%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU394+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n026.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 08:38:40 AM UTC 2026
% Result : Theorem 10.14s 13.88s
% Output : Refutation 11.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 118
% Syntax : Number of formulae : 238 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 1261 ( 43 equ; 0 cnn)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 3606 ( 265 ~; 2 |; 798 &;2318 @)
% ( 5 <=>; 218 =>; 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 : 59 ( 57 usr; 2 con; 0-4 aty)
% Number of variables : 408 ( 0 ^; 333 !; 75 ?; 408 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_decl,type,
empty_carrier: $i > $o ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(filtered_subset_decl,type,
filtered_subset: $i > $i > $o ).
thf(boole_POSet_decl,type,
boole_POSet: $i > $i ).
thf(cast_as_carrier_subset_decl,type,
cast_as_carrier_subset: $i > $i ).
thf(upper_relstr_subset_decl,type,
upper_relstr_subset: $i > $i > $o ).
thf(proper_element_decl,type,
proper_element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(filter_of_net_str_decl,type,
filter_of_net_str: $i > $i > $i ).
thf(net_of_bool_filter_decl,type,
net_of_bool_filter: $i > $i > $i > $i ).
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(in_decl,type,
in: $i > $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(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(rel_str_of_decl,type,
rel_str_of: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(strict_rel_str_decl,type,
strict_rel_str: $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(function_decl,type,
function: $i > $o ).
thf(quasi_total_decl,type,
quasi_total: $i > $i > $i > $o ).
thf(strict_net_str_decl,type,
strict_net_str: $i > $i > $o ).
thf(net_str_of_decl,type,
net_str_of: $i > $i > $i > $i > $i ).
thf(net_str_decl,type,
net_str: $i > $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(with_suprema_relstr_decl,type,
with_suprema_relstr: $i > $o ).
thf(with_infima_relstr_decl,type,
with_infima_relstr: $i > $o ).
thf(directed_subset_decl,type,
directed_subset: $i > $i > $o ).
thf(trivial_carrier_decl,type,
trivial_carrier: $i > $o ).
thf(connected_relstr_decl,type,
connected_relstr: $i > $o ).
thf(directed_relstr_decl,type,
directed_relstr: $i > $o ).
thf(lower_relstr_subset_decl,type,
lower_relstr_subset: $i > $i > $o ).
thf(a_2_1_yellow19_decl,type,
a_2_1_yellow19: $i > $i > $i ).
thf(is_eventually_in_decl,type,
is_eventually_in: $i > $i > $i > $o ).
thf(the_mapping_decl,type,
the_mapping: $i > $i > $i ).
thf(the_InternalRel_decl,type,
the_InternalRel: $i > $i ).
thf(61,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/sandbox2/benchmark/theBenchmark.p',cc12_waybel_0) ).
thf(436,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)],[61]) ).
thf(52,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/sandbox2/benchmark/theBenchmark.p',cc14_waybel_0) ).
thf(376,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)],[52]) ).
thf(36,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/sandbox2/benchmark/theBenchmark.p',rc1_waybel_0) ).
thf(307,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)],[36]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ~ ( B @ empty )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ strict_net_str ) )
& ~ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ empty_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_waybel_0) ).
thf(479,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ~ ( B @ empty )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ strict_net_str ) )
& ~ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(94,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_waybel_7) ).
thf(628,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)],[94]) ).
thf(80,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/sandbox2/benchmark/theBenchmark.p',rc7_waybel_0) ).
thf(582,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)],[80]) ).
thf(109,axiom,
? [A: $i] :
( ( A @ directed_relstr )
& ( A @ transitive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_yellow_6) ).
