relstr_subset ) )
& ( A @ ( B @ filtered_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(111,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ? [B: $i] :
( ( A @ ( B @ upper_relstr_subset ) )
& ( A @ ( B @ lower_relstr_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_waybel_0) ).
thf(730,plain,
! [A: $i] :
( ( A @ rel_str )
=> ? [B: $i] :
( ( A @ ( B @ upper_relstr_subset ) )
& ( A @ ( B @ lower_relstr_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(269,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( B @ powerset @ ( A @ element ) ) )
& ( ( B @ powerset @ ( A @ element ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ the_carrier @ ( C @ element ) )
& ( B @ top_str )
& ( B @ topological_space )
& ~ ( B @ empty_carrier ) )
=> ( ( C @ ( B @ a_2_0_yellow19 ) @ ( A @ in ) )
<=> ? [D: $i] :
( ( A = D )
& ( C @ ( B @ ( D @ point_neighbourhood ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_yellow19) ).
thf(440,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ the_carrier @ ( C @ element ) )
& ( B @ top_str )
& ( B @ topological_space )
& ~ ( B @ empty_carrier ) )
=> ( ( ? [D: $i] :
( ( A = D )
& ( C @ ( B @ ( D @ point_neighbourhood ) ) ) )
=> ( C @ ( B @ a_2_0_yellow19 ) @ ( A @ in ) ) )
& ( ( C @ ( B @ a_2_0_yellow19 ) @ ( A @ in ) )
=> ? [D: $i] :
( ( A = D )
& ( C @ ( B @ ( D @ point_neighbourhood ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(101,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tops_1) ).
thf(655,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(85,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(550,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(109,axiom,
! [A: $i] :
( ( A @ top_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(715,plain,
! [A: $i] :
( ( A @ top_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(76,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr ) )
=> ? [B: $i] :
( ( A @ ( B @ upper_relstr_subset ) )
& ( A @ ( B @ lower_relstr_subset ) )
& ( A @ ( B @ filtered_subset ) )
& ( A @ ( B @ directed_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc11_waybel_0) ).
thf(472,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr ) )
=> ? [B: $i] :
( ( A @ ( B @ upper_relstr_subset ) )
& ( A @ ( B @ lower_relstr_subset ) )
& ( A @ ( B @ filtered_subset ) )
& ( A @ ( B @ directed_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(113,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ open_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tops_1) ).
thf(747,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ open_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ boole_POSet @ rel_str )
& ( A @ boole_POSet @ strict_rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
thf(174,plain,
! [A: $i] :
( ( A @ boole_POSet @ rel_str )
& ( A @ boole_POSet @ strict_rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(107,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(709,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ trivial_carrier )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ connected_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_waybel_0) ).
thf(288,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ trivial_carrier )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ connected_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(43,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ( A @ ( B @ boundary_set ) )
& ( A @ ( B @ closed_subset ) ) )
=> ( ( A @ ( B @ nowhere_dense ) )
& ( A @ ( B @ boundary_set ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_tops_1) ).
thf(301,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ( A @ ( B @ boundary_set ) )
& ( A @ ( B @ closed_subset ) ) )
=> ( ( A @ ( B @ nowhere_dense ) )
& ( A @ ( B @ boundary_set ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complete_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_yellow_0) ).
thf(436,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complete_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(100,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ upper_bounded_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ ( A @ cast_as_carrier_subset @ directed_subset ) )
& ~ ( A @ cast_as_carrier_subset @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_waybel_0) ).
thf(651,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ upper_bounded_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ ( A @ cast_as_carrier_subset @ directed_subset ) )
& ~ ( A @ cast_as_carrier_subset @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(105,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(702,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(3,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(125,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(37,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(284,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_suprema_relstr )
=> ~ ( A @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattice3) ).
thf(416,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_suprema_relstr )
=> ~ ( A @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(71,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( A @ cast_as_carrier_subset @ closed_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_pre_topc) ).
thf(448,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( A @ cast_as_carrier_subset @ closed_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complete_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc10_waybel_0) ).
thf(216,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complete_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_waybel_7) ).
thf(591,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( A @ the_carrier @ powerset @ ( A @ cast_as_carrier_subset @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(353,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( A @ the_carrier @ powerset @ ( A @ cast_as_carrier_subset @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ join_complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ with_infima_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc13_waybel_0) ).
