%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU387+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 : 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 7.91s 3.43s
% Output : Refutation 8.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 78
% Syntax : Number of formulae : 158 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 813 ( 14 equ; 0 cnn)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 2026 ( 158 ~; 2 |; 518 &;1213 @)
% ( 3 <=>; 132 =>; 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 : 45 ( 43 usr; 2 con; 0-3 aty)
% Number of variables : 236 ( 0 ^; 182 !; 54 ?; 236 :)
% Comments :
%------------------------------------------------------------------------------
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(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(in_decl,type,
in: $i > $i > $o ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(rel_str_decl,type,
rel_str: $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(bounded_relstr_decl,type,
bounded_relstr: $i > $o ).
thf(empty_carrier_decl,type,
empty_carrier: $i > $o ).
thf(reflexive_relstr_decl,type,
reflexive_relstr: $i > $o ).
thf(trivial_carrier_decl,type,
trivial_carrier: $i > $o ).
thf(transitive_relstr_decl,type,
transitive_relstr: $i > $o ).
thf(antisymmetric_relstr_decl,type,
antisymmetric_relstr: $i > $o ).
thf(complete_relstr_decl,type,
complete_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(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(join_complete_relstr_decl,type,
join_complete_relstr: $i > $o ).
thf(strict_rel_str_decl,type,
strict_rel_str: $i > $o ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(up_complete_relstr_decl,type,
up_complete_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(rel_str_of_decl,type,
rel_str_of: $i > $i > $i ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(directed_relstr_decl,type,
directed_relstr: $i > $o ).
thf(connected_relstr_decl,type,
connected_relstr: $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(bottom_of_relstr_decl,type,
bottom_of_relstr: $i > $i ).
thf(the_InternalRel_decl,type,
the_InternalRel: $i > $i ).
thf(41,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(347,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(49,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(372,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)],[49]) ).
thf(34,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(285,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)],[34]) ).
thf(59,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(420,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(28,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(245,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)],[28]) ).
thf(42,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(351,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(76,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(523,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(7,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(115,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,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(185,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)],[18]) ).
thf(38,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(301,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)],[38]) ).
thf(4,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(93,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)],[4]) ).
thf(58,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ ( B @ upper_relstr_subset ) )
& ( A @ ( B @ filtered_subset ) )
& ~ ( B @ empty ) )
=> ( ( A @ the_carrier @ powerset @ ( B @ proper_element ) )
<=> ~ ( B @ ( A @ bottom_of_relstr @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_waybel_7) ).
thf(416,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ the_carrier @ powerset @ ( B @ element ) )
& ( A @ ( B @ upper_relstr_subset ) )
& ( A @ ( B @ filtered_subset ) )
& ~ ( B @ empty ) )
=> ( ( ~ ( B @ ( A @ bottom_of_relstr @ in ) )
=> ( A @ the_carrier @ powerset @ ( B @ proper_element ) ) )
& ( ( A @ the_carrier @ powerset @ ( B @ proper_element ) )
=> ~ ( B @ ( A @ bottom_of_relstr @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_suprema_relstr )
=> ~ ( A @ empty_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattice3) ).
thf(152,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_suprema_relstr )
=> ~ ( A @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(24,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(228,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(22,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(216,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)],[22]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(376,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(26,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(238,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)],[26]) ).
thf(9,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(121,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)],[9]) ).
thf(43,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(353,plain,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_infima_relstr )
=> ~ ( A @ empty_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(293,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_infima_relstr )
=> ~ ( A @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ boole_POSet @ bottom_of_relstr )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_yellow_1) ).
thf(411,plain,
! [A: $i] :
( ( A @ boole_POSet @ bottom_of_relstr )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(27,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(243,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(62,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(428,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)],[62]) ).
thf(69,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(452,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(66,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(439,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)],[66]) ).
thf(19,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(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)],[19]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(366,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(6,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(102,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)],[6]) ).
thf(16,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(160,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)],[16]) ).
thf(37,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(297,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(11,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(137,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)],[11]) ).
thf(74,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(488,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)],[74]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(339,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)],[39]) ).
thf(79,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ bottom_of_relstr @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_0) ).
thf(554,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ bottom_of_relstr @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(54,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(393,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)],[54]) ).
thf(70,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(457,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)],[70]) ).
thf(10,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(128,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)],[10]) ).
thf(45,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(360,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(20,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(205,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)],[20]) ).
thf(78,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(530,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)],[78]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(425,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(63,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(430,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(17,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(166,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)],[17]) ).
thf(12,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)],[12]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(279,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(60,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(423,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)],[60]) ).
thf(33,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(281,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)],[33]) ).