thf(741,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)],[109]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ cast_as_carrier_subset @ boole_POSet @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ cast_as_carrier_subset @ boole_POSet @ the_carrier @ powerset @ ( B @ proper_element ) )
& ( A @ cast_as_carrier_subset @ boole_POSet @ ( B @ upper_relstr_subset ) )
& ( A @ cast_as_carrier_subset @ boole_POSet @ ( B @ filtered_subset ) )
& ~ ( B @ empty ) )
=> ( B
= ( B @ ( A @ cast_as_carrier_subset @ ( A @ net_of_bool_filter ) ) @ ( A @ filter_of_net_str ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_yellow19) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ cast_as_carrier_subset @ boole_POSet @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ cast_as_carrier_subset @ boole_POSet @ the_carrier @ powerset @ ( B @ proper_element ) )
& ( A @ cast_as_carrier_subset @ boole_POSet @ ( B @ upper_relstr_subset ) )
& ( A @ cast_as_carrier_subset @ boole_POSet @ ( B @ filtered_subset ) )
& ~ ( B @ empty ) )
=> ( B
= ( B @ ( A @ cast_as_carrier_subset @ ( A @ net_of_bool_filter ) ) @ ( A @ filter_of_net_str ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(120,plain,
~ ! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ cast_as_carrier_subset @ boole_POSet @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ cast_as_carrier_subset @ boole_POSet @ the_carrier @ powerset @ ( B @ proper_element ) )
& ( A @ cast_as_carrier_subset @ boole_POSet @ ( B @ upper_relstr_subset ) )
& ( A @ cast_as_carrier_subset @ boole_POSet @ ( B @ filtered_subset ) )
& ~ ( B @ empty ) )
=> ( B
= ( B @ ( A @ cast_as_carrier_subset @ ( A @ net_of_bool_filter ) ) @ ( A @ filter_of_net_str ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(614,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
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/sandbox2/benchmark/theBenchmark.p',rc8_waybel_0) ).
thf(587,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(43,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(344,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(196,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_difference ) @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(157,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_difference ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(106,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(702,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(111,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(751,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(96,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ! [B: $i] :
( ( ( A @ boole_POSet @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ boole_POSet @ the_carrier @ powerset @ ( B @ proper_element ) )
& ( A @ boole_POSet @ ( B @ upper_relstr_subset ) )
& ( A @ boole_POSet @ ( B @ filtered_subset ) )
& ~ ( B @ empty ) )
=> ! [C: $i] :
~ ( ( C @ empty )
& ( B @ ( C @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_yellow19) ).
thf(638,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ! [B: $i] :
( ( ( A @ boole_POSet @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ boole_POSet @ the_carrier @ powerset @ ( B @ proper_element ) )
& ( A @ boole_POSet @ ( B @ upper_relstr_subset ) )
& ( A @ boole_POSet @ ( B @ filtered_subset ) )
& ~ ( B @ empty ) )
=> ! [C: $i] :
~ ( ( C @ empty )
& ( B @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(88,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(606,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(32,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ cast_as_carrier_subset @ boole_POSet @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ cast_as_carrier_subset @ boole_POSet @ ( B @ upper_relstr_subset ) )
& ( A @ cast_as_carrier_subset @ boole_POSet @ ( B @ filtered_subset ) )
& ~ ( B @ empty ) )
=> ( ( empty_set @ singleton @ ( B @ set_difference ) )
= ( B @ ( A @ cast_as_carrier_subset @ ( A @ net_of_bool_filter ) ) @ ( A @ filter_of_net_str ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_yellow19) ).
thf(284,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ cast_as_carrier_subset @ boole_POSet @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ cast_as_carrier_subset @ boole_POSet @ ( B @ upper_relstr_subset ) )
& ( A @ cast_as_carrier_subset @ boole_POSet @ ( B @ filtered_subset ) )
& ~ ( B @ empty ) )
=> ( ( empty_set @ singleton @ ( B @ set_difference ) )
= ( B @ ( A @ cast_as_carrier_subset @ ( A @ net_of_bool_filter ) ) @ ( A @ filter_of_net_str ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(325,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ singleton @ finite )
& ~ ( A @ singleton @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(448,plain,
! [A: $i] :
( ( A @ singleton @ finite )
& ~ ( A @ singleton @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(602,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ cast_as_carrier_subset @ boole_POSet @ ( B @ ( A @ filter_of_net_str ) @ upper_relstr_subset ) )
& ~ ( B @ ( A @ filter_of_net_str ) @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_yellow19) ).