thf(480,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ join_complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ with_infima_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(79,axiom,
! [A: $i] :
( ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_yellow_1) ).
thf(492,plain,
! [A: $i] :
( ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(16,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ with_suprema_relstr ) )
=> ( ( A @ ( A @ cast_as_carrier_subset @ directed_subset ) )
& ~ ( A @ cast_as_carrier_subset @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_waybel_0) ).
thf(164,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ with_suprema_relstr ) )
=> ( ( A @ ( A @ cast_as_carrier_subset @ directed_subset ) )
& ~ ( A @ cast_as_carrier_subset @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(29,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(211,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(99,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ join_complete_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lower_bounded_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc11_waybel_0) ).
thf(646,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ join_complete_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lower_bounded_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(103,axiom,
? [A: $i] :
( ( A @ directed_relstr )
& ( A @ transitive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_yellow_6) ).
thf(692,plain,
? [A: $i] :
( ( A @ directed_relstr )
& ( A @ transitive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(293,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(6,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(133,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(102,axiom,
! [A: $i] :
( ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ~ ( A @ boole_POSet @ v1_yellow_3 )
& ( A @ boole_POSet @ join_complete_relstr )
& ( A @ boole_POSet @ up_complete_relstr )
& ( A @ boole_POSet @ directed_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_yellow_6) ).
thf(660,plain,
! [A: $i] :
( ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ~ ( A @ boole_POSet @ v1_yellow_3 )
& ( A @ boole_POSet @ join_complete_relstr )
& ( A @ boole_POSet @ up_complete_relstr )
& ( A @ boole_POSet @ directed_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(411,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(73,axiom,
? [A: $i] :
( ( A @ trivial_carrier )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_yellow_0) ).
thf(452,plain,
? [A: $i] :
( ( A @ trivial_carrier )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ( ( B @ ( A @ rel_str_of ) @ rel_str )
& ( B @ ( A @ rel_str_of ) @ strict_rel_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(201,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ( ( B @ ( A @ rel_str_of ) @ rel_str )
& ( B @ ( A @ rel_str_of ) @ strict_rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(49,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ empty )
=> ( A @ ( B @ nowhere_dense ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_tops_1) ).
thf(334,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ empty )
=> ( A @ ( B @ nowhere_dense ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(32,axiom,
? [A: $i] : ( A @ top_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(260,plain,
? [A: $i] : ( A @ top_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(15,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(160,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(87,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_tops_1) ).
thf(561,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ point_neighbourhood ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_connsp_2) ).
thf(297,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ point_neighbourhood ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ trivial_carrier )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_yellow_0) ).
thf(275,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ trivial_carrier )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(197,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ join_complete_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ upper_bounded_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc14_waybel_0) ).
thf(361,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ join_complete_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ upper_bounded_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(22,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(188,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
<=> ( B @ ( C @ in ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(388,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) )
& ( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
<=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(205,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ) )
& ( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(82,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ relation_of2_as_subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(541,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ relation_of2_as_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(67,axiom,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ empty )
=> ( A @ ( B @ boundary_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_tops_1) ).
thf(430,plain,
! [A: $i] :
( ( A @ top_str )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ empty )
=> ( A @ ( B @ boundary_set ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(148,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ rel_str_of ) )
= ( D @ ( C @ rel_str_of ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(180,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ rel_str_of ) )
= ( D @ ( C @ rel_str_of ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(94,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ( ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ boolean_relstr )
& ( A @ boole_POSet @ complemented_relstr )
& ( A @ boole_POSet @ heyting_relstr )
& ( A @ boole_POSet @ distributive_relstr )
& ~ ( A @ boole_POSet @ v1_yellow_3 )
& ( A @ boole_POSet @ join_complete_relstr )
& ( A @ boole_POSet @ up_complete_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ trivial_carrier )
& ~ ( A @ boole_POSet @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_waybel_7) ).
thf(601,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ( ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ boolean_relstr )
& ( A @ boole_POSet @ complemented_relstr )
& ( A @ boole_POSet @ heyting_relstr )
& ( A @ boole_POSet @ distributive_relstr )
& ~ ( A @ boole_POSet @ v1_yellow_3 )
& ( A @ boole_POSet @ join_complete_relstr )
& ( A @ boole_POSet @ up_complete_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ trivial_carrier )
& ~ ( A @ boole_POSet @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(23,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ with_infima_relstr ) )
=> ( ( A @ ( A @ cast_as_carrier_subset @ filtered_subset ) )
& ~ ( A @ cast_as_carrier_subset @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_waybel_0) ).