thf(67,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(445,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)],[67]) ).
thf(52,axiom,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(382,plain,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(40,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(345,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(3,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(91,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(75,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(520,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)],[75]) ).
thf(29,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(251,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)],[29]) ).
thf(23,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(223,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)],[23]) ).
thf(31,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(267,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)],[31]) ).
thf(1,conjecture,
! [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(2,negated_conjecture,
~ ! [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(neg_conjecture,[status(cth)],[1]) ).
thf(80,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)],[2]) ).
thf(77,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(525,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(36,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(295,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(13,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(150,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(30,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(263,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)],[30]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(414,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(5,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(95,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)],[5]) ).
thf(15,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(154,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)],[15]) ).
thf(53,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(386,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)],[53]) ).
thf(46,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(363,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(72,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(482,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(48,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(368,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(71,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(478,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(8,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(119,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ cartesian_product2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(51,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(378,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(68,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(447,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)],[68]) ).
thf(64,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(432,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(55,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(405,plain,
! [A: $i] :
( ( A @ boole_POSet @ rel_str )
& ( A @ boole_POSet @ strict_rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(21,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(210,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)],[21]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(358,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(65,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(437,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(486,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(25,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(232,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)],[25]) ).
thf(562,plain,
$false,
inference(e,[status(thm)],[347,372,285,420,245,351,523,115,185,301,93,416,152,228,216,376,238,121,353,293,411,243,428,452,439,201,366,102,160,297,137,488,339,554,393,457,128,360,205,530,425,430,166,148,279,423,281,445,382,345,91,520,251,223,267,80,525,295,150,263,414,95,154,386,363,482,368,478,119,378,447,432,405,210,358,437,486,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU387+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % 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
% 0.11/0.39 % Computer : n018.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sat Sep 26 09:26:37 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 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
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.49/1.25 % [INFO] Parsing done (263ms).
% 1.49/1.27 % [INFO] Running in sequential loop mode.
% 2.56/1.67 % [INFO] eprover registered as external prover.
% 2.56/1.68 % [INFO] Scanning for conjecture ...
% 2.99/1.81 % [INFO] Found a conjecture (or negated_conjecture) and 84 axioms. Running axiom selection ...
% 3.21/1.93 % [INFO] Axiom selection finished. Selected 77 axioms (removed 7 axioms).
% 3.58/2.05 % [INFO] Problem is first-order (TPTP FOF).
% 3.58/2.07 % [INFO] Type checking passed.
% 3.58/2.07 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 7.91/3.42 % External prover 'e' found a proof!
% 7.91/3.42 % [INFO] Killing All external provers ...
% 7.91/3.42 % Time passed: 2879ms (effective reasoning time: 2149ms)
% 7.91/3.42 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 7.91/3.43 % Axioms used in derivation (77): redefinition_m2_relset_1, cc2_finset_1, rc4_finset_1, rc2_yellow_0, dt_u1_orders_2, rc1_lattice3, t4_subset, fc14_finset_1, fc4_relat_1, t1_subset, fc4_subset_1, fc8_yellow_6, t8_waybel_7, 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, dt_k3_yellow_1, rc2_lattice3, rc3_relat_1, t6_boole, rc2_subset_1, cc5_waybel_0, rc2_waybel_7, rc1_waybel_7, t5_subset, fc1_waybel_7, cc9_waybel_0, existence_m1_relset_1, cc2_yellow_0, rc3_waybel_7, fc8_yellow_1, t7_boole, existence_l1_orders_2, rc3_struct_0, fc1_subset_1, rc4_waybel_7, cc13_waybel_0, dt_g1_orders_2, rc1_subset_1, abstractness_v1_orders_2, cc4_yellow_0, t3_subset, cc1_relset_1, existence_m1_subset_1, dt_k3_yellow_0, rc2_relat_1, existence_m2_relset_1, t18_yellow_1, dt_l1_orders_2, free_g1_orders_2, fc1_struct_0, rc1_relat_1, reflexivity_r1_tarski, rc10_waybel_0, cc10_waybel_0, cc5_yellow_0, rc3_finset_1, rc1_finset_1, cc1_finset_1, cc1_yellow_0, t8_boole, rc5_struct_0, t2_subset, fc12_relat_1, rc1_yellow_0, cc2_lattice3, existence_l1_struct_0, fc7_yellow_1, rc12_waybel_0, cc3_yellow_0, antisymmetry_r2_hidden
% 7.91/3.43 % No. of inferences in proof: 158
% 7.91/3.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2879 ms resp. 2149 ms w/o parsing
% 8.28/3.56 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.28/3.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------