thf(428,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ cast_as_carrier_subset @ boole_POSet @ ( B @ ( A @ filter_of_net_str ) @ upper_relstr_subset ) )
& ~ ( B @ ( A @ filter_of_net_str ) @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(37,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(312,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ boole_POSet @ the_carrier @ powerset @ ( C @ element ) )
& ( B @ boole_POSet @ the_carrier @ powerset @ ( C @ proper_element ) )
& ( B @ boole_POSet @ ( C @ upper_relstr_subset ) )
& ( B @ boole_POSet @ ( C @ filtered_subset ) )
& ~ ( C @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) )
& ~ ( B @ empty )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ directed_relstr )
& ( A @ ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ strict_net_str ) )
& ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ transitive_relstr )
& ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ reflexive_relstr )
& ~ ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ empty_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_yellow19) ).
thf(334,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ boole_POSet @ the_carrier @ powerset @ ( C @ element ) )
& ( B @ boole_POSet @ the_carrier @ powerset @ ( C @ proper_element ) )
& ( B @ boole_POSet @ ( C @ upper_relstr_subset ) )
& ( B @ boole_POSet @ ( C @ filtered_subset ) )
& ~ ( C @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) )
& ~ ( B @ empty )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ directed_relstr )
& ( A @ ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ strict_net_str ) )
& ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ transitive_relstr )
& ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ reflexive_relstr )
& ~ ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(598,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)],[84]) ).
thf(78,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/sandbox2/benchmark/theBenchmark.p',rc1_waybel_7) ).
thf(561,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)],[78]) ).
thf(54,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/sandbox2/benchmark/theBenchmark.p',rc2_lattice3) ).
thf(392,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)],[54]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
<=> ( B @ ( C @ in ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(137,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)],[5]) ).
thf(13,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(165,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] :
( ( B @ directed_relstr )
& ( A @ ( B @ strict_net_str ) )
& ( B @ antisymmetric_relstr )
& ( B @ transitive_relstr )
& ( B @ reflexive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ ( B @ net_str ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_waybel_0) ).
thf(467,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] :
( ( B @ directed_relstr )
& ( A @ ( B @ strict_net_str ) )
& ( B @ antisymmetric_relstr )
& ( B @ transitive_relstr )
& ( B @ reflexive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ ( B @ net_str ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( A @ the_carrier @ powerset @ ( A @ cast_as_carrier_subset @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(361,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)],[48]) ).
thf(55,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ upper_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ trivial_carrier )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ upper_relstr_subset ) )
& ( A @ ( B @ filtered_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ proper_element ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_waybel_7) ).
thf(403,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ upper_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ trivial_carrier )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ( A @ ( B @ upper_relstr_subset ) )
& ( A @ ( B @ filtered_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ proper_element ) )
& ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(169,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)],[15]) ).
thf(82,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ relation_of2_as_subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(593,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(70,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/sandbox2/benchmark/theBenchmark.p',fc4_waybel_0) ).
thf(499,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)],[70]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ boole_POSet @ the_carrier @ powerset @ ( C @ element ) )
& ( B @ boole_POSet @ ( C @ upper_relstr_subset ) )
& ( B @ boole_POSet @ ( C @ filtered_subset ) )
& ~ ( C @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) )
& ~ ( B @ empty )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ strict_net_str ) )
& ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ transitive_relstr )
& ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ reflexive_relstr )
& ~ ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ empty_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_yellow19) ).
thf(328,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ boole_POSet @ the_carrier @ powerset @ ( C @ element ) )
& ( B @ boole_POSet @ ( C @ upper_relstr_subset ) )
& ( B @ boole_POSet @ ( C @ filtered_subset ) )
& ~ ( C @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) )
& ~ ( B @ empty )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ strict_net_str ) )
& ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ transitive_relstr )
& ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ reflexive_relstr )
& ~ ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(112,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(753,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(77,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/sandbox2/benchmark/theBenchmark.p',fc8_yellow_1) ).
thf(537,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)],[77]) ).
thf(102,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/sandbox2/benchmark/theBenchmark.p',cc11_waybel_0) ).
thf(686,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)],[102]) ).
thf(66,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(476,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(92,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/sandbox2/benchmark/theBenchmark.p',fc5_waybel_0) ).