thf(191,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ with_infima_relstr ) )
=> ( ( A @ ( A @ cast_as_carrier_subset @ filtered_subset ) )
& ~ ( A @ cast_as_carrier_subset @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(89,axiom,
? [A: $i] :
( ( A @ connected_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc12_waybel_0) ).
thf(577,plain,
? [A: $i] :
( ( A @ connected_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(84,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_pre_topc) ).
thf(545,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(64,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ neighborhood_system ) )
= ( B @ ( A @ a_2_0_yellow19 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_yellow19) ).
thf(413,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ neighborhood_system ) )
= ( B @ ( A @ a_2_0_yellow19 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(108,axiom,
! [A: $i] :
( ( A @ top_str )
=> ( A @ ( A @ cast_as_carrier_subset @ dense ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_tops_1) ).
thf(713,plain,
! [A: $i] :
( ( A @ top_str )
=> ( A @ ( A @ cast_as_carrier_subset @ dense ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(106,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complete_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_yellow_0) ).
thf(704,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complete_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(18,axiom,
? [A: $i] : ( A @ rel_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(172,plain,
? [A: $i] : ( A @ rel_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(60,axiom,
? [A: $i] :
( ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_lattice3) ).
thf(377,plain,
? [A: $i] :
( ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ top_str )
=> ? [B: $i] :
( ( A @ ( B @ boundary_set ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_tops_1) ).
thf(567,plain,
! [A: $i] :
( ( A @ top_str )
=> ? [B: $i] :
( ( A @ ( B @ boundary_set ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(45,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_waybel_7) ).
thf(318,plain,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(81,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ upper_relstr_subset ) )
& ( A @ ( B @ lower_relstr_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc8_waybel_0) ).
thf(535,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ upper_relstr_subset ) )
& ( A @ ( B @ lower_relstr_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ? [B: $i] :
( ( A @ ( B @ filtered_subset ) )
& ( A @ ( B @ directed_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_waybel_0) ).
thf(323,plain,
! [A: $i] :
( ( A @ rel_str )
=> ? [B: $i] :
( ( A @ ( B @ filtered_subset ) )
& ( A @ ( B @ directed_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_yellow_1) ).
thf(399,plain,
! [A: $i] :
( ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(7,axiom,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(135,plain,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(299,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(589,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(80,axiom,
? [A: $i] :
( ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ boolean_relstr )
& ( A @ complemented_relstr )
& ( A @ heyting_relstr )
& ( A @ distributive_relstr )
& ~ ( A @ v1_yellow_3 )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ trivial_carrier )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_waybel_7) ).
thf(516,plain,
? [A: $i] :
( ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ boolean_relstr )
& ( A @ complemented_relstr )
& ( A @ heyting_relstr )
& ( A @ distributive_relstr )
& ~ ( A @ v1_yellow_3 )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ trivial_carrier )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(52,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ ( A @ cast_as_carrier_subset @ upper_relstr_subset ) )
& ( A @ ( A @ cast_as_carrier_subset @ lower_relstr_subset ) )
& ~ ( A @ cast_as_carrier_subset @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc15_waybel_0) ).
thf(342,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ ( A @ cast_as_carrier_subset @ upper_relstr_subset ) )
& ( A @ ( A @ cast_as_carrier_subset @ lower_relstr_subset ) )
& ~ ( A @ cast_as_carrier_subset @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(56,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(355,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(40,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ nowhere_dense ) )
=> ( A @ ( B @ boundary_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_tops_1) ).
thf(295,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( A @ ( B @ nowhere_dense ) )
=> ( A @ ( B @ boundary_set ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(36,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(282,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(12,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(150,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(199,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(48,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(331,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(90,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ lower_bounded_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ ( A @ cast_as_carrier_subset @ filtered_subset ) )
& ~ ( A @ cast_as_carrier_subset @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_waybel_0) ).
thf(585,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ lower_bounded_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ ( A @ cast_as_carrier_subset @ filtered_subset ) )
& ~ ( A @ cast_as_carrier_subset @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(110,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ nowhere_dense ) )
& ( A @ ( B @ boundary_set ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_tops_1) ).
thf(717,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ nowhere_dense ) )
& ( A @ ( B @ boundary_set ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(4,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(127,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(51,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(338,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(75,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ cast_as_carrier_subset @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pre_topc) ).