thf(622,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)],[92]) ).
thf(73,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ cast_as_carrier_subset @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pre_topc) ).
thf(515,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ cast_as_carrier_subset @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( A @ singleton @ ( A @ singleton @ ( B @ relation_of2 ) ) )
=> ( ( B @ ( A @ singleton @ rel_str_of ) @ trivial_carrier )
& ( B @ ( A @ singleton @ rel_str_of ) @ strict_rel_str )
& ~ ( B @ ( A @ singleton @ rel_str_of ) @ empty_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_yellow_0) ).
thf(779,plain,
! [A: $i,B: $i] :
( ( A @ singleton @ ( A @ singleton @ ( B @ relation_of2 ) ) )
=> ( ( B @ ( A @ singleton @ rel_str_of ) @ trivial_carrier )
& ( B @ ( A @ singleton @ rel_str_of ) @ strict_rel_str )
& ~ ( B @ ( A @ singleton @ rel_str_of ) @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ boole_POSet @ the_carrier @ powerset @ ( C @ element ) )
& ( B @ boole_POSet @ ( C @ upper_relstr_subset ) )
& ( B @ boole_POSet @ ( C @ filtered_subset ) )
& ~ ( C @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) )
& ~ ( B @ empty )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ net_str ) )
& ( A @ ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ strict_net_str ) )
& ~ ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ empty_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow19) ).
thf(371,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ boole_POSet @ the_carrier @ powerset @ ( C @ element ) )
& ( B @ boole_POSet @ ( C @ upper_relstr_subset ) )
& ( B @ boole_POSet @ ( C @ filtered_subset ) )
& ~ ( C @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) )
& ~ ( B @ empty )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ net_str ) )
& ( A @ ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ strict_net_str ) )
& ~ ( C @ ( B @ ( A @ net_of_bool_filter ) ) @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(71,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/sandbox2/benchmark/theBenchmark.p',rc9_waybel_0) ).
thf(503,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)],[71]) ).
thf(95,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(633,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(22,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(205,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(98,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_infima_relstr )
=> ~ ( A @ empty_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(662,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_infima_relstr )
=> ~ ( A @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(6,axiom,
? [A: $i] : ( A @ rel_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(148,plain,
? [A: $i] : ( A @ rel_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',cc2_yellow_0) ).
thf(264,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)],[27]) ).
thf(11,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(161,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(97,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/sandbox2/benchmark/theBenchmark.p',fc2_waybel_7) ).
thf(641,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)],[97]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( B @ strict_net_str ) )
=> ( B
= ( B @ ( A @ the_mapping ) @ ( B @ the_InternalRel @ ( B @ the_carrier @ ( A @ net_str_of ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v6_waybel_0) ).
thf(611,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( B @ strict_net_str ) )
=> ( B
= ( B @ ( A @ the_mapping ) @ ( B @ the_InternalRel @ ( B @ the_carrier @ ( A @ net_str_of ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(107,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/sandbox2/benchmark/theBenchmark.p',fc8_yellow_6) ).
thf(704,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)],[107]) ).
thf(45,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(350,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)],[45]) ).
thf(10,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(159,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] : ( A @ ( B @ net_str ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_waybel_0) ).
thf(604,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] : ( A @ ( B @ net_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ cast_as_carrier_subset @ boole_POSet @ the_carrier @ powerset @ ( B @ ( A @ filter_of_net_str ) @ proper_element ) )
& ( A @ cast_as_carrier_subset @ boole_POSet @ ( B @ ( A @ filter_of_net_str ) @ upper_relstr_subset ) )
& ( A @ cast_as_carrier_subset @ boole_POSet @ ( B @ ( A @ filter_of_net_str ) @ filtered_subset ) )
& ~ ( B @ ( A @ filter_of_net_str ) @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_yellow19) ).
thf(784,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ cast_as_carrier_subset @ boole_POSet @ the_carrier @ powerset @ ( B @ ( A @ filter_of_net_str ) @ proper_element ) )
& ( A @ cast_as_carrier_subset @ boole_POSet @ ( B @ ( A @ filter_of_net_str ) @ upper_relstr_subset ) )
& ( A @ cast_as_carrier_subset @ boole_POSet @ ( B @ ( A @ filter_of_net_str ) @ filtered_subset ) )
& ~ ( B @ ( A @ filter_of_net_str ) @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_waybel_0) ).
thf(736,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(91,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/sandbox2/benchmark/theBenchmark.p',rc10_waybel_0) ).
thf(616,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)],[91]) ).
thf(28,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(271,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function )
& ( B @ ( A @ the_mapping ) @ relation )
& ~ ( B @ ( A @ the_mapping ) @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc15_yellow_6) ).
thf(509,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function )
& ( B @ ( A @ the_mapping ) @ relation )
& ~ ( B @ ( A @ the_mapping ) @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_suprema_relstr )
=> ~ ( A @ empty_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattice3) ).
thf(434,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_suprema_relstr )
=> ~ ( A @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(113,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/sandbox2/benchmark/theBenchmark.p',cc1_yellow_0) ).
thf(758,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)],[113]) ).
thf(50,axiom,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(367,plain,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',fc1_waybel_7) ).
thf(213,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)],[24]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] :
( ( A @ ( B @ strict_net_str ) )
& ( A @ ( B @ net_str ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_waybel_0) ).
thf(483,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] :
( ( A @ ( B @ strict_net_str ) )
& ( A @ ( B @ net_str ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',rc2_waybel_0) ).
thf(251,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)],[25]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(626,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)],[93]) ).
thf(100,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/sandbox2/benchmark/theBenchmark.p',rc13_waybel_0) ).
thf(668,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)],[100]) ).
thf(104,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(695,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ cartesian_product2 ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(135,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ cartesian_product2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(167,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(76,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/sandbox2/benchmark/theBenchmark.p',cc9_waybel_0) ).
thf(531,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)],[76]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ net_str ) )
& ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ strict_net_str ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_waybel_0) ).
thf(209,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ net_str ) )
& ( A @ ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) @ strict_net_str ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(69,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/sandbox2/benchmark/theBenchmark.p',rc1_yellow_0) ).
thf(487,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)],[69]) ).
thf(75,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/sandbox2/benchmark/theBenchmark.p',cc13_waybel_0) ).
thf(525,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)],[75]) ).
thf(79,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(580,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(282,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ bounded_relstr )
=> ( ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_yellow_0) ).
thf(150,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)],[7]) ).
thf(21,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/sandbox2/benchmark/theBenchmark.p',cc10_waybel_0) ).
thf(199,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)],[21]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complete_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_yellow_0) ).
thf(463,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)],[64]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(359,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(8,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(154,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ cast_as_carrier_subset @ boole_POSet @ the_carrier @ powerset @ ( B @ ( A @ filter_of_net_str ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_yellow19) ).
thf(600,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ cast_as_carrier_subset @ boole_POSet @ the_carrier @ powerset @ ( B @ ( A @ filter_of_net_str ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_difference ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(175,plain,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_difference ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(595,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(49,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(363,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(116,axiom,
? [A: $i] :
( ( A @ connected_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc12_waybel_0) ).
thf(771,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)],[116]) ).
thf(105,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ( ( B @ ( A @ filter_of_net_str ) )
= ( B @ ( A @ a_2_1_yellow19 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_yellow19) ).
thf(699,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ( ( B @ ( A @ filter_of_net_str ) )
= ( B @ ( A @ a_2_1_yellow19 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(74,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/sandbox2/benchmark/theBenchmark.p',rc11_waybel_0) ).
thf(517,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)],[74]) ).
thf(110,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ strict_rel_str )
=> ( A
= ( A @ the_InternalRel @ ( A @ the_carrier @ rel_str_of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(748,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)],[110]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(258,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)],[26]) ).
thf(18,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/sandbox2/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(186,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)],[18]) ).
thf(114,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(763,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',rc1_lattice3) ).
thf(383,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)],[53]) ).
thf(101,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ cast_as_carrier_subset @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_yellow_0) ).
thf(684,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ cast_as_carrier_subset @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(44,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(346,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',rc2_yellow_0) ).
thf(287,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)],[33]) ).
thf(34,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_waybel_7) ).