thf(470,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ cast_as_carrier_subset @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ point_neighbourhood ) ) )
=> ( A @ the_carrier @ powerset @ ( C @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_connsp_2) ).
thf(359,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ point_neighbourhood ) ) )
=> ( A @ the_carrier @ powerset @ ( C @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(336,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(13,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(154,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(143,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ( A @ cast_as_carrier_subset @ boole_POSet @ the_carrier @ powerset @ ( B @ ( A @ neighborhood_system ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow19) ).
thf(450,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ( A @ cast_as_carrier_subset @ boole_POSet @ the_carrier @ powerset @ ( B @ ( A @ neighborhood_system ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(59,axiom,
? [A: $i] :
( ( A @ complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_lattice3) ).
thf(368,plain,
? [A: $i] :
( ( A @ complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(104,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ strict_rel_str )
=> ( A
= ( A @ the_InternalRel @ ( A @ the_carrier @ rel_str_of ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(699,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ strict_rel_str )
=> ( A
= ( A @ the_InternalRel @ ( A @ the_carrier @ rel_str_of ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(21,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(186,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( B @ ( A @ neighborhood_system ) @ ( C @ in ) )
<=> ( B @ ( A @ ( C @ point_neighbourhood ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_yellow19) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( B @ ( A @ neighborhood_system ) @ ( C @ in ) )
<=> ( B @ ( A @ ( C @ point_neighbourhood ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(114,plain,
~ ! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ point_neighbourhood ) ) )
=> ( B @ ( A @ neighborhood_system ) @ ( C @ in ) ) )
& ( ( B @ ( A @ neighborhood_system ) @ ( C @ in ) )
=> ( B @ ( A @ ( C @ point_neighbourhood ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ bounded_relstr )
=> ( ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_yellow_0) ).
thf(139,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ bounded_relstr )
=> ( ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ up_complete_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc12_waybel_0) ).
thf(418,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ up_complete_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr ) )
=> ( A @ bounded_relstr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_yellow_0) ).
thf(158,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr ) )
=> ( A @ bounded_relstr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(351,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(68,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ empty )
=> ( ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_tops_1) ).
thf(432,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( B @ empty )
=> ( ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(10,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(146,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(112,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ( A @ ( B @ nowhere_dense ) )
& ( A @ ( B @ open_subset ) ) )
=> ( ( A @ ( B @ nowhere_dense ) )
& ( A @ ( B @ boundary_set ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ( B @ empty ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_tops_1) ).
thf(735,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ( ( ( A @ ( B @ nowhere_dense ) )
& ( A @ ( B @ open_subset ) ) )
=> ( ( A @ ( B @ nowhere_dense ) )
& ( A @ ( B @ boundary_set ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( A @ ( B @ closed_subset ) )
& ( A @ ( B @ open_subset ) )
& ( B @ empty ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(17,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(168,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(33,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ filtered_subset ) )
& ( A @ ( B @ directed_subset ) )
& ( B @ finite )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_waybel_0) ).
thf(262,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ filtered_subset ) )
& ( A @ ( B @ directed_subset ) )
& ( B @ finite )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(44,axiom,
? [A: $i] :
( ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_yellow_0) ).
thf(305,plain,
? [A: $i] :
( ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(195,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(96,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(624,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(74,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ lower_relstr_subset ) )
& ( A @ ( B @ directed_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc9_waybel_0) ).
thf(464,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ lower_relstr_subset ) )
& ( A @ ( B @ directed_subset ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(93,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(596,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(98,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ cast_as_carrier_subset @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_yellow_0) ).
thf(644,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ cast_as_carrier_subset @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ cartesian_product2 ) @ finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(131,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ cartesian_product2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ up_complete_relstr )
& ( A @ with_suprema_relstr )
& ( A @ reflexive_relstr ) )
=> ( ( A @ upper_bounded_relstr )
& ( A @ with_suprema_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc9_waybel_0) ).
thf(486,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ up_complete_relstr )
& ( A @ with_suprema_relstr )
& ( A @ reflexive_relstr ) )
=> ( ( A @ upper_bounded_relstr )
& ( A @ with_suprema_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(543,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ boolean_relstr )
& ( A @ boole_POSet @ complemented_relstr )
& ( A @ boole_POSet @ heyting_relstr )
& ( A @ boole_POSet @ distributive_relstr )
& ~ ( A @ boole_POSet @ v1_yellow_3 )
& ( A @ boole_POSet @ join_complete_relstr )
& ( A @ boole_POSet @ up_complete_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_waybel_7) ).