thf(300,plain,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ( A @ one_sorted_str ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) )
= ( H @ ( G @ ( F @ ( E @ net_str_of ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_waybel_0) ).
thf(315,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( B @ ( D @ relation_of2 ) ) )
& ( A @ the_carrier @ ( B @ ( D @ quasi_total ) ) )
& ( D @ function )
& ( B @ ( B @ ( C @ relation_of2 ) ) )
& ( A @ one_sorted_str ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ net_str_of ) ) ) )
= ( H @ ( G @ ( F @ ( E @ net_str_of ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(59,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(432,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(56,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/sandbox2/benchmark/theBenchmark.p',fc7_yellow_1) ).
thf(410,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)],[56]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
<=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(190,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)],[19]) ).
thf(29,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(273,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ boole_POSet @ rel_str )
& ( A @ boole_POSet @ strict_rel_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
thf(422,plain,
! [A: $i] :
( ( A @ boole_POSet @ rel_str )
& ( A @ boole_POSet @ strict_rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(119,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ( B @ rel_str ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
thf(790,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ( B @ rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(305,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(42,axiom,
! [A: $i] :
~ ( A @ singleton @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(341,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(115,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/sandbox2/benchmark/theBenchmark.p',fc2_waybel_0) ).
thf(767,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)],[115]) ).
thf(99,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(664,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(3,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(131,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr ) )
=> ( A @ bounded_relstr ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_yellow_0) ).
thf(163,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)],[12]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( B @ singleton @ ( A @ set_difference ) )
= A )
<=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(178,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ in ) )
=> ( ( B @ singleton @ ( A @ set_difference ) )
= A ) )
& ( ( ( B @ singleton @ ( A @ set_difference ) )
= A )
=> ~ ( A @ ( B @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(30,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/sandbox2/benchmark/theBenchmark.p',cc5_waybel_0) ).
thf(277,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)],[30]) ).
thf(103,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/sandbox2/benchmark/theBenchmark.p',fc3_waybel_0) ).
thf(691,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)],[103]) ).
thf(46,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/sandbox2/benchmark/theBenchmark.p',fc15_waybel_0) ).
thf(354,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)],[46]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ net_str ) )
& ~ ( C @ empty_carrier )
& ( B @ one_sorted_str )
& ~ ( B @ empty_carrier ) )
=> ( ( C @ ( B @ a_2_1_yellow19 ) @ ( A @ in ) )
<=> ? [D: $i] :
( ( D @ ( C @ ( B @ is_eventually_in ) ) )
& ( A = D )
& ( B @ the_carrier @ powerset @ ( D @ element ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_yellow19) ).
thf(454,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ net_str ) )
& ~ ( C @ empty_carrier )
& ( B @ one_sorted_str )
& ~ ( B @ empty_carrier ) )
=> ( ( ? [D: $i] :
( ( D @ ( C @ ( B @ is_eventually_in ) ) )
& ( A = D )
& ( B @ the_carrier @ powerset @ ( D @ element ) ) )
=> ( C @ ( B @ a_2_1_yellow19 ) @ ( A @ in ) ) )
& ( ( C @ ( B @ a_2_1_yellow19 ) @ ( A @ in ) )
=> ? [D: $i] :
( ( D @ ( C @ ( B @ is_eventually_in ) ) )
& ( A = D )
& ( B @ the_carrier @ powerset @ ( D @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(792,plain,
$false,
inference(e,[status(thm)],[436,376,307,479,628,582,741,120,614,587,344,196,157,702,751,638,606,284,325,448,602,428,312,334,598,561,392,137,165,467,361,403,169,593,499,328,753,537,686,476,622,515,779,371,503,633,205,662,148,264,161,641,611,704,350,159,604,784,736,616,271,509,434,758,367,213,483,251,626,668,695,135,167,531,209,487,525,580,282,150,199,463,359,154,600,175,595,363,771,699,517,748,258,186,763,383,684,346,287,300,315,432,410,190,273,422,790,305,341,767,664,131,163,178,277,691,354,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU394+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.16/10.43 % Computer : n026.cluster.edu
% 0.16/10.43 % Model : x86_64 x86_64
% 0.16/10.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/10.43 % Memory : 8046.5625MB
% 0.16/10.43 % OS : Linux 6.8.0-71-generic
% 0.16/10.43 % CPULimit : 300
% 0.16/10.43 % WCLimit : 300
% 0.16/10.43 % DateTime : Sat Sep 26 09:28:36 UTC 2026
% 0.16/10.44 % CPUTime :
% 0.16/10.44 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.19/11.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.79/11.33 % [INFO] Parsing done (319ms).