thf(222,plain,
! [A: $i] :
( ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ boolean_relstr )
& ( A @ boole_POSet @ complemented_relstr )
& ( A @ boole_POSet @ heyting_relstr )
& ( A @ boole_POSet @ distributive_relstr )
& ~ ( A @ boole_POSet @ v1_yellow_3 )
& ( A @ boole_POSet @ join_complete_relstr )
& ( A @ boole_POSet @ up_complete_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(796,plain,
$false,
inference(e,[status(thm)],[328,622,347,628,555,730,269,440,655,550,715,472,747,174,709,288,301,436,651,702,125,284,416,448,216,591,353,480,492,164,211,646,692,293,133,660,411,452,201,334,260,160,561,297,275,197,361,188,388,205,541,430,148,180,601,191,577,545,413,713,704,172,377,567,318,535,323,399,135,299,589,516,342,355,295,282,150,199,331,585,717,127,338,470,359,336,154,143,450,368,699,186,114,139,418,158,351,432,146,735,168,262,305,195,624,464,596,644,131,486,543,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU388+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.41 % Computer : n018.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 09:26:22 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.50/1.27 % [INFO] Parsing done (281ms).
% 1.50/1.29 % [INFO] Running in sequential loop mode.
% 2.46/1.70 % [INFO] eprover registered as external prover.
% 2.67/1.70 % [INFO] Scanning for conjecture ...
% 2.90/1.85 % [INFO] Found a conjecture (or negated_conjecture) and 118 axioms. Running axiom selection ...
% 3.10/1.98 % [INFO] Axiom selection finished. Selected 111 axioms (removed 7 axioms).
% 3.84/2.13 % [INFO] Problem is first-order (TPTP FOF).
% 3.84/2.15 % [INFO] Type checking passed.
% 3.84/2.15 % [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 ...
% 10.42/3.93 % External prover 'e' found a proof!
% 10.42/3.93 % [INFO] Killing All external provers ...
% 10.42/3.93 % Time passed: 3373ms (effective reasoning time: 2638ms)
% 10.42/3.93 % 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)>
% 10.42/3.93 % Axioms used in derivation (111): t4_subset, existence_m1_connsp_2, fc14_finset_1, 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, d1_yellow19, t1_subset, rc3_tops_1, fc4_relat_1, fc4_subset_1, fc8_yellow_6, fc2_waybel_0, rc2_yellow_0, dt_k1_yellow19, 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, rc11_waybel_0, dt_u1_orders_2, rc6_pre_topc, 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, t2_tarski, fc8_yellow_1, rc4_tops_1, fc2_yellow_0, cc6_tops_1, rc8_waybel_0, t7_boole, existence_l1_orders_2, fc9_tops_1, rc3_struct_0, fc1_subset_1, cc13_waybel_0, dt_g1_orders_2, rc9_waybel_0, rc1_subset_1, abstractness_v1_orders_2, cc4_yellow_0, t3_subset, cc1_relset_1, existence_m1_subset_1, cc2_tops_1, rc2_relat_1, existence_m2_relset_1, dt_m1_connsp_2, dt_l1_orders_2, free_g1_orders_2, fc1_struct_0, existence_l1_pre_topc, rc1_relat_1, reflexivity_r1_tarski, fraenkel_a_2_0_yellow19, rc10_waybel_0, cc10_waybel_0, rc7_pre_topc, cc5_yellow_0, rc3_finset_1, rc1_finset_1, rc2_tops_1, cc1_finset_1, cc1_yellow_0, t8_boole, t2_subset, fc12_relat_1, rc5_struct_0, cc4_tops_1, rc1_yellow_0, cc2_lattice3, existence_l1_struct_0, fc3_waybel_0, rc7_waybel_0, fc7_yellow_1, rc1_waybel_0, rc12_waybel_0, cc3_yellow_0, antisymmetry_r2_hidden, fc4_waybel_0, dt_k2_pre_topc
% 10.42/3.93 % No. of inferences in proof: 226
% 10.42/3.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3373 ms resp. 2638 ms w/o parsing
% 11.32/4.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.32/4.11 % [INFO] Killing All external provers ...
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