% 1.79/11.35 % [INFO] Running in sequential loop mode.
% 2.72/11.74 % [INFO] eprover registered as external prover.
% 2.72/11.75 % [INFO] Scanning for conjecture ...
% 3.19/11.90 % [INFO] Found a conjecture (or negated_conjecture) and 126 axioms. Running axiom selection ...
% 3.62/12.03 % [INFO] Axiom selection finished. Selected 117 axioms (removed 9 axioms).
% 3.91/12.19 % [INFO] Problem is first-order (TPTP FOF).
% 4.08/12.21 % [INFO] Type checking passed.
% 4.08/12.22 % [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 ...
% 10.14/13.88 % External prover 'e' found a proof!
% 10.14/13.88 % [INFO] Killing All external provers ...
% 10.14/13.88 % Time passed: 3306ms (effective reasoning time: 2528ms)
% 10.14/13.88 % 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)>
% 10.14/13.88 % Axioms used in derivation (117): redefinition_m2_relset_1, fc1_finset_1, dt_l1_orders_2, fc15_waybel_0, cc2_finset_1, rc2_waybel_0, rc4_finset_1, fc2_pre_topc, fraenkel_a_2_1_yellow19, fc4_relat_1, t1_subset, fc4_subset_1, fc8_yellow_6, fc2_waybel_0, fc3_relat_1, fc3_yellow19, rc2_yellow_0, cc12_waybel_0, rc4_yellow_6, fc2_waybel_7, cc1_lattice3, dt_m2_relset_1, cc1_relat_1, cc14_waybel_0, cc11_waybel_0, rc13_waybel_0, t2_yellow19, dt_k2_yellow19, dt_u1_orders_2, dt_u1_waybel_0, rc11_waybel_0, dt_g1_waybel_0, rc5_waybel_0, rc1_lattice3, dt_k3_yellow_1, rc2_lattice3, rc3_relat_1, t6_boole, rc2_subset_1, cc5_waybel_0, rc2_waybel_7, fc5_waybel_0, rc1_waybel_7, t5_subset, fc1_waybel_7, cc9_waybel_0, existence_m1_relset_1, cc2_yellow_0, fc2_subset_1, rc3_waybel_7, dt_l1_waybel_0, abstractness_v6_waybel_0, t2_tarski, fc8_yellow_1, existence_l1_waybel_0, t4_boole, t4_subset, dt_k3_yellow19, fc2_yellow_0, rc8_waybel_0, t7_boole, existence_l1_orders_2, 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, fc6_waybel_0, rc2_relat_1, existence_m2_relset_1, fc1_yellow_0, fc4_yellow19, free_g1_orders_2, fc1_struct_0, rc1_relat_1, reflexivity_r1_tarski, rc10_waybel_0, free_g1_waybel_0, cc10_waybel_0, cc5_yellow_0, rc3_finset_1, rc1_finset_1, cc1_finset_1, fc12_finset_1, cc1_yellow_0, t8_boole, rc5_struct_0, t14_yellow19, t2_subset, fc5_yellow19, fc12_relat_1, d3_yellow19, rc1_yellow_0, cc2_lattice3, existence_l1_struct_0, fc3_waybel_0, rc7_waybel_0, t3_boole, fc7_yellow_1, rc1_waybel_0, rc12_waybel_0, fc14_finset_1, fc2_yellow19, cc3_yellow_0, t65_zfmisc_1, antisymmetry_r2_hidden, fc4_waybel_0, dt_k2_pre_topc
% 10.14/13.88 % No. of inferences in proof: 238
% 10.14/13.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3306 ms resp. 2528 ms w/o parsing
% 11.27/14.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.27/14.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------